diff --git a/.gitignore b/.gitignore
index 191faa64d4cb4bc050f36124c20763478c71bac3..423a52d16b06a08d3f9e81333eb2f10abb2542ab 100644
--- a/.gitignore
+++ b/.gitignore
@@ -4,11 +4,13 @@
*.png
!docs/logo/*.png
*.svg
+!examples/model-comparison/reference/*.svg
*.zip
*.vtu
*.vtp
*.pvd
*.pkl
+!examples/model-comparison/reference/*.pkl
# Ignore __pycache__ directories
*/__pycache__/
@@ -24,3 +26,4 @@ examples/*/.ipynb_checkpoints
# Ignore Outputs_*
examples/*/Outputs_*
*/Outputs_*
+
diff --git a/examples/OHagan-function/OHagan.py b/examples/OHagan-function/OHagan.py
new file mode 100644
index 0000000000000000000000000000000000000000..71a58e092600bcd5edd0aca320d0ba6b840e9152
--- /dev/null
+++ b/examples/OHagan-function/OHagan.py
@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Mon Nov 19 08:56:21 2018
+
+@author: farid
+"""
+import numpy as np
+
+
+def OHagan(xx, *args):
+ """
+ Oakley & O'Hagan (2004) Function
+
+ This function's a-coefficients are chosen so that 5 of the input variables
+ contribute significantly to the output variance, 5 have a much smaller
+ effect, and the remaining 5 have almost no effect on the output variance.
+
+ O'Hagan, 2004, Probabilistic sensitivity analysis of complex models: a
+ Bayesian approach J. R. Statist. Soc. B (2004) 66, Part 3, pp. 751-769.
+
+ Parameters
+ ----------
+ xx : array of shape (n_samples, n_params)
+ Input parameter sets.
+
+ Returns
+ -------
+ output: dict
+ Ourput value.
+
+ """
+ n_samples, n_params = xx.shape
+
+ # Read M
+ M = np.loadtxt('data/M.csv', delimiter=',')
+
+ a_1 = np.array([0.0118, 0.0456, 0.2297, 0.0393, 0.1177, 0.3865, 0.3897,
+ 0.6061, 0.6159, 0.4005, 1.0741, 1.1474, 0.7880, 1.1242,
+ 1.1982])
+ a_2 = np.array([0.4341, 0.0887, 0.0512, 0.3233, 0.1489, 1.0360, 0.9892,
+ 0.9672, 0.8977, 0.8083, 1.8426, 2.4712, 2.3946, 2.0045,
+ 2.2621])
+ a_3 = np.array([0.1044, 0.2057, 0.0774, 0.2730, 0.1253, 0.7526, 0.8570,
+ 1.0331, 0.8388, 0.7970, 2.2145, 2.0382, 2.4004, 2.0541,
+ 1.9845])
+
+ # Compute response
+ xx_M = np.dot(xx, M)
+ last_term = np.sum(xx_M * xx, axis=1)
+
+ y = np.dot(xx, a_1) + np.dot(np.sin(xx), a_2) + np.dot(np.cos(xx), a_3)
+ y += last_term
+
+ # Prepare output dict using standard bayesvalidrox format
+ output = {'x_values': np.zeros(1), 'Z': y.T}
+
+ return output
diff --git a/examples/OHagan-function/data/M.csv b/examples/OHagan-function/data/M.csv
new file mode 100644
index 0000000000000000000000000000000000000000..98ec96817d7910bac21cd1ea54d54d7a5f432ad8
--- /dev/null
+++ b/examples/OHagan-function/data/M.csv
@@ -0,0 +1,15 @@
+-0.022482886,-0.18501666,0.13418263,0.36867264,0.17172785,0.13651143,-0.44034404,-0.081422854,0.71321025,-0.44361072,0.50383394,-0.024101458,-0.045939684,0.21666181,0.055887417
+0.2565963,0.053792287,0.25800381,0.23795905,-0.59125756,-0.081627077,-0.28749073,0.41581639,0.49752241,0.083893165,-0.11056683,0.033222351,-0.13979497,-0.031020556,-0.22318721
+-0.055999811,0.19542252,0.095529005,-0.2862653,-0.14441303,0.22369356,0.14527412,0.28998481,0.2310501,-0.31929879,-0.29039128,-0.20956898,0.43139047,0.024429152,0.044904409
+0.66448103,0.43069872,0.29924645,-0.16202441,-0.31479544,-0.39026802,0.17679822,0.057952663,0.17230342,0.13466011,-0.3527524,0.25146896,-0.018810529,0.36482392,-0.32504618
+-0.121278,0.12463327,0.10656519,0.046562296,-0.21678617,0.19492172,-0.065521126,0.024404669,-0.09682886,0.19366196,0.33354757,0.31295994,-0.083615456,-0.25342082,0.37325717
+-0.2837623,-0.32820154,-0.10496068,-0.22073452,-0.13708154,-0.14426375,-0.11503319,0.22424151,-0.030395022,-0.51505615,0.017254978,0.038957118,0.36069184,0.30902452,0.050030193
+-0.077875893,0.003745656,0.88685604,-0.26590028,-0.079325357,-0.042734919,-0.18653782,-0.35604718,-0.17497421,0.088699956,0.40025886,-0.055979693,0.13724479,0.21485613,-0.011265799
+-0.09229473,0.59209563,0.031338285,-0.033080861,-0.24308858,-0.099798547,0.034460195,0.095119813,-0.3380162,0.0063860024,-0.61207299,0.081325416,0.88683114,0.14254905,0.14776204
+-0.13189434,0.52878496,0.12652391,0.045113625,0.58373514,0.37291503,0.11395325,-0.29479222,-0.57014085,0.46291592,-0.094050179,0.13959097,-0.38607402,-0.4489706,-0.14602419
+0.058107658,-0.32289338,0.093139162,0.072427234,-0.56919401,0.52554237,0.23656926,-0.011782016,0.071820601,0.078277291,-0.13355752,0.22722721,0.14369455,-0.45198935,-0.55574794
+0.66145875,0.34633299,0.14098019,0.51882591,-0.28019898,-0.1603226,-0.068413337,-0.20428242,0.069672173,0.23112577,-0.044368579,-0.16455425,0.21620977,0.0042702105,-0.087399014
+0.31599556,-0.027551859,0.13434254,0.13497371,0.05400568,-0.17374789,0.17525393,0.060258929,-0.17914162,-0.31056619,-0.25358691,0.025847535,-0.43006001,-0.62266361,-0.033996882
+-0.29038151,0.03410127,0.034903413,-0.12121764,0.026030714,-0.33546274,-0.41424111,0.05324838,-0.27099455,-0.026251302,0.41024137,0.26636349,0.15582891,-0.18666254,0.019895831
+-0.24388652,-0.44098852,0.012618825,0.24945112,0.071101888,0.24623792,0.17484502,0.0085286769,0.2514707,-0.14659862,-0.08462515,0.36931333,-0.29955293,0.1104436,-0.75690139
+0.041494323,-0.25980564,0.46402128,-0.36112127,-0.94980789,-0.16504063,0.0030943325,0.052792942,0.22523648,0.38390366,0.45562427,-0.18631744,0.0082333995,0.16670803,0.16045688
diff --git a/examples/OHagan-function/data/sparse_solver_comparison.py b/examples/OHagan-function/data/sparse_solver_comparison.py
new file mode 100644
index 0000000000000000000000000000000000000000..5245bb89d56ecba9967e2c1f1ddb90438dc23ce9
--- /dev/null
+++ b/examples/OHagan-function/data/sparse_solver_comparison.py
@@ -0,0 +1,240 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Sat Sep 10 09:44:05 2022
+
+@author: farid
+"""
+
+import numpy as np
+import joblib
+import os
+import scipy.stats as st
+
+import sys
+sys.path.append("../../../src/bayesvalidrox/")
+
+from pylink.pylink import PyLinkForwardModel
+from surrogate_models.inputs import Input
+from surrogate_models.surrogate_models import MetaModel
+from post_processing.post_processing import PostProcessing
+from bayes_inference.bayes_inference import BayesInference
+from bayes_inference.discrepancy import Discrepancy
+import matplotlib
+matplotlib.use('agg')
+from matplotlib.backends.backend_pdf import PdfPages
+import matplotlib.ticker as ticker
+from matplotlib.offsetbox import AnchoredText
+from matplotlib.patches import Patch
+import matplotlib.pyplot as plt
+# Load the mplstyle
+plt.style.use(os.path.join(
+ os.path.split(__file__)[0],
+ '../../../src/bayesvalidrox/', 'bayesvalidrox.mplstyle'))
+
+
+def plot_seq_design_diagnostics(meta_model, util_funcs,
+ ref_BME_KLD=None, save_fig=True):
+ """
+ Plots the Bayesian Model Evidence (BME) and Kullback-Leibler divergence
+ (KLD) for the sequential design.
+
+ Parameters
+ ----------
+ ref_BME_KLD : array, optional
+ Reference BME and KLD . The default is `None`.
+ save_fig : bool, optional
+ Whether to save the figures. The default is `True`.
+
+ Returns
+ -------
+ None.
+
+ """
+ n_init_samples = meta_model.ExpDesign.n_init_samples
+ n_total_samples = meta_model.ExpDesign.X.shape[0]
+
+ if save_fig:
+ newpath = f'{path}/boxplot_{model_name}/'
+ if not os.path.exists(newpath):
+ os.makedirs(newpath)
+
+ plotList = ['Modified LOO error', 'Validation error', 'KLD', 'BME',
+ 'RMSEMean', 'RMSEStd', 'Hellinger distance']
+ seqList = [meta_model.SeqModifiedLOO, meta_model.seqValidError,
+ meta_model.SeqKLD, meta_model.SeqBME, meta_model.seqRMSEMean,
+ meta_model.seqRMSEStd, meta_model.SeqDistHellinger]
+
+ markers = ('x', 'o', 'd', '*', '+')
+ colors = ('k', 'darkgreen', 'b', 'navy', 'darkred')
+
+ # Plot the evolution of the diagnostic criteria of the
+ # Sequential Experimental Design.
+ for plotidx, plot in enumerate(plotList):
+ fig, ax = plt.subplots(figsize=(27, 15))
+ seq_dict = seqList[plotidx]
+ name_util = list(seq_dict.keys())
+
+ if len(name_util) == 0:
+ continue
+
+ # Box plot when Replications have been detected.
+ if any(int(name.split("rep_", 1)[1]) > 1 for name in name_util):
+ # Extract the values from dict
+ sorted_seq_opt = {}
+ # Number of replications
+ n_reps = meta_model.ExpDesign.n_replication
+
+ # Get the list of utility function names
+ # Handle if only one UtilityFunction is provided
+ if not isinstance(util_funcs, list):
+ util_funcs = [util_funcs]
+
+ for util in util_funcs:
+ sortedSeq = {}
+ # min number of runs available from reps
+ n_runs = min([seq_dict[f'{util}_rep_{i+1}'].shape[0]
+ for i in range(n_reps)])
+
+ for runIdx in range(n_runs):
+ values = []
+ for key in seq_dict.keys():
+ if util in key:
+ values.append(seq_dict[key][runIdx].mean())
+ sortedSeq['SeqItr_'+str(runIdx)] = np.array(values)
+ sorted_seq_opt[util] = sortedSeq
+
+ # BoxPlot
+ def draw_plot(data, labels, edge_color, fill_color, idx):
+ pos = labels - (4*idx-6)
+ bp = plt.boxplot(data, positions=pos, labels=labels,
+ patch_artist=True, sym='', widths=3)
+
+ ax.plot(pos, np.median(data, axis=0), lw=4, color=fill_color[idx])
+
+ elements = ['boxes', 'whiskers', 'fliers', 'means',
+ 'medians', 'caps']
+ for element in elements:
+ plt.setp(bp[element], color=edge_color[idx], alpha=0.6)
+
+ for patch in bp['boxes']:
+ patch.set(facecolor=fill_color[idx], alpha=0.6)
+
+ if meta_model.ExpDesign.n_new_samples != 1:
+ step1 = meta_model.ExpDesign.n_new_samples
+ step2 = 1
+ else:
+ step1 = 10
+ step2 = 10
+ edge_color = ['red', 'blue', 'green', 'black']
+ fill_color = ['tan', 'cyan', 'lightgreen', 'grey']
+ plot_label = plot
+ # Plot for different Utility Functions
+ for idx, util in enumerate(util_funcs):
+ all_errors = np.empty((n_reps, 0))
+
+ for key in list(sorted_seq_opt[util].keys()):
+ errors = sorted_seq_opt.get(util, {}).get(key)[:, None]
+ all_errors = np.hstack((all_errors, errors))
+
+ # Special cases for BME and KLD
+ if plot == 'KLD' or plot == 'BME':
+ # BME convergence if refBME is provided
+ if ref_BME_KLD is not None:
+ if plot == 'BME':
+ refValue = ref_BME_KLD[0]
+ plot_label = r'BME/BME$^{Ref.}$'
+ if plot == 'KLD':
+ refValue = ref_BME_KLD[1]
+ plot_label = '$D_{KL}[p(\\theta|y_*),p(\\theta)]'\
+ ' / D_{KL}^{Ref.}[p(\\theta|y_*), '\
+ 'p(\\theta)]$'
+
+ # Difference between BME/KLD and the ref. values
+ all_errors = np.divide(all_errors,
+ np.full((all_errors.shape),
+ refValue))
+
+ # Plot baseline for zero, i.e. no difference
+ plt.axhline(y=1.0, xmin=0, xmax=1, c='green',
+ ls='--', lw=2)
+
+ # Plot each UtilFuncs
+ labels = np.arange(n_init_samples, n_total_samples+1, step1)
+ draw_plot(all_errors[:, ::step2], labels, edge_color,
+ fill_color, idx)
+ # labels = np.array([10, 30, 50, 70, 90, 120, 150, 200])
+ # indices = [0, 20, 40, 60, 80, 110, 140, 190]
+ # draw_plot(all_errors[:, indices], labels, edge_color,
+ # fill_color, idx)
+
+ plt.xticks(labels)
+ # Set the major and minor locators
+ # ax.xaxis.set_major_locator(ticker.AutoLocator())
+ # ax.xaxis.set_minor_locator(ticker.AutoMinorLocator())
+ # ax.xaxis.grid(True, which='major', linestyle='-')
+ # ax.xaxis.grid(True, which='minor', linestyle='--')
+
+ # Shade
+ for center in labels[::2]:
+ ax.axvspan(center-8, center+8, alpha=0.1, color='grey')
+
+ # Legend
+ legend_elements = []
+ for idx, util in enumerate(util_funcs):
+ legend_elements.append(Patch(facecolor=fill_color[idx],
+ edgecolor=edge_color[idx],
+ label=util))
+ plt.legend(handles=legend_elements[::-1], loc='best')
+
+ if plot != 'BME' and plot != 'KLD':
+ plt.yscale('log')
+ plt.autoscale(True)
+ # ax.yaxis.set_minor_locator(ticker.LogLocator(numticks=999, subs="auto"))
+ ax.yaxis.grid(True, which='minor', linestyle='--')
+ plt.xlabel('\\# of training samples', fontsize=f_size)
+ plt.ylabel(plot_label, fontsize=f_size)
+ # plt.title(plot)
+ plt.xticks(fontsize=f_size)
+ plt.yticks(fontsize=f_size)
+
+ if save_fig:
+ # save the current figure
+ plot_name = plot.replace(' ', '_')
+ fig.savefig(
+ f'{newpath}/boxplot_solver_ishigami_{plot_name}.pdf',
+ bbox_inches='tight'
+ )
+ # Destroy the current plot
+ plt.clf()
+ return
+
+
+if __name__ == "__main__":
+ # Set variables
+ model_name = 'borehole'
+ solvers = ['BCS', 'FastARD', 'OMP', 'OLS']
+ path = f'/home/farid/bwSyncShare/Scientific_LH2/Promotion/dissertation/surrogate/data-borehole/'
+ f_size = 45
+
+ all_loo_errors = {}
+ all_valid_errors = {}
+ for solver in solvers:
+ # reading the data from the file
+ with open(f"{path}/{solver}/PCEModel_{model_name}.pkl", "rb") as input:
+ meta_model = joblib.load(input)
+
+ # Update name and Concatenate
+ all_valid_errors.update({key.replace('ALM', solver): value
+ for key, value in
+ meta_model.seqValidError.items()
+ })
+ all_loo_errors.update({key.replace('ALM', solver): value
+ for key, value in
+ meta_model.SeqModifiedLOO.items()
+ })
+ meta_model.seqValidError = all_valid_errors
+ meta_model.SeqModifiedLOO = all_loo_errors
+
+ # Plot box plot
+ plot_seq_design_diagnostics(meta_model, solvers)
diff --git a/examples/OHagan-function/data/valid_outputs.npy b/examples/OHagan-function/data/valid_outputs.npy
new file mode 100644
index 0000000000000000000000000000000000000000..6b0f28b72e05d71f6a0c7a677f416e9493301ac0
Binary files /dev/null and b/examples/OHagan-function/data/valid_outputs.npy differ
diff --git a/examples/OHagan-function/data/valid_samples.npy b/examples/OHagan-function/data/valid_samples.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2a2a38e1a1718d94f39243fac3d0f047fdd870d1
Binary files /dev/null and b/examples/OHagan-function/data/valid_samples.npy differ
diff --git a/examples/OHagan-function/test_OHagan.py b/examples/OHagan-function/test_OHagan.py
new file mode 100644
index 0000000000000000000000000000000000000000..2fc629d3423d7ef3312e0182a8f15d1f0fd18ba0
--- /dev/null
+++ b/examples/OHagan-function/test_OHagan.py
@@ -0,0 +1,191 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+This test deals with the surrogate modeling of O'Hagan function with 15
+parameters.
+
+You will see how to:
+ Check the quality of your regression model
+ Perform sensitivity analysis via Sobol Indices
+
+Author: Farid Mohammadi, M.Sc.
+E-Mail: farid.mohammadi@iws.uni-stuttgart.de
+Department of Hydromechanics and Modelling of Hydrosystems (LH2)
+Institute for Modelling Hydraulic and Environmental Systems (IWS), University
+of Stuttgart, www.iws.uni-stuttgart.de/lh2/
+Pfaffenwaldring 61
+70569 Stuttgart
+
+Created on Wed Jul 10 2019
+
+"""
+
+import numpy as np
+import joblib
+
+# import bayesvalidrox
+# Add BayesValidRox path
+import sys
+sys.path.append("../../src/bayesvalidrox/")
+
+from pylink.pylink import PyLinkForwardModel
+from surrogate_models.inputs import Input
+from surrogate_models.surrogate_models import MetaModel
+from surrogate_models.meta_model_engine import MetaModelEngine
+from post_processing.post_processing import PostProcessing
+from bayes_inference.bayes_inference import BayesInference
+from bayes_inference.discrepancy import Discrepancy
+import matplotlib
+matplotlib.use('agg')
+
+if __name__ == "__main__":
+
+ # =====================================================
+ # ============= COMPUTATIONAL MODEL ================
+ # =====================================================
+ Model = PyLinkForwardModel()
+
+ # Define model options
+ Model.link_type = 'Function'
+ Model.py_file = 'OHagan'
+ Model.name = 'OHagan'
+
+ Model.Output.names = ['Z']
+
+ # =====================================================
+ # ========= PROBABILISTIC INPUT MODEL ==============
+ # =====================================================
+ Inputs = Input()
+
+ n_dim = 15
+
+ for i in range(n_dim):
+ Inputs.add_marginals()
+ Inputs.Marginals[i].name = "$\\theta_{"+str(i+1)+"}$"
+ Inputs.Marginals[i].dist_type = 'normal'
+ Inputs.Marginals[i].parameters = [0, 1]
+
+ # =====================================================
+ # ====== POLYNOMIAL CHAOS EXPANSION METAMODELS ======
+ # =====================================================
+ MetaModelOpts = MetaModel(Inputs, Model)
+
+ # Select your metamodel method
+ # 1) PCE (Polynomial Chaos Expansion) 2) aPCE (arbitrary PCE)
+ # 3) GPE (Gaussian Process Emulator)
+ MetaModelOpts.meta_model_type = 'aPCE'
+
+ # ------------------------------------------------
+ # ------------- PCE Specification ----------------
+ # ------------------------------------------------
+ # Select the sparse least-square minimization method for
+ # the PCE coefficients calculation:
+ # 1)OLS: Ordinary Least Square 2)BRR: Bayesian Ridge Regression
+ # 3)LARS: Least angle regression 4)ARD: Bayesian ARD Regression
+ # 5)FastARD: Fast Bayesian ARD Regression
+ # 6)BCS: Bayesian Compressive Sensing
+ # 7)OMP: Orthogonal Matching Pursuit
+ # 8)VBL: Variational Bayesian Learning
+ # 9)EBL: Emperical Bayesian Learning
+ MetaModelOpts.pce_reg_method = 'FastARD'
+
+ # Specify the max degree to be compared by the adaptive algorithm:
+ # The degree with the lowest Leave-One-Out cross-validation (LOO)
+ # error (or the highest score=1-LOO)estimator is chosen as the final
+ # metamodel. pce_deg accepts degree as a scalar or a range.
+ MetaModelOpts.pce_deg = 7
+
+ # q-quasi-norm 0<q<1 (default=1)
+ MetaModelOpts.pce_q_norm = 0.65
+
+ # Print summary of the regression results
+ # MetaModelOpts.verbose = True
+
+ # ------------------------------------------------
+ # ------ Experimental Design Configuration -------
+ # ------------------------------------------------
+ MetaModelOpts.add_ExpDesign()
+
+ # One-shot (normal) or Sequential Adaptive (sequential) Design
+ MetaModelOpts.ExpDesign.method = 'sequential'
+ MetaModelOpts.ExpDesign.n_init_samples = 100
+
+ # Sampling methods
+ # 1) random 2) latin_hypercube 3) sobol 4) halton 5) hammersley 6) korobov
+ # 7) chebyshev(FT) 8) grid(FT) 9) nested_grid(FT) 10)user
+ MetaModelOpts.ExpDesign.sampling_method = 'latin_hypercube'
+
+ # Provide the experimental design object with a hdf5 file
+ # MetaModelOpts.ExpDesign.hdf5_file = 'ExpDesign_OHagan_orig.hdf5'
+
+ # Sequential experimental design (needed only for sequential ExpDesign)
+ MetaModelOpts.ExpDesign.n_new_samples = 1
+ MetaModelOpts.ExpDesign.n_max_samples = 500 # 150
+ MetaModelOpts.ExpDesign.mod_LOO_threshold = 1e-16
+
+ # ------------------------------------------------
+ # ------- Sequential Design configuration --------
+ # ------------------------------------------------
+ # 1) None 2) 'equal' 3)'epsilon-decreasing' 4) 'adaptive'
+ MetaModelOpts.ExpDesign.tradeoff_scheme = None
+ # MetaModelOpts.ExpDesign.n_replication = 50
+ # -------- Exploration ------
+ # 1)'Voronoi' 2)'random' 3)'latin_hypercube' 4)'dual annealing'
+ MetaModelOpts.ExpDesign.explore_method = 'latin_hypercube'
+
+ # Use when 'dual annealing' chosen
+ MetaModelOpts.ExpDesign.max_func_itr = 200
+
+ # Use when 'Voronoi' or 'random' or 'latin_hypercube' chosen
+ MetaModelOpts.ExpDesign.n_canddidate = 10000
+ MetaModelOpts.ExpDesign.n_cand_groups = 4
+
+ # -------- Exploitation ------
+ # 1)'BayesOptDesign' 2)'VarOptDesign' 3)'alphabetic' 4)'Space-filling'
+ MetaModelOpts.ExpDesign.exploit_method = 'Space-filling'
+
+ # BayesOptDesign -> when data is available
+ # 1)DKL (Kullback-Leibler Divergence) 2)DPP (D-Posterior-percision)
+ # 3)APP (A-Posterior-percision)
+ # MetaModelOpts.ExpDesign.util_func = 'DKL'
+
+ # VarBasedOptDesign -> when data is not available
+ # Only with Vornoi >>> 1)Entropy 2)EIGF, 3)ALM, 4)LOOCV
+ MetaModelOpts.ExpDesign.util_func = 'ALM'
+
+ # alphabetic
+ # 1)D-Opt (D-Optimality) 2)A-Opt (A-Optimality)
+ # 3)K-Opt (K-Optimality)
+ # MetaModelOpts.ExpDesign.util_func = 'D-Opt'
+
+ MetaModelOpts.valid_samples = np.load("data/valid_samples.npy")
+ MetaModelOpts.valid_model_runs = {
+ 'Z': np.load("data/valid_outputs.npy")
+ }
+ # >>>>>>>>>>>>>>>>>>>>>> Build Surrogate <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
+ meta_model_engine = MetaModelEngine(MetaModelOpts)
+ meta_model_engine.run()
+ PCEModel = meta_model_engine.MetaModel
+
+ # Save PCE models
+ with open(f'PCEModel_{Model.name}.pkl', 'wb') as output:
+ joblib.dump(PCEModel, output, 2)
+
+ # =====================================================
+ # ========= POST PROCESSING OF METAMODELS ===========
+ # =====================================================
+ PostPCE = PostProcessing(PCEModel)
+
+ # Plot to check validation visually.
+ PostPCE.valid_metamodel(n_samples=200)
+
+ # PostPCE.eval_PCEmodel_3D()
+ # Compute and print RMSE error
+ PostPCE.check_accuracy(n_samples=3000)
+
+ # Plot the evolution of the KLD,BME, and Modified LOOCV error
+ if MetaModelOpts.ExpDesign.method == 'sequential':
+ PostPCE.plot_seq_design_diagnostics()
+
+ # Plot the sobol indices
+ total_sobol = PostPCE.sobol_indices(plot_type='bar')
diff --git a/examples/analytical_function/analytical_function.py b/examples/analytical-function/analytical_function.py
similarity index 76%
rename from examples/analytical_function/analytical_function.py
rename to examples/analytical-function/analytical_function.py
index 7d1075a0195c7e3ab3db40465f02b840cebf28dc..c7dfaca489abd3dcd2a147f3192c22af8be0c810 100644
--- a/examples/analytical_function/analytical_function.py
+++ b/examples/analytical-function/analytical_function.py
@@ -61,11 +61,12 @@ def analytical_function(xx, t=None):
Output = term4 + np.repeat(const[:, None], len(t), axis=1)
- return np.vstack((t, Output))
+ return {'x_values': t, 'Z': Output[0]}
+
if __name__ == "__main__":
- MCSize = 10000 #1000000
+ MCSize = 10000
ndim = 10
sigma = 2
@@ -75,7 +76,7 @@ if __name__ == "__main__":
t = np.arange(0, 10, 1.) / 9
MAP = np.zeros((1, ndim))
- synthethicData = AnalyticalFunction(MAP, t=t)
+ synthethicData = analytical_function(MAP, t=t)
# -------------------------------------------------------------------------
# ---------------------- Generate Prior distribution ----------------------
@@ -83,22 +84,25 @@ if __name__ == "__main__":
xx = np.zeros((MCSize, ndim))
- params = (-5,5)
+ params = (-5, 5)
for idxDim in range(ndim):
lower, upper = params
- xx[:,idxDim] = stats.uniform(loc=lower, scale=upper-lower).rvs(size=MCSize)
+ xx[:, idxDim] = stats.uniform(
+ loc=lower, scale=upper-lower).rvs(size=MCSize)
# -------------------------------------------------------------------------
# ------------- BME and Kullback-Leibler Divergence -----------------------
# -------------------------------------------------------------------------
- Outputs = AnalyticalFunction(xx, t=t)
+ Outputs = analytical_function(xx, t=t)
cov_matrix = np.diag(np.repeat(sigma**2, synthethicData.shape[1]))
- Likelihoods = st.multivariate_normal.pdf(Outputs[1:], mean=synthethicData[1], cov=cov_matrix)
+ Likelihoods = st.multivariate_normal.pdf(
+ Outputs['Z'], mean=synthethicData[1], cov=cov_matrix)
- sns.kdeplot(np.log(Likelihoods[Likelihoods>0]), shade=True, color="g", label='Ref. Likelihood')
+ sns.kdeplot(np.log(Likelihoods[Likelihoods > 0]),
+ shade=True, color="g", label='Ref. Likelihood')
normLikelihood = Likelihoods / np.nanmax(Likelihoods)
# Random numbers between 0 and 1
@@ -109,23 +113,23 @@ if __name__ == "__main__":
# Prior-based estimation of BME
logBME = np.log(np.nanmean(Likelihoods))
- print('\nThe Naive MC-Estimation of BME is %.5f.'%(logBME))
+ print(f'\nThe Naive MC-Estimation of BME is {logBME:.5f}.')
# Posterior-based expectation of likelihoods
postExpLikelihoods = np.mean(np.log(Likelihoods[accepted]))
# Calculate Kullback-Leibler Divergence
KLD = postExpLikelihoods - logBME
- print("The Kullback-Leibler divergence estimation is %.5f."%KLD)
+ print("The Kullback-Leibler divergence estimation is {KLD:.5f}.")
# -------------------------------------------------------------------------
# ----------------- Save the arrays as .npy files -------------------------
# -------------------------------------------------------------------------
if MCSize > 500000:
- np.save("data/refBME_KLD_"+str(ndim)+".npy", (logBME, KLD))
- np.save("data/mean_"+str(ndim)+".npy", np.mean(Outputs[1:],axis=0))
- np.save("data/std_"+str(ndim)+".npy", np.std(Outputs[1:],axis=0))
+ np.save(f"data/refBME_KLD_{ndim}.npy", (logBME, KLD))
+ np.save(f"data/mean_{ndim}.npy", np.mean(Outputs['Z'], axis=0))
+ np.save(f"data/std_{ndim}.npy", np.std(Outputs['Z'], axis=0))
else:
- np.save("data/Prior_"+str(ndim)+".npy", xx)
- np.save("data/origModelOutput_"+str(ndim)+".npy", Outputs[1:])
- np.save("data/validLikelihoods_"+str(ndim)+".npy", Likelihoods)
+ np.save(f"data/Prior_{ndim}.npy", xx)
+ np.save(f"data/origModelOutput_{ndim}.npy", Outputs[1:])
+ np.save(f"data/validLikelihoods_{ndim}.npy", Likelihoods)
diff --git a/examples/analytical_function/data/InputParameters_10.npy b/examples/analytical-function/data/InputParameters_10.npy
similarity index 100%
rename from examples/analytical_function/data/InputParameters_10.npy
rename to examples/analytical-function/data/InputParameters_10.npy
diff --git a/examples/analytical_function/data/InputParameters_2.npy b/examples/analytical-function/data/InputParameters_2.npy
similarity index 100%
rename from examples/analytical_function/data/InputParameters_2.npy
rename to examples/analytical-function/data/InputParameters_2.npy
diff --git a/examples/analytical_function/data/Prior_10.npy b/examples/analytical-function/data/Prior_10.npy
similarity index 100%
rename from examples/analytical_function/data/Prior_10.npy
rename to examples/analytical-function/data/Prior_10.npy
diff --git a/examples/analytical_function/data/Prior_2.npy b/examples/analytical-function/data/Prior_2.npy
similarity index 100%
rename from examples/analytical_function/data/Prior_2.npy
rename to examples/analytical-function/data/Prior_2.npy
diff --git a/examples/analytical_function/data/Samples.npy b/examples/analytical-function/data/Samples.npy
similarity index 100%
rename from examples/analytical_function/data/Samples.npy
rename to examples/analytical-function/data/Samples.npy
diff --git a/examples/analytical_function/data/mean_10.npy b/examples/analytical-function/data/mean_10.npy
similarity index 100%
rename from examples/analytical_function/data/mean_10.npy
rename to examples/analytical-function/data/mean_10.npy
diff --git a/examples/analytical_function/data/mean_2.npy b/examples/analytical-function/data/mean_2.npy
similarity index 100%
rename from examples/analytical_function/data/mean_2.npy
rename to examples/analytical-function/data/mean_2.npy
diff --git a/examples/analytical_function/data/origModelOutput_10.npy b/examples/analytical-function/data/origModelOutput_10.npy
similarity index 100%
rename from examples/analytical_function/data/origModelOutput_10.npy
rename to examples/analytical-function/data/origModelOutput_10.npy
diff --git a/examples/analytical_function/data/origModelOutput_2.npy b/examples/analytical-function/data/origModelOutput_2.npy
similarity index 100%
rename from examples/analytical_function/data/origModelOutput_2.npy
rename to examples/analytical-function/data/origModelOutput_2.npy
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_1.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_1.npy
new file mode 100644
index 0000000000000000000000000000000000000000..58d2650394f650a6436ed5932bbda05b7f6f90ab
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_1.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_10.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..3c42a71708a6510d7f7493880c667d0460a613e1
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_10.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_11.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_11.npy
new file mode 100644
index 0000000000000000000000000000000000000000..8408441185940760cb6dc02b12630fc7770cfcf9
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_11.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_12.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..83e60bd054704f07d5f25bbee1fe6d593b572ff4
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_12.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_13.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_13.npy
new file mode 100644
index 0000000000000000000000000000000000000000..8dd26b3f277753998c4f47daa43cd0d773a3ee19
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_13.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_14.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..06911cd4722a51d726d36b79ab9bc600c9e82ffb
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_14.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_15.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_15.npy
new file mode 100644
index 0000000000000000000000000000000000000000..d5ee2de4c138728f05cc3d6388f9ff421931e677
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_15.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_16.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..86a34893a169b05e50a21ddd71be260f4c2e9b55
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_16.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_17.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_17.npy
new file mode 100644
index 0000000000000000000000000000000000000000..d4f57970f31a6774401fdfd166c3599b14ef7467
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_17.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_18.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..ecf2f77f270f6f857eff0ea891e8c4b22bbd266f
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_18.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_19.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_19.npy
new file mode 100644
index 0000000000000000000000000000000000000000..fcc94211eb35cabc00b5f7a6767b8e8f7a087050
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_19.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_2.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_2.npy
new file mode 100644
index 0000000000000000000000000000000000000000..11e20672d5b9f3360bccd90dd1a6a4d56d576d1d
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_2.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_20.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..23c02b1104973eb291bf8f027094cb32f74e840d
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_20.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_21.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_21.npy
new file mode 100644
index 0000000000000000000000000000000000000000..747fddb486983ce0bd0dc1c96f8f6e25b23e36fa
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_21.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_22.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..1e1ffe72d4aca881f29430d809fff3c0892dd17f
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_22.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_23.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_23.npy
new file mode 100644
index 0000000000000000000000000000000000000000..824932636e400de9c958f01ea00e5d20104e6d2c
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_23.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_24.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_24.npy
new file mode 100644
index 0000000000000000000000000000000000000000..acce8e21984b60caa1a7d03b176920660175ea62
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_24.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_25.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_25.npy
new file mode 100644
index 0000000000000000000000000000000000000000..ef2ed1ed90e72903967f07a6811684d43fabeeae
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_25.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_26.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_26.npy
new file mode 100644
index 0000000000000000000000000000000000000000..3826ff6805364488b2cd200ae2d98c87b8d83a2e
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_26.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_27.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_27.npy
new file mode 100644
index 0000000000000000000000000000000000000000..3e5e74b92da1704803ef6a2374647bf5a67f4382
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_27.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_28.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_28.npy
new file mode 100644
index 0000000000000000000000000000000000000000..ab8507910ab4311ac6ed8b8660c2beb6b95cbc10
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_28.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_29.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_29.npy
new file mode 100644
index 0000000000000000000000000000000000000000..1e37fada5b7832715c44db653285ace0e3bbcb6b
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_29.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_3.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_3.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a21fe8a3fc7c1044a7e150a3023807e958bb8bc1
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_3.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_30.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_30.npy
new file mode 100644
index 0000000000000000000000000000000000000000..958941edb482c3af37dc9c5aa11996e5628cfeb0
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_30.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_31.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_31.npy
new file mode 100644
index 0000000000000000000000000000000000000000..209c7b52c447685885d4935892fc83435c0831b6
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_31.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_32.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_32.npy
new file mode 100644
index 0000000000000000000000000000000000000000..4e0864f38b0c96424cdfe0b924c5cd67e6e65322
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_32.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_33.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_33.npy
new file mode 100644
index 0000000000000000000000000000000000000000..8279b27ac1716c694f5bbff93f0f2cb0c2ee1029
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_33.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_34.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_34.npy
new file mode 100644
index 0000000000000000000000000000000000000000..069937840094083adbd1bbca9760e178401d9b50
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_34.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_35.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_35.npy
new file mode 100644
index 0000000000000000000000000000000000000000..f03f2b9452ff2ff96578ff6e4346f0f1a7990225
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_35.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_36.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_36.npy
new file mode 100644
index 0000000000000000000000000000000000000000..d17ddeb0517bdf395d710163cf2ed96a65033154
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_36.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_37.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_37.npy
new file mode 100644
index 0000000000000000000000000000000000000000..050bd926cd62c0e199bcdd8924cfc48fd56321d6
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_37.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_38.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_38.npy
new file mode 100644
index 0000000000000000000000000000000000000000..1cc12ec60aa9586880c5ac322273c7ec13491ac8
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_38.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_39.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_39.npy
new file mode 100644
index 0000000000000000000000000000000000000000..795c7d7a1bfa4058b21a0615937c78c018b1003c
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_39.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_4.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..1f85637a22c0e1ad06de73c82e86d89173901a1f
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_4.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_40.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_40.npy
new file mode 100644
index 0000000000000000000000000000000000000000..1d155926d4edf4f46012ce11a2bd4ac527368199
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_40.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_41.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_41.npy
new file mode 100644
index 0000000000000000000000000000000000000000..9bf4183344f47fecbf4a119ebb0555b2b6dc5a77
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_41.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_42.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_42.npy
new file mode 100644
index 0000000000000000000000000000000000000000..83c25fe4b1457399191ec15c291e89f63a6cac86
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_42.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_43.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_43.npy
new file mode 100644
index 0000000000000000000000000000000000000000..bf30ffcd3284dc6f3c78e10500f383ead29570d8
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_43.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_44.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_44.npy
new file mode 100644
index 0000000000000000000000000000000000000000..23be23b1ce4fedaee1f547e6b39b30110b02eae8
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_44.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_45.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_45.npy
new file mode 100644
index 0000000000000000000000000000000000000000..144f305f3baac6c7f984bac654f29e6054acb0e4
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_45.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_46.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_46.npy
new file mode 100644
index 0000000000000000000000000000000000000000..7fe93e468eb90eb4be3f555ac2e063b4b14ba017
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_46.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_47.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_47.npy
new file mode 100644
index 0000000000000000000000000000000000000000..cb61fefd4c793cae614be1a3edeb58da28731f0d
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_47.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_48.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_48.npy
new file mode 100644
index 0000000000000000000000000000000000000000..5664ea3b4a0313420cb96643647cab662e2d5408
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_48.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_5.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_5.npy
new file mode 100644
index 0000000000000000000000000000000000000000..87d29e876d5a7fe28529d210fb5931ae99bb85dd
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_5.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_6.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..568d390111d31aef703453bb2622cd86ba6e4b55
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_6.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_7.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_7.npy
new file mode 100644
index 0000000000000000000000000000000000000000..4e12137059b7a1ed03a8aea854576f0d45a23677
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_7.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_8.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..0ccbc53d605e6b18ef3ef8f2c99f76defbdca16b
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_8.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_9.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_9.npy
new file mode 100644
index 0000000000000000000000000000000000000000..ddfa0fc1d41a9e7716c4e20b09a88541f438806a
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_9.npy differ
diff --git a/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_init.npy b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_init.npy
new file mode 100644
index 0000000000000000000000000000000000000000..38a4eb43f12ef5dfe406a35bec20bfd494b80f43
Binary files /dev/null and b/examples/analytical-function/data/posterior/AL_MI/SeqPosterior_init.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_1.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_1.npy
new file mode 100644
index 0000000000000000000000000000000000000000..c34775a4fcc7ea1095eebb63e39fbdc934cb7631
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_1.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_10.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..cab61893e562500c707c7b1947de0957487bb4ae
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_10.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_11.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_11.npy
new file mode 100644
index 0000000000000000000000000000000000000000..49adae27f0b52aa6f18c4777023f4cb5d810c0e6
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_11.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_12.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..3f5151347c895a778e2d8df393b6dfef328037b6
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_12.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_13.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_13.npy
new file mode 100644
index 0000000000000000000000000000000000000000..50f04221c5d66bba8f36bb1e979b87c75be95c61
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_13.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_14.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..43f3c0e9a2e72b391e1643b6e1542400e7dba7de
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_14.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_15.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_15.npy
new file mode 100644
index 0000000000000000000000000000000000000000..43c9b76a6921dcb00600a6fa2ffb30926d99c3bc
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_15.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_16.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..ab44393d17afb2da51d4308143db99fa21ac4922
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_16.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_17.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_17.npy
new file mode 100644
index 0000000000000000000000000000000000000000..93bc74d44b2ce909ff52a77e0fda780d8f2ba814
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_17.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_18.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..ea7200ceb535182df10a280a118283e327f2b5a4
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_18.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_19.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_19.npy
new file mode 100644
index 0000000000000000000000000000000000000000..f624fd4a9982a74f9882d1a53629297833396dfb
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_19.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_2.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_2.npy
new file mode 100644
index 0000000000000000000000000000000000000000..777d6b42bfcd7eca9957b9a188bc3341c4cfc2a5
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_2.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_20.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..eb2599e7d5533da07d4eb7baa2641cb44e9a2525
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_20.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_21.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_21.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a024ba5b3bcf534bf37819b545384c927ffb43b5
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_21.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_22.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..fe01856a91d758d36fb9c94daa9fc94b125ec74b
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_22.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_23.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_23.npy
new file mode 100644
index 0000000000000000000000000000000000000000..e78c794045249cd88a770ffba0cb645587e038bc
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_23.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_24.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_24.npy
new file mode 100644
index 0000000000000000000000000000000000000000..123c525632549c9aa3135fd2db1052256a1be531
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_24.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_25.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_25.npy
new file mode 100644
index 0000000000000000000000000000000000000000..41fc49bc8f4d36c0a949f7ecafe24e54a03ce638
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_25.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_26.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_26.npy
new file mode 100644
index 0000000000000000000000000000000000000000..da0f0ba273e9b5304ade216a9cc033da587cae32
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_26.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_27.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_27.npy
new file mode 100644
index 0000000000000000000000000000000000000000..148015b740c668bab7727b63bfb5c532766a9554
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_27.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_28.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_28.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a2e9734751a86bdf3caa2b4c34c06f3333b0f567
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_28.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_29.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_29.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2e7288954075a2f0d639765022fe3c0b9e457223
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_29.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_3.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_3.npy
new file mode 100644
index 0000000000000000000000000000000000000000..f589a277b2418b0fe228a53ea98bbdf574719870
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_3.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_30.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_30.npy
new file mode 100644
index 0000000000000000000000000000000000000000..eaea6efbd66fa9ad146b685b7bbdbac8390927a5
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_30.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_31.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_31.npy
new file mode 100644
index 0000000000000000000000000000000000000000..6b1217b9aa0dedbae5efd53f65bb4a8ed963514a
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_31.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_32.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_32.npy
new file mode 100644
index 0000000000000000000000000000000000000000..92c7b6c6b7be9d2743898754cc4920ee03382c94
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_32.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_33.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_33.npy
new file mode 100644
index 0000000000000000000000000000000000000000..e26de7c08182378092a6d0de6a12a1c7081a19bf
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_33.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_34.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_34.npy
new file mode 100644
index 0000000000000000000000000000000000000000..0741feede98ccc7370d19db824a1c9cd489bee34
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_34.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_35.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_35.npy
new file mode 100644
index 0000000000000000000000000000000000000000..e459f827bfea17caddc78276f476d4cdce37e348
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_35.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_36.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_36.npy
new file mode 100644
index 0000000000000000000000000000000000000000..b7190075e5cdd1b26699e0f3abcea2987ddb7ddc
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_36.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_37.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_37.npy
new file mode 100644
index 0000000000000000000000000000000000000000..4ee3216674fa00ce207f6787751707f680b6ffd3
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_37.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_38.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_38.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a9c37c16695a202eeb9d9108d71deebe17aa6db1
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_38.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_39.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_39.npy
new file mode 100644
index 0000000000000000000000000000000000000000..f89804a1adbfde9f9f426e3b03861c0204436a83
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_39.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_4.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..b4aff5c1388dd25bba6c0642f7aafc718217742c
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_4.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_40.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_40.npy
new file mode 100644
index 0000000000000000000000000000000000000000..9e36b2d568d2fd3421701320c6e1df5d0ce0bca6
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_40.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_41.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_41.npy
new file mode 100644
index 0000000000000000000000000000000000000000..55aaeb78facd6c6c75f1b82ca18995f10f9cc627
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_41.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_42.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_42.npy
new file mode 100644
index 0000000000000000000000000000000000000000..0b3dae3cc30bda13736ca486ae901c13ca2be9f2
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_42.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_43.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_43.npy
new file mode 100644
index 0000000000000000000000000000000000000000..9a53d114de5309a25cfcfde96102d507e04c744e
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_43.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_44.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_44.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2eb93e1b29eaf18e32b44a3b0a24e38cbea43be9
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_44.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_45.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_45.npy
new file mode 100644
index 0000000000000000000000000000000000000000..8c0dd9a32b6c5bb887e4db36b1276e8b4621cbcf
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_45.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_46.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_46.npy
new file mode 100644
index 0000000000000000000000000000000000000000..5e0da670a62a624964cb38258219fae55e247654
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_46.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_47.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_47.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2711da8a5ebe1d4ce0b34ef46f0c11f12fa8d6cf
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_47.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_48.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_48.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a294d19315e97f33de7519332728621f127e13cd
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_48.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_5.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_5.npy
new file mode 100644
index 0000000000000000000000000000000000000000..a7c4c5ba912eb3e45f2b9f7ddcb2b56bd2b4701d
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_5.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_6.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2664d172e7f30ef9975575625092ad7fadc4fb8a
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_6.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_7.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_7.npy
new file mode 100644
index 0000000000000000000000000000000000000000..9e26a49798920618950fed29b246343d48946bf9
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_7.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_8.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..7a6ce02d3b0c87a30f93fc585dc31957329892b4
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_8.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_9.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_9.npy
new file mode 100644
index 0000000000000000000000000000000000000000..06e4dddf69d837205acdc47036c7ea8437646b63
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_9.npy differ
diff --git a/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_init.npy b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_init.npy
new file mode 100644
index 0000000000000000000000000000000000000000..f4bd7917b76442f91900be31bb7344b3221853d6
Binary files /dev/null and b/examples/analytical-function/data/posterior/BAL_DKL/SeqPosterior_init.npy differ
diff --git a/examples/analytical-function/data/posterior/BODE_DKL/SeqPosterior_20.npy b/examples/analytical-function/data/posterior/BODE_DKL/SeqPosterior_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..fda8ba1ceab66e45ecac8eb3ef96f12d1a479417
Binary files /dev/null and b/examples/analytical-function/data/posterior/BODE_DKL/SeqPosterior_20.npy differ
diff --git a/examples/analytical-function/data/posterior/BODE_DKL/SeqPosterior_40.npy b/examples/analytical-function/data/posterior/BODE_DKL/SeqPosterior_40.npy
new file mode 100644
index 0000000000000000000000000000000000000000..1b741429b327d9d5bd248a0ba8b6a65f51041141
Binary files /dev/null and b/examples/analytical-function/data/posterior/BODE_DKL/SeqPosterior_40.npy differ
diff --git a/examples/analytical-function/data/posterior/BODE_DKL/SeqPosterior_5.npy b/examples/analytical-function/data/posterior/BODE_DKL/SeqPosterior_5.npy
new file mode 100644
index 0000000000000000000000000000000000000000..c10fa3dc7b589f8e494c6c4e7b688e67f186dcde
Binary files /dev/null and b/examples/analytical-function/data/posterior/BODE_DKL/SeqPosterior_5.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_1.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_1.npy
new file mode 100644
index 0000000000000000000000000000000000000000..6b5413c58ece5a71bd9218d746973c97848524e7
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_1.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_10.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..241e47fa0d0b163f3e124378e395291d467a1799
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_10.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_11.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_11.npy
new file mode 100644
index 0000000000000000000000000000000000000000..c1b0d9da3fc73f6026bc4e501723ae98cd1b5908
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_11.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_12.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..96d8bf9226f83a46348f46e849719fe3eebbd531
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_12.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_13.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_13.npy
new file mode 100644
index 0000000000000000000000000000000000000000..5a4720f22f5c27f067e4386113bb457cc1c6cf46
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_13.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_14.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..1f70c967a90c6d46522c6ea378e8cde3ced45880
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_14.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_15.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_15.npy
new file mode 100644
index 0000000000000000000000000000000000000000..1ac1c383f78dcdbb0081f965768e92f3d63cba67
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_15.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_16.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..3d6a418b0f64254379ee14109e598e422a04cd41
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_16.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_17.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_17.npy
new file mode 100644
index 0000000000000000000000000000000000000000..f7f2731ed4a7fe69bf2f6a14100282ae9572c2a5
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_17.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_18.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..e4b6ffd7e99690060635a2d1c2d02dbab5febd60
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_18.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_19.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_19.npy
new file mode 100644
index 0000000000000000000000000000000000000000..61f190f22b26d7184a31bcd588c01d8b380d67eb
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_19.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_2.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_2.npy
new file mode 100644
index 0000000000000000000000000000000000000000..3ccdca996f02b5d92e4e2b688551c2d55003c264
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_2.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_20.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..b350309abc0c7bbf28d1331576fbd72f4803b954
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_20.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_21.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_21.npy
new file mode 100644
index 0000000000000000000000000000000000000000..c0e350d92cafa7f683f922db74247e6af04c8a30
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_21.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_22.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..19686eaaae0473da2c13ba547c31990bb3c38c41
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_22.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_23.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_23.npy
new file mode 100644
index 0000000000000000000000000000000000000000..ba00848f7a9cb6a510314e327368d326046e3fe4
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_23.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_24.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_24.npy
new file mode 100644
index 0000000000000000000000000000000000000000..9547f11de7a74563ededa94c04654638ec187dd3
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_24.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_25.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_25.npy
new file mode 100644
index 0000000000000000000000000000000000000000..0111a52e70f47f91763b6e02ad42ba29b9931325
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_25.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_26.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_26.npy
new file mode 100644
index 0000000000000000000000000000000000000000..cf4767cc96a74baf71b0d71deced59a01309292a
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_26.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_27.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_27.npy
new file mode 100644
index 0000000000000000000000000000000000000000..838743d630ec7fc04bf62cb298d8346317dec999
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_27.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_28.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_28.npy
new file mode 100644
index 0000000000000000000000000000000000000000..743b5eb5e1ebb5abd4e20eb524683fcf22742cb0
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_28.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_29.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_29.npy
new file mode 100644
index 0000000000000000000000000000000000000000..c93b80f5be8013086d612e207b6592c76f421a22
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_29.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_3.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_3.npy
new file mode 100644
index 0000000000000000000000000000000000000000..984f353f6e897a5e60ee097cd6918fc6a1b3551b
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_3.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_30.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_30.npy
new file mode 100644
index 0000000000000000000000000000000000000000..7160ba971a5510e26f5d11acfe9608257138f878
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_30.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_31.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_31.npy
new file mode 100644
index 0000000000000000000000000000000000000000..8fbe4fc5f504e04ddcaccbcd6184a33e9d59a859
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_31.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_32.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_32.npy
new file mode 100644
index 0000000000000000000000000000000000000000..e894bcb71bf02e62fb763183e130d3b9cc087e81
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_32.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_33.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_33.npy
new file mode 100644
index 0000000000000000000000000000000000000000..34249decfba931a7a4339b8e77e59448c3362e1a
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_33.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_34.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_34.npy
new file mode 100644
index 0000000000000000000000000000000000000000..37839c7f3ea51df637fedd7ecb892ee6fc36e6c9
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_34.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_35.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_35.npy
new file mode 100644
index 0000000000000000000000000000000000000000..5c895454eb6f8d40081b0f79b8c00cc6ecc1574a
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_35.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_36.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_36.npy
new file mode 100644
index 0000000000000000000000000000000000000000..fd20a5f78d5a6cf461ca9c4c1673455127201132
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_36.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_37.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_37.npy
new file mode 100644
index 0000000000000000000000000000000000000000..ed971444870677e639ade70febf414922c66e19c
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_37.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_38.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_38.npy
new file mode 100644
index 0000000000000000000000000000000000000000..552028032255f68aad4752271b40fb9d064d979f
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_38.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_39.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_39.npy
new file mode 100644
index 0000000000000000000000000000000000000000..87782d4449d8fbf4ab1c0a299a76f10d8b77b7fb
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_39.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_4.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2d09c96e6f4b22096fcbc3c057ae3015f38d69e3
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_4.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_40.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_40.npy
new file mode 100644
index 0000000000000000000000000000000000000000..6e8c62be81b8bd5b94ae4cdc18ece4593d4e6546
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_40.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_5.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_5.npy
new file mode 100644
index 0000000000000000000000000000000000000000..0c289921e1866a5a5d8c655eba896119e9c3e742
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_5.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_6.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2927102b083e314abddf6a916c0bde2e6442864e
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_6.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_7.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_7.npy
new file mode 100644
index 0000000000000000000000000000000000000000..64ce5afc104aad7df693b09257681335d055e9bc
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_7.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_8.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..23b0bc224ebd53307557be9247645fa50ce620c4
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_8.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_9.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_9.npy
new file mode 100644
index 0000000000000000000000000000000000000000..d0df70d80536836353307b982c222eb26205c98d
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_9.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_init.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_init.npy
new file mode 100644
index 0000000000000000000000000000000000000000..90cae135df98b14732e1b24d5c5e67d9dfa5eaba
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BAL/SeqPosterior_init.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_1.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_1.npy
new file mode 100644
index 0000000000000000000000000000000000000000..ee0a4e2f642d227bf61c04a7d165cb037e0694d4
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_1.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_10.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_10.npy
new file mode 100644
index 0000000000000000000000000000000000000000..8f4265aea3f09220b8ba2ac265ec8f0fb25897a2
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_10.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_11.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_11.npy
new file mode 100644
index 0000000000000000000000000000000000000000..807281d57783595c1225c590b3c0ea032ca5874b
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_11.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_12.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_12.npy
new file mode 100644
index 0000000000000000000000000000000000000000..acd10283c931b15bb87265c55fd8d4afb7eb3823
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_12.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_13.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_13.npy
new file mode 100644
index 0000000000000000000000000000000000000000..75801891aaf2188184cec607e8b04550ee290c65
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_13.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_14.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_14.npy
new file mode 100644
index 0000000000000000000000000000000000000000..4a27492eda41a607f39c1d944993a03dcd20e511
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_14.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_15.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_15.npy
new file mode 100644
index 0000000000000000000000000000000000000000..55a38d05f60e78123195a683ff9c8db9900d0e24
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_15.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_16.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_16.npy
new file mode 100644
index 0000000000000000000000000000000000000000..571124512d188fcfab8c58157f468ddb0f51828d
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_16.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_17.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_17.npy
new file mode 100644
index 0000000000000000000000000000000000000000..8034e6e94c444f1c8ae9052b193b33b6a1178557
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_17.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_18.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_18.npy
new file mode 100644
index 0000000000000000000000000000000000000000..87bf58d252a03026f6949a360303e46777711b43
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_18.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_19.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_19.npy
new file mode 100644
index 0000000000000000000000000000000000000000..781715681b45c1f18d4eba764e7acfeb2317e0e9
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_19.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_2.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_2.npy
new file mode 100644
index 0000000000000000000000000000000000000000..bf6e74487f47050c54f522bb41d29c08c47a0afe
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_2.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_20.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_20.npy
new file mode 100644
index 0000000000000000000000000000000000000000..fda8ba1ceab66e45ecac8eb3ef96f12d1a479417
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_20.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_21.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_21.npy
new file mode 100644
index 0000000000000000000000000000000000000000..7aaf5dfafe3a3f3fa1932540de52eeb755e8abe9
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_21.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_22.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_22.npy
new file mode 100644
index 0000000000000000000000000000000000000000..d839d72cdf61ccbd30594833381f492587f07747
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_22.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_23.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_23.npy
new file mode 100644
index 0000000000000000000000000000000000000000..cde4d49957a8cf4e281fd9c239a25a73ca8e7ec3
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_23.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_24.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_24.npy
new file mode 100644
index 0000000000000000000000000000000000000000..579458830ff09de5b4f904315f4a7f779df6d0d7
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_24.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_25.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_25.npy
new file mode 100644
index 0000000000000000000000000000000000000000..9211e517b13fe8cb3ab4cf01ad3f936d6adc632f
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_25.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_26.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_26.npy
new file mode 100644
index 0000000000000000000000000000000000000000..82f73f893dfbb112d64ad8fc94c60600bfbd77f7
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_26.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_27.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_27.npy
new file mode 100644
index 0000000000000000000000000000000000000000..3afe7642d7c23c5f3e5e6a336e2eb9fea703af75
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_27.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_28.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_28.npy
new file mode 100644
index 0000000000000000000000000000000000000000..fc15c3a491407ee50db181e262f63f32e95fa72f
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_28.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_29.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_29.npy
new file mode 100644
index 0000000000000000000000000000000000000000..32efa114d37b11439180fb7d31a23a124d4ccc2f
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_29.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_3.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_3.npy
new file mode 100644
index 0000000000000000000000000000000000000000..e1187263971293e3b999ec7b1ba768168e77205b
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_3.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_30.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_30.npy
new file mode 100644
index 0000000000000000000000000000000000000000..2ba02b9ca25de4b48002fc746ba0eefe0a03aa94
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_30.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_31.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_31.npy
new file mode 100644
index 0000000000000000000000000000000000000000..7e6c114100a43d34a3faacef3d4934278ead3048
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_31.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_32.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_32.npy
new file mode 100644
index 0000000000000000000000000000000000000000..e0b1c785ced57cd1d6c6ea3fe5febfc8ec71ece1
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_32.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_33.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_33.npy
new file mode 100644
index 0000000000000000000000000000000000000000..6dcda0817a9b4fd89f0bba8922c2b52cff463dc2
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_33.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_34.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_34.npy
new file mode 100644
index 0000000000000000000000000000000000000000..740a4b631c67944015a19df0767fe61f3738d2d9
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_34.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_35.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_35.npy
new file mode 100644
index 0000000000000000000000000000000000000000..04cf3bcc1dbafa885e39eea988324acbdc63d1a9
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_35.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_36.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_36.npy
new file mode 100644
index 0000000000000000000000000000000000000000..5b24d50a3d1cc7b96409f651340e1db697c8a423
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_36.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_37.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_37.npy
new file mode 100644
index 0000000000000000000000000000000000000000..b3e2c03566cb8aee293f8de816ece3fe2748a3d3
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_37.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_38.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_38.npy
new file mode 100644
index 0000000000000000000000000000000000000000..0d63728879a4c7df148e27a304139985d12e7017
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_38.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_39.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_39.npy
new file mode 100644
index 0000000000000000000000000000000000000000..02d6b3ee69f8f39151920c42f72ff740b3ad58b8
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_39.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_4.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_4.npy
new file mode 100644
index 0000000000000000000000000000000000000000..059a9f5bb18f7fd1039795fb6b749ad08dc585cb
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_4.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_40.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_40.npy
new file mode 100644
index 0000000000000000000000000000000000000000..1b741429b327d9d5bd248a0ba8b6a65f51041141
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_40.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_5.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_5.npy
new file mode 100644
index 0000000000000000000000000000000000000000..c10fa3dc7b589f8e494c6c4e7b688e67f186dcde
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_5.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_6.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_6.npy
new file mode 100644
index 0000000000000000000000000000000000000000..7a95e3fbcec5c58c0f70fd0d5a8bc69b8bf7a963
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_6.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_7.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_7.npy
new file mode 100644
index 0000000000000000000000000000000000000000..b7b20beb1435259ecfc1e7a902805a794ed900eb
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_7.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_8.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_8.npy
new file mode 100644
index 0000000000000000000000000000000000000000..e956155e9421057f0504c616b11ea7ac7c681f41
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_8.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_9.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_9.npy
new file mode 100644
index 0000000000000000000000000000000000000000..03632eea30ff6018ba57324335dcd5ec74d61037
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_9.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_init.npy b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_init.npy
new file mode 100644
index 0000000000000000000000000000000000000000..f573f56fbe19d93deb2d2a4a17c729844832ee2a
Binary files /dev/null and b/examples/analytical-function/data/posterior/posterior_2D_DKL_BODE/SeqPosterior_init.npy differ
diff --git a/examples/analytical-function/data/posterior/posterior_orig.csv b/examples/analytical-function/data/posterior/posterior_orig.csv
new file mode 100644
index 0000000000000000000000000000000000000000..d50c4c4d928097785e4bc3fc46714d1257285c9f
--- /dev/null
+++ b/examples/analytical-function/data/posterior/posterior_orig.csv
@@ -0,0 +1,17791 @@
+$\theta_{1}$,$\theta_{2}$
+-0.5053093321059516,0.3464209655227144
+-0.2503403924088539,1.5610839749457606
+1.3108380934712565,-0.4947653100675753
+-0.4499536611704508,0.33315304638308496
+0.7037002872643395,1.0536446663049537
+0.2639381847880326,-0.08475556473620599
+-0.7692170582461695,0.5628411893581614
+-0.5250575248261623,-0.24129701894736455
+0.27077384266910715,-0.3552056655207011
+-0.1516651180069023,-0.22472514665477483
+-0.4916617502636895,1.3290149861458507
+-1.154466140024725,-0.5264439196906422
+0.8638454401780578,0.6370887961504713
+0.08758184265789484,1.7825424800280465
+-0.8418679509524006,1.239976578898788
+-0.7102087777087558,0.6258584578029999
+-0.6025861531842995,0.6129883355002392
+-0.1635014514977523,0.5285302138061596
+1.2675503545405524,-0.27191599924718635
+1.722623520211238,-2.0093713908710864
+1.1999376790370633,-0.040912844635069945
+-0.4290081160945971,-0.1973312505774666
+-0.014978004247042029,1.9009498970256493
+-0.44167231139542196,-0.23273573437276085
+1.7758149671620844,-2.2146191806542244
+1.7520832346023985,-3.0769987336137845
+0.17564766491733047,-0.17090185930065385
+0.16604397505733415,1.2077947306624552
+1.1635921769861306,0.3250614211287881
+0.6552996494766703,-0.5557980237882176
+-0.5053093321059516,0.3464209655227144
+-0.2503403924088539,1.5610839749457606
+1.3108380934712565,-0.4947653100675753
+1.3410217792991614,-0.8179397142492559
+0.7037002872643395,1.0536446663049537
+0.2639381847880326,-0.08475556473620599
+1.2785176628328716,-1.633038901061103
+-0.5250575248261623,-0.24129701894736455
+-0.9068988352748052,0.8998307366038109
+0.35335586618343995,-0.3539020388514501
+0.1450003084058062,0.9292426607469267
+0.9742155939297248,-1.002879019207505
+1.4080478809050319,-0.4488708718806268
+1.183694781896851,0.5017071455928137
+-0.525339799472231,0.09664647707973373
+-0.18763560912296323,0.3803657962882169
+1.6115304607006014,-1.0510208452744814
+0.31443319961573807,2.0684383430564717
+1.2675503545405524,-0.27191599924718635
+-0.0033082431123794276,-0.08659059889670528
+1.1999376790370633,-0.040912844635069945
+0.19790016572768318,2.2877711796870277
+-0.014978004247042029,1.9009498970256493
+-0.1631074620290083,0.633034958072537
+0.17103405980865966,1.4267765969969046
+1.7520832346023985,-3.0769987336137845
+0.17564766491733047,-0.17090185930065385
+-0.9360854831721612,0.116344808632697
+1.1635921769861306,0.3250614211287881
+-0.7708227824482916,1.551867250464856
+0.6182935674934222,-0.5372486998530183
+-0.2503403924088539,1.5610839749457606
+-0.04879960478928339,1.6647469706753903
+-0.45266763919349096,0.21812156159554602
+0.7037002872643395,1.0536446663049537
+0.2639381847880326,-0.08475556473620599
+1.2785176628328716,-1.633038901061103
+-0.5250575248261623,-0.24129701894736455
+-0.9068988352748052,0.8998307366038109
+0.35335586618343995,-0.3539020388514501
+-0.43373622006151963,-0.32564218152609914
+0.9742155939297248,-1.002879019207505
+0.454046851749124,1.594785377954205
+1.183694781896851,0.5017071455928137
+-0.525339799472231,0.09664647707973373
+0.9407359838370817,1.2360444072800965
+1.6115304607006014,-1.0510208452744814
+0.18524588162757422,2.187815391469033
+1.2675503545405524,-0.27191599924718635
+-0.18067770699301405,1.0717833390219351
+0.46125820449152777,1.3127881784010684
+0.19790016572768318,2.2877711796870277
+-0.014978004247042029,1.9009498970256493
+-0.1631074620290083,0.633034958072537
+0.27647020099787245,2.357860503186485
+0.7499336493026392,-0.4987188155721806
+0.17564766491733047,-0.17090185930065385
+0.22072058423295826,2.0967888817084055
+0.11608176667951817,1.7094562729066778
+1.2088313952441543,-1.6078222956267787
+0.6182935674934222,-0.5372486998530183
+0.4195723739489977,-0.5758257851191217
+0.7085809528909399,-1.0398911654061997
+-0.45266763919349096,0.21812156159554602
+0.7037002872643395,1.0536446663049537
+-0.7848956489111826,0.6910510899230419
+0.7883818564808993,-0.7128685648056312
+-0.5149573041165096,1.5209317071998028
+-0.9068988352748052,0.8998307366038109
+0.35335586618343995,-0.3539020388514501
+-0.43373622006151963,-0.32564218152609914
+0.9742155939297248,-1.002879019207505
+0.599446657119634,1.7611926309209247
+0.5538757163900756,1.1130403981137975
+-0.525339799472231,0.09664647707973373
+0.9407359838370817,1.2360444072800965
+1.6115304607006014,-1.0510208452744814
+0.18524588162757422,2.187815391469033
+-0.6754276638279351,1.460948457551204
+-0.18067770699301405,1.0717833390219351
+-0.7514573838133519,0.598973942314105
+0.19790016572768318,2.2877711796870277
+0.30340850291028176,-0.684924427902603
+-0.1631074620290083,0.633034958072537
+1.1293577456430368,0.6799862689295298
+0.7499336493026392,-0.4987188155721806
+0.17564766491733047,-0.17090185930065385
+0.22072058423295826,2.0967888817084055
+0.11608176667951817,1.7094562729066778
+1.2088313952441543,-1.6078222956267787
+-0.33478579653129426,0.1311124725515458
+0.4195723739489977,-0.5758257851191217
+-0.3253651275477416,0.5066901649853139
+-0.45266763919349096,0.21812156159554602
+0.49107769881087693,-0.037052022114241856
+-0.6226475904351041,0.2589023347908567
+0.7883818564808993,-0.7128685648056312
+-0.5149573041165096,1.5209317071998028
+-0.9633199518581674,0.393072535817966
+0.9552001039599954,0.05422246320616064
+-0.43373622006151963,-0.32564218152609914
+0.9742155939297248,-1.002879019207505
+0.6984415692946255,-0.5720635498627894
+0.5538757163900756,1.1130403981137975
+-0.525339799472231,0.09664647707973373
+-0.11260151022394341,-0.1399176632826965
+1.6115304607006014,-1.0510208452744814
+0.18524588162757422,2.187815391469033
+-0.6754276638279351,1.460948457551204
+-0.596947756878451,0.7821676393989948
+-0.6801760069548315,0.6716094995202454
+0.02235736229315466,-0.030868086597104716
+0.48442792610087876,2.1505050477952667
+-0.6873579130906606,0.5389801365151143
+1.1293577456430368,0.6799862689295298
+0.7499336493026392,-0.4987188155721806
+0.17564766491733047,-0.17090185930065385
+0.22072058423295826,2.0967888817084055
+0.11608176667951817,1.7094562729066778
+1.2088313952441543,-1.6078222956267787
+-0.33478579653129426,0.1311124725515458
+0.4195723739489977,-0.5758257851191217
+-0.11743497836686867,-0.2386424815842973
+0.09756590109008184,1.329888021204482
+-0.5994269936936759,1.1586608446081375
+-0.6226475904351041,0.2589023347908567
+0.7883818564808993,-0.7128685648056312
+-0.24938316724166104,0.5338994785341503
+-0.2418850048764388,-0.12940973560982205
+0.9552001039599954,0.05422246320616064
+0.1745992679990781,1.562124182223414
+0.9742155939297248,-1.002879019207505
+1.0362367792121314,-0.8845173836955289
+-0.7180844898848368,0.6745485430910141
+-0.525339799472231,0.09664647707973373
+-0.11260151022394341,-0.1399176632826965
+1.6115304607006014,-1.0510208452744814
+0.18524588162757422,2.187815391469033
+1.427628766553249,-1.93943220063422
+-0.2045456494104021,2.396569972445869
+0.35849593437306526,1.015133096755812
+0.9780016636442144,0.12710903697812692
+0.48442792610087876,2.1505050477952667
+-0.6873579130906606,0.5389801365151143
+1.3020922892553133,-1.7113863678664565
+0.6730609633311938,-0.5472352522280904
+0.17564766491733047,-0.17090185930065385
+0.22072058423295826,2.0967888817084055
+0.11608176667951817,1.7094562729066778
+0.14581197773190313,0.7538389090294754
+-0.7348755419965166,0.03248451743484049
+0.8927962093043634,0.47092671946058795
+-0.6681120307739363,0.4064718549469103
+1.7029895689954184,-1.7019618696639327
+-0.5926820464971653,0.8080512566681
+-0.6226475904351041,0.2589023347908567
+0.7883818564808993,-0.7128685648056312
+-0.63544631280411,-0.33411925810854615
+-0.12898463652067022,0.4849147194032143
+0.9552001039599954,0.05422246320616064
+-0.6504004418501388,0.29384223326808745
+1.3945954327885872,-1.427166647300416
+1.0362367792121314,-0.8845173836955289
+-0.7180844898848368,0.6745485430910141
+-0.525339799472231,0.09664647707973373
+-0.11260151022394341,-0.1399176632826965
+-1.0923143519018743,-0.5262254018091825
+0.18524588162757422,2.187815391469033
+1.427628766553249,-1.93943220063422
+-0.4176378410089264,1.1272522404760366
+-0.7783721180931695,1.2654744031405272
+0.9780016636442144,0.12710903697812692
+0.48442792610087876,2.1505050477952667
+-0.7953485007033426,0.2902712630085715
+0.17945910330928022,-0.20610572177726993
+1.0863592666900423,-1.0120474432019777
+1.0612840278540154,0.8037326073399161
+0.22072058423295826,2.0967888817084055
+0.11608176667951817,1.7094562729066778
+0.5640726794242966,1.2540194938442863
+0.16191912623411064,0.40231927749796514
+-0.5174589067304702,-0.3706902407586618
+-0.5745719597946655,0.8988884647699387
+1.7029895689954184,-1.7019618696639327
+-0.5926820464971653,0.8080512566681
+-0.6226475904351041,0.2589023347908567
+0.7883818564808993,-0.7128685648056312
+0.5022610043199605,-0.6777302753398546
+-0.12898463652067022,0.4849147194032143
+1.6066189470963137,-1.1136111008520198
+0.7965591828845368,-0.32751229802780424
+1.3945954327885872,-1.427166647300416
+1.0362367792121314,-0.8845173836955289
+-0.7180844898848368,0.6745485430910141
+-0.525339799472231,0.09664647707973373
+-0.11260151022394341,-0.1399176632826965
+-0.5055626851805348,-0.4156086881562447
+0.18524588162757422,2.187815391469033
+-0.9045172078276738,1.1247952992858032
+-0.4176378410089264,1.1272522404760366
+-0.7783721180931695,1.2654744031405272
+0.3976933394943344,1.3344143853506978
+-0.403284268900615,1.8708628424025866
+-0.7953485007033426,0.2902712630085715
+0.17945910330928022,-0.20610572177726993
+1.0863592666900423,-1.0120474432019777
+1.0612840278540154,0.8037326073399161
+0.22072058423295826,2.0967888817084055
+-0.7705495917475944,1.3862932599399758
+0.5640726794242966,1.2540194938442863
+0.16191912623411064,0.40231927749796514
+-0.5174589067304702,-0.3706902407586618
+-0.20501051661305028,0.305368025213353
+0.922993207722996,-0.9163792975476552
+0.7699594110449504,-0.7170576677026601
+-0.6226475904351041,0.2589023347908567
+0.7883818564808993,-0.7128685648056312
+-0.10862278978756301,0.7732117615886062
+-0.12898463652067022,0.4849147194032143
+1.6066189470963137,-1.1136111008520198
+0.7993108041941217,-1.003553085853436
+0.12285700595016104,2.378742127862646
+1.0362367792121314,-0.8845173836955289
+-0.7180844898848368,0.6745485430910141
+-0.525339799472231,0.09664647707973373
+-0.4522432900785449,0.325326531521933
+-0.04651186388704569,0.7797548077587114
+0.18524588162757422,2.187815391469033
+0.20091910584611752,0.6814337532929979
+0.8164034885798728,-0.5908131870764267
+-0.7783721180931695,1.2654744031405272
+1.2409118166612045,-1.3504637931213364
+0.42525544949551963,1.5133533170103624
+-0.8432095021705539,0.3732773058733243
+0.17945910330928022,-0.20610572177726993
+1.0863592666900423,-1.0120474432019777
+1.0612840278540154,0.8037326073399161
+0.22072058423295826,2.0967888817084055
+1.3391702343514453,-1.1214337292809344
+1.8697417018199456,-2.5092354620810315
+0.16191912623411064,0.40231927749796514
+-0.5174589067304702,-0.3706902407586618
+1.4031282417662472,-1.3630717016004295
+-0.4967361447225084,1.252537807949157
+0.7699594110449504,-0.7170576677026601
+-0.15505005100453384,-0.06907639918302308
+0.7883818564808993,-0.7128685648056312
+0.6193518852704646,-0.4885831536852441
+0.09189146199074222,-0.3103021631988357
+1.6066189470963137,-1.1136111008520198
+0.7993108041941217,-1.003553085853436
+-0.1058977705150097,1.2382021994646641
+1.0362367792121314,-0.8845173836955289
+-0.7180844898848368,0.6745485430910141
+-0.525339799472231,0.09664647707973373
+-0.562374163034117,0.6806501681912499
+-0.6265593760563886,0.20643562147527839
+0.18524588162757422,2.187815391469033
+-0.2917379668173985,0.008353609620599611
+0.8164034885798728,-0.5908131870764267
+0.7329508042321565,-0.7894567703596095
+-0.6757512211788298,1.4645360502986566
+0.42525544949551963,1.5133533170103624
+0.8037735810110554,0.09732101142953709
+-0.749719841262179,0.46727391295764337
+1.0863592666900423,-1.0120474432019777
+1.0612840278540154,0.8037326073399161
+0.22072058423295826,2.0967888817084055
+-0.3383846885906139,0.8343285051002605
+1.8697417018199456,-2.5092354620810315
+1.4028912059085172,-1.0879767165835172
+-0.6197976713811776,0.9905846157954286
+0.4277994672870295,0.31117752425973927
+-0.4967361447225084,1.252537807949157
+1.5006050781759672,-0.5682360602901709
+-0.15505005100453384,-0.06907639918302308
+0.538371392273679,0.26388453634741593
+1.339597638263306,-0.6216366207014237
+0.09189146199074222,-0.3103021631988357
+0.9297653063844111,-0.5124125583475931
+-0.7654081507658069,0.007636047634596951
+-0.7808609954446696,0.00968419690805089
+1.0362367792121314,-0.8845173836955289
+0.24926111037960885,1.4310787516609644
+1.0276208553986867,0.5573523435784178
+-0.562374163034117,0.6806501681912499
+-0.45734734712903774,-0.03363605507623152
+0.18524588162757422,2.187815391469033
+0.7430534282780101,-0.2188970035934631
+0.8164034885798728,-0.5908131870764267
+0.7329508042321565,-0.7894567703596095
+-0.6757512211788298,1.4645360502986566
+0.42525544949551963,1.5133533170103624
+0.8037735810110554,0.09732101142953709
+-0.749719841262179,0.46727391295764337
+1.0863592666900423,-1.0120474432019777
+1.0612840278540154,0.8037326073399161
+0.22072058423295826,2.0967888817084055
+-0.3383846885906139,0.8343285051002605
+1.8697417018199456,-2.5092354620810315
+0.1966192691594344,-0.4376765395933403
+-0.6197976713811776,0.9905846157954286
+-0.577210622552996,1.7678463266622706
+0.8678801611507725,-1.1966075837756058
+1.249113331644049,-0.47176874785431444
+1.0798131336224124,-0.9540500145880517
+1.453258951426073,-1.2429034832615429
+1.339597638263306,-0.6216366207014237
+0.2864729168815008,0.16784217746368402
+-0.18172852672510725,-0.09956506105715701
+-0.7654081507658069,0.007636047634596951
+-0.19411635104206665,-0.11291645526747662
+-0.5100460101286504,0.46841252700182195
+-0.020217910873387923,-0.152191509353375
+1.0276208553986867,0.5573523435784178
+1.0193010586664288,-0.7100774306592084
+-0.45734734712903774,-0.03363605507623152
+0.18524588162757422,2.187815391469033
+0.7430534282780101,-0.2188970035934631
+0.4040891990322401,-0.5135309949965021
+-0.4222237829193909,1.1232040420525178
+-0.359984063356492,0.972156885868937
+0.42525544949551963,1.5133533170103624
+0.8037735810110554,0.09732101142953709
+-0.2325401053515746,0.99983792324578
+0.20157162855604305,2.22024030681062
+1.261173988723529,0.22510981475037517
+0.22072058423295826,2.0967888817084055
+1.2673278147640576,-1.120253577970324
+1.8697417018199456,-2.5092354620810315
+1.6921502687001537,-1.6307893820873005
+-0.6197976713811776,0.9905846157954286
+-0.577210622552996,1.7678463266622706
+0.7512576575528925,1.5976020844510335
+0.5492363824625133,-0.250792056384667
+1.0798131336224124,-0.9540500145880517
+1.453258951426073,-1.2429034832615429
+1.339597638263306,-0.6216366207014237
+1.2129728869630274,-0.1740742516035489
+-0.18172852672510725,-0.09956506105715701
+0.00618518629146958,1.2206994184380902
+0.15607438286746997,-0.4263540044268943
+-0.5100460101286504,0.46841252700182195
+0.15959445406437334,0.19345570527252487
+1.0276208553986867,0.5573523435784178
+-0.13764988107291265,-0.22761747640445507
+-0.45734734712903774,-0.03363605507623152
+0.7381355528391419,1.704323422391908
+0.8431885253932445,-0.06564356403721372
+0.4040891990322401,-0.5135309949965021
+0.4123714596804531,1.8524258973270817
+-0.359984063356492,0.972156885868937
+0.42525544949551963,1.5133533170103624
+0.13757581657266518,0.11800903083011827
+-0.2325401053515746,0.99983792324578
+0.9138542956856225,1.0802184956736034
+1.261173988723529,0.22510981475037517
+0.22072058423295826,2.0967888817084055
+-0.8878764535176389,0.8407193758765554
+0.7299410348000539,-0.7130440664351931
+1.6921502687001537,-1.6307893820873005
+-0.6197976713811776,0.9905846157954286
+-0.577210622552996,1.7678463266622706
+-0.2563568527353878,0.42267514832726083
+0.5712997398913231,-0.6396657566895774
+1.0798131336224124,-0.9540500145880517
+0.16467862037920988,2.3707041846067742
+1.339597638263306,-0.6216366207014237
+1.2129728869630274,-0.1740742516035489
+0.7407181158151038,-0.8347315178725216
+0.7407568750757356,0.7200049747227439
+-0.06202720630207914,1.8169561572121664
+-0.1817443668811746,0.1587133396465245
+0.15959445406437334,0.19345570527252487
+1.0276208553986867,0.5573523435784178
+-0.13764988107291265,-0.22761747640445507
+-0.45734734712903774,-0.03363605507623152
+-0.2949979906734477,1.1445755459908296
+0.9633186609386701,-0.20030680997360223
+0.014255394895904605,0.2609462213891709
+0.4123714596804531,1.8524258973270817
+0.219353885150393,2.19358819458457
+1.0946677436327423,-0.6264963779207244
+0.13757581657266518,0.11800903083011827
+-0.12934456736519473,0.18768847785142728
+1.2839112075373198,0.0949764469956389
+-0.5858317027549806,1.3638637592459695
+0.22072058423295826,2.0967888817084055
+-0.8878764535176389,0.8407193758765554
+0.7928440716707081,-0.9937701425216839
+1.6921502687001537,-1.6307893820873005
+-0.6197976713811776,0.9905846157954286
+-0.577210622552996,1.7678463266622706
+-0.2563568527353878,0.42267514832726083
+1.2227555561568857,-0.8510028758235189
+0.9322987644624694,1.3346800697817638
+0.16467862037920988,2.3707041846067742
+0.1460235148131448,-0.07474932482558144
+1.4519062558340856,-1.4310517774342562
+0.8636798586253789,-0.36150129221395183
+0.5327399678674061,-0.6142090933437763
+-0.15958507224383583,2.5495537211004926
+0.24580214017818622,1.7183223440025606
+0.7409801025075142,-0.984737003972104
+1.0276208553986867,0.5573523435784178
+-0.13764988107291265,-0.22761747640445507
+-0.45734734712903774,-0.03363605507623152
+0.9108254404418489,0.841079320173217
+0.9633186609386701,-0.20030680997360223
+0.014255394895904605,0.2609462213891709
+0.4123714596804531,1.8524258973270817
+0.219353885150393,2.19358819458457
+1.0946677436327423,-0.6264963779207244
+0.13757581657266518,0.11800903083011827
+-0.12934456736519473,0.18768847785142728
+0.06067101318672152,-0.28440313865415223
+-0.5858317027549806,1.3638637592459695
+0.4955360155211592,1.6535484551304362
+-0.8878764535176389,0.8407193758765554
+0.7928440716707081,-0.9937701425216839
+1.6351843362806453,-1.2969909005932614
+-0.6197976713811776,0.9905846157954286
+-0.577210622552996,1.7678463266622706
+-0.2563568527353878,0.42267514832726083
+1.2227555561568857,-0.8510028758235189
+0.9322987644624694,1.3346800697817638
+0.16467862037920988,2.3707041846067742
+0.1460235148131448,-0.07474932482558144
+1.4519062558340856,-1.4310517774342562
+0.8636798586253789,-0.36150129221395183
+0.5327399678674061,-0.6142090933437763
+1.1639419154672477,-1.8876990343237743
+0.24580214017818622,1.7183223440025606
+0.7409801025075142,-0.984737003972104
+1.0276208553986867,0.5573523435784178
+-0.13764988107291265,-0.22761747640445507
+-0.7640236747778975,0.5978317159083829
+-0.7764251344303268,0.6778732962580112
+0.9633186609386701,-0.20030680997360223
+0.5131195528387468,-0.007772842630351995
+0.4123714596804531,1.8524258973270817
+0.1486612273770691,0.035434704889841184
+1.0946677436327423,-0.6264963779207244
+0.13757581657266518,0.11800903083011827
+-0.17480108230296618,0.7212319883163519
+-0.8706058425064462,0.48025938610860175
+-0.5858317027549806,1.3638637592459695
+0.4955360155211592,1.6535484551304362
+-0.47724980230819547,-0.17601424523460818
+-0.3056190507325021,2.0127268961530866
+0.9416800442966607,0.25732556514007704
+-0.6197976713811776,0.9905846157954286
+-0.5563206199849793,-0.03488319153706168
+-0.21761048752652284,0.16599449143059314
+0.295422947680666,2.3504467266845612
+0.7701461857419032,0.6141169594509859
+1.0058162423380583,0.9067848212086931
+0.1460235148131448,-0.07474932482558144
+-0.19290757555540775,0.8110779404702647
+0.8636798586253789,-0.36150129221395183
+0.8640838772993594,0.465496576649854
+0.5630195491890806,0.25198772556764076
+0.24580214017818622,1.7183223440025606
+0.6915819275481158,1.0348907906811389
+1.0276208553986867,0.5573523435784178
+-0.13764988107291265,-0.22761747640445507
+-0.7640236747778975,0.5978317159083829
+0.5887872014104362,-0.7608357355208953
+0.9633186609386701,-0.20030680997360223
+1.3335967858005242,-1.9517855301936797
+0.4123714596804531,1.8524258973270817
+0.9274883272767281,-0.8671006236909593
+0.003037641401061386,2.313019869451193
+0.13757581657266518,0.11800903083011827
+1.749264953563672,-1.9194079532827752
+1.3539297112834008,-1.567449933011139
+-0.5858317027549806,1.3638637592459695
+0.4955360155211592,1.6535484551304362
+-0.47724980230819547,-0.17601424523460818
+-0.3056190507325021,2.0127268961530866
+0.9416800442966607,0.25732556514007704
+0.1555299955506278,2.096900740749002
+-0.5563206199849793,-0.03488319153706168
+-0.21761048752652284,0.16599449143059314
+1.6810731754526387,-1.7406868015427719
+-0.08091241606181776,2.5045709628545403
+1.0058162423380583,0.9067848212086931
+0.1460235148131448,-0.07474932482558144
+-0.19290757555540775,0.8110779404702647
+0.4638140048761582,0.35620193105039866
+0.7299439937678682,1.4452573987939137
+0.8332745700774429,-0.37231002897993115
+0.24580214017818622,1.7183223440025606
+-0.3333530750722078,1.3218894484849248
+1.3629293830032287,-1.3769545235716205
+-0.13764988107291265,-0.22761747640445507
+0.6838909627773953,1.6573029227842766
+1.059340582846612,0.629185639133528
+0.9633186609386701,-0.20030680997360223
+1.3335967858005242,-1.9517855301936797
+0.4123714596804531,1.8524258973270817
+0.9274883272767281,-0.8671006236909593
+0.003037641401061386,2.313019869451193
+0.337127042754364,0.772898290120486
+0.3808835913290728,1.2211114247165822
+0.4994811468662761,1.3860459099353606
+-0.5858317027549806,1.3638637592459695
+0.4955360155211592,1.6535484551304362
+-0.47724980230819547,-0.17601424523460818
+-0.3056190507325021,2.0127268961530866
+0.5831781118268866,1.6227303595170288
+1.4061369997130613,-0.2907311438029457
+-0.5563206199849793,-0.03488319153706168
+-0.21761048752652284,0.16599449143059314
+1.6810731754526387,-1.7406868015427719
+-0.08091241606181776,2.5045709628545403
+1.056897483931173,0.6236762877423453
+0.1460235148131448,-0.07474932482558144
+-0.19290757555540775,0.8110779404702647
+-0.9045957038655589,0.639810470119952
+1.2796826304389224,-0.2744419774595908
+0.04546897064007327,1.374276904516188
+0.24580214017818622,1.7183223440025606
+-0.3333530750722078,1.3218894484849248
+1.3629293830032287,-1.3769545235716205
+-0.13764988107291265,-0.22761747640445507
+-0.4208103825570006,1.7222189866165978
+1.059340582846612,0.629185639133528
+0.9633186609386701,-0.20030680997360223
+0.5495273365652522,1.7576229094464058
+0.4123714596804531,1.8524258973270817
+0.9274883272767281,-0.8671006236909593
+1.0679030660134416,1.0398841150643294
+-0.15229857580433648,1.5772059177235631
+0.3808835913290728,1.2211114247165822
+0.4994811468662761,1.3860459099353606
+-0.5858317027549806,1.3638637592459695
+1.284777693657457,-1.878796129548339
+-0.47724980230819547,-0.17601424523460818
+-0.3056190507325021,2.0127268961530866
+0.5831781118268866,1.6227303595170288
+1.4061369997130613,-0.2907311438029457
+-0.5563206199849793,-0.03488319153706168
+-0.21761048752652284,0.16599449143059314
+0.0668489154355204,1.6610488967867874
+0.6834254234265726,-0.5106114748792773
+-0.26749114135267316,0.3071682213420852
+0.7273441115693877,-0.6761481436589697
+-0.19290757555540775,0.8110779404702647
+0.919862632140398,-0.1969436890340459
+1.2796826304389224,-0.2744419774595908
+-0.7293115819293836,0.13092755825891386
+0.24580214017818622,1.7183223440025606
+-0.3333530750722078,1.3218894484849248
+1.3629293830032287,-1.3769545235716205
+-0.13764988107291265,-0.22761747640445507
+0.5474286176699372,-0.024930538477265785
+1.4846627350744883,-1.0018607897820437
+0.23349653797746178,2.283528868797296
+0.5495273365652522,1.7576229094464058
+0.4123714596804531,1.8524258973270817
+1.162753168468668,-0.7357901053216125
+0.07212107420328123,1.4973708016860654
+-0.6309909639074616,-0.34515681144138965
+0.3808835913290728,1.2211114247165822
+0.47405801024380406,1.6631497240479096
+-0.5858317027549806,1.3638637592459695
+1.284777693657457,-1.878796129548339
+0.6294929312640741,0.9338399614186432
+-0.3056190507325021,2.0127268961530866
+0.5831781118268866,1.6227303595170288
+1.4061369997130613,-0.2907311438029457
+-0.5563206199849793,-0.03488319153706168
+-0.21761048752652284,0.16599449143059314
+0.0668489154355204,1.6610488967867874
+0.6834254234265726,-0.5106114748792773
+-0.4985524720835245,-0.4965759967835648
+1.2717326755558966,-1.2976112810415588
+1.5726269604347625,-1.8190189689523077
+0.6662515562560418,-0.16326306011084324
+1.2796826304389224,-0.2744419774595908
+0.25825717232160805,0.04088161199750312
+0.24580214017818622,1.7183223440025606
+-0.15959414545240053,1.502268253626175
+1.3629293830032287,-1.3769545235716205
+-0.13764988107291265,-0.22761747640445507
+0.5474286176699372,-0.024930538477265785
+0.25735473337876985,1.7730578188972048
+0.23349653797746178,2.283528868797296
+0.5495273365652522,1.7576229094464058
+-0.00647350530119678,0.4342999231842476
+1.162753168468668,-0.7357901053216125
+0.07212107420328123,1.4973708016860654
+-0.12115067073042955,1.0821903041725855
+0.3808835913290728,1.2211114247165822
+0.14181667168040707,-0.4901912326979158
+-0.5858317027549806,1.3638637592459695
+0.78242451862788,1.2485643206180748
+0.6294929312640741,0.9338399614186432
+-0.3056190507325021,2.0127268961530866
+0.25582133347099945,1.9172814191911125
+1.4061369997130613,-0.2907311438029457
+1.0823148343631182,-0.39671160600206257
+-0.21761048752652284,0.16599449143059314
+-0.06722526046428567,0.6683171253639167
+0.6834254234265726,-0.5106114748792773
+0.006414193659293729,1.366374464281983
+1.3197521418419196,-1.7644563272887144
+-0.27506524208384087,0.2576017208612762
+-0.1266755590992561,2.251788380057598
+1.475058506656059,-1.597803860699713
+-0.5046683723026861,1.4564792518704226
+0.24580214017818622,1.7183223440025606
+-0.15959414545240053,1.502268253626175
+1.3629293830032287,-1.3769545235716205
+-0.13764988107291265,-0.22761747640445507
+-0.059777720816655736,2.0091974276272775
+0.25735473337876985,1.7730578188972048
+0.23349653797746178,2.283528868797296
+0.5495273365652522,1.7576229094464058
+0.010369414034276048,-0.2416899614047941
+0.158914142816727,0.4076441339305835
+-0.6123759093335387,1.8285144338092358
+-0.12115067073042955,1.0821903041725855
+-0.2332110007452023,1.9050456381085383
+1.1350836699919413,-0.10488367753763031
+-0.5381915754291811,0.5663100630535651
+-0.35742917512850847,-0.17224093906144428
+0.15330829011831293,1.1968486218979533
+0.5178641649238076,1.893312607258689
+0.25582133347099945,1.9172814191911125
+1.4061369997130613,-0.2907311438029457
+1.0823148343631182,-0.39671160600206257
+-0.21761048752652284,0.16599449143059314
+-0.24290437799911027,0.31730410656034125
+0.6834254234265726,-0.5106114748792773
+-0.11044763302849331,1.3694780898040102
+1.3197521418419196,-1.7644563272887144
+-0.27506524208384087,0.2576017208612762
+-0.5815116718496713,0.2658904418448459
+1.475058506656059,-1.597803860699713
+-0.5046683723026861,1.4564792518704226
+0.24580214017818622,1.7183223440025606
+-0.15959414545240053,1.502268253626175
+1.3629293830032287,-1.3769545235716205
+0.38069269306144804,1.4347787220267816
+-0.6943837657354685,0.8535566644785626
+1.4194938539720479,-0.5715525340871319
+0.23349653797746178,2.283528868797296
+0.5495273365652522,1.7576229094464058
+1.013791470547586,-1.223304105773275
+0.158914142816727,0.4076441339305835
+-0.6123759093335387,1.8285144338092358
+-0.12115067073042955,1.0821903041725855
+0.45327117676198586,-0.019125049626885826
+1.1350836699919413,-0.10488367753763031
+-0.5381915754291811,0.5663100630535651
+0.6652681515262548,1.7559426251583057
+-0.3136893196512578,2.426774478986558
+0.5178641649238076,1.893312607258689
+1.5245018155781285,-1.239036790250112
+1.4061369997130613,-0.2907311438029457
+1.0823148343631182,-0.39671160600206257
+-0.33297428523568906,1.3568455300312494
+-0.09721107123033654,0.3063241655716611
+-0.2529051508206548,0.26139105536560736
+-0.11044763302849331,1.3694780898040102
+1.7374192538407736,-2.2491186943832204
+-0.27506524208384087,0.2576017208612762
+0.27309242271004,0.4806174987986163
+1.475058506656059,-1.597803860699713
+1.5364939400644169,-1.7512093902525276
+0.24580214017818622,1.7183223440025606
+-0.15959414545240053,1.502268253626175
+-0.5395865391862176,1.1147393581890652
+0.39574877698198874,2.0241663321520935
+0.5434552336192018,-0.29341912463672104
+0.4944494377241129,1.8732154850573632
+0.2619514233968961,0.5002969419629121
+0.5495273365652522,1.7576229094464058
+1.1988259494445646,-1.3715838270960632
+0.22960344938270183,0.3775037236921687
+-0.6123759093335387,1.8285144338092358
+0.34325256250702674,-0.1698845657680308
+1.006329788102986,0.10977995008191699
+-0.7390982754973587,0.4997399676890179
+1.3096306908488984,0.41635008422535713
+0.6652681515262548,1.7559426251583057
+-0.994745589870548,0.9385110341417264
+-0.2543206490363833,2.497229450522481
+-0.22910680633412434,0.36296161859203413
+1.4061369997130613,-0.2907311438029457
+0.435353121299894,0.8942162742989905
+-0.33297428523568906,1.3568455300312494
+-0.09721107123033654,0.3063241655716611
+-0.2529051508206548,0.26139105536560736
+-0.11044763302849331,1.3694780898040102
+0.007246503789721248,0.03308653200946382
+-0.27506524208384087,0.2576017208612762
+0.08612319349445718,0.27707991107111857
+1.475058506656059,-1.597803860699713
+1.5364939400644169,-1.7512093902525276
+-0.5647462592261323,0.9192803335861466
+1.0842094451043573,0.7227801103901017
+0.20309209820281743,2.153667065353245
+-0.3468361225057024,0.07940651787644237
+-0.44130222674722563,2.100534788683657
+-0.6171201840100109,0.5219828012864138
+1.3453716047023807,-0.7830133444630382
+0.5495273365652522,1.7576229094464058
+1.1988259494445646,-1.3715838270960632
+0.22960344938270183,0.3775037236921687
+-0.6123759093335387,1.8285144338092358
+0.34325256250702674,-0.1698845657680308
+0.331002905052772,1.731127835305921
+-0.7390982754973587,0.4997399676890179
+0.7461549161885507,-0.3010913592936829
+-0.32088847703676215,1.3661739586077684
+-0.3220720322038296,0.6469908823775906
+0.6686056971476616,1.9651904647338003
+-0.22910680633412434,0.36296161859203413
+-0.4542109250743719,0.32688519281564016
+-0.2946518281133231,1.508235737734875
+-0.33297428523568906,1.3568455300312494
+0.08605065399834319,0.09579211952507316
+-0.2529051508206548,0.26139105536560736
+-0.11044763302849331,1.3694780898040102
+1.3158604408697723,-0.6114404970462768
+-0.27506524208384087,0.2576017208612762
+-0.8058884055683975,-0.26252883481113287
+1.475058506656059,-1.597803860699713
+-0.10710781199032537,0.5366152685914558
+-0.051187663680789725,-0.3246116047594698
+1.0842094451043573,0.7227801103901017
+0.20309209820281743,2.153667065353245
+-0.6281968520015535,1.2882427150913687
+-0.44130222674722563,2.100534788683657
+-0.6171201840100109,0.5219828012864138
+1.3453716047023807,-0.7830133444630382
+0.5495273365652522,1.7576229094464058
+1.1988259494445646,-1.3715838270960632
+-0.27368608835545694,0.36389058355448567
+-0.6123759093335387,1.8285144338092358
+0.34325256250702674,-0.1698845657680308
+0.331002905052772,1.731127835305921
+-0.7390982754973587,0.4997399676890179
+0.7461549161885507,-0.3010913592936829
+-0.32088847703676215,1.3661739586077684
+-0.037405707175172886,0.03452434203221655
+1.341429860306229,-0.1278249144277086
+-0.5278823505186715,-0.5038107537220833
+-0.4542109250743719,0.32688519281564016
+0.1666810605372801,1.8334382371593119
+0.9513317594301796,0.02962250651487852
+0.08605065399834319,0.09579211952507316
+0.9167273783068495,0.9821538320749145
+1.0727985741363804,-0.11257416140285283
+1.3158604408697723,-0.6114404970462768
+0.5601058288375871,0.9717438741019873
+-0.8058884055683975,-0.26252883481113287
+1.475058506656059,-1.597803860699713
+-0.10710781199032537,0.5366152685914558
+-0.051187663680789725,-0.3246116047594698
+1.0842094451043573,0.7227801103901017
+0.20309209820281743,2.153667065353245
+0.08945536308230623,1.1323378879380201
+-0.44130222674722563,2.100534788683657
+-0.6171201840100109,0.5219828012864138
+-0.4478488514838951,-0.33457230822780304
+0.5495273365652522,1.7576229094464058
+1.1988259494445646,-1.3715838270960632
+-0.5256137598745055,1.2630469300098728
+-0.3620692166260574,0.8909937401522092
+-0.40249291023409306,0.5529807111367505
+0.331002905052772,1.731127835305921
+-0.7390982754973587,0.4997399676890179
+-0.203036909702822,1.698174646826269
+-0.32088847703676215,1.3661739586077684
+-0.037405707175172886,0.03452434203221655
+1.341429860306229,-0.1278249144277086
+-0.5278823505186715,-0.5038107537220833
+-0.4542109250743719,0.32688519281564016
+0.1666810605372801,1.8334382371593119
+0.3275577231275953,1.9252654823282525
+0.08605065399834319,0.09579211952507316
+0.9167273783068495,0.9821538320749145
+1.0036614370546608,0.06857964625052715
+0.6140696533119498,1.631821202811619
+-0.5422805902361678,-0.20604389743532792
+1.5380719249923367,-1.8588211900956166
+1.475058506656059,-1.597803860699713
+-0.4750866428344256,0.00643839093742915
+-0.051187663680789725,-0.3246116047594698
+1.0842094451043573,0.7227801103901017
+0.20309209820281743,2.153667065353245
+-0.20999993420928367,2.2103095530041235
+-0.44130222674722563,2.100534788683657
+-0.6171201840100109,0.5219828012864138
+-0.48825918445798344,-0.43101350960086227
+0.5495273365652522,1.7576229094464058
+0.7095832316792442,-0.3965825803206849
+-0.11471418617486148,0.37941092275932853
+1.1956614915376758,-1.3605751840091336
+-0.051482348712375225,1.743741522283246
+-0.8336685808917432,-0.310864902011023
+-0.7390982754973587,0.4997399676890179
+-0.203036909702822,1.698174646826269
+-0.32088847703676215,1.3661739586077684
+-0.31669754712758247,0.33936081903315607
+1.341429860306229,-0.1278249144277086
+-0.5278823505186715,-0.5038107537220833
+-0.4542109250743719,0.32688519281564016
+1.6494974034902299,-2.001793074623033
+0.17133094532302523,0.2175683262182741
+0.08605065399834319,0.09579211952507316
+0.9167273783068495,0.9821538320749145
+1.0036614370546608,0.06857964625052715
+0.6140696533119498,1.631821202811619
+-0.12671363033005645,2.333725239902757
+-0.23839042302029503,1.4934350373363603
+-0.04933504033454508,1.877490511008261
+-0.4750866428344256,0.00643839093742915
+-0.051187663680789725,-0.3246116047594698
+1.0842094451043573,0.7227801103901017
+0.20309209820281743,2.153667065353245
+-0.20999993420928367,2.2103095530041235
+-0.14772036134774458,0.3936155357367722
+-0.7357446406496926,0.30772425055997116
+1.4596629988215135,-0.7870350422283396
+0.5495273365652522,1.7576229094464058
+0.7095832316792442,-0.3965825803206849
+-0.11471418617486148,0.37941092275932853
+1.1956614915376758,-1.3605751840091336
+-0.051482348712375225,1.743741522283246
+0.2621540503038641,0.15196143463422312
+0.12263265667185766,1.8158684202243311
+-0.203036909702822,1.698174646826269
+-0.7263057167092788,0.20418759632265127
+-0.31669754712758247,0.33936081903315607
+1.341429860306229,-0.1278249144277086
+0.20975039503630666,1.035946845310432
+-0.1208502278919231,2.111778586656669
+1.349459920122863,-1.4166617130095316
+0.5266099574356693,1.5468397672913878
+-0.5156568542180481,-0.12367506574681317
+0.9167273783068495,0.9821538320749145
+1.0036614370546608,0.06857964625052715
+0.6140696533119498,1.631821202811619
+1.6273077430099865,-1.9359103924891237
+0.5465335470725514,0.023784260695190573
+0.7319774742629195,1.362191352111813
+-0.4750866428344256,0.00643839093742915
+-0.051187663680789725,-0.3246116047594698
+1.0842094451043573,0.7227801103901017
+0.20309209820281743,2.153667065353245
+-1.1739796356742322,-0.6305396527746236
+0.030724765811479315,-0.07570739066972385
+-0.7357446406496926,0.30772425055997116
+1.4596629988215135,-0.7870350422283396
+0.8442257865852412,-0.3258644420703314
+0.7095832316792442,-0.3965825803206849
+1.2050354022728862,-0.2777646603883557
+-0.9622921573843433,-0.6525006340657085
+1.4840927743336334,-1.1297060735087299
+0.2621540503038641,0.15196143463422312
+0.12263265667185766,1.8158684202243311
+-0.203036909702822,1.698174646826269
+-0.7263057167092788,0.20418759632265127
+0.9260534199001125,0.9089216707527437
+0.4241110500787162,1.9056470737645517
+0.20975039503630666,1.035946845310432
+-0.1208502278919231,2.111778586656669
+1.349459920122863,-1.4166617130095316
+-0.6670947040031743,-0.19550214653304632
+1.3815838230248445,-1.1525196660618025
+0.7426385550493957,1.5515037958242126
+-0.33542220307801573,0.5140787571963329
+0.6140696533119498,1.631821202811619
+1.6273077430099865,-1.9359103924891237
+0.21160397536115966,0.662038121894555
+0.7319774742629195,1.362191352111813
+-0.4750866428344256,0.00643839093742915
+-0.051187663680789725,-0.3246116047594698
+1.0842094451043573,0.7227801103901017
+-0.9367856236552163,0.6467984608933983
+-1.1739796356742322,-0.6305396527746236
+0.030724765811479315,-0.07570739066972385
+-0.7357446406496926,0.30772425055997116
+1.4596629988215135,-0.7870350422283396
+0.8442257865852412,-0.3258644420703314
+0.556001117513534,1.4836257268997548
+1.3740429556514178,-0.6230871484765956
+-0.04654952524295897,2.1744297099319403
+1.4840927743336334,-1.1297060735087299
+0.2621540503038641,0.15196143463422312
+0.6348922159374122,1.4831975085911386
+-0.203036909702822,1.698174646826269
+-0.7263057167092788,0.20418759632265127
+0.36927507868205,-0.4011443460787072
+0.4241110500787162,1.9056470737645517
+-0.053215906818847025,0.47945065391260655
+-0.1208502278919231,2.111778586656669
+1.349459920122863,-1.4166617130095316
+-0.6670947040031743,-0.19550214653304632
+1.3815838230248445,-1.1525196660618025
+0.7426385550493957,1.5515037958242126
+-0.33542220307801573,0.5140787571963329
+-0.9287231462984,0.1511991384399634
+1.6273077430099865,-1.9359103924891237
+-0.6104732789870635,1.9410884503201353
+0.7319774742629195,1.362191352111813
+-0.4750866428344256,0.00643839093742915
+-0.051187663680789725,-0.3246116047594698
+1.0842094451043573,0.7227801103901017
+1.1439419797926986,0.860803788216442
+1.0493934727353496,1.27429091384551
+1.528575674765952,-1.932673243375019
+-0.7357446406496926,0.30772425055997116
+1.1275538880827944,0.09431597285698246
+1.4069252184229624,-1.3162228732965502
+0.556001117513534,1.4836257268997548
+-0.24886202450798775,0.2874801682967898
+-0.04654952524295897,2.1744297099319403
+1.4840927743336334,-1.1297060735087299
+0.2621540503038641,0.15196143463422312
+0.6348922159374122,1.4831975085911386
+-0.203036909702822,1.698174646826269
+1.2930111319223694,0.016648145993017574
+0.36927507868205,-0.4011443460787072
+-0.6682564978667466,0.523597871613683
+-0.24915908779454726,-0.09126083043045102
+-0.1208502278919231,2.111778586656669
+1.349459920122863,-1.4166617130095316
+-0.6670947040031743,-0.19550214653304632
+1.3815838230248445,-1.1525196660618025
+-0.04915236489580338,0.5071635493081947
+-0.33542220307801573,0.5140787571963329
+-0.9287231462984,0.1511991384399634
+0.8776136158506181,1.101937382882034
+-0.6104732789870635,1.9410884503201353
+0.7319774742629195,1.362191352111813
+-0.4750866428344256,0.00643839093742915
+1.5089603490010062,-1.0723384463692274
+1.0842094451043573,0.7227801103901017
+1.3531320318019873,-1.3243806882732936
+-0.6355350987047171,1.0335547496211417
+-0.8820875287130816,-0.11509604547775265
+-0.5879243293639729,0.3346525115568223
+1.1275538880827944,0.09431597285698246
+0.715746642420964,-0.20282106270923392
+-0.07333356927183271,2.287759546452317
+-0.24886202450798775,0.2874801682967898
+0.5618182976744743,0.6346507277209967
+1.5193510215483113,-0.5001986839629105
+0.2621540503038641,0.15196143463422312
+1.6638515862154708,-1.4637713014128113
+-0.203036909702822,1.698174646826269
+-0.3327891736032751,0.2985010197572714
+0.36927507868205,-0.4011443460787072
+0.9994740387805094,1.3245198084630947
+0.3516202277102889,-0.044293700509957235
+-0.1208502278919231,2.111778586656669
+1.349459920122863,-1.4166617130095316
+-0.6670947040031743,-0.19550214653304632
+1.5543095220721976,-2.1798364029087733
+-0.04727062592323039,0.33497546704622394
+0.25370170970141037,-0.2741998341701033
+-0.9287231462984,0.1511991384399634
+0.8776136158506181,1.101937382882034
+0.9344445372491514,0.05052637693582626
+0.7319774742629195,1.362191352111813
+-0.4750866428344256,0.00643839093742915
+1.019021129361066,0.32560269643912426
+-0.02343083942881663,0.12249988023512917
+1.3531320318019873,-1.3243806882732936
+-0.6355350987047171,1.0335547496211417
+-0.810917543735224,-0.8265434328766645
+0.5090275708078553,0.4800271697407422
+1.5971393117737502,-0.6803053116308502
+0.715746642420964,-0.20282106270923392
+-0.07333356927183271,2.287759546452317
+0.2550097587095146,1.62057593611415
+0.5618182976744743,0.6346507277209967
+0.8551089024878868,-0.6412927384792757
+1.427505544249627,-0.9821504846277782
+0.3035473733192566,1.5473989015126488
+1.6255504941183059,-0.6855424891312749
+1.91124946694094,-2.422936015388687
+1.0587359511907746,-0.3465031282465664
+-0.6064828043081543,1.7456139164973121
+0.3516202277102889,-0.044293700509957235
+-0.1208502278919231,2.111778586656669
+0.837039622022313,-0.7593824531816183
+0.8393644396512074,0.7180993939019387
+1.5543095220721976,-2.1798364029087733
+-0.5883286855548215,-0.4261288045517057
+-0.7103845994199904,1.5778816969815508
+-0.9287231462984,0.1511991384399634
+0.8776136158506181,1.101937382882034
+0.18691305046976936,0.12591458423656257
+0.7319774742629195,1.362191352111813
+-0.4750866428344256,0.00643839093742915
+1.019021129361066,0.32560269643912426
+-0.02343083942881663,0.12249988023512917
+1.3531320318019873,-1.3243806882732936
+-0.6355350987047171,1.0335547496211417
+-0.810917543735224,-0.8265434328766645
+0.6818007745835952,0.40788826178464244
+1.5971393117737502,-0.6803053116308502
+0.715746642420964,-0.20282106270923392
+-0.07333356927183271,2.287759546452317
+0.2550097587095146,1.62057593611415
+0.5618182976744743,0.6346507277209967
+-0.5970051036584914,0.3576392819673589
+1.427505544249627,-0.9821504846277782
+0.3035473733192566,1.5473989015126488
+1.6255504941183059,-0.6855424891312749
+-0.8438447003336329,0.1164281213497427
+0.7223781113302781,1.6116828899160083
+0.7294493895374978,-0.40784517758577776
+0.3516202277102889,-0.044293700509957235
+-0.1208502278919231,2.111778586656669
+1.6613921866781904,-1.6820084203390773
+0.8393644396512074,0.7180993939019387
+1.5543095220721976,-2.1798364029087733
+-0.5883286855548215,-0.4261288045517057
+-0.753668006124099,0.9397389795957094
+-0.44318962356516745,2.121353683164382
+0.8776136158506181,1.101937382882034
+0.18691305046976936,0.12591458423656257
+0.4734245920406963,0.773592119792974
+-0.6175258713219953,0.10736264289522117
+1.019021129361066,0.32560269643912426
+-0.02343083942881663,0.12249988023512917
+1.3531320318019873,-1.3243806882732936
+-0.6355350987047171,1.0335547496211417
+0.8364031290258416,-0.620006090256386
+-0.5467556590447314,-0.24451377904283164
+-0.09187054052241495,0.06101012367503156
+0.715746642420964,-0.20282106270923392
+-0.07333356927183271,2.287759546452317
+-0.5034515079000184,1.298710376695775
+-0.3785507759682868,0.9055952547103743
+1.4359483983330148,-1.5163676381203415
+0.6038245183117672,1.235909406156023
+0.8865501912162197,1.4035506240856996
+-0.6097238235682666,0.9599087857871466
+-0.8438447003336329,0.1164281213497427
+-1.0216226120701442,0.07802026316741384
+0.7294493895374978,-0.40784517758577776
+-0.5305615547425018,-0.1846125755503444
+-0.5258494333600681,0.25276257948002645
+0.9084963454295302,0.6856969626110273
+-0.8343690562397231,-0.6076735888187368
+1.5543095220721976,-2.1798364029087733
+-0.5883286855548215,-0.4261288045517057
+1.4947172526565962,-1.5858020367418768
+-0.9215300607824739,0.40278818340199307
+0.8776136158506181,1.101937382882034
+0.18691305046976936,0.12591458423656257
+0.4734245920406963,0.773592119792974
+-0.6175258713219953,0.10736264289522117
+1.019021129361066,0.32560269643912426
+-0.02343083942881663,0.12249988023512917
+1.3531320318019873,-1.3243806882732936
+-0.6355350987047171,1.0335547496211417
+0.8364031290258416,-0.620006090256386
+-0.5467556590447314,-0.24451377904283164
+-0.09187054052241495,0.06101012367503156
+0.715746642420964,-0.20282106270923392
+-0.07333356927183271,2.287759546452317
+-0.5034515079000184,1.298710376695775
+-0.3785507759682868,0.9055952547103743
+-0.36699935075198775,-0.27674367193055305
+0.6038245183117672,1.235909406156023
+-0.2874532583723888,1.2637646422883795
+-0.6097238235682666,0.9599087857871466
+0.572748020327026,0.9684507157056861
+-1.0216226120701442,0.07802026316741384
+0.7294493895374978,-0.40784517758577776
+-0.5305615547425018,-0.1846125755503444
+-0.5258494333600681,0.25276257948002645
+0.9084963454295302,0.6856969626110273
+0.28241329342667637,-0.21475825217713918
+1.5543095220721976,-2.1798364029087733
+0.4087567117673866,0.3468103622789519
+1.4947172526565962,-1.5858020367418768
+-0.9215300607824739,0.40278818340199307
+0.13542358672593124,0.5234880027307365
+0.18691305046976936,0.12591458423656257
+0.4734245920406963,0.773592119792974
+-0.6175258713219953,0.10736264289522117
+0.4508345660012219,-0.2865597038874732
+-0.02343083942881663,0.12249988023512917
+-0.5486882046661731,1.1557974482137063
+-0.6355350987047171,1.0335547496211417
+0.8364031290258416,-0.620006090256386
+0.27467509909703564,1.5507620202800063
+-0.09187054052241495,0.06101012367503156
+0.715746642420964,-0.20282106270923392
+-0.07333356927183271,2.287759546452317
+-0.5034515079000184,1.298710376695775
+-0.3785507759682868,0.9055952547103743
+-0.36699935075198775,-0.27674367193055305
+0.6038245183117672,1.235909406156023
+-0.2874532583723888,1.2637646422883795
+-0.6097238235682666,0.9599087857871466
+-0.19637699000510955,0.46104282256029805
+-1.0216226120701442,0.07802026316741384
+0.7294493895374978,-0.40784517758577776
+0.025144449182426087,1.4711590539519197
+0.06892708701965546,0.05730625905696206
+0.2217760578570207,0.9623200522753763
+1.4153436409481008,-1.082079891410346
+1.5543095220721976,-2.1798364029087733
+0.07261938463325435,0.38060337336083805
+1.4947172526565962,-1.5858020367418768
+-0.9215300607824739,0.40278818340199307
+0.4810593641836022,-0.6830065773900456
+-0.07036243404433914,1.0885052133958377
+-0.025374845956917927,0.3720735394444541
+-0.6175258713219953,0.10736264289522117
+0.6673437851565512,1.2825130429100844
+0.09073675239775444,-0.0050420581163198586
+-0.25353458614567015,1.0207634121302038
+-0.21483225992367705,0.45498797015191994
+0.9845133204290155,-1.1042226044354073
+0.27467509909703564,1.5507620202800063
+0.8561087473647206,-0.9655633481658901
+0.46449025900780605,-0.2939948405898738
+-0.07333356927183271,2.287759546452317
+-0.5034515079000184,1.298710376695775
+-0.3785507759682868,0.9055952547103743
+-0.36699935075198775,-0.27674367193055305
+0.08391092119398942,-0.16917215868880844
+-0.2874532583723888,1.2637646422883795
+-0.5265114491852236,1.956652815718153
+-0.19637699000510955,0.46104282256029805
+-1.0216226120701442,0.07802026316741384
+1.6169754698419774,-1.8361352988452637
+0.025144449182426087,1.4711590539519197
+0.06892708701965546,0.05730625905696206
+0.2217760578570207,0.9623200522753763
+0.5382155659632037,-0.20423907517252426
+1.5543095220721976,-2.1798364029087733
+0.07261938463325435,0.38060337336083805
+1.4947172526565962,-1.5858020367418768
+-0.9215300607824739,0.40278818340199307
+0.976227584615317,1.4052359936500318
+0.36216535958350965,1.1897706332851388
+-0.025374845956917927,0.3720735394444541
+-0.6175258713219953,0.10736264289522117
+0.6673437851565512,1.2825130429100844
+-0.5676507760750342,1.155448023555264
+-0.6035562601723347,1.5082905598874736
+-0.7730477580710463,0.9911085547427695
+0.07872775854583859,0.4537593248585239
+0.27467509909703564,1.5507620202800063
+0.5571422840587987,1.7040337446431977
+-0.3959969202306823,1.2582233710938915
+-0.07333356927183271,2.287759546452317
+-0.08211534334615467,0.09118091642644727
+-0.3785507759682868,0.9055952547103743
+-0.36699935075198775,-0.27674367193055305
+0.08391092119398942,-0.16917215868880844
+-0.39592819922936684,0.25632121382862627
+-0.38890270988082504,-0.04579025660380852
+0.4129200419782866,2.1152418220222358
+-1.0216226120701442,0.07802026316741384
+1.3303324863010824,-1.0754963487861944
+-0.6640272332588493,0.9768904435689993
+-0.0004406376682483115,-0.3421043839122822
+0.2217760578570207,0.9623200522753763
+0.5382155659632037,-0.20423907517252426
+1.5543095220721976,-2.1798364029087733
+-0.34366916530342234,0.4381123312756002
+1.4947172526565962,-1.5858020367418768
+-0.9215300607824739,0.40278818340199307
+-0.48738514872854966,0.4391326919856475
+0.072855373538042,-0.3040815730871951
+-0.28503987957510435,0.020516117025411673
+-0.26356946071556336,-0.21072161749639418
+0.6673437851565512,1.2825130429100844
+-0.5676507760750342,1.155448023555264
+-0.22464083689661773,1.7430668694674636
+0.37621062869312655,-0.27154693133816565
+0.07872775854583859,0.4537593248585239
+-0.4390186169323701,-0.16102568732798297
+0.5571422840587987,1.7040337446431977
+-0.3959969202306823,1.2582233710938915
+-0.07333356927183271,2.287759546452317
+0.1378780437997441,0.09743954252065645
+-0.3405234968258333,0.7374067981372237
+1.3495512269448182,-0.37828299248149655
+-0.6739922813241332,0.43233781879179345
+1.443442267371532,-0.8884135624599289
+-0.03086923626810878,2.589990116369016
+0.4129200419782866,2.1152418220222358
+-1.0216226120701442,0.07802026316741384
+1.3303324863010824,-1.0754963487861944
+-0.6640272332588493,0.9768904435689993
+-0.035113440996402456,1.6182080713645184
+1.467418542746094,-0.8405330914641768
+0.5382155659632037,-0.20423907517252426
+1.5543095220721976,-2.1798364029087733
+-0.34366916530342234,0.4381123312756002
+1.4947172526565962,-1.5858020367418768
+0.6558850237904946,1.8942338411225084
+1.0187873873363262,-0.6874907721363424
+0.072855373538042,-0.3040815730871951
+-0.12821010844475714,0.47115747195442853
+-0.26356946071556336,-0.21072161749639418
+0.6673437851565512,1.2825130429100844
+-0.5676507760750342,1.155448023555264
+0.460751762776165,-0.4052853045861413
+1.4429997685342568,-1.5356554078340616
+0.45556167486042803,1.1570242391583285
+-0.4390186169323701,-0.16102568732798297
+0.5571422840587987,1.7040337446431977
+-0.9209889324644156,-0.19422797828534033
+-0.35620530626136504,0.8976807356836201
+0.8918331322939956,0.5393282127435612
+-0.3405234968258333,0.7374067981372237
+0.9814639819857331,0.23624516320137573
+-0.6829866523908239,0.718481711187785
+-0.13628903296413866,-0.18196450852738666
+-0.03086923626810878,2.589990116369016
+0.4129200419782866,2.1152418220222358
+-0.09647572569393092,2.493449614822875
+1.3303324863010824,-1.0754963487861944
+-0.005641700390454307,0.49033916876096895
+-0.035113440996402456,1.6182080713645184
+0.7765602495912951,1.0064010706789694
+0.5382155659632037,-0.20423907517252426
+1.5543095220721976,-2.1798364029087733
+-0.34366916530342234,0.4381123312756002
+1.4947172526565962,-1.5858020367418768
+0.184141382541546,1.2172202905565848
+1.428220294553217,-1.8419823500870136
+0.22787464650245112,-0.5614661988832095
+1.9128493717970383,-2.2877669840527033
+-0.4089535137507917,-0.41268874219716045
+0.6673437851565512,1.2825130429100844
+-0.349418469985176,1.4445982951911045
+1.3602583971285531,0.025245772043837045
+1.4429997685342568,-1.5356554078340616
+1.248093999925318,-1.7656968390817072
+-0.4390186169323701,-0.16102568732798297
+0.5571422840587987,1.7040337446431977
+-0.9209889324644156,-0.19422797828534033
+-0.406564087478926,0.1765222418171628
+0.8918331322939956,0.5393282127435612
+-0.3405234968258333,0.7374067981372237
+-0.46768290649398125,0.65658729807344
+-0.6829866523908239,0.718481711187785
+-0.13628903296413866,-0.18196450852738666
+1.418602671338399,-1.7749844402179307
+0.7200591527561951,-0.142482881126082
+0.31446341576295317,0.6723848402078735
+1.3303324863010824,-1.0754963487861944
+-0.005641700390454307,0.49033916876096895
+-0.035113440996402456,1.6182080713645184
+0.7765602495912951,1.0064010706789694
+0.5382155659632037,-0.20423907517252426
+-0.35182634627311393,1.358332490093926
+-0.34366916530342234,0.4381123312756002
+0.8797504019753025,-0.7653634285385226
+0.6058461348530092,-0.8755526431419922
+0.6926069323893786,1.5843184816988474
+0.27088405061330134,-0.33695178096126
+1.9128493717970383,-2.2877669840527033
+0.45085960602751896,1.5947794763894825
+-0.7029230792573502,1.040533896437231
+1.2282852008344767,-0.3552751208700733
+1.3602583971285531,0.025245772043837045
+-0.5543329975590164,0.5253166621880729
+1.248093999925318,-1.7656968390817072
+0.9179575894221405,1.2284620511029947
+0.5571422840587987,1.7040337446431977
+-0.9209889324644156,-0.19422797828534033
+-0.406564087478926,0.1765222418171628
+0.8918331322939956,0.5393282127435612
+1.3252489376558554,-1.9799044453153045
+-0.46768290649398125,0.65658729807344
+-0.6829866523908239,0.718481711187785
+0.0834005315057444,0.3262852305128433
+1.1239237577824546,0.61210072917211
+-0.46430829402983254,-0.48399514142123534
+0.31446341576295317,0.6723848402078735
+1.3303324863010824,-1.0754963487861944
+0.6156475172228184,-0.2719658587727736
+-0.11253481745125331,1.6896425442527268
+0.7765602495912951,1.0064010706789694
+0.5382155659632037,-0.20423907517252426
+-0.35182634627311393,1.358332490093926
+0.23385886415303775,-0.5251101300832276
+0.5796725190493351,-0.7330406337974096
+0.10828230313098498,1.2634315597718517
+1.2381285135477602,-0.2519957769927609
+-0.6770828048960512,1.8865518727495496
+0.5388906671042059,1.5931751503495613
+-0.012116187306585646,0.43396357640010286
+-0.41369609418586534,0.7315509406099961
+1.2282852008344767,-0.3552751208700733
+1.3602583971285531,0.025245772043837045
+1.1217148473195313,-1.0036552218867156
+1.248093999925318,-1.7656968390817072
+0.6390689064085266,1.1289149682957584
+0.5571422840587987,1.7040337446431977
+-0.12014012172115207,1.8674959155051192
+0.34294386944291994,1.927061941536456
+0.8918331322939956,0.5393282127435612
+1.3252489376558554,-1.9799044453153045
+-0.46768290649398125,0.65658729807344
+-0.6829866523908239,0.718481711187785
+0.0834005315057444,0.3262852305128433
+1.1239237577824546,0.61210072917211
+0.719778794469403,-0.21894125190408276
+0.5080599349394436,1.4121170572271224
+1.3303324863010824,-1.0754963487861944
+0.6156475172228184,-0.2719658587727736
+-0.11253481745125331,1.6896425442527268
+0.7765602495912951,1.0064010706789694
+-0.5718768801467669,0.44134930369355024
+1.4003042863720143,-1.914366472534956
+0.23385886415303775,-0.5251101300832276
+1.1239632206870451,0.31793728214854944
+0.9686750750154064,-1.364422856615779
+1.2381285135477602,-0.2519957769927609
+-0.6770828048960512,1.8865518727495496
+0.45920208807214014,-0.16712663741828315
+-0.012116187306585646,0.43396357640010286
+-0.41369609418586534,0.7315509406099961
+1.2282852008344767,-0.3552751208700733
+-0.16237650485822935,1.5236849694211219
+1.1217148473195313,-1.0036552218867156
+1.248093999925318,-1.7656968390817072
+0.9616747297866876,-0.8357892352113446
+0.5571422840587987,1.7040337446431977
+-0.12014012172115207,1.8674959155051192
+0.34294386944291994,1.927061941536456
+0.8139610113393242,-0.519477131372873
+1.391607456319729,-1.769670590962079
+-0.46768290649398125,0.65658729807344
+-0.6829866523908239,0.718481711187785
+1.187861250485821,-1.3300508068578527
+1.1239237577824546,0.61210072917211
+0.719778794469403,-0.21894125190408276
+1.048590122706207,-0.37869294580582313
+0.09389888556814541,2.309418787600795
+0.1167952849590197,0.6074787400878074
+-0.11253481745125331,1.6896425442527268
+0.7765602495912951,1.0064010706789694
+-0.5718768801467669,0.44134930369355024
+1.4003042863720143,-1.914366472534956
+-0.34965338504970084,0.8354167253635756
+0.38882532743234194,1.6163632629092914
+0.2129212747331422,1.3575443313498288
+0.9318467526791842,-1.3543451057587472
+0.7588101358939062,-0.3284383175698087
+0.0074653824137529134,-0.13281487449516421
+1.1948496561951054,-0.8162111302395341
+-0.07629834244058759,1.602050346905704
+0.1270462827706451,0.6043212146761678
+-0.16237650485822935,1.5236849694211219
+1.1217148473195313,-1.0036552218867156
+1.248093999925318,-1.7656968390817072
+0.9616747297866876,-0.8357892352113446
+0.5571422840587987,1.7040337446431977
+-0.12014012172115207,1.8674959155051192
+0.34294386944291994,1.927061941536456
+0.8931782688085413,0.23213942023562506
+1.0000216282314498,0.9151451802645223
+-0.46768290649398125,0.65658729807344
+-0.6829866523908239,0.718481711187785
+1.116683224281162,-0.9256452388799029
+1.1239237577824546,0.61210072917211
+0.719778794469403,-0.21894125190408276
+-0.004889091110951205,1.0310858490302497
+-0.75380299744088,0.4292286488460058
+-0.6053450597690987,0.5653199736634718
+-0.5165905537014904,0.4430260607651752
+0.7162733061724013,0.12298416746501034
+-0.6665819971138374,0.8876591613019704
+1.4003042863720143,-1.914366472534956
+0.8440835700887639,-0.7542295397278724
+0.38882532743234194,1.6163632629092914
+0.6524666496889278,0.21802985402986136
+0.9318467526791842,-1.3543451057587472
+-0.4076582629878488,0.1860811994674515
+1.1412644027931436,-1.2128580025088214
+-0.35847116781872335,2.0754757504401193
+-0.07629834244058759,1.602050346905704
+-0.7026252384895,-0.422837091600618
+-0.16237650485822935,1.5236849694211219
+1.1217148473195313,-1.0036552218867156
+-0.20244850096708805,1.6630099929525997
+1.74404630141653,-2.3882998802757265
+0.5571422840587987,1.7040337446431977
+-0.12014012172115207,1.8674959155051192
+1.6735629786356279,-1.9864879763985757
+0.8931782688085413,0.23213942023562506
+0.7848161354324072,-0.3174531961502969
+-0.5132146673169378,-0.3230598621354476
+-0.6829866523908239,0.718481711187785
+-0.3698499104047988,1.8331371004998727
+-0.5843094835888868,0.6037600866504078
+0.719778794469403,-0.21894125190408276
+-0.09665824039714949,-0.17218227583431317
+1.5696825102197591,-2.3148577591519706
+0.1458326223419753,-0.25483915540128166
+-0.3792707700559737,0.0571404145294534
+0.7162733061724013,0.12298416746501034
+1.6203337264074327,-2.082219310399113
+0.9888826905681996,0.3275261552376963
+0.8440835700887639,-0.7542295397278724
+0.38882532743234194,1.6163632629092914
+0.6524666496889278,0.21802985402986136
+0.3622955676176106,-0.41182866643639515
+-0.5551762428209305,0.04890537321969578
+0.14813895717267356,0.7605753540440878
+1.011359666038826,-0.7759104951373188
+1.3570163498917946,-1.392723198252334
+-0.7026252384895,-0.422837091600618
+-0.16237650485822935,1.5236849694211219
+1.1217148473195313,-1.0036552218867156
+0.11607558576117694,0.6600377523922671
+1.74404630141653,-2.3882998802757265
+0.5571422840587987,1.7040337446431977
+-0.12014012172115207,1.8674959155051192
+-0.4587502837974817,0.6391798930075505
+1.3052786901841609,-1.688466012507873
+0.7848161354324072,-0.3174531961502969
+-0.5132146673169378,-0.3230598621354476
+0.3915158811511924,0.17440290504486816
+-0.3698499104047988,1.8331371004998727
+1.1851742197356727,0.279026903111008
+0.6241827945355922,0.23141776023201754
+1.6648698183696615,-1.943142769353786
+1.5696825102197591,-2.3148577591519706
+0.1458326223419753,-0.25483915540128166
+-0.3792707700559737,0.0571404145294534
+0.5660023936148406,0.18936788069878646
+1.6203337264074327,-2.082219310399113
+0.9888826905681996,0.3275261552376963
+0.8440835700887639,-0.7542295397278724
+0.49571941973594436,1.3146415034167573
+1.2227145156428818,-0.6205823260568635
+0.3622955676176106,-0.41182866643639515
+-0.5551762428209305,0.04890537321969578
+0.7053061863557466,-0.26373394123758453
+0.8838957322149662,-0.08855766509239021
+-1.077659638023223,-0.15797911595519365
+-0.7026252384895,-0.422837091600618
+-0.16237650485822935,1.5236849694211219
+-0.02379021389459257,0.2975580094639546
+-0.5271345071460172,1.1349555375959066
+1.74404630141653,-2.3882998802757265
+1.4196369709089653,-1.0808499583971376
+-0.12014012172115207,1.8674959155051192
+0.6388090563001716,0.9389724570821278
+-0.48959686937462726,1.6809721884132356
+1.1690058995352375,-1.2328408341891373
+-0.5132146673169378,-0.3230598621354476
+-0.5291688005336626,0.18103097607630528
+-0.3698499104047988,1.8331371004998727
+1.1851742197356727,0.279026903111008
+-0.47348784360844487,1.2689697768866917
+1.6648698183696615,-1.943142769353786
+0.8494946855562816,-0.907449364106086
+0.1458326223419753,-0.25483915540128166
+-0.15456351970261573,0.04108713877011083
+0.28639292510148207,-0.4660523358289332
+0.23636008050466017,-0.03493314066284098
+0.9888826905681996,0.3275261552376963
+-0.07752974436540871,1.1465242440718886
+-0.45532568440178056,1.6395268560201297
+-0.7597142390510496,0.05774768961007004
+0.3622955676176106,-0.41182866643639515
+0.08188272281915313,1.587294476805944
+0.4332984512326601,1.6513728849712601
+-0.08204775293813944,1.7972969546243558
+-1.077659638023223,-0.15797911595519365
+0.3543054037429678,-0.07663857344536945
+-0.35189605124996615,0.09308273539567179
+-0.8074389775928712,-0.012139870923214294
+-0.5271345071460172,1.1349555375959066
+1.74404630141653,-2.3882998802757265
+1.4196369709089653,-1.0808499583971376
+-0.12014012172115207,1.8674959155051192
+-0.7848584546249613,-0.11630331236662983
+-0.14518982038353356,0.12720781901966327
+-0.6865848338853147,-0.1813738482953669
+0.5758058711427921,1.7333928875794817
+-0.5291688005336626,0.18103097607630528
+0.7601260227922402,1.0698277418476785
+1.1851742197356727,0.279026903111008
+-0.2941164516499264,0.7157580784638117
+1.6648698183696615,-1.943142769353786
+0.7535250393413846,0.8680730942917789
+0.1458326223419753,-0.25483915540128166
+-0.15456351970261573,0.04108713877011083
+0.34304466079950724,-0.7551294271689318
+0.9295844808599056,-0.25498544683269403
+-0.43628808956084514,1.5504893805270505
+0.07741666619840631,0.09232283451670831
+-0.45532568440178056,1.6395268560201297
+-0.7164228313679566,-0.21402277640707051
+-0.645335668654773,0.8375936279675471
+0.08188272281915313,1.587294476805944
+0.4332984512326601,1.6513728849712601
+-0.08204775293813944,1.7972969546243558
+-0.3086142726731139,-0.12077280340737248
+-0.5911710863651527,1.0090796630654313
+-0.35189605124996615,0.09308273539567179
+-0.8074389775928712,-0.012139870923214294
+-0.5271345071460172,1.1349555375959066
+1.74404630141653,-2.3882998802757265
+1.4196369709089653,-1.0808499583971376
+-0.12014012172115207,1.8674959155051192
+-0.7848584546249613,-0.11630331236662983
+-0.03160623939852758,-0.11092015652408127
+-0.6865848338853147,-0.1813738482953669
+0.5758058711427921,1.7333928875794817
+-0.5291688005336626,0.18103097607630528
+-0.6427235397488298,1.3763456865754833
+1.1851742197356727,0.279026903111008
+-0.2941164516499264,0.7157580784638117
+1.6648698183696615,-1.943142769353786
+0.2964214422859211,-0.27819793928472364
+0.24256027407507144,-0.5880764817304032
+-0.15456351970261573,0.04108713877011083
+1.009851738858747,-1.5682394368201416
+-0.008588179089503524,0.5013629009391581
+-0.43628808956084514,1.5504893805270505
+0.9801088762573694,1.0223243149985546
+-0.45532568440178056,1.6395268560201297
+-0.7164228313679566,-0.21402277640707051
+-0.645335668654773,0.8375936279675471
+0.08188272281915313,1.587294476805944
+0.4332984512326601,1.6513728849712601
+-0.08204775293813944,1.7972969546243558
+0.31573575998319725,1.4312916275794407
+-0.5134315339197787,1.508910617984204
+-0.35189605124996615,0.09308273539567179
+-0.46280633463157417,1.6860988470925116
+-0.40488476792970374,0.7168712594173321
+1.74404630141653,-2.3882998802757265
+1.4196369709089653,-1.0808499583971376
+-0.2546238641318609,0.5672873619841796
+-0.7848584546249613,-0.11630331236662983
+-0.03160623939852758,-0.11092015652408127
+-0.6865848338853147,-0.1813738482953669
+0.8702918325564195,-0.5356462559270471
+-0.8251047101924929,1.1019992611116072
+1.0514732728727036,-1.247191217040586
+1.1851742197356727,0.279026903111008
+-0.2941164516499264,0.7157580784638117
+1.6648698183696615,-1.943142769353786
+-0.9618911469916492,0.11488258393278344
+-0.42550771854969077,0.8080610107144952
+-0.4342893061915721,1.8642711765200115
+0.09248010892002806,0.7028552154584972
+-0.008588179089503524,0.5013629009391581
+-0.6278349934368427,0.7410493800233193
+0.36399666820346543,1.4983656703483959
+-0.45532568440178056,1.6395268560201297
+0.5909327548385852,-0.5483711075990642
+1.3863748847109663,-0.8612940457072411
+0.08188272281915313,1.587294476805944
+0.4332984512326601,1.6513728849712601
+-0.08204775293813944,1.7972969546243558
+1.7821144089978112,-1.9101508817808481
+1.1666549087128666,-0.31559427120709715
+-0.35189605124996615,0.09308273539567179
+-0.46280633463157417,1.6860988470925116
+0.15676596292893819,0.02029891318373982
+-0.43798969247229624,1.6163537552472163
+1.4196369709089653,-1.0808499583971376
+1.1956356179203393,-1.433624065847971
+1.9334847915887392,-2.196206705772928
+1.172334575880923,-0.8660775386994444
+-0.6865848338853147,-0.1813738482953669
+-0.397047973895515,0.5721709239684325
+-0.03736537688491748,0.10356626042985717
+-0.8473450887433427,0.8827634123163695
+1.1851742197356727,0.279026903111008
+-0.2941164516499264,0.7157580784638117
+1.1898196523163878,-1.3515358955908254
+0.20535505990351555,-0.31945152816280364
+-0.16549737986528315,1.4941938571881843
+-0.4342893061915721,1.8642711765200115
+0.3310976186706845,1.8409989845680217
+-0.008588179089503524,0.5013629009391581
+-0.6278349934368427,0.7410493800233193
+1.0262360885966662,-0.873340773823429
+-0.4875486931716049,1.6514938307133498
+0.5909327548385852,-0.5483711075990642
+0.9261827685456552,0.3126769311684412
+0.08188272281915313,1.587294476805944
+-0.44926972164163304,0.35896941669202664
+1.2185289570540117,-1.171181459475265
+1.063953915276417,-0.07500420988639667
+0.04773827378362128,0.6201811956235012
+-0.35189605124996615,0.09308273539567179
+1.6733278042004829,-1.826052300334176
+1.280574169599579,-0.8800013156801089
+-0.43798969247229624,1.6163537552472163
+-0.1668052580662197,-0.05409844554030274
+1.1956356179203393,-1.433624065847971
+-0.8373378509930822,1.097898008121029
+1.491639329525936,-1.7072571187472108
+-0.6865848338853147,-0.1813738482953669
+0.6218247846278486,-0.7558843418493747
+-0.03736537688491748,0.10356626042985717
+-0.09113449038418503,1.9676322813055194
+1.1851742197356727,0.279026903111008
+0.21316621227028737,-0.3955576977964286
+-0.5469772623303779,1.7312449143228732
+0.9011788880009786,0.5957070111874455
+-0.16549737986528315,1.4941938571881843
+0.8465797572829996,0.89131755159318
+0.3310976186706845,1.8409989845680217
+-0.008588179089503524,0.5013629009391581
+-0.35745401980760527,0.0371376976110406
+1.942133111644701,-2.315943282524354
+0.6363124707794388,-0.6359227767559825
+0.5909327548385852,-0.5483711075990642
+0.9261827685456552,0.3126769311684412
+1.327024042739688,-0.44388337009685974
+-0.44926972164163304,0.35896941669202664
+-0.2242852088731668,1.6194228018626728
+1.063953915276417,-0.07500420988639667
+0.7430723448563451,-0.9197366050466322
+-0.35189605124996615,0.09308273539567179
+-0.23627446331138005,1.2709093585757807
+1.3201853444188962,-0.2411355448235173
+0.736761893492325,1.6672553621289985
+1.0163031904631934,0.18745270571344852
+1.1956356179203393,-1.433624065847971
+0.569077570160428,-0.41011734382089776
+1.491639329525936,-1.7072571187472108
+-0.6865848338853147,-0.1813738482953669
+-0.1481453428598291,0.8341557481581627
+-0.03736537688491748,0.10356626042985717
+-0.09113449038418503,1.9676322813055194
+1.1851742197356727,0.279026903111008
+-0.7176148978686852,0.0004386902061034731
+-0.5469772623303779,1.7312449143228732
+0.9011788880009786,0.5957070111874455
+-0.16549737986528315,1.4941938571881843
+0.8465797572829996,0.89131755159318
+0.9371787027954417,-0.6694198495190219
+-0.008588179089503524,0.5013629009391581
+-0.5285917947321879,1.086266271863758
+0.06855534292006316,0.5149820551048718
+0.6363124707794388,-0.6359227767559825
+0.7836477908742321,0.6231269334204789
+-0.4279150642202494,0.8874023414431758
+1.327024042739688,-0.44388337009685974
+-0.28730215150798083,1.1034434782664593
+-0.2242852088731668,1.6194228018626728
+1.1360953522805686,0.17469688313132364
+-0.5155275689125153,1.167580365749196
+-0.35189605124996615,0.09308273539567179
+0.8419523347737852,1.260302147321147
+1.3201853444188962,-0.2411355448235173
+0.736761893492325,1.6672553621289985
+1.0163031904631934,0.18745270571344852
+0.916919383915529,-0.6024861925263217
+0.569077570160428,-0.41011734382089776
+1.491639329525936,-1.7072571187472108
+-0.6865848338853147,-0.1813738482953669
+-0.1481453428598291,0.8341557481581627
+-0.03736537688491748,0.10356626042985717
+-0.09113449038418503,1.9676322813055194
+0.9904289465547353,-0.517703764626144
+0.2408609891831725,0.036578467032666206
+-0.5469772623303779,1.7312449143228732
+0.9011788880009786,0.5957070111874455
+0.26763938647829544,0.11913444046873212
+-0.9680959858843823,-0.5790219179527407
+1.9116849696940639,-2.7414038942559555
+-0.008588179089503524,0.5013629009391581
+-0.5285917947321879,1.086266271863758
+0.06855534292006316,0.5149820551048718
+-0.5163457682309138,0.4946286277455875
+2.02786691215436,-2.7971807708915826
+-0.7329117132578497,-0.1001211850735421
+1.3578318917586092,-1.8113514231618129
+1.4968061291843882,-2.3053724283029107
+-0.46389990348003385,1.768721333351891
+1.1360953522805686,0.17469688313132364
+0.7949526311660573,-0.0789740937801584
+-0.6854076607072643,1.192375098470856
+0.8419523347737852,1.260302147321147
+1.3201853444188962,-0.2411355448235173
+-1.2302549996156986,0.004723809963623038
+1.0788000342198663,0.5085132233071634
+0.916919383915529,-0.6024861925263217
+-1.1010971255427526,0.3654575971434849
+0.7898101731352392,1.5274178784860661
+-0.6986813643252263,-0.09285952910854034
+0.36576702941384087,0.13688924640107022
+-0.03736537688491748,0.10356626042985717
+-0.09113449038418503,1.9676322813055194
+-0.6450104537587895,0.8184406241598364
+0.2408609891831725,0.036578467032666206
+-0.5469772623303779,1.7312449143228732
+0.9011788880009786,0.5957070111874455
+0.26763938647829544,0.11913444046873212
+0.4614723316906497,-0.5528992458141427
+1.9116849696940639,-2.7414038942559555
+-0.008588179089503524,0.5013629009391581
+1.6665830402799595,-1.9686914101351147
+0.06855534292006316,0.5149820551048718
+0.5313615154150318,1.7132268001914874
+2.02786691215436,-2.7971807708915826
+-0.7329117132578497,-0.1001211850735421
+1.3578318917586092,-1.8113514231618129
+1.4968061291843882,-2.3053724283029107
+-0.46389990348003385,1.768721333351891
+1.1360953522805686,0.17469688313132364
+0.02727787000074569,2.0349007044384315
+-0.945059969195186,0.30379397821248244
+0.2606793042728228,1.5224737035624571
+1.3201853444188962,-0.2411355448235173
+0.6604504529602114,-0.23782117137149578
+1.0788000342198663,0.5085132233071634
+0.916919383915529,-0.6024861925263217
+-0.48064305073882485,0.16239404405908664
+0.7898101731352392,1.5274178784860661
+-0.6986813643252263,-0.09285952910854034
+-0.12486220310672408,2.3255443710201593
+-0.03736537688491748,0.10356626042985717
+-0.09113449038418503,1.9676322813055194
+0.1549985649433161,2.2210613616077945
+0.2408609891831725,0.036578467032666206
+-0.5124271521479431,1.62877035247617
+0.2775666823814288,-0.03208113497433818
+0.26763938647829544,0.11913444046873212
+-0.33038145820905207,1.5751275550362456
+1.9116849696940639,-2.7414038942559555
+-0.2575246942625886,-0.38860600652997995
+1.6665830402799595,-1.9686914101351147
+0.06855534292006316,0.5149820551048718
+0.5313615154150318,1.7132268001914874
+-0.34794564802862693,1.0997382558417748
+-0.7329117132578497,-0.1001211850735421
+1.6662670204052203,-1.8142901363061466
+0.09981152683140879,2.338080903635517
+-0.46389990348003385,1.768721333351891
+1.1360953522805686,0.17469688313132364
+0.02727787000074569,2.0349007044384315
+-0.945059969195186,0.30379397821248244
+0.2606793042728228,1.5224737035624571
+1.3201853444188962,-0.2411355448235173
+-0.0832591889067541,0.5659371040888043
+1.0788000342198663,0.5085132233071634
+0.916919383915529,-0.6024861925263217
+0.6400954629094214,-0.298660214710748
+1.4922348598688642,-0.5393704517882081
+-0.03193063753703812,2.2000337711650877
+-0.12486220310672408,2.3255443710201593
+-0.03736537688491748,0.10356626042985717
+-0.09113449038418503,1.9676322813055194
+0.1549985649433161,2.2210613616077945
+-0.2061254782711009,1.656166468978354
+-0.5124271521479431,1.62877035247617
+-0.5914385599061658,1.61074364327616
+-0.6131811457896645,1.1041640960560186
+0.8673833616881145,0.6849361284900781
+1.9116849696940639,-2.7414038942559555
+1.6630033294534394,-2.10515448731562
+1.6665830402799595,-1.9686914101351147
+0.06855534292006316,0.5149820551048718
+-0.26186150422357235,-0.030925931885480706
+1.2727408955668515,-0.4287599911462048
+0.6259101196866612,1.9601636527734132
+1.6662670204052203,-1.8142901363061466
+0.09981152683140879,2.338080903635517
+0.28381290977850626,1.152520488852774
+1.1360953522805686,0.17469688313132364
+0.02727787000074569,2.0349007044384315
+-0.945059969195186,0.30379397821248244
+0.2606793042728228,1.5224737035624571
+0.6484116699811986,-0.010669152263736104
+-0.0832591889067541,0.5659371040888043
+1.0788000342198663,0.5085132233071634
+0.7028573391042859,0.8568381452445857
+0.5521062086042776,-0.24508143236486768
+1.4922348598688642,-0.5393704517882081
+-0.599267327024372,0.9304577432400765
+-0.12486220310672408,2.3255443710201593
+0.447220145454809,-0.4793404829345376
+-0.09113449038418503,1.9676322813055194
+1.1122709020927108,-0.9621618795471552
+0.3374359930462501,2.2115216062628384
+-0.5124271521479431,1.62877035247617
+-0.46023398670918314,0.3393856342405746
+-0.6131811457896645,1.1041640960560186
+0.8673833616881145,0.6849361284900781
+1.9116849696940639,-2.7414038942559555
+1.6630033294534394,-2.10515448731562
+1.6665830402799595,-1.9686914101351147
+1.6481656599686323,-2.544569373645433
+-0.26186150422357235,-0.030925931885480706
+1.2727408955668515,-0.4287599911462048
+0.15961711394592082,-0.2199382008017895
+1.6662670204052203,-1.8142901363061466
+1.3429089490134944,-0.05915201006219728
+-0.41689024796275564,0.6895268110302983
+-0.06523569096876047,1.3168075545979896
+0.02727787000074569,2.0349007044384315
+-0.945059969195186,0.30379397821248244
+0.2606793042728228,1.5224737035624571
+0.6484116699811986,-0.010669152263736104
+-0.0832591889067541,0.5659371040888043
+1.0788000342198663,0.5085132233071634
+1.4515175140058367,-2.1831992959720536
+0.5521062086042776,-0.24508143236486768
+1.562253440757905,-0.5768382527827003
+-0.599267327024372,0.9304577432400765
+-0.427746825734088,0.44658237471299
+0.447220145454809,-0.4793404829345376
+-0.09113449038418503,1.9676322813055194
+1.1122709020927108,-0.9621618795471552
+0.3374359930462501,2.2115216062628384
+0.8401675280152672,-0.7795945883454634
+-0.04762388837524534,0.28693850512480656
+0.30114937532821906,0.09833265787926898
+-0.43540263291482484,-0.3163043778824158
+1.9116849696940639,-2.7414038942559555
+1.4877519124586154,-0.9014747453846826
+1.2277999170523612,-0.8128771486207353
+-0.4451464440959846,-0.14428266795406952
+-0.26186150422357235,-0.030925931885480706
+1.2727408955668515,-0.4287599911462048
+1.6284299337103243,-2.276390944618203
+-0.43383383354904514,2.0820443959192594
+1.3429089490134944,-0.05915201006219728
+-0.41689024796275564,0.6895268110302983
+-0.06413086974887441,0.8437255710722901
+1.1738258156112629,-0.7281493091679294
+-0.945059969195186,0.30379397821248244
+0.2606793042728228,1.5224737035624571
+-0.1834532689314467,1.2945151558020294
+-0.0832591889067541,0.5659371040888043
+1.0788000342198663,0.5085132233071634
+1.4515175140058367,-2.1831992959720536
+-0.6748608789005239,-0.3672769075916011
+1.562253440757905,-0.5768382527827003
+-0.599267327024372,0.9304577432400765
+-0.427746825734088,0.44658237471299
+-0.40786075697183855,1.5053761695711625
+-0.09113449038418503,1.9676322813055194
+1.1122709020927108,-0.9621618795471552
+0.3374359930462501,2.2115216062628384
+-0.711285092338142,0.36592560299201227
+-0.5973210321093207,1.889200664991451
+-0.4937832471263278,0.6241823150535907
+1.5736258340587503,-0.6338437868184076
+1.590900798458108,-2.5370187651013367
+0.936060529555713,1.0551544354169207
+1.2277999170523612,-0.8128771486207353
+-0.4451464440959846,-0.14428266795406952
+0.7778628419129696,-0.6218401365242596
+0.5242948043061273,0.056065268913000676
+1.3221727511136572,-1.150855525283117
+0.8799755042285475,-0.13960114613778818
+0.5233230408859528,1.8267047416411644
+-0.41689024796275564,0.6895268110302983
+0.08637410325278916,-0.3792722796765736
+-0.636799722882924,0.6999552865541274
+1.5160591697515815,-0.6834968541704526
+0.2606793042728228,1.5224737035624571
+-0.1834532689314467,1.2945151558020294
+-0.0832591889067541,0.5659371040888043
+0.14037260598387902,0.4581638458266918
+0.6710199735225755,-0.04268069747841985
+-0.6748608789005239,-0.3672769075916011
+1.562253440757905,-0.5768382527827003
+0.9801514331886017,-1.088952022305231
+-0.8314403716374582,-0.04721658033210363
+0.5998843334458043,0.6844436697116059
+-0.47452803265353827,-0.4478925362937423
+1.1122709020927108,-0.9621618795471552
+0.3374359930462501,2.2115216062628384
+-0.711285092338142,0.36592560299201227
+-0.5973210321093207,1.889200664991451
+1.1909744275596985,-2.137432204869869
+0.7166415389654367,1.0056952690800245
+1.590900798458108,-2.5370187651013367
+0.936060529555713,1.0551544354169207
+1.2277999170523612,-0.8128771486207353
+-0.4451464440959846,-0.14428266795406952
+0.7063458403877104,-0.6862013066600516
+0.5242948043061273,0.056065268913000676
+1.3221727511136572,-1.150855525283117
+0.8799755042285475,-0.13960114613778818
+0.36905552831088334,0.7401069244805641
+0.31752648494430036,-0.5567117093774522
+0.6781334716832502,-0.2773751065687531
+-0.636799722882924,0.6999552865541274
+0.24175298411606544,0.316077428749017
+0.6930842680348441,-0.8626391441518078
+-0.1834532689314467,1.2945151558020294
+0.7412457001692887,-0.7471976142792156
+-0.8537246612156864,0.09572139206749372
+0.6928813081495588,0.6567594189372276
+-0.2691561828613924,0.6917360995945872
+-0.7790589292427288,0.8861209158419778
+0.9801514331886017,-1.088952022305231
+-0.8314403716374582,-0.04721658033210363
+-0.7989229574352532,-0.5039294559553252
+0.8892676995406888,-0.6816788227055492
+1.1122709020927108,-0.9621618795471552
+0.8091823226375315,-0.033651754451322874
+-0.711285092338142,0.36592560299201227
+1.1610414360042218,-0.8813015232983847
+-0.6630924370339166,1.4203981251466211
+-0.40809058349288463,0.7870362883818347
+1.590900798458108,-2.5370187651013367
+0.936060529555713,1.0551544354169207
+0.500076035706693,-0.1256331940744987
+-0.4451464440959846,-0.14428266795406952
+-1.0492380283330736,0.2923275425053744
+0.5242948043061273,0.056065268913000676
+-0.2276322840003685,0.5102763389229281
+-0.2344859862631362,0.8566733597367167
+0.36905552831088334,0.7401069244805641
+0.31752648494430036,-0.5567117093774522
+0.6781334716832502,-0.2773751065687531
+0.21866470417618888,1.6516554198538895
+0.858815408865529,-0.9184905882474982
+0.6930842680348441,-0.8626391441518078
+0.21303132609852748,0.006307595097716112
+0.35991227922169533,0.2443429017757708
+-0.8537246612156864,0.09572139206749372
+-0.6777330322822226,0.348418837455167
+-0.2691561828613924,0.6917360995945872
+-0.7790589292427288,0.8861209158419778
+0.8682540836966219,-0.47576387869237124
+0.6488106632121393,1.0486677910081295
+-0.21758434444437452,2.418938926740918
+0.6621373205853627,-0.36441105514238437
+1.1122709020927108,-0.9621618795471552
+-0.7018441306827191,0.8195954962521752
+0.9528428908984965,0.05490373281411132
+0.8564927000052045,1.0413064906557743
+0.7334911032164918,1.4101659684247432
+-1.117411043679451,-0.4644147258154281
+0.9706051125805699,-0.7508712116085222
+0.936060529555713,1.0551544354169207
+0.613059801486083,-0.3699530515043645
+0.3389437450754026,-0.541867830792663
+-0.15775007407744973,0.5928909594520113
+0.5242948043061273,0.056065268913000676
+0.9391876440554048,-0.6135287429310651
+-0.2344859862631362,0.8566733597367167
+-0.1987347880637994,0.33933968702655876
+0.5945797963795673,-0.6260087304265782
+0.6781334716832502,-0.2773751065687531
+0.21866470417618888,1.6516554198538895
+0.858815408865529,-0.9184905882474982
+1.0163840085260256,0.7821182545477331
+-0.12943438724815104,1.1176767584275416
+1.483659759560854,-2.32737300559953
+-0.8537246612156864,0.09572139206749372
+0.8737442041769535,-0.43361553181597945
+-0.2691561828613924,0.6917360995945872
+-0.5548887246065255,0.39242822194581356
+0.6408094776273036,-0.790512766967201
+-0.2797333623953703,2.407466230956976
+-0.21758434444437452,2.418938926740918
+-0.41574689394430425,0.053031191869913674
+-0.6022181029146186,0.4986937935928059
+-0.7018441306827191,0.8195954962521752
+0.9528428908984965,0.05490373281411132
+0.8564927000052045,1.0413064906557743
+0.7334911032164918,1.4101659684247432
+-1.117411043679451,-0.4644147258154281
+0.9706051125805699,-0.7508712116085222
+0.433733197203489,1.203439874400284
+0.613059801486083,-0.3699530515043645
+-0.5819152928925438,0.10232737974793138
+-0.15775007407744973,0.5928909594520113
+-0.45362484872447323,0.5220941394657983
+0.9391876440554048,-0.6135287429310651
+-0.2344859862631362,0.8566733597367167
+1.6219880040560872,-1.5688334972573408
+0.5945797963795673,-0.6260087304265782
+1.1709981153132385,-0.2212008753241238
+0.21866470417618888,1.6516554198538895
+-0.6214710890994297,0.12718595152810275
+1.0163840085260256,0.7821182545477331
+-0.8862103159561202,0.24502507470700785
+1.483659759560854,-2.32737300559953
+-0.8537246612156864,0.09572139206749372
+0.47602435717827835,2.1278628987955113
+1.3903923612045186,-0.8456931477049128
+-0.27207765206551815,1.4722728130318052
+0.6408094776273036,-0.790512766967201
+-0.2797333623953703,2.407466230956976
+-0.21758434444437452,2.418938926740918
+0.7334293665321892,-0.06642093520388814
+-0.6022181029146186,0.4986937935928059
+0.6094759799092945,0.7064829728878954
+0.9528428908984965,0.05490373281411132
+-0.48806255742491417,1.0707834309045887
+1.208680737356222,-1.2340622513982349
+-1.117411043679451,-0.4644147258154281
+0.9706051125805699,-0.7508712116085222
+0.5786204597907348,0.9026810382048664
+1.0699525541442496,0.9559082805455044
+-0.5819152928925438,0.10232737974793138
+1.4589114421489937,-0.40957980226922763
+-0.45362484872447323,0.5220941394657983
+0.9391876440554048,-0.6135287429310651
+-0.2344859862631362,0.8566733597367167
+1.6219880040560872,-1.5688334972573408
+0.615246646531643,-0.43874180149128716
+-0.9161353776692289,0.11147030918068067
+-0.7661755598293649,1.3603724380659066
+-0.6214710890994297,0.12718595152810275
+1.0163840085260256,0.7821182545477331
+-0.5488221950330913,0.1392485405455649
+1.483659759560854,-2.32737300559953
+-0.8537246612156864,0.09572139206749372
+0.47602435717827835,2.1278628987955113
+1.941756216348554,-3.4721607462518183
+-0.8245434116292925,0.37971558250240545
+0.44807351671220286,0.1081562877154636
+0.92248402754293,-0.4737859947845221
+1.1178208882992906,-1.5604993173417925
+0.15765324491976868,1.5473989970100084
+0.789006068210531,1.55997042920765
+0.6094759799092945,0.7064829728878954
+0.9528428908984965,0.05490373281411132
+-0.48806255742491417,1.0707834309045887
+1.208680737356222,-1.2340622513982349
+-1.117411043679451,-0.4644147258154281
+0.9706051125805699,-0.7508712116085222
+0.20988200957566472,2.0693041576162834
+0.041168450418358704,-0.34283232952955045
+-0.5819152928925438,0.10232737974793138
+0.6063992902934248,1.5396857528066519
+-0.45362484872447323,0.5220941394657983
+0.09006099045547228,1.455052324363008
+0.266922152203527,0.2971085982370048
+1.6219880040560872,-1.5688334972573408
+0.615246646531643,-0.43874180149128716
+-0.9161353776692289,0.11147030918068067
+-0.7661755598293649,1.3603724380659066
+0.43686628274458306,0.12695510098407733
+1.0163840085260256,0.7821182545477331
+-0.10273801923154174,2.0999373899976828
+1.483659759560854,-2.32737300559953
+-0.8537246612156864,0.09572139206749372
+0.6121371681054653,1.1772080595811616
+1.941756216348554,-3.4721607462518183
+0.6451266770166011,0.04664465670900797
+-0.20412467204147766,0.7545452814664717
+0.09512419672091621,2.0276706093393737
+1.1178208882992906,-1.5604993173417925
+0.15765324491976868,1.5473989970100084
+0.789006068210531,1.55997042920765
+0.6094759799092945,0.7064829728878954
+0.1907258555772161,1.8278376901630615
+-0.48806255742491417,1.0707834309045887
+0.1498051424705544,0.19074265929980325
+-1.117411043679451,-0.4644147258154281
+0.9706051125805699,-0.7508712116085222
+-0.4753187168245504,0.9012192600751661
+0.041168450418358704,-0.34283232952955045
+-0.5819152928925438,0.10232737974793138
+0.6063992902934248,1.5396857528066519
+-0.05897820058717762,0.09844781802745106
+1.0323654627002574,0.026846822711109164
+0.9593411082509451,-1.1937200275181128
+1.6219880040560872,-1.5688334972573408
+0.09993206235941274,-0.5218386727717309
+-0.31236605253749494,1.0575683308800727
+1.059425553720423,-0.2907914628210798
+0.43686628274458306,0.12695510098407733
+1.0163840085260256,0.7821182545477331
+0.67538832117497,1.050875283833744
+1.483659759560854,-2.32737300559953
+-0.8537246612156864,0.09572139206749372
+0.5556991323539631,1.7713603110164884
+1.2197948691878149,-1.1881802191289856
+0.7674160174449355,0.8783251476216163
+0.197253910887694,0.12340464665792591
+0.09512419672091621,2.0276706093393737
+-0.213126588345949,1.561891845184845
+-0.2453714482567488,2.4683076175554097
+1.521425275831054,-1.630105286355692
+-0.03021657151303403,-0.23983183955274562
+0.7721181786495478,0.0667520895226722
+0.6641525728455747,-0.26031265435814555
+0.1498051424705544,0.19074265929980325
+-0.8843705598172261,0.9487076282305194
+1.0449777265829836,0.3166670031896439
+1.7231590014768647,-1.2189335926204836
+0.5597716631425215,-0.20838882482756557
+-0.5819152928925438,0.10232737974793138
+0.6063992902934248,1.5396857528066519
+1.5481089455026784,-1.3310586913029825
+1.0323654627002574,0.026846822711109164
+0.9593411082509451,-1.1937200275181128
+1.2123676610897889,-1.5493524164545749
+0.09993206235941274,-0.5218386727717309
+0.844921493746392,0.1892128574236711
+1.8062423414032136,-2.689079765221871
+0.6269805100520616,0.19434381592681488
+1.0163840085260256,0.7821182545477331
+0.67538832117497,1.050875283833744
+-0.6244130789758924,1.1470910690467468
+-0.8537246612156864,0.09572139206749372
+0.7209429228684949,-0.8330229310608994
+1.2197948691878149,-1.1881802191289856
+-0.3710653181494413,0.41435797828351906
+0.197253910887694,0.12340464665792591
+0.09512419672091621,2.0276706093393737
+-0.213126588345949,1.561891845184845
+0.04878919147514882,2.2448960871704737
+0.8701948359857854,0.1749642497093654
+-0.03021657151303403,-0.23983183955274562
+0.7721181786495478,0.0667520895226722
+0.6641525728455747,-0.26031265435814555
+0.1498051424705544,0.19074265929980325
+0.44808988735977945,1.738639763576544
+0.9313461682958526,0.6561051495758172
+-0.18143778193744106,0.9612992170261372
+0.7613045878387096,-0.4823343342916653
+-0.5819152928925438,0.10232737974793138
+0.6063992902934248,1.5396857528066519
+1.5481089455026784,-1.3310586913029825
+-0.21824540725828365,0.4948848830524066
+0.15945830485822776,-0.1014076245135348
+0.1080341747315734,1.4497673269649063
+-0.5397224431790257,0.7150597218134687
+0.844921493746392,0.1892128574236711
+1.8062423414032136,-2.689079765221871
+1.1158850557519382,0.8702056956455708
+0.13566750711066716,2.133305623910819
+-0.308354635205612,-0.1329706913833716
+-0.6244130789758924,1.1470910690467468
+-0.8537246612156864,0.09572139206749372
+0.6439154135896158,-0.5283458189202801
+1.2197948691878149,-1.1881802191289856
+-0.3710653181494413,0.41435797828351906
+0.197253910887694,0.12340464665792591
+-0.5081793877943144,1.3693483246752174
+-0.213126588345949,1.561891845184845
+0.04878919147514882,2.2448960871704737
+0.8028170822942589,-0.9210774128117454
+-0.03021657151303403,-0.23983183955274562
+0.7721181786495478,0.0667520895226722
+-0.657594969277096,1.594718480684995
+-0.6183544904232208,-0.2569212075298558
+0.44808988735977945,1.738639763576544
+0.9313461682958526,0.6561051495758172
+-0.18143778193744106,0.9612992170261372
+0.7613045878387096,-0.4823343342916653
+-0.5819152928925438,0.10232737974793138
+0.5692697038323908,1.217166684980213
+1.3849842187855501,-1.4022717077474103
+-0.21824540725828365,0.4948848830524066
+0.4321630255045852,0.9373482081310379
+0.1080341747315734,1.4497673269649063
+-0.5397224431790257,0.7150597218134687
+-0.778000323927563,0.7474585560572738
+1.8062423414032136,-2.689079765221871
+1.129692271232511,0.30670196853349574
+0.13566750711066716,2.133305623910819
+-0.10742230915251583,-0.24637920519049084
+0.07040586248825498,1.9045061654795012
+-0.8537246612156864,0.09572139206749372
+0.6439154135896158,-0.5283458189202801
+1.2197948691878149,-1.1881802191289856
+0.16998184225196467,-0.021519968340215356
+1.019998982548987,1.0839452280628374
+-0.30202393902600333,0.7051186350056131
+-0.213126588345949,1.561891845184845
+0.04878919147514882,2.2448960871704737
+0.8028170822942589,-0.9210774128117454
+-0.06077080288353587,1.7727710838144066
+-0.631542706211149,1.2108368322787355
+0.607565409531545,-0.8522432673948093
+-0.6183544904232208,-0.2569212075298558
+0.44808988735977945,1.738639763576544
+0.9313461682958526,0.6561051495758172
+-0.18143778193744106,0.9612992170261372
+0.7613045878387096,-0.4823343342916653
+-0.5819152928925438,0.10232737974793138
+-0.1990466069597528,-0.5427068815097285
+1.3849842187855501,-1.4022717077474103
+-0.21824540725828365,0.4948848830524066
+1.0229947127125167,-0.12349095043535785
+0.6183536725788816,0.9448588999161276
+1.3963132746251152,-0.23649226446819727
+-0.778000323927563,0.7474585560572738
+1.8062423414032136,-2.689079765221871
+1.129692271232511,0.30670196853349574
+0.2688787977863326,-0.017538668327713836
+0.08309084393409483,2.1609241199721487
+0.8265524133553572,0.6281714488838182
+-0.1997247999310819,2.3419297686744964
+-0.667372707809024,0.43669485031493827
+1.2197948691878149,-1.1881802191289856
+0.16998184225196467,-0.021519968340215356
+1.019998982548987,1.0839452280628374
+0.6395973086591643,1.7419011958526285
+0.6666505221506722,-0.4731244466104904
+-0.24299116884262523,1.8784353850245636
+0.8028170822942589,-0.9210774128117454
+-0.06077080288353587,1.7727710838144066
+-0.631542706211149,1.2108368322787355
+-0.7975036620062503,-0.06428709364612062
+0.3781228457092899,1.1661548386728118
+0.743756224329923,0.47466497843253674
+0.28878828516754484,0.3301765417064899
+-0.18143778193744106,0.9612992170261372
+0.20452446988388845,1.932107625872469
+-0.5819152928925438,0.10232737974793138
+-0.1990466069597528,-0.5427068815097285
+0.43440146499867716,1.535226661707851
+-0.21824540725828365,0.4948848830524066
+0.38423515866993885,2.1657273692036707
+0.4906385253481518,0.7817867544277899
+1.3963132746251152,-0.23649226446819727
+-0.778000323927563,0.7474585560572738
+1.8062423414032136,-2.689079765221871
+0.22389126562602668,2.3285471969464746
+0.2688787977863326,-0.017538668327713836
+1.082589876405453,-1.0881601073860059
+0.7536730768529504,-0.5669030241931575
+-0.15260328766397002,1.108131425970832
+-0.6467649248439773,-0.004163530787149261
+1.2197948691878149,-1.1881802191289856
+0.9545032786232122,0.08262553208148204
+1.019998982548987,1.0839452280628374
+0.6395973086591643,1.7419011958526285
+0.6666505221506722,-0.4731244466104904
+0.15303657846409804,2.348669643858655
+0.8028170822942589,-0.9210774128117454
+0.004269649295520789,0.06763071874351734
+-0.0762506312307076,1.9983141706007914
+-0.44907241591765457,0.3282714909265546
+-0.016075178256929612,1.683769506638195
+0.743756224329923,0.47466497843253674
+0.28878828516754484,0.3301765417064899
+0.454802833094453,0.05338349356670062
+0.20452446988388845,1.932107625872469
+-0.5819152928925438,0.10232737974793138
+0.027637293992943124,0.3602877432909474
+0.43440146499867716,1.535226661707851
+0.6343863519112234,-0.21100326797660734
+-0.6354152304945068,0.42781689333545975
+0.8690493657736994,1.1542049282362952
+0.1945622355067004,2.191993453834893
+-0.778000323927563,0.7474585560572738
+1.8062423414032136,-2.689079765221871
+0.22389126562602668,2.3285471969464746
+0.34976904486661464,-0.0011914929810522348
+1.082589876405453,-1.0881601073860059
+0.7536730768529504,-0.5669030241931575
+-0.15260328766397002,1.108131425970832
+-0.6467649248439773,-0.004163530787149261
+1.2197948691878149,-1.1881802191289856
+0.16955672822099238,-0.30885583302409725
+-0.6930736737376727,-0.018522311092164512
+0.7515491447424002,1.3589639869546493
+0.6666505221506722,-0.4731244466104904
+0.6360839912414135,-0.453369184821506
+0.6382376126002293,-0.4480317228838947
+0.38965301730921265,0.8077886796753854
+-0.0762506312307076,1.9983141706007914
+0.7709454973613029,1.4537872972928625
+1.0779023270114874,0.3760819636809361
+-0.16030251880456134,0.6087729661931277
+0.19656974612526243,2.0716417990508265
+1.0145785100005498,0.6764512568892186
+0.20452446988388845,1.932107625872469
+-0.4511438855071423,1.7822794611289137
+0.027637293992943124,0.3602877432909474
+0.43440146499867716,1.535226661707851
+-0.7802752024617547,-0.31959262762850565
+1.0315835617574318,-0.8582210383523996
+0.8690493657736994,1.1542049282362952
+0.1945622355067004,2.191993453834893
+0.5362030405500754,1.4077838461829875
+-0.7102415948088086,0.33208988566355235
+1.1709737208815736,0.4188835012876011
+1.2129411514177215,-1.4314358843855173
+1.082589876405453,-1.0881601073860059
+0.7536730768529504,-0.5669030241931575
+-0.15260328766397002,1.108131425970832
+-0.88281035686051,0.1483586392387147
+1.2197948691878149,-1.1881802191289856
+0.16955672822099238,-0.30885583302409725
+-0.6930736737376727,-0.018522311092164512
+-0.17492985329762298,2.335122384796981
+0.6666505221506722,-0.4731244466104904
+0.6360839912414135,-0.453369184821506
+-0.9367991647215891,-0.5799731841242557
+0.4526531125904356,-0.44570651991793686
+-0.0762506312307076,1.9983141706007914
+0.5881512920479184,-0.6728930489590752
+1.486291461120073,-0.4354166184135988
+-0.16030251880456134,0.6087729661931277
+0.19656974612526243,2.0716417990508265
+0.6337552702317079,1.2555122790003033
+1.2309239284570948,-0.38496357694458844
+-0.4511438855071423,1.7822794611289137
+-0.047063700884379334,0.7083846594441054
+0.43440146499867716,1.535226661707851
+-0.7802752024617547,-0.31959262762850565
+0.2641597105469201,0.44786603425213367
+-0.1595592905795807,1.3906615290663207
+0.1945622355067004,2.191993453834893
+0.5362030405500754,1.4077838461829875
+-0.7102415948088086,0.33208988566355235
+1.1709737208815736,0.4188835012876011
+1.2129411514177215,-1.4314358843855173
+1.082589876405453,-1.0881601073860059
+0.7536730768529504,-0.5669030241931575
+-0.15260328766397002,1.108131425970832
+-0.88281035686051,0.1483586392387147
+1.2197948691878149,-1.1881802191289856
+-0.05417782029290788,-0.047936339948049
+-0.6930736737376727,-0.018522311092164512
+-0.17492985329762298,2.335122384796981
+1.0364763141163684,-0.9504452679762767
+0.219115894791895,-0.08847958869635913
+-0.9367991647215891,-0.5799731841242557
+0.4526531125904356,-0.44570651991793686
+-0.0762506312307076,1.9983141706007914
+0.5881512920479184,-0.6728930489590752
+1.486291461120073,-0.4354166184135988
+1.2910783051504415,-1.209768396146065
+0.19656974612526243,2.0716417990508265
+0.6337552702317079,1.2555122790003033
+-0.16810179345131154,0.6892786867107441
+-0.23566885151316067,0.9934043907239112
+-0.5290239065764876,1.6383597854625125
+0.43440146499867716,1.535226661707851
+-0.7802752024617547,-0.31959262762850565
+-0.22236656345352318,1.4715866560933226
+-0.1595592905795807,1.3906615290663207
+0.1945622355067004,2.191993453834893
+0.5362030405500754,1.4077838461829875
+-0.7102415948088086,0.33208988566355235
+1.1709737208815736,0.4188835012876011
+1.2129411514177215,-1.4314358843855173
+0.7211271140182107,0.03328491562261371
+0.5127357246812586,-0.5441889665850362
+0.3265510872912223,-0.36758190676219943
+-0.88281035686051,0.1483586392387147
+-0.0030618087374918446,1.5803172309347067
+1.0141675032631405,-0.7483583646873433
+1.3270143613262717,-1.670773476828578
+-0.47234221302789353,0.6644770074783513
+-0.12669542309580473,-0.5249779507126815
+-0.11622199093981656,1.5677483190865926
+-0.2866732103849353,1.4325997374917694
+0.8182522299937117,1.1434939437118052
+-0.5808301433951373,1.761164725522335
+-0.760869076847132,0.8494513881041669
+1.486291461120073,-0.4354166184135988
+1.2910783051504415,-1.209768396146065
+0.19656974612526243,2.0716417990508265
+-0.337155054264932,1.0968719583414093
+0.6487175015137207,-0.01810238792058705
+-0.23566885151316067,0.9934043907239112
+-0.5290239065764876,1.6383597854625125
+1.3444362904598697,-0.6070536252645801
+-0.7802752024617547,-0.31959262762850565
+-0.6909761114935127,1.0436982442491005
+-0.1595592905795807,1.3906615290663207
+0.1945622355067004,2.191993453834893
+0.5362030405500754,1.4077838461829875
+-0.7102415948088086,0.33208988566355235
+1.1709737208815736,0.4188835012876011
+1.2129411514177215,-1.4314358843855173
+0.7211271140182107,0.03328491562261371
+0.5127357246812586,-0.5441889665850362
+1.3508682992175767,0.10057193828012578
+-0.88281035686051,0.1483586392387147
+0.3866876670089884,1.8301449482657013
+1.158553554609077,-1.2842483024815772
+1.3270143613262717,-1.670773476828578
+-0.5800624003674053,0.669017730514047
+1.1344512672806117,-0.6870046631067953
+0.529399559476575,-0.6423628347127173
+-0.2866732103849353,1.4325997374917694
+0.8182522299937117,1.1434939437118052
+-0.5808301433951373,1.761164725522335
+-0.760869076847132,0.8494513881041669
+0.5330363005502511,-0.2969004693492949
+1.2910783051504415,-1.209768396146065
+0.7359251208431437,1.1380648826615198
+-0.735278614956279,0.5459649448191621
+0.16641530420781425,1.5549784404506979
+-0.23566885151316067,0.9934043907239112
+-0.5290239065764876,1.6383597854625125
+-0.33285572943358865,1.6097690270752545
+-0.7802752024617547,-0.31959262762850565
+0.3363640284782574,1.0479904941311493
+-0.1595592905795807,1.3906615290663207
+-0.7702876355062833,1.3358857516644984
+0.5362030405500754,1.4077838461829875
+-0.7102415948088086,0.33208988566355235
+1.1709737208815736,0.4188835012876011
+1.2129411514177215,-1.4314358843855173
+-0.21302367085070203,1.6066363717571113
+0.5127357246812586,-0.5441889665850362
+1.4506792920680966,-1.4533627237405753
+-0.4874157868184006,1.1665009338271946
+0.3866876670089884,1.8301449482657013
+-0.3044174152613668,1.183275969637104
+1.3270143613262717,-1.670773476828578
+1.2190196958347093,-0.31182386986264443
+-0.6550616316521086,0.7393783520872
+0.529399559476575,-0.6423628347127173
+1.3580150114346945,-1.4216746976214987
+0.53489272592124,1.5711218856759435
+0.737973531060388,1.5141982543671102
+-0.760869076847132,0.8494513881041669
+0.4886708067156961,0.423497669948939
+1.0428160129695647,0.1617042716460113
+0.7359251208431437,1.1380648826615198
+-0.24319192872977113,-0.03573712572790322
+0.16641530420781425,1.5549784404506979
+-0.23566885151316067,0.9934043907239112
+-0.5290239065764876,1.6383597854625125
+0.8057618870184806,0.4736740888350486
+-0.7802752024617547,-0.31959262762850565
+-0.007644090649552848,0.412884654299479
+0.3804655733535166,1.3508388502940232
+1.4837562060711276,-2.1224842639164514
+1.2696608512154453,-0.8422976522936451
+-0.4013575237679121,2.3452091092103404
+0.31350181147937894,1.7129249431418105
+1.2129411514177215,-1.4314358843855173
+-0.21302367085070203,1.6066363717571113
+0.5127357246812586,-0.5441889665850362
+1.4506792920680966,-1.4533627237405753
+-0.4874157868184006,1.1665009338271946
+0.3866876670089884,1.8301449482657013
+0.48244598800943783,0.7389438447342065
+0.8219263566301307,-0.9086314919452115
+1.2190196958347093,-0.31182386986264443
+0.11966498353639049,1.8094926047465467
+0.7415999661552233,-0.20675350753054503
+1.3580150114346945,-1.4216746976214987
+0.53489272592124,1.5711218856759435
+0.737973531060388,1.5141982543671102
+-0.760869076847132,0.8494513881041669
+1.540392908830821,-1.2782911120275013
+-0.5200396300566205,1.0185113571624143
+0.7359251208431437,1.1380648826615198
+-0.24319192872977113,-0.03573712572790322
+0.07133803450307527,1.451352395758872
+0.802325743256573,-0.6585394401127218
+-0.5290239065764876,1.6383597854625125
+0.6325039164154125,0.8958325020804304
+-0.7802752024617547,-0.31959262762850565
+1.4777744012036458,-1.8898351063062517
+0.3804655733535166,1.3508388502940232
+1.4837562060711276,-2.1224842639164514
+0.6718654838267109,-0.6803720059580657
+-0.4013575237679121,2.3452091092103404
+-0.7002415003709077,0.9566225505227612
+1.2129411514177215,-1.4314358843855173
+-0.21302367085070203,1.6066363717571113
+0.5127357246812586,-0.5441889665850362
+1.4506792920680966,-1.4533627237405753
+-0.4874157868184006,1.1665009338271946
+-0.791093830657823,0.8803018912081875
+-0.16883239183897547,1.4215192201590163
+0.303932101642179,1.2888434116291596
+0.9327501724886373,0.7355268872395024
+0.11966498353639049,1.8094926047465467
+0.7714147416497317,-0.3600981538523418
+1.3580150114346945,-1.4216746976214987
+-0.12320366627218624,0.6253847598661535
+0.737973531060388,1.5141982543671102
+1.1457346010760987,0.25845222118485855
+1.540392908830821,-1.2782911120275013
+-0.5200396300566205,1.0185113571624143
+0.7359251208431437,1.1380648826615198
+0.9087009599966424,-0.42988416064473567
+0.07133803450307527,1.451352395758872
+0.802325743256573,-0.6585394401127218
+0.22004628912997598,0.23464453525263285
+-0.6843679478905327,0.8816547970107307
+-0.7802752024617547,-0.31959262762850565
+0.31089890182519403,1.0761158785900393
+0.3804655733535166,1.3508388502940232
+-0.2074431464288552,0.3103845467818134
+0.6718654838267109,-0.6803720059580657
+1.342882369909837,-1.4474919766852505
+-0.7002415003709077,0.9566225505227612
+0.01086637007636948,-0.013059740208104579
+-0.5110857930260454,0.4443509309055964
+0.5127357246812586,-0.5441889665850362
+0.696624300968828,0.6702993483689029
+-0.4874157868184006,1.1665009338271946
+-0.3982005308892142,0.7523247396028755
+-0.16883239183897547,1.4215192201590163
+-0.431982019841878,-0.1001111890099119
+0.9327501724886373,0.7355268872395024
+0.11966498353639049,1.8094926047465467
+0.7714147416497317,-0.3600981538523418
+1.3580150114346945,-1.4216746976214987
+-0.5108611932679166,0.8896786981082645
+0.737973531060388,1.5141982543671102
+1.5922189668369542,-1.3248068965211084
+1.540392908830821,-1.2782911120275013
+-0.5200396300566205,1.0185113571624143
+0.7359251208431437,1.1380648826615198
+1.151073172785002,-0.24365815860704765
+0.1448438101714615,2.050233815224754
+0.802325743256573,-0.6585394401127218
+0.6777138015709525,1.4557952788004473
+0.610546313502653,1.076866812763275
+-0.7802752024617547,-0.31959262762850565
+0.31089890182519403,1.0761158785900393
+0.3804655733535166,1.3508388502940232
+0.3363467595880479,1.7863360568178275
+1.1105271898378546,0.9847005134643096
+-0.18869033508074745,0.08109521112038637
+-0.7002415003709077,0.9566225505227612
+0.01086637007636948,-0.013059740208104579
+-0.5110857930260454,0.4443509309055964
+0.5495814409509454,1.2137961952779632
+0.039153440485090854,0.9006284690277379
+0.7925685872511965,-0.5131280640736158
+0.0658471286118697,0.9301883404211378
+-0.16883239183897547,1.4215192201590163
+0.7605803594749548,1.3296712463480864
+-0.3566411917637936,2.259679632903972
+0.11966498353639049,1.8094926047465467
+0.7714147416497317,-0.3600981538523418
+1.242423087386121,-1.5879485953698058
+0.5285274840527985,0.14723672969477597
+0.5369427574466248,1.7267065712434762
+1.5922189668369542,-1.3248068965211084
+-1.136525321415806,-0.09397721842045223
+-0.5200396300566205,1.0185113571624143
+0.919196604914919,0.5652604161657775
+1.151073172785002,-0.24365815860704765
+0.1448438101714615,2.050233815224754
+0.802325743256573,-0.6585394401127218
+0.3895812022748029,1.6090250509382504
+0.610546313502653,1.076866812763275
+-0.7802752024617547,-0.31959262762850565
+0.31089890182519403,1.0761158785900393
+0.3804655733535166,1.3508388502940232
+0.3363467595880479,1.7863360568178275
+-0.6603276431008878,-0.2216437450943309
+-0.18869033508074745,0.08109521112038637
+-0.7002415003709077,0.9566225505227612
+0.01086637007636948,-0.013059740208104579
+-0.5110857930260454,0.4443509309055964
+0.5495814409509454,1.2137961952779632
+-0.09965380743127816,1.5569499855976976
+0.7925685872511965,-0.5131280640736158
+0.5645530693789402,1.3657044770502709
+-0.5060121828888304,0.009986730713937797
+0.7605803594749548,1.3296712463480864
+-0.28755039143480665,1.0158962999261838
+0.11966498353639049,1.8094926047465467
+0.6865954959817342,0.674708787033081
+1.242423087386121,-1.5879485953698058
+0.1887445889625457,1.7368023521341176
+-0.8265245379278837,0.48542858512898623
+1.5922189668369542,-1.3248068965211084
+-1.136525321415806,-0.09397721842045223
+-0.26208928989923125,0.14509844518936243
+0.16705500313913949,2.389485448852072
+-0.3653303605838274,0.5371166545175377
+0.1448438101714615,2.050233815224754
+0.802325743256573,-0.6585394401127218
+-0.8076763119942296,0.32840303567687246
+0.5556329052104774,1.511724543696776
+-0.049012916862190725,2.202532398903881
+0.3319728119739508,-0.661475011040713
+1.2961602303960953,-0.7500740390881871
+0.3609279762675382,1.6663228295520098
+-0.6603276431008878,-0.2216437450943309
+-0.18869033508074745,0.08109521112038637
+-0.7002415003709077,0.9566225505227612
+0.01086637007636948,-0.013059740208104579
+-0.5110857930260454,0.4443509309055964
+0.23904017092165342,1.0349773682437986
+0.017035380172740977,0.30536085239665145
+-0.7189651392641999,1.1761178837399264
+-0.711499060625069,0.6180609604154539
+0.12354690906212745,2.354406660614174
+0.7605803594749548,1.3296712463480864
+-0.28755039143480665,1.0158962999261838
+0.11966498353639049,1.8094926047465467
+0.6865954959817342,0.674708787033081
+1.242423087386121,-1.5879485953698058
+0.8065749851694183,-0.5516203011715612
+-0.08364546816987123,1.977223385814415
+1.5922189668369542,-1.3248068965211084
+-1.136525321415806,-0.09397721842045223
+0.30877155367624254,0.15594540674386254
+0.6715303164504761,0.19844285844430232
+0.29315679653483323,0.9825779951381862
+0.1448438101714615,2.050233815224754
+0.45349872388274637,-0.5882866980965333
+0.9032350976863452,0.8525259476112776
+-0.33120995726857466,1.5240106325248302
+-0.061320865175459094,0.40446237609087954
+1.5394280895282157,-0.6197388368275807
+1.2961602303960953,-0.7500740390881871
+0.3609279762675382,1.6663228295520098
+-0.10357041237274349,1.561956471059856
+0.7223075353202381,0.07853453283717055
+-0.7002415003709077,0.9566225505227612
+0.01086637007636948,-0.013059740208104579
+-0.5110857930260454,0.4443509309055964
+-0.8075370009808456,0.3571484750264183
+0.33888555197797066,-0.7090869950155604
+1.1632409222280695,0.029086341004690874
+-0.711499060625069,0.6180609604154539
+0.6138516211334114,0.43507513180782664
+0.7605803594749548,1.3296712463480864
+-0.28755039143480665,1.0158962999261838
+-0.027374481750982227,1.9294570646361933
+-0.49404081624868196,-0.05060545332639754
+1.348211425197416,-1.954958992747892
+1.4916387862021414,-1.1499831734027919
+-0.08364546816987123,1.977223385814415
+1.5922189668369542,-1.3248068965211084
+-1.136525321415806,-0.09397721842045223
+0.30877155367624254,0.15594540674386254
+-0.11493124796742749,1.0944840940410563
+0.29315679653483323,0.9825779951381862
+0.1448438101714615,2.050233815224754
+0.45349872388274637,-0.5882866980965333
+1.5800377580266356,-1.2491275784957083
+-0.33120995726857466,1.5240106325248302
+-0.061320865175459094,0.40446237609087954
+1.5394280895282157,-0.6197388368275807
+1.2961602303960953,-0.7500740390881871
+0.3609279762675382,1.6663228295520098
+0.6143659161667288,1.339018733895423
+0.12443256198032229,1.3105656323218593
+0.8915138362634347,1.676199794617322
+0.01086637007636948,-0.013059740208104579
+-0.5110857930260454,0.4443509309055964
+-0.8075370009808456,0.3571484750264183
+-0.04981157716205209,0.7223388501100099
+0.46719025331916897,-0.2312059444784771
+0.09050548458017982,0.9745652505435156
+0.5715603278717658,0.9127490335882599
+0.7605803594749548,1.3296712463480864
+-0.20393012030285365,2.4599406398694597
+-0.027374481750982227,1.9294570646361933
+-0.29849154887418305,1.9816782885621302
+1.348211425197416,-1.954958992747892
+1.4916387862021414,-1.1499831734027919
+-0.08364546816987123,1.977223385814415
+1.5922189668369542,-1.3248068965211084
+-1.136525321415806,-0.09397721842045223
+0.30877155367624254,0.15594540674386254
+-0.11493124796742749,1.0944840940410563
+0.29315679653483323,0.9825779951381862
+0.1448438101714615,2.050233815224754
+1.1938338888125117,0.1440360053914307
+-0.4480338521591736,0.904293661505978
+0.666959939712901,1.4390198289790426
+0.8346410381009259,0.39151869241943105
+1.4428520223447314,-0.24157984489181095
+1.1927005605842975,0.7889711931964583
+0.3609279762675382,1.6663228295520098
+-0.13446996189702135,2.0441357794442654
+0.12443256198032229,1.3105656323218593
+0.509741970242916,-0.389032652125994
+0.01086637007636948,-0.013059740208104579
+-0.5110857930260454,0.4443509309055964
+-0.8075370009808456,0.3571484750264183
+-0.04981157716205209,0.7223388501100099
+0.46719025331916897,-0.2312059444784771
+0.2788495920518239,1.033531660361003
+1.4922454569651902,-0.585851607672949
+0.7605803594749548,1.3296712463480864
+-0.20393012030285365,2.4599406398694597
+-0.4393207873838739,-0.1169913517933655
+-0.29849154887418305,1.9816782885621302
+1.348211425197416,-1.954958992747892
+1.4916387862021414,-1.1499831734027919
+-0.08364546816987123,1.977223385814415
+1.5922189668369542,-1.3248068965211084
+-1.136525321415806,-0.09397721842045223
+1.0506915367556608,0.11267272687440144
+0.7496929847005389,-0.7713604738890419
+-0.18215280498779352,1.0023272887008665
+0.8883632583182393,-0.3041832263935744
+-0.5784582846667417,0.14104276006088792
+-0.4480338521591736,0.904293661505978
+0.666959939712901,1.4390198289790426
+0.4250373701894733,1.9713196669618864
+-0.11044043457606051,0.3180706487967808
+1.1927005605842975,0.7889711931964583
+0.3609279762675382,1.6663228295520098
+-0.13446996189702135,2.0441357794442654
+-0.6455739025543217,0.07719356444818834
+0.509741970242916,-0.389032652125994
+1.1710804541729667,0.7811206643243781
+-0.5110857930260454,0.4443509309055964
+-0.8075370009808456,0.3571484750264183
+-0.3243141584849304,-0.30017109642389117
+0.46719025331916897,-0.2312059444784771
+-0.42639168630174956,0.6230420417438025
+-0.07636025091611365,-0.02352098195461827
+0.26409777169797005,2.2339993045269266
+-0.5102687720912787,-0.04614378675019182
+0.7138489063389228,-0.4747648695914112
+-0.29849154887418305,1.9816782885621302
+1.348211425197416,-1.954958992747892
+1.3112549883211417,-0.38867162565930824
+-0.7794496368718207,0.7436542789954481
+0.7179132985689429,-0.8037663120930904
+1.1813180338517613,0.2128064570507161
+0.2717257554196131,-0.30032676515353085
+0.7496929847005389,-0.7713604738890419
+-0.18215280498779352,1.0023272887008665
+0.8883632583182393,-0.3041832263935744
+-0.2315438512810211,1.362680873297349
+-0.527805760642217,-0.2092096577915276
+0.666959939712901,1.4390198289790426
+0.4250373701894733,1.9713196669618864
+-0.16094256694129833,0.7633913226458268
+1.1927005605842975,0.7889711931964583
+0.4260037459219853,1.9244150709105317
+-0.13446996189702135,2.0441357794442654
+-0.6455739025543217,0.07719356444818834
+0.509741970242916,-0.389032652125994
+1.1710804541729667,0.7811206643243781
+0.8717582905491835,1.2159985764022108
+-0.020699879040282254,0.6186939067027102
+-0.3243141584849304,-0.30017109642389117
+0.46719025331916897,-0.2312059444784771
+-0.42639168630174956,0.6230420417438025
+0.4221028617127678,1.3193059949531536
+-0.22261550787031886,1.8458115898342315
+1.472994519834086,-0.5801537117358284
+-0.41375771479223555,1.2207477386646304
+-0.29849154887418305,1.9816782885621302
+1.348211425197416,-1.954958992747892
+0.4347552427157545,-0.020609975468280917
+-0.7794496368718207,0.7436542789954481
+0.7179132985689429,-0.8037663120930904
+1.1813180338517613,0.2128064570507161
+0.2717257554196131,-0.30032676515353085
+0.300571254805592,-0.6066773524606829
+1.4880207746305247,-1.7745403500247905
+0.8883632583182393,-0.3041832263935744
+0.5851101409807222,0.39513471772159
+-0.8720500176608195,0.020946188398878116
+0.666959939712901,1.4390198289790426
+-0.5657171253847195,-0.14443902952540472
+-0.2937736664524351,1.0659305546954887
+1.1927005605842975,0.7889711931964583
+0.4260037459219853,1.9244150709105317
+-0.13446996189702135,2.0441357794442654
+-0.6455739025543217,0.07719356444818834
+0.509741970242916,-0.389032652125994
+1.1710804541729667,0.7811206643243781
+0.8717582905491835,1.2159985764022108
+0.6185215273902884,-0.4065281595949899
+-0.3243141584849304,-0.30017109642389117
+0.46719025331916897,-0.2312059444784771
+-0.42639168630174956,0.6230420417438025
+0.4221028617127678,1.3193059949531536
+0.23601386582953232,-0.43574013964478747
+0.181973234563653,-0.2599646075435841
+-0.41375771479223555,1.2207477386646304
+-0.29849154887418305,1.9816782885621302
+1.348211425197416,-1.954958992747892
+0.4347552427157545,-0.020609975468280917
+-0.7794496368718207,0.7436542789954481
+0.8390996556898427,-1.1371941130183059
+1.1813180338517613,0.2128064570507161
+0.2717257554196131,-0.30032676515353085
+1.1306229506017524,-0.1969427960860647
+1.4880207746305247,-1.7745403500247905
+0.8883632583182393,-0.3041832263935744
+0.8477497417893031,0.48362073287329665
+-0.8720500176608195,0.020946188398878116
+0.666959939712901,1.4390198289790426
+-0.5657171253847195,-0.14443902952540472
+-0.2937736664524351,1.0659305546954887
+1.1927005605842975,0.7889711931964583
+1.590043571359757,-1.810043747510181
+-0.13446996189702135,2.0441357794442654
+-0.6455739025543217,0.07719356444818834
+-0.13013836292632697,1.5547228402336257
+1.1710804541729667,0.7811206643243781
+0.5306363186290219,-0.7458278677704882
+1.091152843106359,0.48642318632176407
+-0.3243141584849304,-0.30017109642389117
+0.46719025331916897,-0.2312059444784771
+2.3189238767672933,-4.020030190114723
+-0.21949579386639617,-0.3390154745028251
+0.23601386582953232,-0.43574013964478747
+0.181973234563653,-0.2599646075435841
+-0.41375771479223555,1.2207477386646304
+-0.29849154887418305,1.9816782885621302
+0.9689144799894148,-0.624468794674603
+0.4347552427157545,-0.020609975468280917
+0.9382972405877146,1.0570653218691333
+-0.25468536715638235,2.441523133953132
+-0.36957553964149403,0.2792575766284601
+0.2717257554196131,-0.30032676515353085
+0.30469619297770456,1.1871488537000874
+1.4880207746305247,-1.7745403500247905
+0.8883632583182393,-0.3041832263935744
+0.32727331613901905,1.805606561346485
+-0.8720500176608195,0.020946188398878116
+0.6828808072611056,-0.374677012964746
+-0.5657171253847195,-0.14443902952540472
+0.5473111920547762,0.18149987856238664
+0.00043174530934003696,1.1236747320270282
+0.49540505642337995,0.4854105894973906
+-0.13446996189702135,2.0441357794442654
+-0.6455739025543217,0.07719356444818834
+1.5545509052069173,-0.3100319160790347
+-0.5766174621378474,0.5167222061016175
+0.2953946482928238,0.003412634662583791
+1.091152843106359,0.48642318632176407
+0.8814523711204038,-1.104209290959166
+0.46719025331916897,-0.2312059444784771
+1.0610957160658743,0.4729676366027611
+-0.14379624327465834,0.387743144561697
+0.11290996813777135,-0.1252845227718694
+0.181973234563653,-0.2599646075435841
+-0.41375771479223555,1.2207477386646304
+0.5640912844297077,1.6513924902963808
+0.9689144799894148,-0.624468794674603
+1.1583149997582494,0.07363648496673358
+0.9382972405877146,1.0570653218691333
+-0.7663060406510832,1.3535026316196428
+-0.36957553964149403,0.2792575766284601
+0.2717257554196131,-0.30032676515353085
+1.0841242911868236,-1.0048557888297256
+1.4880207746305247,-1.7745403500247905
+0.2999116594731986,2.032453075813098
+-0.6334343680045866,-0.055971926884967105
+-0.8720500176608195,0.020946188398878116
+0.6828808072611056,-0.374677012964746
+1.6698781136861827,-1.178950287017678
+1.392830084030244,-1.961731851340192
+-0.7022033965729945,1.1727490009419852
+0.49540505642337995,0.4854105894973906
+-0.13446996189702135,2.0441357794442654
+-0.6455739025543217,0.07719356444818834
+-0.783266028270128,1.697147282909762
+-0.5766174621378474,0.5167222061016175
+-0.7377660089701266,0.48412349757293927
+1.091152843106359,0.48642318632176407
+0.8814523711204038,-1.104209290959166
+0.5518658451832108,-0.4663558822485133
+0.6695179669538769,0.9416158225207061
+0.3686565248066751,1.3942945111618337
+-0.9329934454803455,0.3156562233368311
+0.181973234563653,-0.2599646075435841
+-0.41375771479223555,1.2207477386646304
+-0.509804894096402,0.9179763834184195
+0.9689144799894148,-0.624468794674603
+-0.37596694353561383,1.4143502096035512
+0.9382972405877146,1.0570653218691333
+1.0362594727949734,0.5180176286174262
+-0.2860867721071214,0.6900216599527127
+0.2717257554196131,-0.30032676515353085
+1.0841242911868236,-1.0048557888297256
+0.5918182217253397,0.15827478426763109
+1.42982720327451,-1.000371417370115
+0.8589785872446646,-0.5086188352778322
+-0.8720500176608195,0.020946188398878116
+0.7791236188024405,1.684155329151719
+-0.3453091149287994,1.809166132133998
+1.392830084030244,-1.961731851340192
+0.2870755228869936,-0.4236962790763022
+0.49540505642337995,0.4854105894973906
+-0.13446996189702135,2.0441357794442654
+-0.6455739025543217,0.07719356444818834
+0.28544210703579703,2.4657619947785365
+1.5854486257129996,-0.6669647513003358
+-0.7377660089701266,0.48412349757293927
+-0.06151319218385626,0.2783244293241084
+-0.9705095051633528,0.7481051954265239
+0.5518658451832108,-0.4663558822485133
+1.1397836792937857,-1.530662009566325
+0.3686565248066751,1.3942945111618337
+0.6086673077863136,-0.1933411494193873
+0.2302267411484754,-0.0904956761383246
+-0.6599256125266371,1.2242972722558818
+-0.509804894096402,0.9179763834184195
+-0.45429186783836917,1.5628199767901974
+1.0667220380329039,0.7644531500079574
+0.9382972405877146,1.0570653218691333
+1.0362594727949734,0.5180176286174262
+1.0925388694952172,0.9498990291332492
+0.2717257554196131,-0.30032676515353085
+1.0841242911868236,-1.0048557888297256
+1.6345992659996602,-1.1370839854911114
+-0.2688557182899189,0.579439446083407
+0.8589785872446646,-0.5086188352778322
+0.3728627660366252,1.7536129058688237
+1.0519179676713553,0.9005674734033531
+-0.3453091149287994,1.809166132133998
+0.5111771395534086,1.3079378024576578
+0.2870755228869936,-0.4236962790763022
+1.2798968650831528,-1.2526992557830068
+-0.13446996189702135,2.0441357794442654
+-0.6455739025543217,0.07719356444818834
+0.28544210703579703,2.4657619947785365
+-1.025927107556821,0.22414960574336593
+-0.7377660089701266,0.48412349757293927
+1.4165302024547486,-1.024994041388208
+-0.9705095051633528,0.7481051954265239
+1.3729394089046445,-0.41801240558964015
+0.8633719831847326,0.9931195392920283
+0.6404642209200793,1.8059751958494799
+0.45112617984911724,-0.4908274462551007
+1.1391575902111124,0.7565574323513309
+0.5296567263878844,1.5774775221549975
+-0.21842252067271045,0.995757858773747
+-0.45429186783836917,1.5628199767901974
+1.0667220380329039,0.7644531500079574
+0.9382972405877146,1.0570653218691333
+1.0362594727949734,0.5180176286174262
+1.385017096659596,-1.6514331818474308
+0.2717257554196131,-0.30032676515353085
+1.0841242911868236,-1.0048557888297256
+1.6345992659996602,-1.1370839854911114
+-0.20438162788809838,0.29470047128734056
+0.8589785872446646,-0.5086188352778322
+0.3728627660366252,1.7536129058688237
+1.0519179676713553,0.9005674734033531
+-0.3453091149287994,1.809166132133998
+0.8214143093888432,0.3647374940399728
+-0.018953735992245258,0.30639197642687366
+1.3033865815321155,-0.18545665573613535
+-0.13446996189702135,2.0441357794442654
+0.4223291353840479,0.43126970472154436
+1.201433155415087,-0.5641771943663808
+-1.025927107556821,0.22414960574336593
+-0.7377660089701266,0.48412349757293927
+1.4165302024547486,-1.024994041388208
+0.47252879486334076,0.5202934301325591
+1.3729394089046445,-0.41801240558964015
+0.3593512831273141,0.4115908402540773
+0.6404642209200793,1.8059751958494799
+1.0522196937414234,-0.67647376452962
+1.1391575902111124,0.7565574323513309
+-0.6657025313980299,0.9463668178312856
+-0.629670795455643,0.6043054165808502
+-0.45429186783836917,1.5628199767901974
+1.4277830750211764,-1.8146881427742723
+1.3609297894120322,-1.3104416654590767
+1.0362594727949734,0.5180176286174262
+1.385017096659596,-1.6514331818474308
+0.2717257554196131,-0.30032676515353085
+-0.40404363914927877,0.8597630295696621
+-0.39396732380212984,2.253841359988296
+-0.20438162788809838,0.29470047128734056
+0.8250342332574323,0.9248561016382473
+0.3728627660366252,1.7536129058688237
+1.0495319404867232,-0.4591735590268805
+-0.3453091149287994,1.809166132133998
+0.8214143093888432,0.3647374940399728
+0.8276604777018473,-0.6111044222230053
+-0.6610054962042847,0.8799985920864558
+-0.13446996189702135,2.0441357794442654
+0.22244048561532423,1.4795013182827967
+-0.09468146206862799,0.25258563677643775
+-1.025927107556821,0.22414960574336593
+1.0257856069259699,-1.1929264168804208
+1.4165302024547486,-1.024994041388208
+0.47252879486334076,0.5202934301325591
+1.3729394089046445,-0.41801240558964015
+0.3593512831273141,0.4115908402540773
+0.6404642209200793,1.8059751958494799
+0.24069161509442066,-0.10324565476250341
+1.1391575902111124,0.7565574323513309
+-0.012623775369619228,1.9908108610507047
+-0.1689849034269666,-0.10107251743620518
+-0.45429186783836917,1.5628199767901974
+1.4277830750211764,-1.8146881427742723
+1.560266930978047,-1.0724681861050902
+1.68184952608451,-1.2972933672798679
+1.385017096659596,-1.6514331818474308
+0.2717257554196131,-0.30032676515353085
+0.4589122873929885,-0.16333829749511858
+0.8792526961572803,0.12540202993925886
+-0.20438162788809838,0.29470047128734056
+-0.01826919998617854,1.532960736967985
+0.3728627660366252,1.7536129058688237
+1.354185455257093,-1.1584672395148161
+-0.10303731931526106,0.7038137626586938
+1.3783806321662664,-0.9650870675867522
+0.8276604777018473,-0.6111044222230053
+-0.6610054962042847,0.8799985920864558
+-0.13446996189702135,2.0441357794442654
+0.22244048561532423,1.4795013182827967
+1.2538005064425688,-0.780169615068334
+0.8844570394882555,-0.867732134638496
+1.0257856069259699,-1.1929264168804208
+0.6536117334628305,1.7169316655606617
+0.47252879486334076,0.5202934301325591
+-0.08866912352016043,2.1379182521802464
+-0.7187991870953941,1.1462783619810666
+0.6404642209200793,1.8059751958494799
+0.24069161509442066,-0.10324565476250341
+1.1391575902111124,0.7565574323513309
+-0.012623775369619228,1.9908108610507047
+-0.1689849034269666,-0.10107251743620518
+-0.45429186783836917,1.5628199767901974
+0.03758383793584033,-0.14556324797265396
+0.021667632413574736,1.7291064809477985
+1.4475356048213754,-0.01596213254507628
+1.385017096659596,-1.6514331818474308
+0.2717257554196131,-0.30032676515353085
+0.4589122873929885,-0.16333829749511858
+0.8792526961572803,0.12540202993925886
+0.6243265311424462,1.3184498448428685
+-0.01826919998617854,1.532960736967985
+-0.32502872880184386,2.383950323065615
+1.354185455257093,-1.1584672395148161
+-0.10303731931526106,0.7038137626586938
+-0.7644880007524328,0.6854235021217066
+0.8276604777018473,-0.6111044222230053
+-0.6610054962042847,0.8799985920864558
+-0.13446996189702135,2.0441357794442654
+-0.5151054988020263,0.6251676391196953
+1.2808542587383238,-0.8598896766024323
+0.8844570394882555,-0.867732134638496
+-0.7182371155617235,1.03490711885486
+0.6536117334628305,1.7169316655606617
+0.2751410115142433,0.3017021796456798
+-0.08866912352016043,2.1379182521802464
+-0.7187991870953941,1.1462783619810666
+0.6404642209200793,1.8059751958494799
+-0.7168860252008514,0.7960263850362651
+1.1391575902111124,0.7565574323513309
+-0.09624503089795222,0.05860374112482522
+-0.1689849034269666,-0.10107251743620518
+-0.45429186783836917,1.5628199767901974
+0.03758383793584033,-0.14556324797265396
+0.021667632413574736,1.7291064809477985
+0.979852845596739,1.1452523265969843
+1.385017096659596,-1.6514331818474308
+0.2717257554196131,-0.30032676515353085
+1.616013851560628,-1.1591049068807024
+1.1116223761915083,0.736884423228254
+0.6243265311424462,1.3184498448428685
+1.2363017077975236,-1.4512725524184702
+-0.39762551439740906,0.6889972528304273
+1.354185455257093,-1.1584672395148161
+1.460410029536884,-1.5246579865346783
+-0.18842001372863953,-0.3750493063066409
+0.6686986429943891,-0.15582368474617847
+-0.6610054962042847,0.8799985920864558
+-0.13446996189702135,2.0441357794442654
+-0.5412500456712609,0.526483547102415
+1.2808542587383238,-0.8598896766024323
+-0.22269597244387684,-0.051827471288905025
+-0.4307779695442077,-0.47173600648216507
+0.6536117334628305,1.7169316655606617
+0.2751410115142433,0.3017021796456798
+-0.08866912352016043,2.1379182521802464
+-0.37768791193848394,0.31609879179546685
+0.6404642209200793,1.8059751958494799
+-0.7552241749836239,0.3309287737820922
+1.1391575902111124,0.7565574323513309
+-0.8094880724336098,1.1374632710404389
+-0.5598910164143176,1.2911537980904888
+1.2882643648796168,-0.8388413332314116
+-0.6136759654503463,0.592279286800463
+0.021667632413574736,1.7291064809477985
+0.30130151171276576,-0.12802312531221605
+1.385017096659596,-1.6514331818474308
+0.2717257554196131,-0.30032676515353085
+0.8460031982860079,0.5731503212658273
+-0.19707958845809098,0.5705436755616649
+0.6243265311424462,1.3184498448428685
+-0.625230679722908,0.8226404657184299
+1.5138886442556772,-0.7991458220569714
+1.354185455257093,-1.1584672395148161
+1.460410029536884,-1.5246579865346783
+0.0947458975294665,-0.18144004176076634
+0.22881841665070712,0.4087417871923118
+-0.6610054962042847,0.8799985920864558
+-0.13446996189702135,2.0441357794442654
+0.14573323521104808,2.1529754131101564
+-0.1997933957966762,0.6596230006452066
+-0.22269597244387684,-0.051827471288905025
+0.8714865430950913,0.49486151237878895
+0.6536117334628305,1.7169316655606617
+0.2751410115142433,0.3017021796456798
+-0.08866912352016043,2.1379182521802464
+-0.37768791193848394,0.31609879179546685
+0.6404642209200793,1.8059751958494799
+-0.7552241749836239,0.3309287737820922
+-0.7272532430726129,0.35588450752144374
+0.43769953934441086,1.4527650096713887
+0.44663569345393317,0.10502145153641829
+1.2882643648796168,-0.8388413332314116
+-0.6136759654503463,0.592279286800463
+0.021667632413574736,1.7291064809477985
+0.9053349539328485,1.121611511999356
+1.385017096659596,-1.6514331818474308
+-0.056146775880333455,-0.18508379233777916
+0.8460031982860079,0.5731503212658273
+-0.4733885965016867,1.4672559151297988
+0.5601214088613837,-0.3140102608676424
+-0.625230679722908,0.8226404657184299
+0.010942222449170425,0.12232250482725163
+-0.12014346950293141,0.30753102538153254
+1.460410029536884,-1.5246579865346783
+0.9801563114749864,0.035955889534547536
+0.15764189081175173,1.3625536860386076
+-0.6610054962042847,0.8799985920864558
+-0.13446996189702135,2.0441357794442654
+-0.21285775592619754,1.7490391469896687
+1.2680204652907359,-0.4595703849869943
+0.726380845543688,-0.5729719547380453
+0.8714865430950913,0.49486151237878895
+0.6536117334628305,1.7169316655606617
+0.2751410115142433,0.3017021796456798
+1.6879895252114736,-1.8980496880292992
+-0.37768791193848394,0.31609879179546685
+0.6404642209200793,1.8059751958494799
+-0.7552241749836239,0.3309287737820922
+1.265395178645548,0.3580264967285419
+0.43769953934441086,1.4527650096713887
+-0.6359739587747574,0.16193102521501224
+1.2882643648796168,-0.8388413332314116
+-0.6136759654503463,0.592279286800463
+0.021667632413574736,1.7291064809477985
+0.1915068827308875,2.143598876482239
+1.385017096659596,-1.6514331818474308
+0.8886000775211613,1.4786749597825226
+0.8460031982860079,0.5731503212658273
+0.8014395484575891,-0.3304527008341131
+0.5601214088613837,-0.3140102608676424
+-0.625230679722908,0.8226404657184299
+0.9547094987680695,-0.9410112839061542
+-0.12014346950293141,0.30753102538153254
+0.5984377519960471,1.4894540433050474
+0.8013958942439071,0.6818351885884888
+0.15764189081175173,1.3625536860386076
+-0.6610054962042847,0.8799985920864558
+-0.031439619790731066,0.7058859143955951
+1.2590720618668083,-0.8566123425838357
+1.2680204652907359,-0.4595703849869943
+-0.5179220657745369,2.004793239010856
+-0.4941455066191496,0.6379337006653789
+0.6536117334628305,1.7169316655606617
+-0.5614552286917474,-0.2566327144709697
+1.6879895252114736,-1.8980496880292992
+0.20553905109323545,2.0672160082453663
+1.628673108736594,-1.509313612553432
+-0.7552241749836239,0.3309287737820922
+1.265395178645548,0.3580264967285419
+-0.26443902213574694,-0.05126242478577664
+0.37007266082952933,-0.08685336274665267
+-0.05604129743328787,1.9037909536183706
+1.407806226161067,-1.6289718361417878
+0.7343171699495931,-0.7402941984158176
+0.1915068827308875,2.143598876482239
+0.30124138420309393,0.7173995212558291
+-1.0012982895911653,-0.3584819106614756
+1.3226984056624047,-1.8024081014567352
+-0.23959518402885233,1.4939184925790188
+0.762922118368357,-0.3226161097396014
+-0.625230679722908,0.8226404657184299
+0.9547094987680695,-0.9410112839061542
+1.0548112803147816,-0.6434027031961072
+-0.09960053458622509,0.27881266517186565
+0.7966535329215321,0.6757334606455457
+-0.3586608476629348,2.081684606995581
+0.49831875869784104,1.9422610875464696
+0.9019372972684039,0.6639230393388218
+-0.01305074193559519,1.8327779085317824
+1.0966889786192877,-0.6479762097590798
+-0.5179220657745369,2.004793239010856
+0.31799877131284854,0.16006345037154734
+0.6536117334628305,1.7169316655606617
+-0.5614552286917474,-0.2566327144709697
+1.6879895252114736,-1.8980496880292992
+0.20553905109323545,2.0672160082453663
+1.628673108736594,-1.509313612553432
+-0.7552241749836239,0.3309287737820922
+1.265395178645548,0.3580264967285419
+1.7786298730282684,-1.5778701496125096
+0.37007266082952933,-0.08685336274665267
+-0.19826729712410218,1.6846072091439939
+0.32775062176213066,2.204299621490223
+0.4406025729136588,-0.11482882716112985
+0.1915068827308875,2.143598876482239
+0.00921283908660836,0.8763942772160929
+-1.0012982895911653,-0.3584819106614756
+-0.5512504952616595,1.4292671819311662
+-0.24902099248491466,1.3473917586783313
+0.762922118368357,-0.3226161097396014
+-0.625230679722908,0.8226404657184299
+-0.49552364775706925,1.437084396645193
+1.0548112803147816,-0.6434027031961072
+-0.09960053458622509,0.27881266517186565
+0.7966535329215321,0.6757334606455457
+-0.3586608476629348,2.081684606995581
+-0.42594663029418606,1.8854799238018811
+1.1549561646173925,-1.1703521399243308
+-0.5666873990403599,-0.022415039128913766
+1.0966889786192877,-0.6479762097590798
+-0.5179220657745369,2.004793239010856
+0.5220909848908231,-0.1896965104926217
+0.7618921522657065,1.5702865719889596
+-0.5614552286917474,-0.2566327144709697
+1.6879895252114736,-1.8980496880292992
+0.20553905109323545,2.0672160082453663
+1.628673108736594,-1.509313612553432
+-0.7552241749836239,0.3309287737820922
+0.45519633712295415,0.7438641794453582
+1.7786298730282684,-1.5778701496125096
+0.37007266082952933,-0.08685336274665267
+-0.19826729712410218,1.6846072091439939
+-0.30703655327534357,0.4206424870673699
+0.04484339759507061,1.8235467931781033
+0.1915068827308875,2.143598876482239
+1.0359224483508735,-1.2721210463390062
+-0.5780668951048592,1.72816354094207
+-0.5512504952616595,1.4292671819311662
+-0.24902099248491466,1.3473917586783313
+-0.04984150537168153,0.6447551097723724
+-0.14480256941533529,1.2855935034188128
+-0.49552364775706925,1.437084396645193
+1.0548112803147816,-0.6434027031961072
+-0.6853668183601235,-0.06919309356936237
+-0.7512626790338519,0.9734628663854044
+0.7341055558383068,1.945163340087982
+-0.1964438960067459,1.5183741898858796
+-0.48231494869568603,-0.017398673034990077
+-0.5666873990403599,-0.022415039128913766
+1.0966889786192877,-0.6479762097590798
+-0.5179220657745369,2.004793239010856
+0.5220909848908231,-0.1896965104926217
+-0.0719486250903773,1.1552686690561509
+-0.3736477526689609,1.6328691834194031
+1.6879895252114736,-1.8980496880292992
+0.4850531029274158,1.6274265594913717
+1.628673108736594,-1.509313612553432
+0.5799292154841881,1.6110542637629466
+-0.6057268580387827,0.7207246362875093
+-0.5698234710784286,1.5705043658474782
+0.37007266082952933,-0.08685336274665267
+0.17700200209205705,1.4092803555703137
+-0.30703655327534357,0.4206424870673699
+0.04484339759507061,1.8235467931781033
+0.1915068827308875,2.143598876482239
+-0.49005500396880836,1.8819636424094397
+-0.5780668951048592,1.72816354094207
+-0.34423230238654046,0.3127266402965746
+0.8843787211170417,-0.39685064121323116
+-0.04984150537168153,0.6447551097723724
+1.2118214425813887,-0.6877858018296902
+-0.49552364775706925,1.437084396645193
+1.0548112803147816,-0.6434027031961072
+-0.6853668183601235,-0.06919309356936237
+-0.42700236451041207,-0.028946096663685472
+0.7341055558383068,1.945163340087982
+0.9870053043711012,1.2231836572380872
+-0.48231494869568603,-0.017398673034990077
+-0.5666873990403599,-0.022415039128913766
+1.0966889786192877,-0.6479762097590798
+-0.30406941685205036,1.3222971738009446
+0.5220909848908231,-0.1896965104926217
+-0.0719486250903773,1.1552686690561509
+-0.424571484813714,2.086574756323016
+1.6879895252114736,-1.8980496880292992
+-1.0085260120309332,0.3479527538381725
+1.628673108736594,-1.509313612553432
+0.5799292154841881,1.6110542637629466
+-0.6057268580387827,0.7207246362875093
+-0.5698234710784286,1.5705043658474782
+0.37007266082952933,-0.08685336274665267
+-0.5292157161147202,1.2715723507543897
+0.14723509369294951,-0.042224049364407046
+1.1894474587342654,-0.6300646663326732
+0.1915068827308875,2.143598876482239
+-0.898395089957416,0.6130789913124359
+-0.5780668951048592,1.72816354094207
+1.1023937311997565,-0.8120569177038153
+0.8843787211170417,-0.39685064121323116
+-0.04984150537168153,0.6447551097723724
+1.2118214425813887,-0.6877858018296902
+0.053938883442391186,1.6574000798010098
+0.15994858277453491,1.6453912511268232
+-0.49779386412032556,0.5729470221641597
+-0.42700236451041207,-0.028946096663685472
+0.20087749080296358,-0.08315996047207971
+0.9870053043711012,1.2231836572380872
+-0.2164090688724274,-0.23294830341259076
+-0.5666873990403599,-0.022415039128913766
+0.8013975160535889,-0.42729203020948314
+0.6364041823764893,-0.22310511989469328
+-0.3919456310048448,0.712749812987912
+-0.8126935621830724,0.9883822287593832
+-0.424571484813714,2.086574756323016
+1.6879895252114736,-1.8980496880292992
+-1.0085260120309332,0.3479527538381725
+-0.557131933623182,1.4909533503538368
+0.5799292154841881,1.6110542637629466
+-0.6057268580387827,0.7207246362875093
+-0.5698234710784286,1.5705043658474782
+0.37007266082952933,-0.08685336274665267
+0.17528608567606413,2.2105423236698907
+0.14723509369294951,-0.042224049364407046
+1.021979531333628,-0.8371428836306876
+1.556057890492565,-1.3769967877597924
+-0.898395089957416,0.6130789913124359
+-0.5780668951048592,1.72816354094207
+-0.35559924949512767,1.7335574127215878
+1.0343251961152258,-0.7605934422038403
+-0.04984150537168153,0.6447551097723724
+1.2118214425813887,-0.6877858018296902
+0.053938883442391186,1.6574000798010098
+0.15994858277453491,1.6453912511268232
+-0.49779386412032556,0.5729470221641597
+-0.42700236451041207,-0.028946096663685472
+0.20087749080296358,-0.08315996047207971
+-0.3314765474817386,-0.007246152469401683
+-0.2164090688724274,-0.23294830341259076
+-0.5666873990403599,-0.022415039128913766
+-0.15368332418169856,1.5324007262234014
+0.6364041823764893,-0.22310511989469328
+-0.3919456310048448,0.712749812987912
+-0.8126935621830724,0.9883822287593832
+-0.424571484813714,2.086574756323016
+1.6879895252114736,-1.8980496880292992
+-0.002374810238768066,-0.18296695681339936
+0.46312905022191797,0.04018027210690467
+0.5799292154841881,1.6110542637629466
+0.8229041449117163,0.7878696082934058
+-0.38835477060330226,0.36791363315508185
+0.3242533195596943,-0.4921501540045311
+-0.2047621812722841,2.4185978713435823
+0.14723509369294951,-0.042224049364407046
+-0.40630504529937783,-0.24132072124435877
+1.556057890492565,-1.3769967877597924
+-0.898395089957416,0.6130789913124359
+-0.5780668951048592,1.72816354094207
+0.02488745057202285,2.3307398100792613
+-0.1284606894375966,0.42812818304015976
+0.2277586123952502,-0.12172582539571583
+1.2118214425813887,-0.6877858018296902
+0.053938883442391186,1.6574000798010098
+1.0923992082515632,0.9120695117627148
+-0.23775471806417267,2.345203571724306
+-0.42700236451041207,-0.028946096663685472
+0.8159034055323103,-0.3179037288053006
+-0.3314765474817386,-0.007246152469401683
+-0.2164090688724274,-0.23294830341259076
+-0.03738717275940667,1.3808119280229139
+-0.31922889203730986,0.5760915435841186
+0.6364041823764893,-0.22310511989469328
+1.0926738809420353,-1.1108746619559908
+-0.8126935621830724,0.9883822287593832
+0.4813976023093312,0.7555421373081652
+1.6879895252114736,-1.8980496880292992
+-0.002374810238768066,-0.18296695681339936
+-0.08227063776043259,0.6767640635666571
+0.5799292154841881,1.6110542637629466
+0.8229041449117163,0.7878696082934058
+-0.38835477060330226,0.36791363315508185
+0.3242533195596943,-0.4921501540045311
+0.6879046716525568,0.36569779840527294
+0.10503159786040703,1.2747684057270323
+-0.40630504529937783,-0.24132072124435877
+1.556057890492565,-1.3769967877597924
+-0.898395089957416,0.6130789913124359
+-0.5780668951048592,1.72816354094207
+0.02488745057202285,2.3307398100792613
+-0.1284606894375966,0.42812818304015976
+0.2277586123952502,-0.12172582539571583
+1.2118214425813887,-0.6877858018296902
+0.053938883442391186,1.6574000798010098
+1.0923992082515632,0.9120695117627148
+1.5008668145064838,-0.8879886719302743
+-0.42700236451041207,-0.028946096663685472
+0.5410226040076752,-0.482542199738645
+0.15369730792669206,1.172452471998945
+0.4174183444993208,0.5107941524918481
+0.5771760450688609,0.31688743456239543
+0.9509018555508137,-0.16962234706046556
+-0.9348866080594933,-0.07421139097311491
+1.0926738809420353,-1.1108746619559908
+-0.8126935621830724,0.9883822287593832
+0.7052039785522718,-0.42985246179785896
+1.365354991310136,-1.238192043966083
+-0.9457216032308872,-0.12365616192568142
+0.7562504061332576,1.2085881191807695
+0.5799292154841881,1.6110542637629466
+0.8229041449117163,0.7878696082934058
+-0.38835477060330226,0.36791363315508185
+1.3079276244069151,-0.39131168382944337
+0.7876248046101848,0.43050044923295444
+1.3256643611122585,0.37272436751354193
+0.708938593136406,-0.5069147924175084
+1.2000103500349453,-0.04476631768989321
+-0.702799028516502,-0.04052205770639661
+-0.5780668951048592,1.72816354094207
+0.02488745057202285,2.3307398100792613
+-0.1284606894375966,0.42812818304015976
+0.24944950061810883,1.477134241524218
+0.7104838189796792,1.631282258411082
+0.053938883442391186,1.6574000798010098
+1.0923992082515632,0.9120695117627148
+1.5008668145064838,-0.8879886719302743
+-0.42700236451041207,-0.028946096663685472
+0.5410226040076752,-0.482542199738645
+-0.579506253947105,-0.150459331173325
+0.6724148348909199,0.04237361230346648
+0.42546774718500646,-0.5097295546856814
+-0.01579156019940256,1.1247786874059107
+-0.21320246300368395,1.8798832331883022
+1.0926738809420353,-1.1108746619559908
+-0.8126935621830724,0.9883822287593832
+-0.19026649736029566,1.1278051666654263
+1.365354991310136,-1.238192043966083
+-0.9457216032308872,-0.12365616192568142
+0.7562504061332576,1.2085881191807695
+0.5799292154841881,1.6110542637629466
+0.18070897236518446,0.6704011177161106
+-0.38835477060330226,0.36791363315508185
+1.3079276244069151,-0.39131168382944337
+0.7876248046101848,0.43050044923295444
+-0.12904445509082355,2.255461233707802
+0.708938593136406,-0.5069147924175084
+1.2000103500349453,-0.04476631768989321
+-0.2795521769017577,1.428125010455924
+-0.015215195244028479,-0.07900883642517745
+0.02488745057202285,2.3307398100792613
+-0.1284606894375966,0.42812818304015976
+0.5345689305038335,-0.3440649218892592
+-0.9860875073363881,-0.42204574415627355
+0.053938883442391186,1.6574000798010098
+1.0923992082515632,0.9120695117627148
+0.25774189557713034,0.11970661638646768
+-0.42700236451041207,-0.028946096663685472
+-0.13094782542924815,0.9210280974006131
+1.2946523414115556,-0.8142293624943335
+-0.05381852009312993,0.06448246120070245
+0.42546774718500646,-0.5097295546856814
+-0.01579156019940256,1.1247786874059107
+-0.21320246300368395,1.8798832331883022
+-0.510288920813571,2.2458843269655873
+-0.5727001601318663,1.8793977527334205
+-0.19026649736029566,1.1278051666654263
+1.365354991310136,-1.238192043966083
+-0.9457216032308872,-0.12365616192568142
+0.7562504061332576,1.2085881191807695
+0.5799292154841881,1.6110542637629466
+0.1875475587967409,-0.2231299968197884
+-0.38835477060330226,0.36791363315508185
+1.0860374562559487,-1.113767531400942
+0.14525167461594735,-0.2692458396437468
+-0.12904445509082355,2.255461233707802
+0.708938593136406,-0.5069147924175084
+1.2000103500349453,-0.04476631768989321
+0.8121323602460411,-1.0604070937179952
+0.5598199912779744,-0.6595947933301797
+0.02488745057202285,2.3307398100792613
+-0.8184980387845773,-0.006665186912546736
+0.5345689305038335,-0.3440649218892592
+0.8203974424748104,-0.7169653942018235
+-0.38010839897027476,0.8878075732792828
+0.45526761548929706,-0.35298749840946636
+-0.2943445582562033,1.899109116055913
+-0.42700236451041207,-0.028946096663685472
+-0.13094782542924815,0.9210280974006131
+0.18179279948573818,0.0646156101227231
+-0.05381852009312993,0.06448246120070245
+0.42546774718500646,-0.5097295546856814
+-0.01579156019940256,1.1247786874059107
+0.4148367788047994,1.8982400348062975
+-0.510288920813571,2.2458843269655873
+-0.5727001601318663,1.8793977527334205
+0.8849587197928178,-0.8385271547993618
+0.7539629227384135,1.401411550774977
+-0.9457216032308872,-0.12365616192568142
+0.7562504061332576,1.2085881191807695
+0.5799292154841881,1.6110542637629466
+0.1875475587967409,-0.2231299968197884
+-0.38835477060330226,0.36791363315508185
+-1.0036411870749864,0.16535076476965965
+0.14525167461594735,-0.2692458396437468
+1.439515647940711,-1.6457276474881222
+-0.7585908324539974,0.09892751809571353
+1.2000103500349453,-0.04476631768989321
+0.8121323602460411,-1.0604070937179952
+-0.222881005948097,0.5164955471743338
+0.02488745057202285,2.3307398100792613
+-0.8184980387845773,-0.006665186912546736
+0.5345689305038335,-0.3440649218892592
+0.8203974424748104,-0.7169653942018235
+-0.38010839897027476,0.8878075732792828
+0.45526761548929706,-0.35298749840946636
+-0.2943445582562033,1.899109116055913
+1.2435457741781708,-0.33837222354129726
+1.1906996337355382,-1.3049298161576264
+1.7101293826224646,-2.5995323759716005
+0.08362669976892581,1.2966423054187652
+-1.4328020283982346,-0.70506102470605
+-0.0729570269949586,1.6392447255954337
+0.7684540061854005,1.7422776581571837
+0.7312535066540424,-1.0060538728794124
+-0.5727001601318663,1.8793977527334205
+0.8849587197928178,-0.8385271547993618
+0.7539629227384135,1.401411550774977
+1.245277241311023,-1.799045401235379
+0.7562504061332576,1.2085881191807695
+0.5799292154841881,1.6110542637629466
+1.4410208917788079,-0.8684123163308591
+0.635516198558913,1.2569991625644492
+-1.0036411870749864,0.16535076476965965
+0.14525167461594735,-0.2692458396437468
+1.439515647940711,-1.6457276474881222
+1.0540084758105144,0.013042589560245545
+1.2000103500349453,-0.04476631768989321
+0.27468345465421784,2.273515747288122
+-0.222881005948097,0.5164955471743338
+1.7386093842489332,-1.4055214733217463
+-0.8184980387845773,-0.006665186912546736
+0.7198458151994126,0.17693877194444751
+-0.13221888284678776,0.30635597654274377
+0.5893588308973563,-0.48608380717559685
+1.3073649518639543,-1.0673168923567693
+-0.2943445582562033,1.899109116055913
+0.5022217980814644,0.9788786737401669
+1.1906996337355382,-1.3049298161576264
+0.26686008312678455,-0.30876851609458766
+-0.2877180147880257,1.602403288577322
+-1.4328020283982346,-0.70506102470605
+-0.07450620101568858,0.43081470309752223
+-0.34263276923099806,2.2437524007793908
+0.7312535066540424,-1.0060538728794124
+1.0227104906021232,-0.36898387428719537
+0.8849587197928178,-0.8385271547993618
+0.7539629227384135,1.401411550774977
+-0.16492022462953737,-0.019336245923159835
+1.7765644901738362,-1.960550858794135
+0.5799292154841881,1.6110542637629466
+1.4410208917788079,-0.8684123163308591
+0.635516198558913,1.2569991625644492
+-1.0036411870749864,0.16535076476965965
+1.012858662267527,-0.31726645902277073
+-0.14098678170011714,0.7081911527834837
+0.6282268535609747,0.04730717793777983
+1.2000103500349453,-0.04476631768989321
+1.2224635051872947,0.05573237712140722
+-0.222881005948097,0.5164955471743338
+1.7386093842489332,-1.4055214733217463
+1.2582364984060328,0.17170615515333493
+-0.2076521105354052,1.746823655916041
+0.26991621215169626,-0.112737094655192
+0.5893588308973563,-0.48608380717559685
+0.5547346387755017,1.340028081920725
+-0.3179996961993261,-0.2246585869788198
+0.5022217980814644,0.9788786737401669
+1.1906996337355382,-1.3049298161576264
+0.26686008312678455,-0.30876851609458766
+-1.0001963188738168,0.5639436501736521
+1.338089289702097,-0.834308866354727
+-0.7872591384155652,0.9098839435064592
+-0.34263276923099806,2.2437524007793908
+0.7312535066540424,-1.0060538728794124
+1.1506912027993748,0.594296662448357
+0.8849587197928178,-0.8385271547993618
+1.2781081891655564,-1.6676011353838938
+-0.16492022462953737,-0.019336245923159835
+1.7765644901738362,-1.960550858794135
+0.5799292154841881,1.6110542637629466
+0.7708165832415529,-0.4030022528671527
+0.635516198558913,1.2569991625644492
+-1.0036411870749864,0.16535076476965965
+1.012858662267527,-0.31726645902277073
+0.8004560164908381,-0.7862080044799663
+1.1720439715449458,-0.7966508821451878
+0.36244096951054555,1.8617832918155874
+-0.36320344815265126,0.6960680491551529
+-0.222881005948097,0.5164955471743338
+1.7386093842489332,-1.4055214733217463
+1.2582364984060328,0.17170615515333493
+-0.2076521105354052,1.746823655916041
+0.26991621215169626,-0.112737094655192
+0.5893588308973563,-0.48608380717559685
+1.3553692532515411,-1.45788811304763
+-0.3179996961993261,-0.2246585869788198
+-0.05048385224480162,1.9272988649163179
+0.22937277902608408,1.4803609671028695
+0.4132109329523918,1.962470125033899
+-0.1092348150583431,1.8976413098253082
+1.338089289702097,-0.834308866354727
+-0.7872591384155652,0.9098839435064592
+-0.9058144737435941,0.7226126618996213
+-0.3645271142663037,-0.03661748487081112
+1.1506912027993748,0.594296662448357
+0.8849587197928178,-0.8385271547993618
+1.2781081891655564,-1.6676011353838938
+0.37826178302986735,1.5755613415341163
+0.2911626581081762,1.133328422151638
+0.36465461720158054,1.8722362226583291
+0.7708165832415529,-0.4030022528671527
+0.635516198558913,1.2569991625644492
+-1.0036411870749864,0.16535076476965965
+0.12030724284702501,0.8625883395887484
+0.8004560164908381,-0.7862080044799663
+1.0154285215428749,-0.3811337317560477
+0.07048310586629042,1.8966641246961116
+-0.36320344815265126,0.6960680491551529
+-0.222881005948097,0.5164955471743338
+0.06579151523037055,1.8484632289416054
+-0.4558765763412158,1.6563010812948704
+-0.2076521105354052,1.746823655916041
+0.26991621215169626,-0.112737094655192
+0.5893588308973563,-0.48608380717559685
+0.27094378281658216,-0.5349476221917797
+-0.3179996961993261,-0.2246585869788198
+0.6009959932587934,0.757110483769715
+1.422699397870286,-1.5556965655236776
+0.4132109329523918,1.962470125033899
+-0.1092348150583431,1.8976413098253082
+-0.1886143628730872,1.65434376390216
+-0.7872591384155652,0.9098839435064592
+0.7078623675211798,-0.39859959766017344
+-0.029213152190969205,0.7994772228418925
+1.1506912027993748,0.594296662448357
+0.8075870530650413,0.7804838831787503
+0.8204511810085835,-0.23169816257654652
+-0.4984962650606961,-0.5081385422407829
+-0.20210115528986528,1.437002064959752
+0.36465461720158054,1.8722362226583291
+-0.18016843313225384,0.13700704380795314
+-0.06341222560153259,0.19469387751489936
+-1.0036411870749864,0.16535076476965965
+0.29209686588294115,1.3123215872856857
+0.9808985140523027,0.042686449633400014
+1.3313606632695532,-1.268016700986244
+1.1608887747962073,-0.7242299843892376
+-0.36320344815265126,0.6960680491551529
+-0.496096305977068,1.1192323880311157
+0.06579151523037055,1.8484632289416054
+-0.4558765763412158,1.6563010812948704
+-0.2076521105354052,1.746823655916041
+0.26991621215169626,-0.112737094655192
+1.411449307200885,-2.1271128472738843
+0.18803564323660726,1.4218395397425945
+-0.3179996961993261,-0.2246585869788198
+-1.243030633744628,-0.15351574312164734
+1.422699397870286,-1.5556965655236776
+-0.23128235362115152,1.6377619273053823
+-0.9520467715045948,0.4063813115806023
+0.11323274858356636,2.3242618579992067
+-0.7872591384155652,0.9098839435064592
+0.36015063472826336,0.748122581719078
+0.31723975678468447,0.40085537119742
+1.1506912027993748,0.594296662448357
+1.6413148318029633,-2.0515909482686245
+0.07387217847524796,0.16957363936402714
+-0.4984962650606961,-0.5081385422407829
+-0.03434864037254845,1.478611012622926
+1.608791515525227,-2.100129451249687
+-0.18016843313225384,0.13700704380795314
+1.0516244619848498,0.1598541903252496
+-1.0036411870749864,0.16535076476965965
+0.29209686588294115,1.3123215872856857
+0.3943626002078947,1.0128777837310692
+-0.6098104217755886,0.7826340373835415
+1.1608887747962073,-0.7242299843892376
+0.6548472030476626,0.17620213672567125
+-0.496096305977068,1.1192323880311157
+1.4241992881534495,0.13643547629599664
+-0.4558765763412158,1.6563010812948704
+-0.2076521105354052,1.746823655916041
+0.8466259877821576,-0.8389088976071173
+1.411449307200885,-2.1271128472738843
+1.0995405929308542,-1.6043070679379032
+-0.3714919104837127,0.32450081925728425
+-1.243030633744628,-0.15351574312164734
+1.422699397870286,-1.5556965655236776
+1.348550665136857,-0.17483648085640674
+0.7357137605299308,-0.0681526476188102
+-0.3823964383838636,0.5649190199283378
+0.2985813329933066,-0.0708160089446094
+0.8499146854073285,-0.09750517722778951
+-0.18055652232566144,-0.04319291264601238
+1.1556812353591153,-0.43003470666773636
+1.6413148318029633,-2.0515909482686245
+1.194731005336828,0.00928579308785471
+0.7330403099696783,0.7200388229111081
+-0.03434864037254845,1.478611012622926
+1.608791515525227,-2.100129451249687
+0.2633693159337933,-0.4134535421551584
+-0.05153077845009346,0.14862489580853383
+1.054611981505734,-0.7813606849940135
+0.8360596453671499,-0.39017888027643305
+0.3943626002078947,1.0128777837310692
+-0.43509618333059863,1.579065464421849
+1.1608887747962073,-0.7242299843892376
+0.34636532733675507,-0.48939108220510263
+-0.496096305977068,1.1192323880311157
+0.7618257667030712,-1.011385359259127
+-0.4558765763412158,1.6563010812948704
+-0.2076521105354052,1.746823655916041
+1.252462809413319,-0.4593740612709425
+1.24253548947969,0.8626610322044908
+1.0995405929308542,-1.6043070679379032
+-0.3714919104837127,0.32450081925728425
+-1.243030633744628,-0.15351574312164734
+1.422699397870286,-1.5556965655236776
+-0.3663882794546741,1.599577199620853
+1.331755348659721,-0.7675618031666891
+-0.3823964383838636,0.5649190199283378
+0.14979441751569045,1.6702750850974457
+0.3751157556021722,-0.14463680255917227
+-0.18055652232566144,-0.04319291264601238
+0.5438658766876032,1.125283544091816
+1.6413148318029633,-2.0515909482686245
+1.194731005336828,0.00928579308785471
+0.7330403099696783,0.7200388229111081
+1.318595706872132,-1.178025072911399
+0.9724534733058836,0.6333531462872863
+0.23783065817771748,1.334376772138424
+-0.0730689342306534,0.17232572005649366
+0.6230651749753484,0.07111828381730753
+0.8360596453671499,-0.39017888027643305
+1.183649049002018,-0.5778285881038592
+-0.43509618333059863,1.579065464421849
+-0.33548519090661266,-0.4011883383986693
+0.34636532733675507,-0.48939108220510263
+0.542374873193271,-0.7848775816097575
+0.17042310152747442,0.029256054422752528
+-0.4558765763412158,1.6563010812948704
+0.31730635261006346,-0.4060028175981324
+0.6098307322359509,0.005673153026088507
+0.9764725463299564,-0.6503628117717813
+-0.1306626323325567,1.6428325420960612
+-0.3714919104837127,0.32450081925728425
+-1.243030633744628,-0.15351574312164734
+1.422699397870286,-1.5556965655236776
+-0.3663882794546741,1.599577199620853
+-0.6133142077473834,1.46127578343512
+-0.3823964383838636,0.5649190199283378
+0.14979441751569045,1.6702750850974457
+0.3751157556021722,-0.14463680255917227
+-0.18055652232566144,-0.04319291264601238
+1.2734925071763201,0.3767654615969307
+0.11898163531576211,0.13950221966458487
+1.194731005336828,0.00928579308785471
+0.3313806474938241,-0.057018320340135986
+1.318595706872132,-1.178025072911399
+0.42646851469586333,0.9734533610209635
+0.23783065817771748,1.334376772138424
+-0.07828189132399344,1.6822895912084674
+0.6230651749753484,0.07111828381730753
+0.4272449129244468,0.5176595676451627
+1.183649049002018,-0.5778285881038592
+1.739000331780394,-2.5239338366333386
+-0.33548519090661266,-0.4011883383986693
+-0.12247962310260385,0.47641431368494425
+-1.1915212435936626,-0.47778726274360617
+0.17042310152747442,0.029256054422752528
+-0.4558765763412158,1.6563010812948704
+0.31730635261006346,-0.4060028175981324
+0.6098307322359509,0.005673153026088507
+0.9764725463299564,-0.6503628117717813
+-0.1306626323325567,1.6428325420960612
+-0.3714919104837127,0.32450081925728425
+-1.243030633744628,-0.15351574312164734
+0.29425213666319416,0.18727832849350132
+-0.3663882794546741,1.599577199620853
+-0.6133142077473834,1.46127578343512
+-0.3823964383838636,0.5649190199283378
+-0.27393794128973076,-0.1474874186068731
+0.02728437106898185,0.046282063163225085
+0.03085518350650146,-0.03255913270540445
+1.2734925071763201,0.3767654615969307
+1.3802976962724527,-0.3497070725360454
+1.194731005336828,0.00928579308785471
+1.5272760164284689,-1.1856260242486687
+1.3836809711314748,-1.46253937910747
+0.42646851469586333,0.9734533610209635
+1.8349167804857685,-1.8588401029188655
+-0.07828189132399344,1.6822895912084674
+0.8532482960866186,1.103220789059565
+0.5285909364083036,-0.682252122186528
+1.573827340922096,-1.4977814115959311
+0.33831287828624024,-0.2870951530886193
+-0.33548519090661266,-0.4011883383986693
+-0.12247962310260385,0.47641431368494425
+-1.1915212435936626,-0.47778726274360617
+0.9787518561952958,-0.48225026614495303
+-0.4558765763412158,1.6563010812948704
+0.31730635261006346,-0.4060028175981324
+0.40704855588633426,0.11048882041516317
+-0.2837053001640443,0.24425155757242942
+-0.1306626323325567,1.6428325420960612
+-0.3714919104837127,0.32450081925728425
+-1.243030633744628,-0.15351574312164734
+-0.04876699758602275,0.1553992849141329
+0.9552538884635953,-1.2903653005329563
+0.6896182384719838,-0.5299253798344294
+-0.5670811562318889,0.028890948172459102
+-0.27393794128973076,-0.1474874186068731
+1.0748709592042824,-0.6974494988419997
+-0.26752099435920973,1.177734938399801
+1.2734925071763201,0.3767654615969307
+1.3802976962724527,-0.3497070725360454
+1.194731005336828,0.00928579308785471
+1.5272760164284689,-1.1856260242486687
+1.3836809711314748,-1.46253937910747
+1.6630109461468487,-1.3185675784377566
+-0.35218909315802566,0.7182556912436657
+-0.07828189132399344,1.6822895912084674
+0.8532482960866186,1.103220789059565
+1.1379783918610242,0.6159615323052803
+0.3187907131327927,-0.7129875757658897
+-0.38839429035146145,0.9131171025629152
+0.09565571760820601,-0.2384601855917288
+0.28899351196263284,0.49741612642326516
+-0.009384698791653323,0.12321372673917708
+0.9787518561952958,-0.48225026614495303
+-0.4558765763412158,1.6563010812948704
+0.31730635261006346,-0.4060028175981324
+-0.6534364131393252,0.4649961721539737
+-0.2837053001640443,0.24425155757242942
+1.3029810011121457,-1.1528771751957732
+0.8949873250639937,-0.7479134148290546
+-1.243030633744628,-0.15351574312164734
+1.5910048088726043,-0.7276456040854635
+-0.10402406325369097,1.2829588393422482
+-0.4983241249240829,0.9577512866104109
+-0.5670811562318889,0.028890948172459102
+1.132293971801393,-0.14313522121940775
+1.0748709592042824,-0.6974494988419997
+-0.26752099435920973,1.177734938399801
+-0.9053197284412993,0.9068263845440114
+1.3802976962724527,-0.3497070725360454
+-0.22758193858608194,0.038883927586819356
+1.1925529863019761,-0.22909147543528732
+1.3836809711314748,-1.46253937910747
+1.6630109461468487,-1.3185675784377566
+-0.35218909315802566,0.7182556912436657
+-0.07828189132399344,1.6822895912084674
+0.8532482960866186,1.103220789059565
+-0.6920934985655969,0.7529453764337921
+-0.2175690584642874,0.7160449882870704
+-0.38839429035146145,0.9131171025629152
+0.014446346540631927,0.29853996833203555
+0.8037653255463826,0.06418811196507401
+-0.009384698791653323,0.12321372673917708
+1.3557835615392413,-1.3796540278295915
+-0.4558765763412158,1.6563010812948704
+0.119805751089604,1.3802512085114536
+0.5409186568981803,0.17780297129835398
+0.41480694081523195,1.2312695437234895
+1.3029810011121457,-1.1528771751957732
+0.8949873250639937,-0.7479134148290546
+-1.243030633744628,-0.15351574312164734
+1.0826055238206658,-0.8284260654331396
+-0.10402406325369097,1.2829588393422482
+-0.4983241249240829,0.9577512866104109
+-0.5670811562318889,0.028890948172459102
+1.849228165269999,-1.5309899691802868
+-0.10251362588877166,0.8295763722690567
+0.3294898289010407,1.3346719471902748
+-0.9053197284412993,0.9068263845440114
+-0.29606574075623304,1.5076782713460997
+-0.22758193858608194,0.038883927586819356
+0.7539928451378577,1.7266695695916745
+1.3836809711314748,-1.46253937910747
+1.6630109461468487,-1.3185675784377566
+0.15121321610202917,-0.364753967382485
+-0.07828189132399344,1.6822895912084674
+0.8532482960866186,1.103220789059565
+-0.6920934985655969,0.7529453764337921
+-0.2175690584642874,0.7160449882870704
+-0.5873684464196146,1.5645637407307151
+0.014446346540631927,0.29853996833203555
+0.8037653255463826,0.06418811196507401
+0.46745478061798373,2.0921329095438943
+0.47507839842543836,0.25542303219004425
+-0.4558765763412158,1.6563010812948704
+-0.39276493411113933,1.101018285790954
+0.13610581732724528,1.9622339316669126
+0.2866094319042907,1.4684465084106861
+-0.05812474320065847,2.020504787101614
+0.8949873250639937,-0.7479134148290546
+0.15944298881084573,-0.2008863755154039
+0.6302874642919452,1.6424834062591624
+1.1316974945652192,0.17947115694300067
+0.38607859611004486,-0.10096656698812384
+-0.5670811562318889,0.028890948172459102
+1.1929827075599182,0.4946053432882048
+-0.7031164657083162,0.5461108351181387
+0.7114761913460557,0.12295071734820934
+1.378732163011621,-0.4870969234302456
+-0.29606574075623304,1.5076782713460997
+-0.22758193858608194,0.038883927586819356
+0.7539928451378577,1.7266695695916745
+1.3836809711314748,-1.46253937910747
+0.7358337972876912,-0.9869478230587367
+-0.5255957567923636,1.5952165786581258
+-0.07828189132399344,1.6822895912084674
+0.8532482960866186,1.103220789059565
+-0.1441792030378366,0.109943630414824
+-0.8263229762305758,0.40634974949899205
+-0.5873684464196146,1.5645637407307151
+1.021878406072544,0.5284310620643883
+0.9833334372233964,0.19748039385304056
+0.46745478061798373,2.0921329095438943
+0.47507839842543836,0.25542303219004425
+-0.4558765763412158,1.6563010812948704
+-0.39276493411113933,1.101018285790954
+0.13610581732724528,1.9622339316669126
+1.311638411606707,0.3915051606479878
+-0.05812474320065847,2.020504787101614
+0.8949873250639937,-0.7479134148290546
+0.46835008796745337,-0.7382084796124587
+0.6302874642919452,1.6424834062591624
+1.1316974945652192,0.17947115694300067
+0.38607859611004486,-0.10096656698812384
+-0.5670811562318889,0.028890948172459102
+-0.5641264184877705,0.5652354876611613
+-0.7031164657083162,0.5461108351181387
+0.7114761913460557,0.12295071734820934
+1.378732163011621,-0.4870969234302456
+-0.9318590449451732,0.231196331321522
+-0.22758193858608194,0.038883927586819356
+0.7539928451378577,1.7266695695916745
+1.3836809711314748,-1.46253937910747
+0.7358337972876912,-0.9869478230587367
+-0.5255957567923636,1.5952165786581258
+-0.07828189132399344,1.6822895912084674
+0.8532482960866186,1.103220789059565
+-0.1441792030378366,0.109943630414824
+-0.7019561108539066,0.9969737372950103
+-0.5873684464196146,1.5645637407307151
+1.021878406072544,0.5284310620643883
+1.1579833081462314,0.3453181652454755
+0.46745478061798373,2.0921329095438943
+0.20265902885640352,-0.11818875538828044
+-0.4558765763412158,1.6563010812948704
+-0.583010166377037,0.44390383156939733
+0.8754777966226956,1.5634295195517551
+0.5305130762012863,1.2636697688545668
+-0.05812474320065847,2.020504787101614
+0.8949873250639937,-0.7479134148290546
+0.46835008796745337,-0.7382084796124587
+0.8241280129854978,0.2172085218770745
+1.1316974945652192,0.17947115694300067
+-0.7744919413252437,0.11927904661838952
+-0.14593037393408803,0.9924320978602663
+-0.5641264184877705,0.5652354876611613
+-0.7031164657083162,0.5461108351181387
+-0.44369233155328963,0.6148560153939243
+0.3090925183369466,-0.7728598940292155
+0.33494829166658174,-0.24661919103676755
+-0.6501139899943604,-0.2731677034017628
+-0.3047011887968862,1.5919512153943267
+1.3836809711314748,-1.46253937910747
+-0.5374610507437702,1.7985187489104797
+-0.5255957567923636,1.5952165786581258
+-0.07828189132399344,1.6822895912084674
+-0.6110557177333638,0.6612136791046876
+-0.1441792030378366,0.109943630414824
+-0.7019561108539066,0.9969737372950103
+-0.5873684464196146,1.5645637407307151
+-0.46057671771444775,0.2445544734238257
+1.1579833081462314,0.3453181652454755
+0.46745478061798373,2.0921329095438943
+0.20265902885640352,-0.11818875538828044
+-0.4558765763412158,1.6563010812948704
+0.8393947258201868,-0.13310276973757496
+0.9497864302020926,-0.08619839237857163
+0.5305130762012863,1.2636697688545668
+-0.05812474320065847,2.020504787101614
+0.8949873250639937,-0.7479134148290546
+0.8633606914086649,-0.28998855948582203
+2.0100866613323807,-3.2106381913082247
+1.5452047541103042,-1.985733334899018
+1.3040697326895407,-1.6498419713651593
+0.6636127026134542,-0.8610080448016045
+0.008899926989435897,1.6737548391296009
+-0.7031164657083162,0.5461108351181387
+0.691223000815081,0.260424773194154
+0.20092332791643291,-0.15841576065737378
+-0.22831991690112952,-0.11044771968608902
+0.19891868073631258,1.7525566213037325
+-0.3047011887968862,1.5919512153943267
+1.3836809711314748,-1.46253937910747
+-0.3962757823284208,2.1878226588890946
+-0.5255957567923636,1.5952165786581258
+-0.07828189132399344,1.6822895912084674
+-0.6110557177333638,0.6612136791046876
+1.7038390881357994,-1.9702378246285943
+0.28766371683988773,-0.33865074225895553
+1.6564221824441274,-1.03432296774754
+0.8746858196694212,-0.7421755084878979
+1.1579833081462314,0.3453181652454755
+0.46745478061798373,2.0921329095438943
+0.20265902885640352,-0.11818875538828044
+-0.4558765763412158,1.6563010812948704
+-0.37920043031700507,0.6741623145021958
+-0.40390782200338576,0.21395656560322823
+1.5536729092907657,-2.3257062414975844
+-0.05812474320065847,2.020504787101614
+-0.5757042783072338,0.008248453121037058
+0.8633606914086649,-0.28998855948582203
+1.2961764226591614,-1.2132072360502064
+1.5452047541103042,-1.985733334899018
+-0.8795584269261186,0.5191758496404016
+0.6636127026134542,-0.8610080448016045
+0.7205674603028893,1.4595262889377085
+-0.7031164657083162,0.5461108351181387
+0.691223000815081,0.260424773194154
+0.9897875353001451,-1.4801258152041867
+-0.22831991690112952,-0.11044771968608902
+1.0720924143098056,0.22441617582276338
+-0.23797349462511563,2.174488950672813
+1.3836809711314748,-1.46253937910747
+1.4832461178586371,-0.16440390954777329
+-0.5255957567923636,1.5952165786581258
+-0.33934312049408616,1.2445315746466188
+-0.3622979394703635,0.7760690128775787
+1.7038390881357994,-1.9702378246285943
+0.7277175961085885,-0.08653609465818277
+-0.8295994039458239,0.8198667839149298
+0.8746858196694212,-0.7421755084878979
+1.0557442621188649,-0.9247697126012513
+0.46745478061798373,2.0921329095438943
+-0.5182906414656008,1.0116540692441272
+-0.4558765763412158,1.6563010812948704
+-0.37920043031700507,0.6741623145021958
+-0.40390782200338576,0.21395656560322823
+1.5536729092907657,-2.3257062414975844
+-0.05812474320065847,2.020504787101614
+-0.5757042783072338,0.008248453121037058
+0.8633606914086649,-0.28998855948582203
+0.1708723955623842,0.524684420941849
+1.5452047541103042,-1.985733334899018
+1.32674253122146,-0.4464755184359126
+0.6636127026134542,-0.8610080448016045
+0.7205674603028893,1.4595262889377085
+-0.5576531211820371,-0.21975279981592238
+0.691223000815081,0.260424773194154
+-0.382678305104382,1.5155864435663047
+-0.22831991690112952,-0.11044771968608902
+0.9096839897947726,-0.850914711723395
+0.5692257835551793,-0.5191122150904222
+0.48870951538322055,1.293130338182169
+0.8016104609042165,1.2767538909094358
+-0.34504555660214137,0.5841097817412176
+-0.33934312049408616,1.2445315746466188
+0.5132639780604382,1.9997938079543442
+-0.7527205789201297,0.5060331434258842
+-0.25573479824076906,-0.07053126000496326
+-0.8295994039458239,0.8198667839149298
+0.3990738307094435,1.800066795593854
+1.0557442621188649,-0.9247697126012513
+0.46745478061798373,2.0921329095438943
+0.34421956475362553,1.6058808209048523
+-0.4558765763412158,1.6563010812948704
+-0.15240226049617722,1.269466385804919
+-0.40390782200338576,0.21395656560322823
+-0.5117638606896959,0.9031574684994746
+-0.05812474320065847,2.020504787101614
+-0.33970864514430243,1.6719560049374804
+-0.15509371464674143,0.6579833201949068
+1.4144064525220068,0.05088059638957115
+1.5452047541103042,-1.985733334899018
+1.32674253122146,-0.4464755184359126
+-0.2724171021262871,0.8480525247264555
+0.05428770958054063,-0.4048015492142869
+1.194865214439465,0.7410770606127357
+0.691223000815081,0.260424773194154
+-0.382678305104382,1.5155864435663047
+1.2177337555690115,-1.217489517973843
+0.9096839897947726,-0.850914711723395
+0.5692257835551793,-0.5191122150904222
+-0.6252132134561011,0.31501625240932446
+1.411726795290622,-0.9183448218633976
+-0.20972124690327656,0.5524227339522111
+-0.33934312049408616,1.2445315746466188
+0.5132639780604382,1.9997938079543442
+0.18722644746704953,0.28994725954002887
+-0.7729742606146973,0.3785426524484946
+-0.8295994039458239,0.8198667839149298
+0.3990738307094435,1.800066795593854
+1.0557442621188649,-0.9247697126012513
+0.9126539664147434,-1.2591434637087346
+0.34421956475362553,1.6058808209048523
+-0.4558765763412158,1.6563010812948704
+0.9813956254269793,-0.7500483907826628
+0.07220435455705845,-0.20884359423505686
+0.14936495453425574,0.6261998892007451
+0.6149846425399741,1.867833503834195
+-0.33970864514430243,1.6719560049374804
+0.9394549026512646,0.5842821900075488
+1.4144064525220068,0.05088059638957115
+1.5452047541103042,-1.985733334899018
+1.0667647133007403,-1.3162870588268905
+-0.2724171021262871,0.8480525247264555
+0.022911388880640815,-0.10277568154457578
+1.194865214439465,0.7410770606127357
+0.7981244870758875,-1.0223687447879388
+0.44287307674219634,1.5500601860888508
+-0.09818504035212794,1.506087630615429
+0.35804273245497154,2.0026438731044665
+1.5499397140055917,-0.21955857346933683
+-0.6252132134561011,0.31501625240932446
+1.411726795290622,-0.9183448218633976
+1.1565872494065894,0.01527198999248508
+1.4853233291344459,-1.4897248111626407
+0.5132639780604382,1.9997938079543442
+0.11672970973509136,2.156094488289266
+-0.7729742606146973,0.3785426524484946
+-0.8295994039458239,0.8198667839149298
+0.3990738307094435,1.800066795593854
+1.0557442621188649,-0.9247697126012513
+-0.5428770615102971,-0.251575791161712
+0.34421956475362553,1.6058808209048523
+-0.4558765763412158,1.6563010812948704
+0.9813956254269793,-0.7500483907826628
+0.07220435455705845,-0.20884359423505686
+1.1406801678220708,0.5887708963420291
+0.6149846425399741,1.867833503834195
+-0.33970864514430243,1.6719560049374804
+0.30979021401734863,0.35183343939523515
+0.7044761674187033,-0.8670867227795156
+0.1426124597720986,1.8790506746546698
+1.0667647133007403,-1.3162870588268905
+-0.2724171021262871,0.8480525247264555
+1.4849641149872668,-1.0984872587800312
+1.5542393151244789,-1.8578932477029602
+-0.19569157614560717,-0.5424885026779765
+0.44287307674219634,1.5500601860888508
+-0.4114024699518479,-0.1466840430169753
+0.6939744975059847,-0.6488032135982869
+0.98643890852839,-1.5378657723463172
+-0.6252132134561011,0.31501625240932446
+0.05847404496518949,0.5728654597905198
+0.4213077138464103,1.2536021680897145
+1.4853233291344459,-1.4897248111626407
+0.5132639780604382,1.9997938079543442
+0.11672970973509136,2.156094488289266
+-0.7729742606146973,0.3785426524484946
+-0.8295994039458239,0.8198667839149298
+0.3990738307094435,1.800066795593854
+1.472869494366021,-2.3333410956969307
+-0.43740778100551825,0.9536420029189149
+1.2286967352673461,-0.8387819116135486
+-0.4558765763412158,1.6563010812948704
+-0.29917855255162357,-0.1850736175696901
+-0.22077368929142965,0.4263583019849492
+1.1406801678220708,0.5887708963420291
+0.6149846425399741,1.867833503834195
+-0.2549885547388834,-0.11385122039618803
+0.30979021401734863,0.35183343939523515
+0.7044761674187033,-0.8670867227795156
+0.1426124597720986,1.8790506746546698
+1.0667647133007403,-1.3162870588268905
+-0.7661198299441951,0.6728946580326648
+1.4849641149872668,-1.0984872587800312
+-0.6899270797149789,0.6235619733160125
+0.6393715416137399,-1.2102199058745313
+0.923841863490886,0.04668156899968645
+-0.2583736262493441,-0.1845466232805654
+1.239299323727763,-0.5844145803225651
+0.98643890852839,-1.5378657723463172
+-0.6252132134561011,0.31501625240932446
+0.6642189636820321,-1.0440973974167973
+-0.5878783577420148,1.0887175343375328
+0.7606243127446112,1.1984810803360546
+0.8983478098084949,-0.8193946154279723
+0.11672970973509136,2.156094488289266
+0.07517434687056024,-0.41704334257009823
+0.6944184467019929,0.9809371565098584
+0.3990738307094435,1.800066795593854
+0.5101570168433864,1.564704588704412
+-0.43740778100551825,0.9536420029189149
+1.2286967352673461,-0.8387819116135486
+-0.4558765763412158,1.6563010812948704
+-0.29917855255162357,-0.1850736175696901
+-0.22077368929142965,0.4263583019849492
+0.5198878155354151,0.18896733633017193
+0.6149846425399741,1.867833503834195
+-0.2549885547388834,-0.11385122039618803
+0.07495457673972583,0.14107397314859427
+-0.471845126590825,1.2320551636164667
+0.1426124597720986,1.8790506746546698
+0.45095325435329875,-0.6006076016460197
+0.08077507656152685,2.420688661947642
+1.4849641149872668,-1.0984872587800312
+-0.6899270797149789,0.6235619733160125
+-0.6209626306205458,-0.69900045941736
+-0.7885837817809241,0.9893477181778153
+0.12734668372243663,1.4475114692444282
+-0.35451107248684177,1.3249070156579965
+0.98643890852839,-1.5378657723463172
+-0.6252132134561011,0.31501625240932446
+1.3054360989951315,-1.2781729051116657
+1.4243796775735102,-1.442996478185174
+0.31710751499544065,-0.3623979258203853
+0.8983478098084949,-0.8193946154279723
+0.11672970973509136,2.156094488289266
+0.07517434687056024,-0.41704334257009823
+1.5274629177001702,-0.5234103280889202
+0.3990738307094435,1.800066795593854
+0.5101570168433864,1.564704588704412
+-1.0986190497994095,-0.22993300711090475
+1.2286967352673461,-0.8387819116135486
+-0.4558765763412158,1.6563010812948704
+0.3879330994657516,-0.44174266408027774
+-0.22077368929142965,0.4263583019849492
+0.5198878155354151,0.18896733633017193
+0.6149846425399741,1.867833503834195
+-0.2549885547388834,-0.11385122039618803
+0.07495457673972583,0.14107397314859427
+-0.471845126590825,1.2320551636164667
+-0.10972718573813739,2.2550288945612382
+-0.4956362291074272,0.29839448105276345
+0.08077507656152685,2.420688661947642
+1.0704318049388295,0.6314625634946782
+-0.8069940916149513,0.13468792964822773
+-0.6209626306205458,-0.69900045941736
+-0.7101383569503812,0.2505301649825459
+-0.6735830145014953,-0.21147698772632867
+-0.35451107248684177,1.3249070156579965
+0.18961873580282984,2.202944502350669
+-0.6252132134561011,0.31501625240932446
+0.3829423124376454,0.6119309781572646
+1.4243796775735102,-1.442996478185174
+0.31710751499544065,-0.3623979258203853
+0.6888695106823287,-0.21056605478427803
+0.11672970973509136,2.156094488289266
+0.07517434687056024,-0.41704334257009823
+1.1689084838591401,-1.6413198144833792
+0.3990738307094435,1.800066795593854
+0.5101570168433864,1.564704588704412
+-1.0986190497994095,-0.22993300711090475
+0.264682368576049,2.0113949256383936
+-0.4558765763412158,1.6563010812948704
+0.3879330994657516,-0.44174266408027774
+-0.22077368929142965,0.4263583019849492
+0.5198878155354151,0.18896733633017193
+-0.15792656343370476,2.2339899614968237
+-0.7295087971440142,0.6810172186310518
+0.07495457673972583,0.14107397314859427
+-0.471845126590825,1.2320551636164667
+-0.10972718573813739,2.2550288945612382
+-0.46398433736901484,0.14648355760559748
+-0.47909165232584205,0.8324449743692963
+-0.5260510136127621,0.03164145114560887
+-0.8069940916149513,0.13468792964822773
+-0.6438670599619984,0.20150582790694965
+0.629071873083151,0.9328054894340003
+-0.6735830145014953,-0.21147698772632867
+-0.35451107248684177,1.3249070156579965
+0.7127342978523612,0.39780695098138374
+0.5741145245498764,0.04001165379535776
+0.2313208033643897,0.9805223658992619
+1.4243796775735102,-1.442996478185174
+0.31710751499544065,-0.3623979258203853
+-0.658797889856322,-0.48627317039028284
+0.4846652363356345,1.9067470758768277
+-0.2669202609122876,-0.34476101068162124
+0.26266756688482146,1.5784204112062574
+0.3990738307094435,1.800066795593854
+-0.523486117030636,-0.36419818189455155
+-1.0986190497994095,-0.22993300711090475
+-0.8466145043932546,0.4864935201991873
+-0.4558765763412158,1.6563010812948704
+0.3879330994657516,-0.44174266408027774
+0.333523354779425,-0.4861085591989984
+-0.33170337584960496,-0.07057182403865153
+-0.15792656343370476,2.2339899614968237
+-0.7295087971440142,0.6810172186310518
+-0.26072714406308506,0.835219710912907
+-0.26872573581006876,0.5101478749013242
+-0.6949923275201191,1.1985202889083753
+-0.46398433736901484,0.14648355760559748
+-0.47909165232584205,0.8324449743692963
+-0.5260510136127621,0.03164145114560887
+0.19993497513692526,1.9523564827139306
+-0.35432291184017817,1.7618699949056573
+-0.4634825803236568,-0.25557523166289264
+0.3643325668871208,1.7211190767607503
+0.13048604423455568,0.2921800284527417
+0.7127342978523612,0.39780695098138374
+0.6428078940268339,1.4446338310317666
+0.6257632820878011,0.3172909349717862
+1.4243796775735102,-1.442996478185174
+0.31710751499544065,-0.3623979258203853
+-0.9587657487409915,0.22149247638840427
+-0.4677274572033366,0.26813877876761694
+-0.2669202609122876,-0.34476101068162124
+0.26266756688482146,1.5784204112062574
+0.3990738307094435,1.800066795593854
+-0.2086944876775078,0.881013597307161
+-1.0986190497994095,-0.22993300711090475
+0.042391003317187814,-0.19104074278833916
+-0.4558765763412158,1.6563010812948704
+0.3879330994657516,-0.44174266408027774
+0.4795086946780299,1.6638689407885954
+-0.6993272466943535,1.0403325715578866
+-0.15792656343370476,2.2339899614968237
+0.40306656655547535,-0.28316990949345205
+-0.26072714406308506,0.835219710912907
+-0.00727501717142881,0.9990775720207016
+0.9348829951874448,-0.3358847469560292
+-0.46398433736901484,0.14648355760559748
+-0.47909165232584205,0.8324449743692963
+-0.5260510136127621,0.03164145114560887
+0.19993497513692526,1.9523564827139306
+-0.35432291184017817,1.7618699949056573
+-0.4634825803236568,-0.25557523166289264
+0.3643325668871208,1.7211190767607503
+1.0047120904018452,0.3371627965722278
+0.7127342978523612,0.39780695098138374
+0.6428078940268339,1.4446338310317666
+0.6711930571627546,1.7704387432876905
+1.4243796775735102,-1.442996478185174
+0.31710751499544065,-0.3623979258203853
+-0.9587657487409915,0.22149247638840427
+-0.6647600937530153,0.9633732101283191
+-0.8251916414660079,1.0065840139956488
+0.26266756688482146,1.5784204112062574
+0.3990738307094435,1.800066795593854
+-0.2086944876775078,0.881013597307161
+0.9535155984398926,0.5359496010729966
+0.042391003317187814,-0.19104074278833916
+-0.4558765763412158,1.6563010812948704
+0.3879330994657516,-0.44174266408027774
+0.4795086946780299,1.6638689407885954
+-0.6993272466943535,1.0403325715578866
+-0.15792656343370476,2.2339899614968237
+-0.6271435311328117,0.2104330292323715
+-0.26072714406308506,0.835219710912907
+-0.23847782546541002,-0.07151373415473677
+1.0225567899077637,1.311990466154266
+-0.20893206306879286,-0.012241734173398772
+-1.0158558057196196,-0.36015685218347715
+1.5392491187905912,-0.38659785728874363
+0.24683353738193645,-0.01710394170158519
+-0.35432291184017817,1.7618699949056573
+-0.4634825803236568,-0.25557523166289264
+-0.8363817259236592,-0.19270194680983943
+1.0047120904018452,0.3371627965722278
+-0.5089728012538379,1.03043133425505
+0.6428078940268339,1.4446338310317666
+0.6711930571627546,1.7704387432876905
+1.4243796775735102,-1.442996478185174
+0.31710751499544065,-0.3623979258203853
+-0.3953777970844389,1.0769809843792328
+-0.6647600937530153,0.9633732101283191
+1.3046635104624826,-1.7881257526816188
+-0.15466869609129696,0.09240616338926744
+0.3990738307094435,1.800066795593854
+-0.2086944876775078,0.881013597307161
+0.9535155984398926,0.5359496010729966
+0.042391003317187814,-0.19104074278833916
+-0.1889737700669042,0.1342042915801659
+0.3879330994657516,-0.44174266408027774
+0.4795086946780299,1.6638689407885954
+-0.0923570039623841,1.4947793352340684
+-0.15792656343370476,2.2339899614968237
+-0.6271435311328117,0.2104330292323715
+-0.813970779963734,-0.4259010109985125
+-0.23847782546541002,-0.07151373415473677
+-0.45437990238186454,1.8342414561885572
+-0.20893206306879286,-0.012241734173398772
+-1.0158558057196196,-0.36015685218347715
+1.5392491187905912,-0.38659785728874363
+1.2839465351827122,-1.7156572355567192
+0.6541784356798579,-0.4781137032861422
+-1.1402382933219435,-0.14205564956122096
+-0.8363817259236592,-0.19270194680983943
+1.0047120904018452,0.3371627965722278
+-0.5089728012538379,1.03043133425505
+0.6428078940268339,1.4446338310317666
+0.7084902031697193,-0.6280203603724627
+1.4243796775735102,-1.442996478185174
+0.31710751499544065,-0.3623979258203853
+-0.3943008011105113,-0.4573773999295598
+-0.6647600937530153,0.9633732101283191
+1.3046635104624826,-1.7881257526816188
+-0.15466869609129696,0.09240616338926744
+0.3990738307094435,1.800066795593854
+-0.15302388995843386,0.5967024005752449
+0.9535155984398926,0.5359496010729966
+0.042391003317187814,-0.19104074278833916
+-0.1889737700669042,0.1342042915801659
+1.6063200285036916,-0.7714974318869063
+-0.09748519279850038,-0.06887783493693693
+-0.5606196940586533,1.2890310429636118
+-0.15792656343370476,2.2339899614968237
+0.4802265817353262,1.478705716798209
+-0.813970779963734,-0.4259010109985125
+-0.23847782546541002,-0.07151373415473677
+-0.45437990238186454,1.8342414561885572
+-0.20893206306879286,-0.012241734173398772
+-1.0158558057196196,-0.36015685218347715
+1.5392491187905912,-0.38659785728874363
+1.2839465351827122,-1.7156572355567192
+-0.3430239972297233,0.7736540958845096
+1.4453966523658348,-0.26726408552186093
+1.13657962044155,-0.14846388195632754
+1.0047120904018452,0.3371627965722278
+-0.5089728012538379,1.03043133425505
+0.6428078940268339,1.4446338310317666
+0.7084902031697193,-0.6280203603724627
+0.7098208155304121,0.44142774655773953
+-0.9093225458115197,0.39164352121496915
+-0.3943008011105113,-0.4573773999295598
+-0.6647600937530153,0.9633732101283191
+-0.8483711720749372,0.33012833750700743
+-0.4113591384913133,0.32547075468071074
+0.4550981177296013,0.6089244054406073
+-0.5095101433082394,0.9794812739944244
+-1.0391036070769126,0.08579627128766054
+0.042391003317187814,-0.19104074278833916
+0.151890896749373,-0.41394915849867586
+1.6063200285036916,-0.7714974318869063
+-0.09748519279850038,-0.06887783493693693
+1.4079977505487344,-0.6748057322492271
+-0.15792656343370476,2.2339899614968237
+0.4802265817353262,1.478705716798209
+1.4878732371537342,-1.245619142413011
+1.4804121596497275,-0.9723504241296995
+-0.45437990238186454,1.8342414561885572
+-0.20893206306879286,-0.012241734173398772
+-1.0158558057196196,-0.36015685218347715
+0.04405499900436188,-0.036977385659243654
+1.2839465351827122,-1.7156572355567192
+0.2312224152968127,0.698120760314978
+1.4453966523658348,-0.26726408552186093
+0.4745920834536685,-0.026393066322377368
+-0.6487856129664076,0.54961909314238
+-0.5089728012538379,1.03043133425505
+0.6428078940268339,1.4446338310317666
+0.7084902031697193,-0.6280203603724627
+0.7098208155304121,0.44142774655773953
+-0.16192093751441483,0.9878094559070351
+-0.7766059698371737,-0.06753973896018153
+-0.6647600937530153,0.9633732101283191
+-0.16390870720062933,-0.07395612501434716
+-0.4113591384913133,0.32547075468071074
+0.4550981177296013,0.6089244054406073
+-0.5095101433082394,0.9794812739944244
+-1.0391036070769126,0.08579627128766054
+0.042391003317187814,-0.19104074278833916
+0.151890896749373,-0.41394915849867586
+0.08051798787141462,1.0546370177653646
+-0.09748519279850038,-0.06887783493693693
+1.4079977505487344,-0.6748057322492271
+-0.15792656343370476,2.2339899614968237
+0.4802265817353262,1.478705716798209
+1.4878732371537342,-1.245619142413011
+0.5325939384214351,-0.580267827519349
+-0.45437990238186454,1.8342414561885572
+-0.20893206306879286,-0.012241734173398772
+-1.0158558057196196,-0.36015685218347715
+0.04405499900436188,-0.036977385659243654
+0.5030771988426048,1.0518200595328882
+1.5471946154057121,-1.6417211029886944
+1.4453966523658348,-0.26726408552186093
+0.4745920834536685,-0.026393066322377368
+1.0057957541920994,0.8440707540220675
+-0.5089728012538379,1.03043133425505
+0.7246087742762607,-0.3703337560835316
+0.6634925500708032,0.012025408705223284
+-0.418444672060704,0.38054092688218666
+-0.8651495572477684,-1.7375034620169608e-05
+1.4342734593389683,-0.927291603918216
+-0.6647600937530153,0.9633732101283191
+-0.16390870720062933,-0.07395612501434716
+1.0749365424525648,-0.477881788476743
+0.529636463798165,1.415051657275616
+-0.5095101433082394,0.9794812739944244
+-1.0391036070769126,0.08579627128766054
+0.042391003317187814,-0.19104074278833916
+0.151890896749373,-0.41394915849867586
+1.7150227681460821,-1.5008401450687687
+1.1880482127439407,-0.7988448262221519
+-0.7979463592512397,-0.08582839366277062
+-0.15792656343370476,2.2339899614968237
+0.4802265817353262,1.478705716798209
+1.372145055458603,-0.31403504140867966
+-0.15990265080670446,0.6474977951420444
+-0.45437990238186454,1.8342414561885572
+0.45673311087677054,-0.46561048223161083
+-1.0158558057196196,-0.36015685218347715
+-0.7675331880622382,0.6315659717432592
+-0.3096919310770261,1.5572361410434739
+-0.7399845171057966,1.137319213771014
+0.6556513156017187,-0.29908348226411535
+0.4745920834536685,-0.026393066322377368
+1.0057957541920994,0.8440707540220675
+-0.5089728012538379,1.03043133425505
+0.9254097982109226,0.8397662701532447
+0.974188698812576,0.3763043581134954
+-0.418444672060704,0.38054092688218666
+1.4607232407463584,-1.354536395633251
+0.8104827607602787,1.173551459072093
+-0.6647600937530153,0.9633732101283191
+-0.13356180680507787,0.5327186423738675
+-0.5522683202912821,0.03321240906318634
+1.2578224591472764,-1.1598631651483082
+-0.5095101433082394,0.9794812739944244
+1.540945587246552,-1.8290013542438512
+0.042391003317187814,-0.19104074278833916
+0.12493621006633826,0.6369903435493316
+-0.4852053066201117,2.1103305670189387
+1.1397650546585272,-1.1703878149848626
+-0.7979463592512397,-0.08582839366277062
+-0.15792656343370476,2.2339899614968237
+-0.1677540072630604,0.5728895966445218
+1.372145055458603,-0.31403504140867966
+-0.4918805928763509,0.47686181293897045
+-0.45437990238186454,1.8342414561885572
+-0.6304876798591719,0.761141786471931
+1.6991286348147212,-1.3999990695072397
+-0.5610489023370748,0.5065884927191822
+-0.5077256981544337,1.6303409812087866
+-0.7399845171057966,1.137319213771014
+-0.5974579160530358,1.4398578966466369
+0.8422443628959959,-0.5026312028562858
+-0.38687361291362465,0.43118702820730115
+0.08070370914651881,0.1400039461901167
+0.9254097982109226,0.8397662701532447
+-0.6371375700699144,0.8430115495981927
+0.0143187319135019,1.4591032222424336
+1.4607232407463584,-1.354536395633251
+0.8104827607602787,1.173551459072093
+0.40629465035579837,-0.7196823492281152
+0.8430482041796458,1.2843141769183346
+-0.23488601673200044,0.14514101281573577
+1.2578224591472764,-1.1598631651483082
+-0.5095101433082394,0.9794812739944244
+1.540945587246552,-1.8290013542438512
+0.042391003317187814,-0.19104074278833916
+0.2828759517312587,1.0659597676359527
+-0.4852053066201117,2.1103305670189387
+1.1397650546585272,-1.1703878149848626
+-0.5132114971671871,0.15806736444174113
+-0.15792656343370476,2.2339899614968237
+-0.1677540072630604,0.5728895966445218
+1.372145055458603,-0.31403504140867966
+1.3351903866849664,-0.8033170270671047
+-0.5345830701018339,0.38031306072242343
+-0.6304876798591719,0.761141786471931
+1.1687104099878334,-0.3820325118387222
+0.7717851108072533,1.2517517816170822
+-0.5077256981544337,1.6303409812087866
+-0.7399845171057966,1.137319213771014
+1.0873440176586189,-1.360553542244313
+-0.8698525395339693,-0.07272590427443766
+-0.38687361291362465,0.43118702820730115
+0.7769950795034195,-0.795510777677288
+0.9254097982109226,0.8397662701532447
+0.012359662728215037,-0.32523457621404817
+1.45883785734306,-1.3591828547266176
+-0.6395310865190947,1.2229377376121742
+0.8104827607602787,1.173551459072093
+0.40629465035579837,-0.7196823492281152
+0.8430482041796458,1.2843141769183346
+0.05802248424756096,1.8980563868332836
+1.2578224591472764,-1.1598631651483082
+-0.5095101433082394,0.9794812739944244
+1.540945587246552,-1.8290013542438512
+0.44164113973260943,-0.4601679227169009
+0.2828759517312587,1.0659597676359527
+1.3500618859767568,-0.06617575793049868
+1.1397650546585272,-1.1703878149848626
+-0.5132114971671871,0.15806736444174113
+-0.007462890475764816,0.9580421389426187
+-0.1677540072630604,0.5728895966445218
+1.372145055458603,-0.31403504140867966
+0.9551692557507929,-0.7449125759312434
+-0.5345830701018339,0.38031306072242343
+-0.6304876798591719,0.761141786471931
+1.1687104099878334,-0.3820325118387222
+0.7717851108072533,1.2517517816170822
+-0.5077256981544337,1.6303409812087866
+-0.7399845171057966,1.137319213771014
+1.0422986183428526,0.21314445793244918
+-0.8698525395339693,-0.07272590427443766
+1.0206218739943846,-0.5271825703198489
+1.5505633873132227,-1.2933177640648537
+0.9254097982109226,0.8397662701532447
+1.2513802745983695,-1.0126921583495896
+1.8208850314969813,-2.409598927083083
+-0.441394375440495,1.8446861397545447
+0.8104827607602787,1.173551459072093
+-0.21589295458147423,1.4085582833810986
+0.8430482041796458,1.2843141769183346
+0.05802248424756096,1.8980563868332836
+1.2578224591472764,-1.1598631651483082
+1.095574575171249,-0.09526434292243513
+1.540945587246552,-1.8290013542438512
+-0.6749032772394734,-0.4523397324331202
+0.6947376602124334,0.45599271087892956
+1.3500618859767568,-0.06617575793049868
+1.1397650546585272,-1.1703878149848626
+-0.5132114971671871,0.15806736444174113
+0.5238042186204035,-0.027220517360686036
+-0.1677540072630604,0.5728895966445218
+0.8755832630330652,-0.6523017488532629
+0.7973879615911569,0.18909417174226328
+-0.5345830701018339,0.38031306072242343
+-0.3854021664618691,-0.005382651592998555
+0.8332309025927007,1.4810891259227874
+0.7717851108072533,1.2517517816170822
+1.5178704527626814,-1.7157460237437892
+0.8901860182358576,1.4690764792896736
+0.3817599892178357,1.9872029521604904
+-0.8698525395339693,-0.07272590427443766
+0.3143840918060805,1.0954745014290543
+0.20111544130900588,-0.26201294048755686
+0.48974034394234245,2.132210455826556
+-0.8913880123425606,0.417306948148924
+1.8208850314969813,-2.409598927083083
+-0.441394375440495,1.8446861397545447
+0.8104827607602787,1.173551459072093
+0.9041056289940604,0.5303210872902133
+-0.8305984531165621,0.1197272335613852
+0.43260849207729607,-0.11186201430389953
+0.198663611383005,0.02511655558339554
+-0.542814042172567,1.6887030101151133
+-0.23483888231654912,1.5579001165197872
+-0.6749032772394734,-0.4523397324331202
+-0.4548456944180962,0.7411968036580203
+0.5980176638800828,-0.42669471266804077
+1.1397650546585272,-1.1703878149848626
+-0.5132114971671871,0.15806736444174113
+0.5238042186204035,-0.027220517360686036
+-0.1677540072630604,0.5728895966445218
+0.8755832630330652,-0.6523017488532629
+0.7973879615911569,0.18909417174226328
+-0.5345830701018339,0.38031306072242343
+-0.739179308306271,0.42222847755771314
+0.8332309025927007,1.4810891259227874
+1.170659787279276,-0.7969273249194765
+1.5178704527626814,-1.7157460237437892
+0.8901860182358576,1.4690764792896736
+-0.3509587137663055,0.5397509249611434
+-0.8698525395339693,-0.07272590427443766
+1.1612155346160953,-1.4524159880416139
+0.9182576974761987,-0.6939601139962404
+0.48974034394234245,2.132210455826556
+-0.8913880123425606,0.417306948148924
+1.8208850314969813,-2.409598927083083
+-0.441394375440495,1.8446861397545447
+0.39894787731306514,1.2792082492484813
+0.9041056289940604,0.5303210872902133
+-0.8305984531165621,0.1197272335613852
+-0.43411504114841315,1.0530387487865855
+0.198663611383005,0.02511655558339554
+-0.542814042172567,1.6887030101151133
+0.00711292051988166,0.3968000472865904
+0.10882362200697787,1.049599994423121
+-0.4548456944180962,0.7411968036580203
+0.5980176638800828,-0.42669471266804077
+1.1397650546585272,-1.1703878149848626
+-0.5132114971671871,0.15806736444174113
+0.5238042186204035,-0.027220517360686036
+-0.1677540072630604,0.5728895966445218
+0.07901147620155506,0.8456652281660513
+-0.28349462905158657,1.1560021775306273
+0.5843215995756312,0.6183496551979941
+1.3787233361177091,-0.016941014183954328
+0.7328119559498943,-0.45701605058708716
+0.9796199969528747,-0.41136919980540976
+1.611045832089315,-1.8367424972556448
+0.8901860182358576,1.4690764792896736
+-0.3509587137663055,0.5397509249611434
+-0.8698525395339693,-0.07272590427443766
+1.1612155346160953,-1.4524159880416139
+0.754235913164502,-0.0314022578934679
+0.48974034394234245,2.132210455826556
+-0.8913880123425606,0.417306948148924
+1.8208850314969813,-2.409598927083083
+-0.441394375440495,1.8446861397545447
+-0.2681572630684024,0.11111407314632905
+0.9041056289940604,0.5303210872902133
+0.6294791183488833,1.0041886787632772
+1.6232451512266657,-1.1665642434594243
+0.198663611383005,0.02511655558339554
+-0.17381107281654035,1.3078190299526766
+0.00711292051988166,0.3968000472865904
+1.0245371268287278,-0.3348620621381837
+-0.4548456944180962,0.7411968036580203
+0.5980176638800828,-0.42669471266804077
+1.1397650546585272,-1.1703878149848626
+-0.5132114971671871,0.15806736444174113
+0.5238042186204035,-0.027220517360686036
+-0.6360383246758765,1.3010410542013844
+-0.09665376001108072,1.503557467387433
+0.5528002734993434,0.013614889954422171
+1.2686752550920928,0.5588386730331548
+1.3787233361177091,-0.016941014183954328
+0.13314372836108423,0.4685091167470413
+0.17244888309718986,0.7804451292594629
+1.611045832089315,-1.8367424972556448
+0.8901860182358576,1.4690764792896736
+-0.3509587137663055,0.5397509249611434
+-0.8698525395339693,-0.07272590427443766
+0.6011786602593875,1.5814637984937425
+1.240342533291465,-0.11564611735988164
+0.48974034394234245,2.132210455826556
+0.13641932540605645,1.0339402581413812
+1.8208850314969813,-2.409598927083083
+1.5531188740205084,-1.3529326205330576
+-0.2681572630684024,0.11111407314632905
+0.9041056289940604,0.5303210872902133
+0.6294791183488833,1.0041886787632772
+1.6232451512266657,-1.1665642434594243
+0.198663611383005,0.02511655558339554
+-0.3759029883742874,0.2448398303913312
+0.9360973230731985,-0.19965528014931927
+1.0245371268287278,-0.3348620621381837
+-0.7286498064445847,0.6821373444485765
+0.5980176638800828,-0.42669471266804077
+-0.2515262468481148,-0.3867265128787068
+-0.5132114971671871,0.15806736444174113
+-0.6711040297504144,1.068252208781043
+0.8629421136221204,-0.6993907378982605
+-0.09665376001108072,1.503557467387433
+-0.1989459203646342,1.5644763424217367
+-0.21215578189557374,1.0433695420540743
+-0.5625650149940262,-0.24842075048992163
+0.09292269116227223,0.9118109933491851
+-0.4965896846761327,2.1839066616414096
+1.611045832089315,-1.8367424972556448
+0.8248374794865363,0.6674807423724256
+0.769305529039561,0.8683758094948966
+-0.8698525395339693,-0.07272590427443766
+0.6011786602593875,1.5814637984937425
+1.240342533291465,-0.11564611735988164
+0.48974034394234245,2.132210455826556
+0.13641932540605645,1.0339402581413812
+1.8208850314969813,-2.409598927083083
+1.2115146308777605,0.21600742053507122
+-0.2681572630684024,0.11111407314632905
+0.19675167309361685,0.4219766825493653
+-0.48415154088313694,1.3930158847354732
+1.6232451512266657,-1.1665642434594243
+1.4805976566489607,-1.5872900389740554
+1.4725448937663725,-0.4049516126108841
+1.5067423874257375,-1.2247319528521732
+1.3194150108773774,-0.5036595011505847
+-0.7195022687131276,0.6658124514085464
+0.5980176638800828,-0.42669471266804077
+0.9109629657362166,-0.8200133854764833
+-0.5132114971671871,0.15806736444174113
+-0.6711040297504144,1.068252208781043
+-0.4189858891802561,0.08069766960255365
+0.8919171429443667,-0.5548662650993212
+-0.1989459203646342,1.5644763424217367
+-0.6422552479114564,1.9702117649072093
+1.4752936754467856,-1.5362387362347771
+0.09292269116227223,0.9118109933491851
+1.5088861784215513,-1.2930247498167573
+0.846481148970009,0.8098818414392489
+0.5545769565978778,1.352018774009567
+0.769305529039561,0.8683758094948966
+-0.8698525395339693,-0.07272590427443766
+0.6011786602593875,1.5814637984937425
+-0.07754380318927212,0.18846616825132484
+0.5876705695410813,1.5002495836417817
+-0.2932140414019141,1.2247096297474704
+-0.6292978557093248,1.5049728211143663
+-0.2390590892569292,-0.017365649446612764
+-0.2681572630684024,0.11111407314632905
+0.19675167309361685,0.4219766825493653
+-0.48415154088313694,1.3930158847354732
+1.6232451512266657,-1.1665642434594243
+-0.39929903550788015,0.318245048772811
+0.46389673521922825,0.00994661846367606
+-0.16913646690404271,1.6607455735494685
+1.3194150108773774,-0.5036595011505847
+1.630103156766126,-1.7601755701667883
+0.5980176638800828,-0.42669471266804077
+0.9109629657362166,-0.8200133854764833
+0.6872541793371152,-0.36355800032307434
+-0.6711040297504144,1.068252208781043
+-0.4189858891802561,0.08069766960255365
+0.6833475769383259,-1.0399781887929223
+-0.1989459203646342,1.5644763424217367
+-0.6422552479114564,1.9702117649072093
+1.4752936754467856,-1.5362387362347771
+0.478074985660273,1.8816913015797085
+1.5088861784215513,-1.2930247498167573
+-0.28722836828524156,0.27001266995903367
+0.015824466034106144,1.5075127222168834
+0.769305529039561,0.8683758094948966
+-0.5172186020142304,-0.2560325396369758
+0.6011786602593875,1.5814637984937425
+-0.07754380318927212,0.18846616825132484
+0.32296453436224243,2.078882486199162
+-0.21564733891037646,1.862042965116866
+-0.6292978557093248,1.5049728211143663
+0.004328846515930906,2.09134197506176
+-0.2681572630684024,0.11111407314632905
+0.4614225409624835,1.789240503275698
+-0.48415154088313694,1.3930158847354732
+0.1361975688364429,1.6541096547492775
+-0.39929903550788015,0.318245048772811
+0.46389673521922825,0.00994661846367606
+0.1391917177691629,1.7429397302168554
+0.8598679154363267,-0.3372097370218854
+-0.06545280346808907,0.591241579483473
+0.5980176638800828,-0.42669471266804077
+0.6824858403521702,-0.5023430952647088
+0.6872541793371152,-0.36355800032307434
+-0.6711040297504144,1.068252208781043
+-0.7281986361396089,0.7306544472565732
+0.6833475769383259,-1.0399781887929223
+-0.1989459203646342,1.5644763424217367
+-0.3004192641348772,1.3056826622177022
+1.4752936754467856,-1.5362387362347771
+-0.7653544600672385,-0.3521063136741687
+1.5088861784215513,-1.2930247498167573
+1.0693868081450735,-0.03882250374805074
+0.41699889413034164,0.4152599335128347
+0.769305529039561,0.8683758094948966
+-0.7201511037026225,1.4893464205430589
+0.6011786602593875,1.5814637984937425
+-0.07754380318927212,0.18846616825132484
+0.32296453436224243,2.078882486199162
+-0.21564733891037646,1.862042965116866
+-0.6292978557093248,1.5049728211143663
+0.004328846515930906,2.09134197506176
+-0.2681572630684024,0.11111407314632905
+0.4614225409624835,1.789240503275698
+-0.1740994872810404,2.121754210716446
+-0.6869631508345171,1.4723805647887749
+-0.39929903550788015,0.318245048772811
+0.7301873670890959,0.3104119059108838
+-0.03939109448670608,2.321394795864097
+0.8598679154363267,-0.3372097370218854
+-0.23699023442904976,2.074706369846509
+-0.771629923037905,0.9772884975844256
+0.7856619908481188,1.355814162859699
+0.6872541793371152,-0.36355800032307434
+0.2730127917135545,1.8003438098814786
+-0.29963892631906774,0.30824359006254043
+0.6833475769383259,-1.0399781887929223
+-0.1989459203646342,1.5644763424217367
+1.1211072753362692,-0.7573167429941635
+1.4752936754467856,-1.5362387362347771
+-0.7653544600672385,-0.3521063136741687
+1.5088861784215513,-1.2930247498167573
+1.284695900707864,-1.1150150438258182
+1.4879534416223097,-0.7347172894400703
+0.769305529039561,0.8683758094948966
+-0.7201511037026225,1.4893464205430589
+0.6011786602593875,1.5814637984937425
+-0.07754380318927212,0.18846616825132484
+1.7076794712628725,-1.9051577367624632
+-0.1895139536438628,0.12198505440413498
+-0.6292978557093248,1.5049728211143663
+1.235701276559453,-0.16425095126622058
+-0.8679801021566569,0.8662266254103925
+0.4614225409624835,1.789240503275698
+-0.1740994872810404,2.121754210716446
+-0.848101961301301,1.3617619529383698
+-0.6178953661385994,1.7384918548349668
+0.012569112682233152,1.8928959785700388
+1.7478654850071256,-2.3874986401375153
+0.8598679154363267,-0.3372097370218854
+-0.23699023442904976,2.074706369846509
+-0.771629923037905,0.9772884975844256
+0.7856619908481188,1.355814162859699
+1.596130480163475,-2.1326077769339147
+0.5765254571464801,-0.3364305011049853
+-0.29963892631906774,0.30824359006254043
+1.2718616582958413,-0.22806373469118835
+-0.1989459203646342,1.5644763424217367
+0.07253764540695828,1.6127518068444016
+1.4752936754467856,-1.5362387362347771
+-0.7653544600672385,-0.3521063136741687
+0.36760875391288633,-0.293647619570215
+0.10820621014065057,0.11928500955504695
+0.8474938262364154,-0.48610141323656875
+0.3693372039435698,0.2832138478974635
+1.8738550787104316,-2.7585459900581895
+0.6011786602593875,1.5814637984937425
+0.12403436562882719,2.058350860908136
+-0.5314094806391543,1.5967284942823923
+-0.6963836362900835,0.9168550108911603
+0.5977170614133925,-0.4745111452179862
+1.235701276559453,-0.16425095126622058
+-0.8679801021566569,0.8662266254103925
+-0.02856625238407756,0.16042243593001784
+-0.1740994872810404,2.121754210716446
+-0.848101961301301,1.3617619529383698
+-0.04787678642778492,-0.24307118716589715
+0.012569112682233152,1.8928959785700388
+1.7478654850071256,-2.3874986401375153
+0.10823202920757186,-0.01687155623250919
+-0.23699023442904976,2.074706369846509
+-0.771629923037905,0.9772884975844256
+0.7856619908481188,1.355814162859699
+1.596130480163475,-2.1326077769339147
+0.5765254571464801,-0.3364305011049853
+-0.29963892631906774,0.30824359006254043
+-0.6074851348477064,1.5038805328356033
+-0.1989459203646342,1.5644763424217367
+1.5344775532936936,-1.5796722408385722
+1.4752936754467856,-1.5362387362347771
+-0.7653544600672385,-0.3521063136741687
+0.6513655278153015,-0.32290995471918427
+0.10820621014065057,0.11928500955504695
+0.8474938262364154,-0.48610141323656875
+0.3693372039435698,0.2832138478974635
+0.06344674512530102,-0.3452004844966048
+1.3660481222541168,0.1574452618404868
+-0.4556973819681305,1.0689753143231786
+0.36247617619689304,0.14464032594019943
+0.9577567189699914,0.8031792774831145
+1.2586183850273762,0.2195835567898219
+1.235701276559453,-0.16425095126622058
+1.5242835078170418,-1.7053734607798836
+0.23785512790500077,-0.0006934060540908817
+1.775478171733375,-3.0323558355615874
+-0.5528233768389834,0.7132400161410578
+-0.04787678642778492,-0.24307118716589715
+0.012569112682233152,1.8928959785700388
+0.7733754007699801,-0.8050525163978471
+-0.32723632850163253,1.735928615646137
+0.26712093464952086,0.04855498031100415
+-0.3368297636156261,0.26844868927425036
+0.7856619908481188,1.355814162859699
+1.596130480163475,-2.1326077769339147
+0.5765254571464801,-0.3364305011049853
+1.394988835401801,-0.7815594167582955
+0.7607369684354911,1.1508966299111147
+-0.9484636185668951,0.7078758152566409
+1.5344775532936936,-1.5796722408385722
+0.0071075151777172385,1.5725249645520463
+1.5932180486587544,-0.7219877135317463
+0.6513655278153015,-0.32290995471918427
+0.10820621014065057,0.11928500955504695
+-0.6783331982817921,0.10229428986005373
+0.3152340482488998,-0.48078753385419215
+-0.5849616370951936,0.4355763840465402
+1.446711188465898,-0.6688144763192871
+-0.4556973819681305,1.0689753143231786
+-0.6554663413767396,1.0917457693977477
+-0.8060206006345343,0.78047886245266
+1.2586183850273762,0.2195835567898219
+1.235701276559453,-0.16425095126622058
+-0.009558454885570448,1.7523046488768121
+0.23785512790500077,-0.0006934060540908817
+1.775478171733375,-3.0323558355615874
+-0.2039484172152907,1.6224334687172635
+-0.20653832519029316,2.055830949339578
+0.5587782766332416,0.13780266129266325
+0.7733754007699801,-0.8050525163978471
+-0.32723632850163253,1.735928615646137
+0.5239013301975746,1.1842941021661897
+1.0668361086538012,0.5642764066587049
+0.7856619908481188,1.355814162859699
+1.606222991447206,-1.2301734571075111
+0.9783896219728125,0.01483949537060325
+-0.4607909668681044,1.4040555723135157
+0.24392525510606744,1.667329904381455
+1.5949602922952095,-0.9967023894380591
+1.5344775532936936,-1.5796722408385722
+-0.6934436703018675,0.3366198646923896
+0.7297760007659222,-0.12768416434953714
+0.6513655278153015,-0.32290995471918427
+0.10820621014065057,0.11928500955504695
+-0.6783331982817921,0.10229428986005373
+0.3152340482488998,-0.48078753385419215
+-0.5849616370951936,0.4355763840465402
+-0.035145325350629655,2.301209297373837
+0.40183027129087245,1.935236775722271
+-0.6554663413767396,1.0917457693977477
+0.941906744669736,1.062397215371869
+1.2586183850273762,0.2195835567898219
+0.09591752899900526,1.4826182742459888
+-0.15516261554685973,2.119868670896825
+0.5112465621192837,-0.26160312686988285
+1.775478171733375,-3.0323558355615874
+0.09383702584425378,2.251727191214885
+-0.20653832519029316,2.055830949339578
+0.5587782766332416,0.13780266129266325
+1.02055443763368,-1.4533516940485678
+0.7927890789345351,0.9793849714301195
+0.5239013301975746,1.1842941021661897
+1.318276543147908,-0.717533476760378
+0.7856619908481188,1.355814162859699
+1.606222991447206,-1.2301734571075111
+0.9783896219728125,0.01483949537060325
+-0.013312120876164624,1.9732268231275591
+0.24392525510606744,1.667329904381455
+0.055079968376442634,0.10639639346305574
+1.5344775532936936,-1.5796722408385722
+-0.06498299039182887,0.18991551720426414
+0.3631637767382192,0.3241663116433198
+-0.6637805565297221,1.2671150630190056
+0.10820621014065057,0.11928500955504695
+-0.6783331982817921,0.10229428986005373
+-1.0785507371078706,0.9519082820198472
+-0.5849616370951936,0.4355763840465402
+1.7584346103262825,-1.8220214365304441
+1.352723018885526,-1.2019126225917467
+-0.24855620046832794,1.1505916360281505
+0.941906744669736,1.062397215371869
+1.2586183850273762,0.2195835567898219
+-0.016820862538537595,0.06509145809253791
+-0.15516261554685973,2.119868670896825
+0.5112465621192837,-0.26160312686988285
+1.8626761909174134,-1.7836978578058018
+0.09383702584425378,2.251727191214885
+-0.3468183774710674,0.849451577653332
+-0.7255687479043382,0.18803627668348433
+1.2504923083308546,-0.05263496342657015
+-0.4704504098619544,2.1231677316520337
+0.5239013301975746,1.1842941021661897
+1.651664512916681,-2.087141310807109
+0.7856619908481188,1.355814162859699
+0.8299622357773778,0.5972648043437465
+0.9783896219728125,0.01483949537060325
+-0.013312120876164624,1.9732268231275591
+0.6559583924331602,1.6766858226479382
+0.055079968376442634,0.10639639346305574
+0.6481524091644687,-0.27537014033182555
+-0.06498299039182887,0.18991551720426414
+1.1880687213750751,0.7196821598877788
+-0.6637805565297221,1.2671150630190056
+0.04005223784205114,1.0548124964811025
+-0.6187126791697293,0.6770837971114492
+-0.49502091557595845,1.7005065451945587
+0.8822661812593999,0.9552280621718634
+-0.12479116549825406,1.3273835140036483
+1.352723018885526,-1.2019126225917467
+-0.6269587041840223,-0.5353527390985107
+0.20872120593071564,1.2024039026502642
+1.2586183850273762,0.2195835567898219
+-0.016820862538537595,0.06509145809253791
+-0.1078145957265405,1.4533205720983828
+0.5112465621192837,-0.26160312686988285
+1.4655224383415024,-0.011510818563483544
+0.09383702584425378,2.251727191214885
+-0.3468183774710674,0.849451577653332
+-0.7255687479043382,0.18803627668348433
+-0.8673646633389034,-0.3371912566867542
+0.3675941447180763,2.078364482002739
+-0.32345807656951014,1.3397559753752197
+1.651664512916681,-2.087141310807109
+0.7856619908481188,1.355814162859699
+0.8299622357773778,0.5972648043437465
+0.9783896219728125,0.01483949537060325
+-0.7469323303652122,0.7028499212897474
+0.6559583924331602,1.6766858226479382
+-0.3752646279217855,1.59223114048207
+0.6481524091644687,-0.27537014033182555
+-0.06498299039182887,0.18991551720426414
+1.1880687213750751,0.7196821598877788
+-0.6637805565297221,1.2671150630190056
+-0.25419064176865647,0.00510170093758322
+-0.6187126791697293,0.6770837971114492
+-0.49502091557595845,1.7005065451945587
+0.534067832733304,1.5594045464375257
+-0.17718853720407668,0.8070523030408963
+1.352723018885526,-1.2019126225917467
+0.8794346470694127,0.5642443385224507
+0.3084508006369237,1.917672319852015
+0.8312330778909947,0.02535845929554445
+-0.2491244449556727,1.4110820530536
+-1.0237568572948301,-0.12931154731294042
+0.5112465621192837,-0.26160312686988285
+0.8059282554408551,1.629396022484391
+-0.3271003932627143,1.8277112169737053
+-0.3468183774710674,0.849451577653332
+-0.7255687479043382,0.18803627668348433
+0.46275832621218577,0.7249715874345206
+0.3675941447180763,2.078364482002739
+-0.32345807656951014,1.3397559753752197
+1.651664512916681,-2.087141310807109
+0.7856619908481188,1.355814162859699
+-0.16671624896437903,1.6786451489931256
+0.9783896219728125,0.01483949537060325
+0.10654171085817338,0.07191479727725025
+0.6559583924331602,1.6766858226479382
+0.8840860243767188,-0.7229534112131075
+0.6481524091644687,-0.27537014033182555
+0.2254162218816943,2.220808011782677
+1.395262033262247,-0.34539986318421
+1.44660310485942,0.04438379156721828
+0.0007076882380407656,0.01873380997307164
+-0.6187126791697293,0.6770837971114492
+1.1001710527928221,0.8187281489086278
+0.534067832733304,1.5594045464375257
+0.416024092659793,1.325591139453519
+0.28499511204853106,-0.15056572392595738
+1.4084203051465267,0.10623621921908977
+1.0893922946851662,-0.4693911070383303
+-0.6153652921700132,1.1095563201225613
+1.5902034105774185,-1.656146623253745
+-1.0237568572948301,-0.12931154731294042
+0.5112465621192837,-0.26160312686988285
+0.8059282554408551,1.629396022484391
+-0.3271003932627143,1.8277112169737053
+1.009162728635887,-0.27249266637872366
+-0.7255687479043382,0.18803627668348433
+0.46275832621218577,0.7249715874345206
+0.3675941447180763,2.078364482002739
+-0.32345807656951014,1.3397559753752197
+1.651664512916681,-2.087141310807109
+0.7856619908481188,1.355814162859699
+-0.16671624896437903,1.6786451489931256
+0.934903955925113,0.7783115470891285
+0.10654171085817338,0.07191479727725025
+0.9477595915183821,0.9901381114127062
+0.8840860243767188,-0.7229534112131075
+0.6481524091644687,-0.27537014033182555
+0.2254162218816943,2.220808011782677
+-0.7645240647098537,1.074089126390235
+1.2591088393500507,-1.0441827179332261
+0.0007076882380407656,0.01873380997307164
+1.6199417148513806,-1.269869626408302
+1.1001710527928221,0.8187281489086278
+0.9633334552145053,0.7829803104284986
+0.416024092659793,1.325591139453519
+0.28499511204853106,-0.15056572392595738
+0.42664826352168195,1.4015245090167272
+0.4885052933296645,0.20389532261793764
+-0.6153652921700132,1.1095563201225613
+-0.4962005058302217,0.024401299159115812
+-1.0237568572948301,-0.12931154731294042
+0.5112465621192837,-0.26160312686988285
+1.073866797235382,-1.0762970783709649
+-0.3271003932627143,1.8277112169737053
+1.1594448657307237,0.5041213165937042
+-0.29079451575017234,2.2383011257498877
+1.444773167279991,-1.9423546048655287
+0.3675941447180763,2.078364482002739
+-0.299994371381823,0.16989678241834347
+1.651664512916681,-2.087141310807109
+0.7856619908481188,1.355814162859699
+-0.16671624896437903,1.6786451489931256
+0.01368306537895747,2.0716774522083217
+0.10654171085817338,0.07191479727725025
+0.9477595915183821,0.9901381114127062
+0.8840860243767188,-0.7229534112131075
+0.7021142141128923,1.2738149818806428
+0.2254162218816943,2.220808011782677
+0.7177035082265463,1.47272078857989
+1.2591088393500507,-1.0441827179332261
+-0.6280905694217824,0.39898016084829746
+1.5125441847124463,-1.8061055070067997
+1.1001710527928221,0.8187281489086278
+0.9633334552145053,0.7829803104284986
+1.4367605742896274,-0.9703119956106068
+0.28499511204853106,-0.15056572392595738
+0.42664826352168195,1.4015245090167272
+-0.09467139196106433,-0.23559933634580377
+-0.6153652921700132,1.1095563201225613
+-0.4962005058302217,0.024401299159115812
+-1.0237568572948301,-0.12931154731294042
+0.5112465621192837,-0.26160312686988285
+1.073866797235382,-1.0762970783709649
+-0.3271003932627143,1.8277112169737053
+0.7867547727440594,0.18200639714485323
+-0.29079451575017234,2.2383011257498877
+-0.4511790402331486,-0.6490466576323419
+0.3675941447180763,2.078364482002739
+-0.299994371381823,0.16989678241834347
+1.651664512916681,-2.087141310807109
+0.7856619908481188,1.355814162859699
+-0.16671624896437903,1.6786451489931256
+-0.6878489809877664,1.5341241286809706
+0.08428225368922371,2.3460348386194783
+-0.2831513856176035,0.624258589685659
+0.8840860243767188,-0.7229534112131075
+0.7021142141128923,1.2738149818806428
+-0.06816967164451226,1.834942355081092
+0.8761567362706144,-0.550941206798943
+0.23082938183333185,-0.15187397187154122
+-0.6280905694217824,0.39898016084829746
+1.5125441847124463,-1.8061055070067997
+-0.10375317495028974,0.1961621867920192
+0.9633334552145053,0.7829803104284986
+0.48871432117533253,1.6851385645423325
+0.28499511204853106,-0.15056572392595738
+0.42664826352168195,1.4015245090167272
+-0.09467139196106433,-0.23559933634580377
+1.2860310569536382,-0.29752532370806006
+-0.4962005058302217,0.024401299159115812
+-1.0237568572948301,-0.12931154731294042
+-0.5090570032827761,0.753764001055485
+1.0310141294600432,-1.0208411051177504
+-0.3271003932627143,1.8277112169737053
+0.7866094554487753,0.3476221809249631
+-0.07122953214512398,-0.2576134627249912
+1.5079265191935889,-0.5859669757108525
+0.3675941447180763,2.078364482002739
+-0.18849277142121362,1.631872849091707
+1.651664512916681,-2.087141310807109
+0.7856619908481188,1.355814162859699
+-0.16671624896437903,1.6786451489931256
+-0.6878489809877664,1.5341241286809706
+-0.9357107682735001,0.632621150931653
+-0.2831513856176035,0.624258589685659
+0.8840860243767188,-0.7229534112131075
+-0.7305796854575342,0.8360011181807323
+-0.06816967164451226,1.834942355081092
+0.8761567362706144,-0.550941206798943
+0.685194754759311,1.3781130774900059
+-0.3133927942427147,0.4584899883003409
+0.9303478499777138,0.1766086782432097
+0.4709151810227632,-0.35625118249787047
+0.9633334552145053,0.7829803104284986
+0.48871432117533253,1.6851385645423325
+0.28499511204853106,-0.15056572392595738
+0.42664826352168195,1.4015245090167272
+-0.09467139196106433,-0.23559933634580377
+1.2860310569536382,-0.29752532370806006
+-0.4962005058302217,0.024401299159115812
+-0.13438790515747787,0.5140810357047537
+-0.5090570032827761,0.753764001055485
+1.0310141294600432,-1.0208411051177504
+-0.3271003932627143,1.8277112169737053
+-0.5380479562757876,0.889543249125974
+-0.07122953214512398,-0.2576134627249912
+1.5079265191935889,-0.5859669757108525
+0.22736248061659226,0.9328682554368566
+0.9778655984185451,-0.9483743089985259
+1.651664512916681,-2.087141310807109
+0.7856619908481188,1.355814162859699
+-0.16671624896437903,1.6786451489931256
+-0.6878489809877664,1.5341241286809706
+-0.9357107682735001,0.632621150931653
+0.14214183077581422,0.08264725185796062
+1.23198684887045,0.3520649169222969
+-0.7305796854575342,0.8360011181807323
+0.9626847443486259,-0.18696612042555727
+0.8761567362706144,-0.550941206798943
+0.685194754759311,1.3781130774900059
+-0.3133927942427147,0.4584899883003409
+0.4432626679184344,1.2406921790016645
+0.4709151810227632,-0.35625118249787047
+0.9633334552145053,0.7829803104284986
+0.48871432117533253,1.6851385645423325
+0.7571791625134134,-0.8096741397265512
+-0.5678128442473387,0.7740789273697949
+-0.21392105343656265,1.6049977668621058
+1.2860310569536382,-0.29752532370806006
+-0.4962005058302217,0.024401299159115812
+0.5586160462019341,1.650532336394704
+-0.5090570032827761,0.753764001055485
+-0.4106644787174827,1.2189553170142469
+-0.3271003932627143,1.8277112169737053
+-0.5380479562757876,0.889543249125974
+-0.07122953214512398,-0.2576134627249912
+-0.7418925725083365,0.6201607385650565
+0.2540079450958108,0.296871893224107
+0.9778655984185451,-0.9483743089985259
+1.651664512916681,-2.087141310807109
+0.7856619908481188,1.355814162859699
+-0.16671624896437903,1.6786451489931256
+0.7154398923198673,1.3670747674042982
+0.36561477687214783,0.2561245952544264
+0.14214183077581422,0.08264725185796062
+1.23198684887045,0.3520649169222969
+-0.7305796854575342,0.8360011181807323
+0.9626847443486259,-0.18696612042555727
+0.8890073247975023,1.0248541049723139
+0.685194754759311,1.3781130774900059
+-0.3133927942427147,0.4584899883003409
+0.4432626679184344,1.2406921790016645
+0.4709151810227632,-0.35625118249787047
+0.9633334552145053,0.7829803104284986
+0.8640957371921858,-0.9046943201326553
+0.7571791625134134,-0.8096741397265512
+-0.5678128442473387,0.7740789273697949
+0.9684341672612682,0.7108702475861146
+1.2860310569536382,-0.29752532370806006
+0.32842265860595693,-0.26925293414053836
+-0.596610640336354,0.1781800509499074
+-0.5090570032827761,0.753764001055485
+-0.4106644787174827,1.2189553170142469
+0.8841557700356694,-0.8821759468433281
+-0.7526444529612109,0.819880674858839
+-0.07122953214512398,-0.2576134627249912
+-0.7418925725083365,0.6201607385650565
+0.2540079450958108,0.296871893224107
+0.7404572286421902,-0.6085374242136432
+1.651664512916681,-2.087141310807109
+0.7856619908481188,1.355814162859699
+-0.16671624896437903,1.6786451489931256
+0.7154398923198673,1.3670747674042982
+0.36561477687214783,0.2561245952544264
+-0.4776361758680415,0.9512952981988606
+-0.28087684314320227,1.0616377498086633
+-0.3508952750393083,-0.15559077790059733
+0.1253007628379037,0.81616918319388
+0.8890073247975023,1.0248541049723139
+0.5968274377141292,-0.40077911742669725
+-0.3133927942427147,0.4584899883003409
+1.3215823546171552,0.36116318052684726
+0.4709151810227632,-0.35625118249787047
+-0.7832783567589261,0.7060168821608546
+0.8640957371921858,-0.9046943201326553
+0.7571791625134134,-0.8096741397265512
+-0.5678128442473387,0.7740789273697949
+1.3725180240749846,-0.11865673599857163
+1.2860310569536382,-0.29752532370806006
+0.32842265860595693,-0.26925293414053836
+-0.3649631957457528,-0.11486871029051493
+0.18091959535528285,-0.15284829493372193
+-0.4106644787174827,1.2189553170142469
+-0.7626892101895165,1.1730220177549886
+-0.44524602174163735,0.12201692247036788
+-0.5474358896287804,2.1035858675679364
+-0.7418925725083365,0.6201607385650565
+-0.2539983721973088,1.6303991035665366
+0.7404572286421902,-0.6085374242136432
+1.651664512916681,-2.087141310807109
+0.7856619908481188,1.355814162859699
+0.7407707744316077,-0.4110752546349267
+0.7154398923198673,1.3670747674042982
+-0.45354125784352517,0.6749696369506804
+0.34606566278474077,1.2823488906307843
+-0.28087684314320227,1.0616377498086633
+-0.3508952750393083,-0.15559077790059733
+-0.2855320145772172,0.9341202011035644
+-0.002659823536773742,0.3634383960033948
+0.5968274377141292,-0.40077911742669725
+0.7511356887192862,0.4696868836732774
+1.3215823546171552,0.36116318052684726
+0.4709151810227632,-0.35625118249787047
+-0.3664461480011983,1.3078634348639073
+0.8640957371921858,-0.9046943201326553
+1.6471337049184387,-0.681017276377657
+-0.5678128442473387,0.7740789273697949
+1.3725180240749846,-0.11865673599857163
+1.2860310569536382,-0.29752532370806006
+0.32842265860595693,-0.26925293414053836
+-0.3649631957457528,-0.11486871029051493
+1.190840080536386,0.5558687212673765
+0.9580750286095507,0.3207969386763615
+-0.7626892101895165,1.1730220177549886
+-0.44524602174163735,0.12201692247036788
+-0.5474358896287804,2.1035858675679364
+-0.7418925725083365,0.6201607385650565
+-0.2539983721973088,1.6303991035665366
+0.13542542926683127,0.06726933373267852
+1.651664512916681,-2.087141310807109
+0.7856619908481188,1.355814162859699
+0.7407707744316077,-0.4110752546349267
+0.7154398923198673,1.3670747674042982
+0.30551984402023347,0.4192732388628262
+0.2552683019671167,0.011969725704612522
+0.897774839854019,-0.9256618566736527
+-0.3508952750393083,-0.15559077790059733
+-0.6871060335093788,0.29229886325939697
+-0.908241260723994,0.5714243036201786
+0.1511994856864034,0.2460851128259643
+1.100532407923273,-0.5638963962548256
+1.3215823546171552,0.36116318052684726
+1.3505811234853136,-1.4268501635297919
+-0.3664461480011983,1.3078634348639073
+0.8640957371921858,-0.9046943201326553
+1.6471337049184387,-0.681017276377657
+0.5117417186908211,1.5157284587558408
+1.3725180240749846,-0.11865673599857163
+1.2860310569536382,-0.29752532370806006
+1.5441769528071174,-1.310534949552508
+0.6034613858987323,0.2633848973355195
+0.06481087445424549,1.5199180225619564
+-0.09752684778504833,0.11442274292732962
+-0.7626892101895165,1.1730220177549886
+-0.44524602174163735,0.12201692247036788
+0.6867366993163885,1.0175338660020508
+-0.7418925725083365,0.6201607385650565
+1.0585947320926647,1.0442415017008457
+0.13542542926683127,0.06726933373267852
+-0.9073265985000397,0.6214970689022079
+0.7856619908481188,1.355814162859699
+-0.021291985580359357,1.3992705074767677
+1.0808050318693205,0.8025772833071833
+0.8658759168474082,-1.081890389469822
+0.2552683019671167,0.011969725704612522
+0.897774839854019,-0.9256618566736527
+-0.3508952750393083,-0.15559077790059733
+-0.6871060335093788,0.29229886325939697
+1.115654429366101,0.29912515941044393
+0.3481472204946674,0.5493894008219489
+1.1733987759018132,0.1591941282639462
+1.3215823546171552,0.36116318052684726
+1.492375390553483,-1.17356723557715
+-0.3664461480011983,1.3078634348639073
+0.8640957371921858,-0.9046943201326553
+1.6471337049184387,-0.681017276377657
+0.5117417186908211,1.5157284587558408
+0.4575399561539518,2.1005786392838077
+0.9574048415199807,-0.23659294736399494
+1.5441769528071174,-1.310534949552508
+1.1931877308909133,-1.1447153527136265
+0.06481087445424549,1.5199180225619564
+1.2744089709481488,-1.5220726099042818
+-0.7626892101895165,1.1730220177549886
+-0.44524602174163735,0.12201692247036788
+-0.7852269702289711,0.4997151233373156
+1.0218784195549424,-0.930384450562354
+-0.5063496065473642,0.2488892701945019
+0.15792609840755634,0.10778935049855973
+-0.9073265985000397,0.6214970689022079
+-0.4071622112703898,0.6930920061554697
+-0.08428289132924943,1.0456162877347162
+1.0808050318693205,0.8025772833071833
+1.7532769664442998,-2.4024191000781903
+0.2552683019671167,0.011969725704612522
+0.897774839854019,-0.9256618566736527
+-0.3508952750393083,-0.15559077790059733
+0.7395640746102127,-0.7520986152587604
+1.115654429366101,0.29912515941044393
+-0.03812472633342075,1.5641076867378565
+1.1733987759018132,0.1591941282639462
+0.5581829203656999,-0.665639773364511
+1.183763012103882,0.5387620790077379
+0.006487328337923183,1.7392670072036929
+1.4361955736184542,-0.8176357027053089
+-0.4015881962544426,1.373383801195457
+0.5117417186908211,1.5157284587558408
+1.771071933996569,-1.3784056716579034
+1.1960631015034113,-0.46750781221624227
+1.5441769528071174,-1.310534949552508
+1.6275099426158404,-2.181096961438422
+0.06481087445424549,1.5199180225619564
+-0.5547100418792421,1.432221138570748
+0.8616931949729125,0.4238081293388737
+0.0809350298354119,1.9274676469053513
+-0.7852269702289711,0.4997151233373156
+0.35735981398663696,2.0345778821176133
+-0.5063496065473642,0.2488892701945019
+0.15792609840755634,0.10778935049855973
+-0.6694016324728286,1.4805853971527354
+-0.4071622112703898,0.6930920061554697
+-0.19356704534088776,-0.34235266318105495
+-0.6158071185939938,-0.5004777797537969
+1.7532769664442998,-2.4024191000781903
+0.2552683019671167,0.011969725704612522
+-0.4807407277012229,0.5835243606362616
+-0.3508952750393083,-0.15559077790059733
+0.7395640746102127,-0.7520986152587604
+1.115654429366101,0.29912515941044393
+-0.5810934655574935,0.17951575319014768
+1.1733987759018132,0.1591941282639462
+0.04386694972516717,2.4747727329481957
+-0.9245414455015506,0.5569407777878861
+0.006487328337923183,1.7392670072036929
+-0.3129012277323896,1.220772001746654
+-0.4015881962544426,1.373383801195457
+0.5117417186908211,1.5157284587558408
+0.9982506841144995,0.04566608864747046
+1.1960631015034113,-0.46750781221624227
+1.5441769528071174,-1.310534949552508
+0.8480850115122526,1.753383315773295
+0.06481087445424549,1.5199180225619564
+-0.5547100418792421,1.432221138570748
+-0.5742073529269778,1.4308422008909636
+1.2835620546670505,0.02450563771436609
+-0.7852269702289711,0.4997151233373156
+0.35735981398663696,2.0345778821176133
+-0.5063496065473642,0.2488892701945019
+0.15792609840755634,0.10778935049855973
+-0.3829476222675736,0.6205969375348832
+-0.4071622112703898,0.6930920061554697
+0.7500533698642592,0.747680812837169
+-0.6158071185939938,-0.5004777797537969
+1.7532769664442998,-2.4024191000781903
+0.2552683019671167,0.011969725704612522
+0.5659046662534418,1.9555574949773282
+-0.3508952750393083,-0.15559077790059733
+0.7395640746102127,-0.7520986152587604
+0.5133893054115743,0.06709927989667108
+0.08116277421840418,1.7553856110842632
+1.1733987759018132,0.1591941282639462
+-0.6749425182262331,1.1312689099227318
+-0.9245414455015506,0.5569407777878861
+0.4354639836570129,-0.49495180504037994
+-0.3129012277323896,1.220772001746654
+-0.02174845457325554,2.2514227605157897
+0.5117417186908211,1.5157284587558408
+0.9982506841144995,0.04566608864747046
+1.1960631015034113,-0.46750781221624227
+1.5441769528071174,-1.310534949552508
+-0.6001619963883786,-0.2019982213417435
+0.06481087445424549,1.5199180225619564
+-0.5547100418792421,1.432221138570748
+-0.14111350994830013,0.2735906286660382
+-0.9563481870963404,-0.4197813433455706
+-0.7852269702289711,0.4997151233373156
+0.35735981398663696,2.0345778821176133
+-0.5063496065473642,0.2488892701945019
+1.4134804191641481,-1.0760991077908797
+-0.3829476222675736,0.6205969375348832
+1.1547660795771746,-0.702541546374582
+1.1485659655711458,-0.2773157481670182
+-0.6158071185939938,-0.5004777797537969
+1.7532769664442998,-2.4024191000781903
+0.2552683019671167,0.011969725704612522
+0.5659046662534418,1.9555574949773282
+-0.34997389616651786,0.7248574278212507
+0.7395640746102127,-0.7520986152587604
+0.5133893054115743,0.06709927989667108
+-0.22693266670880372,0.020933053304777127
+1.1733987759018132,0.1591941282639462
+-0.6749425182262331,1.1312689099227318
+0.9817217222814347,-0.4597690354630151
+0.4354639836570129,-0.49495180504037994
+-0.7077843469204352,1.1475080708142205
+0.2230958393480916,1.7039452415843608
+0.5117417186908211,1.5157284587558408
+-0.4957843470945084,0.685347135448073
+-0.5940136247594955,0.9488468107101408
+-0.33065321273342363,1.2854151378844993
+0.3947180399740887,-0.5471010803297622
+0.06481087445424549,1.5199180225619564
+-0.06459042854898803,1.6292792613480147
+1.1752336388402,0.6134580807514275
+-0.9563481870963404,-0.4197813433455706
+-0.7852269702289711,0.4997151233373156
+-0.685268459808086,0.7773654154349094
+1.0343423209954152,-0.528216527311828
+1.4134804191641481,-1.0760991077908797
+1.7325616505726738,-3.075263774647504
+1.4205907802871423,-1.333177576889011
+1.1485659655711458,-0.2773157481670182
+-0.6158071185939938,-0.5004777797537969
+1.7532769664442998,-2.4024191000781903
+0.2517859729958757,-0.1006259512564397
+0.5659046662534418,1.9555574949773282
+-0.34997389616651786,0.7248574278212507
+0.7395640746102127,-0.7520986152587604
+0.6605491351394047,-0.691134401942035
+-0.22693266670880372,0.020933053304777127
+-0.7065950270542516,0.2649582636542859
+-0.6749425182262331,1.1312689099227318
+0.9817217222814347,-0.4597690354630151
+1.2696955634709277,-1.259909216091036
+-0.3286309573468276,0.7846595091171054
+-0.17169222974918674,0.04752037572384116
+0.5117417186908211,1.5157284587558408
+1.5807856725784344,-1.8706346521924107
+-0.5940136247594955,0.9488468107101408
+1.1176664568414463,-0.7027112307733163
+0.3947180399740887,-0.5471010803297622
+0.06481087445424549,1.5199180225619564
+-0.06459042854898803,1.6292792613480147
+1.1752336388402,0.6134580807514275
+0.5997745711027291,-0.4530762361485282
+-0.36348847483770724,0.2355586917538077
+-0.685268459808086,0.7773654154349094
+0.11915437948549168,1.9559685795534785
+-0.66434988194826,0.7556878636467641
+1.7325616505726738,-3.075263774647504
+1.1813842610192395,0.5694013545373857
+-0.12368880235065431,1.0128021574297756
+-0.6158071185939938,-0.5004777797537969
+1.7532769664442998,-2.4024191000781903
+0.2517859729958757,-0.1006259512564397
+0.5659046662534418,1.9555574949773282
+-0.34997389616651786,0.7248574278212507
+0.7395640746102127,-0.7520986152587604
+0.6605491351394047,-0.691134401942035
+-0.22693266670880372,0.020933053304777127
+-0.7065950270542516,0.2649582636542859
+0.8443822416067573,-1.0411918511657736
+0.9817217222814347,-0.4597690354630151
+1.2696955634709277,-1.259909216091036
+-0.3286309573468276,0.7846595091171054
+-0.17169222974918674,0.04752037572384116
+0.5117417186908211,1.5157284587558408
+1.5807856725784344,-1.8706346521924107
+-0.2183121742399023,-0.040904488835026204
+-0.6237990072964628,-0.4037124082783161
+0.3947180399740887,-0.5471010803297622
+0.06481087445424549,1.5199180225619564
+-0.06459042854898803,1.6292792613480147
+1.1752336388402,0.6134580807514275
+0.5997745711027291,-0.4530762361485282
+0.30462247742445164,0.8360325459895231
+-0.685268459808086,0.7773654154349094
+0.11915437948549168,1.9559685795534785
+1.4702566081855843,-1.40192739013371
+0.6851793080638611,-0.04098546245077672
+1.049916181522013,-0.265748411783271
+1.8386876761732818,-2.2379382066106337
+-0.6158071185939938,-0.5004777797537969
+1.7532769664442998,-2.4024191000781903
+0.2517859729958757,-0.1006259512564397
+1.1825975737318124,-0.9356199826437954
+-0.34997389616651786,0.7248574278212507
+-0.8055310297945519,0.4682278406349634
+0.6605491351394047,-0.691134401942035
+-0.5105745424863568,0.368769998303468
+-0.7065950270542516,0.2649582636542859
+0.8443822416067573,-1.0411918511657736
+0.9817217222814347,-0.4597690354630151
+1.2696955634709277,-1.259909216091036
+-0.3286309573468276,0.7846595091171054
+-0.17169222974918674,0.04752037572384116
+0.5117417186908211,1.5157284587558408
+0.19379393925766764,-0.028613789324960157
+-0.2183121742399023,-0.040904488835026204
+0.2728253973201449,-0.5132540208828378
+0.4059717525212966,1.7688283034050303
+0.5694246642480587,1.126367281013097
+-0.06459042854898803,1.6292792613480147
+1.1752336388402,0.6134580807514275
+0.5997745711027291,-0.4530762361485282
+0.30462247742445164,0.8360325459895231
+-0.685268459808086,0.7773654154349094
+-0.6853022557259605,1.404372628047919
+1.4702566081855843,-1.40192739013371
+0.6851793080638611,-0.04098546245077672
+0.7570774928679346,-0.6891972600578884
+1.8386876761732818,-2.2379382066106337
+-0.6158071185939938,-0.5004777797537969
+1.7532769664442998,-2.4024191000781903
+0.2517859729958757,-0.1006259512564397
+1.1825975737318124,-0.9356199826437954
+-0.34997389616651786,0.7248574278212507
+-0.8055310297945519,0.4682278406349634
+-0.5232409375731057,0.5291805356776706
+0.6645053763810054,0.9835489175561363
+0.025729833680048886,1.986906883811663
+-0.09134610787340952,1.655691583558201
+0.9817217222814347,-0.4597690354630151
+0.9907198501199602,1.0863810659419517
+0.5181735118102815,-0.7792510529937688
+-0.17169222974918674,0.04752037572384116
+-0.62293606972348,0.6810913777993548
+-0.7744681962623824,0.3425294922954614
+1.276741033121473,-1.4596936695635963
+0.2728253973201449,-0.5132540208828378
+1.661244426766285,-1.8012982340327708
+0.5694246642480587,1.126367281013097
+-0.06459042854898803,1.6292792613480147
+1.1752336388402,0.6134580807514275
+0.7546563798907724,-0.43048605781383575
+-0.15461732504206124,-0.172736760265038
+-0.685268459808086,0.7773654154349094
+-0.6853022557259605,1.404372628047919
+1.4702566081855843,-1.40192739013371
+0.6851793080638611,-0.04098546245077672
+0.7570774928679346,-0.6891972600578884
+-0.6630579421159407,-0.2788023032256984
+-0.6158071185939938,-0.5004777797537969
+0.7080840919156777,1.7906301701441358
+0.2517859729958757,-0.1006259512564397
+-0.7308385534197572,1.451479306177567
+0.5043794234331502,-0.8484597290914623
+-0.8055310297945519,0.4682278406349634
+0.27994109810919615,1.7024756167072368
+0.6645053763810054,0.9835489175561363
+0.025729833680048886,1.986906883811663
+1.116213291000399,1.0124243183186517
+-0.7059505365669024,0.8144681675895693
+0.5903999053488153,1.3551760101713892
+0.5181735118102815,-0.7792510529937688
+-0.17169222974918674,0.04752037572384116
+-0.12534403061735022,1.3685577231625645
+-0.7744681962623824,0.3425294922954614
+1.276741033121473,-1.4596936695635963
+0.2728253973201449,-0.5132540208828378
+-0.449746409978414,1.2676263465063693
+0.5694246642480587,1.126367281013097
+-0.3559558499917419,1.3138681959217995
+0.43832634350578514,-0.5867673902951023
+-0.8115400805676449,0.42326284646990486
+-0.7254401382501778,1.3651065420265458
+-0.12599797407967908,2.1753604903229506
+0.028964269452301128,1.8801861800009334
+1.4702566081855843,-1.40192739013371
+0.10253749020153063,-0.00010674164419080534
+0.7570774928679346,-0.6891972600578884
+-0.6630579421159407,-0.2788023032256984
+-0.5105519123721758,1.5568856119778607
+0.7253216192303162,-0.7250206207404036
+1.0543838010955953,0.5524282843094488
+-0.7308385534197572,1.451479306177567
+-0.2962729431456908,1.1363052395259574
+-0.8055310297945519,0.4682278406349634
+1.258384255218169,-0.6374217185638836
+0.6645053763810054,0.9835489175561363
+0.025729833680048886,1.986906883811663
+0.3874049359569885,0.5370472728362525
+0.0714227240041688,-0.08751557242541137
+0.5903999053488153,1.3551760101713892
+0.9877733421311344,0.8707196206914325
+-0.17169222974918674,0.04752037572384116
+-0.12534403061735022,1.3685577231625645
+-0.7744681962623824,0.3425294922954614
+1.276741033121473,-1.4596936695635963
+0.2728253973201449,-0.5132540208828378
+-0.3459991635865517,0.8928725869475707
+1.9147995660383499,-2.762758599878806
+0.9031406912961766,1.2042855820608604
+-0.11451022615260706,1.7510749200118136
+0.03331711204142865,0.22771785469832648
+-0.7254401382501778,1.3651065420265458
+0.04029601730865451,0.444908014122836
+0.028964269452301128,1.8801861800009334
+0.4706677581602972,0.09889654761711819
+1.6320010603614905,-1.6456951150711887
+-0.7099856742006236,0.02606864005199444
+-0.6630579421159407,-0.2788023032256984
+-0.7154005284399629,-0.0769458144141601
+0.7253216192303162,-0.7250206207404036
+0.5906889899259098,0.8962596655491472
+1.2227439677634355,-1.262649945690578
+-0.2962729431456908,1.1363052395259574
+0.8602339319544231,-0.5015741454746907
+1.258384255218169,-0.6374217185638836
+0.8282751181467296,0.3954321187402796
+0.025729833680048886,1.986906883811663
+0.8970859353474623,1.234794822458657
+0.0714227240041688,-0.08751557242541137
+-0.2658383106184654,-0.2394500500147864
+0.9877733421311344,0.8707196206914325
+-0.17169222974918674,0.04752037572384116
+-0.12534403061735022,1.3685577231625645
+-0.6481262288059824,-0.2091850027822504
+1.276741033121473,-1.4596936695635963
+1.2297427862617671,-1.2553200336451473
+-0.3459991635865517,0.8928725869475707
+1.9147995660383499,-2.762758599878806
+0.9031406912961766,1.2042855820608604
+-0.11451022615260706,1.7510749200118136
+0.03331711204142865,0.22771785469832648
+0.03648846069901546,0.31950490581136326
+0.04029601730865451,0.444908014122836
+0.6186445718397343,-0.43949067072610315
+0.4706677581602972,0.09889654761711819
+0.06432799247056653,0.3848737088098144
+-0.7099856742006236,0.02606864005199444
+0.8250344631269615,-0.8230559750768633
+-0.7154005284399629,-0.0769458144141601
+0.5455100531246877,-0.1829948363666405
+0.9920837438424777,0.8104464011985126
+0.9325014941340161,0.9274673320765217
+-0.2962729431456908,1.1363052395259574
+0.8602339319544231,-0.5015741454746907
+1.0413559527705654,-1.224777521042914
+0.8282751181467296,0.3954321187402796
+0.025729833680048886,1.986906883811663
+0.4419249120697729,-0.21099548314457836
+0.0714227240041688,-0.08751557242541137
+-0.2658383106184654,-0.2394500500147864
+0.9877733421311344,0.8707196206914325
+0.5338194530776719,-0.24701012752748264
+1.1752220501852788,-1.3721694356102443
+-0.4830524940382873,0.992985269638565
+-0.32515416706153794,1.429350265809171
+1.2297427862617671,-1.2553200336451473
+-0.3459991635865517,0.8928725869475707
+1.9147995660383499,-2.762758599878806
+0.9031406912961766,1.2042855820608604
+-0.11451022615260706,1.7510749200118136
+1.337283563073216,-1.458964855074196
+0.03648846069901546,0.31950490581136326
+0.04029601730865451,0.444908014122836
+0.6186445718397343,-0.43949067072610315
+0.4706677581602972,0.09889654761711819
+0.06432799247056653,0.3848737088098144
+-0.7099856742006236,0.02606864005199444
+-1.1085976421276655,0.01916800150340804
+-0.7154005284399629,-0.0769458144141601
+-0.6702619462240533,-0.4550499020773205
+0.9920837438424777,0.8104464011985126
+0.9325014941340161,0.9274673320765217
+-0.5306275698872102,1.0124596495405374
+0.5808149711208391,-0.7588617281933899
+1.0413559527705654,-1.224777521042914
+0.8282751181467296,0.3954321187402796
+0.025729833680048886,1.986906883811663
+0.4419249120697729,-0.21099548314457836
+0.0714227240041688,-0.08751557242541137
+-0.2658383106184654,-0.2394500500147864
+0.9877733421311344,0.8707196206914325
+-0.08610296857594482,1.4680585606469876
+0.3134637873237518,-0.3225146454526263
+-0.4507993434407451,0.21678775795559768
+0.9043315961177707,0.619832815927315
+1.2297427862617671,-1.2553200336451473
+-0.03304730941889358,-0.4984936449047772
+1.9147995660383499,-2.762758599878806
+0.9031406912961766,1.2042855820608604
+0.6604804298413306,-0.28563257583808954
+1.2823039250290353,-0.03277744675413791
+0.6809347165237261,0.6830526363476283
+0.6039634820186631,-0.795719096130866
+0.6186445718397343,-0.43949067072610315
+0.6737708921701934,-0.2574836277986384
+0.06432799247056653,0.3848737088098144
+-0.029207580723080023,0.5263126387926751
+0.7162568047126614,-0.5291138329332783
+-0.7154005284399629,-0.0769458144141601
+-0.23162236183994517,1.1547800463620694
+0.05711713410195329,1.4134036681564879
+0.9325014941340161,0.9274673320765217
+-0.5306275698872102,1.0124596495405374
+0.5808149711208391,-0.7588617281933899
+0.6775195363814697,1.6528500136591457
+-0.5267237078269192,0.5905548888786831
+0.025729833680048886,1.986906883811663
+0.3821146451053013,0.16109883793852842
+0.16478465084577176,0.0628579351428773
+-0.2658383106184654,-0.2394500500147864
+0.36967113075671126,-0.25207799326041397
+0.5006657183631231,-0.7627976787909811
+1.1123132970672684,-0.5309452186622989
+-0.4507993434407451,0.21678775795559768
+0.9043315961177707,0.619832815927315
+1.2297427862617671,-1.2553200336451473
+-0.03304730941889358,-0.4984936449047772
+1.9147995660383499,-2.762758599878806
+0.04320679168897483,0.492623218961124
+0.6604804298413306,-0.28563257583808954
+-0.33864938506155695,0.37524370042115185
+1.0382231286324175,-1.1400600383793194
+0.1528070136909545,-0.1261800793297681
+0.6186445718397343,-0.43949067072610315
+0.6737708921701934,-0.2574836277986384
+0.37495706782874627,-0.09069432010047207
+1.0597807417530685,-1.0765084280073052
+0.7162568047126614,-0.5291138329332783
+-0.7154005284399629,-0.0769458144141601
+-0.42484015565136835,1.328380063505369
+0.05711713410195329,1.4134036681564879
+0.4271726716145866,-0.17085318841097014
+0.9906566505521094,-0.8397269063643151
+1.156867413486057,-0.7554288501612183
+0.6775195363814697,1.6528500136591457
+1.000828131392995,0.8583213686836387
+0.025729833680048886,1.986906883811663
+-0.4487496990204597,0.02465798165745986
+0.5667209301243944,-0.1669409353859797
+0.01728541357638025,0.08764093825298863
+0.9641255138846524,-1.3855562407987008
+0.5006657183631231,-0.7627976787909811
+0.8909233466135804,-0.16988207196565086
+-0.4507993434407451,0.21678775795559768
+0.9043315961177707,0.619832815927315
+1.2297427862617671,-1.2553200336451473
+-0.38704822639093067,0.9510343664613023
+1.9147995660383499,-2.762758599878806
+1.0464544617877756,-1.3220376376136045
+-0.6544395767851875,1.375978606473412
+-0.33864938506155695,0.37524370042115185
+1.0382231286324175,-1.1400600383793194
+0.14303740183398067,-0.4791548458334477
+0.002740326051366433,2.443715661817333
+-0.8437804257455088,0.6261620884116941
+0.8808338717843772,-1.0409997686483394
+1.0597807417530685,-1.0765084280073052
+0.7162568047126614,-0.5291138329332783
+-0.7154005284399629,-0.0769458144141601
+-0.42484015565136835,1.328380063505369
+0.05711713410195329,1.4134036681564879
+0.4271726716145866,-0.17085318841097014
+0.9906566505521094,-0.8397269063643151
+1.156867413486057,-0.7554288501612183
+0.6775195363814697,1.6528500136591457
+1.000828131392995,0.8583213686836387
+0.025729833680048886,1.986906883811663
+-0.8703710358579517,0.6132249171011721
+0.5667209301243944,-0.1669409353859797
+1.5174906480278803,-2.084834269344597
+0.9641255138846524,-1.3855562407987008
+-0.4855807283451256,-0.4262357780369066
+-0.36583916353717577,1.953738359619571
+1.6202529967585508,-2.4964561559837644
+0.9043315961177707,0.619832815927315
+1.2297427862617671,-1.2553200336451473
+0.3258779287788571,0.17921351076126307
+1.9147995660383499,-2.762758599878806
+-0.519598316467292,0.6133553198696723
+-0.6544395767851875,1.375978606473412
+-0.5016050973095287,1.2250422825656146
+0.9157814229155525,-0.5549374572588
+0.14303740183398067,-0.4791548458334477
+0.002740326051366433,2.443715661817333
+-0.4061283822382279,2.013524711862506
+-0.09151296249097463,0.8409402502734983
+-0.8106373281768953,0.7783967036209434
+0.7162568047126614,-0.5291138329332783
+0.2414412621848795,-0.2417763208790552
+0.9599782846511168,0.4645990859524376
+0.32303960855304104,-0.044542391142212756
+0.4271726716145866,-0.17085318841097014
+0.9906566505521094,-0.8397269063643151
+1.156867413486057,-0.7554288501612183
+0.6775195363814697,1.6528500136591457
+1.000828131392995,0.8583213686836387
+0.025729833680048886,1.986906883811663
+-0.1650169270904465,1.4685434064057254
+-0.7041546287196268,0.40205019535475917
+1.5174906480278803,-2.084834269344597
+-0.27470203251675784,0.16492108497069458
+-0.4855807283451256,-0.4262357780369066
+-0.36583916353717577,1.953738359619571
+1.6202529967585508,-2.4964561559837644
+-0.9615098875144276,-0.14851471102212122
+1.2297427862617671,-1.2553200336451473
+0.3258779287788571,0.17921351076126307
+1.9147995660383499,-2.762758599878806
+0.9876708945177166,-0.9368742457262542
+-0.6544395767851875,1.375978606473412
+-0.5016050973095287,1.2250422825656146
+0.10301059811077745,-0.28996151751956717
+-0.3933776220017008,0.4953525487103607
+0.002740326051366433,2.443715661817333
+-0.4061283822382279,2.013524711862506
+0.008141419305818576,1.5596598647305093
+-0.7107858196387026,0.8713236431227518
+0.7162568047126614,-0.5291138329332783
+-0.3848156013771457,1.5886319052406077
+0.9599782846511168,0.4645990859524376
+1.0854946720265681,-0.5720959072047427
+0.4271726716145866,-0.17085318841097014
+0.9906566505521094,-0.8397269063643151
+-0.06344646898457024,2.0983808651856393
+0.6775195363814697,1.6528500136591457
+1.002769080623611,-0.30963035505160164
+0.025729833680048886,1.986906883811663
+-0.1650169270904465,1.4685434064057254
+0.5857938042322941,-0.10758098771858851
+1.5174906480278803,-2.084834269344597
+-0.27470203251675784,0.16492108497069458
+-0.6575162135760437,-0.3472860416000374
+-0.8077887712020317,1.023210819564808
+-0.5152567540196769,1.6929380309610478
+-0.9615098875144276,-0.14851471102212122
+1.2297427862617671,-1.2553200336451473
+0.05596119618648687,0.0775490074787033
+1.9147995660383499,-2.762758599878806
+1.4927210441981626,-1.768244285242506
+1.2584421178523033,-1.0872102958572918
+-0.5016050973095287,1.2250422825656146
+0.15299776257006192,0.119799673584015
+-0.3933776220017008,0.4953525487103607
+0.002740326051366433,2.443715661817333
+-0.4061283822382279,2.013524711862506
+0.008141419305818576,1.5596598647305093
+-0.7107858196387026,0.8713236431227518
+0.7162568047126614,-0.5291138329332783
+-0.3848156013771457,1.5886319052406077
+0.9599782846511168,0.4645990859524376
+1.0854946720265681,-0.5720959072047427
+0.4271726716145866,-0.17085318841097014
+0.8788589810214865,-0.02764112506104066
+-0.06344646898457024,2.0983808651856393
+0.6775195363814697,1.6528500136591457
+1.002769080623611,-0.30963035505160164
+0.025729833680048886,1.986906883811663
+1.8140461881591299,-1.7526669372999042
+0.5857938042322941,-0.10758098771858851
+0.7293703911636092,-0.6444825584826387
+-0.27470203251675784,0.16492108497069458
+-0.6575162135760437,-0.3472860416000374
+-0.8077887712020317,1.023210819564808
+-0.5152567540196769,1.6929380309610478
+-0.01856447661392613,1.5305488273808332
+1.2297427862617671,-1.2553200336451473
+0.6956069172015087,0.03603451188272011
+1.9147995660383499,-2.762758599878806
+1.5668312459305462,-1.0799696997537187
+1.027868761696139,-0.5301500504067809
+-0.5016050973095287,1.2250422825656146
+0.40319158356270013,-0.3554783310073605
+-0.3933776220017008,0.4953525487103607
+0.8484352804465844,0.21022679779198794
+-0.4061283822382279,2.013524711862506
+1.5947206915535312,-0.4679230561891538
+0.6204679681113145,-0.975768308133941
+0.7162568047126614,-0.5291138329332783
+-0.3848156013771457,1.5886319052406077
+0.6728596390822198,-1.0434449270765005
+1.0854946720265681,-0.5720959072047427
+0.4271726716145866,-0.17085318841097014
+-0.4099515930683826,2.0130499002138205
+-0.43624808890596545,1.1890236341129723
+0.6775195363814697,1.6528500136591457
+-0.9919627101979198,0.30825432220464843
+0.4941003821905792,-0.6241898646057922
+1.8140461881591299,-1.7526669372999042
+0.5857938042322941,-0.10758098771858851
+-0.08480034565681786,1.5678468138937636
+0.4424976315828224,0.13030086516981473
+-0.6575162135760437,-0.3472860416000374
+0.04507400776669118,-0.19743619738968682
+-0.5152567540196769,1.6929380309610478
+0.3210683779236455,0.11187771544450453
+0.9387264493246369,-0.31955793608112965
+-0.7160574906891843,1.722894955581744
+-0.45442344005206714,0.6303795536882477
+1.5668312459305462,-1.0799696997537187
+-0.027534488380019484,2.5792987567379533
+-0.5016050973095287,1.2250422825656146
+0.40319158356270013,-0.3554783310073605
+-0.3933776220017008,0.4953525487103607
+1.8738833507758808,-1.8064085343083232
+-0.4061283822382279,2.013524711862506
+1.5947206915535312,-0.4679230561891538
+0.8798106933816023,-0.3245027566314128
+0.9716211270978559,-0.28214693067023244
+-0.3848156013771457,1.5886319052406077
+0.6819730621323594,0.12460401528147103
+1.0105398904480882,-1.1976165092918623
+-0.76803891159292,1.0747737345597328
+-0.4099515930683826,2.0130499002138205
+-0.43624808890596545,1.1890236341129723
+0.6775195363814697,1.6528500136591457
+-0.9919627101979198,0.30825432220464843
+-0.03201019133431776,1.9728575005375217
+1.8140461881591299,-1.7526669372999042
+0.3163963342036775,0.24916905291721364
+1.4696837883897753,-1.905178104668282
+0.6807074505054672,-0.16652173045357216
+-0.3597424284110574,-0.45063111982524184
+-0.7442497524498444,0.7207767696228563
+-0.5152567540196769,1.6929380309610478
+0.3210683779236455,0.11187771544450453
+0.9387264493246369,-0.31955793608112965
+0.8106005754333956,-0.8322975459872366
+1.056360889568078,-0.6667797595860192
+0.8770810956161452,0.060597303220150556
+-0.027534488380019484,2.5792987567379533
+0.4840731795253029,0.7475421095700769
+0.40319158356270013,-0.3554783310073605
+-0.3933776220017008,0.4953525487103607
+1.8738833507758808,-1.8064085343083232
+-0.4061283822382279,2.013524711862506
+0.5235730556029803,0.5919701187427571
+-0.3420277221313962,0.4825433882528281
+0.43211266270581516,-0.5714570968152328
+-0.3848156013771457,1.5886319052406077
+0.6864107861353952,-0.42018014889556454
+1.0105398904480882,-1.1976165092918623
+1.4600047214561096,-2.1877760703792584
+-0.4099515930683826,2.0130499002138205
+-0.43624808890596545,1.1890236341129723
+-0.5967414872820569,0.015156157720752628
+-0.9919627101979198,0.30825432220464843
+-0.03201019133431776,1.9728575005375217
+-0.6692668762149655,1.7317351429195276
+1.221382959847122,0.7435723788584616
+1.602476136898845,-1.295860141250381
+0.7183676838791724,-0.06711737822102049
+-0.3597424284110574,-0.45063111982524184
+-0.7442497524498444,0.7207767696228563
+0.808476656192933,0.19305389469762277
+0.3210683779236455,0.11187771544450453
+0.1248412940604775,0.25280368312384227
+0.8106005754333956,-0.8322975459872366
+-0.10604725967043424,0.1613669391457181
+1.3328138548248012,-1.5299853557482173
+0.9418276622871788,-1.4357043254486213
+0.9723357689192441,-0.6609138258227023
+-0.0009016479361981244,0.41672689075981456
+-0.3933776220017008,0.4953525487103607
+1.8738833507758808,-1.8064085343083232
+-0.4061283822382279,2.013524711862506
+0.5001918099066531,-0.8279018145019856
+-0.3420277221313962,0.4825433882528281
+0.43211266270581516,-0.5714570968152328
+-0.3848156013771457,1.5886319052406077
+0.8118426885885268,0.8132173843171523
+0.03586734855975701,-0.12892314645316277
+1.4600047214561096,-2.1877760703792584
+-0.4099515930683826,2.0130499002138205
+-0.43624808890596545,1.1890236341129723
+-0.5967414872820569,0.015156157720752628
+0.061294615179108614,0.21341048926703016
+-0.03201019133431776,1.9728575005375217
+0.8811508371647627,-0.9946137998500504
+1.221382959847122,0.7435723788584616
+1.602476136898845,-1.295860141250381
+-0.29731429953632615,-0.07854294977443549
+1.3799779338142721,-1.0944984039931032
+1.6901328219822114,-0.7394623236677146
+0.48982536183007763,0.5702226827915431
+0.852002777312419,-0.748497252973731
+0.1248412940604775,0.25280368312384227
+-0.4234784873860531,0.05523598137683439
+-0.10604725967043424,0.1613669391457181
+0.31117116873224493,0.6947688727797763
+0.2224078413378842,-0.05252808510185333
+0.9723357689192441,-0.6609138258227023
+1.4129824937714837,-1.0578741218251442
+-0.3933776220017008,0.4953525487103607
+1.4206516235195399,-1.271822600207205
+1.3320111354044222,-0.8530479264906132
+0.5001918099066531,-0.8279018145019856
+-0.4425450966876885,-0.028391931605986083
+-0.5008288254349412,0.7006240008539795
+-0.3848156013771457,1.5886319052406077
+-0.6060292071167533,0.9944834056128344
+-0.20728254864437906,1.6742727833108102
+1.4600047214561096,-2.1877760703792584
+0.1117936530533463,0.9345673529177876
+-0.43624808890596545,1.1890236341129723
+0.8107371987958619,-0.4549324866320805
+0.061294615179108614,0.21341048926703016
+-0.6397316748889895,0.6913300539506448
+0.8811508371647627,-0.9946137998500504
+1.221382959847122,0.7435723788584616
+0.8582659710160577,0.10195141415773967
+-0.29731429953632615,-0.07854294977443549
+1.6058530750716025,-1.277914075498575
+0.6354977717461221,0.41624741586270453
+0.48982536183007763,0.5702226827915431
+0.852002777312419,-0.748497252973731
+0.1248412940604775,0.25280368312384227
+-0.4234784873860531,0.05523598137683439
+0.8869662766923759,-0.84168624757332
+0.5391281263441496,-0.626650664371439
+0.2224078413378842,-0.05252808510185333
+0.5135114155644002,-0.14643000602201828
+1.4129824937714837,-1.0578741218251442
+0.03859807807159629,-0.33805143087811157
+0.7641528800625704,-0.5020380470120454
+1.3320111354044222,-0.8530479264906132
+0.5335942312188809,-0.3221429442878915
+-0.4425450966876885,-0.028391931605986083
+0.9884763956462119,-1.0200360173731713
+-0.3848156013771457,1.5886319052406077
+1.117762281709411,-1.3431860384510108
+-0.20728254864437906,1.6742727833108102
+1.4600047214561096,-2.1877760703792584
+0.9129770148581722,-0.7252183138396474
+-0.43624808890596545,1.1890236341129723
+0.20352268446609917,-0.06192766600870225
+1.441627600860417,-1.0860086120009524
+0.10371507682831782,-0.12493993650317559
+-0.5355155898783965,1.1764162559027218
+1.221382959847122,0.7435723788584616
+0.8582659710160577,0.10195141415773967
+0.837980891277991,-0.15887228595230907
+1.1968256002105213,-1.1694659700523604
+0.6354977717461221,0.41624741586270453
+0.48982536183007763,0.5702226827915431
+0.852002777312419,-0.748497252973731
+0.1248412940604775,0.25280368312384227
+-0.4234784873860531,0.05523598137683439
+-0.6471149541004146,1.069706406246684
+0.3361835118885895,0.28050207597800786
+-0.5729839160292524,0.6791970230572326
+0.1562147247841717,0.23913695848674618
+0.43798692500477054,-0.10993118839690497
+0.03859807807159629,-0.33805143087811157
+-0.38422660329315284,0.2406215018049958
+1.3320111354044222,-0.8530479264906132
+0.5335942312188809,-0.3221429442878915
+-0.4425450966876885,-0.028391931605986083
+0.9884763956462119,-1.0200360173731713
+-0.3848156013771457,1.5886319052406077
+1.258915932322819,-1.428464182172747
+-0.20728254864437906,1.6742727833108102
+1.3581057626934518,-0.17206784214385562
+0.9129770148581722,-0.7252183138396474
+-0.30169193991546506,0.8080931775288152
+1.16392298033275,-0.976910827477879
+-0.6251087465303639,0.44602842392517816
+0.10371507682831782,-0.12493993650317559
+-0.5355155898783965,1.1764162559027218
+-0.7147538391685275,0.9036763373861405
+1.4773789973367575,-1.7507131320116847
+0.837980891277991,-0.15887228595230907
+1.1968256002105213,-1.1694659700523604
+0.17455212923206148,0.13666644348861917
+-0.08006856545755094,0.2197850741636615
+0.852002777312419,-0.748497252973731
+0.8000084854306724,-0.7005766359201666
+-0.4234784873860531,0.05523598137683439
+-0.6471149541004146,1.069706406246684
+0.7132171640925727,1.435558503857359
+-0.6054564920517859,0.9045876714347423
+0.18797991777621637,1.244633929231178
+1.1134315514208915,-1.2006030440174924
+0.03859807807159629,-0.33805143087811157
+-0.2583469313505161,2.034270950456886
+1.3320111354044222,-0.8530479264906132
+-0.4231520760380695,0.4729565184250412
+-0.4425450966876885,-0.028391931605986083
+0.6890401058664306,-0.8588048202065242
+0.8639015786596359,-0.7737322263642126
+1.258915932322819,-1.428464182172747
+1.346284102648693,-0.8110713696117473
+1.3581057626934518,-0.17206784214385562
+0.6341449448036962,1.1115272062253088
+-0.30169193991546506,0.8080931775288152
+-0.6013699771752394,-0.5899363099579062
+-0.6251087465303639,0.44602842392517816
+0.10371507682831782,-0.12493993650317559
+-0.5355155898783965,1.1764162559027218
+1.156876600693826,-0.6775208641761817
+1.4773789973367575,-1.7507131320116847
+0.5204135321126102,2.1504508005301943
+-0.6499692894715112,1.6680875616893673
+0.7768398636852498,-0.3762417662732849
+1.0532388681842346,-1.3757870859395753
+-0.2844018533944036,-0.27638288382136117
+0.8121376568303514,1.4766060682196613
+-0.4234784873860531,0.05523598137683439
+-0.09073225806853913,1.2774485708910706
+0.7132171640925727,1.435558503857359
+-0.6054564920517859,0.9045876714347423
+0.18797991777621637,1.244633929231178
+1.1134315514208915,-1.2006030440174924
+-0.16454154161654194,0.07511269339737081
+-0.2583469313505161,2.034270950456886
+1.3320111354044222,-0.8530479264906132
+-0.3015831036096229,1.839693752197661
+-0.4425450966876885,-0.028391931605986083
+-0.2932045748497669,1.4135369311789907
+0.8639015786596359,-0.7737322263642126
+0.019739021194706843,0.8666257444780048
+1.346284102648693,-0.8110713696117473
+1.3581057626934518,-0.17206784214385562
+0.5584051784311156,0.7255166930233397
+0.572845049213925,-0.25710945993512635
+-0.20892054103316182,0.8316273708576932
+-0.6251087465303639,0.44602842392517816
+0.10371507682831782,-0.12493993650317559
+1.4500265655278266,-1.9055601044463448
+1.156876600693826,-0.6775208641761817
+1.4773789973367575,-1.7507131320116847
+0.19497095622719152,0.026360452283654023
+-0.6966098455025723,1.0876786927431232
+0.7768398636852498,-0.3762417662732849
+-0.7478333575038474,1.3266588954151644
+0.8410707089475871,1.1692913765568334
+0.8121376568303514,1.4766060682196613
+-0.4234784873860531,0.05523598137683439
+-0.09073225806853913,1.2774485708910706
+0.7132171640925727,1.435558503857359
+-0.6054564920517859,0.9045876714347423
+0.6953730005076475,1.0203880307660413
+0.3151516948609374,1.2824756494657221
+-0.16454154161654194,0.07511269339737081
+0.25100254364172603,2.0296250530735196
+0.038349345213420954,1.6547833598215935
+0.18033698844187174,0.670983828430556
+-0.4425450966876885,-0.028391931605986083
+0.5770516076504413,-0.36453912195957305
+0.8639015786596359,-0.7737322263642126
+0.25360879651909823,-0.025219245697709516
+1.346284102648693,-0.8110713696117473
+1.3581057626934518,-0.17206784214385562
+0.5584051784311156,0.7255166930233397
+0.572845049213925,-0.25710945993512635
+-0.04082616877295642,-0.1247986132426051
+-0.08829748567607787,1.1141252496744853
+-0.8711058959603248,0.496468464696853
+1.985104454465197,-2.501271013091576
+1.156876600693826,-0.6775208641761817
+1.4773789973367575,-1.7507131320116847
+-0.10676105850695866,0.26833660301684814
+-0.08909376958910797,0.01750919038243482
+-0.4086651026416649,1.132566680758726
+1.0623758387753839,0.3800872612844546
+-0.40389984278842006,0.8747636088415288
+0.8121376568303514,1.4766060682196613
+-0.4234784873860531,0.05523598137683439
+-0.4611481691267813,0.0004825414590426541
+0.2813411995879867,-0.14428306175449834
+-0.6054564920517859,0.9045876714347423
+1.3158300156460156,-1.3749104982192106
+0.3151516948609374,1.2824756494657221
+0.7671022227737131,-0.28253722581775265
+0.25100254364172603,2.0296250530735196
+0.038349345213420954,1.6547833598215935
+1.0236639591474535,0.6351182286894461
+1.1980036584249962,-0.160855914918704
+0.5770516076504413,-0.36453912195957305
+-0.5659397781853654,-0.34142355290253024
+0.3828934054578351,0.12843453589090176
+1.346284102648693,-0.8110713696117473
+1.0446563040334884,-0.5458267954454367
+-0.2816896026314667,1.8671842783535122
+1.5815898193408215,-1.3508110770649058
+0.17151027403852456,2.1654618021731022
+-0.08829748567607787,1.1141252496744853
+-0.8711058959603248,0.496468464696853
+-0.014981354901024257,1.9963569310259284
+0.5692691711869307,0.8017935493482191
+1.4773789973367575,-1.7507131320116847
+-0.4967854410549867,0.043831924478202056
+-0.08909376958910797,0.01750919038243482
+-0.4086651026416649,1.132566680758726
+-0.36961363806353165,-0.004562881664649243
+1.1685351277859721,0.5027594036682602
+0.8121376568303514,1.4766060682196613
+-0.4234784873860531,0.05523598137683439
+-0.4611481691267813,0.0004825414590426541
+0.2813411995879867,-0.14428306175449834
+-0.6054564920517859,0.9045876714347423
+1.3158300156460156,-1.3749104982192106
+-0.5163123200153918,0.35610107986063066
+0.7671022227737131,-0.28253722581775265
+0.25100254364172603,2.0296250530735196
+1.483863937227767,-1.2765185090973046
+1.0236639591474535,0.6351182286894461
+1.1980036584249962,-0.160855914918704
+0.5770516076504413,-0.36453912195957305
+-0.5659397781853654,-0.34142355290253024
+-0.14092159839622465,0.18704807317297417
+1.346284102648693,-0.8110713696117473
+1.3334431937134852,-0.464642253400774
+-0.2816896026314667,1.8671842783535122
+1.3252783665142338,-1.5108568614245494
+0.17151027403852456,2.1654618021731022
+-0.9727290051116072,-0.38779460833212914
+1.6955332568616053,-1.9765194645280375
+-0.014981354901024257,1.9963569310259284
+0.5692691711869307,0.8017935493482191
+1.4773789973367575,-1.7507131320116847
+-0.4967854410549867,0.043831924478202056
+-0.08909376958910797,0.01750919038243482
+-0.4086651026416649,1.132566680758726
+-0.9329472788050229,-0.1706329099931863
+1.1685351277859721,0.5027594036682602
+0.8121376568303514,1.4766060682196613
+-0.4234784873860531,0.05523598137683439
+1.3379145059406796,-0.7321041242428288
+0.2813411995879867,-0.14428306175449834
+-0.6054564920517859,0.9045876714347423
+1.3158300156460156,-1.3749104982192106
+-0.5163123200153918,0.35610107986063066
+0.06549238930398593,1.9866280514698884
+0.25100254364172603,2.0296250530735196
+1.483863937227767,-1.2765185090973046
+1.0236639591474535,0.6351182286894461
+1.1980036584249962,-0.160855914918704
+0.5770516076504413,-0.36453912195957305
+0.2985474486198274,0.6084072512047896
+-0.45460280154396804,1.9990717989377074
+1.3454304440949731,-1.8908306185427255
+0.1975792666460321,0.023044233104634326
+-0.41279949760325263,-0.37832579830583735
+1.3252783665142338,-1.5108568614245494
+-0.6137159123918148,1.565377561172856
+-0.9727290051116072,-0.38779460833212914
+1.2813589621759922,-1.8007669287922465
+-0.014981354901024257,1.9963569310259284
+0.5692691711869307,0.8017935493482191
+1.4773789973367575,-1.7507131320116847
+-0.33881196360395116,1.8430601642195483
+-0.08909376958910797,0.01750919038243482
+0.5978394394698106,-0.054545953150203046
+-0.9329472788050229,-0.1706329099931863
+1.1685351277859721,0.5027594036682602
+0.8121376568303514,1.4766060682196613
+-0.4234784873860531,0.05523598137683439
+0.17720076901756582,-0.08739789283367894
+-0.27858236442552486,0.1948175594262024
+-0.5152257778629157,0.12546624179305532
+0.9468289022241956,-0.9848413059466534
+-0.5163123200153918,0.35610107986063066
+0.06549238930398593,1.9866280514698884
+-0.19732885314129534,-0.09556082466526061
+-0.1457281079378005,0.7820795629426404
+0.29008759754216634,-0.6001105470705128
+1.2786288449920615,-0.6907369493898392
+0.5770516076504413,-0.36453912195957305
+1.2564785018346014,-0.3058795087913581
+-0.45460280154396804,1.9990717989377074
+0.5214216177794271,0.4576629097709777
+-0.7287059929594765,0.4254739350108019
+0.7250919931291162,-0.25030459765377755
+-0.4938742631295487,1.6853627084366947
+-0.6137159123918148,1.565377561172856
+-0.4148830854935964,1.032031752788209
+0.5236434872295637,1.0649040454712448
+-0.014981354901024257,1.9963569310259284
+1.0829630837242181,-1.169254633292987
+1.4773789973367575,-1.7507131320116847
+-0.33881196360395116,1.8430601642195483
+-0.08909376958910797,0.01750919038243482
+0.5978394394698106,-0.054545953150203046
+1.0074237076240276,-0.7044542380524415
+1.1685351277859721,0.5027594036682602
+0.8121376568303514,1.4766060682196613
+-0.4234784873860531,0.05523598137683439
+0.17720076901756582,-0.08739789283367894
+0.7665291933986382,-1.0390365343985335
+-0.5152257778629157,0.12546624179305532
+-0.5319354526895067,0.05133712179578981
+-0.5163123200153918,0.35610107986063066
+0.06549238930398593,1.9866280514698884
+-0.19732885314129534,-0.09556082466526061
+0.7618072785844995,0.24415490969506115
+1.4095209887572357,-0.5543037031682427
+1.2786288449920615,-0.6907369493898392
+0.5770516076504413,-0.36453912195957305
+1.2564785018346014,-0.3058795087913581
+0.8302767902411458,1.1124548265326384
+0.5214216177794271,0.4576629097709777
+-0.8420322376373869,-0.38990758521714947
+0.7250919931291162,-0.25030459765377755
+-0.4938742631295487,1.6853627084366947
+-0.6137159123918148,1.565377561172856
+-0.8891006668087443,0.1234721712300248
+0.5236434872295637,1.0649040454712448
+-0.014981354901024257,1.9963569310259284
+1.0829630837242181,-1.169254633292987
+1.4773789973367575,-1.7507131320116847
+-0.33881196360395116,1.8430601642195483
+-0.08909376958910797,0.01750919038243482
+-0.08589563760703722,1.5498857718720702
+1.0074237076240276,-0.7044542380524415
+1.1685351277859721,0.5027594036682602
+0.8747716694712798,0.5278587714103254
+-0.4234784873860531,0.05523598137683439
+0.43176352009571206,-0.18083140894587096
+0.7665291933986382,-1.0390365343985335
+-0.5152257778629157,0.12546624179305532
+-0.41398647048062004,-0.1354869230638116
+-0.38127457599567527,0.9690936580442033
+0.06549238930398593,1.9866280514698884
+-0.19732885314129534,-0.09556082466526061
+0.8087035919288161,-0.35774282035779426
+0.5264087100924477,-0.3392814955277549
+1.2786288449920615,-0.6907369493898392
+-0.3623552810020975,0.4282646852184283
+1.2564785018346014,-0.3058795087913581
+0.8302767902411458,1.1124548265326384
+-0.011241930869600777,-0.23089597703714443
+-0.8420322376373869,-0.38990758521714947
+0.9211518316015676,-0.8171705624287453
+-0.4938742631295487,1.6853627084366947
+-0.6137159123918148,1.565377561172856
+-0.8891006668087443,0.1234721712300248
+0.5236434872295637,1.0649040454712448
+-0.014981354901024257,1.9963569310259284
+1.0829630837242181,-1.169254633292987
+1.4773789973367575,-1.7507131320116847
+-0.33881196360395116,1.8430601642195483
+-0.08909376958910797,0.01750919038243482
+-0.08589563760703722,1.5498857718720702
+0.6307267818754636,0.90400633506001
+1.1685351277859721,0.5027594036682602
+0.8747716694712798,0.5278587714103254
+-0.4234784873860531,0.05523598137683439
+0.43176352009571206,-0.18083140894587096
+0.7665291933986382,-1.0390365343985335
+-0.5152257778629157,0.12546624179305532
+1.0903486072105837,-0.5157662555083653
+-0.42775038727896836,-0.019286137853632646
+0.06549238930398593,1.9866280514698884
+-0.19732885314129534,-0.09556082466526061
+-0.45027695757508396,1.2745247521082639
+0.7597961988832689,-1.0502104458484278
+1.2786288449920615,-0.6907369493898392
+-0.039832591999700157,-0.29416357668844606
+1.2564785018346014,-0.3058795087913581
+0.8302767902411458,1.1124548265326384
+1.4196854072666447,-0.24787398051988185
+-0.8420322376373869,-0.38990758521714947
+0.9211518316015676,-0.8171705624287453
+-0.4938742631295487,1.6853627084366947
+-0.6137159123918148,1.565377561172856
+-0.8891006668087443,0.1234721712300248
+0.21643700303620728,-0.4877991644437148
+-0.014981354901024257,1.9963569310259284
+1.0829630837242181,-1.169254633292987
+1.4773789973367575,-1.7507131320116847
+-0.33881196360395116,1.8430601642195483
+-0.08909376958910797,0.01750919038243482
+0.7886603498126182,0.6392359657213318
+-0.3872776614940838,0.6959672994143913
+1.1685351277859721,0.5027594036682602
+0.8747716694712798,0.5278587714103254
+-0.4234784873860531,0.05523598137683439
+-0.5972243113715976,1.4033709091805386
+0.5480674533191121,-0.22890137168755476
+0.25864971911653234,0.21261524313672558
+1.0903486072105837,-0.5157662555083653
+-0.42775038727896836,-0.019286137853632646
+0.06549238930398593,1.9866280514698884
+1.1178470509751985,-1.8479605390477667
+-0.45027695757508396,1.2745247521082639
+0.9162650958563293,-0.729722123706943
+0.03634603701450499,2.3128211783426766
+-0.221293460625758,0.9752621612121726
+1.0098941739239689,-0.4160953417421236
+0.8302767902411458,1.1124548265326384
+0.14972063369152674,2.404065601156384
+-0.32307158466533664,1.7519869380108735
+1.1065317334289009,0.4461203486741926
+-0.4018830590236899,1.5946881118481921
+0.6633372223113527,-0.19831990097570185
+-0.8891006668087443,0.1234721712300248
+0.21643700303620728,-0.4877991644437148
+0.4233453679490111,1.4878104801242549
+1.0829630837242181,-1.169254633292987
+1.4773789973367575,-1.7507131320116847
+-0.33881196360395116,1.8430601642195483
+0.44338365042956673,-0.20186508546570092
+0.2816254467347983,-0.4523055538310447
+0.23444321073377128,0.9567082196898521
+1.1685351277859721,0.5027594036682602
+0.09270783641200694,1.5061894015491843
+-0.6446425078985574,-0.11894265184638397
+-0.5972243113715976,1.4033709091805386
+1.2790683104006024,-1.6424414499658146
+-0.4203244982078127,0.016476422755099668
+1.0903486072105837,-0.5157662555083653
+1.4879288608253272,-1.6469531440509966
+0.06549238930398593,1.9866280514698884
+-0.3276430661121169,2.4336783545381664
+-0.45027695757508396,1.2745247521082639
+0.9162650958563293,-0.729722123706943
+0.03634603701450499,2.3128211783426766
+-0.221293460625758,0.9752621612121726
+1.0098941739239689,-0.4160953417421236
+0.8302767902411458,1.1124548265326384
+0.14972063369152674,2.404065601156384
+1.4041819906011024,-0.22180892372875438
+-0.184661625533173,-0.15735704131720196
+-0.4018830590236899,1.5946881118481921
+0.3432094788144334,-0.5685993103957903
+-0.8891006668087443,0.1234721712300248
+0.2680484985816183,1.3093205366336376
+-0.4184083627354045,1.2417926672467534
+1.0829630837242181,-1.169254633292987
+1.4773789973367575,-1.7507131320116847
+-0.33881196360395116,1.8430601642195483
+0.44338365042956673,-0.20186508546570092
+-0.018456752768006235,-0.0839803435114456
+0.3486978847948775,2.2044623679878894
+1.6405168078574353,-1.5653874582496892
+0.09270783641200694,1.5061894015491843
+-0.6446425078985574,-0.11894265184638397
+-0.5972243113715976,1.4033709091805386
+1.2790683104006024,-1.6424414499658146
+-0.4203244982078127,0.016476422755099668
+0.8255658892108602,-0.9431177126136984
+0.47835815305041574,1.6457003893578457
+0.06549238930398593,1.9866280514698884
+-0.3276430661121169,2.4336783545381664
+-0.45027695757508396,1.2745247521082639
+0.9162650958563293,-0.729722123706943
+0.03634603701450499,2.3128211783426766
+-0.221293460625758,0.9752621612121726
+1.0098941739239689,-0.4160953417421236
+0.8302767902411458,1.1124548265326384
+0.14972063369152674,2.404065601156384
+-0.12624614796881398,-0.25267491831569155
+-0.49787453010662097,1.2478379675488271
+0.7923631525712828,1.188816781137772
+0.3432094788144334,-0.5685993103957903
+-0.8891006668087443,0.1234721712300248
+0.3495735105387548,0.4796153833958837
+-0.4402941766746128,0.18031319217430064
+0.07780022688383487,-0.3280618702278184
+1.4773789973367575,-1.7507131320116847
+-0.33881196360395116,1.8430601642195483
+-0.4348379242465097,-0.1674668972810589
+-0.018456752768006235,-0.0839803435114456
+0.7745366858227989,1.1504211296817608
+0.4597482599091104,0.3907352478015653
+1.634144229182924,-1.2459933708278708
+-0.6446425078985574,-0.11894265184638397
+-0.5972243113715976,1.4033709091805386
+0.442617106933708,-0.408531376544935
+0.549901426984402,-1.0400826639970968
+0.8255658892108602,-0.9431177126136984
+0.47835815305041574,1.6457003893578457
+0.9224632829223007,-0.38583586749595844
+0.021669230870766484,1.415627943517534
+-0.45027695757508396,1.2745247521082639
+0.9162650958563293,-0.729722123706943
+-0.5436737929095293,1.5465846492549418
+0.5792411287595365,1.4714789909362882
+-0.2685093074485986,1.126070526259222
+0.8302767902411458,1.1124548265326384
+0.152734328060951,1.2540614737427376
+-0.12624614796881398,-0.25267491831569155
+-0.49787453010662097,1.2478379675488271
+0.7923631525712828,1.188816781137772
+-0.10316785646604199,0.7210974927498275
+1.2328062856206288,-0.8920387723188867
+0.5723454331976623,1.2975783056003227
+-0.4402941766746128,0.18031319217430064
+1.0497011253271011,-0.6032912013296313
+1.4773789973367575,-1.7507131320116847
+-0.33881196360395116,1.8430601642195483
+0.16694592582993645,1.9526280313449909
+0.7077618232822855,0.945959552972164
+-0.4259864675121209,0.5344411611607494
+0.011572870116693446,1.3855023891095293
+1.634144229182924,-1.2459933708278708
+-0.6446425078985574,-0.11894265184638397
+0.7670556910262364,1.2967110300268676
+0.442617106933708,-0.408531376544935
+1.0891849184004099,-0.5909034879483545
+0.8255658892108602,-0.9431177126136984
+0.9757591549624565,-0.8932835543568913
+0.9224632829223007,-0.38583586749595844
+-0.41458126125359285,1.8077438620378088
+-0.7700659401116932,0.7689698633014473
+1.4869705376585127,-0.9341046460360405
+-0.5436737929095293,1.5465846492549418
+-0.5406153397909916,0.5589039829794418
+0.6560215910280672,1.1161861155930606
+1.539968808572783,-0.679641688554663
+-0.08416168602236229,1.9138317835669578
+1.6713760759222254,-1.321378659112193
+-0.49787453010662097,1.2478379675488271
+0.7923631525712828,1.188816781137772
+1.031364267854212,-0.8172707525451732
+1.2328062856206288,-0.8920387723188867
+0.9554131031156817,-0.4984102977250574
+-0.4402941766746128,0.18031319217430064
+-0.1295454965889251,0.1665649571468064
+-0.5397279212210566,-0.03120549248675769
+-0.33881196360395116,1.8430601642195483
+1.0211411251842089,0.907215626376682
+1.5613695347040082,-0.5756237386617733
+-0.4259864675121209,0.5344411611607494
+1.0097662594489514,0.57022644055546
+1.247805542292508,-1.42748960138467
+-0.6446425078985574,-0.11894265184638397
+0.06350276731212168,1.3876885887224266
+0.442617106933708,-0.408531376544935
+-0.02156944430245831,1.2801596583069326
+0.6091858489031149,0.1165851720251706
+0.9757591549624565,-0.8932835543568913
+1.2081600940248318,-0.9548319615676734
+-0.41458126125359285,1.8077438620378088
+1.6586891302565516,-1.8692055807737933
+1.4869705376585127,-0.9341046460360405
+-0.5436737929095293,1.5465846492549418
+-0.5406153397909916,0.5589039829794418
+-0.3804165259776259,0.026344881579961177
+1.539968808572783,-0.679641688554663
+-0.6514324958356958,1.2520212916142146
+1.631492319367944,-1.0646333810371231
+-0.49787453010662097,1.2478379675488271
+0.7923631525712828,1.188816781137772
+-0.7184353533110683,0.7624865345731373
+0.6936055113686489,-0.10288433686969056
+-0.6278059504178588,0.17344894990685214
+0.4149482452079273,1.6655635699833884
+-0.1295454965889251,0.1665649571468064
+-0.5397279212210566,-0.03120549248675769
+-0.33881196360395116,1.8430601642195483
+1.0211411251842089,0.907215626376682
+0.5846846294749138,0.9690326881081432
+0.7649879838565078,-0.4454366489889159
+1.0097662594489514,0.57022644055546
+1.8059916691629596,-2.122514997807558
+-0.6446425078985574,-0.11894265184638397
+0.5600986098910951,-0.6032379269272979
+-0.11426554298242408,1.3606706167794247
+0.5325695517485947,1.74162929237756
+0.5713310587558826,0.23811253326501958
+0.9757591549624565,-0.8932835543568913
+0.9938572799767682,0.15709096389903388
+-0.41458126125359285,1.8077438620378088
+1.6586891302565516,-1.8692055807737933
+-0.5823085043829469,0.727523912085021
+1.6363460166473625,-1.119088118063324
+-0.5406153397909916,0.5589039829794418
+-0.3833300522597898,2.035989244566828
+-0.3507401688918213,0.3859679142336978
+1.308781131262219,0.2518808838753317
+-0.4471487319724215,0.13737890543069517
+-0.49787453010662097,1.2478379675488271
+0.7923631525712828,1.188816781137772
+-0.36640203271006183,1.6230632494091535
+0.6936055113686489,-0.10288433686969056
+-0.6278059504178588,0.17344894990685214
+0.4149482452079273,1.6655635699833884
+-0.1295454965889251,0.1665649571468064
+-0.5397279212210566,-0.03120549248675769
+0.042252163844870266,0.07503828613902248
+1.0211411251842089,0.907215626376682
+-0.23741917804056623,-0.22965394551260976
+0.21257356058152654,0.6530340155487566
+1.0097662594489514,0.57022644055546
+1.8059916691629596,-2.122514997807558
+-0.014423908619973669,0.02737185311135018
+1.3690638273464653,-0.39829650571377195
+0.6633180209243252,-0.6247355923523145
+0.5325695517485947,1.74162929237756
+1.4219242849362166,-1.1590105454195447
+0.29510966936384325,1.783567165567434
+0.9938572799767682,0.15709096389903388
+-0.41458126125359285,1.8077438620378088
+1.6586891302565516,-1.8692055807737933
+-0.5823085043829469,0.727523912085021
+1.6363460166473625,-1.119088118063324
+-0.5406153397909916,0.5589039829794418
+-0.3833300522597898,2.035989244566828
+-0.3507401688918213,0.3859679142336978
+1.308781131262219,0.2518808838753317
+-0.4713339056649571,1.3179925862524566
+-0.49787453010662097,1.2478379675488271
+0.5391052756440501,0.12708256447569174
+0.39540479373818055,1.5745948620742756
+0.6936055113686489,-0.10288433686969056
+-0.6278059504178588,0.17344894990685214
+0.4149482452079273,1.6655635699833884
+-0.1295454965889251,0.1665649571468064
+-0.5397279212210566,-0.03120549248675769
+1.0140224869275403,-1.6918265013144982
+-0.6313311994498845,1.1329958772819253
+-0.23741917804056623,-0.22965394551260976
+0.7654196652150721,0.10287804456670047
+-0.6825952293615454,1.5432872863701197
+1.34641529403345,-0.15559210730597778
+-0.014423908619973669,0.02737185311135018
+-0.07740073827510408,-0.11836317795617368
+0.6633180209243252,-0.6247355923523145
+0.5325695517485947,1.74162929237756
+1.4219242849362166,-1.1590105454195447
+0.29510966936384325,1.783567165567434
+0.9938572799767682,0.15709096389903388
+-0.41458126125359285,1.8077438620378088
+1.6329118324716299,-1.4159763395100136
+-0.22207587927437383,0.2925006978294923
+0.2582922055381912,1.9487485928456987
+1.4472413749140247,-1.6460027862414233
+-0.3833300522597898,2.035989244566828
+0.2942326124673982,-0.263313566759687
+1.308781131262219,0.2518808838753317
+-0.4713339056649571,1.3179925862524566
+1.1149896870089404,-1.001927971982859
+0.8331427520561713,0.1049808086984243
+-0.36955602177417146,1.0575648138842644
+-0.3526707446501983,0.21397992856591866
+1.4144698431682334,-0.21400031061616298
+-0.505749262093363,1.197182869598248
+-0.009299275443455657,2.1774999339955388
+-0.15711196676803332,1.7532129022588088
+-0.47663411651706356,2.2204183139266687
+-0.5895401616292414,0.7034966808035825
+-0.5081387873517726,2.090123663961557
+1.2596640277757791,-0.6464532196827167
+0.4947112002261408,1.771065330210633
+1.34641529403345,-0.15559210730597778
+-0.014423908619973669,0.02737185311135018
+1.117083820346399,-0.9428819755226504
+0.19969512542676726,1.103196363947181
+0.5325695517485947,1.74162929237756
+-0.16904661263027632,-0.05553707962274572
+0.29510966936384325,1.783567165567434
+-0.22950069877960044,1.9577646924353695
+-0.41458126125359285,1.8077438620378088
+-0.8975679797965223,0.7127787592172883
+-0.07418688232659848,1.3042480793403528
+0.2582922055381912,1.9487485928456987
+1.4472413749140247,-1.6460027862414233
+-0.3833300522597898,2.035989244566828
+-0.3762658905065542,-0.01592241387402417
+1.0855194557293952,-0.3915536449280105
+-0.4569847456930641,0.5356376194839798
+1.1149896870089404,-1.001927971982859
+-0.7652154289629551,0.888420665566132
+-0.36955602177417146,1.0575648138842644
+-0.3526707446501983,0.21397992856591866
+0.6802798499886513,-0.18897828073194506
+1.1190767578418632,0.3210198009555102
+-0.009299275443455657,2.1774999339955388
+-0.15711196676803332,1.7532129022588088
+1.3717179960903234,-1.3128852147067576
+-0.5895401616292414,0.7034966808035825
+-0.6227870309176998,0.6797571401365132
+0.5147053746470145,-0.8201901567040351
+-0.4298777214275912,0.12844971573941355
+-0.071173604785929,2.2098404897969943
+0.6535421423924113,-0.038515636143764076
+1.117083820346399,-0.9428819755226504
+-0.6791031004652861,1.339876031334133
+0.5325695517485947,1.74162929237756
+-0.16904661263027632,-0.05553707962274572
+0.29510966936384325,1.783567165567434
+1.3174468122737932,-1.2126125416576221
+-0.41458126125359285,1.8077438620378088
+1.7059650575558591,-1.75473810256733
+1.162908545060792,0.6841989713916842
+0.2582922055381912,1.9487485928456987
+1.4472413749140247,-1.6460027862414233
+-0.3833300522597898,2.035989244566828
+-0.3762658905065542,-0.01592241387402417
+1.0855194557293952,-0.3915536449280105
+-0.12188716276338754,1.749680942243715
+1.1149896870089404,-1.001927971982859
+-0.7652154289629551,0.888420665566132
+-0.36955602177417146,1.0575648138842644
+-0.3526707446501983,0.21397992856591866
+0.30092355954172234,0.6854713768431995
+1.1190767578418632,0.3210198009555102
+-0.009299275443455657,2.1774999339955388
+-0.15711196676803332,1.7532129022588088
+1.3717179960903234,-1.3128852147067576
+-0.13209548732027077,2.0247389191147116
+-0.6227870309176998,0.6797571401365132
+1.3051993165137965,-0.567277382300303
+-0.4298777214275912,0.12844971573941355
+0.9711532573564674,0.042860383047289785
+0.2532841348638982,-0.6155673481861135
+1.117083820346399,-0.9428819755226504
+0.15777778258383363,0.7931458115996436
+1.5442657044033605,-0.3798045976992352
+-0.16904661263027632,-0.05553707962274572
+0.29510966936384325,1.783567165567434
+0.04971295370006726,-0.4529065307451171
+-0.7477457269405093,0.20010342354662664
+0.5033790908838478,1.4916826934950373
+-0.16040720734240063,1.733562077997591
+0.2582922055381912,1.9487485928456987
+1.4472413749140247,-1.6460027862414233
+-0.7650345588950478,1.2056616832645988
+-0.3762658905065542,-0.01592241387402417
+-0.47934777515436505,1.6737396855271913
+0.5038368234265416,0.7521554889138207
+1.1149896870089404,-1.001927971982859
+-0.7652154289629551,0.888420665566132
+-0.36955602177417146,1.0575648138842644
+-0.6120054958465104,1.4170112291273047
+-0.5747856342183221,-0.30285223199130595
+1.1190767578418632,0.3210198009555102
+-0.878259591805787,0.3453498856332562
+0.39777983708829157,-0.6803627324468722
+1.3717179960903234,-1.3128852147067576
+1.1677093903929254,-0.5391266764279087
+0.14341527831730017,-0.14601781493730587
+1.207228127441181,-1.0989617418764248
+-0.276296500672476,0.20344710835511493
+-0.1388229221236655,-0.3866192331863084
+0.09703642526165521,0.549930106012956
+1.117083820346399,-0.9428819755226504
+0.15777778258383363,0.7931458115996436
+1.5442657044033605,-0.3798045976992352
+-0.24375476943578714,1.906045419821746
+0.29510966936384325,1.783567165567434
+0.04971295370006726,-0.4529065307451171
+-0.7477457269405093,0.20010342354662664
+0.5033790908838478,1.4916826934950373
+-0.16040720734240063,1.733562077997591
+0.2582922055381912,1.9487485928456987
+1.4472413749140247,-1.6460027862414233
+-0.7650345588950478,1.2056616832645988
+0.3306993090845134,0.40776013409267675
+-0.49653059932986654,0.6223056788048678
+0.6741081121162094,-0.8758080189646288
+1.1149896870089404,-1.001927971982859
+0.18794052611218975,-0.24708970730331759
+-0.36955602177417146,1.0575648138842644
+-0.6120054958465104,1.4170112291273047
+0.5925748989411252,1.3172490344909147
+1.1190767578418632,0.3210198009555102
+-0.878259591805787,0.3453498856332562
+0.43330769150887993,1.6503806191257973
+1.3717179960903234,-1.3128852147067576
+-0.19104295201748922,1.907936113779514
+0.33224727913154883,1.4269381365018399
+-0.4306686134580012,0.24241933382589972
+-0.276296500672476,0.20344710835511493
+-0.1388229221236655,-0.3866192331863084
+0.09703642526165521,0.549930106012956
+0.7786214655743374,-0.9286134950511931
+0.15777778258383363,0.7931458115996436
+0.9743030954913786,0.3875024898154643
+-0.6976141863014294,0.38375992455469876
+0.29510966936384325,1.783567165567434
+0.04971295370006726,-0.4529065307451171
+-0.9833526200463076,0.2907805090600878
+-0.6123946154335642,-0.10673334335233182
+0.7920040573883816,-0.6244700795288558
+0.2582922055381912,1.9487485928456987
+1.4472413749140247,-1.6460027862414233
+-0.7650345588950478,1.2056616832645988
+0.3306993090845134,0.40776013409267675
+-0.7925173754295581,0.9372386613910284
+0.6741081121162094,-0.8758080189646288
+1.1149896870089404,-1.001927971982859
+-0.2682093281729897,0.38820849125191115
+1.723053031586352,-1.1747674448688175
+-0.5703990487585499,-0.10399353400426914
+-0.6830785675125678,0.8588197655222325
+1.1190767578418632,0.3210198009555102
+-0.4812463303926203,0.699496500438495
+-0.939200395531649,0.340641344328221
+1.3717179960903234,-1.3128852147067576
+-0.4379565400817136,1.9713341289827389
+0.1838193704863979,-0.24576953839400473
+-0.24577118295341596,1.1193888134984529
+-0.276296500672476,0.20344710835511493
+0.17815756196343957,-0.0009196696716419483
+0.43841826078652635,0.28234337677431565
+0.7786214655743374,-0.9286134950511931
+0.440603887023845,-0.6692043686333717
+0.9743030954913786,0.3875024898154643
+-0.6976141863014294,0.38375992455469876
+0.29510966936384325,1.783567165567434
+-0.7151771080897029,1.718089479703083
+-0.9833526200463076,0.2907805090600878
+-0.6123946154335642,-0.10673334335233182
+0.033229103013582506,1.6532616983445168
+0.2582922055381912,1.9487485928456987
+-0.517993623784005,0.8358359970104077
+-0.7650345588950478,1.2056616832645988
+0.3306993090845134,0.40776013409267675
+-0.7925173754295581,0.9372386613910284
+-0.5848264946330798,0.5702015331304496
+1.1149896870089404,-1.001927971982859
+-0.2682093281729897,0.38820849125191115
+1.1314825296741717,0.15291253300203614
+-0.5703990487585499,-0.10399353400426914
+-0.589099173396793,-0.19144857110903712
+1.1190767578418632,0.3210198009555102
+1.6288664146201783,-1.9693392634666105
+-0.6996782941867782,0.4835725612791837
+1.3717179960903234,-1.3128852147067576
+-0.4379565400817136,1.9713341289827389
+0.03508153763541583,0.293163902901874
+0.6767811885819981,-0.7568580860492847
+1.3479436096732211,-0.515487192599532
+0.17815756196343957,-0.0009196696716419483
+-0.5641675798692537,1.0425961392041414
+0.7786214655743374,-0.9286134950511931
+0.14781418728298498,-0.2712421368579423
+0.9743030954913786,0.3875024898154643
+-0.8754564813183823,-0.36560582709511735
+0.29510966936384325,1.783567165567434
+-0.2897282547530965,2.2857245845271663
+0.5862578015211588,-0.6534388479396572
+-0.6123946154335642,-0.10673334335233182
+0.033229103013582506,1.6532616983445168
+0.2582922055381912,1.9487485928456987
+1.050205239722049,-0.037442584183211836
+-0.7650345588950478,1.2056616832645988
+0.3306993090845134,0.40776013409267675
+-0.7925173754295581,0.9372386613910284
+-0.5783848410559067,-0.19212298823019766
+1.1149896870089404,-1.001927971982859
+0.9053768205604669,0.4832473939390153
+1.1314825296741717,0.15291253300203614
+0.38702330900833015,1.2766432705305677
+-0.589099173396793,-0.19144857110903712
+1.1190767578418632,0.3210198009555102
+1.6288664146201783,-1.9693392634666105
+0.46942167706501214,0.8858809373115615
+1.5923223895617946,-1.9668002398165887
+-0.4379565400817136,1.9713341289827389
+0.03508153763541583,0.293163902901874
+-0.2018726429437815,0.3635267744101872
+-0.4884643192847541,1.5425910994661745
+-0.17053038498753104,0.16759465673641114
+-0.5641675798692537,1.0425961392041414
+0.7786214655743374,-0.9286134950511931
+-0.5251911385339858,1.0701427958908956
+1.3683194529948834,-1.4639252713303867
+-0.8754564813183823,-0.36560582709511735
+-1.1334347827108888,-0.11683199583102477
+1.11287930048155,0.9421505683096739
+0.4073553712521823,-0.7020385231964351
+-0.6123946154335642,-0.10673334335233182
+0.033229103013582506,1.6532616983445168
+0.2582922055381912,1.9487485928456987
+-0.8049902341660878,1.1398032355549144
+-0.7650345588950478,1.2056616832645988
+0.3306993090845134,0.40776013409267675
+-0.7925173754295581,0.9372386613910284
+-0.5783848410559067,-0.19212298823019766
+1.1149896870089404,-1.001927971982859
+0.9053768205604669,0.4832473939390153
+-0.45196680418650254,2.133464521732502
+-0.5603708890775418,0.7154708926871223
+-0.8341972121851189,-0.10467007662288184
+1.1190767578418632,0.3210198009555102
+1.6288664146201783,-1.9693392634666105
+0.04860846061850016,1.4439336445744981
+1.5923223895617946,-1.9668002398165887
+1.4223996108888124,-0.9795894620786328
+0.0036178231597924215,1.0760755816246772
+-0.29584930312515495,0.5047618504352865
+-0.10497667586391046,-0.09733437148594426
+-0.17053038498753104,0.16759465673641114
+-0.5641675798692537,1.0425961392041414
+1.639409276495501,-0.31507813660329986
+-0.5251911385339858,1.0701427958908956
+1.3683194529948834,-1.4639252713303867
+-0.6026194800880129,0.6809617610000535
+-1.1334347827108888,-0.11683199583102477
+1.11287930048155,0.9421505683096739
+0.4073553712521823,-0.7020385231964351
+-0.6123946154335642,-0.10673334335233182
+0.033229103013582506,1.6532616983445168
+0.2582922055381912,1.9487485928456987
+-0.8049902341660878,1.1398032355549144
+-0.7650345588950478,1.2056616832645988
+1.7081863522785772,-2.38355118103169
+-0.7925173754295581,0.9372386613910284
+0.1653908579654585,0.08208067887684434
+1.1149896870089404,-1.001927971982859
+0.9053768205604669,0.4832473939390153
+-0.45196680418650254,2.133464521732502
+-0.07872202960175881,0.27577354243859964
+-0.8341972121851189,-0.10467007662288184
+1.1190767578418632,0.3210198009555102
+1.6288664146201783,-1.9693392634666105
+0.04860846061850016,1.4439336445744981
+1.5923223895617946,-1.9668002398165887
+1.4223996108888124,-0.9795894620786328
+0.0036178231597924215,1.0760755816246772
+0.6846687391046782,0.22393278385067578
+-0.5982693441151952,0.18541931483867985
+-0.17053038498753104,0.16759465673641114
+-0.5641675798692537,1.0425961392041414
+1.3701325987308675,-0.1372085094183726
+-0.5251911385339858,1.0701427958908956
+1.3683194529948834,-1.4639252713303867
+-0.4386170201135344,0.48161598774954284
+-1.1334347827108888,-0.11683199583102477
+1.11287930048155,0.9421505683096739
+-0.39728463612253795,1.6075385696450861
+-0.6123946154335642,-0.10673334335233182
+0.033229103013582506,1.6532616983445168
+0.2582922055381912,1.9487485928456987
+-0.8049902341660878,1.1398032355549144
+0.1173884208766226,-0.1546717791361305
+1.7081863522785772,-2.38355118103169
+-0.08049885727325023,0.32112502231527174
+0.1653908579654585,0.08208067887684434
+0.3030625038718005,1.1217670259366508
+0.947357140391351,-0.2939384149030059
+-0.45196680418650254,2.133464521732502
+-0.20462769955008644,1.209309915308573
+-0.4879403632411787,0.24706178727014694
+1.1190767578418632,0.3210198009555102
+1.6288664146201783,-1.9693392634666105
+-0.7602540348811371,0.9006364309474317
+1.5923223895617946,-1.9668002398165887
+1.4223996108888124,-0.9795894620786328
+0.0036178231597924215,1.0760755816246772
+1.3634937593937906,-0.6106526530412192
+-0.5982693441151952,0.18541931483867985
+-0.28369609341952273,-0.00023752857345027412
+-0.5641675798692537,1.0425961392041414
+1.3701325987308675,-0.1372085094183726
+-0.33788554133392734,2.1801826672314055
+0.5643593947181047,-0.4573291833547517
+-0.16759674744939523,0.15111729403093532
+0.6315637726434411,1.1759155878294103
+1.11287930048155,0.9421505683096739
+-0.3550468135137298,1.4675289053530873
+-0.6123946154335642,-0.10673334335233182
+0.033229103013582506,1.6532616983445168
+-0.47585578553875657,0.9324382342474026
+-0.8049902341660878,1.1398032355549144
+0.1173884208766226,-0.1546717791361305
+1.2387807412188825,-1.2443585806623338
+-0.08049885727325023,0.32112502231527174
+0.1653908579654585,0.08208067887684434
+-0.20438223904540676,1.7350801357463326
+0.6598582366256436,0.9093023158393226
+-0.6213078228154837,-0.38483903738560366
+0.210439660828586,1.9999359484243697
+-0.578762993963152,0.04774323227164079
+1.1190767578418632,0.3210198009555102
+1.6288664146201783,-1.9693392634666105
+-0.7602540348811371,0.9006364309474317
+0.6862210786647148,0.1371685577779873
+1.4223996108888124,-0.9795894620786328
+0.7079182336858237,-0.6872314427732541
+1.3634937593937906,-0.6106526530412192
+-0.5982693441151952,0.18541931483867985
+-0.28369609341952273,-0.00023752857345027412
+0.18827686832491353,-0.30986455343457864
+1.3701325987308675,-0.1372085094183726
+-0.33788554133392734,2.1801826672314055
+0.30266494007673983,1.6835829580967911
+0.2291692561479063,-0.09047669838235455
+0.6315637726434411,1.1759155878294103
+1.11287930048155,0.9421505683096739
+-0.3550468135137298,1.4675289053530873
+0.3667076037925187,1.9098819298078011
+0.033229103013582506,1.6532616983445168
+0.09252983511783608,1.6908461674593798
+-0.8049902341660878,1.1398032355549144
+0.1173884208766226,-0.1546717791361305
+1.2387807412188825,-1.2443585806623338
+-0.5620767270755028,-0.07863352623850783
+0.1653908579654585,0.08208067887684434
+-0.20438223904540676,1.7350801357463326
+0.4781315003973279,0.2956732995163832
+-0.6256494180283575,0.6960997669378933
+-0.5051489777111583,0.42188405221167846
+-0.578762993963152,0.04774323227164079
+0.5774818468817811,0.14409657881106042
+1.6288664146201783,-1.9693392634666105
+-0.7602540348811371,0.9006364309474317
+0.21816758964623484,0.5423688907673629
+1.4223996108888124,-0.9795894620786328
+-0.23299414931623036,-0.2810156978269138
+1.1198055021825506,-1.061884685446019
+-0.3753640965458461,0.12589420206980767
+-0.28369609341952273,-0.00023752857345027412
+0.056677995866301345,1.9688229831483819
+-0.18052291704269036,-0.28392152992069597
+-0.5310530506013516,-0.10888855599199368
+-0.5032931607999114,0.6699010185195243
+0.5963823384180964,1.1793297271971366
+0.7859665646620473,1.4464311835420534
+1.11287930048155,0.9421505683096739
+-0.3550468135137298,1.4675289053530873
+0.7246504904402121,1.2390121385123432
+-0.32195413317184784,0.46716229929722264
+0.09252983511783608,1.6908461674593798
+-0.8049902341660878,1.1398032355549144
+0.19441287443684682,1.474413455412281
+1.2387807412188825,-1.2443585806623338
+0.11105211046795936,1.2861109835199154
+0.1653908579654585,0.08208067887684434
+-0.20438223904540676,1.7350801357463326
+-0.12429669703323507,0.420999426769624
+-0.6256494180283575,0.6960997669378933
+-0.5748999723557049,0.9166251148951701
+-0.3317079127090857,-0.10700102641453679
+0.5774818468817811,0.14409657881106042
+1.6288664146201783,-1.9693392634666105
+0.46872841137451005,1.8635739195540515
+0.3712770153100479,1.2179389731738264
+-0.60750102428782,0.061038061784120634
+-0.566631211987118,0.5414742654059397
+1.1198055021825506,-1.061884685446019
+-0.3753640965458461,0.12589420206980767
+-0.37038267815825354,2.1692872320825636
+0.5141567020654958,1.3120125481759968
+-0.8392055555530622,0.8730082445275161
+-0.5310530506013516,-0.10888855599199368
+0.9187807356052811,-0.7991936842318578
+0.5963823384180964,1.1793297271971366
+0.7859665646620473,1.4464311835420534
+0.8725062660046543,0.9602397045083052
+-0.3550468135137298,1.4675289053530873
+0.7246504904402121,1.2390121385123432
+-0.32195413317184784,0.46716229929722264
+0.09252983511783608,1.6908461674593798
+-0.8049902341660878,1.1398032355549144
+0.09929841781343762,1.122672792226789
+1.2387807412188825,-1.2443585806623338
+0.5759042582891737,1.2593910362933312
+1.013999590986626,-1.0600947632891788
+-0.20438223904540676,1.7350801357463326
+-0.8066663136370751,0.782835007661122
+-0.35888770064443226,1.445479173787981
+-0.5748999723557049,0.9166251148951701
+-0.3317079127090857,-0.10700102641453679
+0.5774818468817811,0.14409657881106042
+1.6288664146201783,-1.9693392634666105
+0.46872841137451005,1.8635739195540515
+-0.06906405901710311,2.57473225661566
+-0.60750102428782,0.061038061784120634
+-0.566631211987118,0.5414742654059397
+0.03989377905947156,1.3976289070373682
+-0.01036930125667651,1.2691488817643006
+-0.37038267815825354,2.1692872320825636
+0.5141567020654958,1.3120125481759968
+-0.8392055555530622,0.8730082445275161
+-0.5310530506013516,-0.10888855599199368
+0.9187807356052811,-0.7991936842318578
+1.4863713264543432,-1.3298652395104251
+0.7859665646620473,1.4464311835420534
+0.8725062660046543,0.9602397045083052
+-0.027008044996951475,1.3905860833775427
+1.632184146588106,-0.9125899430053819
+-0.32195413317184784,0.46716229929722264
+1.3944126509407895,-0.43129740512186165
+-0.8049902341660878,1.1398032355549144
+0.09929841781343762,1.122672792226789
+1.2387807412188825,-1.2443585806623338
+0.5759042582891737,1.2593910362933312
+1.013999590986626,-1.0600947632891788
+-0.20438223904540676,1.7350801357463326
+-0.0857827106577109,-0.38607971752271464
+1.2916914022055932,0.3480660654206168
+-0.5748999723557049,0.9166251148951701
+-0.3317079127090857,-0.10700102641453679
+0.5774818468817811,0.14409657881106042
+1.6288664146201783,-1.9693392634666105
+0.46872841137451005,1.8635739195540515
+-0.06906405901710311,2.57473225661566
+-0.60750102428782,0.061038061784120634
+1.1550351132775774,0.6012230131873635
+0.03989377905947156,1.3976289070373682
+0.43519706911411726,0.6721249865667709
+-0.21667478859855696,0.9224474218951892
+-0.38356449284214367,1.0829085686757833
+-0.47997088148800465,1.3221748529055593
+1.4353372867163343,-0.2932304743551779
+0.9187807356052811,-0.7991936842318578
+0.47447551992050874,1.4769896290338638
+0.7859665646620473,1.4464311835420534
+0.8725062660046543,0.9602397045083052
+-0.027008044996951475,1.3905860833775427
+1.632184146588106,-0.9125899430053819
+-0.32195413317184784,0.46716229929722264
+1.3944126509407895,-0.43129740512186165
+0.644124522906089,1.3356895978155514
+1.076708470547805,-0.5124416368677096
+1.2387807412188825,-1.2443585806623338
+-0.3894263175759865,0.6789093342941466
+-0.40790681403827783,1.322244639433926
+-0.1311423870331822,1.954460835242931
+-0.0857827106577109,-0.38607971752271464
+0.28543272724113866,1.8183737936407165
+-0.23115087305188062,0.4281769454342952
+-0.5503503695641098,1.0841387168120329
+-0.7100337140542687,1.4608538869419987
+1.6288664146201783,-1.9693392634666105
+-0.5150092412287401,1.0691996074531533
+-0.06906405901710311,2.57473225661566
+-0.60750102428782,0.061038061784120634
+-0.5633644510497153,-0.5238302723477241
+0.3892627330652396,-0.5012423958907958
+0.7262044001664559,-0.30772629183863887
+-0.6180178892404179,1.4096089147249171
+-0.38356449284214367,1.0829085686757833
+-0.47997088148800465,1.3221748529055593
+-0.3957723222055409,2.2731353784148634
+0.9187807356052811,-0.7991936842318578
+0.47447551992050874,1.4769896290338638
+-0.5029918271344789,-0.4404944147176359
+0.023551141599012504,1.0884662583820794
+-0.027008044996951475,1.3905860833775427
+1.632184146588106,-0.9125899430053819
+-0.32195413317184784,0.46716229929722264
+1.3944126509407895,-0.43129740512186165
+-0.5405521520560659,1.2688536560366823
+0.39038005295365763,1.9075751357251334
+1.0723149137831598,-0.9615775446855326
+-0.10127953204133683,1.5905177570710334
+-0.40790681403827783,1.322244639433926
+-0.019919648773723382,0.5541598675116365
+-0.0857827106577109,-0.38607971752271464
+0.28543272724113866,1.8183737936407165
+1.2479200364925376,0.8028466417705196
+-0.5503503695641098,1.0841387168120329
+-0.7100337140542687,1.4608538869419987
+1.6288664146201783,-1.9693392634666105
+1.4560396177319403,-2.252566787227776
+0.520307604372154,0.3046443961568579
+-0.60750102428782,0.061038061784120634
+0.955991378923145,1.1017463882668548
+-0.9379171185077091,0.2923997418184808
+-0.8501013019343795,0.266354103703557
+-0.9705116045440708,0.3669516082828153
+-0.38356449284214367,1.0829085686757833
+-0.47997088148800465,1.3221748529055593
+-0.3957723222055409,2.2731353784148634
+1.0131435493123901,0.6316781000810257
+-0.9470701152697978,-0.10834417411050346
+-0.34744230542266763,1.7396476736464013
+0.3298444725891666,0.7725413960472656
+-0.10459692453234853,1.515738780629329
+1.2837879720742669,-1.7256787132707978
+-0.32195413317184784,0.46716229929722264
+0.07551498360112807,1.5351934421933766
+1.205173151276417,0.02958182564196471
+0.6922134399820377,-0.7959857126326487
+0.7803887342097245,1.6361092500933374
+0.018433164803544178,2.0066382749632137
+0.34284421339429494,1.2703625249745945
+0.2942919646541039,0.7508923110568332
+0.7059336392982658,1.2201851556049343
+0.20788536205653974,-0.33927888127324485
+-0.1507600751538749,0.4010677981746273
+-0.5503503695641098,1.0841387168120329
+-0.7100337140542687,1.4608538869419987
+1.6288664146201783,-1.9693392634666105
+0.1382693043610493,1.6503074483892854
+1.036280578122847,-1.1827450402939872
+-0.60750102428782,0.061038061784120634
+0.955991378923145,1.1017463882668548
+-0.9379171185077091,0.2923997418184808
+-0.8501013019343795,0.266354103703557
+-0.9705116045440708,0.3669516082828153
+-0.38356449284214367,1.0829085686757833
+0.7906728167961645,0.18385944740878202
+-0.3957723222055409,2.2731353784148634
+1.0131435493123901,0.6316781000810257
+-0.9470701152697978,-0.10834417411050346
+-0.34744230542266763,1.7396476736464013
+0.9890611252245817,1.3116073151485803
+-0.10459692453234853,1.515738780629329
+-0.5578554313844131,1.16128731336985
+-0.32195413317184784,0.46716229929722264
+0.9858919775778195,0.8509804232933758
+-0.042083608737277456,1.3097616293335976
+0.6922134399820377,-0.7959857126326487
+0.26041541860629064,1.033808842701879
+0.018433164803544178,2.0066382749632137
+0.03095230864401108,1.335304922201705
+0.2942919646541039,0.7508923110568332
+0.9010406568316787,1.048130659002777
+0.20788536205653974,-0.33927888127324485
+0.8932160271255369,1.1226992289574118
+-0.5503503695641098,1.0841387168120329
+0.47188261963122435,-0.0012027062801834854
+1.6288664146201783,-1.9693392634666105
+-0.1835161281213541,0.8119294533872964
+1.036280578122847,-1.1827450402939872
+0.5374572545243901,1.57034652888397
+0.955991378923145,1.1017463882668548
+-0.9379171185077091,0.2923997418184808
+-0.714724946506188,0.4902410733242274
+-0.06656460862490765,0.5590673778650677
+-0.38356449284214367,1.0829085686757833
+-0.2736197807379101,1.218133934244483
+-0.3957723222055409,2.2731353784148634
+1.0131435493123901,0.6316781000810257
+-0.9470701152697978,-0.10834417411050346
+0.13891345165636795,0.1783637682916014
+0.9890611252245817,1.3116073151485803
+-0.10459692453234853,1.515738780629329
+-0.5578554313844131,1.16128731336985
+-0.32195413317184784,0.46716229929722264
+0.9858919775778195,0.8509804232933758
+-0.2988052499346042,2.237439462445278
+0.6922134399820377,-0.7959857126326487
+0.7992674673808975,-0.8045650429691646
+0.018433164803544178,2.0066382749632137
+0.03095230864401108,1.335304922201705
+0.24686121177492304,0.21522093762310293
+0.9010406568316787,1.048130659002777
+-0.041190546403716555,1.994448508680785
+0.6910681322861445,-1.0991396216584686
+-0.5503503695641098,1.0841387168120329
+-0.021929118171270412,-0.47180259090287757
+1.6288664146201783,-1.9693392634666105
+-0.7636578766018749,1.2187543128493106
+1.036280578122847,-1.1827450402939872
+0.5374572545243901,1.57034652888397
+0.955991378923145,1.1017463882668548
+-0.9379171185077091,0.2923997418184808
+-0.714724946506188,0.4902410733242274
+1.1653590307020258,-0.6323673790287193
+-0.38356449284214367,1.0829085686757833
+0.16850209888169268,1.7069331356867397
+1.2003987173237674,-0.78821061252342
+1.0131435493123901,0.6316781000810257
+-0.9470701152697978,-0.10834417411050346
+0.5553578604839868,0.12315518357405722
+-0.10034153915311425,1.4449745692918734
+-0.577550814218532,0.48878500475788156
+-0.5578554313844131,1.16128731336985
+-0.32195413317184784,0.46716229929722264
+0.9858919775778195,0.8509804232933758
+-0.5767976744193168,0.11375107843128193
+0.6922134399820377,-0.7959857126326487
+-0.0907420790892062,0.7307023508788082
+0.018433164803544178,2.0066382749632137
+0.8405531596419864,0.3400445353755157
+0.7494076038807622,1.2661428044147955
+-0.5499121782140233,-0.023263638298980288
+-0.041190546403716555,1.994448508680785
+0.6910681322861445,-1.0991396216584686
+-0.88401608830967,-0.03794641757734052
+-0.021929118171270412,-0.47180259090287757
+1.6288664146201783,-1.9693392634666105
+-0.03624450725554251,0.21598274491120834
+1.036280578122847,-1.1827450402939872
+0.5374572545243901,1.57034652888397
+0.955991378923145,1.1017463882668548
+-0.9379171185077091,0.2923997418184808
+0.9425487178378658,-0.2021874045845895
+1.1653590307020258,-0.6323673790287193
+-0.38356449284214367,1.0829085686757833
+-0.3171881466053957,0.2539186855124067
+0.9616232195016055,0.7270158796143932
+1.3002108293223857,-0.9629378219396665
+-0.9470701152697978,-0.10834417411050346
+0.5553578604839868,0.12315518357405722
+-0.10034153915311425,1.4449745692918734
+-0.577550814218532,0.48878500475788156
+-0.5578554313844131,1.16128731336985
+-0.32195413317184784,0.46716229929722264
+0.9858919775778195,0.8509804232933758
+1.0137535528471555,-0.9174105719506003
+0.396439286639367,1.9198245933916271
+-0.0907420790892062,0.7307023508788082
+0.018433164803544178,2.0066382749632137
+-0.475424860803522,0.41756613547781063
+1.5299834972934059,-0.6655569133871244
+-0.5499121782140233,-0.023263638298980288
+-0.6136207516342609,0.5123883344457442
+0.7448304141708547,-0.7037831868397396
+0.6936128243262847,-0.21069700535886596
+0.546160130493983,1.3620944196351883
+0.8559043254596258,-0.36567665050523657
+-0.03624450725554251,0.21598274491120834
+1.036280578122847,-1.1827450402939872
+0.5374572545243901,1.57034652888397
+0.16000415606911753,1.720852138554482
+-0.9379171185077091,0.2923997418184808
+0.9425487178378658,-0.2021874045845895
+1.1653590307020258,-0.6323673790287193
+-0.25934333448411706,0.4021896076819933
+-0.22879266519192626,2.352960639253764
+0.9616232195016055,0.7270158796143932
+-0.28436210999447437,-0.2718939601701599
+-0.1853443185407443,0.5922386191501319
+0.9239542746643769,-0.5859432144020952
+-0.10034153915311425,1.4449745692918734
+-0.577550814218532,0.48878500475788156
+0.7023694059293023,1.8007570101251629
+0.2659143457374882,0.11813682235435101
+0.9858919775778195,0.8509804232933758
+1.0137535528471555,-0.9174105719506003
+0.396439286639367,1.9198245933916271
+-0.0907420790892062,0.7307023508788082
+0.018433164803544178,2.0066382749632137
+-0.475424860803522,0.41756613547781063
+1.5299834972934059,-0.6655569133871244
+-0.5499121782140233,-0.023263638298980288
+-0.6020288666792182,0.7041678890688355
+0.7448304141708547,-0.7037831868397396
+-0.6364107330815083,1.171685618643131
+1.215308820582259,-0.9297014056435728
+0.8559043254596258,-0.36567665050523657
+-0.11653743079589526,-0.3474635797464397
+1.460523077591365,-1.3947062512365833
+0.5374572545243901,1.57034652888397
+1.31526129405576,-1.2329086694272637
+-0.9379171185077091,0.2923997418184808
+-0.32185261819313693,0.7131308470635087
+0.9752176090639242,-0.3657729544192341
+0.3991826901390064,0.06480755358107004
+-0.22879266519192626,2.352960639253764
+0.3295246150971228,2.050063565817675
+-0.16846713043435824,0.15557502342010965
+-0.321409305422574,0.28928632122994924
+-0.45048701896543714,1.9765425706327344
+-0.10034153915311425,1.4449745692918734
+-0.577550814218532,0.48878500475788156
+0.05848940184773321,0.5010258343699665
+1.2775837205910432,-0.5931079550053172
+0.46567716419633676,1.931001216337703
+0.7932548362859749,-0.019734507932623768
+0.396439286639367,1.9198245933916271
+0.5186702415913692,1.0797621035524885
+0.018433164803544178,2.0066382749632137
+-0.07387146033209685,0.9528036577522645
+0.19400777487345933,2.3478942227583843
+-0.5499121782140233,-0.023263638298980288
+-0.2759278232321648,0.02543596446265417
+-0.17865851727645,1.000903421294374
+0.5506410322329726,1.658138140687854
+1.215308820582259,-0.9297014056435728
+-0.2507907799884695,0.12971893066799867
+-0.2752907935467609,0.9024393136934137
+1.460523077591365,-1.3947062512365833
+0.5374572545243901,1.57034652888397
+-0.18955829404094532,-0.09980565665138963
+0.8020827775165674,0.29217919225503086
+-0.32185261819313693,0.7131308470635087
+1.125162831836036,0.2638489445781562
+0.3431980162224032,0.25758150853761225
+0.07838180608487649,1.42399791310493
+-0.47741779749088475,0.6181727607512785
+-0.16846713043435824,0.15557502342010965
+-0.321409305422574,0.28928632122994924
+-0.45048701896543714,1.9765425706327344
+0.7708511754720051,1.1790249672844286
+-0.577550814218532,0.48878500475788156
+0.05848940184773321,0.5010258343699665
+1.2775837205910432,-0.5931079550053172
+0.46567716419633676,1.931001216337703
+-0.30101182923720493,0.443387528118603
+0.15313853832376517,-0.35623182353165594
+0.5186702415913692,1.0797621035524885
+0.018433164803544178,2.0066382749632137
+-0.4504967750859114,0.559752406458067
+0.6257707639322041,1.8310401025528824
+-0.5499121782140233,-0.023263638298980288
+0.3514579371203439,1.665659252396494
+-0.004482375784605197,2.377808292970849
+0.5506410322329726,1.658138140687854
+1.215308820582259,-0.9297014056435728
+-0.2507907799884695,0.12971893066799867
+-0.2752907935467609,0.9024393136934137
+1.6607220653334673,-1.5511666783829716
+0.5450741207881111,2.160870749799658
+0.7584099044682684,0.010404172702318248
+0.4397033957498425,1.3432132877036251
+-0.0025659587181940946,-0.2576458035408995
+1.618994834723882,-1.1017836505624072
+0.7348173514192068,0.5339731116992759
+0.07838180608487649,1.42399791310493
+0.032015201830465176,0.3465358112982866
+-0.16846713043435824,0.15557502342010965
+-0.4120307027486301,0.5413285675830133
+-0.45048701896543714,1.9765425706327344
+-0.3762837652629126,0.35928342019372095
+-0.577550814218532,0.48878500475788156
+0.5290910168041238,1.8747393926521614
+1.2775837205910432,-0.5931079550053172
+-0.25081842114036373,-0.3665989021534494
+-0.30101182923720493,0.443387528118603
+0.15313853832376517,-0.35623182353165594
+0.4865763091069928,2.223325634185268
+0.018433164803544178,2.0066382749632137
+-0.32315179364431923,0.5477406797789202
+-0.4045560442342112,1.1826927801459852
+-0.5499121782140233,-0.023263638298980288
+-0.436838647151103,-0.04159256169871678
+-0.7772909894077391,0.9012431724209145
+0.8786554430309136,0.15269021941960909
+1.215308820582259,-0.9297014056435728
+-1.0083151900249747,0.4280779286677941
+-0.0665382029128323,1.2227659899743308
+1.6607220653334673,-1.5511666783829716
+0.8010531357952975,0.614006839363973
+0.7584099044682684,0.010404172702318248
+0.47714556375181627,1.512672713879173
+-0.0025659587181940946,-0.2576458035408995
+1.618994834723882,-1.1017836505624072
+0.43709724168320185,1.6210224846098649
+1.2929623523149525,-0.3121442595124736
+0.555451210478212,1.445365039520834
+0.8847051440831235,-0.8043694087004819
+-0.4120307027486301,0.5413285675830133
+-0.45048701896543714,1.9765425706327344
+0.21853905877647328,-0.37916780101102215
+0.9453886353944062,-0.8401558511909583
+0.5290910168041238,1.8747393926521614
+-0.37220579650564206,0.4559974356310401
+-0.6220618772652192,1.080972281170107
+0.3149042891332458,-0.18542062950495994
+1.4472657268470301,-1.593348131567993
+0.4865763091069928,2.223325634185268
+-0.7103081673753502,0.5933507523238427
+-0.7429462779315241,-0.33384467063842027
+-0.619372110248976,1.2396959966376935
+-0.7095045506695435,-0.40799417469346644
+-0.436838647151103,-0.04159256169871678
+0.035119964920441865,0.20856929425458803
+0.4597097301261448,0.21942376882195713
+-0.4254922925742793,0.0013178547914916017
+-1.0083151900249747,0.4280779286677941
+-0.0665382029128323,1.2227659899743308
+1.6607220653334673,-1.5511666783829716
+1.4236738636761115,-1.200232926318888
+0.26446902383417403,-0.5985078732618165
+1.3099743158966979,-1.334797549847216
+-0.23223486130714546,-0.12688570313020597
+-0.929062986964466,0.41943404164282755
+0.7089195704516145,-0.40848355266284814
+-0.583409122549227,-0.4165831072082894
+0.555451210478212,1.445365039520834
+0.8847051440831235,-0.8043694087004819
+-0.4120307027486301,0.5413285675830133
+-0.45048701896543714,1.9765425706327344
+0.21853905877647328,-0.37916780101102215
+0.08541565218617686,-0.11239949572323392
+-0.3386036867446948,-0.031385992821681696
+-0.37220579650564206,0.4559974356310401
+-0.6220618772652192,1.080972281170107
+-0.7281211753845716,0.2619374287002388
+-0.758494431953396,0.5800830099280944
+0.4865763091069928,2.223325634185268
+-0.7103081673753502,0.5933507523238427
+1.8697380688441474,-2.0863345046196957
+-0.619372110248976,1.2396959966376935
+-0.6535095984844087,0.1822946886583322
+-0.436838647151103,-0.04159256169871678
+-0.541497509353285,0.9545805935995204
+0.4597097301261448,0.21942376882195713
+0.32465139643339197,2.0473327248846265
+0.19032549603169818,-0.17770436042941917
+-0.0665382029128323,1.2227659899743308
+-0.8035560604391857,0.5179862172364282
+1.4236738636761115,-1.200232926318888
+0.580820334563338,1.0230738627075697
+1.3099743158966979,-1.334797549847216
+-0.23223486130714546,-0.12688570313020597
+-0.929062986964466,0.41943404164282755
+0.7089195704516145,-0.40848355266284814
+0.9302444250129553,0.55916841416549
+0.555451210478212,1.445365039520834
+0.8847051440831235,-0.8043694087004819
+-0.4120307027486301,0.5413285675830133
+-0.45048701896543714,1.9765425706327344
+0.21853905877647328,-0.37916780101102215
+-0.40340912322955075,-0.2889029913827586
+-0.3386036867446948,-0.031385992821681696
+-0.37220579650564206,0.4559974356310401
+-0.8987295799969586,-0.32517408971187794
+-0.21806344382691845,-0.39384224793991446
+-0.3005403815236962,-0.1495269698140466
+1.2549396572972535,-0.4603838634524767
+-0.7103081673753502,0.5933507523238427
+1.8697380688441474,-2.0863345046196957
+-0.619372110248976,1.2396959966376935
+1.0649066396975697,0.6801762096932675
+-0.436838647151103,-0.04159256169871678
+-0.211744993397386,1.7461396001973337
+0.7709522207900101,-0.5419290544599096
+0.32465139643339197,2.0473327248846265
+0.19032549603169818,-0.17770436042941917
+-0.0665382029128323,1.2227659899743308
+-0.24535748616557118,1.5431551082386306
+1.4236738636761115,-1.200232926318888
+0.580820334563338,1.0230738627075697
+-0.9365460940188814,0.4959088814936989
+0.4486642307891466,2.067119701102314
+-0.929062986964466,0.41943404164282755
+0.5041253519824964,1.654763118734455
+-1.016641614246116,0.2593502653857524
+0.555451210478212,1.445365039520834
+0.8847051440831235,-0.8043694087004819
+-0.4120307027486301,0.5413285675830133
+-0.45048701896543714,1.9765425706327344
+0.649269443856388,0.07220198647771359
+-0.4975089832577262,0.6769176517474675
+0.46340439704483977,-0.32690403334241847
+-0.8176959080337842,-0.287925684059866
+-0.8987295799969586,-0.32517408971187794
+0.2891080651875344,-0.3774333744623396
+-0.4656178686891862,0.8711508553944722
+1.2549396572972535,-0.4603838634524767
+-0.7103081673753502,0.5933507523238427
+0.08921157187307588,1.0521745781871634
+0.42105824447096,1.144343687910275
+1.1561427221466896,0.28333803854982587
+-0.7289018999585815,0.8655242952100131
+-0.211744993397386,1.7461396001973337
+0.7709522207900101,-0.5419290544599096
+0.32465139643339197,2.0473327248846265
+0.19032549603169818,-0.17770436042941917
+0.6539715390285227,0.6462292223868878
+-0.24348529877669817,0.9330404142492303
+1.4236738636761115,-1.200232926318888
+0.580820334563338,1.0230738627075697
+0.4944502147874235,0.050178362678068356
+1.01027231178876,0.16278136346544736
+1.350751416490891,-0.8322956811428204
+-0.21628613882972736,-0.4068512557627039
+-0.52177122568082,0.3124910255226349
+0.555451210478212,1.445365039520834
+-0.5330714063092592,-0.012878817076524385
+-0.08915561587111648,1.6035391971480042
+-0.45048701896543714,1.9765425706327344
+0.649269443856388,0.07220198647771359
+-0.4975089832577262,0.6769176517474675
+0.46340439704483977,-0.32690403334241847
+-0.1854062029536242,1.1335422826308
+-0.8987295799969586,-0.32517408971187794
+1.2907234811041368,-1.4120876179648194
+-0.4656178686891862,0.8711508553944722
+1.2549396572972535,-0.4603838634524767
+-0.7103081673753502,0.5933507523238427
+1.0997952743560722,-0.019119158193081187
+0.995921412778936,-0.20997332728850399
+0.6344096778254256,1.0416118787523017
+0.9409710844590213,0.6308707462859334
+-0.211744993397386,1.7461396001973337
+0.7709522207900101,-0.5419290544599096
+0.32465139643339197,2.0473327248846265
+-0.03187116653508029,1.8752834913003555
+1.1636313228796873,-0.2826368471172245
+0.49260028462329936,2.050049545936956
+-0.8503253323969957,0.8235556535032414
+0.11229622288333618,-0.593140075713994
+0.8577782118705723,0.7648878150902492
+-0.1899012708931032,1.9860563246121075
+1.350751416490891,-0.8322956811428204
+0.6732404471437314,1.86298422486482
+0.13179426336023908,2.237129918652383
+-0.31117665967057934,2.1398999873307973
+-0.5330714063092592,-0.012878817076524385
+0.5936627325643546,-0.27834671889919005
+0.9623850511502743,0.5827911309964953
+0.649269443856388,0.07220198647771359
+-0.4975089832577262,0.6769176517474675
+0.46340439704483977,-0.32690403334241847
+-0.24468168987368216,0.6761094846318312
+-0.8987295799969586,-0.32517408971187794
+1.2907234811041368,-1.4120876179648194
+-0.1491572084400109,1.819649146702421
+-0.33595329507041416,-0.18889681524975221
+-0.7103081673753502,0.5933507523238427
+0.06623389251158135,1.277231720839641
+0.995921412778936,-0.20997332728850399
+0.6344096778254256,1.0416118787523017
+0.9409710844590213,0.6308707462859334
+0.5919164784428349,0.8159293893836079
+0.24475869747614976,0.2852450307945644
+0.7013433514256519,-0.10126943160513685
+-0.03187116653508029,1.8752834913003555
+0.34571239807351317,-0.28132584220191537
+-0.28649251427140304,0.04233979980870006
+-0.8503253323969957,0.8235556535032414
+-0.08103942004964501,1.6193500630676825
+-0.278503964401513,1.5686764869459435
+0.1947484970506928,1.555056294233278
+1.350751416490891,-0.8322956811428204
+0.6732404471437314,1.86298422486482
+0.13179426336023908,2.237129918652383
+-0.43047900866517214,1.0506326541314361
+-0.5330714063092592,-0.012878817076524385
+0.15410254066017387,2.273748124684401
+0.7477181294883632,-0.6901503088295502
+0.649269443856388,0.07220198647771359
+-0.4975089832577262,0.6769176517474675
+0.46340439704483977,-0.32690403334241847
+-0.24468168987368216,0.6761094846318312
+-0.8987295799969586,-0.32517408971187794
+1.2907234811041368,-1.4120876179648194
+-0.5340607611637729,1.7030511895437817
+-0.33595329507041416,-0.18889681524975221
+0.8097137378786335,-0.1459072082545731
+0.06623389251158135,1.277231720839641
+1.1951279174461802,-0.9322643265861063
+0.15700855234776548,1.3968000059845591
+1.657374547279998,-1.9623302387260404
+0.5858422192957389,0.744139652176332
+0.24475869747614976,0.2852450307945644
+1.3914216095179983,-0.14828082660975717
+-0.03187116653508029,1.8752834913003555
+1.4927910236758781,-0.7894798107736947
+-0.28649251427140304,0.04233979980870006
+0.8997357778062453,-0.06937430611540307
+0.5919433774898025,1.1390398752485693
+-0.278503964401513,1.5686764869459435
+-0.5569282444623226,1.514945623607672
+1.350751416490891,-0.8322956811428204
+0.6732404471437314,1.86298422486482
+0.13179426336023908,2.237129918652383
+-0.43047900866517214,1.0506326541314361
+0.7779807250417363,-0.5803268597852882
+0.15410254066017387,2.273748124684401
+0.5322805318375653,0.031999003437353346
+0.6200508407235213,0.06657920563483166
+0.13764884891655693,0.04451315947404297
+0.46340439704483977,-0.32690403334241847
+-0.24468168987368216,0.6761094846318312
+0.028440601762813156,1.3359397452217916
+-1.0205572058370893,0.26406429715609653
+-0.683020361813268,0.9791155348836428
+-0.33595329507041416,-0.18889681524975221
+-0.27176208699729876,0.23307025597445527
+0.7148926298484637,-0.7590469591249084
+1.1951279174461802,-0.9322643265861063
+0.15700855234776548,1.3968000059845591
+1.657374547279998,-1.9623302387260404
+-0.5888662788123254,1.1857751420703027
+0.24475869747614976,0.2852450307945644
+1.3914216095179983,-0.14828082660975717
+-0.03187116653508029,1.8752834913003555
+1.4927910236758781,-0.7894798107736947
+0.6403982774084016,-0.351200361011332
+1.410856965036488,-0.7117853675694654
+0.0725930719612985,0.32677866883410217
+-0.278503964401513,1.5686764869459435
+0.4539841145095479,0.15734040522366463
+1.350751416490891,-0.8322956811428204
+0.6732404471437314,1.86298422486482
+-0.7590166825297946,0.7625721574492597
+-0.43047900866517214,1.0506326541314361
+0.7779807250417363,-0.5803268597852882
+0.15410254066017387,2.273748124684401
+0.5322805318375653,0.031999003437353346
+1.5221188921308997,-0.7569359432488831
+0.13764884891655693,0.04451315947404297
+-0.1455088046086092,0.2275504790597893
+-0.7291473830101012,-0.33460418875323367
+0.028440601762813156,1.3359397452217916
+-1.0205572058370893,0.26406429715609653
+0.5562932889509501,-0.5076618805431505
+-0.33595329507041416,-0.18889681524975221
+-0.27176208699729876,0.23307025597445527
+1.4486377337635952,-2.119534612443845
+1.1951279174461802,-0.9322643265861063
+0.15700855234776548,1.3968000059845591
+1.657374547279998,-1.9623302387260404
+-0.5888662788123254,1.1857751420703027
+0.24475869747614976,0.2852450307945644
+1.3914216095179983,-0.14828082660975717
+-0.03187116653508029,1.8752834913003555
+1.4927910236758781,-0.7894798107736947
+0.7511457667576491,-0.9023915986771971
+1.410856965036488,-0.7117853675694654
+-0.6515710585187902,0.49728500019679894
+-0.278503964401513,1.5686764869459435
+-0.7027723289066858,0.6968781647696313
+-0.6442256653914356,-0.4475908774642252
+0.6732404471437314,1.86298422486482
+-0.7590166825297946,0.7625721574492597
+0.5612246459658633,0.17986413867326811
+0.7779807250417363,-0.5803268597852882
+0.15410254066017387,2.273748124684401
+-0.09237132826100014,0.13262534224362726
+1.5221188921308997,-0.7569359432488831
+-1.0497895863809075,-0.45032616413260596
+0.41190472278129575,-0.6649093780742599
+-0.7291473830101012,-0.33460418875323367
+1.2608249568840213,-0.20337952683258675
+-1.0205572058370893,0.26406429715609653
+-0.33232935682931686,0.29225204234902136
+0.41851724638550675,0.8471581515552008
+0.8566152739836517,-0.9335286628547133
+1.4486377337635952,-2.119534612443845
+-0.5279426628873668,-0.15896629801808676
+-0.4438128754338474,0.3311915350852881
+1.657374547279998,-1.9623302387260404
+-0.7203294078777933,-0.09659839541215892
+0.24475869747614976,0.2852450307945644
+0.9685544404478821,0.7956404645121591
+-0.03187116653508029,1.8752834913003555
+1.4927910236758781,-0.7894798107736947
+0.6224336941337543,1.265910938602277
+-0.7222995134478437,0.4977769538977269
+-0.031288575096114296,0.7177939335861518
+0.549163677554577,1.7530888903961994
+0.5935973576259754,1.1866956255738328
+-0.5628576245105013,-0.011951624382502635
+0.17777753642629757,0.604160903164399
+-0.7590166825297946,0.7625721574492597
+-0.9831140529341572,0.4547382355390276
+0.7779807250417363,-0.5803268597852882
+0.15410254066017387,2.273748124684401
+-0.09237132826100014,0.13262534224362726
+1.5221188921308997,-0.7569359432488831
+0.43833712074468784,1.2181195219621004
+0.41190472278129575,-0.6649093780742599
+-0.5741637133072701,1.4776532131937765
+1.2608249568840213,-0.20337952683258675
+0.4751863130013323,2.0136859694970273
+-0.33232935682931686,0.29225204234902136
+0.41851724638550675,0.8471581515552008
+-0.4342438447029414,-0.01826697362641616
+1.4486377337635952,-2.119534612443845
+-0.5279426628873668,-0.15896629801808676
+0.8874537608092703,-0.47403708926939964
+1.1047783128366109,0.48119504784169703
+-0.7203294078777933,-0.09659839541215892
+0.9707786106363764,0.5538998093564842
+-0.44549984962358324,0.1756915693137985
+-0.03187116653508029,1.8752834913003555
+1.4927910236758781,-0.7894798107736947
+0.8323940842631332,0.9662834432189255
+-0.7222995134478437,0.4977769538977269
+-0.13122924803319702,1.1927636848660177
+0.549163677554577,1.7530888903961994
+0.5935973576259754,1.1866956255738328
+-0.8565130127854574,1.012045886114959
+-0.46494954002700317,1.4814458342068764
+-0.1590163476432943,-0.3590655925288051
+-0.9831140529341572,0.4547382355390276
+0.7779807250417363,-0.5803268597852882
+0.15410254066017387,2.273748124684401
+0.4737559246361558,1.0809140909373078
+1.5221188921308997,-0.7569359432488831
+-0.24563574128169574,-0.2881987873342766
+0.41190472278129575,-0.6649093780742599
+0.25320758194971116,-0.15149869120228787
+1.2608249568840213,-0.20337952683258675
+0.4751863130013323,2.0136859694970273
+-0.33232935682931686,0.29225204234902136
+0.41851724638550675,0.8471581515552008
+-0.4342438447029414,-0.01826697362641616
+1.4486377337635952,-2.119534612443845
+-0.006833206596626257,1.1887096780474506
+0.8874537608092703,-0.47403708926939964
+0.7961598270480219,-0.36887188786240405
+-0.7203294078777933,-0.09659839541215892
+0.9613635386675095,0.5807984544368263
+-0.44549984962358324,0.1756915693137985
+-0.03187116653508029,1.8752834913003555
+1.4927910236758781,-0.7894798107736947
+-0.6721255681252015,0.5131619998964005
+-0.7222995134478437,0.4977769538977269
+-0.13122924803319702,1.1927636848660177
+0.549163677554577,1.7530888903961994
+0.5935973576259754,1.1866956255738328
+-0.8565130127854574,1.012045886114959
+-0.46494954002700317,1.4814458342068764
+-0.46509313574972844,0.0950574490547467
+-0.6796449449964759,0.6578681332371996
+0.7779807250417363,-0.5803268597852882
+0.15410254066017387,2.273748124684401
+0.6780848396539659,-0.5641750130944488
+1.5221188921308997,-0.7569359432488831
+-0.696535221116253,0.798857802487787
+0.6365082771424149,-0.3657950790765885
+0.5562442948098854,-0.06196774824707346
+1.2608249568840213,-0.20337952683258675
+0.8336621779672001,-0.27984605794743334
+-0.6155824390994118,0.6850168489730278
+0.41851724638550675,0.8471581515552008
+-0.27998100464766323,0.14382989260482265
+1.4486377337635952,-2.119534612443845
+1.6547058811358841,-1.6273523232651887
+-0.16794015048416183,0.4346107102821788
+1.2756993957596967,-1.099170549723929
+-0.10667582831432487,1.5951023927198733
+0.9613635386675095,0.5807984544368263
+-0.44549984962358324,0.1756915693137985
+-0.03187116653508029,1.8752834913003555
+1.1805279475097168,-0.11489152487477858
+-0.38665549270439387,1.7484334870977352
+-0.7222995134478437,0.4977769538977269
+0.7335818774653549,1.531102195392405
+0.549163677554577,1.7530888903961994
+1.0850825317017088,0.27576407265962355
+0.6661745830460802,-0.11775374028425373
+-0.46494954002700317,1.4814458342068764
+0.7316102369049284,-0.950216360364542
+-0.6796449449964759,0.6578681332371996
+0.7779807250417363,-0.5803268597852882
+0.15410254066017387,2.273748124684401
+0.6780848396539659,-0.5641750130944488
+1.5221188921308997,-0.7569359432488831
+-0.696535221116253,0.798857802487787
+0.27140417164221253,-0.16274070111053202
+0.002542160562828466,1.388245837632165
+1.2608249568840213,-0.20337952683258675
+1.5237021105140036,-2.547231374395446
+1.02945292407831,0.1400615850493612
+0.41851724638550675,0.8471581515552008
+-0.27998100464766323,0.14382989260482265
+-0.6549653075323583,1.326357758959122
+1.6547058811358841,-1.6273523232651887
+0.3140152119215684,-0.13599812760319904
+0.34275666940828564,1.385607399750153
+0.42494437113804295,1.8479986504854966
+-0.6110644222676087,0.21560368803214508
+-0.44549984962358324,0.1756915693137985
+-0.03187116653508029,1.8752834913003555
+1.1805279475097168,-0.11489152487477858
+-0.38665549270439387,1.7484334870977352
+-0.7222995134478437,0.4977769538977269
+0.7335818774653549,1.531102195392405
+0.549163677554577,1.7530888903961994
+1.0850825317017088,0.27576407265962355
+-0.7753646229991417,0.39993647356203904
+-0.46494954002700317,1.4814458342068764
+0.7316102369049284,-0.950216360364542
+-0.6796449449964759,0.6578681332371996
+-0.2759782689386732,1.2776241883474966
+0.15410254066017387,2.273748124684401
+0.6780848396539659,-0.5641750130944488
+-0.618392932224704,1.0669023859730988
+1.554355545026568,-1.3270946424596786
+0.8210305326542591,0.11768508887973955
+1.330631104614104,-0.4390472959795276
+1.2608249568840213,-0.20337952683258675
+1.5237021105140036,-2.547231374395446
+1.02945292407831,0.1400615850493612
+-0.36563276714574444,1.152246384751542
+1.1646405411063634,-0.7364931032901075
+-0.6549653075323583,1.326357758959122
+-0.06640867944577095,2.1680155882744394
+0.3140152119215684,-0.13599812760319904
+1.0939586386448825,-0.9232864808939747
+0.42494437113804295,1.8479986504854966
+-0.6110644222676087,0.21560368803214508
+-0.44549984962358324,0.1756915693137985
+-0.03187116653508029,1.8752834913003555
+1.1805279475097168,-0.11489152487477858
+-0.38665549270439387,1.7484334870977352
+-0.7222995134478437,0.4977769538977269
+0.7335818774653549,1.531102195392405
+1.9749847038473425,-3.302787755820022
+-0.654313252707105,0.22851100593669743
+0.00098471605268724,2.028344798366845
+-0.46494954002700317,1.4814458342068764
+0.7316102369049284,-0.950216360364542
+-0.6796449449964759,0.6578681332371996
+-0.2759782689386732,1.2776241883474966
+-0.8212020412178143,0.05178174759402346
+0.6780848396539659,-0.5641750130944488
+1.4077420112058996,-1.1704361302411008
+1.554355545026568,-1.3270946424596786
+0.7471294596363028,-0.604444970422166
+1.330631104614104,-0.4390472959795276
+1.2608249568840213,-0.20337952683258675
+-0.16240807869647778,0.0902970435058188
+0.5877854353809409,1.2071224761268942
+-0.2556496393411486,1.745917563023712
+1.0307197230683691,0.016645883957576935
+-0.6549653075323583,1.326357758959122
+-0.06640867944577095,2.1680155882744394
+-0.44524396524548354,2.286180642788967
+0.1772535454704176,1.0116804703519917
+0.8904343686869878,-1.0633296192372683
+-0.13726508804390664,1.8901527613319289
+-0.44549984962358324,0.1756915693137985
+0.7335218908611311,1.6240698182841935
+1.1805279475097168,-0.11489152487477858
+-0.38665549270439387,1.7484334870977352
+-0.0026623198928450442,-0.12635368019156468
+0.7335818774653549,1.531102195392405
+1.9749847038473425,-3.302787755820022
+0.7849340729921774,1.1878758435232624
+0.00098471605268724,2.028344798366845
+-0.44995640763705624,1.8022799982895952
+0.7316102369049284,-0.950216360364542
+-0.321347063564389,2.0523048381719877
+1.0867661746630983,-0.9971337985546059
+-0.3577369456655477,0.9574736195519279
+-0.7767388503225071,1.0521054595308859
+0.29064374061095927,2.0510267092626706
+1.554355545026568,-1.3270946424596786
+0.7471294596363028,-0.604444970422166
+1.330631104614104,-0.4390472959795276
+1.2608249568840213,-0.20337952683258675
+-0.16240807869647778,0.0902970435058188
+0.5877854353809409,1.2071224761268942
+1.2475663021322614,-1.2000258001563824
+1.6686707257233968,-1.9185657394997915
+-0.6549653075323583,1.326357758959122
+-0.06640867944577095,2.1680155882744394
+2.0985664493740672,-3.2461646631468146
+-0.6756245096643564,0.7261745483525062
+0.8407576579525472,-0.9991761462910703
+1.5836618077778477,-1.6048061305876304
+-0.1877697209363161,-0.5190919553551083
+0.7335218908611311,1.6240698182841935
+1.5160911550415825,-1.3610676187971689
+-0.38665549270439387,1.7484334870977352
+-0.0026623198928450442,-0.12635368019156468
+0.12924293943563125,1.917010332572886
+1.9749847038473425,-3.302787755820022
+0.7849340729921774,1.1878758435232624
+0.00098471605268724,2.028344798366845
+-0.44995640763705624,1.8022799982895952
+-0.7698267141326471,1.3368712563381873
+-0.321347063564389,2.0523048381719877
+1.0867661746630983,-0.9971337985546059
+1.2737730182416382,-1.5349456271047006
+0.9507387915048633,1.2478677392705428
+0.701281041309047,1.7252971032324087
+1.554355545026568,-1.3270946424596786
+0.7471294596363028,-0.604444970422166
+1.7943386110340065,-1.6650030874225155
+1.2608249568840213,-0.20337952683258675
+-0.16240807869647778,0.0902970435058188
+1.4450806686172968,-2.3572341694531644
+1.2475663021322614,-1.2000258001563824
+1.6686707257233968,-1.9185657394997915
+0.03836529039300704,1.630959845534624
+-0.06640867944577095,2.1680155882744394
+2.0985664493740672,-3.2461646631468146
+-0.6756245096643564,0.7261745483525062
+1.2679423187539698,-1.579270678359245
+1.5836618077778477,-1.6048061305876304
+-0.1877697209363161,-0.5190919553551083
+0.7335218908611311,1.6240698182841935
+1.5160911550415825,-1.3610676187971689
+-0.5336221406817557,1.2314703135215126
+-0.0026623198928450442,-0.12635368019156468
+0.12924293943563125,1.917010332572886
+1.9749847038473425,-3.302787755820022
+0.8136841892224844,-0.5542366605212348
+0.00098471605268724,2.028344798366845
+0.7941377450782197,1.2940570147806307
+0.8016129498533925,1.6875419842285624
+1.164145144517698,-1.0518161559982737
+0.9423987451809951,1.0969750933224516
+1.2737730182416382,-1.5349456271047006
+1.0414169910216642,0.7465792249608507
+0.8278927846669535,1.2186347660461196
+1.213486775330221,-1.7303068237410852
+0.7471294596363028,-0.604444970422166
+1.7943386110340065,-1.6650030874225155
+1.2608249568840213,-0.20337952683258675
+0.16383627280784102,0.9564275377596912
+0.07727960709243042,1.6287924496900288
+-0.2224935767786659,1.8880025914096796
+-0.2631464276290066,1.4599778027498425
+0.48411894606621053,-0.6199013931929276
+-0.06640867944577095,2.1680155882744394
+0.45778497451320255,1.8905474283792738
+-0.6756245096643564,0.7261745483525062
+1.2418794778212487,-1.381017190303555
+1.4716955322579013,-1.0145169963155392
+-0.1877697209363161,-0.5190919553551083
+0.7335218908611311,1.6240698182841935
+1.1194864608578705,-0.7761161397762135
+-0.5336221406817557,1.2314703135215126
+-0.0026623198928450442,-0.12635368019156468
+0.12924293943563125,1.917010332572886
+1.9749847038473425,-3.302787755820022
+0.8136841892224844,-0.5542366605212348
+0.07024878152616809,1.7165321702591854
+0.7941377450782197,1.2940570147806307
+0.8016129498533925,1.6875419842285624
+0.2466923757592423,-0.5527125678412086
+1.1613087909241064,0.5126556018270854
+1.2737730182416382,-1.5349456271047006
+0.3509555160470564,-0.33653608604220386
+0.8278927846669535,1.2186347660461196
+-0.07249226728414171,2.565642105273821
+0.7471294596363028,-0.604444970422166
+0.060436673129211166,-0.505143993489486
+0.3262931253280439,1.2767396390949446
+0.16383627280784102,0.9564275377596912
+0.07727960709243042,1.6287924496900288
+-0.2224935767786659,1.8880025914096796
+-0.2631464276290066,1.4599778027498425
+0.07543896005817025,1.6959183843382535
+1.4688073069378587,-0.3557077500978554
+0.45778497451320255,1.8905474283792738
+-0.6756245096643564,0.7261745483525062
+0.42559462723728625,1.3986102959216042
+1.4716955322579013,-1.0145169963155392
+-0.1877697209363161,-0.5190919553551083
+0.9537421085247029,1.240184845777399
+0.8247271811007315,1.6670455981648835
+-0.5336221406817557,1.2314703135215126
+1.2424534727069603,-0.9811795320861971
+0.025868070583538127,2.1859129163587907
+0.48250617167421805,1.3867279945280149
+0.6415291260346041,-0.2859530179102526
+0.34956727215843086,0.013686689991201595
+0.7941377450782197,1.2940570147806307
+0.8016129498533925,1.6875419842285624
+-0.13528418585705293,1.4820706659497425
+1.1613087909241064,0.5126556018270854
+1.2737730182416382,-1.5349456271047006
+0.3509555160470564,-0.33653608604220386
+0.7078359131282913,-0.3996594235095776
+0.08918510194599594,2.136858593462571
+0.7471294596363028,-0.604444970422166
+0.060436673129211166,-0.505143993489486
+0.7492633958168167,-0.17188678436250726
+0.5315107839529222,-0.5206757138488604
+1.5642364924072565,-0.8630161917582968
+0.21011053692825563,1.9383725182694378
+-0.2631464276290066,1.4599778027498425
+0.07543896005817025,1.6959183843382535
+-0.028519133852043965,-0.03100470914220116
+0.45778497451320255,1.8905474283792738
+-0.6756245096643564,0.7261745483525062
+0.09834773607470959,1.06866040472062
+1.4716955322579013,-1.0145169963155392
+-0.1877697209363161,-0.5190919553551083
+0.03233791409871212,1.9183313985658077
+0.6168827427647527,-0.23272903046244492
+-0.24754676158809727,1.906185866095835
+1.9490175088962771,-2.5632891784408334
+0.025868070583538127,2.1859129163587907
+0.48250617167421805,1.3867279945280149
+0.12221510354514253,0.13143892644102484
+0.34956727215843086,0.013686689991201595
+0.8720023633958289,-0.10042115213590252
+0.8016129498533925,1.6875419842285624
+-0.13528418585705293,1.4820706659497425
+1.1613087909241064,0.5126556018270854
+1.2737730182416382,-1.5349456271047006
+0.6655024837671607,-0.5359914207125741
+1.3391815056005534,-0.9580762743677345
+0.017717903187900313,-0.4272621557409192
+0.7471294596363028,-0.604444970422166
+0.060436673129211166,-0.505143993489486
+0.729008491451632,0.8122258625306542
+0.5315107839529222,-0.5206757138488604
+1.5642364924072565,-0.8630161917582968
+0.21011053692825563,1.9383725182694378
+0.06911140335268967,0.958065467427464
+0.41048389644079947,0.1895801373647621
+1.4640463966465505,-2.4444678405080604
+-0.2066367876047867,-0.5173058180559453
+-0.6756245096643564,0.7261745483525062
+0.2185400198977811,0.41838984452182887
+0.3530579098641619,0.2312376468208952
+0.05734403401380456,-0.2642010153216927
+1.3708335804506668,-0.7339557092179863
+0.6168827427647527,-0.23272903046244492
+-0.24754676158809727,1.906185866095835
+1.9490175088962771,-2.5632891784408334
+0.025868070583538127,2.1859129163587907
+0.16917664445945724,0.5367444270217486
+-0.3203930978795086,0.05655471515378835
+1.2501256957408093,-0.7373882894107826
+0.8720023633958289,-0.10042115213590252
+0.8016129498533925,1.6875419842285624
+-0.13528418585705293,1.4820706659497425
+1.1613087909241064,0.5126556018270854
+1.2737730182416382,-1.5349456271047006
+0.6655024837671607,-0.5359914207125741
+0.20539581038163257,0.18908546284400762
+-0.20506598224144645,1.7132713977757876
+0.8112677011648698,0.7882212766320622
+1.438530106804081,0.005277727187581127
+0.729008491451632,0.8122258625306542
+0.5315107839529222,-0.5206757138488604
+-0.5162145286776467,1.3546766917270416
+0.21011053692825563,1.9383725182694378
+-0.061466164700842624,1.5500583680615234
+0.41048389644079947,0.1895801373647621
+1.4640463966465505,-2.4444678405080604
+-0.2066367876047867,-0.5173058180559453
+-0.6756245096643564,0.7261745483525062
+-0.2775220878128133,1.661733073851928
+0.7091088365848087,0.5362284381063875
+0.05734403401380456,-0.2642010153216927
+-0.08395601040421827,-0.35313123847682387
+0.6168827427647527,-0.23272903046244492
+0.6749926653383925,-0.08327643672532659
+1.9490175088962771,-2.5632891784408334
+0.025868070583538127,2.1859129163587907
+0.8304084799992801,-0.1674946937043364
+-0.3203930978795086,0.05655471515378835
+0.5292308336073339,1.2161939628626182
+1.5624458666495786,-1.7985127299093029
+0.8016129498533925,1.6875419842285624
+-0.13528418585705293,1.4820706659497425
+-0.42558674957968945,1.4055954530523647
+1.2737730182416382,-1.5349456271047006
+0.8310975119790305,-0.3810381561111855
+1.488091778353866,-0.19409384329776858
+1.4461662688565093,-1.0450530276338366
+0.4266654177614964,1.7705162237260437
+0.40361428138010785,-0.5691760046047758
+1.3275496693894255,-0.7379479781503316
+-0.23029210618305646,1.3117627337635267
+1.5381865063937386,-2.56315326696064
+0.21011053692825563,1.9383725182694378
+0.3179729778998387,1.7841583631829103
+0.22816356514473063,-0.010497610964486837
+0.9406844492339591,-0.8940850662963293
+0.4026681627228774,-0.51908265120213
+-0.6756245096643564,0.7261745483525062
+-0.2775220878128133,1.661733073851928
+1.0680364935129973,-1.5913060752608674
+0.033975349350585604,1.1432571594655054
+-0.08395601040421827,-0.35313123847682387
+0.5212926081754361,1.8577798866877195
+1.7190332995786974,-1.5361855108967857
+0.9964878745221393,0.8388119518844706
+0.025868070583538127,2.1859129163587907
+0.5157095738736307,-0.016974486586660564
+-0.3203930978795086,0.05655471515378835
+0.45433889821741086,-0.59103648400135
+-0.5682038840771955,1.7958496934748536
+0.0447152847496346,-0.01574819167382402
+-0.13528418585705293,1.4820706659497425
+-0.42558674957968945,1.4055954530523647
+1.2737730182416382,-1.5349456271047006
+0.8310975119790305,-0.3810381561111855
+1.488091778353866,-0.19409384329776858
+1.4461662688565093,-1.0450530276338366
+0.4266654177614964,1.7705162237260437
+0.40361428138010785,-0.5691760046047758
+1.3275496693894255,-0.7379479781503316
+-0.23029210618305646,1.3117627337635267
+1.5381865063937386,-2.56315326696064
+0.21011053692825563,1.9383725182694378
+0.3179729778998387,1.7841583631829103
+0.5627217081087597,1.8565429414294765
+-0.10763929575432296,0.3793679891954481
+0.19199467382055402,1.9259399220784463
+-0.6756245096643564,0.7261745483525062
+0.2670147885678944,1.035504856861125
+0.9445048359353467,1.2283795288286563
+0.033975349350585604,1.1432571594655054
+-0.08395601040421827,-0.35313123847682387
+0.029302563191694553,2.0546945664299128
+1.7190332995786974,-1.5361855108967857
+0.3042232460336109,1.843711015164943
+0.10201404805283462,-0.01491015423507036
+0.5157095738736307,-0.016974486586660564
+1.09197154489162,-0.44319046135761897
+-0.7496578335328536,0.11468937267383894
+0.26633577723519614,1.5248028641099014
+0.0447152847496346,-0.01574819167382402
+-0.13528418585705293,1.4820706659497425
+-0.42558674957968945,1.4055954530523647
+1.2737730182416382,-1.5349456271047006
+0.43450294567211123,1.8809119405720927
+1.488091778353866,-0.19409384329776858
+1.4461662688565093,-1.0450530276338366
+0.4266654177614964,1.7705162237260437
+0.40361428138010785,-0.5691760046047758
+1.3275496693894255,-0.7379479781503316
+0.7679508875230497,0.4098307126434222
+1.5381865063937386,-2.56315326696064
+0.21011053692825563,1.9383725182694378
+0.5108484887378737,0.10160319545818997
+0.5627217081087597,1.8565429414294765
+0.971706343089014,-0.40514629378670963
+0.19199467382055402,1.9259399220784463
+-0.6756245096643564,0.7261745483525062
+0.2670147885678944,1.035504856861125
+0.9445048359353467,1.2283795288286563
+0.033975349350585604,1.1432571594655054
+-0.08395601040421827,-0.35313123847682387
+0.3565525882386855,1.686892703773142
+1.1683918569193137,-0.2215300692040281
+0.3042232460336109,1.843711015164943
+0.10201404805283462,-0.01491015423507036
+0.9746266692489101,-1.2328104542139615
+1.09197154489162,-0.44319046135761897
+-0.7496578335328536,0.11468937267383894
+0.26633577723519614,1.5248028641099014
+1.1478986628346992,-0.12233744444344986
+1.5979988906933495,-1.5730279464323484
+-0.42558674957968945,1.4055954530523647
+1.2737730182416382,-1.5349456271047006
+1.24076668777484,-1.4426635351647397
+-0.7970407289374221,0.05313036525397605
+1.4461662688565093,-1.0450530276338366
+-0.6249372577490473,0.7020449813673051
+0.40361428138010785,-0.5691760046047758
+-0.5398513684291377,-0.058733859016793066
+0.11832854211413218,0.35636035977085584
+-0.29825846157128966,2.197873914426695
+-0.4017760025094532,1.0157490962145586
+0.5108484887378737,0.10160319545818997
+1.498867365190862,-1.059698107419857
+0.971706343089014,-0.40514629378670963
+0.19199467382055402,1.9259399220784463
+-0.6756245096643564,0.7261745483525062
+0.04582231932346581,1.341837762226167
+0.48006958986755277,1.1621092982771382
+-0.09515518201119372,0.8123775080316196
+-0.04808312501702941,0.7270637927551052
+-0.6215931375394737,1.1208667876645821
+-0.2822505269843996,1.8322573606716899
+0.3042232460336109,1.843711015164943
+0.7922506008012571,1.244684945855036
+-0.36229881637638894,1.7297510080045533
+0.2870250578332558,0.1577728035186272
+-0.025588130577039514,2.005963689471
+0.26633577723519614,1.5248028641099014
+1.1478986628346992,-0.12233744444344986
+1.5979988906933495,-1.5730279464323484
+-0.42558674957968945,1.4055954530523647
+0.6231240186634873,1.5409678971106682
+1.24076668777484,-1.4426635351647397
+-0.7970407289374221,0.05313036525397605
+1.4461662688565093,-1.0450530276338366
+0.20042030601258531,1.2947688860978233
+-0.8072240404087141,0.3992158321922684
+-0.5398513684291377,-0.058733859016793066
+1.2503004865611462,0.6082757577225197
+-0.041743335407166904,0.8744605231110578
+-0.4325018664278719,0.21810735708554618
+0.503563565964633,1.0707070621558517
+1.498867365190862,-1.059698107419857
+0.971706343089014,-0.40514629378670963
+-0.11616032583613661,2.1046511421136844
+-0.6756245096643564,0.7261745483525062
+0.04582231932346581,1.341837762226167
+0.52130344521401,1.0449249804402077
+-0.09515518201119372,0.8123775080316196
+-0.48975308306288834,0.45891199475927047
+-0.6215931375394737,1.1208667876645821
+-0.2822505269843996,1.8322573606716899
+0.3042232460336109,1.843711015164943
+0.7922506008012571,1.244684945855036
+-0.5193921996720066,0.6725414575620801
+-0.3212631997931049,2.33753706078012
+1.0016997872015905,0.412437774519519
+0.26633577723519614,1.5248028641099014
+1.1478986628346992,-0.12233744444344986
+1.5979988906933495,-1.5730279464323484
+-0.42558674957968945,1.4055954530523647
+0.6231240186634873,1.5409678971106682
+1.24076668777484,-1.4426635351647397
+-0.7970407289374221,0.05313036525397605
+0.49434011214108886,0.6020471395920757
+0.20042030601258531,1.2947688860978233
+-0.8072240404087141,0.3992158321922684
+-0.5398513684291377,-0.058733859016793066
+1.6174115332994443,-1.8036790947249208
+-0.041743335407166904,0.8744605231110578
+-0.24477503530831685,0.018358607344611255
+-0.5210603522050952,1.5755532049843701
+1.498867365190862,-1.059698107419857
+0.971706343089014,-0.40514629378670963
+-0.11616032583613661,2.1046511421136844
+-0.6756245096643564,0.7261745483525062
+-0.2536441962108027,-0.16624265348286682
+0.5396974884493648,0.9921612675304778
+-0.04892240688356103,1.874378248636096
+-0.5671638799136667,1.6537809843219877
+-0.6215931375394737,1.1208667876645821
+-0.13600732993618603,1.358922637198896
+0.3042232460336109,1.843711015164943
+0.7922506008012571,1.244684945855036
+-0.5193921996720066,0.6725414575620801
+-0.8172153491384526,0.7124409706352892
+1.0016997872015905,0.412437774519519
+-0.28775953066454263,2.210275598522293
+1.1478986628346992,-0.12233744444344986
+1.5979988906933495,-1.5730279464323484
+-0.42558674957968945,1.4055954530523647
+0.6231240186634873,1.5409678971106682
+1.6924800958386441,-1.5863290469170253
+-0.7970407289374221,0.05313036525397605
+1.7036287390142908,-3.1033473150626425
+0.20042030601258531,1.2947688860978233
+-0.8072240404087141,0.3992158321922684
+-0.647596069455912,-0.24599444467716758
+0.6782778285464064,1.2117533970230225
+-0.22081951115123555,0.6839716916848338
+0.5812474880843056,1.5215817060671695
+-0.5210603522050952,1.5755532049843701
+1.498867365190862,-1.059698107419857
+0.23815244667825447,1.7658391955847876
+-0.11616032583613661,2.1046511421136844
+-0.03287187628652016,1.941531298192185
+-0.5320082693857269,1.8247631655415546
+0.5396974884493648,0.9921612675304778
+-0.3130880116982178,1.3891255314343554
+-0.46849323761648815,0.12250683899909498
+-0.6215931375394737,1.1208667876645821
+-0.5157397025394674,0.4250656108643706
+0.3042232460336109,1.843711015164943
+0.20840758508373425,2.2897505194466596
+-0.31398491916223836,1.6572997430770222
+-0.8172153491384526,0.7124409706352892
+1.385833332930012,-1.1431156176673976
+-0.28775953066454263,2.210275598522293
+1.1478986628346992,-0.12233744444344986
+1.5979988906933495,-1.5730279464323484
+0.13738164226545813,-0.13092138768344053
+0.6231240186634873,1.5409678971106682
+-0.5798097941427282,1.6077283533066427
+-0.7970407289374221,0.05313036525397605
+1.7036287390142908,-3.1033473150626425
+0.20042030601258531,1.2947688860978233
+-0.8072240404087141,0.3992158321922684
+-0.647596069455912,-0.24599444467716758
+0.6782778285464064,1.2117533970230225
+-0.22081951115123555,0.6839716916848338
+-0.6220667636183035,0.31858363489356967
+-0.5210603522050952,1.5755532049843701
+1.498867365190862,-1.059698107419857
+-0.6554926879521564,0.20180588544804753
+-0.11616032583613661,2.1046511421136844
+-0.03287187628652016,1.941531298192185
+-0.011310748366509249,-0.29526912200344924
+0.5396974884493648,0.9921612675304778
+0.14119311904465975,-0.27538579129127116
+-0.46849323761648815,0.12250683899909498
+-0.33732539191092553,0.4603901254685255
+-0.5157397025394674,0.4250656108643706
+0.7441815255723647,1.8081901761016288
+0.4507804019435732,1.6179406866987132
+-0.49970069682119256,1.7213654287360511
+-0.08326181636244095,0.11977129029277228
+1.3417811646441082,-1.738841007798048
+1.3973235961555899,-0.19128243123803304
+1.1478986628346992,-0.12233744444344986
+1.5979988906933495,-1.5730279464323484
+0.13738164226545813,-0.13092138768344053
+-0.5539408513059649,1.8809855920740712
+-0.3230915584852102,-0.051702977372847625
+-1.1910877960957125,-0.5944502969316077
+1.7036287390142908,-3.1033473150626425
+-0.009573921119461426,0.7247457801232862
+-0.8072240404087141,0.3992158321922684
+-0.5995053986550991,-0.11027714345847903
+0.6782778285464064,1.2117533970230225
+-0.6216010746143209,0.775237421117519
+1.6860120976456987,-1.3804317223462685
+-0.5210603522050952,1.5755532049843701
+1.498867365190862,-1.059698107419857
+0.8328316484090521,0.7400090260117392
+-0.11616032583613661,2.1046511421136844
+-0.03287187628652016,1.941531298192185
+-0.216381294665202,1.7291179931718068
+0.5396974884493648,0.9921612675304778
+-0.8565753305350596,0.43994190565141733
+1.431847575899824,-0.48162600871858674
+-0.16239460165051406,-0.3016610787209051
+0.8109882011136587,-0.4658772102174219
+0.7441815255723647,1.8081901761016288
+0.63453537386509,1.3103215150094116
+-0.43368317242218096,1.04051848592485
+-0.08326181636244095,0.11977129029277228
+1.3417811646441082,-1.738841007798048
+1.3973235961555899,-0.19128243123803304
+1.1478986628346992,-0.12233744444344986
+-0.28856670509935944,1.3765657524322035
+0.04296425060174114,1.6880755156555014
+-0.31893963904139677,2.0985849554471514
+-0.3230915584852102,-0.051702977372847625
+-0.35326515158964245,2.113462734015473
+-0.020092017712041936,2.3962182664713
+-0.009573921119461426,0.7247457801232862
+-0.8072240404087141,0.3992158321922684
+-0.5995053986550991,-0.11027714345847903
+0.6782778285464064,1.2117533970230225
+-0.6216010746143209,0.775237421117519
+1.6860120976456987,-1.3804317223462685
+-0.5210603522050952,1.5755532049843701
+1.498867365190862,-1.059698107419857
+0.8328316484090521,0.7400090260117392
+-0.2921519022260332,0.44788060453685097
+-0.03287187628652016,1.941531298192185
+-1.0128420559751201,0.48796468202035614
+0.5396974884493648,0.9921612675304778
+0.6108600989963406,1.59140922891058
+-0.6057067587045754,1.2769639736070033
+0.9195101383449334,-0.9733817801874609
+-0.06709388150774598,2.091166791067054
+0.7441815255723647,1.8081901761016288
+0.557608670433919,1.0722216625884897
+-0.43368317242218096,1.04051848592485
+1.6204634267202094,-0.9947229651683882
+1.3417811646441082,-1.738841007798048
+1.3973235961555899,-0.19128243123803304
+1.1478986628346992,-0.12233744444344986
+-0.28856670509935944,1.3765657524322035
+0.684126738581993,1.1212295936602048
+-0.31893963904139677,2.0985849554471514
+-0.3230915584852102,-0.051702977372847625
+-0.35326515158964245,2.113462734015473
+-0.020092017712041936,2.3962182664713
+-0.4229857534199546,-0.15399430184770502
+-0.7939766872012306,-0.4668396045725637
+-0.5995053986550991,-0.11027714345847903
+-0.3500734383032143,1.5523131935232382
+0.9541013402654587,-0.4674216969058823
+1.6860120976456987,-1.3804317223462685
+-0.5210603522050952,1.5755532049843701
+1.498867365190862,-1.059698107419857
+0.8328316484090521,0.7400090260117392
+-0.2921519022260332,0.44788060453685097
+-0.03287187628652016,1.941531298192185
+-0.9809393258063972,0.3617182156801374
+0.5396974884493648,0.9921612675304778
+0.6108600989963406,1.59140922891058
+-0.6057067587045754,1.2769639736070033
+0.9195101383449334,-0.9733817801874609
+1.6229086734327494,-1.8632261717227392
+1.182102304668745,0.07600858833756018
+0.3905528388952648,0.2843686824105985
+-0.43368317242218096,1.04051848592485
+-0.17201155853384587,0.6048095025507659
+1.3417811646441082,-1.738841007798048
+1.3973235961555899,-0.19128243123803304
+1.1478986628346992,-0.12233744444344986
+-0.7249568374858737,1.1945243441632745
+0.684126738581993,1.1212295936602048
+0.26012021335947216,1.832515429710612
+0.12959281141334633,0.004976282183912495
+1.0242246897344525,-0.6294180872056033
+-0.9468423396165794,-0.051165691195900864
+-0.598271963776351,1.754561004856287
+0.4286715398108718,-0.17815973167704258
+-0.5995053986550991,-0.11027714345847903
+-0.3500734383032143,1.5523131935232382
+-0.5369946010507447,1.3543600988473115
+-0.04788933758154623,0.7539871212214033
+-0.5210603522050952,1.5755532049843701
+1.498867365190862,-1.059698107419857
+0.04827266468642122,1.2163877045008311
+0.5792413705363799,-0.8627340635836589
+-0.03287187628652016,1.941531298192185
+-0.9809393258063972,0.3617182156801374
+0.5396974884493648,0.9921612675304778
+-0.746280895781118,1.0799557153236745
+-0.6057067587045754,1.2769639736070033
+0.9195101383449334,-0.9733817801874609
+1.6229086734327494,-1.8632261717227392
+0.08957935397715056,-0.13666630368564292
+0.40533320266849615,1.7338823521574784
+-0.4917640154511187,-0.01801264816519907
+-0.8983278501287013,0.11732331612560379
+1.3417811646441082,-1.738841007798048
+1.3973235961555899,-0.19128243123803304
+1.1478986628346992,-0.12233744444344986
+-0.7249568374858737,1.1945243441632745
+0.684126738581993,1.1212295936602048
+0.2985803504610981,1.5819774439878778
+0.12959281141334633,0.004976282183912495
+0.45576816137030807,-0.796287517093682
+-0.9468423396165794,-0.051165691195900864
+-0.26071651336952895,-0.11795278626410294
+0.4286715398108718,-0.17815973167704258
+-0.5995053986550991,-0.11027714345847903
+-0.3500734383032143,1.5523131935232382
+0.7842560988199263,-0.7641358494446029
+-0.04788933758154623,0.7539871212214033
+-0.5210603522050952,1.5755532049843701
+0.15532865530122952,1.350489650267718
+1.5940738045023226,-1.772434038227321
+0.7163377804111357,-0.22429643836159385
+-0.03287187628652016,1.941531298192185
+-0.9809393258063972,0.3617182156801374
+0.5396974884493648,0.9921612675304778
+0.8713127003988725,0.22890214045402657
+-0.6057067587045754,1.2769639736070033
+0.9195101383449334,-0.9733817801874609
+0.9073489644604291,-0.5937786210611604
+1.1916979230412394,-1.391884519911375
+-0.343753162191497,1.624795501592215
+-0.4917640154511187,-0.01801264816519907
+-0.8983278501287013,0.11732331612560379
+1.3417811646441082,-1.738841007798048
+1.3973235961555899,-0.19128243123803304
+1.1478986628346992,-0.12233744444344986
+-0.0019614149393560876,1.4134692482339806
+-0.9265686343682575,-0.5864143412508741
+1.6970619096509258,-2.1459497065628073
+-0.3649371286929459,1.202601001538203
+0.45576816137030807,-0.796287517093682
+-0.9468423396165794,-0.051165691195900864
+-0.26071651336952895,-0.11795278626410294
+0.4286715398108718,-0.17815973167704258
+1.7472517635494822,-2.6194746476922037
+-0.3500734383032143,1.5523131935232382
+0.7842560988199263,-0.7641358494446029
+1.3316709191021654,-0.708067629051565
+-0.5210603522050952,1.5755532049843701
+-0.0934878686141,2.1381174109745453
+1.4028158404290654,-1.3590119139151287
+1.7288468606927945,-2.55831596059513
+-0.03287187628652016,1.941531298192185
+0.7804574397316134,0.06809905749984835
+0.5396974884493648,0.9921612675304778
+-0.23284987327843348,0.205159513614795
+-0.6057067587045754,1.2769639736070033
+0.5938557189951839,-0.5638210298598054
+1.5813428014327537,-2.053345442563199
+1.1916979230412394,-1.391884519911375
+-0.343753162191497,1.624795501592215
+0.4043071234452301,1.6960042961885802
+0.2731791871370249,0.5846855790504262
+0.1808494264148286,1.4458310157385128
+1.3973235961555899,-0.19128243123803304
+1.6178316588252935,-0.9417992179309981
+1.1594030164410516,-1.4976334686899966
+-0.5585460947825441,0.6263377188676045
+1.6970619096509258,-2.1459497065628073
+1.3331413646013228,-1.1373412030930932
+0.45576816137030807,-0.796287517093682
+-0.9468423396165794,-0.051165691195900864
+-0.385826774203745,0.7002204224586706
+0.4286715398108718,-0.17815973167704258
+1.349714520177023,-2.0763431593350323
+-0.3500734383032143,1.5523131935232382
+0.43136094232602074,-0.6448277750377249
+0.9100361570640864,-0.9152732515028179
+-0.5210603522050952,1.5755532049843701
+-0.0934878686141,2.1381174109745453
+0.988090388411874,0.050103671949279116
+1.7288468606927945,-2.55831596059513
+-0.03287187628652016,1.941531298192185
+1.0646387247161595,0.5516927844176314
+-0.005183479367272259,-0.003568948260702781
+0.06549831073617896,0.5078762344323513
+-0.6057067587045754,1.2769639736070033
+0.9680541493216774,0.6089844921821187
+1.894460067391323,-3.0533765232290495
+0.20340703466597418,2.4249036054406545
+1.1580999190847725,-0.21574832617810547
+0.4043071234452301,1.6960042961885802
+1.6476298489735468,-1.4001096270510194
+0.1808494264148286,1.4458310157385128
+1.3973235961555899,-0.19128243123803304
+1.6178316588252935,-0.9417992179309981
+1.1594030164410516,-1.4976334686899966
+-0.5585460947825441,0.6263377188676045
+0.671459897817404,0.8100947221141193
+0.32530924111904874,0.05757663577391825
+0.08669874185845784,-0.18234241211649657
+-0.9468423396165794,-0.051165691195900864
+-0.385826774203745,0.7002204224586706
+0.4286715398108718,-0.17815973167704258
+1.349714520177023,-2.0763431593350323
+-0.47676181696111253,1.8752897652766247
+0.43136094232602074,-0.6448277750377249
+0.29174221341538875,-0.6548574491188774
+-0.5210603522050952,1.5755532049843701
+-0.1567388173299129,-0.37574503465236236
+-0.26174393566201504,2.472376886337879
+0.15081451624584652,0.5196424586169198
+-0.03287187628652016,1.941531298192185
+1.0646387247161595,0.5516927844176314
+-0.29412203199961917,-0.1641946613428445
+0.49669463672927927,1.109677711648694
+1.02872562517402,0.07884399534204112
+0.9680541493216774,0.6089844921821187
+1.894460067391323,-3.0533765232290495
+-0.18382949157459832,0.29423474762358875
+0.7510133404415686,-0.4947010360877463
+0.45021384154865396,1.5266542015454845
+1.6476298489735468,-1.4001096270510194
+0.20781512517336784,1.25586067299411
+0.547631501008365,1.1476878047724663
+1.6178316588252935,-0.9417992179309981
+0.02906673152923027,0.5021516928625076
+-0.9012961556150507,0.9714136036578966
+0.17039267486617302,0.11315536530114552
+-0.5650456785285842,1.6638913876932524
+0.08669874185845784,-0.18234241211649657
+-0.9468423396165794,-0.051165691195900864
+-0.3391678899292642,0.24561113662322548
+0.4286715398108718,-0.17815973167704258
+1.349714520177023,-2.0763431593350323
+0.9681035763920188,0.43596790741754765
+0.9697338167987516,0.03861203319132411
+-0.23343300091165112,0.9099947470297917
+-0.5210603522050952,1.5755532049843701
+0.0024802715048601043,0.42324576417435883
+-0.26174393566201504,2.472376886337879
+-0.7044146751074701,-0.22703861011658016
+-0.5027088069939679,0.463696222487132
+1.0646387247161595,0.5516927844176314
+-0.8224511773509638,0.48432993094526816
+-0.5654491911623751,0.6802170856474126
+-0.09296985886850728,0.38929750061894774
+-0.6126527390681189,-0.3368382895828492
+1.894460067391323,-3.0533765232290495
+-0.18382949157459832,0.29423474762358875
+0.7246587325697659,1.2700306375752144
+0.45021384154865396,1.5266542015454845
+-0.20823758841057366,0.47150642579806135
+0.20781512517336784,1.25586067299411
+0.547631501008365,1.1476878047724663
+1.6178316588252935,-0.9417992179309981
+1.1022797758353373,0.4385570283265244
+-0.9012961556150507,0.9714136036578966
+-0.56770759947395,-0.25741193821734204
+-0.6437192031741852,1.5076488781651498
+-0.6244739577330832,-0.23616497174892254
+-0.6684956907882482,0.2048727788602578
+-0.3391678899292642,0.24561113662322548
+0.4286715398108718,-0.17815973167704258
+1.349714520177023,-2.0763431593350323
+1.1456954680212896,0.38488029602081236
+-0.9387443311519178,0.17582736275305588
+0.5184200743462981,1.6866989716143068
+-1.1341351634781636,-0.14952507584306873
+0.31222429473977975,1.4644813701483506
+-0.26174393566201504,2.472376886337879
+-0.7044146751074701,-0.22703861011658016
+0.44342016861431854,0.13376146015254853
+1.0646387247161595,0.5516927844176314
+-0.8224511773509638,0.48432993094526816
+-0.5654491911623751,0.6802170856474126
+-0.40596795118573614,0.37261726979662146
+-0.6126527390681189,-0.3368382895828492
+1.894460067391323,-3.0533765232290495
+-0.18382949157459832,0.29423474762358875
+0.07638521503393825,1.7623933219071524
+1.2633254836988719,0.24259053486770563
+0.06416917975499031,1.016766940806015
+0.8854517973285182,-0.02946609326849467
+0.547631501008365,1.1476878047724663
+0.5002433728701252,1.983846975344442
+-0.14405139478044682,0.1135969887573523
+-0.45051880827462387,1.7028227624753272
+1.128667543449237,-0.05065128578348871
+0.7363559354935875,-1.075001355167312
+-0.6244739577330832,-0.23616497174892254
+0.1318399388555374,1.3682848682522706
+-0.9338698745679822,0.09236182189706788
+-0.9131264229106385,-0.013989799936713315
+1.349714520177023,-2.0763431593350323
+1.1456954680212896,0.38488029602081236
+0.8100499987982117,-0.5268130741135907
+-0.03386732365816428,2.3990119135281227
+-0.629368393876558,0.09237779144400932
+0.31222429473977975,1.4644813701483506
+-0.1299040345792405,2.327457791516533
+-0.6514397798441426,0.6941184010319148
+0.6788379646234888,0.7167961254624011
+1.20856628848858,-1.4186395954374127
+0.8974969385594882,1.4960647942435226
+-0.5654491911623751,0.6802170856474126
+-0.40596795118573614,0.37261726979662146
+0.5308744651766744,0.21998043554184044
+1.894460067391323,-3.0533765232290495
+0.948734163327209,0.007963747768557572
+0.07638521503393825,1.7623933219071524
+1.2633254836988719,0.24259053486770563
+0.46549621693048293,0.7331149331465519
+-0.8006072500391768,0.4247631919877683
+0.547631501008365,1.1476878047724663
+0.45649528091465497,-0.4660112645012804
+-0.6748636515327935,0.4683511385619208
+-0.45051880827462387,1.7028227624753272
+1.128667543449237,-0.05065128578348871
+0.7363559354935875,-1.075001355167312
+0.9384563430891818,-1.1354594604705155
+-0.4473353033405385,1.2211134976933893
+-0.9338698745679822,0.09236182189706788
+-0.9131264229106385,-0.013989799936713315
+1.349714520177023,-2.0763431593350323
+1.1456954680212896,0.38488029602081236
+0.8100499987982117,-0.5268130741135907
+-0.03386732365816428,2.3990119135281227
+0.45236393107504536,1.9459854518283881
+0.31222429473977975,1.4644813701483506
+-0.1299040345792405,2.327457791516533
+0.5555921491749485,1.6832351634260576
+1.5597199963209034,-2.32790442102406
+1.3670715745223014,-1.7161914668842306
+1.1652040595229978,0.9117580675662827
+-0.5654491911623751,0.6802170856474126
+-0.40596795118573614,0.37261726979662146
+0.5308744651766744,0.21998043554184044
+1.894460067391323,-3.0533765232290495
+0.31604388606428513,1.7327152185728318
+1.2127874028730232,-0.7895993132352437
+1.2633254836988719,0.24259053486770563
+-0.5495527677079364,2.068906715129394
+-0.8006072500391768,0.4247631919877683
+0.547631501008365,1.1476878047724663
+0.45649528091465497,-0.4660112645012804
+-0.6748636515327935,0.4683511385619208
+1.0081334459396587,1.0907577363481793
+1.128667543449237,-0.05065128578348871
+-0.29288953059678224,0.567379931340255
+1.4013901223898317,-0.3363149488316521
+-0.4473353033405385,1.2211134976933893
+-0.9338698745679822,0.09236182189706788
+-0.9131264229106385,-0.013989799936713315
+1.5654667174375165,-1.7977875052562127
+-0.9035130506417903,0.37772576786998197
+0.8100499987982117,-0.5268130741135907
+1.4774297110733359,-0.6454731409613621
+1.2326905761198552,-1.0303059340845486
+0.31222429473977975,1.4644813701483506
+-0.1299040345792405,2.327457791516533
+0.5555921491749485,1.6832351634260576
+-0.2509454955051975,1.9109114558758322
+1.3670715745223014,-1.7161914668842306
+1.1652040595229978,0.9117580675662827
+-0.5654491911623751,0.6802170856474126
+-0.40596795118573614,0.37261726979662146
+0.5308744651766744,0.21998043554184044
+0.7503843857762829,-0.7647640532264215
+-0.1047791361448428,1.1614181017902112
+0.6075425979087907,0.9234482566550155
+1.2633254836988719,0.24259053486770563
+0.9743209791743211,0.8105370068966932
+-0.8006072500391768,0.4247631919877683
+0.547631501008365,1.1476878047724663
+0.45649528091465497,-0.4660112645012804
+-0.6748636515327935,0.4683511385619208
+1.0081334459396587,1.0907577363481793
+0.6341006606922605,0.6216495656591087
+-0.29288953059678224,0.567379931340255
+1.4013901223898317,-0.3363149488316521
+1.0091798975630257,0.3708406430726362
+-0.21051054074292672,-0.11118939440670655
+-0.9131264229106385,-0.013989799936713315
+1.5654667174375165,-1.7977875052562127
+-0.8181647483051833,0.26415326149466034
+0.8100499987982117,-0.5268130741135907
+1.4774297110733359,-0.6454731409613621
+1.2326905761198552,-1.0303059340845486
+0.31222429473977975,1.4644813701483506
+-0.1299040345792405,2.327457791516533
+-0.2113015093350189,0.3213088228003216
+-0.2509454955051975,1.9109114558758322
+0.6167666382446377,1.4716962314815896
+0.535121210210102,0.6511121080489558
+-0.5654491911623751,0.6802170856474126
+-0.13315519411652457,1.479304690812937
+0.03725188038930771,-0.22472808138815453
+0.7503843857762829,-0.7647640532264215
+0.07544657887975831,2.034884468286415
+-0.6646217112443651,-0.2628851451633596
+1.130366836403214,-1.312318696184559
+0.01987989160814127,0.07974203697243323
+-0.11068594204436724,0.20174939578701062
+-0.8352467043537702,0.4400485785900761
+0.45649528091465497,-0.4660112645012804
+-0.6748636515327935,0.4683511385619208
+1.0081334459396587,1.0907577363481793
+0.6341006606922605,0.6216495656591087
+-0.29288953059678224,0.567379931340255
+1.4013901223898317,-0.3363149488316521
+1.0091798975630257,0.3708406430726362
+-0.21051054074292672,-0.11118939440670655
+1.3564850344850874,-1.433169417346538
+1.5654667174375165,-1.7977875052562127
+-0.8181647483051833,0.26415326149466034
+0.8100499987982117,-0.5268130741135907
+1.4774297110733359,-0.6454731409613621
+1.2326905761198552,-1.0303059340845486
+0.31222429473977975,1.4644813701483506
+-0.5879201692936913,1.830905903726526
+-0.11096463452923178,1.0385557591003225
+-0.2509454955051975,1.9109114558758322
+0.6167666382446377,1.4716962314815896
+0.058060550184620724,1.0421506214608767
+-0.5654491911623751,0.6802170856474126
+-0.13315519411652457,1.479304690812937
+0.03725188038930771,-0.22472808138815453
+0.7503843857762829,-0.7647640532264215
+0.07544657887975831,2.034884468286415
+-0.6646217112443651,-0.2628851451633596
+0.08719422375100237,-0.33194961469831163
+1.7488918955733217,-1.8473774703771904
+-0.11068594204436724,0.20174939578701062
+1.7008234005278928,-2.667292439982092
+0.18516597365691967,0.435990374782694
+-0.6748636515327935,0.4683511385619208
+0.3088704809956415,0.17184607919571532
+0.8044522874892769,0.2859634041610315
+0.3840750630928207,-0.24487719379570638
+1.2699746193458872,-0.951995150208296
+1.0091798975630257,0.3708406430726362
+-0.47489443033580714,0.9703110353146362
+1.3564850344850874,-1.433169417346538
+1.5654667174375165,-1.7977875052562127
+-0.29581453134908775,0.32428648960265616
+0.8100499987982117,-0.5268130741135907
+1.4774297110733359,-0.6454731409613621
+1.2326905761198552,-1.0303059340845486
+0.31222429473977975,1.4644813701483506
+-0.5879201692936913,1.830905903726526
+0.46727592531673956,-0.39891814033501694
+-0.2509454955051975,1.9109114558758322
+0.6167666382446377,1.4716962314815896
+0.058060550184620724,1.0421506214608767
+-0.5654491911623751,0.6802170856474126
+-0.13315519411652457,1.479304690812937
+0.03725188038930771,-0.22472808138815453
+0.8730392793552239,-0.49895100612740495
+0.07544657887975831,2.034884468286415
+-0.6646217112443651,-0.2628851451633596
+1.316742819964597,-0.12768421755171055
+1.7488918955733217,-1.8473774703771904
+-0.11068594204436724,0.20174939578701062
+-0.2628095399173944,1.9251201638492796
+0.18516597365691967,0.435990374782694
+-0.6748636515327935,0.4683511385619208
+-0.49593534789057425,0.11612432507738547
+0.8044522874892769,0.2859634041610315
+0.3840750630928207,-0.24487719379570638
+0.5514723503086968,-0.44876520016260835
+1.0091798975630257,0.3708406430726362
+1.234766832544969,0.05224225615943251
+1.3564850344850874,-1.433169417346538
+1.3548430420482718,-0.10789696700953355
+-0.29581453134908775,0.32428648960265616
+0.8100499987982117,-0.5268130741135907
+1.4774297110733359,-0.6454731409613621
+1.0258024688655074,-0.859077926980836
+-0.22456822481570796,1.6312268416617761
+-0.5879201692936913,1.830905903726526
+0.46727592531673956,-0.39891814033501694
+-0.2509454955051975,1.9109114558758322
+0.6167666382446377,1.4716962314815896
+-0.20996828527581518,-0.15294466773291637
+-0.5654491911623751,0.6802170856474126
+0.5797992549752338,-0.707792936411166
+0.03725188038930771,-0.22472808138815453
+0.9265628259804359,-1.2032369718199263
+0.07544657887975831,2.034884468286415
+-0.6646217112443651,-0.2628851451633596
+1.316742819964597,-0.12768421755171055
+1.230761667458845,0.4866566062600431
+-0.11068594204436724,0.20174939578701062
+-0.2628095399173944,1.9251201638492796
+0.41827090769147407,-0.48844499450136325
+-0.6748636515327935,0.4683511385619208
+-0.11376491295689012,2.435308339805766
+0.08279491568795733,2.1619265270584234
+0.3840750630928207,-0.24487719379570638
+0.2563635770198347,0.7575673226095502
+-0.25201910947970074,1.3458025161488205
+1.234766832544969,0.05224225615943251
+1.3564850344850874,-1.433169417346538
+1.3548430420482718,-0.10789696700953355
+0.6150822036551866,1.4830417840538526
+0.8100499987982117,-0.5268130741135907
+0.252897917919505,1.57244523540297
+0.02789972226681256,2.2254765272431936
+0.14959730949548494,0.2575382808287464
+1.5932330343377001,-0.7235634684892349
+0.46727592531673956,-0.39891814033501694
+-0.2509454955051975,1.9109114558758322
+1.6101474930291948,-0.9045353190317349
+-0.20996828527581518,-0.15294466773291637
+-0.5654491911623751,0.6802170856474126
+0.4604363114973121,-0.31574974576062154
+0.9300730569872662,-0.9455132501848847
+0.9577330226448433,1.1511123095793194
+0.6757307208249395,0.15833825200125656
+-0.6646217112443651,-0.2628851451633596
+1.316742819964597,-0.12768421755171055
+0.870885446091114,-0.9311152602230601
+1.725942249345154,-1.4402925019719153
+-0.2628095399173944,1.9251201638492796
+1.179718871661899,-1.1481736737999593
+0.31273271763709987,0.5417502231341557
+0.4633834922429983,0.4632553091808903
+1.3782277481447092,-1.5828528685683114
+0.3840750630928207,-0.24487719379570638
+0.2563635770198347,0.7575673226095502
+-0.25201910947970074,1.3458025161488205
+1.234766832544969,0.05224225615943251
+1.281286872510619,-0.29380723231202754
+1.3548430420482718,-0.10789696700953355
+0.6150822036551866,1.4830417840538526
+0.8100499987982117,-0.5268130741135907
+1.0270902489205755,0.648214800079008
+1.3599427194618634,-0.37563437061919935
+-0.20193095567369673,1.807976597075576
+1.3510453000528213,-1.5821479549934536
+0.46727592531673956,-0.39891814033501694
+-0.2509454955051975,1.9109114558758322
+0.9189019715924446,0.8537201130828417
+-0.20996828527581518,-0.15294466773291637
+-0.5654491911623751,0.6802170856474126
+0.4604363114973121,-0.31574974576062154
+0.49026706341340487,1.684885968950855
+0.9577330226448433,1.1511123095793194
+-0.1291203000510247,-0.01438862403927263
+-0.6646217112443651,-0.2628851451633596
+1.316742819964597,-0.12768421755171055
+0.1721854423781202,-0.06139861425356413
+-0.17352731919781728,1.6556099965170537
+-0.2628095399173944,1.9251201638492796
+1.179718871661899,-1.1481736737999593
+1.144245559107198,-1.2679341751600308
+0.4633834922429983,0.4632553091808903
+-0.24343498839100444,2.054631599796968
+0.5939083315058138,0.49370160711540223
+-0.4764234319331444,2.158402544278988
+-0.25201910947970074,1.3458025161488205
+0.034602789406729895,1.8190499785672904
+1.281286872510619,-0.29380723231202754
+0.5401905594403229,-0.588377558718249
+0.6150822036551866,1.4830417840538526
+-0.6813373752989305,0.5477121169246078
+0.8966728048904131,0.3105101122667785
+1.3599427194618634,-0.37563437061919935
+-0.20193095567369673,1.807976597075576
+1.3510453000528213,-1.5821479549934536
+0.46727592531673956,-0.39891814033501694
+-0.2509454955051975,1.9109114558758322
+0.9189019715924446,0.8537201130828417
+-0.20996828527581518,-0.15294466773291637
+-0.5654491911623751,0.6802170856474126
+0.4604363114973121,-0.31574974576062154
+0.49026706341340487,1.684885968950855
+0.9577330226448433,1.1511123095793194
+0.013012530524336902,1.892745669478854
+-0.6646217112443651,-0.2628851451633596
+1.316742819964597,-0.12768421755171055
+0.0051671440364097765,0.27223038858143156
+-0.17352731919781728,1.6556099965170537
+1.4685622680731016,-0.7859099658930561
+-0.17256828864086338,0.18552458285910706
+1.144245559107198,-1.2679341751600308
+-0.3110409280514573,-0.2369841792274247
+-0.24343498839100444,2.054631599796968
+0.8440631368838488,1.678776574375409
+0.32655477184675463,-0.5961261261497515
+-0.25201910947970074,1.3458025161488205
+0.7075265222155804,0.8635592763394824
+0.42630218986270807,1.9921279371349576
+0.5401905594403229,-0.588377558718249
+0.6150822036551866,1.4830417840538526
+-0.7818493123744832,1.12366388565102
+1.266911286262741,-1.3939234464443389
+1.3599427194618634,-0.37563437061919935
+-0.8563556245549533,-0.01207101063654989
+1.3510453000528213,-1.5821479549934536
+0.46727592531673956,-0.39891814033501694
+-0.2509454955051975,1.9109114558758322
+-0.5914998805669713,-0.23918104658197825
+0.664662528583518,-0.19290712459211368
+0.016981732071819966,2.2927054719479862
+0.4604363114973121,-0.31574974576062154
+0.20018602383431278,0.46402649283715924
+0.9577330226448433,1.1511123095793194
+0.013012530524336902,1.892745669478854
+0.19074624490780645,1.737941434535275
+-0.5256029156925768,0.7083719132581848
+0.15017628180962495,2.326431074489738
+0.5944896838666238,-0.5617323490016894
+1.4685622680731016,-0.7859099658930561
+-0.17256828864086338,0.18552458285910706
+1.144245559107198,-1.2679341751600308
+-0.3984486442853291,0.6067290327330521
+-0.24343498839100444,2.054631599796968
+1.409743440864417,-1.5027728687840138
+0.19593476589999936,-0.21304849407053045
+1.3030911409687806,-0.927533605862577
+-0.11587356363133644,0.9493905250240492
+0.42630218986270807,1.9921279371349576
+-0.0990365207753359,1.7411314020242599
+0.6150822036551866,1.4830417840538526
+-0.45476615503423995,0.7131571243700299
+1.266911286262741,-1.3939234464443389
+1.3599427194618634,-0.37563437061919935
+-0.8563556245549533,-0.01207101063654989
+0.22537141857371268,-0.18395569384310267
+0.46727592531673956,-0.39891814033501694
+-0.2509454955051975,1.9109114558758322
+-0.5914998805669713,-0.23918104658197825
+0.7182756337042167,-0.3730306153715699
+-0.09095897347270232,0.7702078347873449
+0.5073815996770656,1.6692672365085426
+0.6030486139712155,1.522534678611752
+0.9577330226448433,1.1511123095793194
+0.013012530524336902,1.892745669478854
+-0.16347979934392834,1.054709777422285
+0.8431577042636527,-0.6859172564557945
+0.15017628180962495,2.326431074489738
+0.5944896838666238,-0.5617323490016894
+0.8335190546107024,0.9415702453353586
+1.281462510867263,-1.4582378792483857
+1.144245559107198,-1.2679341751600308
+-0.5220731920977418,1.621849025431918
+-0.5426033070617904,1.62924622793816
+1.3811884717853005,-0.9388514889582427
+0.19593476589999936,-0.21304849407053045
+1.3030911409687806,-0.927533605862577
+1.4070538612962906,-0.80836849405188
+1.7124233067122412,-1.9779307159588466
+-0.0990365207753359,1.7411314020242599
+0.4357223527551332,1.9976309906992766
+-0.45476615503423995,0.7131571243700299
+1.266911286262741,-1.3939234464443389
+-0.8144481586170256,0.8867339011952781
+-0.8563556245549533,-0.01207101063654989
+-0.10239459310773821,2.206885895885195
+-0.3166182199968658,1.9376322848555376
+0.16322597165860248,1.9753394301911062
+1.0703960158401893,-0.6677256531660511
+0.7182756337042167,-0.3730306153715699
+1.3354140308341342,-1.1152363482870946
+0.5073815996770656,1.6692672365085426
+0.6030486139712155,1.522534678611752
+-0.29602851984069206,0.22196837472405817
+0.6520714052101417,1.073975458797608
+1.1465352482865447,-0.9915410446451501
+0.9108246661305275,-0.07498373594449248
+0.8020933413107296,-0.9255998738553444
+0.5944896838666238,-0.5617323490016894
+-0.16213747869649353,1.2621186070253474
+1.336029591398861,-1.8210623108958395
+1.144245559107198,-1.2679341751600308
+1.8490660488731883,-2.066559991536337
+-0.5426033070617904,1.62924622793816
+1.3683561225313894,-0.2906936253442135
+1.4419045258432641,-1.3577458711916335
+1.61246115528993,-0.989490467859101
+1.0879401723155278,-0.7247690697798114
+-0.38923172064464134,0.6822643057303986
+-0.07992949037653024,0.6411457974590402
+0.4357223527551332,1.9976309906992766
+1.5826269648626177,-2.371974895773103
+1.6444849323110466,-2.1740934667434177
+-0.8144481586170256,0.8867339011952781
+-0.8563556245549533,-0.01207101063654989
+-0.409644044191553,1.3732175513773883
+-0.3166182199968658,1.9376322848555376
+0.16322597165860248,1.9753394301911062
+0.9841098613732537,-0.6407403822573234
+-0.351984482094881,0.7504875665616746
+1.3354140308341342,-1.1152363482870946
+0.4598800712059249,0.5982251199648501
+0.6030486139712155,1.522534678611752
+-0.29602851984069206,0.22196837472405817
+0.6520714052101417,1.073975458797608
+1.1465352482865447,-0.9915410446451501
+0.9108246661305275,-0.07498373594449248
+0.8020933413107296,-0.9255998738553444
+-0.37987130258538965,0.5738784634893288
+-0.16213747869649353,1.2621186070253474
+1.1881067839656834,0.021752733394033497
+1.144245559107198,-1.2679341751600308
+1.8490660488731883,-2.066559991536337
+-0.5426033070617904,1.62924622793816
+-0.1057744411353965,2.318943391521577
+-0.5444908044969188,0.5263605205731798
+-0.2244264697570179,0.8707071598066866
+-0.038044156167674814,0.25340457326289834
+1.0297229474205043,1.0466025218767947
+-0.20871246679340916,1.702052602314103
+0.4357223527551332,1.9976309906992766
+0.02271052747558555,1.7294627910981255
+1.8035647118394342,-1.7212724237337853
+-0.8144481586170256,0.8867339011952781
+-0.8563556245549533,-0.01207101063654989
+-0.7125475336703334,1.2724531990928278
+0.44456004461949206,1.954981991267006
+0.16322597165860248,1.9753394301911062
+0.9841098613732537,-0.6407403822573234
+-0.351984482094881,0.7504875665616746
+1.3354140308341342,-1.1152363482870946
+-0.1954184956007794,0.4962327519018799
+0.6030486139712155,1.522534678611752
+0.18794022976430275,1.9282421464557604
+0.6520714052101417,1.073975458797608
+1.284073473174256,-1.6608294801494332
+-0.5763886678797879,1.0356798852396925
+0.9351744420159167,0.9605542531970264
+-0.37987130258538965,0.5738784634893288
+-0.8470132651999085,0.332484931302402
+1.1881067839656834,0.021752733394033497
+1.144245559107198,-1.2679341751600308
+0.45421641097018495,-0.00040860004807175
+1.4344894036390599,-0.3992228815608235
+-0.4402650139339345,1.5438443885260233
+-0.5444908044969188,0.5263605205731798
+-0.2244264697570179,0.8707071598066866
+0.0517104754925207,1.4642972945711885
+1.0297229474205043,1.0466025218767947
+-0.20871246679340916,1.702052602314103
+0.4357223527551332,1.9976309906992766
+0.02271052747558555,1.7294627910981255
+0.22313655745445252,-0.4230431937714515
+-0.6413753601843469,-0.2701621785195515
+-0.8563556245549533,-0.01207101063654989
+-0.7125475336703334,1.2724531990928278
+0.44456004461949206,1.954981991267006
+0.16322597165860248,1.9753394301911062
+-0.5262315269928899,0.9879727130671676
+-0.351984482094881,0.7504875665616746
+1.3354140308341342,-1.1152363482870946
+-0.5521969021536289,0.33097335517688403
+0.6030486139712155,1.522534678611752
+0.18794022976430275,1.9282421464557604
+0.7253306339053499,0.9999581534661991
+0.05781987552767709,0.9107561426821875
+0.4867598986287458,1.119866678072237
+1.5764801647960125,-1.1719766221667087
+-0.5903164512182902,-0.3224530835479048
+-0.8470132651999085,0.332484931302402
+1.1881067839656834,0.021752733394033497
+1.144245559107198,-1.2679341751600308
+0.45421641097018495,-0.00040860004807175
+0.9767890704576838,-0.2711308946148827
+-0.4402650139339345,1.5438443885260233
+-0.025635785449540704,2.058340068850073
+-0.2244264697570179,0.8707071598066866
+0.2559583430209902,2.11779842585426
+1.0297229474205043,1.0466025218767947
+-0.20871246679340916,1.702052602314103
+0.4357223527551332,1.9976309906992766
+1.5658268955957066,-0.723935742793102
+0.22313655745445252,-0.4230431937714515
+-0.6413753601843469,-0.2701621785195515
+-0.8563556245549533,-0.01207101063654989
+-0.7125475336703334,1.2724531990928278
+0.44456004461949206,1.954981991267006
+-0.4953612712248654,1.1487964838634515
+-0.5262315269928899,0.9879727130671676
+0.6938035858785137,0.9885993197071185
+1.3354140308341342,-1.1152363482870946
+-0.5521969021536289,0.33097335517688403
+-0.7668971855116272,1.6430892900133407
+0.18794022976430275,1.9282421464557604
+-0.7253790363700436,1.1254475509180553
+1.0500135298354658,-0.8450450058221037
+-0.6908746019623454,0.4036508743161793
+1.5764801647960125,-1.1719766221667087
+-0.4914060192319184,-0.180311939096318
+-0.8470132651999085,0.332484931302402
+0.15092326854129984,-0.1430232464949157
+1.144245559107198,-1.2679341751600308
+0.45421641097018495,-0.00040860004807175
+0.9767890704576838,-0.2711308946148827
+-0.4402650139339345,1.5438443885260233
+-0.23881929647065736,0.4583017779755124
+0.6380403181062437,0.8418263354828599
+-0.4812813315019433,-0.46696089955953424
+1.0297229474205043,1.0466025218767947
+0.33506680170513015,1.5429185153145464
+0.4357223527551332,1.9976309906992766
+-0.7142486035386441,0.8026447015325023
+-0.35308588651726064,0.5402048196446148
+0.47826070961169903,0.8048733011430612
+-0.9898039108224623,0.5021503434367328
+-0.7125475336703334,1.2724531990928278
+-0.6720122872124518,1.6592401001148354
+-0.4953612712248654,1.1487964838634515
+0.4556084189751731,-0.4637465264673234
+-0.10277825660183293,0.5326288356941392
+-0.5058233441167022,0.684719701873072
+0.22995606676678582,0.12632051938870825
+-0.7668971855116272,1.6430892900133407
+0.18794022976430275,1.9282421464557604
+-0.37749198745649815,0.5517148930792577
+1.0500135298354658,-0.8450450058221037
+-0.6908746019623454,0.4036508743161793
+1.5764801647960125,-1.1719766221667087
+-0.4914060192319184,-0.180311939096318
+-0.04716035011539588,1.6126009998730264
+1.0201762778946109,-1.474956643646735
+1.144245559107198,-1.2679341751600308
+0.45421641097018495,-0.00040860004807175
+-1.0642213974843846,-0.36652206972473267
+-0.9004207750492548,0.3262236081547162
+-0.23881929647065736,0.4583017779755124
+0.6380403181062437,0.8418263354828599
+-0.9920771196312985,0.14670575328449997
+0.19951737851786566,0.21457323847211307
+0.33506680170513015,1.5429185153145464
+0.4357223527551332,1.9976309906992766
+-0.789749508057014,0.1724125370697019
+1.2562041312580006,-1.712853943930795
+0.7544812039462467,1.6774132730813143
+0.833626692337759,1.4320250750457875
+-0.28931716852493194,1.1909875515851267
+-0.6720122872124518,1.6592401001148354
+-0.08469036948578124,0.3452521923889773
+0.4556084189751731,-0.4637465264673234
+-0.10277825660183293,0.5326288356941392
+0.8567767746158577,1.4740812073908969
+0.22995606676678582,0.12632051938870825
+-0.7668971855116272,1.6430892900133407
+0.18794022976430275,1.9282421464557604
+-0.37749198745649815,0.5517148930792577
+1.0500135298354658,-0.8450450058221037
+-0.6908746019623454,0.4036508743161793
+1.5764801647960125,-1.1719766221667087
+-0.4914060192319184,-0.180311939096318
+1.5743418232114956,-2.3548504474583813
+0.5080519901296775,-0.35393763818333546
+1.144245559107198,-1.2679341751600308
+0.3919527092401135,1.132777551640431
+1.1051701111342842,-0.6320430476158025
+0.8031844855995995,0.1306386409041176
+-0.23881929647065736,0.4583017779755124
+0.8027623738631094,0.7452002756499907
+-0.9920771196312985,0.14670575328449997
+0.19951737851786566,0.21457323847211307
+0.8699049686842105,0.8080012140446409
+0.4357223527551332,1.9976309906992766
+-0.789749508057014,0.1724125370697019
+0.6530349941816652,-0.838810936978184
+0.7544812039462467,1.6774132730813143
+0.628959583827636,1.9123250149910773
+-0.045963161386905566,1.059861866038938
+-0.6720122872124518,1.6592401001148354
+-0.08469036948578124,0.3452521923889773
+0.7367338524634905,1.308754121622509
+0.47415001935523826,1.4355927534920634
+0.8567767746158577,1.4740812073908969
+0.22995606676678582,0.12632051938870825
+-0.7668971855116272,1.6430892900133407
+0.18794022976430275,1.9282421464557604
+0.30042754071832956,1.8177307052046134
+1.0500135298354658,-0.8450450058221037
+-0.6908746019623454,0.4036508743161793
+1.1521860483148083,-0.8742578144785558
+0.3869387822779445,2.000440306524884
+0.8710776234696704,1.1756201118094058
+0.5080519901296775,-0.35393763818333546
+1.144245559107198,-1.2679341751600308
+0.3919527092401135,1.132777551640431
+1.1051701111342842,-0.6320430476158025
+0.8031844855995995,0.1306386409041176
+-0.23881929647065736,0.4583017779755124
+0.717871048621308,-0.775977857780407
+-0.9920771196312985,0.14670575328449997
+-0.3953301316897943,0.7721040382804656
+-0.013277745890499681,2.0984413293864024
+0.4357223527551332,1.9976309906992766
+-0.6389819380439727,1.455286708165021
+0.6530349941816652,-0.838810936978184
+0.4423837393876533,1.6137804994236302
+0.628959583827636,1.9123250149910773
+0.267225611279276,0.5188766853994863
+0.06801647186694709,0.3979581056155149
+-0.08469036948578124,0.3452521923889773
+0.9715174337668709,-0.10445129662312716
+1.2226936859362239,-1.0828401201056137
+-0.24250383825569555,0.17887467468432244
+0.22995606676678582,0.12632051938870825
+1.519648042095278,-0.9578115811273243
+0.18794022976430275,1.9282421464557604
+0.028156629385991686,1.0644001290769791
+1.0500135298354658,-0.8450450058221037
+-0.2843108904599606,0.9775781193711003
+1.1521860483148083,-0.8742578144785558
+0.3869387822779445,2.000440306524884
+0.13506139729688157,1.5638766384442402
+0.5080519901296775,-0.35393763818333546
+1.144245559107198,-1.2679341751600308
+0.13080597331907967,0.8174782168724579
+1.1051701111342842,-0.6320430476158025
+0.6100233854945964,-0.40115708512254633
+0.44706022323759537,1.1737036308517028
+-0.8670603394793923,-0.12332649885238595
+-0.9920771196312985,0.14670575328449997
+-0.3953301316897943,0.7721040382804656
+1.1292319437551273,-0.9812420764086682
+0.097525319480906,2.162821663171164
+0.21257131627824,-0.08499228301095252
+-0.5302804435036874,0.9630837954075118
+-0.27255813299058795,0.7044947282126077
+0.8475929149775854,-0.8669696261397015
+1.1123922614914972,-1.0019321775650352
+0.7791053480145304,-0.9750144906132842
+1.476853255518527,-1.7003613282867847
+0.9715174337668709,-0.10445129662312716
+1.240000156231843,-0.11893329923446318
+-0.24250383825569555,0.17887467468432244
+1.1125521007236765,-0.9891557587261979
+1.519648042095278,-0.9578115811273243
+0.18794022976430275,1.9282421464557604
+0.028156629385991686,1.0644001290769791
+1.0500135298354658,-0.8450450058221037
+0.8856612197217462,0.8352460656200015
+-0.7244311483059285,1.104571953342719
+-0.6562440208297586,0.4653266190088354
+0.8588440689846485,0.42319961911610093
+0.5080519901296775,-0.35393763818333546
+1.144245559107198,-1.2679341751600308
+0.07728420463283729,1.9370238373673025
+0.6518802153583129,1.4582486272570119
+0.6100233854945964,-0.40115708512254633
+0.44706022323759537,1.1737036308517028
+-0.8670603394793923,-0.12332649885238595
+-0.9920771196312985,0.14670575328449997
+-0.3953301316897943,0.7721040382804656
+1.1292319437551273,-0.9812420764086682
+0.4281067286145762,1.6700227023246523
+0.5298273943197245,-0.5493369031738692
+-0.5302804435036874,0.9630837954075118
+-0.7228065137795314,0.09561662546993663
+0.8475929149775854,-0.8669696261397015
+1.1123922614914972,-1.0019321775650352
+0.35177283898388567,-0.003954518779295951
+1.3255775308986821,-0.72012730753872
+0.9715174337668709,-0.10445129662312716
+1.240000156231843,-0.11893329923446318
+1.171994566656522,-1.1353225327314638
+1.1125521007236765,-0.9891557587261979
+-0.414758442151839,0.22582653451639711
+0.18794022976430275,1.9282421464557604
+0.20953525081702123,0.4000680060781908
+0.1622263635825355,0.008614479457651009
+0.8856612197217462,0.8352460656200015
+-0.7244311483059285,1.104571953342719
+-0.4752767415341318,0.6665758379884648
+-0.2392518693118597,-0.3635131476481446
+-0.41912647610844184,1.5966224751416722
+0.5311346222408759,-0.14408445861578784
+0.07728420463283729,1.9370238373673025
+0.6492875144474118,-0.15564258729746228
+0.6100233854945964,-0.40115708512254633
+0.31199625522641516,1.6619977524949139
+-0.8670603394793923,-0.12332649885238595
+-0.9920771196312985,0.14670575328449997
+-0.22415360249880742,1.0932821260282906
+0.700578897406956,0.5528251560738675
+0.09389256942195978,-0.1834158308330992
+0.5298273943197245,-0.5493369031738692
+-0.5302804435036874,0.9630837954075118
+-0.7228065137795314,0.09561662546993663
+1.5822916106422298,-1.269543715416467
+1.1123922614914972,-1.0019321775650352
+0.35177283898388567,-0.003954518779295951
+-0.20886505162453867,0.8414514000700422
+0.1317397952124273,-0.2920308942707609
+1.240000156231843,-0.11893329923446318
+1.171994566656522,-1.1353225327314638
+-0.7050927463161665,0.2948567483232851
+1.2856087506549125,0.41135671361637327
+0.18794022976430275,1.9282421464557604
+0.15455460932461584,-0.24949111205137348
+0.14922122682708366,0.2816402460807589
+0.8856612197217462,0.8352460656200015
+-0.7244311483059285,1.104571953342719
+-0.4752767415341318,0.6665758379884648
+-0.2392518693118597,-0.3635131476481446
+-0.41912647610844184,1.5966224751416722
+0.5311346222408759,-0.14408445861578784
+0.07728420463283729,1.9370238373673025
+-0.5968938392014485,0.7247024425902062
+0.6100233854945964,-0.40115708512254633
+0.31199625522641516,1.6619977524949139
+-0.8670603394793923,-0.12332649885238595
+-0.9920771196312985,0.14670575328449997
+-0.13042219583051845,0.740081018660178
+1.54222275478028,-1.0094735573359808
+0.09389256942195978,-0.1834158308330992
+-0.24799146881733458,2.373534156110849
+-0.6028680360167121,0.7677443444205908
+-0.7228065137795314,0.09561662546993663
+1.5822916106422298,-1.269543715416467
+1.1123922614914972,-1.0019321775650352
+0.35177283898388567,-0.003954518779295951
+-0.3187867785494492,2.1027532400889988
+0.5577360096019945,-0.19305415619402655
+1.240000156231843,-0.11893329923446318
+1.171994566656522,-1.1353225327314638
+-0.7050927463161665,0.2948567483232851
+-0.773962230752628,-0.22079268575608063
+0.18794022976430275,1.9282421464557604
+-0.8080813656546044,0.8021396441579223
+1.1978442829805576,0.588431184514203
+0.8856612197217462,0.8352460656200015
+-0.7244311483059285,1.104571953342719
+0.06278020266352147,1.773607784433203
+-0.2392518693118597,-0.3635131476481446
+0.7809288164832782,1.2747464089572278
+0.5311346222408759,-0.14408445861578784
+0.07728420463283729,1.9370238373673025
+-0.5968938392014485,0.7247024425902062
+0.6100233854945964,-0.40115708512254633
+0.6068583513354793,-0.5021233342566628
+-0.24442093772003198,1.3032485496201716
+1.2242133478195996,0.21944831622214223
+0.5401617334271481,1.6621033676081136
+1.54222275478028,-1.0094735573359808
+-0.6386622243118097,0.3630706656086178
+-0.24799146881733458,2.373534156110849
+-0.6028680360167121,0.7677443444205908
+0.7523196294125698,-0.42982768381304665
+1.5822916106422298,-1.269543715416467
+1.1123922614914972,-1.0019321775650352
+0.4950744919347486,0.338269706346352
+-0.3187867785494492,2.1027532400889988
+0.5577360096019945,-0.19305415619402655
+1.240000156231843,-0.11893329923446318
+1.171994566656522,-1.1353225327314638
+-0.7050927463161665,0.2948567483232851
+0.2609819544774813,1.4832090364601775
+0.18794022976430275,1.9282421464557604
+-0.8080813656546044,0.8021396441579223
+1.1978442829805576,0.588431184514203
+0.148778924901651,0.5192382900114314
+0.5874454892789595,1.0053836013172452
+-0.09592927185802845,2.1947015600041353
+-0.5716056697766833,0.5404962969865572
+0.04569787895697824,2.4181391222524504
+0.5311346222408759,-0.14408445861578784
+0.07728420463283729,1.9370238373673025
+-0.5968938392014485,0.7247024425902062
+0.18314656005180652,2.223992639118866
+0.8991754075302805,0.5920738731998141
+-0.24442093772003198,1.3032485496201716
+1.2242133478195996,0.21944831622214223
+0.5401617334271481,1.6621033676081136
+1.54222275478028,-1.0094735573359808
+-0.6386622243118097,0.3630706656086178
+-0.24799146881733458,2.373534156110849
+1.5605523365446534,-1.2957941116890372
+0.7523196294125698,-0.42982768381304665
+0.47254887659908673,-0.43825566071200694
+1.1123922614914972,-1.0019321775650352
+-0.034239834556616,0.6645351508559902
+-0.3187867785494492,2.1027532400889988
+0.5577360096019945,-0.19305415619402655
+0.7115838672799583,1.856220024609073
+0.8127520515531794,-0.35093315623942134
+0.32234665147986347,2.1895884351864146
+0.2609819544774813,1.4832090364601775
+0.18794022976430275,1.9282421464557604
+-0.8080813656546044,0.8021396441579223
+1.1978442829805576,0.588431184514203
+0.7155821151493388,-0.8186906946165516
+0.21965851029983136,0.32767229587438496
+0.6477661851073373,-0.3247959139994937
+-0.5716056697766833,0.5404962969865572
+1.8413392463742453,-1.911256458496693
+0.5311346222408759,-0.14408445861578784
+1.2824228977708225,-1.2800401766046472
+0.8144808866876565,-0.0373719870368005
+-0.35748883276981047,2.0174716958070342
+1.1748563484891426,-1.4261883902727845
+0.40998054891440905,-0.1898141137190107
+1.2242133478195996,0.21944831622214223
+0.5401617334271481,1.6621033676081136
+-0.2091588401355094,1.03552579894326
+-0.6386622243118097,0.3630706656086178
+-0.24799146881733458,2.373534156110849
+1.5605523365446534,-1.2957941116890372
+0.0480986511863577,0.879803004106372
+-0.014031528005575167,0.02413066895949112
+1.1123922614914972,-1.0019321775650352
+-0.034239834556616,0.6645351508559902
+-0.3187867785494492,2.1027532400889988
+0.5577360096019945,-0.19305415619402655
+0.7115838672799583,1.856220024609073
+0.3730152552407219,-0.11629263249425326
+0.6259351265757349,1.9519105393727116
+0.24223970743192244,-0.5347934790374034
+0.8818484420115702,-0.8076009462871163
+1.292185046965874,-1.5996344299356253
+1.1978442829805576,0.588431184514203
+0.7155821151493388,-0.8186906946165516
+1.0209568532979298,-0.986793971575225
+0.6477661851073373,-0.3247959139994937
+-0.5716056697766833,0.5404962969865572
+1.8413392463742453,-1.911256458496693
+0.5311346222408759,-0.14408445861578784
+-0.021489460853293063,-0.02475438011055564
+1.601140115992574,-1.2953502516207989
+-0.35748883276981047,2.0174716958070342
+1.0898613520856617,0.15831915019791826
+0.9736255882690481,-0.658421955590184
+1.2242133478195996,0.21944831622214223
+0.5401617334271481,1.6621033676081136
+-0.4700670192125471,-0.052446262105768304
+0.5747388115759138,0.12106074782499365
+-0.24799146881733458,2.373534156110849
+1.5605523365446534,-1.2957941116890372
+1.325709449038993,0.41121678226253955
+1.4151747903873408,-1.3301876255973677
+1.1123922614914972,-1.0019321775650352
+0.25610115288842783,-0.5392181596488338
+-0.3187867785494492,2.1027532400889988
+0.4637149124481171,0.3251263206652023
+0.7115838672799583,1.856220024609073
+0.10851295129732261,0.40062482575482905
+0.6259351265757349,1.9519105393727116
+1.399065942618738,-2.008608811571875
+-0.2651354289332696,0.9193570990380553
+1.292185046965874,-1.5996344299356253
+1.1978442829805576,0.588431184514203
+0.7155821151493388,-0.8186906946165516
+1.0209568532979298,-0.986793971575225
+0.5819122744048801,1.6965776890746698
+-0.5716056697766833,0.5404962969865572
+1.6925560225350025,-1.7824510777405016
+0.6955429890296069,-0.407644987058437
+-0.021489460853293063,-0.02475438011055564
+0.774352369665605,-0.8724498809215729
+-0.35748883276981047,2.0174716958070342
+1.9189232903799498,-2.8447881691793304
+0.9736255882690481,-0.658421955590184
+1.2242133478195996,0.21944831622214223
+0.5401617334271481,1.6621033676081136
+-0.2562438769507599,1.1648743892507019
+0.5747388115759138,0.12106074782499365
+-0.3274746042903124,-0.3894059718593588
+1.5605523365446534,-1.2957941116890372
+2.1044727106158216,-4.120755689198509
+1.4151747903873408,-1.3301876255973677
+1.1123922614914972,-1.0019321775650352
+0.25610115288842783,-0.5392181596488338
+-0.3187867785494492,2.1027532400889988
+0.4637149124481171,0.3251263206652023
+1.249932939103577,-1.4582782588756962
+0.19911009153233825,0.3451490750709406
+1.0757387050857277,-1.0333855442296984
+1.399065942618738,-2.008608811571875
+-0.2651354289332696,0.9193570990380553
+1.292185046965874,-1.5996344299356253
+1.1978442829805576,0.588431184514203
+0.7155821151493388,-0.8186906946165516
+-0.2009399185697588,0.2382380107677603
+1.6816983100280796,-2.055083952974513
+-0.5716056697766833,0.5404962969865572
+0.3158707231654774,-0.5037104992154144
+0.6955429890296069,-0.407644987058437
+-0.021489460853293063,-0.02475438011055564
+0.774352369665605,-0.8724498809215729
+1.2693623587832268,-0.38313373432864617
+1.9189232903799498,-2.8447881691793304
+-0.10260929279248104,0.9869428619430627
+1.2242133478195996,0.21944831622214223
+0.5401617334271481,1.6621033676081136
+-0.2562438769507599,1.1648743892507019
+1.069326359810908,-0.825568897583187
+-0.3307160131578577,1.208927670196069
+1.5605523365446534,-1.2957941116890372
+2.1044727106158216,-4.120755689198509
+-0.4137819683981374,0.1717109213726737
+0.27446758607508087,1.219638012251412
+-0.368503357282152,0.9343605721760465
+-0.3187867785494492,2.1027532400889988
+0.7672263919085909,-0.1766648125398984
+1.2831067344976468,-2.1387647360738113
+0.19911009153233825,0.3451490750709406
+0.46586005792683305,-0.17640807854572726
+1.3677257272761218,-0.6290478727875887
+-0.2651354289332696,0.9193570990380553
+0.8836241530359914,-0.5796245907659192
+1.1949566387328725,0.040330195481795617
+0.5205068888991775,-0.6091102072605774
+-0.2009399185697588,0.2382380107677603
+0.6975683969570659,0.18267786985719514
+-0.5716056697766833,0.5404962969865572
+1.0191891986611412,-0.7894056659113761
+0.6955429890296069,-0.407644987058437
+-0.021489460853293063,-0.02475438011055564
+0.774352369665605,-0.8724498809215729
+1.2693623587832268,-0.38313373432864617
+1.9189232903799498,-2.8447881691793304
+0.3828702759372721,0.7263317277828149
+1.2242133478195996,0.21944831622214223
+0.5401617334271481,1.6621033676081136
+-0.2562438769507599,1.1648743892507019
+0.337052517848806,1.509404992113552
+-0.3307160131578577,1.208927670196069
+0.8171098762253972,-0.19442647134001723
+0.22234275393380074,-0.08826798497373146
+-0.4137819683981374,0.1717109213726737
+-0.010593031100403022,0.13056166660206012
+-0.368503357282152,0.9343605721760465
+-0.3187867785494492,2.1027532400889988
+0.7672263919085909,-0.1766648125398984
+1.7318870122383658,-1.0183891051062641
+0.19911009153233825,0.3451490750709406
+0.46586005792683305,-0.17640807854572726
+1.4699797944405788,-1.2619078613790746
+-0.20684006087546705,0.4961026965243164
+0.8046102845543186,-0.9021531316631494
+1.1949566387328725,0.040330195481795617
+-0.25032605578275474,-0.04360546245413055
+-0.12772870838872377,0.3127414996189393
+0.07695187763726502,0.009688830107089985
+-0.5716056697766833,0.5404962969865572
+-0.18569813226403648,1.9239157212850482
+0.6955429890296069,-0.407644987058437
+-0.021489460853293063,-0.02475438011055564
+0.5303434422949729,-0.683002381647995
+-0.031746789962585224,-0.6160417071003197
+1.9189232903799498,-2.8447881691793304
+-0.39501468286709096,1.3100266721257623
+1.2242133478195996,0.21944831622214223
+0.5401617334271481,1.6621033676081136
+-0.32043590511012565,-0.10333313748610462
+0.337052517848806,1.509404992113552
+0.9720243128074735,1.1526112475722752
+0.8171098762253972,-0.19442647134001723
+-0.2745149159969174,1.6194903401413323
+0.08668025835316279,-0.08444751956642726
+-0.1372779596858658,0.08985995255814905
+-0.09445445805656741,1.15409904819522
+-0.3187867785494492,2.1027532400889988
+0.7672263919085909,-0.1766648125398984
+-0.4218142571422082,0.8786098933212961
+-0.009625130536865145,-0.21088200231079085
+-0.01955567156775337,1.6069399643528308
+1.4033361106155657,-0.5286578137220295
+-0.20684006087546705,0.4961026965243164
+-0.03783443694033002,0.09508070260200388
+-0.01801013796625918,1.1153115033338397
+-0.5715147763680255,1.3582096406451567
+-0.12772870838872377,0.3127414996189393
+0.07695187763726502,0.009688830107089985
+-0.5716056697766833,0.5404962969865572
+-0.18569813226403648,1.9239157212850482
+0.6955429890296069,-0.407644987058437
+-0.06439883281535178,-0.24290033103011333
+1.239634292714152,-0.2171058540769614
+0.12911056261327072,-0.21544130348278936
+1.9189232903799498,-2.8447881691793304
+-0.39501468286709096,1.3100266721257623
+1.2242133478195996,0.21944831622214223
+0.5401617334271481,1.6621033676081136
+-0.8833547339558796,0.9204629119282379
+0.337052517848806,1.509404992113552
+0.9720243128074735,1.1526112475722752
+-0.37478639665816077,0.140938447031409
+-0.2745149159969174,1.6194903401413323
+0.08668025835316279,-0.08444751956642726
+-0.21751181558882576,0.5177264829609622
+0.23496222215021445,-0.10898426105590353
+-0.3187867785494492,2.1027532400889988
+0.15987885141196478,0.1234279362878864
+-0.030768000554620395,0.12781260429027902
+1.0330357098827854,0.5685503739877935
+0.3573959945315641,-0.4881291577332939
+1.4033361106155657,-0.5286578137220295
+-0.3902646883455373,0.34963984217666993
+-0.6061889511116348,0.1990000420111925
+-0.01801013796625918,1.1153115033338397
+1.0717298316130754,0.581360177563603
+-0.6295565073961142,0.05965564784440744
+0.07695187763726502,0.009688830107089985
+-0.5424464509222044,-0.10023514749473095
+-0.6514292170147102,1.0517663890015942
+1.2185852796065675,0.23421578550987598
+-0.07955803312433725,1.5774327095571588
+0.35539317550757143,0.8831073626772686
+0.12911056261327072,-0.21544130348278936
+1.9189232903799498,-2.8447881691793304
+0.0007794831075410777,0.8728586110819675
+1.2242133478195996,0.21944831622214223
+0.5401617334271481,1.6621033676081136
+-0.8833547339558796,0.9204629119282379
+0.337052517848806,1.509404992113552
+0.9720243128074735,1.1526112475722752
+-0.37478639665816077,0.140938447031409
+0.10980872968811192,0.16885590925198146
+0.26292535197057043,0.017527824663501813
+-0.21751181558882576,0.5177264829609622
+1.488911789757878,-0.43824245002129314
+0.3909492765036241,0.8421936644241821
+0.39159877037606966,1.8665102159759095
+0.7228538877991956,1.0999012913397066
+1.0330357098827854,0.5685503739877935
+0.4774717654488964,1.973310302053368
+1.4033361106155657,-0.5286578137220295
+0.3630570634130864,1.7088132155161124
+-0.6061889511116348,0.1990000420111925
+0.674954998464049,1.6739456953666065
+0.7325810278793142,-0.6155534903609329
+-0.6295565073961142,0.05965564784440744
+0.07695187763726502,0.009688830107089985
+-0.5424464509222044,-0.10023514749473095
+-0.6514292170147102,1.0517663890015942
+-0.7257130332143167,0.6158910756353423
+-0.07955803312433725,1.5774327095571588
+0.35539317550757143,0.8831073626772686
+-0.30602420704312916,-0.1366947223897788
+1.9189232903799498,-2.8447881691793304
+0.42931409911779156,0.022559384673503935
+1.2242133478195996,0.21944831622214223
+0.5401617334271481,1.6621033676081136
+0.32231856375315604,-0.11218793313404785
+1.4161765051835256,0.009792731632913138
+0.9720243128074735,1.1526112475722752
+0.6818348436723456,0.2636643275867618
+0.10980872968811192,0.16885590925198146
+0.7254273472342105,1.6164410638370441
+1.5786226716901042,-0.9535317111738567
+-0.3842997289875579,0.38482794623245503
+0.3909492765036241,0.8421936644241821
+0.8929633667636966,0.39842071149077907
+0.2354971696564468,1.1157077005036569
+1.0330357098827854,0.5685503739877935
+0.4774717654488964,1.973310302053368
+0.28435344104306964,-0.32175237377439764
+0.3630570634130864,1.7088132155161124
+0.09110688432706227,1.902235660464991
+-0.4707296581613149,0.30420948204643744
+0.7325810278793142,-0.6155534903609329
+-0.38600631538030566,1.6718293824626385
+0.05893371130477837,2.5287571756777396
+-0.5424464509222044,-0.10023514749473095
+0.49447572166221904,1.58674730559781
+-0.7257130332143167,0.6158910756353423
+-0.3289562202755613,0.2006381215415889
+0.7742695996931312,0.738173880151976
+-0.30602420704312916,-0.1366947223897788
+1.9189232903799498,-2.8447881691793304
+-0.4956298856945775,-0.024794104782045856
+-0.454541512842514,1.7425300611590937
+0.5401617334271481,1.6621033676081136
+0.32231856375315604,-0.11218793313404785
+-0.6861452798343406,0.44176595163020266
+0.9720243128074735,1.1526112475722752
+0.33110288359458084,1.0304286393230786
+0.10980872968811192,0.16885590925198146
+0.7254273472342105,1.6164410638370441
+1.5786226716901042,-0.9535317111738567
+-0.3842997289875579,0.38482794623245503
+0.3909492765036241,0.8421936644241821
+-0.6920314149585183,-0.4033521496423946
+0.8917497300798795,-0.9899937539256838
+1.0330357098827854,0.5685503739877935
+0.4774717654488964,1.973310302053368
+0.28435344104306964,-0.32175237377439764
+1.0365547283581034,-1.1872668561758124
+0.09110688432706227,1.902235660464991
+-0.4707296581613149,0.30420948204643744
+0.7325810278793142,-0.6155534903609329
+-0.38600631538030566,1.6718293824626385
+-0.5155411115790196,2.0959016543843143
+-0.5424464509222044,-0.10023514749473095
+-0.383047545645512,2.299033992885642
+-0.7257130332143167,0.6158910756353423
+-0.4196833631288471,1.0972162869599598
+0.7399672208869644,0.2070842097773741
+1.0054926076530448,0.6613534030123576
+1.9189232903799498,-2.8447881691793304
+-0.9069619337168747,0.8390160531940081
+0.6965893959831392,1.7599132660827168
+0.7415057023413055,0.8155008204399428
+0.32231856375315604,-0.11218793313404785
+0.43095792573050146,-0.2361235533882488
+0.9720243128074735,1.1526112475722752
+0.33110288359458084,1.0304286393230786
+0.10980872968811192,0.16885590925198146
+0.06823985699233959,1.9655671196317153
+1.5786226716901042,-0.9535317111738567
+-0.3842997289875579,0.38482794623245503
+-0.19959198894089647,2.24139319534564
+-0.6920314149585183,-0.4033521496423946
+0.6435167523376812,-0.601024730860332
+1.0330357098827854,0.5685503739877935
+0.4774717654488964,1.973310302053368
+0.28435344104306964,-0.32175237377439764
+0.8325970529793458,-0.7336663179477567
+0.09110688432706227,1.902235660464991
+0.7744179022330031,-0.6038504632938249
+0.2016300793482783,1.3108185637373038
+-0.38600631538030566,1.6718293824626385
+0.6711087931019692,1.1901511954313313
+1.4784801485053325,-1.7169120294953517
+0.7560040547400564,-0.055953775832546904
+-0.7257130332143167,0.6158910756353423
+0.17305515601794252,1.7319856778898446
+1.177977856365027,-1.048064452965492
+1.0054926076530448,0.6613534030123576
+1.9189232903799498,-2.8447881691793304
+-0.9069619337168747,0.8390160531940081
+0.6557300331089154,1.3111238457032472
+0.6183172995005327,-0.2764294658078663
+0.32231856375315604,-0.11218793313404785
+0.8774237824041221,-0.1081263299187688
+0.9720243128074735,1.1526112475722752
+-1.0518366172689217,-0.4910248558139485
+0.10980872968811192,0.16885590925198146
+0.06823985699233959,1.9655671196317153
+-0.3962675639401452,-0.1374042486794706
+-0.3842997289875579,0.38482794623245503
+-0.19959198894089647,2.24139319534564
+-0.6920314149585183,-0.4033521496423946
+0.5654665566600098,0.16461470012189372
+1.3991824984603545,-0.9612461756327418
+-0.08938190538228119,2.2830303151099067
+0.28435344104306964,-0.32175237377439764
+0.4212667832695135,-0.38611493822609
+0.09110688432706227,1.902235660464991
+0.7744179022330031,-0.6038504632938249
+0.2016300793482783,1.3108185637373038
+0.3979334562496379,1.8129856104549957
+0.6711087931019692,1.1901511954313313
+1.4784801485053325,-1.7169120294953517
+1.5917318708242225,-1.8866369444040827
+-0.7257130332143167,0.6158910756353423
+0.17305515601794252,1.7319856778898446
+1.177977856365027,-1.048064452965492
+1.0054926076530448,0.6613534030123576
+1.9189232903799498,-2.8447881691793304
+0.8187524835816111,-0.38285952057061134
+0.6557300331089154,1.3111238457032472
+-0.25893573501778955,-0.08295066288610531
+1.4841146569882007,-1.0976655279827292
+0.8774237824041221,-0.1081263299187688
+0.9720243128074735,1.1526112475722752
+-1.0518366172689217,-0.4910248558139485
+0.10980872968811192,0.16885590925198146
+0.06823985699233959,1.9655671196317153
+-0.3962675639401452,-0.1374042486794706
+-0.3842997289875579,0.38482794623245503
+1.34666915938756,-1.8723253969427003
+0.8916927665416753,-0.758861885663868
+0.8549084545193024,1.3702891485774156
+1.3991824984603545,-0.9612461756327418
+-0.08938190538228119,2.2830303151099067
+0.4813576739062555,-0.2234832384072889
+0.4212667832695135,-0.38611493822609
+0.09110688432706227,1.902235660464991
+0.04856423863611534,1.0377822022676912
+0.16791967076038816,0.7691131154972757
+0.3979334562496379,1.8129856104549957
+0.6711087931019692,1.1901511954313313
+0.7155468764672271,-0.8391270941627127
+1.5917318708242225,-1.8866369444040827
+0.47522106914855,0.13644123522709584
+0.17305515601794252,1.7319856778898446
+1.177977856365027,-1.048064452965492
+-0.7945702586581502,0.5469320185025506
+-0.20117102017380548,1.2888945901550173
+0.8187524835816111,-0.38285952057061134
+0.6557300331089154,1.3111238457032472
+-0.25893573501778955,-0.08295066288610531
+-0.9363259676015274,0.4762395483212571
+-0.057740477246507355,-0.35885677923151643
+0.9720243128074735,1.1526112475722752
+1.0552650957743914,-0.9243040998249991
+-0.6890376365814945,-0.3221166988234308
+1.4141892386910273,-0.45610497048112303
+-0.3962675639401452,-0.1374042486794706
+-0.3187140975682694,-0.15636436916582855
+-0.3234483688809472,0.2714326716033463
+0.8916927665416753,-0.758861885663868
+-0.5232804930857466,1.500984424670635
+1.3991824984603545,-0.9612461756327418
+0.5123357053900215,1.3595912088660882
+0.4813576739062555,-0.2234832384072889
+0.4212667832695135,-0.38611493822609
+0.09110688432706227,1.902235660464991
+-0.012696030870237685,0.2747135312883651
+-0.6798904042266558,0.5112166505637166
+0.3979334562496379,1.8129856104549957
+0.8341421823439513,0.172938753659303
+0.29019332073207005,1.272054544010613
+1.5917318708242225,-1.8866369444040827
+0.47522106914855,0.13644123522709584
+0.7553015385973738,1.1204208032505159
+0.8763036681074134,-0.39004819970019255
+-0.7945702586581502,0.5469320185025506
+-0.20117102017380548,1.2888945901550173
+0.8187524835816111,-0.38285952057061134
+0.6557300331089154,1.3111238457032472
+-0.5511250068837434,0.07341829681065937
+-0.513524008314511,0.70722704175163
+0.6860986362062393,-0.8939322355168774
+-0.23922058279857927,0.08439050426365341
+1.0552650957743914,-0.9243040998249991
+1.1440018031681616,-1.3012811396442094
+1.4141892386910273,-0.45610497048112303
+-0.3962675639401452,-0.1374042486794706
+-0.23535538712667203,0.11429466803573812
+0.3110955224427844,1.9393746888492098
+0.8916927665416753,-0.758861885663868
+-0.5232804930857466,1.500984424670635
+1.3991824984603545,-0.9612461756327418
+1.7102669166032072,-1.8489104622413546
+1.7869667536481575,-2.1626722947697257
+0.4082896163433207,1.7539293169769556
+0.008647698067531795,0.14810551427500152
+-0.012696030870237685,0.2747135312883651
+-0.7525357384753707,1.53643071470771
+0.3979334562496379,1.8129856104549957
+0.8341421823439513,0.172938753659303
+-0.09516002819393837,0.3972051740892245
+1.5917318708242225,-1.8866369444040827
+1.2288745202927822,-1.5541028461461606
+0.7553015385973738,1.1204208032505159
+0.8959292162734492,-0.8376770450435997
+-0.3312690484395425,2.3184297324454874
+0.36974117884660684,1.616737353859176
+-0.2052791531086583,1.5829011145099985
+0.3084267796174873,0.5156749608064017
+-0.5511250068837434,0.07341829681065937
+-0.513524008314511,0.70722704175163
+0.6860986362062393,-0.8939322355168774
+1.8426753669055689,-1.6242687427084568
+-0.22290863367844915,0.9197270900431707
+-0.5524735823898184,0.12683270584848272
+1.4141892386910273,-0.45610497048112303
+-0.3962675639401452,-0.1374042486794706
+-0.45012947364816863,0.8718605969507416
+0.3110955224427844,1.9393746888492098
+0.8916927665416753,-0.758861885663868
+-0.5232804930857466,1.500984424670635
+1.3991824984603545,-0.9612461756327418
+1.7102669166032072,-1.8489104622413546
+1.692228432410481,-2.645507538332108
+0.7456280710115523,0.07735092969894691
+-0.1922523455833085,1.0323983661128424
+-0.012696030870237685,0.2747135312883651
+-0.7525357384753707,1.53643071470771
+0.3979334562496379,1.8129856104549957
+0.8341421823439513,0.172938753659303
+0.17543816458977946,0.4280498067711231
+1.5917318708242225,-1.8866369444040827
+0.21285227972352627,0.07327244382684187
+-0.7001512421868696,0.6415871641387656
+0.8959292162734492,-0.8376770450435997
+-0.3312690484395425,2.3184297324454874
+1.506622453050058,-2.0307599767302555
+-0.2052791531086583,1.5829011145099985
+0.3084267796174873,0.5156749608064017
+-0.5511250068837434,0.07341829681065937
+-0.45244780447382377,-0.47543618353939726
+0.6860986362062393,-0.8939322355168774
+0.5184924882729383,-0.6691904225943003
+-0.26108304098456786,-0.29303460861854846
+-0.5524735823898184,0.12683270584848272
+0.1238942931662328,-0.1756921603155387
+-0.6168784385655337,0.3780508460233284
+0.03210643366346427,1.7626543748033867
+1.267480299982617,-0.9168460971879865
+0.35563950400332867,-0.43094083979904374
+0.42363802242150905,1.6038129182925929
+1.3991824984603545,-0.9612461756327418
+0.1815523946532105,1.3406018453767687
+1.692228432410481,-2.645507538332108
+0.7456280710115523,0.07735092969894691
+-0.1922523455833085,1.0323983661128424
+-0.012696030870237685,0.2747135312883651
+-0.7525357384753707,1.53643071470771
+-0.9298794944484585,0.774376932783131
+1.361330300223673,-0.7507517123795381
+0.5217061467866931,1.269082630574512
+1.5917318708242225,-1.8866369444040827
+-0.361908836328584,0.19280166531263987
+1.7089538351535036,-1.8131987481151344
+0.8959292162734492,-0.8376770450435997
+-0.3312690484395425,2.3184297324454874
+0.8171187002602329,-0.5966544762853803
+-0.2052791531086583,1.5829011145099985
+0.5872756700894652,-0.8468179517475909
+-0.2303483584901171,0.9244674743945736
+0.2420458694196811,1.651262352782904
+0.5989231717916887,-0.52464066713193
+-0.40236050992938965,0.22075021811144907
+-0.26108304098456786,-0.29303460861854846
+1.5209507110854055,-1.4481283483666854
+0.6383883445143055,0.8950852569503861
+-0.6168784385655337,0.3780508460233284
+0.03210643366346427,1.7626543748033867
+-0.8459139419188918,0.5382221345407727
+0.35563950400332867,-0.43094083979904374
+-0.5152153114181806,2.033407364476588
+1.3991824984603545,-0.9612461756327418
+1.5336374625309803,-0.8770191087832824
+0.9956665353907242,0.10630065025847402
+0.7456280710115523,0.07735092969894691
+-0.1922523455833085,1.0323983661128424
+-0.012696030870237685,0.2747135312883651
+-0.4060012685041491,0.04110486013947595
+-0.9298794944484585,0.774376932783131
+1.361330300223673,-0.7507517123795381
+0.8214149214037393,-0.047106518018782365
+1.5917318708242225,-1.8866369444040827
+0.8973106759052446,0.9130143167933975
+0.183198978915299,2.1709311583001156
+1.1423196314998052,0.08541688859388656
+1.2688978045414316,-0.25097030391692154
+0.8673532715445214,-0.49907675043687033
+0.5013656531829618,-0.01281956739052792
+0.28736387441646893,1.2195073430119618
+-0.2303483584901171,0.9244674743945736
+0.2420458694196811,1.651262352782904
+0.17633033103455287,0.149114401845157
+-0.40236050992938965,0.22075021811144907
+-0.26108304098456786,-0.29303460861854846
+1.5209507110854055,-1.4481283483666854
+-0.22475873933972879,1.9931579430035824
+-0.6168784385655337,0.3780508460233284
+1.3685446303324111,0.32083256623669343
+-0.8459139419188918,0.5382221345407727
+-0.12279844281834931,2.0504776882340834
+-0.5152153114181806,2.033407364476588
+0.1635058917437408,1.6982391351776118
+1.3885959990788854,-0.5807400857150007
+1.2718722766926,-0.39474319931216506
+0.7456280710115523,0.07735092969894691
+-0.0174589324603186,0.4322819765740823
+0.3028820970255866,1.4692416579938645
+-0.4060012685041491,0.04110486013947595
+-0.9298794944484585,0.774376932783131
+1.361330300223673,-0.7507517123795381
+0.7601355884350989,0.7139419389689508
+-0.23145376686130456,1.905864426584621
+0.8973106759052446,0.9130143167933975
+0.183198978915299,2.1709311583001156
+1.1423196314998052,0.08541688859388656
+1.2688978045414316,-0.25097030391692154
+-0.23034148329965773,1.9634617323419352
+0.6571606370812999,0.7420750567328102
+0.23816088375396127,0.34804497590707806
+-0.2303483584901171,0.9244674743945736
+0.2420458694196811,1.651262352782904
+0.17633033103455287,0.149114401845157
+0.007255032811246065,0.9727325488312356
+-0.26108304098456786,-0.29303460861854846
+1.168668427157107,-0.4097183901381224
+-0.7105884080023241,0.03816186672644184
+-0.3896192627902732,2.022928738768945
+1.3685446303324111,0.32083256623669343
+-0.8459139419188918,0.5382221345407727
+-0.12279844281834931,2.0504776882340834
+1.4698443439173399,-1.2592934404332656
+0.1635058917437408,1.6982391351776118
+0.05868862829636401,-0.18179623690908278
+1.1616277791465055,0.3778932596717482
+-0.6971415875993032,1.8446854749047468
+-0.0174589324603186,0.4322819765740823
+0.3028820970255866,1.4692416579938645
+-0.4060012685041491,0.04110486013947595
+1.3981584221141383,-0.4234480819847709
+1.361330300223673,-0.7507517123795381
+0.6396321871458248,1.8158754399514363
+0.42043515224254124,-0.045481822537780145
+0.8973106759052446,0.9130143167933975
+0.183198978915299,2.1709311583001156
+0.20474836272831265,0.06316621491794783
+1.2688978045414316,-0.25097030391692154
+-0.23034148329965773,1.9634617323419352
+0.0888989178282625,0.5223135547803595
+0.23816088375396127,0.34804497590707806
+0.8655062975972021,-0.27206857162978526
+0.24914616797401212,0.8822993645402344
+0.17633033103455287,0.149114401845157
+0.30420365211325207,0.8661094543021961
+1.613841306126257,-1.0860686796231658
+1.168668427157107,-0.4097183901381224
+0.3037269602272161,2.075349670875984
+-0.3896192627902732,2.022928738768945
+1.207638880767871,-1.2875972760941128
+-0.6511339627363033,0.487665529939549
+-0.12279844281834931,2.0504776882340834
+1.4698443439173399,-1.2592934404332656
+0.1635058917437408,1.6982391351776118
+0.05868862829636401,-0.18179623690908278
+-0.4023559123753765,1.51295990741552
+-0.17936295985202252,-0.015915975666955594
+-0.0174589324603186,0.4322819765740823
+0.3028820970255866,1.4692416579938645
+1.432051161429719,-1.049440145570835
+1.3981584221141383,-0.4234480819847709
+1.361330300223673,-0.7507517123795381
+0.6396321871458248,1.8158754399514363
+0.42043515224254124,-0.045481822537780145
+0.8973106759052446,0.9130143167933975
+-0.5259272103836963,-0.06384064187434503
+0.20474836272831265,0.06316621491794783
+-0.2403109361232419,-0.1535488672546022
+-0.23034148329965773,1.9634617323419352
+-0.11370700607502862,0.42716214493747856
+0.5772475522874589,0.8249734266599862
+0.531553185779351,1.333091609668221
+0.24914616797401212,0.8822993645402344
+0.5526360654042879,1.1964856049501396
+-0.36628999780578475,0.2801811302427275
+1.613841306126257,-1.0860686796231658
+0.19927646218762995,0.11638452099144153
+0.3037269602272161,2.075349670875984
+0.022121204222145474,-0.2931142505341513
+1.207638880767871,-1.2875972760941128
+0.9454727361082769,0.7672793464127563
+-0.12279844281834931,2.0504776882340834
+0.45618608158127105,1.2266454031170526
+-0.13745805153110163,1.8897183463582463
+1.0062818667398483,-0.7583136014960783
+0.7581618864573721,-0.24952291798655124
+-0.04605751401318944,2.26576245631132
+-0.7064714794231368,1.7082604667202743
+0.36457182259266385,-0.11183440148315085
+1.432051161429719,-1.049440145570835
+0.17736223033980747,-0.2208821925610549
+1.0262806634924135,0.17952545057047536
+0.6396321871458248,1.8158754399514363
+0.42043515224254124,-0.045481822537780145
+0.8973106759052446,0.9130143167933975
+-0.5259272103836963,-0.06384064187434503
+-0.549780916171878,1.6844616386646558
+0.3762734481114097,1.7444614153426639
+1.2205139325998016,-1.5131537362625858
+-0.11370700607502862,0.42716214493747856
+0.5772475522874589,0.8249734266599862
+-0.11068307290641544,1.6539011342059315
+-1.0527496548892983,0.3638993336890138
+-0.8238176247442284,1.635095289726013
+-0.36628999780578475,0.2801811302427275
+-0.40704532529340776,2.365356874999213
+-0.1872929053475224,0.8879176489634011
+0.3037269602272161,2.075349670875984
+0.022121204222145474,-0.2931142505341513
+1.2218191489019277,-1.6000818158128967
+0.6006730182006632,0.4455219166166276
+-0.12279844281834931,2.0504776882340834
+0.45618608158127105,1.2266454031170526
+1.013289904662015,0.9849610215880622
+1.0062818667398483,-0.7583136014960783
+0.24005144433565326,-0.2198643383369655
+0.19309284228511542,1.4498411499835777
+1.0466241364297537,-1.2658703067053998
+0.8542226129957893,0.08971447109359376
+1.432051161429719,-1.049440145570835
+0.17736223033980747,-0.2208821925610549
+-0.38021726472736184,2.1120269587786393
+0.6396321871458248,1.8158754399514363
+-0.10333006852174687,2.165708141139229
+0.8973106759052446,0.9130143167933975
+-0.5259272103836963,-0.06384064187434503
+-0.549780916171878,1.6844616386646558
+0.3762734481114097,1.7444614153426639
+1.2205139325998016,-1.5131537362625858
+-0.11370700607502862,0.42716214493747856
+0.360569225923531,1.906665243567234
+-0.11068307290641544,1.6539011342059315
+-1.0527496548892983,0.3638993336890138
+-0.8238176247442284,1.635095289726013
+-0.36628999780578475,0.2801811302427275
+0.1525777308454651,0.11680202993922473
+0.10248073344541504,1.2742038094287396
+0.3037269602272161,2.075349670875984
+0.022121204222145474,-0.2931142505341513
+1.2218191489019277,-1.6000818158128967
+0.126629034691999,2.5240942936227895
+-0.1828966288062494,1.5266907125392286
+0.6608484969386271,1.13077633952347
+1.013289904662015,0.9849610215880622
+0.5694725272120942,-0.6094359230295049
+0.24005144433565326,-0.2198643383369655
+-0.5889829238044734,1.0818954886131318
+1.0466241364297537,-1.2658703067053998
+0.8542226129957893,0.08971447109359376
+0.33892600379782756,0.277284273559086
+0.17736223033980747,-0.2208821925610549
+-0.38021726472736184,2.1120269587786393
+0.6396321871458248,1.8158754399514363
+0.8340938581278019,1.373104493593252
+0.8973106759052446,0.9130143167933975
+-0.5259272103836963,-0.06384064187434503
+-0.65634980512076,-0.004707088241589774
+-0.3280920332530515,0.3660978982062522
+1.2205139325998016,-1.5131537362625858
+-0.11370700607502862,0.42716214493747856
+0.360569225923531,1.906665243567234
+0.1534785184641438,2.2339718755515956
+0.6348226618907938,0.5334419574508058
+1.7629497773861154,-2.8666313117409117
+-0.36628999780578475,0.2801811302427275
+0.1525777308454651,0.11680202993922473
+1.643325509522382,-0.6785207537422336
+0.3037269602272161,2.075349670875984
+-0.8178404471976439,-0.6350206831722878
+0.513727575532583,-0.3967752691581101
+0.126629034691999,2.5240942936227895
+-0.1828966288062494,1.5266907125392286
+0.6608484969386271,1.13077633952347
+-0.3522274109931895,1.0860998846143333
+-0.4528753458667777,1.2382589516832212
+0.24005144433565326,-0.2198643383369655
+-0.5889829238044734,1.0818954886131318
+1.0466241364297537,-1.2658703067053998
+0.8542226129957893,0.08971447109359376
+0.33892600379782756,0.277284273559086
+0.17736223033980747,-0.2208821925610549
+-0.41846717412263923,1.5731302389968842
+-0.08356385600692906,-0.029579954320922378
+0.8340938581278019,1.373104493593252
+0.8973106759052446,0.9130143167933975
+-0.2649175360777722,0.18767854809467222
+-0.65634980512076,-0.004707088241589774
+0.8466517420741053,1.0354417045712667
+1.2205139325998016,-1.5131537362625858
+-0.11370700607502862,0.42716214493747856
+0.360569225923531,1.906665243567234
+0.1534785184641438,2.2339718755515956
+0.6348226618907938,0.5334419574508058
+1.7629497773861154,-2.8666313117409117
+1.636631132474323,-1.445836162919346
+-0.4426276880672608,0.1376238475488181
+1.643325509522382,-0.6785207537422336
+0.3037269602272161,2.075349670875984
+0.8665856629727996,-0.5293020019541266
+0.21183493155072664,-0.40254492636696837
+-0.28134369964570394,0.9316971834209069
+-0.764830412138427,0.4629489585545934
+0.6608484969386271,1.13077633952347
+0.6027332851259197,-0.16838677901234655
+-0.4528753458667777,1.2382589516832212
+0.24005144433565326,-0.2198643383369655
+1.1922201462547737,0.18995709630459673
+1.0466241364297537,-1.2658703067053998
+0.8542226129957893,0.08971447109359376
+0.33892600379782756,0.277284273559086
+-0.6971432850696786,0.7903662181553489
+-0.41846717412263923,1.5731302389968842
+0.8316436234208828,0.18260287754316729
+0.8340938581278019,1.373104493593252
+0.8973106759052446,0.9130143167933975
+-0.2649175360777722,0.18767854809467222
+-0.65634980512076,-0.004707088241589774
+0.8466517420741053,1.0354417045712667
+1.2205139325998016,-1.5131537362625858
+0.9549989007128762,-1.1482131206919373
+0.750758445416513,1.256255272246288
+0.1534785184641438,2.2339718755515956
+0.24249838341878593,0.591776924592299
+1.7629497773861154,-2.8666313117409117
+1.636631132474323,-1.445836162919346
+-0.4426276880672608,0.1376238475488181
+1.643325509522382,-0.6785207537422336
+0.3037269602272161,2.075349670875984
+0.8665856629727996,-0.5293020019541266
+1.2090038489288868,0.2054279355720552
+0.7966595745485655,-0.5419698483693239
+-0.764830412138427,0.4629489585545934
+0.5829370833888567,0.9598245285265705
+0.9968171836870054,0.7328772662645349
+-0.4528753458667777,1.2382589516832212
+0.37635754995529025,1.6523711487973731
+1.8837626030507737,-2.613387405510413
+0.5918546445347086,0.2673443849129604
+0.05087381900620863,1.2696532381018228
+0.3134771785573481,1.501717958165347
+0.5256321560788496,1.3404379265743471
+-0.41846717412263923,1.5731302389968842
+0.8316436234208828,0.18260287754316729
+0.8340938581278019,1.373104493593252
+-0.07261754169759238,1.8697149229260583
+0.30600343833504917,0.04344409674506988
+-0.65634980512076,-0.004707088241589774
+0.8466517420741053,1.0354417045712667
+1.2205139325998016,-1.5131537362625858
+0.9549989007128762,-1.1482131206919373
+0.5854158511597525,0.005461692706610788
+-0.5914957574062258,0.1847111482767685
+0.24249838341878593,0.591776924592299
+0.9651300605660695,-0.8673333065318038
+1.636631132474323,-1.445836162919346
+-0.4426276880672608,0.1376238475488181
+-0.40046082365466257,-0.5040073495850371
+0.46735067476414144,0.07370874442093078
+0.8665856629727996,-0.5293020019541266
+1.2090038489288868,0.2054279355720552
+0.7966595745485655,-0.5419698483693239
+-0.764830412138427,0.4629489585545934
+0.5829370833888567,0.9598245285265705
+-0.778210850909743,0.35055810328771897
+-0.4528753458667777,1.2382589516832212
+0.37635754995529025,1.6523711487973731
+1.8837626030507737,-2.613387405510413
+0.5918546445347086,0.2673443849129604
+-0.7366569803399438,1.5136270870566704
+0.3134771785573481,1.501717958165347
+0.5256321560788496,1.3404379265743471
+1.31060446831714,-0.12600240662016127
+1.4372382893746338,-1.0254406395993139
+0.4094305653834532,1.1522221898935934
+-0.07261754169759238,1.8697149229260583
+0.30600343833504917,0.04344409674506988
+-0.6871001135706275,-0.19116489123799552
+0.8466517420741053,1.0354417045712667
+1.2205139325998016,-1.5131537362625858
+-0.518546367589582,0.10291220253449061
+0.5854158511597525,0.005461692706610788
+-0.5914957574062258,0.1847111482767685
+0.24249838341878593,0.591776924592299
+0.8515171795262735,-0.5768989342801522
+1.636631132474323,-1.445836162919346
+-0.4426276880672608,0.1376238475488181
+-0.2604205937969315,0.9278494404441382
+0.46735067476414144,0.07370874442093078
+1.786496325822496,-2.2179697890545014
+1.2090038489288868,0.2054279355720552
+0.7966595745485655,-0.5419698483693239
+-0.764830412138427,0.4629489585545934
+1.307268476110759,0.3360008129544585
+-0.778210850909743,0.35055810328771897
+-0.4528753458667777,1.2382589516832212
+0.8335789978307604,0.6382584839328599
+-0.8391473403471071,0.344720355667136
+-0.40058582484241756,-0.4564617058701449
+-0.030771511409894425,1.0646143303328683
+0.972403940905836,-0.06681688551034197
+-0.8257516247804115,-0.22111068756294194
+-0.4972454613962945,1.0423911261184302
+0.029314434708966275,0.2460152147008709
+1.3490807010774493,-1.1345582879297398
+-0.07261754169759238,1.8697149229260583
+-0.5918724339013464,0.25677951843308094
+-0.6871001135706275,-0.19116489123799552
+0.998075246474073,0.5967686436968765
+1.2205139325998016,-1.5131537362625858
+-0.518546367589582,0.10291220253449061
+0.5847507975008884,-0.49252604472088
+-0.545607405491664,0.048185969310337994
+0.8207410448384842,-0.8462863444001285
+-0.6571211920946347,-0.12983388565096937
+-0.11563343472113363,1.339768947430672
+-0.4426276880672608,0.1376238475488181
+-0.2604205937969315,0.9278494404441382
+0.46735067476414144,0.07370874442093078
+1.786496325822496,-2.2179697890545014
+1.2090038489288868,0.2054279355720552
+1.3700062690298327,-1.3033262137602413
+-0.764830412138427,0.4629489585545934
+-0.685500717435734,-0.0693876549369587
+-0.778210850909743,0.35055810328771897
+-0.4528753458667777,1.2382589516832212
+0.8335789978307604,0.6382584839328599
+-0.4106464446014623,-0.28202563739072206
+-0.4436196260773645,-0.0642080491069339
+-0.030771511409894425,1.0646143303328683
+0.12207112846346468,1.2356404243404138
+-0.8257516247804115,-0.22111068756294194
+-0.008210004859726339,1.0701835669127422
+-0.25230885633680644,0.22880293245503738
+0.5810220525983003,0.5667397004452622
+-0.07261754169759238,1.8697149229260583
+1.5461788229620606,-1.6631738639101994
+-0.8401464961398492,0.4251964038382032
+0.998075246474073,0.5967686436968765
+1.2205139325998016,-1.5131537362625858
+-0.518546367589582,0.10291220253449061
+0.26746535124088766,0.7205627949506991
+-0.7662716061892697,1.1223916292348763
+0.8207410448384842,-0.8462863444001285
+-0.6571211920946347,-0.12983388565096937
+-0.11563343472113363,1.339768947430672
+-0.4426276880672608,0.1376238475488181
+-0.6522457689728173,0.32444334271970937
+0.46735067476414144,0.07370874442093078
+1.786496325822496,-2.2179697890545014
+1.2090038489288868,0.2054279355720552
+-0.6079745509966662,-0.0642583391149536
+-0.764830412138427,0.4629489585545934
+-0.685500717435734,-0.0693876549369587
+-0.778210850909743,0.35055810328771897
+-0.4528753458667777,1.2382589516832212
+0.9074387939088493,-0.7881674830591914
+-0.21831759581774263,0.0009531959554412717
+1.676737119795267,-2.06704166245094
+-0.6297005509978746,1.1374005647429868
+-0.9414975118909631,0.40512992986222746
+-0.4148059453460421,0.3842881701642853
+-0.8998060091010479,-0.44897355473104444
+-0.25230885633680644,0.22880293245503738
+-0.796692800007684,0.5868026933795196
+-0.07261754169759238,1.8697149229260583
+1.5461788229620606,-1.6631738639101994
+-0.6458947706714482,0.7921878946696197
+0.998075246474073,0.5967686436968765
+1.2205139325998016,-1.5131537362625858
+-0.7174180687355172,1.3331694449108062
+0.27568505463236737,0.28438310182501003
+-0.27093216498562833,0.30534717015360946
+1.6489600590053932,-1.5665783090521739
+-0.3237988587894088,0.49030654442268395
+-0.11563343472113363,1.339768947430672
+-0.4426276880672608,0.1376238475488181
+-0.6522457689728173,0.32444334271970937
+0.10235209640689263,-0.20604927505432413
+1.786496325822496,-2.2179697890545014
+-0.749516353290934,0.15708914261999773
+-0.46492296877556427,-0.1535018111897199
+0.6899297818855187,1.2692696044559737
+0.7605192043768989,0.9399187027557916
+-0.6892094008591562,0.4068185856773986
+-0.4528753458667777,1.2382589516832212
+0.9074387939088493,-0.7881674830591914
+-0.21831759581774263,0.0009531959554412717
+1.676737119795267,-2.06704166245094
+-0.4281189275576453,-0.23108294994140732
+-0.4274614576084525,1.2434099069045035
+-0.4148059453460421,0.3842881701642853
+-0.8998060091010479,-0.44897355473104444
+-0.14536713913201688,0.3562167946503596
+-0.687306631667642,1.4894160392960722
+-0.07261754169759238,1.8697149229260583
+1.5461788229620606,-1.6631738639101994
+-0.9323679311213344,0.31135855136241797
+0.998075246474073,0.5967686436968765
+0.548743025023204,0.21637868459788
+-0.7174180687355172,1.3331694449108062
+0.9494609467744837,0.6982482458658239
+-1.0297110600912116,-0.12205329563146622
+0.579024260103356,-0.6487239343795882
+-0.3237988587894088,0.49030654442268395
+-0.11563343472113363,1.339768947430672
+-0.4426276880672608,0.1376238475488181
+-0.6522457689728173,0.32444334271970937
+-0.2491356146405621,1.6960723109168654
+1.786496325822496,-2.2179697890545014
+-0.749516353290934,0.15708914261999773
+-0.6227343165935366,0.7217332886817263
+0.6899297818855187,1.2692696044559737
+0.7605192043768989,0.9399187027557916
+-0.521787919516054,-0.5903815809805866
+0.5078532737118806,1.703800319103269
+0.9074387939088493,-0.7881674830591914
+-0.21831759581774263,0.0009531959554412717
+1.676737119795267,-2.06704166245094
+-0.043497447235686715,1.938484216238092
+-0.4274614576084525,1.2434099069045035
+0.012336831912906687,0.004683952106533884
+0.9890640043159207,0.5930779784460737
+-0.14536713913201688,0.3562167946503596
+-0.687306631667642,1.4894160392960722
+-0.07261754169759238,1.8697149229260583
+1.5461788229620606,-1.6631738639101994
+-0.06732410685102069,1.037561486759391
+0.998075246474073,0.5967686436968765
+1.4861432101167116,-2.350912231256654
+-0.861623842964617,-0.5845132474997582
+1.345326860994715,-0.9804522258240008
+1.376000243737363,-1.764542000985237
+0.4468734902010882,-0.13182780202772132
+0.7532118050303401,0.48921580244810037
+0.09934322575558652,0.4240801846335913
+-0.4426276880672608,0.1376238475488181
+-0.6522457689728173,0.32444334271970937
+-0.2491356146405621,1.6960723109168654
+1.786496325822496,-2.2179697890545014
+-0.749516353290934,0.15708914261999773
+-0.6227343165935366,0.7217332886817263
+0.6899297818855187,1.2692696044559737
+0.7605192043768989,0.9399187027557916
+-0.521787919516054,-0.5903815809805866
+0.5078532737118806,1.703800319103269
+0.9074387939088493,-0.7881674830591914
+-0.21831759581774263,0.0009531959554412717
+1.676737119795267,-2.06704166245094
+-0.043497447235686715,1.938484216238092
+-0.4274614576084525,1.2434099069045035
+-0.9672612907600509,-0.2917239823371988
+0.9890640043159207,0.5930779784460737
+-0.14536713913201688,0.3562167946503596
+-0.687306631667642,1.4894160392960722
+-0.07261754169759238,1.8697149229260583
+1.5461788229620606,-1.6631738639101994
+-0.06732410685102069,1.037561486759391
+0.998075246474073,0.5967686436968765
+-0.591480130979712,-0.3056833441594104
+-0.724873089428332,1.302016523348071
+1.345326860994715,-0.9804522258240008
+1.376000243737363,-1.764542000985237
+0.4468734902010882,-0.13182780202772132
+1.5091230182711606,-1.0202220505476298
+0.06183649162421728,2.486908127824319
+-0.4426276880672608,0.1376238475488181
+1.7239230911498304,-2.3889838184599523
+-0.9109882612350068,-0.006155341827990046
+0.7309188370320887,1.5707004189352118
+-0.4096412982106955,-0.13745412489451939
+-0.6227343165935366,0.7217332886817263
+0.627656156144317,0.8516840451197634
+0.4510062009085377,1.1595839765340545
+-0.521787919516054,-0.5903815809805866
+0.5078532737118806,1.703800319103269
+0.9074387939088493,-0.7881674830591914
+-0.25292599325610426,1.9923083062960263
+1.423557697893242,-1.4299695802153352
+1.603863376957526,-2.4936302914058524
+-0.4274614576084525,1.2434099069045035
+-0.9672612907600509,-0.2917239823371988
+-0.372942311858289,2.0787383182150108
+0.5524287322567051,1.0776505541229728
+-0.5652739902985191,0.38504298269418036
+-0.07261754169759238,1.8697149229260583
+1.5461788229620606,-1.6631738639101994
+0.0054191598587287615,-0.3890114056871229
+0.998075246474073,0.5967686436968765
+1.7699342280432506,-2.218102757355452
+-0.019639742139087923,0.6386149960922933
+1.4652546807004971,-2.037469401096258
+1.376000243737363,-1.764542000985237
+0.4468734902010882,-0.13182780202772132
+1.5091230182711606,-1.0202220505476298
+-0.2630307472037064,1.0015430542909878
+2.137569268591293,-3.7572072092967006
+1.7239230911498304,-2.3889838184599523
+1.3093039609005013,-0.4140701689129873
+1.087356743800824,-1.2627927243239165
+1.1770803549149778,0.5423809077429419
+-0.6227343165935366,0.7217332886817263
+0.627656156144317,0.8516840451197634
+0.4510062009085377,1.1595839765340545
+0.6788559315289804,0.9710057957135534
+0.5078532737118806,1.703800319103269
+0.9074387939088493,-0.7881674830591914
+-0.5725851029738143,0.6081904899920141
+1.423557697893242,-1.4299695802153352
+1.603863376957526,-2.4936302914058524
+-0.4274614576084525,1.2434099069045035
+-0.9672612907600509,-0.2917239823371988
+-0.9056264464640107,-0.5653550312250951
+0.46069424912602347,1.6718530110295764
+0.9477341219776814,0.8897031203423093
+-0.07261754169759238,1.8697149229260583
+1.5461788229620606,-1.6631738639101994
+0.0054191598587287615,-0.3890114056871229
+0.998075246474073,0.5967686436968765
+1.7699342280432506,-2.218102757355452
+-0.019639742139087923,0.6386149960922933
+-1.1462904498589306,-0.00995986798008841
+-0.7678832990564775,0.041056871363260417
+-0.8259542698708247,0.6983325766535138
+1.5091230182711606,-1.0202220505476298
+1.5030656867158398,-0.8779782124538802
+1.6776833999296203,-1.6389018116491392
+1.7239230911498304,-2.3889838184599523
+0.7364660891800149,-0.23783399901642
+1.087356743800824,-1.2627927243239165
+0.8289379515486283,1.0065710078668026
+-0.6227343165935366,0.7217332886817263
+0.10367091398970002,0.5083767156320601
+0.2732786285849125,0.40875317793764765
+0.6788559315289804,0.9710057957135534
+0.5078532737118806,1.703800319103269
+0.6230382624658133,-0.5197315057209979
+-0.5725851029738143,0.6081904899920141
+1.423557697893242,-1.4299695802153352
+-0.38046720286656516,-0.5268622038049704
+1.249497600033644,-1.014572972639645
+-0.4640730152497774,0.7871066135276202
+0.23273962420825295,0.6537625014791937
+0.46069424912602347,1.6718530110295764
+0.45472844008123386,-0.3316654219666352
+0.2723696049006076,-0.13649788959718556
+-0.2982867647840848,1.775502783453174
+0.0054191598587287615,-0.3890114056871229
+0.998075246474073,0.5967686436968765
+1.3368151882149273,-1.7625637154636142
+-0.019639742139087923,0.6386149960922933
+0.9123565928066787,1.1778715607964774
+-0.7678832990564775,0.041056871363260417
+-0.8259542698708247,0.6983325766535138
+1.5091230182711606,-1.0202220505476298
+1.5030656867158398,-0.8779782124538802
+1.6776833999296203,-1.6389018116491392
+1.7239230911498304,-2.3889838184599523
+0.7364660891800149,-0.23783399901642
+-0.3850361200184419,1.2208980812164953
+0.8289379515486283,1.0065710078668026
+-0.6227343165935366,0.7217332886817263
+1.407642964823763,-1.3307768907418085
+0.28085737020626567,0.1603885780241716
+0.6788559315289804,0.9710057957135534
+0.5078532737118806,1.703800319103269
+-0.09295983943227326,-0.13788115115803093
+-0.5725851029738143,0.6081904899920141
+1.423557697893242,-1.4299695802153352
+1.6921981426474182,-2.3909942762242458
+1.249497600033644,-1.014572972639645
+-0.4640730152497774,0.7871066135276202
+-0.5806957697730322,-0.7037787454882587
+0.46069424912602347,1.6718530110295764
+-0.2989728227849846,-0.11449946119135185
+0.2723696049006076,-0.13649788959718556
+-0.2982867647840848,1.775502783453174
+0.3978431431884601,-0.24173593020741546
+0.998075246474073,0.5967686436968765
+1.3368151882149273,-1.7625637154636142
+-0.8925709547714825,-0.14311114726915208
+0.9123565928066787,1.1778715607964774
+-0.7678832990564775,0.041056871363260417
+-0.8259542698708247,0.6983325766535138
+1.1705857267155915,-0.7137226860584274
+1.496318611405665,-1.6640204426377325
+0.9629203259762952,-0.451628997728033
+-0.14089342158878687,0.6404947023822429
+0.7364660891800149,-0.23783399901642
+-0.3850361200184419,1.2208980812164953
+0.8289379515486283,1.0065710078668026
+-0.6227343165935366,0.7217332886817263
+1.407642964823763,-1.3307768907418085
+0.28085737020626567,0.1603885780241716
+0.6788559315289804,0.9710057957135534
+0.5078532737118806,1.703800319103269
+0.6771908152951487,-0.4021878691595387
+-0.5725851029738143,0.6081904899920141
+1.423557697893242,-1.4299695802153352
+1.6921981426474182,-2.3909942762242458
+-0.8950240686857242,0.749496216056634
+1.558599834859295,-1.1159344686609762
+-0.5806957697730322,-0.7037787454882587
+-0.9604852961133356,-0.4606284370116086
+-0.2989728227849846,-0.11449946119135185
+0.2723696049006076,-0.13649788959718556
+-0.6147319159632958,0.245427788315627
+0.8420211327567869,1.391600087689959
+0.998075246474073,0.5967686436968765
+1.3368151882149273,-1.7625637154636142
+-0.8925709547714825,-0.14311114726915208
+0.9123565928066787,1.1778715607964774
+-0.7678832990564775,0.041056871363260417
+-0.6576064066261911,1.2902210176427957
+1.1705857267155915,-0.7137226860584274
+-0.5592176124140766,1.5967504764009792
+0.9629203259762952,-0.451628997728033
+-0.14089342158878687,0.6404947023822429
+0.7364660891800149,-0.23783399901642
+-0.3850361200184419,1.2208980812164953
+0.6030389174719639,0.3802231696257179
+0.9979715137982468,-0.350642178969488
+1.407642964823763,-1.3307768907418085
+1.1920970412639178,0.25546076615824004
+0.6788559315289804,0.9710057957135534
+0.5078532737118806,1.703800319103269
+0.6771908152951487,-0.4021878691595387
+-0.5725851029738143,0.6081904899920141
+1.423557697893242,-1.4299695802153352
+1.6921981426474182,-2.3909942762242458
+1.2717605821305624,0.08769556450319645
+1.558599834859295,-1.1159344686609762
+1.127300262604713,0.1541824454179454
+-0.9604852961133356,-0.4606284370116086
+-0.2989728227849846,-0.11449946119135185
+0.2723696049006076,-0.13649788959718556
+1.1344340770663113,0.15733811883317717
+0.8420211327567869,1.391600087689959
+1.2750443319430596,-1.4179818258104837
+1.3368151882149273,-1.7625637154636142
+-0.8925709547714825,-0.14311114726915208
+0.9123565928066787,1.1778715607964774
+-0.7678832990564775,0.041056871363260417
+-0.6576064066261911,1.2902210176427957
+1.1705857267155915,-0.7137226860584274
+-0.5592176124140766,1.5967504764009792
+-0.7272087776944633,1.5579749878179698
+-0.14089342158878687,0.6404947023822429
+0.7364660891800149,-0.23783399901642
+-0.3850361200184419,1.2208980812164953
+1.2984398888519122,-1.2339515575276103
+0.9979715137982468,-0.350642178969488
+0.4053783758622999,1.989854322793359
+0.9265503493648651,1.0252006707602896
+0.03573882666739103,2.049445882510178
+0.5078532737118806,1.703800319103269
+0.7356671957896422,-0.5286754036477581
+0.7172789686076849,-0.8977814509695415
+1.423557697893242,-1.4299695802153352
+1.6921981426474182,-2.3909942762242458
+1.2717605821305624,0.08769556450319645
+0.9312969044561991,-0.9882886767693675
+-0.5477667547033408,1.9224600249715031
+-0.9604852961133356,-0.4606284370116086
+-0.2989728227849846,-0.11449946119135185
+0.2723696049006076,-0.13649788959718556
+1.1344340770663113,0.15733811883317717
+0.8420211327567869,1.391600087689959
+0.2239810864358166,-0.2772693214922307
+-0.24261623247394326,1.277432298645924
+-0.8925709547714825,-0.14311114726915208
+-0.23966990715591718,0.32628417753735295
+-0.7678832990564775,0.041056871363260417
+-0.6576064066261911,1.2902210176427957
+-0.15887762062727576,0.7164468541663507
+0.6433299549291229,1.6880397172508992
+0.5106179886473574,-0.4286564462621649
+0.9578089076639796,-1.008105258628515
+-0.17920682768294302,1.3295228508763
+0.0052728888243388505,-0.20880250199027114
+-0.32908779097792534,2.214109623223252
+-0.6876097239159815,-0.10060031408247888
+0.4053783758622999,1.989854322793359
+-0.10286972536803418,1.2184206542886824
+0.03573882666739103,2.049445882510178
+0.5078532737118806,1.703800319103269
+1.4498322117551012,-1.7324513634049579
+0.22438581882293887,2.192136955283646
+-0.8805325845627637,-0.024659532156883338
+1.6921981426474182,-2.3909942762242458
+1.2717605821305624,0.08769556450319645
+0.9312969044561991,-0.9882886767693675
+0.4702493614248761,-0.21319876486218975
+0.09931244961693209,1.132984118401825
+-0.2994398966301223,0.4053817641952641
+0.2723696049006076,-0.13649788959718556
+1.1344340770663113,0.15733811883317717
+1.3859047197038454,-1.014735908988421
+-0.7347501291843539,-0.1029458749327648
+-0.12117889974659796,0.028300985676250445
+0.7874085511061941,1.333934443120606
+-0.23966990715591718,0.32628417753735295
+-0.7678832990564775,0.041056871363260417
+-0.6576064066261911,1.2902210176427957
+-0.572423503995731,0.6541473872279877
+0.6433299549291229,1.6880397172508992
+-1.0490890738004803,-0.8013460338277192
+0.9578089076639796,-1.008105258628515
+-0.10397851890075965,2.2454901834925027
+0.0052728888243388505,-0.20880250199027114
+-0.32908779097792534,2.214109623223252
+-0.7271540503875529,0.46243433341963847
+0.4053783758622999,1.989854322793359
+-0.10286972536803418,1.2184206542886824
+0.03573882666739103,2.049445882510178
+0.5078532737118806,1.703800319103269
+1.4498322117551012,-1.7324513634049579
+-0.3829758748970512,0.5469867034670924
+-0.8805325845627637,-0.024659532156883338
+1.6921981426474182,-2.3909942762242458
+0.8240284185812069,0.4665654753169871
+0.9312969044561991,-0.9882886767693675
+1.0541223185009319,-1.1958061928774546
+0.09931244961693209,1.132984118401825
+0.6032081902738018,-0.6796297431424546
+0.2723696049006076,-0.13649788959718556
+1.1344340770663113,0.15733811883317717
+1.3859047197038454,-1.014735908988421
+-0.7347501291843539,-0.1029458749327648
+1.1042594032838262,0.6548254666505451
+0.7874085511061941,1.333934443120606
+0.43671338370852464,1.8180624629704405
+-0.7678832990564775,0.041056871363260417
+-0.6576064066261911,1.2902210176427957
+-0.572423503995731,0.6541473872279877
+0.49037947942514604,-0.12819514241428004
+-1.0490890738004803,-0.8013460338277192
+0.9578089076639796,-1.008105258628515
+-0.10397851890075965,2.2454901834925027
+1.0067815138076486,-0.6906390823044528
+-0.32908779097792534,2.214109623223252
+0.9167039775355806,-0.7371039758786101
+-0.08310606364233109,0.26252818549179036
+-0.10286972536803418,1.2184206542886824
+0.03573882666739103,2.049445882510178
+0.41223040176366976,0.3597621098307813
+-0.26353449439067045,0.10652778425832227
+-0.3829758748970512,0.5469867034670924
+0.8568020065765062,-0.9809386841883827
+1.6921981426474182,-2.3909942762242458
+0.8240284185812069,0.4665654753169871
+0.2522522414394358,-0.3728353277068682
+0.4682493616485439,0.1654410804175666
+-0.057492227301752616,1.4040005458319849
+0.3293565287028895,0.9652541833663981
+0.2723696049006076,-0.13649788959718556
+1.1344340770663113,0.15733811883317717
+1.3859047197038454,-1.014735908988421
+-0.0127782192471122,0.21469733185029116
+1.1042594032838262,0.6548254666505451
+0.7874085511061941,1.333934443120606
+0.43671338370852464,1.8180624629704405
+-0.7678832990564775,0.041056871363260417
+-0.6576064066261911,1.2902210176427957
+1.6980953686892177,-1.3411609082751421
+1.5783554525498635,-1.6758625007194583
+-1.0490890738004803,-0.8013460338277192
+1.3885975845495515,-1.2028146018962373
+0.49591493035186973,-0.025449935338721863
+1.0067815138076486,-0.6906390823044528
+-0.8042211486039329,0.45288081312158135
+0.9167039775355806,-0.7371039758786101
+-0.08310606364233109,0.26252818549179036
+-0.10286972536803418,1.2184206542886824
+0.03573882666739103,2.049445882510178
+-0.7539722456809452,1.595794185749405
+-0.26353449439067045,0.10652778425832227
+0.7889571202667596,1.3847651703185198
+0.8568020065765062,-0.9809386841883827
+1.6921981426474182,-2.3909942762242458
+0.8240284185812069,0.4665654753169871
+0.2522522414394358,-0.3728353277068682
+-1.112093884928954,-0.3004015394505398
+-0.9232246941975261,-0.44342697588060737
+0.3293565287028895,0.9652541833663981
+-0.3076690056059008,2.0119143675500584
+0.05367611045056647,1.805570590435459
+1.3859047197038454,-1.014735908988421
+-0.0127782192471122,0.21469733185029116
+1.1042594032838262,0.6548254666505451
+0.22044560252543977,0.05980055460564926
+0.43671338370852464,1.8180624629704405
+-0.7678832990564775,0.041056871363260417
+-0.6576064066261911,1.2902210176427957
+-0.6526884373593234,1.2122100583219173
+1.5783554525498635,-1.6758625007194583
+-1.0490890738004803,-0.8013460338277192
+0.13106928896979975,-0.09622348762775251
+0.8143785147027375,1.0557455487274074
+1.0067815138076486,-0.6906390823044528
+0.861929646228021,1.0576876969438447
+1.1884212717139597,-0.8741895555832545
+-0.08310606364233109,0.26252818549179036
+-0.8392900601124702,0.9544740170062721
+1.1160626263826614,0.8823644392104741
+-0.7539722456809452,1.595794185749405
+-0.17317503625569752,0.17348660558352869
+0.7889571202667596,1.3847651703185198
+0.8568020065765062,-0.9809386841883827
+1.6921981426474182,-2.3909942762242458
+1.2878481733145606,-0.37347538636911576
+0.2522522414394358,-0.3728353277068682
+-1.112093884928954,-0.3004015394505398
+-0.9232246941975261,-0.44342697588060737
+0.3293565287028895,0.9652541833663981
+-0.3076690056059008,2.0119143675500584
+0.05367611045056647,1.805570590435459
+1.3859047197038454,-1.014735908988421
+-0.0127782192471122,0.21469733185029116
+1.1042594032838262,0.6548254666505451
+0.22044560252543977,0.05980055460564926
+0.43671338370852464,1.8180624629704405
+-0.7678832990564775,0.041056871363260417
+-0.6576064066261911,1.2902210176427957
+-0.6526884373593234,1.2122100583219173
+1.5783554525498635,-1.6758625007194583
+-1.0490890738004803,-0.8013460338277192
+0.13106928896979975,-0.09622348762775251
+0.5034756534624699,1.992293539891883
+0.9453283445069784,-0.9661433657272067
+0.8852378368718221,0.5000984528726915
+1.3645758623558815,-0.6146719748184639
+-0.08310606364233109,0.26252818549179036
+-0.8392900601124702,0.9544740170062721
+0.4037033298318768,1.7678798276617294
+-0.7539722456809452,1.595794185749405
+-0.17317503625569752,0.17348660558352869
+0.7889571202667596,1.3847651703185198
+0.8568020065765062,-0.9809386841883827
+1.6921981426474182,-2.3909942762242458
+1.2878481733145606,-0.37347538636911576
+0.2474011925440122,1.756124769079228
+0.515121721395766,1.3239544493915816
+-0.7087503137275043,-0.04051394886364719
+-0.31968268182572224,0.4343928451878006
+-0.3076690056059008,2.0119143675500584
+0.05367611045056647,1.805570590435459
+-0.4055117231054068,1.0379696305628028
+-0.0127782192471122,0.21469733185029116
+1.1042594032838262,0.6548254666505451
+0.23068881237120586,2.5754142571948693
+0.43671338370852464,1.8180624629704405
+-0.7678832990564775,0.041056871363260417
+-0.6576064066261911,1.2902210176427957
+-0.8011233755663137,0.7119934184826997
+1.5783554525498635,-1.6758625007194583
+-1.0490890738004803,-0.8013460338277192
+-0.5710160760624794,1.3735895356837342
+0.5034756534624699,1.992293539891883
+0.29789705455884546,-0.026238540443812797
+-0.6611878317128076,0.9322722466246931
+1.3645758623558815,-0.6146719748184639
+0.4446692763657934,1.5712737040395113
+-0.8392900601124702,0.9544740170062721
+0.12768991503437005,1.9809590275000466
+0.3867846248070477,0.16062004245612632
+-0.17317503625569752,0.17348660558352869
+0.648439234234687,0.3063728762522399
+0.8568020065765062,-0.9809386841883827
+1.6921981426474182,-2.3909942762242458
+0.7118606664452553,1.2254822204638922
+0.2474011925440122,1.756124769079228
+0.515121721395766,1.3239544493915816
+-0.7087503137275043,-0.04051394886364719
+0.22833924792016336,1.0447898626655454
+0.396671890261756,2.3841147431767715
+0.05367611045056647,1.805570590435459
+-0.4055117231054068,1.0379696305628028
+1.3199644543895799,-0.31065250464079597
+1.1042594032838262,0.6548254666505451
+0.7317781140866173,-0.9686660796958798
+0.43671338370852464,1.8180624629704405
+-0.7678832990564775,0.041056871363260417
+-0.7305848076131176,1.4316031782872354
+0.12631517247227053,1.0834210041541295
+1.5783554525498635,-1.6758625007194583
+-0.9855130663970088,1.0703333138857618
+-0.5710160760624794,1.3735895356837342
+-0.42718919001631317,-0.41113757861404454
+0.29789705455884546,-0.026238540443812797
+-0.6611878317128076,0.9322722466246931
+1.3645758623558815,-0.6146719748184639
+0.4446692763657934,1.5712737040395113
+1.5456816305034669,-0.595167781802902
+0.11614386544280747,1.4498917463969017
+0.3731015330439523,0.05363790614495012
+0.7401810770295387,1.4316956572783368
+0.648439234234687,0.3063728762522399
+-0.37330109174373866,0.7863305407870061
+1.6921981426474182,-2.3909942762242458
+0.7118606664452553,1.2254822204638922
+0.2474011925440122,1.756124769079228
+-0.01838792831545416,0.4029297309865851
+-0.5670521832228059,0.5356248521485744
+0.04976910603153356,0.24326207638675365
+-0.5988232931979987,0.719607187264732
+-0.9025040390373272,-0.12874173950838907
+-0.6763391121607498,-0.20790051908203855
+-0.2637083466158442,0.8250136242351479
+1.1042594032838262,0.6548254666505451
+-0.2265293827393985,0.3599575436967516
+0.43671338370852464,1.8180624629704405
+-0.7678832990564775,0.041056871363260417
+1.7179834804944734,-0.9078317585915906
+0.12631517247227053,1.0834210041541295
+1.5783554525498635,-1.6758625007194583
+-0.12265883125463464,-0.24215789395057805
+-0.5710160760624794,1.3735895356837342
+0.35139126595542675,-0.04775769395336049
+0.29789705455884546,-0.026238540443812797
+0.40562456587382145,0.05562926494418702
+-0.2044459465626357,0.8285224632415417
+0.19139024137774205,0.22365558746873432
+1.5456816305034669,-0.595167781802902
+-0.4326785501720017,-0.07583707719085092
+-0.6129383378314222,1.0506817331021154
+0.7401810770295387,1.4316956572783368
+1.3576046017782981,-1.2454486291225155
+-0.37330109174373866,0.7863305407870061
+1.6921981426474182,-2.3909942762242458
+0.7118606664452553,1.2254822204638922
+0.2474011925440122,1.756124769079228
+-0.01838792831545416,0.4029297309865851
+-0.5670521832228059,0.5356248521485744
+-0.925063992531501,0.5665500700978984
+-0.9726715986493706,-0.8530843499136793
+-0.9025040390373272,-0.12874173950838907
+-0.7969065156917619,0.5311781366682082
+1.051969310259973,0.7979302265786623
+1.1042594032838262,0.6548254666505451
+1.4907167538567072,-1.8507632773328666
+0.43671338370852464,1.8180624629704405
+-0.7678832990564775,0.041056871363260417
+0.38729177978109747,-0.7749490096530001
+0.5932518123547262,1.2861609547869062
+0.5422543209204918,-0.556761543639856
+0.42279716531713935,1.9310772670156926
+-0.5710160760624794,1.3735895356837342
+0.35139126595542675,-0.04775769395336049
+0.5178151861706259,1.9909379083447072
+0.5065382590389501,1.3385645452673223
+-0.7153818335551163,0.6066345458973469
+-0.614161269856689,0.8745556001936852
+1.5456816305034669,-0.595167781802902
+-0.4326785501720017,-0.07583707719085092
+-0.6129383378314222,1.0506817331021154
+1.4128551639416131,-2.2761488868321518
+1.3576046017782981,-1.2454486291225155
+0.3837926052021395,-0.4935005346811421
+1.6921981426474182,-2.3909942762242458
+0.7118606664452553,1.2254822204638922
+0.6830930676161676,-0.8054926697555916
+-0.01838792831545416,0.4029297309865851
+-0.5670521832228059,0.5356248521485744
+0.3242331954894834,0.47953233875142465
+0.888363889952363,-0.03701908263772036
+-0.9025040390373272,-0.12874173950838907
+0.41955074976882606,1.7699636652551256
+1.051969310259973,0.7979302265786623
+1.6319383150215456,-1.715482403477185
+-0.018998051171529307,0.552050874179753
+0.43671338370852464,1.8180624629704405
+-0.7678832990564775,0.041056871363260417
+1.7171280680845027,-1.1554760820356471
+0.6425975412473179,-0.424992557532722
+0.5422543209204918,-0.556761543639856
+0.42279716531713935,1.9310772670156926
+-0.5710160760624794,1.3735895356837342
+0.35139126595542675,-0.04775769395336049
+0.5178151861706259,1.9909379083447072
+0.7423823008295882,0.5542479147653961
+-0.7153818335551163,0.6066345458973469
+-0.614161269856689,0.8745556001936852
+1.5456816305034669,-0.595167781802902
+-0.4326785501720017,-0.07583707719085092
+-0.6129383378314222,1.0506817331021154
+1.4128551639416131,-2.2761488868321518
+1.3576046017782981,-1.2454486291225155
+1.2559868424859566,-1.3357729325826164
+1.6921981426474182,-2.3909942762242458
+0.7118606664452553,1.2254822204638922
+0.6830930676161676,-0.8054926697555916
+-0.01838792831545416,0.4029297309865851
+-0.5670521832228059,0.5356248521485744
+1.2743961678787792,-0.4370878778187772
+1.2810682397367055,0.43526443537011106
+-0.9025040390373272,-0.12874173950838907
+0.8023663734513657,-1.081098360391922
+1.051969310259973,0.7979302265786623
+1.6319383150215456,-1.715482403477185
+0.5075477745461836,-0.6808394906098207
+0.43671338370852464,1.8180624629704405
+-0.7678832990564775,0.041056871363260417
+-0.7496628293432094,1.2095844773730198
+0.6425975412473179,-0.424992557532722
+0.5422543209204918,-0.556761543639856
+0.42279716531713935,1.9310772670156926
+0.5098539671428743,1.4937692332529955
+-0.7576445075871775,0.6388327980680798
+-0.5292841495027562,1.9984929622894159
+-0.9658433041771761,-0.2282410883302522
+-0.5864085918427528,0.12053955692886625
+-0.614161269856689,0.8745556001936852
+1.5456816305034669,-0.595167781802902
+0.5084535925373614,0.3924154879676591
+-0.6129383378314222,1.0506817331021154
+1.4128551639416131,-2.2761488868321518
+-0.6754564329812506,0.7962468915428111
+1.3273413783510213,-1.976762974758714
+1.6921981426474182,-2.3909942762242458
+0.7118606664452553,1.2254822204638922
+0.6830930676161676,-0.8054926697555916
+-0.01838792831545416,0.4029297309865851
+0.8554776979831094,-0.20621908142834816
+1.2743961678787792,-0.4370878778187772
+0.06523477657402121,-0.0883930799051571
+-0.9025040390373272,-0.12874173950838907
+0.8023663734513657,-1.081098360391922
+1.051969310259973,0.7979302265786623
+1.6319383150215456,-1.715482403477185
+0.5075477745461836,-0.6808394906098207
+0.43671338370852464,1.8180624629704405
+-0.7678832990564775,0.041056871363260417
+-0.15365957888099868,-0.073426359628686
+0.6425975412473179,-0.424992557532722
+0.5422543209204918,-0.556761543639856
+0.42279716531713935,1.9310772670156926
+-0.23679919014218725,-0.05759415124436984
+-0.7576445075871775,0.6388327980680798
+-0.5292841495027562,1.9984929622894159
+-0.29767658994417134,-0.35076948574055167
+-0.5864085918427528,0.12053955692886625
+0.2552243035272738,0.44469395473188617
+1.5456816305034669,-0.595167781802902
+0.5084535925373614,0.3924154879676591
+-0.6129383378314222,1.0506817331021154
+1.4128551639416131,-2.2761488868321518
+-0.6754564329812506,0.7962468915428111
+1.3273413783510213,-1.976762974758714
+1.6921981426474182,-2.3909942762242458
+0.7118606664452553,1.2254822204638922
+0.6830930676161676,-0.8054926697555916
+0.16400088727333512,1.8287047843697988
+-0.2849316135894179,1.3206969621174842
+0.11584637640021767,0.13109401799213527
+0.06523477657402121,-0.0883930799051571
+-0.9025040390373272,-0.12874173950838907
+0.8411136785967264,0.3363705481420984
+-0.892216370414931,0.4020129655643974
+1.6319383150215456,-1.715482403477185
+0.5075477745461836,-0.6808394906098207
+0.43671338370852464,1.8180624629704405
+-0.7678832990564775,0.041056871363260417
+1.58663316635235,-0.37151135896904863
+-0.6187745098824541,1.1455550724432009
+0.5422543209204918,-0.556761543639856
+-0.7769415398816131,0.6551076577812195
+0.39989447461217253,-0.27699810859447016
+-0.7576445075871775,0.6388327980680798
+1.0156017836708235,-1.1862061106561406
+1.3170663942837917,-1.3513831712750282
+-0.5864085918427528,0.12053955692886625
+0.2552243035272738,0.44469395473188617
+1.5456816305034669,-0.595167781802902
+-0.5027184083548136,0.45851022402941694
+1.382023038809956,-1.0311471190161234
+-0.1628381170249656,1.791589881176621
+-0.6754564329812506,0.7962468915428111
+-0.5924245445900443,0.1329086416881634
+1.6921981426474182,-2.3909942762242458
+0.7118606664452553,1.2254822204638922
+0.6830930676161676,-0.8054926697555916
+0.16400088727333512,1.8287047843697988
+0.3609927240942492,-0.5549963402393968
+0.11584637640021767,0.13109401799213527
+1.140853096271259,-1.5401850181853889
+-0.9025040390373272,-0.12874173950838907
+0.8411136785967264,0.3363705481420984
+-0.892216370414931,0.4020129655643974
+1.6319383150215456,-1.715482403477185
+-0.03050196917558301,1.0753076719257366
+0.8555261847691218,-0.10559171533345302
+-0.7678832990564775,0.041056871363260417
+-0.1174898980842634,1.1513639436154575
+-0.6187745098824541,1.1455550724432009
+0.5422543209204918,-0.556761543639856
+0.8749371886670136,0.6675263333701369
+-0.4743887384115908,1.3396708934233421
+1.2712261319023659,-0.05743383563906351
+0.38991905207677663,-0.3932307487497089
+1.3170663942837917,-1.3513831712750282
+0.8545421515778981,-0.26000341128464954
+0.6522824670031695,1.3885788548735827
+1.5456816305034669,-0.595167781802902
+0.7643929151602793,0.6783760892755251
+1.4686052430892444,-0.9124228130803584
+-0.1628381170249656,1.791589881176621
+-0.6754564329812506,0.7962468915428111
+-0.5924245445900443,0.1329086416881634
+1.6921981426474182,-2.3909942762242458
+0.7118606664452553,1.2254822204638922
+0.06161234978928376,0.2988479734954857
+0.16400088727333512,1.8287047843697988
+0.7610482612684635,1.6232149358654244
+1.0288517632274006,0.7729120403530196
+1.140853096271259,-1.5401850181853889
+-0.9025040390373272,-0.12874173950838907
+0.520392516520895,1.2078725163454953
+-0.892216370414931,0.4020129655643974
+1.6319383150215456,-1.715482403477185
+-0.6042377143669772,0.570567364682371
+0.8555261847691218,-0.10559171533345302
+-0.7678832990564775,0.041056871363260417
+0.9700426654782338,-0.556519901228089
+-0.6187745098824541,1.1455550724432009
+0.5422543209204918,-0.556761543639856
+0.8749371886670136,0.6675263333701369
+-0.4743887384115908,1.3396708934233421
+-0.3040801932371507,0.8128666136006424
+1.305794751157706,-0.12705096139938143
+1.3170663942837917,-1.3513831712750282
+0.8545421515778981,-0.26000341128464954
+0.6522824670031695,1.3885788548735827
+0.35043095737842933,1.4548593866492185
+0.7643929151602793,0.6783760892755251
+0.9452048403356876,1.147742912362877
+1.3179258679173302,-0.6312378283802006
+-0.6754564329812506,0.7962468915428111
+0.5678490044026416,-0.4284181128607282
+1.6921981426474182,-2.3909942762242458
+0.7118606664452553,1.2254822204638922
+0.06161234978928376,0.2988479734954857
+0.9865925287786532,0.439174154403263
+-0.8054605861761304,1.5251782196372239
+0.09715973096528185,2.476582534298336
+1.140853096271259,-1.5401850181853889
+-0.9025040390373272,-0.12874173950838907
+0.7784808881303428,-0.40532426298360447
+-0.892216370414931,0.4020129655643974
+1.6319383150215456,-1.715482403477185
+1.1776887865725023,-0.5577939356291424
+1.873161856637595,-2.543387639658394
+0.9397368455139836,0.6590734624980721
+1.2458753580872113,-1.528862419145387
+-0.6187745098824541,1.1455550724432009
+-0.9456923507767738,-0.1292491946135998
+0.8749371886670136,0.6675263333701369
+-0.4743887384115908,1.3396708934233421
+0.6112917487463988,-0.512304001706546
+1.305794751157706,-0.12705096139938143
+1.3170663942837917,-1.3513831712750282
+1.6291521163507585,-1.0671588737162394
+0.6522824670031695,1.3885788548735827
+0.35043095737842933,1.4548593866492185
+0.7499062294882777,0.4950452548799703
+-0.8337783997966631,0.0861490216047952
+1.3179258679173302,-0.6312378283802006
+-0.6540573672028126,0.4333519031386551
+0.5678490044026416,-0.4284181128607282
+1.5581851189220848,-0.8875858612481531
+0.934523576422888,0.0857557861556022
+0.7232593442250856,-0.8814096679569378
+0.9865925287786532,0.439174154403263
+0.16614583597755994,2.320119184730582
+0.09715973096528185,2.476582534298336
+1.9583472722053548,-3.665707861595992
+-0.9025040390373272,-0.12874173950838907
+0.0008466725181743573,2.2484175436907146
+-0.892216370414931,0.4020129655643974
+-0.9403871201395427,0.014652692110375051
+1.1776887865725023,-0.5577939356291424
+1.873161856637595,-2.543387639658394
+-0.41791865792587457,1.9628473185013726
+0.41931819426783123,-0.4411779872087762
+-0.6187745098824541,1.1455550724432009
+1.6391067019487353,-1.16405694065247
+-0.2143393580330285,-0.09647235538766316
+-0.4743887384115908,1.3396708934233421
+0.6112917487463988,-0.512304001706546
+-0.7472107598385387,-0.14192797514494265
+1.3170663942837917,-1.3513831712750282
+-0.11920646160550619,0.014011737910249122
+0.6522824670031695,1.3885788548735827
+0.35043095737842933,1.4548593866492185
+-0.8078609810420586,-0.2838547609967768
+-0.8337783997966631,0.0861490216047952
+-0.4932884039626826,1.0470051814348478
+-0.6540573672028126,0.4333519031386551
+0.5678490044026416,-0.4284181128607282
+-0.442330406985872,1.6851781667143344
+0.934523576422888,0.0857557861556022
+0.7232593442250856,-0.8814096679569378
+0.9865925287786532,0.439174154403263
+-0.16503513536129688,0.16446763018114452
+0.09715973096528185,2.476582534298336
+1.6239559298685193,-0.6227792380900891
+1.3387940490056072,-1.413552055988859
+0.0008466725181743573,2.2484175436907146
+-0.3955374386932869,0.7041180697457597
+-0.9403871201395427,0.014652692110375051
+1.1776887865725023,-0.5577939356291424
+1.873161856637595,-2.543387639658394
+-0.5321194030450367,0.8478136066207997
+-0.4290719670163625,0.439655687408861
+-0.6187745098824541,1.1455550724432009
+1.6391067019487353,-1.16405694065247
+-0.2143393580330285,-0.09647235538766316
+-0.4743887384115908,1.3396708934233421
+-0.7045680478049454,0.5578282614483349
+-0.7472107598385387,-0.14192797514494265
+-0.5706615040158372,1.0265047616643037
+-0.11920646160550619,0.014011737910249122
+0.6522824670031695,1.3885788548735827
+0.35043095737842933,1.4548593866492185
+-0.5066822945630611,0.6301100715099289
+-0.8337783997966631,0.0861490216047952
+-0.4932884039626826,1.0470051814348478
+0.7626034743896319,0.15165012746997447
+-0.8342619256400788,-0.2755877315194837
+-0.442330406985872,1.6851781667143344
+0.934523576422888,0.0857557861556022
+-0.05792499864173456,0.029483496053440916
+0.1330989772478503,-0.366401739327073
+-0.16503513536129688,0.16446763018114452
+0.09715973096528185,2.476582534298336
+1.6239559298685193,-0.6227792380900891
+1.3387940490056072,-1.413552055988859
+-0.5207496516442903,-0.24220379733233188
+-0.2634350960238815,0.7201109863341406
+-0.00861387149045012,1.3631866088404836
+1.5168255601083518,-2.166803608205088
+1.873161856637595,-2.543387639658394
+-0.5321194030450367,0.8478136066207997
+-0.4290719670163625,0.439655687408861
+-0.4540410346064814,1.8096121429051801
+-0.35284483700141667,0.41201882788428207
+-0.43706637060035747,1.9617192879011296
+1.155995970252476,-0.5526622117945361
+-0.30128941420646493,-0.14715534766118166
+0.7986568733802232,-0.39334201724033563
+1.5379976027425701,-1.087211749959514
+-0.11920646160550619,0.014011737910249122
+0.6522824670031695,1.3885788548735827
+1.2632320375607937,-1.0067475090293088
+0.630547229485114,0.2597218182060704
+-0.06511917997647232,1.9363051293547517
+-0.5891720556123774,0.1484888440575814
+1.745927348373678,-1.7753318183790816
+-0.8342619256400788,-0.2755877315194837
+-0.442330406985872,1.6851781667143344
+-0.9189786909870485,0.1771952394680235
+-0.05792499864173456,0.029483496053440916
+0.1330989772478503,-0.366401739327073
+-0.16503513536129688,0.16446763018114452
+0.26616465276976753,-0.27960612996343887
+-0.6019495372783785,1.7090615849040356
+1.3387940490056072,-1.413552055988859
+-0.05566987608143853,0.3084276014622065
+1.3779547361289126,-0.9279378695244
+-0.7022485976431345,0.5225530589685828
+1.5168255601083518,-2.166803608205088
+1.873161856637595,-2.543387639658394
+-0.9218842219433149,0.2738829972281545
+-0.36780494162727395,-0.2673992284342459
+-0.7023303330135009,0.869630930336831
+-0.35284483700141667,0.41201882788428207
+-0.43706637060035747,1.9617192879011296
+0.4711383965829826,0.22153333051692542
+0.038957494899431344,-0.058339705888535265
+0.7986568733802232,-0.39334201724033563
+0.792937177521237,-0.4152133134776602
+-0.11920646160550619,0.014011737910249122
+0.6522824670031695,1.3885788548735827
+1.2632320375607937,-1.0067475090293088
+0.6815238581518794,1.5415702621529441
+-0.06511917997647232,1.9363051293547517
+-0.5891720556123774,0.1484888440575814
+1.745927348373678,-1.7753318183790816
+-0.8342619256400788,-0.2755877315194837
+-0.09005449036855614,0.5296651692401879
+-0.9189786909870485,0.1771952394680235
+-0.05792499864173456,0.029483496053440916
+0.9928023201771945,-0.8339076503850146
+1.203537024940574,-1.2288331086286497
+-0.9349151247792165,-0.5222415885655808
+-0.6019495372783785,1.7090615849040356
+0.7164415335349685,1.0906174283075698
+-0.05566987608143853,0.3084276014622065
+1.4053949581858238,-1.1525334960893747
+-0.7022485976431345,0.5225530589685828
+1.5168255601083518,-2.166803608205088
+1.873161856637595,-2.543387639658394
+-0.9218842219433149,0.2738829972281545
+-0.36780494162727395,-0.2673992284342459
+-0.5575274608665217,1.292167516239095
+1.4623470453398781,-0.44642283381820236
+-0.43706637060035747,1.9617192879011296
+0.4711383965829826,0.22153333051692542
+0.038957494899431344,-0.058339705888535265
+0.7986568733802232,-0.39334201724033563
+0.6687805836753359,-0.8315988664232583
+1.248189985975462,-1.110377820034368
+0.6522824670031695,1.3885788548735827
+1.2632320375607937,-1.0067475090293088
+0.6815238581518794,1.5415702621529441
+-0.06511917997647232,1.9363051293547517
+-0.5891720556123774,0.1484888440575814
+1.745927348373678,-1.7753318183790816
+-0.8342619256400788,-0.2755877315194837
+-0.09005449036855614,0.5296651692401879
+-0.9189786909870485,0.1771952394680235
+-0.05792499864173456,0.029483496053440916
+-0.35319506906407944,1.3864659909817656
+1.203537024940574,-1.2288331086286497
+-0.9349151247792165,-0.5222415885655808
+1.0821637301608453,1.013242259534372
+0.7164415335349685,1.0906174283075698
+-0.05566987608143853,0.3084276014622065
+1.1908857511944562,-1.1772429269778188
+-0.7022485976431345,0.5225530589685828
+1.5168255601083518,-2.166803608205088
+1.873161856637595,-2.543387639658394
+-0.9218842219433149,0.2738829972281545
+-0.36780494162727395,-0.2673992284342459
+-0.5575274608665217,1.292167516239095
+1.0129598538621205,0.08627840890169625
+-0.43706637060035747,1.9617192879011296
+1.9972488218472084,-2.5513020452184927
+0.038957494899431344,-0.058339705888535265
+0.7986568733802232,-0.39334201724033563
+0.6839094447529329,0.007480623596098301
+1.248189985975462,-1.110377820034368
+0.6522824670031695,1.3885788548735827
+1.2632320375607937,-1.0067475090293088
+0.6815238581518794,1.5415702621529441
+-0.06511917997647232,1.9363051293547517
+-0.5891720556123774,0.1484888440575814
+1.745927348373678,-1.7753318183790816
+0.9646291558224072,-1.1323750382923587
+0.34736133389534535,1.4662188129561842
+-0.9189786909870485,0.1771952394680235
+1.235989489747933,-0.5409401610088544
+-0.11765740560511229,1.7539880145510311
+0.9014094637266266,-0.625681051775121
+-0.9349151247792165,-0.5222415885655808
+1.0821637301608453,1.013242259534372
+0.7164415335349685,1.0906174283075698
+-0.05566987608143853,0.3084276014622065
+-0.89916748725617,-0.28018352429025645
+1.2830472969209115,0.13968641642433116
+1.5168255601083518,-2.166803608205088
+-0.04348342961391203,0.4657137348615427
+-0.9218842219433149,0.2738829972281545
+-0.36780494162727395,-0.2673992284342459
+0.43460290323642403,1.9913431592429571
+1.0129598538621205,0.08627840890169625
+0.06508991815568993,1.958605887897993
+-0.7351977840062169,1.249783902947206
+0.038957494899431344,-0.058339705888535265
+1.2591935375234695,-0.14019269690470465
+1.2881799823583562,-0.35685667918608077
+1.248189985975462,-1.110377820034368
+0.6152521695091372,1.6150750734106287
+1.2632320375607937,-1.0067475090293088
+-0.2939322471010432,0.8888333374067676
+-0.06511917997647232,1.9363051293547517
+-0.5891720556123774,0.1484888440575814
+1.745927348373678,-1.7753318183790816
+-0.11716742249044065,0.15637182258741003
+0.34736133389534535,1.4662188129561842
+-0.9189786909870485,0.1771952394680235
+1.235989489747933,-0.5409401610088544
+-0.11765740560511229,1.7539880145510311
+0.6591899899550253,-0.15799918815022995
+-0.32878880897244545,1.705643531618426
+1.0821637301608453,1.013242259534372
+0.7164415335349685,1.0906174283075698
+-0.05566987608143853,0.3084276014622065
+-0.89916748725617,-0.28018352429025645
+1.2830472969209115,0.13968641642433116
+-0.32968014320619854,1.5009582166784896
+0.3977688546503678,0.3470209963681204
+-0.9218842219433149,0.2738829972281545
+-0.18033742580842982,1.4412421939978797
+0.43460290323642403,1.9913431592429571
+0.6266540127191546,1.5618323658530568
+0.06508991815568993,1.958605887897993
+-0.7351977840062169,1.249783902947206
+0.12315671883753032,0.003600615265664242
+1.2591935375234695,-0.14019269690470465
+1.2881799823583562,-0.35685667918608077
+-0.5084524633646652,1.4744756146866558
+-0.012261120582326646,0.09429485154701472
+1.2632320375607937,-1.0067475090293088
+-0.5386027950756618,1.5122119504029534
+1.2623303888865993,0.017081637724359958
+-0.5891720556123774,0.1484888440575814
+-0.07282629614993918,-0.09442039626579839
+0.6554307968099222,-0.22680685529107153
+0.6738227253364097,-0.04401043623642428
+0.5222083125299763,-0.6043674070810361
+-0.24154124617936,1.7538029064717109
+-0.11765740560511229,1.7539880145510311
+0.8332578050540891,-1.0020471008010143
+-0.32878880897244545,1.705643531618426
+1.0821637301608453,1.013242259534372
+-0.7253651842311298,1.0932310639753917
+0.8491786120874453,1.2097504753760913
+-0.89916748725617,-0.28018352429025645
+1.1347904200537786,0.125978570263228
+1.0284402646528121,-0.4583313052785892
+0.5129039206393189,-0.5124666139102757
+-0.9218842219433149,0.2738829972281545
+-0.13113749812845105,1.2008163484532524
+0.43460290323642403,1.9913431592429571
+0.6266540127191546,1.5618323658530568
+1.0957936132980537,-0.8143998620160487
+-0.7351977840062169,1.249783902947206
+0.12315671883753032,0.003600615265664242
+1.2591935375234695,-0.14019269690470465
+1.2881799823583562,-0.35685667918608077
+-0.5084524633646652,1.4744756146866558
+0.10726437613465481,1.3306446072716407
+0.9278955005227536,0.5307238381645141
+1.102644653274761,-0.09131325362182968
+1.2623303888865993,0.017081637724359958
+-0.5891720556123774,0.1484888440575814
+-0.07282629614993918,-0.09442039626579839
+0.7661968661697199,-0.7789935798787755
+0.9756032578174116,0.5748214833683913
+0.16610865836918248,2.1074128989444274
+-0.24154124617936,1.7538029064717109
+-0.11765740560511229,1.7539880145510311
+0.396347968769962,2.2731513903038763
+1.6364170689111777,-1.2345126932427952
+1.0821637301608453,1.013242259534372
+0.8828094209489076,1.1273536225914884
+1.0995789178714561,-0.7113043495793694
+-0.89916748725617,-0.28018352429025645
+0.5488455969468201,-0.007674219315597419
+-0.6705537367210234,0.3014997443504562
+0.5129039206393189,-0.5124666139102757
+-0.9218842219433149,0.2738829972281545
+-0.13113749812845105,1.2008163484532524
+-0.46643255823208485,1.1455442657696273
+0.7135939479365812,1.6091074465338275
+-0.20672797649478825,1.0291777719331636
+-0.7351977840062169,1.249783902947206
+0.12315671883753032,0.003600615265664242
+1.2591935375234695,-0.14019269690470465
+1.4601019879728185,-1.4135565557991008
+-0.5084524633646652,1.4744756146866558
+0.10726437613465481,1.3306446072716407
+-0.5745675152204924,0.04214519113109941
+0.6236744220251315,-0.3715706105285459
+-0.5902913522478578,-0.38765006084090137
+-0.5891720556123774,0.1484888440575814
+1.4860065300276437,-0.5223950309597009
+0.6798802847188113,0.7302902979300712
+1.6902915960485592,-1.7047805617951783
+0.16610865836918248,2.1074128989444274
+0.43073498148624323,1.898358320577258
+-0.6000945347149695,0.970235254318038
+0.28354526394252677,-0.7147129162374902
+1.6364170689111777,-1.2345126932427952
+1.2333268674243554,-1.57780300183141
+0.8828094209489076,1.1273536225914884
+-0.6850554801976264,-0.3343050234680519
+-0.89916748725617,-0.28018352429025645
+-0.6053337224385842,1.1620476616827493
+-0.6705537367210234,0.3014997443504562
+0.5129039206393189,-0.5124666139102757
+0.41742405887246437,1.8841318104121059
+-0.7116204167181565,-0.2795327553358692
+0.2344815681639842,2.1258362164146223
+0.7135939479365812,1.6091074465338275
+-0.4798704398165694,1.377874743866482
+-0.7351977840062169,1.249783902947206
+1.1339215993584633,-1.1133811526625355
+1.2591935375234695,-0.14019269690470465
+1.4601019879728185,-1.4135565557991008
+-0.5084524633646652,1.4744756146866558
+0.10726437613465481,1.3306446072716407
+-0.5745675152204924,0.04214519113109941
+0.6236744220251315,-0.3715706105285459
+-0.5902913522478578,-0.38765006084090137
+0.03804847815148982,-0.24928257528964531
+1.4860065300276437,-0.5223950309597009
+0.6798802847188113,0.7302902979300712
+1.0070233363814758,-1.278301650121819
+0.05812983459188237,0.3743665698526538
+0.43073498148624323,1.898358320577258
+1.0705013559029446,0.21609605919632952
+0.28354526394252677,-0.7147129162374902
+1.236011914500596,-0.4669674464089072
+0.07060072410502632,0.27565025199868576
+0.8828094209489076,1.1273536225914884
+0.03138518440414467,0.3768299772721848
+-0.89916748725617,-0.28018352429025645
+1.4378066507478937,-0.15453609378542832
+-0.40828895655813435,1.5806826337018072
+1.7350565697349478,-1.9345284645315952
+0.23780657819512213,1.7274741472233495
+-0.7116204167181565,-0.2795327553358692
+-0.2610661662217798,0.8169958595150966
+0.7135939479365812,1.6091074465338275
+-0.2665893920238629,1.4266267409629396
+-0.7351977840062169,1.249783902947206
+0.22509666920773586,0.5904561741072627
+0.19613447512635945,0.7812531997409964
+1.4601019879728185,-1.4135565557991008
+-0.5084524633646652,1.4744756146866558
+0.10726437613465481,1.3306446072716407
+-0.5745675152204924,0.04214519113109941
+0.6236744220251315,-0.3715706105285459
+-0.5902913522478578,-0.38765006084090137
+1.237863141126378,-0.9631816659570469
+1.4860065300276437,-0.5223950309597009
+-0.3095166347056878,1.0348090808094033
+1.764855240897379,-1.7017333797382244
+0.05812983459188237,0.3743665698526538
+0.25989191156272995,2.3726291308200067
+0.4415916937476648,-0.2607529676057663
+-0.2002877160291906,1.4692250382507142
+1.236011914500596,-0.4669674464089072
+0.8986131980343584,0.4650941874515505
+0.8828094209489076,1.1273536225914884
+0.6438609249573249,0.866892344203554
+-0.89916748725617,-0.28018352429025645
+1.4378066507478937,-0.15453609378542832
+1.409272959555957,-0.7602342422118407
+1.7350565697349478,-1.9345284645315952
+1.3837286447200692,-1.127803796880518
+0.6475974554976915,-0.4914067234547381
+0.8854697303463303,-0.7331762675174007
+0.7135939479365812,1.6091074465338275
+0.4673861765769847,-0.3883252004475205
+0.6708218605359911,-0.6150953512881027
+0.8089386307411454,-1.1101248454966055
+0.314208344786356,0.43091940952166274
+1.4601019879728185,-1.4135565557991008
+-0.5084524633646652,1.4744756146866558
+-0.6464261686170202,1.0642977620918965
+0.021462618967469704,1.208434635416011
+0.6236744220251315,-0.3715706105285459
+-0.5902913522478578,-0.38765006084090137
+1.237863141126378,-0.9631816659570469
+0.06296223867147668,0.18904597748524712
+1.141407132713989,-0.5343600482193032
+0.40129115678967714,-0.20431307655007958
+-0.3004318173452014,1.7575789773505082
+1.811799717561572,-1.8271434992137803
+0.4415916937476648,-0.2607529676057663
+-0.003069574335942793,0.43870470118141436
+-0.6717597760272204,1.1113903307534936
+0.8986131980343584,0.4650941874515505
+0.5376295957159511,0.24053553384054532
+0.5499401767506634,1.653070031550368
+0.9743255503449937,0.9743558587691573
+1.4378066507478937,-0.15453609378542832
+1.409272959555957,-0.7602342422118407
+0.895371121942475,-0.18369480871679988
+1.1280338625127424,-1.294686084465764
+-0.09209254943092292,2.0694544737036518
+0.8854697303463303,-0.7331762675174007
+0.7135939479365812,1.6091074465338275
+0.4673861765769847,-0.3883252004475205
+1.0894202202559773,-0.7677773919848161
+0.8089386307411454,-1.1101248454966055
+0.9238250611733212,0.3912960337685186
+1.4601019879728185,-1.4135565557991008
+-0.5084524633646652,1.4744756146866558
+-0.08734774769520348,1.2538979701063324
+1.41607724996195,-1.4108714080039424
+0.6236744220251315,-0.3715706105285459
+-0.5902913522478578,-0.38765006084090137
+1.237863141126378,-0.9631816659570469
+0.06296223867147668,0.18904597748524712
+0.4686819987146583,1.5258866166631222
+0.40129115678967714,-0.20431307655007958
+-0.3004318173452014,1.7575789773505082
+1.811799717561572,-1.8271434992137803
+0.05012772541749305,1.3418420985357873
+0.6436978076676203,1.1386500156639499
+-0.6717597760272204,1.1113903307534936
+0.8986131980343584,0.4650941874515505
+0.6418295804968446,-0.4764874935753659
+0.5499401767506634,1.653070031550368
+0.9743255503449937,0.9743558587691573
+0.5669302987727959,0.6627029706182341
+1.409272959555957,-0.7602342422118407
+1.4039000327639954,-1.4601689971129863
+0.08215116711900744,1.9462509846572673
+-0.09209254943092292,2.0694544737036518
+0.5649921016996077,0.6055703017034015
+0.15692102753536563,-0.6141897934436584
+0.9397980356641081,1.1734820888171487
+1.1564851830909522,-0.7051109478531201
+0.8089386307411454,-1.1101248454966055
+0.9238250611733212,0.3912960337685186
+1.3761147926328454,-0.16180546257547912
+-0.5084524633646652,1.4744756146866558
+-0.08734774769520348,1.2538979701063324
+-0.45052756127374144,0.8142348304314239
+0.6236744220251315,-0.3715706105285459
+-0.5902913522478578,-0.38765006084090137
+1.237863141126378,-0.9631816659570469
+0.06296223867147668,0.18904597748524712
+-0.10477816062005778,1.639295085210199
+1.1515040771965626,-1.6472948992017715
+-0.3004318173452014,1.7575789773505082
+-0.0325077098659163,0.8170372604094975
+-0.037477486761426704,0.45641033918680096
+0.5735317122199511,-0.45304689231195994
+-0.05378899216859359,0.5672429395968068
+-0.5420519897372738,1.2917299019711956
+0.021933326383159646,-0.42483097586163054
+0.5499401767506634,1.653070031550368
+0.23784652704361614,0.4760034596770917
+0.3073141366721029,0.3665873450831597
+-0.2304720112237877,1.7791719267001092
+-0.331767321462706,1.7171435897877543
+0.08215116711900744,1.9462509846572673
+-0.09209254943092292,2.0694544737036518
+0.47319166858243,1.5996950086460442
+1.1186976814335308,-0.861043430324188
+-0.5832887724011735,0.2567021374286612
+0.2747936342334297,0.6606320700421872
+0.7541575935201539,-0.9755322294489722
+-0.39172236128082055,0.3231357253776365
+1.3761147926328454,-0.16180546257547912
+1.1645423132226593,-1.3323193202058232
+-0.44586356661169424,1.004883152425449
+-0.45052756127374144,0.8142348304314239
+0.6236744220251315,-0.3715706105285459
+-0.5902913522478578,-0.38765006084090137
+1.237863141126378,-0.9631816659570469
+0.06296223867147668,0.18904597748524712
+0.6539797137187093,-0.5084153206548737
+0.2934474664095792,-0.6038669343939082
+-0.023505402551546636,-0.30682879964364396
+-0.42821353352510105,1.1201154972621095
+-0.037477486761426704,0.45641033918680096
+0.5735317122199511,-0.45304689231195994
+1.379051895641249,-0.6113766378707859
+1.3289429972785343,0.6754925058350086
+0.0879476644202879,0.9491097612789002
+0.0802401528604686,-0.22756013005840117
+-0.16266571306313032,1.4420509080180137
+0.3073141366721029,0.3665873450831597
+-0.2304720112237877,1.7791719267001092
+-0.2816541450549899,1.4682245950075794
+0.5308253357376274,-0.5434983894523213
+-0.33577357976768674,0.05765676411462403
+0.47319166858243,1.5996950086460442
+1.1186976814335308,-0.861043430324188
+-0.10541908201203798,0.39184816827610175
+-0.44924056980647586,0.8617644467886778
+-0.38811606146422406,1.9801729104019805
+-0.39172236128082055,0.3231357253776365
+1.3761147926328454,-0.16180546257547912
+0.13608774788392908,1.9272684235646111
+-0.44586356661169424,1.004883152425449
+0.34299638495432083,1.2871042701038347
+-0.0903864951124845,0.3206950187795873
+0.26790217746322637,-0.09019103769302372
+-0.5393887434248248,0.6693074475855949
+0.06296223867147668,0.18904597748524712
+-0.4473275647257351,1.1044841149314446
+-0.01429894323474723,-0.1601644850695405
+0.39343967590165124,2.0296164798990226
+-0.42821353352510105,1.1201154972621095
+0.18817026303741358,0.4494671851168689
+0.543524307752688,-0.331167608241672
+0.19643613141696492,1.591179283074152
+0.060243675168895165,0.22917506196495316
+0.0879476644202879,0.9491097612789002
+0.30981186023407825,0.5667677188687834
+-0.6017869030975751,0.984151870728346
+0.32301935992303354,0.06260747718184197
+0.1751041859314135,2.1202884946025264
+-0.2816541450549899,1.4682245950075794
+1.1005997238470113,-1.3231236994329842
+-0.46767078799993306,-0.09100379829387106
+-0.5921313817752618,1.0817096656979563
+1.1186976814335308,-0.861043430324188
+-0.10541908201203798,0.39184816827610175
+1.4098013084070649,-1.5506127408412385
+-0.38811606146422406,1.9801729104019805
+-0.4762243953176847,1.6402136999297938
+1.3761147926328454,-0.16180546257547912
+0.30263821065111496,1.7915939169375483
+-0.44586356661169424,1.004883152425449
+0.34299638495432083,1.2871042701038347
+-0.22755439104441494,0.6278311052098295
+0.26790217746322637,-0.09019103769302372
+1.3710122184113165,0.052203485752536416
+0.06296223867147668,0.18904597748524712
+0.6292595373392067,-0.09384326631029428
+-0.11151126003206922,1.7910607661062103
+0.27798656867560834,1.9767994738664205
+-0.34810943639109976,0.6219905680701352
+-0.4572899404375226,2.1381685518415723
+0.37127034469578807,2.0901882397241267
+0.31511375255649277,1.9368864702808488
+-0.13304832838824265,0.6553665699946142
+-0.09386104376314064,1.971445135374369
+-0.6148758972418868,1.5710493998290769
+0.2503595081512474,0.7956430322835213
+1.1675560473806126,-1.3973078643909755
+0.1751041859314135,2.1202884946025264
+-0.2816541450549899,1.4682245950075794
+1.1005997238470113,-1.3231236994329842
+1.0961197306015544,-1.045273104756119
+-0.2925062617552531,-0.031334215931068055
+1.1186976814335308,-0.861043430324188
+-0.10541908201203798,0.39184816827610175
+1.4098013084070649,-1.5506127408412385
+0.378691279263358,2.321809747227545
+-0.8418393230332326,0.9975130324468666
+1.3761147926328454,-0.16180546257547912
+0.30263821065111496,1.7915939169375483
+-0.44586356661169424,1.004883152425449
+1.4571425516055243,-0.6626157982455064
+0.290349047180698,2.0822484131540704
+0.26790217746322637,-0.09019103769302372
+1.3710122184113165,0.052203485752536416
+1.3269432091015578,-1.4258429262317422
+0.4214385132778257,1.5879916287992202
+-0.11151126003206922,1.7910607661062103
+0.27798656867560834,1.9767994738664205
+0.11841671885577576,0.14604886870697392
+-0.4572899404375226,2.1381685518415723
+0.37127034469578807,2.0901882397241267
+0.31511375255649277,1.9368864702808488
+0.23371642738737228,0.17844863888418494
+-0.09386104376314064,1.971445135374369
+0.9799189177161215,-1.080358027062745
+-0.19256505217202347,1.7111480261689278
+-0.3979494701482672,2.1864563422793455
+0.3847088275727433,0.7041603574875017
+0.012870161428850613,0.4335041470146197
+1.6686941009463157,-1.8656434188919184
+1.115497471814453,-1.6134401794699764
+-0.2925062617552531,-0.031334215931068055
+-0.3095983263645621,0.7531726939028117
+-0.025746903756590583,0.04913448737422338
+0.21103613861708598,-0.1274440378810619
+-0.4420430147632973,1.2551982356891713
+-0.07160884207042514,0.788469956086391
+1.3761147926328454,-0.16180546257547912
+1.4481020654261128,-0.8281544629006902
+-0.23754578721427141,0.7847067855229851
+1.4571425516055243,-0.6626157982455064
+0.290349047180698,2.0822484131540704
+0.26790217746322637,-0.09019103769302372
+0.24533005529379748,0.26083598790482876
+1.3269432091015578,-1.4258429262317422
+0.6273660968880195,0.24884166521076695
+-0.098009385488561,0.4791826983305937
+0.27798656867560834,1.9767994738664205
+0.11841671885577576,0.14604886870697392
+-0.4572899404375226,2.1381685518415723
+0.37127034469578807,2.0901882397241267
+0.31511375255649277,1.9368864702808488
+0.23371642738737228,0.17844863888418494
+-0.09386104376314064,1.971445135374369
+-0.06514816325358724,1.8441770229366745
+0.3541594921019359,0.5815690480379347
+-0.3979494701482672,2.1864563422793455
+0.029939991019187207,0.8038716076698201
+-0.4175934935665892,0.5313337984698947
+0.21683865074687622,0.9867361269732942
+1.115497471814453,-1.6134401794699764
+-0.2925062617552531,-0.031334215931068055
+-0.3095983263645621,0.7531726939028117
+0.6695657263101039,-0.6790241317375156
+-0.030802880995262294,2.3247172294067946
+0.03103192279185929,1.9125856418415408
+-0.07160884207042514,0.788469956086391
+1.3761147926328454,-0.16180546257547912
+0.6105465169348864,1.2509764682470084
+-0.23754578721427141,0.7847067855229851
+1.4571425516055243,-0.6626157982455064
+0.290349047180698,2.0822484131540704
+0.046797154457501544,0.23034200673912256
+-0.18083952378248996,0.04715412689336951
+1.3269432091015578,-1.4258429262317422
+0.46586114175828675,2.269836566494029
+0.432782450010287,0.21312699256903123
+1.0695125953793845,0.9502711193939406
+0.11841671885577576,0.14604886870697392
+-0.28833185116765747,1.7847189149941984
+0.37127034469578807,2.0901882397241267
+0.48720367720898483,0.1634743160456481
+0.9992169833686286,-0.9816509904766446
+-0.09386104376314064,1.971445135374369
+-0.06514816325358724,1.8441770229366745
+0.3541594921019359,0.5815690480379347
+-0.70029397764126,1.234868807113687
+-0.203544463972864,1.2977995658997532
+-0.014772077070736814,0.6331526140317205
+0.7907803293574333,0.47662625544066906
+1.115497471814453,-1.6134401794699764
+-0.2925062617552531,-0.031334215931068055
+0.10741978103993016,2.3381640230454024
+-0.38224869139050555,0.5708039513116603
+-0.030802880995262294,2.3247172294067946
+0.03103192279185929,1.9125856418415408
+-0.5986569604223969,0.27428164594319326
+1.3761147926328454,-0.16180546257547912
+0.6105465169348864,1.2509764682470084
+-0.23754578721427141,0.7847067855229851
+0.22043277080402804,0.7975217923322786
+1.2578816649093398,-1.227227918735512
+-0.26320753811564,1.3651299073019465
+-0.18083952378248996,0.04715412689336951
+1.3269432091015578,-1.4258429262317422
+0.9516765909289137,-0.32993291072327796
+-0.24365003069671243,0.7272438409465737
+-0.43526451516293563,0.168969003935586
+0.11841671885577576,0.14604886870697392
+-0.18049058405956675,2.3907188495730107
+0.37127034469578807,2.0901882397241267
+0.48720367720898483,0.1634743160456481
+0.953290260710572,0.2730243176348398
+0.7107377140511228,-0.8294980913563629
+0.53269023316157,1.9545364598232964
+0.694566310000758,0.38185692381397585
+0.28241451005006213,-0.05819106930094353
+-0.5858318964721039,-0.42734987167902483
+0.5202441536757063,-0.30773946163482
+-0.7851622394219611,0.16407624826281914
+1.115497471814453,-1.6134401794699764
+0.5560642583485158,1.7767556393150081
+0.10741978103993016,2.3381640230454024
+-0.38224869139050555,0.5708039513116603
+-0.030802880995262294,2.3247172294067946
+0.7148719108984288,1.4228020269115425
+0.9218307418954835,0.6765618147699588
+1.3761147926328454,-0.16180546257547912
+-0.6780339794982709,0.9615507609649574
+-0.23510030943661858,1.9851165523108116
+0.22043277080402804,0.7975217923322786
+1.2578816649093398,-1.227227918735512
+-0.26320753811564,1.3651299073019465
+-0.24819772983760782,-0.4705542822715652
+1.3269432091015578,-1.4258429262317422
+-0.8551124518578123,-0.11938275322436531
+-0.24365003069671243,0.7272438409465737
+-0.43526451516293563,0.168969003935586
+-0.716866160397136,0.2899352639701364
+-0.35137234578202897,1.6295707586905634
+0.37127034469578807,2.0901882397241267
+-0.006475959898337574,1.1819994940250707
+-0.5211269695890611,0.5000201491106193
+0.7107377140511228,-0.8294980913563629
+0.53269023316157,1.9545364598232964
+-0.6198929532867392,-0.2089137663401714
+0.28241451005006213,-0.05819106930094353
+-0.5858318964721039,-0.42734987167902483
+0.5202441536757063,-0.30773946163482
+-0.7851622394219611,0.16407624826281914
+-0.03648371710422216,1.9716884761975484
+0.5560642583485158,1.7767556393150081
+-0.06938024614540944,0.018511948223220887
+-0.38224869139050555,0.5708039513116603
+-0.10670498995232734,1.7622971456133387
+0.26853936767338743,-0.16251089799856655
+0.4326655838125496,2.0847106514044667
+1.3761147926328454,-0.16180546257547912
+-0.6780339794982709,0.9615507609649574
+-1.0638930327430791,-0.050098011466587045
+-0.3207199725577167,2.149398053798279
+1.2578816649093398,-1.227227918735512
+-0.26320753811564,1.3651299073019465
+-0.9331154037893676,-0.26431683916783766
+1.3269432091015578,-1.4258429262317422
+-0.8551124518578123,-0.11938275322436531
+1.117610430267375,-0.10861743167261377
+-0.43526451516293563,0.168969003935586
+0.5659821842619136,2.283419481275046
+-0.6841578022122661,1.6359731895557412
+0.1263287840668082,0.34288733323791365
+-0.006475959898337574,1.1819994940250707
+0.2659066729599622,0.4247991096828493
+0.7107377140511228,-0.8294980913563629
+0.53269023316157,1.9545364598232964
+-0.6198929532867392,-0.2089137663401714
+0.28241451005006213,-0.05819106930094353
+-0.5858318964721039,-0.42734987167902483
+0.6457611003308606,-0.15467066029132975
+-0.7851622394219611,0.16407624826281914
+-0.03648371710422216,1.9716884761975484
+0.5560642583485158,1.7767556393150081
+-0.008782544280929033,0.40516131684457285
+-1.0046277229907556,1.3643145075525906
+0.08891691262918991,1.0635492003483058
+-0.5093362450500942,0.5478947548442041
+0.4326655838125496,2.0847106514044667
+1.3761147926328454,-0.16180546257547912
+-0.6780339794982709,0.9615507609649574
+1.449376640044044,-0.6767271937464503
+-0.3207199725577167,2.149398053798279
+1.2578816649093398,-1.227227918735512
+-0.26320753811564,1.3651299073019465
+-0.8532281627548591,-0.3057528944426161
+1.3269432091015578,-1.4258429262317422
+-0.5551980243823733,0.8549488529451313
+1.117610430267375,-0.10861743167261377
+-0.43526451516293563,0.168969003935586
+0.1429266297680308,1.659202502452458
+-0.769184633691084,1.5061456954067838
+0.1263287840668082,0.34288733323791365
+1.7270629004610156,-2.814725820786233
+0.5451249439017362,0.20883736174260203
+0.7107377140511228,-0.8294980913563629
+0.53269023316157,1.9545364598232964
+-0.6198929532867392,-0.2089137663401714
+-0.0554256114748094,1.0450659522731336
+-0.5858318964721039,-0.42734987167902483
+0.5253972498504522,-0.05267236418857879
+-0.7851622394219611,0.16407624826281914
+-0.03648371710422216,1.9716884761975484
+0.5560642583485158,1.7767556393150081
+1.2769084007713976,-0.28079958739367866
+-1.0046277229907556,1.3643145075525906
+-0.2018610929513423,1.8584945709213507
+-0.24670864612676535,-0.26924345823116036
+-0.127304468408181,0.025536547423795547
+1.3761147926328454,-0.16180546257547912
+-0.6780339794982709,0.9615507609649574
+1.449376640044044,-0.6767271937464503
+0.991695841793483,0.40358894562946596
+1.2578816649093398,-1.227227918735512
+-0.26320753811564,1.3651299073019465
+-0.8532281627548591,-0.3057528944426161
+1.3269432091015578,-1.4258429262317422
+-0.5551980243823733,0.8549488529451313
+1.117610430267375,-0.10861743167261377
+0.8319297612524532,0.06917381981723317
+0.1429266297680308,1.659202502452458
+-0.769184633691084,1.5061456954067838
+0.1263287840668082,0.34288733323791365
+1.7270629004610156,-2.814725820786233
+-0.25041120799931604,0.6410467245205613
+0.5642182292387263,1.3058156299436272
+-0.39557264860734676,1.2031064499435797
+0.6428293738228722,-0.7482567735733167
+-0.7670948736074239,-0.505012937471618
+1.1461446725770126,-0.9444693868731762
+1.3810653493726903,-0.8464511385732041
+-0.7851622394219611,0.16407624826281914
+-0.03648371710422216,1.9716884761975484
+-0.3589208103645295,0.3645399193509533
+1.2769084007713976,-0.28079958739367866
+1.1533489047362062,-1.2110032445583112
+-0.2018610929513423,1.8584945709213507
+-0.24670864612676535,-0.26924345823116036
+1.0605724574340565,-0.7144134206013768
+1.3761147926328454,-0.16180546257547912
+0.7250289881831044,-0.6266043889336157
+0.7094750765629494,0.16898583509262333
+0.991695841793483,0.40358894562946596
+1.0153900173110153,0.04398062550086407
+-0.26320753811564,1.3651299073019465
+-0.8532281627548591,-0.3057528944426161
+0.13199717680465706,0.6612114695889276
+-0.5551980243823733,0.8549488529451313
+1.117610430267375,-0.10861743167261377
+1.288443978276687,-0.05718980204577151
+1.1763923315154792,-1.3312870116010505
+-0.769184633691084,1.5061456954067838
+0.1263287840668082,0.34288733323791365
+1.7270629004610156,-2.814725820786233
+-0.25041120799931604,0.6410467245205613
+1.1353100627669979,-1.623638538674811
+-0.39557264860734676,1.2031064499435797
+0.0860823076508237,0.03687549749149921
+-0.6121761378477608,0.2141340836619413
+1.1461446725770126,-0.9444693868731762
+1.3810653493726903,-0.8464511385732041
+1.5208108000890688,-2.294479665396001
+-0.03648371710422216,1.9716884761975484
+-0.3589208103645295,0.3645399193509533
+1.2769084007713976,-0.28079958739367866
+1.1533489047362062,-1.2110032445583112
+-0.727798251979173,0.9770443995861168
+0.192861425981676,0.8888517925722741
+1.170453650560779,-0.5602813554802095
+1.3761147926328454,-0.16180546257547912
+-0.15557740346040017,1.4801649597980566
+0.12216257521938345,1.7103931826373762
+1.4066425806708747,-1.4635627077426658
+1.0153900173110153,0.04398062550086407
+-0.26320753811564,1.3651299073019465
+0.343262270056107,-0.45398055378011715
+-0.5074482992413525,0.69223547600357
+-0.1869141493493175,-0.19935900990861466
+-0.8465054037962272,-0.8052918149483925
+0.7337914656022427,-0.7309292095352736
+-0.774272881797387,1.0580302575235634
+1.288506580996631,-1.8230395682755347
+-1.0082352827371983,-0.4947075801881614
+1.0777059365177046,-0.9924337227202218
+-0.25041120799931604,0.6410467245205613
+-0.3314045976972815,1.912051530501299
+1.5653325908030333,-1.939328494114974
+0.0860823076508237,0.03687549749149921
+-0.6121761378477608,0.2141340836619413
+-0.8614133057533601,-0.7309137991035086
+0.27351007070605354,0.41745299700744243
+1.5208108000890688,-2.294479665396001
+0.008315453621464464,-0.010931095640383193
+0.28822172027199594,-0.27107895286556316
+0.1224820980333888,-0.21517759950956494
+1.1533489047362062,-1.2110032445583112
+0.14532506442498658,0.9784224990808942
+-1.0141146181405596,0.5573244693283836
+0.7950571037651541,-0.6563043116568341
+1.1698578764440992,0.6956753600393548
+0.07513068841404615,-0.13309056008085407
+-1.139175274989265,-0.7437054860133807
+-0.49707793833443437,0.012735050999614334
+1.0153900173110153,0.04398062550086407
+0.6436094967902752,-0.6128595583139439
+-0.26955396348875343,-0.145448067025377
+-0.5074482992413525,0.69223547600357
+-0.6806941760197682,0.84197106481838
+-1.0427260363338122,1.0219936823642397
+0.7337914656022427,-0.7309292095352736
+-0.774272881797387,1.0580302575235634
+-0.025555014729594427,1.0813983157146487
+0.5965330133910766,0.03644642876030635
+1.0777059365177046,-0.9924337227202218
+-0.04139692293258618,1.502137640916396
+0.02406110881364726,0.31019174747158906
+1.5653325908030333,-1.939328494114974
+-0.43353641349771443,1.618680654564794
+-0.2066149141161041,-0.20214383504555397
+-0.8395733192947675,-0.3839491755111903
+0.7124901555498542,-0.482458208433832
+-0.29675110078929623,1.3700206094689653
+1.1357154587255662,0.009762990697922636
+0.28822172027199594,-0.27107895286556316
+0.12586431470614073,1.089693004588403
+-0.07258853203444045,-0.3388837943416393
+1.2103301265516906,-0.3235902345356564
+0.6756091354469496,0.9531147321984232
+0.6917204003540052,-0.11598999971396298
+1.1698578764440992,0.6956753600393548
+1.1283059674041134,-0.43597361879689955
+0.3191042715929018,0.4825047884576712
+1.1007295417948812,-0.7747877133278618
+1.0153900173110153,0.04398062550086407
+-0.37293382760803906,1.1805921203133012
+0.6026430685950337,-0.1543764045878186
+-0.5074482992413525,0.69223547600357
+0.09821766708871638,0.3378657829760476
+0.5039089646420445,-0.3950112369249969
+0.7337914656022427,-0.7309292095352736
+-0.774272881797387,1.0580302575235634
+0.13612961264301549,1.218601445609933
+0.5190514319294096,-0.1341180256379656
+1.0777059365177046,-0.9924337227202218
+-0.04139692293258618,1.502137640916396
+-0.43610049295281134,1.1735366310292605
+1.5653325908030333,-1.939328494114974
+-0.43353641349771443,1.618680654564794
+-0.2066149141161041,-0.20214383504555397
+-0.8395733192947675,-0.3839491755111903
+-0.04108288273530791,0.006791592519775791
+-0.46084378884569005,0.2857459274305727
+-0.36105114744581235,1.3592370193279542
+0.28822172027199594,-0.27107895286556316
+1.5384775449464554,-1.7570457848185441
+0.3924324229216851,0.6158439197663121
+0.6785613684149159,-0.21029994027491739
+0.14807574389305245,-0.08516883152051799
+0.6917204003540052,-0.11598999971396298
+1.1698578764440992,0.6956753600393548
+0.6682849940378494,0.21796501863404705
+0.3191042715929018,0.4825047884576712
+0.5166474929802625,-0.04555628759636886
+-0.22805994078565217,1.2397371884952935
+0.1252669667196668,-0.3995935844584757
+0.02910754785663544,1.055754567131571
+0.2087947226693393,1.5695824580428097
+0.15831354136789522,0.8291128294785695
+-0.39859995031614337,-0.11059088040670428
+0.7337914656022427,-0.7309292095352736
+0.7506393450610837,-0.34332634918340893
+-0.1200825127084465,1.0831455717977065
+1.2397556960392615,-0.8359315442108064
+0.37183769548665735,-0.6028892608273664
+-0.04139692293258618,1.502137640916396
+1.487334891387257,-0.23436023711242782
+1.5653325908030333,-1.939328494114974
+-0.43353641349771443,1.618680654564794
+-0.2066149141161041,-0.20214383504555397
+-0.8395733192947675,-0.3839491755111903
+1.0564398158890147,-0.6201732001908737
+-0.46084378884569005,0.2857459274305727
+-0.36105114744581235,1.3592370193279542
+0.28822172027199594,-0.27107895286556316
+1.5384775449464554,-1.7570457848185441
+1.3982147365786397,-0.7276929854917297
+1.5228849546919634,-0.5540017195212887
+0.1881683177453019,0.08563126524240558
+-0.3453292099887642,1.654886119870711
+1.1698578764440992,0.6956753600393548
+-0.36961000712567105,0.608021585771375
+1.0464095243965685,1.1719178352875779
+0.8440937385683389,1.5801050067889224
+-0.22805994078565217,1.2397371884952935
+0.05346298379643005,0.11854276929852728
+-0.029250025751393023,-0.2917810499967618
+0.2087947226693393,1.5695824580428097
+1.4922739878378866,-0.9310010341335215
+1.0324077524501805,-0.25299027874952346
+0.2917939077272128,0.14606158387242396
+0.7506393450610837,-0.34332634918340893
+-0.1200825127084465,1.0831455717977065
+0.3611814867141955,-0.5328772274861857
+0.261810281656831,1.5810288679509332
+-0.17271472490768777,0.07370434464241207
+-0.10094253083545235,-0.2865327472288445
+-0.5759159567736906,-0.2810373699675901
+-0.8039610959141366,0.0987261432169288
+-0.8999566926769386,0.7071767077318389
+-0.21892977826270238,1.8713526564631866
+-0.5993982870163641,-0.1578365363901585
+-0.942563709860823,-0.21347599336251089
+-0.36105114744581235,1.3592370193279542
+0.28822172027199594,-0.27107895286556316
+1.5384775449464554,-1.7570457848185441
+0.7648612979474565,0.47892929558374603
+1.5228849546919634,-0.5540017195212887
+-0.16229718147467598,1.8643150972107232
+-0.3453292099887642,1.654886119870711
+1.1698578764440992,0.6956753600393548
+-0.6373449600778548,0.3277888972772489
+1.0464095243965685,1.1719178352875779
+0.8440937385683389,1.5801050067889224
+-0.22805994078565217,1.2397371884952935
+0.10626013314530362,0.3413255452587308
+-0.10176980829248339,0.32116856082651485
+0.2087947226693393,1.5695824580428097
+-0.01951383704818832,0.7709980422650266
+-0.9106273205295066,0.4348505753342018
+0.2917939077272128,0.14606158387242396
+0.7506393450610837,-0.34332634918340893
+1.1993204462775153,-0.27087958429679176
+-0.3730489021020842,0.8298695895437589
+0.261810281656831,1.5810288679509332
+-0.22868845169086371,0.349238952772409
+-0.10094253083545235,-0.2865327472288445
+-0.5759159567736906,-0.2810373699675901
+-0.8039610959141366,0.0987261432169288
+-0.8999566926769386,0.7071767077318389
+-0.21892977826270238,1.8713526564631866
+-0.5993982870163641,-0.1578365363901585
+-0.31639714741313085,-0.019498703683823115
+1.6471631682000358,-1.026470285621761
+0.28822172027199594,-0.27107895286556316
+1.5384775449464554,-1.7570457848185441
+-0.4281577747457384,1.0686467301895222
+1.5228849546919634,-0.5540017195212887
+0.05159102068194554,1.9664602245686345
+0.8477620470824905,-0.48876419211750344
+-0.5290968658477423,0.030501871848537532
+-0.3929368660623921,0.13391964220866337
+0.5353105387312002,-0.3935739316086715
+0.8440937385683389,1.5801050067889224
+-0.7596937136716191,0.8944443008495592
+-0.8795772325528073,0.35625220178343575
+-0.10176980829248339,0.32116856082651485
+1.4380288009698459,-0.6237688103321901
+-0.01951383704818832,0.7709980422650266
+-0.5470269393136694,0.9799146571607531
+0.2917939077272128,0.14606158387242396
+-0.6161680018722998,0.5814102389134684
+1.1993204462775153,-0.27087958429679176
+-0.3730489021020842,0.8298695895437589
+0.2132059147996324,1.98191881448954
+0.7990404429990294,1.4140133898835212
+1.505441043619403,-1.7499694728877406
+-0.5759159567736906,-0.2810373699675901
+-0.3694134548307399,-0.049258371816703936
+0.6695797878287328,-0.36255688491572213
+-0.21892977826270238,1.8713526564631866
+0.7614038056377503,-0.4292522243865242
+-0.31639714741313085,-0.019498703683823115
+-0.8997041776080947,1.2442275916151184
+0.1715517448776337,0.670949213179735
+1.5384775449464554,-1.7570457848185441
+-0.5910668337580279,-0.6940822061870711
+0.4313967231200908,-0.05739775816855042
+0.05159102068194554,1.9664602245686345
+0.8477620470824905,-0.48876419211750344
+-0.5290968658477423,0.030501871848537532
+1.6425478858062454,-2.0162944634567204
+0.5353105387312002,-0.3935739316086715
+1.1489532592098786,0.8243023055024981
+-0.7596937136716191,0.8944443008495592
+1.2300549895320645,-0.015243793681924023
+-0.5396198639898508,0.3790551017242315
+0.3287852833682121,-0.5956951007401345
+0.08002478965290313,1.9236774121907174
+0.5663984021935138,-0.4496151037032069
+0.2917939077272128,0.14606158387242396
+-0.4297222986561715,0.2737472773698435
+1.1993204462775153,-0.27087958429679176
+0.7422275337958637,0.9457503329775913
+0.2132059147996324,1.98191881448954
+0.7990404429990294,1.4140133898835212
+1.505441043619403,-1.7499694728877406
+-0.5759159567736906,-0.2810373699675901
+0.33393557641085053,-0.37083226903966404
+-0.02116040629015875,1.5984825205798598
+-0.21892977826270238,1.8713526564631866
+0.948447524348025,1.1193174806323487
+-0.31639714741313085,-0.019498703683823115
+-0.8997041776080947,1.2442275916151184
+0.21653335642989302,0.31237746409223976
+1.5384775449464554,-1.7570457848185441
+0.41755724172755815,1.0169102994438568
+-0.5259301205537434,-0.13470221680694267
+0.05159102068194554,1.9664602245686345
+0.0781841335207025,2.095133861089093
+0.5174310646740266,-0.260876113685576
+1.6425478858062454,-2.0162944634567204
+0.25255984912903007,1.8282621584300818
+1.1489532592098786,0.8243023055024981
+-0.8293353637620688,-0.5750826862827872
+1.2300549895320645,-0.015243793681924023
+-0.0022868814807255333,2.0808478944563644
+0.15145793980117683,-0.509290650183855
+-0.3770045807032038,0.13035774886123594
+0.589163377576227,1.6369267706557498
+1.4884245964806118,-0.18111201909283348
+-0.4297222986561715,0.2737472773698435
+0.24172068792019796,1.515800280933223
+1.7045326750122758,-1.8283924948622488
+0.2132059147996324,1.98191881448954
+0.7990404429990294,1.4140133898835212
+1.505441043619403,-1.7499694728877406
+0.84443782984847,-0.8630051892768013
+0.33393557641085053,-0.37083226903966404
+0.20954129461085658,0.32407296456553675
+-0.21892977826270238,1.8713526564631866
+-0.472629850625842,0.8018864443356745
+-0.31639714741313085,-0.019498703683823115
+-0.8997041776080947,1.2442275916151184
+0.21653335642989302,0.31237746409223976
+1.5384775449464554,-1.7570457848185441
+0.6652890507216495,1.8532702820582538
+-0.5259301205537434,-0.13470221680694267
+0.8224430848429866,1.48607416770788
+0.0781841335207025,2.095133861089093
+0.5174310646740266,-0.260876113685576
+0.3850173165394105,1.5361046149189672
+0.2795840772676531,1.9129425281420878
+-0.18521119199870345,1.5952710183701264
+-0.8293353637620688,-0.5750826862827872
+1.2300549895320645,-0.015243793681924023
+-0.0022868814807255333,2.0808478944563644
+0.15145793980117683,-0.509290650183855
+-0.3770045807032038,0.13035774886123594
+0.589163377576227,1.6369267706557498
+-0.48678394068405134,0.5724008247519365
+-0.13206692097265407,1.1120887574206453
+-0.04128588954611545,0.8367747891234941
+1.7045326750122758,-1.8283924948622488
+0.2132059147996324,1.98191881448954
+0.7990404429990294,1.4140133898835212
+1.505441043619403,-1.7499694728877406
+0.84443782984847,-0.8630051892768013
+-0.536474630365175,0.7240091769968121
+-0.26351067617155843,-0.27303575231088495
+-0.21892977826270238,1.8713526564631866
+-0.472629850625842,0.8018864443356745
+1.4997608507519966,-1.679669873046991
+0.6767502888856702,-0.052161702771608365
+0.5750926588227462,-0.8578837687004583
+1.5384775449464554,-1.7570457848185441
+0.9360235422212395,-1.246078133177251
+0.19664801134086402,-0.2653980898566511
+-0.1889621307196945,-0.053165623532791306
+0.0781841335207025,2.095133861089093
+1.2598539185018165,-0.9810548424434313
+0.3850173165394105,1.5361046149189672
+-0.7052616517068275,-0.06027005881053582
+-0.18521119199870345,1.5952710183701264
+0.2987138347553349,-0.6012684101994934
+1.2300549895320645,-0.015243793681924023
+-0.0022868814807255333,2.0808478944563644
+-0.6755810912453613,0.6801629671218461
+-0.3770045807032038,0.13035774886123594
+0.589163377576227,1.6369267706557498
+-0.48678394068405134,0.5724008247519365
+-0.3462966019608895,0.6869343770444246
+-0.1446863788874025,0.42199975865961753
+-0.5516990919887683,-0.04662486116410458
+0.2132059147996324,1.98191881448954
+0.7990404429990294,1.4140133898835212
+1.505441043619403,-1.7499694728877406
+0.84443782984847,-0.8630051892768013
+1.2907922974856718,-0.4010438337064963
+0.6676158973697679,1.5959443348649205
+-0.21892977826270238,1.8713526564631866
+1.030663610675854,-0.3152327600846656
+-0.15333293811235166,1.754062698663659
+0.6767502888856702,-0.052161702771608365
+0.5750926588227462,-0.8578837687004583
+1.5384775449464554,-1.7570457848185441
+0.9360235422212395,-1.246078133177251
+0.19664801134086402,-0.2653980898566511
+-0.1889621307196945,-0.053165623532791306
+0.0781841335207025,2.095133861089093
+1.2598539185018165,-0.9810548424434313
+0.3850173165394105,1.5361046149189672
+-0.7052616517068275,-0.06027005881053582
+-0.18521119199870345,1.5952710183701264
+-0.44274923737934996,-0.4338631426677932
+1.2300549895320645,-0.015243793681924023
+-0.0022868814807255333,2.0808478944563644
+-0.6755810912453613,0.6801629671218461
+0.15260601135433982,1.7525326475903287
+0.589163377576227,1.6369267706557498
+-0.48678394068405134,0.5724008247519365
+0.23443176562980259,0.4310008019529524
+-0.43415131961866416,-0.5713831949748507
+-0.5516990919887683,-0.04662486116410458
+0.2132059147996324,1.98191881448954
+0.7990404429990294,1.4140133898835212
+1.505441043619403,-1.7499694728877406
+-0.5530542790374176,0.7764282147786166
+1.2907922974856718,-0.4010438337064963
+-0.02972494959857816,0.6999970924591906
+-0.2749140155396069,1.933888894091801
+1.030663610675854,-0.3152327600846656
+-0.15333293811235166,1.754062698663659
+0.6767502888856702,-0.052161702771608365
+-0.2776244072384581,1.6448509407708618
+0.5528945168042158,1.846683300058006
+0.9360235422212395,-1.246078133177251
+-0.1977190595754653,2.0792870453011973
+-0.1889621307196945,-0.053165623532791306
+0.0781841335207025,2.095133861089093
+1.2598539185018165,-0.9810548424434313
+0.3850173165394105,1.5361046149189672
+-0.7052616517068275,-0.06027005881053582
+-0.18521119199870345,1.5952710183701264
+0.8969010168074507,1.4594942696354458
+0.179775025722132,-0.09055832351701298
+-0.0022868814807255333,2.0808478944563644
+0.5123696577666177,-0.7483415294476928
+0.15260601135433982,1.7525326475903287
+0.10952943444907001,-0.2696225915818789
+-0.48678394068405134,0.5724008247519365
+0.33471624144518786,1.3155304461239072
+0.618351259451056,0.49465701720334787
+-0.4985186070277551,0.1409549792764937
+-0.2726968008118097,0.6676697029995163
+0.7990404429990294,1.4140133898835212
+1.505441043619403,-1.7499694728877406
+-0.5530542790374176,0.7764282147786166
+0.13150444966595304,1.074218320349781
+0.5252756312256018,0.31103634231047084
+-0.9076951891510696,0.4237179830432455
+-0.6301884089361598,1.0994943814447455
+-0.15333293811235166,1.754062698663659
+-0.07456962432357524,1.2447430917814006
+0.11628756394782473,1.478703617811267
+0.5528945168042158,1.846683300058006
+-0.9193602658925926,0.18236728070704888
+0.3442462751089216,-0.2375310170066267
+-0.31854350022313077,0.3496839754915526
+0.0781841335207025,2.095133861089093
+1.2598539185018165,-0.9810548424434313
+-0.28488960460379964,0.49948040289580103
+-0.7052616517068275,-0.06027005881053582
+-0.01138743957119659,2.2114568967896218
+0.8969010168074507,1.4594942696354458
+0.39664888865636916,0.7804218034703525
+-0.6196564600787794,1.165246051931652
+0.5123696577666177,-0.7483415294476928
+0.15260601135433982,1.7525326475903287
+0.10952943444907001,-0.2696225915818789
+1.1553688979119943,0.35804997441551056
+-0.18857900972298738,0.13950875583656974
+0.19357112334628548,1.9159043075285114
+-0.4985186070277551,0.1409549792764937
+-0.2726968008118097,0.6676697029995163
+0.7990404429990294,1.4140133898835212
+1.505441043619403,-1.7499694728877406
+-0.5530542790374176,0.7764282147786166
+-0.1881705219942627,-0.00445120877349503
+-0.45567050206334886,1.4275260691762237
+-0.9076951891510696,0.4237179830432455
+-0.6301884089361598,1.0994943814447455
+0.3596699988141616,0.6462173095239648
+0.35306369676882254,2.0582829032996006
+0.11628756394782473,1.478703617811267
+1.4421969838771622,-0.6196894877464278
+1.0642911198615335,-0.17613823650352423
+0.035592970593008644,-0.14215041979332943
+-0.31854350022313077,0.3496839754915526
+0.0781841335207025,2.095133861089093
+1.2598539185018165,-0.9810548424434313
+-0.29809053160463317,0.8239393574850146
+-0.7052616517068275,-0.06027005881053582
+-0.01138743957119659,2.2114568967896218
+1.4734967395181486,-1.2035627927968309
+0.39664888865636916,0.7804218034703525
+-0.6196564600787794,1.165246051931652
+-0.6272231572525881,-0.0008374437732196205
+0.06331711401156498,0.15845757367929936
+0.47630276800195104,-0.07781675312876454
+1.1553688979119943,0.35804997441551056
+0.21467657185282893,0.990198333048653
+-0.6355024531666861,-0.27930574628529703
+-0.4985186070277551,0.1409549792764937
+0.4084891903827357,1.4904711657372811
+0.6822869996231338,-0.7705206989863075
+1.505441043619403,-1.7499694728877406
+-0.4421510734859663,0.24914027813516304
+-0.1881705219942627,-0.00445120877349503
+-0.45567050206334886,1.4275260691762237
+-0.24031016442363545,-0.2693025788008178
+-0.6301884089361598,1.0994943814447455
+0.8308687676885287,-0.06608925768523721
+0.35306369676882254,2.0582829032996006
+0.11628756394782473,1.478703617811267
+1.4421969838771622,-0.6196894877464278
+1.0642911198615335,-0.17613823650352423
+-0.7358503224996833,1.6477855267070283
+-0.31854350022313077,0.3496839754915526
+-0.8706017520377549,0.7800583244340903
+1.2598539185018165,-0.9810548424434313
+0.04770380431956234,1.1905839008881394
+-0.7052616517068275,-0.06027005881053582
+-0.01138743957119659,2.2114568967896218
+1.4734967395181486,-1.2035627927968309
+0.39664888865636916,0.7804218034703525
+0.351454169610907,0.7594787135626051
+-0.6272231572525881,-0.0008374437732196205
+0.06331711401156498,0.15845757367929936
+1.1837122443596546,-0.1257349425110661
+1.1553688979119943,0.35804997441551056
+0.2638709679236697,-0.25260096705049895
+-0.6355024531666861,-0.27930574628529703
+1.453367920790972,-0.7500478273969496
+0.4084891903827357,1.4904711657372811
+0.6822869996231338,-0.7705206989863075
+-0.23690420148018215,0.6472278513526137
+1.0285365445044918,-1.0295900456257392
+0.9456606300032014,0.5674571885801132
+-0.45567050206334886,1.4275260691762237
+-0.9784006960387471,0.38749037136137887
+1.1103539067287258,0.7780658838537198
+0.10281521280904626,-0.4033823106803808
+0.963161294920728,0.46774003461998664
+0.11628756394782473,1.478703617811267
+1.069626190932353,0.0667162408597235
+1.0642911198615335,-0.17613823650352423
+1.0422425144411758,-0.5690070327100695
+-0.31854350022313077,0.3496839754915526
+0.3932488304654058,-0.02830149226705536
+0.9211815422263359,-0.766694331471013
+-0.5628043215374543,1.1798886981995924
+-0.7052616517068275,-0.06027005881053582
+-0.01138743957119659,2.2114568967896218
+1.5183683100514709,-1.3494295653155493
+1.3832813904363008,-0.4025676871263226
+0.3894348700346435,0.21392211423225194
+-0.6272231572525881,-0.0008374437732196205
+0.06331711401156498,0.15845757367929936
+-0.68309187167379,-0.12351490839084629
+-0.12113342667124369,0.2674024038580934
+0.2638709679236697,-0.25260096705049895
+-0.6355024531666861,-0.27930574628529703
+-0.4159230689378024,0.4958851775586625
+-0.0794140854266497,2.490681709067074
+0.6822869996231338,-0.7705206989863075
+-0.074841891510764,0.5150330230417928
+1.0285365445044918,-1.0295900456257392
+0.9456606300032014,0.5674571885801132
+-0.45567050206334886,1.4275260691762237
+-1.2073903580157372,0.08002669621020206
+1.1103539067287258,0.7780658838537198
+0.10281521280904626,-0.4033823106803808
+0.963161294920728,0.46774003461998664
+0.11628756394782473,1.478703617811267
+1.069626190932353,0.0667162408597235
+1.0642911198615335,-0.17613823650352423
+1.0422425144411758,-0.5690070327100695
+-0.24165816381070637,0.6233289564386751
+0.3932488304654058,-0.02830149226705536
+0.9211815422263359,-0.766694331471013
+-0.5628043215374543,1.1798886981995924
+-0.7052616517068275,-0.06027005881053582
+-0.01138743957119659,2.2114568967896218
+1.5183683100514709,-1.3494295653155493
+0.05267969256994423,0.013388197573154459
+-0.4638628048697925,0.5188424653888748
+-0.6272231572525881,-0.0008374437732196205
+0.019503078297155363,0.1860924686669314
+-0.68309187167379,-0.12351490839084629
+-0.6970988082988421,-0.24271096987926716
+0.2638709679236697,-0.25260096705049895
+1.0994327209981263,-0.5221210133407771
+-0.36365551245472205,-0.48009578827663746
+-0.0794140854266497,2.490681709067074
+0.6822869996231338,-0.7705206989863075
+-0.074841891510764,0.5150330230417928
+-0.014113879068140434,0.8456404714847991
+0.7486492160356533,-0.4246046869896805
+-0.45567050206334886,1.4275260691762237
+-0.13094378774875362,0.16160291595049725
+-0.05408440137432735,-0.10923358929315666
+0.9207057415627968,-0.8610492467278266
+-0.09689057786915269,2.3196777562125157
+0.11628756394782473,1.478703617811267
+0.6966961419823828,0.4518483039647095
+1.2078943438890308,0.6977016881462431
+1.0422425144411758,-0.5690070327100695
+0.2795967648943421,0.6904153451875621
+0.47167384853034183,-0.005514182647034183
+1.103070973147871,0.2966215702654392
+1.2998088140336448,-1.1836570203204144
+-0.7052616517068275,-0.06027005881053582
+-0.256832740358897,0.1887458615209618
+1.5183683100514709,-1.3494295653155493
+0.05267969256994423,0.013388197573154459
+-0.096872950100673,1.732840828069146
+-0.6272231572525881,-0.0008374437732196205
+0.6702411911952887,-0.3275025446494712
+1.0970708374560072,0.8203754219725065
+-0.6970988082988421,-0.24271096987926716
+0.2638709679236697,-0.25260096705049895
+1.0994327209981263,-0.5221210133407771
+-0.36365551245472205,-0.48009578827663746
+-0.0794140854266497,2.490681709067074
+1.1217099894874711,-0.7052659671988344
+1.277578921942807,-0.0012366246003737702
+-0.7388694498091768,1.6494919996497415
+0.7486492160356533,-0.4246046869896805
+-0.38688726088457515,1.6623492884315878
+-0.7587069890744722,0.09463182238672221
+-0.05408440137432735,-0.10923358929315666
+-0.14774771595557568,1.2889408502249957
+-0.09689057786915269,2.3196777562125157
+1.2297614211376848,0.019235918369437055
+-0.1347977724513174,1.2886970316496777
+1.2078943438890308,0.6977016881462431
+1.0422425144411758,-0.5690070327100695
+-0.4486922911819146,1.4259354149535661
+0.47167384853034183,-0.005514182647034183
+-0.1702438276285873,1.8816678263727218
+1.2998088140336448,-1.1836570203204144
+-0.464150708464649,0.29744094505051166
+-0.256832740358897,0.1887458615209618
+-0.9014466688486602,-0.07735129351156356
+0.05267969256994423,0.013388197573154459
+-0.1586683113997674,1.1865511446924968
+-0.6272231572525881,-0.0008374437732196205
+0.6702411911952887,-0.3275025446494712
+1.0970708374560072,0.8203754219725065
+-0.6970988082988421,-0.24271096987926716
+0.2638709679236697,-0.25260096705049895
+1.0994327209981263,-0.5221210133407771
+-0.5024069919831937,-0.2809460513756151
+-0.0794140854266497,2.490681709067074
+0.28147325853486277,0.4353873131883791
+1.277578921942807,-0.0012366246003737702
+-0.7388694498091768,1.6494919996497415
+1.4992006377264948,-0.8432603932060312
+-0.38688726088457515,1.6623492884315878
+-0.7587069890744722,0.09463182238672221
+-0.05408440137432735,-0.10923358929315666
+0.07284557796194557,0.727504459239762
+-1.061065735636507,-0.2739257993747184
+1.2297614211376848,0.019235918369437055
+1.034587783432058,0.9986787303067776
+1.2078943438890308,0.6977016881462431
+-0.2690489241387751,1.9195431808276868
+-0.4486922911819146,1.4259354149535661
+-0.35749263572641765,0.2033861579997831
+-0.5183312572017341,1.9304218349612707
+1.2998088140336448,-1.1836570203204144
+-0.464150708464649,0.29744094505051166
+-0.681965535005304,0.38204718689256734
+0.7283482006559283,0.9917268905387563
+1.0260777113989898,-0.13014610685144556
+0.01585031379097579,-0.22664669290282896
+-0.5588087603644326,-0.053440761294585803
+0.6702411911952887,-0.3275025446494712
+0.2623651817054151,-0.24648786143116588
+0.534028209238911,-0.7678346038877518
+1.2199574686647947,0.3371805659248868
+-0.7000973668160424,0.3234117914468645
+-0.5024069919831937,-0.2809460513756151
+-0.13322547360719378,0.26212998802987725
+0.28147325853486277,0.4353873131883791
+1.277578921942807,-0.0012366246003737702
+0.33420070761649634,-0.5068590490776362
+1.4992006377264948,-0.8432603932060312
+-0.38688726088457515,1.6623492884315878
+-0.7587069890744722,0.09463182238672221
+-0.0351829441183672,1.8325289445854414
+1.2962314350643276,-0.2974350156731337
+-1.061065735636507,-0.2739257993747184
+0.23842660215801043,1.6131238419109855
+0.6148946297458329,-0.368281370453284
+0.8429677837377515,1.1206401104822108
+-0.2690489241387751,1.9195431808276868
+0.9515521272728624,1.1965261479593874
+-0.35749263572641765,0.2033861579997831
+-0.5183312572017341,1.9304218349612707
+1.2998088140336448,-1.1836570203204144
+-0.11341254027315635,0.22259437268183402
+0.9112938172959529,0.24256883499585372
+-0.30748597057575655,0.178688116853695
+0.6813923807433948,0.26193560633272517
+0.01585031379097579,-0.22664669290282896
+-0.5588087603644326,-0.053440761294585803
+0.49917909836508434,0.31080323800013043
+0.9535900759614238,0.576257720648619
+0.7912821464797538,0.754673183958006
+1.2199574686647947,0.3371805659248868
+0.026082869302141654,0.3294741236160654
+-0.5024069919831937,-0.2809460513756151
+1.3605932367848674,-0.9476528288947614
+0.28147325853486277,0.4353873131883791
+1.277578921942807,-0.0012366246003737702
+-0.7277606234009797,1.4172205598469505
+1.4992006377264948,-0.8432603932060312
+-0.38688726088457515,1.6623492884315878
+1.4118405994835248,-0.8001902675326229
+-0.0351829441183672,1.8325289445854414
+0.23853414803349626,1.8521512781643958
+-1.061065735636507,-0.2739257993747184
+0.23842660215801043,1.6131238419109855
+-0.9040561724540381,0.7447412262852691
+0.8429677837377515,1.1206401104822108
+-0.2690489241387751,1.9195431808276868
+0.9515521272728624,1.1965261479593874
+1.2396374381305866,0.6017004598766014
+-0.5183312572017341,1.9304218349612707
+1.2998088140336448,-1.1836570203204144
+-0.11341254027315635,0.22259437268183402
+-0.3021216766611312,0.9495544211562037
+-0.30748597057575655,0.178688116853695
+0.6813923807433948,0.26193560633272517
+0.13553519384538978,0.7273350212500309
+-0.5588087603644326,-0.053440761294585803
+0.49917909836508434,0.31080323800013043
+-0.288934636732601,-0.24621201349462368
+0.7912821464797538,0.754673183958006
+1.2199574686647947,0.3371805659248868
+0.026082869302141654,0.3294741236160654
+-0.5024069919831937,-0.2809460513756151
+1.3605932367848674,-0.9476528288947614
+1.3266822998839674,-0.33008953664610974
+1.277578921942807,-0.0012366246003737702
+0.6857026395120291,-0.1935049074629694
+1.4992006377264948,-0.8432603932060312
+-0.38688726088457515,1.6623492884315878
+1.4118405994835248,-0.8001902675326229
+-0.0351829441183672,1.8325289445854414
+0.23853414803349626,1.8521512781643958
+-1.061065735636507,-0.2739257993747184
+0.23842660215801043,1.6131238419109855
+-0.9040561724540381,0.7447412262852691
+0.8429677837377515,1.1206401104822108
+-0.2690489241387751,1.9195431808276868
+1.243651721276692,-0.446231156642489
+0.0760069069348898,0.5522351585141352
+0.6716960587025582,-0.649485184753738
+0.7927939302295899,-0.6623925667091949
+-0.11341254027315635,0.22259437268183402
+1.184421888142956,-1.2268955526405998
+-0.6778755944799104,1.7540659483774388
+-0.5768566280625207,1.8404511423487675
+0.13553519384538978,0.7273350212500309
+-0.5588087603644326,-0.053440761294585803
+0.4283491597609513,-0.6561779993588172
+-0.288934636732601,-0.24621201349462368
+0.7912821464797538,0.754673183958006
+1.6558828750970316,-1.6172056783879571
+0.34368173903549903,0.07186713451213753
+-0.5024069919831937,-0.2809460513756151
+0.17722403625307942,-0.10233546716676556
+-0.09099674911713973,0.6345304532400998
+1.277578921942807,-0.0012366246003737702
+-0.4355235397518692,1.5904835681458924
+1.4992006377264948,-0.8432603932060312
+-0.6534788663032043,0.9693894084669591
+1.4118405994835248,-0.8001902675326229
+0.3814538001465433,0.9040687995441095
+0.23853414803349626,1.8521512781643958
+-1.061065735636507,-0.2739257993747184
+0.23842660215801043,1.6131238419109855
+-0.9040561724540381,0.7447412262852691
+0.8429677837377515,1.1206401104822108
+0.8501387624586837,-0.4779945056930742
+1.1518831243574836,-0.8299107952091689
+0.7538407302842361,0.5101592566489159
+0.6716960587025582,-0.649485184753738
+0.31494206185381335,1.7635490278650572
+-0.11341254027315635,0.22259437268183402
+1.184421888142956,-1.2268955526405998
+0.5105889667402984,0.5323870284327992
+0.31023106341175444,1.9128633698608648
+-0.7178837631328585,1.5714839416562425
+-0.5588087603644326,-0.053440761294585803
+0.4283491597609513,-0.6561779993588172
+-0.4268621479661151,1.2787639604869245
+1.0314309880545465,-0.10736610495154819
+1.6558828750970316,-1.6172056783879571
+0.34368173903549903,0.07186713451213753
+-0.5024069919831937,-0.2809460513756151
+0.17722403625307942,-0.10233546716676556
+-0.09099674911713973,0.6345304532400998
+1.277578921942807,-0.0012366246003737702
+-0.4355235397518692,1.5904835681458924
+1.4992006377264948,-0.8432603932060312
+-0.6534788663032043,0.9693894084669591
+1.4652610592119917,-1.2144324079450026
+0.8709351920376124,-0.9796138903858704
+-0.31838903628577386,-0.006201530964469293
+-1.061065735636507,-0.2739257993747184
+0.23842660215801043,1.6131238419109855
+1.2683592386919977,-1.4667758544424292
+0.8429677837377515,1.1206401104822108
+0.8501387624586837,-0.4779945056930742
+1.1518831243574836,-0.8299107952091689
+0.6555289552270965,-0.4785783259739109
+-0.14810271178865092,1.2314998975349285
+0.9546642310310054,1.0933216855349421
+1.3477893645763817,-1.685319837254551
+1.184421888142956,-1.2268955526405998
+0.5105889667402984,0.5323870284327992
+0.31023106341175444,1.9128633698608648
+0.3745875933536883,1.328389736943573
+-0.5588087603644326,-0.053440761294585803
+0.7543670259659802,-0.7671761091954972
+-0.4268621479661151,1.2787639604869245
+1.6270910734732535,-0.8464706678088371
+1.6558828750970316,-1.6172056783879571
+0.34368173903549903,0.07186713451213753
+-0.5024069919831937,-0.2809460513756151
+0.8942951589489603,-1.108259145673864
+-0.6191911166328926,1.1600465203370596
+0.2068296207193575,1.6132606712711604
+-0.4355235397518692,1.5904835681458924
+-0.8551523154233767,0.23228279356337656
+-0.15621771575698376,1.1493679903577672
+1.4652610592119917,-1.2144324079450026
+-0.4559425984850138,1.7612220789599469
+-0.31838903628577386,-0.006201530964469293
+1.2442729651887334,-0.05350612198919835
+0.23842660215801043,1.6131238419109855
+-0.4987212219106947,-0.2293859301423337
+0.13056216306354995,-0.08241763721229156
+1.7061576441267436,-2.0927144443100962
+1.1518831243574836,-0.8299107952091689
+0.6555289552270965,-0.4785783259739109
+-0.7701790338778953,1.4016978089125183
+1.064649073490998,0.3440943857570494
+1.8200903072654004,-2.163359963116161
+1.8924304472723834,-3.0559721022104895
+0.5105889667402984,0.5323870284327992
+-0.5566343343004156,0.9626033129114456
+0.3745875933536883,1.328389736943573
+-0.5588087603644326,-0.053440761294585803
+0.7543670259659802,-0.7671761091954972
+-0.4268621479661151,1.2787639604869245
+1.6270910734732535,-0.8464706678088371
+1.6558828750970316,-1.6172056783879571
+0.34368173903549903,0.07186713451213753
+-0.5024069919831937,-0.2809460513756151
+1.176262615665156,-0.6061348352795299
+-0.6191911166328926,1.1600465203370596
+-0.8174480509904993,0.7878320873913511
+-0.4355235397518692,1.5904835681458924
+-0.19837099057866192,0.07516825788672354
+-0.15621771575698376,1.1493679903577672
+-0.5418803080270742,0.5194767945233726
+-0.4559425984850138,1.7612220789599469
+-0.31838903628577386,-0.006201530964469293
+1.2442729651887334,-0.05350612198919835
+0.23842660215801043,1.6131238419109855
+0.5891967703764167,-0.5486875013400057
+0.13056216306354995,-0.08241763721229156
+1.7061576441267436,-2.0927144443100962
+-0.59020274265602,0.5596598475350836
+0.6225489436712127,1.6436373766192836
+0.22141071142808777,0.8179649731139131
+-0.3257822685478379,-0.3042571330844961
+0.9789670774005185,0.6085221584752165
+1.8924304472723834,-3.0559721022104895
+0.5105889667402984,0.5323870284327992
+-0.5566343343004156,0.9626033129114456
+-0.5961182443042512,0.4147138890318565
+0.9998714216482726,-0.9526775339664231
+0.5662967879271156,0.2994668860753633
+0.9267603431696982,0.5901920633026977
+1.6270910734732535,-0.8464706678088371
+1.6558828750970316,-1.6172056783879571
+-0.7607363323387645,0.3820225171499263
+-0.5024069919831937,-0.2809460513756151
+0.5178631150747728,-0.7601270625123852
+-0.6892986654396758,0.4553947432762202
+-0.5783526974028377,0.7153404412320509
+-0.4355235397518692,1.5904835681458924
+0.6050237662579261,-0.34185211463095444
+0.4138940776070549,-0.632750420753214
+1.2221706405449893,-1.3722050733152518
+-0.4559425984850138,1.7612220789599469
+-0.970080232309711,0.45199526322388084
+1.2926688081262094,-1.2065512282932627
+0.6883577213393358,1.6236182345760064
+-1.1467078210693047,-0.23731432287327486
+1.7069213675603687,-2.2309503481590336
+1.7061576441267436,-2.0927144443100962
+-0.59020274265602,0.5596598475350836
+0.6225489436712127,1.6436373766192836
+0.80490522983906,-0.43725078782321636
+-0.3257822685478379,-0.3042571330844961
+0.9789670774005185,0.6085221584752165
+0.8237699787975341,-0.2915296766995779
+0.5105889667402984,0.5323870284327992
+-0.5566343343004156,0.9626033129114456
+-0.9208370887297042,0.013077969620158614
+0.8572706586744072,-0.12641630448801533
+0.5662967879271156,0.2994668860753633
+0.8044906238731642,1.627483407021994
+1.506112370351351,-2.4992482592954604
+0.6557375874139295,-0.9982278501848493
+1.0853022920999964,-0.6141612487716089
+-0.5024069919831937,-0.2809460513756151
+-0.5170345092687011,1.83011703201514
+-0.6892986654396758,0.4553947432762202
+0.5935263858070344,1.5353689598134193
+-0.4355235397518692,1.5904835681458924
+-0.6398540340765699,1.1539286044926969
+-0.5399472175987775,1.5906458832981234
+0.3275854401666706,1.7047580761338803
+0.9235415056198805,-0.9954382235984673
+-0.970080232309711,0.45199526322388084
+-0.3415491581484177,0.2950780143604931
+0.6883577213393358,1.6236182345760064
+0.6334637616524759,-0.6165032423053668
+1.7069213675603687,-2.2309503481590336
+-0.48206197296317665,0.48506933310728517
+-0.9548662909718506,-0.43987402550324484
+0.6225489436712127,1.6436373766192836
+0.80490522983906,-0.43725078782321636
+0.20974946650885362,-0.13900754528790987
+0.9789670774005185,0.6085221584752165
+0.8237699787975341,-0.2915296766995779
+1.3901582472795,-0.8981544201780869
+0.39171976045184886,-0.5416316952927855
+0.01378981028308357,0.15650108006401453
+-0.6121553897551816,0.12239396520105983
+0.11893999515214485,1.878417380420022
+-0.31108750635701615,-0.21725677855175873
+1.506112370351351,-2.4992482592954604
+-0.5930890984668733,1.7882149183018252
+1.0853022920999964,-0.6141612487716089
+-0.5024069919831937,-0.2809460513756151
+-0.6014785500457883,0.4954064809491132
+-0.6892986654396758,0.4553947432762202
+1.7828335499986014,-2.1383912538353287
+-0.4355235397518692,1.5904835681458924
+1.5143514148403172,-2.0805093309786113
+-0.5399472175987775,1.5906458832981234
+0.8847305614928354,1.1977252640466096
+0.9235415056198805,-0.9954382235984673
+-0.970080232309711,0.45199526322388084
+0.1824716631465546,1.0116314366252217
+0.6883577213393358,1.6236182345760064
+0.6334637616524759,-0.6165032423053668
+1.7069213675603687,-2.2309503481590336
+0.2627606335415573,1.615599345569081
+-0.9548662909718506,-0.43987402550324484
+0.6225489436712127,1.6436373766192836
+0.7740678243691812,0.08694257788261577
+0.20974946650885362,-0.13900754528790987
+0.9789670774005185,0.6085221584752165
+0.8237699787975341,-0.2915296766995779
+1.3901582472795,-0.8981544201780869
+0.11178356540427126,0.34441237995432405
+0.29132906378442436,1.5671478745654868
+-0.6121553897551816,0.12239396520105983
+1.7454853481427317,-2.6335441120883982
+1.5553762602038517,-1.8466149175560438
+0.37974295160235405,-0.01493700266141651
+-0.5930890984668733,1.7882149183018252
+1.529820964392926,-1.8775511177495008
+-0.7258656336539678,1.278519043865516
+-0.6014785500457883,0.4954064809491132
+0.43355112655500777,2.2482620325469402
+0.4886092915501026,-0.08401232459891539
+0.3560054323141397,-0.7320786076137555
+1.5143514148403172,-2.0805093309786113
+-0.9802279005603818,0.5986802600670428
+0.8847305614928354,1.1977252640466096
+0.5223735984934943,-0.5865629884008949
+0.1667497171702303,0.32396497814666997
+0.49980148182735384,1.5199756040384085
+0.539813738277357,-0.7528305170799647
+0.6334637616524759,-0.6165032423053668
+-0.1200729538362304,1.413700346233091
+0.2627606335415573,1.615599345569081
+-0.9548662909718506,-0.43987402550324484
+0.6225489436712127,1.6436373766192836
+-0.9211473765238931,0.5347564411488714
+0.20974946650885362,-0.13900754528790987
+0.9789670774005185,0.6085221584752165
+0.6949661154047044,-0.5097609640071791
+-0.06742749100660062,0.13690267479253904
+0.11178356540427126,0.34441237995432405
+0.11357566919257656,0.04260060731257598
+1.209749647077314,0.2688968450347097
+1.7454853481427317,-2.6335441120883982
+-0.4755956461172199,0.3193047131515804
+0.37974295160235405,-0.01493700266141651
+-0.5930890984668733,1.7882149183018252
+1.529820964392926,-1.8775511177495008
+-0.7258656336539678,1.278519043865516
+-0.6014785500457883,0.4954064809491132
+1.0090478192568613,0.10681533699814394
+0.4886092915501026,-0.08401232459891539
+0.3560054323141397,-0.7320786076137555
+1.5139405121788954,-0.8625608080098071
+-0.9802279005603818,0.5986802600670428
+0.8847305614928354,1.1977252640466096
+0.5223735984934943,-0.5865629884008949
+0.1667497171702303,0.32396497814666997
+0.49980148182735384,1.5199756040384085
+1.3541650262459437,-0.5014828899353811
+0.6334637616524759,-0.6165032423053668
+0.6818337289610641,1.64559471173881
+0.2627606335415573,1.615599345569081
+0.5092480462945129,1.687876722097455
+0.9202725476859264,-1.041887812853593
+-0.9211473765238931,0.5347564411488714
+0.17390085921709458,-0.684960430767913
+0.9789670774005185,0.6085221584752165
+0.6949661154047044,-0.5097609640071791
+-0.06742749100660062,0.13690267479253904
+0.11178356540427126,0.34441237995432405
+0.39922436035353964,1.991531044173423
+1.209749647077314,0.2688968450347097
+1.7454853481427317,-2.6335441120883982
+-0.4755956461172199,0.3193047131515804
+0.37974295160235405,-0.01493700266141651
+0.7015064881728843,-0.5430813188215796
+1.529820964392926,-1.8775511177495008
+-0.6964059749974478,0.3270811268913409
+0.46525198838266807,-0.06011816062832972
+1.0090478192568613,0.10681533699814394
+0.4886092915501026,-0.08401232459891539
+0.17868418318302282,1.9909670485561768
+1.5139405121788954,-0.8625608080098071
+-0.9802279005603818,0.5986802600670428
+0.8847305614928354,1.1977252640466096
+0.9707707512348809,-0.8081259500887724
+0.1667497171702303,0.32396497814666997
+0.49980148182735384,1.5199756040384085
+1.73301783497816,-2.248794385911477
+0.6334637616524759,-0.6165032423053668
+0.6818337289610641,1.64559471173881
+0.2627606335415573,1.615599345569081
+0.20267445149305302,-0.24700968021523595
+0.9202725476859264,-1.041887812853593
+-0.9211473765238931,0.5347564411488714
+0.17390085921709458,-0.684960430767913
+0.9789670774005185,0.6085221584752165
+0.6949661154047044,-0.5097609640071791
+-0.06742749100660062,0.13690267479253904
+0.11178356540427126,0.34441237995432405
+0.39922436035353964,1.991531044173423
+1.209749647077314,0.2688968450347097
+1.7454853481427317,-2.6335441120883982
+1.3277690139287057,-1.5110595122651784
+0.4470484645937507,0.19995054366591586
+0.7015064881728843,-0.5430813188215796
+1.529820964392926,-1.8775511177495008
+-0.6964059749974478,0.3270811268913409
+0.46525198838266807,-0.06011816062832972
+1.104916239139932,-0.6776059950753903
+0.4886092915501026,-0.08401232459891539
+0.17868418318302282,1.9909670485561768
+1.5139405121788954,-0.8625608080098071
+-0.9802279005603818,0.5986802600670428
+0.8847305614928354,1.1977252640466096
+1.2253282387969033,-1.933383571622859
+0.9658374923620732,0.016805349003701897
+0.8901163834304041,0.8410698233107172
+0.950269796734813,-0.5605242132523957
+0.6334637616524759,-0.6165032423053668
+0.6818337289610641,1.64559471173881
+0.2627606335415573,1.615599345569081
+0.20267445149305302,-0.24700968021523595
+0.9202725476859264,-1.041887812853593
+-0.9112631941913786,1.0337886765231983
+0.17390085921709458,-0.684960430767913
+0.9789670774005185,0.6085221584752165
+0.6949661154047044,-0.5097609640071791
+0.6619098935332483,0.3273628351793285
+0.11178356540427126,0.34441237995432405
+0.21359638258500946,-0.21767649017412227
+1.209749647077314,0.2688968450347097
+0.2273042345691778,2.441186016067874
+1.3277690139287057,-1.5110595122651784
+0.368778921327878,-0.4213865051680329
+-0.22948835265735196,1.818262850854532
+-0.17755097282073012,-0.1622044082589459
+-0.6964059749974478,0.3270811268913409
+-0.06724523510795216,1.993531495105302
+1.104916239139932,-0.6776059950753903
+-0.1892933139444219,1.2526525062480243
+0.17868418318302282,1.9909670485561768
+1.5139405121788954,-0.8625608080098071
+0.43062086481049966,1.8324363829839991
+0.8847305614928354,1.1977252640466096
+0.8041948982880465,0.3689512528899671
+-0.4260672525760308,0.5908435027903128
+0.7905006198595411,1.5527496360268722
+0.950269796734813,-0.5605242132523957
+-0.7373956494604859,0.6298245827911608
+-0.5710885460021717,0.9548323801789771
+0.2627606335415573,1.615599345569081
+1.1664457866799494,-1.8537328760989011
+0.9202725476859264,-1.041887812853593
+-0.9112631941913786,1.0337886765231983
+0.17390085921709458,-0.684960430767913
+-0.24993341943601521,0.7666045011986798
+0.6949661154047044,-0.5097609640071791
+0.6619098935332483,0.3273628351793285
+-0.3877820360069679,0.6471233332841482
+0.21359638258500946,-0.21767649017412227
+1.209749647077314,0.2688968450347097
+0.48932865851634844,-0.03829022278036398
+1.3277690139287057,-1.5110595122651784
+1.4520458662821296,-1.1956702367127794
+-0.22948835265735196,1.818262850854532
+1.4015333041755254,-1.6242825649265704
+-0.6964059749974478,0.3270811268913409
+-0.3349896920651101,0.8806611029212112
+0.30560730182209794,0.1596730308093044
+1.3544534732313867,-0.8308096574913955
+0.17868418318302282,1.9909670485561768
+1.5139405121788954,-0.8625608080098071
+0.43062086481049966,1.8324363829839991
+0.8847305614928354,1.1977252640466096
+0.3059689174840977,1.6231750542695087
+-0.4260672525760308,0.5908435027903128
+-0.5407917118899472,1.4431745048273346
+0.950269796734813,-0.5605242132523957
+-0.7373956494604859,0.6298245827911608
+-0.24486715561502279,0.9254288658116745
+0.2627606335415573,1.615599345569081
+1.160541231516044,-0.5993659005591776
+0.9202725476859264,-1.041887812853593
+-0.9112631941913786,1.0337886765231983
+0.17390085921709458,-0.684960430767913
+-0.4832521575787937,1.47448408807294
+0.6949661154047044,-0.5097609640071791
+-1.0244663579523003,0.6213487137472392
+-0.3877820360069679,0.6471233332841482
+1.279434257631549,-0.9713309359609947
+1.209749647077314,0.2688968450347097
+0.31218193190588944,0.11572050944885245
+-0.462901300911044,1.7563154056381731
+1.4142411270175894,-1.4558832504470636
+-0.22948835265735196,1.818262850854532
+1.4015333041755254,-1.6242825649265704
+1.4040851323231016,-0.36015748728027347
+-0.3349896920651101,0.8806611029212112
+0.4501930789428613,-0.11295213000186882
+1.3544534732313867,-0.8308096574913955
+-0.9342594905402933,0.6363524976743875
+1.5139405121788954,-0.8625608080098071
+0.43062086481049966,1.8324363829839991
+0.8847305614928354,1.1977252640466096
+1.248813856841346,-1.949673293591021
+0.833719086708791,-0.48351476974453894
+-0.5407917118899472,1.4431745048273346
+0.950269796734813,-0.5605242132523957
+0.9205529108689228,-0.8726189957499824
+0.33668272639831687,2.456811725911463
+-0.3646763886312001,1.6650089295407455
+1.084016566026219,0.1930084286636422
+0.32665905842878756,0.27520528888588836
+-0.9112631941913786,1.0337886765231983
+0.17390085921709458,-0.684960430767913
+-0.4832521575787937,1.47448408807294
+0.6949661154047044,-0.5097609640071791
+-1.0244663579523003,0.6213487137472392
+-0.3877820360069679,0.6471233332841482
+1.279434257631549,-0.9713309359609947
+1.209749647077314,0.2688968450347097
+0.7611225298459171,-0.5100941825001429
+0.9111898184261522,0.7950285558680263
+1.0297536983983706,0.08418824202367614
+-0.22948835265735196,1.818262850854532
+0.15138935834404316,1.915938207141934
+0.3714734615104889,0.13062388647809675
+0.9622782113807045,-1.1174472209393365
+1.8101250344089723,-1.9325890813229079
+0.20835840820744794,0.41474331462133585
+1.9206462581343198,-2.115237719313317
+1.5139405121788954,-0.8625608080098071
+0.43062086481049966,1.8324363829839991
+0.362251269765029,0.817257840432169
+1.248813856841346,-1.949673293591021
+-0.6973177579137071,0.2571949620929661
+-0.5407917118899472,1.4431745048273346
+0.950269796734813,-0.5605242132523957
+0.9205529108689228,-0.8726189957499824
+0.33668272639831687,2.456811725911463
+1.2820152687836517,-0.5550940654568568
+1.084016566026219,0.1930084286636422
+-0.12418866371889553,2.0836359222954903
+-0.9112631941913786,1.0337886765231983
+0.24424593705662248,1.0562215540124273
+0.5736414120433626,1.4474543410502276
+0.6949661154047044,-0.5097609640071791
+-1.0244663579523003,0.6213487137472392
+-0.225179919561578,0.5549781729891623
+1.3570509733635536,-1.3497592740007234
+0.21110186266423164,1.2976358819712055
+-0.04351493425525005,1.7688299918252965
+0.764615633982157,0.05178056161293454
+0.44365206936557744,1.3361658371774987
+-0.22948835265735196,1.818262850854532
+0.15138935834404316,1.915938207141934
+0.3714734615104889,0.13062388647809675
+1.442275857844289,0.07273452751168108
+1.8101250344089723,-1.9325890813229079
+0.993178470312709,0.8065253009706093
+0.568312048643173,-0.9284978376916071
+1.5139405121788954,-0.8625608080098071
+-0.35265151080015644,1.461777165086822
+0.5467285861154743,1.7617827093942278
+-0.4338601749531385,1.7396750284044264
+-0.6973177579137071,0.2571949620929661
+1.3846589366932147,-0.3373042181603733
+1.798717766819896,-3.2407087731083433
+0.9205529108689228,-0.8726189957499824
+-1.1401782343366542,0.33462347738313053
+1.2820152687836517,-0.5550940654568568
+1.0172504215594118,-0.7942381496063444
+-0.12418866371889553,2.0836359222954903
+-0.9112631941913786,1.0337886765231983
+-1.0330109605857234,-0.0011593921530135831
+0.5736414120433626,1.4474543410502276
+0.6949661154047044,-0.5097609640071791
+0.1405496694366461,0.6445940557679688
+-0.225179919561578,0.5549781729891623
+1.3570509733635536,-1.3497592740007234
+0.21110186266423164,1.2976358819712055
+-0.04351493425525005,1.7688299918252965
+1.7228212668520548,-1.6070609394989432
+1.3912194345392175,-1.9366504867574705
+-0.22948835265735196,1.818262850854532
+0.15138935834404316,1.915938207141934
+-0.3606925418772957,1.8890577068214067
+0.4993107335697491,1.3726228494044488
+1.5779505065601176,-2.299092611178204
+0.993178470312709,0.8065253009706093
+1.422985178080866,-1.6811274556813085
+1.317157380977229,-0.7238409720550653
+-0.35265151080015644,1.461777165086822
+0.5467285861154743,1.7617827093942278
+-0.18313428545633526,2.132662021612408
+0.061074808584244966,1.1121147889846608
+1.3846589366932147,-0.3373042181603733
+0.38395808930382197,0.7695216404352094
+0.9205529108689228,-0.8726189957499824
+-1.1401782343366542,0.33462347738313053
+1.2820152687836517,-0.5550940654568568
+1.2501986490559924,-1.134044249304001
+0.32605452129777185,2.243724995753445
+0.960318281056638,0.5329624446210686
+-1.0330109605857234,-0.0011593921530135831
+0.5736414120433626,1.4474543410502276
+0.6949661154047044,-0.5097609640071791
+0.1405496694366461,0.6445940557679688
+-0.225179919561578,0.5549781729891623
+1.3570509733635536,-1.3497592740007234
+-0.050942173207914804,0.4411458899231341
+-0.04351493425525005,1.7688299918252965
+-0.5686038682283049,1.4634405277995886
+1.3912194345392175,-1.9366504867574705
+-0.22948835265735196,1.818262850854532
+0.15138935834404316,1.915938207141934
+-0.3606925418772957,1.8890577068214067
+0.4993107335697491,1.3726228494044488
+-0.6130152061639946,1.2729541152898238
+0.993178470312709,0.8065253009706093
+1.422985178080866,-1.6811274556813085
+1.317157380977229,-0.7238409720550653
+1.1821116843147723,-1.1948406297338698
+0.5467285861154743,1.7617827093942278
+-0.18313428545633526,2.132662021612408
+0.061074808584244966,1.1121147889846608
+-0.06649004827862207,0.3785485310315988
+0.007053201400834631,0.40345042626065
+0.9205529108689228,-0.8726189957499824
+-1.1401782343366542,0.33462347738313053
+1.2820152687836517,-0.5550940654568568
+-0.051331018006247585,0.8870905207401014
+0.6422207154643673,-0.8546269615151314
+0.9826862674434511,-0.7722604722176343
+-1.0330109605857234,-0.0011593921530135831
+0.5736414120433626,1.4474543410502276
+1.2142828341205736,-1.8079913184192278
+-0.22569681999837243,-0.5811731749478508
+-0.9983827794683096,0.2524409892537013
+0.6890142159451111,-0.7403985796809609
+-0.8387562466337369,0.9562583776085286
+1.6669071927856427,-1.346398210038814
+-0.5686038682283049,1.4634405277995886
+1.3912194345392175,-1.9366504867574705
+-0.22948835265735196,1.818262850854532
+1.5251706607039237,-1.0341198578642705
+-0.3606925418772957,1.8890577068214067
+0.4993107335697491,1.3726228494044488
+-0.6130152061639946,1.2729541152898238
+0.993178470312709,0.8065253009706093
+0.9140388586784445,-1.0059810161049287
+1.521429658064715,-2.3346791584251947
+-0.4818147359374968,0.8892110054475033
+0.5467285861154743,1.7617827093942278
+1.2200081632937612,-0.08965983999819316
+0.061074808584244966,1.1121147889846608
+0.870010843964685,-0.5600778792558925
+0.20661467231941588,-0.07743241994157657
+0.10536818070411691,-0.3625411711599307
+-0.2370962353260044,0.7687715297993125
+-0.08689941028604542,0.0798884106760348
+-0.051331018006247585,0.8870905207401014
+0.6422207154643673,-0.8546269615151314
+1.0335274124363285,-0.7007236901236475
+-1.0330109605857234,-0.0011593921530135831
+0.9708191062787479,-1.1385638075551987
+0.8272382930693011,-0.7332762619935195
+-0.22569681999837243,-0.5811731749478508
+0.6982424844947559,-0.4359765057497374
+0.6890142159451111,-0.7403985796809609
+-0.8387562466337369,0.9562583776085286
+-0.08828447410374579,1.7423274412631415
+1.6578958045214178,-1.6168163589555546
+1.3912194345392175,-1.9366504867574705
+-0.22948835265735196,1.818262850854532
+1.5251706607039237,-1.0341198578642705
+-0.3606925418772957,1.8890577068214067
+0.38832706107889137,-0.38111159644427706
+-0.6130152061639946,1.2729541152898238
+0.993178470312709,0.8065253009706093
+-1.020528074442769,0.7359889047418875
+1.2182992625586706,-1.2950401708339467
+0.6420742371368302,1.6618817089993008
+0.5467285861154743,1.7617827093942278
+1.6802777871890033,-2.481552545551897
+0.12124252692648063,0.14177308722270032
+0.870010843964685,-0.5600778792558925
+0.8409621347663941,-0.9544331532366002
+1.1575240055079348,-1.4672735280389977
+-0.2370962353260044,0.7687715297993125
+-0.5723800128638278,0.9511094279414398
+0.2549798883364869,0.6357480152919786
+-0.5805437009070321,1.2437067355646996
+1.0335274124363285,-0.7007236901236475
+-1.0330109605857234,-0.0011593921530135831
+1.7284875876857482,-1.553951816383472
+0.8272382930693011,-0.7332762619935195
+0.5598712152216856,-0.48710925453785325
+0.6982424844947559,-0.4359765057497374
+0.4485346364702086,-0.25849132962302557
+-0.8387562466337369,0.9562583776085286
+-0.08828447410374579,1.7423274412631415
+1.6578958045214178,-1.6168163589555546
+1.3912194345392175,-1.9366504867574705
+-0.22948835265735196,1.818262850854532
+-0.42849881294145437,0.6389401160277474
+0.0012716985199379138,-0.1667952741464035
+0.38832706107889137,-0.38111159644427706
+-0.10817136240333858,1.9809153432052118
+0.993178470312709,0.8065253009706093
+-0.25880761185269097,1.459181718321894
+1.4514335591916785,-1.898551760144989
+0.2766298114902189,1.6876977537058884
+0.5467285861154743,1.7617827093942278
+1.6802777871890033,-2.481552545551897
+1.340024851519484,-1.2284005776989957
+0.870010843964685,-0.5600778792558925
+0.8409621347663941,-0.9544331532366002
+1.8394072391473109,-1.6870149533405319
+-0.2370962353260044,0.7687715297993125
+0.47218205881902275,-0.21230542511919948
+0.3155761461037746,-0.1331536994014063
+-0.5805437009070321,1.2437067355646996
+1.0335274124363285,-0.7007236901236475
+-1.0330109605857234,-0.0011593921530135831
+0.8638505453525986,-0.6742823708993693
+0.5758761019617822,-0.43906318186008697
+0.1669199105604111,1.7452486570774255
+-0.5530540417064163,1.2499023111189669
+0.8359103604239093,0.28767881309436294
+0.06676949775777241,-0.024925193206543406
+-0.08828447410374579,1.7423274412631415
+1.6578958045214178,-1.6168163589555546
+1.3912194345392175,-1.9366504867574705
+-0.22948835265735196,1.818262850854532
+0.788092327615707,-0.7071875386456442
+0.0012716985199379138,-0.1667952741464035
+0.7421635026102312,-0.11127712236912368
+-0.10817136240333858,1.9809153432052118
+0.993178470312709,0.8065253009706093
+-0.25880761185269097,1.459181718321894
+1.1555375705590116,-0.9237529751870215
+-1.1741881358910242,-0.26475459666733536
+0.7922935327882227,0.2573573026734415
+1.6802777871890033,-2.481552545551897
+1.340024851519484,-1.2284005776989957
+0.870010843964685,-0.5600778792558925
+-0.4862077046798934,0.21056262010855242
+-0.7311597165166888,1.812066678816832
+-0.2370962353260044,0.7687715297993125
+0.8736931359045904,0.8966003037191956
+0.3155761461037746,-0.1331536994014063
+-0.5805437009070321,1.2437067355646996
+1.4088583896334739,-1.777914822488046
+-1.0330109605857234,-0.0011593921530135831
+1.5518620509701926,-2.4442876616151117
+0.5758761019617822,-0.43906318186008697
+-0.3400452806208075,1.575004288564685
+-0.5530540417064163,1.2499023111189669
+0.13199699461740444,-0.26187385865892154
+0.06676949775777241,-0.024925193206543406
+-0.08828447410374579,1.7423274412631415
+1.6504694042470076,-0.8698389137691652
+-0.7615752227921374,0.221265430671338
+-0.22948835265735196,1.818262850854532
+1.1708567295766783,-1.388410175920665
+0.0012716985199379138,-0.1667952741464035
+0.7737857770560349,-0.12925245748490877
+0.09011378652967497,1.8407515070591671
+0.5621611525858712,1.4356177110949724
+-0.25880761185269097,1.459181718321894
+1.1555375705590116,-0.9237529751870215
+-1.1741881358910242,-0.26475459666733536
+0.7922935327882227,0.2573573026734415
+1.6802777871890033,-2.481552545551897
+1.0129297921013407,0.8897519609407428
+0.870010843964685,-0.5600778792558925
+-0.4862077046798934,0.21056262010855242
+0.5005361259390347,-0.4303018902264021
+0.07781669737796937,-0.3760094205003543
+-0.3431633950276989,1.8672566423086472
+0.3155761461037746,-0.1331536994014063
+-0.8155614835681476,0.44014070823752965
+0.8976976368321097,-0.6043073621697787
+1.7281303236378323,-2.2289981133619796
+0.24439955660505225,1.4572975266810348
+0.5758761019617822,-0.43906318186008697
+0.11657282814482461,1.8397516082170537
+-0.5530540417064163,1.2499023111189669
+0.13199699461740444,-0.26187385865892154
+0.06676949775777241,-0.024925193206543406
+-0.08828447410374579,1.7423274412631415
+0.027223133083182194,1.175991192733379
+-0.7615752227921374,0.221265430671338
+-0.22948835265735196,1.818262850854532
+0.24828481176978656,0.03400573972385457
+0.0012716985199379138,-0.1667952741464035
+-0.4358633699958448,1.6107392950058208
+0.7809746687513548,1.31543576583469
+0.5621611525858712,1.4356177110949724
+-0.25880761185269097,1.459181718321894
+1.1555375705590116,-0.9237529751870215
+-1.1741881358910242,-0.26475459666733536
+0.7922935327882227,0.2573573026734415
+1.6802777871890033,-2.481552545551897
+1.0129297921013407,0.8897519609407428
+0.870010843964685,-0.5600778792558925
+-0.4862077046798934,0.21056262010855242
+1.0882368375184843,-1.335740416634906
+0.07781669737796937,-0.3760094205003543
+-0.17480630358702148,2.319660630306739
+0.05854199124605847,2.0822268658449357
+-0.6928770679772247,1.0897272251259194
+0.8976976368321097,-0.6043073621697787
+1.7281303236378323,-2.2289981133619796
+0.47021698973581993,-0.004845348654919389
+0.5758761019617822,-0.43906318186008697
+0.22366143007958955,1.3098226561277404
+-0.5530540417064163,1.2499023111189669
+1.7339846005990744,-2.4516858232857115
+0.06676949775777241,-0.024925193206543406
+-0.08828447410374579,1.7423274412631415
+-0.37767165023028954,-0.4381313061295942
+-0.7615752227921374,0.221265430671338
+-0.22948835265735196,1.818262850854532
+0.24828481176978656,0.03400573972385457
+0.0012716985199379138,-0.1667952741464035
+-0.4358633699958448,1.6107392950058208
+0.7809746687513548,1.31543576583469
+0.5621611525858712,1.4356177110949724
+0.5445062937686871,2.0738245452333426
+1.1555375705590116,-0.9237529751870215
+1.1889128413867556,0.05351249624351772
+0.7922935327882227,0.2573573026734415
+1.6802777871890033,-2.481552545551897
+-0.34731115838424664,0.1467452341910207
+1.7305024255052106,-2.2044608833264667
+-0.26326948409300094,0.18127258438057237
+1.0882368375184843,-1.335740416634906
+-0.44829657398530887,-0.4015416175630193
+-0.17480630358702148,2.319660630306739
+0.05854199124605847,2.0822268658449357
+0.11795760152469854,-0.19528869527923673
+0.8976976368321097,-0.6043073621697787
+0.37058493131422443,-0.05312235431039364
+-0.3910208661181151,-0.012179345120446827
+0.5758761019617822,-0.43906318186008697
+0.22366143007958955,1.3098226561277404
+-0.5530540417064163,1.2499023111189669
+-0.0201058171900554,0.21629048268982978
+-0.030187677080525832,0.01564808383429872
+-0.3841430737111862,0.4992253012347947
+0.7327437651910558,0.425513337123957
+0.3330540885838819,-0.5809467256876449
+-0.22948835265735196,1.818262850854532
+0.24828481176978656,0.03400573972385457
+-0.5363566255362303,0.5469445391571381
+-0.4358633699958448,1.6107392950058208
+-0.13668897891632878,0.4096829472711794
+1.0766908550343306,0.6233426497820483
+0.5445062937686871,2.0738245452333426
+1.1555375705590116,-0.9237529751870215
+1.1889128413867556,0.05351249624351772
+-0.0809305690965626,0.8611445000268594
+1.299263307382342,-1.2575451104599873
+-0.8129794934841944,0.7151781992741438
+1.7305024255052106,-2.2044608833264667
+-0.26326948409300094,0.18127258438057237
+-0.26342646769273953,1.7289799317141483
+-0.5638955362940932,0.3696561577578823
+-0.17480630358702148,2.319660630306739
+0.05854199124605847,2.0822268658449357
+0.11795760152469854,-0.19528869527923673
+0.6544048259777846,-0.13718747739389014
+-0.33952125346568024,0.315021425996037
+-0.3910208661181151,-0.012179345120446827
+0.5758761019617822,-0.43906318186008697
+0.20698234999296378,0.7053274180730396
+-0.5530540417064163,1.2499023111189669
+-0.0201058171900554,0.21629048268982978
+0.0036892257743022794,0.11288116875537069
+0.5128714121958371,-0.578254466665314
+0.7327437651910558,0.425513337123957
+0.3330540885838819,-0.5809467256876449
+-0.22948835265735196,1.818262850854532
+-0.39305271535169994,0.7878452716507145
+-0.5363566255362303,0.5469445391571381
+-0.4358633699958448,1.6107392950058208
+-0.13668897891632878,0.4096829472711794
+1.0766908550343306,0.6233426497820483
+0.5445062937686871,2.0738245452333426
+1.1555375705590116,-0.9237529751870215
+1.1889128413867556,0.05351249624351772
+-0.09645863723569015,0.020425002840486012
+1.299263307382342,-1.2575451104599873
+0.4315677653614832,1.6951905661077329
+1.7305024255052106,-2.2044608833264667
+-0.26326948409300094,0.18127258438057237
+-0.4764288372979673,-0.33936543743523623
+-0.07680993516059875,0.28391165495997617
+-0.2966471101423364,1.1588824738786916
+1.6694683269370385,-1.4377777210976022
+0.11795760152469854,-0.19528869527923673
+0.6544048259777846,-0.13718747739389014
+-0.6634038482698354,0.6673774479356299
+-0.3910208661181151,-0.012179345120446827
+1.9049580055122606,-1.7448624807102122
+0.9568561121656698,0.5169446205212084
+-0.061455893934512756,0.26896825058999146
+0.5905902073247002,1.208632903588212
+-0.5819999845003236,1.6318934856686118
+0.5128714121958371,-0.578254466665314
+-0.43046166953402637,-0.07929280363793645
+0.5777491335155015,0.9300308419610922
+-0.22948835265735196,1.818262850854532
+-0.39305271535169994,0.7878452716507145
+0.947787927845827,-1.2458429926308885
+0.6769679495023012,-0.3056299671606757
+-0.13668897891632878,0.4096829472711794
+1.0766908550343306,0.6233426497820483
+0.5445062937686871,2.0738245452333426
+-0.4462050897112878,1.4670100461559248
+1.1889128413867556,0.05351249624351772
+0.4222189333043671,0.057090752957074775
+1.299263307382342,-1.2575451104599873
+0.4315677653614832,1.6951905661077329
+0.04242889897434654,0.1983880034380917
+-0.26326948409300094,0.18127258438057237
+0.18282498033373817,-0.4595768925016178
+-0.009811017600425798,-0.3605095347938705
+-0.08057513844125241,2.0277508413724834
+1.6694683269370385,-1.4377777210976022
+-0.5064681781839117,1.3347564646162189
+0.6544048259777846,-0.13718747739389014
+0.04904073693359842,-0.3598907639097143
+-0.3910208661181151,-0.012179345120446827
+1.253817825052787,-0.7419226038166054
+0.9568561121656698,0.5169446205212084
+1.4088406869270866,-1.564376535730038
+0.5905902073247002,1.208632903588212
+-0.5819999845003236,1.6318934856686118
+0.5128714121958371,-0.578254466665314
+-0.31851936970808614,0.004874922096757661
+0.5777491335155015,0.9300308419610922
+-0.501067051803218,0.9809854083298134
+-0.39305271535169994,0.7878452716507145
+0.947787927845827,-1.2458429926308885
+0.6769679495023012,-0.3056299671606757
+0.2771274609009053,1.5545893214226474
+1.0766908550343306,0.6233426497820483
+0.9506162961369893,0.5347442393379956
+-0.4462050897112878,1.4670100461559248
+-0.4006746813565435,1.8499213867375301
+0.4222189333043671,0.057090752957074775
+1.299263307382342,-1.2575451104599873
+0.4315677653614832,1.6951905661077329
+-0.11718810319783476,1.6888798489479784
+-0.26326948409300094,0.18127258438057237
+0.8392656329663195,0.8550533314125064
+1.3825681290440817,-0.25861386405965137
+-0.08057513844125241,2.0277508413724834
+1.6694683269370385,-1.4377777210976022
+-0.6831007940026582,1.3514810778432784
+0.6544048259777846,-0.13718747739389014
+-0.36476292426970125,1.1035294353889995
+-0.3910208661181151,-0.012179345120446827
+1.1885451226359123,0.7483502385965124
+0.8395099236983319,0.9970216320738481
+1.4088406869270866,-1.564376535730038
+0.5905902073247002,1.208632903588212
+1.479650206501931,-1.2402230471946099
+1.0320144978739019,0.2766254400990811
+0.3164366634536928,1.4019862787264283
+-0.1506384887995716,-0.008704311444653418
+-0.5940299703113617,1.593618207473633
+-0.39305271535169994,0.7878452716507145
+-0.29743927338021275,-0.2668134670594082
+0.6769679495023012,-0.3056299671606757
+-0.23500372616294996,0.02416321244945343
+0.9108791706398444,-0.31356437443375273
+1.6848521326679076,-1.930965970757837
+0.5654765288289341,-0.4067900909788923
+-0.4006746813565435,1.8499213867375301
+-0.02060802424678998,0.27761541077152563
+1.299263307382342,-1.2575451104599873
+1.1609519951792255,0.6406457501935283
+1.4620222126513145,-0.06458920404473079
+-0.26326948409300094,0.18127258438057237
+0.3342065275606553,-0.4182568359568159
+1.3825681290440817,-0.25861386405965137
+-0.08057513844125241,2.0277508413724834
+0.5873010107794872,-0.44919624483300435
+-0.6831007940026582,1.3514810778432784
+0.26122798860199625,1.747609271065428
+1.3259292527075879,0.1768147688885811
+-0.1511783267872565,2.018396784606809
+1.1885451226359123,0.7483502385965124
+-0.7462441065816188,0.48853184704070396
+1.4088406869270866,-1.564376535730038
+0.5905902073247002,1.208632903588212
+0.5927987838173367,-0.4347159425544765
+0.7663698569658068,1.4578221815212753
+0.3164366634536928,1.4019862787264283
+-0.1506384887995716,-0.008704311444653418
+-0.004098226816138029,1.4769050094186387
+1.6909538186210233,-1.933654582247073
+-0.29743927338021275,-0.2668134670594082
+1.0001568711360396,-1.0090138792403152
+-0.23500372616294996,0.02416321244945343
+0.7466174250360085,0.8364778741180874
+1.6848521326679076,-1.930965970757837
+-0.6000596930716137,1.0143675129540586
+0.7467711034454696,-0.46524654670889676
+-0.02060802424678998,0.27761541077152563
+1.299263307382342,-1.2575451104599873
+1.1609519951792255,0.6406457501935283
+-0.020212975866727184,2.549764727623391
+0.1198320003799509,1.5125831138929384
+0.030590730613378053,1.5770098162280815
+1.3825681290440817,-0.25861386405965137
+0.9060706365026266,-0.6219734014231636
+0.5873010107794872,-0.44919624483300435
+-0.46008623334138443,-0.21205426981007242
+0.26122798860199625,1.747609271065428
+1.3259292527075879,0.1768147688885811
+-0.1511783267872565,2.018396784606809
+1.1885451226359123,0.7483502385965124
+1.3536010969791543,-0.33686093185679244
+1.4088406869270866,-1.564376535730038
+0.5905902073247002,1.208632903588212
+0.5927987838173367,-0.4347159425544765
+-0.8124453821212653,0.13351812358488196
+0.3164366634536928,1.4019862787264283
+-0.1506384887995716,-0.008704311444653418
+-0.004098226816138029,1.4769050094186387
+1.6909538186210233,-1.933654582247073
+-0.29743927338021275,-0.2668134670594082
+1.0001568711360396,-1.0090138792403152
+0.5972241778458204,1.4101491804159927
+0.7504799126619381,-1.0523977141405363
+-0.936676844697747,0.7770568953960565
+-0.6000596930716137,1.0143675129540586
+0.0015685936997077154,1.0652738246809172
+-0.7832788823778477,-0.00040863135157392927
+1.299263307382342,-1.2575451104599873
+1.0267502201346663,-1.437509119236218
+-0.020212975866727184,2.549764727623391
+0.1198320003799509,1.5125831138929384
+1.188272847436922,-1.0815992795350593
+1.3825681290440817,-0.25861386405965137
+0.9060706365026266,-0.6219734014231636
+0.5873010107794872,-0.44919624483300435
+0.3979812174797064,0.1257370030273287
+0.10470318273428852,1.3157280018864148
+1.0552157867364578,0.5800543482096441
+-0.44233179977164994,0.014042429485340069
+1.1885451226359123,0.7483502385965124
+-0.7475884041694489,-0.1360174912299357
+1.4088406869270866,-1.564376535730038
+0.5905902073247002,1.208632903588212
+0.5927987838173367,-0.4347159425544765
+-0.8124453821212653,0.13351812358488196
+-0.1900294246765665,0.9249564563008388
+-0.1506384887995716,-0.008704311444653418
+0.8308585718924699,-0.053852066239817586
+0.010815255579371741,1.6860384933175059
+1.2784776698172737,-1.7407252545177574
+-0.6016486450630587,1.3358304220790438
+0.5972241778458204,1.4101491804159927
+0.5004944821188289,0.7320972671218415
+-0.5207582082230042,1.7911656908618452
+-0.6000596930716137,1.0143675129540586
+1.0292588594037313,-0.13420662718874232
+-0.7832788823778477,-0.00040863135157392927
+0.378273194654507,1.3495695979759275
+0.8909681130887264,0.49933846592429265
+-0.020212975866727184,2.549764727623391
+0.6405915774493749,-0.17786044085561226
+0.9836264420167576,0.7899125655126199
+0.7254335858317379,1.6218038743138248
+0.3686463500961015,1.1282546632812887
+0.5873010107794872,-0.44919624483300435
+0.3979812174797064,0.1257370030273287
+0.10470318273428852,1.3157280018864148
+0.8648839224616903,1.1819366612826567
+0.1308808089376291,-0.37449379237341296
+1.1885451226359123,0.7483502385965124
+-0.7475884041694489,-0.1360174912299357
+1.4088406869270866,-1.564376535730038
+0.19644694962125675,1.805748157382356
+0.5927987838173367,-0.4347159425544765
+-0.8124453821212653,0.13351812358488196
+-0.1900294246765665,0.9249564563008388
+-0.1506384887995716,-0.008704311444653418
+-0.25085648250968584,0.08867824399607639
+0.010815255579371741,1.6860384933175059
+1.0245327180930566,0.7744204191888022
+1.467488614190949,-1.5049187380163258
+0.5972241778458204,1.4101491804159927
+1.7227926774956663,-2.675663713224065
+-0.5207582082230042,1.7911656908618452
+-0.6000596930716137,1.0143675129540586
+1.0292588594037313,-0.13420662718874232
+-0.7680319452001406,0.219519035725708
+1.3529676734278047,-1.1031532302159057
+0.8909681130887264,0.49933846592429265
+-0.020212975866727184,2.549764727623391
+0.7318885328877917,-0.031382494669557004
+1.0683218150051503,0.7483715581957755
+0.7254335858317379,1.6218038743138248
+0.6511185345879277,1.7837996386636605
+-0.4990335672921742,1.9913124705927598
+0.5815290677316602,-0.1706885619289853
+0.19960692564096405,1.6846328444672845
+0.8648839224616903,1.1819366612826567
+0.1308808089376291,-0.37449379237341296
+-0.5068899916154652,0.36303263142536757
+-0.7475884041694489,-0.1360174912299357
+1.4088406869270866,-1.564376535730038
+0.19644694962125675,1.805748157382356
+-0.9463862346333545,0.724729068577167
+-0.8124453821212653,0.13351812358488196
+0.4762337423343966,2.192439230564418
+-0.1506384887995716,-0.008704311444653418
+-0.25085648250968584,0.08867824399607639
+0.9868880573759092,0.7523590258018151
+1.0245327180930566,0.7744204191888022
+1.467488614190949,-1.5049187380163258
+-0.4146366132940126,0.9742882021962207
+1.7227926774956663,-2.675663713224065
+-0.7774486835230054,0.2162562642148722
+-0.35859300720066967,-0.26410131470574516
+-0.1280356126761576,2.169717778552113
+-0.7680319452001406,0.219519035725708
+1.3529676734278047,-1.1031532302159057
+0.8909681130887264,0.49933846592429265
+0.4799807295097376,0.029749814071351244
+0.7318885328877917,-0.031382494669557004
+0.817217430833628,1.566352722923621
+0.7254335858317379,1.6218038743138248
+0.9992856375043626,-0.3124557076645028
+-0.4990335672921742,1.9913124705927598
+-0.47874174559785104,1.6693068569310991
+0.19960692564096405,1.6846328444672845
+0.8648839224616903,1.1819366612826567
+0.1308808089376291,-0.37449379237341296
+1.4546371744311886,-0.8571177487097821
+-0.7475884041694489,-0.1360174912299357
+1.4088406869270866,-1.564376535730038
+0.19644694962125675,1.805748157382356
+0.11822354385140066,-0.46563836756564314
+-0.7622277476586315,1.5341442614041565
+0.4762337423343966,2.192439230564418
+-0.1506384887995716,-0.008704311444653418
+-0.6492067392210373,1.1951285307462052
+-0.9343316669186896,0.3924927302390233
+0.6073114831089086,0.2818139625114159
+1.467488614190949,-1.5049187380163258
+-0.4146366132940126,0.9742882021962207
+1.7227926774956663,-2.675663713224065
+0.2718398080254095,2.242954134902056
+-0.35859300720066967,-0.26410131470574516
+-0.1280356126761576,2.169717778552113
+-0.7680319452001406,0.219519035725708
+1.3529676734278047,-1.1031532302159057
+1.1199638701754986,0.10708186661306018
+0.4799807295097376,0.029749814071351244
+0.3494080581906873,2.3096049910509517
+-0.09132846145814688,1.9155320508670517
+0.7254335858317379,1.6218038743138248
+-0.003518890310637235,1.5866969584651476
+-0.4990335672921742,1.9913124705927598
+-0.47874174559785104,1.6693068569310991
+0.19960692564096405,1.6846328444672845
+0.8648839224616903,1.1819366612826567
+0.3266199336232542,0.2376922156190635
+-0.27264422107726777,1.455799137146697
+1.5520341907444013,-2.509280918296093
+1.4088406869270866,-1.564376535730038
+0.10752538914474483,2.242946381975254
+0.17812897387513982,1.5531156697170836
+-0.7622277476586315,1.5341442614041565
+1.7146975578536947,-1.5693947513059934
+-0.1506384887995716,-0.008704311444653418
+-0.6492067392210373,1.1951285307462052
+-0.9343316669186896,0.3924927302390233
+-0.14195909899567966,1.6545068388393844
+1.467488614190949,-1.5049187380163258
+-0.02068148890139132,2.015489507440587
+1.7227926774956663,-2.675663713224065
+1.0043291180739737,-1.0962873940618876
+-0.35859300720066967,-0.26410131470574516
+-0.1280356126761576,2.169717778552113
+-0.7680319452001406,0.219519035725708
+-0.4296683094001657,0.04880529813953052
+0.7143398552158037,-0.20831310054523922
+-0.2076785162509829,2.2075852542257377
+-0.2655780056219291,0.8579469547495825
+-0.09132846145814688,1.9155320508670517
+-0.6014157268785605,0.09861721922025891
+-0.003518890310637235,1.5866969584651476
+-0.3602827975120006,1.2576076035627894
+-0.47874174559785104,1.6693068569310991
+0.19960692564096405,1.6846328444672845
+1.1603922410820433,0.8485857077115777
+0.3266199336232542,0.2376922156190635
+0.18714532493785987,1.8063608461455656
+1.5520341907444013,-2.509280918296093
+1.4088406869270866,-1.564376535730038
+0.10752538914474483,2.242946381975254
+0.6841961898593715,0.52216318833161
+-0.5197050800034262,1.8016306175315717
+0.277673291274065,1.9479872387104569
+0.11358813953693062,0.9173136172337549
+-0.6492067392210373,1.1951285307462052
+-0.9343316669186896,0.3924927302390233
+-0.4059594148381973,1.819713011705249
+1.467488614190949,-1.5049187380163258
+-0.02068148890139132,2.015489507440587
+1.7227926774956663,-2.675663713224065
+1.3669045609722577,-1.2030521862178039
+-0.7121465505495129,0.7040164798039121
+-0.1280356126761576,2.169717778552113
+-0.7680319452001406,0.219519035725708
+-0.4296683094001657,0.04880529813953052
+0.7143398552158037,-0.20831310054523922
+-0.17318529431269644,1.9592025889073752
+-0.265447087141917,1.1590169347829662
+-0.4465519589982447,1.6170678418473514
+-0.6014157268785605,0.09861721922025891
+-0.003518890310637235,1.5866969584651476
+-0.3602827975120006,1.2576076035627894
+-0.34686959857912675,1.9324795495250031
+1.0751581990367018,-1.2673184114639493
+-0.7173678714555722,0.9624909787567566
+-0.6889303687232936,1.068460381755568
+-0.21012774311163662,1.8267111092736985
+1.2393198566200834,-1.4134103276418561
+1.4088406869270866,-1.564376535730038
+0.10752538914474483,2.242946381975254
+-0.1745938762017143,0.23769390956665837
+-0.5197050800034262,1.8016306175315717
+0.277673291274065,1.9479872387104569
+0.11358813953693062,0.9173136172337549
+0.507826394464442,-0.16417531687769757
+-0.9343316669186896,0.3924927302390233
+-0.4059594148381973,1.819713011705249
+1.467488614190949,-1.5049187380163258
+-0.02068148890139132,2.015489507440587
+1.7227926774956663,-2.675663713224065
+0.8319337439631788,-1.1573621568275998
+-0.48534259771782706,-0.1423777868913152
+0.5346377233106522,0.9782397858054527
+-0.7680319452001406,0.219519035725708
+-0.4296683094001657,0.04880529813953052
+0.45975873862208105,1.5963851196757226
+-0.17318529431269644,1.9592025889073752
+-0.5896840730508828,0.2536942439996887
+0.3730275781727633,0.16020532396010667
+-0.6014157268785605,0.09861721922025891
+-0.0022817921810188713,1.5649615598289792
+1.6949228062334298,-2.0707963060554815
+-0.4008121373850043,0.5973077356026633
+1.0751581990367018,-1.2673184114639493
+-0.7173678714555722,0.9624909787567566
+-0.6889303687232936,1.068460381755568
+1.1123953105600857,-0.6930710208143118
+0.5065278030438577,0.8810986723951235
+1.636796617731259,-2.81224144295342
+0.6562930373443017,1.731083555347058
+-0.6151236326674709,0.9988091912471619
+1.5145866875497709,-1.0591262491224769
+0.277673291274065,1.9479872387104569
+0.11104908299445151,1.4183278380658377
+1.0175392805459629,-0.5737358447605462
+-0.9343316669186896,0.3924927302390233
+-0.4059594148381973,1.819713011705249
+1.467488614190949,-1.5049187380163258
+-0.02068148890139132,2.015489507440587
+0.8133048057718871,0.8475152578847753
+0.8319337439631788,-1.1573621568275998
+1.2310426077210317,0.23901046906988577
+0.5346377233106522,0.9782397858054527
+1.0396390867895364,0.4127749389639325
+-0.4296683094001657,0.04880529813953052
+1.089751005004729,-0.1330432517769965
+-0.17318529431269644,1.9592025889073752
+-0.5896840730508828,0.2536942439996887
+-0.781300424103717,0.7709264587392901
+-0.6014157268785605,0.09861721922025891
+-0.0022817921810188713,1.5649615598289792
+1.6949228062334298,-2.0707963060554815
+-0.4008121373850043,0.5973077356026633
+1.0751581990367018,-1.2673184114639493
+0.10758443208768698,0.1070580278141616
+-0.8595352777641458,0.175957870013756
+1.0721408176924756,-0.4758627759638021
+0.5065278030438577,0.8810986723951235
+1.636796617731259,-2.81224144295342
+0.49871892039228044,-0.6619300437862544
+-0.6151236326674709,0.9988091912471619
+1.5145866875497709,-1.0591262491224769
+0.277673291274065,1.9479872387104569
+-0.0679060405970171,-0.16359748639749577
+0.626927388924158,0.9098244642367622
+-0.36638593698992605,2.1202616711440014
+-0.4059594148381973,1.819713011705249
+1.467488614190949,-1.5049187380163258
+0.35188444569920313,-0.2008252122709851
+-0.16294791381982188,-0.00229474087115121
+0.8319337439631788,-1.1573621568275998
+1.17159597696614,-0.9946040671889994
+0.5346377233106522,0.9782397858054527
+1.0396390867895364,0.4127749389639325
+-0.04471817231286146,1.6620319034036095
+-0.6049195185201397,1.7718263382890047
+-0.17318529431269644,1.9592025889073752
+0.2617417616479785,1.3992018959189352
+0.16834645801372528,0.4698952183035694
+-0.6014157268785605,0.09861721922025891
+-0.5653246410828621,0.6649812158113888
+1.6949228062334298,-2.0707963060554815
+-0.4008121373850043,0.5973077356026633
+0.7265992050778294,-0.14494460992550146
+-0.7587478965330535,0.46950254350956006
+0.8500897817958467,-0.6475576411194994
+1.1307488784785424,-1.8564520205457002
+-0.3709550947407771,0.37549111083587927
+1.636796617731259,-2.81224144295342
+0.49871892039228044,-0.6619300437862544
+0.9068843752549938,1.1536065712213697
+1.5145866875497709,-1.0591262491224769
+1.1268407033286891,0.8555824269299173
+-0.0679060405970171,-0.16359748639749577
+1.2220534001876704,-0.6708889692421909
+-0.36638593698992605,2.1202616711440014
+-0.4059594148381973,1.819713011705249
+0.9020692267077215,-0.3725914199651529
+1.262295020469054,-0.4163793933151737
+-0.16294791381982188,-0.00229474087115121
+0.3199053659785697,0.9418490486853014
+1.4980264855972183,-0.3404060276235419
+0.06303022304674158,-0.1257468727438846
+1.0396390867895364,0.4127749389639325
+0.11190060532818019,-0.7799277011118272
+0.3222516976080564,1.6694451218961774
+-0.4865200836795989,0.8889692715679788
+0.21624628662553635,2.2544494203774663
+-0.17851676669998,0.09747699402950709
+-0.6014157268785605,0.09861721922025891
+0.7843122150101978,0.11499256361823773
+1.6949228062334298,-2.0707963060554815
+1.1452314900934775,-1.1690593091180896
+0.7265992050778294,-0.14494460992550146
+-0.7587478965330535,0.46950254350956006
+0.6878947356729587,1.0151846877946311
+1.012730625204083,0.31590849829270684
+-0.3709550947407771,0.37549111083587927
+1.636796617731259,-2.81224144295342
+1.0925175394057562,-0.25509522646843885
+1.1159234960661786,-0.08138969304732838
+1.5145866875497709,-1.0591262491224769
+-0.10990711900143138,1.6752154122087082
+0.7981925484949312,-0.6582706262114346
+1.523813105514829,-1.4086614763686616
+-0.36638593698992605,2.1202616711440014
+-0.4059594148381973,1.819713011705249
+0.9020692267077215,-0.3725914199651529
+1.262295020469054,-0.4163793933151737
+-0.16294791381982188,-0.00229474087115121
+1.3981472933177659,0.05634541758716172
+1.4980264855972183,-0.3404060276235419
+0.04160444276883116,-0.11827084556003793
+1.0396390867895364,0.4127749389639325
+-0.1188529669877339,-0.2540347780584865
+0.3222516976080564,1.6694451218961774
+-0.4865200836795989,0.8889692715679788
+0.21624628662553635,2.2544494203774663
+-0.7726429002405681,0.8522619249249563
+-0.6014157268785605,0.09861721922025891
+1.0226178960680083,-0.1764218558462668
+1.6949228062334298,-2.0707963060554815
+1.1452314900934775,-1.1690593091180896
+1.6767828153683664,-2.72800737850571
+1.574142053907319,-0.9036017592875041
+0.6878947356729587,1.0151846877946311
+1.1828514237055638,0.11661500824809318
+0.29069479661237996,0.2106404275652956
+1.7489158537175482,-1.3879946094370847
+1.1568586752494034,-0.07314972890035806
+-0.18626006767444475,0.07094726920930958
+0.6297066518106644,-0.5674503708302914
+0.5062460758063398,1.2033306140055386
+0.7981925484949312,-0.6582706262114346
+1.523813105514829,-1.4086614763686616
+-0.36638593698992605,2.1202616711440014
+0.3644821122369376,0.566900185433826
+1.4824703453839239,-2.1807082200804837
+1.262295020469054,-0.4163793933151737
+-0.16294791381982188,-0.00229474087115121
+1.3460016426162267,-0.42670609609346244
+0.31492174485903307,2.1980281038206435
+0.04160444276883116,-0.11827084556003793
+0.9015181709640621,-0.05478664296034892
+-0.1188529669877339,-0.2540347780584865
+0.3222516976080564,1.6694451218961774
+-0.5216853562030043,1.1549611496690266
+0.21624628662553635,2.2544494203774663
+-0.1936186445484495,-0.08993671739672407
+-0.6014157268785605,0.09861721922025891
+1.4104666503943912,-0.16564958090046544
+1.6949228062334298,-2.0707963060554815
+0.026801293729439624,2.468709958760292
+1.6767828153683664,-2.72800737850571
+1.574142053907319,-0.9036017592875041
+0.3212769036316341,0.22426086439822773
+1.2740832968190985,0.03233153820595175
+0.29069479661237996,0.2106404275652956
+1.7489158537175482,-1.3879946094370847
+1.0723941805997768,-0.8097369673695229
+1.1670901858125178,0.06704460554013
+0.6297066518106644,-0.5674503708302914
+0.5062460758063398,1.2033306140055386
+0.751951420207089,-0.6176813495217985
+1.523813105514829,-1.4086614763686616
+-0.36638593698992605,2.1202616711440014
+-0.8361866959087496,1.2215233218957313
+0.7737687856558939,1.0999410611272298
+1.262295020469054,-0.4163793933151737
+0.1151906387188465,-0.1601673470030498
+1.3706330132767321,-0.391215602755502
+0.31492174485903307,2.1980281038206435
+0.04160444276883116,-0.11827084556003793
+-0.4547556936069014,1.7717939795506312
+-0.1188529669877339,-0.2540347780584865
+1.219502269030611,-0.6746701163756339
+-0.5216853562030043,1.1549611496690266
+-0.13054398499357592,2.3338636695351345
+-0.1936186445484495,-0.08993671739672407
+-0.2372721633661509,0.0801638722022644
+-0.07016338928518104,-0.23821737280249822
+1.6949228062334298,-2.0707963060554815
+0.026801293729439624,2.468709958760292
+0.14393801989046792,0.11934298766149726
+1.574142053907319,-0.9036017592875041
+0.12800438193827635,1.3942431315364523
+1.2740832968190985,0.03233153820595175
+0.9116494871217417,-0.7598635038656352
+-0.47293972740374357,1.0857288411534527
+-0.16060766877270677,1.1505007494290649
+1.1670901858125178,0.06704460554013
+0.9199830885689295,0.12509523011071133
+0.5062460758063398,1.2033306140055386
+0.11571292331260079,1.5041680222707925
+1.523813105514829,-1.4086614763686616
+0.172200182609691,0.2007099805226844
+-0.8361866959087496,1.2215233218957313
+0.7737687856558939,1.0999410611272298
+-0.7436552872386626,0.050445136100811555
+-0.33590549263180713,-0.2515499841079983
+1.3706330132767321,-0.391215602755502
+0.07877324417630904,0.4139126655941092
+-0.30504694161416046,0.545658959679236
+-0.4547556936069014,1.7717939795506312
+0.6013289289623226,1.3745235841188386
+1.219502269030611,-0.6746701163756339
+1.7690643651398887,-3.0189019057575592
+0.9957053287372125,-1.3042082781121644
+-0.1936186445484495,-0.08993671739672407
+-0.04941302770056488,0.4170841947401679
+-0.07016338928518104,-0.23821737280249822
+0.17548411127211017,2.051744949792344
+-0.2755784773803932,0.5652379517070613
+0.14393801989046792,0.11934298766149726
+1.574142053907319,-0.9036017592875041
+-0.8815600795708505,0.6925779725815604
+1.2740832968190985,0.03233153820595175
+-0.004561928284528061,1.4070816748605794
+-0.47293972740374357,1.0857288411534527
+0.3430595207565753,1.0085176544261982
+0.4680101410434087,1.341792030039815
+0.9199830885689295,0.12509523011071133
+0.5062460758063398,1.2033306140055386
+0.11571292331260079,1.5041680222707925
+0.8991010375452817,1.1063229613353365
+0.172200182609691,0.2007099805226844
+-0.8361866959087496,1.2215233218957313
+0.7737687856558939,1.0999410611272298
+-0.7352999882862035,1.5343464303668386
+0.9232972470391781,1.4087899974731157
+-0.49368441810504415,0.06870872456162191
+0.36194015984963607,1.5385601620439255
+-0.30504694161416046,0.545658959679236
+0.6757710474676817,1.7160343363463817
+-0.15546303806340434,0.9021000076088171
+1.219502269030611,-0.6746701163756339
+1.7690643651398887,-3.0189019057575592
+0.9957053287372125,-1.3042082781121644
+-0.1936186445484495,-0.08993671739672407
+-0.04941302770056488,0.4170841947401679
+-0.4112057695722629,0.2885116019111301
+0.17548411127211017,2.051744949792344
+-0.02794345993715086,1.50493343895883
+0.05706438242735956,1.527423317874306
+-0.33096887330072133,0.17872076248030533
+-0.22395837434365395,1.7184854394665354
+1.2740832968190985,0.03233153820595175
+-0.4324431785869073,-0.2128903886345067
+-0.10689347076950154,0.08895558498301293
+-0.2846531214339755,-0.36511329562521017
+0.4680101410434087,1.341792030039815
+0.30645621394975203,-0.17371669294952863
+0.15258741607828696,2.2045105755103935
+0.40002835959001126,-0.06986582387808096
+0.8991010375452817,1.1063229613353365
+-0.7402539078412523,-0.06971880518440121
+-0.8361866959087496,1.2215233218957313
+0.7737687856558939,1.0999410611272298
+-0.8011470455104812,0.2361980474332241
+0.9232972470391781,1.4087899974731157
+-0.49368441810504415,0.06870872456162191
+0.36194015984963607,1.5385601620439255
+-0.21006250716284502,-0.028269526762410332
+0.6757710474676817,1.7160343363463817
+-0.309580998560214,1.289876904978929
+0.03598769696300724,1.5609019367124475
+1.7690643651398887,-3.0189019057575592
+0.9957053287372125,-1.3042082781121644
+-0.28019303699848785,1.9944411327181593
+-0.5519212340027714,1.0971183889782843
+1.1622630688726392,0.6688513726009879
+0.17548411127211017,2.051744949792344
+0.487400141928863,0.9165805331782562
+0.03589136498519285,0.42680011628750136
+0.5801411966310788,1.9569049743640008
+0.7091631864976092,-0.3526419272955279
+1.2740832968190985,0.03233153820595175
+0.6705226026804687,-0.4598809198458764
+-0.10689347076950154,0.08895558498301293
+-0.2846531214339755,-0.36511329562521017
+0.30227225203227526,1.321258989682434
+0.30645621394975203,-0.17371669294952863
+0.15258741607828696,2.2045105755103935
+0.40002835959001126,-0.06986582387808096
+0.8991010375452817,1.1063229613353365
+-0.7402539078412523,-0.06971880518440121
+0.2878914205948593,1.3764824108966227
+1.8543372566620238,-2.0955195290039637
+-0.8011470455104812,0.2361980474332241
+0.2279103317646176,2.274676715129398
+-0.2565578762061099,0.08852246311971951
+0.36194015984963607,1.5385601620439255
+0.8871324860707024,-0.6458750234333015
+-0.5592249402397745,1.3081796642060726
+-0.309580998560214,1.289876904978929
+-0.2979865251694341,0.6230248591211102
+1.7690643651398887,-3.0189019057575592
+0.34584981030895323,1.7634795421343674
+0.5987440996703921,1.2507606863431908
+-0.06824187339120236,1.4059889556261538
+1.1622630688726392,0.6688513726009879
+0.21012255909745908,-0.4786282963273907
+0.38236718111945944,-0.28862365486742275
+0.3630069964645585,0.1318044024361209
+-0.4071510872313513,1.2083841250340166
+0.7091631864976092,-0.3526419272955279
+0.843023998531703,-0.6605990411521827
+0.47676020372042915,1.4271786469931835
+-0.10689347076950154,0.08895558498301293
+-0.18503720500735915,-0.13134110661167075
+0.30227225203227526,1.321258989682434
+0.31765093950283785,-0.4950013972855742
+0.15258741607828696,2.2045105755103935
+-0.23040337308884795,2.218361483550066
+-0.6541633184678062,1.9859117126249588
+-0.7402539078412523,-0.06971880518440121
+0.6466175431155564,0.6453230246459412
+1.8543372566620238,-2.0955195290039637
+-0.8011470455104812,0.2361980474332241
+0.2279103317646176,2.274676715129398
+-0.2565578762061099,0.08852246311971951
+0.36194015984963607,1.5385601620439255
+-0.20711656201347328,1.9084765407162565
+0.3214620330808689,1.6080749169617843
+-0.309580998560214,1.289876904978929
+-0.40695477390119583,1.2118056703798659
+1.7690643651398887,-3.0189019057575592
+0.8018937709275499,1.0818345260835818
+0.5987440996703921,1.2507606863431908
+-0.06824187339120236,1.4059889556261538
+-0.08340612671783332,-0.3003702680654874
+0.21012255909745908,-0.4786282963273907
+0.2488992388489395,-0.6282486884079518
+0.3630069964645585,0.1318044024361209
+0.9746876227440122,-0.4412849042982151
+0.7091631864976092,-0.3526419272955279
+0.843023998531703,-0.6605990411521827
+0.47676020372042915,1.4271786469931835
+-0.10689347076950154,0.08895558498301293
+-0.18503720500735915,-0.13134110661167075
+-0.733774403964947,0.9338463031304838
+0.31765093950283785,-0.4950013972855742
+0.15258741607828696,2.2045105755103935
+-0.23040337308884795,2.218361483550066
+-0.7734900861119869,1.7481906219328
+-0.7402539078412523,-0.06971880518440121
+0.6466175431155564,0.6453230246459412
+1.8543372566620238,-2.0955195290039637
+0.06277653066719874,-0.03408829776793815
+0.2279103317646176,2.274676715129398
+-0.7993523433346643,0.1443758110212966
+0.17843646213645403,-0.09693619718680811
+-0.20711656201347328,1.9084765407162565
+-0.113162559294394,1.6461311584392715
+-0.009190242701892781,0.1642424600485714
+-0.40695477390119583,1.2118056703798659
+1.7690643651398887,-3.0189019057575592
+0.8018937709275499,1.0818345260835818
+0.6031209224558863,1.3836666637676107
+-0.2191183658931162,0.05796113959904531
+-0.3141459125863284,1.6947515938210729
+0.21012255909745908,-0.4786282963273907
+0.2488992388489395,-0.6282486884079518
+0.09632004565485686,-0.1861627767434179
+0.9746876227440122,-0.4412849042982151
+-0.7001988544091444,1.386636292138471
+0.843023998531703,-0.6605990411521827
+0.47676020372042915,1.4271786469931835
+0.7162966005281747,0.4154056469785329
+-0.18503720500735915,-0.13134110661167075
+-0.7036173262533023,0.2363096456177577
+0.31765093950283785,-0.4950013972855742
+0.15258741607828696,2.2045105755103935
+-0.738566316542688,1.1712930649710904
+-0.7734900861119869,1.7481906219328
+1.7602143431291706,-2.0786014890010738
+-0.19948382059022532,-0.36340334175368305
+1.8543372566620238,-2.0955195290039637
+-0.1040366218970381,0.040244429267036586
+0.2279103317646176,2.274676715129398
+-0.24962283208987193,0.7626582373184503
+1.8590277702450915,-2.711937518716222
+1.0488019148065915,0.7729336017921788
+-0.1543148544593278,1.3719522475871444
+-0.18296815519836018,0.4041298853632326
+1.0832422158175594,-0.1581985159290734
+1.7690643651398887,-3.0189019057575592
+-0.5392390187433584,1.1410895246080734
+1.7704165170998118,-2.4331241743989342
+-0.2191183658931162,0.05796113959904531
+0.6644830734451382,1.595035858031064
+-0.3204546183981527,0.6569816269228992
+0.43813343418540157,1.5034575802822665
+0.09632004565485686,-0.1861627767434179
+0.9746876227440122,-0.4412849042982151
+-0.7001988544091444,1.386636292138471
+0.9849874380315878,-0.6736493570372755
+0.1390559931249476,1.2663490093057825
+1.541267544517385,-0.6059865850829651
+-0.18503720500735915,-0.13134110661167075
+0.15649223675793594,2.006248855667522
+1.6779335548074186,-1.8182980562402564
+0.9311946030528484,0.961000004041758
+1.7600852672132152,-1.338350811280768
+0.5499212176859426,1.6039283941992162
+1.7602143431291706,-2.0786014890010738
+1.1833389257259934,-1.3471574064151355
+-0.29313761191317567,0.615496374075597
+0.5063399349420192,0.7579210877525233
+0.08054377350003833,2.070787012119701
+-0.10178598167821912,2.3494374821327693
+0.07906143584126207,-0.16395185857341155
+-0.8012808823983022,1.355003539556652
+-0.1543148544593278,1.3719522475871444
+-0.18296815519836018,0.4041298853632326
+0.20052649927526955,0.8853457612961604
+1.3246178816899792,-0.2377271034828033
+1.2656723913180685,-1.0904399153567366
+-0.4516711640433433,0.11387088726841976
+-0.2191183658931162,0.05796113959904531
+1.678565361420979,-1.8880946089411734
+1.0381041803716031,-0.8469828944465592
+0.43813343418540157,1.5034575802822665
+-0.5201806003395025,0.38752050620363915
+0.9746876227440122,-0.4412849042982151
+-0.8282654908911393,0.3389725091520287
+0.74324217528895,-0.3468317958245757
+0.6704930372722587,1.148870957803828
+1.541267544517385,-0.6059865850829651
+-0.18503720500735915,-0.13134110661167075
+1.7369584912066447,-1.8769610696089822
+1.36883829280633,-0.9950828123662447
+-0.3040868618906106,1.2948414956447862
+1.6132834969570429,-0.8022233745332364
+0.5499212176859426,1.6039283941992162
+1.7602143431291706,-2.0786014890010738
+1.1605753178646832,-0.9725815255934434
+0.6958138679603639,1.2108679020691022
+0.5063399349420192,0.7579210877525233
+0.09474980887315862,2.141842306975746
+-0.10178598167821912,2.3494374821327693
+0.046002359336260734,1.1047342631800972
+0.21797170322554849,1.6039924808106367
+0.6032569359577622,1.6654479119940624
+-0.6762531379127256,-0.275643818217267
+-1.1474086556287428,0.15787467350829754
+0.6645461665133696,1.6511264375596597
+0.4560364730017711,-0.5101856404943474
+-0.4516711640433433,0.11387088726841976
+-0.2191183658931162,0.05796113959904531
+1.678565361420979,-1.8880946089411734
+1.0381041803716031,-0.8469828944465592
+0.43813343418540157,1.5034575802822665
+-0.5201806003395025,0.38752050620363915
+0.9746876227440122,-0.4412849042982151
+-0.8282654908911393,0.3389725091520287
+1.6636886897435899,-1.5239671512049262
+0.6704930372722587,1.148870957803828
+1.541267544517385,-0.6059865850829651
+-0.18503720500735915,-0.13134110661167075
+1.7369584912066447,-1.8769610696089822
+1.36883829280633,-0.9950828123662447
+-0.3040868618906106,1.2948414956447862
+0.6828256332362173,0.9003369100144446
+0.5499212176859426,1.6039283941992162
+0.990993310881449,0.6469086374959847
+1.1605753178646832,-0.9725815255934434
+-0.08502262551607853,0.1688321215073787
+-0.4186483101490449,1.2938548221190045
+-0.27115754493839567,0.9875500109444929
+-0.3384635672922257,0.7197335926680857
+0.1775943891740605,-0.4691999274582975
+0.3787145856439459,0.5084936016472043
+0.6032569359577622,1.6654479119940624
+1.7136853637472838,-2.1473823082261836
+0.03927932407770235,0.4134692726982722
+0.6645461665133696,1.6511264375596597
+0.5339106643760284,1.577797146115858
+1.2588605884999575,0.355406156804591
+-0.12881279738936946,0.25059961135441966
+1.678565361420979,-1.8880946089411734
+0.5581459114769733,1.524023444216612
+-0.6260548040550844,1.7222577095914082
+0.6190584100718841,1.7267400303146085
+0.9746876227440122,-0.4412849042982151
+-0.8282654908911393,0.3389725091520287
+1.1869593245697352,-1.021515197234065
+-0.39970974433568485,1.664985654385996
+1.541267544517385,-0.6059865850829651
+-0.18503720500735915,-0.13134110661167075
+1.7369584912066447,-1.8769610696089822
+1.36883829280633,-0.9950828123662447
+0.5358003424853817,-0.24575523822548123
+0.6828256332362173,0.9003369100144446
+0.7960064213653864,1.1126266912744258
+0.15285220647911835,-0.03973747912487152
+1.1605753178646832,-0.9725815255934434
+1.3610432849897933,-0.0842901407942599
+-0.4186483101490449,1.2938548221190045
+-0.27115754493839567,0.9875500109444929
+-0.3384635672922257,0.7197335926680857
+0.8556036051500572,0.7531955836249029
+0.3787145856439459,0.5084936016472043
+1.6363889643904082,-2.3638807902395715
+0.6148262154534025,-0.1955013630564744
+0.4637741724000928,1.9085429393926077
+0.5014629964644958,0.32793452867151696
+0.8106002855398591,-0.5841932455093004
+1.2588605884999575,0.355406156804591
+-0.12881279738936946,0.25059961135441966
+1.678565361420979,-1.8880946089411734
+0.7193365129325211,1.9366575926418952
+-0.6260548040550844,1.7222577095914082
+-0.3547141451917042,0.7493134111161591
+0.6638971279666309,1.5741626111938554
+-0.10805417156105723,1.1608407654471242
+0.9876645862449196,0.7559412808198647
+-0.39970974433568485,1.664985654385996
+1.6678873232674531,-2.165954990483643
+-0.18503720500735915,-0.13134110661167075
+-0.13988403354179357,0.9969942693063744
+-0.5060042185268339,1.078954550679585
+0.5358003424853817,-0.24575523822548123
+-0.7737558106804068,0.8090488424692676
+0.7960064213653864,1.1126266912744258
+0.6488501643481727,1.3845924661588316
+1.5215614391492123,-1.8697323847088887
+1.3610432849897933,-0.0842901407942599
+-0.4186483101490449,1.2938548221190045
+-0.27115754493839567,0.9875500109444929
+-0.3219868960005043,0.9135366985875116
+-0.13532516892177027,0.3903603724630462
+0.4295744136830384,-0.542922074437177
+1.6363889643904082,-2.3638807902395715
+0.6148262154534025,-0.1955013630564744
+0.4637741724000928,1.9085429393926077
+-0.4611334654860101,1.155782702198751
+0.8106002855398591,-0.5841932455093004
+1.2588605884999575,0.355406156804591
+-0.12881279738936946,0.25059961135441966
+1.678565361420979,-1.8880946089411734
+0.23312050085041747,0.04003998258724037
+0.4060537709463934,0.7814093763896994
+-0.3547141451917042,0.7493134111161591
+0.6638971279666309,1.5741626111938554
+0.8919309723998019,-0.33232617177391827
+0.9876645862449196,0.7559412808198647
+-0.39970974433568485,1.664985654385996
+-0.7412941655912556,0.07511661902303679
+1.5476980571445735,-1.8738336277340146
+1.169108963014239,-0.5494880045639163
+-0.5060042185268339,1.078954550679585
+0.5358003424853817,-0.24575523822548123
+1.0644118828667126,-1.360845405912082
+0.7960064213653864,1.1126266912744258
+0.3711599789875534,0.11355943503702626
+1.5215614391492123,-1.8697323847088887
+0.5572520592945952,0.10600265317128171
+-0.4186483101490449,1.2938548221190045
+-0.6534727819978858,0.5498392606918383
+-0.16788094019575506,2.103098659453414
+-0.13532516892177027,0.3903603724630462
+0.6225908452698639,-0.2532021680335341
+1.0105487821452699,1.0592640528561033
+-0.48237230530231723,1.6588423154788534
+0.4637741724000928,1.9085429393926077
+-0.4611334654860101,1.155782702198751
+0.8106002855398591,-0.5841932455093004
+0.3437078799557153,0.02205738427300502
+-0.12881279738936946,0.25059961135441966
+1.678565361420979,-1.8880946089411734
+-0.42345793478746657,0.859219560864061
+0.22864308093926478,0.003975640589536755
+-0.3547141451917042,0.7493134111161591
+-0.5573687956630493,1.3217190632624432
+0.27127857674019595,2.0091650882612333
+0.9876645862449196,0.7559412808198647
+-0.6377096412921925,-0.1255616310761165
+-0.7412941655912556,0.07511661902303679
+0.7563371390598115,0.0861910534187034
+1.169108963014239,-0.5494880045639163
+1.559442388053789,-2.0418210104909855
+0.5358003424853817,-0.24575523822548123
+1.0644118828667126,-1.360845405912082
+1.648497283620983,-1.5161818667065474
+-0.15482549483924504,2.2888601591745084
+-0.26254046641240625,1.9320992523124776
+0.05045391741275357,0.6665172367744472
+0.1193628560410076,2.243104979828651
+-0.6534727819978858,0.5498392606918383
+-0.16788094019575506,2.103098659453414
+-0.13532516892177027,0.3903603724630462
+0.6225908452698639,-0.2532021680335341
+-0.3359327704501455,1.5663407798985423
+0.3154252249871296,1.4288341072902075
+0.564522867381941,0.03839270640110648
+0.587786384849223,1.7708263697806172
+0.8106002855398591,-0.5841932455093004
+0.9143655457604907,0.8322847399891071
+0.7422418851813647,-0.8392350677730767
+1.678565361420979,-1.8880946089411734
+-0.42345793478746657,0.859219560864061
+0.22864308093926478,0.003975640589536755
+-0.694980907744597,1.3174803686219643
+0.0044757651646786245,1.7509915264753109
+1.416569050254513,-0.1667307196380664
+0.9876645862449196,0.7559412808198647
+-0.6377096412921925,-0.1255616310761165
+-0.7412941655912556,0.07511661902303679
+0.7563371390598115,0.0861910534187034
+0.8808596912310804,1.4795048943962985
+1.559442388053789,-2.0418210104909855
+1.3453455529570835,-0.18646456018737328
+0.6961337622012278,-0.12343133766396203
+1.648497283620983,-1.5161818667065474
+-0.6985509815006002,0.07442527335898758
+-0.26254046641240625,1.9320992523124776
+0.05045391741275357,0.6665172367744472
+0.1193628560410076,2.243104979828651
+-0.6534727819978858,0.5498392606918383
+-0.16788094019575506,2.103098659453414
+-0.4026940820222755,1.7541831877966592
+0.6225908452698639,-0.2532021680335341
+-0.3359327704501455,1.5663407798985423
+0.8760163559915657,-0.47591691552502047
+1.3285391737135308,-0.5759763243692402
+0.1400542402908473,1.8635251189215098
+0.10165455472283547,-0.275484549646829
+0.9143655457604907,0.8322847399891071
+1.1717304017565393,-0.6085181247075092
+1.678565361420979,-1.8880946089411734
+-0.42345793478746657,0.859219560864061
+-0.8200986226756357,1.2566457581275436
+1.52212372056922,-0.521671956280855
+1.3234086544195482,-0.7566204946922315
+1.3102784209544223,-0.8064925810260182
+0.9876645862449196,0.7559412808198647
+-0.6377096412921925,-0.1255616310761165
+-0.7412941655912556,0.07511661902303679
+0.4189816289888445,1.4233809974470506
+0.09219159689365625,0.19960343600142946
+1.559442388053789,-2.0418210104909855
+1.3453455529570835,-0.18646456018737328
+0.4290388541746429,-0.311900894425089
+1.648497283620983,-1.5161818667065474
+-0.6985509815006002,0.07442527335898758
+-0.26254046641240625,1.9320992523124776
+0.05045391741275357,0.6665172367744472
+0.5888657373602586,-0.4870436515475405
+-0.14927546954897436,1.127387191901988
+-0.16788094019575506,2.103098659453414
+-0.6290019962687908,0.7921567852477119
+0.3600365098518069,1.170297182535415
+-0.3359327704501455,1.5663407798985423
+-0.0949164295951892,0.7021146123391256
+1.2998926596789695,-0.6745643406230093
+0.3074461321667088,0.15139820888619815
+0.10165455472283547,-0.275484549646829
+0.9143655457604907,0.8322847399891071
+1.1717304017565393,-0.6085181247075092
+1.678565361420979,-1.8880946089411734
+-0.42345793478746657,0.859219560864061
+-0.6649248959590314,0.3592628494715377
+1.2479148177651476,-0.11223507218726653
+1.5306213292746023,-1.5973779459293396
+-0.2922352557222934,1.420349035486943
+0.9876645862449196,0.7559412808198647
+-0.7689080948938223,1.1982320273145173
+-0.7412941655912556,0.07511661902303679
+0.4189816289888445,1.4233809974470506
+-0.6254930788554166,0.4358108919900645
+1.559442388053789,-2.0418210104909855
+1.558508150831843,-2.319799360085433
+-0.27240456707577554,0.9857378980636416
+1.3895683865939386,-0.5759899325821521
+-0.6541405713142582,1.1110962250761687
+-0.26254046641240625,1.9320992523124776
+1.7688283353368435,-2.2497296243013074
+-0.203351944229609,1.599614988056711
+-0.14927546954897436,1.127387191901988
+-0.16788094019575506,2.103098659453414
+1.2605875380606029,-0.6092558893095629
+0.19547703193802335,0.31274228742355836
+-0.29639681313600547,-0.48247855698630937
+-0.0949164295951892,0.7021146123391256
+0.45460378823879577,0.7250567557418831
+0.9749513883121972,0.560745132531547
+0.14328272596699754,1.633472737868579
+0.9143655457604907,0.8322847399891071
+1.1717304017565393,-0.6085181247075092
+1.678565361420979,-1.8880946089411734
+-0.42345793478746657,0.859219560864061
+0.1683965683037506,2.171936819619882
+1.695360404780069,-1.728288624709687
+0.4625930763070169,-0.36944877402126297
+-0.2922352557222934,1.420349035486943
+-0.3702892980907572,1.5973433578297007
+-0.1844729224378776,2.0608351129102953
+-0.7412941655912556,0.07511661902303679
+0.05448566812781068,1.2395514167283512
+-0.6254930788554166,0.4358108919900645
+1.559442388053789,-2.0418210104909855
+1.558508150831843,-2.319799360085433
+-0.27240456707577554,0.9857378980636416
+-0.3634171416445362,2.0674176943424896
+-0.6541405713142582,1.1110962250761687
+1.331458635685729,-0.12865961910173396
+1.7688283353368435,-2.2497296243013074
+0.7363694670166809,-0.14374251656482284
+-0.14927546954897436,1.127387191901988
+0.9210217875698258,0.7785776521004814
+0.08153604452661911,0.5301375675326239
+-0.4611526784596138,-0.27931519919272374
+0.047492993100796965,1.4343782980445083
+-0.0949164295951892,0.7021146123391256
+0.45460378823879577,0.7250567557418831
+0.0260969526503253,1.6793456977628913
+0.14328272596699754,1.633472737868579
+1.5017870171726502,-1.7524220736763971
+1.1717304017565393,-0.6085181247075092
+1.678565361420979,-1.8880946089411734
+-0.42345793478746657,0.859219560864061
+0.1683965683037506,2.171936819619882
+1.3242755587155068,-0.49754809070398615
+0.4625930763070169,-0.36944877402126297
+-0.00858016728053912,0.08333138442415144
+-0.3702892980907572,1.5973433578297007
+-0.1844729224378776,2.0608351129102953
+-0.7412941655912556,0.07511661902303679
+0.05448566812781068,1.2395514167283512
+-0.07772438043028275,0.7470233526923953
+0.7076037512450166,-0.02638992132084017
+1.558508150831843,-2.319799360085433
+1.6944539140139232,-2.047727606518067
+-0.3634171416445362,2.0674176943424896
+-0.6541405713142582,1.1110962250761687
+-0.0926318567629163,0.39958669297240856
+1.3058834477173389,-1.4355479612121689
+0.5629236189734015,-0.48505973387107837
+0.7538993496960096,-0.5967050972234229
+0.9210217875698258,0.7785776521004814
+-0.020041811864123404,2.2892323958308833
+-0.4611526784596138,-0.27931519919272374
+0.047492993100796965,1.4343782980445083
+0.17842414256763744,0.005137231437328582
+1.0280142952647258,-0.9516628868911707
+0.0260969526503253,1.6793456977628913
+0.19350350763907473,1.3246224549480448
+0.5645383932163711,1.3314342740717615
+-0.35327440299397256,1.9935029070748629
+-0.2839168934288952,0.42639512967291116
+-0.38708064151726346,1.0827839382139546
+0.1683965683037506,2.171936819619882
+1.3242755587155068,-0.49754809070398615
+0.4625930763070169,-0.36944877402126297
+-0.00858016728053912,0.08333138442415144
+-0.03951907070759836,1.7380814618181994
+-0.1844729224378776,2.0608351129102953
+-0.7412941655912556,0.07511661902303679
+1.4506305480943535,-1.7183123289325972
+2.049011776680002,-3.885240303795792
+0.21259473189614453,1.8513382450123417
+1.164225293666243,-1.2444088086312202
+1.6944539140139232,-2.047727606518067
+-0.5523404983237298,1.4615082781560962
+-0.6541405713142582,1.1110962250761687
+-0.5355865329262645,1.1766808872225885
+-0.5060011070654636,1.462951285162123
+0.5629236189734015,-0.48505973387107837
+0.7538993496960096,-0.5967050972234229
+0.9210217875698258,0.7785776521004814
+-0.020041811864123404,2.2892323958308833
+-0.4611526784596138,-0.27931519919272374
+0.047492993100796965,1.4343782980445083
+0.17842414256763744,0.005137231437328582
+1.0280142952647258,-0.9516628868911707
+0.0260969526503253,1.6793456977628913
+1.8013073059060742,-2.118547277802682
+1.4802808490322479,-0.91786447082199
+-0.36125187694292493,1.5521323575295785
+-0.2839168934288952,0.42639512967291116
+-0.8852132304485173,0.7928920330793104
+0.1683965683037506,2.171936819619882
+1.3242755587155068,-0.49754809070398615
+0.4625930763070169,-0.36944877402126297
+-0.00858016728053912,0.08333138442415144
+-0.03951907070759836,1.7380814618181994
+-0.1844729224378776,2.0608351129102953
+1.8047754883325178,-2.349521344422179
+-8.04155332357892e-05,1.7203023457708577
+2.049011776680002,-3.885240303795792
+0.21259473189614453,1.8513382450123417
+1.164225293666243,-1.2444088086312202
+1.6944539140139232,-2.047727606518067
+-0.5523404983237298,1.4615082781560962
+-0.6541405713142582,1.1110962250761687
+-0.5355865329262645,1.1766808872225885
+-0.5060011070654636,1.462951285162123
+0.5629236189734015,-0.48505973387107837
+0.7538993496960096,-0.5967050972234229
+0.9210217875698258,0.7785776521004814
+-0.020041811864123404,2.2892323958308833
+-0.4611526784596138,-0.27931519919272374
+0.047492993100796965,1.4343782980445083
+0.17842414256763744,0.005137231437328582
+1.0280142952647258,-0.9516628868911707
+0.0260969526503253,1.6793456977628913
+1.0858095816563167,0.6626876169431697
+1.4802808490322479,-0.91786447082199
+0.7893466723029454,-1.0930412354876706
+1.402217651404589,-0.7162659293908696
+-0.8852132304485173,0.7928920330793104
+0.1683965683037506,2.171936819619882
+1.3242755587155068,-0.49754809070398615
+0.4625930763070169,-0.36944877402126297
+-0.00858016728053912,0.08333138442415144
+-0.08051271179286079,0.6433099915987023
+0.7570099234278429,-0.059003847085585814
+1.8047754883325178,-2.349521344422179
+-0.5696748674574812,1.1835388614880906
+2.049011776680002,-3.885240303795792
+-0.1340695129610993,1.8552971231921103
+1.164225293666243,-1.2444088086312202
+1.2235789529828902,-0.41127816244134774
+1.896086659930467,-2.229993573731642
+0.7861745245252145,-0.31893638852096023
+-0.015397451280685731,0.453332269391251
+-0.5060011070654636,1.462951285162123
+-0.5116466608093371,0.6651642893721119
+-0.19498041019812984,0.1780096905284632
+0.9210217875698258,0.7785776521004814
+-0.020041811864123404,2.2892323958308833
+1.8420691729261554,-2.749512855928177
+0.047492993100796965,1.4343782980445083
+0.17842414256763744,0.005137231437328582
+0.6223020259712988,-0.17851253791089117
+0.0260969526503253,1.6793456977628913
+1.0858095816563167,0.6626876169431697
+1.4802808490322479,-0.91786447082199
+0.13517996407676663,-0.6024790635235079
+1.402217651404589,-0.7162659293908696
+0.2794340083638295,1.9901751700011274
+0.1683965683037506,2.171936819619882
+-0.3300913375073545,2.207897094155329
+0.4625930763070169,-0.36944877402126297
+-0.00858016728053912,0.08333138442415144
+2.090443568378248,-3.449156543144909
+-0.9069586840961754,0.0990898498029773
+1.8047754883325178,-2.349521344422179
+-0.5696748674574812,1.1835388614880906
+-0.1808650588074966,0.8434372215254209
+-0.1340695129610993,1.8552971231921103
+1.2278229266851322,-0.5532786257985889
+0.009373857251201823,0.18596742609781836
+1.5001153424009246,-1.0625351012347855
+-0.07612947623552623,1.9694945283239909
+0.9835963896905404,0.6104015790396051
+-0.5060011070654636,1.462951285162123
+0.878105811133429,-0.32873571238269506
+-0.19498041019812984,0.1780096905284632
+0.9210217875698258,0.7785776521004814
+-0.020041811864123404,2.2892323958308833
+-0.4319740354494277,2.130403998425613
+1.4739374163951546,-1.602385913862028
+0.17842414256763744,0.005137231437328582
+0.6223020259712988,-0.17851253791089117
+0.0260969526503253,1.6793456977628913
+-0.46538385114128233,0.5751914537119884
+-0.17093538352464305,0.670175891061151
+0.6271824121778391,1.4071395735874614
+0.8560481018788929,1.2454598910212664
+-0.1826136832799037,0.21150770488268136
+0.1683965683037506,2.171936819619882
+-0.15180780229360996,1.8768370952456963
+1.1968142553287406,-1.2910145822388017
+-0.00858016728053912,0.08333138442415144
+0.7813074161284075,1.4989251615145975
+-0.9069586840961754,0.0990898498029773
+0.7769566774793111,-0.7543379122314388
+-0.5696748674574812,1.1835388614880906
+0.4743598715926189,2.0443061474242676
+0.8505562512504073,-0.5536412736818379
+1.2278229266851322,-0.5532786257985889
+0.29109081131322184,-0.14044277452018838
+1.5001153424009246,-1.0625351012347855
+-0.07612947623552623,1.9694945283239909
+1.3601608932047535,-1.9379171230035759
+-0.5060011070654636,1.462951285162123
+0.878105811133429,-0.32873571238269506
+-0.19498041019812984,0.1780096905284632
+-0.44787276233701845,0.46468520683310166
+1.021790191756107,-1.2129947473150318
+0.48273436305554573,0.44444119109152014
+1.4739374163951546,-1.602385913862028
+0.17842414256763744,0.005137231437328582
+0.44313170028109583,-0.09572884844169818
+0.0260969526503253,1.6793456977628913
+0.2185408044726837,0.46493661341836023
+-0.17093538352464305,0.670175891061151
+0.6271824121778391,1.4071395735874614
+0.8560481018788929,1.2454598910212664
+-0.1826136832799037,0.21150770488268136
+0.1683965683037506,2.171936819619882
+1.0726544716413204,-0.6401733502348887
+0.09680752322005948,0.1500686176872839
+-0.566380704739904,0.5678641978399777
+0.14062756540697396,2.1763065885138815
+-0.9069586840961754,0.0990898498029773
+0.7769566774793111,-0.7543379122314388
+-0.676742967912933,0.8834260139979178
+-0.12214633037647493,2.228262845905944
+1.5876673598415751,-1.2920532766600998
+1.2278229266851322,-0.5532786257985889
+0.853796685686747,0.05535397833472902
+0.36337207706291963,2.330136003398602
+1.2638135742824346,-0.6808777889122442
+1.3601608932047535,-1.9379171230035759
+-0.5060011070654636,1.462951285162123
+-0.1438108828444459,0.030823990992137423
+-0.19498041019812984,0.1780096905284632
+-0.44787276233701845,0.46468520683310166
+1.2462768052192479,-0.7797535764567307
+0.48273436305554573,0.44444119109152014
+0.5770645896522135,0.038336996725089945
+0.17842414256763744,0.005137231437328582
+0.44313170028109583,-0.09572884844169818
+0.4212933252411263,-0.20812127550665643
+1.0289277529300782,0.37631794848730205
+1.0582653882686166,0.8134861718838841
+0.6271824121778391,1.4071395735874614
+0.8560481018788929,1.2454598910212664
+0.518038862888999,1.7209763906265656
+0.1683965683037506,2.171936819619882
+-0.7184702782669954,1.8135406415437372
+0.09680752322005948,0.1500686176872839
+0.8195714544035863,0.14742921901883332
+0.14062756540697396,2.1763065885138815
+1.3424963934131373,-1.3990451765841898
+1.0680344084989555,-0.48907948206787466
+-0.676742967912933,0.8834260139979178
+1.5080757730500367,-1.9307635833988785
+1.5876673598415751,-1.2920532766600998
+-0.22582518439889548,2.2056817776478477
+1.2902938363428087,0.5254559454662824
+1.4032896513246154,-0.6701771676127816
+1.2638135742824346,-0.6808777889122442
+1.97440850229908,-3.774040371149982
+-0.5060011070654636,1.462951285162123
+-0.1438108828444459,0.030823990992137423
+-0.19498041019812984,0.1780096905284632
+-0.44787276233701845,0.46468520683310166
+0.8693776552074871,-0.8328672916491996
+-0.2472533879914226,0.9776154883240104
+0.5770645896522135,0.038336996725089945
+0.17842414256763744,0.005137231437328582
+-0.4322475204422065,1.3098073492428735
+0.6321652758705276,1.639270176647094
+1.0289277529300782,0.37631794848730205
+1.0582653882686166,0.8134861718838841
+0.40504289886582306,1.2530838322090028
+0.8560481018788929,1.2454598910212664
+0.518038862888999,1.7209763906265656
+0.41155157249589036,0.20454185835052885
+1.014961219535289,-1.0292468614343386
+0.09680752322005948,0.1500686176872839
+-0.42210658625507486,-0.3579435832648805
+-0.3589498157957206,1.0284262467410328
+1.611458536666871,-1.663152181135711
+0.08623050105927972,0.22452337610331394
+-0.676742967912933,0.8834260139979178
+1.5080757730500367,-1.9307635833988785
+1.5876673598415751,-1.2920532766600998
+-0.22582518439889548,2.2056817776478477
+-0.4258078138185887,0.9429895275126006
+1.4032896513246154,-0.6701771676127816
+1.365638342679516,-0.8741794701475263
+1.97440850229908,-3.774040371149982
+-0.5060011070654636,1.462951285162123
+-0.05444313377583759,0.34900492775404357
+0.5513064808995283,-0.6195641781321617
+-0.44787276233701845,0.46468520683310166
+-0.2543386453055729,0.1412933651969342
+0.29663554456750607,1.7677558406829164
+-0.24209355202522453,2.2573743621804887
+0.17842414256763744,0.005137231437328582
+-0.4322475204422065,1.3098073492428735
+0.5589516730832023,2.0259346958657725
+-0.33589214502322634,1.2937091415875206
+1.0582653882686166,0.8134861718838841
+1.45875860545943,-0.8831904075931521
+0.8560481018788929,1.2454598910212664
+-0.18801147563292148,-0.5210353130864044
+-0.653883853078537,1.2012581211895503
+1.014961219535289,-1.0292468614343386
+0.17043715952657235,1.8833188831899237
+-0.42210658625507486,-0.3579435832648805
+0.9986411295414497,1.1732747685679543
+1.611458536666871,-1.663152181135711
+0.08623050105927972,0.22452337610331394
+-0.676742967912933,0.8834260139979178
+1.5080757730500367,-1.9307635833988785
+1.419972914338497,-1.3824202370186662
+-0.22582518439889548,2.2056817776478477
+0.05035979923521278,2.0727169667385543
+1.4032896513246154,-0.6701771676127816
+1.365638342679516,-0.8741794701475263
+1.8305986885029761,-1.7748783553821417
+1.829948959621308,-1.9642928230546164
+-0.45337111966109295,0.3864107431894086
+-0.24969093943718823,1.9109124264814679
+-0.44787276233701845,0.46468520683310166
+0.012703774929543991,2.161944448335232
+1.201179666376245,-1.1774209081838007
+-0.24209355202522453,2.2573743621804887
+0.17842414256763744,0.005137231437328582
+-0.16748456487907282,0.223786466744042
+0.5589516730832023,2.0259346958657725
+-0.3754834571606305,1.6073704296580016
+-0.07200193834022056,-0.12571110353073323
+1.45875860545943,-0.8831904075931521
+0.8560481018788929,1.2454598910212664
+-0.18801147563292148,-0.5210353130864044
+-0.653717739101131,1.364784971033546
+1.014961219535289,-1.0292468614343386
+0.6596520727062192,-0.09180569232777314
+-0.42210658625507486,-0.3579435832648805
+0.9986411295414497,1.1732747685679543
+1.611458536666871,-1.663152181135711
+-0.6484737677879658,0.3347008186117981
+-0.676742967912933,0.8834260139979178
+1.5080757730500367,-1.9307635833988785
+1.419972914338497,-1.3824202370186662
+0.5706071045336424,0.555272753825821
+0.05035979923521278,2.0727169667385543
+0.7759017598182336,0.5126640000239837
+1.044220964054154,0.21390909912651168
+1.1555325672747911,-1.7649516356069497
+-0.2806692589751838,1.0336094206343038
+-0.45337111966109295,0.3864107431894086
+-0.6817039397861747,1.6844217748650405
+1.03202744057318,-0.3339293731069196
+0.012703774929543991,2.161944448335232
+0.8151239517604313,-0.09776060376309881
+1.470101668259923,-1.9667809946834791
+0.18673238457165187,0.060390723556929315
+-0.16748456487907282,0.223786466744042
+0.5998165365314183,-0.7379173928666377
+0.07631832147245399,1.2102560852575943
+1.3667604942138898,-0.9309225505565494
+0.5240929383760455,-0.5683773720265595
+0.8560481018788929,1.2454598910212664
+-0.18801147563292148,-0.5210353130864044
+-0.653717739101131,1.364784971033546
+1.014961219535289,-1.0292468614343386
+0.6596520727062192,-0.09180569232777314
+1.0170955460695992,-0.9863842871219077
+0.9986411295414497,1.1732747685679543
+1.611458536666871,-1.663152181135711
+-0.6484737677879658,0.3347008186117981
+-0.676742967912933,0.8834260139979178
+0.8039337191948972,-0.5790616556411164
+-0.900223670823226,1.2871803665381494
+1.5344002740853164,-1.356724666093747
+-1.0048946074728877,0.7262481383421638
+0.2398399879119757,-0.09532101364460366
+-0.49502863939288044,0.753021657731093
+1.5471923392136424,-0.37363058868793053
+1.4574849268683634,-0.5198102005382363
+-0.45337111966109295,0.3864107431894086
+0.36503803293711623,0.22153442220610042
+-0.6779313057303834,0.6887134403505675
+0.012703774929543991,2.161944448335232
+-0.14271278489002603,0.3186142147177592
+1.470101668259923,-1.9667809946834791
+0.18673238457165187,0.060390723556929315
+-0.3614874516097657,0.8454574997861269
+1.0676214600925473,-0.953900702644161
+0.07631832147245399,1.2102560852575943
+-0.07743070471189195,-0.17211092451957843
+0.676610343037362,-0.31749210353637136
+0.8560481018788929,1.2454598910212664
+-0.23847104209103498,0.32847852253421356
+-0.653717739101131,1.364784971033546
+1.014961219535289,-1.0292468614343386
+0.6596520727062192,-0.09180569232777314
+-0.43135857474705436,1.7919603691573753
+0.9986411295414497,1.1732747685679543
+1.611458536666871,-1.663152181135711
+1.5471224224980025,-1.5064532537144681
+0.1592616549711257,-0.012800507556092258
+0.8039337191948972,-0.5790616556411164
+-0.900223670823226,1.2871803665381494
+-1.0915171619674218,0.8912761077706133
+-1.0048946074728877,0.7262481383421638
+0.6180881539466245,-0.497277294432257
+-0.34007836784764356,0.12257439352686689
+1.5471923392136424,-0.37363058868793053
+1.4574849268683634,-0.5198102005382363
+-0.45337111966109295,0.3864107431894086
+0.36503803293711623,0.22153442220610042
+-0.6779313057303834,0.6887134403505675
+-0.47421250574439067,0.3871264662411763
+1.0620890755021866,-0.7608528295200645
+1.470101668259923,-1.9667809946834791
+0.18673238457165187,0.060390723556929315
+-0.3402127123214089,1.2801305061325328
+1.0676214600925473,-0.953900702644161
+-0.1888139570229667,-0.3569377989417827
+1.1313716962130744,-0.6158163692425815
+0.42237943552492174,-0.629505746398559
+0.8560481018788929,1.2454598910212664
+1.758939015590911,-1.5806130452666451
+-0.653717739101131,1.364784971033546
+-0.16738732364375733,1.574671531299638
+0.1660660389033242,0.2203758734389382
+-0.43135857474705436,1.7919603691573753
+0.9986411295414497,1.1732747685679543
+0.09589982423914578,0.30987010378808805
+1.3945963459933544,-0.6723773274289201
+0.1592616549711257,-0.012800507556092258
+0.8039337191948972,-0.5790616556411164
+-0.7197055651688149,0.9585378994437348
+-0.9285477617875713,0.9089988174416146
+0.3255946547558935,-0.11781879011335936
+0.6180881539466245,-0.497277294432257
+-0.34007836784764356,0.12257439352686689
+0.9968231281154774,-0.4958382341235276
+-0.6268218068733374,0.202411255374029
+0.18562970895410866,0.34686759352464536
+0.36503803293711623,0.22153442220610042
+-0.6779313057303834,0.6887134403505675
+-0.47421250574439067,0.3871264662411763
+0.7239897189485109,1.2332064820026398
+1.470101668259923,-1.9667809946834791
+0.24628792457073465,-0.20256198041173185
+-0.3402127123214089,1.2801305061325328
+1.0676214600925473,-0.953900702644161
+-0.1888139570229667,-0.3569377989417827
+-0.2917819438680248,1.2817877292921822
+-0.20075914160271047,0.02105644656396599
+0.8560481018788929,1.2454598910212664
+1.758939015590911,-1.5806130452666451
+-0.653717739101131,1.364784971033546
+0.8697119076180735,0.042640080807585606
+-0.5307555121378609,0.878834475764618
+0.15559284481746488,0.7955885583620388
+0.9986411295414497,1.1732747685679543
+-0.34891023139132804,1.2969737924439435
+1.3945963459933544,-0.6723773274289201
+0.1592616549711257,-0.012800507556092258
+-0.38762963895973856,0.07214436443295591
+-0.7197055651688149,0.9585378994437348
+0.31985459555078566,0.7730934139627065
+0.09110433290737147,-0.06331726307144198
+0.7247632084824016,-0.5235896745128006
+0.4231842845602374,0.0343762059280428
+0.44517181348071255,-0.4154384527304613
+-0.6268218068733374,0.202411255374029
+1.229753834999006,-1.1310821655439791
+0.36503803293711623,0.22153442220610042
+-0.6779313057303834,0.6887134403505675
+0.6903936746435089,1.8161866885818965
+1.2410802909801688,-0.43934295187340566
+1.470101668259923,-1.9667809946834791
+0.24628792457073465,-0.20256198041173185
+-0.3402127123214089,1.2801305061325328
+1.0676214600925473,-0.953900702644161
+-0.1888139570229667,-0.3569377989417827
+-0.2917819438680248,1.2817877292921822
+-0.20075914160271047,0.02105644656396599
+0.8560481018788929,1.2454598910212664
+-0.5005008192975167,0.8471261919437952
+-0.653717739101131,1.364784971033546
+0.8697119076180735,0.042640080807585606
+1.4603238714233449,-0.5107013291180053
+1.6818733446126282,-0.8731185428794586
+-1.035075249964916,0.10447266533829588
+-0.34891023139132804,1.2969737924439435
+-0.46273882143910516,0.10466625304498707
+-0.6504934219816754,1.1494285667040554
+-0.38762963895973856,0.07214436443295591
+-0.7197055651688149,0.9585378994437348
+0.46398498163979873,1.890751904404921
+0.09110433290737147,-0.06331726307144198
+0.7247632084824016,-0.5235896745128006
+0.9630563746556771,-0.7650337916122629
+0.1431002609750949,0.3303314142604814
+-0.7102132572406104,0.5846225012458358
+0.12351791878106355,1.7866198410175345
+0.36503803293711623,0.22153442220610042
+1.0705817696190707,-0.12563727914217784
+0.6903936746435089,1.8161866885818965
+1.2410802909801688,-0.43934295187340566
+1.470101668259923,-1.9667809946834791
+-0.7360537626419488,0.8917064267920487
+-0.3402127123214089,1.2801305061325328
+1.0676214600925473,-0.953900702644161
+0.7830467597320323,-0.23864136974679806
+-0.2917819438680248,1.2817877292921822
+0.6232864007632727,1.4844270470511347
+0.8560481018788929,1.2454598910212664
+-0.5005008192975167,0.8471261919437952
+-0.653717739101131,1.364784971033546
+1.648644789581698,-2.933857416306759
+0.06889792283331753,1.4716280042362795
+0.5561782001734908,1.7138838028573642
+-1.035075249964916,0.10447266533829588
+-0.34891023139132804,1.2969737924439435
+-0.46273882143910516,0.10466625304498707
+0.6088396995803338,-0.21457694015728723
+-0.38762963895973856,0.07214436443295591
+0.9317524179781731,-0.6474394915451013
+0.46398498163979873,1.890751904404921
+0.09110433290737147,-0.06331726307144198
+0.7247632084824016,-0.5235896745128006
+0.21105877693177244,-0.26412609623848576
+-0.5455010309569949,1.592695636436949
+-0.7102132572406104,0.5846225012458358
+0.05653762278498842,-0.3443878997620866
+0.8586931869727913,0.8618053175313726
+-0.6744327297493751,0.2714088110059659
+0.6903936746435089,1.8161866885818965
+1.2410802909801688,-0.43934295187340566
+1.470101668259923,-1.9667809946834791
+0.5414352357100004,-0.5779185963094464
+-0.3402127123214089,1.2801305061325328
+1.0676214600925473,-0.953900702644161
+0.7830467597320323,-0.23864136974679806
+0.015201297407221787,-0.008845047346208279
+0.6232864007632727,1.4844270470511347
+0.8560481018788929,1.2454598910212664
+-0.7570041582068748,0.007256452009163472
+-0.653717739101131,1.364784971033546
+1.648644789581698,-2.933857416306759
+0.06889792283331753,1.4716280042362795
+0.5561782001734908,1.7138838028573642
+-1.035075249964916,0.10447266533829588
+-0.34891023139132804,1.2969737924439435
+-0.46273882143910516,0.10466625304498707
+0.09855389501933876,-0.45369585908370536
+-0.38762963895973856,0.07214436443295591
+0.9317524179781731,-0.6474394915451013
+0.46398498163979873,1.890751904404921
+-0.09781874562385195,1.090031553670155
+0.7247632084824016,-0.5235896745128006
+0.21105877693177244,-0.26412609623848576
+-0.38073787267420645,0.9693531481974794
+-0.7102132572406104,0.5846225012458358
+0.19000013323282355,-0.2372890877021351
+0.8586931869727913,0.8618053175313726
+0.2989990028273048,-0.25226458753196
+0.6903936746435089,1.8161866885818965
+1.2410802909801688,-0.43934295187340566
+1.470101668259923,-1.9667809946834791
+0.5414352357100004,-0.5779185963094464
+-0.2620847095827641,0.3546476350859886
+1.0880978981479652,0.36601655329459964
+0.5325273832254788,1.4045593124216134
+0.015201297407221787,-0.008845047346208279
+0.6232864007632727,1.4844270470511347
+0.8560481018788929,1.2454598910212664
+-0.7570041582068748,0.007256452009163472
+-0.653717739101131,1.364784971033546
+1.648644789581698,-2.933857416306759
+1.0250225876447754,-0.23648365410959205
+0.5561782001734908,1.7138838028573642
+-1.035075249964916,0.10447266533829588
+-0.34891023139132804,1.2969737924439435
+-0.46273882143910516,0.10466625304498707
+0.09855389501933876,-0.45369585908370536
+-0.38762963895973856,0.07214436443295591
+0.9317524179781731,-0.6474394915451013
+0.46398498163979873,1.890751904404921
+-0.028743306007800895,-0.10204350366292753
+0.7247632084824016,-0.5235896745128006
+0.568066957697736,1.5819475099161493
+-0.38073787267420645,0.9693531481974794
+-0.7102132572406104,0.5846225012458358
+0.19000013323282355,-0.2372890877021351
+0.8586931869727913,0.8618053175313726
+-0.7358141301983867,0.5569046060173629
+1.5329510348138036,-0.6893921321414127
+1.2410802909801688,-0.43934295187340566
+1.470101668259923,-1.9667809946834791
+0.885327456242335,-0.637463291398158
+0.24496380952515223,-0.2407360450416153
+0.2527054228706625,0.0040614831643226434
+0.5325273832254788,1.4045593124216134
+0.015201297407221787,-0.008845047346208279
+0.6232864007632727,1.4844270470511347
+0.8560481018788929,1.2454598910212664
+-0.7570041582068748,0.007256452009163472
+-0.653717739101131,1.364784971033546
+1.648644789581698,-2.933857416306759
+-0.6743344800866293,0.06998200300253027
+0.27215822704042786,-0.544393046428275
+-1.035075249964916,0.10447266533829588
+-0.34891023139132804,1.2969737924439435
+-0.46273882143910516,0.10466625304498707
+0.09855389501933876,-0.45369585908370536
+-0.38762963895973856,0.07214436443295591
+0.9317524179781731,-0.6474394915451013
+0.46398498163979873,1.890751904404921
+1.1011852957597965,0.056712184449092484
+0.7247632084824016,-0.5235896745128006
+1.3338451794902588,-0.13259676409096643
+-0.38073787267420645,0.9693531481974794
+-0.7102132572406104,0.5846225012458358
+0.19000013323282355,-0.2372890877021351
+0.8586931869727913,0.8618053175313726
+-0.7358141301983867,0.5569046060173629
+1.5329510348138036,-0.6893921321414127
+1.2410802909801688,-0.43934295187340566
+1.470101668259923,-1.9667809946834791
+0.885327456242335,-0.637463291398158
+0.24496380952515223,-0.2407360450416153
+-0.8213093299268885,0.4419122298331175
+0.5325273832254788,1.4045593124216134
+0.015201297407221787,-0.008845047346208279
+0.6232864007632727,1.4844270470511347
+1.3201450450699133,-0.21709356904606958
+1.0169750922879004,0.10038438808837502
+-0.653717739101131,1.364784971033546
+1.648644789581698,-2.933857416306759
+-0.6743344800866293,0.06998200300253027
+-0.6091691982692902,0.38423606529184073
+-1.035075249964916,0.10447266533829588
+-0.34891023139132804,1.2969737924439435
+-0.46273882143910516,0.10466625304498707
+0.09855389501933876,-0.45369585908370536
+-0.44077683370081217,0.16107236344805506
+1.5081517330840886,-0.906564625272494
+0.046700626724631045,1.5005460748334054
+0.982778887092941,-0.8976035141559958
+0.7247632084824016,-0.5235896745128006
+1.3338451794902588,-0.13259676409096643
+-0.38073787267420645,0.9693531481974794
+-0.7102132572406104,0.5846225012458358
+0.19000013323282355,-0.2372890877021351
+0.8586931869727913,0.8618053175313726
+-0.16563186567562688,0.3679628107950725
+-0.8463638570206969,0.3601108023964531
+1.2410802909801688,-0.43934295187340566
+1.470101668259923,-1.9667809946834791
+0.6946349072455197,-0.18188884312751144
+0.24496380952515223,-0.2407360450416153
+-0.8213093299268885,0.4419122298331175
+0.7629943441772629,0.9411928443429046
+0.4120039631922038,1.5023268027806949
+0.14093054963489815,-0.29114795790119885
+-0.1619831356749758,2.096223228395942
+1.0169750922879004,0.10038438808837502
+0.05397878952304175,1.8294666004355045
+-0.28212843230031776,0.28231995147721883
+0.3651819172828039,0.7380003015265293
+-0.6091691982692902,0.38423606529184073
+0.24737854110569735,-0.10912380388979226
+-0.34891023139132804,1.2969737924439435
+-0.3707045208211575,-0.2164747842794983
+0.09855389501933876,-0.45369585908370536
+-0.716201381413078,0.45949514306499717
+0.7535060626452784,0.680294590613166
+-0.23332147927153302,0.027727820376580947
+1.081380462631003,0.9765534938261291
+0.021098911358077788,0.6521534769841301
+1.3338451794902588,-0.13259676409096643
+-0.7177382415721595,-0.033688372997397076
+-0.1779411481128249,0.5779418998722117
+0.9749498834078303,0.7536770822452921
+0.8586931869727913,0.8618053175313726
+-0.008869612123593162,-0.2500830540933353
+-0.8463638570206969,0.3601108023964531
+1.2410802909801688,-0.43934295187340566
+1.470101668259923,-1.9667809946834791
+0.6946349072455197,-0.18188884312751144
+0.7865410629519389,1.3175597819295408
+-0.8213093299268885,0.4419122298331175
+0.7629943441772629,0.9411928443429046
+0.4120039631922038,1.5023268027806949
+0.14093054963489815,-0.29114795790119885
+-0.1619831356749758,2.096223228395942
+1.0169750922879004,0.10038438808837502
+0.05397878952304175,1.8294666004355045
+-0.28212843230031776,0.28231995147721883
+0.3651819172828039,0.7380003015265293
+-0.6091691982692902,0.38423606529184073
+0.0029362350246633986,2.309511900409696
+0.051018134835997375,0.2457333629567071
+-0.3707045208211575,-0.2164747842794983
+0.8080434002128011,-0.8263617358705012
+0.5348590594293052,-0.07408434789687901
+-0.002534577183773923,0.6445225359785992
+-0.4819979149120479,0.0743695694068609
+1.081380462631003,0.9765534938261291
+0.48200106232051704,-0.43631023211897685
+1.3338451794902588,-0.13259676409096643
+-0.6215472613529156,0.7259943737261566
+-0.1779411481128249,0.5779418998722117
+0.30877015891423987,0.006696173687606527
+1.6022426581817353,-0.9212579708265844
+-0.008869612123593162,-0.2500830540933353
+-0.8463638570206969,0.3601108023964531
+-0.09153508571804297,1.5510436249637771
+1.470101668259923,-1.9667809946834791
+0.7194413769812384,-0.935225327541186
+0.7865410629519389,1.3175597819295408
+-0.8213093299268885,0.4419122298331175
+1.6992141214023981,-2.3108521476770645
+0.4120039631922038,1.5023268027806949
+0.14093054963489815,-0.29114795790119885
+-0.1619831356749758,2.096223228395942
+-0.834658767323253,0.7922996385656426
+0.05397878952304175,1.8294666004355045
+-0.28212843230031776,0.28231995147721883
+-0.03753207015102218,0.03709220885653641
+-0.6091691982692902,0.38423606529184073
+0.0029362350246633986,2.309511900409696
+0.051018134835997375,0.2457333629567071
+1.4830294837339855,-1.2386941163243563
+0.8080434002128011,-0.8263617358705012
+0.5348590594293052,-0.07408434789687901
+-0.29809702555588224,0.0008332164284721444
+-0.4819979149120479,0.0743695694068609
+1.081380462631003,0.9765534938261291
+0.1449744080759548,1.0733891550835675
+1.3338451794902588,-0.13259676409096643
+-0.6215472613529156,0.7259943737261566
+-0.1779411481128249,0.5779418998722117
+-0.10975096092541248,1.965697784061367
+1.6022426581817353,-0.9212579708265844
+-0.4388535722910355,0.96731794515359
+-0.153064400730859,2.1194492089491415
+-0.5911644416483638,-0.2637949781839295
+1.470101668259923,-1.9667809946834791
+-0.046652626216363915,2.214501086473701
+0.7865410629519389,1.3175597819295408
+-0.7515211867053817,0.3519735683884471
+1.6992141214023981,-2.3108521476770645
+0.4120039631922038,1.5023268027806949
+0.14093054963489815,-0.29114795790119885
+-0.7258628685194892,-0.7195415562725395
+1.2942107832076932,0.06746051044681317
+0.05397878952304175,1.8294666004355045
+0.39551650011188266,0.4555753049865182
+-0.20814594277965565,-0.08209906002727499
+-0.6091691982692902,0.38423606529184073
+0.0029362350246633986,2.309511900409696
+0.051018134835997375,0.2457333629567071
+1.4830294837339855,-1.2386941163243563
+0.8080434002128011,-0.8263617358705012
+0.5348590594293052,-0.07408434789687901
+-0.309695588686708,1.8147347403330056
+-0.7540147311338374,0.9281433890273736
+1.081380462631003,0.9765534938261291
+0.1449744080759548,1.0733891550835675
+1.3338451794902588,-0.13259676409096643
+-0.6215472613529156,0.7259943737261566
+0.5111907720850086,1.1421332168146623
+-0.10975096092541248,1.965697784061367
+1.1120368478740172,-0.5733572324546443
+-0.4388535722910355,0.96731794515359
+1.2332950577354544,-1.604368924259763
+-0.5911644416483638,-0.2637949781839295
+1.470101668259923,-1.9667809946834791
+-0.046652626216363915,2.214501086473701
+-0.3208657284809635,2.090222039237265
+-0.04189229870044536,1.6926918313072163
+1.6992141214023981,-2.3108521476770645
+0.4120039631922038,1.5023268027806949
+0.14093054963489815,-0.29114795790119885
+1.8109049304647447,-2.6193506818738843
+1.2942107832076932,0.06746051044681317
+0.2987296661286323,-0.21333864508228187
+0.39551650011188266,0.4555753049865182
+-0.20814594277965565,-0.08209906002727499
+-0.6091691982692902,0.38423606529184073
+0.0029362350246633986,2.309511900409696
+0.051018134835997375,0.2457333629567071
+-0.6993822502518078,1.2841936646973477
+0.8080434002128011,-0.8263617358705012
+0.1680875139639057,1.8165603203818983
+-0.309695588686708,1.8147347403330056
+-0.7540147311338374,0.9281433890273736
+1.081380462631003,0.9765534938261291
+0.1449744080759548,1.0733891550835675
+1.3338451794902588,-0.13259676409096643
+0.834041478019732,0.6137178389918326
+0.5111907720850086,1.1421332168146623
+1.229960738702296e-05,-0.05638363165854777
+0.5570854242876586,-0.37228047677282816
+1.8359243240247527,-2.6240769668420523
+0.6686820374018354,1.1300688413451323
+-0.5911644416483638,-0.2637949781839295
+1.470101668259923,-1.9667809946834791
+-0.046652626216363915,2.214501086473701
+-0.3208657284809635,2.090222039237265
+-0.04189229870044536,1.6926918313072163
+-0.5466758448364721,0.690468074019571
+0.6648164358575676,1.3712412029985868
+0.14093054963489815,-0.29114795790119885
+1.8109049304647447,-2.6193506818738843
+1.2942107832076932,0.06746051044681317
+-0.044530312706156844,0.11875840073737978
+0.4087337676430649,1.4820351331698527
+-0.4497270582461355,1.0914667559753082
+-0.6091691982692902,0.38423606529184073
+0.30179740482741635,1.766736463852819
+-0.6710370712387331,-0.0006764641752606826
+-0.6993822502518078,1.2841936646973477
+0.8080434002128011,-0.8263617358705012
+0.9121963994165492,-1.0902660393095358
+-0.309695588686708,1.8147347403330056
+0.6652788430263039,-0.7865285797047318
+-0.23993690941173607,0.130573677628254
+0.3457793997139883,1.28887211316075
+1.3338451794902588,-0.13259676409096643
+0.027604698748650125,-0.31848358951963845
+0.5111907720850086,1.1421332168146623
+0.787698850870685,1.450117957445499
+0.07555377452364039,1.435317048694158
+0.9478924318683913,-1.128619342632793
+0.6686820374018354,1.1300688413451323
+-0.5911644416483638,-0.2637949781839295
+0.565742375668429,-0.49327840666385525
+-0.15913761051285197,2.096788826609292
+-0.3208657284809635,2.090222039237265
+-0.39700383214404383,1.7555781166381106
+-0.5466758448364721,0.690468074019571
+1.3285616216294491,-1.090748844640132
+0.14093054963489815,-0.29114795790119885
+1.8109049304647447,-2.6193506818738843
+1.2942107832076932,0.06746051044681317
+-0.044530312706156844,0.11875840073737978
+-0.1345296615426526,0.4591471146932984
+0.3067173258749555,-0.40144201614360264
+0.9398052065664707,-0.8692669027537969
+0.30179740482741635,1.766736463852819
+-0.6710370712387331,-0.0006764641752606826
+-0.38043278643039213,1.2217808151138438
+0.8080434002128011,-0.8263617358705012
+1.0086360353395016,-0.6435470246095868
+-0.731893800757003,1.5940795409565318
+0.5848261098617279,-0.5715360401259599
+-0.23993690941173607,0.130573677628254
+0.3457793997139883,1.28887211316075
+1.3338451794902588,-0.13259676409096643
+-0.20985544605386075,0.10408979683938069
+0.5111907720850086,1.1421332168146623
+-0.494802730769384,1.8677258488692416
+0.08060618131674063,0.21687897353129126
+-0.5548830049417329,0.17388315465706727
+0.6686820374018354,1.1300688413451323
+-0.5911644416483638,-0.2637949781839295
+0.565742375668429,-0.49327840666385525
+1.2084865052156952,-1.0970569041932254
+1.2824836432967437,-0.514272461069148
+-0.39700383214404383,1.7555781166381106
+-0.5466758448364721,0.690468074019571
+-0.6300848834048319,1.2414841311663258
+0.486143030152292,-0.09923131020734921
+1.8109049304647447,-2.6193506818738843
+1.2942107832076932,0.06746051044681317
+0.5141775068098953,1.448671463909901
+0.12076128125636998,1.030423158285819
+0.5774359024760681,0.1853032337435827
+0.9398052065664707,-0.8692669027537969
+0.30179740482741635,1.766736463852819
+0.6500251065496347,1.3107234137206265
+-0.38043278643039213,1.2217808151138438
+1.3678384270638206,-0.16623085887609926
+1.0086360353395016,-0.6435470246095868
+0.0976213813192019,0.8161248681335704
+-0.16616010172993856,-0.12239203678256866
+-0.021527687568058562,2.1085681509478604
+0.5303796412099745,-0.5655753516610306
+1.3338451794902588,-0.13259676409096643
+-0.20985544605386075,0.10408979683938069
+0.007285357508370782,-0.47724844407318223
+-0.29101302297343246,0.9669912407870095
+0.2892131679124463,1.5462016858305452
+-0.5548830049417329,0.17388315465706727
+-0.6818806892262239,1.5195084175845757
+-0.5911644416483638,-0.2637949781839295
+0.6558867879794874,1.9835217290987552
+1.2084865052156952,-1.0970569041932254
+1.2824836432967437,-0.514272461069148
+-0.6555575990481588,1.3079713314639898
+-0.9206974157481757,0.958110379153317
+1.2150326090426984,-1.1082569365092814
+1.1482817821951161,-1.1669188419323397
+1.8109049304647447,-2.6193506818738843
+1.2942107832076932,0.06746051044681317
+0.5141775068098953,1.448671463909901
+0.12076128125636998,1.030423158285819
+0.46784384010957014,0.18685061566347827
+0.9398052065664707,-0.8692669027537969
+0.30179740482741635,1.766736463852819
+0.6500251065496347,1.3107234137206265
+-0.38043278643039213,1.2217808151138438
+-0.036761614723123455,1.5962853628817117
+1.0086360353395016,-0.6435470246095868
+0.5977861078562889,1.42602391713105
+-0.16616010172993856,-0.12239203678256866
+-0.021527687568058562,2.1085681509478604
+0.17201511954905105,1.589340547974317
+1.3338451794902588,-0.13259676409096643
+-0.20985544605386075,0.10408979683938069
+-0.24924817263240212,1.675151637963804
+-0.29101302297343246,0.9669912407870095
+1.1262640846165515,-0.7960719125509679
+-0.5548830049417329,0.17388315465706727
+1.3490786414028544,-0.2341576992098358
+-0.20069316901105097,0.9183021727842562
+-0.019756935323602565,0.31974134053506453
+1.2084865052156952,-1.0970569041932254
+-0.5403377681312602,1.062703031063913
+-0.6555575990481588,1.3079713314639898
+1.4974767762413261,-0.41938353846212173
+1.2150326090426984,-1.1082569365092814
+1.1482817821951161,-1.1669188419323397
+1.8109049304647447,-2.6193506818738843
+1.2942107832076932,0.06746051044681317
+1.3471377726606497,-0.7439462731356323
+0.9285684372441587,1.2453423813679236
+1.642618729832014,-0.9059005602052044
+0.6603222012301766,1.3297727571365368
+0.30179740482741635,1.766736463852819
+0.6500251065496347,1.3107234137206265
+0.49948123322998284,-0.37595670541743265
+1.108708580122744,-0.7718395631340942
+-0.5973345336953622,1.6531222155888852
+0.5977861078562889,1.42602391713105
+0.46585525812170514,-0.2981544172979863
+0.44854360411069594,-0.2463598786647358
+-0.7072530134132013,1.2395732222503657
+1.3338451794902588,-0.13259676409096643
+-0.20985544605386075,0.10408979683938069
+-0.6145235091266211,1.7192800616122865
+0.7359095457346965,1.61314203211393
+0.9392451480097987,-0.017036256433059227
+-0.5548830049417329,0.17388315465706727
+0.8793917043864182,1.2286863261699403
+-0.15476532446124658,0.371281922441462
+1.6842479378312287,-1.7640948233330378
+1.2084865052156952,-1.0970569041932254
+-0.6059951565064359,0.15650940869918317
+0.9930258359108881,-0.012311639317454881
+1.4974767762413261,-0.41938353846212173
+0.6137685078549634,0.5947842013629999
+1.1482817821951161,-1.1669188419323397
+1.8109049304647447,-2.6193506818738843
+1.2942107832076932,0.06746051044681317
+1.3471377726606497,-0.7439462731356323
+0.9285684372441587,1.2453423813679236
+0.9187378344889416,-0.03890464287660339
+-0.4030170730782481,1.4678435323304375
+1.3118549241365134,-0.34366458327246185
+0.2628954562709087,0.44465675801595994
+0.49948123322998284,-0.37595670541743265
+-0.14606565159038742,0.3721063789864174
+-0.5973345336953622,1.6531222155888852
+0.5977861078562889,1.42602391713105
+0.46585525812170514,-0.2981544172979863
+0.44854360411069594,-0.2463598786647358
+-0.7072530134132013,1.2395732222503657
+1.3338451794902588,-0.13259676409096643
+-0.20985544605386075,0.10408979683938069
+-0.6145235091266211,1.7192800616122865
+-0.8633854044074514,0.528364050496417
+0.43234377525538426,1.4221673510315769
+-0.5548830049417329,0.17388315465706727
+0.8793917043864182,1.2286863261699403
+0.6510378833853565,1.3188191133544929
+-0.09025437883100579,0.5152228386471484
+1.2084865052156952,-1.0970569041932254
+-0.6059951565064359,0.15650940869918317
+0.979861484491127,0.2697309538169075
+1.3739832849965374,-1.861119354428118
+-0.14834251373210705,0.876805334606209
+1.1482817821951161,-1.1669188419323397
+1.8109049304647447,-2.6193506818738843
+1.2942107832076932,0.06746051044681317
+1.3471377726606497,-0.7439462731356323
+0.9285684372441587,1.2453423813679236
+1.4838640274520087,-2.1218247057532604
+-0.4865653458736954,0.06874141039904208
+0.8588456606857806,1.5956570794750329
+0.2628954562709087,0.44465675801595994
+1.3595252900762804,-1.4907360174941737
+-0.14606565159038742,0.3721063789864174
+-0.5973345336953622,1.6531222155888852
+0.5977861078562889,1.42602391713105
+0.46585525812170514,-0.2981544172979863
+0.44854360411069594,-0.2463598786647358
+0.5169538902818649,1.4395443765498481
+1.7399264783931987,-2.038314446803226
+-0.13841486024092559,-0.16280058414912835
+-0.6145235091266211,1.7192800616122865
+-0.8633854044074514,0.528364050496417
+-0.7138236309446433,1.1979497324504798
+-0.21517514651065783,2.022810756075636
+-0.41300413042592743,0.08296409180331053
+0.13166806961125843,-0.476120154753523
+-0.09025437883100579,0.5152228386471484
+1.2084865052156952,-1.0970569041932254
+-0.6059951565064359,0.15650940869918317
+-0.5565987714698956,-0.024216219073248335
+1.3739832849965374,-1.861119354428118
+0.32240903906397367,1.0733908832841388
+1.1482817821951161,-1.1669188419323397
+-0.6113334692743739,-0.4043800388522957
+0.21668279073150892,1.4440575929028294
+1.3471377726606497,-0.7439462731356323
+0.9285684372441587,1.2453423813679236
+1.4838640274520087,-2.1218247057532604
+-0.27254498774756225,1.8386821036725105
+1.6722594790871717,-1.9258051334021116
+0.2628954562709087,0.44465675801595994
+0.48146622951072066,1.8321895939377466
+-0.14606565159038742,0.3721063789864174
+-0.20173788080214256,-0.4066042911493572
+0.39568402733078933,0.10646590863156546
+0.46585525812170514,-0.2981544172979863
+0.44854360411069594,-0.2463598786647358
+0.5169538902818649,1.4395443765498481
+0.40841365936344715,1.3450573540711368
+-0.13841486024092559,-0.16280058414912835
+-0.6145235091266211,1.7192800616122865
+0.4140940150577067,2.0481390726664483
+-0.7138236309446433,1.1979497324504798
+-0.21517514651065783,2.022810756075636
+0.14425938761410928,-0.2666548038027299
+-0.776811411746636,-0.2885304321401014
+-0.09025437883100579,0.5152228386471484
+1.2084865052156952,-1.0970569041932254
+-0.6059951565064359,0.15650940869918317
+-0.5565987714698956,-0.024216219073248335
+-0.5962509950514049,2.066299958081997
+0.23797382077521304,1.7684265687861935
+0.5278525649989438,2.1134819595605983
+-0.18310776576503907,0.18700182465667675
+0.31068955263938813,0.6989342987894469
+1.3471377726606497,-0.7439462731356323
+0.9285684372441587,1.2453423813679236
+1.4838640274520087,-2.1218247057532604
+-0.27254498774756225,1.8386821036725105
+1.6722594790871717,-1.9258051334021116
+0.2628954562709087,0.44465675801595994
+-1.1007769443643332,0.5827440218157347
+-0.8266867755751212,-0.8189998025754512
+-0.5157802983946133,-0.4201777507878673
+0.39568402733078933,0.10646590863156546
+0.46585525812170514,-0.2981544172979863
+-0.9733555399648746,0.45272161791490095
+0.4505876004967872,1.5542093340453595
+0.40841365936344715,1.3450573540711368
+-0.13841486024092559,-0.16280058414912835
+-0.6145235091266211,1.7192800616122865
+0.4140940150577067,2.0481390726664483
+-0.7138236309446433,1.1979497324504798
+-0.20703568997640742,-0.099783080672321
+0.852387843049938,0.4158108570327078
+0.29975486703663,-0.45615465592731297
+-0.09025437883100579,0.5152228386471484
+1.2084865052156952,-1.0970569041932254
+0.1472284408843177,2.1699505569192667
+-0.15620841239277986,0.9182055765538133
+-0.4624283306309068,0.12644131856061858
+0.550536906557451,-0.5295890671713178
+0.5278525649989438,2.1134819595605983
+0.4262167129230377,0.025804553311827738
+-0.11973416127746102,1.3387889526067054
+1.3144070235697791,-0.43909309177569766
+-0.3273781000575796,0.6528574064513468
+1.4838640274520087,-2.1218247057532604
+-0.589267193827226,0.370523665950251
+1.064527100617752,-0.6090979701398419
+1.784402071559068,-1.9873159366536208
+0.37767184934690073,0.8699522025128247
+-0.05006844149381259,1.6553584372727217
+0.5004885530521079,1.663879129436948
+-0.26982761524855653,0.41944891297611414
+0.0594218475365286,-0.25007457395128324
+1.0452601190986723,-1.530607947353904
+1.373798107345831,-0.7590409012066516
+0.14082044756532333,1.2563719290841158
+-0.13841486024092559,-0.16280058414912835
+-0.6145235091266211,1.7192800616122865
+0.4140940150577067,2.0481390726664483
+1.0238921122747935,-0.9477327752485418
+0.7180078524874633,-0.31126022758242433
+0.6008097972381103,-0.8832956299679248
+0.29975486703663,-0.45615465592731297
+-0.09025437883100579,0.5152228386471484
+1.1618390645823533,-1.60221467739947
+1.5205849587374558,-0.05251531140187704
+0.3193078462578488,0.018662347956670766
+0.6006645826979213,1.7091698570037934
+1.4332732929443972,-0.9705783591743997
+-0.516652837749732,0.28853825930785126
+1.664081376940413,-0.7118420433280075
+0.1612177602628096,2.197475214236332
+-0.6915936542383063,-0.461080723983736
+-0.5121933580858182,0.52284310650689
+-0.183981742821349,1.3849665440404328
+0.11041698885069784,-0.028326518475957796
+0.4710022284251076,0.02595929375310524
+1.784402071559068,-1.9873159366536208
+1.1123131498349832,-1.1523174452045315
+-0.05006844149381259,1.6553584372727217
+0.5004885530521079,1.663879129436948
+-0.26982761524855653,0.41944891297611414
+-0.3292765254946757,1.0357958430245784
+0.3048030612961203,1.5689063188982402
+-0.7930093718228708,-0.031611510186938585
+1.6732915981459673,-1.5577209995962034
+-0.13841486024092559,-0.16280058414912835
+1.0655430171718192,-0.9713380960744044
+1.1604991814582173,-0.6417474065565747
+1.3295362938844237,-1.2204112582416249
+-0.02026194337756726,0.6377144874005759
+1.568086541025968,-1.0674704997213968
+0.29975486703663,-0.45615465592731297
+-0.09025437883100579,0.5152228386471484
+1.3260648605186232,-0.008576422907598337
+0.9810402670131178,1.7240048716913223
+0.3193078462578488,0.018662347956670766
+0.6006645826979213,1.7091698570037934
+-0.27370657737195897,0.8314632609126936
+-0.516652837749732,0.28853825930785126
+0.16023349813931542,0.6856069839469834
+0.1612177602628096,2.197475214236332
+-0.6915936542383063,-0.461080723983736
+-0.8539530223694061,0.7109808836455
+-0.183981742821349,1.3849665440404328
+0.08235895576605354,2.5524642809138065
+-0.614116894733026,0.3524700837827377
+1.784402071559068,-1.9873159366536208
+1.161218843950682,-1.3087067293909946
+-0.8022829663004765,1.3334309126857797
+0.5004885530521079,1.663879129436948
+-0.8102333973256114,-0.13504926844378373
+-0.06700051526261308,1.6075946114977437
+-0.1968648460758079,0.22620818096679352
+1.3604828774890494,-0.04908908663673894
+0.9237014688515491,-0.7147803490567399
+-0.13841486024092559,-0.16280058414912835
+0.17762414909753577,0.16537876239181548
+1.1604991814582173,-0.6417474065565747
+1.3295362938844237,-1.2204112582416249
+-0.23387301842470753,0.6011486880577555
+2.06115442725506,-3.213167292881698
+-0.8727964015351944,0.796650750762974
+1.2841570258161765,-1.461039296283459
+1.3260648605186232,-0.008576422907598337
+0.23208181554765178,0.14936110590311003
+0.3193078462578488,0.018662347956670766
+0.6006645826979213,1.7091698570037934
+0.8474285179638728,0.16404121529387516
+-0.516652837749732,0.28853825930785126
+0.5508897370629945,0.46963768716084653
+0.1612177602628096,2.197475214236332
+0.6165235240492193,-0.6264396796706733
+-0.8539530223694061,0.7109808836455
+-0.183981742821349,1.3849665440404328
+0.08235895576605354,2.5524642809138065
+-0.614116894733026,0.3524700837827377
+1.2449125978411815,-1.2995603542876029
+1.161218843950682,-1.3087067293909946
+1.3713602777681269,0.16035262510439893
+0.5004885530521079,1.663879129436948
+-0.8102333973256114,-0.13504926844378373
+-0.06700051526261308,1.6075946114977437
+-0.1968648460758079,0.22620818096679352
+-0.5084625090838237,1.391152322194028
+0.9237014688515491,-0.7147803490567399
+-0.3052644103931542,-0.13110483265890938
+0.17762414909753577,0.16537876239181548
+1.1604991814582173,-0.6417474065565747
+1.3295362938844237,-1.2204112582416249
+-0.23387301842470753,0.6011486880577555
+2.06115442725506,-3.213167292881698
+0.5710328393361049,1.5540528837097152
+1.2841570258161765,-1.461039296283459
+0.20551649542324513,0.8897316793711554
+0.8234310318077838,-0.44132207790615086
+0.9807294664633768,0.17871032214166932
+0.6006645826979213,1.7091698570037934
+1.328492745163425,-1.7686272979677484
+-0.516652837749732,0.28853825930785126
+-0.40284443990742697,1.293762404048939
+0.1612177602628096,2.197475214236332
+0.9120149743058048,0.9715538290211889
+-0.8539530223694061,0.7109808836455
+0.9561778237419869,-0.19330678068106943
+1.3923633583508654,-1.9373502650787022
+1.440088732343631,-1.4017518063626988
+1.5571896077266842,-0.8032254589103511
+-0.412710291557905,0.9188666793707181
+1.3713602777681269,0.16035262510439893
+0.5004885530521079,1.663879129436948
+-0.8102333973256114,-0.13504926844378373
+-0.06700051526261308,1.6075946114977437
+-0.1968648460758079,0.22620818096679352
+-0.5084625090838237,1.391152322194028
+0.9237014688515491,-0.7147803490567399
+-0.6547572744938932,0.024795218093369376
+-0.37845152369172563,0.29719534376230117
+0.39295922674393347,1.9562930762969388
+-0.04842794132674466,0.04227089468055438
+0.22769635382412234,1.3215811989859645
+-0.30269566793339875,1.2257513962733757
+0.5710328393361049,1.5540528837097152
+0.42610721206116775,1.7645626450312777
+0.20551649542324513,0.8897316793711554
+0.8234310318077838,-0.44132207790615086
+0.6959476357686991,-0.4908132548490096
+-0.512835460049588,-0.02074393342114171
+1.8568431651668786,-2.599789419446226
+0.8204037021389677,0.3125110013283241
+-0.40284443990742697,1.293762404048939
+0.1612177602628096,2.197475214236332
+0.9120149743058048,0.9715538290211889
+0.2880966133156567,-0.37499931657838825
+0.9561778237419869,-0.19330678068106943
+1.3923633583508654,-1.9373502650787022
+1.440088732343631,-1.4017518063626988
+1.5571896077266842,-0.8032254589103511
+0.8443506054701496,-0.5122977454452858
+1.3713602777681269,0.16035262510439893
+0.5004885530521079,1.663879129436948
+-0.8102333973256114,-0.13504926844378373
+-0.06700051526261308,1.6075946114977437
+0.8934481092969486,-0.22064781965788288
+-0.5084625090838237,1.391152322194028
+-0.685223643212826,1.6888231315673714
+-0.6547572744938932,0.024795218093369376
+-0.37845152369172563,0.29719534376230117
+0.39295922674393347,1.9562930762969388
+-0.04842794132674466,0.04227089468055438
+-0.6298383198948047,1.9487653938862803
+-0.06278575372950912,2.041734756118357
+-0.6688038475803826,1.1900180300564627
+1.2343097005372239,-1.0836918451070097
+0.20551649542324513,0.8897316793711554
+0.701691819861755,1.109356231441659
+0.6959476357686991,-0.4908132548490096
+-0.512835460049588,-0.02074393342114171
+1.8568431651668786,-2.599789419446226
+0.31173528487927304,2.0503606819805738
+-0.40284443990742697,1.293762404048939
+0.1612177602628096,2.197475214236332
+0.054689979623160925,1.8991468100004998
+1.3337489642038602,-1.2099756580593701
+0.6396105692952682,1.506301943068618
+1.3923633583508654,-1.9373502650787022
+1.440088732343631,-1.4017518063626988
+1.5571896077266842,-0.8032254589103511
+0.8443506054701496,-0.5122977454452858
+1.3141451687513108,-1.36154865681436
+0.7903723119315642,-0.799175800023586
+-0.8102333973256114,-0.13504926844378373
+-0.06700051526261308,1.6075946114977437
+1.2898206354107737,-2.0333102199931754
+-0.335931287802066,0.37958033618734244
+0.649525551141477,0.5107156574487288
+-0.6547572744938932,0.024795218093369376
+-0.37845152369172563,0.29719534376230117
+0.39295922674393347,1.9562930762969388
+-0.511010587130151,1.0513666488963294
+1.5107756317800183,-2.420218092808742
+0.37716293062339656,2.1896780777097438
+0.35458735979516837,1.7753346871781333
+-0.120526699778716,1.8041169709233136
+0.20551649542324513,0.8897316793711554
+0.701691819861755,1.109356231441659
+0.6959476357686991,-0.4908132548490096
+-0.512835460049588,-0.02074393342114171
+1.8568431651668786,-2.599789419446226
+0.2082025353601959,0.013342087686952109
+1.770558653214262,-2.497251934740709
+0.1612177602628096,2.197475214236332
+0.689871525876264,-0.18902455479716568
+1.3337489642038602,-1.2099756580593701
+0.6396105692952682,1.506301943068618
+1.3923633583508654,-1.9373502650787022
+1.6964746114467855,-2.0298556346581416
+1.3964025650899734,-0.7968506848500215
+-0.7795284240458911,0.7161860415909227
+1.3141451687513108,-1.36154865681436
+0.7903723119315642,-0.799175800023586
+0.22664524321904939,1.8774806662420538
+-0.06700051526261308,1.6075946114977437
+1.2898206354107737,-2.0333102199931754
+1.5904338367553463,-1.3283096831210137
+-0.34468028018292074,1.9725008380818274
+-0.6547572744938932,0.024795218093369376
+-0.37845152369172563,0.29719534376230117
+0.39295922674393347,1.9562930762969388
+-0.511010587130151,1.0513666488963294
+-0.10199512204357053,0.9479886082869913
+1.2443569782972062,-1.0548758875983337
+-0.634643543661707,1.5375957679984624
+0.5766779336362005,1.2774850576591117
+0.7904773682941705,0.05807981283877939
+0.4614991663400774,2.1511112788924445
+0.6959476357686991,-0.4908132548490096
+-0.512835460049588,-0.02074393342114171
+1.8568431651668786,-2.599789419446226
+0.2082025353601959,0.013342087686952109
+1.770558653214262,-2.497251934740709
+0.1612177602628096,2.197475214236332
+0.689871525876264,-0.18902455479716568
+1.3337489642038602,-1.2099756580593701
+0.6396105692952682,1.506301943068618
+1.3364974054049794,-1.3521939149681543
+-0.24450868903059852,-0.25821643957077256
+0.5883251991955799,1.3813630506839676
+-0.7795284240458911,0.7161860415909227
+-0.6278686519464161,0.9347989420036577
+0.7903723119315642,-0.799175800023586
+0.22664524321904939,1.8774806662420538
+-0.22547658565228845,1.4709498304274442
+1.2898206354107737,-2.0333102199931754
+1.5904338367553463,-1.3283096831210137
+-0.34468028018292074,1.9725008380818274
+-0.6547572744938932,0.024795218093369376
+-0.37845152369172563,0.29719534376230117
+0.39295922674393347,1.9562930762969388
+-0.511010587130151,1.0513666488963294
+-0.10199512204357053,0.9479886082869913
+-0.30147386377324586,2.3736001296796343
+-0.634643543661707,1.5375957679984624
+0.5766779336362005,1.2774850576591117
+0.7904773682941705,0.05807981283877939
+0.4614991663400774,2.1511112788924445
+0.6959476357686991,-0.4908132548490096
+1.2595270086290078,-0.49437656843106004
+1.8568431651668786,-2.599789419446226
+0.2082025353601959,0.013342087686952109
+1.770558653214262,-2.497251934740709
+0.1612177602628096,2.197475214236332
+-0.3221726588135493,1.3712755021170104
+1.3337489642038602,-1.2099756580593701
+0.6396105692952682,1.506301943068618
+1.1946033973165153,-0.9720787403846368
+1.1059977976034494,0.7203190739250276
+0.21103715834376624,-0.015594485969288918
+-0.7795284240458911,0.7161860415909227
+0.8880273151457725,0.16209112186436725
+-0.013619741670957627,-0.2396913023640106
+0.22664524321904939,1.8774806662420538
+-0.22547658565228845,1.4709498304274442
+1.2898206354107737,-2.0333102199931754
+1.5904338367553463,-1.3283096831210137
+-0.34468028018292074,1.9725008380818274
+-0.6547572744938932,0.024795218093369376
+0.39851977302361613,-0.35248540183505644
+-0.39576443488246554,-0.3025738801424134
+1.4462072766317513,-1.0541496224299622
+-0.05852368561378334,0.15533080683590383
+-0.3738012592248924,1.7389325278722914
+-0.634643543661707,1.5375957679984624
+0.5766779336362005,1.2774850576591117
+0.006904864716951176,0.593590428775141
+0.4614991663400774,2.1511112788924445
+1.378559265990421,-1.1278318527736968
+-1.045777411919452,0.5410979641415796
+1.32340947378266,-1.691810103856611
+0.2082025353601959,0.013342087686952109
+1.5290071075910858,-1.1358748620405816
+0.1612177602628096,2.197475214236332
+-0.3221726588135493,1.3712755021170104
+1.3337489642038602,-1.2099756580593701
+0.6396105692952682,1.506301943068618
+-0.062105019945135065,1.6530757701510628
+1.1059977976034494,0.7203190739250276
+0.21103715834376624,-0.015594485969288918
+-0.7795284240458911,0.7161860415909227
+-0.6520215844225239,1.6534642877242733
+1.3420307977461303,-1.0771880601891595
+0.22664524321904939,1.8774806662420538
+1.6656319809734643,-0.827749741499941
+1.2898206354107737,-2.0333102199931754
+1.5904338367553463,-1.3283096831210137
+-0.34468028018292074,1.9725008380818274
+-0.6547572744938932,0.024795218093369376
+-0.39513886215652644,1.3044067851681627
+-0.39576443488246554,-0.3025738801424134
+2.0292585053109535,-2.867201408451707
+0.25019773835499803,0.13726961748511624
+-0.3738012592248924,1.7389325278722914
+-0.634643543661707,1.5375957679984624
+0.5766779336362005,1.2774850576591117
+0.006904864716951176,0.593590428775141
+-0.2986522283174009,0.23726520264855822
+1.378559265990421,-1.1278318527736968
+0.6996187039027109,-0.12860457521766666
+-1.116895424641669,-0.4029652569225053
+0.2082025353601959,0.013342087686952109
+1.5290071075910858,-1.1358748620405816
+0.1612177602628096,2.197475214236332
+-0.3221726588135493,1.3712755021170104
+1.3337489642038602,-1.2099756580593701
+0.6396105692952682,1.506301943068618
+-0.062105019945135065,1.6530757701510628
+0.6838197548561189,-0.37328241206073987
+-0.1846650638494307,2.201994386566477
+-0.7795284240458911,0.7161860415909227
+-0.6520215844225239,1.6534642877242733
+-0.9320887643798885,0.3011320901133
+0.22664524321904939,1.8774806662420538
+1.6656319809734643,-0.827749741499941
+1.2898206354107737,-2.0333102199931754
+1.2116460615406865,-0.8190904397338643
+-0.7461431218771087,0.3168887942732147
+-0.6547572744938932,0.024795218093369376
+-0.39513886215652644,1.3044067851681627
+-0.39576443488246554,-0.3025738801424134
+2.0292585053109535,-2.867201408451707
+0.25019773835499803,0.13726961748511624
+0.9012843488026282,-0.8902448586242386
+-0.634643543661707,1.5375957679984624
+0.4306550943007996,0.5264515442142244
+0.006904864716951176,0.593590428775141
+-0.2986522283174009,0.23726520264855822
+1.378559265990421,-1.1278318527736968
+1.0941624549351041,-1.2751658809915418
+-0.13769008442150854,-0.027262392228823484
+0.2082025353601959,0.013342087686952109
+1.5290071075910858,-1.1358748620405816
+0.1612177602628096,2.197475214236332
+-0.3221726588135493,1.3712755021170104
+1.3337489642038602,-1.2099756580593701
+0.6396105692952682,1.506301943068618
+-0.062105019945135065,1.6530757701510628
+0.9694034807867669,0.19322268765470896
+-0.1846650638494307,2.201994386566477
+-0.7795284240458911,0.7161860415909227
+-0.6520215844225239,1.6534642877242733
+-0.9320887643798885,0.3011320901133
+0.725419065479537,-0.7998374159074182
+-0.5887639393224067,1.500979887556893
+1.6401132995543262,-0.9821374677660049
+1.2116460615406865,-0.8190904397338643
+-0.7461431218771087,0.3168887942732147
+-0.6547572744938932,0.024795218093369376
+1.0665206162535017,-0.6916112892596364
+0.4110433714183279,-0.40299047288408896
+-0.9892964592883553,0.14418513567931832
+0.25019773835499803,0.13726961748511624
+-0.7544288148192786,-0.7168351352559613
+-0.634643543661707,1.5375957679984624
+0.4306550943007996,0.5264515442142244
+0.006904864716951176,0.593590428775141
+1.4678038801758853,-1.8984513871278006
+-0.027183045251307103,1.5505133093033079
+-0.6457822982931704,1.1327916243568956
+-0.13769008442150854,-0.027262392228823484
+0.06160309002902535,2.2771562987645524
+-0.9044417707414417,-0.13202066940002297
+-0.5435666349386671,1.4497380415232306
+-0.7914243945649044,0.16742792184505112
+1.3337489642038602,-1.2099756580593701
+0.6396105692952682,1.506301943068618
+-0.062105019945135065,1.6530757701510628
+0.9694034807867669,0.19322268765470896
+1.4825984944589514,-2.4280219610085894
+1.0566129739984242,-0.8350552213175533
+-0.26674394450435657,0.35715376362600937
+-0.5375313195342468,0.07001119366705977
+0.725419065479537,-0.7998374159074182
+-0.5887639393224067,1.500979887556893
+0.15705558567061007,1.7982838058175805
+-0.7429084961291351,6.37208530139266e-05
+-0.18484581383004905,2.035822904376075
+1.5472345310753808,-2.4726252806650564
+1.0665206162535017,-0.6916112892596364
+0.4110433714183279,-0.40299047288408896
+-1.020212092874981,0.09237588916638928
+0.25019773835499803,0.13726961748511624
+1.2147443250349388,-0.89376971302461
+-0.634643543661707,1.5375957679984624
+0.4306550943007996,0.5264515442142244
+0.006904864716951176,0.593590428775141
+-0.7967610032423034,0.5823724018180753
+-0.027183045251307103,1.5505133093033079
+1.2550748599437882,-0.2533123708572348
+-0.13769008442150854,-0.027262392228823484
+0.06160309002902535,2.2771562987645524
+-0.9044417707414417,-0.13202066940002297
+-0.5435666349386671,1.4497380415232306
+-0.7914243945649044,0.16742792184505112
+-0.4312246335007997,2.161451508690812
+0.6396105692952682,1.506301943068618
+-0.062105019945135065,1.6530757701510628
+0.9694034807867669,0.19322268765470896
+1.4825984944589514,-2.4280219610085894
+1.0566129739984242,-0.8350552213175533
+0.7877762361834894,-0.6909294766134926
+-0.5375313195342468,0.07001119366705977
+-0.3881315368788274,1.1335467827571872
+-0.7306527046621776,-0.6492970955044853
+0.15705558567061007,1.7982838058175805
+-0.7429084961291351,6.37208530139266e-05
+-0.18484581383004905,2.035822904376075
+1.5472345310753808,-2.4726252806650564
+1.0665206162535017,-0.6916112892596364
+0.4110433714183279,-0.40299047288408896
+-0.6283603092354697,0.7707857391173918
+-0.2646263949152987,0.34536884820024005
+1.3014628388575553,-0.701222048398654
+-0.10051765151377329,1.7829297220871356
+-0.8157401353728815,0.8185097485132856
+0.589856401295293,1.7012051089232512
+0.6840631778493781,-0.7620748391145211
+-0.027183045251307103,1.5505133093033079
+0.7747711657139187,-1.3327118623700691
+0.01033744028384509,0.3066370486553165
+0.06160309002902535,2.2771562987645524
+0.5215819214166009,1.1053320940911608
+-0.5435666349386671,1.4497380415232306
+-0.7914243945649044,0.16742792184505112
+-0.4312246335007997,2.161451508690812
+0.6396105692952682,1.506301943068618
+-0.062105019945135065,1.6530757701510628
+0.5473757134560838,-0.028510705165403993
+1.4825984944589514,-2.4280219610085894
+1.0566129739984242,-0.8350552213175533
+0.7877762361834894,-0.6909294766134926
+0.7320769314177797,-0.6410512028321964
+-0.3881315368788274,1.1335467827571872
+-0.20192627202767632,-0.23175747091290766
+0.15705558567061007,1.7982838058175805
+-0.7429084961291351,6.37208530139266e-05
+-0.8995742699373891,0.6455246235889298
+1.5472345310753808,-2.4726252806650564
+0.2863687228383426,-0.30476261669992116
+1.1419609429203719,-1.6886032822606027
+-0.6283603092354697,0.7707857391173918
+-0.2646263949152987,0.34536884820024005
+-0.21000752470669434,2.0775276190658025
+1.2504193729320239,0.5596997578549865
+0.19559702678013283,2.07466960220965
+-0.004733987832368088,0.19444229439027994
+0.6840631778493781,-0.7620748391145211
+1.406851799323611,-0.08993143411895022
+0.631432059368598,0.4055046257044963
+0.295115171916529,0.25207443278532493
+0.11028299603100097,2.0144360890813737
+0.5215819214166009,1.1053320940911608
+-0.5435666349386671,1.4497380415232306
+-0.7914243945649044,0.16742792184505112
+0.8706686997770047,-0.6731075827552335
+0.4932340177296731,1.6622927729548436
+-0.062105019945135065,1.6530757701510628
+0.5473757134560838,-0.028510705165403993
+0.6253637351892728,-0.21267212892311838
+0.22384554944667873,2.0060769381902332
+-0.7675111815504788,0.5848984116706382
+0.7320769314177797,-0.6410512028321964
+-0.3881315368788274,1.1335467827571872
+-0.14221695580251176,1.884488867999473
+-0.22878979541779376,-0.05083252629464652
+-0.7429084961291351,6.37208530139266e-05
+0.013827990228823056,-0.1915864536992153
+-0.4572588051788833,1.8309446098181352
+-0.32046355941449955,0.8725206043014264
+1.1419609429203719,-1.6886032822606027
+0.04758875553355696,0.12818665442190835
+0.9265650922282282,0.2804772615284665
+-0.5695368467131249,0.8150154202736934
+1.2504193729320239,0.5596997578549865
+0.19559702678013283,2.07466960220965
+-0.19359235435158795,1.0170718485155454
+0.6840631778493781,-0.7620748391145211
+1.406851799323611,-0.08993143411895022
+0.631432059368598,0.4055046257044963
+1.2091051415815977,-0.35964254273657503
+-0.1996900862451294,1.7208373597626032
+-0.3634168317159673,1.478825198835362
+-0.5435666349386671,1.4497380415232306
+-0.7914243945649044,0.16742792184505112
+-0.08057551788273369,1.284977374609202
+0.4932340177296731,1.6622927729548436
+0.31882220253281707,1.8153659323868878
+0.5473757134560838,-0.028510705165403993
+-0.5100509069750541,2.2699118929741227
+0.22384554944667873,2.0060769381902332
+-0.7675111815504788,0.5848984116706382
+0.7320769314177797,-0.6410512028321964
+0.6213016393034742,-0.6866859536028087
+1.1365966563408119,-0.06698422986666402
+1.1677175404068345,-1.4811738875885503
+-0.5257718349685829,2.2790305773689763
+0.013827990228823056,-0.1915864536992153
+0.9870481291772033,0.8381826934411558
+-0.32046355941449955,0.8725206043014264
+0.07807221896455491,1.6767301721486298
+0.04758875553355696,0.12818665442190835
+0.9265650922282282,0.2804772615284665
+-0.5695368467131249,0.8150154202736934
+1.2504193729320239,0.5596997578549865
+0.4295961540343155,-0.4709596641729281
+-0.5584323503619856,-0.5170867583931376
+0.14883172885369866,-0.28314795200502785
+-0.11127426641834515,2.109308702002236
+1.249428325217354,-0.9773594087183652
+1.2091051415815977,-0.35964254273657503
+-0.1996900862451294,1.7208373597626032
+0.21560102745262877,-0.1836295536881969
+0.22295893081770696,1.463182724565986
+-0.7914243945649044,0.16742792184505112
+-0.08057551788273369,1.284977374609202
+-0.030344561924308122,-0.12369981228730209
+0.31882220253281707,1.8153659323868878
+0.5473757134560838,-0.028510705165403993
+-0.7409865738523957,0.640689796763118
+0.7125937301426843,-0.2239565272304036
+-0.7675111815504788,0.5848984116706382
+0.2911977387698428,0.13688539422456286
+1.065750339029133,-0.6569995673365316
+1.1365966563408119,-0.06698422986666402
+1.1677175404068345,-1.4811738875885503
+-0.8403967250506643,1.4720053632162227
+0.013827990228823056,-0.1915864536992153
+-0.777787285580212,0.4040675510202789
+-0.32046355941449955,0.8725206043014264
+1.0204491255954256,-0.2000551999044653
+0.04758875553355696,0.12818665442190835
+0.9265650922282282,0.2804772615284665
+0.6417018944106985,1.7404942663938323
+0.18293223945760007,-0.37633371659302783
+0.4295961540343155,-0.4709596641729281
+-0.5584323503619856,-0.5170867583931376
+1.598701968006366,-1.2982351618337247
+-0.11127426641834515,2.109308702002236
+1.249428325217354,-0.9773594087183652
+-0.6156925949599429,0.11937560581590984
+1.5482035710726454,-0.5407747966933755
+0.502426194260533,0.7824088095111872
+0.9959633171897787,0.502385711559151
+0.008510608066173153,1.7992540065204623
+-0.6064843183224309,0.36403189291419025
+-0.030344561924308122,-0.12369981228730209
+0.31882220253281707,1.8153659323868878
+0.5473757134560838,-0.028510705165403993
+-0.7008861922724103,0.9659435347643448
+-1.0021666406422616,0.1719998496688439
+-0.15488751715786117,1.3312876695200344
+1.4328625846982002,-0.7379863442403529
+1.065750339029133,-0.6569995673365316
+1.1365966563408119,-0.06698422986666402
+-0.5415499167858574,0.035887957476866794
+0.03775289788877986,1.4069941507028898
+0.40073302714030373,-0.027881583693059986
+-0.7210430525809859,-0.019219889271475
+-0.32046355941449955,0.8725206043014264
+0.4679883070205785,1.1602657657976267
+-0.4976049889794178,0.3703795666945378
+-0.15606818091611158,1.633980762121287
+-0.7920507443902098,0.9603545608861572
+0.18293223945760007,-0.37633371659302783
+0.4295961540343155,-0.4709596641729281
+0.2822187984704485,1.5273873607972215
+1.598701968006366,-1.2982351618337247
+-0.11127426641834515,2.109308702002236
+1.249428325217354,-0.9773594087183652
+-1.0083067863064399,0.9967765906151629
+-0.4413939305034997,-0.3192408861699151
+-0.43078618412234715,0.24699559789647668
+0.9959633171897787,0.502385711559151
+0.27509073514920485,-0.02687189164841508
+-0.6064843183224309,0.36403189291419025
+0.8110445498438696,-0.5612656466239834
+0.07991100551540171,1.1005445792359092
+-0.49177805393681673,0.5398544167236579
+-0.7008861922724103,0.9659435347643448
+-1.0021666406422616,0.1719998496688439
+-0.851344679327063,-0.08209454955747769
+1.4328625846982002,-0.7379863442403529
+-0.20533380671486307,1.279744868170755
+1.1365966563408119,-0.06698422986666402
+-0.7749285395280032,0.16652913847564
+0.46300376640709295,2.135546853086708
+0.710405572919972,0.6828510772181464
+-0.5663108095520092,1.0032735694329697
+-0.32046355941449955,0.8725206043014264
+-0.6907033284866204,0.751548716394061
+-0.4976049889794178,0.3703795666945378
+-0.15606818091611158,1.633980762121287
+-0.7920507443902098,0.9603545608861572
+-0.4183857352836938,1.5393021317293596
+-0.5422851704442216,-0.36392415056310295
+0.2822187984704485,1.5273873607972215
+1.598701968006366,-1.2982351618337247
+1.2174899202738638,-1.208433620924653
+0.883683354554229,0.8891147548021169
+0.23278221135035215,-0.27771878923810667
+-0.4413939305034997,-0.3192408861699151
+-0.43078618412234715,0.24699559789647668
+0.9959633171897787,0.502385711559151
+1.183562633996586,0.14307361637642768
+-0.6064843183224309,0.36403189291419025
+1.2569369309491825,-0.15556534040715975
+0.07991100551540171,1.1005445792359092
+-0.49177805393681673,0.5398544167236579
+-0.7008861922724103,0.9659435347643448
+0.3583656347325799,-0.748669087410982
+0.486153682658823,1.1954918860468282
+1.4328625846982002,-0.7379863442403529
+-0.20533380671486307,1.279744868170755
+1.1365966563408119,-0.06698422986666402
+-0.7749285395280032,0.16652913847564
+0.9421930526842158,-0.8977989526790514
+-0.7716618649114457,0.17923667536297438
+-0.5663108095520092,1.0032735694329697
+0.6650146007929006,-0.2321064054469129
+-0.3032380318679644,-0.10742192756479861
+0.8516389455742973,-0.9636943085777301
+0.8273259510915357,-0.9681563836494416
+-0.7920507443902098,0.9603545608861572
+-0.4183857352836938,1.5393021317293596
+-0.5422851704442216,-0.36392415056310295
+0.2966705804716733,-0.46861665759907634
+1.598701968006366,-1.2982351618337247
+1.2174899202738638,-1.208433620924653
+0.7073160748177002,1.0731927702453565
+0.23278221135035215,-0.27771878923810667
+1.2637132034150587,-0.2562340775766204
+0.16744586713092352,0.6191833242453718
+0.9959633171897787,0.502385711559151
+0.47191491500603483,0.9079185695315475
+-0.6064843183224309,0.36403189291419025
+1.2569369309491825,-0.15556534040715975
+-0.6681692036994848,-0.023436604955173967
+0.4980770733426365,0.3629962476540185
+-0.05583142397513924,-0.3439763753448935
+0.015761604662508533,0.348713961476094
+0.12602450306078247,1.4024667083804985
+1.4328625846982002,-0.7379863442403529
+0.9449200578694315,-0.46928952366163945
+0.1818494827556667,0.6779658887173892
+-0.7749285395280032,0.16652913847564
+0.9421930526842158,-0.8977989526790514
+0.35774073223739444,0.23888916940829813
+-0.5663108095520092,1.0032735694329697
+0.15495800474688487,0.5114948043496437
+-0.8478441635702479,0.12865959200979055
+0.8516389455742973,-0.9636943085777301
+-0.5595351053865999,-0.21250978327014625
+-0.7920507443902098,0.9603545608861572
+-0.4183857352836938,1.5393021317293596
+0.39681247216215076,0.47819107806555605
+-0.10459319971606074,0.5379985466706453
+1.598701968006366,-1.2982351618337247
+1.2174899202738638,-1.208433620924653
+-0.3629963726619271,1.310411980469413
+0.23278221135035215,-0.27771878923810667
+-0.47993475257590124,-0.30323955927388174
+-0.27530915303079745,-0.37892663854416025
+0.9959633171897787,0.502385711559151
+-0.3296503511233949,0.129521362871334
+-0.6064843183224309,0.36403189291419025
+1.2569369309491825,-0.15556534040715975
+-0.24467673075401059,1.66761554170765
+1.782272269692596,-1.6234533717423822
+-0.05583142397513924,-0.3439763753448935
+0.015761604662508533,0.348713961476094
+-0.06172998010582054,0.9520038970578768
+1.4328625846982002,-0.7379863442403529
+-0.32491287230813537,1.2152219043818013
+0.5572435259998428,1.3155391845437918
+-0.7749285395280032,0.16652913847564
+0.9421930526842158,-0.8977989526790514
+1.2733106487767196,-0.19451905967284916
+0.5373793161456537,0.1840334616010415
+0.8913209626263165,0.5465292531953431
+-0.8478441635702479,0.12865959200979055
+-0.004184629956878544,0.007551822496386418
+1.7701323275733505,-1.2035127736406568
+-0.7920507443902098,0.9603545608861572
+1.1900154980687743,-0.05822617592483137
+0.058055537464744233,-0.44895147442301364
+1.0996907949629802,0.6837663639788316
+1.598701968006366,-1.2982351618337247
+1.2174899202738638,-1.208433620924653
+0.9622788696150378,-0.0009940388854223214
+-0.8063412215589201,0.12858019773890975
+-0.47993475257590124,-0.30323955927388174
+-0.5790826738801602,0.5408028616250706
+0.9959633171897787,0.502385711559151
+-0.3890514471057024,-0.2666061614491112
+0.11238907314388757,0.017222238714494353
+1.5695018826586669,-0.9004863278829747
+-0.24467673075401059,1.66761554170765
+0.41711776876093426,-0.5531274426415684
+0.06743783474626597,0.6759973077477661
+0.015761604662508533,0.348713961476094
+-0.06172998010582054,0.9520038970578768
+1.4328625846982002,-0.7379863442403529
+-0.24456333865284652,-0.0666346526752628
+0.5572435259998428,1.3155391845437918
+-0.7749285395280032,0.16652913847564
+1.2685692965232467,-1.6274611459004675
+0.8022137712706272,-0.8839482849042763
+0.5373793161456537,0.1840334616010415
+0.8913209626263165,0.5465292531953431
+-0.8478441635702479,0.12865959200979055
+-0.004184629956878544,0.007551822496386418
+1.7701323275733505,-1.2035127736406568
+-0.34409932328699777,1.2199317747101022
+1.1900154980687743,-0.05822617592483137
+0.8608785617725384,-0.15883175607577832
+1.0996907949629802,0.6837663639788316
+-0.5636166760221839,-0.5292792761150235
+-0.5331343321965376,1.6206946219369045
+0.684444996321472,-0.7258692718643855
+-0.8063412215589201,0.12858019773890975
+1.0012083579146585,0.6006476646921097
+-0.6285392095299172,0.7891999953203211
+0.9959633171897787,0.502385711559151
+-0.8285640597724393,0.3424915558921258
+0.319879878465673,-0.33610452264162427
+-0.6556512012523673,0.0008258867649472146
+-0.24467673075401059,1.66761554170765
+0.41711776876093426,-0.5531274426415684
+-0.07417902217179523,0.8352224831214239
+1.6539142537284157,-1.8118069042968519
+0.4654830520694627,0.028261865671018183
+1.4328625846982002,-0.7379863442403529
+1.3247385244240422,0.4024874723478394
+0.32328143753077876,-0.08394628482624505
+0.2579469709740907,-0.1967748935415386
+1.2685692965232467,-1.6274611459004675
+0.8022137712706272,-0.8839482849042763
+0.5373793161456537,0.1840334616010415
+0.28778690599840706,-0.2918834493993231
+-0.8478441635702479,0.12865959200979055
+-0.004184629956878544,0.007551822496386418
+-1.0286281002769924,0.9934407494346565
+-0.34409932328699777,1.2199317747101022
+1.1900154980687743,-0.05822617592483137
+0.01631367958834451,0.03847005934898328
+1.0996907949629802,0.6837663639788316
+-0.5636166760221839,-0.5292792761150235
+-0.5331343321965376,1.6206946219369045
+0.684444996321472,-0.7258692718643855
+-0.3464616627370473,0.6142219369797234
+1.0012083579146585,0.6006476646921097
+-0.6285392095299172,0.7891999953203211
+1.4401091773202197,-1.1934380663476247
+-0.8005805124878281,0.9590823265750552
+0.5275003147536337,1.7544889607956993
+-0.6556512012523673,0.0008258867649472146
+-0.24467673075401059,1.66761554170765
+0.41711776876093426,-0.5531274426415684
+-0.07417902217179523,0.8352224831214239
+1.6539142537284157,-1.8118069042968519
+-0.14556149331575774,0.11905198981829584
+1.4328625846982002,-0.7379863442403529
+-0.3454740003778699,-0.4514083628945922
+0.9974614887821758,0.7707015697864064
+1.4611208632268786,-0.544525348302085
+1.2685692965232467,-1.6274611459004675
+0.8022137712706272,-0.8839482849042763
+1.3710603019445184,-0.7133675321822412
+0.8551647383751675,-0.4163839323030733
+1.2996800245459041,-1.2124568151489297
+-0.004184629956878544,0.007551822496386418
+-1.046171401579347,0.8205104181844113
+-0.34409932328699777,1.2199317747101022
+1.1900154980687743,-0.05822617592483137
+0.01631367958834451,0.03847005934898328
+0.5833344053311785,-0.171352164414001
+0.0782594019873169,1.7249023442790317
+0.434912258427936,1.4519108345802576
+1.2244937121794308,0.06705405425002142
+-0.25111739071605826,1.283182285929227
+1.0012083579146585,0.6006476646921097
+-0.6285392095299172,0.7891999953203211
+1.2525155802966867,-0.06819743184693522
+-0.8005805124878281,0.9590823265750552
+0.5275003147536337,1.7544889607956993
+-0.683087376321845,1.3455332411594518
+-0.24467673075401059,1.66761554170765
+0.41711776876093426,-0.5531274426415684
+-0.3565405341349327,0.7496419598797974
+1.6539142537284157,-1.8118069042968519
+-0.14556149331575774,0.11905198981829584
+1.4328625846982002,-0.7379863442403529
+-0.3454740003778699,-0.4514083628945922
+0.6169811874212584,-0.23810414217277837
+0.600175030215606,-0.18997381778213174
+1.2685692965232467,-1.6274611459004675
+1.1116787065350566,0.4129736855269701
+0.1528150161543098,1.4622680660621956
+0.8551647383751675,-0.4163839323030733
+1.2996800245459041,-1.2124568151489297
+1.6732669376870204,-1.233270785692582
+1.1931190050213056,-0.2989573810028986
+-0.34409932328699777,1.2199317747101022
+1.1900154980687743,-0.05822617592483137
+0.01631367958834451,0.03847005934898328
+0.5833344053311785,-0.171352164414001
+0.0782594019873169,1.7249023442790317
+0.434912258427936,1.4519108345802576
+1.2244937121794308,0.06705405425002142
+-0.25111739071605826,1.283182285929227
+0.8419821693568752,-0.5002095285282031
+-0.5677358851218759,0.7283225263887515
+-0.3913304602633366,2.1333315531603674
+-0.6356621672116998,0.9487608187147656
+0.21792522715658552,0.12050207475696836
+-0.683087376321845,1.3455332411594518
+-0.24467673075401059,1.66761554170765
+0.44857456830230313,1.6496310245772168
+0.8354024862915512,1.1887509029370302
+-0.6623940823574739,0.6722246456418091
+0.24136975556407816,0.3867756265059522
+0.30896262946746716,-0.6151436008382349
+0.6934032744659906,1.0363992621004383
+0.6169811874212584,-0.23810414217277837
+0.600175030215606,-0.18997381778213174
+1.2685692965232467,-1.6274611459004675
+1.1116787065350566,0.4129736855269701
+0.1528150161543098,1.4622680660621956
+0.8551647383751675,-0.4163839323030733
+0.6891282248670063,-0.18262312980154002
+1.6732669376870204,-1.233270785692582
+0.3744397712724092,0.592027596862881
+-0.34409932328699777,1.2199317747101022
+1.1900154980687743,-0.05822617592483137
+0.01631367958834451,0.03847005934898328
+0.5833344053311785,-0.171352164414001
+-0.09798827940900112,1.9611261892980458
+0.434912258427936,1.4519108345802576
+1.2244937121794308,0.06705405425002142
+0.9555464228200208,0.39767985483069196
+-0.32570902675680874,1.3412070375191418
+-0.5677358851218759,0.7283225263887515
+-0.3913304602633366,2.1333315531603674
+-0.6356621672116998,0.9487608187147656
+0.18039505194212102,0.3725194824677279
+1.010618861314982,-0.8882776435757975
+0.29802569804888696,0.552830675395772
+0.44857456830230313,1.6496310245772168
+0.8354024862915512,1.1887509029370302
+-0.6623940823574739,0.6722246456418091
+1.6006511140099888,-1.8252275638143192
+1.6570197338238517,-1.2142481755989925
+0.6934032744659906,1.0363992621004383
+1.5283576210143108,-2.0684387304835092
+0.600175030215606,-0.18997381778213174
+1.2685692965232467,-1.6274611459004675
+1.1116787065350566,0.4129736855269701
+0.7409204251480721,1.081434193889055
+0.5645622648701538,-0.3070816389239618
+0.957297395413316,1.183993513084614
+1.6732669376870204,-1.233270785692582
+-0.12559083027726806,0.5518768454499952
+-0.9864718828191089,0.6117328741153452
+1.1900154980687743,-0.05822617592483137
+0.01631367958834451,0.03847005934898328
+1.2699322073028343,-0.8310686215342217
+-0.09798827940900112,1.9611261892980458
+1.1094291265105791,0.5173818416851209
+1.2244937121794308,0.06705405425002142
+0.9555464228200208,0.39767985483069196
+-0.32570902675680874,1.3412070375191418
+-0.5677358851218759,0.7283225263887515
+-0.3913304602633366,2.1333315531603674
+-0.6356621672116998,0.9487608187147656
+-0.6247350640908512,1.0989498125710915
+0.4641369130651839,-0.17413629894390747
+1.3761378360535992,-0.7148839462065104
+0.44857456830230313,1.6496310245772168
+-0.1260446391716199,0.4559404078138128
+-0.6623940823574739,0.6722246456418091
+0.9111080414325979,0.4391961609962961
+1.6570197338238517,-1.2142481755989925
+0.6934032744659906,1.0363992621004383
+1.5283576210143108,-2.0684387304835092
+0.9556657583504857,0.6397739569916842
+1.2685692965232467,-1.6274611459004675
+-1.0875297593077344,-0.20101043509907146
+1.2548267926650043,-1.65944944875132
+0.5645622648701538,-0.3070816389239618
+0.3808964318930598,1.3266294392957578
+1.6732669376870204,-1.233270785692582
+1.1614348731444588,-1.5782433688605915
+-0.7956563634624745,-0.38259140082976195
+0.3344548684516735,0.7977850346012394
+0.01631367958834451,0.03847005934898328
+1.2699322073028343,-0.8310686215342217
+-0.09798827940900112,1.9611261892980458
+1.1094291265105791,0.5173818416851209
+1.457206093153376,-0.5268084988792778
+1.226691372102128,-0.6118065378208637
+-0.021647041178529614,0.8131902142811654
+-0.5677358851218759,0.7283225263887515
+-0.3913304602633366,2.1333315531603674
+-0.6356621672116998,0.9487608187147656
+-0.6247350640908512,1.0989498125710915
+-0.29561430469230715,0.24772203815191163
+-0.4170908779946123,0.18746991942098856
+0.44857456830230313,1.6496310245772168
+-0.1260446391716199,0.4559404078138128
+-0.6623940823574739,0.6722246456418091
+-0.2538729949075287,1.7570024428822608
+1.1831441038969965,-0.14056708367356396
+0.6934032744659906,1.0363992621004383
+1.5283576210143108,-2.0684387304835092
+0.9556657583504857,0.6397739569916842
+1.2685692965232467,-1.6274611459004675
+-1.0875297593077344,-0.20101043509907146
+1.2548267926650043,-1.65944944875132
+0.7319565264848632,-0.8949803204400737
+0.3808964318930598,1.3266294392957578
+1.6732669376870204,-1.233270785692582
+1.1614348731444588,-1.5782433688605915
+-0.6010104137799317,1.0134718282852644
+0.3344548684516735,0.7977850346012394
+0.01631367958834451,0.03847005934898328
+-0.44194538663624094,1.2607923430299266
+-0.09798827940900112,1.9611261892980458
+-0.9105797137308992,0.17011372751986292
+1.457206093153376,-0.5268084988792778
+1.226691372102128,-0.6118065378208637
+-0.23331417597361412,1.6125081337428395
+-0.6313099882143149,0.5878938048555933
+-0.3913304602633366,2.1333315531603674
+-0.3589114576994924,1.3073723092788563
+0.07908979337850097,1.986157699434358
+-0.29561430469230715,0.24772203815191163
+-0.4170908779946123,0.18746991942098856
+0.44857456830230313,1.6496310245772168
+-0.32656174489259016,0.3701925346564444
+-0.6623940823574739,0.6722246456418091
+-0.2538729949075287,1.7570024428822608
+-0.19154455728903758,0.11333733543639979
+0.6934032744659906,1.0363992621004383
+1.5283576210143108,-2.0684387304835092
+0.9556657583504857,0.6397739569916842
+0.37172930104641566,1.2274191799194258
+-1.0875297593077344,-0.20101043509907146
+-0.24202748166597177,0.32904354758251847
+0.7319565264848632,-0.8949803204400737
+0.3808964318930598,1.3266294392957578
+1.6732669376870204,-1.233270785692582
+1.1614348731444588,-1.5782433688605915
+-0.6010104137799317,1.0134718282852644
+0.3344548684516735,0.7977850346012394
+1.194520830519426,-1.3400846987555632
+-0.44194538663624094,1.2607923430299266
+-0.09798827940900112,1.9611261892980458
+-0.9105797137308992,0.17011372751986292
+1.457206093153376,-0.5268084988792778
+1.226691372102128,-0.6118065378208637
+-0.23331417597361412,1.6125081337428395
+0.9387030604489562,-0.1135660432594221
+0.9472927800966031,0.9556567778589822
+0.798261028220262,1.0223439222279598
+0.07908979337850097,1.986157699434358
+-0.29561430469230715,0.24772203815191163
+-0.4170908779946123,0.18746991942098856
+0.17093248875223807,0.24060644885753132
+-0.32656174489259016,0.3701925346564444
+-0.6623940823574739,0.6722246456418091
+-0.2538729949075287,1.7570024428822608
+-0.19154455728903758,0.11333733543639979
+0.6934032744659906,1.0363992621004383
+1.5283576210143108,-2.0684387304835092
+0.5523660543261745,-0.6178467158570404
+0.18628010031465586,-0.2489579720506293
+-0.7724667314309797,-0.05956191395773852
+0.16892528857950573,0.15478635855619263
+0.7319565264848632,-0.8949803204400737
+1.3402120627157066,-1.817145136109431
+1.6732669376870204,-1.233270785692582
+1.0552066548270516,0.0650819046167761
+-0.6010104137799317,1.0134718282852644
+0.3344548684516735,0.7977850346012394
+1.194520830519426,-1.3400846987555632
+-0.594822390914426,0.7038827525872009
+-0.09798827940900112,1.9611261892980458
+-0.9105797137308992,0.17011372751986292
+1.457206093153376,-0.5268084988792778
+-0.652304210530018,1.3741998439340877
+-0.23331417597361412,1.6125081337428395
+0.9387030604489562,-0.1135660432594221
+-0.4923733156844098,-0.17596879539781907
+0.798261028220262,1.0223439222279598
+0.07908979337850097,1.986157699434358
+-0.10837251827546557,-0.2725027709270416
+1.2085652221599266,-1.3171026120609073
+0.17093248875223807,0.24060644885753132
+-0.32656174489259016,0.3701925346564444
+-0.4494271128266655,-0.08965783188688162
+1.750884817900733,-2.6320075950911517
+-0.19154455728903758,0.11333733543639979
+0.6934032744659906,1.0363992621004383
+1.5283576210143108,-2.0684387304835092
+-0.75843783935881,0.6912152964381773
+-0.4927423856670893,1.1950483170883093
+-0.7724667314309797,-0.05956191395773852
+-1.2144882306576585,-0.35807759851613574
+0.7319565264848632,-0.8949803204400737
+1.3402120627157066,-1.817145136109431
+1.6732669376870204,-1.233270785692582
+-0.9748086913573625,0.7203553107500354
+-0.6010104137799317,1.0134718282852644
+1.3525571258453954,-0.576095675021297
+0.9548120807026637,0.8632994906865954
+0.27807395350976355,0.1013727524226804
+-0.5146545814265742,0.9702861438611285
+-0.9105797137308992,0.17011372751986292
+1.457206093153376,-0.5268084988792778
+1.2722307321992967,-0.7216979246242481
+0.4603168382328299,0.7907882308479608
+0.9387030604489562,-0.1135660432594221
+0.613736720313198,-0.254339097970933
+0.798261028220262,1.0223439222279598
+0.07908979337850097,1.986157699434358
+-0.10837251827546557,-0.2725027709270416
+1.2085652221599266,-1.3171026120609073
+0.17093248875223807,0.24060644885753132
+-0.5468035474083899,-0.09713524504752805
+-0.6842564731130867,0.7715172882603585
+1.750884817900733,-2.6320075950911517
+-0.19154455728903758,0.11333733543639979
+0.11979425557287347,0.22527442255842514
+1.1648364519648857,-1.3762326998470202
+-0.75843783935881,0.6912152964381773
+-0.4927423856670893,1.1950483170883093
+-0.7724667314309797,-0.05956191395773852
+-1.2144882306576585,-0.35807759851613574
+0.7319565264848632,-0.8949803204400737
+1.3402120627157066,-1.817145136109431
+1.6732669376870204,-1.233270785692582
+-0.9748086913573625,0.7203553107500354
+-0.6010104137799317,1.0134718282852644
+1.3525571258453954,-0.576095675021297
+0.9548120807026637,0.8632994906865954
+0.27807395350976355,0.1013727524226804
+0.6589325774487171,0.10636388310049394
+0.7029926040399237,0.5235242009284738
+1.457206093153376,-0.5268084988792778
+1.2722307321992967,-0.7216979246242481
+0.4603168382328299,0.7907882308479608
+0.4049951478862912,-0.6679137208503603
+-0.1561891090681916,0.601821759204602
+-0.03585868434778866,1.4681822783797833
+0.07908979337850097,1.986157699434358
+-0.10837251827546557,-0.2725027709270416
+1.2085652221599266,-1.3171026120609073
+0.909954477175442,-0.8329610543376416
+-0.5511013396770246,0.057091964316167296
+-0.6842564731130867,0.7715172882603585
+-0.24126391675602576,1.7866460543111855
+0.18579489683843686,-0.20791608180076282
+0.11979425557287347,0.22527442255842514
+1.1648364519648857,-1.3762326998470202
+-0.75843783935881,0.6912152964381773
+-0.4927423856670893,1.1950483170883093
+0.9981062828346232,-0.7195147017589101
+-1.2144882306576585,-0.35807759851613574
+1.5589532352494773,-1.89224876883101
+0.4941048004624833,0.07539149718825805
+1.6732669376870204,-1.233270785692582
+-0.40564356895721254,-0.04357307026542945
+-0.6010104137799317,1.0134718282852644
+-0.4778493499728589,0.47924279126034475
+0.9548120807026637,0.8632994906865954
+0.27807395350976355,0.1013727524226804
+1.4961729747929455,-0.673047509086691
+0.8247232481190471,-0.14213007500164065
+1.457206093153376,-0.5268084988792778
+0.5092413284268217,-0.3096718545629444
+0.39869535785822785,1.4145429605491413
+0.4049951478862912,-0.6679137208503603
+1.4104187707741775,-0.9396905627043501
+-0.03585868434778866,1.4681822783797833
+0.07908979337850097,1.986157699434358
+0.9477359755100893,-1.094782052083073
+1.267112536999106,-1.2285827445121824
+0.9636095527020099,-0.6754240408339813
+-0.5511013396770246,0.057091964316167296
+-0.6842564731130867,0.7715172882603585
+0.2133677450939553,1.452708994057824
+0.18579489683843686,-0.20791608180076282
+-0.13246723483549672,0.5912465378647435
+-0.50307523858999,0.003312748911362587
+-0.75843783935881,0.6912152964381773
+-0.7895941116594488,-0.04298252524763646
+0.9981062828346232,-0.7195147017589101
+-1.2144882306576585,-0.35807759851613574
+1.5589532352494773,-1.89224876883101
+0.4941048004624833,0.07539149718825805
+1.2099535820215448,0.1493846107048758
+0.4079600280710788,-0.313122673077784
+-0.04100262865904209,0.8384766339904053
+-0.6827344968059692,-0.18447504852634544
+0.9548120807026637,0.8632994906865954
+0.27807395350976355,0.1013727524226804
+1.4961729747929455,-0.673047509086691
+0.33649048771211243,-0.7511910834263525
+1.457206093153376,-0.5268084988792778
+0.5092413284268217,-0.3096718545629444
+0.480093435217547,-0.3224989457357321
+0.0865451214891706,1.1439438609738124
+0.8631476060664853,-0.3452511471670655
+-0.07877791519733723,0.0871363193223682
+0.07908979337850097,1.986157699434358
+0.9477359755100893,-1.094782052083073
+-0.6827324951517539,1.2460852166860281
+-0.8533809923059894,-0.18081260280449357
+0.0816163617560437,0.7428475990079635
+-0.6842564731130867,0.7715172882603585
+0.2133677450939553,1.452708994057824
+1.1866934248797516,0.19729962699329173
+1.263318934654816,-1.4185221551149105
+-0.50307523858999,0.003312748911362587
+-0.75843783935881,0.6912152964381773
+-0.7895941116594488,-0.04298252524763646
+-0.5738588051959657,0.4532691637049314
+0.1915796252730565,1.2607742053700646
+1.5589532352494773,-1.89224876883101
+0.4941048004624833,0.07539149718825805
+1.2099535820215448,0.1493846107048758
+0.4079600280710788,-0.313122673077784
+-0.04100262865904209,0.8384766339904053
+-0.6827344968059692,-0.18447504852634544
+0.8087193580530547,0.253341451638137
+0.27807395350976355,0.1013727524226804
+1.4961729747929455,-0.673047509086691
+0.33649048771211243,-0.7511910834263525
+1.457206093153376,-0.5268084988792778
+0.5092413284268217,-0.3096718545629444
+-0.6415037204680634,-0.04198598957048613
+0.0865451214891706,1.1439438609738124
+0.8631476060664853,-0.3452511471670655
+0.193549674983731,0.8492478017376229
+-0.43484843410570556,0.14354940268762117
+0.9477359755100893,-1.094782052083073
+-0.6827324951517539,1.2460852166860281
+-0.732776482562886,0.5838397967748113
+-0.811606392814459,0.09668937140731837
+0.29255264409862447,1.278892145759225
+0.2133677450939553,1.452708994057824
+-0.38719646389155804,2.082934262481008
+1.263318934654816,-1.4185221551149105
+-0.8053704379627467,0.9054735070305069
+0.10458224719360965,-0.3260042499984875
+0.06865052773221217,1.3354211127548887
+0.27707717846338287,0.27815459564792133
+0.1915796252730565,1.2607742053700646
+1.5589532352494773,-1.89224876883101
+1.0058058277047648,1.1798561185378005
+1.2099535820215448,0.1493846107048758
+0.4079600280710788,-0.313122673077784
+0.20514864085967208,0.8843777399640149
+0.5142560945123458,-0.48145638470827257
+-0.26614397371125487,2.1480846979990575
+0.27807395350976355,0.1013727524226804
+1.4961729747929455,-0.673047509086691
+-0.25225958051782543,2.0726986980802398
+1.457206093153376,-0.5268084988792778
+0.5092413284268217,-0.3096718545629444
+-0.1482636676678562,0.2654588002488791
+0.0865451214891706,1.1439438609738124
+-0.6495257796489327,-0.16094321937298722
+0.193549674983731,0.8492478017376229
+-0.43484843410570556,0.14354940268762117
+0.9477359755100893,-1.094782052083073
+-0.6592562313872302,0.6967235753024827
+1.3898678918972673,-1.5263840871358567
+-0.8317462338704271,0.8572668344071304
+0.22589061304790364,1.860861886060417
+0.6483120852924463,1.489219937252231
+-0.38719646389155804,2.082934262481008
+-0.18424349540068738,1.919545123874071
+1.114451984916088,-0.7419534327109287
+0.10458224719360965,-0.3260042499984875
+0.06865052773221217,1.3354211127548887
+0.6061643229033886,-0.013134101762246997
+0.1915796252730565,1.2607742053700646
+1.5589532352494773,-1.89224876883101
+0.1950413376011415,0.09934745851214344
+1.0886399342188473,0.3530522511045102
+0.4079600280710788,-0.313122673077784
+0.20514864085967208,0.8843777399640149
+0.5869557670363226,0.1442386264014988
+-0.26614397371125487,2.1480846979990575
+1.557614100816,-2.0311990886921576
+-0.8691486787564622,0.6931108680103453
+-0.375419634445903,0.33668480713778703
+1.457206093153376,-0.5268084988792778
+0.5092413284268217,-0.3096718545629444
+-0.5252650314126154,0.4098034595541055
+0.17855829354328917,2.107931918442554
+-0.6495257796489327,-0.16094321937298722
+0.9871783801728498,-0.9124281818490318
+0.33102564464157463,-0.3040469312412039
+-0.5925877684414743,0.27965684892265535
+-0.6592562313872302,0.6967235753024827
+1.3898678918972673,-1.5263840871358567
+0.3114398319816758,1.9601543892145028
+0.06891842027567141,-0.4279067343213021
+0.6483120852924463,1.489219937252231
+-0.38719646389155804,2.082934262481008
+-0.18424349540068738,1.919545123874071
+1.114451984916088,-0.7419534327109287
+-0.17785264837636583,0.5253725832037085
+-0.557196171149626,0.8017125806636323
+0.6061643229033886,-0.013134101762246997
+-0.31993601351640655,0.2543828634466322
+1.5589532352494773,-1.89224876883101
+0.1950413376011415,0.09934745851214344
+1.0886399342188473,0.3530522511045102
+0.7248315385207159,0.6040268319464035
+0.20514864085967208,0.8843777399640149
+0.5271834609311747,1.528003219337573
+-0.26614397371125487,2.1480846979990575
+-0.8836994118942341,0.4523561440866382
+-0.3076386139592864,0.0011996010184512906
+-0.375419634445903,0.33668480713778703
+0.4394604091957019,1.5714302264623239
+0.6615744137850584,1.4459551847564942
+-0.5252650314126154,0.4098034595541055
+0.17855829354328917,2.107931918442554
+-0.6495257796489327,-0.16094321937298722
+1.6155574687373007,-1.4351530497778346
+0.33102564464157463,-0.3040469312412039
+1.1940247564500943,-0.8105049745002584
+-0.6592562313872302,0.6967235753024827
+1.3898678918972673,-1.5263840871358567
+0.3114398319816758,1.9601543892145028
+0.06891842027567141,-0.4279067343213021
+0.6483120852924463,1.489219937252231
+-0.38719646389155804,2.082934262481008
+0.22479795743490072,-0.3448771952608294
+1.114451984916088,-0.7419534327109287
+-0.3104863576435703,0.08083274186391498
+-0.557196171149626,0.8017125806636323
+0.6061643229033886,-0.013134101762246997
+0.0623483613305289,0.14354762561507634
+1.5589532352494773,-1.89224876883101
+-0.6861653102893247,0.2950815379221395
+1.0886399342188473,0.3530522511045102
+0.7248315385207159,0.6040268319464035
+0.20514864085967208,0.8843777399640149
+1.4363985374656294,-1.3351592242568089
+-0.26614397371125487,2.1480846979990575
+-0.17646893546840142,2.1709015864008916
+1.1845683486450815,-1.374300702911914
+-0.375419634445903,0.33668480713778703
+-0.19529093677971332,2.1202518418813256
+0.6615744137850584,1.4459551847564942
+1.5380658853626408,-1.8024091555678186
+-0.782450541775222,1.2215677266499392
+-0.6495257796489327,-0.16094321937298722
+1.6155574687373007,-1.4351530497778346
+0.33102564464157463,-0.3040469312412039
+0.5083214831262071,1.9461420915329253
+-0.6592562313872302,0.6967235753024827
+1.7639491199838806,-1.674364387956122
+1.0577480543433868,0.5650847558818082
+0.9810400812442394,1.0374221985239895
+0.6483120852924463,1.489219937252231
+-0.38719646389155804,2.082934262481008
+-0.5065522707473323,-0.24565282751487466
+1.6549189674465186,-2.4079554269139094
+-0.3104863576435703,0.08083274186391498
+-0.05764488890529354,1.237032570175823
+1.3888829074223645,-1.576424612944133
+0.0623483613305289,0.14354762561507634
+1.5589532352494773,-1.89224876883101
+-0.6456394433358298,0.5280975849724083
+1.0886399342188473,0.3530522511045102
+0.7248315385207159,0.6040268319464035
+-0.1084823253445335,0.1727034856320509
+1.4363985374656294,-1.3351592242568089
+-0.26614397371125487,2.1480846979990575
+0.4419876574190687,1.890195207693562
+1.1845683486450815,-1.374300702911914
+-0.375419634445903,0.33668480713778703
+-0.19529093677971332,2.1202518418813256
+0.6615744137850584,1.4459551847564942
+1.5380658853626408,-1.8024091555678186
+-0.782450541775222,1.2215677266499392
+0.374566327340363,0.4408640088040976
+0.7030404596517974,-0.7051863613173494
+0.33102564464157463,-0.3040469312412039
+0.5083214831262071,1.9461420915329253
+-0.6592562313872302,0.6967235753024827
+-0.33757695327156684,0.113803920235997
+1.0577480543433868,0.5650847558818082
+0.5327727046744996,-0.5806887765635955
+0.6483120852924463,1.489219937252231
+0.15683099036774228,1.5448639820913492
+0.315823332046519,1.783860640623921
+0.9286397544537686,0.5065565991050617
+-0.3104863576435703,0.08083274186391498
+0.20984813219370663,0.4624160397758644
+-0.33869700027824123,0.08980114844407433
+0.0623483613305289,0.14354762561507634
+1.5589532352494773,-1.89224876883101
+0.5016884294866948,-0.39810213201432804
+1.0886399342188473,0.3530522511045102
+-0.8743126390420057,0.1490684927394731
+0.1854284533935916,1.914079128606659
+1.4363985374656294,-1.3351592242568089
+-0.13504442578712927,0.4150994068246325
+0.4419876574190687,1.890195207693562
+0.5638809171369286,-0.584358554626252
+-0.22458485278094478,2.2567062330933005
+0.8127523519924372,-0.7777090915873404
+0.41678834981100726,-0.09982813818326608
+1.5380658853626408,-1.8024091555678186
+0.21227916079696033,1.740523120551251
+-0.3743247894211635,0.8268486970327285
+0.3103465071297966,1.3539000455592753
+0.4044295460061481,0.66835281495801
+1.6248780336781945,-1.3436045161742747
+-0.6592562313872302,0.6967235753024827
+-0.33757695327156684,0.113803920235997
+-0.31836470052522825,1.7305098199776858
+-0.1039897182600687,2.103391967616695
+1.5161352216914834,-0.44506675792761274
+-0.30908401054288814,-0.280601653992535
+0.7803149907113861,-0.7863866375820434
+-0.027763653981903447,-0.19269709007899471
+-0.3104863576435703,0.08083274186391498
+0.6565623324227248,-0.9114128703919488
+-0.5608888367910628,-0.13420104294151658
+0.5740572606642168,1.2996328588497894
+1.1554667461984405,-1.2121691378408264
+0.5016884294866948,-0.39810213201432804
+1.0886399342188473,0.3530522511045102
+-0.8743126390420057,0.1490684927394731
+0.1854284533935916,1.914079128606659
+1.4363985374656294,-1.3351592242568089
+-0.13504442578712927,0.4150994068246325
+0.4419876574190687,1.890195207693562
+0.5638809171369286,-0.584358554626252
+-0.22458485278094478,2.2567062330933005
+0.8127523519924372,-0.7777090915873404
+1.0221752519777163,0.8618260916317981
+0.4476498360265038,1.7200485331874722
+-0.4776094362022159,1.0577482212725948
+-0.3743247894211635,0.8268486970327285
+-0.7026620335385791,0.8636188365955986
+0.4044295460061481,0.66835281495801
+1.6248780336781945,-1.3436045161742747
+-0.6592562313872302,0.6967235753024827
+0.897175880809894,1.2156418021495186
+0.3133680482372218,1.5249933410558225
+-0.37117995372393503,0.7343100916247601
+1.5161352216914834,-0.44506675792761274
+-0.30908401054288814,-0.280601653992535
+1.0639061908471934,-0.5246346470466461
+-0.027763653981903447,-0.19269709007899471
+-0.5271483632672902,0.033125905808022035
+-0.0675640842911936,1.6024699774381468
+-0.5608888367910628,-0.13420104294151658
+0.34063116122463577,-0.1129176563859825
+1.1554667461984405,-1.2121691378408264
+0.5016884294866948,-0.39810213201432804
+1.0886399342188473,0.3530522511045102
+-0.8743126390420057,0.1490684927394731
+0.18659181499041605,0.5624608086203158
+1.4363985374656294,-1.3351592242568089
+1.3109596483546013,0.21141147657624382
+0.4419876574190687,1.890195207693562
+0.5638809171369286,-0.584358554626252
+-0.22458485278094478,2.2567062330933005
+0.8127523519924372,-0.7777090915873404
+1.0221752519777163,0.8618260916317981
+0.4476498360265038,1.7200485331874722
+0.3290798669859627,2.2460307070873347
+-0.3743247894211635,0.8268486970327285
+-0.7026620335385791,0.8636188365955986
+0.4044295460061481,0.66835281495801
+1.6248780336781945,-1.3436045161742747
+-0.6592562313872302,0.6967235753024827
+0.897175880809894,1.2156418021495186
+0.3133680482372218,1.5249933410558225
+-0.37117995372393503,0.7343100916247601
+1.5161352216914834,-0.44506675792761274
+-0.30908401054288814,-0.280601653992535
+1.0639061908471934,-0.5246346470466461
+-0.027763653981903447,-0.19269709007899471
+0.08864610230648912,-0.09987360820593333
+-0.0675640842911936,1.6024699774381468
+0.5410530376632907,-0.4442650180426991
+0.34063116122463577,-0.1129176563859825
+1.1554667461984405,-1.2121691378408264
+0.5016884294866948,-0.39810213201432804
+1.0886399342188473,0.3530522511045102
+-0.6444194422016803,1.6056356465913764
+0.033238526956228504,0.7146507428220358
+1.4363985374656294,-1.3351592242568089
+1.3109596483546013,0.21141147657624382
+-0.2544212298843167,1.7988639599001053
+0.5638809171369286,-0.584358554626252
+-0.22458485278094478,2.2567062330933005
+0.8127523519924372,-0.7777090915873404
+1.0221752519777163,0.8618260916317981
+1.6343084593959314,-2.1101316097096205
+0.3290798669859627,2.2460307070873347
+0.14345693056516945,0.18967251486898834
+-0.7026620335385791,0.8636188365955986
+1.0981930427106137,0.6495549065255687
+1.6248780336781945,-1.3436045161742747
+-0.21454627657975872,0.8927743831466227
+-0.026663681607142387,1.4535106474560768
+1.7038472925178778,-2.3225911731551285
+-0.37117995372393503,0.7343100916247601
+1.0484566895057514,-0.1284295386221933
+-0.30908401054288814,-0.280601653992535
+-0.40635972816409116,0.5121687015119658
+-0.45203914355466845,1.3844808993744813
+1.4946516751690562,-1.8647659108864647
+-0.0675640842911936,1.6024699774381468
+0.5410530376632907,-0.4442650180426991
+0.34063116122463577,-0.1129176563859825
+1.1554667461984405,-1.2121691378408264
+-0.11547552866470234,0.191590955904605
+0.8259270301204089,1.1995459716526509
+-0.6444194422016803,1.6056356465913764
+0.9416347089236743,-1.0270482554249107
+1.4363985374656294,-1.3351592242568089
+-0.6260230909861626,1.2071622034906688
+1.3582048628345773,-1.4741006439406465
+0.23726117823041548,0.4207899507595798
+-0.22458485278094478,2.2567062330933005
+0.3810998393508307,0.2832114524506001
+-0.04190346104870124,0.05208619929820811
+1.6343084593959314,-2.1101316097096205
+1.4071235778823432,-1.1926876425649358
+1.4917953527209808,-2.073372718681295
+-0.7026620335385791,0.8636188365955986
+-0.02410049385454688,1.9133087189974856
+1.6248780336781945,-1.3436045161742747
+-0.22306417607301626,1.2932798713688833
+0.9637859197185794,0.9851764701030066
+1.7038472925178778,-2.3225911731551285
+-0.37117995372393503,0.7343100916247601
+1.1353351317481268,-1.3578225250395768
+-0.30908401054288814,-0.280601653992535
+0.5669006458742112,0.0809551922263424
+-0.45203914355466845,1.3844808993744813
+0.03114798076133382,-0.10969639498519035
+0.5180058194232304,-0.2532287341038016
+0.5410530376632907,-0.4442650180426991
+0.34063116122463577,-0.1129176563859825
+1.353504288869721,-0.8127341716291047
+-0.11547552866470234,0.191590955904605
+0.8259270301204089,1.1995459716526509
+1.1568890266389944,-0.8241207009132008
+0.9416347089236743,-1.0270482554249107
+1.4363985374656294,-1.3351592242568089
+-0.6260230909861626,1.2071622034906688
+1.335541868196232,-0.07125866756907262
+1.228562376313773,-1.1470146603778455
+-0.22458485278094478,2.2567062330933005
+0.3810998393508307,0.2832114524506001
+1.1618146094361832,-0.8228544511619563
+1.4069610971945017,-0.9577731646070878
+1.3293066039554067,-1.8971599234865215
+0.057502309565905935,1.8670952357704398
+-0.7026620335385791,0.8636188365955986
+0.8410988627589675,0.7810961264194238
+1.6248780336781945,-1.3436045161742747
+-0.22306417607301626,1.2932798713688833
+0.9637859197185794,0.9851764701030066
+1.4693055322097879,-0.5910667327129882
+-0.0698621347582894,1.8651216123893253
+1.1353351317481268,-1.3578225250395768
+-0.6851874298241377,0.919027394632713
+-0.32494876906732834,1.8799079884805066
+0.4844620322252542,2.0198293024631258
+0.03114798076133382,-0.10969639498519035
+0.5180058194232304,-0.2532287341038016
+0.5410530376632907,-0.4442650180426991
+0.34063116122463577,-0.1129176563859825
+1.353504288869721,-0.8127341716291047
+-0.11547552866470234,0.191590955904605
+0.8259270301204089,1.1995459716526509
+0.39299945128990565,-0.15850246249838587
+1.2325928938165096,0.19140690774993518
+1.0445949542320518,0.4149016740074074
+-0.6260230909861626,1.2071622034906688
+0.5344432215719297,2.126185974160037
+1.3405303684263346,-1.1355896708909472
+-0.21832112409051377,0.5100119551101797
+0.4619750280491382,1.6263847129622508
+1.655062606177684,-1.1284972212733793
+1.4069610971945017,-0.9577731646070878
+1.0131160341574386,0.7963326088040197
+0.057502309565905935,1.8670952357704398
+-0.7026620335385791,0.8636188365955986
+-0.6733380121877746,1.3525911550769296
+0.6978570978515759,1.483561949379376
+-0.37602218651223396,0.18087104033180867
+0.9637859197185794,0.9851764701030066
+1.4693055322097879,-0.5910667327129882
+-0.0698621347582894,1.8651216123893253
+-0.2947038611995108,2.453899977814136
+1.6707544873988531,-1.774469961045393
+1.164149168590157,-0.6987498754012285
+0.4844620322252542,2.0198293024631258
+0.45660058935801695,-0.32773514361578027
+0.5180058194232304,-0.2532287341038016
+0.5410530376632907,-0.4442650180426991
+0.5854401616425855,0.10557040813260876
+1.353504288869721,-0.8127341716291047
+-0.11547552866470234,0.191590955904605
+-0.501407910005112,1.9827992639833047
+1.584679938110507,-1.1413293691107753
+1.2325928938165096,0.19140690774993518
+1.0445949542320518,0.4149016740074074
+-0.6260230909861626,1.2071622034906688
+1.5242777255552413,-2.2966587640979004
+1.3405303684263346,-1.1355896708909472
+-0.21832112409051377,0.5100119551101797
+-0.5163621185777999,1.746421745322126
+1.655062606177684,-1.1284972212733793
+1.4069610971945017,-0.9577731646070878
+1.0131160341574386,0.7963326088040197
+0.057502309565905935,1.8670952357704398
+0.4248592029639318,-0.13627949259417171
+-0.6733380121877746,1.3525911550769296
+0.6978570978515759,1.483561949379376
+-0.37602218651223396,0.18087104033180867
+-0.3451049462606201,0.26165157184438687
+1.2483276217416557,-0.5258140731631982
+-0.0698621347582894,1.8651216123893253
+0.853719554331677,0.02992313254404988
+1.6707544873988531,-1.774469961045393
+0.15336906655138155,0.0469681778991172
+0.4844620322252542,2.0198293024631258
+0.5966037609195863,-0.8090167943943818
+0.5605386495262364,1.2123669464508324
+0.5410530376632907,-0.4442650180426991
+0.5854401616425855,0.10557040813260876
+1.353504288869721,-0.8127341716291047
+-0.04713910318026393,0.3431224470045123
+-0.47440570642217084,0.4809695959612028
+0.07455275404988734,0.271075595940408
+1.2325928938165096,0.19140690774993518
+1.0445949542320518,0.4149016740074074
+-0.013585418457580656,1.241379512417402
+1.5242777255552413,-2.2966587640979004
+0.36180928498005765,-0.05782781207075434
+-0.21832112409051377,0.5100119551101797
+-0.5163621185777999,1.746421745322126
+1.655062606177684,-1.1284972212733793
+1.4069610971945017,-0.9577731646070878
+1.0131160341574386,0.7963326088040197
+0.057502309565905935,1.8670952357704398
+0.4248592029639318,-0.13627949259417171
+-0.6733380121877746,1.3525911550769296
+0.6978570978515759,1.483561949379376
+-0.03388589361616991,1.7167770640179247
+0.20411728983414257,0.5183800503450766
+1.4014346635666408,-0.4154312500704368
+0.6163245441913257,1.663841933723584
+0.7627456428334926,-0.18974370223823156
+1.6707544873988531,-1.774469961045393
+-0.9331867059418506,0.8324480242516683
+-0.004868346828201253,1.6171766710908575
+0.5966037609195863,-0.8090167943943818
+0.5605386495262364,1.2123669464508324
+0.05854560666132386,-0.3498679676798728
+-0.46470656378939706,1.3798169992382332
+1.353504288869721,-0.8127341716291047
+-0.04713910318026393,0.3431224470045123
+-0.47440570642217084,0.4809695959612028
+0.07455275404988734,0.271075595940408
+1.2325928938165096,0.19140690774993518
+1.6677638356096391,-1.4609912426725953
+1.123321346809153,-1.686322794493118
+-0.6807097354993445,1.0638585171484887
+0.7737135517289278,0.9326291294131946
+0.28984100918763533,0.46617189702501816
+-0.5163621185777999,1.746421745322126
+1.655062606177684,-1.1284972212733793
+1.4069610971945017,-0.9577731646070878
+1.0401555936064333,0.7366138261299214
+0.057502309565905935,1.8670952357704398
+-0.9080413234665773,0.9422309448069593
+1.596988178846632,-1.5164118838962106
+0.6978570978515759,1.483561949379376
+0.09421617103372977,0.9711224193582182
+-0.8797693925133905,0.503855870752709
+1.4014346635666408,-0.4154312500704368
+0.6163245441913257,1.663841933723584
+0.7627456428334926,-0.18974370223823156
+-0.4760761271181928,-0.256121401662743
+-0.46115912815142623,0.8417331775500037
+-0.3290883310649779,1.4857820848135193
+-0.23924240975712396,-0.18842170344544096
+0.5605386495262364,1.2123669464508324
+1.1939167564502546,-0.6919460669147783
+-0.46470656378939706,1.3798169992382332
+1.353504288869721,-0.8127341716291047
+-0.09943228148558847,-0.44102074592062057
+-0.47440570642217084,0.4809695959612028
+0.788585299435687,-0.8523414737288254
+1.2325928938165096,0.19140690774993518
+1.6677638356096391,-1.4609912426725953
+1.123321346809153,-1.686322794493118
+-0.6807097354993445,1.0638585171484887
+0.7854875062172035,-0.9306402539605558
+-0.7022028099273782,0.30228905649781956
+-0.5163621185777999,1.746421745322126
+1.655062606177684,-1.1284972212733793
+1.4069610971945017,-0.9577731646070878
+1.0401555936064333,0.7366138261299214
+0.9500207980343723,-0.7455544418887502
+-0.9080413234665773,0.9422309448069593
+1.1915642519743943,-0.343891706663718
+-0.9856994005593656,0.6497071554199669
+1.0139846387328022,0.5963561336630897
+-0.8797693925133905,0.503855870752709
+1.4014346635666408,-0.4154312500704368
+1.2503723302316838,-1.2947679193099466
+1.0822522422895486,-0.6593730002971797
+-0.13565355700738757,0.23552733695954264
+-0.46115912815142623,0.8417331775500037
+-0.3290883310649779,1.4857820848135193
+-0.23924240975712396,-0.18842170344544096
+-0.32531129122784913,0.013597761254766833
+1.1529295451001025,-0.43473477619936185
+-0.46470656378939706,1.3798169992382332
+0.47768050871207113,1.2411300896028103
+-0.09943228148558847,-0.44102074592062057
+-0.5663976777278784,1.5811362722484434
+0.788585299435687,-0.8523414737288254
+1.2325928938165096,0.19140690774993518
+1.1170489571721545,-0.8040415381710247
+1.123321346809153,-1.686322794493118
+-0.6807097354993445,1.0638585171484887
+0.9685112765522277,0.42540761775191227
+-0.7022028099273782,0.30228905649781956
+-0.5163621185777999,1.746421745322126
+1.655062606177684,-1.1284972212733793
+-0.3561300806108175,2.2433072372482714
+1.0401555936064333,0.7366138261299214
+1.5435933122456373,-1.702043693899964
+0.5716876376471791,0.8973181487209014
+1.1915642519743943,-0.343891706663718
+0.6441910983634609,-0.6969339116164031
+1.7179569900577225,-2.27212537144357
+-0.8797693925133905,0.503855870752709
+1.4014346635666408,-0.4154312500704368
+1.5720463994328902,-1.2755754783557207
+-0.19717463746165054,-0.16603631054387008
+-0.5593454509866069,0.28703974392034953
+-0.7373521512755491,0.8077051757531442
+0.8562483032365649,-1.0415595219071054
+-0.23924240975712396,-0.18842170344544096
+-0.32531129122784913,0.013597761254766833
+1.5669259450402884,-1.174194349088674
+-0.46470656378939706,1.3798169992382332
+0.47768050871207113,1.2411300896028103
+-0.09943228148558847,-0.44102074592062057
+-0.8056936869995927,1.2182067899603921
+0.788585299435687,-0.8523414737288254
+0.6063542358673215,0.9050212607407045
+-0.5149063807974157,1.8134983323852363
+0.19890623980435768,2.2814928663173606
+-0.6807097354993445,1.0638585171484887
+-0.20686817951778647,0.754734650714362
+-0.7022028099273782,0.30228905649781956
+-0.689656845602286,1.0440112836076718
+1.655062606177684,-1.1284972212733793
+0.12471256354556735,1.68275564874552
+1.0401555936064333,0.7366138261299214
+0.6450077053857247,-0.4968223621832115
+0.5716876376471791,0.8973181487209014
+1.2318013936101408,0.19371216629603882
+-0.9487865760752245,0.2748164044024659
+1.7179569900577225,-2.27212537144357
+-0.8797693925133905,0.503855870752709
+-0.7620423724948878,0.5190998524594956
+1.6023744413661778,-1.5488392754035696
+-0.19717463746165054,-0.16603631054387008
+0.4664897201538345,1.43985121104078
+-0.538929003787983,-0.07415127182916884
+0.8562483032365649,-1.0415595219071054
+-0.23924240975712396,-0.18842170344544096
+0.7610308696696914,1.2019661961395676
+1.659851383271969,-2.5117080402391494
+-0.46470656378939706,1.3798169992382332
+0.47302431113670196,0.7051125515222547
+-0.09943228148558847,-0.44102074592062057
+1.6025421277243015,-1.0366904490162052
+1.3483328554861005,-0.34405785553097334
+0.6063542358673215,0.9050212607407045
+-0.5149063807974157,1.8134983323852363
+0.19890623980435768,2.2814928663173606
+-0.6807097354993445,1.0638585171484887
+0.7837909974811982,-0.9263580210757891
+-0.7022028099273782,0.30228905649781956
+-0.689656845602286,1.0440112836076718
+1.655062606177684,-1.1284972212733793
+-0.14305309188788512,0.2669168091594994
+1.0401555936064333,0.7366138261299214
+0.13455590720515342,-0.0705181123141253
+0.6980646054862438,0.023492021343436753
+-0.08889145338608817,2.4514415911341527
+-0.9487865760752245,0.2748164044024659
+1.7179569900577225,-2.27212537144357
+-0.872270881120812,0.2387473408917787
+-0.7620423724948878,0.5190998524594956
+1.6023744413661778,-1.5488392754035696
+-0.7405286433793867,0.8182178046160512
+0.4664897201538345,1.43985121104078
+0.050896153587958404,1.8561308659264522
+0.8562483032365649,-1.0415595219071054
+-0.23924240975712396,-0.18842170344544096
+0.7610308696696914,1.2019661961395676
+1.659851383271969,-2.5117080402391494
+-0.46470656378939706,1.3798169992382332
+0.47302431113670196,0.7051125515222547
+-0.09943228148558847,-0.44102074592062057
+1.6025421277243015,-1.0366904490162052
+0.38042878047528106,0.07592559147247635
+0.6063542358673215,0.9050212607407045
+-0.5149063807974157,1.8134983323852363
+0.19890623980435768,2.2814928663173606
+-0.3748933695668394,1.189157980733141
+0.7837909974811982,-0.9263580210757891
+-0.7022028099273782,0.30228905649781956
+-1.188499102959464,0.1449283071655039
+1.655062606177684,-1.1284972212733793
+-0.14305309188788512,0.2669168091594994
+1.0401555936064333,0.7366138261299214
+0.13455590720515342,-0.0705181123141253
+0.7769260543968319,-0.2708958894841331
+-0.08889145338608817,2.4514415911341527
+-0.9487865760752245,0.2748164044024659
+1.7179569900577225,-2.27212537144357
+-0.872270881120812,0.2387473408917787
+-0.7620423724948878,0.5190998524594956
+1.549488177140771,-1.4359720637244795
+-0.9917512578204617,0.38655363393663067
+0.4664897201538345,1.43985121104078
+-0.2233176315212343,0.5784389508817505
+0.8562483032365649,-1.0415595219071054
+1.4047141063228903,0.15639426490586716
+0.7610308696696914,1.2019661961395676
+1.659851383271969,-2.5117080402391494
+-0.8033558183799433,0.5550579790227544
+1.6267733700731424,-1.1834230832901524
+-0.2876873885381517,1.5279505085781722
+1.6025421277243015,-1.0366904490162052
+-0.02556071101459602,0.3556835946748136
+0.23570592132021365,2.139068831910946
+-0.5149063807974157,1.8134983323852363
+0.7764336613231583,0.08312534638502717
+-0.3748933695668394,1.189157980733141
+0.7837909974811982,-0.9263580210757891
+0.5459590873866198,1.0431012950506486
+0.848203918977638,0.4758874511154615
+1.655062606177684,-1.1284972212733793
+-0.1515786322261189,-0.12956035058881907
+1.0401555936064333,0.7366138261299214
+0.3805074548574372,1.9588230610079518
+0.7769260543968319,-0.2708958894841331
+1.2802404742655638,-1.1734858715796022
+-0.7030951492206422,0.2065692649395843
+1.7179569900577225,-2.27212537144357
+-0.872270881120812,0.2387473408917787
+0.1149172112050969,1.3467911682899474
+-0.36216533917560856,0.9038206260855544
+0.6332075342019468,-0.7565076414800068
+1.520599174529758,-1.66062704208478
+1.0600391683007053,0.18883762740167587
+-0.2667650606479024,-0.1965091852801254
+0.8385513383856399,-0.7012850198861103
+0.7610308696696914,1.2019661961395676
+1.659851383271969,-2.5117080402391494
+0.8099379484690381,1.443285588170451
+1.6267733700731424,-1.1834230832901524
+-0.2876873885381517,1.5279505085781722
+0.7462329047517235,1.1842753884008506
+-0.02556071101459602,0.3556835946748136
+0.23570592132021365,2.139068831910946
+1.629808018872363,-1.1952184924441547
+1.2374100951290554,-1.9093029404840496
+-0.5279581379646052,1.8628101471722607
+0.7837909974811982,-0.9263580210757891
+0.45681486312073705,-0.43393761804407216
+0.818442575498995,-0.32046899078425684
+0.8159575282207531,-0.7751241625031637
+-0.1515786322261189,-0.12956035058881907
+1.0401555936064333,0.7366138261299214
+0.3805074548574372,1.9588230610079518
+0.500992283679762,1.3286456757846365
+1.2802404742655638,-1.1734858715796022
+-0.017450742814250575,1.5520912520147496
+1.7179569900577225,-2.27212537144357
+-0.872270881120812,0.2387473408917787
+1.2640190199171593,-1.1470793645863984
+-0.36216533917560856,0.9038206260855544
+0.05671433627105976,1.5185913362745243
+1.520599174529758,-1.66062704208478
+1.0600391683007053,0.18883762740167587
+-0.28466183480234186,2.253659302904905
+0.8385513383856399,-0.7012850198861103
+0.7610308696696914,1.2019661961395676
+1.659851383271969,-2.5117080402391494
+1.439737688304593,-1.0836805102600704
+0.6278339195601073,1.1685764677232684
+-0.2876873885381517,1.5279505085781722
+0.7497386040309697,-1.0989928172804169
+-0.02556071101459602,0.3556835946748136
+0.23570592132021365,2.139068831910946
+1.0800320799559968,0.9400742002124011
+1.3780543180518845,-1.5556451903574646
+-0.5279581379646052,1.8628101471722607
+-0.141537760020739,2.0204724074795446
+-0.383205515954286,0.669489222592522
+0.818442575498995,-0.32046899078425684
+0.8159575282207531,-0.7751241625031637
+0.6747783345763082,1.138525643848899
+1.0401555936064333,0.7366138261299214
+0.3805074548574372,1.9588230610079518
+0.500992283679762,1.3286456757846365
+1.2802404742655638,-1.1734858715796022
+1.0219384463538441,0.2479822645786045
+0.7962666502236375,-0.4375060482485562
+-0.01653817081203779,-0.17951669410253582
+1.2771406459887804,-0.5275380629082864
+-0.6686971128882346,1.551771103367491
+0.7046970742890377,-0.5401007158927142
+1.520599174529758,-1.66062704208478
+0.018753583621624048,1.3400044489264695
+0.25176485979436636,0.30361663750052537
+0.8385513383856399,-0.7012850198861103
+-0.167866702481781,0.8572919776392799
+1.659851383271969,-2.5117080402391494
+1.439737688304593,-1.0836805102600704
+-0.5298980691827858,1.7005400428451025
+-0.2876873885381517,1.5279505085781722
+0.7497386040309697,-1.0989928172804169
+0.2870687009543045,2.2972688484791046
+-0.4665886800740928,1.631562464416791
+1.0800320799559968,0.9400742002124011
+1.3780543180518845,-1.5556451903574646
+-0.6411302935809028,1.0107226841362684
+-0.141537760020739,2.0204724074795446
+0.5056331195584159,0.12689652153538145
+0.818442575498995,-0.32046899078425684
+1.415663869301723,-0.6371429503939015
+0.6747783345763082,1.138525643848899
+1.2000713060486878,-0.6432325439997829
+1.1048023901281445,-1.8628166704283617
+0.500992283679762,1.3286456757846365
+0.09909402239353479,0.6953659829411527
+1.7161760835678823,-1.765805464466759
+0.42608499915202114,1.61319438901121
+-0.06621486471306831,-0.023711362458398222
+1.2771406459887804,-0.5275380629082864
+0.3714852598503921,1.4988822037745044
+0.7046970742890377,-0.5401007158927142
+1.520599174529758,-1.66062704208478
+0.018753583621624048,1.3400044489264695
+1.227812440506634,-1.7895296785715735
+0.8385513383856399,-0.7012850198861103
+-0.1681096909524904,1.8867440489863023
+1.3977788454868607,-0.6274783068342283
+-0.8004125132052518,0.1454785859418939
+-0.5298980691827858,1.7005400428451025
+-0.2876873885381517,1.5279505085781722
+-0.4741908131166956,2.200337212962925
+0.2870687009543045,2.2972688484791046
+-0.3394708345961541,0.4994406125839257
+1.5459872975589903,-1.4823031048003454
+1.3780543180518845,-1.5556451903574646
+-0.6411302935809028,1.0107226841362684
+1.711441183568525,-1.7525020181725899
+-0.14772769075308187,1.9557026915485514
+0.818442575498995,-0.32046899078425684
+-0.7234604641257979,0.9045261242566982
+1.7664844912926263,-1.3396476549816587
+1.2000713060486878,-0.6432325439997829
+0.7930348228537695,-1.4592761897916446
+0.13907130645040305,1.4937799581585631
+-0.5905805312220964,1.3819372622453676
+1.7161760835678823,-1.765805464466759
+0.42608499915202114,1.61319438901121
+-0.06621486471306831,-0.023711362458398222
+1.122669516490616,-1.0599718683323087
+1.7465051403177156,-2.5506831242943213
+0.7046970742890377,-0.5401007158927142
+1.3823738519450015,-0.08987227625343108
+0.8782167395669898,0.1955622069069416
+1.227812440506634,-1.7895296785715735
+0.8385513383856399,-0.7012850198861103
+0.9173929410897279,1.3851730948470629
+1.3977788454868607,-0.6274783068342283
+-0.8004125132052518,0.1454785859418939
+-0.5298980691827858,1.7005400428451025
+-0.2876873885381517,1.5279505085781722
+0.6008338188981632,-0.7119565817088463
+-0.06328279352855737,0.14273928994662655
+-0.5077650596403934,1.6190249743754916
+1.5459872975589903,-1.4823031048003454
+1.3780543180518845,-1.5556451903574646
+-0.6411302935809028,1.0107226841362684
+0.36692939829923477,1.3663557758634597
+-0.14772769075308187,1.9557026915485514
+0.818442575498995,-0.32046899078425684
+0.21492312795880075,-0.07073970228441095
+1.74141730540398,-2.449611861457524
+0.25828807903627615,-0.0462871884677547
+0.7930348228537695,-1.4592761897916446
+1.4203239774695429,-1.5508140080619186
+-0.5905805312220964,1.3819372622453676
+0.8031674600916358,0.26952999635908337
+0.42608499915202114,1.61319438901121
+-0.8408600405886498,-0.22048639688358562
+1.122669516490616,-1.0599718683323087
+1.7465051403177156,-2.5506831242943213
+-0.2741585644592176,0.0665677104631417
+-0.2159522749584882,0.5840581075860138
+0.8782167395669898,0.1955622069069416
+1.227812440506634,-1.7895296785715735
+-0.7348458359356912,-0.0591611075596255
+0.9173929410897279,1.3851730948470629
+1.3977788454868607,-0.6274783068342283
+-0.8004125132052518,0.1454785859418939
+-0.5298980691827858,1.7005400428451025
+-0.2876873885381517,1.5279505085781722
+0.6008338188981632,-0.7119565817088463
+-0.06328279352855737,0.14273928994662655
diff --git a/examples/analytical-function/data/posterior/posterior_plot.py b/examples/analytical-function/data/posterior/posterior_plot.py
new file mode 100644
index 0000000000000000000000000000000000000000..840d0bcd7717f903750e6cadf8978e5d7df6b06a
--- /dev/null
+++ b/examples/analytical-function/data/posterior/posterior_plot.py
@@ -0,0 +1,52 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu May 19 14:31:50 2022
+
+@author: farid
+"""
+import matplotlib.pyplot as plt
+import os
+import pandas as pd
+import seaborn as sns
+import numpy as np
+# Load the mplstyle
+plt.style.use(os.path.join(
+ os.path.split(__file__)[0],
+ '../../../../src/bayesvalidrox/', 'bayesvalidrox.mplstyle'))
+
+font_size = 80
+
+posterior_df = pd.read_csv('posterior_orig.csv')
+par_names = list(posterior_df.keys())
+n_params = len(par_names)
+posterior = posterior_df.values
+bound_tuples = [(-5, 5), (-5, 5)]
+
+folder = 'BAL_DKL'
+file = 'SeqPosterior_45'
+posterior = np.load(f'{folder}/{file}.npy')
+
+figPosterior, ax = plt.subplots(figsize=(15, 15))
+
+sns.kdeplot(x=posterior[:, 0], y=posterior[:, 1],
+ fill=True, ax=ax, cmap=plt.cm.jet,
+ clip=bound_tuples)
+# Axis labels
+plt.xlabel(par_names[0], fontsize=font_size)
+plt.ylabel(par_names[1], fontsize=font_size)
+
+# Set axis limit
+plt.xlim(bound_tuples[0])
+plt.ylim(bound_tuples[1])
+
+# Increase font size
+plt.xticks(fontsize=font_size)
+plt.yticks(fontsize=font_size)
+
+# Switch off the grids
+plt.grid(False)
+plt.show()
+# figPosterior.savefig("orig_posterior.pdf", bbox_inches='tight')
+figPosterior.savefig(f"seq_posterior_45_{folder}.pdf", bbox_inches='tight')
+plt.close()
diff --git a/examples/analytical_function/data/refBME_KLD_10.npy b/examples/analytical-function/data/refBME_KLD_10.npy
similarity index 100%
rename from examples/analytical_function/data/refBME_KLD_10.npy
rename to examples/analytical-function/data/refBME_KLD_10.npy
diff --git a/examples/analytical_function/data/refBME_KLD_2.npy b/examples/analytical-function/data/refBME_KLD_2.npy
similarity index 100%
rename from examples/analytical_function/data/refBME_KLD_2.npy
rename to examples/analytical-function/data/refBME_KLD_2.npy
diff --git a/examples/analytical_function/data/std_10.npy b/examples/analytical-function/data/std_10.npy
similarity index 100%
rename from examples/analytical_function/data/std_10.npy
rename to examples/analytical-function/data/std_10.npy
diff --git a/examples/analytical_function/data/std_2.npy b/examples/analytical-function/data/std_2.npy
similarity index 100%
rename from examples/analytical_function/data/std_2.npy
rename to examples/analytical-function/data/std_2.npy
diff --git a/examples/analytical_function/data/validLikelihoods_10.npy b/examples/analytical-function/data/validLikelihoods_10.npy
similarity index 100%
rename from examples/analytical_function/data/validLikelihoods_10.npy
rename to examples/analytical-function/data/validLikelihoods_10.npy
diff --git a/examples/analytical_function/data/validLikelihoods_2.npy b/examples/analytical-function/data/validLikelihoods_2.npy
similarity index 100%
rename from examples/analytical_function/data/validLikelihoods_2.npy
rename to examples/analytical-function/data/validLikelihoods_2.npy
diff --git a/examples/analytical_function/example_analytical_function.ipynb b/examples/analytical-function/example_analytical_function.ipynb
similarity index 100%
rename from examples/analytical_function/example_analytical_function.ipynb
rename to examples/analytical-function/example_analytical_function.ipynb
diff --git a/examples/analytical_function/test_analytical_function.py b/examples/analytical-function/test_analytical_function.py
similarity index 75%
rename from examples/analytical_function/test_analytical_function.py
rename to examples/analytical-function/test_analytical_function.py
index c832c4f0483a49beb3ee0430a291932e7a693b93..fa3daf3ea324416e74c649d521d98f87690e5863 100755
--- a/examples/analytical_function/test_analytical_function.py
+++ b/examples/analytical-function/test_analytical_function.py
@@ -22,12 +22,12 @@ import sys
import joblib
# import bayesvalidrox
# Add BayesValidRox path
-import sys
sys.path.append("../../src/bayesvalidrox/")
from pylink.pylink import PyLinkForwardModel
from surrogate_models.inputs import Input
from surrogate_models.surrogate_models import MetaModel
+from surrogate_models.meta_model_engine import MetaModelEngine
from post_processing.post_processing import PostProcessing
from bayes_inference.bayes_inference import BayesInference
from bayes_inference.discrepancy import Discrepancy
@@ -38,7 +38,7 @@ matplotlib.use('agg')
if __name__ == "__main__":
# Number of parameters
- ndim = 2 # 2, 10
+ ndim = 10 # 2, 10
# =====================================================
# ============= COMPUTATIONAL MODEL ================
@@ -74,7 +74,7 @@ if __name__ == "__main__":
for i in range(ndim):
Inputs.add_marginals()
- Inputs.Marginals[i].name = f'$X_{i+1}$'
+ Inputs.Marginals[i].name = "$\\theta_{"+str(i+1)+"}$"
Inputs.Marginals[i].dist_type = 'uniform'
Inputs.Marginals[i].parameters = [-5, 5]
@@ -88,12 +88,12 @@ if __name__ == "__main__":
# =====================================================
# ========== DEFINITION OF THE METAMODEL ============
# =====================================================
- MetaModelOpts = MetaModel(Inputs)
+ MetaModelOpts = MetaModel(Inputs, Model)
# Select if you want to preserve the spatial/temporal depencencies
# MetaModelOpts.dim_red_method = 'PCA'
# MetaModelOpts.var_pca_threshold = 99.999
- # MetaModelOpts.n_pca_components = 12
+ # MetaModelOpts.n_pca_components = 10
# Select your metamodel method
# 1) PCE (Polynomial Chaos Expansion) 2) aPCE (arbitrary PCE)
@@ -108,19 +108,25 @@ if __name__ == "__main__":
# 1)OLS: Ordinary Least Square 2)BRR: Bayesian Ridge Regression
# 3)LARS: Least angle regression 4)ARD: Bayesian ARD Regression
# 5)FastARD: Fast Bayesian ARD Regression
- # 6)VBL: Variational Bayesian Learning
- # 7)EBL: Emperical Bayesian Learning
+ # 6)BCS: Bayesian Compressive Sensing
+ # 7)OMP: Orthogonal Matching Pursuit
+ # 8)VBL: Variational Bayesian Learning
+ # 9)EBL: Emperical Bayesian Learning
MetaModelOpts.pce_reg_method = 'FastARD'
+ # Bootstraping
+ # 1) normal 2) fast
+ MetaModelOpts.bootstrap_method = 'fast'
+ MetaModelOpts.n_bootstrap_itrs = 1
+
# Specify the max degree to be compared by the adaptive algorithm:
# The degree with the lowest Leave-One-Out cross-validation (LOO)
# error (or the highest score=1-LOO)estimator is chosen as the final
# metamodel. pce_deg accepts degree as a scalar or a range.
- MetaModelOpts.pce_deg = np.arange(9)
+ MetaModelOpts.pce_deg = 12
# q-quasi-norm 0<q<1 (default=1)
- MetaModelOpts.pce_q_norm = 0.75 if ndim < 5 else 0.5
- # MetaModelOpts.pce_q_norm = np.linspace(0.25,0.75, 3)
+ MetaModelOpts.pce_q_norm = 0.85 if ndim < 5 else 0.5
# Print summary of the regression results
# MetaModelOpts.verbose = True
@@ -131,12 +137,12 @@ if __name__ == "__main__":
MetaModelOpts.add_ExpDesign()
# One-shot (normal) or Sequential Adaptive (sequential) Design
- MetaModelOpts.ExpDesign.method = 'normal'
- MetaModelOpts.ExpDesign.n_init_samples = 75 # 5*ndim
+ MetaModelOpts.ExpDesign.method = 'sequential'
+ MetaModelOpts.ExpDesign.n_init_samples = 3*ndim
# Sampling methods
- # 1) random 2) latin_hypercube 3) sobol 4) halton 5) hammersley 6) korobov
- # 7) chebyshev(FT) 8) grid(FT) 9) nested_grid(FT) 10)user
+ # 1) random 2) latin_hypercube 3) sobol 4) halton 5) hammersley
+ # 6) chebyshev(FT) 7) grid(FT) 8)user
MetaModelOpts.ExpDesign.sampling_method = 'latin_hypercube'
# Provide the experimental design object with a hdf5 file
@@ -147,38 +153,44 @@ if __name__ == "__main__":
# ------------------------------------------------
# Set the sampling parameters
MetaModelOpts.ExpDesign.n_new_samples = 1
- MetaModelOpts.ExpDesign.n_max_samples = 25 # 150
+ MetaModelOpts.ExpDesign.n_max_samples = 150
MetaModelOpts.ExpDesign.mod_LOO_threshold = 1e-16
- MetaModelOpts.adapt_verbose = True
+ # MetaModelOpts.adapt_verbose = True
# 1) None 2) 'equal' 3)'epsilon-decreasing' 4) 'adaptive'
MetaModelOpts.ExpDesign.tradeoff_scheme = None
- # MetaModelOpts.ExpDesign.n_replication = 20
+ # MetaModelOpts.ExpDesign.n_replication = 5
# -------- Exploration ------
# 1)'Voronoi' 2)'random' 3)'latin_hypercube' 4)'LOOCV' 5)'dual annealing'
- MetaModelOpts.ExpDesign.explore_method = 'Voronoi'
+ MetaModelOpts.ExpDesign.explore_method = 'random'
# Use when 'dual annealing' chosen
- MetaModelOpts.ExpDesign.max_func_itr = 200
+ MetaModelOpts.ExpDesign.max_func_itr = 1000
# Use when 'Voronoi' or 'random' or 'latin_hypercube' chosen
- MetaModelOpts.ExpDesign.n_canddidate = 5000
- MetaModelOpts.ExpDesign.n_cand_groups = 4 # 8
+ MetaModelOpts.ExpDesign.n_canddidate = 1000
+ MetaModelOpts.ExpDesign.n_cand_groups = 4
# -------- Exploitation ------
# 1)'BayesOptDesign' 2)'BayesActDesign' 3)'VarOptDesign' 4)'alphabetic'
# 5)'Space-filling'
- MetaModelOpts.ExpDesign.exploit_method = 'VarOptDesign'
+ MetaModelOpts.ExpDesign.exploit_method = 'BayesActDesign'
- # BayesOptDesign -> when data is available
- # 1)DKL (Kullback-Leibler Divergence) 2)DPP (D-Posterior-percision)
- # 3)APP (A-Posterior-percision) # ['DKL', 'BME', 'infEntropy']
+ # BayesOptDesign/BayesActDesign -> when data is available
+ # 1) MI (Mutual information) 2) ALC (Active learning McKay)
+ # 2)DKL (Kullback-Leibler Divergence) 3)DPP (D-Posterior-percision)
+ # 4)APP (A-Posterior-percision) # ['DKL', 'BME', 'infEntropy']
# MetaModelOpts.ExpDesign.util_func = 'DKL'
+ # BayesActDesign -> when data is available
+ # 1) BME (Bayesian model evidence) 2) infEntropy (Information entropy)
+ # 2)DKL (Kullback-Leibler Divergence)
+ MetaModelOpts.ExpDesign.util_func = 'DKL'
+
# VarBasedOptDesign -> when data is not available
- # 1)Entropy 2)EIGF, 3)LOOCV
+ # 1)ALM 2)EIGF, 3)LOOCV
# or a combination as a list
- MetaModelOpts.ExpDesign.util_func = 'Entropy'
+ # MetaModelOpts.ExpDesign.util_func = 'EIGF'
# alphabetic
# 1)D-Opt (D-Optimality) 2)A-Opt (A-Optimality)
@@ -201,20 +213,22 @@ if __name__ == "__main__":
prior = np.load(f"data/Prior_{ndim}.npy")
prior_outputs = np.load(f"data/origModelOutput_{ndim}.npy")
likelihood = np.load(f"data/validLikelihoods_{ndim}.npy")
- MetaModelOpts.valid_samples = prior
- MetaModelOpts.valid_model_runs = {'Z': prior_outputs}
- MetaModelOpts.valid_likelihoods = likelihood
+ MetaModelOpts.valid_samples = prior[:500]
+ MetaModelOpts.valid_model_runs = {'Z': prior_outputs[:500]}
+ # MetaModelOpts.valid_likelihoods = likelihood
# >>>>>>>>>>>>>>>>>>>>>> Build Surrogate <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
# Train the meta model
- PCEModel = MetaModelOpts.create_metamodel(Model)
+ meta_model_engine = MetaModelEngine(MetaModelOpts)
+ meta_model_engine.run()
+ PCEModel = meta_model_engine.MetaModel
# Save PCE models
with open(f'PCEModel_{Model.name}.pkl', 'wb') as output:
joblib.dump(PCEModel, output, 2)
- # Load PCEModel
- # with open(f'PCEModel_{Model.name}.pkl', 'rb') as input:
+ # Load the objects
+ # with open(f"PCEModel_{Model.name}.pkl", "rb") as input:
# PCEModel = joblib.load(input)
# =====================================================
@@ -223,7 +237,10 @@ if __name__ == "__main__":
PostPCE = PostProcessing(PCEModel)
# Plot to check validation visually.
- PostPCE.valid_metamodel(n_samples=3)
+ PostPCE.valid_metamodel(n_samples=1)
+
+ # Compute and print RMSE error
+ PostPCE.check_accuracy(n_samples=300)
# Compute the moments and compare with the Monte-Carlo reference
if MetaModelOpts.meta_model_type != 'GPE':
@@ -236,11 +253,8 @@ if __name__ == "__main__":
# Plot the sobol indices
if MetaModelOpts.meta_model_type != 'GPE':
- sobol_cell, total_sobol = PostPCE.sobol_indices()
+ total_sobol = PostPCE.sobol_indices()
- # Compute and print RMSE error
- PostPCE.check_accuracy(n_samples=200)
- # sys.exit()
# =====================================================
# ======== Bayesian inference with Emulator ==========
# =====================================================
@@ -310,44 +324,3 @@ if __name__ == "__main__":
# Save class objects
with open(f'Bayes_{Model.name}.pkl', 'wb') as output:
joblib.dump(Bayes_PCE, output, 2)
-
- sys.exit('STOP!!')
- # =====================================================
- # ====== Bayesian inference with Forward Model ========
- # =====================================================
- if ndim < 7:
- PCEModel.ModelObj.Name = 'OrigAnalyticFunc'
-
- BayesOptsModel = bayesvalidrox.BayesInference(PCEModel)
- BayesOptsModel.emulator = False
- BayesOptsModel.NrofSamples = 10000
-
- # Evaluation of forward model predictions for the surrogate posterior
- # BayesOptsModel.Samples = Bayes_PCE.Samples
- # BayesOptsModel.SamplingMethod = 'MCMC'
-
- # Bootstrap for BME calulations
- BayesOptsModel.Bootstrap = True
- BayesOptsModel.BootstrapItrNr = 1
- BayesOptsModel.BootstrapNoise = 0.05
-
- BayesOptsModel.PlotPostDist = True
- BayesOptsModel.PlotPostPred = False
-
- # ----- Define the discrepancy model -------
- BayesOptsModel.MeasurementError = obsData
- # (Option B)
- DiscrepancyOpts = bayesvalidrox.Discrepancy('')
- DiscrepancyOpts.Type = 'Gaussian'
- DiscrepancyOpts.Parameters = obsData ** 2
- BayesOptsModel.Discrepancy = DiscrepancyOpts
-
- # Start the infernce
- Bayes_Model = BayesOptsModel.create_Inference()
-
- # =====================================================
- # ============== Save class objects =================
- # =====================================================
- if ndim < 7:
- with open('AnalyticFunc_Results.pkl', 'wb') as output:
- joblib.dump(Bayes_Model, output, 2)
diff --git a/examples/analytical_function/util/AnalytFuncValid_Test.py b/examples/analytical-function/util/AnalytFuncValid_Test.py
similarity index 100%
rename from examples/analytical_function/util/AnalytFuncValid_Test.py
rename to examples/analytical-function/util/AnalytFuncValid_Test.py
diff --git a/examples/analytical_function/util/AnalyticFunc_Demo.py b/examples/analytical-function/util/AnalyticFunc_Demo.py
similarity index 100%
rename from examples/analytical_function/util/AnalyticFunc_Demo.py
rename to examples/analytical-function/util/AnalyticFunc_Demo.py
diff --git a/examples/analytical_function/util/AnalyticalFunction.py b/examples/analytical-function/util/AnalyticalFunction.py
similarity index 100%
rename from examples/analytical_function/util/AnalyticalFunction.py
rename to examples/analytical-function/util/AnalyticalFunction.py
diff --git a/examples/analytical_function/util/PCE_vs_Chaospy.py b/examples/analytical-function/util/PCE_vs_Chaospy.py
similarity index 100%
rename from examples/analytical_function/util/PCE_vs_Chaospy.py
rename to examples/analytical-function/util/PCE_vs_Chaospy.py
diff --git a/examples/analytical_function/util/Psi_BayesValidRox.npy b/examples/analytical-function/util/Psi_BayesValidRox.npy
similarity index 100%
rename from examples/analytical_function/util/Psi_BayesValidRox.npy
rename to examples/analytical-function/util/Psi_BayesValidRox.npy
diff --git a/examples/analytical_function/util/Psi_Chaospy.npy b/examples/analytical-function/util/Psi_Chaospy.npy
similarity index 100%
rename from examples/analytical_function/util/Psi_Chaospy.npy
rename to examples/analytical-function/util/Psi_Chaospy.npy
diff --git a/examples/analytical_function/util/__pycache__/AnalyticalFunction.cpython-38.pyc b/examples/analytical-function/util/__pycache__/AnalyticalFunction.cpython-38.pyc
similarity index 100%
rename from examples/analytical_function/util/__pycache__/AnalyticalFunction.cpython-38.pyc
rename to examples/analytical-function/util/__pycache__/AnalyticalFunction.cpython-38.pyc
diff --git a/examples/analytical_function/util/dynamic_image.py b/examples/analytical-function/util/dynamic_image.py
similarity index 100%
rename from examples/analytical_function/util/dynamic_image.py
rename to examples/analytical-function/util/dynamic_image.py
diff --git a/examples/analytical_function/util/indices_bayesValid.npy b/examples/analytical-function/util/indices_bayesValid.npy
similarity index 100%
rename from examples/analytical_function/util/indices_bayesValid.npy
rename to examples/analytical-function/util/indices_bayesValid.npy
diff --git a/examples/analytical_function/util/indices_chaospy.npy b/examples/analytical-function/util/indices_chaospy.npy
similarity index 100%
rename from examples/analytical_function/util/indices_chaospy.npy
rename to examples/analytical-function/util/indices_chaospy.npy
diff --git a/examples/analytical-function/util/svg_gif.py b/examples/analytical-function/util/svg_gif.py
new file mode 100644
index 0000000000000000000000000000000000000000..4430de69c299a495bba9642ea5d5115e7452bdda
--- /dev/null
+++ b/examples/analytical-function/util/svg_gif.py
@@ -0,0 +1,47 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Mon May 16 10:51:20 2022
+
+@author: farid
+"""
+
+import imageio
+import os
+import re
+
+
+def tryint(s):
+ try:
+ return int(s)
+ except:
+ return s
+
+
+def alphanum_key(s):
+ """ Turn a string into a list of string and number chunks.
+ "z23a" -> ["z", 23, "a"]
+ """
+ return [tryint(c) for c in re.split('([0-9]+)', s)]
+
+
+def sort_nicely(input_list):
+ """ Sort the given list in the way that humans expect.
+ """
+ input_list.sort(key=alphanum_key)
+
+
+path = '../adaptivePlots'
+file_ext = 'pdf'
+
+
+filenames = []
+for file in os.listdir(path):
+ if file.endswith(f'.{file_ext}'):
+ filenames.append(os.path.join(path, file))
+sort_nicely(filenames)
+
+images = []
+for filename in filenames:
+ images.append(imageio.imread(filename))
+imageio.mimsave(f'{path}/movie.gif', images)
diff --git a/examples/analytical_function/.ipynb_checkpoints/example_analytical_function-checkpoint.ipynb b/examples/analytical_function/.ipynb_checkpoints/example_analytical_function-checkpoint.ipynb
deleted file mode 100644
index e63948ddc4e636a1e0eef9834c706a40f5be6890..0000000000000000000000000000000000000000
--- a/examples/analytical_function/.ipynb_checkpoints/example_analytical_function-checkpoint.ipynb
+++ /dev/null
@@ -1,926 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "markdown",
- "id": "13c8e941",
- "metadata": {},
- "source": [
- "# Example: Surrogate Model"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "de58892b",
- "metadata": {},
- "source": [
- "In this example, we train a surrogate model via the `bayesvalidrox` package. We aim at training a Polynomial Chaos Expansion to a simple analytical function. \n",
- "The PCE representation of the computational model $M$ provides the dependence of this model on the uncertain model's parameters $\\mathbf{\\theta}$ using projection onto an orthonormal polynomial basis. It could be also seen as a linear regression that includes linear combinations of a fixed set of nonlinear functions with respect to the input variables, known as polynomial basis function"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "2890d7ef",
- "metadata": {},
- "source": [
- "\\begin{equation}\n",
- "\\label{eq:PCE_Trunc}\n",
- " M(x,y,z,t, \\mathbf{\\theta}) \\approx \\sum_{\\mathbf{\\alpha} \\in \\mathcal{A} } c_{\\mathbf{\\alpha}} (x,y,z,t) \\Psi_{\\mathbf{\\alpha}}(\\mathbf{\\theta}) \\, .\n",
- "\\end{equation}"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "bccdaebc",
- "metadata": {},
- "source": [
- "Here, $x,y,z,t$ are the spatial and temporal components of the quantity of interest, $\\mathbf{\\theta}$ is the vector of the $N$ uncertain parameters of model $M$, $c_{\\mathbf{\\alpha}}(x,y,z,t) \\in \\mathbb{R}$ are the corresponding expansion coefficients that are functions of space and time, and $\\Psi_{\\mathbf{\\alpha}}(\\mathbf{\\theta})$ represents multivariate polynomials orthogonal with respect to a multi-index $\\mathbf{\\alpha}$. "
- ]
- },
- {
- "cell_type": "markdown",
- "id": "50023bea",
- "metadata": {},
- "source": [
- "The latter represents the combinatoric information how to enumerate all possible products of $N$ individual univariate basis functions with respect to the total degree of expansions less or equal to polynomial degree $d$:"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "538c43c8",
- "metadata": {},
- "source": [
- "\\begin{equation}\n",
- "\\label{eq:truncation}\n",
- "\\begin{split}\n",
- " \\mathcal{A}^{N, d} = \\{ \\alpha \\in \\mathbb{N}^{N} \\ : \\ |\\alpha|\\leq d\\} \\, , \\qquad\n",
- " \\text{card} \\ \\mathcal{A}^{N, d} \\equiv P = \\binom{N+d}{d}.\n",
- "\\end{split}\n",
- "\\end{equation}"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "b22c0ccb",
- "metadata": {},
- "source": [
- "The multivariate polynomials $\\Psi_{\\alpha}(\\mathbf{\\theta})$ are comprised of the tensor product of univariate polynomials"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "41eeb9d3",
- "metadata": {},
- "source": [
- "\\begin{equation}\n",
- "\\label{eq:Psi}\n",
- " \\Psi_{\\alpha}(\\mathbf{\\theta}_k) := \\prod_{i=1}^{N_k} \\psi_{\\alpha_i}^{(i)}(\\mathbf{\\theta}_{k,i}) \\, ,\n",
- "\\end{equation}"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "860cbcbd",
- "metadata": {},
- "source": [
- "where the univariate orthonormal polynomials $\\psi_{\\alpha_i}^{(i)}(\\mathbf{\\theta}_{i})$ must satisfy "
- ]
- },
- {
- "cell_type": "markdown",
- "id": "459de9cc",
- "metadata": {},
- "source": [
- "\\begin{equation}\n",
- "\\label{eq:univPsi}\n",
- " \\langle \\psi_j^{(i)}(\\mathbf{\\theta}_{k,i}), \\psi_l^{(i)}(\\mathbf{\\theta}_{k,i}) \\rangle := \\int_{\\Theta_{k,i}} \\psi_j^{(i)}(\\mathbf{\\theta}_{k,i}) \\psi_l^{(i)}(\\mathbf{\\theta}_{k,i}) f_{\\Theta_{k,i}} (\\mathbf{\\theta}_{k,i})d \\mathbf{\\theta}_{k,i} = \\delta_{j l} \\, .\n",
- "\\end{equation}"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "34403fc6",
- "metadata": {},
- "source": [
- "Here, $i$ represents the input variable with respect to which the polynomials are orthogonal as well as the corresponding polynomial family, $j$ and $l$ are the corresponding polynomial degree, $f_{\\Theta_{i}}(\\mathbf{\\theta}_{i})$ is the $i$th-input marginal distribution and $\\delta_{j l}$ is the Kronecker delta.\n",
- "We use an arbitrary polynomial chaos expansion (aPCE), introduced by [Oladyshkin & Nowak (2012)](https://www.sciencedirect.com/science/article/pii/S0951832012000853?casa_token=pbisUgY4niQAAAAA:8WsqMi1mCyfUIJ3GnFGdv6FXFA6a4g8MB75kjGGdEvocV64cd4E8LxcSh8_fwZTeI2ONlUalq_8), that can operate with probability measures that may be implicitly and incompletely defined via their statistical moments. Using aPCE, one can build the multivariate orthonormal polynomials even in the absence of the exact probability density function $f_{\\Theta}(\\theta)$"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "3bd3feba",
- "metadata": {},
- "source": [
- "In this tutorial, we use an extension of aPCE as Bayesian sparse arbitrary polynomial chaos (BsaPCE) representation. This method computes the coefficients $c_\\alpha$ in a Bayesian setting via a so-called Bayesian sparse learning approach, introduced by [Tipping (2001)](https://www.jmlr.org/papers/volume1/tipping01a/tipping01a.pdf?ref=https://githubhelp.com)."
- ]
- },
- {
- "cell_type": "markdown",
- "id": "6a291027",
- "metadata": {},
- "source": [
- "The posterior distribution of the expansion coefficients, conditioned on the model responses $\\mathrm{\\mathbf{Y}}$ resulting from the training sets $\\mathbf{X}$, is given by the combination of a Gaussian likelihood and a Gaussian prior distribution over the unknown expansion coefficients $\\mathbf{c}$ according to Bayes' rule. Then, the posterior of the expansion coefficients given the model responses $\\mathrm{\\mathbf{Y}}$ and values of hyper-parameters $\\mathbf{\\alpha}$ and $\\beta$ describing the Gauss process, can take the following form"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "3127c49a",
- "metadata": {},
- "source": [
- "\\begin{equation}\n",
- "\\label{eq:PCE_Posterior}\n",
- " p(\\mathrm{\\mathbf{c}}|\\mathbf{Y},\\mathbf{\\alpha}, \\beta) = \\frac{p(\\mathrm{\\mathbf{Y}}|\\mathbf{X},\\mathbf{c}, \\beta) p(\\mathbf{c}|\\mathbf{\\alpha})}{p(\\mathrm{\\mathbf{Y}}| \\mathbf{X}, \\mathbf{\\alpha} , \\beta)},\n",
- "\\end{equation}"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "46381c6d",
- "metadata": {},
- "source": [
- "which is also Gaussian defined by $\\mathcal{N}( \\mathbf{c}| \\mathbf{\\mu}, \\mathbf{\\Sigma})$ with"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "515d47e6",
- "metadata": {},
- "source": [
- "\\begin{equation}\n",
- "\\label{eq:PCE_Posterior_moments}\n",
- " \\mathbf{\\mu} = \\beta \\mathbf{\\Sigma} \\mathbf{\\Psi}^{\\top} \\mathrm{\\mathbf{Y}} \\, , \\qquad\n",
- " \\mathbf{\\Sigma} = \\left(\\mathbf{A}+ \\mathbf{\\Psi}^{\\top} \\beta \\mathbf{\\Psi} \\right)^{-1} \\, .\n",
- "\\end{equation}"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "ce4636d9",
- "metadata": {},
- "source": [
- "Here, $\\mathbf{\\Psi}$ is the design matrix of size $E \\times N$ with elements $\\Psi_{ni}=\\psi_i(x_n)$, where $E$ represents the number of model evaluations using the training samples, and $\\mathbf{A}=\\mathrm{diag}(\\alpha_i)$. The values of $\\mathbf{\\alpha}$ and $\\beta$ can be determined via type-II maximum likelihood [Berger (2013)](https://books.google.com/books?hl=en&lr=&id=1CDaBwAAQBAJ&oi=fnd&pg=PA1&dq=Statistical+decision+theory+and+Bayesian+analysis.++berger+2013&ots=LMulrdTL3O&sig=xMTVRCVf5scWBLQi98BgUie5d-M)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "c50a317d",
- "metadata": {},
- "source": [
- "## Problem description: Analytical function"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "d13b9da3",
- "metadata": {},
- "source": [
- "This test shows a surrogate-assisted Bayesian calibration of a time dependent non-linear analytical function of ten ($n=10$) uncertain parameters $\\omega=\\{\\omega_1, ..., \\omega_n\\}$, which reads as:"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "b715ea87",
- "metadata": {},
- "source": [
- "\\begin{equation}\n",
- "\\mathbf{y}(\\boldsymbol{\\omega}, t)=\\left(\\omega_{1}^{2}+\\omega_{2}-1\\right)^{2}+\\omega_{1}^{2}+0.1 \\omega_{1} \\exp \\left(\\omega_{2}\\right)-2 \\omega_{1} \\sqrt{0.5 t}+1+\\sum_{i=2}^{n} \\frac{\\omega_{i}^{3}}{i}\n",
- "\\end{equation}"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "6625cdf6",
- "metadata": {},
- "source": [
- "where the prior parameter distribution $p(\\omega)$ is considered to be independent and uniform with $\\omega_i \\sim \\mathcal{U} (-5, 5)$."
- ]
- },
- {
- "cell_type": "markdown",
- "id": "efe8f59c",
- "metadata": {},
- "source": [
- "## Import necessary libraries"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "id": "31b60d45",
- "metadata": {},
- "outputs": [],
- "source": [
- "import numpy as np\n",
- "import pandas as pd\n",
- "import sys\n",
- "import joblib\n",
- "from IPython.display import IFrame"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "6d44d5af",
- "metadata": {},
- "source": [
- "## Define the model with PyLinkForwardModel"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "bf3f4dfe",
- "metadata": {},
- "source": [
- "We use the`PyLinkForwardModel`object for this purpose. Fistly, we are going to import the `bayesvalidrox` package and then, we instantiate the `PyLinkForwardModel` object."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "id": "25a3b65a",
- "metadata": {},
- "outputs": [],
- "source": [
- "from bayesvalidrox import PyLinkForwardModel\n",
- "Model = PyLinkForwardModel()"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "0452955f",
- "metadata": {},
- "source": [
- "Next, we will pass the `link_type`, `name` and `py_file` variables to the `Model` object. Since the analytical function is implmented as a python function in a separate file, we only need to pass it's name (without `.py` extension) to the object variable `py_file`. Note that the function name in the python script should match that of the script. For models implemented as a separate python file, the `link_type` is `Function` to be given as a string. The `name` variable takes any user defined string."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "id": "f26dbacd",
- "metadata": {},
- "outputs": [],
- "source": [
- "Model.link_type = 'Function'\n",
- "Model.py_file = 'analytical_function'\n",
- "Model.name = 'AnalyticFunc'"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "e12ef2ab",
- "metadata": {},
- "source": [
- "The model output name is defined as follows:"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "id": "c2778a83",
- "metadata": {},
- "outputs": [],
- "source": [
- "Model.Output.names = ['Z'] # As a list of strings"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "d4106fb6",
- "metadata": {},
- "source": [
- "**Bonus**: For this example, we have a Monte-Carlo reference solution for the first moements (mean and standard deviation) of the analytical function. The numpy (`*.npy`) files can be found in the `data\\` directory. We will discuss the first two moments with our estimate moments using the surrogate model. These values can be passed in a form of a dictionary to the object variable `mc_reference`."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "id": "9dc9e177",
- "metadata": {},
- "outputs": [],
- "source": [
- "Model.mc_reference = {}\n",
- "Model.mc_reference['Time [s]'] = np.arange(0, 10, 1.) / 9\n",
- "Model.mc_reference['mean'] = np.load(f\"data/mean_2.npy\")\n",
- "Model.mc_reference['std'] = np.load(f\"data/std_2.npy\")"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "c2c68eee",
- "metadata": {},
- "source": [
- "## Define probablistic input model"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "af7f7d8f",
- "metadata": {},
- "source": [
- "Now, we define the distribution of the model inputs. `bayesvalidrox` accepts the definition in two ways: by defining the distribution directly or by passing available data. The latter is handy, when little information is available on the parameters or they do not follow any typical distributions. We will use the second option and read the input parameters form a numpy file in the `data/` directory."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "id": "f1d2deb0",
- "metadata": {},
- "outputs": [],
- "source": [
- "# Import and instantiate the input object\n",
- "from bayesvalidrox import Input\n",
- "Inputs = Input()\n",
- "\n",
- "# Option I: Define distribution directy with their name, type and parameters \n",
- "\n",
- "# First parameter\n",
- "Inputs.add_marginals()\n",
- "Inputs.Marginals[0].name = '$X_1$'\n",
- "Inputs.Marginals[0].dist_type = 'unif'\n",
- "Inputs.Marginals[0].parameters = [-5, 5]\n",
- "\n",
- "# Second parameter\n",
- "Inputs.add_marginals()\n",
- "Inputs.Marginals[1].name = '$X_2$'\n",
- "Inputs.Marginals[1].dist_type = 'unif'\n",
- "Inputs.Marginals[1].parameters = [-5, 5]\n",
- "\n",
- "# ----------------------------------------------------------------------------\n",
- "\n",
- "# Option II: Pass available data for input parameters\n",
- "# inputParams = np.load('data/InputParameters_2.npy')\n",
- "\n",
- "# First parameter\n",
- "# Inputs.add_marginals()\n",
- "# Inputs.Marginals[0].name = '$X_1$'\n",
- "# Inputs.Marginals[0].input_data = inputParams[:, 0]\n",
- "\n",
- "# Second parameter\n",
- "# Inputs.add_marginals()\n",
- "# Inputs.Marginals[1].name = '$X_2$'\n",
- "# Inputs.Marginals[1].input_data = inputParams[:, 1]"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "10ff4b23",
- "metadata": {},
- "source": [
- "## Define surrogate (meta) model"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "d0e8a911",
- "metadata": {},
- "source": [
- "In this example, we use a Polynomial Chaos Expansion (PCE) as our meta model. Like before, we need to import the `MetaModel` object from `bayesvalidrox` package and instantiate a meta-model object. This object, however, accepts the input object (`Input`) as an argument."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "id": "7256d8f0",
- "metadata": {},
- "outputs": [],
- "source": [
- "from bayesvalidrox import MetaModel\n",
- "MetaModelOpts = MetaModel(Inputs)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "aa7756f5",
- "metadata": {},
- "source": [
- "Let us define now the meta model type, the regression type, degree of the polynomials and the trunction norm `q_norm` which lies between 0 and 1. This parameter defines hyperbolic truncation scheme. As for `meta_model_type`, there are two PCE implementations available in `bayesvalidrox`, namely generalized PCE (`PCE`) [Xiu & Karniadakis (2002)](https://doi.org/10.1137/S1064827501387826) or its arbitrary extension (`aPCE`) [Oladyshkin & Nowak (2012)](https://doi.org/10.1016/j.ress.2012.05.002)."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "id": "39a2ece3",
- "metadata": {},
- "outputs": [],
- "source": [
- "# Select your metamodel method\n",
- "# Options: PCE and aPCE\n",
- "MetaModelOpts.meta_model_type = 'aPCE'\n",
- "\n",
- "# Select the regression method for calculation of the PCE coefficients:\n",
- "# 1)OLS: Ordinary Least Square 2)BRR: Bayesian Ridge Regression\n",
- "# 3)LARS: Least angle regression 4)ARD: Bayesian ARD Regression\n",
- "# 5)FastARD: Fast Bayesian ARD Regression\n",
- "# 6)VBL: Variational Bayesian Learning\n",
- "# 7)EBL: Emperical Bayesian Learning\n",
- "MetaModelOpts.pce_reg_method = 'FastARD'\n",
- "\n",
- "\n",
- "# Specify the polynomial degree to be compared by the adaptive algorithm:\n",
- "# The degree with the lowest Leave-One-Out cross-validation (LOO)\n",
- "# error (or the highest score=1-LOO)estimator is chosen as the final\n",
- "# metamodel. pce_deg accepts degree as a scalar or a range.\n",
- "MetaModelOpts.pce_deg = np.arange(9)\n",
- "\n",
- "# Hyperbolic truncation scheme 0<q<1 (default=1)\n",
- "MetaModelOpts.pce_q_norm = 0.75"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "a3048f38",
- "metadata": {},
- "source": [
- "After defining the metamodel type, we need to define the so-called experimental design (ExpDesign). ExpDesign basically provides instruction on how to samplie the input parameter space."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "id": "f8e1bf2d",
- "metadata": {},
- "outputs": [],
- "source": [
- "# ------------------------------------------------\n",
- "# ------ Experimental Design Configuration -------\n",
- "# ------------------------------------------------\n",
- "MetaModelOpts.add_ExpDesign()\n",
- "\n",
- "# One-shot (normal) or Sequential Adaptive (sequential) Design\n",
- "MetaModelOpts.ExpDesign.Method = 'normal'\n",
- "MetaModelOpts.ExpDesign.n_init_samples = 100\n",
- "\n",
- "# Sampling methods\n",
- "# 1) random 2) latin_hypercube 3) sobol 4) halton 5) hammersley 6) korobov\n",
- "# 7) chebyshev(FT) 8) grid(FT) 9) nested_grid(FT) 10)user\n",
- "MetaModelOpts.ExpDesign.sampling_method = 'latin_hypercube'"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "8f7cd8dc",
- "metadata": {},
- "source": [
- "Now, we can start training the surrogate (meta-) model by using the `create_metamodel` method and passing the model object as the only argument."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "id": "82fffca5",
- "metadata": {},
- "outputs": [
- {
- "name": "stderr",
- "output_type": "stream",
- "text": [
- "Computing orth. polynomial coeffs: 100%|##########| 2/2 [00:02<00:00, 1.42s/it]"
- ]
- },
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "\n",
- " Now the forward model needs to be run!\n",
- "\n"
- ]
- },
- {
- "name": "stderr",
- "output_type": "stream",
- "text": [
- "\n",
- "Running forward model : 100%|██████████| 100/100 [00:00<00:00, 6414.49it/s]\n",
- "Fitting regression: 0%| | 0/1 [00:00<?, ?it/s]"
- ]
- },
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "\n",
- ">>>> Training the aPCE metamodel started. <<<<<<\n",
- "\n"
- ]
- },
- {
- "name": "stderr",
- "output_type": "stream",
- "text": [
- "Fitting regression: 100%|██████████| 1/1 [00:04<00:00, 4.51s/it]"
- ]
- },
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "\n",
- ">>>> Training the aPCE metamodel sucessfully completed. <<<<<<\n",
- "\n"
- ]
- },
- {
- "name": "stderr",
- "output_type": "stream",
- "text": [
- "\n"
- ]
- }
- ],
- "source": [
- "# Train the meta model\n",
- "PCEModel = MetaModelOpts.create_metamodel(Model)\n",
- "\n",
- "# Save PCE models as pkl object for further deployment for example on a cloud\n",
- "with open(f'PCEModel_{Model.name}.pkl', 'wb') as output:\n",
- " joblib.dump(PCEModel, output, 2)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "4b2b6a1b",
- "metadata": {},
- "source": [
- "## Post-processing"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "64ea5912",
- "metadata": {},
- "source": [
- "As before, we need to import the `PostProcessing` module of `bayesvalidrox` and instantiate it. Bear in mind that it accepts the meta-model object `PCEModel` as the only argument."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 11,
- "id": "d51e4195",
- "metadata": {},
- "outputs": [],
- "source": [
- "from bayesvalidrox import PostProcessing\n",
- "PostPCE = PostProcessing(PCEModel)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "51aed43d",
- "metadata": {},
- "source": [
- "### Moment comparison"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "69de7856",
- "metadata": {},
- "source": [
- "Since the reference moments obtained from a Monte-Carlo simulation is available, we only need to call the `plotMoments` method from the PostProcessing object. This method generates a plot and stores it in `Outputs_PostProcessing_calib` directory."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 13,
- "id": "96e85fb9",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- " Time [s] mean std\n",
- "0 0.000000 126.943408 170.920339\n",
- "1 0.111111 126.941468 170.889593\n",
- "2 0.222222 126.940664 170.880029\n",
- "3 0.333333 126.940047 170.873950\n",
- "4 0.444444 126.939527 170.869675\n",
- "5 0.555556 126.939069 170.866553\n",
- "6 0.666667 126.938655 170.864251\n",
- "7 0.777778 126.938274 170.862569\n",
- "8 0.888889 126.937919 170.861378\n",
- "9 1.000000 126.937586 170.860589\n",
- "\n",
- ">>>>> Moments of Z <<<<<\n",
- "\n",
- "Index | Mean | Std. deviation\n",
- "-----------------------------------\n",
- "1 | 1.266e+02 | 1.705e+02\n",
- "2 | 1.266e+02 | 1.705e+02\n",
- "3 | 1.266e+02 | 1.705e+02\n",
- "4 | 1.266e+02 | 1.705e+02\n",
- "5 | 1.266e+02 | 1.705e+02\n",
- "6 | 1.266e+02 | 1.705e+02\n",
- "7 | 1.266e+02 | 1.705e+02\n",
- "8 | 1.266e+02 | 1.705e+02\n",
- "9 | 1.266e+02 | 1.705e+02\n",
- "10 | 1.266e+02 | 1.705e+02\n",
- "----------------------------------------\n"
- ]
- },
- {
- "data": {
- "text/html": [
- "\n",
- " <iframe\n",
- " width=\"900\"\n",
- " height=\"600\"\n",
- " src=\"./Outputs_PostProcessing_calib/Mean_Std_PCE.pdf\"\n",
- " frameborder=\"0\"\n",
- " allowfullscreen\n",
- " ></iframe>\n",
- " "
- ],
- "text/plain": [
- "<IPython.lib.display.IFrame at 0x7f44a48ed670>"
- ]
- },
- "execution_count": 13,
- "metadata": {},
- "output_type": "execute_result"
- },
- {
- "data": {
- "text/plain": [
- "<Figure size 1728x1152 with 0 Axes>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "# Compute the moments and compare with the Monte-Carlo reference\n",
- "PostPCE.plot_moments()\n",
- "# Show the pdf\n",
- "IFrame(\"./Outputs_PostProcessing_calib/Mean_Std_PCE.pdf\", width=900, height=600)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "a6cf5333",
- "metadata": {},
- "source": [
- "### Validation of the metamodel"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "9d506ae2",
- "metadata": {},
- "source": [
- "Let us first visually compare the results of the metamodel and the original model, i.e. `Analyrical Function` for 3 randomly drawn samples for the prior parameter distribution. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "id": "cfd42c02",
- "metadata": {},
- "outputs": [
- {
- "name": "stderr",
- "output_type": "stream",
- "text": [
- "Running forward model valid: 100%|██████████| 3/3 [00:00<00:00, 3583.85it/s]\n"
- ]
- },
- {
- "data": {
- "text/html": [
- "\n",
- " <iframe\n",
- " width=\"900\"\n",
- " height=\"600\"\n",
- " src=\"./Outputs_PostProcessing_calib/Model_vs_PCEModel.pdf\"\n",
- " frameborder=\"0\"\n",
- " allowfullscreen\n",
- " ></iframe>\n",
- " "
- ],
- "text/plain": [
- "<IPython.lib.display.IFrame at 0x7f44a47a7bb0>"
- ]
- },
- "execution_count": 15,
- "metadata": {},
- "output_type": "execute_result"
- },
- {
- "data": {
- "text/plain": [
- "<Figure size 1728x1152 with 0 Axes>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "# Plot to check validation visually.\n",
- "PostPCE.valid_metamodel(n_samples=3)\n",
- "# Show the pdf\n",
- "IFrame(\"./Outputs_PostProcessing_calib/Model_vs_PCEModel.pdf\", width=900, height=600)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "3b39e05f",
- "metadata": {},
- "source": [
- "Another way to check the accuracy of the meta model is to use the `accuracyCheckMetaModel` method to show the Root Mean Square Error and the validation error. "
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 14,
- "id": "e2f83de2",
- "metadata": {},
- "outputs": [
- {
- "name": "stderr",
- "output_type": "stream",
- "text": [
- "Running forward model validSet: 100%|██████████| 200/200 [00:00<00:00, 8584.59it/s]"
- ]
- },
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "\n",
- ">>>>> Errors of Z <<<<<\n",
- "\n",
- "Index | RMSE | Validation Error\n",
- "-----------------------------------\n",
- "1 | 4.415e-01 | 3.393e-08\n",
- "2 | 4.415e-01 | 3.399e-08\n",
- "3 | 4.415e-01 | 3.402e-08\n",
- "4 | 4.415e-01 | 3.404e-08\n",
- "5 | 4.415e-01 | 3.406e-08\n",
- "6 | 4.416e-01 | 3.408e-08\n",
- "7 | 4.418e-01 | 3.412e-08\n",
- "8 | 4.458e-01 | 3.475e-08\n",
- "9 | 4.410e-01 | 3.401e-08\n",
- "10 | 4.412e-01 | 3.405e-08\n"
- ]
- },
- {
- "name": "stderr",
- "output_type": "stream",
- "text": [
- "\n"
- ]
- }
- ],
- "source": [
- "# Compute and print RMSE error\n",
- "PostPCE.accuracyCheckMetaModel(nSamples=200)"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "ef686ae7",
- "metadata": {},
- "source": [
- "### Global sensitivity analysis with Sobol indices"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "1ffecd15",
- "metadata": {},
- "source": [
- "Here, we analyze how the variability of the model response quantity (`Z`) is affected by the variability of each input variable or combinations thereof. Here, we use the so-called Sobol indices ([Sobol original paper](https://mae.ufl.edu/haftka/eoed/protected/Sobol%20Original%20Paper.pdf)), derived from a variance decomposition of model outputs in terms of contributions of each input parameter or combinations thereof. \n",
- "Using Sobol decomposition, one can describe the total variance of the model in terms of the sum of the summands' variances. Once the PC representation of the model is available, the expansion coefficients are simply gathered according to the dependency of each basis polynomial, square-summed and normalized"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "3e95b594",
- "metadata": {},
- "source": [
- "\\begin{equation}\n",
- "\\label{eq:pce-sobol-1st}\n",
- "\\begin{array}{l}\n",
- "S_{i_{1}, \\ldots, i_{s}}=\\frac{\\sum\\limits_{j=1}^{M} \\chi_{j} c_{j}^{2}}{\\sum\\limits_{j=1}^{M} c_{j}^{2}} \\, ,\\qquad\n",
- "\\chi_{j}=\\left\\{\\begin{array}{ll}\n",
- "1, & \\text { if } \\alpha_{j}^{k}>0, \\quad \\forall j \\in\\left(i_{1}, \\ldots, i_{s}\\right) \\\\[0.5em]\n",
- "0, & \\text { if } \\alpha_{j}^{k}=0, \\quad \\exists j \\in\\left(i_{1}, \\ldots, i_{s}\\right)\n",
- "\\end{array}\\right\\} \\, .\n",
- "\\end{array}\n",
- "\\end{equation}"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "a255fc43",
- "metadata": {},
- "source": [
- "Here, $S_{i_{1}, \\ldots, i_{s}}$ is the Sobol index that indicates what fraction of total variance of the response quantity can be traced back to the joint contributions of the parameters $\\theta_{i_{1}}, \\ldots, \\theta_{i_{s}}.$ The index selection operator $\\chi_{j}$ indicates where the chosen parameters $\\theta$ numbered as $i_{1}, \\ldots, i_{s}$ (i.e., $\\left.\\theta_{i_{1}}, \\ldots, \\theta_{i_{s}}\\right)$ have concurrent contributions to the variance within the overall expansion. Simply put, it selects all polynomial terms with the specified combination $i_{1}, \\ldots, i_{s}$ of model parameters."
- ]
- },
- {
- "cell_type": "markdown",
- "id": "025e4a83",
- "metadata": {},
- "source": [
- "A complementing measure for sensitivity analysis is the Sobol Total Index. It expresses the total contribution to the variance of model output due to the uncertainty of an individual parameter $\\theta_j$ in all cross-combinations with other parameters"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "9da5d910",
- "metadata": {},
- "source": [
- "\\begin{equation}\n",
- "\\label{eq:pce-sobol-total}\n",
- "S_{j}^{T}=\\sum_{\\left\\{i_{1}, \\ldots, i_{s}\\right\\} \\supset j} S_{i_{1}, \\ldots, i_{s}},\n",
- "\\end{equation}"
- ]
- },
- {
- "cell_type": "markdown",
- "id": "59413b8c",
- "metadata": {},
- "source": [
- "where $S_{j}^{T}$ is simply a summation of all Sobol indices in which the variable $\\theta_j$ appears as univariate as well as joint influences.\n",
- "The Total Sobol indices sum to one, if input variables are independent. When dealing with correlated variables, however, this is not the case."
- ]
- },
- {
- "cell_type": "markdown",
- "id": "962bf769",
- "metadata": {},
- "source": [
- "To perform the sensitivity analysis with `bayesvalidrox` package, we need to call the `sobolIndicesPCE` of the `PostProcessing` object. This returns two dictionaries containing the single sobol indices and the total ones. Moreover, it plots the Total Sobol Indices and stores the plots in `pdf` format in `Outputs_PostProcessing_calib` directory."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 15,
- "id": "135173d6",
- "metadata": {
- "scrolled": true
- },
- "outputs": [
- {
- "data": {
- "text/html": [
- "\n",
- " <iframe\n",
- " width=\"900\"\n",
- " height=\"600\"\n",
- " src=\"./Outputs_PostProcessing_calib/Sobol_indices.pdf\"\n",
- " frameborder=\"0\"\n",
- " allowfullscreen\n",
- " ></iframe>\n",
- " "
- ],
- "text/plain": [
- "<IPython.lib.display.IFrame at 0x7fe0b57d1340>"
- ]
- },
- "execution_count": 15,
- "metadata": {},
- "output_type": "execute_result"
- },
- {
- "data": {
- "text/plain": [
- "<Figure size 1728x1152 with 0 Axes>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "# Plot the sobol indices\n",
- "sobol_cell, total_sobol = PostPCE.sobolIndicesPCE()\n",
- "# Show the pdf\n",
- "IFrame(\"./Outputs_PostProcessing_calib/Sobol_indices.pdf\", width=900, height=600)"
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Python 3",
- "language": "python",
- "name": "python3"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 3
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython3",
- "version": "3.9.4"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/examples/analytical_function/util/polyCoeffs/par_1.npy b/examples/analytical_function/util/polyCoeffs/par_1.npy
deleted file mode 100644
index 79baeb5e7d4dc4d2f02168707818177a697fab9d..0000000000000000000000000000000000000000
Binary files a/examples/analytical_function/util/polyCoeffs/par_1.npy and /dev/null differ
diff --git a/examples/analytical_function/util/polyCoeffs/par_10.npy b/examples/analytical_function/util/polyCoeffs/par_10.npy
deleted file mode 100644
index bdee15afb5c89f9d1d883e9711635863998dcc08..0000000000000000000000000000000000000000
Binary files a/examples/analytical_function/util/polyCoeffs/par_10.npy and /dev/null differ
diff --git a/examples/analytical_function/util/polyCoeffs/par_2.npy b/examples/analytical_function/util/polyCoeffs/par_2.npy
deleted file mode 100644
index 7fd65ab9c91bb5b424abf6b432380891e762c04d..0000000000000000000000000000000000000000
Binary files a/examples/analytical_function/util/polyCoeffs/par_2.npy and /dev/null differ
diff --git a/examples/analytical_function/util/polyCoeffs/par_3.npy b/examples/analytical_function/util/polyCoeffs/par_3.npy
deleted file mode 100644
index d11d47a390a8de627b23d3aea01d5936d646bc19..0000000000000000000000000000000000000000
Binary files a/examples/analytical_function/util/polyCoeffs/par_3.npy and /dev/null differ
diff --git a/examples/analytical_function/util/polyCoeffs/par_4.npy b/examples/analytical_function/util/polyCoeffs/par_4.npy
deleted file mode 100644
index 9f09d03cf6d85fb57e35c1b421787af780cfe673..0000000000000000000000000000000000000000
Binary files a/examples/analytical_function/util/polyCoeffs/par_4.npy and /dev/null differ
diff --git a/examples/analytical_function/util/polyCoeffs/par_5.npy b/examples/analytical_function/util/polyCoeffs/par_5.npy
deleted file mode 100644
index cbb5f48e9648edeafa7bf04e922143b23f086eb4..0000000000000000000000000000000000000000
Binary files a/examples/analytical_function/util/polyCoeffs/par_5.npy and /dev/null differ
diff --git a/examples/analytical_function/util/polyCoeffs/par_6.npy b/examples/analytical_function/util/polyCoeffs/par_6.npy
deleted file mode 100644
index 27df138ae67857b1eefd616a4d3bad00b97acbbc..0000000000000000000000000000000000000000
Binary files a/examples/analytical_function/util/polyCoeffs/par_6.npy and /dev/null differ
diff --git a/examples/analytical_function/util/polyCoeffs/par_7.npy b/examples/analytical_function/util/polyCoeffs/par_7.npy
deleted file mode 100644
index 4dd2be13d4ac52cd836c85c133f181d2d8f4d05b..0000000000000000000000000000000000000000
Binary files a/examples/analytical_function/util/polyCoeffs/par_7.npy and /dev/null differ
diff --git a/examples/analytical_function/util/polyCoeffs/par_8.npy b/examples/analytical_function/util/polyCoeffs/par_8.npy
deleted file mode 100644
index 5d6d9dff5c015d5bcb9aedd6137d38c0bcbc37e0..0000000000000000000000000000000000000000
Binary files a/examples/analytical_function/util/polyCoeffs/par_8.npy and /dev/null differ
diff --git a/examples/analytical_function/util/polyCoeffs/par_9.npy b/examples/analytical_function/util/polyCoeffs/par_9.npy
deleted file mode 100644
index 4a608a2b60db69ce5402bcc561f3e260a832aaaa..0000000000000000000000000000000000000000
Binary files a/examples/analytical_function/util/polyCoeffs/par_9.npy and /dev/null differ
diff --git a/examples/beam/data/MCrefs_MeanStd.csv b/examples/beam/data/MCrefs_MeanStd.csv
index 435da6a3fa0d17ead4712f67b90b1707f704a495..e9592bf45db032790f95259b8cedd7f961e70a81 100644
--- a/examples/beam/data/MCrefs_MeanStd.csv
+++ b/examples/beam/data/MCrefs_MeanStd.csv
@@ -1,12 +1,12 @@
x [m],mean,std
0,0,0
-0.555555555555556,-0.002623091088022,6.21E-07
-1.11111111111111,-0.004962749295994,2.22E-06
-1.66666666666667,-0.006794367435948,4.16E-06
-2.22222222222222,-0.007957511802197,5.71E-06
-2.77777777777778,-0.008355922171325,6.3E-06
-3.33333333333333,-0.007957511802197,5.71E-06
-3.88888888888889,-0.006794367435948,4.16E-06
-4.44444444444444,-0.004962749295994,2.22E-06
-5,-0.002623091088022,6.21E-07
-5.55555555555556,0,0
+0.1,-0.002623091088022,8.06E-04
+0.2,-0.004962749295994,0.001525818175278
+0.3,-0.006794367435948,0.002088956887598
+0.4,-0.007957511802197,0.002446570522429
+0.5,-0.008355922171325,0.002569063468612
+0.6,-0.007957511802197,0.002446570522429
+0.7,-0.006794367435948,0.002088956887598
+0.8,-0.004962749295994,0.001525818175278
+0.9,-0.002623091088022,8.06E-04
+1,0,0
diff --git a/examples/beam/read_Beam_Deflection.py b/examples/beam/read_Beam_Deflection.py
index 92ae490334e47c07e63c117ef70a47c2d11dd10f..cd7a5e26ee498496abd6b49fed201e1506e14823 100644
--- a/examples/beam/read_Beam_Deflection.py
+++ b/examples/beam/read_Beam_Deflection.py
@@ -12,11 +12,14 @@ import numpy as np
def read_Beam_Deflection(FileNames):
df_Mean = pd.read_csv(FileNames[0], header=None, delimiter=' ')
- x_values = np.arange(0, 5.6, 5./9) # [1:]
- Deflection = df_Mean[df_Mean.columns[0]]
+ x_values = np.linspace(0, 1, 11)
+ deflection = df_Mean[df_Mean.columns[0]]
- Deflection_zero = np.zeros((1))
- Deflection_mid = np.append(Deflection_zero, Deflection)
- Deflection_Final = np.append(Deflection_mid, Deflection_zero)
+ deflection_zero = np.zeros((1))
+ deflection_mid = np.append(deflection_zero, deflection)
+ deflection_final = np.append(deflection_mid, deflection_zero)
- return np.vstack((x_values, Deflection_Final))
+ # Prepare output dict using standard bayesvalidrox format
+ output = {'x_values': x_values, 'Deflection [m]': deflection_final}
+
+ return output
diff --git a/examples/beam/test_beam.py b/examples/beam/test_beam.py
index e1d1ababc8da4b3bd6d96e14dbc9e82c48259549..8e17a42408ea7405b7b0d45f615a86a38216509f 100644
--- a/examples/beam/test_beam.py
+++ b/examples/beam/test_beam.py
@@ -1,9 +1,9 @@
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
-This test shows a surrogate-assisted Bayesian calibration of a beam deflection
- model. This example also illustrate how a model with an executable and a
- input file can be linked with the bayesvalidrox package.
+This test shows a surrogate for a beam deflection model can be created.
+This example also illustrate how a model with an executable and a
+input file can be linked with the bayesvalidrox package.
Author: Farid Mohammadi, M.Sc.
E-Mail: farid.mohammadi@iws.uni-stuttgart.de
@@ -16,10 +16,6 @@ Pfaffenwaldring 61
Created on Wed Jul 10 2019
"""
-import os
-import numpy as np
-import pandas as pd
-import joblib
# Add BayesValidRox path
import sys
sys.path.append("../../src/bayesvalidrox/")
@@ -86,7 +82,7 @@ if __name__ == "__main__":
# =====================================================
# ========== DEFINITION OF THE METAMODEL ============
# =====================================================
- MetaModelOpts = MetaModel(Inputs)
+ MetaModelOpts = MetaModel(Inputs, Model)
# Select if you want to preserve the spatial/temporal depencencies
# MetaModelOpts.dim_red_method = 'PCA'
@@ -96,7 +92,7 @@ if __name__ == "__main__":
# Select your metamodel method
# 1) PCE (Polynomial Chaos Expansion) 2) aPCE (arbitrary PCE)
# 3) GPE (Gaussian Process Emulator)
- MetaModelOpts.meta_model_type = 'aPCE'
+ MetaModelOpts.meta_model_type = 'PCE'
# ------------------------------------------------
# ------------- PCE Specification ----------------
@@ -106,15 +102,17 @@ if __name__ == "__main__":
# 1)OLS: Ordinary Least Square 2)BRR: Bayesian Ridge Regression
# 3)LARS: Least angle regression 4)ARD: Bayesian ARD Regression
# 5)FastARD: Fast Bayesian ARD Regression
- # 6)VBL: Variational Bayesian Learning
- # 7)EBL: Emperical Bayesian Learning
+ # 6)BCS: Bayesian Compressive Sensing
+ # 7)OMP: Orthogonal Matching Pursuit
+ # 8)VBL: Variational Bayesian Learning
+ # 9)EBL: Emperical Bayesian Learning
MetaModelOpts.pce_reg_method = 'FastARD'
# Specify the max degree to be compared by the adaptive algorithm:
# The degree with the lowest Leave-One-Out cross-validation (LOO)
# error (or the highest score=1-LOO)estimator is chosen as the final
# metamodel. pce_deg accepts degree as a scalar or a range.
- MetaModelOpts.pce_deg = np.arange(6)
+ MetaModelOpts.pce_deg = 6
# q-quasi-norm 0<q<1 (default=1)
MetaModelOpts.pce_q_norm = 0.75
@@ -126,18 +124,18 @@ if __name__ == "__main__":
# One-shot (normal) or Sequential Adaptive (sequential) Design
MetaModelOpts.ExpDesign.method = 'normal'
- MetaModelOpts.ExpDesign.n_init_samples = 20
+ MetaModelOpts.ExpDesign.n_init_samples = 100
# Sampling methods
# 1) random 2) latin_hypercube 3) sobol 4) halton 5) hammersley
- # 6) chebyshev(FT) 7) korobov 8) grid(FT) 9) nested_grid(FT) 10)user
+ # 6) chebyshev(FT) 7) grid(FT) 8)user
MetaModelOpts.ExpDesign.sampling_method = 'latin_hypercube'
# Provide the experimental design object with a hdf5 file
# MetaModelOpts.ExpDesign.hdf5_file = 'ExpDesign_Beam9points.hdf5'
# ------ Train the surrogate model ------
- PCEModel = MetaModelOpts.create_metamodel(Model)
+ PCEModel = MetaModelOpts.create_metamodel()
# =====================================================
# ========= POST PROCESSING OF METAMODELS ===========
@@ -145,37 +143,11 @@ if __name__ == "__main__":
PostPCE = PostProcessing(PCEModel)
# Compute the moments and compare with the Monte-Carlo reference
- PostPCE.plot_moments()
+ PostPCE.plot_moments(xlabel='$\\mathrm{L_{rel}}$ (-)')
# Plot the sobol indices
if MetaModelOpts.meta_model_type != 'GPE':
- sobol_cell, total_sobol = PostPCE.sobol_indices()
+ total_sobol = PostPCE.sobol_indices()
# Plot to check validation visually.
PostPCE.valid_metamodel(n_samples=3)
-
- # =====================================================
- # ============ Bayesian calibration =================
- # =====================================================
- BayesOpts = BayesInference(PCEModel)
- BayesOpts.name = 'Calib'
- BayesOpts.emulator = True
-
- # Bootstrap for BME calulations
- BayesOpts.bootstrap = True
- BayesOpts.n_bootstrap_itrs = 100
- BayesOpts.bootstrap_noise = 0.05
-
- # -------- Discrepancy model ------
- DiscrepancyOpts = Discrepancy('')
- DiscrepancyOpts.type = 'Gaussian'
- obsData = pd.read_csv(Model.meas_file)
- DiscrepancyOpts.parameters = (0.01*obsData)**2
- BayesOpts.Discrepancy = DiscrepancyOpts
-
- Bayes_Calib = BayesOpts.create_inference()
-
- with open('Beam_Results.pkl', 'wb') as output:
- joblib.dump(PCEModel, output, 2)
- joblib.dump(PostPCE, output, 2)
- joblib.dump(Bayes_Calib, output, 2)
diff --git a/examples/borehole/borehole.py b/examples/borehole/borehole.py
new file mode 100644
index 0000000000000000000000000000000000000000..b2a0dcd4a08091e05b74cceae3eda3709308ae49
--- /dev/null
+++ b/examples/borehole/borehole.py
@@ -0,0 +1,73 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Author: Farid Mohammadi, M.Sc.
+E-Mail: farid.mohammadi@iws.uni-stuttgart.de
+Department of Hydromechanics and Modelling of Hydrosystems (LH2)
+Institute for Modelling Hydraulic and Environmental Systems (IWS), University
+of Stuttgart, www.iws.uni-stuttgart.de/lh2/
+Pfaffenwaldring 61
+70569 Stuttgart
+
+Created on Mon Sep 12 2022
+
+"""
+import numpy as np
+
+
+def borehole(xx, *args):
+ """
+ BOREHOLE FUNCTION
+
+ Authors: Sonja Surjanovic, Simon Fraser University
+ Derek Bingham, Simon Fraser University
+ Questions/Comments: Please email Derek Bingham at dbingham@stat.sfu.ca.
+
+ Copyright 2013. Derek Bingham, Simon Fraser University.
+
+ THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY
+ FOR THE USE OF THIS SOFTWARE. If software is modified to produce
+ derivative works, such modified software should be clearly marked.
+ Additionally, this program is free software; you can redistribute it
+ and/or modify it under the terms of the GNU General Public License as
+ published by the Free Software Foundation; version 2.0 of the License.
+ Accordingly, this program is distributed in the hope that it will be
+ useful, but WITHOUT ANY WARRANTY; without even the implied warranty
+ of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ General Public License for more details.
+
+ For function details and reference information, see:
+ https://www.sfu.ca/~ssurjano/ishigami.html
+
+ Parameters
+ ----------
+ xx : array of shape (n_samples, n_params)
+ Input parameter sets. [rw, L, kw, Tu, Tl, Hu, Hl, r]
+
+ Returns
+ -------
+ output: dict
+ Water flow rate.
+
+ """
+ rw = xx[:, 0]
+ L = xx[:, 1]
+ Kw = xx[:, 2]
+ Tu = xx[:, 3]
+ Tl = xx[:, 4]
+ Hu = xx[:, 5]
+ Hl = xx[:, 6]
+ r = xx[:, 7]
+
+ frac1 = 2 * np.pi * Tu * (Hu-Hl)
+
+ frac2a = 2*L*Tu / (np.log(r/rw)*(rw**2)*Kw)
+ frac2b = Tu / Tl
+ frac2 = np.log(r/rw) * (1 + frac2a + frac2b)
+
+ y = frac1 / frac2
+
+ # Prepare output dict using standard bayesvalidrox format
+ output = {'x_values': np.zeros(1), 'flow rate [m$^3$/yr]': y}
+
+ return output
diff --git a/examples/borehole/data/sparse_solver_comparison.py b/examples/borehole/data/sparse_solver_comparison.py
new file mode 100644
index 0000000000000000000000000000000000000000..c438162f8e167ee420ca2b521eae917b30eb4130
--- /dev/null
+++ b/examples/borehole/data/sparse_solver_comparison.py
@@ -0,0 +1,240 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Sat Sep 10 09:44:05 2022
+
+@author: farid
+"""
+
+import numpy as np
+import joblib
+import os
+import scipy.stats as st
+
+import sys
+sys.path.append("../../../src/bayesvalidrox/")
+
+from pylink.pylink import PyLinkForwardModel
+from surrogate_models.inputs import Input
+from surrogate_models.surrogate_models import MetaModel
+from post_processing.post_processing import PostProcessing
+from bayes_inference.bayes_inference import BayesInference
+from bayes_inference.discrepancy import Discrepancy
+import matplotlib
+matplotlib.use('agg')
+from matplotlib.backends.backend_pdf import PdfPages
+import matplotlib.ticker as ticker
+from matplotlib.offsetbox import AnchoredText
+from matplotlib.patches import Patch
+import matplotlib.pyplot as plt
+# Load the mplstyle
+plt.style.use(os.path.join(
+ os.path.split(__file__)[0],
+ '../../../src/bayesvalidrox/', 'bayesvalidrox.mplstyle'))
+
+
+def plot_seq_design_diagnostics(meta_model, util_funcs,
+ ref_BME_KLD=None, save_fig=True):
+ """
+ Plots the Bayesian Model Evidence (BME) and Kullback-Leibler divergence
+ (KLD) for the sequential design.
+
+ Parameters
+ ----------
+ ref_BME_KLD : array, optional
+ Reference BME and KLD . The default is `None`.
+ save_fig : bool, optional
+ Whether to save the figures. The default is `True`.
+
+ Returns
+ -------
+ None.
+
+ """
+ n_init_samples = meta_model.ExpDesign.n_init_samples
+ n_total_samples = meta_model.ExpDesign.X.shape[0]
+
+ if save_fig:
+ newpath = f'{path}/boxplot_{model_name}/'
+ if not os.path.exists(newpath):
+ os.makedirs(newpath)
+
+ plotList = ['Modified LOO error', 'Validation error', 'KLD', 'BME',
+ 'RMSEMean', 'RMSEStd', 'Hellinger distance']
+ seqList = [meta_model.SeqModifiedLOO, meta_model.seqValidError,
+ meta_model.SeqKLD, meta_model.SeqBME, meta_model.seqRMSEMean,
+ meta_model.seqRMSEStd, meta_model.SeqDistHellinger]
+
+ markers = ('x', 'o', 'd', '*', '+')
+ colors = ('k', 'darkgreen', 'b', 'navy', 'darkred')
+
+ # Plot the evolution of the diagnostic criteria of the
+ # Sequential Experimental Design.
+ for plotidx, plot in enumerate(plotList):
+ fig, ax = plt.subplots(figsize=(27, 15))
+ seq_dict = seqList[plotidx]
+ name_util = list(seq_dict.keys())
+
+ if len(name_util) == 0:
+ continue
+
+ # Box plot when Replications have been detected.
+ if any(int(name.split("rep_", 1)[1]) > 1 for name in name_util):
+ # Extract the values from dict
+ sorted_seq_opt = {}
+ # Number of replications
+ n_reps = meta_model.ExpDesign.n_replication
+
+ # Get the list of utility function names
+ # Handle if only one UtilityFunction is provided
+ if not isinstance(util_funcs, list):
+ util_funcs = [util_funcs]
+
+ for util in util_funcs:
+ sortedSeq = {}
+ # min number of runs available from reps
+ n_runs = min([seq_dict[f'{util}_rep_{i+1}'].shape[0]
+ for i in range(n_reps)])
+
+ for runIdx in range(n_runs):
+ values = []
+ for key in seq_dict.keys():
+ if util in key:
+ values.append(seq_dict[key][runIdx].mean())
+ sortedSeq['SeqItr_'+str(runIdx)] = np.array(values)
+ sorted_seq_opt[util] = sortedSeq
+
+ # BoxPlot
+ def draw_plot(data, labels, edge_color, fill_color, idx):
+ pos = labels - (4*idx-6)
+ bp = plt.boxplot(data, positions=pos, labels=labels,
+ patch_artist=True, sym='', widths=3)
+
+ ax.plot(pos, np.median(data, axis=0), lw=4, color=fill_color[idx])
+
+ elements = ['boxes', 'whiskers', 'fliers', 'means',
+ 'medians', 'caps']
+ for element in elements:
+ plt.setp(bp[element], color=edge_color[idx], alpha=0.6)
+
+ for patch in bp['boxes']:
+ patch.set(facecolor=fill_color[idx], alpha=0.6)
+
+ if meta_model.ExpDesign.n_new_samples != 1:
+ step1 = meta_model.ExpDesign.n_new_samples
+ step2 = 1
+ else:
+ step1 = 25
+ step2 = 25
+ edge_color = ['red', 'blue', 'green', 'black']
+ fill_color = ['tan', 'cyan', 'lightgreen', 'grey']
+ plot_label = plot
+ # Plot for different Utility Functions
+ for idx, util in enumerate(util_funcs):
+ all_errors = np.empty((n_reps, 0))
+
+ for key in list(sorted_seq_opt[util].keys()):
+ errors = sorted_seq_opt.get(util, {}).get(key)[:, None]
+ all_errors = np.hstack((all_errors, errors))
+
+ # Special cases for BME and KLD
+ if plot == 'KLD' or plot == 'BME':
+ # BME convergence if refBME is provided
+ if ref_BME_KLD is not None:
+ if plot == 'BME':
+ refValue = ref_BME_KLD[0]
+ plot_label = r'BME/BME$^{Ref.}$'
+ if plot == 'KLD':
+ refValue = ref_BME_KLD[1]
+ plot_label = '$D_{KL}[p(\\theta|y_*),p(\\theta)]'\
+ ' / D_{KL}^{Ref.}[p(\\theta|y_*), '\
+ 'p(\\theta)]$'
+
+ # Difference between BME/KLD and the ref. values
+ all_errors = np.divide(all_errors,
+ np.full((all_errors.shape),
+ refValue))
+
+ # Plot baseline for zero, i.e. no difference
+ plt.axhline(y=1.0, xmin=0, xmax=1, c='green',
+ ls='--', lw=2)
+
+ # Plot each UtilFuncs
+ labels = np.arange(n_init_samples, n_total_samples+1, step1)
+ draw_plot(all_errors[:, ::step2], labels, edge_color,
+ fill_color, idx)
+ # labels = np.array([10, 30, 50, 70, 90, 120, 150, 200])
+ # indices = [0, 20, 40, 60, 80, 110, 140, 190]
+ # draw_plot(all_errors[:, indices], labels, edge_color,
+ # fill_color, idx)
+
+ plt.xticks(labels)
+ # Set the major and minor locators
+ # ax.xaxis.set_major_locator(ticker.AutoLocator())
+ # ax.xaxis.set_minor_locator(ticker.AutoMinorLocator())
+ # ax.xaxis.grid(True, which='major', linestyle='-')
+ # ax.xaxis.grid(True, which='minor', linestyle='--')
+
+ # Shade
+ for center in labels[::2]:
+ ax.axvspan(center-8, center+8, alpha=0.1, color='grey')
+
+ # Legend
+ legend_elements = []
+ for idx, util in enumerate(util_funcs):
+ legend_elements.append(Patch(facecolor=fill_color[idx],
+ edgecolor=edge_color[idx],
+ label=util))
+ plt.legend(handles=legend_elements[::-1], loc='best')
+
+ if plot != 'BME' and plot != 'KLD':
+ plt.yscale('log')
+ plt.autoscale(True)
+ # ax.yaxis.set_minor_locator(ticker.LogLocator(numticks=999, subs="auto"))
+ #ax.yaxis.grid(True, which='minor', linestyle='--')
+ plt.xlabel('\\# of training samples', fontsize=f_size)
+ plt.ylabel(plot_label, fontsize=f_size)
+ # plt.title(plot)
+ plt.xticks(fontsize=f_size)
+ plt.yticks(fontsize=f_size)
+
+ if save_fig:
+ # save the current figure
+ plot_name = plot.replace(' ', '_')
+ fig.savefig(
+ f'{newpath}/boxplot_solver_{model_name}_{plot_name}.pdf',
+ bbox_inches='tight'
+ )
+ # Destroy the current plot
+ plt.clf()
+ return
+
+
+if __name__ == "__main__":
+ # Set variables
+ model_name = 'borehole'
+ solvers = ['FastLaplace', 'FastARD', 'OMP', 'OLS']
+ path = '../solver_comparison'
+ f_size = 45
+
+ all_loo_errors = {}
+ all_valid_errors = {}
+ for solver in solvers:
+ # reading the data from the file
+ with open(f"{path}/{solver}/PCEModel_{model_name}.pkl", "rb") as input:
+ meta_model = joblib.load(input)
+
+ # Update name and Concatenate
+ all_valid_errors.update({key.replace('ALM', solver): value
+ for key, value in
+ meta_model.seqValidError.items()
+ })
+ all_loo_errors.update({key.replace('ALM', solver): value
+ for key, value in
+ meta_model.SeqModifiedLOO.items()
+ })
+ meta_model.seqValidError = all_valid_errors
+ meta_model.SeqModifiedLOO = all_loo_errors
+
+ # Plot box plot
+ plot_seq_design_diagnostics(meta_model, solvers)
diff --git a/examples/borehole/data/valid_outputs.npy b/examples/borehole/data/valid_outputs.npy
new file mode 100644
index 0000000000000000000000000000000000000000..076320cebb087989776523cbfd6e1dd122c84b63
Binary files /dev/null and b/examples/borehole/data/valid_outputs.npy differ
diff --git a/examples/borehole/data/valid_samples.npy b/examples/borehole/data/valid_samples.npy
new file mode 100644
index 0000000000000000000000000000000000000000..27564f822ee863e5d75d7b8c71fcd8a763d5bc63
Binary files /dev/null and b/examples/borehole/data/valid_samples.npy differ
diff --git a/examples/borehole/test_borehole.py b/examples/borehole/test_borehole.py
new file mode 100644
index 0000000000000000000000000000000000000000..e28e9a30f76afa9deb158e23532af12623f2d8e2
--- /dev/null
+++ b/examples/borehole/test_borehole.py
@@ -0,0 +1,235 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+This test deals with the surrogate modeling of a Borehole function.
+
+You will see how to:
+ Check the quality of your regression model
+ Perform sensitivity analysis via Sobol Indices
+
+Author: Farid Mohammadi, M.Sc.
+E-Mail: farid.mohammadi@iws.uni-stuttgart.de
+Department of Hydromechanics and Modelling of Hydrosystems (LH2)
+Institute for Modelling Hydraulic and Environmental Systems (IWS), University
+of Stuttgart, www.iws.uni-stuttgart.de/lh2/
+Pfaffenwaldring 61
+70569 Stuttgart
+
+Created on Sep 12 2022
+
+"""
+
+import numpy as np
+import joblib
+
+# import bayesvalidrox
+# Add BayesValidRox path
+import sys
+sys.path.append("../../src/bayesvalidrox/")
+
+from pylink.pylink import PyLinkForwardModel
+from surrogate_models.inputs import Input
+from surrogate_models.surrogate_models import MetaModel
+from post_processing.post_processing import PostProcessing
+from bayes_inference.bayes_inference import BayesInference
+from bayes_inference.discrepancy import Discrepancy
+from surrogate_models.meta_model_engine import MetaModelEngine
+
+import matplotlib
+matplotlib.use('agg')
+
+if __name__ == "__main__":
+
+ # =====================================================
+ # ============= COMPUTATIONAL MODEL ================
+ # =====================================================
+ Model = PyLinkForwardModel()
+
+ # Define model options
+ Model.link_type = 'Function'
+ Model.py_file = 'borehole'
+ Model.name = 'borehole'
+
+ Model.Output.names = ['flow rate [m$^3$/yr]']
+
+ # =====================================================
+ # ========= PROBABILISTIC INPUT MODEL ==============
+ # =====================================================
+ Inputs = Input()
+
+ # borehole radius
+ Inputs.add_marginals()
+ Inputs.Marginals[0].name = '$r_w$'
+ Inputs.Marginals[0].dist_type = 'normal'
+ Inputs.Marginals[0].parameters = [0.10, 0.0161812]
+
+ # borehole length
+ Inputs.add_marginals()
+ Inputs.Marginals[1].name = '$L$'
+ Inputs.Marginals[1].dist_type = 'unif'
+ Inputs.Marginals[1].parameters = [1120, 1680]
+
+ # borehole hydraulic conductivity
+ Inputs.add_marginals()
+ Inputs.Marginals[2].name = '$K_w$'
+ Inputs.Marginals[2].dist_type = 'unif'
+ Inputs.Marginals[2].parameters = [9855, 12045]
+
+ # transmissivity of upper aquifer
+ Inputs.add_marginals()
+ Inputs.Marginals[3].name = '$T_u$'
+ Inputs.Marginals[3].dist_type = 'unif'
+ Inputs.Marginals[3].parameters = [63070, 115600]
+
+ # transmissivity of lower aquifer
+ Inputs.add_marginals()
+ Inputs.Marginals[4].name = '$T_l$'
+ Inputs.Marginals[4].dist_type = 'unif'
+ Inputs.Marginals[4].parameters = [63.1, 116]
+
+ # potentiometric head of upper aquifer
+ Inputs.add_marginals()
+ Inputs.Marginals[5].name = '$H_u$'
+ Inputs.Marginals[5].dist_type = 'unif'
+ Inputs.Marginals[5].parameters = [990, 1110]
+
+ # potentiometric head of lower aquifer
+ Inputs.add_marginals()
+ Inputs.Marginals[6].name = '$H_l$'
+ Inputs.Marginals[6].dist_type = 'unif'
+ Inputs.Marginals[6].parameters = [700, 820]
+
+ # radius of influence
+ Inputs.add_marginals()
+ Inputs.Marginals[7].name = '$r$'
+ Inputs.Marginals[7].dist_type = 'lognorm'
+ Inputs.Marginals[7].parameters = [7.71, 1.0056]
+
+ # =====================================================
+ # ====== POLYNOMIAL CHAOS EXPANSION METAMODELS ======
+ # =====================================================
+ MetaModelOpts = MetaModel(Inputs, Model)
+
+ # Select your metamodel method
+ # 1) PCE (Polynomial Chaos Expansion) 2) aPCE (arbitrary PCE)
+ # 3) GPE (Gaussian Process Emulator)
+ MetaModelOpts.meta_model_type = 'aPCE'
+
+ # ------------------------------------------------
+ # ------------- PCE Specification ----------------
+ # ------------------------------------------------
+ # Select the sparse least-square minimization method for
+ # the PCE coefficients calculation:
+ # 1)OLS: Ordinary Least Square 2)BRR: Bayesian Ridge Regression
+ # 3)LARS: Least angle regression 4)ARD: Bayesian ARD Regression
+ # 5)FastARD: Fast Bayesian ARD Regression
+ # 6)BCS: Bayesian Compressive Sensing
+ # 7)OMP: Orthogonal Matching Pursuit
+ # 8)VBL: Variational Bayesian Learning
+ # 9)EBL: Emperical Bayesian Learning
+ MetaModelOpts.pce_reg_method = 'OMP'
+
+ # Specify the max degree to be compared by the adaptive algorithm:
+ # The degree with the lowest Leave-One-Out cross-validation (LOO)
+ # error (or the highest score=1-LOO)estimator is chosen as the final
+ # metamodel. pce_deg accepts degree as a scalar or a range.
+ MetaModelOpts.pce_deg = 5
+
+ # q-quasi-norm 0<q<1 (default=1)
+ MetaModelOpts.pce_q_norm = 1.0
+
+ # Print summary of the regression results
+ # MetaModelOpts.verbose = True
+
+ # ------------------------------------------------
+ # ------ Experimental Design Configuration -------
+ # ------------------------------------------------
+ MetaModelOpts.add_ExpDesign()
+
+ # One-shot (normal) or Sequential Adaptive (sequential) Design
+ MetaModelOpts.ExpDesign.method = 'sequential'
+ MetaModelOpts.ExpDesign.n_init_samples = 50
+
+ # Sampling methods
+ # 1) random 2) latin_hypercube 3) sobol 4) halton 5) hammersley 6) korobov
+ # 7) chebyshev(FT) 8) grid(FT) 9) nested_grid(FT) 10)user
+ MetaModelOpts.ExpDesign.sampling_method = 'latin_hypercube'
+
+ # Provide the experimental design object with a hdf5 file
+ # MetaModelOpts.ExpDesign.hdf5_file = 'ExpDesign_borehole.hdf5'
+
+ # Sequential experimental design (needed only for sequential ExpDesign)
+ MetaModelOpts.ExpDesign.n_new_samples = 1
+ MetaModelOpts.ExpDesign.n_max_samples = 300
+ MetaModelOpts.ExpDesign.mod_LOO_threshold = 1e-16
+
+ # ------------------------------------------------
+ # ------- Sequential Design configuration --------
+ # ------------------------------------------------
+ # 1) None 2) 'equal' 3)'epsilon-decreasing' 4) 'adaptive'
+ MetaModelOpts.ExpDesign.tradeoff_scheme = None
+ # MetaModelOpts.ExpDesign.n_replication = 50
+ # -------- Exploration ------
+ # 1)'Voronoi' 2)'random' 3)'latin_hypercube' 4)'dual annealing'
+ MetaModelOpts.ExpDesign.explore_method = 'latin_hypercube'
+
+ # Use when 'dual annealing' chosen
+ MetaModelOpts.ExpDesign.max_func_itr = 200
+
+ # Use when 'Voronoi' or 'random' or 'latin_hypercube' chosen
+ MetaModelOpts.ExpDesign.n_canddidate = 5000
+ MetaModelOpts.ExpDesign.n_cand_groups = 4
+
+ # -------- Exploitation ------
+ # 1)'BayesOptDesign' 2)'VarOptDesign' 3)'alphabetic' 4)'Space-filling'
+ MetaModelOpts.ExpDesign.exploit_method = 'Space-filling'
+
+ # BayesOptDesign -> when data is available
+ # 1)DKL (Kullback-Leibler Divergence) 2)DPP (D-Posterior-percision)
+ # 3)APP (A-Posterior-percision)
+ # MetaModelOpts.ExpDesign.util_func = 'DKL'
+
+ # VarBasedOptDesign -> when data is not available
+ # Only with Vornoi >>> 1)Entropy 2)EIGF, 3)ALM, 4)LOOCV
+ MetaModelOpts.ExpDesign.util_func = 'ALM'
+
+ # alphabetic
+ # 1)D-Opt (D-Optimality) 2)A-Opt (A-Optimality)
+ # 3)K-Opt (K-Optimality)
+ # MetaModelOpts.ExpDesign.util_func = 'D-Opt'
+
+ MetaModelOpts.valid_samples = np.load("data/valid_samples.npy")
+ MetaModelOpts.valid_model_runs = {
+ 'flow rate [m$^3$/yr]': np.load("data/valid_outputs.npy")
+ }
+ # >>>>>>>>>>>>>>>>>>>>>> Build Surrogate <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
+ # Use MetaModelEngine for sequential experimental design
+ meta_model_engine = MetaModelEngine(MetaModelOpts)
+ meta_model_engine.run()
+ PCEModel = meta_model_engine.MetaModel
+
+ # Save PCE models
+ with open(f'PCEModel_{Model.name}.pkl', 'wb') as output:
+ joblib.dump(PCEModel, output, 2)
+
+ # =====================================================
+ # ========= POST PROCESSING OF METAMODELS ===========
+ # =====================================================
+ PostPCE = PostProcessing(PCEModel)
+
+ # Plot to check validation visually.
+ PostPCE.valid_metamodel(n_samples=200)
+
+ # Check the quality of your regression model
+ PostPCE.check_reg_quality()
+
+ # PostPCE.eval_PCEmodel_3D()
+ # Compute and print RMSE error
+ PostPCE.check_accuracy(n_samples=3000)
+
+ # Plot the evolution of the KLD,BME, and Modified LOOCV error
+ if MetaModelOpts.ExpDesign.method == 'sequential':
+ PostPCE.plot_seq_design_diagnostics()
+
+ # Plot the sobol indices
+ total_sobol = PostPCE.sobol_indices(plot_type='bar')
diff --git a/examples/ishigami/Ishigami.py b/examples/ishigami/Ishigami.py
index a2efe98eed2fe5269ee2e2ce7af59fdfa3b50894..9a60daae698f40bb2425c81fe40fe5f7a6f6292b 100644
--- a/examples/ishigami/Ishigami.py
+++ b/examples/ishigami/Ishigami.py
@@ -9,51 +9,51 @@ import numpy as np
def Ishigami(xx, *args):
+ """
+ ISHIGAMI FUNCTION
+
+ Authors: Sonja Surjanovic, Simon Fraser University
+ Derek Bingham, Simon Fraser University
+ Questions/Comments: Please email Derek Bingham at dbingham@stat.sfu.ca.
+
+ Copyright 2013. Derek Bingham, Simon Fraser University.
+
+ THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY
+ FOR THE USE OF THIS SOFTWARE. If software is modified to produce
+ derivative works, such modified software should be clearly marked.
+ Additionally, this program is free software; you can redistribute it
+ and/or modify it under the terms of the GNU General Public License as
+ published by the Free Software Foundation; version 2.0 of the License.
+ Accordingly, this program is distributed in the hope that it will be
+ useful, but WITHOUT ANY WARRANTY; without even the implied warranty
+ of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ General Public License for more details.
+
+ For function details and reference information, see:
+ https://www.sfu.ca/~ssurjano/ishigami.html
+
+ Parameters
+ ----------
+ xx : array of shape (n_samples, n_params)
+ Input parameter sets.
+ *args : coefficients
+ a = coefficient (optional), with default value 7
+ b = coefficient (optional), with default value 0.1
+
+ Returns
+ -------
+ output: dict
+ Output with x_values.
- """#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- #%
- #% ISHIGAMI FUNCTION
- #%
- #% Authors: Sonja Surjanovic, Simon Fraser University
- #% Derek Bingham, Simon Fraser University
- #% Questions/Comments: Please email Derek Bingham at dbingham@stat.sfu.ca.
- #%
- #% Copyright 2013. Derek Bingham, Simon Fraser University.
- #%
- #% THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY
- #% FOR THE USE OF THIS SOFTWARE. If software is modified to produce
- #% derivative works, such modified software should be clearly marked.
- #% Additionally, this program is free software; you can redistribute it
- #% and/or modify it under the terms of the GNU General Public License as
- #% published by the Free Software Foundation; version 2.0 of the License.
- #% Accordingly, this program is distributed in the hope that it will be
- #% useful, but WITHOUT ANY WARRANTY; without even the implied warranty
- #% of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- #% General Public License for more details.
- #%
- #% For function details and reference information, see:
- #% https://www.sfu.ca/~ssurjano/ishigami.html
- #%
- #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- #%
- #% INPUTS:
- #%
- #% xx = [x1, x2, x3]
- #% a = coefficient (optional), with default value 7
- #% b = coefficient (optional), with default value 0.1
- #%
- #%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
"""
-
- x1 = xx[:,0]
- x2 = xx[:,1]
- x3 = xx[:,2]
-
+
+ x1, x2, x3 = xx[:, 0], xx[:, 1], xx[:, 2]
+
if (len(args) == 0):
- a = 7
- b = 0.1
+ a = 7
+ b = 0.1
elif (len(args) == 1):
- b = 0.1
+ b = 0.1
term1 = np.sin(x1)
term2 = a * (np.sin(x2))**2
@@ -61,9 +61,7 @@ def Ishigami(xx, *args):
y = term1 + term2 + term3
-
- return np.vstack((np.zeros(1),y))
-
-
-
-
\ No newline at end of file
+ # Prepare output dict using standard bayesvalidrox format
+ output = {'x_values': np.zeros(1), 'Z': y}
+
+ return output
diff --git a/examples/ishigami/data/sparse_solver_comparison.py b/examples/ishigami/data/sparse_solver_comparison.py
new file mode 100644
index 0000000000000000000000000000000000000000..8bf8e00ca4b32c46ba7df8651397f969669c735b
--- /dev/null
+++ b/examples/ishigami/data/sparse_solver_comparison.py
@@ -0,0 +1,240 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Sat Sep 10 09:44:05 2022
+
+@author: farid
+"""
+
+import numpy as np
+import joblib
+import os
+import scipy.stats as st
+
+import sys
+sys.path.append("../../../src/bayesvalidrox/")
+
+from pylink.pylink import PyLinkForwardModel
+from surrogate_models.inputs import Input
+from surrogate_models.surrogate_models import MetaModel
+from post_processing.post_processing import PostProcessing
+from bayes_inference.bayes_inference import BayesInference
+from bayes_inference.discrepancy import Discrepancy
+import matplotlib
+matplotlib.use('agg')
+from matplotlib.backends.backend_pdf import PdfPages
+import matplotlib.ticker as ticker
+from matplotlib.offsetbox import AnchoredText
+from matplotlib.patches import Patch
+import matplotlib.pyplot as plt
+# Load the mplstyle
+plt.style.use(os.path.join(
+ os.path.split(__file__)[0],
+ '../../../src/bayesvalidrox/', 'bayesvalidrox.mplstyle'))
+
+
+def plot_seq_design_diagnostics(meta_model, util_funcs,
+ ref_BME_KLD=None, save_fig=True):
+ """
+ Plots the Bayesian Model Evidence (BME) and Kullback-Leibler divergence
+ (KLD) for the sequential design.
+
+ Parameters
+ ----------
+ ref_BME_KLD : array, optional
+ Reference BME and KLD . The default is `None`.
+ save_fig : bool, optional
+ Whether to save the figures. The default is `True`.
+
+ Returns
+ -------
+ None.
+
+ """
+ n_init_samples = meta_model.ExpDesign.n_init_samples
+ n_total_samples = meta_model.ExpDesign.X.shape[0]
+
+ if save_fig:
+ newpath = f'{path}/boxplot_{model_name}/'
+ if not os.path.exists(newpath):
+ os.makedirs(newpath)
+
+ plotList = ['Modified LOO error', 'Validation error', 'KLD', 'BME',
+ 'RMSEMean', 'RMSEStd', 'Hellinger distance']
+ seqList = [meta_model.SeqModifiedLOO, meta_model.seqValidError,
+ meta_model.SeqKLD, meta_model.SeqBME, meta_model.seqRMSEMean,
+ meta_model.seqRMSEStd, meta_model.SeqDistHellinger]
+
+ markers = ('x', 'o', 'd', '*', '+')
+ colors = ('k', 'darkgreen', 'b', 'navy', 'darkred')
+
+ # Plot the evolution of the diagnostic criteria of the
+ # Sequential Experimental Design.
+ for plotidx, plot in enumerate(plotList):
+ fig, ax = plt.subplots(figsize=(27, 15))
+ seq_dict = seqList[plotidx]
+ name_util = list(seq_dict.keys())
+
+ if len(name_util) == 0:
+ continue
+
+ # Box plot when Replications have been detected.
+ if any(int(name.split("rep_", 1)[1]) > 1 for name in name_util):
+ # Extract the values from dict
+ sorted_seq_opt = {}
+ # Number of replications
+ n_reps = meta_model.ExpDesign.n_replication
+
+ # Get the list of utility function names
+ # Handle if only one UtilityFunction is provided
+ if not isinstance(util_funcs, list):
+ util_funcs = [util_funcs]
+
+ for util in util_funcs:
+ sortedSeq = {}
+ # min number of runs available from reps
+ n_runs = min([seq_dict[f'{util}_rep_{i+1}'].shape[0]
+ for i in range(n_reps)])
+
+ for runIdx in range(n_runs):
+ values = []
+ for key in seq_dict.keys():
+ if util in key:
+ values.append(seq_dict[key][runIdx].mean())
+ sortedSeq['SeqItr_'+str(runIdx)] = np.array(values)
+ sorted_seq_opt[util] = sortedSeq
+
+ # BoxPlot
+ def draw_plot(data, labels, edge_color, fill_color, idx):
+ pos = labels - (4*idx-6)
+ bp = plt.boxplot(data, positions=pos, labels=labels,
+ patch_artist=True, sym='', widths=3)
+
+ ax.plot(pos, np.median(data, axis=0), lw=4, color=fill_color[idx])
+
+ elements = ['boxes', 'whiskers', 'fliers', 'means',
+ 'medians', 'caps']
+ for element in elements:
+ plt.setp(bp[element], color=edge_color[idx], alpha=0.6)
+
+ for patch in bp['boxes']:
+ patch.set(facecolor=fill_color[idx], alpha=0.6)
+
+ if meta_model.ExpDesign.n_new_samples != 1:
+ step1 = meta_model.ExpDesign.n_new_samples
+ step2 = 1
+ else:
+ step1 = 10
+ step2 = 10
+ edge_color = ['red', 'blue', 'green', 'black']
+ fill_color = ['tan', 'cyan', 'lightgreen', 'grey']
+ plot_label = plot
+ # Plot for different Utility Functions
+ for idx, util in enumerate(util_funcs):
+ all_errors = np.empty((n_reps, 0))
+
+ for key in list(sorted_seq_opt[util].keys()):
+ errors = sorted_seq_opt.get(util, {}).get(key)[:, None]
+ all_errors = np.hstack((all_errors, errors))
+
+ # Special cases for BME and KLD
+ if plot == 'KLD' or plot == 'BME':
+ # BME convergence if refBME is provided
+ if ref_BME_KLD is not None:
+ if plot == 'BME':
+ refValue = ref_BME_KLD[0]
+ plot_label = r'BME/BME$^{Ref.}$'
+ if plot == 'KLD':
+ refValue = ref_BME_KLD[1]
+ plot_label = '$D_{KL}[p(\\theta|y_*),p(\\theta)]'\
+ ' / D_{KL}^{Ref.}[p(\\theta|y_*), '\
+ 'p(\\theta)]$'
+
+ # Difference between BME/KLD and the ref. values
+ all_errors = np.divide(all_errors,
+ np.full((all_errors.shape),
+ refValue))
+
+ # Plot baseline for zero, i.e. no difference
+ plt.axhline(y=1.0, xmin=0, xmax=1, c='green',
+ ls='--', lw=2)
+
+ # Plot each UtilFuncs
+ # labels = np.arange(n_init_samples, n_total_samples+1, step1)
+ labels = np.array([10, 30, 50, 70, 90, 120, 150, 200])
+ indices = [0, 20, 40, 60, 80, 110, 140, 190]
+ draw_plot(all_errors[:, indices], labels, edge_color,
+ fill_color, idx)
+ # draw_plot(all_errors[:, ::step2], labels, edge_color,
+ # fill_color, idx)
+
+ plt.xticks(labels)
+ # Set the major and minor locators
+ # ax.xaxis.set_major_locator(ticker.AutoLocator())
+ # ax.xaxis.set_minor_locator(ticker.AutoMinorLocator())
+ # ax.xaxis.grid(True, which='major', linestyle='-')
+ # ax.xaxis.grid(True, which='minor', linestyle='--')
+
+ # Shade
+ for center in [30, 70, 120, 200]:#labels[::2]:
+ ax.axvspan(center-8, center+8, alpha=0.1, color='grey')
+
+ # Legend
+ legend_elements = []
+ for idx, util in enumerate(util_funcs):
+ legend_elements.append(Patch(facecolor=fill_color[idx],
+ edgecolor=edge_color[idx],
+ label=util))
+ plt.legend(handles=legend_elements[::-1], loc='best')
+
+ if plot != 'BME' and plot != 'KLD':
+ plt.yscale('log')
+ plt.autoscale(True)
+ # ax.yaxis.set_minor_locator(ticker.LogLocator(numticks=999, subs="auto"))
+ ax.yaxis.grid(True, which='minor', linestyle='--')
+ plt.xlabel('\\# of training samples', fontsize=f_size)
+ plt.ylabel(plot_label, fontsize=f_size)
+ # plt.title(plot)
+ plt.xticks(fontsize=f_size)
+ plt.yticks(fontsize=f_size)
+
+ if save_fig:
+ # save the current figure
+ plot_name = plot.replace(' ', '_')
+ fig.savefig(
+ f'{newpath}/boxplot_solver_ishigami_{plot_name}.pdf',
+ bbox_inches='tight'
+ )
+ # Destroy the current plot
+ plt.clf()
+ return
+
+
+if __name__ == "__main__":
+ # Set variables
+ model_name = 'Ishigami'
+ solvers = ['FastLaplace', 'FastARD', 'OMP', 'OLS']
+ path = f'/home/farid/bwSyncShare/Scientific_LH2/Promotion/dissertation/surrogate/data-ishigami/'
+ f_size = 45
+
+ all_loo_errors = {}
+ all_valid_errors = {}
+ for solver in solvers:
+ # reading the data from the file
+ with open(f"{path}/{solver}/PCEModel_{model_name}.pkl", "rb") as input:
+ meta_model = joblib.load(input)
+
+ # Update name and Concatenate
+ all_valid_errors.update({key.replace('ALM', solver): value
+ for key, value in
+ meta_model.seqValidError.items()
+ })
+ all_loo_errors.update({key.replace('ALM', solver): value
+ for key, value in
+ meta_model.SeqModifiedLOO.items()
+ })
+ meta_model.seqValidError = all_valid_errors
+ meta_model.SeqModifiedLOO = all_loo_errors
+
+ # Plot box plot
+ plot_seq_design_diagnostics(meta_model, solvers)
diff --git a/examples/ishigami/data/valid_outputs.npy b/examples/ishigami/data/valid_outputs.npy
new file mode 100644
index 0000000000000000000000000000000000000000..049f39311e41b8f0b00d443078068385470af45f
Binary files /dev/null and b/examples/ishigami/data/valid_outputs.npy differ
diff --git a/examples/ishigami/data/valid_samples.npy b/examples/ishigami/data/valid_samples.npy
new file mode 100644
index 0000000000000000000000000000000000000000..882ca288df7951d0025dd36e2ed4823c3ae361f9
Binary files /dev/null and b/examples/ishigami/data/valid_samples.npy differ
diff --git a/examples/ishigami/test_ishigami.py b/examples/ishigami/test_ishigami.py
index 3e37246d4c83b321cbb6286f6bbc301a742a59db..313ad38280acfe6bf3a4b8c29b1f94d74da399b7 100644
--- a/examples/ishigami/test_ishigami.py
+++ b/examples/ishigami/test_ishigami.py
@@ -20,6 +20,7 @@ Created on Wed Jul 10 2019
"""
import numpy as np
+import joblib
# import bayesvalidrox
# Add BayesValidRox path
@@ -29,6 +30,7 @@ sys.path.append("../../src/bayesvalidrox/")
from pylink.pylink import PyLinkForwardModel
from surrogate_models.inputs import Input
from surrogate_models.surrogate_models import MetaModel
+from surrogate_models.meta_model_engine import MetaModelEngine
from post_processing.post_processing import PostProcessing
from bayes_inference.bayes_inference import BayesInference
from bayes_inference.discrepancy import Discrepancy
@@ -72,7 +74,7 @@ if __name__ == "__main__":
# =====================================================
# ====== POLYNOMIAL CHAOS EXPANSION METAMODELS ======
# =====================================================
- MetaModelOpts = MetaModel(Inputs)
+ MetaModelOpts = MetaModel(Inputs, Model)
# Select your metamodel method
# 1) PCE (Polynomial Chaos Expansion) 2) aPCE (arbitrary PCE)
@@ -87,19 +89,24 @@ if __name__ == "__main__":
# 1)OLS: Ordinary Least Square 2)BRR: Bayesian Ridge Regression
# 3)LARS: Least angle regression 4)ARD: Bayesian ARD Regression
# 5)FastARD: Fast Bayesian ARD Regression
- # 6)VBL: Variational Bayesian Learning
- # 7)EBL: Emperical Bayesian Learning
- MetaModelOpts.pce_reg_method = 'FastARD'
+ # 6)BCS: Bayesian Compressive Sensing
+ # 7)OMP: Orthogonal Matching Pursuit
+ # 8)VBL: Variational Bayesian Learning
+ # 9)EBL: Emperical Bayesian Learning
+ MetaModelOpts.pce_reg_method = 'BCS'
# Specify the max degree to be compared by the adaptive algorithm:
# The degree with the lowest Leave-One-Out cross-validation (LOO)
# error (or the highest score=1-LOO)estimator is chosen as the final
# metamodel. pce_deg accepts degree as a scalar or a range.
- MetaModelOpts.pce_deg = np.arange(9)
+ MetaModelOpts.pce_deg = 14
# q-quasi-norm 0<q<1 (default=1)
MetaModelOpts.pce_q_norm = 1.0
+ # Print summary of the regression results
+ # MetaModelOpts.verbose = True
+
# ------------------------------------------------
# ------ Experimental Design Configuration -------
# ------------------------------------------------
@@ -107,7 +114,7 @@ if __name__ == "__main__":
# One-shot (normal) or Sequential Adaptive (sequential) Design
MetaModelOpts.ExpDesign.method = 'normal'
- MetaModelOpts.ExpDesign.n_init_samples = 100
+ MetaModelOpts.ExpDesign.n_init_samples = 50
# Sampling methods
# 1) random 2) latin_hypercube 3) sobol 4) halton 5) hammersley 6) korobov
@@ -119,7 +126,7 @@ if __name__ == "__main__":
# Sequential experimental design (needed only for sequential ExpDesign)
MetaModelOpts.ExpDesign.n_new_samples = 1
- MetaModelOpts.ExpDesign.n_max_samples = 100 # 150
+ MetaModelOpts.ExpDesign.n_max_samples = 200 # 150
MetaModelOpts.ExpDesign.mod_LOO_threshold = 1e-16
# ------------------------------------------------
@@ -127,10 +134,10 @@ if __name__ == "__main__":
# ------------------------------------------------
# 1) None 2) 'equal' 3)'epsilon-decreasing' 4) 'adaptive'
MetaModelOpts.ExpDesign.tradeoff_scheme = None
- # MetaModelOpts.ExpDesign.n_replication = 20
+ # MetaModelOpts.ExpDesign.n_replication = 50
# -------- Exploration ------
# 1)'Voronoi' 2)'random' 3)'latin_hypercube' 4)'dual annealing'
- MetaModelOpts.ExpDesign.explore_method = 'Voronoi'
+ MetaModelOpts.ExpDesign.explore_method = 'latin_hypercube'
# Use when 'dual annealing' chosen
MetaModelOpts.ExpDesign.max_func_itr = 200
@@ -141,7 +148,7 @@ if __name__ == "__main__":
# -------- Exploitation ------
# 1)'BayesOptDesign' 2)'VarOptDesign' 3)'alphabetic' 4)'Space-filling'
- MetaModelOpts.ExpDesign.exploit_method = 'VarOptDesign'
+ MetaModelOpts.ExpDesign.exploit_method = 'Space-filling'
# BayesOptDesign -> when data is available
# 1)DKL (Kullback-Leibler Divergence) 2)DPP (D-Posterior-percision)
@@ -150,16 +157,23 @@ if __name__ == "__main__":
# VarBasedOptDesign -> when data is not available
# Only with Vornoi >>> 1)Entropy 2)EIGF, 3)ALM, 4)LOOCV
- MetaModelOpts.ExpDesign.util_func = 'Entropy'
+ MetaModelOpts.ExpDesign.util_func = 'ALM'
# alphabetic
# 1)D-Opt (D-Optimality) 2)A-Opt (A-Optimality)
# 3)K-Opt (K-Optimality)
# MetaModelOpts.ExpDesign.util_func = 'D-Opt'
+ MetaModelOpts.valid_samples = np.load("data/valid_samples.npy")
+ MetaModelOpts.valid_model_runs = {'Z': np.load("data/valid_outputs.npy")}
# >>>>>>>>>>>>>>>>>>>>>> Build Surrogate <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
- # Adaptive sparse arbitrary polynomial chaos expansion
- PCEModel = MetaModelOpts.create_metamodel(Model)
+ meta_model_engine = MetaModelEngine(MetaModelOpts)
+ meta_model_engine.run()
+ PCEModel = meta_model_engine.MetaModel
+
+ # Save PCE models
+ with open(f'PCEModel_{Model.name}.pkl', 'wb') as output:
+ joblib.dump(PCEModel, output, 2)
# =====================================================
# ========= POST PROCESSING OF METAMODELS ===========
@@ -181,4 +195,4 @@ if __name__ == "__main__":
PostPCE.plot_seq_design_diagnostics()
# Plot the sobol indices
- sobol_cell, total_sobol = PostPCE.sobol_indices(plot_type='bar')
+ total_sobol = PostPCE.sobol_indices(plot_type='bar')
diff --git a/examples/model-comparison/L2_model.py b/examples/model-comparison/L2_model.py
new file mode 100644
index 0000000000000000000000000000000000000000..6b28c818101e25859bdb222b82cfd9bee741d381
--- /dev/null
+++ b/examples/model-comparison/L2_model.py
@@ -0,0 +1,57 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+This is a simple linear model.
+
+The code for this numerical experiments is available at
+https://github.com/MichaelSinsbeck/paper_sequential-design-model-selection.
+
+Author: Farid Mohammadi, M.Sc.
+E-Mail: farid.mohammadi@iws.uni-stuttgart.de
+Department of Hydromechanics and Modelling of Hydrosystems (LH2)
+Institute for Modelling Hydraulic and Environmental Systems (IWS),
+University of Stuttgart, www.iws.uni-stuttgart.de/lh2/
+Pfaffenwaldring 61
+70569 Stuttgart
+
+Created on Fri Oct 8 2021
+
+"""
+import numpy as np
+
+
+def L2_model(xx):
+ """
+ Linear model y = a*x+b
+
+ Models adapted from Anneli Guthke's paper:
+ ch€oniger, A., T. W€ohling, L. Samaniego,and W. Nowak (2014), Model
+ selection on solid ground: Rigorous comparison ofnine ways to evaluate
+ Bayesian modelevidence,Water Resour. Res.,50,9484–9513,
+ doi:10.1002/2014WR016062
+
+ Parameters
+ ----------
+ xx : array
+ Parameters a and b.
+
+ Returns
+ -------
+ 2D-array
+ The first row contains the measurement locations.
+ The second row contains the model outputs.
+
+ """
+ n_output = 15
+ meas_loc = np.linspace(0.25, 4.75, n_output)
+
+ # L2_model
+ L2_model = xx[:, 0] * meas_loc + xx[:, 1]
+
+ # Output
+ output = {
+ 'x_values': meas_loc,
+ 'Z': L2_model
+ }
+
+ return output
diff --git a/examples/model-comparison/NL2_model.py b/examples/model-comparison/NL2_model.py
new file mode 100644
index 0000000000000000000000000000000000000000..5fd4820e76a9756b85b891b0d8272404e81d3361
--- /dev/null
+++ b/examples/model-comparison/NL2_model.py
@@ -0,0 +1,57 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+This is a nonlinear cosine model.
+
+The code for this numerical experiments is available at
+https://github.com/MichaelSinsbeck/paper_sequential-design-model-selection.
+
+Author: Farid Mohammadi, M.Sc.
+E-Mail: farid.mohammadi@iws.uni-stuttgart.de
+Department of Hydromechanics and Modelling of Hydrosystems (LH2)
+Institute for Modelling Hydraulic and Environmental Systems (IWS),
+University of Stuttgart, www.iws.uni-stuttgart.de/lh2/
+Pfaffenwaldring 61
+70569 Stuttgart
+
+Created on Fri Oct 8 2021
+
+"""
+import numpy as np
+
+
+def NL2_model(xx):
+ """
+ Nonlinear model y = exp(a*x) + b
+
+ Models adapted from Anneli Guthke's paper:
+ ch€oniger, A., T. W€ohling, L. Samaniego,and W. Nowak (2014), Model
+ selection on solid ground: Rigorous comparison ofnine ways to evaluate
+ Bayesian modelevidence,Water Resour. Res.,50,9484–9513,
+ doi:10.1002/2014WR016062
+
+ Parameters
+ ----------
+ xx : array
+ Parameters a and b.
+
+ Returns
+ -------
+ 2D-array
+ The first row contains the measurement locations.
+ The second row contains the model outputs.
+
+ """
+ n_output = 15
+ meas_loc = np.linspace(0.25, 4.75, n_output)
+
+ # NL2_model
+ NL2_model = np.exp(xx[:, 0] * meas_loc) + xx[:, 1]
+
+ # Output
+ output = {
+ 'x_values': meas_loc,
+ 'Z': NL2_model
+ }
+
+ return output
diff --git a/examples/model-comparison/NL4_model.py b/examples/model-comparison/NL4_model.py
new file mode 100644
index 0000000000000000000000000000000000000000..5ca495306d9a6d277ec654a3efbdfb84bfc28ce1
--- /dev/null
+++ b/examples/model-comparison/NL4_model.py
@@ -0,0 +1,57 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+This is a nonlinear cosine model.
+
+The code for this numerical experiments is available at
+https://github.com/MichaelSinsbeck/paper_sequential-design-model-selection.
+
+Author: Farid Mohammadi, M.Sc.
+E-Mail: farid.mohammadi@iws.uni-stuttgart.de
+Department of Hydromechanics and Modelling of Hydrosystems (LH2)
+Institute for Modelling Hydraulic and Environmental Systems (IWS),
+University of Stuttgart, www.iws.uni-stuttgart.de/lh2/
+Pfaffenwaldring 61
+70569 Stuttgart
+
+Created on Fri Oct 8 2021
+
+"""
+import numpy as np
+
+
+def NL4_model(xx):
+ """
+ Nonlinear model y = a*cos(b*x+c)+d
+
+ Models adapted from Anneli Guthke's paper:
+ ch€oniger, A., T. W€ohling, L. Samaniego,and W. Nowak (2014), Model
+ selection on solid ground: Rigorous comparison ofnine ways to evaluate
+ Bayesian modelevidence,Water Resour. Res.,50,9484–9513,
+ doi:10.1002/2014WR016062
+
+ Parameters
+ ----------
+ xx : array
+ Parameters a and b.
+
+ Returns
+ -------
+ 2D-array
+ The first row contains the measurement locations.
+ The second row contains the model outputs.
+
+ """
+ n_output = 15
+ meas_loc = np.linspace(0.25, 4.75, n_output)
+
+ # NL4_model
+ NL4_model = xx[:, 0] * np.cos(xx[:, 1] * meas_loc + xx[:, 2]) + xx[:, 3]
+
+ # Output
+ output = {
+ 'x_values': meas_loc,
+ 'Z': NL4_model
+ }
+
+ return output
diff --git a/examples/model-comparison/__init__.py b/examples/model-comparison/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..4287ca8617970fa8fc025b75cb319c7032706910
--- /dev/null
+++ b/examples/model-comparison/__init__.py
@@ -0,0 +1 @@
+#
\ No newline at end of file
diff --git a/examples/model-comparison/data/synth_data.mat b/examples/model-comparison/data/synth_data.mat
new file mode 100644
index 0000000000000000000000000000000000000000..352697fc3848c73bf8ae8819f065b873a62907f5
Binary files /dev/null and b/examples/model-comparison/data/synth_data.mat differ
diff --git a/examples/model-comparison/reference/confusionMatrix_ND_1.svg b/examples/model-comparison/reference/confusionMatrix_ND_1.svg
new file mode 100644
index 0000000000000000000000000000000000000000..97ca52daed28161e3096b51ffc42713b51011477
--- /dev/null
+++ b/examples/model-comparison/reference/confusionMatrix_ND_1.svg
@@ -0,0 +1,1539 @@
+<?xml version="1.0" encoding="utf-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<svg height="953.484441pt" version="1.1" viewBox="0 0 1313.889331 953.484441" width="1313.889331pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+ <metadata>
+ <rdf:RDF xmlns:cc="http://creativecommons.org/ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
+ <cc:Work>
+ <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
+ <dc:date>2022-06-03T16:06:05.065575</dc:date>
+ <dc:format>image/svg+xml</dc:format>
+ <dc:creator>
+ <cc:Agent>
+ <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>
+ </cc:Agent>
+ </dc:creator>
+ </cc:Work>
+ </rdf:RDF>
+ </metadata>
+ <defs>
+ <style type="text/css">*{stroke-linecap:butt;stroke-linejoin:round;}</style>
+ </defs>
+ <g id="figure_1">
+ <g id="patch_1">
+ <path d="M 0 953.484441
+L 1313.889331 953.484441
+L 1313.889331 0
+L 0 0
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="axes_1">
+ <g id="patch_2">
+ <path d="M 82.337891 946.284441
+L 1153.697891 946.284441
+L 1153.697891 76.524441
+L 82.337891 76.524441
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="QuadMesh_1">
+ <path clip-path="url(#p3a944e23f5)" d="M 82.337891 76.524441
+L 350.177891 76.524441
+L 350.177891 366.444441
+L 82.337891 366.444441
+L 82.337891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#p3a944e23f5)" d="M 350.177891 76.524441
+L 618.017891 76.524441
+L 618.017891 366.444441
+L 350.177891 366.444441
+L 350.177891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#p3a944e23f5)" d="M 618.017891 76.524441
+L 885.857891 76.524441
+L 885.857891 366.444441
+L 618.017891 366.444441
+L 618.017891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#p3a944e23f5)" d="M 885.857891 76.524441
+L 1153.697891 76.524441
+L 1153.697891 366.444441
+L 885.857891 366.444441
+L 885.857891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#p3a944e23f5)" d="M 82.337891 366.444441
+L 350.177891 366.444441
+L 350.177891 656.364441
+L 82.337891 656.364441
+L 82.337891 366.444441
+" style="fill:#08306b;"/>
+ <path clip-path="url(#p3a944e23f5)" d="M 350.177891 366.444441
+L 618.017891 366.444441
+L 618.017891 656.364441
+L 350.177891 656.364441
+L 350.177891 366.444441
+" style="fill:#08316d;"/>
+ <path clip-path="url(#p3a944e23f5)" d="M 618.017891 366.444441
+L 885.857891 366.444441
+L 885.857891 656.364441
+L 618.017891 656.364441
+L 618.017891 366.444441
+" style="fill:#08306b;"/>
+ <path clip-path="url(#p3a944e23f5)" d="M 885.857891 366.444441
+L 1153.697891 366.444441
+L 1153.697891 656.364441
+L 885.857891 656.364441
+L 885.857891 366.444441
+" style="fill:#08306b;"/>
+ <path clip-path="url(#p3a944e23f5)" d="M 82.337891 656.364441
+L 350.177891 656.364441
+L 350.177891 946.284441
+L 82.337891 946.284441
+L 82.337891 656.364441
+" style="fill:#08316d;"/>
+ <path clip-path="url(#p3a944e23f5)" d="M 350.177891 656.364441
+L 618.017891 656.364441
+L 618.017891 946.284441
+L 350.177891 946.284441
+L 350.177891 656.364441
+" style="fill:#08306b;"/>
+ <path clip-path="url(#p3a944e23f5)" d="M 618.017891 656.364441
+L 885.857891 656.364441
+L 885.857891 946.284441
+L 618.017891 946.284441
+L 618.017891 656.364441
+" style="fill:#08316d;"/>
+ <path clip-path="url(#p3a944e23f5)" d="M 885.857891 656.364441
+L 1153.697891 656.364441
+L 1153.697891 946.284441
+L 885.857891 946.284441
+L 885.857891 656.364441
+" style="fill:#08316d;"/>
+ </g>
+ <g id="matplotlib.axis_1">
+ <g id="xtick_1">
+ <g id="line2d_1">
+ <defs>
+ <path d="M 0 0
+L 0 -3.5
+" id="md4ad71d0d3" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="216.257891" xlink:href="#md4ad71d0d3" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_1">
+ <!-- Observation -->
+ <g transform="translate(144.303789 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 4307 2166
+C 4307 3488 3366 4480 2304 4480
+C 1216 4480 294 3475 294 2166
+C 294 857 1229 -128 2298 -128
+C 3392 -128 4307 876 4307 2166
+z
+M 2304 -13
+C 1574 -13 781 722 781 2250
+C 781 3771 1651 4364 2298 4364
+C 2976 4364 3821 3752 3821 2250
+C 3821 696 3008 -13 2304 -13
+z
+" id="CMR17-4f" transform="scale(0.015625)"/>
+ <path d="M 960 4416
+L 198 4345
+L 198 4179
+C 576 4179 634 4141 634 3843
+L 634 -13
+L 749 -13
+L 934 445
+C 1120 141 1395 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2209 2477 2816 1830 2816
+C 1434 2816 1152 2603 960 2351
+L 960 4416
+z
+M 973 2022
+C 973 2138 973 2157 1062 2293
+C 1312 2681 1670 2713 1792 2713
+C 1984 2713 2643 2610 2643 1388
+C 2643 109 1888 38 1734 38
+C 1536 38 1248 115 1043 490
+C 973 613 973 626 973 742
+L 973 2022
+z
+" id="CMR17-62" transform="scale(0.015625)"/>
+ <path d="M 1978 2688
+C 1978 2803 1971 2809 1933 2809
+C 1907 2809 1901 2803 1824 2707
+C 1805 2681 1747 2617 1728 2592
+C 1523 2809 1235 2816 1126 2816
+C 416 2816 160 2444 160 2073
+C 160 1497 813 1363 998 1324
+C 1402 1241 1542 1216 1677 1100
+C 1760 1024 1901 883 1901 652
+C 1901 384 1747 38 1158 38
+C 602 38 403 460 288 1024
+C 269 1113 269 1120 218 1120
+C 166 1120 160 1113 160 985
+L 160 64
+C 160 -52 166 -58 205 -58
+C 237 -58 243 -52 275 0
+C 314 57 410 211 448 275
+C 576 102 800 -64 1158 -64
+C 1792 -64 2131 281 2131 780
+C 2131 1107 1958 1280 1875 1356
+C 1683 1555 1459 1600 1190 1651
+C 838 1728 390 1817 390 2208
+C 390 2374 480 2726 1126 2726
+C 1811 2726 1850 2086 1862 1881
+C 1869 1849 1901 1843 1920 1843
+C 1978 1843 1978 1862 1978 1971
+L 1978 2688
+z
+" id="CMR17-73" transform="scale(0.015625)"/>
+ <path d="M 2438 1503
+C 2464 1529 2464 1542 2464 1606
+C 2464 2251 2118 2816 1389 2816
+C 710 2816 173 2175 173 1394
+C 173 554 781 -64 1459 -64
+C 2176 -64 2458 619 2458 755
+C 2458 800 2419 800 2406 800
+C 2362 800 2355 787 2330 709
+C 2189 270 1837 51 1504 51
+C 1229 51 954 206 781 490
+C 582 819 582 1200 582 1503
+L 2438 1503
+z
+M 589 1600
+C 634 2511 1126 2713 1382 2713
+C 1818 2713 2112 2308 2118 1600
+L 589 1600
+z
+" id="CMR17-65" transform="scale(0.015625)"/>
+ <path d="M 960 1517
+C 960 2134 1222 2713 1702 2713
+C 1747 2713 1792 2707 1837 2687
+C 1837 2687 1696 2642 1696 2475
+C 1696 2321 1818 2257 1914 2257
+C 1990 2257 2131 2302 2131 2482
+C 2131 2687 1926 2816 1709 2816
+C 1222 2816 1011 2340 947 2115
+L 941 2115
+L 941 2816
+L 198 2745
+L 198 2578
+C 576 2578 634 2540 634 2231
+L 634 443
+C 634 198 608 166 198 166
+L 198 0
+C 352 12 646 12 813 12
+C 998 12 1325 12 1498 0
+L 1498 166
+C 1037 166 960 166 960 455
+L 960 1517
+z
+" id="CMR17-72" transform="scale(0.015625)"/>
+ <path d="M 2502 2173
+C 2560 2315 2662 2572 3034 2585
+L 3034 2752
+C 2912 2745 2752 2739 2630 2739
+C 2496 2739 2285 2739 2157 2752
+L 2157 2585
+C 2317 2572 2406 2495 2406 2328
+C 2406 2270 2406 2257 2368 2167
+L 1664 379
+L 902 2308
+C 864 2392 864 2405 864 2431
+C 864 2585 1075 2585 1171 2585
+L 1171 2752
+C 1018 2739 736 2739 576 2739
+C 403 2739 205 2739 64 2752
+L 64 2585
+C 307 2585 442 2585 518 2386
+L 1446 44
+C 1485 -52 1491 -64 1549 -64
+C 1606 -64 1613 -52 1651 44
+L 2502 2173
+z
+" id="CMR17-76" transform="scale(0.015625)"/>
+ <path d="M 2304 1656
+C 2304 2048 2304 2275 2035 2534
+C 1798 2751 1523 2816 1306 2816
+C 800 2816 435 2408 435 1977
+C 435 1740 627 1728 666 1728
+C 749 1728 896 1779 896 1958
+C 896 2118 774 2188 666 2188
+C 640 2188 608 2182 589 2176
+C 723 2594 1069 2713 1293 2713
+C 1613 2713 1965 2421 1965 1875
+L 1965 1632
+C 1587 1619 1133 1568 774 1373
+C 371 1147 256 822 256 576
+C 256 77 832 -64 1171 -64
+C 1523 -64 1850 135 1990 505
+C 2003 219 2182 -39 2464 -39
+C 2598 -39 2938 51 2938 563
+L 2938 926
+L 2822 926
+L 2822 557
+C 2822 161 2650 109 2566 109
+C 2304 109 2304 446 2304 732
+L 2304 1656
+z
+M 1965 887
+C 1965 323 1568 38 1216 38
+C 896 38 646 278 646 576
+C 646 771 730 1114 1101 1322
+C 1408 1497 1760 1523 1965 1536
+L 1965 887
+z
+" id="CMR17-61" transform="scale(0.015625)"/>
+ <path d="M 966 2585
+L 1862 2585
+L 1862 2752
+L 966 2752
+L 966 3968
+L 851 3968
+C 838 3292 614 2700 70 2687
+L 70 2585
+L 627 2585
+L 627 778
+C 627 655 627 -64 1370 -64
+C 1747 -64 1965 308 1965 784
+L 1965 1151
+L 1850 1151
+L 1850 790
+C 1850 347 1677 51 1408 51
+C 1222 51 966 179 966 765
+L 966 2585
+z
+" id="CMR17-74" transform="scale(0.015625)"/>
+ <path d="M 992 3961
+C 992 4102 877 4224 730 4224
+C 589 4224 467 4108 467 3961
+C 467 3820 582 3699 730 3699
+C 870 3699 992 3814 992 3961
+z
+M 243 2745
+L 243 2579
+C 602 2579 653 2540 653 2231
+L 653 443
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 646 12 806 12
+C 960 12 1222 12 1370 0
+L 1370 166
+C 992 166 979 205 979 436
+L 979 2816
+L 243 2745
+z
+" id="CMR17-69" transform="scale(0.015625)"/>
+ <path d="M 2758 1356
+C 2758 2176 2163 2816 1466 2816
+C 768 2816 173 2176 173 1356
+C 173 550 768 -64 1466 -64
+C 2163 -64 2758 550 2758 1356
+z
+M 1466 51
+C 1165 51 909 230 762 480
+C 602 768 582 1126 582 1408
+C 582 1676 595 2009 762 2297
+C 890 2508 1139 2713 1466 2713
+C 1754 2713 1997 2553 2150 2329
+C 2349 2028 2349 1606 2349 1408
+C 2349 1158 2336 774 2163 467
+C 1984 172 1709 51 1466 51
+z
+" id="CMR17-6f" transform="scale(0.015625)"/>
+ <path d="M 2656 1954
+C 2656 2282 2592 2816 1837 2816
+C 1331 2816 1069 2424 973 2166
+L 966 2166
+L 966 2816
+L 211 2745
+L 211 2578
+C 589 2578 646 2540 646 2231
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1954
+z
+" id="CMR17-6e" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-4f"/>
+ <use transform="translate(71.714788 0)scale(0.996264)" xlink:href="#CMR17-62"/>
+ <use transform="translate(122.610158 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(158.411496 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(198.897156 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ <use transform="translate(234.177924 0)scale(0.996264)" xlink:href="#CMR17-76"/>
+ <use transform="translate(277.266023 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(322.9565 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(358.237268 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(383.108327 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(428.798804 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_2">
+ <g id="line2d_2">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="484.097891" xlink:href="#md4ad71d0d3" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_2">
+ <!-- linear -->
+ <g transform="translate(450.783747 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 979 4416
+L 218 4345
+L 218 4179
+C 595 4179 653 4141 653 3835
+L 653 439
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 653 12 813 12
+C 979 12 1261 12 1414 0
+L 1414 166
+C 1005 166 979 191 979 439
+L 979 4416
+z
+" id="CMR17-6c" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_3">
+ <g id="line2d_3">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="751.937891" xlink:href="#md4ad71d0d3" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_3">
+ <!-- exponential -->
+ <g transform="translate(683.18479 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1664 1491
+C 1856 1740 2074 2022 2253 2233
+C 2464 2476 2707 2579 2989 2585
+L 2989 2752
+C 2880 2745 2656 2739 2541 2739
+C 2368 2739 2170 2739 2022 2752
+L 2022 2585
+C 2112 2572 2163 2508 2163 2419
+C 2163 2304 2099 2233 2067 2188
+L 1594 1587
+L 1030 2323
+C 973 2393 973 2406 973 2438
+C 973 2515 1037 2579 1146 2585
+L 1146 2752
+C 992 2739 717 2739 557 2739
+C 384 2739 179 2739 38 2752
+L 38 2585
+C 384 2585 461 2560 614 2368
+L 1350 1414
+C 1363 1401 1395 1363 1395 1344
+C 1395 1318 838 633 768 544
+C 480 198 179 172 6 166
+L 6 0
+C 115 6 339 12 454 12
+C 582 12 864 12 979 0
+L 979 166
+C 941 172 838 185 838 332
+C 838 448 890 518 947 595
+L 1478 1248
+L 2035 524
+C 2086 454 2163 358 2163 313
+C 2163 224 2086 172 1984 166
+L 1984 0
+C 2138 12 2413 12 2573 12
+C 2746 12 2950 12 3091 0
+L 3091 166
+C 2771 166 2675 179 2522 377
+L 1664 1491
+z
+" id="CMR17-78" transform="scale(0.015625)"/>
+ <path d="M 1408 -1114
+C 998 -1114 973 -1088 973 -834
+L 973 380
+C 1158 109 1427 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2196 2496 2816 1837 2816
+C 1453 2816 1139 2603 960 2345
+L 960 2816
+L 198 2745
+L 198 2577
+C 576 2577 634 2539 634 2228
+L 634 -834
+C 634 -1081 608 -1114 198 -1114
+L 198 -1280
+C 352 -1268 634 -1268 800 -1268
+C 966 -1268 1254 -1268 1408 -1280
+L 1408 -1114
+z
+M 973 2015
+C 973 2106 973 2241 1222 2481
+C 1254 2506 1472 2700 1792 2700
+C 2259 2700 2643 2112 2643 1376
+C 2643 639 2234 38 1728 38
+C 1498 38 1248 148 1056 451
+C 973 594 973 632 973 736
+L 973 2015
+z
+" id="CMR17-70" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_4">
+ <g id="line2d_4">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1019.777891" xlink:href="#md4ad71d0d3" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_4">
+ <!-- cosine -->
+ <g transform="translate(984.043472 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2234 2240
+C 2112 2240 1933 2240 1933 2015
+C 1933 1836 2080 1785 2163 1785
+C 2208 1785 2394 1804 2394 2028
+C 2394 2476 1958 2816 1466 2816
+C 787 2816 211 2201 211 1379
+C 211 521 813 -64 1466 -64
+C 2259 -64 2458 676 2458 747
+C 2458 773 2451 792 2406 792
+C 2362 792 2355 786 2330 702
+C 2163 180 1798 51 1523 51
+C 1114 51 621 431 621 1385
+C 621 2358 1094 2700 1472 2700
+C 1722 2700 2093 2582 2234 2240
+z
+" id="CMR17-63" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_5">
+ <!-- \textbf{Data generated by:} -->
+ <g transform="translate(476.949653 27.955495)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 243 4416
+L 243 4140
+L 922 4140
+L 922 275
+L 243 275
+L 243 0
+L 2938 0
+C 4166 0 5114 790 5114 2169
+C 5114 3625 4141 4416 2938 4416
+L 243 4416
+z
+M 1734 275
+L 1734 4140
+L 2694 4140
+C 3251 4140 3699 3921 3936 3586
+C 4122 3322 4243 3006 4243 2175
+C 4243 1421 4147 1086 3923 784
+C 3699 487 3270 275 2694 275
+L 1734 275
+z
+" id="CMBX12-44" transform="scale(0.015625)"/>
+ <path d="M 2944 1894
+C 2944 2483 2477 2880 1574 2880
+C 1216 2880 461 2847 461 2310
+C 461 2041 666 1926 838 1926
+C 1030 1926 1216 2060 1216 2303
+C 1216 2425 1171 2540 1062 2611
+C 1274 2668 1427 2668 1549 2668
+C 1984 2668 2246 2425 2246 1900
+L 2246 1644
+C 1235 1644 218 1362 218 648
+C 218 64 960 -64 1402 -64
+C 1894 -64 2208 205 2336 488
+C 2336 250 2336 -26 2982 -26
+L 3309 -26
+C 3443 -26 3494 -26 3494 115
+C 3494 250 3437 250 3347 250
+C 2944 256 2944 359 2944 507
+L 2944 1894
+z
+M 2246 867
+C 2246 262 1709 147 1504 147
+C 1190 147 928 359 928 655
+C 928 1240 1619 1439 2246 1472
+L 2246 867
+z
+" id="CMBX12-61" transform="scale(0.015625)"/>
+ <path d="M 1350 2540
+L 2272 2540
+L 2272 2816
+L 1350 2816
+L 1350 4032
+L 1082 4032
+C 1075 3401 768 2771 134 2751
+L 134 2540
+L 653 2540
+L 653 761
+C 653 83 1178 -64 1638 -64
+C 2112 -64 2394 294 2394 768
+L 2394 1107
+L 2125 1107
+L 2125 774
+C 2125 352 1933 166 1734 166
+C 1350 166 1350 595 1350 742
+L 1350 2540
+z
+" id="CMBX12-74" transform="scale(0.015625)"/>
+ <path d="M 832 1177
+C 1139 1011 1498 1011 1594 1011
+C 2477 1011 2829 1506 2829 1958
+C 2829 2287 2643 2519 2566 2584
+C 2752 2687 2906 2713 3014 2726
+C 2995 2694 2976 2668 2976 2584
+C 2976 2448 3066 2326 3232 2326
+C 3398 2326 3488 2448 3488 2584
+C 3488 2739 3373 2944 3104 2944
+C 2829 2944 2566 2809 2432 2694
+C 2170 2847 1920 2905 1594 2905
+C 710 2905 358 2410 358 1958
+C 358 1758 422 1493 691 1274
+C 582 1151 467 926 467 693
+C 467 416 614 179 749 76
+C 595 38 198 -109 198 -474
+C 198 -852 614 -1280 1792 -1280
+C 2854 -1280 3392 -935 3392 -455
+C 3392 108 3021 294 2861 371
+C 2554 524 2144 524 1581 524
+C 1421 524 1139 524 1107 531
+C 832 576 755 823 755 946
+C 755 998 762 1094 832 1177
+z
+M 1594 1216
+C 1037 1216 1037 1661 1037 1958
+C 1037 2255 1037 2700 1594 2700
+C 2150 2700 2150 2255 2150 1958
+C 2150 1661 2150 1216 1594 1216
+z
+M 1952 -64
+C 2419 -64 2867 -148 2867 -480
+C 2867 -704 2643 -1076 1798 -1076
+C 954 -1076 723 -717 723 -474
+C 723 -64 1126 -64 1222 -64
+L 1952 -64
+z
+" id="CMBX12-67" transform="scale(0.015625)"/>
+ <path d="M 2893 1408
+C 3040 1408 3078 1408 3078 1568
+C 3078 1758 3034 2232 2739 2529
+C 2470 2796 2112 2880 1741 2880
+C 742 2880 198 2232 198 1433
+C 198 523 858 -64 1824 -64
+C 2790 -64 3078 621 3078 731
+C 3078 829 2982 829 2944 829
+C 2842 829 2835 809 2797 725
+C 2630 302 2208 166 1901 166
+C 973 166 966 1043 966 1408
+L 2893 1408
+z
+M 966 1593
+C 979 1852 986 2099 1120 2327
+C 1242 2529 1466 2668 1741 2668
+C 2426 2668 2483 1909 2490 1593
+L 966 1593
+z
+" id="CMBX12-65" transform="scale(0.015625)"/>
+ <path d="M 3398 1958
+C 3398 2566 3136 2880 2432 2880
+C 1971 2880 1574 2656 1357 2176
+L 1350 2176
+L 1350 2880
+L 269 2828
+L 269 2553
+C 666 2553 710 2553 710 2304
+L 710 275
+L 269 275
+L 269 0
+C 416 12 877 12 1056 12
+C 1235 12 1702 12 1850 0
+L 1850 275
+L 1408 275
+L 1408 1638
+C 1408 2329 1920 2668 2330 2668
+C 2566 2668 2701 2515 2701 2028
+L 2701 275
+L 2259 275
+L 2259 0
+C 2406 12 2867 12 3046 12
+C 3226 12 3693 12 3840 0
+L 3840 275
+L 3398 275
+L 3398 1958
+z
+" id="CMBX12-6e" transform="scale(0.015625)"/>
+ <path d="M 1331 1440
+C 1331 1651 1376 2668 2125 2668
+C 2035 2598 1990 2489 1990 2374
+C 1990 2112 2202 2003 2362 2003
+C 2522 2003 2733 2112 2733 2374
+C 2733 2700 2400 2880 2093 2880
+C 1587 2880 1370 2438 1280 2169
+L 1274 2169
+L 1274 2880
+L 224 2828
+L 224 2553
+C 621 2553 666 2553 666 2304
+L 666 275
+L 224 275
+L 224 0
+C 371 12 851 12 1030 12
+C 1216 12 1734 12 1888 0
+L 1888 275
+L 1331 275
+L 1331 1440
+z
+" id="CMBX12-72" transform="scale(0.015625)"/>
+ <path d="M 2221 4428
+L 2221 4153
+C 2618 4153 2662 4153 2662 3896
+L 2662 2571
+C 2522 2694 2240 2880 1798 2880
+C 890 2880 243 2313 243 1408
+C 243 483 877 -64 1728 -64
+C 2080 -64 2381 57 2630 270
+L 2630 -64
+L 3770 -26
+L 3770 250
+C 3373 250 3328 250 3328 502
+L 3328 4480
+L 2221 4428
+z
+M 2630 625
+C 2362 231 2035 147 1805 147
+C 1011 147 1011 968 1011 1395
+C 1011 1699 1011 2022 1152 2268
+C 1350 2630 1728 2668 1875 2668
+C 2138 2668 2419 2552 2630 2268
+L 2630 625
+z
+" id="CMBX12-64" transform="scale(0.015625)"/>
+ <path d="M 1331 4480
+L 224 4428
+L 224 4153
+C 621 4153 666 4153 666 3896
+L 666 -26
+L 934 -26
+C 1043 96 1152 218 1254 347
+C 1581 6 1933 -64 2189 -64
+C 3072 -64 3750 476 3750 1414
+C 3750 2300 3149 2880 2272 2880
+C 1894 2880 1594 2758 1331 2552
+L 1331 4480
+z
+M 1363 2242
+C 1587 2552 1920 2668 2189 2668
+C 2982 2668 2982 1847 2982 1420
+C 2982 1130 2982 761 2829 522
+C 2630 211 2330 147 2125 147
+C 1690 147 1453 457 1363 599
+L 1363 2242
+z
+" id="CMBX12-62" transform="scale(0.015625)"/>
+ <path d="M 3168 2400
+C 3206 2489 3232 2540 3642 2540
+L 3642 2816
+C 3424 2803 3398 2803 3136 2803
+C 2963 2803 2950 2803 2586 2816
+L 2586 2540
+C 2592 2540 2893 2540 2893 2457
+C 2893 2438 2874 2400 2867 2381
+L 2118 780
+L 1299 2540
+L 1651 2540
+L 1651 2816
+C 1498 2803 1062 2803 883 2803
+C 698 2803 320 2803 154 2816
+L 154 2540
+L 563 2540
+L 1747 -8
+C 1715 -84 1626 -269 1594 -345
+C 1459 -631 1254 -1069 806 -1069
+C 781 -1069 704 -1069 634 -1031
+C 646 -1025 838 -949 838 -707
+C 838 -497 685 -364 493 -364
+C 294 -364 141 -497 141 -713
+C 141 -1012 422 -1280 806 -1280
+C 1331 -1280 1677 -809 1805 -529
+L 3168 2400
+z
+" id="CMBX12-79" transform="scale(0.015625)"/>
+ <path d="M 1459 2355
+C 1459 2617 1248 2816 998 2816
+C 749 2816 538 2617 538 2355
+C 538 2092 749 1894 998 1894
+C 1248 1894 1459 2092 1459 2355
+z
+M 1459 460
+C 1459 723 1248 921 998 921
+C 749 921 538 723 538 460
+C 538 198 749 0 998 0
+C 1248 0 1459 198 1459 460
+z
+" id="CMBX12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMBX12-44"/>
+ <use transform="translate(85.904786 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(140.387974 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(183.974524 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(275.817613 0)scale(0.996264)" xlink:href="#CMBX12-67"/>
+ <use transform="translate(331.857463 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(382.99673 0)scale(0.996264)" xlink:href="#CMBX12-6e"/>
+ <use transform="translate(445.263231 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(496.402498 0)scale(0.996264)" xlink:href="#CMBX12-72"/>
+ <use transform="translate(542.180006 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(596.663194 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(640.249744 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(691.389011 0)scale(0.996264)" xlink:href="#CMBX12-64"/>
+ <use transform="translate(791.015412 0)scale(0.996264)" xlink:href="#CMBX12-62"/>
+ <use transform="translate(850.168588 0)scale(0.996264)" xlink:href="#CMBX12-79"/>
+ <use transform="translate(909.321763 0)scale(0.996264)" xlink:href="#CMBX12-3a"/>
+ </g>
+ </g>
+ </g>
+ <g id="matplotlib.axis_2">
+ <g id="ytick_1">
+ <g id="line2d_5">
+ <defs>
+ <path d="M 0 0
+L -3.5 0
+" id="m079c559b9a" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#m079c559b9a" y="221.484441"/>
+ </g>
+ </g>
+ <g id="text_6">
+ <!-- linear -->
+ <g transform="translate(69.524441 277.73498)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_2">
+ <g id="line2d_6">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#m079c559b9a" y="511.404441"/>
+ </g>
+ </g>
+ <g id="text_7">
+ <!-- exponential -->
+ <g transform="translate(69.524441 638.532895)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_3">
+ <g id="line2d_7">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#m079c559b9a" y="801.324441"/>
+ </g>
+ </g>
+ <g id="text_8">
+ <!-- cosine -->
+ <g transform="translate(69.524441 862.415532)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_9">
+ <!-- \textbf{Model weight for:} -->
+ <g transform="translate(27.955495 642.025756)rotate(-90)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 3411 816
+L 1875 4281
+C 1818 4416 1760 4416 1626 4416
+L 262 4416
+L 262 4140
+L 941 4140
+L 941 468
+C 941 326 934 320 768 294
+C 653 281 525 275 410 275
+L 262 275
+L 262 0
+C 410 12 909 12 1088 12
+C 1267 12 1773 12 1920 0
+L 1920 275
+L 1773 275
+C 1600 275 1587 275 1434 294
+C 1248 320 1242 326 1242 468
+L 1242 4063
+L 1248 4063
+L 2989 134
+C 3021 64 3059 0 3168 0
+C 3277 0 3315 64 3347 134
+L 5120 4140
+L 5126 4140
+L 5126 275
+L 4448 275
+L 4448 0
+C 4621 12 5286 12 5504 12
+C 5722 12 6387 12 6560 0
+L 6560 275
+L 5882 275
+L 5882 4140
+L 6560 4140
+L 6560 4416
+L 5197 4416
+C 5062 4416 5005 4416 4947 4281
+L 3411 816
+z
+" id="CMBX12-4d" transform="scale(0.015625)"/>
+ <path d="M 3392 1379
+C 3392 2245 2803 2880 1798 2880
+C 755 2880 198 2213 198 1379
+C 198 538 787 -64 1792 -64
+C 2835 -64 3392 570 3392 1379
+z
+M 1798 166
+C 966 166 966 917 966 1443
+C 966 1744 966 2065 1088 2296
+C 1229 2553 1517 2668 1792 2668
+C 2157 2668 2387 2495 2496 2315
+C 2624 2084 2624 1751 2624 1443
+C 2624 910 2624 166 1798 166
+z
+" id="CMBX12-6f" transform="scale(0.015625)"/>
+ <path d="M 1389 4480
+L 282 4428
+L 282 4153
+C 678 4153 723 4153 723 3901
+L 723 275
+L 282 275
+L 282 0
+C 429 12 883 12 1056 12
+C 1229 12 1683 12 1830 0
+L 1830 275
+L 1389 275
+L 1389 4480
+z
+" id="CMBX12-6c" transform="scale(0.015625)"/>
+ <path d="M 4608 2386
+C 4653 2496 4672 2540 5043 2540
+L 5043 2816
+C 4858 2803 4774 2803 4544 2803
+C 4282 2803 4198 2803 3968 2816
+L 3968 2540
+C 4026 2540 4339 2540 4339 2457
+C 4339 2451 4339 2444 4314 2380
+L 3642 712
+L 2906 2540
+L 3270 2540
+L 3270 2816
+C 3117 2803 2739 2803 2566 2803
+C 2240 2803 2227 2803 1907 2816
+L 1907 2540
+L 2285 2540
+C 2304 2489 2336 2406 2362 2348
+C 2381 2309 2445 2155 2445 2123
+C 2445 2111 2426 2066 2419 2046
+L 1933 834
+L 1242 2540
+L 1606 2540
+L 1606 2816
+C 1459 2803 1024 2803 851 2803
+C 646 2803 339 2803 147 2816
+L 147 2540
+L 525 2540
+L 1504 96
+C 1549 -20 1574 -64 1715 -64
+C 1786 -64 1862 -64 1914 64
+L 2592 1764
+L 3270 76
+C 3328 -64 3398 -64 3475 -64
+C 3616 -64 3635 -26 3680 89
+L 4608 2386
+z
+" id="CMBX12-77" transform="scale(0.015625)"/>
+ <path d="M 1427 4019
+C 1427 4281 1216 4480 966 4480
+C 704 4480 506 4262 506 4019
+C 506 3775 704 3558 966 3558
+C 1216 3558 1427 3756 1427 4019
+z
+M 301 2828
+L 301 2553
+C 678 2553 723 2553 723 2303
+L 723 275
+L 282 275
+L 282 0
+C 429 12 870 12 1043 12
+C 1222 12 1632 12 1786 0
+L 1786 275
+L 1389 275
+L 1389 2880
+L 301 2828
+z
+" id="CMBX12-69" transform="scale(0.015625)"/>
+ <path d="M 3398 1958
+C 3398 2566 3136 2880 2432 2880
+C 1786 2880 1472 2425 1382 2233
+L 1376 2233
+L 1376 4480
+L 269 4428
+L 269 4153
+C 666 4153 710 4153 710 3896
+L 710 275
+L 269 275
+L 269 0
+C 416 12 877 12 1056 12
+C 1235 12 1702 12 1850 0
+L 1850 275
+L 1408 275
+L 1408 1638
+C 1408 2329 1920 2668 2330 2668
+C 2566 2668 2701 2515 2701 2028
+L 2701 275
+L 2259 275
+L 2259 0
+C 2406 12 2867 12 3046 12
+C 3226 12 3693 12 3840 0
+L 3840 275
+L 3398 275
+L 3398 1958
+z
+" id="CMBX12-68" transform="scale(0.015625)"/>
+ <path d="M 1389 2540
+L 2118 2540
+L 2118 2816
+L 1357 2816
+L 1357 3466
+C 1357 4122 1779 4224 1990 4224
+C 2061 4224 2074 4217 2112 4204
+C 2016 4141 1958 4034 1958 3901
+C 1958 3649 2163 3535 2330 3535
+C 2470 3535 2701 3630 2701 3908
+C 2701 4167 2470 4435 2016 4435
+C 1434 4435 723 4192 723 3459
+L 723 2816
+L 250 2816
+L 250 2540
+L 723 2540
+L 723 275
+L 282 275
+L 282 0
+C 429 12 909 12 1088 12
+C 1274 12 1792 12 1946 0
+L 1946 275
+L 1389 275
+L 1389 2540
+z
+" id="CMBX12-66" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMBX12-4d"/>
+ <use transform="translate(106.314425 0)scale(0.996264)" xlink:href="#CMBX12-6f"/>
+ <use transform="translate(165.467601 0)scale(0.996264)" xlink:href="#CMBX12-64"/>
+ <use transform="translate(227.734101 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(278.873369 0)scale(0.996264)" xlink:href="#CMBX12-6c"/>
+ <use transform="translate(347.366519 0)scale(0.996264)" xlink:href="#CMBX12-77"/>
+ <use transform="translate(425.199645 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(476.338912 0)scale(0.996264)" xlink:href="#CMBX12-69"/>
+ <use transform="translate(507.472162 0)scale(0.996264)" xlink:href="#CMBX12-67"/>
+ <use transform="translate(563.512013 0)scale(0.996264)" xlink:href="#CMBX12-68"/>
+ <use transform="translate(622.665189 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(703.611639 0)scale(0.996264)" xlink:href="#CMBX12-66"/>
+ <use transform="translate(737.858215 0)scale(0.996264)" xlink:href="#CMBX12-6f"/>
+ <use transform="translate(793.898065 0)scale(0.996264)" xlink:href="#CMBX12-72"/>
+ <use transform="translate(839.675573 0)scale(0.996264)" xlink:href="#CMBX12-3a"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_10">
+ <!-- 0.00033 -->
+ <g style="fill:#262626;" transform="translate(171.405807 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2688 2038
+C 2688 2430 2682 3099 2413 3613
+C 2176 4063 1798 4224 1466 4224
+C 1158 4224 768 4082 525 3620
+C 269 3137 243 2539 243 2038
+C 243 1671 250 1112 448 623
+C 723 -39 1216 -128 1466 -128
+C 1760 -128 2208 -7 2470 604
+C 2662 1048 2688 1568 2688 2038
+z
+M 1466 -26
+C 1056 -26 813 328 723 816
+C 653 1196 653 1749 653 2109
+C 653 2604 653 3015 736 3407
+C 858 3954 1216 4121 1466 4121
+C 1728 4121 2067 3947 2189 3420
+C 2272 3054 2278 2623 2278 2109
+C 2278 1691 2278 1176 2202 797
+C 2067 96 1690 -26 1466 -26
+z
+" id="CMR17-30" transform="scale(0.015625)"/>
+ <path d="M 1062 262
+C 1062 422 934 524 800 524
+C 672 524 538 422 538 262
+C 538 102 666 0 800 0
+C 928 0 1062 102 1062 262
+z
+" id="CMR17-2e" transform="scale(0.015625)"/>
+ <path d="M 1414 2176
+C 1984 2176 2234 1673 2234 1094
+C 2234 322 1824 25 1453 25
+C 1114 25 563 193 390 691
+C 422 678 454 678 486 678
+C 640 678 755 780 755 947
+C 755 1132 614 1216 486 1216
+C 378 1216 211 1164 211 927
+C 211 335 787 -128 1466 -128
+C 2176 -128 2720 432 2720 1087
+C 2720 1718 2208 2176 1600 2246
+C 2086 2347 2554 2776 2554 3353
+C 2554 3856 2048 4224 1472 4224
+C 890 4224 378 3862 378 3347
+C 378 3123 544 3084 627 3084
+C 762 3084 877 3167 877 3334
+C 877 3500 762 3584 627 3584
+C 602 3584 570 3584 544 3571
+C 730 3999 1235 4076 1459 4076
+C 1683 4076 2106 3966 2106 3347
+C 2106 3167 2080 2851 1862 2574
+C 1670 2329 1453 2316 1242 2297
+C 1210 2297 1062 2284 1037 2284
+C 992 2278 966 2272 966 2227
+C 966 2182 973 2176 1101 2176
+L 1414 2176
+z
+" id="CMR17-33" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(161.94249 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(207.632967 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ <use transform="translate(253.323444 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ <g id="text_11">
+ <!-- 0.00047 -->
+ <g style="fill:#262626;" transform="translate(439.245807 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2150 4147
+C 2150 4281 2144 4288 2029 4288
+L 128 1254
+L 128 1088
+L 1779 1088
+L 1779 460
+C 1779 230 1766 166 1318 166
+L 1197 166
+L 1197 0
+C 1402 12 1747 12 1965 12
+C 2182 12 2528 12 2733 0
+L 2733 166
+L 2611 166
+C 2163 166 2150 230 2150 460
+L 2150 1088
+L 2803 1088
+L 2803 1254
+L 2150 1254
+L 2150 4147
+z
+M 1798 3723
+L 1798 1254
+L 256 1254
+L 1798 3723
+z
+" id="CMR17-34" transform="scale(0.015625)"/>
+ <path d="M 2886 3955
+L 2886 4096
+L 1382 4096
+C 634 4096 621 4166 595 4288
+L 480 4288
+L 294 3104
+L 410 3104
+C 429 3226 474 3552 550 3673
+C 589 3724 1062 3724 1171 3724
+L 2579 3724
+L 1869 2670
+C 1395 1961 1069 1003 1069 166
+C 1069 89 1069 -128 1299 -128
+C 1530 -128 1530 89 1530 172
+L 1530 466
+C 1530 1514 1709 2204 2003 2644
+L 2886 3955
+z
+" id="CMR17-37" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(161.94249 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(207.632967 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(253.323444 0)scale(0.996264)" xlink:href="#CMR17-37"/>
+ </g>
+ </g>
+ <g id="text_12">
+ <!-- 0.00031 -->
+ <g style="fill:#262626;" transform="translate(707.085807 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1702 4083
+C 1702 4217 1696 4224 1606 4224
+C 1357 3927 979 3833 621 3820
+C 602 3820 570 3820 563 3808
+C 557 3795 557 3782 557 3648
+C 755 3648 1088 3686 1344 3839
+L 1344 467
+C 1344 243 1331 166 781 166
+L 589 166
+L 589 0
+C 896 6 1216 12 1523 12
+C 1830 12 2150 6 2458 0
+L 2458 166
+L 2266 166
+C 1715 166 1702 236 1702 467
+L 1702 4083
+z
+" id="CMR17-31" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(161.94249 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(207.632967 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ <use transform="translate(253.323444 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ <g id="text_13">
+ <!-- 0.00031 -->
+ <g style="fill:#262626;" transform="translate(974.925807 228.955463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(161.94249 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(207.632967 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ <use transform="translate(253.323444 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ <g id="text_14">
+ <!-- 0.5 -->
+ <g style="fill:#ffffff;" transform="translate(198.820094 518.875463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 730 3750
+C 794 3724 1056 3641 1325 3641
+C 1920 3641 2246 3961 2432 4140
+C 2432 4191 2432 4224 2394 4224
+C 2387 4224 2374 4224 2323 4198
+C 2099 4102 1837 4032 1517 4032
+C 1325 4032 1037 4055 723 4191
+C 653 4224 640 4224 634 4224
+C 602 4224 595 4217 595 4090
+L 595 2231
+C 595 2113 595 2080 659 2080
+C 691 2080 704 2093 736 2139
+C 941 2435 1222 2560 1542 2560
+C 1766 2560 2246 2415 2246 1293
+C 2246 1087 2246 716 2054 422
+C 1894 159 1645 25 1370 25
+C 947 25 518 319 403 812
+C 429 806 480 793 506 793
+C 589 793 749 838 749 1036
+C 749 1209 627 1280 506 1280
+C 358 1280 262 1190 262 1011
+C 262 454 704 -128 1382 -128
+C 2042 -128 2669 441 2669 1267
+C 2669 2054 2170 2662 1549 2662
+C 1222 2662 947 2540 730 2304
+L 730 3750
+z
+" id="CMR17-35" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_15">
+ <!-- 0.5 -->
+ <g style="fill:#ffffff;" transform="translate(466.660094 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_16">
+ <!-- 0.5 -->
+ <g style="fill:#ffffff;" transform="translate(734.500094 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_17">
+ <!-- 0.5 -->
+ <g style="fill:#ffffff;" transform="translate(1002.340094 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_18">
+ <!-- 0.5 -->
+ <g style="fill:#ffffff;" transform="translate(198.820094 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_19">
+ <!-- 0.5 -->
+ <g style="fill:#ffffff;" transform="translate(466.660094 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_20">
+ <!-- 0.5 -->
+ <g style="fill:#ffffff;" transform="translate(734.500094 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_21">
+ <!-- 0.5 -->
+ <g style="fill:#ffffff;" transform="translate(1002.340094 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ <g id="axes_2">
+ <g id="patch_3">
+ <path d="M 1220.657891 946.284441
+L 1264.145891 946.284441
+L 1264.145891 76.524441
+L 1220.657891 76.524441
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="patch_4">
+ <path clip-path="url(#pe1c5aaa433)" d="M 1220.657891 946.284441
+L 1220.657891 942.886941
+L 1220.657891 79.921941
+L 1220.657891 76.524441
+L 1264.145891 76.524441
+L 1264.145891 79.921941
+L 1264.145891 942.886941
+L 1264.145891 946.284441
+L 1264.145891 946.284441
+z
+" style="fill:#ffffff;stroke:#ffffff;stroke-linejoin:miter;stroke-width:0.01;"/>
+ </g>
+ <image height="870" id="image4de93ebaed" transform="scale(1 -1)translate(0 -870)" width="43" x="1221" xlink:href="data:image/png;base64,
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" y="-76"/>
+ <g id="matplotlib.axis_3"/>
+ <g id="matplotlib.axis_4">
+ <g id="ytick_4">
+ <g id="line2d_8">
+ <defs>
+ <path d="M 0 0
+L 3.5 0
+" id="m161a9fc761" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m161a9fc761" y="773.351004"/>
+ </g>
+ </g>
+ <g id="text_22">
+ <!-- $\mathdefault{0.1}$ -->
+ <g transform="translate(1271.145891 783.728752)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1178 307
+C 1178 492 1024 620 870 620
+C 685 620 557 467 557 313
+C 557 128 710 0 864 0
+C 1050 0 1178 153 1178 307
+z
+" id="CMMI12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_5">
+ <g id="line2d_9">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m161a9fc761" y="599.878057"/>
+ </g>
+ </g>
+ <g id="text_23">
+ <!-- $\mathdefault{0.2}$ -->
+ <g transform="translate(1271.145891 610.255805)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2669 990
+L 2554 990
+C 2490 537 2438 460 2413 422
+C 2381 371 1920 371 1830 371
+L 602 371
+C 832 620 1280 1073 1824 1596
+C 2214 1966 2669 2400 2669 3033
+C 2669 3788 2067 4224 1395 4224
+C 691 4224 262 3603 262 3027
+C 262 2777 448 2745 525 2745
+C 589 2745 781 2783 781 3007
+C 781 3206 614 3264 525 3264
+C 486 3264 448 3257 422 3244
+C 544 3788 915 4057 1306 4057
+C 1862 4057 2227 3616 2227 3033
+C 2227 2477 1901 1998 1536 1583
+L 262 147
+L 262 0
+L 2515 0
+L 2669 990
+z
+" id="CMR17-32" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_6">
+ <g id="line2d_10">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m161a9fc761" y="426.40511"/>
+ </g>
+ </g>
+ <g id="text_24">
+ <!-- $\mathdefault{0.3}$ -->
+ <g transform="translate(1271.145891 436.782858)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_7">
+ <g id="line2d_11">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m161a9fc761" y="252.932163"/>
+ </g>
+ </g>
+ <g id="text_25">
+ <!-- $\mathdefault{0.4}$ -->
+ <g transform="translate(1271.145891 263.309911)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_8">
+ <g id="line2d_12">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m161a9fc761" y="79.459216"/>
+ </g>
+ </g>
+ <g id="text_26">
+ <!-- $\mathdefault{0.5}$ -->
+ <g transform="translate(1271.145891 89.836963)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ </g>
+ <g id="LineCollection_1"/>
+ <g id="patch_5">
+ <path d="M 1220.657891 946.284441
+L 1220.657891 942.886941
+L 1220.657891 79.921941
+L 1220.657891 76.524441
+L 1264.145891 76.524441
+L 1264.145891 79.921941
+L 1264.145891 942.886941
+L 1264.145891 946.284441
+z
+" style="fill:none;"/>
+ </g>
+ </g>
+ </g>
+ <defs>
+ <clipPath id="p3a944e23f5">
+ <rect height="869.76" width="1071.36" x="82.337891" y="76.524441"/>
+ </clipPath>
+ <clipPath id="pe1c5aaa433">
+ <rect height="869.76" width="43.488" x="1220.657891" y="76.524441"/>
+ </clipPath>
+ </defs>
+</svg>
diff --git a/examples/model-comparison/reference/confusionMatrix_ND_11.svg b/examples/model-comparison/reference/confusionMatrix_ND_11.svg
new file mode 100644
index 0000000000000000000000000000000000000000..b4d2b667af46dddde4bfd4969d9737fce3911fda
--- /dev/null
+++ b/examples/model-comparison/reference/confusionMatrix_ND_11.svg
@@ -0,0 +1,1633 @@
+<?xml version="1.0" encoding="utf-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<svg height="969.675639pt" version="1.1" viewBox="0 0 1313.889331 969.675639" width="1313.889331pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+ <metadata>
+ <rdf:RDF xmlns:cc="http://creativecommons.org/ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
+ <cc:Work>
+ <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
+ <dc:date>2022-06-03T16:06:11.367292</dc:date>
+ <dc:format>image/svg+xml</dc:format>
+ <dc:creator>
+ <cc:Agent>
+ <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>
+ </cc:Agent>
+ </dc:creator>
+ </cc:Work>
+ </rdf:RDF>
+ </metadata>
+ <defs>
+ <style type="text/css">*{stroke-linecap:butt;stroke-linejoin:round;}</style>
+ </defs>
+ <g id="figure_1">
+ <g id="patch_1">
+ <path d="M 0 969.675639
+L 1313.889331 969.675639
+L 1313.889331 0
+L 0 0
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="axes_1">
+ <g id="patch_2">
+ <path d="M 82.337891 946.284441
+L 1153.697891 946.284441
+L 1153.697891 76.524441
+L 82.337891 76.524441
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="QuadMesh_1">
+ <path clip-path="url(#p8b993e097e)" d="M 82.337891 76.524441
+L 350.177891 76.524441
+L 350.177891 366.444441
+L 82.337891 366.444441
+L 82.337891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#p8b993e097e)" d="M 350.177891 76.524441
+L 618.017891 76.524441
+L 618.017891 366.444441
+L 350.177891 366.444441
+L 350.177891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#p8b993e097e)" d="M 618.017891 76.524441
+L 885.857891 76.524441
+L 885.857891 366.444441
+L 618.017891 366.444441
+L 618.017891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#p8b993e097e)" d="M 885.857891 76.524441
+L 1153.697891 76.524441
+L 1153.697891 366.444441
+L 885.857891 366.444441
+L 885.857891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#p8b993e097e)" d="M 82.337891 366.444441
+L 350.177891 366.444441
+L 350.177891 656.364441
+L 82.337891 656.364441
+L 82.337891 366.444441
+" style="fill:#3181bd;"/>
+ <path clip-path="url(#p8b993e097e)" d="M 350.177891 366.444441
+L 618.017891 366.444441
+L 618.017891 656.364441
+L 350.177891 656.364441
+L 350.177891 366.444441
+" style="fill:#08306b;"/>
+ <path clip-path="url(#p8b993e097e)" d="M 618.017891 366.444441
+L 885.857891 366.444441
+L 885.857891 656.364441
+L 618.017891 656.364441
+L 618.017891 366.444441
+" style="fill:#2d7dbb;"/>
+ <path clip-path="url(#p8b993e097e)" d="M 885.857891 366.444441
+L 1153.697891 366.444441
+L 1153.697891 656.364441
+L 885.857891 656.364441
+L 885.857891 366.444441
+" style="fill:#2d7dbb;"/>
+ <path clip-path="url(#p8b993e097e)" d="M 82.337891 656.364441
+L 350.177891 656.364441
+L 350.177891 946.284441
+L 82.337891 946.284441
+L 82.337891 656.364441
+" style="fill:#083877;"/>
+ <path clip-path="url(#p8b993e097e)" d="M 350.177891 656.364441
+L 618.017891 656.364441
+L 618.017891 946.284441
+L 350.177891 946.284441
+L 350.177891 656.364441
+" style="fill:#3a8ac2;"/>
+ <path clip-path="url(#p8b993e097e)" d="M 618.017891 656.364441
+L 885.857891 656.364441
+L 885.857891 946.284441
+L 618.017891 946.284441
+L 618.017891 656.364441
+" style="fill:#083c7d;"/>
+ <path clip-path="url(#p8b993e097e)" d="M 885.857891 656.364441
+L 1153.697891 656.364441
+L 1153.697891 946.284441
+L 885.857891 946.284441
+L 885.857891 656.364441
+" style="fill:#083c7d;"/>
+ </g>
+ <g id="matplotlib.axis_1">
+ <g id="xtick_1">
+ <g id="line2d_1">
+ <defs>
+ <path d="M 0 0
+L 0 -3.5
+" id="m87820abdbd" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="216.257891" xlink:href="#m87820abdbd" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_1">
+ <!-- Observation -->
+ <g transform="translate(144.303789 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 4307 2166
+C 4307 3488 3366 4480 2304 4480
+C 1216 4480 294 3475 294 2166
+C 294 857 1229 -128 2298 -128
+C 3392 -128 4307 876 4307 2166
+z
+M 2304 -13
+C 1574 -13 781 722 781 2250
+C 781 3771 1651 4364 2298 4364
+C 2976 4364 3821 3752 3821 2250
+C 3821 696 3008 -13 2304 -13
+z
+" id="CMR17-4f" transform="scale(0.015625)"/>
+ <path d="M 960 4416
+L 198 4345
+L 198 4179
+C 576 4179 634 4141 634 3843
+L 634 -13
+L 749 -13
+L 934 445
+C 1120 141 1395 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2209 2477 2816 1830 2816
+C 1434 2816 1152 2603 960 2351
+L 960 4416
+z
+M 973 2022
+C 973 2138 973 2157 1062 2293
+C 1312 2681 1670 2713 1792 2713
+C 1984 2713 2643 2610 2643 1388
+C 2643 109 1888 38 1734 38
+C 1536 38 1248 115 1043 490
+C 973 613 973 626 973 742
+L 973 2022
+z
+" id="CMR17-62" transform="scale(0.015625)"/>
+ <path d="M 1978 2688
+C 1978 2803 1971 2809 1933 2809
+C 1907 2809 1901 2803 1824 2707
+C 1805 2681 1747 2617 1728 2592
+C 1523 2809 1235 2816 1126 2816
+C 416 2816 160 2444 160 2073
+C 160 1497 813 1363 998 1324
+C 1402 1241 1542 1216 1677 1100
+C 1760 1024 1901 883 1901 652
+C 1901 384 1747 38 1158 38
+C 602 38 403 460 288 1024
+C 269 1113 269 1120 218 1120
+C 166 1120 160 1113 160 985
+L 160 64
+C 160 -52 166 -58 205 -58
+C 237 -58 243 -52 275 0
+C 314 57 410 211 448 275
+C 576 102 800 -64 1158 -64
+C 1792 -64 2131 281 2131 780
+C 2131 1107 1958 1280 1875 1356
+C 1683 1555 1459 1600 1190 1651
+C 838 1728 390 1817 390 2208
+C 390 2374 480 2726 1126 2726
+C 1811 2726 1850 2086 1862 1881
+C 1869 1849 1901 1843 1920 1843
+C 1978 1843 1978 1862 1978 1971
+L 1978 2688
+z
+" id="CMR17-73" transform="scale(0.015625)"/>
+ <path d="M 2438 1503
+C 2464 1529 2464 1542 2464 1606
+C 2464 2251 2118 2816 1389 2816
+C 710 2816 173 2175 173 1394
+C 173 554 781 -64 1459 -64
+C 2176 -64 2458 619 2458 755
+C 2458 800 2419 800 2406 800
+C 2362 800 2355 787 2330 709
+C 2189 270 1837 51 1504 51
+C 1229 51 954 206 781 490
+C 582 819 582 1200 582 1503
+L 2438 1503
+z
+M 589 1600
+C 634 2511 1126 2713 1382 2713
+C 1818 2713 2112 2308 2118 1600
+L 589 1600
+z
+" id="CMR17-65" transform="scale(0.015625)"/>
+ <path d="M 960 1517
+C 960 2134 1222 2713 1702 2713
+C 1747 2713 1792 2707 1837 2687
+C 1837 2687 1696 2642 1696 2475
+C 1696 2321 1818 2257 1914 2257
+C 1990 2257 2131 2302 2131 2482
+C 2131 2687 1926 2816 1709 2816
+C 1222 2816 1011 2340 947 2115
+L 941 2115
+L 941 2816
+L 198 2745
+L 198 2578
+C 576 2578 634 2540 634 2231
+L 634 443
+C 634 198 608 166 198 166
+L 198 0
+C 352 12 646 12 813 12
+C 998 12 1325 12 1498 0
+L 1498 166
+C 1037 166 960 166 960 455
+L 960 1517
+z
+" id="CMR17-72" transform="scale(0.015625)"/>
+ <path d="M 2502 2173
+C 2560 2315 2662 2572 3034 2585
+L 3034 2752
+C 2912 2745 2752 2739 2630 2739
+C 2496 2739 2285 2739 2157 2752
+L 2157 2585
+C 2317 2572 2406 2495 2406 2328
+C 2406 2270 2406 2257 2368 2167
+L 1664 379
+L 902 2308
+C 864 2392 864 2405 864 2431
+C 864 2585 1075 2585 1171 2585
+L 1171 2752
+C 1018 2739 736 2739 576 2739
+C 403 2739 205 2739 64 2752
+L 64 2585
+C 307 2585 442 2585 518 2386
+L 1446 44
+C 1485 -52 1491 -64 1549 -64
+C 1606 -64 1613 -52 1651 44
+L 2502 2173
+z
+" id="CMR17-76" transform="scale(0.015625)"/>
+ <path d="M 2304 1656
+C 2304 2048 2304 2275 2035 2534
+C 1798 2751 1523 2816 1306 2816
+C 800 2816 435 2408 435 1977
+C 435 1740 627 1728 666 1728
+C 749 1728 896 1779 896 1958
+C 896 2118 774 2188 666 2188
+C 640 2188 608 2182 589 2176
+C 723 2594 1069 2713 1293 2713
+C 1613 2713 1965 2421 1965 1875
+L 1965 1632
+C 1587 1619 1133 1568 774 1373
+C 371 1147 256 822 256 576
+C 256 77 832 -64 1171 -64
+C 1523 -64 1850 135 1990 505
+C 2003 219 2182 -39 2464 -39
+C 2598 -39 2938 51 2938 563
+L 2938 926
+L 2822 926
+L 2822 557
+C 2822 161 2650 109 2566 109
+C 2304 109 2304 446 2304 732
+L 2304 1656
+z
+M 1965 887
+C 1965 323 1568 38 1216 38
+C 896 38 646 278 646 576
+C 646 771 730 1114 1101 1322
+C 1408 1497 1760 1523 1965 1536
+L 1965 887
+z
+" id="CMR17-61" transform="scale(0.015625)"/>
+ <path d="M 966 2585
+L 1862 2585
+L 1862 2752
+L 966 2752
+L 966 3968
+L 851 3968
+C 838 3292 614 2700 70 2687
+L 70 2585
+L 627 2585
+L 627 778
+C 627 655 627 -64 1370 -64
+C 1747 -64 1965 308 1965 784
+L 1965 1151
+L 1850 1151
+L 1850 790
+C 1850 347 1677 51 1408 51
+C 1222 51 966 179 966 765
+L 966 2585
+z
+" id="CMR17-74" transform="scale(0.015625)"/>
+ <path d="M 992 3961
+C 992 4102 877 4224 730 4224
+C 589 4224 467 4108 467 3961
+C 467 3820 582 3699 730 3699
+C 870 3699 992 3814 992 3961
+z
+M 243 2745
+L 243 2579
+C 602 2579 653 2540 653 2231
+L 653 443
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 646 12 806 12
+C 960 12 1222 12 1370 0
+L 1370 166
+C 992 166 979 205 979 436
+L 979 2816
+L 243 2745
+z
+" id="CMR17-69" transform="scale(0.015625)"/>
+ <path d="M 2758 1356
+C 2758 2176 2163 2816 1466 2816
+C 768 2816 173 2176 173 1356
+C 173 550 768 -64 1466 -64
+C 2163 -64 2758 550 2758 1356
+z
+M 1466 51
+C 1165 51 909 230 762 480
+C 602 768 582 1126 582 1408
+C 582 1676 595 2009 762 2297
+C 890 2508 1139 2713 1466 2713
+C 1754 2713 1997 2553 2150 2329
+C 2349 2028 2349 1606 2349 1408
+C 2349 1158 2336 774 2163 467
+C 1984 172 1709 51 1466 51
+z
+" id="CMR17-6f" transform="scale(0.015625)"/>
+ <path d="M 2656 1954
+C 2656 2282 2592 2816 1837 2816
+C 1331 2816 1069 2424 973 2166
+L 966 2166
+L 966 2816
+L 211 2745
+L 211 2578
+C 589 2578 646 2540 646 2231
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1954
+z
+" id="CMR17-6e" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-4f"/>
+ <use transform="translate(71.714788 0)scale(0.996264)" xlink:href="#CMR17-62"/>
+ <use transform="translate(122.610158 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(158.411496 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(198.897156 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ <use transform="translate(234.177924 0)scale(0.996264)" xlink:href="#CMR17-76"/>
+ <use transform="translate(277.266023 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(322.9565 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(358.237268 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(383.108327 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(428.798804 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_2">
+ <g id="line2d_2">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="484.097891" xlink:href="#m87820abdbd" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_2">
+ <!-- linear -->
+ <g transform="translate(450.783747 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 979 4416
+L 218 4345
+L 218 4179
+C 595 4179 653 4141 653 3835
+L 653 439
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 653 12 813 12
+C 979 12 1261 12 1414 0
+L 1414 166
+C 1005 166 979 191 979 439
+L 979 4416
+z
+" id="CMR17-6c" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_3">
+ <g id="line2d_3">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="751.937891" xlink:href="#m87820abdbd" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_3">
+ <!-- exponential -->
+ <g transform="translate(683.18479 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1664 1491
+C 1856 1740 2074 2022 2253 2233
+C 2464 2476 2707 2579 2989 2585
+L 2989 2752
+C 2880 2745 2656 2739 2541 2739
+C 2368 2739 2170 2739 2022 2752
+L 2022 2585
+C 2112 2572 2163 2508 2163 2419
+C 2163 2304 2099 2233 2067 2188
+L 1594 1587
+L 1030 2323
+C 973 2393 973 2406 973 2438
+C 973 2515 1037 2579 1146 2585
+L 1146 2752
+C 992 2739 717 2739 557 2739
+C 384 2739 179 2739 38 2752
+L 38 2585
+C 384 2585 461 2560 614 2368
+L 1350 1414
+C 1363 1401 1395 1363 1395 1344
+C 1395 1318 838 633 768 544
+C 480 198 179 172 6 166
+L 6 0
+C 115 6 339 12 454 12
+C 582 12 864 12 979 0
+L 979 166
+C 941 172 838 185 838 332
+C 838 448 890 518 947 595
+L 1478 1248
+L 2035 524
+C 2086 454 2163 358 2163 313
+C 2163 224 2086 172 1984 166
+L 1984 0
+C 2138 12 2413 12 2573 12
+C 2746 12 2950 12 3091 0
+L 3091 166
+C 2771 166 2675 179 2522 377
+L 1664 1491
+z
+" id="CMR17-78" transform="scale(0.015625)"/>
+ <path d="M 1408 -1114
+C 998 -1114 973 -1088 973 -834
+L 973 380
+C 1158 109 1427 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2196 2496 2816 1837 2816
+C 1453 2816 1139 2603 960 2345
+L 960 2816
+L 198 2745
+L 198 2577
+C 576 2577 634 2539 634 2228
+L 634 -834
+C 634 -1081 608 -1114 198 -1114
+L 198 -1280
+C 352 -1268 634 -1268 800 -1268
+C 966 -1268 1254 -1268 1408 -1280
+L 1408 -1114
+z
+M 973 2015
+C 973 2106 973 2241 1222 2481
+C 1254 2506 1472 2700 1792 2700
+C 2259 2700 2643 2112 2643 1376
+C 2643 639 2234 38 1728 38
+C 1498 38 1248 148 1056 451
+C 973 594 973 632 973 736
+L 973 2015
+z
+" id="CMR17-70" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_4">
+ <g id="line2d_4">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1019.777891" xlink:href="#m87820abdbd" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_4">
+ <!-- cosine -->
+ <g transform="translate(984.043472 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2234 2240
+C 2112 2240 1933 2240 1933 2015
+C 1933 1836 2080 1785 2163 1785
+C 2208 1785 2394 1804 2394 2028
+C 2394 2476 1958 2816 1466 2816
+C 787 2816 211 2201 211 1379
+C 211 521 813 -64 1466 -64
+C 2259 -64 2458 676 2458 747
+C 2458 773 2451 792 2406 792
+C 2362 792 2355 786 2330 702
+C 2163 180 1798 51 1523 51
+C 1114 51 621 431 621 1385
+C 621 2358 1094 2700 1472 2700
+C 1722 2700 2093 2582 2234 2240
+z
+" id="CMR17-63" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_5">
+ <!-- \textbf{Data generated by:} -->
+ <g transform="translate(476.949653 27.955495)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 243 4416
+L 243 4140
+L 922 4140
+L 922 275
+L 243 275
+L 243 0
+L 2938 0
+C 4166 0 5114 790 5114 2169
+C 5114 3625 4141 4416 2938 4416
+L 243 4416
+z
+M 1734 275
+L 1734 4140
+L 2694 4140
+C 3251 4140 3699 3921 3936 3586
+C 4122 3322 4243 3006 4243 2175
+C 4243 1421 4147 1086 3923 784
+C 3699 487 3270 275 2694 275
+L 1734 275
+z
+" id="CMBX12-44" transform="scale(0.015625)"/>
+ <path d="M 2944 1894
+C 2944 2483 2477 2880 1574 2880
+C 1216 2880 461 2847 461 2310
+C 461 2041 666 1926 838 1926
+C 1030 1926 1216 2060 1216 2303
+C 1216 2425 1171 2540 1062 2611
+C 1274 2668 1427 2668 1549 2668
+C 1984 2668 2246 2425 2246 1900
+L 2246 1644
+C 1235 1644 218 1362 218 648
+C 218 64 960 -64 1402 -64
+C 1894 -64 2208 205 2336 488
+C 2336 250 2336 -26 2982 -26
+L 3309 -26
+C 3443 -26 3494 -26 3494 115
+C 3494 250 3437 250 3347 250
+C 2944 256 2944 359 2944 507
+L 2944 1894
+z
+M 2246 867
+C 2246 262 1709 147 1504 147
+C 1190 147 928 359 928 655
+C 928 1240 1619 1439 2246 1472
+L 2246 867
+z
+" id="CMBX12-61" transform="scale(0.015625)"/>
+ <path d="M 1350 2540
+L 2272 2540
+L 2272 2816
+L 1350 2816
+L 1350 4032
+L 1082 4032
+C 1075 3401 768 2771 134 2751
+L 134 2540
+L 653 2540
+L 653 761
+C 653 83 1178 -64 1638 -64
+C 2112 -64 2394 294 2394 768
+L 2394 1107
+L 2125 1107
+L 2125 774
+C 2125 352 1933 166 1734 166
+C 1350 166 1350 595 1350 742
+L 1350 2540
+z
+" id="CMBX12-74" transform="scale(0.015625)"/>
+ <path d="M 832 1177
+C 1139 1011 1498 1011 1594 1011
+C 2477 1011 2829 1506 2829 1958
+C 2829 2287 2643 2519 2566 2584
+C 2752 2687 2906 2713 3014 2726
+C 2995 2694 2976 2668 2976 2584
+C 2976 2448 3066 2326 3232 2326
+C 3398 2326 3488 2448 3488 2584
+C 3488 2739 3373 2944 3104 2944
+C 2829 2944 2566 2809 2432 2694
+C 2170 2847 1920 2905 1594 2905
+C 710 2905 358 2410 358 1958
+C 358 1758 422 1493 691 1274
+C 582 1151 467 926 467 693
+C 467 416 614 179 749 76
+C 595 38 198 -109 198 -474
+C 198 -852 614 -1280 1792 -1280
+C 2854 -1280 3392 -935 3392 -455
+C 3392 108 3021 294 2861 371
+C 2554 524 2144 524 1581 524
+C 1421 524 1139 524 1107 531
+C 832 576 755 823 755 946
+C 755 998 762 1094 832 1177
+z
+M 1594 1216
+C 1037 1216 1037 1661 1037 1958
+C 1037 2255 1037 2700 1594 2700
+C 2150 2700 2150 2255 2150 1958
+C 2150 1661 2150 1216 1594 1216
+z
+M 1952 -64
+C 2419 -64 2867 -148 2867 -480
+C 2867 -704 2643 -1076 1798 -1076
+C 954 -1076 723 -717 723 -474
+C 723 -64 1126 -64 1222 -64
+L 1952 -64
+z
+" id="CMBX12-67" transform="scale(0.015625)"/>
+ <path d="M 2893 1408
+C 3040 1408 3078 1408 3078 1568
+C 3078 1758 3034 2232 2739 2529
+C 2470 2796 2112 2880 1741 2880
+C 742 2880 198 2232 198 1433
+C 198 523 858 -64 1824 -64
+C 2790 -64 3078 621 3078 731
+C 3078 829 2982 829 2944 829
+C 2842 829 2835 809 2797 725
+C 2630 302 2208 166 1901 166
+C 973 166 966 1043 966 1408
+L 2893 1408
+z
+M 966 1593
+C 979 1852 986 2099 1120 2327
+C 1242 2529 1466 2668 1741 2668
+C 2426 2668 2483 1909 2490 1593
+L 966 1593
+z
+" id="CMBX12-65" transform="scale(0.015625)"/>
+ <path d="M 3398 1958
+C 3398 2566 3136 2880 2432 2880
+C 1971 2880 1574 2656 1357 2176
+L 1350 2176
+L 1350 2880
+L 269 2828
+L 269 2553
+C 666 2553 710 2553 710 2304
+L 710 275
+L 269 275
+L 269 0
+C 416 12 877 12 1056 12
+C 1235 12 1702 12 1850 0
+L 1850 275
+L 1408 275
+L 1408 1638
+C 1408 2329 1920 2668 2330 2668
+C 2566 2668 2701 2515 2701 2028
+L 2701 275
+L 2259 275
+L 2259 0
+C 2406 12 2867 12 3046 12
+C 3226 12 3693 12 3840 0
+L 3840 275
+L 3398 275
+L 3398 1958
+z
+" id="CMBX12-6e" transform="scale(0.015625)"/>
+ <path d="M 1331 1440
+C 1331 1651 1376 2668 2125 2668
+C 2035 2598 1990 2489 1990 2374
+C 1990 2112 2202 2003 2362 2003
+C 2522 2003 2733 2112 2733 2374
+C 2733 2700 2400 2880 2093 2880
+C 1587 2880 1370 2438 1280 2169
+L 1274 2169
+L 1274 2880
+L 224 2828
+L 224 2553
+C 621 2553 666 2553 666 2304
+L 666 275
+L 224 275
+L 224 0
+C 371 12 851 12 1030 12
+C 1216 12 1734 12 1888 0
+L 1888 275
+L 1331 275
+L 1331 1440
+z
+" id="CMBX12-72" transform="scale(0.015625)"/>
+ <path d="M 2221 4428
+L 2221 4153
+C 2618 4153 2662 4153 2662 3896
+L 2662 2571
+C 2522 2694 2240 2880 1798 2880
+C 890 2880 243 2313 243 1408
+C 243 483 877 -64 1728 -64
+C 2080 -64 2381 57 2630 270
+L 2630 -64
+L 3770 -26
+L 3770 250
+C 3373 250 3328 250 3328 502
+L 3328 4480
+L 2221 4428
+z
+M 2630 625
+C 2362 231 2035 147 1805 147
+C 1011 147 1011 968 1011 1395
+C 1011 1699 1011 2022 1152 2268
+C 1350 2630 1728 2668 1875 2668
+C 2138 2668 2419 2552 2630 2268
+L 2630 625
+z
+" id="CMBX12-64" transform="scale(0.015625)"/>
+ <path d="M 1331 4480
+L 224 4428
+L 224 4153
+C 621 4153 666 4153 666 3896
+L 666 -26
+L 934 -26
+C 1043 96 1152 218 1254 347
+C 1581 6 1933 -64 2189 -64
+C 3072 -64 3750 476 3750 1414
+C 3750 2300 3149 2880 2272 2880
+C 1894 2880 1594 2758 1331 2552
+L 1331 4480
+z
+M 1363 2242
+C 1587 2552 1920 2668 2189 2668
+C 2982 2668 2982 1847 2982 1420
+C 2982 1130 2982 761 2829 522
+C 2630 211 2330 147 2125 147
+C 1690 147 1453 457 1363 599
+L 1363 2242
+z
+" id="CMBX12-62" transform="scale(0.015625)"/>
+ <path d="M 3168 2400
+C 3206 2489 3232 2540 3642 2540
+L 3642 2816
+C 3424 2803 3398 2803 3136 2803
+C 2963 2803 2950 2803 2586 2816
+L 2586 2540
+C 2592 2540 2893 2540 2893 2457
+C 2893 2438 2874 2400 2867 2381
+L 2118 780
+L 1299 2540
+L 1651 2540
+L 1651 2816
+C 1498 2803 1062 2803 883 2803
+C 698 2803 320 2803 154 2816
+L 154 2540
+L 563 2540
+L 1747 -8
+C 1715 -84 1626 -269 1594 -345
+C 1459 -631 1254 -1069 806 -1069
+C 781 -1069 704 -1069 634 -1031
+C 646 -1025 838 -949 838 -707
+C 838 -497 685 -364 493 -364
+C 294 -364 141 -497 141 -713
+C 141 -1012 422 -1280 806 -1280
+C 1331 -1280 1677 -809 1805 -529
+L 3168 2400
+z
+" id="CMBX12-79" transform="scale(0.015625)"/>
+ <path d="M 1459 2355
+C 1459 2617 1248 2816 998 2816
+C 749 2816 538 2617 538 2355
+C 538 2092 749 1894 998 1894
+C 1248 1894 1459 2092 1459 2355
+z
+M 1459 460
+C 1459 723 1248 921 998 921
+C 749 921 538 723 538 460
+C 538 198 749 0 998 0
+C 1248 0 1459 198 1459 460
+z
+" id="CMBX12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMBX12-44"/>
+ <use transform="translate(85.904786 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(140.387974 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(183.974524 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(275.817613 0)scale(0.996264)" xlink:href="#CMBX12-67"/>
+ <use transform="translate(331.857463 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(382.99673 0)scale(0.996264)" xlink:href="#CMBX12-6e"/>
+ <use transform="translate(445.263231 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(496.402498 0)scale(0.996264)" xlink:href="#CMBX12-72"/>
+ <use transform="translate(542.180006 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(596.663194 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(640.249744 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(691.389011 0)scale(0.996264)" xlink:href="#CMBX12-64"/>
+ <use transform="translate(791.015412 0)scale(0.996264)" xlink:href="#CMBX12-62"/>
+ <use transform="translate(850.168588 0)scale(0.996264)" xlink:href="#CMBX12-79"/>
+ <use transform="translate(909.321763 0)scale(0.996264)" xlink:href="#CMBX12-3a"/>
+ </g>
+ </g>
+ </g>
+ <g id="matplotlib.axis_2">
+ <g id="ytick_1">
+ <g id="line2d_5">
+ <defs>
+ <path d="M 0 0
+L -3.5 0
+" id="m9d15884c53" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#m9d15884c53" y="221.484441"/>
+ </g>
+ </g>
+ <g id="text_6">
+ <!-- linear -->
+ <g transform="translate(69.524441 277.73498)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_2">
+ <g id="line2d_6">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#m9d15884c53" y="511.404441"/>
+ </g>
+ </g>
+ <g id="text_7">
+ <!-- exponential -->
+ <g transform="translate(69.524441 638.532895)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_3">
+ <g id="line2d_7">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#m9d15884c53" y="801.324441"/>
+ </g>
+ </g>
+ <g id="text_8">
+ <!-- cosine -->
+ <g transform="translate(69.524441 862.415532)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_9">
+ <!-- \textbf{Model weight for:} -->
+ <g transform="translate(27.955495 642.025756)rotate(-90)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 3411 816
+L 1875 4281
+C 1818 4416 1760 4416 1626 4416
+L 262 4416
+L 262 4140
+L 941 4140
+L 941 468
+C 941 326 934 320 768 294
+C 653 281 525 275 410 275
+L 262 275
+L 262 0
+C 410 12 909 12 1088 12
+C 1267 12 1773 12 1920 0
+L 1920 275
+L 1773 275
+C 1600 275 1587 275 1434 294
+C 1248 320 1242 326 1242 468
+L 1242 4063
+L 1248 4063
+L 2989 134
+C 3021 64 3059 0 3168 0
+C 3277 0 3315 64 3347 134
+L 5120 4140
+L 5126 4140
+L 5126 275
+L 4448 275
+L 4448 0
+C 4621 12 5286 12 5504 12
+C 5722 12 6387 12 6560 0
+L 6560 275
+L 5882 275
+L 5882 4140
+L 6560 4140
+L 6560 4416
+L 5197 4416
+C 5062 4416 5005 4416 4947 4281
+L 3411 816
+z
+" id="CMBX12-4d" transform="scale(0.015625)"/>
+ <path d="M 3392 1379
+C 3392 2245 2803 2880 1798 2880
+C 755 2880 198 2213 198 1379
+C 198 538 787 -64 1792 -64
+C 2835 -64 3392 570 3392 1379
+z
+M 1798 166
+C 966 166 966 917 966 1443
+C 966 1744 966 2065 1088 2296
+C 1229 2553 1517 2668 1792 2668
+C 2157 2668 2387 2495 2496 2315
+C 2624 2084 2624 1751 2624 1443
+C 2624 910 2624 166 1798 166
+z
+" id="CMBX12-6f" transform="scale(0.015625)"/>
+ <path d="M 1389 4480
+L 282 4428
+L 282 4153
+C 678 4153 723 4153 723 3901
+L 723 275
+L 282 275
+L 282 0
+C 429 12 883 12 1056 12
+C 1229 12 1683 12 1830 0
+L 1830 275
+L 1389 275
+L 1389 4480
+z
+" id="CMBX12-6c" transform="scale(0.015625)"/>
+ <path d="M 4608 2386
+C 4653 2496 4672 2540 5043 2540
+L 5043 2816
+C 4858 2803 4774 2803 4544 2803
+C 4282 2803 4198 2803 3968 2816
+L 3968 2540
+C 4026 2540 4339 2540 4339 2457
+C 4339 2451 4339 2444 4314 2380
+L 3642 712
+L 2906 2540
+L 3270 2540
+L 3270 2816
+C 3117 2803 2739 2803 2566 2803
+C 2240 2803 2227 2803 1907 2816
+L 1907 2540
+L 2285 2540
+C 2304 2489 2336 2406 2362 2348
+C 2381 2309 2445 2155 2445 2123
+C 2445 2111 2426 2066 2419 2046
+L 1933 834
+L 1242 2540
+L 1606 2540
+L 1606 2816
+C 1459 2803 1024 2803 851 2803
+C 646 2803 339 2803 147 2816
+L 147 2540
+L 525 2540
+L 1504 96
+C 1549 -20 1574 -64 1715 -64
+C 1786 -64 1862 -64 1914 64
+L 2592 1764
+L 3270 76
+C 3328 -64 3398 -64 3475 -64
+C 3616 -64 3635 -26 3680 89
+L 4608 2386
+z
+" id="CMBX12-77" transform="scale(0.015625)"/>
+ <path d="M 1427 4019
+C 1427 4281 1216 4480 966 4480
+C 704 4480 506 4262 506 4019
+C 506 3775 704 3558 966 3558
+C 1216 3558 1427 3756 1427 4019
+z
+M 301 2828
+L 301 2553
+C 678 2553 723 2553 723 2303
+L 723 275
+L 282 275
+L 282 0
+C 429 12 870 12 1043 12
+C 1222 12 1632 12 1786 0
+L 1786 275
+L 1389 275
+L 1389 2880
+L 301 2828
+z
+" id="CMBX12-69" transform="scale(0.015625)"/>
+ <path d="M 3398 1958
+C 3398 2566 3136 2880 2432 2880
+C 1786 2880 1472 2425 1382 2233
+L 1376 2233
+L 1376 4480
+L 269 4428
+L 269 4153
+C 666 4153 710 4153 710 3896
+L 710 275
+L 269 275
+L 269 0
+C 416 12 877 12 1056 12
+C 1235 12 1702 12 1850 0
+L 1850 275
+L 1408 275
+L 1408 1638
+C 1408 2329 1920 2668 2330 2668
+C 2566 2668 2701 2515 2701 2028
+L 2701 275
+L 2259 275
+L 2259 0
+C 2406 12 2867 12 3046 12
+C 3226 12 3693 12 3840 0
+L 3840 275
+L 3398 275
+L 3398 1958
+z
+" id="CMBX12-68" transform="scale(0.015625)"/>
+ <path d="M 1389 2540
+L 2118 2540
+L 2118 2816
+L 1357 2816
+L 1357 3466
+C 1357 4122 1779 4224 1990 4224
+C 2061 4224 2074 4217 2112 4204
+C 2016 4141 1958 4034 1958 3901
+C 1958 3649 2163 3535 2330 3535
+C 2470 3535 2701 3630 2701 3908
+C 2701 4167 2470 4435 2016 4435
+C 1434 4435 723 4192 723 3459
+L 723 2816
+L 250 2816
+L 250 2540
+L 723 2540
+L 723 275
+L 282 275
+L 282 0
+C 429 12 909 12 1088 12
+C 1274 12 1792 12 1946 0
+L 1946 275
+L 1389 275
+L 1389 2540
+z
+" id="CMBX12-66" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMBX12-4d"/>
+ <use transform="translate(106.314425 0)scale(0.996264)" xlink:href="#CMBX12-6f"/>
+ <use transform="translate(165.467601 0)scale(0.996264)" xlink:href="#CMBX12-64"/>
+ <use transform="translate(227.734101 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(278.873369 0)scale(0.996264)" xlink:href="#CMBX12-6c"/>
+ <use transform="translate(347.366519 0)scale(0.996264)" xlink:href="#CMBX12-77"/>
+ <use transform="translate(425.199645 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(476.338912 0)scale(0.996264)" xlink:href="#CMBX12-69"/>
+ <use transform="translate(507.472162 0)scale(0.996264)" xlink:href="#CMBX12-67"/>
+ <use transform="translate(563.512013 0)scale(0.996264)" xlink:href="#CMBX12-68"/>
+ <use transform="translate(622.665189 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(703.611639 0)scale(0.996264)" xlink:href="#CMBX12-66"/>
+ <use transform="translate(737.858215 0)scale(0.996264)" xlink:href="#CMBX12-6f"/>
+ <use transform="translate(793.898065 0)scale(0.996264)" xlink:href="#CMBX12-72"/>
+ <use transform="translate(839.675573 0)scale(0.996264)" xlink:href="#CMBX12-3a"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_10">
+ <!-- 3.5e-18 -->
+ <g style="fill:#262626;" transform="translate(174.52871 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1414 2176
+C 1984 2176 2234 1673 2234 1094
+C 2234 322 1824 25 1453 25
+C 1114 25 563 193 390 691
+C 422 678 454 678 486 678
+C 640 678 755 780 755 947
+C 755 1132 614 1216 486 1216
+C 378 1216 211 1164 211 927
+C 211 335 787 -128 1466 -128
+C 2176 -128 2720 432 2720 1087
+C 2720 1718 2208 2176 1600 2246
+C 2086 2347 2554 2776 2554 3353
+C 2554 3856 2048 4224 1472 4224
+C 890 4224 378 3862 378 3347
+C 378 3123 544 3084 627 3084
+C 762 3084 877 3167 877 3334
+C 877 3500 762 3584 627 3584
+C 602 3584 570 3584 544 3571
+C 730 3999 1235 4076 1459 4076
+C 1683 4076 2106 3966 2106 3347
+C 2106 3167 2080 2851 1862 2574
+C 1670 2329 1453 2316 1242 2297
+C 1210 2297 1062 2284 1037 2284
+C 992 2278 966 2272 966 2227
+C 966 2182 973 2176 1101 2176
+L 1414 2176
+z
+" id="CMR17-33" transform="scale(0.015625)"/>
+ <path d="M 1062 262
+C 1062 422 934 524 800 524
+C 672 524 538 422 538 262
+C 538 102 666 0 800 0
+C 928 0 1062 102 1062 262
+z
+" id="CMR17-2e" transform="scale(0.015625)"/>
+ <path d="M 730 3750
+C 794 3724 1056 3641 1325 3641
+C 1920 3641 2246 3961 2432 4140
+C 2432 4191 2432 4224 2394 4224
+C 2387 4224 2374 4224 2323 4198
+C 2099 4102 1837 4032 1517 4032
+C 1325 4032 1037 4055 723 4191
+C 653 4224 640 4224 634 4224
+C 602 4224 595 4217 595 4090
+L 595 2231
+C 595 2113 595 2080 659 2080
+C 691 2080 704 2093 736 2139
+C 941 2435 1222 2560 1542 2560
+C 1766 2560 2246 2415 2246 1293
+C 2246 1087 2246 716 2054 422
+C 1894 159 1645 25 1370 25
+C 947 25 518 319 403 812
+C 429 806 480 793 506 793
+C 589 793 749 838 749 1036
+C 749 1209 627 1280 506 1280
+C 358 1280 262 1190 262 1011
+C 262 454 704 -128 1382 -128
+C 2042 -128 2669 441 2669 1267
+C 2669 2054 2170 2662 1549 2662
+C 1222 2662 947 2540 730 2304
+L 730 3750
+z
+" id="CMR17-35" transform="scale(0.015625)"/>
+ <path d="M 1632 1254
+L 1632 1536
+L 26 1536
+L 26 1254
+L 1632 1254
+z
+" id="CMR17-2d" transform="scale(0.015625)"/>
+ <path d="M 1702 4083
+C 1702 4217 1696 4224 1606 4224
+C 1357 3927 979 3833 621 3820
+C 602 3820 570 3820 563 3808
+C 557 3795 557 3782 557 3648
+C 755 3648 1088 3686 1344 3839
+L 1344 467
+C 1344 243 1331 166 781 166
+L 589 166
+L 589 0
+C 896 6 1216 12 1523 12
+C 1830 12 2150 6 2458 0
+L 2458 166
+L 2266 166
+C 1715 166 1702 236 1702 467
+L 1702 4083
+z
+" id="CMR17-31" transform="scale(0.015625)"/>
+ <path d="M 1741 2289
+C 2144 2494 2554 2803 2554 3298
+C 2554 3884 1990 4224 1472 4224
+C 890 4224 378 3800 378 3215
+C 378 3054 416 2777 666 2533
+C 730 2469 998 2276 1171 2154
+C 883 2006 211 1652 211 945
+C 211 282 838 -128 1459 -128
+C 2144 -128 2720 366 2720 1022
+C 2720 1607 2330 1877 2074 2051
+L 1741 2289
+z
+M 902 2855
+C 851 2887 595 3086 595 3388
+C 595 3781 998 4076 1459 4076
+C 1965 4076 2336 3716 2336 3298
+C 2336 2700 1670 2359 1638 2359
+C 1632 2359 1626 2359 1574 2398
+L 902 2855
+z
+M 2080 1536
+C 2176 1466 2483 1253 2483 861
+C 2483 385 2010 25 1472 25
+C 890 25 448 443 448 951
+C 448 1459 838 1884 1280 2083
+L 2080 1536
+z
+" id="CMR17-38" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-33"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-38"/>
+ </g>
+ </g>
+ <g id="text_11">
+ <!-- 1.3e-07 -->
+ <g style="fill:#262626;" transform="translate(442.36871 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2688 2038
+C 2688 2430 2682 3099 2413 3613
+C 2176 4063 1798 4224 1466 4224
+C 1158 4224 768 4082 525 3620
+C 269 3137 243 2539 243 2038
+C 243 1671 250 1112 448 623
+C 723 -39 1216 -128 1466 -128
+C 1760 -128 2208 -7 2470 604
+C 2662 1048 2688 1568 2688 2038
+z
+M 1466 -26
+C 1056 -26 813 328 723 816
+C 653 1196 653 1749 653 2109
+C 653 2604 653 3015 736 3407
+C 858 3954 1216 4121 1466 4121
+C 1728 4121 2067 3947 2189 3420
+C 2272 3054 2278 2623 2278 2109
+C 2278 1691 2278 1176 2202 797
+C 2067 96 1690 -26 1466 -26
+z
+" id="CMR17-30" transform="scale(0.015625)"/>
+ <path d="M 2886 3955
+L 2886 4096
+L 1382 4096
+C 634 4096 621 4166 595 4288
+L 480 4288
+L 294 3104
+L 410 3104
+C 429 3226 474 3552 550 3673
+C 589 3724 1062 3724 1171 3724
+L 2579 3724
+L 1869 2670
+C 1395 1961 1069 1003 1069 166
+C 1069 89 1069 -128 1299 -128
+C 1530 -128 1530 89 1530 172
+L 1530 466
+C 1530 1514 1709 2204 2003 2644
+L 2886 3955
+z
+" id="CMR17-37" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-37"/>
+ </g>
+ </g>
+ <g id="text_12">
+ <!-- 3.2e-20 -->
+ <g style="fill:#262626;" transform="translate(710.20871 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2669 990
+L 2554 990
+C 2490 537 2438 460 2413 422
+C 2381 371 1920 371 1830 371
+L 602 371
+C 832 620 1280 1073 1824 1596
+C 2214 1966 2669 2400 2669 3033
+C 2669 3788 2067 4224 1395 4224
+C 691 4224 262 3603 262 3027
+C 262 2777 448 2745 525 2745
+C 589 2745 781 2783 781 3007
+C 781 3206 614 3264 525 3264
+C 486 3264 448 3257 422 3244
+C 544 3788 915 4057 1306 4057
+C 1862 4057 2227 3616 2227 3033
+C 2227 2477 1901 1998 1536 1583
+L 262 147
+L 262 0
+L 2515 0
+L 2669 990
+z
+" id="CMR17-32" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-33"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ </g>
+ </g>
+ <g id="text_13">
+ <!-- 3.2e-20 -->
+ <g style="fill:#262626;" transform="translate(978.04871 228.955463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-33"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ </g>
+ </g>
+ <g id="text_14">
+ <!-- 0.42 -->
+ <g style="fill:#ffffff;" transform="translate(191.966522 518.875463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2150 4147
+C 2150 4281 2144 4288 2029 4288
+L 128 1254
+L 128 1088
+L 1779 1088
+L 1779 460
+C 1779 230 1766 166 1318 166
+L 1197 166
+L 1197 0
+C 1402 12 1747 12 1965 12
+C 2182 12 2528 12 2733 0
+L 2733 166
+L 2611 166
+C 2163 166 2150 230 2150 460
+L 2150 1088
+L 2803 1088
+L 2803 1254
+L 2150 1254
+L 2150 4147
+z
+M 1798 3723
+L 1798 1254
+L 256 1254
+L 1798 3723
+z
+" id="CMR17-34" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ <g id="text_15">
+ <!-- 0.6 -->
+ <g style="fill:#ffffff;" transform="translate(466.660094 518.875463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 678 2198
+C 678 3712 1395 4076 1811 4076
+C 1946 4076 2272 4049 2400 3782
+C 2298 3782 2106 3782 2106 3558
+C 2106 3385 2246 3328 2336 3328
+C 2394 3328 2566 3353 2566 3571
+C 2566 3987 2246 4224 1805 4224
+C 1043 4224 243 3411 243 2011
+C 243 257 966 -128 1478 -128
+C 2099 -128 2688 431 2688 1295
+C 2688 2101 2170 2688 1517 2688
+C 1126 2688 838 2430 678 1979
+L 678 2198
+z
+M 1478 25
+C 691 25 691 1212 691 1450
+C 691 1914 909 2585 1504 2585
+C 1613 2585 1926 2585 2138 2140
+C 2253 1889 2253 1624 2253 1302
+C 2253 954 2253 696 2118 438
+C 1978 173 1773 25 1478 25
+z
+" id="CMR17-36" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ <g id="text_16">
+ <!-- 0.43 -->
+ <g style="fill:#ffffff;" transform="translate(727.646522 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ <g id="text_17">
+ <!-- 0.43 -->
+ <g style="fill:#ffffff;" transform="translate(995.486522 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ <g id="text_18">
+ <!-- 0.58 -->
+ <g style="fill:#ffffff;" transform="translate(191.966522 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-38"/>
+ </g>
+ </g>
+ <g id="text_19">
+ <!-- 0.4 -->
+ <g style="fill:#ffffff;" transform="translate(466.660094 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ <g id="text_20">
+ <!-- 0.57 -->
+ <g style="fill:#ffffff;" transform="translate(727.646522 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-37"/>
+ </g>
+ </g>
+ <g id="text_21">
+ <!-- 0.57 -->
+ <g style="fill:#ffffff;" transform="translate(995.486522 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-37"/>
+ </g>
+ </g>
+ </g>
+ <g id="axes_2">
+ <g id="patch_3">
+ <path d="M 1220.657891 946.284441
+L 1264.145891 946.284441
+L 1264.145891 76.524441
+L 1220.657891 76.524441
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="patch_4">
+ <path clip-path="url(#pde8f792f02)" d="M 1220.657891 946.284441
+L 1220.657891 942.886941
+L 1220.657891 79.921941
+L 1220.657891 76.524441
+L 1264.145891 76.524441
+L 1264.145891 79.921941
+L 1264.145891 942.886941
+L 1264.145891 946.284441
+L 1264.145891 946.284441
+z
+" style="fill:#ffffff;stroke:#ffffff;stroke-linejoin:miter;stroke-width:0.01;"/>
+ </g>
+ <image height="870" id="image141f2ad2aa" transform="scale(1 -1)translate(0 -870)" width="43" x="1221" xlink:href="data:image/png;base64,
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" y="-76"/>
+ <g id="matplotlib.axis_3"/>
+ <g id="matplotlib.axis_4">
+ <g id="ytick_4">
+ <g id="line2d_8">
+ <defs>
+ <path d="M 0 0
+L 3.5 0
+" id="mcad016c4b8" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#mcad016c4b8" y="946.284441"/>
+ </g>
+ </g>
+ <g id="text_22">
+ <!-- $\mathdefault{0.0}$ -->
+ <g transform="translate(1271.145891 956.662188)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1178 307
+C 1178 492 1024 620 870 620
+C 685 620 557 467 557 313
+C 557 128 710 0 864 0
+C 1050 0 1178 153 1178 307
+z
+" id="CMMI12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_5">
+ <g id="line2d_9">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#mcad016c4b8" y="802.291672"/>
+ </g>
+ </g>
+ <g id="text_23">
+ <!-- $\mathdefault{0.1}$ -->
+ <g transform="translate(1271.145891 812.669419)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_6">
+ <g id="line2d_10">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#mcad016c4b8" y="658.298903"/>
+ </g>
+ </g>
+ <g id="text_24">
+ <!-- $\mathdefault{0.2}$ -->
+ <g transform="translate(1271.145891 668.676651)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_7">
+ <g id="line2d_11">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#mcad016c4b8" y="514.306134"/>
+ </g>
+ </g>
+ <g id="text_25">
+ <!-- $\mathdefault{0.3}$ -->
+ <g transform="translate(1271.145891 524.683882)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_8">
+ <g id="line2d_12">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#mcad016c4b8" y="370.313365"/>
+ </g>
+ </g>
+ <g id="text_26">
+ <!-- $\mathdefault{0.4}$ -->
+ <g transform="translate(1271.145891 380.691113)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_9">
+ <g id="line2d_13">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#mcad016c4b8" y="226.320597"/>
+ </g>
+ </g>
+ <g id="text_27">
+ <!-- $\mathdefault{0.5}$ -->
+ <g transform="translate(1271.145891 236.698344)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_10">
+ <g id="line2d_14">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#mcad016c4b8" y="82.327828"/>
+ </g>
+ </g>
+ <g id="text_28">
+ <!-- $\mathdefault{0.6}$ -->
+ <g transform="translate(1271.145891 92.705575)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ </g>
+ </g>
+ <g id="LineCollection_1"/>
+ <g id="patch_5">
+ <path d="M 1220.657891 946.284441
+L 1220.657891 942.886941
+L 1220.657891 79.921941
+L 1220.657891 76.524441
+L 1264.145891 76.524441
+L 1264.145891 79.921941
+L 1264.145891 942.886941
+L 1264.145891 946.284441
+z
+" style="fill:none;"/>
+ </g>
+ </g>
+ </g>
+ <defs>
+ <clipPath id="p8b993e097e">
+ <rect height="869.76" width="1071.36" x="82.337891" y="76.524441"/>
+ </clipPath>
+ <clipPath id="pde8f792f02">
+ <rect height="869.76" width="43.488" x="1220.657891" y="76.524441"/>
+ </clipPath>
+ </defs>
+</svg>
diff --git a/examples/model-comparison/reference/confusionMatrix_ND_13.svg b/examples/model-comparison/reference/confusionMatrix_ND_13.svg
new file mode 100644
index 0000000000000000000000000000000000000000..6518b5b8622a3f1b611aa1037aca1aa32b393d48
--- /dev/null
+++ b/examples/model-comparison/reference/confusionMatrix_ND_13.svg
@@ -0,0 +1,1614 @@
+<?xml version="1.0" encoding="utf-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<svg height="969.675639pt" version="1.1" viewBox="0 0 1313.889331 969.675639" width="1313.889331pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+ <metadata>
+ <rdf:RDF xmlns:cc="http://creativecommons.org/ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
+ <cc:Work>
+ <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
+ <dc:date>2022-06-03T16:06:12.794421</dc:date>
+ <dc:format>image/svg+xml</dc:format>
+ <dc:creator>
+ <cc:Agent>
+ <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>
+ </cc:Agent>
+ </dc:creator>
+ </cc:Work>
+ </rdf:RDF>
+ </metadata>
+ <defs>
+ <style type="text/css">*{stroke-linecap:butt;stroke-linejoin:round;}</style>
+ </defs>
+ <g id="figure_1">
+ <g id="patch_1">
+ <path d="M 0 969.675639
+L 1313.889331 969.675639
+L 1313.889331 0
+L 0 0
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="axes_1">
+ <g id="patch_2">
+ <path d="M 82.337891 946.284441
+L 1153.697891 946.284441
+L 1153.697891 76.524441
+L 82.337891 76.524441
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="QuadMesh_1">
+ <path clip-path="url(#p4d2d3adaac)" d="M 82.337891 76.524441
+L 350.177891 76.524441
+L 350.177891 366.444441
+L 82.337891 366.444441
+L 82.337891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#p4d2d3adaac)" d="M 350.177891 76.524441
+L 618.017891 76.524441
+L 618.017891 366.444441
+L 350.177891 366.444441
+L 350.177891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#p4d2d3adaac)" d="M 618.017891 76.524441
+L 885.857891 76.524441
+L 885.857891 366.444441
+L 618.017891 366.444441
+L 618.017891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#p4d2d3adaac)" d="M 885.857891 76.524441
+L 1153.697891 76.524441
+L 1153.697891 366.444441
+L 885.857891 366.444441
+L 885.857891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#p4d2d3adaac)" d="M 82.337891 366.444441
+L 350.177891 366.444441
+L 350.177891 656.364441
+L 82.337891 656.364441
+L 82.337891 366.444441
+" style="fill:#08306b;"/>
+ <path clip-path="url(#p4d2d3adaac)" d="M 350.177891 366.444441
+L 618.017891 366.444441
+L 618.017891 656.364441
+L 350.177891 656.364441
+L 350.177891 366.444441
+" style="fill:#083979;"/>
+ <path clip-path="url(#p4d2d3adaac)" d="M 618.017891 366.444441
+L 885.857891 366.444441
+L 885.857891 656.364441
+L 618.017891 656.364441
+L 618.017891 366.444441
+" style="fill:#083776;"/>
+ <path clip-path="url(#p4d2d3adaac)" d="M 885.857891 366.444441
+L 1153.697891 366.444441
+L 1153.697891 656.364441
+L 885.857891 656.364441
+L 885.857891 366.444441
+" style="fill:#083776;"/>
+ <path clip-path="url(#p4d2d3adaac)" d="M 82.337891 656.364441
+L 350.177891 656.364441
+L 350.177891 946.284441
+L 82.337891 946.284441
+L 82.337891 656.364441
+" style="fill:#084488;"/>
+ <path clip-path="url(#p4d2d3adaac)" d="M 350.177891 656.364441
+L 618.017891 656.364441
+L 618.017891 946.284441
+L 350.177891 946.284441
+L 350.177891 656.364441
+" style="fill:#083979;"/>
+ <path clip-path="url(#p4d2d3adaac)" d="M 618.017891 656.364441
+L 885.857891 656.364441
+L 885.857891 946.284441
+L 618.017891 946.284441
+L 618.017891 656.364441
+" style="fill:#083b7c;"/>
+ <path clip-path="url(#p4d2d3adaac)" d="M 885.857891 656.364441
+L 1153.697891 656.364441
+L 1153.697891 946.284441
+L 885.857891 946.284441
+L 885.857891 656.364441
+" style="fill:#083b7c;"/>
+ </g>
+ <g id="matplotlib.axis_1">
+ <g id="xtick_1">
+ <g id="line2d_1">
+ <defs>
+ <path d="M 0 0
+L 0 -3.5
+" id="m03797c84b0" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="216.257891" xlink:href="#m03797c84b0" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_1">
+ <!-- Observation -->
+ <g transform="translate(144.303789 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 4307 2166
+C 4307 3488 3366 4480 2304 4480
+C 1216 4480 294 3475 294 2166
+C 294 857 1229 -128 2298 -128
+C 3392 -128 4307 876 4307 2166
+z
+M 2304 -13
+C 1574 -13 781 722 781 2250
+C 781 3771 1651 4364 2298 4364
+C 2976 4364 3821 3752 3821 2250
+C 3821 696 3008 -13 2304 -13
+z
+" id="CMR17-4f" transform="scale(0.015625)"/>
+ <path d="M 960 4416
+L 198 4345
+L 198 4179
+C 576 4179 634 4141 634 3843
+L 634 -13
+L 749 -13
+L 934 445
+C 1120 141 1395 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2209 2477 2816 1830 2816
+C 1434 2816 1152 2603 960 2351
+L 960 4416
+z
+M 973 2022
+C 973 2138 973 2157 1062 2293
+C 1312 2681 1670 2713 1792 2713
+C 1984 2713 2643 2610 2643 1388
+C 2643 109 1888 38 1734 38
+C 1536 38 1248 115 1043 490
+C 973 613 973 626 973 742
+L 973 2022
+z
+" id="CMR17-62" transform="scale(0.015625)"/>
+ <path d="M 1978 2688
+C 1978 2803 1971 2809 1933 2809
+C 1907 2809 1901 2803 1824 2707
+C 1805 2681 1747 2617 1728 2592
+C 1523 2809 1235 2816 1126 2816
+C 416 2816 160 2444 160 2073
+C 160 1497 813 1363 998 1324
+C 1402 1241 1542 1216 1677 1100
+C 1760 1024 1901 883 1901 652
+C 1901 384 1747 38 1158 38
+C 602 38 403 460 288 1024
+C 269 1113 269 1120 218 1120
+C 166 1120 160 1113 160 985
+L 160 64
+C 160 -52 166 -58 205 -58
+C 237 -58 243 -52 275 0
+C 314 57 410 211 448 275
+C 576 102 800 -64 1158 -64
+C 1792 -64 2131 281 2131 780
+C 2131 1107 1958 1280 1875 1356
+C 1683 1555 1459 1600 1190 1651
+C 838 1728 390 1817 390 2208
+C 390 2374 480 2726 1126 2726
+C 1811 2726 1850 2086 1862 1881
+C 1869 1849 1901 1843 1920 1843
+C 1978 1843 1978 1862 1978 1971
+L 1978 2688
+z
+" id="CMR17-73" transform="scale(0.015625)"/>
+ <path d="M 2438 1503
+C 2464 1529 2464 1542 2464 1606
+C 2464 2251 2118 2816 1389 2816
+C 710 2816 173 2175 173 1394
+C 173 554 781 -64 1459 -64
+C 2176 -64 2458 619 2458 755
+C 2458 800 2419 800 2406 800
+C 2362 800 2355 787 2330 709
+C 2189 270 1837 51 1504 51
+C 1229 51 954 206 781 490
+C 582 819 582 1200 582 1503
+L 2438 1503
+z
+M 589 1600
+C 634 2511 1126 2713 1382 2713
+C 1818 2713 2112 2308 2118 1600
+L 589 1600
+z
+" id="CMR17-65" transform="scale(0.015625)"/>
+ <path d="M 960 1517
+C 960 2134 1222 2713 1702 2713
+C 1747 2713 1792 2707 1837 2687
+C 1837 2687 1696 2642 1696 2475
+C 1696 2321 1818 2257 1914 2257
+C 1990 2257 2131 2302 2131 2482
+C 2131 2687 1926 2816 1709 2816
+C 1222 2816 1011 2340 947 2115
+L 941 2115
+L 941 2816
+L 198 2745
+L 198 2578
+C 576 2578 634 2540 634 2231
+L 634 443
+C 634 198 608 166 198 166
+L 198 0
+C 352 12 646 12 813 12
+C 998 12 1325 12 1498 0
+L 1498 166
+C 1037 166 960 166 960 455
+L 960 1517
+z
+" id="CMR17-72" transform="scale(0.015625)"/>
+ <path d="M 2502 2173
+C 2560 2315 2662 2572 3034 2585
+L 3034 2752
+C 2912 2745 2752 2739 2630 2739
+C 2496 2739 2285 2739 2157 2752
+L 2157 2585
+C 2317 2572 2406 2495 2406 2328
+C 2406 2270 2406 2257 2368 2167
+L 1664 379
+L 902 2308
+C 864 2392 864 2405 864 2431
+C 864 2585 1075 2585 1171 2585
+L 1171 2752
+C 1018 2739 736 2739 576 2739
+C 403 2739 205 2739 64 2752
+L 64 2585
+C 307 2585 442 2585 518 2386
+L 1446 44
+C 1485 -52 1491 -64 1549 -64
+C 1606 -64 1613 -52 1651 44
+L 2502 2173
+z
+" id="CMR17-76" transform="scale(0.015625)"/>
+ <path d="M 2304 1656
+C 2304 2048 2304 2275 2035 2534
+C 1798 2751 1523 2816 1306 2816
+C 800 2816 435 2408 435 1977
+C 435 1740 627 1728 666 1728
+C 749 1728 896 1779 896 1958
+C 896 2118 774 2188 666 2188
+C 640 2188 608 2182 589 2176
+C 723 2594 1069 2713 1293 2713
+C 1613 2713 1965 2421 1965 1875
+L 1965 1632
+C 1587 1619 1133 1568 774 1373
+C 371 1147 256 822 256 576
+C 256 77 832 -64 1171 -64
+C 1523 -64 1850 135 1990 505
+C 2003 219 2182 -39 2464 -39
+C 2598 -39 2938 51 2938 563
+L 2938 926
+L 2822 926
+L 2822 557
+C 2822 161 2650 109 2566 109
+C 2304 109 2304 446 2304 732
+L 2304 1656
+z
+M 1965 887
+C 1965 323 1568 38 1216 38
+C 896 38 646 278 646 576
+C 646 771 730 1114 1101 1322
+C 1408 1497 1760 1523 1965 1536
+L 1965 887
+z
+" id="CMR17-61" transform="scale(0.015625)"/>
+ <path d="M 966 2585
+L 1862 2585
+L 1862 2752
+L 966 2752
+L 966 3968
+L 851 3968
+C 838 3292 614 2700 70 2687
+L 70 2585
+L 627 2585
+L 627 778
+C 627 655 627 -64 1370 -64
+C 1747 -64 1965 308 1965 784
+L 1965 1151
+L 1850 1151
+L 1850 790
+C 1850 347 1677 51 1408 51
+C 1222 51 966 179 966 765
+L 966 2585
+z
+" id="CMR17-74" transform="scale(0.015625)"/>
+ <path d="M 992 3961
+C 992 4102 877 4224 730 4224
+C 589 4224 467 4108 467 3961
+C 467 3820 582 3699 730 3699
+C 870 3699 992 3814 992 3961
+z
+M 243 2745
+L 243 2579
+C 602 2579 653 2540 653 2231
+L 653 443
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 646 12 806 12
+C 960 12 1222 12 1370 0
+L 1370 166
+C 992 166 979 205 979 436
+L 979 2816
+L 243 2745
+z
+" id="CMR17-69" transform="scale(0.015625)"/>
+ <path d="M 2758 1356
+C 2758 2176 2163 2816 1466 2816
+C 768 2816 173 2176 173 1356
+C 173 550 768 -64 1466 -64
+C 2163 -64 2758 550 2758 1356
+z
+M 1466 51
+C 1165 51 909 230 762 480
+C 602 768 582 1126 582 1408
+C 582 1676 595 2009 762 2297
+C 890 2508 1139 2713 1466 2713
+C 1754 2713 1997 2553 2150 2329
+C 2349 2028 2349 1606 2349 1408
+C 2349 1158 2336 774 2163 467
+C 1984 172 1709 51 1466 51
+z
+" id="CMR17-6f" transform="scale(0.015625)"/>
+ <path d="M 2656 1954
+C 2656 2282 2592 2816 1837 2816
+C 1331 2816 1069 2424 973 2166
+L 966 2166
+L 966 2816
+L 211 2745
+L 211 2578
+C 589 2578 646 2540 646 2231
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1954
+z
+" id="CMR17-6e" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-4f"/>
+ <use transform="translate(71.714788 0)scale(0.996264)" xlink:href="#CMR17-62"/>
+ <use transform="translate(122.610158 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(158.411496 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(198.897156 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ <use transform="translate(234.177924 0)scale(0.996264)" xlink:href="#CMR17-76"/>
+ <use transform="translate(277.266023 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(322.9565 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(358.237268 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(383.108327 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(428.798804 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_2">
+ <g id="line2d_2">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="484.097891" xlink:href="#m03797c84b0" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_2">
+ <!-- linear -->
+ <g transform="translate(450.783747 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 979 4416
+L 218 4345
+L 218 4179
+C 595 4179 653 4141 653 3835
+L 653 439
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 653 12 813 12
+C 979 12 1261 12 1414 0
+L 1414 166
+C 1005 166 979 191 979 439
+L 979 4416
+z
+" id="CMR17-6c" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_3">
+ <g id="line2d_3">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="751.937891" xlink:href="#m03797c84b0" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_3">
+ <!-- exponential -->
+ <g transform="translate(683.18479 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1664 1491
+C 1856 1740 2074 2022 2253 2233
+C 2464 2476 2707 2579 2989 2585
+L 2989 2752
+C 2880 2745 2656 2739 2541 2739
+C 2368 2739 2170 2739 2022 2752
+L 2022 2585
+C 2112 2572 2163 2508 2163 2419
+C 2163 2304 2099 2233 2067 2188
+L 1594 1587
+L 1030 2323
+C 973 2393 973 2406 973 2438
+C 973 2515 1037 2579 1146 2585
+L 1146 2752
+C 992 2739 717 2739 557 2739
+C 384 2739 179 2739 38 2752
+L 38 2585
+C 384 2585 461 2560 614 2368
+L 1350 1414
+C 1363 1401 1395 1363 1395 1344
+C 1395 1318 838 633 768 544
+C 480 198 179 172 6 166
+L 6 0
+C 115 6 339 12 454 12
+C 582 12 864 12 979 0
+L 979 166
+C 941 172 838 185 838 332
+C 838 448 890 518 947 595
+L 1478 1248
+L 2035 524
+C 2086 454 2163 358 2163 313
+C 2163 224 2086 172 1984 166
+L 1984 0
+C 2138 12 2413 12 2573 12
+C 2746 12 2950 12 3091 0
+L 3091 166
+C 2771 166 2675 179 2522 377
+L 1664 1491
+z
+" id="CMR17-78" transform="scale(0.015625)"/>
+ <path d="M 1408 -1114
+C 998 -1114 973 -1088 973 -834
+L 973 380
+C 1158 109 1427 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2196 2496 2816 1837 2816
+C 1453 2816 1139 2603 960 2345
+L 960 2816
+L 198 2745
+L 198 2577
+C 576 2577 634 2539 634 2228
+L 634 -834
+C 634 -1081 608 -1114 198 -1114
+L 198 -1280
+C 352 -1268 634 -1268 800 -1268
+C 966 -1268 1254 -1268 1408 -1280
+L 1408 -1114
+z
+M 973 2015
+C 973 2106 973 2241 1222 2481
+C 1254 2506 1472 2700 1792 2700
+C 2259 2700 2643 2112 2643 1376
+C 2643 639 2234 38 1728 38
+C 1498 38 1248 148 1056 451
+C 973 594 973 632 973 736
+L 973 2015
+z
+" id="CMR17-70" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_4">
+ <g id="line2d_4">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1019.777891" xlink:href="#m03797c84b0" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_4">
+ <!-- cosine -->
+ <g transform="translate(984.043472 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2234 2240
+C 2112 2240 1933 2240 1933 2015
+C 1933 1836 2080 1785 2163 1785
+C 2208 1785 2394 1804 2394 2028
+C 2394 2476 1958 2816 1466 2816
+C 787 2816 211 2201 211 1379
+C 211 521 813 -64 1466 -64
+C 2259 -64 2458 676 2458 747
+C 2458 773 2451 792 2406 792
+C 2362 792 2355 786 2330 702
+C 2163 180 1798 51 1523 51
+C 1114 51 621 431 621 1385
+C 621 2358 1094 2700 1472 2700
+C 1722 2700 2093 2582 2234 2240
+z
+" id="CMR17-63" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_5">
+ <!-- \textbf{Data generated by:} -->
+ <g transform="translate(476.949653 27.955495)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 243 4416
+L 243 4140
+L 922 4140
+L 922 275
+L 243 275
+L 243 0
+L 2938 0
+C 4166 0 5114 790 5114 2169
+C 5114 3625 4141 4416 2938 4416
+L 243 4416
+z
+M 1734 275
+L 1734 4140
+L 2694 4140
+C 3251 4140 3699 3921 3936 3586
+C 4122 3322 4243 3006 4243 2175
+C 4243 1421 4147 1086 3923 784
+C 3699 487 3270 275 2694 275
+L 1734 275
+z
+" id="CMBX12-44" transform="scale(0.015625)"/>
+ <path d="M 2944 1894
+C 2944 2483 2477 2880 1574 2880
+C 1216 2880 461 2847 461 2310
+C 461 2041 666 1926 838 1926
+C 1030 1926 1216 2060 1216 2303
+C 1216 2425 1171 2540 1062 2611
+C 1274 2668 1427 2668 1549 2668
+C 1984 2668 2246 2425 2246 1900
+L 2246 1644
+C 1235 1644 218 1362 218 648
+C 218 64 960 -64 1402 -64
+C 1894 -64 2208 205 2336 488
+C 2336 250 2336 -26 2982 -26
+L 3309 -26
+C 3443 -26 3494 -26 3494 115
+C 3494 250 3437 250 3347 250
+C 2944 256 2944 359 2944 507
+L 2944 1894
+z
+M 2246 867
+C 2246 262 1709 147 1504 147
+C 1190 147 928 359 928 655
+C 928 1240 1619 1439 2246 1472
+L 2246 867
+z
+" id="CMBX12-61" transform="scale(0.015625)"/>
+ <path d="M 1350 2540
+L 2272 2540
+L 2272 2816
+L 1350 2816
+L 1350 4032
+L 1082 4032
+C 1075 3401 768 2771 134 2751
+L 134 2540
+L 653 2540
+L 653 761
+C 653 83 1178 -64 1638 -64
+C 2112 -64 2394 294 2394 768
+L 2394 1107
+L 2125 1107
+L 2125 774
+C 2125 352 1933 166 1734 166
+C 1350 166 1350 595 1350 742
+L 1350 2540
+z
+" id="CMBX12-74" transform="scale(0.015625)"/>
+ <path d="M 832 1177
+C 1139 1011 1498 1011 1594 1011
+C 2477 1011 2829 1506 2829 1958
+C 2829 2287 2643 2519 2566 2584
+C 2752 2687 2906 2713 3014 2726
+C 2995 2694 2976 2668 2976 2584
+C 2976 2448 3066 2326 3232 2326
+C 3398 2326 3488 2448 3488 2584
+C 3488 2739 3373 2944 3104 2944
+C 2829 2944 2566 2809 2432 2694
+C 2170 2847 1920 2905 1594 2905
+C 710 2905 358 2410 358 1958
+C 358 1758 422 1493 691 1274
+C 582 1151 467 926 467 693
+C 467 416 614 179 749 76
+C 595 38 198 -109 198 -474
+C 198 -852 614 -1280 1792 -1280
+C 2854 -1280 3392 -935 3392 -455
+C 3392 108 3021 294 2861 371
+C 2554 524 2144 524 1581 524
+C 1421 524 1139 524 1107 531
+C 832 576 755 823 755 946
+C 755 998 762 1094 832 1177
+z
+M 1594 1216
+C 1037 1216 1037 1661 1037 1958
+C 1037 2255 1037 2700 1594 2700
+C 2150 2700 2150 2255 2150 1958
+C 2150 1661 2150 1216 1594 1216
+z
+M 1952 -64
+C 2419 -64 2867 -148 2867 -480
+C 2867 -704 2643 -1076 1798 -1076
+C 954 -1076 723 -717 723 -474
+C 723 -64 1126 -64 1222 -64
+L 1952 -64
+z
+" id="CMBX12-67" transform="scale(0.015625)"/>
+ <path d="M 2893 1408
+C 3040 1408 3078 1408 3078 1568
+C 3078 1758 3034 2232 2739 2529
+C 2470 2796 2112 2880 1741 2880
+C 742 2880 198 2232 198 1433
+C 198 523 858 -64 1824 -64
+C 2790 -64 3078 621 3078 731
+C 3078 829 2982 829 2944 829
+C 2842 829 2835 809 2797 725
+C 2630 302 2208 166 1901 166
+C 973 166 966 1043 966 1408
+L 2893 1408
+z
+M 966 1593
+C 979 1852 986 2099 1120 2327
+C 1242 2529 1466 2668 1741 2668
+C 2426 2668 2483 1909 2490 1593
+L 966 1593
+z
+" id="CMBX12-65" transform="scale(0.015625)"/>
+ <path d="M 3398 1958
+C 3398 2566 3136 2880 2432 2880
+C 1971 2880 1574 2656 1357 2176
+L 1350 2176
+L 1350 2880
+L 269 2828
+L 269 2553
+C 666 2553 710 2553 710 2304
+L 710 275
+L 269 275
+L 269 0
+C 416 12 877 12 1056 12
+C 1235 12 1702 12 1850 0
+L 1850 275
+L 1408 275
+L 1408 1638
+C 1408 2329 1920 2668 2330 2668
+C 2566 2668 2701 2515 2701 2028
+L 2701 275
+L 2259 275
+L 2259 0
+C 2406 12 2867 12 3046 12
+C 3226 12 3693 12 3840 0
+L 3840 275
+L 3398 275
+L 3398 1958
+z
+" id="CMBX12-6e" transform="scale(0.015625)"/>
+ <path d="M 1331 1440
+C 1331 1651 1376 2668 2125 2668
+C 2035 2598 1990 2489 1990 2374
+C 1990 2112 2202 2003 2362 2003
+C 2522 2003 2733 2112 2733 2374
+C 2733 2700 2400 2880 2093 2880
+C 1587 2880 1370 2438 1280 2169
+L 1274 2169
+L 1274 2880
+L 224 2828
+L 224 2553
+C 621 2553 666 2553 666 2304
+L 666 275
+L 224 275
+L 224 0
+C 371 12 851 12 1030 12
+C 1216 12 1734 12 1888 0
+L 1888 275
+L 1331 275
+L 1331 1440
+z
+" id="CMBX12-72" transform="scale(0.015625)"/>
+ <path d="M 2221 4428
+L 2221 4153
+C 2618 4153 2662 4153 2662 3896
+L 2662 2571
+C 2522 2694 2240 2880 1798 2880
+C 890 2880 243 2313 243 1408
+C 243 483 877 -64 1728 -64
+C 2080 -64 2381 57 2630 270
+L 2630 -64
+L 3770 -26
+L 3770 250
+C 3373 250 3328 250 3328 502
+L 3328 4480
+L 2221 4428
+z
+M 2630 625
+C 2362 231 2035 147 1805 147
+C 1011 147 1011 968 1011 1395
+C 1011 1699 1011 2022 1152 2268
+C 1350 2630 1728 2668 1875 2668
+C 2138 2668 2419 2552 2630 2268
+L 2630 625
+z
+" id="CMBX12-64" transform="scale(0.015625)"/>
+ <path d="M 1331 4480
+L 224 4428
+L 224 4153
+C 621 4153 666 4153 666 3896
+L 666 -26
+L 934 -26
+C 1043 96 1152 218 1254 347
+C 1581 6 1933 -64 2189 -64
+C 3072 -64 3750 476 3750 1414
+C 3750 2300 3149 2880 2272 2880
+C 1894 2880 1594 2758 1331 2552
+L 1331 4480
+z
+M 1363 2242
+C 1587 2552 1920 2668 2189 2668
+C 2982 2668 2982 1847 2982 1420
+C 2982 1130 2982 761 2829 522
+C 2630 211 2330 147 2125 147
+C 1690 147 1453 457 1363 599
+L 1363 2242
+z
+" id="CMBX12-62" transform="scale(0.015625)"/>
+ <path d="M 3168 2400
+C 3206 2489 3232 2540 3642 2540
+L 3642 2816
+C 3424 2803 3398 2803 3136 2803
+C 2963 2803 2950 2803 2586 2816
+L 2586 2540
+C 2592 2540 2893 2540 2893 2457
+C 2893 2438 2874 2400 2867 2381
+L 2118 780
+L 1299 2540
+L 1651 2540
+L 1651 2816
+C 1498 2803 1062 2803 883 2803
+C 698 2803 320 2803 154 2816
+L 154 2540
+L 563 2540
+L 1747 -8
+C 1715 -84 1626 -269 1594 -345
+C 1459 -631 1254 -1069 806 -1069
+C 781 -1069 704 -1069 634 -1031
+C 646 -1025 838 -949 838 -707
+C 838 -497 685 -364 493 -364
+C 294 -364 141 -497 141 -713
+C 141 -1012 422 -1280 806 -1280
+C 1331 -1280 1677 -809 1805 -529
+L 3168 2400
+z
+" id="CMBX12-79" transform="scale(0.015625)"/>
+ <path d="M 1459 2355
+C 1459 2617 1248 2816 998 2816
+C 749 2816 538 2617 538 2355
+C 538 2092 749 1894 998 1894
+C 1248 1894 1459 2092 1459 2355
+z
+M 1459 460
+C 1459 723 1248 921 998 921
+C 749 921 538 723 538 460
+C 538 198 749 0 998 0
+C 1248 0 1459 198 1459 460
+z
+" id="CMBX12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMBX12-44"/>
+ <use transform="translate(85.904786 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(140.387974 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(183.974524 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(275.817613 0)scale(0.996264)" xlink:href="#CMBX12-67"/>
+ <use transform="translate(331.857463 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(382.99673 0)scale(0.996264)" xlink:href="#CMBX12-6e"/>
+ <use transform="translate(445.263231 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(496.402498 0)scale(0.996264)" xlink:href="#CMBX12-72"/>
+ <use transform="translate(542.180006 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(596.663194 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(640.249744 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(691.389011 0)scale(0.996264)" xlink:href="#CMBX12-64"/>
+ <use transform="translate(791.015412 0)scale(0.996264)" xlink:href="#CMBX12-62"/>
+ <use transform="translate(850.168588 0)scale(0.996264)" xlink:href="#CMBX12-79"/>
+ <use transform="translate(909.321763 0)scale(0.996264)" xlink:href="#CMBX12-3a"/>
+ </g>
+ </g>
+ </g>
+ <g id="matplotlib.axis_2">
+ <g id="ytick_1">
+ <g id="line2d_5">
+ <defs>
+ <path d="M 0 0
+L -3.5 0
+" id="m894c9f5256" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#m894c9f5256" y="221.484441"/>
+ </g>
+ </g>
+ <g id="text_6">
+ <!-- linear -->
+ <g transform="translate(69.524441 277.73498)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_2">
+ <g id="line2d_6">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#m894c9f5256" y="511.404441"/>
+ </g>
+ </g>
+ <g id="text_7">
+ <!-- exponential -->
+ <g transform="translate(69.524441 638.532895)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_3">
+ <g id="line2d_7">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#m894c9f5256" y="801.324441"/>
+ </g>
+ </g>
+ <g id="text_8">
+ <!-- cosine -->
+ <g transform="translate(69.524441 862.415532)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_9">
+ <!-- \textbf{Model weight for:} -->
+ <g transform="translate(27.955495 642.025756)rotate(-90)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 3411 816
+L 1875 4281
+C 1818 4416 1760 4416 1626 4416
+L 262 4416
+L 262 4140
+L 941 4140
+L 941 468
+C 941 326 934 320 768 294
+C 653 281 525 275 410 275
+L 262 275
+L 262 0
+C 410 12 909 12 1088 12
+C 1267 12 1773 12 1920 0
+L 1920 275
+L 1773 275
+C 1600 275 1587 275 1434 294
+C 1248 320 1242 326 1242 468
+L 1242 4063
+L 1248 4063
+L 2989 134
+C 3021 64 3059 0 3168 0
+C 3277 0 3315 64 3347 134
+L 5120 4140
+L 5126 4140
+L 5126 275
+L 4448 275
+L 4448 0
+C 4621 12 5286 12 5504 12
+C 5722 12 6387 12 6560 0
+L 6560 275
+L 5882 275
+L 5882 4140
+L 6560 4140
+L 6560 4416
+L 5197 4416
+C 5062 4416 5005 4416 4947 4281
+L 3411 816
+z
+" id="CMBX12-4d" transform="scale(0.015625)"/>
+ <path d="M 3392 1379
+C 3392 2245 2803 2880 1798 2880
+C 755 2880 198 2213 198 1379
+C 198 538 787 -64 1792 -64
+C 2835 -64 3392 570 3392 1379
+z
+M 1798 166
+C 966 166 966 917 966 1443
+C 966 1744 966 2065 1088 2296
+C 1229 2553 1517 2668 1792 2668
+C 2157 2668 2387 2495 2496 2315
+C 2624 2084 2624 1751 2624 1443
+C 2624 910 2624 166 1798 166
+z
+" id="CMBX12-6f" transform="scale(0.015625)"/>
+ <path d="M 1389 4480
+L 282 4428
+L 282 4153
+C 678 4153 723 4153 723 3901
+L 723 275
+L 282 275
+L 282 0
+C 429 12 883 12 1056 12
+C 1229 12 1683 12 1830 0
+L 1830 275
+L 1389 275
+L 1389 4480
+z
+" id="CMBX12-6c" transform="scale(0.015625)"/>
+ <path d="M 4608 2386
+C 4653 2496 4672 2540 5043 2540
+L 5043 2816
+C 4858 2803 4774 2803 4544 2803
+C 4282 2803 4198 2803 3968 2816
+L 3968 2540
+C 4026 2540 4339 2540 4339 2457
+C 4339 2451 4339 2444 4314 2380
+L 3642 712
+L 2906 2540
+L 3270 2540
+L 3270 2816
+C 3117 2803 2739 2803 2566 2803
+C 2240 2803 2227 2803 1907 2816
+L 1907 2540
+L 2285 2540
+C 2304 2489 2336 2406 2362 2348
+C 2381 2309 2445 2155 2445 2123
+C 2445 2111 2426 2066 2419 2046
+L 1933 834
+L 1242 2540
+L 1606 2540
+L 1606 2816
+C 1459 2803 1024 2803 851 2803
+C 646 2803 339 2803 147 2816
+L 147 2540
+L 525 2540
+L 1504 96
+C 1549 -20 1574 -64 1715 -64
+C 1786 -64 1862 -64 1914 64
+L 2592 1764
+L 3270 76
+C 3328 -64 3398 -64 3475 -64
+C 3616 -64 3635 -26 3680 89
+L 4608 2386
+z
+" id="CMBX12-77" transform="scale(0.015625)"/>
+ <path d="M 1427 4019
+C 1427 4281 1216 4480 966 4480
+C 704 4480 506 4262 506 4019
+C 506 3775 704 3558 966 3558
+C 1216 3558 1427 3756 1427 4019
+z
+M 301 2828
+L 301 2553
+C 678 2553 723 2553 723 2303
+L 723 275
+L 282 275
+L 282 0
+C 429 12 870 12 1043 12
+C 1222 12 1632 12 1786 0
+L 1786 275
+L 1389 275
+L 1389 2880
+L 301 2828
+z
+" id="CMBX12-69" transform="scale(0.015625)"/>
+ <path d="M 3398 1958
+C 3398 2566 3136 2880 2432 2880
+C 1786 2880 1472 2425 1382 2233
+L 1376 2233
+L 1376 4480
+L 269 4428
+L 269 4153
+C 666 4153 710 4153 710 3896
+L 710 275
+L 269 275
+L 269 0
+C 416 12 877 12 1056 12
+C 1235 12 1702 12 1850 0
+L 1850 275
+L 1408 275
+L 1408 1638
+C 1408 2329 1920 2668 2330 2668
+C 2566 2668 2701 2515 2701 2028
+L 2701 275
+L 2259 275
+L 2259 0
+C 2406 12 2867 12 3046 12
+C 3226 12 3693 12 3840 0
+L 3840 275
+L 3398 275
+L 3398 1958
+z
+" id="CMBX12-68" transform="scale(0.015625)"/>
+ <path d="M 1389 2540
+L 2118 2540
+L 2118 2816
+L 1357 2816
+L 1357 3466
+C 1357 4122 1779 4224 1990 4224
+C 2061 4224 2074 4217 2112 4204
+C 2016 4141 1958 4034 1958 3901
+C 1958 3649 2163 3535 2330 3535
+C 2470 3535 2701 3630 2701 3908
+C 2701 4167 2470 4435 2016 4435
+C 1434 4435 723 4192 723 3459
+L 723 2816
+L 250 2816
+L 250 2540
+L 723 2540
+L 723 275
+L 282 275
+L 282 0
+C 429 12 909 12 1088 12
+C 1274 12 1792 12 1946 0
+L 1946 275
+L 1389 275
+L 1389 2540
+z
+" id="CMBX12-66" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMBX12-4d"/>
+ <use transform="translate(106.314425 0)scale(0.996264)" xlink:href="#CMBX12-6f"/>
+ <use transform="translate(165.467601 0)scale(0.996264)" xlink:href="#CMBX12-64"/>
+ <use transform="translate(227.734101 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(278.873369 0)scale(0.996264)" xlink:href="#CMBX12-6c"/>
+ <use transform="translate(347.366519 0)scale(0.996264)" xlink:href="#CMBX12-77"/>
+ <use transform="translate(425.199645 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(476.338912 0)scale(0.996264)" xlink:href="#CMBX12-69"/>
+ <use transform="translate(507.472162 0)scale(0.996264)" xlink:href="#CMBX12-67"/>
+ <use transform="translate(563.512013 0)scale(0.996264)" xlink:href="#CMBX12-68"/>
+ <use transform="translate(622.665189 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(703.611639 0)scale(0.996264)" xlink:href="#CMBX12-66"/>
+ <use transform="translate(737.858215 0)scale(0.996264)" xlink:href="#CMBX12-6f"/>
+ <use transform="translate(793.898065 0)scale(0.996264)" xlink:href="#CMBX12-72"/>
+ <use transform="translate(839.675573 0)scale(0.996264)" xlink:href="#CMBX12-3a"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_10">
+ <!-- 2.7e-14 -->
+ <g style="fill:#262626;" transform="translate(174.52871 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2669 990
+L 2554 990
+C 2490 537 2438 460 2413 422
+C 2381 371 1920 371 1830 371
+L 602 371
+C 832 620 1280 1073 1824 1596
+C 2214 1966 2669 2400 2669 3033
+C 2669 3788 2067 4224 1395 4224
+C 691 4224 262 3603 262 3027
+C 262 2777 448 2745 525 2745
+C 589 2745 781 2783 781 3007
+C 781 3206 614 3264 525 3264
+C 486 3264 448 3257 422 3244
+C 544 3788 915 4057 1306 4057
+C 1862 4057 2227 3616 2227 3033
+C 2227 2477 1901 1998 1536 1583
+L 262 147
+L 262 0
+L 2515 0
+L 2669 990
+z
+" id="CMR17-32" transform="scale(0.015625)"/>
+ <path d="M 1062 262
+C 1062 422 934 524 800 524
+C 672 524 538 422 538 262
+C 538 102 666 0 800 0
+C 928 0 1062 102 1062 262
+z
+" id="CMR17-2e" transform="scale(0.015625)"/>
+ <path d="M 2886 3955
+L 2886 4096
+L 1382 4096
+C 634 4096 621 4166 595 4288
+L 480 4288
+L 294 3104
+L 410 3104
+C 429 3226 474 3552 550 3673
+C 589 3724 1062 3724 1171 3724
+L 2579 3724
+L 1869 2670
+C 1395 1961 1069 1003 1069 166
+C 1069 89 1069 -128 1299 -128
+C 1530 -128 1530 89 1530 172
+L 1530 466
+C 1530 1514 1709 2204 2003 2644
+L 2886 3955
+z
+" id="CMR17-37" transform="scale(0.015625)"/>
+ <path d="M 1632 1254
+L 1632 1536
+L 26 1536
+L 26 1254
+L 1632 1254
+z
+" id="CMR17-2d" transform="scale(0.015625)"/>
+ <path d="M 1702 4083
+C 1702 4217 1696 4224 1606 4224
+C 1357 3927 979 3833 621 3820
+C 602 3820 570 3820 563 3808
+C 557 3795 557 3782 557 3648
+C 755 3648 1088 3686 1344 3839
+L 1344 467
+C 1344 243 1331 166 781 166
+L 589 166
+L 589 0
+C 896 6 1216 12 1523 12
+C 1830 12 2150 6 2458 0
+L 2458 166
+L 2266 166
+C 1715 166 1702 236 1702 467
+L 1702 4083
+z
+" id="CMR17-31" transform="scale(0.015625)"/>
+ <path d="M 2150 4147
+C 2150 4281 2144 4288 2029 4288
+L 128 1254
+L 128 1088
+L 1779 1088
+L 1779 460
+C 1779 230 1766 166 1318 166
+L 1197 166
+L 1197 0
+C 1402 12 1747 12 1965 12
+C 2182 12 2528 12 2733 0
+L 2733 166
+L 2611 166
+C 2163 166 2150 230 2150 460
+L 2150 1088
+L 2803 1088
+L 2803 1254
+L 2150 1254
+L 2150 4147
+z
+M 1798 3723
+L 1798 1254
+L 256 1254
+L 1798 3723
+z
+" id="CMR17-34" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-32"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-37"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ <g id="text_11">
+ <!-- 4.7e-06 -->
+ <g style="fill:#262626;" transform="translate(442.36871 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2688 2038
+C 2688 2430 2682 3099 2413 3613
+C 2176 4063 1798 4224 1466 4224
+C 1158 4224 768 4082 525 3620
+C 269 3137 243 2539 243 2038
+C 243 1671 250 1112 448 623
+C 723 -39 1216 -128 1466 -128
+C 1760 -128 2208 -7 2470 604
+C 2662 1048 2688 1568 2688 2038
+z
+M 1466 -26
+C 1056 -26 813 328 723 816
+C 653 1196 653 1749 653 2109
+C 653 2604 653 3015 736 3407
+C 858 3954 1216 4121 1466 4121
+C 1728 4121 2067 3947 2189 3420
+C 2272 3054 2278 2623 2278 2109
+C 2278 1691 2278 1176 2202 797
+C 2067 96 1690 -26 1466 -26
+z
+" id="CMR17-30" transform="scale(0.015625)"/>
+ <path d="M 678 2198
+C 678 3712 1395 4076 1811 4076
+C 1946 4076 2272 4049 2400 3782
+C 2298 3782 2106 3782 2106 3558
+C 2106 3385 2246 3328 2336 3328
+C 2394 3328 2566 3353 2566 3571
+C 2566 3987 2246 4224 1805 4224
+C 1043 4224 243 3411 243 2011
+C 243 257 966 -128 1478 -128
+C 2099 -128 2688 431 2688 1295
+C 2688 2101 2170 2688 1517 2688
+C 1126 2688 838 2430 678 1979
+L 678 2198
+z
+M 1478 25
+C 691 25 691 1212 691 1450
+C 691 1914 909 2585 1504 2585
+C 1613 2585 1926 2585 2138 2140
+C 2253 1889 2253 1624 2253 1302
+C 2253 954 2253 696 2118 438
+C 1978 173 1773 25 1478 25
+z
+" id="CMR17-36" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-37"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ <g id="text_12">
+ <!-- 4.6e-15 -->
+ <g style="fill:#262626;" transform="translate(710.20871 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 730 3750
+C 794 3724 1056 3641 1325 3641
+C 1920 3641 2246 3961 2432 4140
+C 2432 4191 2432 4224 2394 4224
+C 2387 4224 2374 4224 2323 4198
+C 2099 4102 1837 4032 1517 4032
+C 1325 4032 1037 4055 723 4191
+C 653 4224 640 4224 634 4224
+C 602 4224 595 4217 595 4090
+L 595 2231
+C 595 2113 595 2080 659 2080
+C 691 2080 704 2093 736 2139
+C 941 2435 1222 2560 1542 2560
+C 1766 2560 2246 2415 2246 1293
+C 2246 1087 2246 716 2054 422
+C 1894 159 1645 25 1370 25
+C 947 25 518 319 403 812
+C 429 806 480 793 506 793
+C 589 793 749 838 749 1036
+C 749 1209 627 1280 506 1280
+C 358 1280 262 1190 262 1011
+C 262 454 704 -128 1382 -128
+C 2042 -128 2669 441 2669 1267
+C 2669 2054 2170 2662 1549 2662
+C 1222 2662 947 2540 730 2304
+L 730 3750
+z
+" id="CMR17-35" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_13">
+ <!-- 4.6e-15 -->
+ <g style="fill:#262626;" transform="translate(978.04871 228.955463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_14">
+ <!-- 0.52 -->
+ <g style="fill:#ffffff;" transform="translate(191.966522 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ <g id="text_15">
+ <!-- 0.5 -->
+ <g style="fill:#ffffff;" transform="translate(466.660094 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_16">
+ <!-- 0.5 -->
+ <g style="fill:#ffffff;" transform="translate(734.500094 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_17">
+ <!-- 0.5 -->
+ <g style="fill:#ffffff;" transform="translate(1002.340094 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_18">
+ <!-- 0.48 -->
+ <g style="fill:#ffffff;" transform="translate(191.966522 808.795463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1741 2289
+C 2144 2494 2554 2803 2554 3298
+C 2554 3884 1990 4224 1472 4224
+C 890 4224 378 3800 378 3215
+C 378 3054 416 2777 666 2533
+C 730 2469 998 2276 1171 2154
+C 883 2006 211 1652 211 945
+C 211 282 838 -128 1459 -128
+C 2144 -128 2720 366 2720 1022
+C 2720 1607 2330 1877 2074 2051
+L 1741 2289
+z
+M 902 2855
+C 851 2887 595 3086 595 3388
+C 595 3781 998 4076 1459 4076
+C 1965 4076 2336 3716 2336 3298
+C 2336 2700 1670 2359 1638 2359
+C 1632 2359 1626 2359 1574 2398
+L 902 2855
+z
+M 2080 1536
+C 2176 1466 2483 1253 2483 861
+C 2483 385 2010 25 1472 25
+C 890 25 448 443 448 951
+C 448 1459 838 1884 1280 2083
+L 2080 1536
+z
+" id="CMR17-38" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-38"/>
+ </g>
+ </g>
+ <g id="text_19">
+ <!-- 0.5 -->
+ <g style="fill:#ffffff;" transform="translate(466.660094 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_20">
+ <!-- 0.5 -->
+ <g style="fill:#ffffff;" transform="translate(734.500094 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_21">
+ <!-- 0.5 -->
+ <g style="fill:#ffffff;" transform="translate(1002.340094 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ <g id="axes_2">
+ <g id="patch_3">
+ <path d="M 1220.657891 946.284441
+L 1264.145891 946.284441
+L 1264.145891 76.524441
+L 1220.657891 76.524441
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="patch_4">
+ <path clip-path="url(#p7d3937ad3b)" d="M 1220.657891 946.284441
+L 1220.657891 942.886941
+L 1220.657891 79.921941
+L 1220.657891 76.524441
+L 1264.145891 76.524441
+L 1264.145891 79.921941
+L 1264.145891 942.886941
+L 1264.145891 946.284441
+L 1264.145891 946.284441
+z
+" style="fill:#ffffff;stroke:#ffffff;stroke-linejoin:miter;stroke-width:0.01;"/>
+ </g>
+ <image height="870" id="image0b6f4e5b6f" transform="scale(1 -1)translate(0 -870)" width="43" x="1221" xlink:href="data:image/png;base64,
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" y="-76"/>
+ <g id="matplotlib.axis_3"/>
+ <g id="matplotlib.axis_4">
+ <g id="ytick_4">
+ <g id="line2d_8">
+ <defs>
+ <path d="M 0 0
+L 3.5 0
+" id="m5dda3d42e1" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m5dda3d42e1" y="946.284441"/>
+ </g>
+ </g>
+ <g id="text_22">
+ <!-- $\mathdefault{0.0}$ -->
+ <g transform="translate(1271.145891 956.662188)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1178 307
+C 1178 492 1024 620 870 620
+C 685 620 557 467 557 313
+C 557 128 710 0 864 0
+C 1050 0 1178 153 1178 307
+z
+" id="CMMI12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_5">
+ <g id="line2d_9">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m5dda3d42e1" y="778.968017"/>
+ </g>
+ </g>
+ <g id="text_23">
+ <!-- $\mathdefault{0.1}$ -->
+ <g transform="translate(1271.145891 789.345765)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_6">
+ <g id="line2d_10">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m5dda3d42e1" y="611.651594"/>
+ </g>
+ </g>
+ <g id="text_24">
+ <!-- $\mathdefault{0.2}$ -->
+ <g transform="translate(1271.145891 622.029341)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_7">
+ <g id="line2d_11">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m5dda3d42e1" y="444.33517"/>
+ </g>
+ </g>
+ <g id="text_25">
+ <!-- $\mathdefault{0.3}$ -->
+ <g transform="translate(1271.145891 454.712918)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1414 2176
+C 1984 2176 2234 1673 2234 1094
+C 2234 322 1824 25 1453 25
+C 1114 25 563 193 390 691
+C 422 678 454 678 486 678
+C 640 678 755 780 755 947
+C 755 1132 614 1216 486 1216
+C 378 1216 211 1164 211 927
+C 211 335 787 -128 1466 -128
+C 2176 -128 2720 432 2720 1087
+C 2720 1718 2208 2176 1600 2246
+C 2086 2347 2554 2776 2554 3353
+C 2554 3856 2048 4224 1472 4224
+C 890 4224 378 3862 378 3347
+C 378 3123 544 3084 627 3084
+C 762 3084 877 3167 877 3334
+C 877 3500 762 3584 627 3584
+C 602 3584 570 3584 544 3571
+C 730 3999 1235 4076 1459 4076
+C 1683 4076 2106 3966 2106 3347
+C 2106 3167 2080 2851 1862 2574
+C 1670 2329 1453 2316 1242 2297
+C 1210 2297 1062 2284 1037 2284
+C 992 2278 966 2272 966 2227
+C 966 2182 973 2176 1101 2176
+L 1414 2176
+z
+" id="CMR17-33" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_8">
+ <g id="line2d_12">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m5dda3d42e1" y="277.018747"/>
+ </g>
+ </g>
+ <g id="text_26">
+ <!-- $\mathdefault{0.4}$ -->
+ <g transform="translate(1271.145891 287.396495)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_9">
+ <g id="line2d_13">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m5dda3d42e1" y="109.702324"/>
+ </g>
+ </g>
+ <g id="text_27">
+ <!-- $\mathdefault{0.5}$ -->
+ <g transform="translate(1271.145891 120.080071)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ </g>
+ <g id="LineCollection_1"/>
+ <g id="patch_5">
+ <path d="M 1220.657891 946.284441
+L 1220.657891 942.886941
+L 1220.657891 79.921941
+L 1220.657891 76.524441
+L 1264.145891 76.524441
+L 1264.145891 79.921941
+L 1264.145891 942.886941
+L 1264.145891 946.284441
+z
+" style="fill:none;"/>
+ </g>
+ </g>
+ </g>
+ <defs>
+ <clipPath id="p4d2d3adaac">
+ <rect height="869.76" width="1071.36" x="82.337891" y="76.524441"/>
+ </clipPath>
+ <clipPath id="p7d3937ad3b">
+ <rect height="869.76" width="43.488" x="1220.657891" y="76.524441"/>
+ </clipPath>
+ </defs>
+</svg>
diff --git a/examples/model-comparison/reference/confusionMatrix_ND_15.svg b/examples/model-comparison/reference/confusionMatrix_ND_15.svg
new file mode 100644
index 0000000000000000000000000000000000000000..881f2a12da0fcf1493c65b560e094c416be60360
--- /dev/null
+++ b/examples/model-comparison/reference/confusionMatrix_ND_15.svg
@@ -0,0 +1,1592 @@
+<?xml version="1.0" encoding="utf-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<svg height="953.484441pt" version="1.1" viewBox="0 0 1313.889331 953.484441" width="1313.889331pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+ <metadata>
+ <rdf:RDF xmlns:cc="http://creativecommons.org/ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
+ <cc:Work>
+ <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
+ <dc:date>2022-06-03T16:06:13.582877</dc:date>
+ <dc:format>image/svg+xml</dc:format>
+ <dc:creator>
+ <cc:Agent>
+ <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>
+ </cc:Agent>
+ </dc:creator>
+ </cc:Work>
+ </rdf:RDF>
+ </metadata>
+ <defs>
+ <style type="text/css">*{stroke-linecap:butt;stroke-linejoin:round;}</style>
+ </defs>
+ <g id="figure_1">
+ <g id="patch_1">
+ <path d="M 0 953.484441
+L 1313.889331 953.484441
+L 1313.889331 0
+L 0 0
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="axes_1">
+ <g id="patch_2">
+ <path d="M 82.337891 946.284441
+L 1153.697891 946.284441
+L 1153.697891 76.524441
+L 82.337891 76.524441
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="QuadMesh_1">
+ <path clip-path="url(#pc5cc66efae)" d="M 82.337891 76.524441
+L 350.177891 76.524441
+L 350.177891 366.444441
+L 82.337891 366.444441
+L 82.337891 76.524441
+" style="fill:#c3daee;"/>
+ <path clip-path="url(#pc5cc66efae)" d="M 350.177891 76.524441
+L 618.017891 76.524441
+L 618.017891 366.444441
+L 350.177891 366.444441
+L 350.177891 76.524441
+" style="fill:#08306b;"/>
+ <path clip-path="url(#pc5cc66efae)" d="M 618.017891 76.524441
+L 885.857891 76.524441
+L 885.857891 366.444441
+L 618.017891 366.444441
+L 618.017891 76.524441
+" style="fill:#e7f0fa;"/>
+ <path clip-path="url(#pc5cc66efae)" d="M 885.857891 76.524441
+L 1153.697891 76.524441
+L 1153.697891 366.444441
+L 885.857891 366.444441
+L 885.857891 76.524441
+" style="fill:#e7f0fa;"/>
+ <path clip-path="url(#pc5cc66efae)" d="M 82.337891 366.444441
+L 350.177891 366.444441
+L 350.177891 656.364441
+L 82.337891 656.364441
+L 82.337891 366.444441
+" style="fill:#9fcae1;"/>
+ <path clip-path="url(#pc5cc66efae)" d="M 350.177891 366.444441
+L 618.017891 366.444441
+L 618.017891 656.364441
+L 350.177891 656.364441
+L 350.177891 366.444441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#pc5cc66efae)" d="M 618.017891 366.444441
+L 885.857891 366.444441
+L 885.857891 656.364441
+L 618.017891 656.364441
+L 618.017891 366.444441
+" style="fill:#7cb7da;"/>
+ <path clip-path="url(#pc5cc66efae)" d="M 885.857891 366.444441
+L 1153.697891 366.444441
+L 1153.697891 656.364441
+L 885.857891 656.364441
+L 885.857891 366.444441
+" style="fill:#7cb7da;"/>
+ <path clip-path="url(#pc5cc66efae)" d="M 82.337891 656.364441
+L 350.177891 656.364441
+L 350.177891 946.284441
+L 82.337891 946.284441
+L 82.337891 656.364441
+" style="fill:#a0cbe2;"/>
+ <path clip-path="url(#pc5cc66efae)" d="M 350.177891 656.364441
+L 618.017891 656.364441
+L 618.017891 946.284441
+L 350.177891 946.284441
+L 350.177891 656.364441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#pc5cc66efae)" d="M 618.017891 656.364441
+L 885.857891 656.364441
+L 885.857891 946.284441
+L 618.017891 946.284441
+L 618.017891 656.364441
+" style="fill:#7cb7da;"/>
+ <path clip-path="url(#pc5cc66efae)" d="M 885.857891 656.364441
+L 1153.697891 656.364441
+L 1153.697891 946.284441
+L 885.857891 946.284441
+L 885.857891 656.364441
+" style="fill:#7cb7da;"/>
+ </g>
+ <g id="matplotlib.axis_1">
+ <g id="xtick_1">
+ <g id="line2d_1">
+ <defs>
+ <path d="M 0 0
+L 0 -3.5
+" id="mff7cabf4e2" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="216.257891" xlink:href="#mff7cabf4e2" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_1">
+ <!-- Observation -->
+ <g transform="translate(144.303789 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 4307 2166
+C 4307 3488 3366 4480 2304 4480
+C 1216 4480 294 3475 294 2166
+C 294 857 1229 -128 2298 -128
+C 3392 -128 4307 876 4307 2166
+z
+M 2304 -13
+C 1574 -13 781 722 781 2250
+C 781 3771 1651 4364 2298 4364
+C 2976 4364 3821 3752 3821 2250
+C 3821 696 3008 -13 2304 -13
+z
+" id="CMR17-4f" transform="scale(0.015625)"/>
+ <path d="M 960 4416
+L 198 4345
+L 198 4179
+C 576 4179 634 4141 634 3843
+L 634 -13
+L 749 -13
+L 934 445
+C 1120 141 1395 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2209 2477 2816 1830 2816
+C 1434 2816 1152 2603 960 2351
+L 960 4416
+z
+M 973 2022
+C 973 2138 973 2157 1062 2293
+C 1312 2681 1670 2713 1792 2713
+C 1984 2713 2643 2610 2643 1388
+C 2643 109 1888 38 1734 38
+C 1536 38 1248 115 1043 490
+C 973 613 973 626 973 742
+L 973 2022
+z
+" id="CMR17-62" transform="scale(0.015625)"/>
+ <path d="M 1978 2688
+C 1978 2803 1971 2809 1933 2809
+C 1907 2809 1901 2803 1824 2707
+C 1805 2681 1747 2617 1728 2592
+C 1523 2809 1235 2816 1126 2816
+C 416 2816 160 2444 160 2073
+C 160 1497 813 1363 998 1324
+C 1402 1241 1542 1216 1677 1100
+C 1760 1024 1901 883 1901 652
+C 1901 384 1747 38 1158 38
+C 602 38 403 460 288 1024
+C 269 1113 269 1120 218 1120
+C 166 1120 160 1113 160 985
+L 160 64
+C 160 -52 166 -58 205 -58
+C 237 -58 243 -52 275 0
+C 314 57 410 211 448 275
+C 576 102 800 -64 1158 -64
+C 1792 -64 2131 281 2131 780
+C 2131 1107 1958 1280 1875 1356
+C 1683 1555 1459 1600 1190 1651
+C 838 1728 390 1817 390 2208
+C 390 2374 480 2726 1126 2726
+C 1811 2726 1850 2086 1862 1881
+C 1869 1849 1901 1843 1920 1843
+C 1978 1843 1978 1862 1978 1971
+L 1978 2688
+z
+" id="CMR17-73" transform="scale(0.015625)"/>
+ <path d="M 2438 1503
+C 2464 1529 2464 1542 2464 1606
+C 2464 2251 2118 2816 1389 2816
+C 710 2816 173 2175 173 1394
+C 173 554 781 -64 1459 -64
+C 2176 -64 2458 619 2458 755
+C 2458 800 2419 800 2406 800
+C 2362 800 2355 787 2330 709
+C 2189 270 1837 51 1504 51
+C 1229 51 954 206 781 490
+C 582 819 582 1200 582 1503
+L 2438 1503
+z
+M 589 1600
+C 634 2511 1126 2713 1382 2713
+C 1818 2713 2112 2308 2118 1600
+L 589 1600
+z
+" id="CMR17-65" transform="scale(0.015625)"/>
+ <path d="M 960 1517
+C 960 2134 1222 2713 1702 2713
+C 1747 2713 1792 2707 1837 2687
+C 1837 2687 1696 2642 1696 2475
+C 1696 2321 1818 2257 1914 2257
+C 1990 2257 2131 2302 2131 2482
+C 2131 2687 1926 2816 1709 2816
+C 1222 2816 1011 2340 947 2115
+L 941 2115
+L 941 2816
+L 198 2745
+L 198 2578
+C 576 2578 634 2540 634 2231
+L 634 443
+C 634 198 608 166 198 166
+L 198 0
+C 352 12 646 12 813 12
+C 998 12 1325 12 1498 0
+L 1498 166
+C 1037 166 960 166 960 455
+L 960 1517
+z
+" id="CMR17-72" transform="scale(0.015625)"/>
+ <path d="M 2502 2173
+C 2560 2315 2662 2572 3034 2585
+L 3034 2752
+C 2912 2745 2752 2739 2630 2739
+C 2496 2739 2285 2739 2157 2752
+L 2157 2585
+C 2317 2572 2406 2495 2406 2328
+C 2406 2270 2406 2257 2368 2167
+L 1664 379
+L 902 2308
+C 864 2392 864 2405 864 2431
+C 864 2585 1075 2585 1171 2585
+L 1171 2752
+C 1018 2739 736 2739 576 2739
+C 403 2739 205 2739 64 2752
+L 64 2585
+C 307 2585 442 2585 518 2386
+L 1446 44
+C 1485 -52 1491 -64 1549 -64
+C 1606 -64 1613 -52 1651 44
+L 2502 2173
+z
+" id="CMR17-76" transform="scale(0.015625)"/>
+ <path d="M 2304 1656
+C 2304 2048 2304 2275 2035 2534
+C 1798 2751 1523 2816 1306 2816
+C 800 2816 435 2408 435 1977
+C 435 1740 627 1728 666 1728
+C 749 1728 896 1779 896 1958
+C 896 2118 774 2188 666 2188
+C 640 2188 608 2182 589 2176
+C 723 2594 1069 2713 1293 2713
+C 1613 2713 1965 2421 1965 1875
+L 1965 1632
+C 1587 1619 1133 1568 774 1373
+C 371 1147 256 822 256 576
+C 256 77 832 -64 1171 -64
+C 1523 -64 1850 135 1990 505
+C 2003 219 2182 -39 2464 -39
+C 2598 -39 2938 51 2938 563
+L 2938 926
+L 2822 926
+L 2822 557
+C 2822 161 2650 109 2566 109
+C 2304 109 2304 446 2304 732
+L 2304 1656
+z
+M 1965 887
+C 1965 323 1568 38 1216 38
+C 896 38 646 278 646 576
+C 646 771 730 1114 1101 1322
+C 1408 1497 1760 1523 1965 1536
+L 1965 887
+z
+" id="CMR17-61" transform="scale(0.015625)"/>
+ <path d="M 966 2585
+L 1862 2585
+L 1862 2752
+L 966 2752
+L 966 3968
+L 851 3968
+C 838 3292 614 2700 70 2687
+L 70 2585
+L 627 2585
+L 627 778
+C 627 655 627 -64 1370 -64
+C 1747 -64 1965 308 1965 784
+L 1965 1151
+L 1850 1151
+L 1850 790
+C 1850 347 1677 51 1408 51
+C 1222 51 966 179 966 765
+L 966 2585
+z
+" id="CMR17-74" transform="scale(0.015625)"/>
+ <path d="M 992 3961
+C 992 4102 877 4224 730 4224
+C 589 4224 467 4108 467 3961
+C 467 3820 582 3699 730 3699
+C 870 3699 992 3814 992 3961
+z
+M 243 2745
+L 243 2579
+C 602 2579 653 2540 653 2231
+L 653 443
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 646 12 806 12
+C 960 12 1222 12 1370 0
+L 1370 166
+C 992 166 979 205 979 436
+L 979 2816
+L 243 2745
+z
+" id="CMR17-69" transform="scale(0.015625)"/>
+ <path d="M 2758 1356
+C 2758 2176 2163 2816 1466 2816
+C 768 2816 173 2176 173 1356
+C 173 550 768 -64 1466 -64
+C 2163 -64 2758 550 2758 1356
+z
+M 1466 51
+C 1165 51 909 230 762 480
+C 602 768 582 1126 582 1408
+C 582 1676 595 2009 762 2297
+C 890 2508 1139 2713 1466 2713
+C 1754 2713 1997 2553 2150 2329
+C 2349 2028 2349 1606 2349 1408
+C 2349 1158 2336 774 2163 467
+C 1984 172 1709 51 1466 51
+z
+" id="CMR17-6f" transform="scale(0.015625)"/>
+ <path d="M 2656 1954
+C 2656 2282 2592 2816 1837 2816
+C 1331 2816 1069 2424 973 2166
+L 966 2166
+L 966 2816
+L 211 2745
+L 211 2578
+C 589 2578 646 2540 646 2231
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1954
+z
+" id="CMR17-6e" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-4f"/>
+ <use transform="translate(71.714788 0)scale(0.996264)" xlink:href="#CMR17-62"/>
+ <use transform="translate(122.610158 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(158.411496 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(198.897156 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ <use transform="translate(234.177924 0)scale(0.996264)" xlink:href="#CMR17-76"/>
+ <use transform="translate(277.266023 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(322.9565 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(358.237268 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(383.108327 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(428.798804 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_2">
+ <g id="line2d_2">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="484.097891" xlink:href="#mff7cabf4e2" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_2">
+ <!-- linear -->
+ <g transform="translate(450.783747 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 979 4416
+L 218 4345
+L 218 4179
+C 595 4179 653 4141 653 3835
+L 653 439
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 653 12 813 12
+C 979 12 1261 12 1414 0
+L 1414 166
+C 1005 166 979 191 979 439
+L 979 4416
+z
+" id="CMR17-6c" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_3">
+ <g id="line2d_3">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="751.937891" xlink:href="#mff7cabf4e2" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_3">
+ <!-- exponential -->
+ <g transform="translate(683.18479 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1664 1491
+C 1856 1740 2074 2022 2253 2233
+C 2464 2476 2707 2579 2989 2585
+L 2989 2752
+C 2880 2745 2656 2739 2541 2739
+C 2368 2739 2170 2739 2022 2752
+L 2022 2585
+C 2112 2572 2163 2508 2163 2419
+C 2163 2304 2099 2233 2067 2188
+L 1594 1587
+L 1030 2323
+C 973 2393 973 2406 973 2438
+C 973 2515 1037 2579 1146 2585
+L 1146 2752
+C 992 2739 717 2739 557 2739
+C 384 2739 179 2739 38 2752
+L 38 2585
+C 384 2585 461 2560 614 2368
+L 1350 1414
+C 1363 1401 1395 1363 1395 1344
+C 1395 1318 838 633 768 544
+C 480 198 179 172 6 166
+L 6 0
+C 115 6 339 12 454 12
+C 582 12 864 12 979 0
+L 979 166
+C 941 172 838 185 838 332
+C 838 448 890 518 947 595
+L 1478 1248
+L 2035 524
+C 2086 454 2163 358 2163 313
+C 2163 224 2086 172 1984 166
+L 1984 0
+C 2138 12 2413 12 2573 12
+C 2746 12 2950 12 3091 0
+L 3091 166
+C 2771 166 2675 179 2522 377
+L 1664 1491
+z
+" id="CMR17-78" transform="scale(0.015625)"/>
+ <path d="M 1408 -1114
+C 998 -1114 973 -1088 973 -834
+L 973 380
+C 1158 109 1427 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2196 2496 2816 1837 2816
+C 1453 2816 1139 2603 960 2345
+L 960 2816
+L 198 2745
+L 198 2577
+C 576 2577 634 2539 634 2228
+L 634 -834
+C 634 -1081 608 -1114 198 -1114
+L 198 -1280
+C 352 -1268 634 -1268 800 -1268
+C 966 -1268 1254 -1268 1408 -1280
+L 1408 -1114
+z
+M 973 2015
+C 973 2106 973 2241 1222 2481
+C 1254 2506 1472 2700 1792 2700
+C 2259 2700 2643 2112 2643 1376
+C 2643 639 2234 38 1728 38
+C 1498 38 1248 148 1056 451
+C 973 594 973 632 973 736
+L 973 2015
+z
+" id="CMR17-70" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_4">
+ <g id="line2d_4">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1019.777891" xlink:href="#mff7cabf4e2" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_4">
+ <!-- cosine -->
+ <g transform="translate(984.043472 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2234 2240
+C 2112 2240 1933 2240 1933 2015
+C 1933 1836 2080 1785 2163 1785
+C 2208 1785 2394 1804 2394 2028
+C 2394 2476 1958 2816 1466 2816
+C 787 2816 211 2201 211 1379
+C 211 521 813 -64 1466 -64
+C 2259 -64 2458 676 2458 747
+C 2458 773 2451 792 2406 792
+C 2362 792 2355 786 2330 702
+C 2163 180 1798 51 1523 51
+C 1114 51 621 431 621 1385
+C 621 2358 1094 2700 1472 2700
+C 1722 2700 2093 2582 2234 2240
+z
+" id="CMR17-63" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_5">
+ <!-- \textbf{Data generated by:} -->
+ <g transform="translate(476.949653 27.955495)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 243 4416
+L 243 4140
+L 922 4140
+L 922 275
+L 243 275
+L 243 0
+L 2938 0
+C 4166 0 5114 790 5114 2169
+C 5114 3625 4141 4416 2938 4416
+L 243 4416
+z
+M 1734 275
+L 1734 4140
+L 2694 4140
+C 3251 4140 3699 3921 3936 3586
+C 4122 3322 4243 3006 4243 2175
+C 4243 1421 4147 1086 3923 784
+C 3699 487 3270 275 2694 275
+L 1734 275
+z
+" id="CMBX12-44" transform="scale(0.015625)"/>
+ <path d="M 2944 1894
+C 2944 2483 2477 2880 1574 2880
+C 1216 2880 461 2847 461 2310
+C 461 2041 666 1926 838 1926
+C 1030 1926 1216 2060 1216 2303
+C 1216 2425 1171 2540 1062 2611
+C 1274 2668 1427 2668 1549 2668
+C 1984 2668 2246 2425 2246 1900
+L 2246 1644
+C 1235 1644 218 1362 218 648
+C 218 64 960 -64 1402 -64
+C 1894 -64 2208 205 2336 488
+C 2336 250 2336 -26 2982 -26
+L 3309 -26
+C 3443 -26 3494 -26 3494 115
+C 3494 250 3437 250 3347 250
+C 2944 256 2944 359 2944 507
+L 2944 1894
+z
+M 2246 867
+C 2246 262 1709 147 1504 147
+C 1190 147 928 359 928 655
+C 928 1240 1619 1439 2246 1472
+L 2246 867
+z
+" id="CMBX12-61" transform="scale(0.015625)"/>
+ <path d="M 1350 2540
+L 2272 2540
+L 2272 2816
+L 1350 2816
+L 1350 4032
+L 1082 4032
+C 1075 3401 768 2771 134 2751
+L 134 2540
+L 653 2540
+L 653 761
+C 653 83 1178 -64 1638 -64
+C 2112 -64 2394 294 2394 768
+L 2394 1107
+L 2125 1107
+L 2125 774
+C 2125 352 1933 166 1734 166
+C 1350 166 1350 595 1350 742
+L 1350 2540
+z
+" id="CMBX12-74" transform="scale(0.015625)"/>
+ <path d="M 832 1177
+C 1139 1011 1498 1011 1594 1011
+C 2477 1011 2829 1506 2829 1958
+C 2829 2287 2643 2519 2566 2584
+C 2752 2687 2906 2713 3014 2726
+C 2995 2694 2976 2668 2976 2584
+C 2976 2448 3066 2326 3232 2326
+C 3398 2326 3488 2448 3488 2584
+C 3488 2739 3373 2944 3104 2944
+C 2829 2944 2566 2809 2432 2694
+C 2170 2847 1920 2905 1594 2905
+C 710 2905 358 2410 358 1958
+C 358 1758 422 1493 691 1274
+C 582 1151 467 926 467 693
+C 467 416 614 179 749 76
+C 595 38 198 -109 198 -474
+C 198 -852 614 -1280 1792 -1280
+C 2854 -1280 3392 -935 3392 -455
+C 3392 108 3021 294 2861 371
+C 2554 524 2144 524 1581 524
+C 1421 524 1139 524 1107 531
+C 832 576 755 823 755 946
+C 755 998 762 1094 832 1177
+z
+M 1594 1216
+C 1037 1216 1037 1661 1037 1958
+C 1037 2255 1037 2700 1594 2700
+C 2150 2700 2150 2255 2150 1958
+C 2150 1661 2150 1216 1594 1216
+z
+M 1952 -64
+C 2419 -64 2867 -148 2867 -480
+C 2867 -704 2643 -1076 1798 -1076
+C 954 -1076 723 -717 723 -474
+C 723 -64 1126 -64 1222 -64
+L 1952 -64
+z
+" id="CMBX12-67" transform="scale(0.015625)"/>
+ <path d="M 2893 1408
+C 3040 1408 3078 1408 3078 1568
+C 3078 1758 3034 2232 2739 2529
+C 2470 2796 2112 2880 1741 2880
+C 742 2880 198 2232 198 1433
+C 198 523 858 -64 1824 -64
+C 2790 -64 3078 621 3078 731
+C 3078 829 2982 829 2944 829
+C 2842 829 2835 809 2797 725
+C 2630 302 2208 166 1901 166
+C 973 166 966 1043 966 1408
+L 2893 1408
+z
+M 966 1593
+C 979 1852 986 2099 1120 2327
+C 1242 2529 1466 2668 1741 2668
+C 2426 2668 2483 1909 2490 1593
+L 966 1593
+z
+" id="CMBX12-65" transform="scale(0.015625)"/>
+ <path d="M 3398 1958
+C 3398 2566 3136 2880 2432 2880
+C 1971 2880 1574 2656 1357 2176
+L 1350 2176
+L 1350 2880
+L 269 2828
+L 269 2553
+C 666 2553 710 2553 710 2304
+L 710 275
+L 269 275
+L 269 0
+C 416 12 877 12 1056 12
+C 1235 12 1702 12 1850 0
+L 1850 275
+L 1408 275
+L 1408 1638
+C 1408 2329 1920 2668 2330 2668
+C 2566 2668 2701 2515 2701 2028
+L 2701 275
+L 2259 275
+L 2259 0
+C 2406 12 2867 12 3046 12
+C 3226 12 3693 12 3840 0
+L 3840 275
+L 3398 275
+L 3398 1958
+z
+" id="CMBX12-6e" transform="scale(0.015625)"/>
+ <path d="M 1331 1440
+C 1331 1651 1376 2668 2125 2668
+C 2035 2598 1990 2489 1990 2374
+C 1990 2112 2202 2003 2362 2003
+C 2522 2003 2733 2112 2733 2374
+C 2733 2700 2400 2880 2093 2880
+C 1587 2880 1370 2438 1280 2169
+L 1274 2169
+L 1274 2880
+L 224 2828
+L 224 2553
+C 621 2553 666 2553 666 2304
+L 666 275
+L 224 275
+L 224 0
+C 371 12 851 12 1030 12
+C 1216 12 1734 12 1888 0
+L 1888 275
+L 1331 275
+L 1331 1440
+z
+" id="CMBX12-72" transform="scale(0.015625)"/>
+ <path d="M 2221 4428
+L 2221 4153
+C 2618 4153 2662 4153 2662 3896
+L 2662 2571
+C 2522 2694 2240 2880 1798 2880
+C 890 2880 243 2313 243 1408
+C 243 483 877 -64 1728 -64
+C 2080 -64 2381 57 2630 270
+L 2630 -64
+L 3770 -26
+L 3770 250
+C 3373 250 3328 250 3328 502
+L 3328 4480
+L 2221 4428
+z
+M 2630 625
+C 2362 231 2035 147 1805 147
+C 1011 147 1011 968 1011 1395
+C 1011 1699 1011 2022 1152 2268
+C 1350 2630 1728 2668 1875 2668
+C 2138 2668 2419 2552 2630 2268
+L 2630 625
+z
+" id="CMBX12-64" transform="scale(0.015625)"/>
+ <path d="M 1331 4480
+L 224 4428
+L 224 4153
+C 621 4153 666 4153 666 3896
+L 666 -26
+L 934 -26
+C 1043 96 1152 218 1254 347
+C 1581 6 1933 -64 2189 -64
+C 3072 -64 3750 476 3750 1414
+C 3750 2300 3149 2880 2272 2880
+C 1894 2880 1594 2758 1331 2552
+L 1331 4480
+z
+M 1363 2242
+C 1587 2552 1920 2668 2189 2668
+C 2982 2668 2982 1847 2982 1420
+C 2982 1130 2982 761 2829 522
+C 2630 211 2330 147 2125 147
+C 1690 147 1453 457 1363 599
+L 1363 2242
+z
+" id="CMBX12-62" transform="scale(0.015625)"/>
+ <path d="M 3168 2400
+C 3206 2489 3232 2540 3642 2540
+L 3642 2816
+C 3424 2803 3398 2803 3136 2803
+C 2963 2803 2950 2803 2586 2816
+L 2586 2540
+C 2592 2540 2893 2540 2893 2457
+C 2893 2438 2874 2400 2867 2381
+L 2118 780
+L 1299 2540
+L 1651 2540
+L 1651 2816
+C 1498 2803 1062 2803 883 2803
+C 698 2803 320 2803 154 2816
+L 154 2540
+L 563 2540
+L 1747 -8
+C 1715 -84 1626 -269 1594 -345
+C 1459 -631 1254 -1069 806 -1069
+C 781 -1069 704 -1069 634 -1031
+C 646 -1025 838 -949 838 -707
+C 838 -497 685 -364 493 -364
+C 294 -364 141 -497 141 -713
+C 141 -1012 422 -1280 806 -1280
+C 1331 -1280 1677 -809 1805 -529
+L 3168 2400
+z
+" id="CMBX12-79" transform="scale(0.015625)"/>
+ <path d="M 1459 2355
+C 1459 2617 1248 2816 998 2816
+C 749 2816 538 2617 538 2355
+C 538 2092 749 1894 998 1894
+C 1248 1894 1459 2092 1459 2355
+z
+M 1459 460
+C 1459 723 1248 921 998 921
+C 749 921 538 723 538 460
+C 538 198 749 0 998 0
+C 1248 0 1459 198 1459 460
+z
+" id="CMBX12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMBX12-44"/>
+ <use transform="translate(85.904786 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(140.387974 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(183.974524 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(275.817613 0)scale(0.996264)" xlink:href="#CMBX12-67"/>
+ <use transform="translate(331.857463 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(382.99673 0)scale(0.996264)" xlink:href="#CMBX12-6e"/>
+ <use transform="translate(445.263231 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(496.402498 0)scale(0.996264)" xlink:href="#CMBX12-72"/>
+ <use transform="translate(542.180006 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(596.663194 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(640.249744 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(691.389011 0)scale(0.996264)" xlink:href="#CMBX12-64"/>
+ <use transform="translate(791.015412 0)scale(0.996264)" xlink:href="#CMBX12-62"/>
+ <use transform="translate(850.168588 0)scale(0.996264)" xlink:href="#CMBX12-79"/>
+ <use transform="translate(909.321763 0)scale(0.996264)" xlink:href="#CMBX12-3a"/>
+ </g>
+ </g>
+ </g>
+ <g id="matplotlib.axis_2">
+ <g id="ytick_1">
+ <g id="line2d_5">
+ <defs>
+ <path d="M 0 0
+L -3.5 0
+" id="md905bc3807" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#md905bc3807" y="221.484441"/>
+ </g>
+ </g>
+ <g id="text_6">
+ <!-- linear -->
+ <g transform="translate(69.524441 277.73498)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_2">
+ <g id="line2d_6">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#md905bc3807" y="511.404441"/>
+ </g>
+ </g>
+ <g id="text_7">
+ <!-- exponential -->
+ <g transform="translate(69.524441 638.532895)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_3">
+ <g id="line2d_7">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#md905bc3807" y="801.324441"/>
+ </g>
+ </g>
+ <g id="text_8">
+ <!-- cosine -->
+ <g transform="translate(69.524441 862.415532)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_9">
+ <!-- \textbf{Model weight for:} -->
+ <g transform="translate(27.955495 642.025756)rotate(-90)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 3411 816
+L 1875 4281
+C 1818 4416 1760 4416 1626 4416
+L 262 4416
+L 262 4140
+L 941 4140
+L 941 468
+C 941 326 934 320 768 294
+C 653 281 525 275 410 275
+L 262 275
+L 262 0
+C 410 12 909 12 1088 12
+C 1267 12 1773 12 1920 0
+L 1920 275
+L 1773 275
+C 1600 275 1587 275 1434 294
+C 1248 320 1242 326 1242 468
+L 1242 4063
+L 1248 4063
+L 2989 134
+C 3021 64 3059 0 3168 0
+C 3277 0 3315 64 3347 134
+L 5120 4140
+L 5126 4140
+L 5126 275
+L 4448 275
+L 4448 0
+C 4621 12 5286 12 5504 12
+C 5722 12 6387 12 6560 0
+L 6560 275
+L 5882 275
+L 5882 4140
+L 6560 4140
+L 6560 4416
+L 5197 4416
+C 5062 4416 5005 4416 4947 4281
+L 3411 816
+z
+" id="CMBX12-4d" transform="scale(0.015625)"/>
+ <path d="M 3392 1379
+C 3392 2245 2803 2880 1798 2880
+C 755 2880 198 2213 198 1379
+C 198 538 787 -64 1792 -64
+C 2835 -64 3392 570 3392 1379
+z
+M 1798 166
+C 966 166 966 917 966 1443
+C 966 1744 966 2065 1088 2296
+C 1229 2553 1517 2668 1792 2668
+C 2157 2668 2387 2495 2496 2315
+C 2624 2084 2624 1751 2624 1443
+C 2624 910 2624 166 1798 166
+z
+" id="CMBX12-6f" transform="scale(0.015625)"/>
+ <path d="M 1389 4480
+L 282 4428
+L 282 4153
+C 678 4153 723 4153 723 3901
+L 723 275
+L 282 275
+L 282 0
+C 429 12 883 12 1056 12
+C 1229 12 1683 12 1830 0
+L 1830 275
+L 1389 275
+L 1389 4480
+z
+" id="CMBX12-6c" transform="scale(0.015625)"/>
+ <path d="M 4608 2386
+C 4653 2496 4672 2540 5043 2540
+L 5043 2816
+C 4858 2803 4774 2803 4544 2803
+C 4282 2803 4198 2803 3968 2816
+L 3968 2540
+C 4026 2540 4339 2540 4339 2457
+C 4339 2451 4339 2444 4314 2380
+L 3642 712
+L 2906 2540
+L 3270 2540
+L 3270 2816
+C 3117 2803 2739 2803 2566 2803
+C 2240 2803 2227 2803 1907 2816
+L 1907 2540
+L 2285 2540
+C 2304 2489 2336 2406 2362 2348
+C 2381 2309 2445 2155 2445 2123
+C 2445 2111 2426 2066 2419 2046
+L 1933 834
+L 1242 2540
+L 1606 2540
+L 1606 2816
+C 1459 2803 1024 2803 851 2803
+C 646 2803 339 2803 147 2816
+L 147 2540
+L 525 2540
+L 1504 96
+C 1549 -20 1574 -64 1715 -64
+C 1786 -64 1862 -64 1914 64
+L 2592 1764
+L 3270 76
+C 3328 -64 3398 -64 3475 -64
+C 3616 -64 3635 -26 3680 89
+L 4608 2386
+z
+" id="CMBX12-77" transform="scale(0.015625)"/>
+ <path d="M 1427 4019
+C 1427 4281 1216 4480 966 4480
+C 704 4480 506 4262 506 4019
+C 506 3775 704 3558 966 3558
+C 1216 3558 1427 3756 1427 4019
+z
+M 301 2828
+L 301 2553
+C 678 2553 723 2553 723 2303
+L 723 275
+L 282 275
+L 282 0
+C 429 12 870 12 1043 12
+C 1222 12 1632 12 1786 0
+L 1786 275
+L 1389 275
+L 1389 2880
+L 301 2828
+z
+" id="CMBX12-69" transform="scale(0.015625)"/>
+ <path d="M 3398 1958
+C 3398 2566 3136 2880 2432 2880
+C 1786 2880 1472 2425 1382 2233
+L 1376 2233
+L 1376 4480
+L 269 4428
+L 269 4153
+C 666 4153 710 4153 710 3896
+L 710 275
+L 269 275
+L 269 0
+C 416 12 877 12 1056 12
+C 1235 12 1702 12 1850 0
+L 1850 275
+L 1408 275
+L 1408 1638
+C 1408 2329 1920 2668 2330 2668
+C 2566 2668 2701 2515 2701 2028
+L 2701 275
+L 2259 275
+L 2259 0
+C 2406 12 2867 12 3046 12
+C 3226 12 3693 12 3840 0
+L 3840 275
+L 3398 275
+L 3398 1958
+z
+" id="CMBX12-68" transform="scale(0.015625)"/>
+ <path d="M 1389 2540
+L 2118 2540
+L 2118 2816
+L 1357 2816
+L 1357 3466
+C 1357 4122 1779 4224 1990 4224
+C 2061 4224 2074 4217 2112 4204
+C 2016 4141 1958 4034 1958 3901
+C 1958 3649 2163 3535 2330 3535
+C 2470 3535 2701 3630 2701 3908
+C 2701 4167 2470 4435 2016 4435
+C 1434 4435 723 4192 723 3459
+L 723 2816
+L 250 2816
+L 250 2540
+L 723 2540
+L 723 275
+L 282 275
+L 282 0
+C 429 12 909 12 1088 12
+C 1274 12 1792 12 1946 0
+L 1946 275
+L 1389 275
+L 1389 2540
+z
+" id="CMBX12-66" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMBX12-4d"/>
+ <use transform="translate(106.314425 0)scale(0.996264)" xlink:href="#CMBX12-6f"/>
+ <use transform="translate(165.467601 0)scale(0.996264)" xlink:href="#CMBX12-64"/>
+ <use transform="translate(227.734101 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(278.873369 0)scale(0.996264)" xlink:href="#CMBX12-6c"/>
+ <use transform="translate(347.366519 0)scale(0.996264)" xlink:href="#CMBX12-77"/>
+ <use transform="translate(425.199645 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(476.338912 0)scale(0.996264)" xlink:href="#CMBX12-69"/>
+ <use transform="translate(507.472162 0)scale(0.996264)" xlink:href="#CMBX12-67"/>
+ <use transform="translate(563.512013 0)scale(0.996264)" xlink:href="#CMBX12-68"/>
+ <use transform="translate(622.665189 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(703.611639 0)scale(0.996264)" xlink:href="#CMBX12-66"/>
+ <use transform="translate(737.858215 0)scale(0.996264)" xlink:href="#CMBX12-6f"/>
+ <use transform="translate(793.898065 0)scale(0.996264)" xlink:href="#CMBX12-72"/>
+ <use transform="translate(839.675573 0)scale(0.996264)" xlink:href="#CMBX12-3a"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_10">
+ <!-- 0.29 -->
+ <g style="fill:#262626;" transform="translate(191.966522 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2688 2038
+C 2688 2430 2682 3099 2413 3613
+C 2176 4063 1798 4224 1466 4224
+C 1158 4224 768 4082 525 3620
+C 269 3137 243 2539 243 2038
+C 243 1671 250 1112 448 623
+C 723 -39 1216 -128 1466 -128
+C 1760 -128 2208 -7 2470 604
+C 2662 1048 2688 1568 2688 2038
+z
+M 1466 -26
+C 1056 -26 813 328 723 816
+C 653 1196 653 1749 653 2109
+C 653 2604 653 3015 736 3407
+C 858 3954 1216 4121 1466 4121
+C 1728 4121 2067 3947 2189 3420
+C 2272 3054 2278 2623 2278 2109
+C 2278 1691 2278 1176 2202 797
+C 2067 96 1690 -26 1466 -26
+z
+" id="CMR17-30" transform="scale(0.015625)"/>
+ <path d="M 1062 262
+C 1062 422 934 524 800 524
+C 672 524 538 422 538 262
+C 538 102 666 0 800 0
+C 928 0 1062 102 1062 262
+z
+" id="CMR17-2e" transform="scale(0.015625)"/>
+ <path d="M 2669 990
+L 2554 990
+C 2490 537 2438 460 2413 422
+C 2381 371 1920 371 1830 371
+L 602 371
+C 832 620 1280 1073 1824 1596
+C 2214 1966 2669 2400 2669 3033
+C 2669 3788 2067 4224 1395 4224
+C 691 4224 262 3603 262 3027
+C 262 2777 448 2745 525 2745
+C 589 2745 781 2783 781 3007
+C 781 3206 614 3264 525 3264
+C 486 3264 448 3257 422 3244
+C 544 3788 915 4057 1306 4057
+C 1862 4057 2227 3616 2227 3033
+C 2227 2477 1901 1998 1536 1583
+L 262 147
+L 262 0
+L 2515 0
+L 2669 990
+z
+" id="CMR17-32" transform="scale(0.015625)"/>
+ <path d="M 2253 1871
+C 2253 448 1670 25 1190 25
+C 1043 25 685 43 538 281
+C 704 256 826 345 826 505
+C 826 678 685 736 595 736
+C 538 736 365 710 365 492
+C 365 68 742 -128 1203 -128
+C 1939 -128 2688 665 2688 2090
+C 2688 3857 1971 4224 1485 4224
+C 851 4224 243 3664 243 2800
+C 243 2000 762 1408 1414 1408
+C 1952 1408 2189 1910 2253 2122
+L 2253 1871
+z
+M 1427 1510
+C 1254 1510 1011 1542 813 1929
+C 678 2181 678 2477 678 2793
+C 678 3174 678 3438 858 3722
+C 947 3857 1114 4076 1485 4076
+C 2240 4076 2240 2909 2240 2651
+C 2240 2193 2035 1510 1427 1510
+z
+" id="CMR17-39" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-39"/>
+ </g>
+ </g>
+ <g id="text_11">
+ <!-- 0.71 -->
+ <g style="fill:#ffffff;" transform="translate(459.806522 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2886 3955
+L 2886 4096
+L 1382 4096
+C 634 4096 621 4166 595 4288
+L 480 4288
+L 294 3104
+L 410 3104
+C 429 3226 474 3552 550 3673
+C 589 3724 1062 3724 1171 3724
+L 2579 3724
+L 1869 2670
+C 1395 1961 1069 1003 1069 166
+C 1069 89 1069 -128 1299 -128
+C 1530 -128 1530 89 1530 172
+L 1530 466
+C 1530 1514 1709 2204 2003 2644
+L 2886 3955
+z
+" id="CMR17-37" transform="scale(0.015625)"/>
+ <path d="M 1702 4083
+C 1702 4217 1696 4224 1606 4224
+C 1357 3927 979 3833 621 3820
+C 602 3820 570 3820 563 3808
+C 557 3795 557 3782 557 3648
+C 755 3648 1088 3686 1344 3839
+L 1344 467
+C 1344 243 1331 166 781 166
+L 589 166
+L 589 0
+C 896 6 1216 12 1523 12
+C 1830 12 2150 6 2458 0
+L 2458 166
+L 2266 166
+C 1715 166 1702 236 1702 467
+L 1702 4083
+z
+" id="CMR17-31" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-37"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ <g id="text_12">
+ <!-- 0.19 -->
+ <g style="fill:#262626;" transform="translate(727.646522 228.955463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-39"/>
+ </g>
+ </g>
+ <g id="text_13">
+ <!-- 0.19 -->
+ <g style="fill:#262626;" transform="translate(995.486522 228.955463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-39"/>
+ </g>
+ </g>
+ <g id="text_14">
+ <!-- 0.36 -->
+ <g style="fill:#262626;" transform="translate(191.966522 518.875463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1414 2176
+C 1984 2176 2234 1673 2234 1094
+C 2234 322 1824 25 1453 25
+C 1114 25 563 193 390 691
+C 422 678 454 678 486 678
+C 640 678 755 780 755 947
+C 755 1132 614 1216 486 1216
+C 378 1216 211 1164 211 927
+C 211 335 787 -128 1466 -128
+C 2176 -128 2720 432 2720 1087
+C 2720 1718 2208 2176 1600 2246
+C 2086 2347 2554 2776 2554 3353
+C 2554 3856 2048 4224 1472 4224
+C 890 4224 378 3862 378 3347
+C 378 3123 544 3084 627 3084
+C 762 3084 877 3167 877 3334
+C 877 3500 762 3584 627 3584
+C 602 3584 570 3584 544 3571
+C 730 3999 1235 4076 1459 4076
+C 1683 4076 2106 3966 2106 3347
+C 2106 3167 2080 2851 1862 2574
+C 1670 2329 1453 2316 1242 2297
+C 1210 2297 1062 2284 1037 2284
+C 992 2278 966 2272 966 2227
+C 966 2182 973 2176 1101 2176
+L 1414 2176
+z
+" id="CMR17-33" transform="scale(0.015625)"/>
+ <path d="M 678 2198
+C 678 3712 1395 4076 1811 4076
+C 1946 4076 2272 4049 2400 3782
+C 2298 3782 2106 3782 2106 3558
+C 2106 3385 2246 3328 2336 3328
+C 2394 3328 2566 3353 2566 3571
+C 2566 3987 2246 4224 1805 4224
+C 1043 4224 243 3411 243 2011
+C 243 257 966 -128 1478 -128
+C 2099 -128 2688 431 2688 1295
+C 2688 2101 2170 2688 1517 2688
+C 1126 2688 838 2430 678 1979
+L 678 2198
+z
+M 1478 25
+C 691 25 691 1212 691 1450
+C 691 1914 909 2585 1504 2585
+C 1613 2585 1926 2585 2138 2140
+C 2253 1889 2253 1624 2253 1302
+C 2253 954 2253 696 2118 438
+C 1978 173 1773 25 1478 25
+z
+" id="CMR17-36" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ <g id="text_15">
+ <!-- 0.15 -->
+ <g style="fill:#262626;" transform="translate(459.806522 518.875463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 730 3750
+C 794 3724 1056 3641 1325 3641
+C 1920 3641 2246 3961 2432 4140
+C 2432 4191 2432 4224 2394 4224
+C 2387 4224 2374 4224 2323 4198
+C 2099 4102 1837 4032 1517 4032
+C 1325 4032 1037 4055 723 4191
+C 653 4224 640 4224 634 4224
+C 602 4224 595 4217 595 4090
+L 595 2231
+C 595 2113 595 2080 659 2080
+C 691 2080 704 2093 736 2139
+C 941 2435 1222 2560 1542 2560
+C 1766 2560 2246 2415 2246 1293
+C 2246 1087 2246 716 2054 422
+C 1894 159 1645 25 1370 25
+C 947 25 518 319 403 812
+C 429 806 480 793 506 793
+C 589 793 749 838 749 1036
+C 749 1209 627 1280 506 1280
+C 358 1280 262 1190 262 1011
+C 262 454 704 -128 1382 -128
+C 2042 -128 2669 441 2669 1267
+C 2669 2054 2170 2662 1549 2662
+C 1222 2662 947 2540 730 2304
+L 730 3750
+z
+" id="CMR17-35" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_16">
+ <!-- 0.4 -->
+ <g style="fill:#262626;" transform="translate(734.500094 518.875463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2150 4147
+C 2150 4281 2144 4288 2029 4288
+L 128 1254
+L 128 1088
+L 1779 1088
+L 1779 460
+C 1779 230 1766 166 1318 166
+L 1197 166
+L 1197 0
+C 1402 12 1747 12 1965 12
+C 2182 12 2528 12 2733 0
+L 2733 166
+L 2611 166
+C 2163 166 2150 230 2150 460
+L 2150 1088
+L 2803 1088
+L 2803 1254
+L 2150 1254
+L 2150 4147
+z
+M 1798 3723
+L 1798 1254
+L 256 1254
+L 1798 3723
+z
+" id="CMR17-34" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ <g id="text_17">
+ <!-- 0.4 -->
+ <g style="fill:#262626;" transform="translate(1002.340094 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ <g id="text_18">
+ <!-- 0.35 -->
+ <g style="fill:#262626;" transform="translate(191.966522 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_19">
+ <!-- 0.15 -->
+ <g style="fill:#262626;" transform="translate(459.806522 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_20">
+ <!-- 0.4 -->
+ <g style="fill:#262626;" transform="translate(734.500094 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ <g id="text_21">
+ <!-- 0.4 -->
+ <g style="fill:#262626;" transform="translate(1002.340094 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="axes_2">
+ <g id="patch_3">
+ <path d="M 1220.657891 946.284441
+L 1264.145891 946.284441
+L 1264.145891 76.524441
+L 1220.657891 76.524441
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="patch_4">
+ <path clip-path="url(#p638d850c7b)" d="M 1220.657891 946.284441
+L 1220.657891 942.886941
+L 1220.657891 79.921941
+L 1220.657891 76.524441
+L 1264.145891 76.524441
+L 1264.145891 79.921941
+L 1264.145891 942.886941
+L 1264.145891 946.284441
+L 1264.145891 946.284441
+z
+" style="fill:#ffffff;stroke:#ffffff;stroke-linejoin:miter;stroke-width:0.01;"/>
+ </g>
+ <image height="870" id="imagebb63b95cf5" transform="scale(1 -1)translate(0 -870)" width="43" x="1221" xlink:href="data:image/png;base64,
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" y="-76"/>
+ <g id="matplotlib.axis_3"/>
+ <g id="matplotlib.axis_4">
+ <g id="ytick_4">
+ <g id="line2d_8">
+ <defs>
+ <path d="M 0 0
+L 3.5 0
+" id="mc89ad4dc12" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#mc89ad4dc12" y="861.575857"/>
+ </g>
+ </g>
+ <g id="text_22">
+ <!-- $\mathdefault{0.2}$ -->
+ <g transform="translate(1271.145891 871.953604)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1178 307
+C 1178 492 1024 620 870 620
+C 685 620 557 467 557 313
+C 557 128 710 0 864 0
+C 1050 0 1178 153 1178 307
+z
+" id="CMMI12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_5">
+ <g id="line2d_9">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#mc89ad4dc12" y="707.290216"/>
+ </g>
+ </g>
+ <g id="text_23">
+ <!-- $\mathdefault{0.3}$ -->
+ <g transform="translate(1271.145891 717.667964)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_6">
+ <g id="line2d_10">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#mc89ad4dc12" y="553.004576"/>
+ </g>
+ </g>
+ <g id="text_24">
+ <!-- $\mathdefault{0.4}$ -->
+ <g transform="translate(1271.145891 563.382323)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_7">
+ <g id="line2d_11">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#mc89ad4dc12" y="398.718935"/>
+ </g>
+ </g>
+ <g id="text_25">
+ <!-- $\mathdefault{0.5}$ -->
+ <g transform="translate(1271.145891 409.096682)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_8">
+ <g id="line2d_12">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#mc89ad4dc12" y="244.433294"/>
+ </g>
+ </g>
+ <g id="text_26">
+ <!-- $\mathdefault{0.6}$ -->
+ <g transform="translate(1271.145891 254.811042)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_9">
+ <g id="line2d_13">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#mc89ad4dc12" y="90.147654"/>
+ </g>
+ </g>
+ <g id="text_27">
+ <!-- $\mathdefault{0.7}$ -->
+ <g transform="translate(1271.145891 100.525401)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-37"/>
+ </g>
+ </g>
+ </g>
+ </g>
+ <g id="LineCollection_1"/>
+ <g id="patch_5">
+ <path d="M 1220.657891 946.284441
+L 1220.657891 942.886941
+L 1220.657891 79.921941
+L 1220.657891 76.524441
+L 1264.145891 76.524441
+L 1264.145891 79.921941
+L 1264.145891 942.886941
+L 1264.145891 946.284441
+z
+" style="fill:none;"/>
+ </g>
+ </g>
+ </g>
+ <defs>
+ <clipPath id="pc5cc66efae">
+ <rect height="869.76" width="1071.36" x="82.337891" y="76.524441"/>
+ </clipPath>
+ <clipPath id="p638d850c7b">
+ <rect height="869.76" width="43.488" x="1220.657891" y="76.524441"/>
+ </clipPath>
+ </defs>
+</svg>
diff --git a/examples/model-comparison/reference/confusionMatrix_ND_3.svg b/examples/model-comparison/reference/confusionMatrix_ND_3.svg
new file mode 100644
index 0000000000000000000000000000000000000000..8bfe4259be5437dc668348180a2406627cb21238
--- /dev/null
+++ b/examples/model-comparison/reference/confusionMatrix_ND_3.svg
@@ -0,0 +1,1573 @@
+<?xml version="1.0" encoding="utf-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<svg height="953.484441pt" version="1.1" viewBox="0 0 1313.889331 953.484441" width="1313.889331pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+ <metadata>
+ <rdf:RDF xmlns:cc="http://creativecommons.org/ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
+ <cc:Work>
+ <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
+ <dc:date>2022-06-03T16:06:06.149900</dc:date>
+ <dc:format>image/svg+xml</dc:format>
+ <dc:creator>
+ <cc:Agent>
+ <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>
+ </cc:Agent>
+ </dc:creator>
+ </cc:Work>
+ </rdf:RDF>
+ </metadata>
+ <defs>
+ <style type="text/css">*{stroke-linecap:butt;stroke-linejoin:round;}</style>
+ </defs>
+ <g id="figure_1">
+ <g id="patch_1">
+ <path d="M 0 953.484441
+L 1313.889331 953.484441
+L 1313.889331 0
+L 0 0
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="axes_1">
+ <g id="patch_2">
+ <path d="M 82.337891 946.284441
+L 1153.697891 946.284441
+L 1153.697891 76.524441
+L 82.337891 76.524441
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="QuadMesh_1">
+ <path clip-path="url(#pcc8f1eefc5)" d="M 82.337891 76.524441
+L 350.177891 76.524441
+L 350.177891 366.444441
+L 82.337891 366.444441
+L 82.337891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#pcc8f1eefc5)" d="M 350.177891 76.524441
+L 618.017891 76.524441
+L 618.017891 366.444441
+L 350.177891 366.444441
+L 350.177891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#pcc8f1eefc5)" d="M 618.017891 76.524441
+L 885.857891 76.524441
+L 885.857891 366.444441
+L 618.017891 366.444441
+L 618.017891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#pcc8f1eefc5)" d="M 885.857891 76.524441
+L 1153.697891 76.524441
+L 1153.697891 366.444441
+L 885.857891 366.444441
+L 885.857891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#pcc8f1eefc5)" d="M 82.337891 366.444441
+L 350.177891 366.444441
+L 350.177891 656.364441
+L 82.337891 656.364441
+L 82.337891 366.444441
+" style="fill:#083d7f;"/>
+ <path clip-path="url(#pcc8f1eefc5)" d="M 350.177891 366.444441
+L 618.017891 366.444441
+L 618.017891 656.364441
+L 350.177891 656.364441
+L 350.177891 366.444441
+" style="fill:#083674;"/>
+ <path clip-path="url(#pcc8f1eefc5)" d="M 618.017891 366.444441
+L 885.857891 366.444441
+L 885.857891 656.364441
+L 618.017891 656.364441
+L 618.017891 366.444441
+" style="fill:#083c7d;"/>
+ <path clip-path="url(#pcc8f1eefc5)" d="M 885.857891 366.444441
+L 1153.697891 366.444441
+L 1153.697891 656.364441
+L 885.857891 656.364441
+L 885.857891 366.444441
+" style="fill:#083c7d;"/>
+ <path clip-path="url(#pcc8f1eefc5)" d="M 82.337891 656.364441
+L 350.177891 656.364441
+L 350.177891 946.284441
+L 82.337891 946.284441
+L 82.337891 656.364441
+" style="fill:#08306b;"/>
+ <path clip-path="url(#pcc8f1eefc5)" d="M 350.177891 656.364441
+L 618.017891 656.364441
+L 618.017891 946.284441
+L 350.177891 946.284441
+L 350.177891 656.364441
+" style="fill:#083776;"/>
+ <path clip-path="url(#pcc8f1eefc5)" d="M 618.017891 656.364441
+L 885.857891 656.364441
+L 885.857891 946.284441
+L 618.017891 946.284441
+L 618.017891 656.364441
+" style="fill:#08316d;"/>
+ <path clip-path="url(#pcc8f1eefc5)" d="M 885.857891 656.364441
+L 1153.697891 656.364441
+L 1153.697891 946.284441
+L 885.857891 946.284441
+L 885.857891 656.364441
+" style="fill:#08316d;"/>
+ </g>
+ <g id="matplotlib.axis_1">
+ <g id="xtick_1">
+ <g id="line2d_1">
+ <defs>
+ <path d="M 0 0
+L 0 -3.5
+" id="mc693ec92f0" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="216.257891" xlink:href="#mc693ec92f0" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_1">
+ <!-- Observation -->
+ <g transform="translate(144.303789 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 4307 2166
+C 4307 3488 3366 4480 2304 4480
+C 1216 4480 294 3475 294 2166
+C 294 857 1229 -128 2298 -128
+C 3392 -128 4307 876 4307 2166
+z
+M 2304 -13
+C 1574 -13 781 722 781 2250
+C 781 3771 1651 4364 2298 4364
+C 2976 4364 3821 3752 3821 2250
+C 3821 696 3008 -13 2304 -13
+z
+" id="CMR17-4f" transform="scale(0.015625)"/>
+ <path d="M 960 4416
+L 198 4345
+L 198 4179
+C 576 4179 634 4141 634 3843
+L 634 -13
+L 749 -13
+L 934 445
+C 1120 141 1395 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2209 2477 2816 1830 2816
+C 1434 2816 1152 2603 960 2351
+L 960 4416
+z
+M 973 2022
+C 973 2138 973 2157 1062 2293
+C 1312 2681 1670 2713 1792 2713
+C 1984 2713 2643 2610 2643 1388
+C 2643 109 1888 38 1734 38
+C 1536 38 1248 115 1043 490
+C 973 613 973 626 973 742
+L 973 2022
+z
+" id="CMR17-62" transform="scale(0.015625)"/>
+ <path d="M 1978 2688
+C 1978 2803 1971 2809 1933 2809
+C 1907 2809 1901 2803 1824 2707
+C 1805 2681 1747 2617 1728 2592
+C 1523 2809 1235 2816 1126 2816
+C 416 2816 160 2444 160 2073
+C 160 1497 813 1363 998 1324
+C 1402 1241 1542 1216 1677 1100
+C 1760 1024 1901 883 1901 652
+C 1901 384 1747 38 1158 38
+C 602 38 403 460 288 1024
+C 269 1113 269 1120 218 1120
+C 166 1120 160 1113 160 985
+L 160 64
+C 160 -52 166 -58 205 -58
+C 237 -58 243 -52 275 0
+C 314 57 410 211 448 275
+C 576 102 800 -64 1158 -64
+C 1792 -64 2131 281 2131 780
+C 2131 1107 1958 1280 1875 1356
+C 1683 1555 1459 1600 1190 1651
+C 838 1728 390 1817 390 2208
+C 390 2374 480 2726 1126 2726
+C 1811 2726 1850 2086 1862 1881
+C 1869 1849 1901 1843 1920 1843
+C 1978 1843 1978 1862 1978 1971
+L 1978 2688
+z
+" id="CMR17-73" transform="scale(0.015625)"/>
+ <path d="M 2438 1503
+C 2464 1529 2464 1542 2464 1606
+C 2464 2251 2118 2816 1389 2816
+C 710 2816 173 2175 173 1394
+C 173 554 781 -64 1459 -64
+C 2176 -64 2458 619 2458 755
+C 2458 800 2419 800 2406 800
+C 2362 800 2355 787 2330 709
+C 2189 270 1837 51 1504 51
+C 1229 51 954 206 781 490
+C 582 819 582 1200 582 1503
+L 2438 1503
+z
+M 589 1600
+C 634 2511 1126 2713 1382 2713
+C 1818 2713 2112 2308 2118 1600
+L 589 1600
+z
+" id="CMR17-65" transform="scale(0.015625)"/>
+ <path d="M 960 1517
+C 960 2134 1222 2713 1702 2713
+C 1747 2713 1792 2707 1837 2687
+C 1837 2687 1696 2642 1696 2475
+C 1696 2321 1818 2257 1914 2257
+C 1990 2257 2131 2302 2131 2482
+C 2131 2687 1926 2816 1709 2816
+C 1222 2816 1011 2340 947 2115
+L 941 2115
+L 941 2816
+L 198 2745
+L 198 2578
+C 576 2578 634 2540 634 2231
+L 634 443
+C 634 198 608 166 198 166
+L 198 0
+C 352 12 646 12 813 12
+C 998 12 1325 12 1498 0
+L 1498 166
+C 1037 166 960 166 960 455
+L 960 1517
+z
+" id="CMR17-72" transform="scale(0.015625)"/>
+ <path d="M 2502 2173
+C 2560 2315 2662 2572 3034 2585
+L 3034 2752
+C 2912 2745 2752 2739 2630 2739
+C 2496 2739 2285 2739 2157 2752
+L 2157 2585
+C 2317 2572 2406 2495 2406 2328
+C 2406 2270 2406 2257 2368 2167
+L 1664 379
+L 902 2308
+C 864 2392 864 2405 864 2431
+C 864 2585 1075 2585 1171 2585
+L 1171 2752
+C 1018 2739 736 2739 576 2739
+C 403 2739 205 2739 64 2752
+L 64 2585
+C 307 2585 442 2585 518 2386
+L 1446 44
+C 1485 -52 1491 -64 1549 -64
+C 1606 -64 1613 -52 1651 44
+L 2502 2173
+z
+" id="CMR17-76" transform="scale(0.015625)"/>
+ <path d="M 2304 1656
+C 2304 2048 2304 2275 2035 2534
+C 1798 2751 1523 2816 1306 2816
+C 800 2816 435 2408 435 1977
+C 435 1740 627 1728 666 1728
+C 749 1728 896 1779 896 1958
+C 896 2118 774 2188 666 2188
+C 640 2188 608 2182 589 2176
+C 723 2594 1069 2713 1293 2713
+C 1613 2713 1965 2421 1965 1875
+L 1965 1632
+C 1587 1619 1133 1568 774 1373
+C 371 1147 256 822 256 576
+C 256 77 832 -64 1171 -64
+C 1523 -64 1850 135 1990 505
+C 2003 219 2182 -39 2464 -39
+C 2598 -39 2938 51 2938 563
+L 2938 926
+L 2822 926
+L 2822 557
+C 2822 161 2650 109 2566 109
+C 2304 109 2304 446 2304 732
+L 2304 1656
+z
+M 1965 887
+C 1965 323 1568 38 1216 38
+C 896 38 646 278 646 576
+C 646 771 730 1114 1101 1322
+C 1408 1497 1760 1523 1965 1536
+L 1965 887
+z
+" id="CMR17-61" transform="scale(0.015625)"/>
+ <path d="M 966 2585
+L 1862 2585
+L 1862 2752
+L 966 2752
+L 966 3968
+L 851 3968
+C 838 3292 614 2700 70 2687
+L 70 2585
+L 627 2585
+L 627 778
+C 627 655 627 -64 1370 -64
+C 1747 -64 1965 308 1965 784
+L 1965 1151
+L 1850 1151
+L 1850 790
+C 1850 347 1677 51 1408 51
+C 1222 51 966 179 966 765
+L 966 2585
+z
+" id="CMR17-74" transform="scale(0.015625)"/>
+ <path d="M 992 3961
+C 992 4102 877 4224 730 4224
+C 589 4224 467 4108 467 3961
+C 467 3820 582 3699 730 3699
+C 870 3699 992 3814 992 3961
+z
+M 243 2745
+L 243 2579
+C 602 2579 653 2540 653 2231
+L 653 443
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 646 12 806 12
+C 960 12 1222 12 1370 0
+L 1370 166
+C 992 166 979 205 979 436
+L 979 2816
+L 243 2745
+z
+" id="CMR17-69" transform="scale(0.015625)"/>
+ <path d="M 2758 1356
+C 2758 2176 2163 2816 1466 2816
+C 768 2816 173 2176 173 1356
+C 173 550 768 -64 1466 -64
+C 2163 -64 2758 550 2758 1356
+z
+M 1466 51
+C 1165 51 909 230 762 480
+C 602 768 582 1126 582 1408
+C 582 1676 595 2009 762 2297
+C 890 2508 1139 2713 1466 2713
+C 1754 2713 1997 2553 2150 2329
+C 2349 2028 2349 1606 2349 1408
+C 2349 1158 2336 774 2163 467
+C 1984 172 1709 51 1466 51
+z
+" id="CMR17-6f" transform="scale(0.015625)"/>
+ <path d="M 2656 1954
+C 2656 2282 2592 2816 1837 2816
+C 1331 2816 1069 2424 973 2166
+L 966 2166
+L 966 2816
+L 211 2745
+L 211 2578
+C 589 2578 646 2540 646 2231
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1954
+z
+" id="CMR17-6e" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-4f"/>
+ <use transform="translate(71.714788 0)scale(0.996264)" xlink:href="#CMR17-62"/>
+ <use transform="translate(122.610158 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(158.411496 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(198.897156 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ <use transform="translate(234.177924 0)scale(0.996264)" xlink:href="#CMR17-76"/>
+ <use transform="translate(277.266023 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(322.9565 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(358.237268 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(383.108327 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(428.798804 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_2">
+ <g id="line2d_2">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="484.097891" xlink:href="#mc693ec92f0" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_2">
+ <!-- linear -->
+ <g transform="translate(450.783747 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 979 4416
+L 218 4345
+L 218 4179
+C 595 4179 653 4141 653 3835
+L 653 439
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 653 12 813 12
+C 979 12 1261 12 1414 0
+L 1414 166
+C 1005 166 979 191 979 439
+L 979 4416
+z
+" id="CMR17-6c" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_3">
+ <g id="line2d_3">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="751.937891" xlink:href="#mc693ec92f0" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_3">
+ <!-- exponential -->
+ <g transform="translate(683.18479 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1664 1491
+C 1856 1740 2074 2022 2253 2233
+C 2464 2476 2707 2579 2989 2585
+L 2989 2752
+C 2880 2745 2656 2739 2541 2739
+C 2368 2739 2170 2739 2022 2752
+L 2022 2585
+C 2112 2572 2163 2508 2163 2419
+C 2163 2304 2099 2233 2067 2188
+L 1594 1587
+L 1030 2323
+C 973 2393 973 2406 973 2438
+C 973 2515 1037 2579 1146 2585
+L 1146 2752
+C 992 2739 717 2739 557 2739
+C 384 2739 179 2739 38 2752
+L 38 2585
+C 384 2585 461 2560 614 2368
+L 1350 1414
+C 1363 1401 1395 1363 1395 1344
+C 1395 1318 838 633 768 544
+C 480 198 179 172 6 166
+L 6 0
+C 115 6 339 12 454 12
+C 582 12 864 12 979 0
+L 979 166
+C 941 172 838 185 838 332
+C 838 448 890 518 947 595
+L 1478 1248
+L 2035 524
+C 2086 454 2163 358 2163 313
+C 2163 224 2086 172 1984 166
+L 1984 0
+C 2138 12 2413 12 2573 12
+C 2746 12 2950 12 3091 0
+L 3091 166
+C 2771 166 2675 179 2522 377
+L 1664 1491
+z
+" id="CMR17-78" transform="scale(0.015625)"/>
+ <path d="M 1408 -1114
+C 998 -1114 973 -1088 973 -834
+L 973 380
+C 1158 109 1427 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2196 2496 2816 1837 2816
+C 1453 2816 1139 2603 960 2345
+L 960 2816
+L 198 2745
+L 198 2577
+C 576 2577 634 2539 634 2228
+L 634 -834
+C 634 -1081 608 -1114 198 -1114
+L 198 -1280
+C 352 -1268 634 -1268 800 -1268
+C 966 -1268 1254 -1268 1408 -1280
+L 1408 -1114
+z
+M 973 2015
+C 973 2106 973 2241 1222 2481
+C 1254 2506 1472 2700 1792 2700
+C 2259 2700 2643 2112 2643 1376
+C 2643 639 2234 38 1728 38
+C 1498 38 1248 148 1056 451
+C 973 594 973 632 973 736
+L 973 2015
+z
+" id="CMR17-70" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_4">
+ <g id="line2d_4">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1019.777891" xlink:href="#mc693ec92f0" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_4">
+ <!-- cosine -->
+ <g transform="translate(984.043472 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2234 2240
+C 2112 2240 1933 2240 1933 2015
+C 1933 1836 2080 1785 2163 1785
+C 2208 1785 2394 1804 2394 2028
+C 2394 2476 1958 2816 1466 2816
+C 787 2816 211 2201 211 1379
+C 211 521 813 -64 1466 -64
+C 2259 -64 2458 676 2458 747
+C 2458 773 2451 792 2406 792
+C 2362 792 2355 786 2330 702
+C 2163 180 1798 51 1523 51
+C 1114 51 621 431 621 1385
+C 621 2358 1094 2700 1472 2700
+C 1722 2700 2093 2582 2234 2240
+z
+" id="CMR17-63" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_5">
+ <!-- \textbf{Data generated by:} -->
+ <g transform="translate(476.949653 27.955495)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 243 4416
+L 243 4140
+L 922 4140
+L 922 275
+L 243 275
+L 243 0
+L 2938 0
+C 4166 0 5114 790 5114 2169
+C 5114 3625 4141 4416 2938 4416
+L 243 4416
+z
+M 1734 275
+L 1734 4140
+L 2694 4140
+C 3251 4140 3699 3921 3936 3586
+C 4122 3322 4243 3006 4243 2175
+C 4243 1421 4147 1086 3923 784
+C 3699 487 3270 275 2694 275
+L 1734 275
+z
+" id="CMBX12-44" transform="scale(0.015625)"/>
+ <path d="M 2944 1894
+C 2944 2483 2477 2880 1574 2880
+C 1216 2880 461 2847 461 2310
+C 461 2041 666 1926 838 1926
+C 1030 1926 1216 2060 1216 2303
+C 1216 2425 1171 2540 1062 2611
+C 1274 2668 1427 2668 1549 2668
+C 1984 2668 2246 2425 2246 1900
+L 2246 1644
+C 1235 1644 218 1362 218 648
+C 218 64 960 -64 1402 -64
+C 1894 -64 2208 205 2336 488
+C 2336 250 2336 -26 2982 -26
+L 3309 -26
+C 3443 -26 3494 -26 3494 115
+C 3494 250 3437 250 3347 250
+C 2944 256 2944 359 2944 507
+L 2944 1894
+z
+M 2246 867
+C 2246 262 1709 147 1504 147
+C 1190 147 928 359 928 655
+C 928 1240 1619 1439 2246 1472
+L 2246 867
+z
+" id="CMBX12-61" transform="scale(0.015625)"/>
+ <path d="M 1350 2540
+L 2272 2540
+L 2272 2816
+L 1350 2816
+L 1350 4032
+L 1082 4032
+C 1075 3401 768 2771 134 2751
+L 134 2540
+L 653 2540
+L 653 761
+C 653 83 1178 -64 1638 -64
+C 2112 -64 2394 294 2394 768
+L 2394 1107
+L 2125 1107
+L 2125 774
+C 2125 352 1933 166 1734 166
+C 1350 166 1350 595 1350 742
+L 1350 2540
+z
+" id="CMBX12-74" transform="scale(0.015625)"/>
+ <path d="M 832 1177
+C 1139 1011 1498 1011 1594 1011
+C 2477 1011 2829 1506 2829 1958
+C 2829 2287 2643 2519 2566 2584
+C 2752 2687 2906 2713 3014 2726
+C 2995 2694 2976 2668 2976 2584
+C 2976 2448 3066 2326 3232 2326
+C 3398 2326 3488 2448 3488 2584
+C 3488 2739 3373 2944 3104 2944
+C 2829 2944 2566 2809 2432 2694
+C 2170 2847 1920 2905 1594 2905
+C 710 2905 358 2410 358 1958
+C 358 1758 422 1493 691 1274
+C 582 1151 467 926 467 693
+C 467 416 614 179 749 76
+C 595 38 198 -109 198 -474
+C 198 -852 614 -1280 1792 -1280
+C 2854 -1280 3392 -935 3392 -455
+C 3392 108 3021 294 2861 371
+C 2554 524 2144 524 1581 524
+C 1421 524 1139 524 1107 531
+C 832 576 755 823 755 946
+C 755 998 762 1094 832 1177
+z
+M 1594 1216
+C 1037 1216 1037 1661 1037 1958
+C 1037 2255 1037 2700 1594 2700
+C 2150 2700 2150 2255 2150 1958
+C 2150 1661 2150 1216 1594 1216
+z
+M 1952 -64
+C 2419 -64 2867 -148 2867 -480
+C 2867 -704 2643 -1076 1798 -1076
+C 954 -1076 723 -717 723 -474
+C 723 -64 1126 -64 1222 -64
+L 1952 -64
+z
+" id="CMBX12-67" transform="scale(0.015625)"/>
+ <path d="M 2893 1408
+C 3040 1408 3078 1408 3078 1568
+C 3078 1758 3034 2232 2739 2529
+C 2470 2796 2112 2880 1741 2880
+C 742 2880 198 2232 198 1433
+C 198 523 858 -64 1824 -64
+C 2790 -64 3078 621 3078 731
+C 3078 829 2982 829 2944 829
+C 2842 829 2835 809 2797 725
+C 2630 302 2208 166 1901 166
+C 973 166 966 1043 966 1408
+L 2893 1408
+z
+M 966 1593
+C 979 1852 986 2099 1120 2327
+C 1242 2529 1466 2668 1741 2668
+C 2426 2668 2483 1909 2490 1593
+L 966 1593
+z
+" id="CMBX12-65" transform="scale(0.015625)"/>
+ <path d="M 3398 1958
+C 3398 2566 3136 2880 2432 2880
+C 1971 2880 1574 2656 1357 2176
+L 1350 2176
+L 1350 2880
+L 269 2828
+L 269 2553
+C 666 2553 710 2553 710 2304
+L 710 275
+L 269 275
+L 269 0
+C 416 12 877 12 1056 12
+C 1235 12 1702 12 1850 0
+L 1850 275
+L 1408 275
+L 1408 1638
+C 1408 2329 1920 2668 2330 2668
+C 2566 2668 2701 2515 2701 2028
+L 2701 275
+L 2259 275
+L 2259 0
+C 2406 12 2867 12 3046 12
+C 3226 12 3693 12 3840 0
+L 3840 275
+L 3398 275
+L 3398 1958
+z
+" id="CMBX12-6e" transform="scale(0.015625)"/>
+ <path d="M 1331 1440
+C 1331 1651 1376 2668 2125 2668
+C 2035 2598 1990 2489 1990 2374
+C 1990 2112 2202 2003 2362 2003
+C 2522 2003 2733 2112 2733 2374
+C 2733 2700 2400 2880 2093 2880
+C 1587 2880 1370 2438 1280 2169
+L 1274 2169
+L 1274 2880
+L 224 2828
+L 224 2553
+C 621 2553 666 2553 666 2304
+L 666 275
+L 224 275
+L 224 0
+C 371 12 851 12 1030 12
+C 1216 12 1734 12 1888 0
+L 1888 275
+L 1331 275
+L 1331 1440
+z
+" id="CMBX12-72" transform="scale(0.015625)"/>
+ <path d="M 2221 4428
+L 2221 4153
+C 2618 4153 2662 4153 2662 3896
+L 2662 2571
+C 2522 2694 2240 2880 1798 2880
+C 890 2880 243 2313 243 1408
+C 243 483 877 -64 1728 -64
+C 2080 -64 2381 57 2630 270
+L 2630 -64
+L 3770 -26
+L 3770 250
+C 3373 250 3328 250 3328 502
+L 3328 4480
+L 2221 4428
+z
+M 2630 625
+C 2362 231 2035 147 1805 147
+C 1011 147 1011 968 1011 1395
+C 1011 1699 1011 2022 1152 2268
+C 1350 2630 1728 2668 1875 2668
+C 2138 2668 2419 2552 2630 2268
+L 2630 625
+z
+" id="CMBX12-64" transform="scale(0.015625)"/>
+ <path d="M 1331 4480
+L 224 4428
+L 224 4153
+C 621 4153 666 4153 666 3896
+L 666 -26
+L 934 -26
+C 1043 96 1152 218 1254 347
+C 1581 6 1933 -64 2189 -64
+C 3072 -64 3750 476 3750 1414
+C 3750 2300 3149 2880 2272 2880
+C 1894 2880 1594 2758 1331 2552
+L 1331 4480
+z
+M 1363 2242
+C 1587 2552 1920 2668 2189 2668
+C 2982 2668 2982 1847 2982 1420
+C 2982 1130 2982 761 2829 522
+C 2630 211 2330 147 2125 147
+C 1690 147 1453 457 1363 599
+L 1363 2242
+z
+" id="CMBX12-62" transform="scale(0.015625)"/>
+ <path d="M 3168 2400
+C 3206 2489 3232 2540 3642 2540
+L 3642 2816
+C 3424 2803 3398 2803 3136 2803
+C 2963 2803 2950 2803 2586 2816
+L 2586 2540
+C 2592 2540 2893 2540 2893 2457
+C 2893 2438 2874 2400 2867 2381
+L 2118 780
+L 1299 2540
+L 1651 2540
+L 1651 2816
+C 1498 2803 1062 2803 883 2803
+C 698 2803 320 2803 154 2816
+L 154 2540
+L 563 2540
+L 1747 -8
+C 1715 -84 1626 -269 1594 -345
+C 1459 -631 1254 -1069 806 -1069
+C 781 -1069 704 -1069 634 -1031
+C 646 -1025 838 -949 838 -707
+C 838 -497 685 -364 493 -364
+C 294 -364 141 -497 141 -713
+C 141 -1012 422 -1280 806 -1280
+C 1331 -1280 1677 -809 1805 -529
+L 3168 2400
+z
+" id="CMBX12-79" transform="scale(0.015625)"/>
+ <path d="M 1459 2355
+C 1459 2617 1248 2816 998 2816
+C 749 2816 538 2617 538 2355
+C 538 2092 749 1894 998 1894
+C 1248 1894 1459 2092 1459 2355
+z
+M 1459 460
+C 1459 723 1248 921 998 921
+C 749 921 538 723 538 460
+C 538 198 749 0 998 0
+C 1248 0 1459 198 1459 460
+z
+" id="CMBX12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMBX12-44"/>
+ <use transform="translate(85.904786 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(140.387974 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(183.974524 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(275.817613 0)scale(0.996264)" xlink:href="#CMBX12-67"/>
+ <use transform="translate(331.857463 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(382.99673 0)scale(0.996264)" xlink:href="#CMBX12-6e"/>
+ <use transform="translate(445.263231 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(496.402498 0)scale(0.996264)" xlink:href="#CMBX12-72"/>
+ <use transform="translate(542.180006 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(596.663194 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(640.249744 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(691.389011 0)scale(0.996264)" xlink:href="#CMBX12-64"/>
+ <use transform="translate(791.015412 0)scale(0.996264)" xlink:href="#CMBX12-62"/>
+ <use transform="translate(850.168588 0)scale(0.996264)" xlink:href="#CMBX12-79"/>
+ <use transform="translate(909.321763 0)scale(0.996264)" xlink:href="#CMBX12-3a"/>
+ </g>
+ </g>
+ </g>
+ <g id="matplotlib.axis_2">
+ <g id="ytick_1">
+ <g id="line2d_5">
+ <defs>
+ <path d="M 0 0
+L -3.5 0
+" id="me8341da3b9" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#me8341da3b9" y="221.484441"/>
+ </g>
+ </g>
+ <g id="text_6">
+ <!-- linear -->
+ <g transform="translate(69.524441 277.73498)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_2">
+ <g id="line2d_6">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#me8341da3b9" y="511.404441"/>
+ </g>
+ </g>
+ <g id="text_7">
+ <!-- exponential -->
+ <g transform="translate(69.524441 638.532895)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_3">
+ <g id="line2d_7">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#me8341da3b9" y="801.324441"/>
+ </g>
+ </g>
+ <g id="text_8">
+ <!-- cosine -->
+ <g transform="translate(69.524441 862.415532)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_9">
+ <!-- \textbf{Model weight for:} -->
+ <g transform="translate(27.955495 642.025756)rotate(-90)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 3411 816
+L 1875 4281
+C 1818 4416 1760 4416 1626 4416
+L 262 4416
+L 262 4140
+L 941 4140
+L 941 468
+C 941 326 934 320 768 294
+C 653 281 525 275 410 275
+L 262 275
+L 262 0
+C 410 12 909 12 1088 12
+C 1267 12 1773 12 1920 0
+L 1920 275
+L 1773 275
+C 1600 275 1587 275 1434 294
+C 1248 320 1242 326 1242 468
+L 1242 4063
+L 1248 4063
+L 2989 134
+C 3021 64 3059 0 3168 0
+C 3277 0 3315 64 3347 134
+L 5120 4140
+L 5126 4140
+L 5126 275
+L 4448 275
+L 4448 0
+C 4621 12 5286 12 5504 12
+C 5722 12 6387 12 6560 0
+L 6560 275
+L 5882 275
+L 5882 4140
+L 6560 4140
+L 6560 4416
+L 5197 4416
+C 5062 4416 5005 4416 4947 4281
+L 3411 816
+z
+" id="CMBX12-4d" transform="scale(0.015625)"/>
+ <path d="M 3392 1379
+C 3392 2245 2803 2880 1798 2880
+C 755 2880 198 2213 198 1379
+C 198 538 787 -64 1792 -64
+C 2835 -64 3392 570 3392 1379
+z
+M 1798 166
+C 966 166 966 917 966 1443
+C 966 1744 966 2065 1088 2296
+C 1229 2553 1517 2668 1792 2668
+C 2157 2668 2387 2495 2496 2315
+C 2624 2084 2624 1751 2624 1443
+C 2624 910 2624 166 1798 166
+z
+" id="CMBX12-6f" transform="scale(0.015625)"/>
+ <path d="M 1389 4480
+L 282 4428
+L 282 4153
+C 678 4153 723 4153 723 3901
+L 723 275
+L 282 275
+L 282 0
+C 429 12 883 12 1056 12
+C 1229 12 1683 12 1830 0
+L 1830 275
+L 1389 275
+L 1389 4480
+z
+" id="CMBX12-6c" transform="scale(0.015625)"/>
+ <path d="M 4608 2386
+C 4653 2496 4672 2540 5043 2540
+L 5043 2816
+C 4858 2803 4774 2803 4544 2803
+C 4282 2803 4198 2803 3968 2816
+L 3968 2540
+C 4026 2540 4339 2540 4339 2457
+C 4339 2451 4339 2444 4314 2380
+L 3642 712
+L 2906 2540
+L 3270 2540
+L 3270 2816
+C 3117 2803 2739 2803 2566 2803
+C 2240 2803 2227 2803 1907 2816
+L 1907 2540
+L 2285 2540
+C 2304 2489 2336 2406 2362 2348
+C 2381 2309 2445 2155 2445 2123
+C 2445 2111 2426 2066 2419 2046
+L 1933 834
+L 1242 2540
+L 1606 2540
+L 1606 2816
+C 1459 2803 1024 2803 851 2803
+C 646 2803 339 2803 147 2816
+L 147 2540
+L 525 2540
+L 1504 96
+C 1549 -20 1574 -64 1715 -64
+C 1786 -64 1862 -64 1914 64
+L 2592 1764
+L 3270 76
+C 3328 -64 3398 -64 3475 -64
+C 3616 -64 3635 -26 3680 89
+L 4608 2386
+z
+" id="CMBX12-77" transform="scale(0.015625)"/>
+ <path d="M 1427 4019
+C 1427 4281 1216 4480 966 4480
+C 704 4480 506 4262 506 4019
+C 506 3775 704 3558 966 3558
+C 1216 3558 1427 3756 1427 4019
+z
+M 301 2828
+L 301 2553
+C 678 2553 723 2553 723 2303
+L 723 275
+L 282 275
+L 282 0
+C 429 12 870 12 1043 12
+C 1222 12 1632 12 1786 0
+L 1786 275
+L 1389 275
+L 1389 2880
+L 301 2828
+z
+" id="CMBX12-69" transform="scale(0.015625)"/>
+ <path d="M 3398 1958
+C 3398 2566 3136 2880 2432 2880
+C 1786 2880 1472 2425 1382 2233
+L 1376 2233
+L 1376 4480
+L 269 4428
+L 269 4153
+C 666 4153 710 4153 710 3896
+L 710 275
+L 269 275
+L 269 0
+C 416 12 877 12 1056 12
+C 1235 12 1702 12 1850 0
+L 1850 275
+L 1408 275
+L 1408 1638
+C 1408 2329 1920 2668 2330 2668
+C 2566 2668 2701 2515 2701 2028
+L 2701 275
+L 2259 275
+L 2259 0
+C 2406 12 2867 12 3046 12
+C 3226 12 3693 12 3840 0
+L 3840 275
+L 3398 275
+L 3398 1958
+z
+" id="CMBX12-68" transform="scale(0.015625)"/>
+ <path d="M 1389 2540
+L 2118 2540
+L 2118 2816
+L 1357 2816
+L 1357 3466
+C 1357 4122 1779 4224 1990 4224
+C 2061 4224 2074 4217 2112 4204
+C 2016 4141 1958 4034 1958 3901
+C 1958 3649 2163 3535 2330 3535
+C 2470 3535 2701 3630 2701 3908
+C 2701 4167 2470 4435 2016 4435
+C 1434 4435 723 4192 723 3459
+L 723 2816
+L 250 2816
+L 250 2540
+L 723 2540
+L 723 275
+L 282 275
+L 282 0
+C 429 12 909 12 1088 12
+C 1274 12 1792 12 1946 0
+L 1946 275
+L 1389 275
+L 1389 2540
+z
+" id="CMBX12-66" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMBX12-4d"/>
+ <use transform="translate(106.314425 0)scale(0.996264)" xlink:href="#CMBX12-6f"/>
+ <use transform="translate(165.467601 0)scale(0.996264)" xlink:href="#CMBX12-64"/>
+ <use transform="translate(227.734101 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(278.873369 0)scale(0.996264)" xlink:href="#CMBX12-6c"/>
+ <use transform="translate(347.366519 0)scale(0.996264)" xlink:href="#CMBX12-77"/>
+ <use transform="translate(425.199645 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(476.338912 0)scale(0.996264)" xlink:href="#CMBX12-69"/>
+ <use transform="translate(507.472162 0)scale(0.996264)" xlink:href="#CMBX12-67"/>
+ <use transform="translate(563.512013 0)scale(0.996264)" xlink:href="#CMBX12-68"/>
+ <use transform="translate(622.665189 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(703.611639 0)scale(0.996264)" xlink:href="#CMBX12-66"/>
+ <use transform="translate(737.858215 0)scale(0.996264)" xlink:href="#CMBX12-6f"/>
+ <use transform="translate(793.898065 0)scale(0.996264)" xlink:href="#CMBX12-72"/>
+ <use transform="translate(839.675573 0)scale(0.996264)" xlink:href="#CMBX12-3a"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_10">
+ <!-- 1.9e-05 -->
+ <g style="fill:#262626;" transform="translate(174.52871 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1702 4083
+C 1702 4217 1696 4224 1606 4224
+C 1357 3927 979 3833 621 3820
+C 602 3820 570 3820 563 3808
+C 557 3795 557 3782 557 3648
+C 755 3648 1088 3686 1344 3839
+L 1344 467
+C 1344 243 1331 166 781 166
+L 589 166
+L 589 0
+C 896 6 1216 12 1523 12
+C 1830 12 2150 6 2458 0
+L 2458 166
+L 2266 166
+C 1715 166 1702 236 1702 467
+L 1702 4083
+z
+" id="CMR17-31" transform="scale(0.015625)"/>
+ <path d="M 1062 262
+C 1062 422 934 524 800 524
+C 672 524 538 422 538 262
+C 538 102 666 0 800 0
+C 928 0 1062 102 1062 262
+z
+" id="CMR17-2e" transform="scale(0.015625)"/>
+ <path d="M 2253 1871
+C 2253 448 1670 25 1190 25
+C 1043 25 685 43 538 281
+C 704 256 826 345 826 505
+C 826 678 685 736 595 736
+C 538 736 365 710 365 492
+C 365 68 742 -128 1203 -128
+C 1939 -128 2688 665 2688 2090
+C 2688 3857 1971 4224 1485 4224
+C 851 4224 243 3664 243 2800
+C 243 2000 762 1408 1414 1408
+C 1952 1408 2189 1910 2253 2122
+L 2253 1871
+z
+M 1427 1510
+C 1254 1510 1011 1542 813 1929
+C 678 2181 678 2477 678 2793
+C 678 3174 678 3438 858 3722
+C 947 3857 1114 4076 1485 4076
+C 2240 4076 2240 2909 2240 2651
+C 2240 2193 2035 1510 1427 1510
+z
+" id="CMR17-39" transform="scale(0.015625)"/>
+ <path d="M 1632 1254
+L 1632 1536
+L 26 1536
+L 26 1254
+L 1632 1254
+z
+" id="CMR17-2d" transform="scale(0.015625)"/>
+ <path d="M 2688 2038
+C 2688 2430 2682 3099 2413 3613
+C 2176 4063 1798 4224 1466 4224
+C 1158 4224 768 4082 525 3620
+C 269 3137 243 2539 243 2038
+C 243 1671 250 1112 448 623
+C 723 -39 1216 -128 1466 -128
+C 1760 -128 2208 -7 2470 604
+C 2662 1048 2688 1568 2688 2038
+z
+M 1466 -26
+C 1056 -26 813 328 723 816
+C 653 1196 653 1749 653 2109
+C 653 2604 653 3015 736 3407
+C 858 3954 1216 4121 1466 4121
+C 1728 4121 2067 3947 2189 3420
+C 2272 3054 2278 2623 2278 2109
+C 2278 1691 2278 1176 2202 797
+C 2067 96 1690 -26 1466 -26
+z
+" id="CMR17-30" transform="scale(0.015625)"/>
+ <path d="M 730 3750
+C 794 3724 1056 3641 1325 3641
+C 1920 3641 2246 3961 2432 4140
+C 2432 4191 2432 4224 2394 4224
+C 2387 4224 2374 4224 2323 4198
+C 2099 4102 1837 4032 1517 4032
+C 1325 4032 1037 4055 723 4191
+C 653 4224 640 4224 634 4224
+C 602 4224 595 4217 595 4090
+L 595 2231
+C 595 2113 595 2080 659 2080
+C 691 2080 704 2093 736 2139
+C 941 2435 1222 2560 1542 2560
+C 1766 2560 2246 2415 2246 1293
+C 2246 1087 2246 716 2054 422
+C 1894 159 1645 25 1370 25
+C 947 25 518 319 403 812
+C 429 806 480 793 506 793
+C 589 793 749 838 749 1036
+C 749 1209 627 1280 506 1280
+C 358 1280 262 1190 262 1011
+C 262 454 704 -128 1382 -128
+C 2042 -128 2669 441 2669 1267
+C 2669 2054 2170 2662 1549 2662
+C 1222 2662 947 2540 730 2304
+L 730 3750
+z
+" id="CMR17-35" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-39"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_11">
+ <!-- 0.00047 -->
+ <g style="fill:#262626;" transform="translate(439.245807 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2150 4147
+C 2150 4281 2144 4288 2029 4288
+L 128 1254
+L 128 1088
+L 1779 1088
+L 1779 460
+C 1779 230 1766 166 1318 166
+L 1197 166
+L 1197 0
+C 1402 12 1747 12 1965 12
+C 2182 12 2528 12 2733 0
+L 2733 166
+L 2611 166
+C 2163 166 2150 230 2150 460
+L 2150 1088
+L 2803 1088
+L 2803 1254
+L 2150 1254
+L 2150 4147
+z
+M 1798 3723
+L 1798 1254
+L 256 1254
+L 1798 3723
+z
+" id="CMR17-34" transform="scale(0.015625)"/>
+ <path d="M 2886 3955
+L 2886 4096
+L 1382 4096
+C 634 4096 621 4166 595 4288
+L 480 4288
+L 294 3104
+L 410 3104
+C 429 3226 474 3552 550 3673
+C 589 3724 1062 3724 1171 3724
+L 2579 3724
+L 1869 2670
+C 1395 1961 1069 1003 1069 166
+C 1069 89 1069 -128 1299 -128
+C 1530 -128 1530 89 1530 172
+L 1530 466
+C 1530 1514 1709 2204 2003 2644
+L 2886 3955
+z
+" id="CMR17-37" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(161.94249 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(207.632967 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(253.323444 0)scale(0.996264)" xlink:href="#CMR17-37"/>
+ </g>
+ </g>
+ <g id="text_12">
+ <!-- 2.4e-05 -->
+ <g style="fill:#262626;" transform="translate(710.20871 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2669 990
+L 2554 990
+C 2490 537 2438 460 2413 422
+C 2381 371 1920 371 1830 371
+L 602 371
+C 832 620 1280 1073 1824 1596
+C 2214 1966 2669 2400 2669 3033
+C 2669 3788 2067 4224 1395 4224
+C 691 4224 262 3603 262 3027
+C 262 2777 448 2745 525 2745
+C 589 2745 781 2783 781 3007
+C 781 3206 614 3264 525 3264
+C 486 3264 448 3257 422 3244
+C 544 3788 915 4057 1306 4057
+C 1862 4057 2227 3616 2227 3033
+C 2227 2477 1901 1998 1536 1583
+L 262 147
+L 262 0
+L 2515 0
+L 2669 990
+z
+" id="CMR17-32" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-32"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_13">
+ <!-- 2.4e-05 -->
+ <g style="fill:#262626;" transform="translate(978.04871 228.955463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-32"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_14">
+ <!-- 0.49 -->
+ <g style="fill:#ffffff;" transform="translate(191.966522 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-39"/>
+ </g>
+ </g>
+ <g id="text_15">
+ <!-- 0.5 -->
+ <g style="fill:#ffffff;" transform="translate(466.660094 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_16">
+ <!-- 0.49 -->
+ <g style="fill:#ffffff;" transform="translate(727.646522 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-39"/>
+ </g>
+ </g>
+ <g id="text_17">
+ <!-- 0.49 -->
+ <g style="fill:#ffffff;" transform="translate(995.486522 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-39"/>
+ </g>
+ </g>
+ <g id="text_18">
+ <!-- 0.51 -->
+ <g style="fill:#ffffff;" transform="translate(191.966522 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ <g id="text_19">
+ <!-- 0.5 -->
+ <g style="fill:#ffffff;" transform="translate(466.660094 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_20">
+ <!-- 0.51 -->
+ <g style="fill:#ffffff;" transform="translate(727.646522 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ <g id="text_21">
+ <!-- 0.51 -->
+ <g style="fill:#ffffff;" transform="translate(995.486522 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ </g>
+ <g id="axes_2">
+ <g id="patch_3">
+ <path d="M 1220.657891 946.284441
+L 1264.145891 946.284441
+L 1264.145891 76.524441
+L 1220.657891 76.524441
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="patch_4">
+ <path clip-path="url(#p29e8ce2b1b)" d="M 1220.657891 946.284441
+L 1220.657891 942.886941
+L 1220.657891 79.921941
+L 1220.657891 76.524441
+L 1264.145891 76.524441
+L 1264.145891 79.921941
+L 1264.145891 942.886941
+L 1264.145891 946.284441
+L 1264.145891 946.284441
+z
+" style="fill:#ffffff;stroke:#ffffff;stroke-linejoin:miter;stroke-width:0.01;"/>
+ </g>
+ <image height="870" id="image5488b0d60f" transform="scale(1 -1)translate(0 -870)" width="43" x="1221" xlink:href="data:image/png;base64,
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" y="-76"/>
+ <g id="matplotlib.axis_3"/>
+ <g id="matplotlib.axis_4">
+ <g id="ytick_4">
+ <g id="line2d_8">
+ <defs>
+ <path d="M 0 0
+L 3.5 0
+" id="m0511830380" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m0511830380" y="776.944289"/>
+ </g>
+ </g>
+ <g id="text_22">
+ <!-- $\mathdefault{0.1}$ -->
+ <g transform="translate(1271.145891 787.322037)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1178 307
+C 1178 492 1024 620 870 620
+C 685 620 557 467 557 313
+C 557 128 710 0 864 0
+C 1050 0 1178 153 1178 307
+z
+" id="CMMI12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_5">
+ <g id="line2d_9">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m0511830380" y="607.57242"/>
+ </g>
+ </g>
+ <g id="text_23">
+ <!-- $\mathdefault{0.2}$ -->
+ <g transform="translate(1271.145891 617.950168)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_6">
+ <g id="line2d_10">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m0511830380" y="438.200551"/>
+ </g>
+ </g>
+ <g id="text_24">
+ <!-- $\mathdefault{0.3}$ -->
+ <g transform="translate(1271.145891 448.578298)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1414 2176
+C 1984 2176 2234 1673 2234 1094
+C 2234 322 1824 25 1453 25
+C 1114 25 563 193 390 691
+C 422 678 454 678 486 678
+C 640 678 755 780 755 947
+C 755 1132 614 1216 486 1216
+C 378 1216 211 1164 211 927
+C 211 335 787 -128 1466 -128
+C 2176 -128 2720 432 2720 1087
+C 2720 1718 2208 2176 1600 2246
+C 2086 2347 2554 2776 2554 3353
+C 2554 3856 2048 4224 1472 4224
+C 890 4224 378 3862 378 3347
+C 378 3123 544 3084 627 3084
+C 762 3084 877 3167 877 3334
+C 877 3500 762 3584 627 3584
+C 602 3584 570 3584 544 3571
+C 730 3999 1235 4076 1459 4076
+C 1683 4076 2106 3966 2106 3347
+C 2106 3167 2080 2851 1862 2574
+C 1670 2329 1453 2316 1242 2297
+C 1210 2297 1062 2284 1037 2284
+C 992 2278 966 2272 966 2227
+C 966 2182 973 2176 1101 2176
+L 1414 2176
+z
+" id="CMR17-33" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_7">
+ <g id="line2d_11">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m0511830380" y="268.828681"/>
+ </g>
+ </g>
+ <g id="text_25">
+ <!-- $\mathdefault{0.4}$ -->
+ <g transform="translate(1271.145891 279.206429)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_8">
+ <g id="line2d_12">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m0511830380" y="99.456812"/>
+ </g>
+ </g>
+ <g id="text_26">
+ <!-- $\mathdefault{0.5}$ -->
+ <g transform="translate(1271.145891 109.83456)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ </g>
+ <g id="LineCollection_1"/>
+ <g id="patch_5">
+ <path d="M 1220.657891 946.284441
+L 1220.657891 942.886941
+L 1220.657891 79.921941
+L 1220.657891 76.524441
+L 1264.145891 76.524441
+L 1264.145891 79.921941
+L 1264.145891 942.886941
+L 1264.145891 946.284441
+z
+" style="fill:none;"/>
+ </g>
+ </g>
+ </g>
+ <defs>
+ <clipPath id="pcc8f1eefc5">
+ <rect height="869.76" width="1071.36" x="82.337891" y="76.524441"/>
+ </clipPath>
+ <clipPath id="p29e8ce2b1b">
+ <rect height="869.76" width="43.488" x="1220.657891" y="76.524441"/>
+ </clipPath>
+ </defs>
+</svg>
diff --git a/examples/model-comparison/reference/confusionMatrix_ND_5.svg b/examples/model-comparison/reference/confusionMatrix_ND_5.svg
new file mode 100644
index 0000000000000000000000000000000000000000..3118ffe6a2d6679c517189e70465b6e35a447b08
--- /dev/null
+++ b/examples/model-comparison/reference/confusionMatrix_ND_5.svg
@@ -0,0 +1,1628 @@
+<?xml version="1.0" encoding="utf-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<svg height="953.484441pt" version="1.1" viewBox="0 0 1313.889331 953.484441" width="1313.889331pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+ <metadata>
+ <rdf:RDF xmlns:cc="http://creativecommons.org/ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
+ <cc:Work>
+ <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
+ <dc:date>2022-06-03T16:06:07.371011</dc:date>
+ <dc:format>image/svg+xml</dc:format>
+ <dc:creator>
+ <cc:Agent>
+ <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>
+ </cc:Agent>
+ </dc:creator>
+ </cc:Work>
+ </rdf:RDF>
+ </metadata>
+ <defs>
+ <style type="text/css">*{stroke-linecap:butt;stroke-linejoin:round;}</style>
+ </defs>
+ <g id="figure_1">
+ <g id="patch_1">
+ <path d="M 0 953.484441
+L 1313.889331 953.484441
+L 1313.889331 0
+L 0 0
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="axes_1">
+ <g id="patch_2">
+ <path d="M 82.337891 946.284441
+L 1153.697891 946.284441
+L 1153.697891 76.524441
+L 82.337891 76.524441
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="QuadMesh_1">
+ <path clip-path="url(#pea58550c9c)" d="M 82.337891 76.524441
+L 350.177891 76.524441
+L 350.177891 366.444441
+L 82.337891 366.444441
+L 82.337891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#pea58550c9c)" d="M 350.177891 76.524441
+L 618.017891 76.524441
+L 618.017891 366.444441
+L 350.177891 366.444441
+L 350.177891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#pea58550c9c)" d="M 618.017891 76.524441
+L 885.857891 76.524441
+L 885.857891 366.444441
+L 618.017891 366.444441
+L 618.017891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#pea58550c9c)" d="M 885.857891 76.524441
+L 1153.697891 76.524441
+L 1153.697891 366.444441
+L 885.857891 366.444441
+L 885.857891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#pea58550c9c)" d="M 82.337891 366.444441
+L 350.177891 366.444441
+L 350.177891 656.364441
+L 82.337891 656.364441
+L 82.337891 366.444441
+" style="fill:#083776;"/>
+ <path clip-path="url(#pea58550c9c)" d="M 350.177891 366.444441
+L 618.017891 366.444441
+L 618.017891 656.364441
+L 350.177891 656.364441
+L 350.177891 366.444441
+" style="fill:#083d7f;"/>
+ <path clip-path="url(#pea58550c9c)" d="M 618.017891 366.444441
+L 885.857891 366.444441
+L 885.857891 656.364441
+L 618.017891 656.364441
+L 618.017891 366.444441
+" style="fill:#08306b;"/>
+ <path clip-path="url(#pea58550c9c)" d="M 885.857891 366.444441
+L 1153.697891 366.444441
+L 1153.697891 656.364441
+L 885.857891 656.364441
+L 885.857891 366.444441
+" style="fill:#08306b;"/>
+ <path clip-path="url(#pea58550c9c)" d="M 82.337891 656.364441
+L 350.177891 656.364441
+L 350.177891 946.284441
+L 82.337891 946.284441
+L 82.337891 656.364441
+" style="fill:#084285;"/>
+ <path clip-path="url(#pea58550c9c)" d="M 350.177891 656.364441
+L 618.017891 656.364441
+L 618.017891 946.284441
+L 350.177891 946.284441
+L 350.177891 656.364441
+" style="fill:#083b7c;"/>
+ <path clip-path="url(#pea58550c9c)" d="M 618.017891 656.364441
+L 885.857891 656.364441
+L 885.857891 946.284441
+L 618.017891 946.284441
+L 618.017891 656.364441
+" style="fill:#084990;"/>
+ <path clip-path="url(#pea58550c9c)" d="M 885.857891 656.364441
+L 1153.697891 656.364441
+L 1153.697891 946.284441
+L 885.857891 946.284441
+L 885.857891 656.364441
+" style="fill:#084990;"/>
+ </g>
+ <g id="matplotlib.axis_1">
+ <g id="xtick_1">
+ <g id="line2d_1">
+ <defs>
+ <path d="M 0 0
+L 0 -3.5
+" id="m8560e00e6a" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="216.257891" xlink:href="#m8560e00e6a" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_1">
+ <!-- Observation -->
+ <g transform="translate(144.303789 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 4307 2166
+C 4307 3488 3366 4480 2304 4480
+C 1216 4480 294 3475 294 2166
+C 294 857 1229 -128 2298 -128
+C 3392 -128 4307 876 4307 2166
+z
+M 2304 -13
+C 1574 -13 781 722 781 2250
+C 781 3771 1651 4364 2298 4364
+C 2976 4364 3821 3752 3821 2250
+C 3821 696 3008 -13 2304 -13
+z
+" id="CMR17-4f" transform="scale(0.015625)"/>
+ <path d="M 960 4416
+L 198 4345
+L 198 4179
+C 576 4179 634 4141 634 3843
+L 634 -13
+L 749 -13
+L 934 445
+C 1120 141 1395 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2209 2477 2816 1830 2816
+C 1434 2816 1152 2603 960 2351
+L 960 4416
+z
+M 973 2022
+C 973 2138 973 2157 1062 2293
+C 1312 2681 1670 2713 1792 2713
+C 1984 2713 2643 2610 2643 1388
+C 2643 109 1888 38 1734 38
+C 1536 38 1248 115 1043 490
+C 973 613 973 626 973 742
+L 973 2022
+z
+" id="CMR17-62" transform="scale(0.015625)"/>
+ <path d="M 1978 2688
+C 1978 2803 1971 2809 1933 2809
+C 1907 2809 1901 2803 1824 2707
+C 1805 2681 1747 2617 1728 2592
+C 1523 2809 1235 2816 1126 2816
+C 416 2816 160 2444 160 2073
+C 160 1497 813 1363 998 1324
+C 1402 1241 1542 1216 1677 1100
+C 1760 1024 1901 883 1901 652
+C 1901 384 1747 38 1158 38
+C 602 38 403 460 288 1024
+C 269 1113 269 1120 218 1120
+C 166 1120 160 1113 160 985
+L 160 64
+C 160 -52 166 -58 205 -58
+C 237 -58 243 -52 275 0
+C 314 57 410 211 448 275
+C 576 102 800 -64 1158 -64
+C 1792 -64 2131 281 2131 780
+C 2131 1107 1958 1280 1875 1356
+C 1683 1555 1459 1600 1190 1651
+C 838 1728 390 1817 390 2208
+C 390 2374 480 2726 1126 2726
+C 1811 2726 1850 2086 1862 1881
+C 1869 1849 1901 1843 1920 1843
+C 1978 1843 1978 1862 1978 1971
+L 1978 2688
+z
+" id="CMR17-73" transform="scale(0.015625)"/>
+ <path d="M 2438 1503
+C 2464 1529 2464 1542 2464 1606
+C 2464 2251 2118 2816 1389 2816
+C 710 2816 173 2175 173 1394
+C 173 554 781 -64 1459 -64
+C 2176 -64 2458 619 2458 755
+C 2458 800 2419 800 2406 800
+C 2362 800 2355 787 2330 709
+C 2189 270 1837 51 1504 51
+C 1229 51 954 206 781 490
+C 582 819 582 1200 582 1503
+L 2438 1503
+z
+M 589 1600
+C 634 2511 1126 2713 1382 2713
+C 1818 2713 2112 2308 2118 1600
+L 589 1600
+z
+" id="CMR17-65" transform="scale(0.015625)"/>
+ <path d="M 960 1517
+C 960 2134 1222 2713 1702 2713
+C 1747 2713 1792 2707 1837 2687
+C 1837 2687 1696 2642 1696 2475
+C 1696 2321 1818 2257 1914 2257
+C 1990 2257 2131 2302 2131 2482
+C 2131 2687 1926 2816 1709 2816
+C 1222 2816 1011 2340 947 2115
+L 941 2115
+L 941 2816
+L 198 2745
+L 198 2578
+C 576 2578 634 2540 634 2231
+L 634 443
+C 634 198 608 166 198 166
+L 198 0
+C 352 12 646 12 813 12
+C 998 12 1325 12 1498 0
+L 1498 166
+C 1037 166 960 166 960 455
+L 960 1517
+z
+" id="CMR17-72" transform="scale(0.015625)"/>
+ <path d="M 2502 2173
+C 2560 2315 2662 2572 3034 2585
+L 3034 2752
+C 2912 2745 2752 2739 2630 2739
+C 2496 2739 2285 2739 2157 2752
+L 2157 2585
+C 2317 2572 2406 2495 2406 2328
+C 2406 2270 2406 2257 2368 2167
+L 1664 379
+L 902 2308
+C 864 2392 864 2405 864 2431
+C 864 2585 1075 2585 1171 2585
+L 1171 2752
+C 1018 2739 736 2739 576 2739
+C 403 2739 205 2739 64 2752
+L 64 2585
+C 307 2585 442 2585 518 2386
+L 1446 44
+C 1485 -52 1491 -64 1549 -64
+C 1606 -64 1613 -52 1651 44
+L 2502 2173
+z
+" id="CMR17-76" transform="scale(0.015625)"/>
+ <path d="M 2304 1656
+C 2304 2048 2304 2275 2035 2534
+C 1798 2751 1523 2816 1306 2816
+C 800 2816 435 2408 435 1977
+C 435 1740 627 1728 666 1728
+C 749 1728 896 1779 896 1958
+C 896 2118 774 2188 666 2188
+C 640 2188 608 2182 589 2176
+C 723 2594 1069 2713 1293 2713
+C 1613 2713 1965 2421 1965 1875
+L 1965 1632
+C 1587 1619 1133 1568 774 1373
+C 371 1147 256 822 256 576
+C 256 77 832 -64 1171 -64
+C 1523 -64 1850 135 1990 505
+C 2003 219 2182 -39 2464 -39
+C 2598 -39 2938 51 2938 563
+L 2938 926
+L 2822 926
+L 2822 557
+C 2822 161 2650 109 2566 109
+C 2304 109 2304 446 2304 732
+L 2304 1656
+z
+M 1965 887
+C 1965 323 1568 38 1216 38
+C 896 38 646 278 646 576
+C 646 771 730 1114 1101 1322
+C 1408 1497 1760 1523 1965 1536
+L 1965 887
+z
+" id="CMR17-61" transform="scale(0.015625)"/>
+ <path d="M 966 2585
+L 1862 2585
+L 1862 2752
+L 966 2752
+L 966 3968
+L 851 3968
+C 838 3292 614 2700 70 2687
+L 70 2585
+L 627 2585
+L 627 778
+C 627 655 627 -64 1370 -64
+C 1747 -64 1965 308 1965 784
+L 1965 1151
+L 1850 1151
+L 1850 790
+C 1850 347 1677 51 1408 51
+C 1222 51 966 179 966 765
+L 966 2585
+z
+" id="CMR17-74" transform="scale(0.015625)"/>
+ <path d="M 992 3961
+C 992 4102 877 4224 730 4224
+C 589 4224 467 4108 467 3961
+C 467 3820 582 3699 730 3699
+C 870 3699 992 3814 992 3961
+z
+M 243 2745
+L 243 2579
+C 602 2579 653 2540 653 2231
+L 653 443
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 646 12 806 12
+C 960 12 1222 12 1370 0
+L 1370 166
+C 992 166 979 205 979 436
+L 979 2816
+L 243 2745
+z
+" id="CMR17-69" transform="scale(0.015625)"/>
+ <path d="M 2758 1356
+C 2758 2176 2163 2816 1466 2816
+C 768 2816 173 2176 173 1356
+C 173 550 768 -64 1466 -64
+C 2163 -64 2758 550 2758 1356
+z
+M 1466 51
+C 1165 51 909 230 762 480
+C 602 768 582 1126 582 1408
+C 582 1676 595 2009 762 2297
+C 890 2508 1139 2713 1466 2713
+C 1754 2713 1997 2553 2150 2329
+C 2349 2028 2349 1606 2349 1408
+C 2349 1158 2336 774 2163 467
+C 1984 172 1709 51 1466 51
+z
+" id="CMR17-6f" transform="scale(0.015625)"/>
+ <path d="M 2656 1954
+C 2656 2282 2592 2816 1837 2816
+C 1331 2816 1069 2424 973 2166
+L 966 2166
+L 966 2816
+L 211 2745
+L 211 2578
+C 589 2578 646 2540 646 2231
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1954
+z
+" id="CMR17-6e" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-4f"/>
+ <use transform="translate(71.714788 0)scale(0.996264)" xlink:href="#CMR17-62"/>
+ <use transform="translate(122.610158 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(158.411496 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(198.897156 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ <use transform="translate(234.177924 0)scale(0.996264)" xlink:href="#CMR17-76"/>
+ <use transform="translate(277.266023 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(322.9565 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(358.237268 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(383.108327 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(428.798804 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_2">
+ <g id="line2d_2">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="484.097891" xlink:href="#m8560e00e6a" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_2">
+ <!-- linear -->
+ <g transform="translate(450.783747 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 979 4416
+L 218 4345
+L 218 4179
+C 595 4179 653 4141 653 3835
+L 653 439
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 653 12 813 12
+C 979 12 1261 12 1414 0
+L 1414 166
+C 1005 166 979 191 979 439
+L 979 4416
+z
+" id="CMR17-6c" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_3">
+ <g id="line2d_3">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="751.937891" xlink:href="#m8560e00e6a" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_3">
+ <!-- exponential -->
+ <g transform="translate(683.18479 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1664 1491
+C 1856 1740 2074 2022 2253 2233
+C 2464 2476 2707 2579 2989 2585
+L 2989 2752
+C 2880 2745 2656 2739 2541 2739
+C 2368 2739 2170 2739 2022 2752
+L 2022 2585
+C 2112 2572 2163 2508 2163 2419
+C 2163 2304 2099 2233 2067 2188
+L 1594 1587
+L 1030 2323
+C 973 2393 973 2406 973 2438
+C 973 2515 1037 2579 1146 2585
+L 1146 2752
+C 992 2739 717 2739 557 2739
+C 384 2739 179 2739 38 2752
+L 38 2585
+C 384 2585 461 2560 614 2368
+L 1350 1414
+C 1363 1401 1395 1363 1395 1344
+C 1395 1318 838 633 768 544
+C 480 198 179 172 6 166
+L 6 0
+C 115 6 339 12 454 12
+C 582 12 864 12 979 0
+L 979 166
+C 941 172 838 185 838 332
+C 838 448 890 518 947 595
+L 1478 1248
+L 2035 524
+C 2086 454 2163 358 2163 313
+C 2163 224 2086 172 1984 166
+L 1984 0
+C 2138 12 2413 12 2573 12
+C 2746 12 2950 12 3091 0
+L 3091 166
+C 2771 166 2675 179 2522 377
+L 1664 1491
+z
+" id="CMR17-78" transform="scale(0.015625)"/>
+ <path d="M 1408 -1114
+C 998 -1114 973 -1088 973 -834
+L 973 380
+C 1158 109 1427 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2196 2496 2816 1837 2816
+C 1453 2816 1139 2603 960 2345
+L 960 2816
+L 198 2745
+L 198 2577
+C 576 2577 634 2539 634 2228
+L 634 -834
+C 634 -1081 608 -1114 198 -1114
+L 198 -1280
+C 352 -1268 634 -1268 800 -1268
+C 966 -1268 1254 -1268 1408 -1280
+L 1408 -1114
+z
+M 973 2015
+C 973 2106 973 2241 1222 2481
+C 1254 2506 1472 2700 1792 2700
+C 2259 2700 2643 2112 2643 1376
+C 2643 639 2234 38 1728 38
+C 1498 38 1248 148 1056 451
+C 973 594 973 632 973 736
+L 973 2015
+z
+" id="CMR17-70" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_4">
+ <g id="line2d_4">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1019.777891" xlink:href="#m8560e00e6a" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_4">
+ <!-- cosine -->
+ <g transform="translate(984.043472 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2234 2240
+C 2112 2240 1933 2240 1933 2015
+C 1933 1836 2080 1785 2163 1785
+C 2208 1785 2394 1804 2394 2028
+C 2394 2476 1958 2816 1466 2816
+C 787 2816 211 2201 211 1379
+C 211 521 813 -64 1466 -64
+C 2259 -64 2458 676 2458 747
+C 2458 773 2451 792 2406 792
+C 2362 792 2355 786 2330 702
+C 2163 180 1798 51 1523 51
+C 1114 51 621 431 621 1385
+C 621 2358 1094 2700 1472 2700
+C 1722 2700 2093 2582 2234 2240
+z
+" id="CMR17-63" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_5">
+ <!-- \textbf{Data generated by:} -->
+ <g transform="translate(476.949653 27.955495)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 243 4416
+L 243 4140
+L 922 4140
+L 922 275
+L 243 275
+L 243 0
+L 2938 0
+C 4166 0 5114 790 5114 2169
+C 5114 3625 4141 4416 2938 4416
+L 243 4416
+z
+M 1734 275
+L 1734 4140
+L 2694 4140
+C 3251 4140 3699 3921 3936 3586
+C 4122 3322 4243 3006 4243 2175
+C 4243 1421 4147 1086 3923 784
+C 3699 487 3270 275 2694 275
+L 1734 275
+z
+" id="CMBX12-44" transform="scale(0.015625)"/>
+ <path d="M 2944 1894
+C 2944 2483 2477 2880 1574 2880
+C 1216 2880 461 2847 461 2310
+C 461 2041 666 1926 838 1926
+C 1030 1926 1216 2060 1216 2303
+C 1216 2425 1171 2540 1062 2611
+C 1274 2668 1427 2668 1549 2668
+C 1984 2668 2246 2425 2246 1900
+L 2246 1644
+C 1235 1644 218 1362 218 648
+C 218 64 960 -64 1402 -64
+C 1894 -64 2208 205 2336 488
+C 2336 250 2336 -26 2982 -26
+L 3309 -26
+C 3443 -26 3494 -26 3494 115
+C 3494 250 3437 250 3347 250
+C 2944 256 2944 359 2944 507
+L 2944 1894
+z
+M 2246 867
+C 2246 262 1709 147 1504 147
+C 1190 147 928 359 928 655
+C 928 1240 1619 1439 2246 1472
+L 2246 867
+z
+" id="CMBX12-61" transform="scale(0.015625)"/>
+ <path d="M 1350 2540
+L 2272 2540
+L 2272 2816
+L 1350 2816
+L 1350 4032
+L 1082 4032
+C 1075 3401 768 2771 134 2751
+L 134 2540
+L 653 2540
+L 653 761
+C 653 83 1178 -64 1638 -64
+C 2112 -64 2394 294 2394 768
+L 2394 1107
+L 2125 1107
+L 2125 774
+C 2125 352 1933 166 1734 166
+C 1350 166 1350 595 1350 742
+L 1350 2540
+z
+" id="CMBX12-74" transform="scale(0.015625)"/>
+ <path d="M 832 1177
+C 1139 1011 1498 1011 1594 1011
+C 2477 1011 2829 1506 2829 1958
+C 2829 2287 2643 2519 2566 2584
+C 2752 2687 2906 2713 3014 2726
+C 2995 2694 2976 2668 2976 2584
+C 2976 2448 3066 2326 3232 2326
+C 3398 2326 3488 2448 3488 2584
+C 3488 2739 3373 2944 3104 2944
+C 2829 2944 2566 2809 2432 2694
+C 2170 2847 1920 2905 1594 2905
+C 710 2905 358 2410 358 1958
+C 358 1758 422 1493 691 1274
+C 582 1151 467 926 467 693
+C 467 416 614 179 749 76
+C 595 38 198 -109 198 -474
+C 198 -852 614 -1280 1792 -1280
+C 2854 -1280 3392 -935 3392 -455
+C 3392 108 3021 294 2861 371
+C 2554 524 2144 524 1581 524
+C 1421 524 1139 524 1107 531
+C 832 576 755 823 755 946
+C 755 998 762 1094 832 1177
+z
+M 1594 1216
+C 1037 1216 1037 1661 1037 1958
+C 1037 2255 1037 2700 1594 2700
+C 2150 2700 2150 2255 2150 1958
+C 2150 1661 2150 1216 1594 1216
+z
+M 1952 -64
+C 2419 -64 2867 -148 2867 -480
+C 2867 -704 2643 -1076 1798 -1076
+C 954 -1076 723 -717 723 -474
+C 723 -64 1126 -64 1222 -64
+L 1952 -64
+z
+" id="CMBX12-67" transform="scale(0.015625)"/>
+ <path d="M 2893 1408
+C 3040 1408 3078 1408 3078 1568
+C 3078 1758 3034 2232 2739 2529
+C 2470 2796 2112 2880 1741 2880
+C 742 2880 198 2232 198 1433
+C 198 523 858 -64 1824 -64
+C 2790 -64 3078 621 3078 731
+C 3078 829 2982 829 2944 829
+C 2842 829 2835 809 2797 725
+C 2630 302 2208 166 1901 166
+C 973 166 966 1043 966 1408
+L 2893 1408
+z
+M 966 1593
+C 979 1852 986 2099 1120 2327
+C 1242 2529 1466 2668 1741 2668
+C 2426 2668 2483 1909 2490 1593
+L 966 1593
+z
+" id="CMBX12-65" transform="scale(0.015625)"/>
+ <path d="M 3398 1958
+C 3398 2566 3136 2880 2432 2880
+C 1971 2880 1574 2656 1357 2176
+L 1350 2176
+L 1350 2880
+L 269 2828
+L 269 2553
+C 666 2553 710 2553 710 2304
+L 710 275
+L 269 275
+L 269 0
+C 416 12 877 12 1056 12
+C 1235 12 1702 12 1850 0
+L 1850 275
+L 1408 275
+L 1408 1638
+C 1408 2329 1920 2668 2330 2668
+C 2566 2668 2701 2515 2701 2028
+L 2701 275
+L 2259 275
+L 2259 0
+C 2406 12 2867 12 3046 12
+C 3226 12 3693 12 3840 0
+L 3840 275
+L 3398 275
+L 3398 1958
+z
+" id="CMBX12-6e" transform="scale(0.015625)"/>
+ <path d="M 1331 1440
+C 1331 1651 1376 2668 2125 2668
+C 2035 2598 1990 2489 1990 2374
+C 1990 2112 2202 2003 2362 2003
+C 2522 2003 2733 2112 2733 2374
+C 2733 2700 2400 2880 2093 2880
+C 1587 2880 1370 2438 1280 2169
+L 1274 2169
+L 1274 2880
+L 224 2828
+L 224 2553
+C 621 2553 666 2553 666 2304
+L 666 275
+L 224 275
+L 224 0
+C 371 12 851 12 1030 12
+C 1216 12 1734 12 1888 0
+L 1888 275
+L 1331 275
+L 1331 1440
+z
+" id="CMBX12-72" transform="scale(0.015625)"/>
+ <path d="M 2221 4428
+L 2221 4153
+C 2618 4153 2662 4153 2662 3896
+L 2662 2571
+C 2522 2694 2240 2880 1798 2880
+C 890 2880 243 2313 243 1408
+C 243 483 877 -64 1728 -64
+C 2080 -64 2381 57 2630 270
+L 2630 -64
+L 3770 -26
+L 3770 250
+C 3373 250 3328 250 3328 502
+L 3328 4480
+L 2221 4428
+z
+M 2630 625
+C 2362 231 2035 147 1805 147
+C 1011 147 1011 968 1011 1395
+C 1011 1699 1011 2022 1152 2268
+C 1350 2630 1728 2668 1875 2668
+C 2138 2668 2419 2552 2630 2268
+L 2630 625
+z
+" id="CMBX12-64" transform="scale(0.015625)"/>
+ <path d="M 1331 4480
+L 224 4428
+L 224 4153
+C 621 4153 666 4153 666 3896
+L 666 -26
+L 934 -26
+C 1043 96 1152 218 1254 347
+C 1581 6 1933 -64 2189 -64
+C 3072 -64 3750 476 3750 1414
+C 3750 2300 3149 2880 2272 2880
+C 1894 2880 1594 2758 1331 2552
+L 1331 4480
+z
+M 1363 2242
+C 1587 2552 1920 2668 2189 2668
+C 2982 2668 2982 1847 2982 1420
+C 2982 1130 2982 761 2829 522
+C 2630 211 2330 147 2125 147
+C 1690 147 1453 457 1363 599
+L 1363 2242
+z
+" id="CMBX12-62" transform="scale(0.015625)"/>
+ <path d="M 3168 2400
+C 3206 2489 3232 2540 3642 2540
+L 3642 2816
+C 3424 2803 3398 2803 3136 2803
+C 2963 2803 2950 2803 2586 2816
+L 2586 2540
+C 2592 2540 2893 2540 2893 2457
+C 2893 2438 2874 2400 2867 2381
+L 2118 780
+L 1299 2540
+L 1651 2540
+L 1651 2816
+C 1498 2803 1062 2803 883 2803
+C 698 2803 320 2803 154 2816
+L 154 2540
+L 563 2540
+L 1747 -8
+C 1715 -84 1626 -269 1594 -345
+C 1459 -631 1254 -1069 806 -1069
+C 781 -1069 704 -1069 634 -1031
+C 646 -1025 838 -949 838 -707
+C 838 -497 685 -364 493 -364
+C 294 -364 141 -497 141 -713
+C 141 -1012 422 -1280 806 -1280
+C 1331 -1280 1677 -809 1805 -529
+L 3168 2400
+z
+" id="CMBX12-79" transform="scale(0.015625)"/>
+ <path d="M 1459 2355
+C 1459 2617 1248 2816 998 2816
+C 749 2816 538 2617 538 2355
+C 538 2092 749 1894 998 1894
+C 1248 1894 1459 2092 1459 2355
+z
+M 1459 460
+C 1459 723 1248 921 998 921
+C 749 921 538 723 538 460
+C 538 198 749 0 998 0
+C 1248 0 1459 198 1459 460
+z
+" id="CMBX12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMBX12-44"/>
+ <use transform="translate(85.904786 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(140.387974 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(183.974524 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(275.817613 0)scale(0.996264)" xlink:href="#CMBX12-67"/>
+ <use transform="translate(331.857463 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(382.99673 0)scale(0.996264)" xlink:href="#CMBX12-6e"/>
+ <use transform="translate(445.263231 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(496.402498 0)scale(0.996264)" xlink:href="#CMBX12-72"/>
+ <use transform="translate(542.180006 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(596.663194 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(640.249744 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(691.389011 0)scale(0.996264)" xlink:href="#CMBX12-64"/>
+ <use transform="translate(791.015412 0)scale(0.996264)" xlink:href="#CMBX12-62"/>
+ <use transform="translate(850.168588 0)scale(0.996264)" xlink:href="#CMBX12-79"/>
+ <use transform="translate(909.321763 0)scale(0.996264)" xlink:href="#CMBX12-3a"/>
+ </g>
+ </g>
+ </g>
+ <g id="matplotlib.axis_2">
+ <g id="ytick_1">
+ <g id="line2d_5">
+ <defs>
+ <path d="M 0 0
+L -3.5 0
+" id="maf00c7b200" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#maf00c7b200" y="221.484441"/>
+ </g>
+ </g>
+ <g id="text_6">
+ <!-- linear -->
+ <g transform="translate(69.524441 277.73498)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_2">
+ <g id="line2d_6">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#maf00c7b200" y="511.404441"/>
+ </g>
+ </g>
+ <g id="text_7">
+ <!-- exponential -->
+ <g transform="translate(69.524441 638.532895)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_3">
+ <g id="line2d_7">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#maf00c7b200" y="801.324441"/>
+ </g>
+ </g>
+ <g id="text_8">
+ <!-- cosine -->
+ <g transform="translate(69.524441 862.415532)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_9">
+ <!-- \textbf{Model weight for:} -->
+ <g transform="translate(27.955495 642.025756)rotate(-90)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 3411 816
+L 1875 4281
+C 1818 4416 1760 4416 1626 4416
+L 262 4416
+L 262 4140
+L 941 4140
+L 941 468
+C 941 326 934 320 768 294
+C 653 281 525 275 410 275
+L 262 275
+L 262 0
+C 410 12 909 12 1088 12
+C 1267 12 1773 12 1920 0
+L 1920 275
+L 1773 275
+C 1600 275 1587 275 1434 294
+C 1248 320 1242 326 1242 468
+L 1242 4063
+L 1248 4063
+L 2989 134
+C 3021 64 3059 0 3168 0
+C 3277 0 3315 64 3347 134
+L 5120 4140
+L 5126 4140
+L 5126 275
+L 4448 275
+L 4448 0
+C 4621 12 5286 12 5504 12
+C 5722 12 6387 12 6560 0
+L 6560 275
+L 5882 275
+L 5882 4140
+L 6560 4140
+L 6560 4416
+L 5197 4416
+C 5062 4416 5005 4416 4947 4281
+L 3411 816
+z
+" id="CMBX12-4d" transform="scale(0.015625)"/>
+ <path d="M 3392 1379
+C 3392 2245 2803 2880 1798 2880
+C 755 2880 198 2213 198 1379
+C 198 538 787 -64 1792 -64
+C 2835 -64 3392 570 3392 1379
+z
+M 1798 166
+C 966 166 966 917 966 1443
+C 966 1744 966 2065 1088 2296
+C 1229 2553 1517 2668 1792 2668
+C 2157 2668 2387 2495 2496 2315
+C 2624 2084 2624 1751 2624 1443
+C 2624 910 2624 166 1798 166
+z
+" id="CMBX12-6f" transform="scale(0.015625)"/>
+ <path d="M 1389 4480
+L 282 4428
+L 282 4153
+C 678 4153 723 4153 723 3901
+L 723 275
+L 282 275
+L 282 0
+C 429 12 883 12 1056 12
+C 1229 12 1683 12 1830 0
+L 1830 275
+L 1389 275
+L 1389 4480
+z
+" id="CMBX12-6c" transform="scale(0.015625)"/>
+ <path d="M 4608 2386
+C 4653 2496 4672 2540 5043 2540
+L 5043 2816
+C 4858 2803 4774 2803 4544 2803
+C 4282 2803 4198 2803 3968 2816
+L 3968 2540
+C 4026 2540 4339 2540 4339 2457
+C 4339 2451 4339 2444 4314 2380
+L 3642 712
+L 2906 2540
+L 3270 2540
+L 3270 2816
+C 3117 2803 2739 2803 2566 2803
+C 2240 2803 2227 2803 1907 2816
+L 1907 2540
+L 2285 2540
+C 2304 2489 2336 2406 2362 2348
+C 2381 2309 2445 2155 2445 2123
+C 2445 2111 2426 2066 2419 2046
+L 1933 834
+L 1242 2540
+L 1606 2540
+L 1606 2816
+C 1459 2803 1024 2803 851 2803
+C 646 2803 339 2803 147 2816
+L 147 2540
+L 525 2540
+L 1504 96
+C 1549 -20 1574 -64 1715 -64
+C 1786 -64 1862 -64 1914 64
+L 2592 1764
+L 3270 76
+C 3328 -64 3398 -64 3475 -64
+C 3616 -64 3635 -26 3680 89
+L 4608 2386
+z
+" id="CMBX12-77" transform="scale(0.015625)"/>
+ <path d="M 1427 4019
+C 1427 4281 1216 4480 966 4480
+C 704 4480 506 4262 506 4019
+C 506 3775 704 3558 966 3558
+C 1216 3558 1427 3756 1427 4019
+z
+M 301 2828
+L 301 2553
+C 678 2553 723 2553 723 2303
+L 723 275
+L 282 275
+L 282 0
+C 429 12 870 12 1043 12
+C 1222 12 1632 12 1786 0
+L 1786 275
+L 1389 275
+L 1389 2880
+L 301 2828
+z
+" id="CMBX12-69" transform="scale(0.015625)"/>
+ <path d="M 3398 1958
+C 3398 2566 3136 2880 2432 2880
+C 1786 2880 1472 2425 1382 2233
+L 1376 2233
+L 1376 4480
+L 269 4428
+L 269 4153
+C 666 4153 710 4153 710 3896
+L 710 275
+L 269 275
+L 269 0
+C 416 12 877 12 1056 12
+C 1235 12 1702 12 1850 0
+L 1850 275
+L 1408 275
+L 1408 1638
+C 1408 2329 1920 2668 2330 2668
+C 2566 2668 2701 2515 2701 2028
+L 2701 275
+L 2259 275
+L 2259 0
+C 2406 12 2867 12 3046 12
+C 3226 12 3693 12 3840 0
+L 3840 275
+L 3398 275
+L 3398 1958
+z
+" id="CMBX12-68" transform="scale(0.015625)"/>
+ <path d="M 1389 2540
+L 2118 2540
+L 2118 2816
+L 1357 2816
+L 1357 3466
+C 1357 4122 1779 4224 1990 4224
+C 2061 4224 2074 4217 2112 4204
+C 2016 4141 1958 4034 1958 3901
+C 1958 3649 2163 3535 2330 3535
+C 2470 3535 2701 3630 2701 3908
+C 2701 4167 2470 4435 2016 4435
+C 1434 4435 723 4192 723 3459
+L 723 2816
+L 250 2816
+L 250 2540
+L 723 2540
+L 723 275
+L 282 275
+L 282 0
+C 429 12 909 12 1088 12
+C 1274 12 1792 12 1946 0
+L 1946 275
+L 1389 275
+L 1389 2540
+z
+" id="CMBX12-66" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMBX12-4d"/>
+ <use transform="translate(106.314425 0)scale(0.996264)" xlink:href="#CMBX12-6f"/>
+ <use transform="translate(165.467601 0)scale(0.996264)" xlink:href="#CMBX12-64"/>
+ <use transform="translate(227.734101 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(278.873369 0)scale(0.996264)" xlink:href="#CMBX12-6c"/>
+ <use transform="translate(347.366519 0)scale(0.996264)" xlink:href="#CMBX12-77"/>
+ <use transform="translate(425.199645 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(476.338912 0)scale(0.996264)" xlink:href="#CMBX12-69"/>
+ <use transform="translate(507.472162 0)scale(0.996264)" xlink:href="#CMBX12-67"/>
+ <use transform="translate(563.512013 0)scale(0.996264)" xlink:href="#CMBX12-68"/>
+ <use transform="translate(622.665189 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(703.611639 0)scale(0.996264)" xlink:href="#CMBX12-66"/>
+ <use transform="translate(737.858215 0)scale(0.996264)" xlink:href="#CMBX12-6f"/>
+ <use transform="translate(793.898065 0)scale(0.996264)" xlink:href="#CMBX12-72"/>
+ <use transform="translate(839.675573 0)scale(0.996264)" xlink:href="#CMBX12-3a"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_10">
+ <!-- 4.5e-07 -->
+ <g style="fill:#262626;" transform="translate(174.52871 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2150 4147
+C 2150 4281 2144 4288 2029 4288
+L 128 1254
+L 128 1088
+L 1779 1088
+L 1779 460
+C 1779 230 1766 166 1318 166
+L 1197 166
+L 1197 0
+C 1402 12 1747 12 1965 12
+C 2182 12 2528 12 2733 0
+L 2733 166
+L 2611 166
+C 2163 166 2150 230 2150 460
+L 2150 1088
+L 2803 1088
+L 2803 1254
+L 2150 1254
+L 2150 4147
+z
+M 1798 3723
+L 1798 1254
+L 256 1254
+L 1798 3723
+z
+" id="CMR17-34" transform="scale(0.015625)"/>
+ <path d="M 1062 262
+C 1062 422 934 524 800 524
+C 672 524 538 422 538 262
+C 538 102 666 0 800 0
+C 928 0 1062 102 1062 262
+z
+" id="CMR17-2e" transform="scale(0.015625)"/>
+ <path d="M 730 3750
+C 794 3724 1056 3641 1325 3641
+C 1920 3641 2246 3961 2432 4140
+C 2432 4191 2432 4224 2394 4224
+C 2387 4224 2374 4224 2323 4198
+C 2099 4102 1837 4032 1517 4032
+C 1325 4032 1037 4055 723 4191
+C 653 4224 640 4224 634 4224
+C 602 4224 595 4217 595 4090
+L 595 2231
+C 595 2113 595 2080 659 2080
+C 691 2080 704 2093 736 2139
+C 941 2435 1222 2560 1542 2560
+C 1766 2560 2246 2415 2246 1293
+C 2246 1087 2246 716 2054 422
+C 1894 159 1645 25 1370 25
+C 947 25 518 319 403 812
+C 429 806 480 793 506 793
+C 589 793 749 838 749 1036
+C 749 1209 627 1280 506 1280
+C 358 1280 262 1190 262 1011
+C 262 454 704 -128 1382 -128
+C 2042 -128 2669 441 2669 1267
+C 2669 2054 2170 2662 1549 2662
+C 1222 2662 947 2540 730 2304
+L 730 3750
+z
+" id="CMR17-35" transform="scale(0.015625)"/>
+ <path d="M 1632 1254
+L 1632 1536
+L 26 1536
+L 26 1254
+L 1632 1254
+z
+" id="CMR17-2d" transform="scale(0.015625)"/>
+ <path d="M 2688 2038
+C 2688 2430 2682 3099 2413 3613
+C 2176 4063 1798 4224 1466 4224
+C 1158 4224 768 4082 525 3620
+C 269 3137 243 2539 243 2038
+C 243 1671 250 1112 448 623
+C 723 -39 1216 -128 1466 -128
+C 1760 -128 2208 -7 2470 604
+C 2662 1048 2688 1568 2688 2038
+z
+M 1466 -26
+C 1056 -26 813 328 723 816
+C 653 1196 653 1749 653 2109
+C 653 2604 653 3015 736 3407
+C 858 3954 1216 4121 1466 4121
+C 1728 4121 2067 3947 2189 3420
+C 2272 3054 2278 2623 2278 2109
+C 2278 1691 2278 1176 2202 797
+C 2067 96 1690 -26 1466 -26
+z
+" id="CMR17-30" transform="scale(0.015625)"/>
+ <path d="M 2886 3955
+L 2886 4096
+L 1382 4096
+C 634 4096 621 4166 595 4288
+L 480 4288
+L 294 3104
+L 410 3104
+C 429 3226 474 3552 550 3673
+C 589 3724 1062 3724 1171 3724
+L 2579 3724
+L 1869 2670
+C 1395 1961 1069 1003 1069 166
+C 1069 89 1069 -128 1299 -128
+C 1530 -128 1530 89 1530 172
+L 1530 466
+C 1530 1514 1709 2204 2003 2644
+L 2886 3955
+z
+" id="CMR17-37" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-37"/>
+ </g>
+ </g>
+ <g id="text_11">
+ <!-- 0.00043 -->
+ <g style="fill:#262626;" transform="translate(439.245807 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1414 2176
+C 1984 2176 2234 1673 2234 1094
+C 2234 322 1824 25 1453 25
+C 1114 25 563 193 390 691
+C 422 678 454 678 486 678
+C 640 678 755 780 755 947
+C 755 1132 614 1216 486 1216
+C 378 1216 211 1164 211 927
+C 211 335 787 -128 1466 -128
+C 2176 -128 2720 432 2720 1087
+C 2720 1718 2208 2176 1600 2246
+C 2086 2347 2554 2776 2554 3353
+C 2554 3856 2048 4224 1472 4224
+C 890 4224 378 3862 378 3347
+C 378 3123 544 3084 627 3084
+C 762 3084 877 3167 877 3334
+C 877 3500 762 3584 627 3584
+C 602 3584 570 3584 544 3571
+C 730 3999 1235 4076 1459 4076
+C 1683 4076 2106 3966 2106 3347
+C 2106 3167 2080 2851 1862 2574
+C 1670 2329 1453 2316 1242 2297
+C 1210 2297 1062 2284 1037 2284
+C 992 2278 966 2272 966 2227
+C 966 2182 973 2176 1101 2176
+L 1414 2176
+z
+" id="CMR17-33" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(161.94249 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(207.632967 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(253.323444 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ <g id="text_12">
+ <!-- 6.7e-08 -->
+ <g style="fill:#262626;" transform="translate(710.20871 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 678 2198
+C 678 3712 1395 4076 1811 4076
+C 1946 4076 2272 4049 2400 3782
+C 2298 3782 2106 3782 2106 3558
+C 2106 3385 2246 3328 2336 3328
+C 2394 3328 2566 3353 2566 3571
+C 2566 3987 2246 4224 1805 4224
+C 1043 4224 243 3411 243 2011
+C 243 257 966 -128 1478 -128
+C 2099 -128 2688 431 2688 1295
+C 2688 2101 2170 2688 1517 2688
+C 1126 2688 838 2430 678 1979
+L 678 2198
+z
+M 1478 25
+C 691 25 691 1212 691 1450
+C 691 1914 909 2585 1504 2585
+C 1613 2585 1926 2585 2138 2140
+C 2253 1889 2253 1624 2253 1302
+C 2253 954 2253 696 2118 438
+C 1978 173 1773 25 1478 25
+z
+" id="CMR17-36" transform="scale(0.015625)"/>
+ <path d="M 1741 2289
+C 2144 2494 2554 2803 2554 3298
+C 2554 3884 1990 4224 1472 4224
+C 890 4224 378 3800 378 3215
+C 378 3054 416 2777 666 2533
+C 730 2469 998 2276 1171 2154
+C 883 2006 211 1652 211 945
+C 211 282 838 -128 1459 -128
+C 2144 -128 2720 366 2720 1022
+C 2720 1607 2330 1877 2074 2051
+L 1741 2289
+z
+M 902 2855
+C 851 2887 595 3086 595 3388
+C 595 3781 998 4076 1459 4076
+C 1965 4076 2336 3716 2336 3298
+C 2336 2700 1670 2359 1638 2359
+C 1632 2359 1626 2359 1574 2398
+L 902 2855
+z
+M 2080 1536
+C 2176 1466 2483 1253 2483 861
+C 2483 385 2010 25 1472 25
+C 890 25 448 443 448 951
+C 448 1459 838 1884 1280 2083
+L 2080 1536
+z
+" id="CMR17-38" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-36"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-37"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-38"/>
+ </g>
+ </g>
+ <g id="text_13">
+ <!-- 6.7e-08 -->
+ <g style="fill:#262626;" transform="translate(978.04871 228.955463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-36"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-37"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-38"/>
+ </g>
+ </g>
+ <g id="text_14">
+ <!-- 0.51 -->
+ <g style="fill:#ffffff;" transform="translate(191.966522 518.875463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1702 4083
+C 1702 4217 1696 4224 1606 4224
+C 1357 3927 979 3833 621 3820
+C 602 3820 570 3820 563 3808
+C 557 3795 557 3782 557 3648
+C 755 3648 1088 3686 1344 3839
+L 1344 467
+C 1344 243 1331 166 781 166
+L 589 166
+L 589 0
+C 896 6 1216 12 1523 12
+C 1830 12 2150 6 2458 0
+L 2458 166
+L 2266 166
+C 1715 166 1702 236 1702 467
+L 1702 4083
+z
+" id="CMR17-31" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ <g id="text_15">
+ <!-- 0.5 -->
+ <g style="fill:#ffffff;" transform="translate(466.660094 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_16">
+ <!-- 0.53 -->
+ <g style="fill:#ffffff;" transform="translate(727.646522 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ <g id="text_17">
+ <!-- 0.53 -->
+ <g style="fill:#ffffff;" transform="translate(995.486522 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ <g id="text_18">
+ <!-- 0.49 -->
+ <g style="fill:#ffffff;" transform="translate(191.966522 808.795463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2253 1871
+C 2253 448 1670 25 1190 25
+C 1043 25 685 43 538 281
+C 704 256 826 345 826 505
+C 826 678 685 736 595 736
+C 538 736 365 710 365 492
+C 365 68 742 -128 1203 -128
+C 1939 -128 2688 665 2688 2090
+C 2688 3857 1971 4224 1485 4224
+C 851 4224 243 3664 243 2800
+C 243 2000 762 1408 1414 1408
+C 1952 1408 2189 1910 2253 2122
+L 2253 1871
+z
+M 1427 1510
+C 1254 1510 1011 1542 813 1929
+C 678 2181 678 2477 678 2793
+C 678 3174 678 3438 858 3722
+C 947 3857 1114 4076 1485 4076
+C 2240 4076 2240 2909 2240 2651
+C 2240 2193 2035 1510 1427 1510
+z
+" id="CMR17-39" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-39"/>
+ </g>
+ </g>
+ <g id="text_19">
+ <!-- 0.5 -->
+ <g style="fill:#ffffff;" transform="translate(466.660094 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ <g id="text_20">
+ <!-- 0.47 -->
+ <g style="fill:#ffffff;" transform="translate(727.646522 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-37"/>
+ </g>
+ </g>
+ <g id="text_21">
+ <!-- 0.47 -->
+ <g style="fill:#ffffff;" transform="translate(995.486522 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-37"/>
+ </g>
+ </g>
+ </g>
+ <g id="axes_2">
+ <g id="patch_3">
+ <path d="M 1220.657891 946.284441
+L 1264.145891 946.284441
+L 1264.145891 76.524441
+L 1220.657891 76.524441
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="patch_4">
+ <path clip-path="url(#p85530c5d57)" d="M 1220.657891 946.284441
+L 1220.657891 942.886941
+L 1220.657891 79.921941
+L 1220.657891 76.524441
+L 1264.145891 76.524441
+L 1264.145891 79.921941
+L 1264.145891 942.886941
+L 1264.145891 946.284441
+L 1264.145891 946.284441
+z
+" style="fill:#ffffff;stroke:#ffffff;stroke-linejoin:miter;stroke-width:0.01;"/>
+ </g>
+ <image height="870" id="imagef6d4731400" transform="scale(1 -1)translate(0 -870)" width="43" x="1221" xlink:href="data:image/png;base64,
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" y="-76"/>
+ <g id="matplotlib.axis_3"/>
+ <g id="matplotlib.axis_4">
+ <g id="ytick_4">
+ <g id="line2d_8">
+ <defs>
+ <path d="M 0 0
+L 3.5 0
+" id="m80979439c7" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m80979439c7" y="780.661049"/>
+ </g>
+ </g>
+ <g id="text_22">
+ <!-- $\mathdefault{0.1}$ -->
+ <g transform="translate(1271.145891 791.038797)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1178 307
+C 1178 492 1024 620 870 620
+C 685 620 557 467 557 313
+C 557 128 710 0 864 0
+C 1050 0 1178 153 1178 307
+z
+" id="CMMI12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_5">
+ <g id="line2d_9">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m80979439c7" y="615.037547"/>
+ </g>
+ </g>
+ <g id="text_23">
+ <!-- $\mathdefault{0.2}$ -->
+ <g transform="translate(1271.145891 625.415294)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2669 990
+L 2554 990
+C 2490 537 2438 460 2413 422
+C 2381 371 1920 371 1830 371
+L 602 371
+C 832 620 1280 1073 1824 1596
+C 2214 1966 2669 2400 2669 3033
+C 2669 3788 2067 4224 1395 4224
+C 691 4224 262 3603 262 3027
+C 262 2777 448 2745 525 2745
+C 589 2745 781 2783 781 3007
+C 781 3206 614 3264 525 3264
+C 486 3264 448 3257 422 3244
+C 544 3788 915 4057 1306 4057
+C 1862 4057 2227 3616 2227 3033
+C 2227 2477 1901 1998 1536 1583
+L 262 147
+L 262 0
+L 2515 0
+L 2669 990
+z
+" id="CMR17-32" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_6">
+ <g id="line2d_10">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m80979439c7" y="449.414044"/>
+ </g>
+ </g>
+ <g id="text_24">
+ <!-- $\mathdefault{0.3}$ -->
+ <g transform="translate(1271.145891 459.791791)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_7">
+ <g id="line2d_11">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m80979439c7" y="283.790541"/>
+ </g>
+ </g>
+ <g id="text_25">
+ <!-- $\mathdefault{0.4}$ -->
+ <g transform="translate(1271.145891 294.168289)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_8">
+ <g id="line2d_12">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m80979439c7" y="118.167039"/>
+ </g>
+ </g>
+ <g id="text_26">
+ <!-- $\mathdefault{0.5}$ -->
+ <g transform="translate(1271.145891 128.544786)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ </g>
+ <g id="LineCollection_1"/>
+ <g id="patch_5">
+ <path d="M 1220.657891 946.284441
+L 1220.657891 942.886941
+L 1220.657891 79.921941
+L 1220.657891 76.524441
+L 1264.145891 76.524441
+L 1264.145891 79.921941
+L 1264.145891 942.886941
+L 1264.145891 946.284441
+z
+" style="fill:none;"/>
+ </g>
+ </g>
+ </g>
+ <defs>
+ <clipPath id="pea58550c9c">
+ <rect height="869.76" width="1071.36" x="82.337891" y="76.524441"/>
+ </clipPath>
+ <clipPath id="p85530c5d57">
+ <rect height="869.76" width="43.488" x="1220.657891" y="76.524441"/>
+ </clipPath>
+ </defs>
+</svg>
diff --git a/examples/model-comparison/reference/confusionMatrix_ND_7.svg b/examples/model-comparison/reference/confusionMatrix_ND_7.svg
new file mode 100644
index 0000000000000000000000000000000000000000..1ec466699a0789aae80c426b53b8012efffe1ef5
--- /dev/null
+++ b/examples/model-comparison/reference/confusionMatrix_ND_7.svg
@@ -0,0 +1,1609 @@
+<?xml version="1.0" encoding="utf-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<svg height="953.484441pt" version="1.1" viewBox="0 0 1313.889331 953.484441" width="1313.889331pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+ <metadata>
+ <rdf:RDF xmlns:cc="http://creativecommons.org/ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
+ <cc:Work>
+ <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
+ <dc:date>2022-06-03T16:06:08.348017</dc:date>
+ <dc:format>image/svg+xml</dc:format>
+ <dc:creator>
+ <cc:Agent>
+ <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>
+ </cc:Agent>
+ </dc:creator>
+ </cc:Work>
+ </rdf:RDF>
+ </metadata>
+ <defs>
+ <style type="text/css">*{stroke-linecap:butt;stroke-linejoin:round;}</style>
+ </defs>
+ <g id="figure_1">
+ <g id="patch_1">
+ <path d="M 0 953.484441
+L 1313.889331 953.484441
+L 1313.889331 0
+L 0 0
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="axes_1">
+ <g id="patch_2">
+ <path d="M 82.337891 946.284441
+L 1153.697891 946.284441
+L 1153.697891 76.524441
+L 82.337891 76.524441
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="QuadMesh_1">
+ <path clip-path="url(#p1ad762eb0e)" d="M 82.337891 76.524441
+L 350.177891 76.524441
+L 350.177891 366.444441
+L 82.337891 366.444441
+L 82.337891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#p1ad762eb0e)" d="M 350.177891 76.524441
+L 618.017891 76.524441
+L 618.017891 366.444441
+L 350.177891 366.444441
+L 350.177891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#p1ad762eb0e)" d="M 618.017891 76.524441
+L 885.857891 76.524441
+L 885.857891 366.444441
+L 618.017891 366.444441
+L 618.017891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#p1ad762eb0e)" d="M 885.857891 76.524441
+L 1153.697891 76.524441
+L 1153.697891 366.444441
+L 885.857891 366.444441
+L 885.857891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#p1ad762eb0e)" d="M 82.337891 366.444441
+L 350.177891 366.444441
+L 350.177891 656.364441
+L 82.337891 656.364441
+L 82.337891 366.444441
+" style="fill:#08306b;"/>
+ <path clip-path="url(#p1ad762eb0e)" d="M 350.177891 366.444441
+L 618.017891 366.444441
+L 618.017891 656.364441
+L 350.177891 656.364441
+L 350.177891 366.444441
+" style="fill:#084387;"/>
+ <path clip-path="url(#p1ad762eb0e)" d="M 618.017891 366.444441
+L 885.857891 366.444441
+L 885.857891 656.364441
+L 618.017891 656.364441
+L 618.017891 366.444441
+" style="fill:#083674;"/>
+ <path clip-path="url(#p1ad762eb0e)" d="M 885.857891 366.444441
+L 1153.697891 366.444441
+L 1153.697891 656.364441
+L 885.857891 656.364441
+L 885.857891 366.444441
+" style="fill:#083674;"/>
+ <path clip-path="url(#p1ad762eb0e)" d="M 82.337891 656.364441
+L 350.177891 656.364441
+L 350.177891 946.284441
+L 82.337891 946.284441
+L 82.337891 656.364441
+" style="fill:#08468b;"/>
+ <path clip-path="url(#p1ad762eb0e)" d="M 350.177891 656.364441
+L 618.017891 656.364441
+L 618.017891 946.284441
+L 350.177891 946.284441
+L 350.177891 656.364441
+" style="fill:#08326e;"/>
+ <path clip-path="url(#p1ad762eb0e)" d="M 618.017891 656.364441
+L 885.857891 656.364441
+L 885.857891 946.284441
+L 618.017891 946.284441
+L 618.017891 656.364441
+" style="fill:#083e81;"/>
+ <path clip-path="url(#p1ad762eb0e)" d="M 885.857891 656.364441
+L 1153.697891 656.364441
+L 1153.697891 946.284441
+L 885.857891 946.284441
+L 885.857891 656.364441
+" style="fill:#083e81;"/>
+ </g>
+ <g id="matplotlib.axis_1">
+ <g id="xtick_1">
+ <g id="line2d_1">
+ <defs>
+ <path d="M 0 0
+L 0 -3.5
+" id="mfc3e427192" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="216.257891" xlink:href="#mfc3e427192" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_1">
+ <!-- Observation -->
+ <g transform="translate(144.303789 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 4307 2166
+C 4307 3488 3366 4480 2304 4480
+C 1216 4480 294 3475 294 2166
+C 294 857 1229 -128 2298 -128
+C 3392 -128 4307 876 4307 2166
+z
+M 2304 -13
+C 1574 -13 781 722 781 2250
+C 781 3771 1651 4364 2298 4364
+C 2976 4364 3821 3752 3821 2250
+C 3821 696 3008 -13 2304 -13
+z
+" id="CMR17-4f" transform="scale(0.015625)"/>
+ <path d="M 960 4416
+L 198 4345
+L 198 4179
+C 576 4179 634 4141 634 3843
+L 634 -13
+L 749 -13
+L 934 445
+C 1120 141 1395 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2209 2477 2816 1830 2816
+C 1434 2816 1152 2603 960 2351
+L 960 4416
+z
+M 973 2022
+C 973 2138 973 2157 1062 2293
+C 1312 2681 1670 2713 1792 2713
+C 1984 2713 2643 2610 2643 1388
+C 2643 109 1888 38 1734 38
+C 1536 38 1248 115 1043 490
+C 973 613 973 626 973 742
+L 973 2022
+z
+" id="CMR17-62" transform="scale(0.015625)"/>
+ <path d="M 1978 2688
+C 1978 2803 1971 2809 1933 2809
+C 1907 2809 1901 2803 1824 2707
+C 1805 2681 1747 2617 1728 2592
+C 1523 2809 1235 2816 1126 2816
+C 416 2816 160 2444 160 2073
+C 160 1497 813 1363 998 1324
+C 1402 1241 1542 1216 1677 1100
+C 1760 1024 1901 883 1901 652
+C 1901 384 1747 38 1158 38
+C 602 38 403 460 288 1024
+C 269 1113 269 1120 218 1120
+C 166 1120 160 1113 160 985
+L 160 64
+C 160 -52 166 -58 205 -58
+C 237 -58 243 -52 275 0
+C 314 57 410 211 448 275
+C 576 102 800 -64 1158 -64
+C 1792 -64 2131 281 2131 780
+C 2131 1107 1958 1280 1875 1356
+C 1683 1555 1459 1600 1190 1651
+C 838 1728 390 1817 390 2208
+C 390 2374 480 2726 1126 2726
+C 1811 2726 1850 2086 1862 1881
+C 1869 1849 1901 1843 1920 1843
+C 1978 1843 1978 1862 1978 1971
+L 1978 2688
+z
+" id="CMR17-73" transform="scale(0.015625)"/>
+ <path d="M 2438 1503
+C 2464 1529 2464 1542 2464 1606
+C 2464 2251 2118 2816 1389 2816
+C 710 2816 173 2175 173 1394
+C 173 554 781 -64 1459 -64
+C 2176 -64 2458 619 2458 755
+C 2458 800 2419 800 2406 800
+C 2362 800 2355 787 2330 709
+C 2189 270 1837 51 1504 51
+C 1229 51 954 206 781 490
+C 582 819 582 1200 582 1503
+L 2438 1503
+z
+M 589 1600
+C 634 2511 1126 2713 1382 2713
+C 1818 2713 2112 2308 2118 1600
+L 589 1600
+z
+" id="CMR17-65" transform="scale(0.015625)"/>
+ <path d="M 960 1517
+C 960 2134 1222 2713 1702 2713
+C 1747 2713 1792 2707 1837 2687
+C 1837 2687 1696 2642 1696 2475
+C 1696 2321 1818 2257 1914 2257
+C 1990 2257 2131 2302 2131 2482
+C 2131 2687 1926 2816 1709 2816
+C 1222 2816 1011 2340 947 2115
+L 941 2115
+L 941 2816
+L 198 2745
+L 198 2578
+C 576 2578 634 2540 634 2231
+L 634 443
+C 634 198 608 166 198 166
+L 198 0
+C 352 12 646 12 813 12
+C 998 12 1325 12 1498 0
+L 1498 166
+C 1037 166 960 166 960 455
+L 960 1517
+z
+" id="CMR17-72" transform="scale(0.015625)"/>
+ <path d="M 2502 2173
+C 2560 2315 2662 2572 3034 2585
+L 3034 2752
+C 2912 2745 2752 2739 2630 2739
+C 2496 2739 2285 2739 2157 2752
+L 2157 2585
+C 2317 2572 2406 2495 2406 2328
+C 2406 2270 2406 2257 2368 2167
+L 1664 379
+L 902 2308
+C 864 2392 864 2405 864 2431
+C 864 2585 1075 2585 1171 2585
+L 1171 2752
+C 1018 2739 736 2739 576 2739
+C 403 2739 205 2739 64 2752
+L 64 2585
+C 307 2585 442 2585 518 2386
+L 1446 44
+C 1485 -52 1491 -64 1549 -64
+C 1606 -64 1613 -52 1651 44
+L 2502 2173
+z
+" id="CMR17-76" transform="scale(0.015625)"/>
+ <path d="M 2304 1656
+C 2304 2048 2304 2275 2035 2534
+C 1798 2751 1523 2816 1306 2816
+C 800 2816 435 2408 435 1977
+C 435 1740 627 1728 666 1728
+C 749 1728 896 1779 896 1958
+C 896 2118 774 2188 666 2188
+C 640 2188 608 2182 589 2176
+C 723 2594 1069 2713 1293 2713
+C 1613 2713 1965 2421 1965 1875
+L 1965 1632
+C 1587 1619 1133 1568 774 1373
+C 371 1147 256 822 256 576
+C 256 77 832 -64 1171 -64
+C 1523 -64 1850 135 1990 505
+C 2003 219 2182 -39 2464 -39
+C 2598 -39 2938 51 2938 563
+L 2938 926
+L 2822 926
+L 2822 557
+C 2822 161 2650 109 2566 109
+C 2304 109 2304 446 2304 732
+L 2304 1656
+z
+M 1965 887
+C 1965 323 1568 38 1216 38
+C 896 38 646 278 646 576
+C 646 771 730 1114 1101 1322
+C 1408 1497 1760 1523 1965 1536
+L 1965 887
+z
+" id="CMR17-61" transform="scale(0.015625)"/>
+ <path d="M 966 2585
+L 1862 2585
+L 1862 2752
+L 966 2752
+L 966 3968
+L 851 3968
+C 838 3292 614 2700 70 2687
+L 70 2585
+L 627 2585
+L 627 778
+C 627 655 627 -64 1370 -64
+C 1747 -64 1965 308 1965 784
+L 1965 1151
+L 1850 1151
+L 1850 790
+C 1850 347 1677 51 1408 51
+C 1222 51 966 179 966 765
+L 966 2585
+z
+" id="CMR17-74" transform="scale(0.015625)"/>
+ <path d="M 992 3961
+C 992 4102 877 4224 730 4224
+C 589 4224 467 4108 467 3961
+C 467 3820 582 3699 730 3699
+C 870 3699 992 3814 992 3961
+z
+M 243 2745
+L 243 2579
+C 602 2579 653 2540 653 2231
+L 653 443
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 646 12 806 12
+C 960 12 1222 12 1370 0
+L 1370 166
+C 992 166 979 205 979 436
+L 979 2816
+L 243 2745
+z
+" id="CMR17-69" transform="scale(0.015625)"/>
+ <path d="M 2758 1356
+C 2758 2176 2163 2816 1466 2816
+C 768 2816 173 2176 173 1356
+C 173 550 768 -64 1466 -64
+C 2163 -64 2758 550 2758 1356
+z
+M 1466 51
+C 1165 51 909 230 762 480
+C 602 768 582 1126 582 1408
+C 582 1676 595 2009 762 2297
+C 890 2508 1139 2713 1466 2713
+C 1754 2713 1997 2553 2150 2329
+C 2349 2028 2349 1606 2349 1408
+C 2349 1158 2336 774 2163 467
+C 1984 172 1709 51 1466 51
+z
+" id="CMR17-6f" transform="scale(0.015625)"/>
+ <path d="M 2656 1954
+C 2656 2282 2592 2816 1837 2816
+C 1331 2816 1069 2424 973 2166
+L 966 2166
+L 966 2816
+L 211 2745
+L 211 2578
+C 589 2578 646 2540 646 2231
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1954
+z
+" id="CMR17-6e" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-4f"/>
+ <use transform="translate(71.714788 0)scale(0.996264)" xlink:href="#CMR17-62"/>
+ <use transform="translate(122.610158 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(158.411496 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(198.897156 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ <use transform="translate(234.177924 0)scale(0.996264)" xlink:href="#CMR17-76"/>
+ <use transform="translate(277.266023 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(322.9565 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(358.237268 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(383.108327 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(428.798804 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_2">
+ <g id="line2d_2">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="484.097891" xlink:href="#mfc3e427192" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_2">
+ <!-- linear -->
+ <g transform="translate(450.783747 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 979 4416
+L 218 4345
+L 218 4179
+C 595 4179 653 4141 653 3835
+L 653 439
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 653 12 813 12
+C 979 12 1261 12 1414 0
+L 1414 166
+C 1005 166 979 191 979 439
+L 979 4416
+z
+" id="CMR17-6c" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_3">
+ <g id="line2d_3">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="751.937891" xlink:href="#mfc3e427192" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_3">
+ <!-- exponential -->
+ <g transform="translate(683.18479 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1664 1491
+C 1856 1740 2074 2022 2253 2233
+C 2464 2476 2707 2579 2989 2585
+L 2989 2752
+C 2880 2745 2656 2739 2541 2739
+C 2368 2739 2170 2739 2022 2752
+L 2022 2585
+C 2112 2572 2163 2508 2163 2419
+C 2163 2304 2099 2233 2067 2188
+L 1594 1587
+L 1030 2323
+C 973 2393 973 2406 973 2438
+C 973 2515 1037 2579 1146 2585
+L 1146 2752
+C 992 2739 717 2739 557 2739
+C 384 2739 179 2739 38 2752
+L 38 2585
+C 384 2585 461 2560 614 2368
+L 1350 1414
+C 1363 1401 1395 1363 1395 1344
+C 1395 1318 838 633 768 544
+C 480 198 179 172 6 166
+L 6 0
+C 115 6 339 12 454 12
+C 582 12 864 12 979 0
+L 979 166
+C 941 172 838 185 838 332
+C 838 448 890 518 947 595
+L 1478 1248
+L 2035 524
+C 2086 454 2163 358 2163 313
+C 2163 224 2086 172 1984 166
+L 1984 0
+C 2138 12 2413 12 2573 12
+C 2746 12 2950 12 3091 0
+L 3091 166
+C 2771 166 2675 179 2522 377
+L 1664 1491
+z
+" id="CMR17-78" transform="scale(0.015625)"/>
+ <path d="M 1408 -1114
+C 998 -1114 973 -1088 973 -834
+L 973 380
+C 1158 109 1427 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2196 2496 2816 1837 2816
+C 1453 2816 1139 2603 960 2345
+L 960 2816
+L 198 2745
+L 198 2577
+C 576 2577 634 2539 634 2228
+L 634 -834
+C 634 -1081 608 -1114 198 -1114
+L 198 -1280
+C 352 -1268 634 -1268 800 -1268
+C 966 -1268 1254 -1268 1408 -1280
+L 1408 -1114
+z
+M 973 2015
+C 973 2106 973 2241 1222 2481
+C 1254 2506 1472 2700 1792 2700
+C 2259 2700 2643 2112 2643 1376
+C 2643 639 2234 38 1728 38
+C 1498 38 1248 148 1056 451
+C 973 594 973 632 973 736
+L 973 2015
+z
+" id="CMR17-70" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_4">
+ <g id="line2d_4">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1019.777891" xlink:href="#mfc3e427192" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_4">
+ <!-- cosine -->
+ <g transform="translate(984.043472 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2234 2240
+C 2112 2240 1933 2240 1933 2015
+C 1933 1836 2080 1785 2163 1785
+C 2208 1785 2394 1804 2394 2028
+C 2394 2476 1958 2816 1466 2816
+C 787 2816 211 2201 211 1379
+C 211 521 813 -64 1466 -64
+C 2259 -64 2458 676 2458 747
+C 2458 773 2451 792 2406 792
+C 2362 792 2355 786 2330 702
+C 2163 180 1798 51 1523 51
+C 1114 51 621 431 621 1385
+C 621 2358 1094 2700 1472 2700
+C 1722 2700 2093 2582 2234 2240
+z
+" id="CMR17-63" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_5">
+ <!-- \textbf{Data generated by:} -->
+ <g transform="translate(476.949653 27.955495)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 243 4416
+L 243 4140
+L 922 4140
+L 922 275
+L 243 275
+L 243 0
+L 2938 0
+C 4166 0 5114 790 5114 2169
+C 5114 3625 4141 4416 2938 4416
+L 243 4416
+z
+M 1734 275
+L 1734 4140
+L 2694 4140
+C 3251 4140 3699 3921 3936 3586
+C 4122 3322 4243 3006 4243 2175
+C 4243 1421 4147 1086 3923 784
+C 3699 487 3270 275 2694 275
+L 1734 275
+z
+" id="CMBX12-44" transform="scale(0.015625)"/>
+ <path d="M 2944 1894
+C 2944 2483 2477 2880 1574 2880
+C 1216 2880 461 2847 461 2310
+C 461 2041 666 1926 838 1926
+C 1030 1926 1216 2060 1216 2303
+C 1216 2425 1171 2540 1062 2611
+C 1274 2668 1427 2668 1549 2668
+C 1984 2668 2246 2425 2246 1900
+L 2246 1644
+C 1235 1644 218 1362 218 648
+C 218 64 960 -64 1402 -64
+C 1894 -64 2208 205 2336 488
+C 2336 250 2336 -26 2982 -26
+L 3309 -26
+C 3443 -26 3494 -26 3494 115
+C 3494 250 3437 250 3347 250
+C 2944 256 2944 359 2944 507
+L 2944 1894
+z
+M 2246 867
+C 2246 262 1709 147 1504 147
+C 1190 147 928 359 928 655
+C 928 1240 1619 1439 2246 1472
+L 2246 867
+z
+" id="CMBX12-61" transform="scale(0.015625)"/>
+ <path d="M 1350 2540
+L 2272 2540
+L 2272 2816
+L 1350 2816
+L 1350 4032
+L 1082 4032
+C 1075 3401 768 2771 134 2751
+L 134 2540
+L 653 2540
+L 653 761
+C 653 83 1178 -64 1638 -64
+C 2112 -64 2394 294 2394 768
+L 2394 1107
+L 2125 1107
+L 2125 774
+C 2125 352 1933 166 1734 166
+C 1350 166 1350 595 1350 742
+L 1350 2540
+z
+" id="CMBX12-74" transform="scale(0.015625)"/>
+ <path d="M 832 1177
+C 1139 1011 1498 1011 1594 1011
+C 2477 1011 2829 1506 2829 1958
+C 2829 2287 2643 2519 2566 2584
+C 2752 2687 2906 2713 3014 2726
+C 2995 2694 2976 2668 2976 2584
+C 2976 2448 3066 2326 3232 2326
+C 3398 2326 3488 2448 3488 2584
+C 3488 2739 3373 2944 3104 2944
+C 2829 2944 2566 2809 2432 2694
+C 2170 2847 1920 2905 1594 2905
+C 710 2905 358 2410 358 1958
+C 358 1758 422 1493 691 1274
+C 582 1151 467 926 467 693
+C 467 416 614 179 749 76
+C 595 38 198 -109 198 -474
+C 198 -852 614 -1280 1792 -1280
+C 2854 -1280 3392 -935 3392 -455
+C 3392 108 3021 294 2861 371
+C 2554 524 2144 524 1581 524
+C 1421 524 1139 524 1107 531
+C 832 576 755 823 755 946
+C 755 998 762 1094 832 1177
+z
+M 1594 1216
+C 1037 1216 1037 1661 1037 1958
+C 1037 2255 1037 2700 1594 2700
+C 2150 2700 2150 2255 2150 1958
+C 2150 1661 2150 1216 1594 1216
+z
+M 1952 -64
+C 2419 -64 2867 -148 2867 -480
+C 2867 -704 2643 -1076 1798 -1076
+C 954 -1076 723 -717 723 -474
+C 723 -64 1126 -64 1222 -64
+L 1952 -64
+z
+" id="CMBX12-67" transform="scale(0.015625)"/>
+ <path d="M 2893 1408
+C 3040 1408 3078 1408 3078 1568
+C 3078 1758 3034 2232 2739 2529
+C 2470 2796 2112 2880 1741 2880
+C 742 2880 198 2232 198 1433
+C 198 523 858 -64 1824 -64
+C 2790 -64 3078 621 3078 731
+C 3078 829 2982 829 2944 829
+C 2842 829 2835 809 2797 725
+C 2630 302 2208 166 1901 166
+C 973 166 966 1043 966 1408
+L 2893 1408
+z
+M 966 1593
+C 979 1852 986 2099 1120 2327
+C 1242 2529 1466 2668 1741 2668
+C 2426 2668 2483 1909 2490 1593
+L 966 1593
+z
+" id="CMBX12-65" transform="scale(0.015625)"/>
+ <path d="M 3398 1958
+C 3398 2566 3136 2880 2432 2880
+C 1971 2880 1574 2656 1357 2176
+L 1350 2176
+L 1350 2880
+L 269 2828
+L 269 2553
+C 666 2553 710 2553 710 2304
+L 710 275
+L 269 275
+L 269 0
+C 416 12 877 12 1056 12
+C 1235 12 1702 12 1850 0
+L 1850 275
+L 1408 275
+L 1408 1638
+C 1408 2329 1920 2668 2330 2668
+C 2566 2668 2701 2515 2701 2028
+L 2701 275
+L 2259 275
+L 2259 0
+C 2406 12 2867 12 3046 12
+C 3226 12 3693 12 3840 0
+L 3840 275
+L 3398 275
+L 3398 1958
+z
+" id="CMBX12-6e" transform="scale(0.015625)"/>
+ <path d="M 1331 1440
+C 1331 1651 1376 2668 2125 2668
+C 2035 2598 1990 2489 1990 2374
+C 1990 2112 2202 2003 2362 2003
+C 2522 2003 2733 2112 2733 2374
+C 2733 2700 2400 2880 2093 2880
+C 1587 2880 1370 2438 1280 2169
+L 1274 2169
+L 1274 2880
+L 224 2828
+L 224 2553
+C 621 2553 666 2553 666 2304
+L 666 275
+L 224 275
+L 224 0
+C 371 12 851 12 1030 12
+C 1216 12 1734 12 1888 0
+L 1888 275
+L 1331 275
+L 1331 1440
+z
+" id="CMBX12-72" transform="scale(0.015625)"/>
+ <path d="M 2221 4428
+L 2221 4153
+C 2618 4153 2662 4153 2662 3896
+L 2662 2571
+C 2522 2694 2240 2880 1798 2880
+C 890 2880 243 2313 243 1408
+C 243 483 877 -64 1728 -64
+C 2080 -64 2381 57 2630 270
+L 2630 -64
+L 3770 -26
+L 3770 250
+C 3373 250 3328 250 3328 502
+L 3328 4480
+L 2221 4428
+z
+M 2630 625
+C 2362 231 2035 147 1805 147
+C 1011 147 1011 968 1011 1395
+C 1011 1699 1011 2022 1152 2268
+C 1350 2630 1728 2668 1875 2668
+C 2138 2668 2419 2552 2630 2268
+L 2630 625
+z
+" id="CMBX12-64" transform="scale(0.015625)"/>
+ <path d="M 1331 4480
+L 224 4428
+L 224 4153
+C 621 4153 666 4153 666 3896
+L 666 -26
+L 934 -26
+C 1043 96 1152 218 1254 347
+C 1581 6 1933 -64 2189 -64
+C 3072 -64 3750 476 3750 1414
+C 3750 2300 3149 2880 2272 2880
+C 1894 2880 1594 2758 1331 2552
+L 1331 4480
+z
+M 1363 2242
+C 1587 2552 1920 2668 2189 2668
+C 2982 2668 2982 1847 2982 1420
+C 2982 1130 2982 761 2829 522
+C 2630 211 2330 147 2125 147
+C 1690 147 1453 457 1363 599
+L 1363 2242
+z
+" id="CMBX12-62" transform="scale(0.015625)"/>
+ <path d="M 3168 2400
+C 3206 2489 3232 2540 3642 2540
+L 3642 2816
+C 3424 2803 3398 2803 3136 2803
+C 2963 2803 2950 2803 2586 2816
+L 2586 2540
+C 2592 2540 2893 2540 2893 2457
+C 2893 2438 2874 2400 2867 2381
+L 2118 780
+L 1299 2540
+L 1651 2540
+L 1651 2816
+C 1498 2803 1062 2803 883 2803
+C 698 2803 320 2803 154 2816
+L 154 2540
+L 563 2540
+L 1747 -8
+C 1715 -84 1626 -269 1594 -345
+C 1459 -631 1254 -1069 806 -1069
+C 781 -1069 704 -1069 634 -1031
+C 646 -1025 838 -949 838 -707
+C 838 -497 685 -364 493 -364
+C 294 -364 141 -497 141 -713
+C 141 -1012 422 -1280 806 -1280
+C 1331 -1280 1677 -809 1805 -529
+L 3168 2400
+z
+" id="CMBX12-79" transform="scale(0.015625)"/>
+ <path d="M 1459 2355
+C 1459 2617 1248 2816 998 2816
+C 749 2816 538 2617 538 2355
+C 538 2092 749 1894 998 1894
+C 1248 1894 1459 2092 1459 2355
+z
+M 1459 460
+C 1459 723 1248 921 998 921
+C 749 921 538 723 538 460
+C 538 198 749 0 998 0
+C 1248 0 1459 198 1459 460
+z
+" id="CMBX12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMBX12-44"/>
+ <use transform="translate(85.904786 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(140.387974 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(183.974524 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(275.817613 0)scale(0.996264)" xlink:href="#CMBX12-67"/>
+ <use transform="translate(331.857463 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(382.99673 0)scale(0.996264)" xlink:href="#CMBX12-6e"/>
+ <use transform="translate(445.263231 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(496.402498 0)scale(0.996264)" xlink:href="#CMBX12-72"/>
+ <use transform="translate(542.180006 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(596.663194 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(640.249744 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(691.389011 0)scale(0.996264)" xlink:href="#CMBX12-64"/>
+ <use transform="translate(791.015412 0)scale(0.996264)" xlink:href="#CMBX12-62"/>
+ <use transform="translate(850.168588 0)scale(0.996264)" xlink:href="#CMBX12-79"/>
+ <use transform="translate(909.321763 0)scale(0.996264)" xlink:href="#CMBX12-3a"/>
+ </g>
+ </g>
+ </g>
+ <g id="matplotlib.axis_2">
+ <g id="ytick_1">
+ <g id="line2d_5">
+ <defs>
+ <path d="M 0 0
+L -3.5 0
+" id="m39d76f3dfe" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#m39d76f3dfe" y="221.484441"/>
+ </g>
+ </g>
+ <g id="text_6">
+ <!-- linear -->
+ <g transform="translate(69.524441 277.73498)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_2">
+ <g id="line2d_6">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#m39d76f3dfe" y="511.404441"/>
+ </g>
+ </g>
+ <g id="text_7">
+ <!-- exponential -->
+ <g transform="translate(69.524441 638.532895)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_3">
+ <g id="line2d_7">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#m39d76f3dfe" y="801.324441"/>
+ </g>
+ </g>
+ <g id="text_8">
+ <!-- cosine -->
+ <g transform="translate(69.524441 862.415532)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_9">
+ <!-- \textbf{Model weight for:} -->
+ <g transform="translate(27.955495 642.025756)rotate(-90)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 3411 816
+L 1875 4281
+C 1818 4416 1760 4416 1626 4416
+L 262 4416
+L 262 4140
+L 941 4140
+L 941 468
+C 941 326 934 320 768 294
+C 653 281 525 275 410 275
+L 262 275
+L 262 0
+C 410 12 909 12 1088 12
+C 1267 12 1773 12 1920 0
+L 1920 275
+L 1773 275
+C 1600 275 1587 275 1434 294
+C 1248 320 1242 326 1242 468
+L 1242 4063
+L 1248 4063
+L 2989 134
+C 3021 64 3059 0 3168 0
+C 3277 0 3315 64 3347 134
+L 5120 4140
+L 5126 4140
+L 5126 275
+L 4448 275
+L 4448 0
+C 4621 12 5286 12 5504 12
+C 5722 12 6387 12 6560 0
+L 6560 275
+L 5882 275
+L 5882 4140
+L 6560 4140
+L 6560 4416
+L 5197 4416
+C 5062 4416 5005 4416 4947 4281
+L 3411 816
+z
+" id="CMBX12-4d" transform="scale(0.015625)"/>
+ <path d="M 3392 1379
+C 3392 2245 2803 2880 1798 2880
+C 755 2880 198 2213 198 1379
+C 198 538 787 -64 1792 -64
+C 2835 -64 3392 570 3392 1379
+z
+M 1798 166
+C 966 166 966 917 966 1443
+C 966 1744 966 2065 1088 2296
+C 1229 2553 1517 2668 1792 2668
+C 2157 2668 2387 2495 2496 2315
+C 2624 2084 2624 1751 2624 1443
+C 2624 910 2624 166 1798 166
+z
+" id="CMBX12-6f" transform="scale(0.015625)"/>
+ <path d="M 1389 4480
+L 282 4428
+L 282 4153
+C 678 4153 723 4153 723 3901
+L 723 275
+L 282 275
+L 282 0
+C 429 12 883 12 1056 12
+C 1229 12 1683 12 1830 0
+L 1830 275
+L 1389 275
+L 1389 4480
+z
+" id="CMBX12-6c" transform="scale(0.015625)"/>
+ <path d="M 4608 2386
+C 4653 2496 4672 2540 5043 2540
+L 5043 2816
+C 4858 2803 4774 2803 4544 2803
+C 4282 2803 4198 2803 3968 2816
+L 3968 2540
+C 4026 2540 4339 2540 4339 2457
+C 4339 2451 4339 2444 4314 2380
+L 3642 712
+L 2906 2540
+L 3270 2540
+L 3270 2816
+C 3117 2803 2739 2803 2566 2803
+C 2240 2803 2227 2803 1907 2816
+L 1907 2540
+L 2285 2540
+C 2304 2489 2336 2406 2362 2348
+C 2381 2309 2445 2155 2445 2123
+C 2445 2111 2426 2066 2419 2046
+L 1933 834
+L 1242 2540
+L 1606 2540
+L 1606 2816
+C 1459 2803 1024 2803 851 2803
+C 646 2803 339 2803 147 2816
+L 147 2540
+L 525 2540
+L 1504 96
+C 1549 -20 1574 -64 1715 -64
+C 1786 -64 1862 -64 1914 64
+L 2592 1764
+L 3270 76
+C 3328 -64 3398 -64 3475 -64
+C 3616 -64 3635 -26 3680 89
+L 4608 2386
+z
+" id="CMBX12-77" transform="scale(0.015625)"/>
+ <path d="M 1427 4019
+C 1427 4281 1216 4480 966 4480
+C 704 4480 506 4262 506 4019
+C 506 3775 704 3558 966 3558
+C 1216 3558 1427 3756 1427 4019
+z
+M 301 2828
+L 301 2553
+C 678 2553 723 2553 723 2303
+L 723 275
+L 282 275
+L 282 0
+C 429 12 870 12 1043 12
+C 1222 12 1632 12 1786 0
+L 1786 275
+L 1389 275
+L 1389 2880
+L 301 2828
+z
+" id="CMBX12-69" transform="scale(0.015625)"/>
+ <path d="M 3398 1958
+C 3398 2566 3136 2880 2432 2880
+C 1786 2880 1472 2425 1382 2233
+L 1376 2233
+L 1376 4480
+L 269 4428
+L 269 4153
+C 666 4153 710 4153 710 3896
+L 710 275
+L 269 275
+L 269 0
+C 416 12 877 12 1056 12
+C 1235 12 1702 12 1850 0
+L 1850 275
+L 1408 275
+L 1408 1638
+C 1408 2329 1920 2668 2330 2668
+C 2566 2668 2701 2515 2701 2028
+L 2701 275
+L 2259 275
+L 2259 0
+C 2406 12 2867 12 3046 12
+C 3226 12 3693 12 3840 0
+L 3840 275
+L 3398 275
+L 3398 1958
+z
+" id="CMBX12-68" transform="scale(0.015625)"/>
+ <path d="M 1389 2540
+L 2118 2540
+L 2118 2816
+L 1357 2816
+L 1357 3466
+C 1357 4122 1779 4224 1990 4224
+C 2061 4224 2074 4217 2112 4204
+C 2016 4141 1958 4034 1958 3901
+C 1958 3649 2163 3535 2330 3535
+C 2470 3535 2701 3630 2701 3908
+C 2701 4167 2470 4435 2016 4435
+C 1434 4435 723 4192 723 3459
+L 723 2816
+L 250 2816
+L 250 2540
+L 723 2540
+L 723 275
+L 282 275
+L 282 0
+C 429 12 909 12 1088 12
+C 1274 12 1792 12 1946 0
+L 1946 275
+L 1389 275
+L 1389 2540
+z
+" id="CMBX12-66" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMBX12-4d"/>
+ <use transform="translate(106.314425 0)scale(0.996264)" xlink:href="#CMBX12-6f"/>
+ <use transform="translate(165.467601 0)scale(0.996264)" xlink:href="#CMBX12-64"/>
+ <use transform="translate(227.734101 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(278.873369 0)scale(0.996264)" xlink:href="#CMBX12-6c"/>
+ <use transform="translate(347.366519 0)scale(0.996264)" xlink:href="#CMBX12-77"/>
+ <use transform="translate(425.199645 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(476.338912 0)scale(0.996264)" xlink:href="#CMBX12-69"/>
+ <use transform="translate(507.472162 0)scale(0.996264)" xlink:href="#CMBX12-67"/>
+ <use transform="translate(563.512013 0)scale(0.996264)" xlink:href="#CMBX12-68"/>
+ <use transform="translate(622.665189 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(703.611639 0)scale(0.996264)" xlink:href="#CMBX12-66"/>
+ <use transform="translate(737.858215 0)scale(0.996264)" xlink:href="#CMBX12-6f"/>
+ <use transform="translate(793.898065 0)scale(0.996264)" xlink:href="#CMBX12-72"/>
+ <use transform="translate(839.675573 0)scale(0.996264)" xlink:href="#CMBX12-3a"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_10">
+ <!-- 5.8e-09 -->
+ <g style="fill:#262626;" transform="translate(174.52871 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 730 3750
+C 794 3724 1056 3641 1325 3641
+C 1920 3641 2246 3961 2432 4140
+C 2432 4191 2432 4224 2394 4224
+C 2387 4224 2374 4224 2323 4198
+C 2099 4102 1837 4032 1517 4032
+C 1325 4032 1037 4055 723 4191
+C 653 4224 640 4224 634 4224
+C 602 4224 595 4217 595 4090
+L 595 2231
+C 595 2113 595 2080 659 2080
+C 691 2080 704 2093 736 2139
+C 941 2435 1222 2560 1542 2560
+C 1766 2560 2246 2415 2246 1293
+C 2246 1087 2246 716 2054 422
+C 1894 159 1645 25 1370 25
+C 947 25 518 319 403 812
+C 429 806 480 793 506 793
+C 589 793 749 838 749 1036
+C 749 1209 627 1280 506 1280
+C 358 1280 262 1190 262 1011
+C 262 454 704 -128 1382 -128
+C 2042 -128 2669 441 2669 1267
+C 2669 2054 2170 2662 1549 2662
+C 1222 2662 947 2540 730 2304
+L 730 3750
+z
+" id="CMR17-35" transform="scale(0.015625)"/>
+ <path d="M 1062 262
+C 1062 422 934 524 800 524
+C 672 524 538 422 538 262
+C 538 102 666 0 800 0
+C 928 0 1062 102 1062 262
+z
+" id="CMR17-2e" transform="scale(0.015625)"/>
+ <path d="M 1741 2289
+C 2144 2494 2554 2803 2554 3298
+C 2554 3884 1990 4224 1472 4224
+C 890 4224 378 3800 378 3215
+C 378 3054 416 2777 666 2533
+C 730 2469 998 2276 1171 2154
+C 883 2006 211 1652 211 945
+C 211 282 838 -128 1459 -128
+C 2144 -128 2720 366 2720 1022
+C 2720 1607 2330 1877 2074 2051
+L 1741 2289
+z
+M 902 2855
+C 851 2887 595 3086 595 3388
+C 595 3781 998 4076 1459 4076
+C 1965 4076 2336 3716 2336 3298
+C 2336 2700 1670 2359 1638 2359
+C 1632 2359 1626 2359 1574 2398
+L 902 2855
+z
+M 2080 1536
+C 2176 1466 2483 1253 2483 861
+C 2483 385 2010 25 1472 25
+C 890 25 448 443 448 951
+C 448 1459 838 1884 1280 2083
+L 2080 1536
+z
+" id="CMR17-38" transform="scale(0.015625)"/>
+ <path d="M 1632 1254
+L 1632 1536
+L 26 1536
+L 26 1254
+L 1632 1254
+z
+" id="CMR17-2d" transform="scale(0.015625)"/>
+ <path d="M 2688 2038
+C 2688 2430 2682 3099 2413 3613
+C 2176 4063 1798 4224 1466 4224
+C 1158 4224 768 4082 525 3620
+C 269 3137 243 2539 243 2038
+C 243 1671 250 1112 448 623
+C 723 -39 1216 -128 1466 -128
+C 1760 -128 2208 -7 2470 604
+C 2662 1048 2688 1568 2688 2038
+z
+M 1466 -26
+C 1056 -26 813 328 723 816
+C 653 1196 653 1749 653 2109
+C 653 2604 653 3015 736 3407
+C 858 3954 1216 4121 1466 4121
+C 1728 4121 2067 3947 2189 3420
+C 2272 3054 2278 2623 2278 2109
+C 2278 1691 2278 1176 2202 797
+C 2067 96 1690 -26 1466 -26
+z
+" id="CMR17-30" transform="scale(0.015625)"/>
+ <path d="M 2253 1871
+C 2253 448 1670 25 1190 25
+C 1043 25 685 43 538 281
+C 704 256 826 345 826 505
+C 826 678 685 736 595 736
+C 538 736 365 710 365 492
+C 365 68 742 -128 1203 -128
+C 1939 -128 2688 665 2688 2090
+C 2688 3857 1971 4224 1485 4224
+C 851 4224 243 3664 243 2800
+C 243 2000 762 1408 1414 1408
+C 1952 1408 2189 1910 2253 2122
+L 2253 1871
+z
+M 1427 1510
+C 1254 1510 1011 1542 813 1929
+C 678 2181 678 2477 678 2793
+C 678 3174 678 3438 858 3722
+C 947 3857 1114 4076 1485 4076
+C 2240 4076 2240 2909 2240 2651
+C 2240 2193 2035 1510 1427 1510
+z
+" id="CMR17-39" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-38"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-39"/>
+ </g>
+ </g>
+ <g id="text_11">
+ <!-- 0.00026 -->
+ <g style="fill:#262626;" transform="translate(439.245807 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2669 990
+L 2554 990
+C 2490 537 2438 460 2413 422
+C 2381 371 1920 371 1830 371
+L 602 371
+C 832 620 1280 1073 1824 1596
+C 2214 1966 2669 2400 2669 3033
+C 2669 3788 2067 4224 1395 4224
+C 691 4224 262 3603 262 3027
+C 262 2777 448 2745 525 2745
+C 589 2745 781 2783 781 3007
+C 781 3206 614 3264 525 3264
+C 486 3264 448 3257 422 3244
+C 544 3788 915 4057 1306 4057
+C 1862 4057 2227 3616 2227 3033
+C 2227 2477 1901 1998 1536 1583
+L 262 147
+L 262 0
+L 2515 0
+L 2669 990
+z
+" id="CMR17-32" transform="scale(0.015625)"/>
+ <path d="M 678 2198
+C 678 3712 1395 4076 1811 4076
+C 1946 4076 2272 4049 2400 3782
+C 2298 3782 2106 3782 2106 3558
+C 2106 3385 2246 3328 2336 3328
+C 2394 3328 2566 3353 2566 3571
+C 2566 3987 2246 4224 1805 4224
+C 1043 4224 243 3411 243 2011
+C 243 257 966 -128 1478 -128
+C 2099 -128 2688 431 2688 1295
+C 2688 2101 2170 2688 1517 2688
+C 1126 2688 838 2430 678 1979
+L 678 2198
+z
+M 1478 25
+C 691 25 691 1212 691 1450
+C 691 1914 909 2585 1504 2585
+C 1613 2585 1926 2585 2138 2140
+C 2253 1889 2253 1624 2253 1302
+C 2253 954 2253 696 2118 438
+C 1978 173 1773 25 1478 25
+z
+" id="CMR17-36" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(161.94249 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(207.632967 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ <use transform="translate(253.323444 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ <g id="text_12">
+ <!-- 2.1e-10 -->
+ <g style="fill:#262626;" transform="translate(710.20871 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1702 4083
+C 1702 4217 1696 4224 1606 4224
+C 1357 3927 979 3833 621 3820
+C 602 3820 570 3820 563 3808
+C 557 3795 557 3782 557 3648
+C 755 3648 1088 3686 1344 3839
+L 1344 467
+C 1344 243 1331 166 781 166
+L 589 166
+L 589 0
+C 896 6 1216 12 1523 12
+C 1830 12 2150 6 2458 0
+L 2458 166
+L 2266 166
+C 1715 166 1702 236 1702 467
+L 1702 4083
+z
+" id="CMR17-31" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-32"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ </g>
+ </g>
+ <g id="text_13">
+ <!-- 2.1e-10 -->
+ <g style="fill:#262626;" transform="translate(978.04871 228.955463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-32"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ </g>
+ </g>
+ <g id="text_14">
+ <!-- 0.52 -->
+ <g style="fill:#ffffff;" transform="translate(191.966522 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ <g id="text_15">
+ <!-- 0.48 -->
+ <g style="fill:#ffffff;" transform="translate(459.806522 518.875463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2150 4147
+C 2150 4281 2144 4288 2029 4288
+L 128 1254
+L 128 1088
+L 1779 1088
+L 1779 460
+C 1779 230 1766 166 1318 166
+L 1197 166
+L 1197 0
+C 1402 12 1747 12 1965 12
+C 2182 12 2528 12 2733 0
+L 2733 166
+L 2611 166
+C 2163 166 2150 230 2150 460
+L 2150 1088
+L 2803 1088
+L 2803 1254
+L 2150 1254
+L 2150 4147
+z
+M 1798 3723
+L 1798 1254
+L 256 1254
+L 1798 3723
+z
+" id="CMR17-34" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-38"/>
+ </g>
+ </g>
+ <g id="text_16">
+ <!-- 0.51 -->
+ <g style="fill:#ffffff;" transform="translate(727.646522 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ <g id="text_17">
+ <!-- 0.51 -->
+ <g style="fill:#ffffff;" transform="translate(995.486522 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ <g id="text_18">
+ <!-- 0.48 -->
+ <g style="fill:#ffffff;" transform="translate(191.966522 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-38"/>
+ </g>
+ </g>
+ <g id="text_19">
+ <!-- 0.52 -->
+ <g style="fill:#ffffff;" transform="translate(459.806522 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ <g id="text_20">
+ <!-- 0.49 -->
+ <g style="fill:#ffffff;" transform="translate(727.646522 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-39"/>
+ </g>
+ </g>
+ <g id="text_21">
+ <!-- 0.49 -->
+ <g style="fill:#ffffff;" transform="translate(995.486522 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-39"/>
+ </g>
+ </g>
+ </g>
+ <g id="axes_2">
+ <g id="patch_3">
+ <path d="M 1220.657891 946.284441
+L 1264.145891 946.284441
+L 1264.145891 76.524441
+L 1220.657891 76.524441
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="patch_4">
+ <path clip-path="url(#p3cacba46cb)" d="M 1220.657891 946.284441
+L 1220.657891 942.886941
+L 1220.657891 79.921941
+L 1220.657891 76.524441
+L 1264.145891 76.524441
+L 1264.145891 79.921941
+L 1264.145891 942.886941
+L 1264.145891 946.284441
+L 1264.145891 946.284441
+z
+" style="fill:#ffffff;stroke:#ffffff;stroke-linejoin:miter;stroke-width:0.01;"/>
+ </g>
+ <image height="870" id="image9ccbbdbe75" transform="scale(1 -1)translate(0 -870)" width="43" x="1221" xlink:href="data:image/png;base64,
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" y="-76"/>
+ <g id="matplotlib.axis_3"/>
+ <g id="matplotlib.axis_4">
+ <g id="ytick_4">
+ <g id="line2d_8">
+ <defs>
+ <path d="M 0 0
+L 3.5 0
+" id="mc4dd4640b4" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#mc4dd4640b4" y="779.480844"/>
+ </g>
+ </g>
+ <g id="text_22">
+ <!-- $\mathdefault{0.1}$ -->
+ <g transform="translate(1271.145891 789.858591)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1178 307
+C 1178 492 1024 620 870 620
+C 685 620 557 467 557 313
+C 557 128 710 0 864 0
+C 1050 0 1178 153 1178 307
+z
+" id="CMMI12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_5">
+ <g id="line2d_9">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#mc4dd4640b4" y="612.677247"/>
+ </g>
+ </g>
+ <g id="text_23">
+ <!-- $\mathdefault{0.2}$ -->
+ <g transform="translate(1271.145891 623.054994)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_6">
+ <g id="line2d_10">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#mc4dd4640b4" y="445.873649"/>
+ </g>
+ </g>
+ <g id="text_24">
+ <!-- $\mathdefault{0.3}$ -->
+ <g transform="translate(1271.145891 456.251397)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1414 2176
+C 1984 2176 2234 1673 2234 1094
+C 2234 322 1824 25 1453 25
+C 1114 25 563 193 390 691
+C 422 678 454 678 486 678
+C 640 678 755 780 755 947
+C 755 1132 614 1216 486 1216
+C 378 1216 211 1164 211 927
+C 211 335 787 -128 1466 -128
+C 2176 -128 2720 432 2720 1087
+C 2720 1718 2208 2176 1600 2246
+C 2086 2347 2554 2776 2554 3353
+C 2554 3856 2048 4224 1472 4224
+C 890 4224 378 3862 378 3347
+C 378 3123 544 3084 627 3084
+C 762 3084 877 3167 877 3334
+C 877 3500 762 3584 627 3584
+C 602 3584 570 3584 544 3571
+C 730 3999 1235 4076 1459 4076
+C 1683 4076 2106 3966 2106 3347
+C 2106 3167 2080 2851 1862 2574
+C 1670 2329 1453 2316 1242 2297
+C 1210 2297 1062 2284 1037 2284
+C 992 2278 966 2272 966 2227
+C 966 2182 973 2176 1101 2176
+L 1414 2176
+z
+" id="CMR17-33" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_7">
+ <g id="line2d_11">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#mc4dd4640b4" y="279.070052"/>
+ </g>
+ </g>
+ <g id="text_25">
+ <!-- $\mathdefault{0.4}$ -->
+ <g transform="translate(1271.145891 289.4478)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_8">
+ <g id="line2d_12">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#mc4dd4640b4" y="112.266455"/>
+ </g>
+ </g>
+ <g id="text_26">
+ <!-- $\mathdefault{0.5}$ -->
+ <g transform="translate(1271.145891 122.644202)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ </g>
+ <g id="LineCollection_1"/>
+ <g id="patch_5">
+ <path d="M 1220.657891 946.284441
+L 1220.657891 942.886941
+L 1220.657891 79.921941
+L 1220.657891 76.524441
+L 1264.145891 76.524441
+L 1264.145891 79.921941
+L 1264.145891 942.886941
+L 1264.145891 946.284441
+z
+" style="fill:none;"/>
+ </g>
+ </g>
+ </g>
+ <defs>
+ <clipPath id="p1ad762eb0e">
+ <rect height="869.76" width="1071.36" x="82.337891" y="76.524441"/>
+ </clipPath>
+ <clipPath id="p3cacba46cb">
+ <rect height="869.76" width="43.488" x="1220.657891" y="76.524441"/>
+ </clipPath>
+ </defs>
+</svg>
diff --git a/examples/model-comparison/reference/confusionMatrix_ND_9.svg b/examples/model-comparison/reference/confusionMatrix_ND_9.svg
new file mode 100644
index 0000000000000000000000000000000000000000..5534b31a4fc5d91cc85d22b5b340bb0b546cb1c6
--- /dev/null
+++ b/examples/model-comparison/reference/confusionMatrix_ND_9.svg
@@ -0,0 +1,1632 @@
+<?xml version="1.0" encoding="utf-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<svg height="969.675639pt" version="1.1" viewBox="0 0 1313.889331 969.675639" width="1313.889331pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+ <metadata>
+ <rdf:RDF xmlns:cc="http://creativecommons.org/ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
+ <cc:Work>
+ <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
+ <dc:date>2022-06-03T16:06:09.611703</dc:date>
+ <dc:format>image/svg+xml</dc:format>
+ <dc:creator>
+ <cc:Agent>
+ <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>
+ </cc:Agent>
+ </dc:creator>
+ </cc:Work>
+ </rdf:RDF>
+ </metadata>
+ <defs>
+ <style type="text/css">*{stroke-linecap:butt;stroke-linejoin:round;}</style>
+ </defs>
+ <g id="figure_1">
+ <g id="patch_1">
+ <path d="M 0 969.675639
+L 1313.889331 969.675639
+L 1313.889331 0
+L 0 0
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="axes_1">
+ <g id="patch_2">
+ <path d="M 82.337891 946.284441
+L 1153.697891 946.284441
+L 1153.697891 76.524441
+L 82.337891 76.524441
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="QuadMesh_1">
+ <path clip-path="url(#pba293bd3d4)" d="M 82.337891 76.524441
+L 350.177891 76.524441
+L 350.177891 366.444441
+L 82.337891 366.444441
+L 82.337891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#pba293bd3d4)" d="M 350.177891 76.524441
+L 618.017891 76.524441
+L 618.017891 366.444441
+L 350.177891 366.444441
+L 350.177891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#pba293bd3d4)" d="M 618.017891 76.524441
+L 885.857891 76.524441
+L 885.857891 366.444441
+L 618.017891 366.444441
+L 618.017891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#pba293bd3d4)" d="M 885.857891 76.524441
+L 1153.697891 76.524441
+L 1153.697891 366.444441
+L 885.857891 366.444441
+L 885.857891 76.524441
+" style="fill:#f7fbff;"/>
+ <path clip-path="url(#pba293bd3d4)" d="M 82.337891 366.444441
+L 350.177891 366.444441
+L 350.177891 656.364441
+L 82.337891 656.364441
+L 82.337891 366.444441
+" style="fill:#3d8dc4;"/>
+ <path clip-path="url(#pba293bd3d4)" d="M 350.177891 366.444441
+L 618.017891 366.444441
+L 618.017891 656.364441
+L 350.177891 656.364441
+L 350.177891 366.444441
+" style="fill:#1460a8;"/>
+ <path clip-path="url(#pba293bd3d4)" d="M 618.017891 366.444441
+L 885.857891 366.444441
+L 885.857891 656.364441
+L 618.017891 656.364441
+L 618.017891 366.444441
+" style="fill:#7fb9da;"/>
+ <path clip-path="url(#pba293bd3d4)" d="M 885.857891 366.444441
+L 1153.697891 366.444441
+L 1153.697891 656.364441
+L 885.857891 656.364441
+L 885.857891 366.444441
+" style="fill:#7fb9da;"/>
+ <path clip-path="url(#pba293bd3d4)" d="M 82.337891 656.364441
+L 350.177891 656.364441
+L 350.177891 946.284441
+L 82.337891 946.284441
+L 82.337891 656.364441
+" style="fill:#1561a9;"/>
+ <path clip-path="url(#pba293bd3d4)" d="M 350.177891 656.364441
+L 618.017891 656.364441
+L 618.017891 946.284441
+L 350.177891 946.284441
+L 350.177891 656.364441
+" style="fill:#3f8fc5;"/>
+ <path clip-path="url(#pba293bd3d4)" d="M 618.017891 656.364441
+L 885.857891 656.364441
+L 885.857891 946.284441
+L 618.017891 946.284441
+L 618.017891 656.364441
+" style="fill:#08306b;"/>
+ <path clip-path="url(#pba293bd3d4)" d="M 885.857891 656.364441
+L 1153.697891 656.364441
+L 1153.697891 946.284441
+L 885.857891 946.284441
+L 885.857891 656.364441
+" style="fill:#08306b;"/>
+ </g>
+ <g id="matplotlib.axis_1">
+ <g id="xtick_1">
+ <g id="line2d_1">
+ <defs>
+ <path d="M 0 0
+L 0 -3.5
+" id="mba46036235" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="216.257891" xlink:href="#mba46036235" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_1">
+ <!-- Observation -->
+ <g transform="translate(144.303789 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 4307 2166
+C 4307 3488 3366 4480 2304 4480
+C 1216 4480 294 3475 294 2166
+C 294 857 1229 -128 2298 -128
+C 3392 -128 4307 876 4307 2166
+z
+M 2304 -13
+C 1574 -13 781 722 781 2250
+C 781 3771 1651 4364 2298 4364
+C 2976 4364 3821 3752 3821 2250
+C 3821 696 3008 -13 2304 -13
+z
+" id="CMR17-4f" transform="scale(0.015625)"/>
+ <path d="M 960 4416
+L 198 4345
+L 198 4179
+C 576 4179 634 4141 634 3843
+L 634 -13
+L 749 -13
+L 934 445
+C 1120 141 1395 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2209 2477 2816 1830 2816
+C 1434 2816 1152 2603 960 2351
+L 960 4416
+z
+M 973 2022
+C 973 2138 973 2157 1062 2293
+C 1312 2681 1670 2713 1792 2713
+C 1984 2713 2643 2610 2643 1388
+C 2643 109 1888 38 1734 38
+C 1536 38 1248 115 1043 490
+C 973 613 973 626 973 742
+L 973 2022
+z
+" id="CMR17-62" transform="scale(0.015625)"/>
+ <path d="M 1978 2688
+C 1978 2803 1971 2809 1933 2809
+C 1907 2809 1901 2803 1824 2707
+C 1805 2681 1747 2617 1728 2592
+C 1523 2809 1235 2816 1126 2816
+C 416 2816 160 2444 160 2073
+C 160 1497 813 1363 998 1324
+C 1402 1241 1542 1216 1677 1100
+C 1760 1024 1901 883 1901 652
+C 1901 384 1747 38 1158 38
+C 602 38 403 460 288 1024
+C 269 1113 269 1120 218 1120
+C 166 1120 160 1113 160 985
+L 160 64
+C 160 -52 166 -58 205 -58
+C 237 -58 243 -52 275 0
+C 314 57 410 211 448 275
+C 576 102 800 -64 1158 -64
+C 1792 -64 2131 281 2131 780
+C 2131 1107 1958 1280 1875 1356
+C 1683 1555 1459 1600 1190 1651
+C 838 1728 390 1817 390 2208
+C 390 2374 480 2726 1126 2726
+C 1811 2726 1850 2086 1862 1881
+C 1869 1849 1901 1843 1920 1843
+C 1978 1843 1978 1862 1978 1971
+L 1978 2688
+z
+" id="CMR17-73" transform="scale(0.015625)"/>
+ <path d="M 2438 1503
+C 2464 1529 2464 1542 2464 1606
+C 2464 2251 2118 2816 1389 2816
+C 710 2816 173 2175 173 1394
+C 173 554 781 -64 1459 -64
+C 2176 -64 2458 619 2458 755
+C 2458 800 2419 800 2406 800
+C 2362 800 2355 787 2330 709
+C 2189 270 1837 51 1504 51
+C 1229 51 954 206 781 490
+C 582 819 582 1200 582 1503
+L 2438 1503
+z
+M 589 1600
+C 634 2511 1126 2713 1382 2713
+C 1818 2713 2112 2308 2118 1600
+L 589 1600
+z
+" id="CMR17-65" transform="scale(0.015625)"/>
+ <path d="M 960 1517
+C 960 2134 1222 2713 1702 2713
+C 1747 2713 1792 2707 1837 2687
+C 1837 2687 1696 2642 1696 2475
+C 1696 2321 1818 2257 1914 2257
+C 1990 2257 2131 2302 2131 2482
+C 2131 2687 1926 2816 1709 2816
+C 1222 2816 1011 2340 947 2115
+L 941 2115
+L 941 2816
+L 198 2745
+L 198 2578
+C 576 2578 634 2540 634 2231
+L 634 443
+C 634 198 608 166 198 166
+L 198 0
+C 352 12 646 12 813 12
+C 998 12 1325 12 1498 0
+L 1498 166
+C 1037 166 960 166 960 455
+L 960 1517
+z
+" id="CMR17-72" transform="scale(0.015625)"/>
+ <path d="M 2502 2173
+C 2560 2315 2662 2572 3034 2585
+L 3034 2752
+C 2912 2745 2752 2739 2630 2739
+C 2496 2739 2285 2739 2157 2752
+L 2157 2585
+C 2317 2572 2406 2495 2406 2328
+C 2406 2270 2406 2257 2368 2167
+L 1664 379
+L 902 2308
+C 864 2392 864 2405 864 2431
+C 864 2585 1075 2585 1171 2585
+L 1171 2752
+C 1018 2739 736 2739 576 2739
+C 403 2739 205 2739 64 2752
+L 64 2585
+C 307 2585 442 2585 518 2386
+L 1446 44
+C 1485 -52 1491 -64 1549 -64
+C 1606 -64 1613 -52 1651 44
+L 2502 2173
+z
+" id="CMR17-76" transform="scale(0.015625)"/>
+ <path d="M 2304 1656
+C 2304 2048 2304 2275 2035 2534
+C 1798 2751 1523 2816 1306 2816
+C 800 2816 435 2408 435 1977
+C 435 1740 627 1728 666 1728
+C 749 1728 896 1779 896 1958
+C 896 2118 774 2188 666 2188
+C 640 2188 608 2182 589 2176
+C 723 2594 1069 2713 1293 2713
+C 1613 2713 1965 2421 1965 1875
+L 1965 1632
+C 1587 1619 1133 1568 774 1373
+C 371 1147 256 822 256 576
+C 256 77 832 -64 1171 -64
+C 1523 -64 1850 135 1990 505
+C 2003 219 2182 -39 2464 -39
+C 2598 -39 2938 51 2938 563
+L 2938 926
+L 2822 926
+L 2822 557
+C 2822 161 2650 109 2566 109
+C 2304 109 2304 446 2304 732
+L 2304 1656
+z
+M 1965 887
+C 1965 323 1568 38 1216 38
+C 896 38 646 278 646 576
+C 646 771 730 1114 1101 1322
+C 1408 1497 1760 1523 1965 1536
+L 1965 887
+z
+" id="CMR17-61" transform="scale(0.015625)"/>
+ <path d="M 966 2585
+L 1862 2585
+L 1862 2752
+L 966 2752
+L 966 3968
+L 851 3968
+C 838 3292 614 2700 70 2687
+L 70 2585
+L 627 2585
+L 627 778
+C 627 655 627 -64 1370 -64
+C 1747 -64 1965 308 1965 784
+L 1965 1151
+L 1850 1151
+L 1850 790
+C 1850 347 1677 51 1408 51
+C 1222 51 966 179 966 765
+L 966 2585
+z
+" id="CMR17-74" transform="scale(0.015625)"/>
+ <path d="M 992 3961
+C 992 4102 877 4224 730 4224
+C 589 4224 467 4108 467 3961
+C 467 3820 582 3699 730 3699
+C 870 3699 992 3814 992 3961
+z
+M 243 2745
+L 243 2579
+C 602 2579 653 2540 653 2231
+L 653 443
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 646 12 806 12
+C 960 12 1222 12 1370 0
+L 1370 166
+C 992 166 979 205 979 436
+L 979 2816
+L 243 2745
+z
+" id="CMR17-69" transform="scale(0.015625)"/>
+ <path d="M 2758 1356
+C 2758 2176 2163 2816 1466 2816
+C 768 2816 173 2176 173 1356
+C 173 550 768 -64 1466 -64
+C 2163 -64 2758 550 2758 1356
+z
+M 1466 51
+C 1165 51 909 230 762 480
+C 602 768 582 1126 582 1408
+C 582 1676 595 2009 762 2297
+C 890 2508 1139 2713 1466 2713
+C 1754 2713 1997 2553 2150 2329
+C 2349 2028 2349 1606 2349 1408
+C 2349 1158 2336 774 2163 467
+C 1984 172 1709 51 1466 51
+z
+" id="CMR17-6f" transform="scale(0.015625)"/>
+ <path d="M 2656 1954
+C 2656 2282 2592 2816 1837 2816
+C 1331 2816 1069 2424 973 2166
+L 966 2166
+L 966 2816
+L 211 2745
+L 211 2578
+C 589 2578 646 2540 646 2231
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1954
+z
+" id="CMR17-6e" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-4f"/>
+ <use transform="translate(71.714788 0)scale(0.996264)" xlink:href="#CMR17-62"/>
+ <use transform="translate(122.610158 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(158.411496 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(198.897156 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ <use transform="translate(234.177924 0)scale(0.996264)" xlink:href="#CMR17-76"/>
+ <use transform="translate(277.266023 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(322.9565 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(358.237268 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(383.108327 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(428.798804 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_2">
+ <g id="line2d_2">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="484.097891" xlink:href="#mba46036235" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_2">
+ <!-- linear -->
+ <g transform="translate(450.783747 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 979 4416
+L 218 4345
+L 218 4179
+C 595 4179 653 4141 653 3835
+L 653 439
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 653 12 813 12
+C 979 12 1261 12 1414 0
+L 1414 166
+C 1005 166 979 191 979 439
+L 979 4416
+z
+" id="CMR17-6c" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_3">
+ <g id="line2d_3">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="751.937891" xlink:href="#mba46036235" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_3">
+ <!-- exponential -->
+ <g transform="translate(683.18479 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1664 1491
+C 1856 1740 2074 2022 2253 2233
+C 2464 2476 2707 2579 2989 2585
+L 2989 2752
+C 2880 2745 2656 2739 2541 2739
+C 2368 2739 2170 2739 2022 2752
+L 2022 2585
+C 2112 2572 2163 2508 2163 2419
+C 2163 2304 2099 2233 2067 2188
+L 1594 1587
+L 1030 2323
+C 973 2393 973 2406 973 2438
+C 973 2515 1037 2579 1146 2585
+L 1146 2752
+C 992 2739 717 2739 557 2739
+C 384 2739 179 2739 38 2752
+L 38 2585
+C 384 2585 461 2560 614 2368
+L 1350 1414
+C 1363 1401 1395 1363 1395 1344
+C 1395 1318 838 633 768 544
+C 480 198 179 172 6 166
+L 6 0
+C 115 6 339 12 454 12
+C 582 12 864 12 979 0
+L 979 166
+C 941 172 838 185 838 332
+C 838 448 890 518 947 595
+L 1478 1248
+L 2035 524
+C 2086 454 2163 358 2163 313
+C 2163 224 2086 172 1984 166
+L 1984 0
+C 2138 12 2413 12 2573 12
+C 2746 12 2950 12 3091 0
+L 3091 166
+C 2771 166 2675 179 2522 377
+L 1664 1491
+z
+" id="CMR17-78" transform="scale(0.015625)"/>
+ <path d="M 1408 -1114
+C 998 -1114 973 -1088 973 -834
+L 973 380
+C 1158 109 1427 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2196 2496 2816 1837 2816
+C 1453 2816 1139 2603 960 2345
+L 960 2816
+L 198 2745
+L 198 2577
+C 576 2577 634 2539 634 2228
+L 634 -834
+C 634 -1081 608 -1114 198 -1114
+L 198 -1280
+C 352 -1268 634 -1268 800 -1268
+C 966 -1268 1254 -1268 1408 -1280
+L 1408 -1114
+z
+M 973 2015
+C 973 2106 973 2241 1222 2481
+C 1254 2506 1472 2700 1792 2700
+C 2259 2700 2643 2112 2643 1376
+C 2643 639 2234 38 1728 38
+C 1498 38 1248 148 1056 451
+C 973 594 973 632 973 736
+L 973 2015
+z
+" id="CMR17-70" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_4">
+ <g id="line2d_4">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1019.777891" xlink:href="#mba46036235" y="76.524441"/>
+ </g>
+ </g>
+ <g id="text_4">
+ <!-- cosine -->
+ <g transform="translate(984.043472 63.71099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2234 2240
+C 2112 2240 1933 2240 1933 2015
+C 1933 1836 2080 1785 2163 1785
+C 2208 1785 2394 1804 2394 2028
+C 2394 2476 1958 2816 1466 2816
+C 787 2816 211 2201 211 1379
+C 211 521 813 -64 1466 -64
+C 2259 -64 2458 676 2458 747
+C 2458 773 2451 792 2406 792
+C 2362 792 2355 786 2330 702
+C 2163 180 1798 51 1523 51
+C 1114 51 621 431 621 1385
+C 621 2358 1094 2700 1472 2700
+C 1722 2700 2093 2582 2234 2240
+z
+" id="CMR17-63" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_5">
+ <!-- \textbf{Data generated by:} -->
+ <g transform="translate(476.949653 27.955495)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 243 4416
+L 243 4140
+L 922 4140
+L 922 275
+L 243 275
+L 243 0
+L 2938 0
+C 4166 0 5114 790 5114 2169
+C 5114 3625 4141 4416 2938 4416
+L 243 4416
+z
+M 1734 275
+L 1734 4140
+L 2694 4140
+C 3251 4140 3699 3921 3936 3586
+C 4122 3322 4243 3006 4243 2175
+C 4243 1421 4147 1086 3923 784
+C 3699 487 3270 275 2694 275
+L 1734 275
+z
+" id="CMBX12-44" transform="scale(0.015625)"/>
+ <path d="M 2944 1894
+C 2944 2483 2477 2880 1574 2880
+C 1216 2880 461 2847 461 2310
+C 461 2041 666 1926 838 1926
+C 1030 1926 1216 2060 1216 2303
+C 1216 2425 1171 2540 1062 2611
+C 1274 2668 1427 2668 1549 2668
+C 1984 2668 2246 2425 2246 1900
+L 2246 1644
+C 1235 1644 218 1362 218 648
+C 218 64 960 -64 1402 -64
+C 1894 -64 2208 205 2336 488
+C 2336 250 2336 -26 2982 -26
+L 3309 -26
+C 3443 -26 3494 -26 3494 115
+C 3494 250 3437 250 3347 250
+C 2944 256 2944 359 2944 507
+L 2944 1894
+z
+M 2246 867
+C 2246 262 1709 147 1504 147
+C 1190 147 928 359 928 655
+C 928 1240 1619 1439 2246 1472
+L 2246 867
+z
+" id="CMBX12-61" transform="scale(0.015625)"/>
+ <path d="M 1350 2540
+L 2272 2540
+L 2272 2816
+L 1350 2816
+L 1350 4032
+L 1082 4032
+C 1075 3401 768 2771 134 2751
+L 134 2540
+L 653 2540
+L 653 761
+C 653 83 1178 -64 1638 -64
+C 2112 -64 2394 294 2394 768
+L 2394 1107
+L 2125 1107
+L 2125 774
+C 2125 352 1933 166 1734 166
+C 1350 166 1350 595 1350 742
+L 1350 2540
+z
+" id="CMBX12-74" transform="scale(0.015625)"/>
+ <path d="M 832 1177
+C 1139 1011 1498 1011 1594 1011
+C 2477 1011 2829 1506 2829 1958
+C 2829 2287 2643 2519 2566 2584
+C 2752 2687 2906 2713 3014 2726
+C 2995 2694 2976 2668 2976 2584
+C 2976 2448 3066 2326 3232 2326
+C 3398 2326 3488 2448 3488 2584
+C 3488 2739 3373 2944 3104 2944
+C 2829 2944 2566 2809 2432 2694
+C 2170 2847 1920 2905 1594 2905
+C 710 2905 358 2410 358 1958
+C 358 1758 422 1493 691 1274
+C 582 1151 467 926 467 693
+C 467 416 614 179 749 76
+C 595 38 198 -109 198 -474
+C 198 -852 614 -1280 1792 -1280
+C 2854 -1280 3392 -935 3392 -455
+C 3392 108 3021 294 2861 371
+C 2554 524 2144 524 1581 524
+C 1421 524 1139 524 1107 531
+C 832 576 755 823 755 946
+C 755 998 762 1094 832 1177
+z
+M 1594 1216
+C 1037 1216 1037 1661 1037 1958
+C 1037 2255 1037 2700 1594 2700
+C 2150 2700 2150 2255 2150 1958
+C 2150 1661 2150 1216 1594 1216
+z
+M 1952 -64
+C 2419 -64 2867 -148 2867 -480
+C 2867 -704 2643 -1076 1798 -1076
+C 954 -1076 723 -717 723 -474
+C 723 -64 1126 -64 1222 -64
+L 1952 -64
+z
+" id="CMBX12-67" transform="scale(0.015625)"/>
+ <path d="M 2893 1408
+C 3040 1408 3078 1408 3078 1568
+C 3078 1758 3034 2232 2739 2529
+C 2470 2796 2112 2880 1741 2880
+C 742 2880 198 2232 198 1433
+C 198 523 858 -64 1824 -64
+C 2790 -64 3078 621 3078 731
+C 3078 829 2982 829 2944 829
+C 2842 829 2835 809 2797 725
+C 2630 302 2208 166 1901 166
+C 973 166 966 1043 966 1408
+L 2893 1408
+z
+M 966 1593
+C 979 1852 986 2099 1120 2327
+C 1242 2529 1466 2668 1741 2668
+C 2426 2668 2483 1909 2490 1593
+L 966 1593
+z
+" id="CMBX12-65" transform="scale(0.015625)"/>
+ <path d="M 3398 1958
+C 3398 2566 3136 2880 2432 2880
+C 1971 2880 1574 2656 1357 2176
+L 1350 2176
+L 1350 2880
+L 269 2828
+L 269 2553
+C 666 2553 710 2553 710 2304
+L 710 275
+L 269 275
+L 269 0
+C 416 12 877 12 1056 12
+C 1235 12 1702 12 1850 0
+L 1850 275
+L 1408 275
+L 1408 1638
+C 1408 2329 1920 2668 2330 2668
+C 2566 2668 2701 2515 2701 2028
+L 2701 275
+L 2259 275
+L 2259 0
+C 2406 12 2867 12 3046 12
+C 3226 12 3693 12 3840 0
+L 3840 275
+L 3398 275
+L 3398 1958
+z
+" id="CMBX12-6e" transform="scale(0.015625)"/>
+ <path d="M 1331 1440
+C 1331 1651 1376 2668 2125 2668
+C 2035 2598 1990 2489 1990 2374
+C 1990 2112 2202 2003 2362 2003
+C 2522 2003 2733 2112 2733 2374
+C 2733 2700 2400 2880 2093 2880
+C 1587 2880 1370 2438 1280 2169
+L 1274 2169
+L 1274 2880
+L 224 2828
+L 224 2553
+C 621 2553 666 2553 666 2304
+L 666 275
+L 224 275
+L 224 0
+C 371 12 851 12 1030 12
+C 1216 12 1734 12 1888 0
+L 1888 275
+L 1331 275
+L 1331 1440
+z
+" id="CMBX12-72" transform="scale(0.015625)"/>
+ <path d="M 2221 4428
+L 2221 4153
+C 2618 4153 2662 4153 2662 3896
+L 2662 2571
+C 2522 2694 2240 2880 1798 2880
+C 890 2880 243 2313 243 1408
+C 243 483 877 -64 1728 -64
+C 2080 -64 2381 57 2630 270
+L 2630 -64
+L 3770 -26
+L 3770 250
+C 3373 250 3328 250 3328 502
+L 3328 4480
+L 2221 4428
+z
+M 2630 625
+C 2362 231 2035 147 1805 147
+C 1011 147 1011 968 1011 1395
+C 1011 1699 1011 2022 1152 2268
+C 1350 2630 1728 2668 1875 2668
+C 2138 2668 2419 2552 2630 2268
+L 2630 625
+z
+" id="CMBX12-64" transform="scale(0.015625)"/>
+ <path d="M 1331 4480
+L 224 4428
+L 224 4153
+C 621 4153 666 4153 666 3896
+L 666 -26
+L 934 -26
+C 1043 96 1152 218 1254 347
+C 1581 6 1933 -64 2189 -64
+C 3072 -64 3750 476 3750 1414
+C 3750 2300 3149 2880 2272 2880
+C 1894 2880 1594 2758 1331 2552
+L 1331 4480
+z
+M 1363 2242
+C 1587 2552 1920 2668 2189 2668
+C 2982 2668 2982 1847 2982 1420
+C 2982 1130 2982 761 2829 522
+C 2630 211 2330 147 2125 147
+C 1690 147 1453 457 1363 599
+L 1363 2242
+z
+" id="CMBX12-62" transform="scale(0.015625)"/>
+ <path d="M 3168 2400
+C 3206 2489 3232 2540 3642 2540
+L 3642 2816
+C 3424 2803 3398 2803 3136 2803
+C 2963 2803 2950 2803 2586 2816
+L 2586 2540
+C 2592 2540 2893 2540 2893 2457
+C 2893 2438 2874 2400 2867 2381
+L 2118 780
+L 1299 2540
+L 1651 2540
+L 1651 2816
+C 1498 2803 1062 2803 883 2803
+C 698 2803 320 2803 154 2816
+L 154 2540
+L 563 2540
+L 1747 -8
+C 1715 -84 1626 -269 1594 -345
+C 1459 -631 1254 -1069 806 -1069
+C 781 -1069 704 -1069 634 -1031
+C 646 -1025 838 -949 838 -707
+C 838 -497 685 -364 493 -364
+C 294 -364 141 -497 141 -713
+C 141 -1012 422 -1280 806 -1280
+C 1331 -1280 1677 -809 1805 -529
+L 3168 2400
+z
+" id="CMBX12-79" transform="scale(0.015625)"/>
+ <path d="M 1459 2355
+C 1459 2617 1248 2816 998 2816
+C 749 2816 538 2617 538 2355
+C 538 2092 749 1894 998 1894
+C 1248 1894 1459 2092 1459 2355
+z
+M 1459 460
+C 1459 723 1248 921 998 921
+C 749 921 538 723 538 460
+C 538 198 749 0 998 0
+C 1248 0 1459 198 1459 460
+z
+" id="CMBX12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMBX12-44"/>
+ <use transform="translate(85.904786 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(140.387974 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(183.974524 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(275.817613 0)scale(0.996264)" xlink:href="#CMBX12-67"/>
+ <use transform="translate(331.857463 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(382.99673 0)scale(0.996264)" xlink:href="#CMBX12-6e"/>
+ <use transform="translate(445.263231 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(496.402498 0)scale(0.996264)" xlink:href="#CMBX12-72"/>
+ <use transform="translate(542.180006 0)scale(0.996264)" xlink:href="#CMBX12-61"/>
+ <use transform="translate(596.663194 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(640.249744 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(691.389011 0)scale(0.996264)" xlink:href="#CMBX12-64"/>
+ <use transform="translate(791.015412 0)scale(0.996264)" xlink:href="#CMBX12-62"/>
+ <use transform="translate(850.168588 0)scale(0.996264)" xlink:href="#CMBX12-79"/>
+ <use transform="translate(909.321763 0)scale(0.996264)" xlink:href="#CMBX12-3a"/>
+ </g>
+ </g>
+ </g>
+ <g id="matplotlib.axis_2">
+ <g id="ytick_1">
+ <g id="line2d_5">
+ <defs>
+ <path d="M 0 0
+L -3.5 0
+" id="m5ac61d4823" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#m5ac61d4823" y="221.484441"/>
+ </g>
+ </g>
+ <g id="text_6">
+ <!-- linear -->
+ <g transform="translate(69.524441 277.73498)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_2">
+ <g id="line2d_6">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#m5ac61d4823" y="511.404441"/>
+ </g>
+ </g>
+ <g id="text_7">
+ <!-- exponential -->
+ <g transform="translate(69.524441 638.532895)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_3">
+ <g id="line2d_7">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="82.337891" xlink:href="#m5ac61d4823" y="801.324441"/>
+ </g>
+ </g>
+ <g id="text_8">
+ <!-- cosine -->
+ <g transform="translate(69.524441 862.415532)rotate(-90)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_9">
+ <!-- \textbf{Model weight for:} -->
+ <g transform="translate(27.955495 642.025756)rotate(-90)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 3411 816
+L 1875 4281
+C 1818 4416 1760 4416 1626 4416
+L 262 4416
+L 262 4140
+L 941 4140
+L 941 468
+C 941 326 934 320 768 294
+C 653 281 525 275 410 275
+L 262 275
+L 262 0
+C 410 12 909 12 1088 12
+C 1267 12 1773 12 1920 0
+L 1920 275
+L 1773 275
+C 1600 275 1587 275 1434 294
+C 1248 320 1242 326 1242 468
+L 1242 4063
+L 1248 4063
+L 2989 134
+C 3021 64 3059 0 3168 0
+C 3277 0 3315 64 3347 134
+L 5120 4140
+L 5126 4140
+L 5126 275
+L 4448 275
+L 4448 0
+C 4621 12 5286 12 5504 12
+C 5722 12 6387 12 6560 0
+L 6560 275
+L 5882 275
+L 5882 4140
+L 6560 4140
+L 6560 4416
+L 5197 4416
+C 5062 4416 5005 4416 4947 4281
+L 3411 816
+z
+" id="CMBX12-4d" transform="scale(0.015625)"/>
+ <path d="M 3392 1379
+C 3392 2245 2803 2880 1798 2880
+C 755 2880 198 2213 198 1379
+C 198 538 787 -64 1792 -64
+C 2835 -64 3392 570 3392 1379
+z
+M 1798 166
+C 966 166 966 917 966 1443
+C 966 1744 966 2065 1088 2296
+C 1229 2553 1517 2668 1792 2668
+C 2157 2668 2387 2495 2496 2315
+C 2624 2084 2624 1751 2624 1443
+C 2624 910 2624 166 1798 166
+z
+" id="CMBX12-6f" transform="scale(0.015625)"/>
+ <path d="M 1389 4480
+L 282 4428
+L 282 4153
+C 678 4153 723 4153 723 3901
+L 723 275
+L 282 275
+L 282 0
+C 429 12 883 12 1056 12
+C 1229 12 1683 12 1830 0
+L 1830 275
+L 1389 275
+L 1389 4480
+z
+" id="CMBX12-6c" transform="scale(0.015625)"/>
+ <path d="M 4608 2386
+C 4653 2496 4672 2540 5043 2540
+L 5043 2816
+C 4858 2803 4774 2803 4544 2803
+C 4282 2803 4198 2803 3968 2816
+L 3968 2540
+C 4026 2540 4339 2540 4339 2457
+C 4339 2451 4339 2444 4314 2380
+L 3642 712
+L 2906 2540
+L 3270 2540
+L 3270 2816
+C 3117 2803 2739 2803 2566 2803
+C 2240 2803 2227 2803 1907 2816
+L 1907 2540
+L 2285 2540
+C 2304 2489 2336 2406 2362 2348
+C 2381 2309 2445 2155 2445 2123
+C 2445 2111 2426 2066 2419 2046
+L 1933 834
+L 1242 2540
+L 1606 2540
+L 1606 2816
+C 1459 2803 1024 2803 851 2803
+C 646 2803 339 2803 147 2816
+L 147 2540
+L 525 2540
+L 1504 96
+C 1549 -20 1574 -64 1715 -64
+C 1786 -64 1862 -64 1914 64
+L 2592 1764
+L 3270 76
+C 3328 -64 3398 -64 3475 -64
+C 3616 -64 3635 -26 3680 89
+L 4608 2386
+z
+" id="CMBX12-77" transform="scale(0.015625)"/>
+ <path d="M 1427 4019
+C 1427 4281 1216 4480 966 4480
+C 704 4480 506 4262 506 4019
+C 506 3775 704 3558 966 3558
+C 1216 3558 1427 3756 1427 4019
+z
+M 301 2828
+L 301 2553
+C 678 2553 723 2553 723 2303
+L 723 275
+L 282 275
+L 282 0
+C 429 12 870 12 1043 12
+C 1222 12 1632 12 1786 0
+L 1786 275
+L 1389 275
+L 1389 2880
+L 301 2828
+z
+" id="CMBX12-69" transform="scale(0.015625)"/>
+ <path d="M 3398 1958
+C 3398 2566 3136 2880 2432 2880
+C 1786 2880 1472 2425 1382 2233
+L 1376 2233
+L 1376 4480
+L 269 4428
+L 269 4153
+C 666 4153 710 4153 710 3896
+L 710 275
+L 269 275
+L 269 0
+C 416 12 877 12 1056 12
+C 1235 12 1702 12 1850 0
+L 1850 275
+L 1408 275
+L 1408 1638
+C 1408 2329 1920 2668 2330 2668
+C 2566 2668 2701 2515 2701 2028
+L 2701 275
+L 2259 275
+L 2259 0
+C 2406 12 2867 12 3046 12
+C 3226 12 3693 12 3840 0
+L 3840 275
+L 3398 275
+L 3398 1958
+z
+" id="CMBX12-68" transform="scale(0.015625)"/>
+ <path d="M 1389 2540
+L 2118 2540
+L 2118 2816
+L 1357 2816
+L 1357 3466
+C 1357 4122 1779 4224 1990 4224
+C 2061 4224 2074 4217 2112 4204
+C 2016 4141 1958 4034 1958 3901
+C 1958 3649 2163 3535 2330 3535
+C 2470 3535 2701 3630 2701 3908
+C 2701 4167 2470 4435 2016 4435
+C 1434 4435 723 4192 723 3459
+L 723 2816
+L 250 2816
+L 250 2540
+L 723 2540
+L 723 275
+L 282 275
+L 282 0
+C 429 12 909 12 1088 12
+C 1274 12 1792 12 1946 0
+L 1946 275
+L 1389 275
+L 1389 2540
+z
+" id="CMBX12-66" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMBX12-4d"/>
+ <use transform="translate(106.314425 0)scale(0.996264)" xlink:href="#CMBX12-6f"/>
+ <use transform="translate(165.467601 0)scale(0.996264)" xlink:href="#CMBX12-64"/>
+ <use transform="translate(227.734101 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(278.873369 0)scale(0.996264)" xlink:href="#CMBX12-6c"/>
+ <use transform="translate(347.366519 0)scale(0.996264)" xlink:href="#CMBX12-77"/>
+ <use transform="translate(425.199645 0)scale(0.996264)" xlink:href="#CMBX12-65"/>
+ <use transform="translate(476.338912 0)scale(0.996264)" xlink:href="#CMBX12-69"/>
+ <use transform="translate(507.472162 0)scale(0.996264)" xlink:href="#CMBX12-67"/>
+ <use transform="translate(563.512013 0)scale(0.996264)" xlink:href="#CMBX12-68"/>
+ <use transform="translate(622.665189 0)scale(0.996264)" xlink:href="#CMBX12-74"/>
+ <use transform="translate(703.611639 0)scale(0.996264)" xlink:href="#CMBX12-66"/>
+ <use transform="translate(737.858215 0)scale(0.996264)" xlink:href="#CMBX12-6f"/>
+ <use transform="translate(793.898065 0)scale(0.996264)" xlink:href="#CMBX12-72"/>
+ <use transform="translate(839.675573 0)scale(0.996264)" xlink:href="#CMBX12-3a"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_10">
+ <!-- 7.9e-13 -->
+ <g style="fill:#262626;" transform="translate(174.52871 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2886 3955
+L 2886 4096
+L 1382 4096
+C 634 4096 621 4166 595 4288
+L 480 4288
+L 294 3104
+L 410 3104
+C 429 3226 474 3552 550 3673
+C 589 3724 1062 3724 1171 3724
+L 2579 3724
+L 1869 2670
+C 1395 1961 1069 1003 1069 166
+C 1069 89 1069 -128 1299 -128
+C 1530 -128 1530 89 1530 172
+L 1530 466
+C 1530 1514 1709 2204 2003 2644
+L 2886 3955
+z
+" id="CMR17-37" transform="scale(0.015625)"/>
+ <path d="M 1062 262
+C 1062 422 934 524 800 524
+C 672 524 538 422 538 262
+C 538 102 666 0 800 0
+C 928 0 1062 102 1062 262
+z
+" id="CMR17-2e" transform="scale(0.015625)"/>
+ <path d="M 2253 1871
+C 2253 448 1670 25 1190 25
+C 1043 25 685 43 538 281
+C 704 256 826 345 826 505
+C 826 678 685 736 595 736
+C 538 736 365 710 365 492
+C 365 68 742 -128 1203 -128
+C 1939 -128 2688 665 2688 2090
+C 2688 3857 1971 4224 1485 4224
+C 851 4224 243 3664 243 2800
+C 243 2000 762 1408 1414 1408
+C 1952 1408 2189 1910 2253 2122
+L 2253 1871
+z
+M 1427 1510
+C 1254 1510 1011 1542 813 1929
+C 678 2181 678 2477 678 2793
+C 678 3174 678 3438 858 3722
+C 947 3857 1114 4076 1485 4076
+C 2240 4076 2240 2909 2240 2651
+C 2240 2193 2035 1510 1427 1510
+z
+" id="CMR17-39" transform="scale(0.015625)"/>
+ <path d="M 1632 1254
+L 1632 1536
+L 26 1536
+L 26 1254
+L 1632 1254
+z
+" id="CMR17-2d" transform="scale(0.015625)"/>
+ <path d="M 1702 4083
+C 1702 4217 1696 4224 1606 4224
+C 1357 3927 979 3833 621 3820
+C 602 3820 570 3820 563 3808
+C 557 3795 557 3782 557 3648
+C 755 3648 1088 3686 1344 3839
+L 1344 467
+C 1344 243 1331 166 781 166
+L 589 166
+L 589 0
+C 896 6 1216 12 1523 12
+C 1830 12 2150 6 2458 0
+L 2458 166
+L 2266 166
+C 1715 166 1702 236 1702 467
+L 1702 4083
+z
+" id="CMR17-31" transform="scale(0.015625)"/>
+ <path d="M 1414 2176
+C 1984 2176 2234 1673 2234 1094
+C 2234 322 1824 25 1453 25
+C 1114 25 563 193 390 691
+C 422 678 454 678 486 678
+C 640 678 755 780 755 947
+C 755 1132 614 1216 486 1216
+C 378 1216 211 1164 211 927
+C 211 335 787 -128 1466 -128
+C 2176 -128 2720 432 2720 1087
+C 2720 1718 2208 2176 1600 2246
+C 2086 2347 2554 2776 2554 3353
+C 2554 3856 2048 4224 1472 4224
+C 890 4224 378 3862 378 3347
+C 378 3123 544 3084 627 3084
+C 762 3084 877 3167 877 3334
+C 877 3500 762 3584 627 3584
+C 602 3584 570 3584 544 3571
+C 730 3999 1235 4076 1459 4076
+C 1683 4076 2106 3966 2106 3347
+C 2106 3167 2080 2851 1862 2574
+C 1670 2329 1453 2316 1242 2297
+C 1210 2297 1062 2284 1037 2284
+C 992 2278 966 2272 966 2227
+C 966 2182 973 2176 1101 2176
+L 1414 2176
+z
+" id="CMR17-33" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-37"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-39"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ <g id="text_11">
+ <!-- 0.00017 -->
+ <g style="fill:#262626;" transform="translate(439.245807 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2688 2038
+C 2688 2430 2682 3099 2413 3613
+C 2176 4063 1798 4224 1466 4224
+C 1158 4224 768 4082 525 3620
+C 269 3137 243 2539 243 2038
+C 243 1671 250 1112 448 623
+C 723 -39 1216 -128 1466 -128
+C 1760 -128 2208 -7 2470 604
+C 2662 1048 2688 1568 2688 2038
+z
+M 1466 -26
+C 1056 -26 813 328 723 816
+C 653 1196 653 1749 653 2109
+C 653 2604 653 3015 736 3407
+C 858 3954 1216 4121 1466 4121
+C 1728 4121 2067 3947 2189 3420
+C 2272 3054 2278 2623 2278 2109
+C 2278 1691 2278 1176 2202 797
+C 2067 96 1690 -26 1466 -26
+z
+" id="CMR17-30" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(161.94249 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(207.632967 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(253.323444 0)scale(0.996264)" xlink:href="#CMR17-37"/>
+ </g>
+ </g>
+ <g id="text_12">
+ <!-- 9.9e-16 -->
+ <g style="fill:#262626;" transform="translate(710.20871 228.955463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 678 2198
+C 678 3712 1395 4076 1811 4076
+C 1946 4076 2272 4049 2400 3782
+C 2298 3782 2106 3782 2106 3558
+C 2106 3385 2246 3328 2336 3328
+C 2394 3328 2566 3353 2566 3571
+C 2566 3987 2246 4224 1805 4224
+C 1043 4224 243 3411 243 2011
+C 243 257 966 -128 1478 -128
+C 2099 -128 2688 431 2688 1295
+C 2688 2101 2170 2688 1517 2688
+C 1126 2688 838 2430 678 1979
+L 678 2198
+z
+M 1478 25
+C 691 25 691 1212 691 1450
+C 691 1914 909 2585 1504 2585
+C 1613 2585 1926 2585 2138 2140
+C 2253 1889 2253 1624 2253 1302
+C 2253 954 2253 696 2118 438
+C 1978 173 1773 25 1478 25
+z
+" id="CMR17-36" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-39"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-39"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ <g id="text_13">
+ <!-- 9.9e-16 -->
+ <g style="fill:#262626;" transform="translate(978.04871 228.955463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-39"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-39"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(156.737673 0)scale(0.996264)" xlink:href="#CMR17-2d"/>
+ <use transform="translate(186.81364 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(232.504117 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ <g id="text_14">
+ <!-- 0.44 -->
+ <g style="fill:#ffffff;" transform="translate(191.966522 518.875463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2150 4147
+C 2150 4281 2144 4288 2029 4288
+L 128 1254
+L 128 1088
+L 1779 1088
+L 1779 460
+C 1779 230 1766 166 1318 166
+L 1197 166
+L 1197 0
+C 1402 12 1747 12 1965 12
+C 2182 12 2528 12 2733 0
+L 2733 166
+L 2611 166
+C 2163 166 2150 230 2150 460
+L 2150 1088
+L 2803 1088
+L 2803 1254
+L 2150 1254
+L 2150 4147
+z
+M 1798 3723
+L 1798 1254
+L 256 1254
+L 1798 3723
+z
+" id="CMR17-34" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ <g id="text_15">
+ <!-- 0.56 -->
+ <g style="fill:#ffffff;" transform="translate(459.806522 518.875463)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 730 3750
+C 794 3724 1056 3641 1325 3641
+C 1920 3641 2246 3961 2432 4140
+C 2432 4191 2432 4224 2394 4224
+C 2387 4224 2374 4224 2323 4198
+C 2099 4102 1837 4032 1517 4032
+C 1325 4032 1037 4055 723 4191
+C 653 4224 640 4224 634 4224
+C 602 4224 595 4217 595 4090
+L 595 2231
+C 595 2113 595 2080 659 2080
+C 691 2080 704 2093 736 2139
+C 941 2435 1222 2560 1542 2560
+C 1766 2560 2246 2415 2246 1293
+C 2246 1087 2246 716 2054 422
+C 1894 159 1645 25 1370 25
+C 947 25 518 319 403 812
+C 429 806 480 793 506 793
+C 589 793 749 838 749 1036
+C 749 1209 627 1280 506 1280
+C 358 1280 262 1190 262 1011
+C 262 454 704 -128 1382 -128
+C 2042 -128 2669 441 2669 1267
+C 2669 2054 2170 2662 1549 2662
+C 1222 2662 947 2540 730 2304
+L 730 3750
+z
+" id="CMR17-35" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ <g id="text_16">
+ <!-- 0.31 -->
+ <g style="fill:#262626;" transform="translate(727.646522 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ <g id="text_17">
+ <!-- 0.31 -->
+ <g style="fill:#262626;" transform="translate(995.486522 518.875463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ <g id="text_18">
+ <!-- 0.56 -->
+ <g style="fill:#ffffff;" transform="translate(191.966522 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ <g id="text_19">
+ <!-- 0.44 -->
+ <g style="fill:#ffffff;" transform="translate(459.806522 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ <g id="text_20">
+ <!-- 0.69 -->
+ <g style="fill:#ffffff;" transform="translate(727.646522 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-39"/>
+ </g>
+ </g>
+ <g id="text_21">
+ <!-- 0.69 -->
+ <g style="fill:#ffffff;" transform="translate(995.486522 808.795463)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(70.561536 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ <use transform="translate(116.252013 0)scale(0.996264)" xlink:href="#CMR17-39"/>
+ </g>
+ </g>
+ </g>
+ <g id="axes_2">
+ <g id="patch_3">
+ <path d="M 1220.657891 946.284441
+L 1264.145891 946.284441
+L 1264.145891 76.524441
+L 1220.657891 76.524441
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="patch_4">
+ <path clip-path="url(#p628abfa176)" d="M 1220.657891 946.284441
+L 1220.657891 942.886941
+L 1220.657891 79.921941
+L 1220.657891 76.524441
+L 1264.145891 76.524441
+L 1264.145891 79.921941
+L 1264.145891 942.886941
+L 1264.145891 946.284441
+L 1264.145891 946.284441
+z
+" style="fill:#ffffff;stroke:#ffffff;stroke-linejoin:miter;stroke-width:0.01;"/>
+ </g>
+ <image height="870" id="imagea549e9aa0d" transform="scale(1 -1)translate(0 -870)" width="43" x="1221" xlink:href="data:image/png;base64,
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" y="-76"/>
+ <g id="matplotlib.axis_3"/>
+ <g id="matplotlib.axis_4">
+ <g id="ytick_4">
+ <g id="line2d_8">
+ <defs>
+ <path d="M 0 0
+L 3.5 0
+" id="m1a6892c68c" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m1a6892c68c" y="946.284441"/>
+ </g>
+ </g>
+ <g id="text_22">
+ <!-- $\mathdefault{0.0}$ -->
+ <g transform="translate(1271.145891 956.662188)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1178 307
+C 1178 492 1024 620 870 620
+C 685 620 557 467 557 313
+C 557 128 710 0 864 0
+C 1050 0 1178 153 1178 307
+z
+" id="CMMI12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_5">
+ <g id="line2d_9">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m1a6892c68c" y="820.153305"/>
+ </g>
+ </g>
+ <g id="text_23">
+ <!-- $\mathdefault{0.1}$ -->
+ <g transform="translate(1271.145891 830.531052)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_6">
+ <g id="line2d_10">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m1a6892c68c" y="694.022169"/>
+ </g>
+ </g>
+ <g id="text_24">
+ <!-- $\mathdefault{0.2}$ -->
+ <g transform="translate(1271.145891 704.399916)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2669 990
+L 2554 990
+C 2490 537 2438 460 2413 422
+C 2381 371 1920 371 1830 371
+L 602 371
+C 832 620 1280 1073 1824 1596
+C 2214 1966 2669 2400 2669 3033
+C 2669 3788 2067 4224 1395 4224
+C 691 4224 262 3603 262 3027
+C 262 2777 448 2745 525 2745
+C 589 2745 781 2783 781 3007
+C 781 3206 614 3264 525 3264
+C 486 3264 448 3257 422 3244
+C 544 3788 915 4057 1306 4057
+C 1862 4057 2227 3616 2227 3033
+C 2227 2477 1901 1998 1536 1583
+L 262 147
+L 262 0
+L 2515 0
+L 2669 990
+z
+" id="CMR17-32" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_7">
+ <g id="line2d_11">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m1a6892c68c" y="567.891033"/>
+ </g>
+ </g>
+ <g id="text_25">
+ <!-- $\mathdefault{0.3}$ -->
+ <g transform="translate(1271.145891 578.26878)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_8">
+ <g id="line2d_12">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m1a6892c68c" y="441.759897"/>
+ </g>
+ </g>
+ <g id="text_26">
+ <!-- $\mathdefault{0.4}$ -->
+ <g transform="translate(1271.145891 452.137644)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_9">
+ <g id="line2d_13">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m1a6892c68c" y="315.628761"/>
+ </g>
+ </g>
+ <g id="text_27">
+ <!-- $\mathdefault{0.5}$ -->
+ <g transform="translate(1271.145891 326.006508)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_10">
+ <g id="line2d_14">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1264.145891" xlink:href="#m1a6892c68c" y="189.497625"/>
+ </g>
+ </g>
+ <g id="text_28">
+ <!-- $\mathdefault{0.6}$ -->
+ <g transform="translate(1271.145891 199.875372)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ </g>
+ </g>
+ <g id="LineCollection_1"/>
+ <g id="patch_5">
+ <path d="M 1220.657891 946.284441
+L 1220.657891 942.886941
+L 1220.657891 79.921941
+L 1220.657891 76.524441
+L 1264.145891 76.524441
+L 1264.145891 79.921941
+L 1264.145891 942.886941
+L 1264.145891 946.284441
+z
+" style="fill:none;"/>
+ </g>
+ </g>
+ </g>
+ <defs>
+ <clipPath id="pba293bd3d4">
+ <rect height="869.76" width="1071.36" x="82.337891" y="76.524441"/>
+ </clipPath>
+ <clipPath id="p628abfa176">
+ <rect height="869.76" width="43.488" x="1220.657891" y="76.524441"/>
+ </clipPath>
+ </defs>
+</svg>
diff --git a/examples/model-comparison/reference/modelWeights_Observation.svg b/examples/model-comparison/reference/modelWeights_Observation.svg
new file mode 100644
index 0000000000000000000000000000000000000000..4bd75c828bd193cbc55fffebba97930573fbbede
--- /dev/null
+++ b/examples/model-comparison/reference/modelWeights_Observation.svg
@@ -0,0 +1,1735 @@
+<?xml version="1.0" encoding="utf-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<svg height="975.053386pt" version="1.1" viewBox="0 0 1426.712385 975.053386" width="1426.712385pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+ <metadata>
+ <rdf:RDF xmlns:cc="http://creativecommons.org/ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
+ <cc:Work>
+ <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
+ <dc:date>2022-06-03T16:06:03.509920</dc:date>
+ <dc:format>image/svg+xml</dc:format>
+ <dc:creator>
+ <cc:Agent>
+ <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>
+ </cc:Agent>
+ </dc:creator>
+ </cc:Work>
+ </rdf:RDF>
+ </metadata>
+ <defs>
+ <style type="text/css">*{stroke-linecap:butt;stroke-linejoin:round;}</style>
+ </defs>
+ <g id="figure_1">
+ <g id="patch_1">
+ <path d="M 0 975.053386
+L 1426.712385 975.053386
+L 1426.712385 0
+L 0 0
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="axes_1">
+ <g id="patch_2">
+ <path d="M 80.312385 903.715495
+L 1419.512385 903.715495
+L 1419.512385 33.955495
+L 80.312385 33.955495
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="matplotlib.axis_1">
+ <g id="xtick_1">
+ <g id="line2d_1">
+ <path clip-path="url(#p390e746ae5)" d="M 141.185112 903.715495
+L 141.185112 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_2">
+ <defs>
+ <path d="M 0 0
+L 0 3.5
+" id="m22d57cdbea" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="141.185112" xlink:href="#m22d57cdbea" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_1">
+ <!-- $\mathdefault{1}$ -->
+ <g transform="translate(134.331541 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1702 4083
+C 1702 4217 1696 4224 1606 4224
+C 1357 3927 979 3833 621 3820
+C 602 3820 570 3820 563 3808
+C 557 3795 557 3782 557 3648
+C 755 3648 1088 3686 1344 3839
+L 1344 467
+C 1344 243 1331 166 781 166
+L 589 166
+L 589 0
+C 896 6 1216 12 1523 12
+C 1830 12 2150 6 2458 0
+L 2458 166
+L 2266 166
+C 1715 166 1702 236 1702 467
+L 1702 4083
+z
+" id="CMR17-31" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_2">
+ <g id="line2d_3">
+ <path clip-path="url(#p390e746ae5)" d="M 228.146151 903.715495
+L 228.146151 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_4">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="228.146151" xlink:href="#m22d57cdbea" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_2">
+ <!-- $\mathdefault{2}$ -->
+ <g transform="translate(221.29258 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2669 990
+L 2554 990
+C 2490 537 2438 460 2413 422
+C 2381 371 1920 371 1830 371
+L 602 371
+C 832 620 1280 1073 1824 1596
+C 2214 1966 2669 2400 2669 3033
+C 2669 3788 2067 4224 1395 4224
+C 691 4224 262 3603 262 3027
+C 262 2777 448 2745 525 2745
+C 589 2745 781 2783 781 3007
+C 781 3206 614 3264 525 3264
+C 486 3264 448 3257 422 3244
+C 544 3788 915 4057 1306 4057
+C 1862 4057 2227 3616 2227 3033
+C 2227 2477 1901 1998 1536 1583
+L 262 147
+L 262 0
+L 2515 0
+L 2669 990
+z
+" id="CMR17-32" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_3">
+ <g id="line2d_5">
+ <path clip-path="url(#p390e746ae5)" d="M 315.10719 903.715495
+L 315.10719 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_6">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="315.10719" xlink:href="#m22d57cdbea" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_3">
+ <!-- $\mathdefault{3}$ -->
+ <g transform="translate(308.253619 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1414 2176
+C 1984 2176 2234 1673 2234 1094
+C 2234 322 1824 25 1453 25
+C 1114 25 563 193 390 691
+C 422 678 454 678 486 678
+C 640 678 755 780 755 947
+C 755 1132 614 1216 486 1216
+C 378 1216 211 1164 211 927
+C 211 335 787 -128 1466 -128
+C 2176 -128 2720 432 2720 1087
+C 2720 1718 2208 2176 1600 2246
+C 2086 2347 2554 2776 2554 3353
+C 2554 3856 2048 4224 1472 4224
+C 890 4224 378 3862 378 3347
+C 378 3123 544 3084 627 3084
+C 762 3084 877 3167 877 3334
+C 877 3500 762 3584 627 3584
+C 602 3584 570 3584 544 3571
+C 730 3999 1235 4076 1459 4076
+C 1683 4076 2106 3966 2106 3347
+C 2106 3167 2080 2851 1862 2574
+C 1670 2329 1453 2316 1242 2297
+C 1210 2297 1062 2284 1037 2284
+C 992 2278 966 2272 966 2227
+C 966 2182 973 2176 1101 2176
+L 1414 2176
+z
+" id="CMR17-33" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_4">
+ <g id="line2d_7">
+ <path clip-path="url(#p390e746ae5)" d="M 402.068229 903.715495
+L 402.068229 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_8">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="402.068229" xlink:href="#m22d57cdbea" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_4">
+ <!-- $\mathdefault{4}$ -->
+ <g transform="translate(395.214658 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2150 4147
+C 2150 4281 2144 4288 2029 4288
+L 128 1254
+L 128 1088
+L 1779 1088
+L 1779 460
+C 1779 230 1766 166 1318 166
+L 1197 166
+L 1197 0
+C 1402 12 1747 12 1965 12
+C 2182 12 2528 12 2733 0
+L 2733 166
+L 2611 166
+C 2163 166 2150 230 2150 460
+L 2150 1088
+L 2803 1088
+L 2803 1254
+L 2150 1254
+L 2150 4147
+z
+M 1798 3723
+L 1798 1254
+L 256 1254
+L 1798 3723
+z
+" id="CMR17-34" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_5">
+ <g id="line2d_9">
+ <path clip-path="url(#p390e746ae5)" d="M 489.029268 903.715495
+L 489.029268 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_10">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="489.029268" xlink:href="#m22d57cdbea" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_5">
+ <!-- $\mathdefault{5}$ -->
+ <g transform="translate(482.175697 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 730 3750
+C 794 3724 1056 3641 1325 3641
+C 1920 3641 2246 3961 2432 4140
+C 2432 4191 2432 4224 2394 4224
+C 2387 4224 2374 4224 2323 4198
+C 2099 4102 1837 4032 1517 4032
+C 1325 4032 1037 4055 723 4191
+C 653 4224 640 4224 634 4224
+C 602 4224 595 4217 595 4090
+L 595 2231
+C 595 2113 595 2080 659 2080
+C 691 2080 704 2093 736 2139
+C 941 2435 1222 2560 1542 2560
+C 1766 2560 2246 2415 2246 1293
+C 2246 1087 2246 716 2054 422
+C 1894 159 1645 25 1370 25
+C 947 25 518 319 403 812
+C 429 806 480 793 506 793
+C 589 793 749 838 749 1036
+C 749 1209 627 1280 506 1280
+C 358 1280 262 1190 262 1011
+C 262 454 704 -128 1382 -128
+C 2042 -128 2669 441 2669 1267
+C 2669 2054 2170 2662 1549 2662
+C 1222 2662 947 2540 730 2304
+L 730 3750
+z
+" id="CMR17-35" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_6">
+ <g id="line2d_11">
+ <path clip-path="url(#p390e746ae5)" d="M 575.990307 903.715495
+L 575.990307 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_12">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="575.990307" xlink:href="#m22d57cdbea" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_6">
+ <!-- $\mathdefault{6}$ -->
+ <g transform="translate(569.136735 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 678 2198
+C 678 3712 1395 4076 1811 4076
+C 1946 4076 2272 4049 2400 3782
+C 2298 3782 2106 3782 2106 3558
+C 2106 3385 2246 3328 2336 3328
+C 2394 3328 2566 3353 2566 3571
+C 2566 3987 2246 4224 1805 4224
+C 1043 4224 243 3411 243 2011
+C 243 257 966 -128 1478 -128
+C 2099 -128 2688 431 2688 1295
+C 2688 2101 2170 2688 1517 2688
+C 1126 2688 838 2430 678 1979
+L 678 2198
+z
+M 1478 25
+C 691 25 691 1212 691 1450
+C 691 1914 909 2585 1504 2585
+C 1613 2585 1926 2585 2138 2140
+C 2253 1889 2253 1624 2253 1302
+C 2253 954 2253 696 2118 438
+C 1978 173 1773 25 1478 25
+z
+" id="CMR17-36" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_7">
+ <g id="line2d_13">
+ <path clip-path="url(#p390e746ae5)" d="M 662.951346 903.715495
+L 662.951346 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_14">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="662.951346" xlink:href="#m22d57cdbea" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_7">
+ <!-- $\mathdefault{7}$ -->
+ <g transform="translate(656.097774 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2886 3955
+L 2886 4096
+L 1382 4096
+C 634 4096 621 4166 595 4288
+L 480 4288
+L 294 3104
+L 410 3104
+C 429 3226 474 3552 550 3673
+C 589 3724 1062 3724 1171 3724
+L 2579 3724
+L 1869 2670
+C 1395 1961 1069 1003 1069 166
+C 1069 89 1069 -128 1299 -128
+C 1530 -128 1530 89 1530 172
+L 1530 466
+C 1530 1514 1709 2204 2003 2644
+L 2886 3955
+z
+" id="CMR17-37" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-37"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_8">
+ <g id="line2d_15">
+ <path clip-path="url(#p390e746ae5)" d="M 749.912385 903.715495
+L 749.912385 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_16">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="749.912385" xlink:href="#m22d57cdbea" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_8">
+ <!-- $\mathdefault{8}$ -->
+ <g transform="translate(743.058813 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1741 2289
+C 2144 2494 2554 2803 2554 3298
+C 2554 3884 1990 4224 1472 4224
+C 890 4224 378 3800 378 3215
+C 378 3054 416 2777 666 2533
+C 730 2469 998 2276 1171 2154
+C 883 2006 211 1652 211 945
+C 211 282 838 -128 1459 -128
+C 2144 -128 2720 366 2720 1022
+C 2720 1607 2330 1877 2074 2051
+L 1741 2289
+z
+M 902 2855
+C 851 2887 595 3086 595 3388
+C 595 3781 998 4076 1459 4076
+C 1965 4076 2336 3716 2336 3298
+C 2336 2700 1670 2359 1638 2359
+C 1632 2359 1626 2359 1574 2398
+L 902 2855
+z
+M 2080 1536
+C 2176 1466 2483 1253 2483 861
+C 2483 385 2010 25 1472 25
+C 890 25 448 443 448 951
+C 448 1459 838 1884 1280 2083
+L 2080 1536
+z
+" id="CMR17-38" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-38"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_9">
+ <g id="line2d_17">
+ <path clip-path="url(#p390e746ae5)" d="M 836.873424 903.715495
+L 836.873424 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_18">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="836.873424" xlink:href="#m22d57cdbea" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_9">
+ <!-- $\mathdefault{9}$ -->
+ <g transform="translate(830.019852 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2253 1871
+C 2253 448 1670 25 1190 25
+C 1043 25 685 43 538 281
+C 704 256 826 345 826 505
+C 826 678 685 736 595 736
+C 538 736 365 710 365 492
+C 365 68 742 -128 1203 -128
+C 1939 -128 2688 665 2688 2090
+C 2688 3857 1971 4224 1485 4224
+C 851 4224 243 3664 243 2800
+C 243 2000 762 1408 1414 1408
+C 1952 1408 2189 1910 2253 2122
+L 2253 1871
+z
+M 1427 1510
+C 1254 1510 1011 1542 813 1929
+C 678 2181 678 2477 678 2793
+C 678 3174 678 3438 858 3722
+C 947 3857 1114 4076 1485 4076
+C 2240 4076 2240 2909 2240 2651
+C 2240 2193 2035 1510 1427 1510
+z
+" id="CMR17-39" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-39"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_10">
+ <g id="line2d_19">
+ <path clip-path="url(#p390e746ae5)" d="M 923.834463 903.715495
+L 923.834463 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_20">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="923.834463" xlink:href="#m22d57cdbea" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_10">
+ <!-- $\mathdefault{10}$ -->
+ <g transform="translate(910.12732 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2688 2038
+C 2688 2430 2682 3099 2413 3613
+C 2176 4063 1798 4224 1466 4224
+C 1158 4224 768 4082 525 3620
+C 269 3137 243 2539 243 2038
+C 243 1671 250 1112 448 623
+C 723 -39 1216 -128 1466 -128
+C 1760 -128 2208 -7 2470 604
+C 2662 1048 2688 1568 2688 2038
+z
+M 1466 -26
+C 1056 -26 813 328 723 816
+C 653 1196 653 1749 653 2109
+C 653 2604 653 3015 736 3407
+C 858 3954 1216 4121 1466 4121
+C 1728 4121 2067 3947 2189 3420
+C 2272 3054 2278 2623 2278 2109
+C 2278 1691 2278 1176 2202 797
+C 2067 96 1690 -26 1466 -26
+z
+" id="CMR17-30" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_11">
+ <g id="line2d_21">
+ <path clip-path="url(#p390e746ae5)" d="M 1010.795502 903.715495
+L 1010.795502 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_22">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1010.795502" xlink:href="#m22d57cdbea" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_11">
+ <!-- $\mathdefault{11}$ -->
+ <g transform="translate(997.088359 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_12">
+ <g id="line2d_23">
+ <path clip-path="url(#p390e746ae5)" d="M 1097.756541 903.715495
+L 1097.756541 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_24">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1097.756541" xlink:href="#m22d57cdbea" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_12">
+ <!-- $\mathdefault{12}$ -->
+ <g transform="translate(1084.049398 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_13">
+ <g id="line2d_25">
+ <path clip-path="url(#p390e746ae5)" d="M 1184.71758 903.715495
+L 1184.71758 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_26">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1184.71758" xlink:href="#m22d57cdbea" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_13">
+ <!-- $\mathdefault{13}$ -->
+ <g transform="translate(1171.010437 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_14">
+ <g id="line2d_27">
+ <path clip-path="url(#p390e746ae5)" d="M 1271.678619 903.715495
+L 1271.678619 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_28">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1271.678619" xlink:href="#m22d57cdbea" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_14">
+ <!-- $\mathdefault{14}$ -->
+ <g transform="translate(1257.971476 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_15">
+ <g id="line2d_29">
+ <path clip-path="url(#p390e746ae5)" d="M 1358.639658 903.715495
+L 1358.639658 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_30">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1358.639658" xlink:href="#m22d57cdbea" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_15">
+ <!-- $\mathdefault{15}$ -->
+ <g transform="translate(1344.932515 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_16">
+ <!-- No. of measurement points -->
+ <g transform="translate(587.401303 962.039936)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1312 4275
+C 1267 4345 1261 4352 1139 4352
+L 326 4352
+L 326 4185
+L 448 4185
+C 704 4185 819 4153 838 4147
+L 838 624
+C 838 465 838 166 326 166
+L 326 0
+C 474 12 742 12 902 12
+C 1062 12 1331 12 1478 0
+L 1478 166
+C 966 166 966 465 966 624
+L 966 4057
+C 1011 4019 1011 4007 1056 3943
+L 3430 76
+C 3475 0 3494 0 3526 0
+C 3590 0 3590 19 3590 140
+L 3590 3726
+C 3590 3885 3590 4185 4102 4185
+L 4102 4352
+C 3955 4339 3686 4339 3526 4339
+C 3366 4339 3098 4339 2950 4352
+L 2950 4185
+C 3462 4185 3462 3885 3462 3726
+L 3462 777
+L 1312 4275
+z
+" id="CMR17-4e" transform="scale(0.015625)"/>
+ <path d="M 2758 1356
+C 2758 2176 2163 2816 1466 2816
+C 768 2816 173 2176 173 1356
+C 173 550 768 -64 1466 -64
+C 2163 -64 2758 550 2758 1356
+z
+M 1466 51
+C 1165 51 909 230 762 480
+C 602 768 582 1126 582 1408
+C 582 1676 595 2009 762 2297
+C 890 2508 1139 2713 1466 2713
+C 1754 2713 1997 2553 2150 2329
+C 2349 2028 2349 1606 2349 1408
+C 2349 1158 2336 774 2163 467
+C 1984 172 1709 51 1466 51
+z
+" id="CMR17-6f" transform="scale(0.015625)"/>
+ <path d="M 1062 262
+C 1062 422 934 524 800 524
+C 672 524 538 422 538 262
+C 538 102 666 0 800 0
+C 928 0 1062 102 1062 262
+z
+" id="CMR17-2e" transform="scale(0.015625)"/>
+ <path d="M 979 2585
+L 1709 2585
+L 1709 2752
+L 966 2752
+L 966 3539
+C 966 4076 1235 4377 1510 4377
+C 1594 4377 1690 4363 1754 4339
+C 1702 4326 1568 4281 1568 4121
+C 1568 3955 1696 3904 1786 3904
+C 1875 3904 2003 3955 2003 4121
+C 2003 4353 1773 4480 1517 4480
+C 1152 4480 653 4211 653 3526
+L 653 2752
+L 141 2752
+L 141 2585
+L 653 2585
+L 653 441
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 666 12 832 12
+C 1018 12 1344 12 1517 0
+L 1517 166
+C 1056 166 979 166 979 454
+L 979 2585
+z
+" id="CMR17-66" transform="scale(0.015625)"/>
+ <path d="M 4326 1954
+C 4326 2276 4269 2816 3507 2816
+C 3072 2816 2771 2520 2656 2173
+L 2650 2173
+C 2573 2700 2195 2816 1837 2816
+C 1331 2816 1069 2424 973 2166
+L 966 2166
+L 966 2816
+L 211 2745
+L 211 2578
+C 589 2578 646 2540 646 2231
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1678
+C 2656 2269 3014 2713 3462 2713
+C 3936 2713 3987 2289 3987 1980
+L 3987 443
+C 3987 198 3962 166 3552 166
+L 3552 0
+C 3706 12 3987 12 4154 12
+C 4320 12 4608 12 4762 0
+L 4762 166
+C 4352 166 4326 192 4326 443
+L 4326 1954
+z
+" id="CMR17-6d" transform="scale(0.015625)"/>
+ <path d="M 2438 1503
+C 2464 1529 2464 1542 2464 1606
+C 2464 2251 2118 2816 1389 2816
+C 710 2816 173 2175 173 1394
+C 173 554 781 -64 1459 -64
+C 2176 -64 2458 619 2458 755
+C 2458 800 2419 800 2406 800
+C 2362 800 2355 787 2330 709
+C 2189 270 1837 51 1504 51
+C 1229 51 954 206 781 490
+C 582 819 582 1200 582 1503
+L 2438 1503
+z
+M 589 1600
+C 634 2511 1126 2713 1382 2713
+C 1818 2713 2112 2308 2118 1600
+L 589 1600
+z
+" id="CMR17-65" transform="scale(0.015625)"/>
+ <path d="M 2304 1656
+C 2304 2048 2304 2275 2035 2534
+C 1798 2751 1523 2816 1306 2816
+C 800 2816 435 2408 435 1977
+C 435 1740 627 1728 666 1728
+C 749 1728 896 1779 896 1958
+C 896 2118 774 2188 666 2188
+C 640 2188 608 2182 589 2176
+C 723 2594 1069 2713 1293 2713
+C 1613 2713 1965 2421 1965 1875
+L 1965 1632
+C 1587 1619 1133 1568 774 1373
+C 371 1147 256 822 256 576
+C 256 77 832 -64 1171 -64
+C 1523 -64 1850 135 1990 505
+C 2003 219 2182 -39 2464 -39
+C 2598 -39 2938 51 2938 563
+L 2938 926
+L 2822 926
+L 2822 557
+C 2822 161 2650 109 2566 109
+C 2304 109 2304 446 2304 732
+L 2304 1656
+z
+M 1965 887
+C 1965 323 1568 38 1216 38
+C 896 38 646 278 646 576
+C 646 771 730 1114 1101 1322
+C 1408 1497 1760 1523 1965 1536
+L 1965 887
+z
+" id="CMR17-61" transform="scale(0.015625)"/>
+ <path d="M 1978 2688
+C 1978 2803 1971 2809 1933 2809
+C 1907 2809 1901 2803 1824 2707
+C 1805 2681 1747 2617 1728 2592
+C 1523 2809 1235 2816 1126 2816
+C 416 2816 160 2444 160 2073
+C 160 1497 813 1363 998 1324
+C 1402 1241 1542 1216 1677 1100
+C 1760 1024 1901 883 1901 652
+C 1901 384 1747 38 1158 38
+C 602 38 403 460 288 1024
+C 269 1113 269 1120 218 1120
+C 166 1120 160 1113 160 985
+L 160 64
+C 160 -52 166 -58 205 -58
+C 237 -58 243 -52 275 0
+C 314 57 410 211 448 275
+C 576 102 800 -64 1158 -64
+C 1792 -64 2131 281 2131 780
+C 2131 1107 1958 1280 1875 1356
+C 1683 1555 1459 1600 1190 1651
+C 838 1728 390 1817 390 2208
+C 390 2374 480 2726 1126 2726
+C 1811 2726 1850 2086 1862 1881
+C 1869 1849 1901 1843 1920 1843
+C 1978 1843 1978 1862 1978 1971
+L 1978 2688
+z
+" id="CMR17-73" transform="scale(0.015625)"/>
+ <path d="M 1882 2745
+L 1882 2579
+C 2259 2579 2317 2540 2317 2229
+L 2317 1053
+C 2317 510 2029 38 1555 38
+C 1030 38 986 355 986 691
+L 986 2816
+L 211 2745
+L 211 2579
+C 467 2579 640 2579 646 2320
+L 646 1079
+C 646 646 646 368 813 187
+C 896 103 1056 -64 1517 -64
+C 2061 -64 2272 400 2323 536
+L 2330 536
+L 2330 -64
+L 3091 -13
+L 3091 154
+C 2714 154 2656 193 2656 503
+L 2656 2816
+L 1882 2745
+z
+" id="CMR17-75" transform="scale(0.015625)"/>
+ <path d="M 960 1517
+C 960 2134 1222 2713 1702 2713
+C 1747 2713 1792 2707 1837 2687
+C 1837 2687 1696 2642 1696 2475
+C 1696 2321 1818 2257 1914 2257
+C 1990 2257 2131 2302 2131 2482
+C 2131 2687 1926 2816 1709 2816
+C 1222 2816 1011 2340 947 2115
+L 941 2115
+L 941 2816
+L 198 2745
+L 198 2578
+C 576 2578 634 2540 634 2231
+L 634 443
+C 634 198 608 166 198 166
+L 198 0
+C 352 12 646 12 813 12
+C 998 12 1325 12 1498 0
+L 1498 166
+C 1037 166 960 166 960 455
+L 960 1517
+z
+" id="CMR17-72" transform="scale(0.015625)"/>
+ <path d="M 2656 1954
+C 2656 2282 2592 2816 1837 2816
+C 1331 2816 1069 2424 973 2166
+L 966 2166
+L 966 2816
+L 211 2745
+L 211 2578
+C 589 2578 646 2540 646 2231
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1954
+z
+" id="CMR17-6e" transform="scale(0.015625)"/>
+ <path d="M 966 2585
+L 1862 2585
+L 1862 2752
+L 966 2752
+L 966 3968
+L 851 3968
+C 838 3292 614 2700 70 2687
+L 70 2585
+L 627 2585
+L 627 778
+C 627 655 627 -64 1370 -64
+C 1747 -64 1965 308 1965 784
+L 1965 1151
+L 1850 1151
+L 1850 790
+C 1850 347 1677 51 1408 51
+C 1222 51 966 179 966 765
+L 966 2585
+z
+" id="CMR17-74" transform="scale(0.015625)"/>
+ <path d="M 1408 -1114
+C 998 -1114 973 -1088 973 -834
+L 973 380
+C 1158 109 1427 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2196 2496 2816 1837 2816
+C 1453 2816 1139 2603 960 2345
+L 960 2816
+L 198 2745
+L 198 2577
+C 576 2577 634 2539 634 2228
+L 634 -834
+C 634 -1081 608 -1114 198 -1114
+L 198 -1280
+C 352 -1268 634 -1268 800 -1268
+C 966 -1268 1254 -1268 1408 -1280
+L 1408 -1114
+z
+M 973 2015
+C 973 2106 973 2241 1222 2481
+C 1254 2506 1472 2700 1792 2700
+C 2259 2700 2643 2112 2643 1376
+C 2643 639 2234 38 1728 38
+C 1498 38 1248 148 1056 451
+C 973 594 973 632 973 736
+L 973 2015
+z
+" id="CMR17-70" transform="scale(0.015625)"/>
+ <path d="M 992 3961
+C 992 4102 877 4224 730 4224
+C 589 4224 467 4108 467 3961
+C 467 3820 582 3699 730 3699
+C 870 3699 992 3814 992 3961
+z
+M 243 2745
+L 243 2579
+C 602 2579 653 2540 653 2231
+L 653 443
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 646 12 806 12
+C 960 12 1222 12 1370 0
+L 1370 166
+C 992 166 979 205 979 436
+L 979 2816
+L 243 2745
+z
+" id="CMR17-69" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-4e"/>
+ <use transform="translate(69.07243 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(114.762907 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(180.119626 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(225.810103 0)scale(0.996264)" xlink:href="#CMR17-66"/>
+ <use transform="translate(283.359582 0)scale(0.996264)" xlink:href="#CMR17-6d"/>
+ <use transform="translate(360.279172 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(400.764832 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(446.455309 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(482.256647 0)scale(0.996264)" xlink:href="#CMR17-75"/>
+ <use transform="translate(533.152017 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ <use transform="translate(568.432784 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(608.918445 0)scale(0.996264)" xlink:href="#CMR17-6d"/>
+ <use transform="translate(685.838035 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(726.323695 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(774.616611 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(839.973345 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(893.471154 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(939.161631 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(964.032689 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(1012.325605 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(1047.606373 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ </g>
+ </g>
+ </g>
+ <g id="matplotlib.axis_2">
+ <g id="ytick_1">
+ <g id="line2d_31">
+ <path clip-path="url(#p390e746ae5)" d="M 80.312385 864.18095
+L 1419.512385 864.18095
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_32">
+ <defs>
+ <path d="M 0 0
+L -3.5 0
+" id="m5427385f90" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#m5427385f90" y="864.18095"/>
+ </g>
+ </g>
+ <g id="text_17">
+ <!-- $\mathdefault{0.0}$ -->
+ <g transform="translate(37.768946 874.558697)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1178 307
+C 1178 492 1024 620 870 620
+C 685 620 557 467 557 313
+C 557 128 710 0 864 0
+C 1050 0 1178 153 1178 307
+z
+" id="CMMI12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_2">
+ <g id="line2d_33">
+ <path clip-path="url(#p390e746ae5)" d="M 80.312385 728.854242
+L 1419.512385 728.854242
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_34">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#m5427385f90" y="728.854242"/>
+ </g>
+ </g>
+ <g id="text_18">
+ <!-- $\mathdefault{0.1}$ -->
+ <g transform="translate(37.768946 739.23199)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_3">
+ <g id="line2d_35">
+ <path clip-path="url(#p390e746ae5)" d="M 80.312385 593.527535
+L 1419.512385 593.527535
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_36">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#m5427385f90" y="593.527535"/>
+ </g>
+ </g>
+ <g id="text_19">
+ <!-- $\mathdefault{0.2}$ -->
+ <g transform="translate(37.768946 603.905283)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_4">
+ <g id="line2d_37">
+ <path clip-path="url(#p390e746ae5)" d="M 80.312385 458.200828
+L 1419.512385 458.200828
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_38">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#m5427385f90" y="458.200828"/>
+ </g>
+ </g>
+ <g id="text_20">
+ <!-- $\mathdefault{0.3}$ -->
+ <g transform="translate(37.768946 468.578575)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_5">
+ <g id="line2d_39">
+ <path clip-path="url(#p390e746ae5)" d="M 80.312385 322.87412
+L 1419.512385 322.87412
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_40">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#m5427385f90" y="322.87412"/>
+ </g>
+ </g>
+ <g id="text_21">
+ <!-- $\mathdefault{0.4}$ -->
+ <g transform="translate(37.768946 333.251868)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_6">
+ <g id="line2d_41">
+ <path clip-path="url(#p390e746ae5)" d="M 80.312385 187.547413
+L 1419.512385 187.547413
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_42">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#m5427385f90" y="187.547413"/>
+ </g>
+ </g>
+ <g id="text_22">
+ <!-- $\mathdefault{0.5}$ -->
+ <g transform="translate(37.768946 197.92516)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_7">
+ <g id="line2d_43">
+ <path clip-path="url(#p390e746ae5)" d="M 80.312385 52.220705
+L 1419.512385 52.220705
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_44">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#m5427385f90" y="52.220705"/>
+ </g>
+ </g>
+ <g id="text_23">
+ <!-- $\mathdefault{0.6}$ -->
+ <g transform="translate(37.768946 62.598453)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_24">
+ <!-- Weights -->
+ <g transform="translate(27.955495 516.492209)rotate(-90)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 5523 3775
+C 5581 3948 5677 4173 6048 4185
+L 6048 4352
+C 5939 4345 5715 4339 5600 4339
+C 5440 4339 5158 4339 5005 4352
+L 5005 4185
+C 5293 4179 5414 4019 5414 3865
+C 5414 3820 5408 3794 5382 3724
+L 4390 557
+L 3347 3890
+C 3328 3955 3322 3980 3322 4006
+C 3322 4185 3603 4185 3725 4185
+L 3725 4352
+C 3539 4339 3219 4339 3021 4339
+C 2861 4339 2573 4339 2426 4352
+L 2426 4185
+C 2720 4185 2797 4166 2861 4051
+C 2886 3993 2989 3660 2989 3640
+C 2989 3615 2976 3576 2970 3557
+L 2029 564
+L 986 3890
+C 954 3980 954 3993 954 4006
+C 954 4185 1235 4185 1363 4185
+L 1363 4352
+C 1178 4339 858 4339 659 4339
+C 493 4339 211 4339 58 4352
+L 58 4185
+C 442 4185 467 4147 531 3942
+L 1779 -20
+C 1811 -116 1811 -128 1869 -128
+C 1920 -128 1939 -116 1965 -26
+L 3053 3448
+L 4141 -26
+C 4166 -116 4186 -128 4237 -128
+C 4294 -128 4294 -116 4326 -20
+L 5523 3775
+z
+" id="CMR17-57" transform="scale(0.015625)"/>
+ <path d="M 710 1165
+C 832 1068 1043 960 1299 960
+C 1805 960 2240 1359 2240 1895
+C 2240 2063 2189 2321 1997 2521
+C 2176 2713 2438 2777 2586 2777
+C 2611 2777 2650 2777 2682 2758
+C 2656 2751 2598 2726 2598 2623
+C 2598 2540 2656 2483 2739 2483
+C 2835 2483 2886 2547 2886 2630
+C 2886 2751 2790 2880 2586 2880
+C 2330 2880 2106 2758 1926 2591
+C 1734 2764 1504 2828 1299 2828
+C 794 2828 358 2431 358 1895
+C 358 1527 570 1294 634 1230
+C 442 1004 442 742 442 710
+C 442 544 506 300 723 166
+C 390 82 128 -184 128 -517
+C 128 -996 736 -1344 1466 -1344
+C 2170 -1344 2803 -1009 2803 -510
+C 2803 384 1856 384 1363 384
+C 1216 384 954 384 922 390
+C 723 422 589 601 589 825
+C 589 883 589 1024 710 1165
+z
+M 1299 1068
+C 736 1068 736 1766 736 1895
+C 736 2024 736 2719 1299 2719
+C 1862 2719 1862 2024 1862 1895
+C 1862 1766 1862 1068 1299 1068
+z
+M 1466 -1236
+C 826 -1236 384 -883 384 -517
+C 384 -311 493 -118 634 -11
+C 794 102 858 102 1293 102
+C 1818 102 2547 102 2547 -517
+C 2547 -883 2106 -1236 1466 -1236
+z
+" id="CMR17-67" transform="scale(0.015625)"/>
+ <path d="M 2656 1954
+C 2656 2282 2592 2816 1837 2816
+C 1312 2816 1056 2392 979 2179
+L 973 2179
+L 973 4416
+L 211 4345
+L 211 4179
+C 589 4179 646 4141 646 3843
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1954
+z
+" id="CMR17-68" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-57"/>
+ <use transform="translate(87.289395 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(127.775055 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(152.646113 0)scale(0.996264)" xlink:href="#CMR17-67"/>
+ <use transform="translate(198.336591 0)scale(0.996264)" xlink:href="#CMR17-68"/>
+ <use transform="translate(246.629506 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(281.910274 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ </g>
+ </g>
+ </g>
+ <g id="line2d_45">
+ <path clip-path="url(#p390e746ae5)" d="M 141.185112 863.735852
+L 228.146151 863.925567
+L 315.10719 864.155607
+L 402.068229 864.177652
+L 489.029268 864.180344
+L 575.990307 864.180853
+L 662.951346 864.180942
+L 749.912385 864.180944
+L 836.873424 864.18095
+L 923.834463 864.18095
+L 1010.795502 864.18095
+L 1097.756541 864.18095
+L 1184.71758 864.18095
+L 1271.678619 864.180901
+L 1358.639658 469.876853
+" style="fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:2;"/>
+ <defs>
+ <path d="M 0 5
+C 1.326016 5 2.597899 4.473168 3.535534 3.535534
+C 4.473168 2.597899 5 1.326016 5 0
+C 5 -1.326016 4.473168 -2.597899 3.535534 -3.535534
+C 2.597899 -4.473168 1.326016 -5 0 -5
+C -1.326016 -5 -2.597899 -4.473168 -3.535534 -3.535534
+C -4.473168 -2.597899 -5 -1.326016 -5 0
+C -5 1.326016 -4.473168 2.597899 -3.535534 3.535534
+C -2.597899 4.473168 -1.326016 5 0 5
+z
+" id="m03e5f5b84b" style="stroke:#1f77b4;"/>
+ </defs>
+ <g clip-path="url(#p390e746ae5)">
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="141.185112" xlink:href="#m03e5f5b84b" y="863.735852"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="228.146151" xlink:href="#m03e5f5b84b" y="863.925567"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="315.10719" xlink:href="#m03e5f5b84b" y="864.155607"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="402.068229" xlink:href="#m03e5f5b84b" y="864.177652"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="489.029268" xlink:href="#m03e5f5b84b" y="864.180344"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="575.990307" xlink:href="#m03e5f5b84b" y="864.180853"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="662.951346" xlink:href="#m03e5f5b84b" y="864.180942"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="749.912385" xlink:href="#m03e5f5b84b" y="864.180944"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="836.873424" xlink:href="#m03e5f5b84b" y="864.18095"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="923.834463" xlink:href="#m03e5f5b84b" y="864.18095"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1010.795502" xlink:href="#m03e5f5b84b" y="864.18095"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1097.756541" xlink:href="#m03e5f5b84b" y="864.18095"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1184.71758" xlink:href="#m03e5f5b84b" y="864.18095"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1271.678619" xlink:href="#m03e5f5b84b" y="864.180901"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1358.639658" xlink:href="#m03e5f5b84b" y="469.876853"/>
+ </g>
+ </g>
+ <g id="line2d_46">
+ <path clip-path="url(#p390e746ae5)" d="M 141.185112 185.584992
+L 228.146151 184.913877
+L 315.10719 205.895528
+L 402.068229 202.094631
+L 489.029268 174.323896
+L 575.990307 151.507301
+L 662.951346 158.550142
+L 749.912385 213.013028
+L 836.873424 266.29479
+L 923.834463 197.341968
+L 1010.795502 301.604785
+L 1097.756541 271.689208
+L 1184.71758 160.712906
+L 1271.678619 208.194053
+L 1358.639658 383.132409
+" style="fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:2;"/>
+ <defs>
+ <path d="M 0 5
+C 1.326016 5 2.597899 4.473168 3.535534 3.535534
+C 4.473168 2.597899 5 1.326016 5 0
+C 5 -1.326016 4.473168 -2.597899 3.535534 -3.535534
+C 2.597899 -4.473168 1.326016 -5 0 -5
+C -1.326016 -5 -2.597899 -4.473168 -3.535534 -3.535534
+C -4.473168 -2.597899 -5 -1.326016 -5 0
+C -5 1.326016 -4.473168 2.597899 -3.535534 3.535534
+C -2.597899 4.473168 -1.326016 5 0 5
+z
+" id="me0316df6ac" style="stroke:#ff7f0e;"/>
+ </defs>
+ <g clip-path="url(#p390e746ae5)">
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="141.185112" xlink:href="#me0316df6ac" y="185.584992"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="228.146151" xlink:href="#me0316df6ac" y="184.913877"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="315.10719" xlink:href="#me0316df6ac" y="205.895528"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="402.068229" xlink:href="#me0316df6ac" y="202.094631"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="489.029268" xlink:href="#me0316df6ac" y="174.323896"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="575.990307" xlink:href="#me0316df6ac" y="151.507301"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="662.951346" xlink:href="#me0316df6ac" y="158.550142"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="749.912385" xlink:href="#me0316df6ac" y="213.013028"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="836.873424" xlink:href="#me0316df6ac" y="266.29479"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="923.834463" xlink:href="#me0316df6ac" y="197.341968"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1010.795502" xlink:href="#me0316df6ac" y="301.604785"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1097.756541" xlink:href="#me0316df6ac" y="271.689208"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1184.71758" xlink:href="#me0316df6ac" y="160.712906"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1271.678619" xlink:href="#me0316df6ac" y="208.194053"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1358.639658" xlink:href="#me0316df6ac" y="383.132409"/>
+ </g>
+ </g>
+ <g id="line2d_47">
+ <path clip-path="url(#p390e746ae5)" d="M 141.185112 189.954931
+L 228.146151 190.436332
+L 315.10719 169.22464
+L 402.068229 173.003493
+L 489.029268 200.771535
+L 575.990307 223.587621
+L 662.951346 216.544691
+L 749.912385 162.081803
+L 836.873424 108.800036
+L 923.834463 177.752858
+L 1010.795502 73.490041
+L 1097.756541 103.405618
+L 1184.71758 214.381919
+L 1271.678619 166.900821
+L 1358.639658 386.266513
+" style="fill:none;stroke:#2ca02c;stroke-linecap:square;stroke-width:2;"/>
+ <defs>
+ <path d="M 0 5
+C 1.326016 5 2.597899 4.473168 3.535534 3.535534
+C 4.473168 2.597899 5 1.326016 5 0
+C 5 -1.326016 4.473168 -2.597899 3.535534 -3.535534
+C 2.597899 -4.473168 1.326016 -5 0 -5
+C -1.326016 -5 -2.597899 -4.473168 -3.535534 -3.535534
+C -4.473168 -2.597899 -5 -1.326016 -5 0
+C -5 1.326016 -4.473168 2.597899 -3.535534 3.535534
+C -2.597899 4.473168 -1.326016 5 0 5
+z
+" id="m085466da6f" style="stroke:#2ca02c;"/>
+ </defs>
+ <g clip-path="url(#p390e746ae5)">
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="141.185112" xlink:href="#m085466da6f" y="189.954931"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="228.146151" xlink:href="#m085466da6f" y="190.436332"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="315.10719" xlink:href="#m085466da6f" y="169.22464"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="402.068229" xlink:href="#m085466da6f" y="173.003493"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="489.029268" xlink:href="#m085466da6f" y="200.771535"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="575.990307" xlink:href="#m085466da6f" y="223.587621"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="662.951346" xlink:href="#m085466da6f" y="216.544691"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="749.912385" xlink:href="#m085466da6f" y="162.081803"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="836.873424" xlink:href="#m085466da6f" y="108.800036"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="923.834463" xlink:href="#m085466da6f" y="177.752858"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1010.795502" xlink:href="#m085466da6f" y="73.490041"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1097.756541" xlink:href="#m085466da6f" y="103.405618"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1184.71758" xlink:href="#m085466da6f" y="214.381919"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1271.678619" xlink:href="#m085466da6f" y="166.900821"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1358.639658" xlink:href="#m085466da6f" y="386.266513"/>
+ </g>
+ </g>
+ <g id="patch_3">
+ <path d="M 80.312385 903.715495
+L 80.312385 33.955495
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:3;"/>
+ </g>
+ <g id="patch_4">
+ <path d="M 1419.512385 903.715495
+L 1419.512385 33.955495
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:3;"/>
+ </g>
+ <g id="patch_5">
+ <path d="M 80.312385 903.715495
+L 1419.512385 903.715495
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:3;"/>
+ </g>
+ <g id="patch_6">
+ <path d="M 80.312385 33.955495
+L 1419.512385 33.955495
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:3;"/>
+ </g>
+ <g id="text_25">
+ <!-- Data generated by: Observation -->
+ <g transform="translate(557.307322 27.955495)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 333 4352
+L 333 4185
+C 774 4185 845 4185 845 3898
+L 845 453
+C 845 166 774 166 333 166
+L 333 0
+L 2368 0
+C 3398 0 4224 943 4224 2140
+C 4224 3344 3411 4352 2368 4352
+L 333 4352
+z
+M 1523 166
+C 1267 166 1254 198 1254 414
+L 1254 3936
+C 1254 4153 1267 4185 1523 4185
+L 2240 4185
+C 2771 4185 3750 3873 3750 2140
+C 3750 1242 3488 879 3366 707
+C 3213 510 2848 166 2240 166
+L 1523 166
+z
+" id="CMR17-44" transform="scale(0.015625)"/>
+ <path d="M 1869 4345
+L 1869 4179
+C 2246 4179 2304 4141 2304 3843
+L 2304 2371
+C 2278 2403 2016 2816 1498 2816
+C 845 2816 211 2228 211 1376
+C 211 529 806 -64 1434 -64
+C 1978 -64 2259 361 2291 406
+L 2291 -64
+L 3066 -13
+L 3066 154
+C 2688 154 2630 193 2630 503
+L 2630 4416
+L 1869 4345
+z
+M 2291 762
+C 2291 568 2176 393 2029 264
+C 1811 70 1594 38 1472 38
+C 1286 38 621 135 621 1369
+C 621 2636 1363 2713 1530 2713
+C 1824 2713 2061 2545 2208 2313
+C 2291 2177 2291 2157 2291 2041
+L 2291 762
+z
+" id="CMR17-64" transform="scale(0.015625)"/>
+ <path d="M 960 4416
+L 198 4345
+L 198 4179
+C 576 4179 634 4141 634 3843
+L 634 -13
+L 749 -13
+L 934 445
+C 1120 141 1395 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2209 2477 2816 1830 2816
+C 1434 2816 1152 2603 960 2351
+L 960 4416
+z
+M 973 2022
+C 973 2138 973 2157 1062 2293
+C 1312 2681 1670 2713 1792 2713
+C 1984 2713 2643 2610 2643 1388
+C 2643 109 1888 38 1734 38
+C 1536 38 1248 115 1043 490
+C 973 613 973 626 973 742
+L 973 2022
+z
+" id="CMR17-62" transform="scale(0.015625)"/>
+ <path d="M 2496 2183
+C 2656 2579 2944 2585 3034 2585
+L 3034 2752
+C 2912 2745 2752 2739 2630 2739
+C 2496 2739 2285 2739 2157 2752
+L 2157 2585
+C 2400 2566 2406 2384 2406 2332
+C 2406 2268 2394 2235 2362 2158
+L 1664 409
+L 902 2300
+C 870 2378 870 2423 870 2430
+C 870 2572 1018 2585 1171 2585
+L 1171 2752
+C 1018 2739 742 2739 582 2739
+C 410 2739 205 2739 64 2752
+L 64 2585
+C 410 2585 448 2553 531 2345
+L 1485 -31
+C 1197 -795 1030 -1242 627 -1242
+C 557 -1242 397 -1223 282 -1106
+C 429 -1093 493 -1002 493 -892
+C 493 -782 416 -685 288 -685
+C 147 -685 77 -782 77 -899
+C 77 -1158 339 -1344 627 -1344
+C 998 -1344 1229 -983 1357 -659
+L 2496 2183
+z
+" id="CMR17-79" transform="scale(0.015625)"/>
+ <path d="M 1062 2489
+C 1062 2649 934 2752 800 2752
+C 672 2752 538 2649 538 2489
+C 538 2329 666 2227 800 2227
+C 928 2227 1062 2329 1062 2489
+z
+M 1062 262
+C 1062 422 934 524 800 524
+C 672 524 538 422 538 262
+C 538 102 666 0 800 0
+C 928 0 1062 102 1062 262
+z
+" id="CMR17-3a" transform="scale(0.015625)"/>
+ <path d="M 4307 2166
+C 4307 3488 3366 4480 2304 4480
+C 1216 4480 294 3475 294 2166
+C 294 857 1229 -128 2298 -128
+C 3392 -128 4307 876 4307 2166
+z
+M 2304 -13
+C 1574 -13 781 722 781 2250
+C 781 3771 1651 4364 2298 4364
+C 2976 4364 3821 3752 3821 2250
+C 3821 696 3008 -13 2304 -13
+z
+" id="CMR17-4f" transform="scale(0.015625)"/>
+ <path d="M 2502 2173
+C 2560 2315 2662 2572 3034 2585
+L 3034 2752
+C 2912 2745 2752 2739 2630 2739
+C 2496 2739 2285 2739 2157 2752
+L 2157 2585
+C 2317 2572 2406 2495 2406 2328
+C 2406 2270 2406 2257 2368 2167
+L 1664 379
+L 902 2308
+C 864 2392 864 2405 864 2431
+C 864 2585 1075 2585 1171 2585
+L 1171 2752
+C 1018 2739 736 2739 576 2739
+C 403 2739 205 2739 64 2752
+L 64 2585
+C 307 2585 442 2585 518 2386
+L 1446 44
+C 1485 -52 1491 -64 1549 -64
+C 1606 -64 1613 -52 1651 44
+L 2502 2173
+z
+" id="CMR17-76" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-44"/>
+ <use transform="translate(70.393556 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(116.084033 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(151.364801 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(227.131244 0)scale(0.996264)" xlink:href="#CMR17-67"/>
+ <use transform="translate(272.821721 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(313.307382 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(364.202752 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(404.688412 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ <use transform="translate(439.96918 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(485.659657 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(520.940425 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(561.426085 0)scale(0.996264)" xlink:href="#CMR17-64"/>
+ <use transform="translate(642.397421 0)scale(0.996264)" xlink:href="#CMR17-62"/>
+ <use transform="translate(690.690337 0)scale(0.996264)" xlink:href="#CMR17-79"/>
+ <use transform="translate(738.983253 0)scale(0.996264)" xlink:href="#CMR17-3a"/>
+ <use transform="translate(804.339972 0)scale(0.996264)" xlink:href="#CMR17-4f"/>
+ <use transform="translate(876.05476 0)scale(0.996264)" xlink:href="#CMR17-62"/>
+ <use transform="translate(926.95013 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(962.751468 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(1003.237128 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ <use transform="translate(1038.517896 0)scale(0.996264)" xlink:href="#CMR17-76"/>
+ <use transform="translate(1081.605995 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(1127.296472 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(1162.57724 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(1187.448299 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(1233.138776 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ </g>
+ </g>
+ <g id="legend_1">
+ <g id="patch_7">
+ <path d="M 101.312385 536.055671
+L 334.818587 536.055671
+Q 340.818587 536.055671 340.818587 530.055671
+L 340.818587 407.61532
+Q 340.818587 401.61532 334.818587 401.61532
+L 101.312385 401.61532
+Q 95.312385 401.61532 95.312385 407.61532
+L 95.312385 530.055671
+Q 95.312385 536.055671 101.312385 536.055671
+z
+" style="fill:#ffffff;opacity:0.8;stroke:#cccccc;stroke-linejoin:miter;"/>
+ </g>
+ <g id="line2d_48">
+ <path d="M 107.312385 424.11532
+L 167.312385 424.11532
+" style="fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:2;"/>
+ </g>
+ <g id="line2d_49">
+ <g>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="137.312385" xlink:href="#m03e5f5b84b" y="424.11532"/>
+ </g>
+ </g>
+ <g id="text_26">
+ <!-- linear -->
+ <g transform="translate(191.312385 434.61532)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 979 4416
+L 218 4345
+L 218 4179
+C 595 4179 653 4141 653 3835
+L 653 439
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 653 12 813 12
+C 979 12 1261 12 1414 0
+L 1414 166
+C 1005 166 979 191 979 439
+L 979 4416
+z
+" id="CMR17-6c" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ <g id="line2d_50">
+ <path d="M 107.312385 465.92877
+L 167.312385 465.92877
+" style="fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:2;"/>
+ </g>
+ <g id="line2d_51">
+ <g>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="137.312385" xlink:href="#me0316df6ac" y="465.92877"/>
+ </g>
+ </g>
+ <g id="text_27">
+ <!-- exponential -->
+ <g transform="translate(191.312385 476.42877)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1664 1491
+C 1856 1740 2074 2022 2253 2233
+C 2464 2476 2707 2579 2989 2585
+L 2989 2752
+C 2880 2745 2656 2739 2541 2739
+C 2368 2739 2170 2739 2022 2752
+L 2022 2585
+C 2112 2572 2163 2508 2163 2419
+C 2163 2304 2099 2233 2067 2188
+L 1594 1587
+L 1030 2323
+C 973 2393 973 2406 973 2438
+C 973 2515 1037 2579 1146 2585
+L 1146 2752
+C 992 2739 717 2739 557 2739
+C 384 2739 179 2739 38 2752
+L 38 2585
+C 384 2585 461 2560 614 2368
+L 1350 1414
+C 1363 1401 1395 1363 1395 1344
+C 1395 1318 838 633 768 544
+C 480 198 179 172 6 166
+L 6 0
+C 115 6 339 12 454 12
+C 582 12 864 12 979 0
+L 979 166
+C 941 172 838 185 838 332
+C 838 448 890 518 947 595
+L 1478 1248
+L 2035 524
+C 2086 454 2163 358 2163 313
+C 2163 224 2086 172 1984 166
+L 1984 0
+C 2138 12 2413 12 2573 12
+C 2746 12 2950 12 3091 0
+L 3091 166
+C 2771 166 2675 179 2522 377
+L 1664 1491
+z
+" id="CMR17-78" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ <g id="line2d_52">
+ <path d="M 107.312385 507.74222
+L 167.312385 507.74222
+" style="fill:none;stroke:#2ca02c;stroke-linecap:square;stroke-width:2;"/>
+ </g>
+ <g id="line2d_53">
+ <g>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="137.312385" xlink:href="#m085466da6f" y="507.74222"/>
+ </g>
+ </g>
+ <g id="text_28">
+ <!-- cosine -->
+ <g transform="translate(191.312385 518.24222)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2234 2240
+C 2112 2240 1933 2240 1933 2015
+C 1933 1836 2080 1785 2163 1785
+C 2208 1785 2394 1804 2394 2028
+C 2394 2476 1958 2816 1466 2816
+C 787 2816 211 2201 211 1379
+C 211 521 813 -64 1466 -64
+C 2259 -64 2458 676 2458 747
+C 2458 773 2451 792 2406 792
+C 2362 792 2355 786 2330 702
+C 2163 180 1798 51 1523 51
+C 1114 51 621 431 621 1385
+C 621 2358 1094 2700 1472 2700
+C 1722 2700 2093 2582 2234 2240
+z
+" id="CMR17-63" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ </g>
+ </g>
+ <defs>
+ <clipPath id="p390e746ae5">
+ <rect height="869.76" width="1339.2" x="80.312385" y="33.955495"/>
+ </clipPath>
+ </defs>
+</svg>
diff --git a/examples/model-comparison/reference/modelWeights_cosine.svg b/examples/model-comparison/reference/modelWeights_cosine.svg
new file mode 100644
index 0000000000000000000000000000000000000000..f7861afd959eece7a243f8f4b7cc2048cab7ca2f
--- /dev/null
+++ b/examples/model-comparison/reference/modelWeights_cosine.svg
@@ -0,0 +1,1652 @@
+<?xml version="1.0" encoding="utf-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<svg height="975.053386pt" version="1.1" viewBox="0 0 1426.712385 975.053386" width="1426.712385pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+ <metadata>
+ <rdf:RDF xmlns:cc="http://creativecommons.org/ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
+ <cc:Work>
+ <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
+ <dc:date>2022-06-03T16:06:04.273208</dc:date>
+ <dc:format>image/svg+xml</dc:format>
+ <dc:creator>
+ <cc:Agent>
+ <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>
+ </cc:Agent>
+ </dc:creator>
+ </cc:Work>
+ </rdf:RDF>
+ </metadata>
+ <defs>
+ <style type="text/css">*{stroke-linecap:butt;stroke-linejoin:round;}</style>
+ </defs>
+ <g id="figure_1">
+ <g id="patch_1">
+ <path d="M 0 975.053386
+L 1426.712385 975.053386
+L 1426.712385 0
+L 0 0
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="axes_1">
+ <g id="patch_2">
+ <path d="M 80.312385 903.715495
+L 1419.512385 903.715495
+L 1419.512385 33.955495
+L 80.312385 33.955495
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="matplotlib.axis_1">
+ <g id="xtick_1">
+ <g id="line2d_1">
+ <path clip-path="url(#pfd5fc2547a)" d="M 141.185112 903.715495
+L 141.185112 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_2">
+ <defs>
+ <path d="M 0 0
+L 0 3.5
+" id="m038b979e94" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="141.185112" xlink:href="#m038b979e94" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_1">
+ <!-- $\mathdefault{1}$ -->
+ <g transform="translate(134.331541 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1702 4083
+C 1702 4217 1696 4224 1606 4224
+C 1357 3927 979 3833 621 3820
+C 602 3820 570 3820 563 3808
+C 557 3795 557 3782 557 3648
+C 755 3648 1088 3686 1344 3839
+L 1344 467
+C 1344 243 1331 166 781 166
+L 589 166
+L 589 0
+C 896 6 1216 12 1523 12
+C 1830 12 2150 6 2458 0
+L 2458 166
+L 2266 166
+C 1715 166 1702 236 1702 467
+L 1702 4083
+z
+" id="CMR17-31" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_2">
+ <g id="line2d_3">
+ <path clip-path="url(#pfd5fc2547a)" d="M 228.146151 903.715495
+L 228.146151 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_4">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="228.146151" xlink:href="#m038b979e94" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_2">
+ <!-- $\mathdefault{2}$ -->
+ <g transform="translate(221.29258 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2669 990
+L 2554 990
+C 2490 537 2438 460 2413 422
+C 2381 371 1920 371 1830 371
+L 602 371
+C 832 620 1280 1073 1824 1596
+C 2214 1966 2669 2400 2669 3033
+C 2669 3788 2067 4224 1395 4224
+C 691 4224 262 3603 262 3027
+C 262 2777 448 2745 525 2745
+C 589 2745 781 2783 781 3007
+C 781 3206 614 3264 525 3264
+C 486 3264 448 3257 422 3244
+C 544 3788 915 4057 1306 4057
+C 1862 4057 2227 3616 2227 3033
+C 2227 2477 1901 1998 1536 1583
+L 262 147
+L 262 0
+L 2515 0
+L 2669 990
+z
+" id="CMR17-32" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_3">
+ <g id="line2d_5">
+ <path clip-path="url(#pfd5fc2547a)" d="M 315.10719 903.715495
+L 315.10719 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_6">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="315.10719" xlink:href="#m038b979e94" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_3">
+ <!-- $\mathdefault{3}$ -->
+ <g transform="translate(308.253619 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1414 2176
+C 1984 2176 2234 1673 2234 1094
+C 2234 322 1824 25 1453 25
+C 1114 25 563 193 390 691
+C 422 678 454 678 486 678
+C 640 678 755 780 755 947
+C 755 1132 614 1216 486 1216
+C 378 1216 211 1164 211 927
+C 211 335 787 -128 1466 -128
+C 2176 -128 2720 432 2720 1087
+C 2720 1718 2208 2176 1600 2246
+C 2086 2347 2554 2776 2554 3353
+C 2554 3856 2048 4224 1472 4224
+C 890 4224 378 3862 378 3347
+C 378 3123 544 3084 627 3084
+C 762 3084 877 3167 877 3334
+C 877 3500 762 3584 627 3584
+C 602 3584 570 3584 544 3571
+C 730 3999 1235 4076 1459 4076
+C 1683 4076 2106 3966 2106 3347
+C 2106 3167 2080 2851 1862 2574
+C 1670 2329 1453 2316 1242 2297
+C 1210 2297 1062 2284 1037 2284
+C 992 2278 966 2272 966 2227
+C 966 2182 973 2176 1101 2176
+L 1414 2176
+z
+" id="CMR17-33" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_4">
+ <g id="line2d_7">
+ <path clip-path="url(#pfd5fc2547a)" d="M 402.068229 903.715495
+L 402.068229 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_8">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="402.068229" xlink:href="#m038b979e94" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_4">
+ <!-- $\mathdefault{4}$ -->
+ <g transform="translate(395.214658 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2150 4147
+C 2150 4281 2144 4288 2029 4288
+L 128 1254
+L 128 1088
+L 1779 1088
+L 1779 460
+C 1779 230 1766 166 1318 166
+L 1197 166
+L 1197 0
+C 1402 12 1747 12 1965 12
+C 2182 12 2528 12 2733 0
+L 2733 166
+L 2611 166
+C 2163 166 2150 230 2150 460
+L 2150 1088
+L 2803 1088
+L 2803 1254
+L 2150 1254
+L 2150 4147
+z
+M 1798 3723
+L 1798 1254
+L 256 1254
+L 1798 3723
+z
+" id="CMR17-34" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_5">
+ <g id="line2d_9">
+ <path clip-path="url(#pfd5fc2547a)" d="M 489.029268 903.715495
+L 489.029268 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_10">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="489.029268" xlink:href="#m038b979e94" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_5">
+ <!-- $\mathdefault{5}$ -->
+ <g transform="translate(482.175697 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 730 3750
+C 794 3724 1056 3641 1325 3641
+C 1920 3641 2246 3961 2432 4140
+C 2432 4191 2432 4224 2394 4224
+C 2387 4224 2374 4224 2323 4198
+C 2099 4102 1837 4032 1517 4032
+C 1325 4032 1037 4055 723 4191
+C 653 4224 640 4224 634 4224
+C 602 4224 595 4217 595 4090
+L 595 2231
+C 595 2113 595 2080 659 2080
+C 691 2080 704 2093 736 2139
+C 941 2435 1222 2560 1542 2560
+C 1766 2560 2246 2415 2246 1293
+C 2246 1087 2246 716 2054 422
+C 1894 159 1645 25 1370 25
+C 947 25 518 319 403 812
+C 429 806 480 793 506 793
+C 589 793 749 838 749 1036
+C 749 1209 627 1280 506 1280
+C 358 1280 262 1190 262 1011
+C 262 454 704 -128 1382 -128
+C 2042 -128 2669 441 2669 1267
+C 2669 2054 2170 2662 1549 2662
+C 1222 2662 947 2540 730 2304
+L 730 3750
+z
+" id="CMR17-35" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_6">
+ <g id="line2d_11">
+ <path clip-path="url(#pfd5fc2547a)" d="M 575.990307 903.715495
+L 575.990307 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_12">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="575.990307" xlink:href="#m038b979e94" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_6">
+ <!-- $\mathdefault{6}$ -->
+ <g transform="translate(569.136735 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 678 2198
+C 678 3712 1395 4076 1811 4076
+C 1946 4076 2272 4049 2400 3782
+C 2298 3782 2106 3782 2106 3558
+C 2106 3385 2246 3328 2336 3328
+C 2394 3328 2566 3353 2566 3571
+C 2566 3987 2246 4224 1805 4224
+C 1043 4224 243 3411 243 2011
+C 243 257 966 -128 1478 -128
+C 2099 -128 2688 431 2688 1295
+C 2688 2101 2170 2688 1517 2688
+C 1126 2688 838 2430 678 1979
+L 678 2198
+z
+M 1478 25
+C 691 25 691 1212 691 1450
+C 691 1914 909 2585 1504 2585
+C 1613 2585 1926 2585 2138 2140
+C 2253 1889 2253 1624 2253 1302
+C 2253 954 2253 696 2118 438
+C 1978 173 1773 25 1478 25
+z
+" id="CMR17-36" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_7">
+ <g id="line2d_13">
+ <path clip-path="url(#pfd5fc2547a)" d="M 662.951346 903.715495
+L 662.951346 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_14">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="662.951346" xlink:href="#m038b979e94" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_7">
+ <!-- $\mathdefault{7}$ -->
+ <g transform="translate(656.097774 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2886 3955
+L 2886 4096
+L 1382 4096
+C 634 4096 621 4166 595 4288
+L 480 4288
+L 294 3104
+L 410 3104
+C 429 3226 474 3552 550 3673
+C 589 3724 1062 3724 1171 3724
+L 2579 3724
+L 1869 2670
+C 1395 1961 1069 1003 1069 166
+C 1069 89 1069 -128 1299 -128
+C 1530 -128 1530 89 1530 172
+L 1530 466
+C 1530 1514 1709 2204 2003 2644
+L 2886 3955
+z
+" id="CMR17-37" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-37"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_8">
+ <g id="line2d_15">
+ <path clip-path="url(#pfd5fc2547a)" d="M 749.912385 903.715495
+L 749.912385 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_16">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="749.912385" xlink:href="#m038b979e94" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_8">
+ <!-- $\mathdefault{8}$ -->
+ <g transform="translate(743.058813 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1741 2289
+C 2144 2494 2554 2803 2554 3298
+C 2554 3884 1990 4224 1472 4224
+C 890 4224 378 3800 378 3215
+C 378 3054 416 2777 666 2533
+C 730 2469 998 2276 1171 2154
+C 883 2006 211 1652 211 945
+C 211 282 838 -128 1459 -128
+C 2144 -128 2720 366 2720 1022
+C 2720 1607 2330 1877 2074 2051
+L 1741 2289
+z
+M 902 2855
+C 851 2887 595 3086 595 3388
+C 595 3781 998 4076 1459 4076
+C 1965 4076 2336 3716 2336 3298
+C 2336 2700 1670 2359 1638 2359
+C 1632 2359 1626 2359 1574 2398
+L 902 2855
+z
+M 2080 1536
+C 2176 1466 2483 1253 2483 861
+C 2483 385 2010 25 1472 25
+C 890 25 448 443 448 951
+C 448 1459 838 1884 1280 2083
+L 2080 1536
+z
+" id="CMR17-38" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-38"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_9">
+ <g id="line2d_17">
+ <path clip-path="url(#pfd5fc2547a)" d="M 836.873424 903.715495
+L 836.873424 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_18">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="836.873424" xlink:href="#m038b979e94" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_9">
+ <!-- $\mathdefault{9}$ -->
+ <g transform="translate(830.019852 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2253 1871
+C 2253 448 1670 25 1190 25
+C 1043 25 685 43 538 281
+C 704 256 826 345 826 505
+C 826 678 685 736 595 736
+C 538 736 365 710 365 492
+C 365 68 742 -128 1203 -128
+C 1939 -128 2688 665 2688 2090
+C 2688 3857 1971 4224 1485 4224
+C 851 4224 243 3664 243 2800
+C 243 2000 762 1408 1414 1408
+C 1952 1408 2189 1910 2253 2122
+L 2253 1871
+z
+M 1427 1510
+C 1254 1510 1011 1542 813 1929
+C 678 2181 678 2477 678 2793
+C 678 3174 678 3438 858 3722
+C 947 3857 1114 4076 1485 4076
+C 2240 4076 2240 2909 2240 2651
+C 2240 2193 2035 1510 1427 1510
+z
+" id="CMR17-39" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-39"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_10">
+ <g id="line2d_19">
+ <path clip-path="url(#pfd5fc2547a)" d="M 923.834463 903.715495
+L 923.834463 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_20">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="923.834463" xlink:href="#m038b979e94" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_10">
+ <!-- $\mathdefault{10}$ -->
+ <g transform="translate(910.12732 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2688 2038
+C 2688 2430 2682 3099 2413 3613
+C 2176 4063 1798 4224 1466 4224
+C 1158 4224 768 4082 525 3620
+C 269 3137 243 2539 243 2038
+C 243 1671 250 1112 448 623
+C 723 -39 1216 -128 1466 -128
+C 1760 -128 2208 -7 2470 604
+C 2662 1048 2688 1568 2688 2038
+z
+M 1466 -26
+C 1056 -26 813 328 723 816
+C 653 1196 653 1749 653 2109
+C 653 2604 653 3015 736 3407
+C 858 3954 1216 4121 1466 4121
+C 1728 4121 2067 3947 2189 3420
+C 2272 3054 2278 2623 2278 2109
+C 2278 1691 2278 1176 2202 797
+C 2067 96 1690 -26 1466 -26
+z
+" id="CMR17-30" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_11">
+ <g id="line2d_21">
+ <path clip-path="url(#pfd5fc2547a)" d="M 1010.795502 903.715495
+L 1010.795502 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_22">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1010.795502" xlink:href="#m038b979e94" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_11">
+ <!-- $\mathdefault{11}$ -->
+ <g transform="translate(997.088359 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_12">
+ <g id="line2d_23">
+ <path clip-path="url(#pfd5fc2547a)" d="M 1097.756541 903.715495
+L 1097.756541 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_24">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1097.756541" xlink:href="#m038b979e94" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_12">
+ <!-- $\mathdefault{12}$ -->
+ <g transform="translate(1084.049398 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_13">
+ <g id="line2d_25">
+ <path clip-path="url(#pfd5fc2547a)" d="M 1184.71758 903.715495
+L 1184.71758 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_26">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1184.71758" xlink:href="#m038b979e94" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_13">
+ <!-- $\mathdefault{13}$ -->
+ <g transform="translate(1171.010437 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_14">
+ <g id="line2d_27">
+ <path clip-path="url(#pfd5fc2547a)" d="M 1271.678619 903.715495
+L 1271.678619 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_28">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1271.678619" xlink:href="#m038b979e94" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_14">
+ <!-- $\mathdefault{14}$ -->
+ <g transform="translate(1257.971476 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_15">
+ <g id="line2d_29">
+ <path clip-path="url(#pfd5fc2547a)" d="M 1358.639658 903.715495
+L 1358.639658 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_30">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1358.639658" xlink:href="#m038b979e94" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_15">
+ <!-- $\mathdefault{15}$ -->
+ <g transform="translate(1344.932515 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_16">
+ <!-- No. of measurement points -->
+ <g transform="translate(587.401303 962.039936)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1312 4275
+C 1267 4345 1261 4352 1139 4352
+L 326 4352
+L 326 4185
+L 448 4185
+C 704 4185 819 4153 838 4147
+L 838 624
+C 838 465 838 166 326 166
+L 326 0
+C 474 12 742 12 902 12
+C 1062 12 1331 12 1478 0
+L 1478 166
+C 966 166 966 465 966 624
+L 966 4057
+C 1011 4019 1011 4007 1056 3943
+L 3430 76
+C 3475 0 3494 0 3526 0
+C 3590 0 3590 19 3590 140
+L 3590 3726
+C 3590 3885 3590 4185 4102 4185
+L 4102 4352
+C 3955 4339 3686 4339 3526 4339
+C 3366 4339 3098 4339 2950 4352
+L 2950 4185
+C 3462 4185 3462 3885 3462 3726
+L 3462 777
+L 1312 4275
+z
+" id="CMR17-4e" transform="scale(0.015625)"/>
+ <path d="M 2758 1356
+C 2758 2176 2163 2816 1466 2816
+C 768 2816 173 2176 173 1356
+C 173 550 768 -64 1466 -64
+C 2163 -64 2758 550 2758 1356
+z
+M 1466 51
+C 1165 51 909 230 762 480
+C 602 768 582 1126 582 1408
+C 582 1676 595 2009 762 2297
+C 890 2508 1139 2713 1466 2713
+C 1754 2713 1997 2553 2150 2329
+C 2349 2028 2349 1606 2349 1408
+C 2349 1158 2336 774 2163 467
+C 1984 172 1709 51 1466 51
+z
+" id="CMR17-6f" transform="scale(0.015625)"/>
+ <path d="M 1062 262
+C 1062 422 934 524 800 524
+C 672 524 538 422 538 262
+C 538 102 666 0 800 0
+C 928 0 1062 102 1062 262
+z
+" id="CMR17-2e" transform="scale(0.015625)"/>
+ <path d="M 979 2585
+L 1709 2585
+L 1709 2752
+L 966 2752
+L 966 3539
+C 966 4076 1235 4377 1510 4377
+C 1594 4377 1690 4363 1754 4339
+C 1702 4326 1568 4281 1568 4121
+C 1568 3955 1696 3904 1786 3904
+C 1875 3904 2003 3955 2003 4121
+C 2003 4353 1773 4480 1517 4480
+C 1152 4480 653 4211 653 3526
+L 653 2752
+L 141 2752
+L 141 2585
+L 653 2585
+L 653 441
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 666 12 832 12
+C 1018 12 1344 12 1517 0
+L 1517 166
+C 1056 166 979 166 979 454
+L 979 2585
+z
+" id="CMR17-66" transform="scale(0.015625)"/>
+ <path d="M 4326 1954
+C 4326 2276 4269 2816 3507 2816
+C 3072 2816 2771 2520 2656 2173
+L 2650 2173
+C 2573 2700 2195 2816 1837 2816
+C 1331 2816 1069 2424 973 2166
+L 966 2166
+L 966 2816
+L 211 2745
+L 211 2578
+C 589 2578 646 2540 646 2231
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1678
+C 2656 2269 3014 2713 3462 2713
+C 3936 2713 3987 2289 3987 1980
+L 3987 443
+C 3987 198 3962 166 3552 166
+L 3552 0
+C 3706 12 3987 12 4154 12
+C 4320 12 4608 12 4762 0
+L 4762 166
+C 4352 166 4326 192 4326 443
+L 4326 1954
+z
+" id="CMR17-6d" transform="scale(0.015625)"/>
+ <path d="M 2438 1503
+C 2464 1529 2464 1542 2464 1606
+C 2464 2251 2118 2816 1389 2816
+C 710 2816 173 2175 173 1394
+C 173 554 781 -64 1459 -64
+C 2176 -64 2458 619 2458 755
+C 2458 800 2419 800 2406 800
+C 2362 800 2355 787 2330 709
+C 2189 270 1837 51 1504 51
+C 1229 51 954 206 781 490
+C 582 819 582 1200 582 1503
+L 2438 1503
+z
+M 589 1600
+C 634 2511 1126 2713 1382 2713
+C 1818 2713 2112 2308 2118 1600
+L 589 1600
+z
+" id="CMR17-65" transform="scale(0.015625)"/>
+ <path d="M 2304 1656
+C 2304 2048 2304 2275 2035 2534
+C 1798 2751 1523 2816 1306 2816
+C 800 2816 435 2408 435 1977
+C 435 1740 627 1728 666 1728
+C 749 1728 896 1779 896 1958
+C 896 2118 774 2188 666 2188
+C 640 2188 608 2182 589 2176
+C 723 2594 1069 2713 1293 2713
+C 1613 2713 1965 2421 1965 1875
+L 1965 1632
+C 1587 1619 1133 1568 774 1373
+C 371 1147 256 822 256 576
+C 256 77 832 -64 1171 -64
+C 1523 -64 1850 135 1990 505
+C 2003 219 2182 -39 2464 -39
+C 2598 -39 2938 51 2938 563
+L 2938 926
+L 2822 926
+L 2822 557
+C 2822 161 2650 109 2566 109
+C 2304 109 2304 446 2304 732
+L 2304 1656
+z
+M 1965 887
+C 1965 323 1568 38 1216 38
+C 896 38 646 278 646 576
+C 646 771 730 1114 1101 1322
+C 1408 1497 1760 1523 1965 1536
+L 1965 887
+z
+" id="CMR17-61" transform="scale(0.015625)"/>
+ <path d="M 1978 2688
+C 1978 2803 1971 2809 1933 2809
+C 1907 2809 1901 2803 1824 2707
+C 1805 2681 1747 2617 1728 2592
+C 1523 2809 1235 2816 1126 2816
+C 416 2816 160 2444 160 2073
+C 160 1497 813 1363 998 1324
+C 1402 1241 1542 1216 1677 1100
+C 1760 1024 1901 883 1901 652
+C 1901 384 1747 38 1158 38
+C 602 38 403 460 288 1024
+C 269 1113 269 1120 218 1120
+C 166 1120 160 1113 160 985
+L 160 64
+C 160 -52 166 -58 205 -58
+C 237 -58 243 -52 275 0
+C 314 57 410 211 448 275
+C 576 102 800 -64 1158 -64
+C 1792 -64 2131 281 2131 780
+C 2131 1107 1958 1280 1875 1356
+C 1683 1555 1459 1600 1190 1651
+C 838 1728 390 1817 390 2208
+C 390 2374 480 2726 1126 2726
+C 1811 2726 1850 2086 1862 1881
+C 1869 1849 1901 1843 1920 1843
+C 1978 1843 1978 1862 1978 1971
+L 1978 2688
+z
+" id="CMR17-73" transform="scale(0.015625)"/>
+ <path d="M 1882 2745
+L 1882 2579
+C 2259 2579 2317 2540 2317 2229
+L 2317 1053
+C 2317 510 2029 38 1555 38
+C 1030 38 986 355 986 691
+L 986 2816
+L 211 2745
+L 211 2579
+C 467 2579 640 2579 646 2320
+L 646 1079
+C 646 646 646 368 813 187
+C 896 103 1056 -64 1517 -64
+C 2061 -64 2272 400 2323 536
+L 2330 536
+L 2330 -64
+L 3091 -13
+L 3091 154
+C 2714 154 2656 193 2656 503
+L 2656 2816
+L 1882 2745
+z
+" id="CMR17-75" transform="scale(0.015625)"/>
+ <path d="M 960 1517
+C 960 2134 1222 2713 1702 2713
+C 1747 2713 1792 2707 1837 2687
+C 1837 2687 1696 2642 1696 2475
+C 1696 2321 1818 2257 1914 2257
+C 1990 2257 2131 2302 2131 2482
+C 2131 2687 1926 2816 1709 2816
+C 1222 2816 1011 2340 947 2115
+L 941 2115
+L 941 2816
+L 198 2745
+L 198 2578
+C 576 2578 634 2540 634 2231
+L 634 443
+C 634 198 608 166 198 166
+L 198 0
+C 352 12 646 12 813 12
+C 998 12 1325 12 1498 0
+L 1498 166
+C 1037 166 960 166 960 455
+L 960 1517
+z
+" id="CMR17-72" transform="scale(0.015625)"/>
+ <path d="M 2656 1954
+C 2656 2282 2592 2816 1837 2816
+C 1331 2816 1069 2424 973 2166
+L 966 2166
+L 966 2816
+L 211 2745
+L 211 2578
+C 589 2578 646 2540 646 2231
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1954
+z
+" id="CMR17-6e" transform="scale(0.015625)"/>
+ <path d="M 966 2585
+L 1862 2585
+L 1862 2752
+L 966 2752
+L 966 3968
+L 851 3968
+C 838 3292 614 2700 70 2687
+L 70 2585
+L 627 2585
+L 627 778
+C 627 655 627 -64 1370 -64
+C 1747 -64 1965 308 1965 784
+L 1965 1151
+L 1850 1151
+L 1850 790
+C 1850 347 1677 51 1408 51
+C 1222 51 966 179 966 765
+L 966 2585
+z
+" id="CMR17-74" transform="scale(0.015625)"/>
+ <path d="M 1408 -1114
+C 998 -1114 973 -1088 973 -834
+L 973 380
+C 1158 109 1427 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2196 2496 2816 1837 2816
+C 1453 2816 1139 2603 960 2345
+L 960 2816
+L 198 2745
+L 198 2577
+C 576 2577 634 2539 634 2228
+L 634 -834
+C 634 -1081 608 -1114 198 -1114
+L 198 -1280
+C 352 -1268 634 -1268 800 -1268
+C 966 -1268 1254 -1268 1408 -1280
+L 1408 -1114
+z
+M 973 2015
+C 973 2106 973 2241 1222 2481
+C 1254 2506 1472 2700 1792 2700
+C 2259 2700 2643 2112 2643 1376
+C 2643 639 2234 38 1728 38
+C 1498 38 1248 148 1056 451
+C 973 594 973 632 973 736
+L 973 2015
+z
+" id="CMR17-70" transform="scale(0.015625)"/>
+ <path d="M 992 3961
+C 992 4102 877 4224 730 4224
+C 589 4224 467 4108 467 3961
+C 467 3820 582 3699 730 3699
+C 870 3699 992 3814 992 3961
+z
+M 243 2745
+L 243 2579
+C 602 2579 653 2540 653 2231
+L 653 443
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 646 12 806 12
+C 960 12 1222 12 1370 0
+L 1370 166
+C 992 166 979 205 979 436
+L 979 2816
+L 243 2745
+z
+" id="CMR17-69" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-4e"/>
+ <use transform="translate(69.07243 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(114.762907 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(180.119626 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(225.810103 0)scale(0.996264)" xlink:href="#CMR17-66"/>
+ <use transform="translate(283.359582 0)scale(0.996264)" xlink:href="#CMR17-6d"/>
+ <use transform="translate(360.279172 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(400.764832 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(446.455309 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(482.256647 0)scale(0.996264)" xlink:href="#CMR17-75"/>
+ <use transform="translate(533.152017 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ <use transform="translate(568.432784 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(608.918445 0)scale(0.996264)" xlink:href="#CMR17-6d"/>
+ <use transform="translate(685.838035 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(726.323695 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(774.616611 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(839.973345 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(893.471154 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(939.161631 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(964.032689 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(1012.325605 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(1047.606373 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ </g>
+ </g>
+ </g>
+ <g id="matplotlib.axis_2">
+ <g id="ytick_1">
+ <g id="line2d_31">
+ <path clip-path="url(#pfd5fc2547a)" d="M 80.312385 864.18095
+L 1419.512385 864.18095
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_32">
+ <defs>
+ <path d="M 0 0
+L -3.5 0
+" id="m05702e7797" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#m05702e7797" y="864.18095"/>
+ </g>
+ </g>
+ <g id="text_17">
+ <!-- $\mathdefault{0.0}$ -->
+ <g transform="translate(37.768946 874.558697)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1178 307
+C 1178 492 1024 620 870 620
+C 685 620 557 467 557 313
+C 557 128 710 0 864 0
+C 1050 0 1178 153 1178 307
+z
+" id="CMMI12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_2">
+ <g id="line2d_33">
+ <path clip-path="url(#pfd5fc2547a)" d="M 80.312385 678.361857
+L 1419.512385 678.361857
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_34">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#m05702e7797" y="678.361857"/>
+ </g>
+ </g>
+ <g id="text_18">
+ <!-- $\mathdefault{0.2}$ -->
+ <g transform="translate(37.768946 688.739605)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_3">
+ <g id="line2d_35">
+ <path clip-path="url(#pfd5fc2547a)" d="M 80.312385 492.542765
+L 1419.512385 492.542765
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_36">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#m05702e7797" y="492.542765"/>
+ </g>
+ </g>
+ <g id="text_19">
+ <!-- $\mathdefault{0.4}$ -->
+ <g transform="translate(37.768946 502.920512)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_4">
+ <g id="line2d_37">
+ <path clip-path="url(#pfd5fc2547a)" d="M 80.312385 306.723672
+L 1419.512385 306.723672
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_38">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#m05702e7797" y="306.723672"/>
+ </g>
+ </g>
+ <g id="text_20">
+ <!-- $\mathdefault{0.6}$ -->
+ <g transform="translate(37.768946 317.10142)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_5">
+ <g id="line2d_39">
+ <path clip-path="url(#pfd5fc2547a)" d="M 80.312385 120.904579
+L 1419.512385 120.904579
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_40">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#m05702e7797" y="120.904579"/>
+ </g>
+ </g>
+ <g id="text_21">
+ <!-- $\mathdefault{0.8}$ -->
+ <g transform="translate(37.768946 131.282327)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-38"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_22">
+ <!-- Weights -->
+ <g transform="translate(27.955495 516.492209)rotate(-90)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 5523 3775
+C 5581 3948 5677 4173 6048 4185
+L 6048 4352
+C 5939 4345 5715 4339 5600 4339
+C 5440 4339 5158 4339 5005 4352
+L 5005 4185
+C 5293 4179 5414 4019 5414 3865
+C 5414 3820 5408 3794 5382 3724
+L 4390 557
+L 3347 3890
+C 3328 3955 3322 3980 3322 4006
+C 3322 4185 3603 4185 3725 4185
+L 3725 4352
+C 3539 4339 3219 4339 3021 4339
+C 2861 4339 2573 4339 2426 4352
+L 2426 4185
+C 2720 4185 2797 4166 2861 4051
+C 2886 3993 2989 3660 2989 3640
+C 2989 3615 2976 3576 2970 3557
+L 2029 564
+L 986 3890
+C 954 3980 954 3993 954 4006
+C 954 4185 1235 4185 1363 4185
+L 1363 4352
+C 1178 4339 858 4339 659 4339
+C 493 4339 211 4339 58 4352
+L 58 4185
+C 442 4185 467 4147 531 3942
+L 1779 -20
+C 1811 -116 1811 -128 1869 -128
+C 1920 -128 1939 -116 1965 -26
+L 3053 3448
+L 4141 -26
+C 4166 -116 4186 -128 4237 -128
+C 4294 -128 4294 -116 4326 -20
+L 5523 3775
+z
+" id="CMR17-57" transform="scale(0.015625)"/>
+ <path d="M 710 1165
+C 832 1068 1043 960 1299 960
+C 1805 960 2240 1359 2240 1895
+C 2240 2063 2189 2321 1997 2521
+C 2176 2713 2438 2777 2586 2777
+C 2611 2777 2650 2777 2682 2758
+C 2656 2751 2598 2726 2598 2623
+C 2598 2540 2656 2483 2739 2483
+C 2835 2483 2886 2547 2886 2630
+C 2886 2751 2790 2880 2586 2880
+C 2330 2880 2106 2758 1926 2591
+C 1734 2764 1504 2828 1299 2828
+C 794 2828 358 2431 358 1895
+C 358 1527 570 1294 634 1230
+C 442 1004 442 742 442 710
+C 442 544 506 300 723 166
+C 390 82 128 -184 128 -517
+C 128 -996 736 -1344 1466 -1344
+C 2170 -1344 2803 -1009 2803 -510
+C 2803 384 1856 384 1363 384
+C 1216 384 954 384 922 390
+C 723 422 589 601 589 825
+C 589 883 589 1024 710 1165
+z
+M 1299 1068
+C 736 1068 736 1766 736 1895
+C 736 2024 736 2719 1299 2719
+C 1862 2719 1862 2024 1862 1895
+C 1862 1766 1862 1068 1299 1068
+z
+M 1466 -1236
+C 826 -1236 384 -883 384 -517
+C 384 -311 493 -118 634 -11
+C 794 102 858 102 1293 102
+C 1818 102 2547 102 2547 -517
+C 2547 -883 2106 -1236 1466 -1236
+z
+" id="CMR17-67" transform="scale(0.015625)"/>
+ <path d="M 2656 1954
+C 2656 2282 2592 2816 1837 2816
+C 1312 2816 1056 2392 979 2179
+L 973 2179
+L 973 4416
+L 211 4345
+L 211 4179
+C 589 4179 646 4141 646 3843
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1954
+z
+" id="CMR17-68" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-57"/>
+ <use transform="translate(87.289395 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(127.775055 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(152.646113 0)scale(0.996264)" xlink:href="#CMR17-67"/>
+ <use transform="translate(198.336591 0)scale(0.996264)" xlink:href="#CMR17-68"/>
+ <use transform="translate(246.629506 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(281.910274 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ </g>
+ </g>
+ </g>
+ <g id="line2d_41">
+ <path clip-path="url(#pfd5fc2547a)" d="M 141.185112 863.891996
+L 228.146151 864.06292
+L 315.10719 864.158733
+L 402.068229 864.1793
+L 489.029268 864.180887
+L 575.990307 864.180948
+L 662.951346 864.180949
+L 749.912385 864.18095
+L 836.873424 864.18095
+L 923.834463 864.18095
+L 1010.795502 864.18095
+L 1097.756541 864.18095
+L 1184.71758 864.18095
+L 1271.678619 864.180918
+L 1358.639658 685.620096
+" style="fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:2;"/>
+ <defs>
+ <path d="M 0 5
+C 1.326016 5 2.597899 4.473168 3.535534 3.535534
+C 4.473168 2.597899 5 1.326016 5 0
+C 5 -1.326016 4.473168 -2.597899 3.535534 -3.535534
+C 2.597899 -4.473168 1.326016 -5 0 -5
+C -1.326016 -5 -2.597899 -4.473168 -3.535534 -3.535534
+C -4.473168 -2.597899 -5 -1.326016 -5 0
+C -5 1.326016 -4.473168 2.597899 -3.535534 3.535534
+C -2.597899 4.473168 -1.326016 5 0 5
+z
+" id="mc4192d3d36" style="stroke:#1f77b4;"/>
+ </defs>
+ <g clip-path="url(#pfd5fc2547a)">
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="141.185112" xlink:href="#mc4192d3d36" y="863.891996"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="228.146151" xlink:href="#mc4192d3d36" y="864.06292"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="315.10719" xlink:href="#mc4192d3d36" y="864.158733"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="402.068229" xlink:href="#mc4192d3d36" y="864.1793"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="489.029268" xlink:href="#mc4192d3d36" y="864.180887"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="575.990307" xlink:href="#mc4192d3d36" y="864.180948"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="662.951346" xlink:href="#mc4192d3d36" y="864.180949"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="749.912385" xlink:href="#mc4192d3d36" y="864.18095"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="836.873424" xlink:href="#mc4192d3d36" y="864.18095"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="923.834463" xlink:href="#mc4192d3d36" y="864.18095"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1010.795502" xlink:href="#mc4192d3d36" y="864.18095"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1097.756541" xlink:href="#mc4192d3d36" y="864.18095"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1184.71758" xlink:href="#mc4192d3d36" y="864.18095"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1271.678619" xlink:href="#mc4192d3d36" y="864.180918"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1358.639658" xlink:href="#mc4192d3d36" y="685.620096"/>
+ </g>
+ </g>
+ <g id="line2d_42">
+ <path clip-path="url(#pfd5fc2547a)" d="M 141.185112 398.061396
+L 228.146151 398.483388
+L 315.10719 409.52644
+L 402.068229 407.615036
+L 489.029268 376.273038
+L 575.990307 376.657206
+L 662.951346 392.619425
+L 749.912385 725.776396
+L 836.873424 575.760023
+L 923.834463 462.354831
+L 1010.795502 468.704043
+L 1097.756541 482.829016
+L 1184.71758 396.27868
+L 1271.678619 409.554051
+L 1358.639658 489.311417
+" style="fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:2;"/>
+ <defs>
+ <path d="M 0 5
+C 1.326016 5 2.597899 4.473168 3.535534 3.535534
+C 4.473168 2.597899 5 1.326016 5 0
+C 5 -1.326016 4.473168 -2.597899 3.535534 -3.535534
+C 2.597899 -4.473168 1.326016 -5 0 -5
+C -1.326016 -5 -2.597899 -4.473168 -3.535534 -3.535534
+C -4.473168 -2.597899 -5 -1.326016 -5 0
+C -5 1.326016 -4.473168 2.597899 -3.535534 3.535534
+C -2.597899 4.473168 -1.326016 5 0 5
+z
+" id="m379ff5238b" style="stroke:#ff7f0e;"/>
+ </defs>
+ <g clip-path="url(#pfd5fc2547a)">
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="141.185112" xlink:href="#m379ff5238b" y="398.061396"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="228.146151" xlink:href="#m379ff5238b" y="398.483388"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="315.10719" xlink:href="#m379ff5238b" y="409.52644"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="402.068229" xlink:href="#m379ff5238b" y="407.615036"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="489.029268" xlink:href="#m379ff5238b" y="376.273038"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="575.990307" xlink:href="#m379ff5238b" y="376.657206"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="662.951346" xlink:href="#m379ff5238b" y="392.619425"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="749.912385" xlink:href="#m379ff5238b" y="725.776396"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="836.873424" xlink:href="#m379ff5238b" y="575.760023"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="923.834463" xlink:href="#m379ff5238b" y="462.354831"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1010.795502" xlink:href="#m379ff5238b" y="468.704043"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1097.756541" xlink:href="#m379ff5238b" y="482.829016"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1184.71758" xlink:href="#m379ff5238b" y="396.27868"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1271.678619" xlink:href="#m379ff5238b" y="409.554051"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1358.639658" xlink:href="#m379ff5238b" y="489.311417"/>
+ </g>
+ </g>
+ <g id="line2d_43">
+ <path clip-path="url(#pfd5fc2547a)" d="M 141.185112 401.493994
+L 228.146151 400.901079
+L 315.10719 389.762213
+L 402.068229 391.65305
+L 489.029268 422.993461
+L 575.990307 422.609232
+L 662.951346 406.647012
+L 749.912385 73.490041
+L 836.873424 223.506414
+L 923.834463 336.911606
+L 1010.795502 330.562394
+L 1097.756541 316.43742
+L 1184.71758 402.987757
+L 1271.678619 389.712417
+L 1358.639658 488.515873
+" style="fill:none;stroke:#2ca02c;stroke-linecap:square;stroke-width:2;"/>
+ <defs>
+ <path d="M 0 5
+C 1.326016 5 2.597899 4.473168 3.535534 3.535534
+C 4.473168 2.597899 5 1.326016 5 0
+C 5 -1.326016 4.473168 -2.597899 3.535534 -3.535534
+C 2.597899 -4.473168 1.326016 -5 0 -5
+C -1.326016 -5 -2.597899 -4.473168 -3.535534 -3.535534
+C -4.473168 -2.597899 -5 -1.326016 -5 0
+C -5 1.326016 -4.473168 2.597899 -3.535534 3.535534
+C -2.597899 4.473168 -1.326016 5 0 5
+z
+" id="mdfedee9bfe" style="stroke:#2ca02c;"/>
+ </defs>
+ <g clip-path="url(#pfd5fc2547a)">
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="141.185112" xlink:href="#mdfedee9bfe" y="401.493994"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="228.146151" xlink:href="#mdfedee9bfe" y="400.901079"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="315.10719" xlink:href="#mdfedee9bfe" y="389.762213"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="402.068229" xlink:href="#mdfedee9bfe" y="391.65305"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="489.029268" xlink:href="#mdfedee9bfe" y="422.993461"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="575.990307" xlink:href="#mdfedee9bfe" y="422.609232"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="662.951346" xlink:href="#mdfedee9bfe" y="406.647012"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="749.912385" xlink:href="#mdfedee9bfe" y="73.490041"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="836.873424" xlink:href="#mdfedee9bfe" y="223.506414"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="923.834463" xlink:href="#mdfedee9bfe" y="336.911606"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1010.795502" xlink:href="#mdfedee9bfe" y="330.562394"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1097.756541" xlink:href="#mdfedee9bfe" y="316.43742"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1184.71758" xlink:href="#mdfedee9bfe" y="402.987757"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1271.678619" xlink:href="#mdfedee9bfe" y="389.712417"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1358.639658" xlink:href="#mdfedee9bfe" y="488.515873"/>
+ </g>
+ </g>
+ <g id="patch_3">
+ <path d="M 80.312385 903.715495
+L 80.312385 33.955495
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:3;"/>
+ </g>
+ <g id="patch_4">
+ <path d="M 1419.512385 903.715495
+L 1419.512385 33.955495
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:3;"/>
+ </g>
+ <g id="patch_5">
+ <path d="M 80.312385 903.715495
+L 1419.512385 903.715495
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:3;"/>
+ </g>
+ <g id="patch_6">
+ <path d="M 80.312385 33.955495
+L 1419.512385 33.955495
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:3;"/>
+ </g>
+ <g id="text_23">
+ <!-- Data generated by: cosine -->
+ <g transform="translate(593.527005 27.955495)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 333 4352
+L 333 4185
+C 774 4185 845 4185 845 3898
+L 845 453
+C 845 166 774 166 333 166
+L 333 0
+L 2368 0
+C 3398 0 4224 943 4224 2140
+C 4224 3344 3411 4352 2368 4352
+L 333 4352
+z
+M 1523 166
+C 1267 166 1254 198 1254 414
+L 1254 3936
+C 1254 4153 1267 4185 1523 4185
+L 2240 4185
+C 2771 4185 3750 3873 3750 2140
+C 3750 1242 3488 879 3366 707
+C 3213 510 2848 166 2240 166
+L 1523 166
+z
+" id="CMR17-44" transform="scale(0.015625)"/>
+ <path d="M 1869 4345
+L 1869 4179
+C 2246 4179 2304 4141 2304 3843
+L 2304 2371
+C 2278 2403 2016 2816 1498 2816
+C 845 2816 211 2228 211 1376
+C 211 529 806 -64 1434 -64
+C 1978 -64 2259 361 2291 406
+L 2291 -64
+L 3066 -13
+L 3066 154
+C 2688 154 2630 193 2630 503
+L 2630 4416
+L 1869 4345
+z
+M 2291 762
+C 2291 568 2176 393 2029 264
+C 1811 70 1594 38 1472 38
+C 1286 38 621 135 621 1369
+C 621 2636 1363 2713 1530 2713
+C 1824 2713 2061 2545 2208 2313
+C 2291 2177 2291 2157 2291 2041
+L 2291 762
+z
+" id="CMR17-64" transform="scale(0.015625)"/>
+ <path d="M 960 4416
+L 198 4345
+L 198 4179
+C 576 4179 634 4141 634 3843
+L 634 -13
+L 749 -13
+L 934 445
+C 1120 141 1395 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2209 2477 2816 1830 2816
+C 1434 2816 1152 2603 960 2351
+L 960 4416
+z
+M 973 2022
+C 973 2138 973 2157 1062 2293
+C 1312 2681 1670 2713 1792 2713
+C 1984 2713 2643 2610 2643 1388
+C 2643 109 1888 38 1734 38
+C 1536 38 1248 115 1043 490
+C 973 613 973 626 973 742
+L 973 2022
+z
+" id="CMR17-62" transform="scale(0.015625)"/>
+ <path d="M 2496 2183
+C 2656 2579 2944 2585 3034 2585
+L 3034 2752
+C 2912 2745 2752 2739 2630 2739
+C 2496 2739 2285 2739 2157 2752
+L 2157 2585
+C 2400 2566 2406 2384 2406 2332
+C 2406 2268 2394 2235 2362 2158
+L 1664 409
+L 902 2300
+C 870 2378 870 2423 870 2430
+C 870 2572 1018 2585 1171 2585
+L 1171 2752
+C 1018 2739 742 2739 582 2739
+C 410 2739 205 2739 64 2752
+L 64 2585
+C 410 2585 448 2553 531 2345
+L 1485 -31
+C 1197 -795 1030 -1242 627 -1242
+C 557 -1242 397 -1223 282 -1106
+C 429 -1093 493 -1002 493 -892
+C 493 -782 416 -685 288 -685
+C 147 -685 77 -782 77 -899
+C 77 -1158 339 -1344 627 -1344
+C 998 -1344 1229 -983 1357 -659
+L 2496 2183
+z
+" id="CMR17-79" transform="scale(0.015625)"/>
+ <path d="M 1062 2489
+C 1062 2649 934 2752 800 2752
+C 672 2752 538 2649 538 2489
+C 538 2329 666 2227 800 2227
+C 928 2227 1062 2329 1062 2489
+z
+M 1062 262
+C 1062 422 934 524 800 524
+C 672 524 538 422 538 262
+C 538 102 666 0 800 0
+C 928 0 1062 102 1062 262
+z
+" id="CMR17-3a" transform="scale(0.015625)"/>
+ <path d="M 2234 2240
+C 2112 2240 1933 2240 1933 2015
+C 1933 1836 2080 1785 2163 1785
+C 2208 1785 2394 1804 2394 2028
+C 2394 2476 1958 2816 1466 2816
+C 787 2816 211 2201 211 1379
+C 211 521 813 -64 1466 -64
+C 2259 -64 2458 676 2458 747
+C 2458 773 2451 792 2406 792
+C 2362 792 2355 786 2330 702
+C 2163 180 1798 51 1523 51
+C 1114 51 621 431 621 1385
+C 621 2358 1094 2700 1472 2700
+C 1722 2700 2093 2582 2234 2240
+z
+" id="CMR17-63" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-44"/>
+ <use transform="translate(70.393556 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(116.084033 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(151.364801 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(227.131244 0)scale(0.996264)" xlink:href="#CMR17-67"/>
+ <use transform="translate(272.821721 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(313.307382 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(364.202752 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(404.688412 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ <use transform="translate(439.96918 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(485.659657 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(520.940425 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(561.426085 0)scale(0.996264)" xlink:href="#CMR17-64"/>
+ <use transform="translate(642.397421 0)scale(0.996264)" xlink:href="#CMR17-62"/>
+ <use transform="translate(690.690337 0)scale(0.996264)" xlink:href="#CMR17-79"/>
+ <use transform="translate(738.983253 0)scale(0.996264)" xlink:href="#CMR17-3a"/>
+ <use transform="translate(804.339972 0)scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(844.825633 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(890.51611 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(926.317447 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(951.188506 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(1002.083876 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ <g id="legend_1">
+ <g id="patch_7">
+ <path d="M 1165.006183 183.395846
+L 1398.512385 183.395846
+Q 1404.512385 183.395846 1404.512385 177.395846
+L 1404.512385 54.955495
+Q 1404.512385 48.955495 1398.512385 48.955495
+L 1165.006183 48.955495
+Q 1159.006183 48.955495 1159.006183 54.955495
+L 1159.006183 177.395846
+Q 1159.006183 183.395846 1165.006183 183.395846
+z
+" style="fill:#ffffff;opacity:0.8;stroke:#cccccc;stroke-linejoin:miter;"/>
+ </g>
+ <g id="line2d_44">
+ <path d="M 1171.006183 71.455495
+L 1231.006183 71.455495
+" style="fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:2;"/>
+ </g>
+ <g id="line2d_45">
+ <g>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1201.006183" xlink:href="#mc4192d3d36" y="71.455495"/>
+ </g>
+ </g>
+ <g id="text_24">
+ <!-- linear -->
+ <g transform="translate(1255.006183 81.955495)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 979 4416
+L 218 4345
+L 218 4179
+C 595 4179 653 4141 653 3835
+L 653 439
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 653 12 813 12
+C 979 12 1261 12 1414 0
+L 1414 166
+C 1005 166 979 191 979 439
+L 979 4416
+z
+" id="CMR17-6c" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ <g id="line2d_46">
+ <path d="M 1171.006183 113.268946
+L 1231.006183 113.268946
+" style="fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:2;"/>
+ </g>
+ <g id="line2d_47">
+ <g>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1201.006183" xlink:href="#m379ff5238b" y="113.268946"/>
+ </g>
+ </g>
+ <g id="text_25">
+ <!-- exponential -->
+ <g transform="translate(1255.006183 123.768946)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1664 1491
+C 1856 1740 2074 2022 2253 2233
+C 2464 2476 2707 2579 2989 2585
+L 2989 2752
+C 2880 2745 2656 2739 2541 2739
+C 2368 2739 2170 2739 2022 2752
+L 2022 2585
+C 2112 2572 2163 2508 2163 2419
+C 2163 2304 2099 2233 2067 2188
+L 1594 1587
+L 1030 2323
+C 973 2393 973 2406 973 2438
+C 973 2515 1037 2579 1146 2585
+L 1146 2752
+C 992 2739 717 2739 557 2739
+C 384 2739 179 2739 38 2752
+L 38 2585
+C 384 2585 461 2560 614 2368
+L 1350 1414
+C 1363 1401 1395 1363 1395 1344
+C 1395 1318 838 633 768 544
+C 480 198 179 172 6 166
+L 6 0
+C 115 6 339 12 454 12
+C 582 12 864 12 979 0
+L 979 166
+C 941 172 838 185 838 332
+C 838 448 890 518 947 595
+L 1478 1248
+L 2035 524
+C 2086 454 2163 358 2163 313
+C 2163 224 2086 172 1984 166
+L 1984 0
+C 2138 12 2413 12 2573 12
+C 2746 12 2950 12 3091 0
+L 3091 166
+C 2771 166 2675 179 2522 377
+L 1664 1491
+z
+" id="CMR17-78" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ <g id="line2d_48">
+ <path d="M 1171.006183 155.082396
+L 1231.006183 155.082396
+" style="fill:none;stroke:#2ca02c;stroke-linecap:square;stroke-width:2;"/>
+ </g>
+ <g id="line2d_49">
+ <g>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1201.006183" xlink:href="#mdfedee9bfe" y="155.082396"/>
+ </g>
+ </g>
+ <g id="text_26">
+ <!-- cosine -->
+ <g transform="translate(1255.006183 165.582396)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ </g>
+ </g>
+ <defs>
+ <clipPath id="pfd5fc2547a">
+ <rect height="869.76" width="1339.2" x="80.312385" y="33.955495"/>
+ </clipPath>
+ </defs>
+</svg>
diff --git a/examples/model-comparison/reference/modelWeights_exponential.svg b/examples/model-comparison/reference/modelWeights_exponential.svg
new file mode 100644
index 0000000000000000000000000000000000000000..040d5a36c30d0ec908dd019793073a01470484a0
--- /dev/null
+++ b/examples/model-comparison/reference/modelWeights_exponential.svg
@@ -0,0 +1,1655 @@
+<?xml version="1.0" encoding="utf-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<svg height="975.053386pt" version="1.1" viewBox="0 0 1426.712385 975.053386" width="1426.712385pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+ <metadata>
+ <rdf:RDF xmlns:cc="http://creativecommons.org/ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
+ <cc:Work>
+ <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
+ <dc:date>2022-06-03T16:06:04.012780</dc:date>
+ <dc:format>image/svg+xml</dc:format>
+ <dc:creator>
+ <cc:Agent>
+ <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>
+ </cc:Agent>
+ </dc:creator>
+ </cc:Work>
+ </rdf:RDF>
+ </metadata>
+ <defs>
+ <style type="text/css">*{stroke-linecap:butt;stroke-linejoin:round;}</style>
+ </defs>
+ <g id="figure_1">
+ <g id="patch_1">
+ <path d="M 0 975.053386
+L 1426.712385 975.053386
+L 1426.712385 0
+L 0 0
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="axes_1">
+ <g id="patch_2">
+ <path d="M 80.312385 903.715495
+L 1419.512385 903.715495
+L 1419.512385 33.955495
+L 80.312385 33.955495
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="matplotlib.axis_1">
+ <g id="xtick_1">
+ <g id="line2d_1">
+ <path clip-path="url(#p94bc642b58)" d="M 141.185112 903.715495
+L 141.185112 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_2">
+ <defs>
+ <path d="M 0 0
+L 0 3.5
+" id="m8e7df65195" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="141.185112" xlink:href="#m8e7df65195" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_1">
+ <!-- $\mathdefault{1}$ -->
+ <g transform="translate(134.331541 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1702 4083
+C 1702 4217 1696 4224 1606 4224
+C 1357 3927 979 3833 621 3820
+C 602 3820 570 3820 563 3808
+C 557 3795 557 3782 557 3648
+C 755 3648 1088 3686 1344 3839
+L 1344 467
+C 1344 243 1331 166 781 166
+L 589 166
+L 589 0
+C 896 6 1216 12 1523 12
+C 1830 12 2150 6 2458 0
+L 2458 166
+L 2266 166
+C 1715 166 1702 236 1702 467
+L 1702 4083
+z
+" id="CMR17-31" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_2">
+ <g id="line2d_3">
+ <path clip-path="url(#p94bc642b58)" d="M 228.146151 903.715495
+L 228.146151 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_4">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="228.146151" xlink:href="#m8e7df65195" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_2">
+ <!-- $\mathdefault{2}$ -->
+ <g transform="translate(221.29258 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2669 990
+L 2554 990
+C 2490 537 2438 460 2413 422
+C 2381 371 1920 371 1830 371
+L 602 371
+C 832 620 1280 1073 1824 1596
+C 2214 1966 2669 2400 2669 3033
+C 2669 3788 2067 4224 1395 4224
+C 691 4224 262 3603 262 3027
+C 262 2777 448 2745 525 2745
+C 589 2745 781 2783 781 3007
+C 781 3206 614 3264 525 3264
+C 486 3264 448 3257 422 3244
+C 544 3788 915 4057 1306 4057
+C 1862 4057 2227 3616 2227 3033
+C 2227 2477 1901 1998 1536 1583
+L 262 147
+L 262 0
+L 2515 0
+L 2669 990
+z
+" id="CMR17-32" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_3">
+ <g id="line2d_5">
+ <path clip-path="url(#p94bc642b58)" d="M 315.10719 903.715495
+L 315.10719 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_6">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="315.10719" xlink:href="#m8e7df65195" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_3">
+ <!-- $\mathdefault{3}$ -->
+ <g transform="translate(308.253619 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1414 2176
+C 1984 2176 2234 1673 2234 1094
+C 2234 322 1824 25 1453 25
+C 1114 25 563 193 390 691
+C 422 678 454 678 486 678
+C 640 678 755 780 755 947
+C 755 1132 614 1216 486 1216
+C 378 1216 211 1164 211 927
+C 211 335 787 -128 1466 -128
+C 2176 -128 2720 432 2720 1087
+C 2720 1718 2208 2176 1600 2246
+C 2086 2347 2554 2776 2554 3353
+C 2554 3856 2048 4224 1472 4224
+C 890 4224 378 3862 378 3347
+C 378 3123 544 3084 627 3084
+C 762 3084 877 3167 877 3334
+C 877 3500 762 3584 627 3584
+C 602 3584 570 3584 544 3571
+C 730 3999 1235 4076 1459 4076
+C 1683 4076 2106 3966 2106 3347
+C 2106 3167 2080 2851 1862 2574
+C 1670 2329 1453 2316 1242 2297
+C 1210 2297 1062 2284 1037 2284
+C 992 2278 966 2272 966 2227
+C 966 2182 973 2176 1101 2176
+L 1414 2176
+z
+" id="CMR17-33" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_4">
+ <g id="line2d_7">
+ <path clip-path="url(#p94bc642b58)" d="M 402.068229 903.715495
+L 402.068229 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_8">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="402.068229" xlink:href="#m8e7df65195" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_4">
+ <!-- $\mathdefault{4}$ -->
+ <g transform="translate(395.214658 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2150 4147
+C 2150 4281 2144 4288 2029 4288
+L 128 1254
+L 128 1088
+L 1779 1088
+L 1779 460
+C 1779 230 1766 166 1318 166
+L 1197 166
+L 1197 0
+C 1402 12 1747 12 1965 12
+C 2182 12 2528 12 2733 0
+L 2733 166
+L 2611 166
+C 2163 166 2150 230 2150 460
+L 2150 1088
+L 2803 1088
+L 2803 1254
+L 2150 1254
+L 2150 4147
+z
+M 1798 3723
+L 1798 1254
+L 256 1254
+L 1798 3723
+z
+" id="CMR17-34" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_5">
+ <g id="line2d_9">
+ <path clip-path="url(#p94bc642b58)" d="M 489.029268 903.715495
+L 489.029268 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_10">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="489.029268" xlink:href="#m8e7df65195" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_5">
+ <!-- $\mathdefault{5}$ -->
+ <g transform="translate(482.175697 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 730 3750
+C 794 3724 1056 3641 1325 3641
+C 1920 3641 2246 3961 2432 4140
+C 2432 4191 2432 4224 2394 4224
+C 2387 4224 2374 4224 2323 4198
+C 2099 4102 1837 4032 1517 4032
+C 1325 4032 1037 4055 723 4191
+C 653 4224 640 4224 634 4224
+C 602 4224 595 4217 595 4090
+L 595 2231
+C 595 2113 595 2080 659 2080
+C 691 2080 704 2093 736 2139
+C 941 2435 1222 2560 1542 2560
+C 1766 2560 2246 2415 2246 1293
+C 2246 1087 2246 716 2054 422
+C 1894 159 1645 25 1370 25
+C 947 25 518 319 403 812
+C 429 806 480 793 506 793
+C 589 793 749 838 749 1036
+C 749 1209 627 1280 506 1280
+C 358 1280 262 1190 262 1011
+C 262 454 704 -128 1382 -128
+C 2042 -128 2669 441 2669 1267
+C 2669 2054 2170 2662 1549 2662
+C 1222 2662 947 2540 730 2304
+L 730 3750
+z
+" id="CMR17-35" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_6">
+ <g id="line2d_11">
+ <path clip-path="url(#p94bc642b58)" d="M 575.990307 903.715495
+L 575.990307 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_12">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="575.990307" xlink:href="#m8e7df65195" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_6">
+ <!-- $\mathdefault{6}$ -->
+ <g transform="translate(569.136735 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 678 2198
+C 678 3712 1395 4076 1811 4076
+C 1946 4076 2272 4049 2400 3782
+C 2298 3782 2106 3782 2106 3558
+C 2106 3385 2246 3328 2336 3328
+C 2394 3328 2566 3353 2566 3571
+C 2566 3987 2246 4224 1805 4224
+C 1043 4224 243 3411 243 2011
+C 243 257 966 -128 1478 -128
+C 2099 -128 2688 431 2688 1295
+C 2688 2101 2170 2688 1517 2688
+C 1126 2688 838 2430 678 1979
+L 678 2198
+z
+M 1478 25
+C 691 25 691 1212 691 1450
+C 691 1914 909 2585 1504 2585
+C 1613 2585 1926 2585 2138 2140
+C 2253 1889 2253 1624 2253 1302
+C 2253 954 2253 696 2118 438
+C 1978 173 1773 25 1478 25
+z
+" id="CMR17-36" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_7">
+ <g id="line2d_13">
+ <path clip-path="url(#p94bc642b58)" d="M 662.951346 903.715495
+L 662.951346 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_14">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="662.951346" xlink:href="#m8e7df65195" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_7">
+ <!-- $\mathdefault{7}$ -->
+ <g transform="translate(656.097774 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2886 3955
+L 2886 4096
+L 1382 4096
+C 634 4096 621 4166 595 4288
+L 480 4288
+L 294 3104
+L 410 3104
+C 429 3226 474 3552 550 3673
+C 589 3724 1062 3724 1171 3724
+L 2579 3724
+L 1869 2670
+C 1395 1961 1069 1003 1069 166
+C 1069 89 1069 -128 1299 -128
+C 1530 -128 1530 89 1530 172
+L 1530 466
+C 1530 1514 1709 2204 2003 2644
+L 2886 3955
+z
+" id="CMR17-37" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-37"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_8">
+ <g id="line2d_15">
+ <path clip-path="url(#p94bc642b58)" d="M 749.912385 903.715495
+L 749.912385 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_16">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="749.912385" xlink:href="#m8e7df65195" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_8">
+ <!-- $\mathdefault{8}$ -->
+ <g transform="translate(743.058813 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1741 2289
+C 2144 2494 2554 2803 2554 3298
+C 2554 3884 1990 4224 1472 4224
+C 890 4224 378 3800 378 3215
+C 378 3054 416 2777 666 2533
+C 730 2469 998 2276 1171 2154
+C 883 2006 211 1652 211 945
+C 211 282 838 -128 1459 -128
+C 2144 -128 2720 366 2720 1022
+C 2720 1607 2330 1877 2074 2051
+L 1741 2289
+z
+M 902 2855
+C 851 2887 595 3086 595 3388
+C 595 3781 998 4076 1459 4076
+C 1965 4076 2336 3716 2336 3298
+C 2336 2700 1670 2359 1638 2359
+C 1632 2359 1626 2359 1574 2398
+L 902 2855
+z
+M 2080 1536
+C 2176 1466 2483 1253 2483 861
+C 2483 385 2010 25 1472 25
+C 890 25 448 443 448 951
+C 448 1459 838 1884 1280 2083
+L 2080 1536
+z
+" id="CMR17-38" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-38"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_9">
+ <g id="line2d_17">
+ <path clip-path="url(#p94bc642b58)" d="M 836.873424 903.715495
+L 836.873424 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_18">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="836.873424" xlink:href="#m8e7df65195" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_9">
+ <!-- $\mathdefault{9}$ -->
+ <g transform="translate(830.019852 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2253 1871
+C 2253 448 1670 25 1190 25
+C 1043 25 685 43 538 281
+C 704 256 826 345 826 505
+C 826 678 685 736 595 736
+C 538 736 365 710 365 492
+C 365 68 742 -128 1203 -128
+C 1939 -128 2688 665 2688 2090
+C 2688 3857 1971 4224 1485 4224
+C 851 4224 243 3664 243 2800
+C 243 2000 762 1408 1414 1408
+C 1952 1408 2189 1910 2253 2122
+L 2253 1871
+z
+M 1427 1510
+C 1254 1510 1011 1542 813 1929
+C 678 2181 678 2477 678 2793
+C 678 3174 678 3438 858 3722
+C 947 3857 1114 4076 1485 4076
+C 2240 4076 2240 2909 2240 2651
+C 2240 2193 2035 1510 1427 1510
+z
+" id="CMR17-39" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-39"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_10">
+ <g id="line2d_19">
+ <path clip-path="url(#p94bc642b58)" d="M 923.834463 903.715495
+L 923.834463 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_20">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="923.834463" xlink:href="#m8e7df65195" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_10">
+ <!-- $\mathdefault{10}$ -->
+ <g transform="translate(910.12732 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2688 2038
+C 2688 2430 2682 3099 2413 3613
+C 2176 4063 1798 4224 1466 4224
+C 1158 4224 768 4082 525 3620
+C 269 3137 243 2539 243 2038
+C 243 1671 250 1112 448 623
+C 723 -39 1216 -128 1466 -128
+C 1760 -128 2208 -7 2470 604
+C 2662 1048 2688 1568 2688 2038
+z
+M 1466 -26
+C 1056 -26 813 328 723 816
+C 653 1196 653 1749 653 2109
+C 653 2604 653 3015 736 3407
+C 858 3954 1216 4121 1466 4121
+C 1728 4121 2067 3947 2189 3420
+C 2272 3054 2278 2623 2278 2109
+C 2278 1691 2278 1176 2202 797
+C 2067 96 1690 -26 1466 -26
+z
+" id="CMR17-30" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_11">
+ <g id="line2d_21">
+ <path clip-path="url(#p94bc642b58)" d="M 1010.795502 903.715495
+L 1010.795502 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_22">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1010.795502" xlink:href="#m8e7df65195" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_11">
+ <!-- $\mathdefault{11}$ -->
+ <g transform="translate(997.088359 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_12">
+ <g id="line2d_23">
+ <path clip-path="url(#p94bc642b58)" d="M 1097.756541 903.715495
+L 1097.756541 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_24">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1097.756541" xlink:href="#m8e7df65195" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_12">
+ <!-- $\mathdefault{12}$ -->
+ <g transform="translate(1084.049398 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_13">
+ <g id="line2d_25">
+ <path clip-path="url(#p94bc642b58)" d="M 1184.71758 903.715495
+L 1184.71758 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_26">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1184.71758" xlink:href="#m8e7df65195" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_13">
+ <!-- $\mathdefault{13}$ -->
+ <g transform="translate(1171.010437 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_14">
+ <g id="line2d_27">
+ <path clip-path="url(#p94bc642b58)" d="M 1271.678619 903.715495
+L 1271.678619 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_28">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1271.678619" xlink:href="#m8e7df65195" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_14">
+ <!-- $\mathdefault{14}$ -->
+ <g transform="translate(1257.971476 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_15">
+ <g id="line2d_29">
+ <path clip-path="url(#p94bc642b58)" d="M 1358.639658 903.715495
+L 1358.639658 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_30">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1358.639658" xlink:href="#m8e7df65195" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_15">
+ <!-- $\mathdefault{15}$ -->
+ <g transform="translate(1344.932515 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_16">
+ <!-- No. of measurement points -->
+ <g transform="translate(587.401303 962.039936)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1312 4275
+C 1267 4345 1261 4352 1139 4352
+L 326 4352
+L 326 4185
+L 448 4185
+C 704 4185 819 4153 838 4147
+L 838 624
+C 838 465 838 166 326 166
+L 326 0
+C 474 12 742 12 902 12
+C 1062 12 1331 12 1478 0
+L 1478 166
+C 966 166 966 465 966 624
+L 966 4057
+C 1011 4019 1011 4007 1056 3943
+L 3430 76
+C 3475 0 3494 0 3526 0
+C 3590 0 3590 19 3590 140
+L 3590 3726
+C 3590 3885 3590 4185 4102 4185
+L 4102 4352
+C 3955 4339 3686 4339 3526 4339
+C 3366 4339 3098 4339 2950 4352
+L 2950 4185
+C 3462 4185 3462 3885 3462 3726
+L 3462 777
+L 1312 4275
+z
+" id="CMR17-4e" transform="scale(0.015625)"/>
+ <path d="M 2758 1356
+C 2758 2176 2163 2816 1466 2816
+C 768 2816 173 2176 173 1356
+C 173 550 768 -64 1466 -64
+C 2163 -64 2758 550 2758 1356
+z
+M 1466 51
+C 1165 51 909 230 762 480
+C 602 768 582 1126 582 1408
+C 582 1676 595 2009 762 2297
+C 890 2508 1139 2713 1466 2713
+C 1754 2713 1997 2553 2150 2329
+C 2349 2028 2349 1606 2349 1408
+C 2349 1158 2336 774 2163 467
+C 1984 172 1709 51 1466 51
+z
+" id="CMR17-6f" transform="scale(0.015625)"/>
+ <path d="M 1062 262
+C 1062 422 934 524 800 524
+C 672 524 538 422 538 262
+C 538 102 666 0 800 0
+C 928 0 1062 102 1062 262
+z
+" id="CMR17-2e" transform="scale(0.015625)"/>
+ <path d="M 979 2585
+L 1709 2585
+L 1709 2752
+L 966 2752
+L 966 3539
+C 966 4076 1235 4377 1510 4377
+C 1594 4377 1690 4363 1754 4339
+C 1702 4326 1568 4281 1568 4121
+C 1568 3955 1696 3904 1786 3904
+C 1875 3904 2003 3955 2003 4121
+C 2003 4353 1773 4480 1517 4480
+C 1152 4480 653 4211 653 3526
+L 653 2752
+L 141 2752
+L 141 2585
+L 653 2585
+L 653 441
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 666 12 832 12
+C 1018 12 1344 12 1517 0
+L 1517 166
+C 1056 166 979 166 979 454
+L 979 2585
+z
+" id="CMR17-66" transform="scale(0.015625)"/>
+ <path d="M 4326 1954
+C 4326 2276 4269 2816 3507 2816
+C 3072 2816 2771 2520 2656 2173
+L 2650 2173
+C 2573 2700 2195 2816 1837 2816
+C 1331 2816 1069 2424 973 2166
+L 966 2166
+L 966 2816
+L 211 2745
+L 211 2578
+C 589 2578 646 2540 646 2231
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1678
+C 2656 2269 3014 2713 3462 2713
+C 3936 2713 3987 2289 3987 1980
+L 3987 443
+C 3987 198 3962 166 3552 166
+L 3552 0
+C 3706 12 3987 12 4154 12
+C 4320 12 4608 12 4762 0
+L 4762 166
+C 4352 166 4326 192 4326 443
+L 4326 1954
+z
+" id="CMR17-6d" transform="scale(0.015625)"/>
+ <path d="M 2438 1503
+C 2464 1529 2464 1542 2464 1606
+C 2464 2251 2118 2816 1389 2816
+C 710 2816 173 2175 173 1394
+C 173 554 781 -64 1459 -64
+C 2176 -64 2458 619 2458 755
+C 2458 800 2419 800 2406 800
+C 2362 800 2355 787 2330 709
+C 2189 270 1837 51 1504 51
+C 1229 51 954 206 781 490
+C 582 819 582 1200 582 1503
+L 2438 1503
+z
+M 589 1600
+C 634 2511 1126 2713 1382 2713
+C 1818 2713 2112 2308 2118 1600
+L 589 1600
+z
+" id="CMR17-65" transform="scale(0.015625)"/>
+ <path d="M 2304 1656
+C 2304 2048 2304 2275 2035 2534
+C 1798 2751 1523 2816 1306 2816
+C 800 2816 435 2408 435 1977
+C 435 1740 627 1728 666 1728
+C 749 1728 896 1779 896 1958
+C 896 2118 774 2188 666 2188
+C 640 2188 608 2182 589 2176
+C 723 2594 1069 2713 1293 2713
+C 1613 2713 1965 2421 1965 1875
+L 1965 1632
+C 1587 1619 1133 1568 774 1373
+C 371 1147 256 822 256 576
+C 256 77 832 -64 1171 -64
+C 1523 -64 1850 135 1990 505
+C 2003 219 2182 -39 2464 -39
+C 2598 -39 2938 51 2938 563
+L 2938 926
+L 2822 926
+L 2822 557
+C 2822 161 2650 109 2566 109
+C 2304 109 2304 446 2304 732
+L 2304 1656
+z
+M 1965 887
+C 1965 323 1568 38 1216 38
+C 896 38 646 278 646 576
+C 646 771 730 1114 1101 1322
+C 1408 1497 1760 1523 1965 1536
+L 1965 887
+z
+" id="CMR17-61" transform="scale(0.015625)"/>
+ <path d="M 1978 2688
+C 1978 2803 1971 2809 1933 2809
+C 1907 2809 1901 2803 1824 2707
+C 1805 2681 1747 2617 1728 2592
+C 1523 2809 1235 2816 1126 2816
+C 416 2816 160 2444 160 2073
+C 160 1497 813 1363 998 1324
+C 1402 1241 1542 1216 1677 1100
+C 1760 1024 1901 883 1901 652
+C 1901 384 1747 38 1158 38
+C 602 38 403 460 288 1024
+C 269 1113 269 1120 218 1120
+C 166 1120 160 1113 160 985
+L 160 64
+C 160 -52 166 -58 205 -58
+C 237 -58 243 -52 275 0
+C 314 57 410 211 448 275
+C 576 102 800 -64 1158 -64
+C 1792 -64 2131 281 2131 780
+C 2131 1107 1958 1280 1875 1356
+C 1683 1555 1459 1600 1190 1651
+C 838 1728 390 1817 390 2208
+C 390 2374 480 2726 1126 2726
+C 1811 2726 1850 2086 1862 1881
+C 1869 1849 1901 1843 1920 1843
+C 1978 1843 1978 1862 1978 1971
+L 1978 2688
+z
+" id="CMR17-73" transform="scale(0.015625)"/>
+ <path d="M 1882 2745
+L 1882 2579
+C 2259 2579 2317 2540 2317 2229
+L 2317 1053
+C 2317 510 2029 38 1555 38
+C 1030 38 986 355 986 691
+L 986 2816
+L 211 2745
+L 211 2579
+C 467 2579 640 2579 646 2320
+L 646 1079
+C 646 646 646 368 813 187
+C 896 103 1056 -64 1517 -64
+C 2061 -64 2272 400 2323 536
+L 2330 536
+L 2330 -64
+L 3091 -13
+L 3091 154
+C 2714 154 2656 193 2656 503
+L 2656 2816
+L 1882 2745
+z
+" id="CMR17-75" transform="scale(0.015625)"/>
+ <path d="M 960 1517
+C 960 2134 1222 2713 1702 2713
+C 1747 2713 1792 2707 1837 2687
+C 1837 2687 1696 2642 1696 2475
+C 1696 2321 1818 2257 1914 2257
+C 1990 2257 2131 2302 2131 2482
+C 2131 2687 1926 2816 1709 2816
+C 1222 2816 1011 2340 947 2115
+L 941 2115
+L 941 2816
+L 198 2745
+L 198 2578
+C 576 2578 634 2540 634 2231
+L 634 443
+C 634 198 608 166 198 166
+L 198 0
+C 352 12 646 12 813 12
+C 998 12 1325 12 1498 0
+L 1498 166
+C 1037 166 960 166 960 455
+L 960 1517
+z
+" id="CMR17-72" transform="scale(0.015625)"/>
+ <path d="M 2656 1954
+C 2656 2282 2592 2816 1837 2816
+C 1331 2816 1069 2424 973 2166
+L 966 2166
+L 966 2816
+L 211 2745
+L 211 2578
+C 589 2578 646 2540 646 2231
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1954
+z
+" id="CMR17-6e" transform="scale(0.015625)"/>
+ <path d="M 966 2585
+L 1862 2585
+L 1862 2752
+L 966 2752
+L 966 3968
+L 851 3968
+C 838 3292 614 2700 70 2687
+L 70 2585
+L 627 2585
+L 627 778
+C 627 655 627 -64 1370 -64
+C 1747 -64 1965 308 1965 784
+L 1965 1151
+L 1850 1151
+L 1850 790
+C 1850 347 1677 51 1408 51
+C 1222 51 966 179 966 765
+L 966 2585
+z
+" id="CMR17-74" transform="scale(0.015625)"/>
+ <path d="M 1408 -1114
+C 998 -1114 973 -1088 973 -834
+L 973 380
+C 1158 109 1427 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2196 2496 2816 1837 2816
+C 1453 2816 1139 2603 960 2345
+L 960 2816
+L 198 2745
+L 198 2577
+C 576 2577 634 2539 634 2228
+L 634 -834
+C 634 -1081 608 -1114 198 -1114
+L 198 -1280
+C 352 -1268 634 -1268 800 -1268
+C 966 -1268 1254 -1268 1408 -1280
+L 1408 -1114
+z
+M 973 2015
+C 973 2106 973 2241 1222 2481
+C 1254 2506 1472 2700 1792 2700
+C 2259 2700 2643 2112 2643 1376
+C 2643 639 2234 38 1728 38
+C 1498 38 1248 148 1056 451
+C 973 594 973 632 973 736
+L 973 2015
+z
+" id="CMR17-70" transform="scale(0.015625)"/>
+ <path d="M 992 3961
+C 992 4102 877 4224 730 4224
+C 589 4224 467 4108 467 3961
+C 467 3820 582 3699 730 3699
+C 870 3699 992 3814 992 3961
+z
+M 243 2745
+L 243 2579
+C 602 2579 653 2540 653 2231
+L 653 443
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 646 12 806 12
+C 960 12 1222 12 1370 0
+L 1370 166
+C 992 166 979 205 979 436
+L 979 2816
+L 243 2745
+z
+" id="CMR17-69" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-4e"/>
+ <use transform="translate(69.07243 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(114.762907 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(180.119626 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(225.810103 0)scale(0.996264)" xlink:href="#CMR17-66"/>
+ <use transform="translate(283.359582 0)scale(0.996264)" xlink:href="#CMR17-6d"/>
+ <use transform="translate(360.279172 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(400.764832 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(446.455309 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(482.256647 0)scale(0.996264)" xlink:href="#CMR17-75"/>
+ <use transform="translate(533.152017 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ <use transform="translate(568.432784 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(608.918445 0)scale(0.996264)" xlink:href="#CMR17-6d"/>
+ <use transform="translate(685.838035 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(726.323695 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(774.616611 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(839.973345 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(893.471154 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(939.161631 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(964.032689 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(1012.325605 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(1047.606373 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ </g>
+ </g>
+ </g>
+ <g id="matplotlib.axis_2">
+ <g id="ytick_1">
+ <g id="line2d_31">
+ <path clip-path="url(#p94bc642b58)" d="M 80.312385 864.18095
+L 1419.512385 864.18095
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_32">
+ <defs>
+ <path d="M 0 0
+L -3.5 0
+" id="m001966780f" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#m001966780f" y="864.18095"/>
+ </g>
+ </g>
+ <g id="text_17">
+ <!-- $\mathdefault{0.0}$ -->
+ <g transform="translate(37.768946 874.558697)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1178 307
+C 1178 492 1024 620 870 620
+C 685 620 557 467 557 313
+C 557 128 710 0 864 0
+C 1050 0 1178 153 1178 307
+z
+" id="CMMI12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_2">
+ <g id="line2d_33">
+ <path clip-path="url(#p94bc642b58)" d="M 80.312385 678.361857
+L 1419.512385 678.361857
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_34">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#m001966780f" y="678.361857"/>
+ </g>
+ </g>
+ <g id="text_18">
+ <!-- $\mathdefault{0.2}$ -->
+ <g transform="translate(37.768946 688.739605)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_3">
+ <g id="line2d_35">
+ <path clip-path="url(#p94bc642b58)" d="M 80.312385 492.542765
+L 1419.512385 492.542765
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_36">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#m001966780f" y="492.542765"/>
+ </g>
+ </g>
+ <g id="text_19">
+ <!-- $\mathdefault{0.4}$ -->
+ <g transform="translate(37.768946 502.920512)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_4">
+ <g id="line2d_37">
+ <path clip-path="url(#p94bc642b58)" d="M 80.312385 306.723672
+L 1419.512385 306.723672
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_38">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#m001966780f" y="306.723672"/>
+ </g>
+ </g>
+ <g id="text_20">
+ <!-- $\mathdefault{0.6}$ -->
+ <g transform="translate(37.768946 317.10142)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_5">
+ <g id="line2d_39">
+ <path clip-path="url(#p94bc642b58)" d="M 80.312385 120.904579
+L 1419.512385 120.904579
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_40">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#m001966780f" y="120.904579"/>
+ </g>
+ </g>
+ <g id="text_21">
+ <!-- $\mathdefault{0.8}$ -->
+ <g transform="translate(37.768946 131.282327)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-38"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_22">
+ <!-- Weights -->
+ <g transform="translate(27.955495 516.492209)rotate(-90)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 5523 3775
+C 5581 3948 5677 4173 6048 4185
+L 6048 4352
+C 5939 4345 5715 4339 5600 4339
+C 5440 4339 5158 4339 5005 4352
+L 5005 4185
+C 5293 4179 5414 4019 5414 3865
+C 5414 3820 5408 3794 5382 3724
+L 4390 557
+L 3347 3890
+C 3328 3955 3322 3980 3322 4006
+C 3322 4185 3603 4185 3725 4185
+L 3725 4352
+C 3539 4339 3219 4339 3021 4339
+C 2861 4339 2573 4339 2426 4352
+L 2426 4185
+C 2720 4185 2797 4166 2861 4051
+C 2886 3993 2989 3660 2989 3640
+C 2989 3615 2976 3576 2970 3557
+L 2029 564
+L 986 3890
+C 954 3980 954 3993 954 4006
+C 954 4185 1235 4185 1363 4185
+L 1363 4352
+C 1178 4339 858 4339 659 4339
+C 493 4339 211 4339 58 4352
+L 58 4185
+C 442 4185 467 4147 531 3942
+L 1779 -20
+C 1811 -116 1811 -128 1869 -128
+C 1920 -128 1939 -116 1965 -26
+L 3053 3448
+L 4141 -26
+C 4166 -116 4186 -128 4237 -128
+C 4294 -128 4294 -116 4326 -20
+L 5523 3775
+z
+" id="CMR17-57" transform="scale(0.015625)"/>
+ <path d="M 710 1165
+C 832 1068 1043 960 1299 960
+C 1805 960 2240 1359 2240 1895
+C 2240 2063 2189 2321 1997 2521
+C 2176 2713 2438 2777 2586 2777
+C 2611 2777 2650 2777 2682 2758
+C 2656 2751 2598 2726 2598 2623
+C 2598 2540 2656 2483 2739 2483
+C 2835 2483 2886 2547 2886 2630
+C 2886 2751 2790 2880 2586 2880
+C 2330 2880 2106 2758 1926 2591
+C 1734 2764 1504 2828 1299 2828
+C 794 2828 358 2431 358 1895
+C 358 1527 570 1294 634 1230
+C 442 1004 442 742 442 710
+C 442 544 506 300 723 166
+C 390 82 128 -184 128 -517
+C 128 -996 736 -1344 1466 -1344
+C 2170 -1344 2803 -1009 2803 -510
+C 2803 384 1856 384 1363 384
+C 1216 384 954 384 922 390
+C 723 422 589 601 589 825
+C 589 883 589 1024 710 1165
+z
+M 1299 1068
+C 736 1068 736 1766 736 1895
+C 736 2024 736 2719 1299 2719
+C 1862 2719 1862 2024 1862 1895
+C 1862 1766 1862 1068 1299 1068
+z
+M 1466 -1236
+C 826 -1236 384 -883 384 -517
+C 384 -311 493 -118 634 -11
+C 794 102 858 102 1293 102
+C 1818 102 2547 102 2547 -517
+C 2547 -883 2106 -1236 1466 -1236
+z
+" id="CMR17-67" transform="scale(0.015625)"/>
+ <path d="M 2656 1954
+C 2656 2282 2592 2816 1837 2816
+C 1312 2816 1056 2392 979 2179
+L 973 2179
+L 973 4416
+L 211 4345
+L 211 4179
+C 589 4179 646 4141 646 3843
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1954
+z
+" id="CMR17-68" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-57"/>
+ <use transform="translate(87.289395 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(127.775055 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(152.646113 0)scale(0.996264)" xlink:href="#CMR17-67"/>
+ <use transform="translate(198.336591 0)scale(0.996264)" xlink:href="#CMR17-68"/>
+ <use transform="translate(246.629506 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(281.910274 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ </g>
+ </g>
+ </g>
+ <g id="line2d_41">
+ <path clip-path="url(#p94bc642b58)" d="M 141.185112 863.891996
+L 228.146151 864.06292
+L 315.10719 864.158733
+L 402.068229 864.1793
+L 489.029268 864.180887
+L 575.990307 864.180948
+L 662.951346 864.180949
+L 749.912385 864.18095
+L 836.873424 864.18095
+L 923.834463 864.18095
+L 1010.795502 864.18095
+L 1097.756541 864.18095
+L 1184.71758 864.18095
+L 1271.678619 864.180918
+L 1358.639658 685.620096
+" style="fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:2;"/>
+ <defs>
+ <path d="M 0 5
+C 1.326016 5 2.597899 4.473168 3.535534 3.535534
+C 4.473168 2.597899 5 1.326016 5 0
+C 5 -1.326016 4.473168 -2.597899 3.535534 -3.535534
+C 2.597899 -4.473168 1.326016 -5 0 -5
+C -1.326016 -5 -2.597899 -4.473168 -3.535534 -3.535534
+C -4.473168 -2.597899 -5 -1.326016 -5 0
+C -5 1.326016 -4.473168 2.597899 -3.535534 3.535534
+C -2.597899 4.473168 -1.326016 5 0 5
+z
+" id="m46385b3834" style="stroke:#1f77b4;"/>
+ </defs>
+ <g clip-path="url(#p94bc642b58)">
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="141.185112" xlink:href="#m46385b3834" y="863.891996"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="228.146151" xlink:href="#m46385b3834" y="864.06292"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="315.10719" xlink:href="#m46385b3834" y="864.158733"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="402.068229" xlink:href="#m46385b3834" y="864.1793"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="489.029268" xlink:href="#m46385b3834" y="864.180887"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="575.990307" xlink:href="#m46385b3834" y="864.180948"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="662.951346" xlink:href="#m46385b3834" y="864.180949"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="749.912385" xlink:href="#m46385b3834" y="864.18095"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="836.873424" xlink:href="#m46385b3834" y="864.18095"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="923.834463" xlink:href="#m46385b3834" y="864.18095"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1010.795502" xlink:href="#m46385b3834" y="864.18095"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1097.756541" xlink:href="#m46385b3834" y="864.18095"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1184.71758" xlink:href="#m46385b3834" y="864.18095"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1271.678619" xlink:href="#m46385b3834" y="864.180918"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1358.639658" xlink:href="#m46385b3834" y="685.620096"/>
+ </g>
+ </g>
+ <g id="line2d_42">
+ <path clip-path="url(#p94bc642b58)" d="M 141.185112 398.061396
+L 228.146151 398.483388
+L 315.10719 409.52644
+L 402.068229 407.615036
+L 489.029268 376.273038
+L 575.990307 376.657206
+L 662.951346 392.619425
+L 749.912385 725.776396
+L 836.873424 575.760023
+L 923.834463 462.354831
+L 1010.795502 468.704043
+L 1097.756541 482.829016
+L 1184.71758 396.27868
+L 1271.678619 409.554051
+L 1358.639658 489.311417
+" style="fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:2;"/>
+ <defs>
+ <path d="M 0 5
+C 1.326016 5 2.597899 4.473168 3.535534 3.535534
+C 4.473168 2.597899 5 1.326016 5 0
+C 5 -1.326016 4.473168 -2.597899 3.535534 -3.535534
+C 2.597899 -4.473168 1.326016 -5 0 -5
+C -1.326016 -5 -2.597899 -4.473168 -3.535534 -3.535534
+C -4.473168 -2.597899 -5 -1.326016 -5 0
+C -5 1.326016 -4.473168 2.597899 -3.535534 3.535534
+C -2.597899 4.473168 -1.326016 5 0 5
+z
+" id="ma649d9850c" style="stroke:#ff7f0e;"/>
+ </defs>
+ <g clip-path="url(#p94bc642b58)">
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="141.185112" xlink:href="#ma649d9850c" y="398.061396"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="228.146151" xlink:href="#ma649d9850c" y="398.483388"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="315.10719" xlink:href="#ma649d9850c" y="409.52644"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="402.068229" xlink:href="#ma649d9850c" y="407.615036"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="489.029268" xlink:href="#ma649d9850c" y="376.273038"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="575.990307" xlink:href="#ma649d9850c" y="376.657206"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="662.951346" xlink:href="#ma649d9850c" y="392.619425"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="749.912385" xlink:href="#ma649d9850c" y="725.776396"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="836.873424" xlink:href="#ma649d9850c" y="575.760023"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="923.834463" xlink:href="#ma649d9850c" y="462.354831"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1010.795502" xlink:href="#ma649d9850c" y="468.704043"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1097.756541" xlink:href="#ma649d9850c" y="482.829016"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1184.71758" xlink:href="#ma649d9850c" y="396.27868"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1271.678619" xlink:href="#ma649d9850c" y="409.554051"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1358.639658" xlink:href="#ma649d9850c" y="489.311417"/>
+ </g>
+ </g>
+ <g id="line2d_43">
+ <path clip-path="url(#p94bc642b58)" d="M 141.185112 401.493994
+L 228.146151 400.901079
+L 315.10719 389.762213
+L 402.068229 391.65305
+L 489.029268 422.993461
+L 575.990307 422.609232
+L 662.951346 406.647012
+L 749.912385 73.490041
+L 836.873424 223.506414
+L 923.834463 336.911606
+L 1010.795502 330.562394
+L 1097.756541 316.43742
+L 1184.71758 402.987757
+L 1271.678619 389.712417
+L 1358.639658 488.515873
+" style="fill:none;stroke:#2ca02c;stroke-linecap:square;stroke-width:2;"/>
+ <defs>
+ <path d="M 0 5
+C 1.326016 5 2.597899 4.473168 3.535534 3.535534
+C 4.473168 2.597899 5 1.326016 5 0
+C 5 -1.326016 4.473168 -2.597899 3.535534 -3.535534
+C 2.597899 -4.473168 1.326016 -5 0 -5
+C -1.326016 -5 -2.597899 -4.473168 -3.535534 -3.535534
+C -4.473168 -2.597899 -5 -1.326016 -5 0
+C -5 1.326016 -4.473168 2.597899 -3.535534 3.535534
+C -2.597899 4.473168 -1.326016 5 0 5
+z
+" id="m439971d2eb" style="stroke:#2ca02c;"/>
+ </defs>
+ <g clip-path="url(#p94bc642b58)">
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="141.185112" xlink:href="#m439971d2eb" y="401.493994"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="228.146151" xlink:href="#m439971d2eb" y="400.901079"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="315.10719" xlink:href="#m439971d2eb" y="389.762213"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="402.068229" xlink:href="#m439971d2eb" y="391.65305"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="489.029268" xlink:href="#m439971d2eb" y="422.993461"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="575.990307" xlink:href="#m439971d2eb" y="422.609232"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="662.951346" xlink:href="#m439971d2eb" y="406.647012"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="749.912385" xlink:href="#m439971d2eb" y="73.490041"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="836.873424" xlink:href="#m439971d2eb" y="223.506414"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="923.834463" xlink:href="#m439971d2eb" y="336.911606"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1010.795502" xlink:href="#m439971d2eb" y="330.562394"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1097.756541" xlink:href="#m439971d2eb" y="316.43742"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1184.71758" xlink:href="#m439971d2eb" y="402.987757"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1271.678619" xlink:href="#m439971d2eb" y="389.712417"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1358.639658" xlink:href="#m439971d2eb" y="488.515873"/>
+ </g>
+ </g>
+ <g id="patch_3">
+ <path d="M 80.312385 903.715495
+L 80.312385 33.955495
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:3;"/>
+ </g>
+ <g id="patch_4">
+ <path d="M 1419.512385 903.715495
+L 1419.512385 33.955495
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:3;"/>
+ </g>
+ <g id="patch_5">
+ <path d="M 80.312385 903.715495
+L 1419.512385 903.715495
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:3;"/>
+ </g>
+ <g id="patch_6">
+ <path d="M 80.312385 33.955495
+L 1419.512385 33.955495
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:3;"/>
+ </g>
+ <g id="text_23">
+ <!-- Data generated by: exponential -->
+ <g transform="translate(560.508324 27.955495)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 333 4352
+L 333 4185
+C 774 4185 845 4185 845 3898
+L 845 453
+C 845 166 774 166 333 166
+L 333 0
+L 2368 0
+C 3398 0 4224 943 4224 2140
+C 4224 3344 3411 4352 2368 4352
+L 333 4352
+z
+M 1523 166
+C 1267 166 1254 198 1254 414
+L 1254 3936
+C 1254 4153 1267 4185 1523 4185
+L 2240 4185
+C 2771 4185 3750 3873 3750 2140
+C 3750 1242 3488 879 3366 707
+C 3213 510 2848 166 2240 166
+L 1523 166
+z
+" id="CMR17-44" transform="scale(0.015625)"/>
+ <path d="M 1869 4345
+L 1869 4179
+C 2246 4179 2304 4141 2304 3843
+L 2304 2371
+C 2278 2403 2016 2816 1498 2816
+C 845 2816 211 2228 211 1376
+C 211 529 806 -64 1434 -64
+C 1978 -64 2259 361 2291 406
+L 2291 -64
+L 3066 -13
+L 3066 154
+C 2688 154 2630 193 2630 503
+L 2630 4416
+L 1869 4345
+z
+M 2291 762
+C 2291 568 2176 393 2029 264
+C 1811 70 1594 38 1472 38
+C 1286 38 621 135 621 1369
+C 621 2636 1363 2713 1530 2713
+C 1824 2713 2061 2545 2208 2313
+C 2291 2177 2291 2157 2291 2041
+L 2291 762
+z
+" id="CMR17-64" transform="scale(0.015625)"/>
+ <path d="M 960 4416
+L 198 4345
+L 198 4179
+C 576 4179 634 4141 634 3843
+L 634 -13
+L 749 -13
+L 934 445
+C 1120 141 1395 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2209 2477 2816 1830 2816
+C 1434 2816 1152 2603 960 2351
+L 960 4416
+z
+M 973 2022
+C 973 2138 973 2157 1062 2293
+C 1312 2681 1670 2713 1792 2713
+C 1984 2713 2643 2610 2643 1388
+C 2643 109 1888 38 1734 38
+C 1536 38 1248 115 1043 490
+C 973 613 973 626 973 742
+L 973 2022
+z
+" id="CMR17-62" transform="scale(0.015625)"/>
+ <path d="M 2496 2183
+C 2656 2579 2944 2585 3034 2585
+L 3034 2752
+C 2912 2745 2752 2739 2630 2739
+C 2496 2739 2285 2739 2157 2752
+L 2157 2585
+C 2400 2566 2406 2384 2406 2332
+C 2406 2268 2394 2235 2362 2158
+L 1664 409
+L 902 2300
+C 870 2378 870 2423 870 2430
+C 870 2572 1018 2585 1171 2585
+L 1171 2752
+C 1018 2739 742 2739 582 2739
+C 410 2739 205 2739 64 2752
+L 64 2585
+C 410 2585 448 2553 531 2345
+L 1485 -31
+C 1197 -795 1030 -1242 627 -1242
+C 557 -1242 397 -1223 282 -1106
+C 429 -1093 493 -1002 493 -892
+C 493 -782 416 -685 288 -685
+C 147 -685 77 -782 77 -899
+C 77 -1158 339 -1344 627 -1344
+C 998 -1344 1229 -983 1357 -659
+L 2496 2183
+z
+" id="CMR17-79" transform="scale(0.015625)"/>
+ <path d="M 1062 2489
+C 1062 2649 934 2752 800 2752
+C 672 2752 538 2649 538 2489
+C 538 2329 666 2227 800 2227
+C 928 2227 1062 2329 1062 2489
+z
+M 1062 262
+C 1062 422 934 524 800 524
+C 672 524 538 422 538 262
+C 538 102 666 0 800 0
+C 928 0 1062 102 1062 262
+z
+" id="CMR17-3a" transform="scale(0.015625)"/>
+ <path d="M 1664 1491
+C 1856 1740 2074 2022 2253 2233
+C 2464 2476 2707 2579 2989 2585
+L 2989 2752
+C 2880 2745 2656 2739 2541 2739
+C 2368 2739 2170 2739 2022 2752
+L 2022 2585
+C 2112 2572 2163 2508 2163 2419
+C 2163 2304 2099 2233 2067 2188
+L 1594 1587
+L 1030 2323
+C 973 2393 973 2406 973 2438
+C 973 2515 1037 2579 1146 2585
+L 1146 2752
+C 992 2739 717 2739 557 2739
+C 384 2739 179 2739 38 2752
+L 38 2585
+C 384 2585 461 2560 614 2368
+L 1350 1414
+C 1363 1401 1395 1363 1395 1344
+C 1395 1318 838 633 768 544
+C 480 198 179 172 6 166
+L 6 0
+C 115 6 339 12 454 12
+C 582 12 864 12 979 0
+L 979 166
+C 941 172 838 185 838 332
+C 838 448 890 518 947 595
+L 1478 1248
+L 2035 524
+C 2086 454 2163 358 2163 313
+C 2163 224 2086 172 1984 166
+L 1984 0
+C 2138 12 2413 12 2573 12
+C 2746 12 2950 12 3091 0
+L 3091 166
+C 2771 166 2675 179 2522 377
+L 1664 1491
+z
+" id="CMR17-78" transform="scale(0.015625)"/>
+ <path d="M 979 4416
+L 218 4345
+L 218 4179
+C 595 4179 653 4141 653 3835
+L 653 439
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 653 12 813 12
+C 979 12 1261 12 1414 0
+L 1414 166
+C 1005 166 979 191 979 439
+L 979 4416
+z
+" id="CMR17-6c" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-44"/>
+ <use transform="translate(70.393556 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(116.084033 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(151.364801 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(227.131244 0)scale(0.996264)" xlink:href="#CMR17-67"/>
+ <use transform="translate(272.821721 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(313.307382 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(364.202752 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(404.688412 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ <use transform="translate(439.96918 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(485.659657 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(520.940425 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(561.426085 0)scale(0.996264)" xlink:href="#CMR17-64"/>
+ <use transform="translate(642.397421 0)scale(0.996264)" xlink:href="#CMR17-62"/>
+ <use transform="translate(690.690337 0)scale(0.996264)" xlink:href="#CMR17-79"/>
+ <use transform="translate(738.983253 0)scale(0.996264)" xlink:href="#CMR17-3a"/>
+ <use transform="translate(804.339972 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(844.825633 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(893.118548 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(946.616357 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(992.306834 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(1043.202204 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(1083.687864 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(1131.98078 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(1167.261548 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(1192.132606 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(1237.823083 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ <g id="legend_1">
+ <g id="patch_7">
+ <path d="M 1165.006183 183.395846
+L 1398.512385 183.395846
+Q 1404.512385 183.395846 1404.512385 177.395846
+L 1404.512385 54.955495
+Q 1404.512385 48.955495 1398.512385 48.955495
+L 1165.006183 48.955495
+Q 1159.006183 48.955495 1159.006183 54.955495
+L 1159.006183 177.395846
+Q 1159.006183 183.395846 1165.006183 183.395846
+z
+" style="fill:#ffffff;opacity:0.8;stroke:#cccccc;stroke-linejoin:miter;"/>
+ </g>
+ <g id="line2d_44">
+ <path d="M 1171.006183 71.455495
+L 1231.006183 71.455495
+" style="fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:2;"/>
+ </g>
+ <g id="line2d_45">
+ <g>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1201.006183" xlink:href="#m46385b3834" y="71.455495"/>
+ </g>
+ </g>
+ <g id="text_24">
+ <!-- linear -->
+ <g transform="translate(1255.006183 81.955495)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ <g id="line2d_46">
+ <path d="M 1171.006183 113.268946
+L 1231.006183 113.268946
+" style="fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:2;"/>
+ </g>
+ <g id="line2d_47">
+ <g>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1201.006183" xlink:href="#ma649d9850c" y="113.268946"/>
+ </g>
+ </g>
+ <g id="text_25">
+ <!-- exponential -->
+ <g transform="translate(1255.006183 123.768946)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ <g id="line2d_48">
+ <path d="M 1171.006183 155.082396
+L 1231.006183 155.082396
+" style="fill:none;stroke:#2ca02c;stroke-linecap:square;stroke-width:2;"/>
+ </g>
+ <g id="line2d_49">
+ <g>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1201.006183" xlink:href="#m439971d2eb" y="155.082396"/>
+ </g>
+ </g>
+ <g id="text_26">
+ <!-- cosine -->
+ <g transform="translate(1255.006183 165.582396)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2234 2240
+C 2112 2240 1933 2240 1933 2015
+C 1933 1836 2080 1785 2163 1785
+C 2208 1785 2394 1804 2394 2028
+C 2394 2476 1958 2816 1466 2816
+C 787 2816 211 2201 211 1379
+C 211 521 813 -64 1466 -64
+C 2259 -64 2458 676 2458 747
+C 2458 773 2451 792 2406 792
+C 2362 792 2355 786 2330 702
+C 2163 180 1798 51 1523 51
+C 1114 51 621 431 621 1385
+C 621 2358 1094 2700 1472 2700
+C 1722 2700 2093 2582 2234 2240
+z
+" id="CMR17-63" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ </g>
+ </g>
+ <defs>
+ <clipPath id="p94bc642b58">
+ <rect height="869.76" width="1339.2" x="80.312385" y="33.955495"/>
+ </clipPath>
+ </defs>
+</svg>
diff --git a/examples/model-comparison/reference/modelWeights_linear.svg b/examples/model-comparison/reference/modelWeights_linear.svg
new file mode 100644
index 0000000000000000000000000000000000000000..a5a947efd336f97837a9a9903066394fa8587273
--- /dev/null
+++ b/examples/model-comparison/reference/modelWeights_linear.svg
@@ -0,0 +1,1652 @@
+<?xml version="1.0" encoding="utf-8" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+ "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<svg height="975.053386pt" version="1.1" viewBox="0 0 1426.712385 975.053386" width="1426.712385pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+ <metadata>
+ <rdf:RDF xmlns:cc="http://creativecommons.org/ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
+ <cc:Work>
+ <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
+ <dc:date>2022-06-03T16:06:03.758650</dc:date>
+ <dc:format>image/svg+xml</dc:format>
+ <dc:creator>
+ <cc:Agent>
+ <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>
+ </cc:Agent>
+ </dc:creator>
+ </cc:Work>
+ </rdf:RDF>
+ </metadata>
+ <defs>
+ <style type="text/css">*{stroke-linecap:butt;stroke-linejoin:round;}</style>
+ </defs>
+ <g id="figure_1">
+ <g id="patch_1">
+ <path d="M 0 975.053386
+L 1426.712385 975.053386
+L 1426.712385 0
+L 0 0
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="axes_1">
+ <g id="patch_2">
+ <path d="M 80.312385 903.715495
+L 1419.512385 903.715495
+L 1419.512385 33.955495
+L 80.312385 33.955495
+z
+" style="fill:#ffffff;"/>
+ </g>
+ <g id="matplotlib.axis_1">
+ <g id="xtick_1">
+ <g id="line2d_1">
+ <path clip-path="url(#p94371e9dc2)" d="M 141.185112 903.715495
+L 141.185112 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_2">
+ <defs>
+ <path d="M 0 0
+L 0 3.5
+" id="mc63b21f2d1" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="141.185112" xlink:href="#mc63b21f2d1" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_1">
+ <!-- $\mathdefault{1}$ -->
+ <g transform="translate(134.331541 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1702 4083
+C 1702 4217 1696 4224 1606 4224
+C 1357 3927 979 3833 621 3820
+C 602 3820 570 3820 563 3808
+C 557 3795 557 3782 557 3648
+C 755 3648 1088 3686 1344 3839
+L 1344 467
+C 1344 243 1331 166 781 166
+L 589 166
+L 589 0
+C 896 6 1216 12 1523 12
+C 1830 12 2150 6 2458 0
+L 2458 166
+L 2266 166
+C 1715 166 1702 236 1702 467
+L 1702 4083
+z
+" id="CMR17-31" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_2">
+ <g id="line2d_3">
+ <path clip-path="url(#p94371e9dc2)" d="M 228.146151 903.715495
+L 228.146151 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_4">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="228.146151" xlink:href="#mc63b21f2d1" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_2">
+ <!-- $\mathdefault{2}$ -->
+ <g transform="translate(221.29258 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2669 990
+L 2554 990
+C 2490 537 2438 460 2413 422
+C 2381 371 1920 371 1830 371
+L 602 371
+C 832 620 1280 1073 1824 1596
+C 2214 1966 2669 2400 2669 3033
+C 2669 3788 2067 4224 1395 4224
+C 691 4224 262 3603 262 3027
+C 262 2777 448 2745 525 2745
+C 589 2745 781 2783 781 3007
+C 781 3206 614 3264 525 3264
+C 486 3264 448 3257 422 3244
+C 544 3788 915 4057 1306 4057
+C 1862 4057 2227 3616 2227 3033
+C 2227 2477 1901 1998 1536 1583
+L 262 147
+L 262 0
+L 2515 0
+L 2669 990
+z
+" id="CMR17-32" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_3">
+ <g id="line2d_5">
+ <path clip-path="url(#p94371e9dc2)" d="M 315.10719 903.715495
+L 315.10719 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_6">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="315.10719" xlink:href="#mc63b21f2d1" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_3">
+ <!-- $\mathdefault{3}$ -->
+ <g transform="translate(308.253619 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1414 2176
+C 1984 2176 2234 1673 2234 1094
+C 2234 322 1824 25 1453 25
+C 1114 25 563 193 390 691
+C 422 678 454 678 486 678
+C 640 678 755 780 755 947
+C 755 1132 614 1216 486 1216
+C 378 1216 211 1164 211 927
+C 211 335 787 -128 1466 -128
+C 2176 -128 2720 432 2720 1087
+C 2720 1718 2208 2176 1600 2246
+C 2086 2347 2554 2776 2554 3353
+C 2554 3856 2048 4224 1472 4224
+C 890 4224 378 3862 378 3347
+C 378 3123 544 3084 627 3084
+C 762 3084 877 3167 877 3334
+C 877 3500 762 3584 627 3584
+C 602 3584 570 3584 544 3571
+C 730 3999 1235 4076 1459 4076
+C 1683 4076 2106 3966 2106 3347
+C 2106 3167 2080 2851 1862 2574
+C 1670 2329 1453 2316 1242 2297
+C 1210 2297 1062 2284 1037 2284
+C 992 2278 966 2272 966 2227
+C 966 2182 973 2176 1101 2176
+L 1414 2176
+z
+" id="CMR17-33" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_4">
+ <g id="line2d_7">
+ <path clip-path="url(#p94371e9dc2)" d="M 402.068229 903.715495
+L 402.068229 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_8">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="402.068229" xlink:href="#mc63b21f2d1" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_4">
+ <!-- $\mathdefault{4}$ -->
+ <g transform="translate(395.214658 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2150 4147
+C 2150 4281 2144 4288 2029 4288
+L 128 1254
+L 128 1088
+L 1779 1088
+L 1779 460
+C 1779 230 1766 166 1318 166
+L 1197 166
+L 1197 0
+C 1402 12 1747 12 1965 12
+C 2182 12 2528 12 2733 0
+L 2733 166
+L 2611 166
+C 2163 166 2150 230 2150 460
+L 2150 1088
+L 2803 1088
+L 2803 1254
+L 2150 1254
+L 2150 4147
+z
+M 1798 3723
+L 1798 1254
+L 256 1254
+L 1798 3723
+z
+" id="CMR17-34" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_5">
+ <g id="line2d_9">
+ <path clip-path="url(#p94371e9dc2)" d="M 489.029268 903.715495
+L 489.029268 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_10">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="489.029268" xlink:href="#mc63b21f2d1" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_5">
+ <!-- $\mathdefault{5}$ -->
+ <g transform="translate(482.175697 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 730 3750
+C 794 3724 1056 3641 1325 3641
+C 1920 3641 2246 3961 2432 4140
+C 2432 4191 2432 4224 2394 4224
+C 2387 4224 2374 4224 2323 4198
+C 2099 4102 1837 4032 1517 4032
+C 1325 4032 1037 4055 723 4191
+C 653 4224 640 4224 634 4224
+C 602 4224 595 4217 595 4090
+L 595 2231
+C 595 2113 595 2080 659 2080
+C 691 2080 704 2093 736 2139
+C 941 2435 1222 2560 1542 2560
+C 1766 2560 2246 2415 2246 1293
+C 2246 1087 2246 716 2054 422
+C 1894 159 1645 25 1370 25
+C 947 25 518 319 403 812
+C 429 806 480 793 506 793
+C 589 793 749 838 749 1036
+C 749 1209 627 1280 506 1280
+C 358 1280 262 1190 262 1011
+C 262 454 704 -128 1382 -128
+C 2042 -128 2669 441 2669 1267
+C 2669 2054 2170 2662 1549 2662
+C 1222 2662 947 2540 730 2304
+L 730 3750
+z
+" id="CMR17-35" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_6">
+ <g id="line2d_11">
+ <path clip-path="url(#p94371e9dc2)" d="M 575.990307 903.715495
+L 575.990307 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_12">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="575.990307" xlink:href="#mc63b21f2d1" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_6">
+ <!-- $\mathdefault{6}$ -->
+ <g transform="translate(569.136735 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 678 2198
+C 678 3712 1395 4076 1811 4076
+C 1946 4076 2272 4049 2400 3782
+C 2298 3782 2106 3782 2106 3558
+C 2106 3385 2246 3328 2336 3328
+C 2394 3328 2566 3353 2566 3571
+C 2566 3987 2246 4224 1805 4224
+C 1043 4224 243 3411 243 2011
+C 243 257 966 -128 1478 -128
+C 2099 -128 2688 431 2688 1295
+C 2688 2101 2170 2688 1517 2688
+C 1126 2688 838 2430 678 1979
+L 678 2198
+z
+M 1478 25
+C 691 25 691 1212 691 1450
+C 691 1914 909 2585 1504 2585
+C 1613 2585 1926 2585 2138 2140
+C 2253 1889 2253 1624 2253 1302
+C 2253 954 2253 696 2118 438
+C 1978 173 1773 25 1478 25
+z
+" id="CMR17-36" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_7">
+ <g id="line2d_13">
+ <path clip-path="url(#p94371e9dc2)" d="M 662.951346 903.715495
+L 662.951346 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_14">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="662.951346" xlink:href="#mc63b21f2d1" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_7">
+ <!-- $\mathdefault{7}$ -->
+ <g transform="translate(656.097774 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2886 3955
+L 2886 4096
+L 1382 4096
+C 634 4096 621 4166 595 4288
+L 480 4288
+L 294 3104
+L 410 3104
+C 429 3226 474 3552 550 3673
+C 589 3724 1062 3724 1171 3724
+L 2579 3724
+L 1869 2670
+C 1395 1961 1069 1003 1069 166
+C 1069 89 1069 -128 1299 -128
+C 1530 -128 1530 89 1530 172
+L 1530 466
+C 1530 1514 1709 2204 2003 2644
+L 2886 3955
+z
+" id="CMR17-37" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-37"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_8">
+ <g id="line2d_15">
+ <path clip-path="url(#p94371e9dc2)" d="M 749.912385 903.715495
+L 749.912385 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_16">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="749.912385" xlink:href="#mc63b21f2d1" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_8">
+ <!-- $\mathdefault{8}$ -->
+ <g transform="translate(743.058813 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1741 2289
+C 2144 2494 2554 2803 2554 3298
+C 2554 3884 1990 4224 1472 4224
+C 890 4224 378 3800 378 3215
+C 378 3054 416 2777 666 2533
+C 730 2469 998 2276 1171 2154
+C 883 2006 211 1652 211 945
+C 211 282 838 -128 1459 -128
+C 2144 -128 2720 366 2720 1022
+C 2720 1607 2330 1877 2074 2051
+L 1741 2289
+z
+M 902 2855
+C 851 2887 595 3086 595 3388
+C 595 3781 998 4076 1459 4076
+C 1965 4076 2336 3716 2336 3298
+C 2336 2700 1670 2359 1638 2359
+C 1632 2359 1626 2359 1574 2398
+L 902 2855
+z
+M 2080 1536
+C 2176 1466 2483 1253 2483 861
+C 2483 385 2010 25 1472 25
+C 890 25 448 443 448 951
+C 448 1459 838 1884 1280 2083
+L 2080 1536
+z
+" id="CMR17-38" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-38"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_9">
+ <g id="line2d_17">
+ <path clip-path="url(#p94371e9dc2)" d="M 836.873424 903.715495
+L 836.873424 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_18">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="836.873424" xlink:href="#mc63b21f2d1" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_9">
+ <!-- $\mathdefault{9}$ -->
+ <g transform="translate(830.019852 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2253 1871
+C 2253 448 1670 25 1190 25
+C 1043 25 685 43 538 281
+C 704 256 826 345 826 505
+C 826 678 685 736 595 736
+C 538 736 365 710 365 492
+C 365 68 742 -128 1203 -128
+C 1939 -128 2688 665 2688 2090
+C 2688 3857 1971 4224 1485 4224
+C 851 4224 243 3664 243 2800
+C 243 2000 762 1408 1414 1408
+C 1952 1408 2189 1910 2253 2122
+L 2253 1871
+z
+M 1427 1510
+C 1254 1510 1011 1542 813 1929
+C 678 2181 678 2477 678 2793
+C 678 3174 678 3438 858 3722
+C 947 3857 1114 4076 1485 4076
+C 2240 4076 2240 2909 2240 2651
+C 2240 2193 2035 1510 1427 1510
+z
+" id="CMR17-39" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-39"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_10">
+ <g id="line2d_19">
+ <path clip-path="url(#p94371e9dc2)" d="M 923.834463 903.715495
+L 923.834463 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_20">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="923.834463" xlink:href="#mc63b21f2d1" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_10">
+ <!-- $\mathdefault{10}$ -->
+ <g transform="translate(910.12732 931.47099)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2688 2038
+C 2688 2430 2682 3099 2413 3613
+C 2176 4063 1798 4224 1466 4224
+C 1158 4224 768 4082 525 3620
+C 269 3137 243 2539 243 2038
+C 243 1671 250 1112 448 623
+C 723 -39 1216 -128 1466 -128
+C 1760 -128 2208 -7 2470 604
+C 2662 1048 2688 1568 2688 2038
+z
+M 1466 -26
+C 1056 -26 813 328 723 816
+C 653 1196 653 1749 653 2109
+C 653 2604 653 3015 736 3407
+C 858 3954 1216 4121 1466 4121
+C 1728 4121 2067 3947 2189 3420
+C 2272 3054 2278 2623 2278 2109
+C 2278 1691 2278 1176 2202 797
+C 2067 96 1690 -26 1466 -26
+z
+" id="CMR17-30" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_11">
+ <g id="line2d_21">
+ <path clip-path="url(#p94371e9dc2)" d="M 1010.795502 903.715495
+L 1010.795502 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_22">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1010.795502" xlink:href="#mc63b21f2d1" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_11">
+ <!-- $\mathdefault{11}$ -->
+ <g transform="translate(997.088359 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-31"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_12">
+ <g id="line2d_23">
+ <path clip-path="url(#p94371e9dc2)" d="M 1097.756541 903.715495
+L 1097.756541 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_24">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1097.756541" xlink:href="#mc63b21f2d1" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_12">
+ <!-- $\mathdefault{12}$ -->
+ <g transform="translate(1084.049398 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_13">
+ <g id="line2d_25">
+ <path clip-path="url(#p94371e9dc2)" d="M 1184.71758 903.715495
+L 1184.71758 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_26">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1184.71758" xlink:href="#mc63b21f2d1" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_13">
+ <!-- $\mathdefault{13}$ -->
+ <g transform="translate(1171.010437 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-33"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_14">
+ <g id="line2d_27">
+ <path clip-path="url(#p94371e9dc2)" d="M 1271.678619 903.715495
+L 1271.678619 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_28">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1271.678619" xlink:href="#mc63b21f2d1" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_14">
+ <!-- $\mathdefault{14}$ -->
+ <g transform="translate(1257.971476 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="xtick_15">
+ <g id="line2d_29">
+ <path clip-path="url(#p94371e9dc2)" d="M 1358.639658 903.715495
+L 1358.639658 33.955495
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_30">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="1358.639658" xlink:href="#mc63b21f2d1" y="903.715495"/>
+ </g>
+ </g>
+ <g id="text_15">
+ <!-- $\mathdefault{15}$ -->
+ <g transform="translate(1344.932515 931.47099)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-31"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMR17-35"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_16">
+ <!-- No. of measurement points -->
+ <g transform="translate(587.401303 962.039936)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1312 4275
+C 1267 4345 1261 4352 1139 4352
+L 326 4352
+L 326 4185
+L 448 4185
+C 704 4185 819 4153 838 4147
+L 838 624
+C 838 465 838 166 326 166
+L 326 0
+C 474 12 742 12 902 12
+C 1062 12 1331 12 1478 0
+L 1478 166
+C 966 166 966 465 966 624
+L 966 4057
+C 1011 4019 1011 4007 1056 3943
+L 3430 76
+C 3475 0 3494 0 3526 0
+C 3590 0 3590 19 3590 140
+L 3590 3726
+C 3590 3885 3590 4185 4102 4185
+L 4102 4352
+C 3955 4339 3686 4339 3526 4339
+C 3366 4339 3098 4339 2950 4352
+L 2950 4185
+C 3462 4185 3462 3885 3462 3726
+L 3462 777
+L 1312 4275
+z
+" id="CMR17-4e" transform="scale(0.015625)"/>
+ <path d="M 2758 1356
+C 2758 2176 2163 2816 1466 2816
+C 768 2816 173 2176 173 1356
+C 173 550 768 -64 1466 -64
+C 2163 -64 2758 550 2758 1356
+z
+M 1466 51
+C 1165 51 909 230 762 480
+C 602 768 582 1126 582 1408
+C 582 1676 595 2009 762 2297
+C 890 2508 1139 2713 1466 2713
+C 1754 2713 1997 2553 2150 2329
+C 2349 2028 2349 1606 2349 1408
+C 2349 1158 2336 774 2163 467
+C 1984 172 1709 51 1466 51
+z
+" id="CMR17-6f" transform="scale(0.015625)"/>
+ <path d="M 1062 262
+C 1062 422 934 524 800 524
+C 672 524 538 422 538 262
+C 538 102 666 0 800 0
+C 928 0 1062 102 1062 262
+z
+" id="CMR17-2e" transform="scale(0.015625)"/>
+ <path d="M 979 2585
+L 1709 2585
+L 1709 2752
+L 966 2752
+L 966 3539
+C 966 4076 1235 4377 1510 4377
+C 1594 4377 1690 4363 1754 4339
+C 1702 4326 1568 4281 1568 4121
+C 1568 3955 1696 3904 1786 3904
+C 1875 3904 2003 3955 2003 4121
+C 2003 4353 1773 4480 1517 4480
+C 1152 4480 653 4211 653 3526
+L 653 2752
+L 141 2752
+L 141 2585
+L 653 2585
+L 653 441
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 666 12 832 12
+C 1018 12 1344 12 1517 0
+L 1517 166
+C 1056 166 979 166 979 454
+L 979 2585
+z
+" id="CMR17-66" transform="scale(0.015625)"/>
+ <path d="M 4326 1954
+C 4326 2276 4269 2816 3507 2816
+C 3072 2816 2771 2520 2656 2173
+L 2650 2173
+C 2573 2700 2195 2816 1837 2816
+C 1331 2816 1069 2424 973 2166
+L 966 2166
+L 966 2816
+L 211 2745
+L 211 2578
+C 589 2578 646 2540 646 2231
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1678
+C 2656 2269 3014 2713 3462 2713
+C 3936 2713 3987 2289 3987 1980
+L 3987 443
+C 3987 198 3962 166 3552 166
+L 3552 0
+C 3706 12 3987 12 4154 12
+C 4320 12 4608 12 4762 0
+L 4762 166
+C 4352 166 4326 192 4326 443
+L 4326 1954
+z
+" id="CMR17-6d" transform="scale(0.015625)"/>
+ <path d="M 2438 1503
+C 2464 1529 2464 1542 2464 1606
+C 2464 2251 2118 2816 1389 2816
+C 710 2816 173 2175 173 1394
+C 173 554 781 -64 1459 -64
+C 2176 -64 2458 619 2458 755
+C 2458 800 2419 800 2406 800
+C 2362 800 2355 787 2330 709
+C 2189 270 1837 51 1504 51
+C 1229 51 954 206 781 490
+C 582 819 582 1200 582 1503
+L 2438 1503
+z
+M 589 1600
+C 634 2511 1126 2713 1382 2713
+C 1818 2713 2112 2308 2118 1600
+L 589 1600
+z
+" id="CMR17-65" transform="scale(0.015625)"/>
+ <path d="M 2304 1656
+C 2304 2048 2304 2275 2035 2534
+C 1798 2751 1523 2816 1306 2816
+C 800 2816 435 2408 435 1977
+C 435 1740 627 1728 666 1728
+C 749 1728 896 1779 896 1958
+C 896 2118 774 2188 666 2188
+C 640 2188 608 2182 589 2176
+C 723 2594 1069 2713 1293 2713
+C 1613 2713 1965 2421 1965 1875
+L 1965 1632
+C 1587 1619 1133 1568 774 1373
+C 371 1147 256 822 256 576
+C 256 77 832 -64 1171 -64
+C 1523 -64 1850 135 1990 505
+C 2003 219 2182 -39 2464 -39
+C 2598 -39 2938 51 2938 563
+L 2938 926
+L 2822 926
+L 2822 557
+C 2822 161 2650 109 2566 109
+C 2304 109 2304 446 2304 732
+L 2304 1656
+z
+M 1965 887
+C 1965 323 1568 38 1216 38
+C 896 38 646 278 646 576
+C 646 771 730 1114 1101 1322
+C 1408 1497 1760 1523 1965 1536
+L 1965 887
+z
+" id="CMR17-61" transform="scale(0.015625)"/>
+ <path d="M 1978 2688
+C 1978 2803 1971 2809 1933 2809
+C 1907 2809 1901 2803 1824 2707
+C 1805 2681 1747 2617 1728 2592
+C 1523 2809 1235 2816 1126 2816
+C 416 2816 160 2444 160 2073
+C 160 1497 813 1363 998 1324
+C 1402 1241 1542 1216 1677 1100
+C 1760 1024 1901 883 1901 652
+C 1901 384 1747 38 1158 38
+C 602 38 403 460 288 1024
+C 269 1113 269 1120 218 1120
+C 166 1120 160 1113 160 985
+L 160 64
+C 160 -52 166 -58 205 -58
+C 237 -58 243 -52 275 0
+C 314 57 410 211 448 275
+C 576 102 800 -64 1158 -64
+C 1792 -64 2131 281 2131 780
+C 2131 1107 1958 1280 1875 1356
+C 1683 1555 1459 1600 1190 1651
+C 838 1728 390 1817 390 2208
+C 390 2374 480 2726 1126 2726
+C 1811 2726 1850 2086 1862 1881
+C 1869 1849 1901 1843 1920 1843
+C 1978 1843 1978 1862 1978 1971
+L 1978 2688
+z
+" id="CMR17-73" transform="scale(0.015625)"/>
+ <path d="M 1882 2745
+L 1882 2579
+C 2259 2579 2317 2540 2317 2229
+L 2317 1053
+C 2317 510 2029 38 1555 38
+C 1030 38 986 355 986 691
+L 986 2816
+L 211 2745
+L 211 2579
+C 467 2579 640 2579 646 2320
+L 646 1079
+C 646 646 646 368 813 187
+C 896 103 1056 -64 1517 -64
+C 2061 -64 2272 400 2323 536
+L 2330 536
+L 2330 -64
+L 3091 -13
+L 3091 154
+C 2714 154 2656 193 2656 503
+L 2656 2816
+L 1882 2745
+z
+" id="CMR17-75" transform="scale(0.015625)"/>
+ <path d="M 960 1517
+C 960 2134 1222 2713 1702 2713
+C 1747 2713 1792 2707 1837 2687
+C 1837 2687 1696 2642 1696 2475
+C 1696 2321 1818 2257 1914 2257
+C 1990 2257 2131 2302 2131 2482
+C 2131 2687 1926 2816 1709 2816
+C 1222 2816 1011 2340 947 2115
+L 941 2115
+L 941 2816
+L 198 2745
+L 198 2578
+C 576 2578 634 2540 634 2231
+L 634 443
+C 634 198 608 166 198 166
+L 198 0
+C 352 12 646 12 813 12
+C 998 12 1325 12 1498 0
+L 1498 166
+C 1037 166 960 166 960 455
+L 960 1517
+z
+" id="CMR17-72" transform="scale(0.015625)"/>
+ <path d="M 2656 1954
+C 2656 2282 2592 2816 1837 2816
+C 1331 2816 1069 2424 973 2166
+L 966 2166
+L 966 2816
+L 211 2745
+L 211 2578
+C 589 2578 646 2540 646 2231
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1954
+z
+" id="CMR17-6e" transform="scale(0.015625)"/>
+ <path d="M 966 2585
+L 1862 2585
+L 1862 2752
+L 966 2752
+L 966 3968
+L 851 3968
+C 838 3292 614 2700 70 2687
+L 70 2585
+L 627 2585
+L 627 778
+C 627 655 627 -64 1370 -64
+C 1747 -64 1965 308 1965 784
+L 1965 1151
+L 1850 1151
+L 1850 790
+C 1850 347 1677 51 1408 51
+C 1222 51 966 179 966 765
+L 966 2585
+z
+" id="CMR17-74" transform="scale(0.015625)"/>
+ <path d="M 1408 -1114
+C 998 -1114 973 -1088 973 -834
+L 973 380
+C 1158 109 1427 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2196 2496 2816 1837 2816
+C 1453 2816 1139 2603 960 2345
+L 960 2816
+L 198 2745
+L 198 2577
+C 576 2577 634 2539 634 2228
+L 634 -834
+C 634 -1081 608 -1114 198 -1114
+L 198 -1280
+C 352 -1268 634 -1268 800 -1268
+C 966 -1268 1254 -1268 1408 -1280
+L 1408 -1114
+z
+M 973 2015
+C 973 2106 973 2241 1222 2481
+C 1254 2506 1472 2700 1792 2700
+C 2259 2700 2643 2112 2643 1376
+C 2643 639 2234 38 1728 38
+C 1498 38 1248 148 1056 451
+C 973 594 973 632 973 736
+L 973 2015
+z
+" id="CMR17-70" transform="scale(0.015625)"/>
+ <path d="M 992 3961
+C 992 4102 877 4224 730 4224
+C 589 4224 467 4108 467 3961
+C 467 3820 582 3699 730 3699
+C 870 3699 992 3814 992 3961
+z
+M 243 2745
+L 243 2579
+C 602 2579 653 2540 653 2231
+L 653 443
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 646 12 806 12
+C 960 12 1222 12 1370 0
+L 1370 166
+C 992 166 979 205 979 436
+L 979 2816
+L 243 2745
+z
+" id="CMR17-69" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-4e"/>
+ <use transform="translate(69.07243 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(114.762907 0)scale(0.996264)" xlink:href="#CMR17-2e"/>
+ <use transform="translate(180.119626 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(225.810103 0)scale(0.996264)" xlink:href="#CMR17-66"/>
+ <use transform="translate(283.359582 0)scale(0.996264)" xlink:href="#CMR17-6d"/>
+ <use transform="translate(360.279172 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(400.764832 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(446.455309 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(482.256647 0)scale(0.996264)" xlink:href="#CMR17-75"/>
+ <use transform="translate(533.152017 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ <use transform="translate(568.432784 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(608.918445 0)scale(0.996264)" xlink:href="#CMR17-6d"/>
+ <use transform="translate(685.838035 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(726.323695 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(774.616611 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(839.973345 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(893.471154 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(939.161631 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(964.032689 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(1012.325605 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(1047.606373 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ </g>
+ </g>
+ </g>
+ <g id="matplotlib.axis_2">
+ <g id="ytick_1">
+ <g id="line2d_31">
+ <path clip-path="url(#p94371e9dc2)" d="M 80.312385 864.181069
+L 1419.512385 864.181069
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_32">
+ <defs>
+ <path d="M 0 0
+L -3.5 0
+" id="mea7fd5c0ac" style="stroke:#000000;stroke-width:0.8;"/>
+ </defs>
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#mea7fd5c0ac" y="864.181069"/>
+ </g>
+ </g>
+ <g id="text_17">
+ <!-- $\mathdefault{0.0}$ -->
+ <g transform="translate(37.768946 874.558817)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1178 307
+C 1178 492 1024 620 870 620
+C 685 620 557 467 557 313
+C 557 128 710 0 864 0
+C 1050 0 1178 153 1178 307
+z
+" id="CMMI12-3a" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-30"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_2">
+ <g id="line2d_33">
+ <path clip-path="url(#p94371e9dc2)" d="M 80.312385 680.594919
+L 1419.512385 680.594919
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_34">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#mea7fd5c0ac" y="680.594919"/>
+ </g>
+ </g>
+ <g id="text_18">
+ <!-- $\mathdefault{0.2}$ -->
+ <g transform="translate(37.768946 690.972666)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-32"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_3">
+ <g id="line2d_35">
+ <path clip-path="url(#p94371e9dc2)" d="M 80.312385 497.008768
+L 1419.512385 497.008768
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_36">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#mea7fd5c0ac" y="497.008768"/>
+ </g>
+ </g>
+ <g id="text_19">
+ <!-- $\mathdefault{0.4}$ -->
+ <g transform="translate(37.768946 507.386515)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-34"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_4">
+ <g id="line2d_37">
+ <path clip-path="url(#p94371e9dc2)" d="M 80.312385 313.422617
+L 1419.512385 313.422617
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_38">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#mea7fd5c0ac" y="313.422617"/>
+ </g>
+ </g>
+ <g id="text_20">
+ <!-- $\mathdefault{0.6}$ -->
+ <g transform="translate(37.768946 323.800365)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-36"/>
+ </g>
+ </g>
+ </g>
+ <g id="ytick_5">
+ <g id="line2d_39">
+ <path clip-path="url(#p94371e9dc2)" d="M 80.312385 129.836466
+L 1419.512385 129.836466
+" style="fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;"/>
+ </g>
+ <g id="line2d_40">
+ <g>
+ <use style="stroke:#000000;stroke-width:0.8;" x="80.312385" xlink:href="#mea7fd5c0ac" y="129.836466"/>
+ </g>
+ </g>
+ <g id="text_21">
+ <!-- $\mathdefault{0.8}$ -->
+ <g transform="translate(37.768946 140.214214)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-30"/>
+ <use transform="translate(45.690477 0)scale(0.996264)" xlink:href="#CMMI12-3a"/>
+ <use transform="translate(72.787654 0)scale(0.996264)" xlink:href="#CMR17-38"/>
+ </g>
+ </g>
+ </g>
+ <g id="text_22">
+ <!-- Weights -->
+ <g transform="translate(27.955495 516.492209)rotate(-90)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 5523 3775
+C 5581 3948 5677 4173 6048 4185
+L 6048 4352
+C 5939 4345 5715 4339 5600 4339
+C 5440 4339 5158 4339 5005 4352
+L 5005 4185
+C 5293 4179 5414 4019 5414 3865
+C 5414 3820 5408 3794 5382 3724
+L 4390 557
+L 3347 3890
+C 3328 3955 3322 3980 3322 4006
+C 3322 4185 3603 4185 3725 4185
+L 3725 4352
+C 3539 4339 3219 4339 3021 4339
+C 2861 4339 2573 4339 2426 4352
+L 2426 4185
+C 2720 4185 2797 4166 2861 4051
+C 2886 3993 2989 3660 2989 3640
+C 2989 3615 2976 3576 2970 3557
+L 2029 564
+L 986 3890
+C 954 3980 954 3993 954 4006
+C 954 4185 1235 4185 1363 4185
+L 1363 4352
+C 1178 4339 858 4339 659 4339
+C 493 4339 211 4339 58 4352
+L 58 4185
+C 442 4185 467 4147 531 3942
+L 1779 -20
+C 1811 -116 1811 -128 1869 -128
+C 1920 -128 1939 -116 1965 -26
+L 3053 3448
+L 4141 -26
+C 4166 -116 4186 -128 4237 -128
+C 4294 -128 4294 -116 4326 -20
+L 5523 3775
+z
+" id="CMR17-57" transform="scale(0.015625)"/>
+ <path d="M 710 1165
+C 832 1068 1043 960 1299 960
+C 1805 960 2240 1359 2240 1895
+C 2240 2063 2189 2321 1997 2521
+C 2176 2713 2438 2777 2586 2777
+C 2611 2777 2650 2777 2682 2758
+C 2656 2751 2598 2726 2598 2623
+C 2598 2540 2656 2483 2739 2483
+C 2835 2483 2886 2547 2886 2630
+C 2886 2751 2790 2880 2586 2880
+C 2330 2880 2106 2758 1926 2591
+C 1734 2764 1504 2828 1299 2828
+C 794 2828 358 2431 358 1895
+C 358 1527 570 1294 634 1230
+C 442 1004 442 742 442 710
+C 442 544 506 300 723 166
+C 390 82 128 -184 128 -517
+C 128 -996 736 -1344 1466 -1344
+C 2170 -1344 2803 -1009 2803 -510
+C 2803 384 1856 384 1363 384
+C 1216 384 954 384 922 390
+C 723 422 589 601 589 825
+C 589 883 589 1024 710 1165
+z
+M 1299 1068
+C 736 1068 736 1766 736 1895
+C 736 2024 736 2719 1299 2719
+C 1862 2719 1862 2024 1862 1895
+C 1862 1766 1862 1068 1299 1068
+z
+M 1466 -1236
+C 826 -1236 384 -883 384 -517
+C 384 -311 493 -118 634 -11
+C 794 102 858 102 1293 102
+C 1818 102 2547 102 2547 -517
+C 2547 -883 2106 -1236 1466 -1236
+z
+" id="CMR17-67" transform="scale(0.015625)"/>
+ <path d="M 2656 1954
+C 2656 2282 2592 2816 1837 2816
+C 1312 2816 1056 2392 979 2179
+L 973 2179
+L 973 4416
+L 211 4345
+L 211 4179
+C 589 4179 646 4141 646 3843
+L 646 443
+C 646 198 621 166 211 166
+L 211 0
+C 365 12 646 12 813 12
+C 979 12 1267 12 1421 0
+L 1421 166
+C 1011 166 986 192 986 443
+L 986 1678
+C 986 2269 1344 2713 1792 2713
+C 2266 2713 2317 2289 2317 1980
+L 2317 443
+C 2317 198 2291 166 1882 166
+L 1882 0
+C 2035 12 2317 12 2483 12
+C 2650 12 2938 12 3091 0
+L 3091 166
+C 2682 166 2656 192 2656 443
+L 2656 1954
+z
+" id="CMR17-68" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-57"/>
+ <use transform="translate(87.289395 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(127.775055 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(152.646113 0)scale(0.996264)" xlink:href="#CMR17-67"/>
+ <use transform="translate(198.336591 0)scale(0.996264)" xlink:href="#CMR17-68"/>
+ <use transform="translate(246.629506 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(281.910274 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ </g>
+ </g>
+ </g>
+ <g id="line2d_41">
+ <path clip-path="url(#p94371e9dc2)" d="M 141.185112 863.753392
+L 228.146151 863.754197
+L 315.10719 863.748938
+L 402.068229 863.752282
+L 489.029268 863.78749
+L 575.990307 863.859182
+L 662.951346 863.942932
+L 749.912385 864.009331
+L 836.873424 864.025767
+L 923.834463 864.179979
+L 1010.795502 864.18095
+L 1097.756541 864.180769
+L 1184.71758 864.176712
+L 1271.678619 852.525037
+L 1358.639658 213.524338
+" style="fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:2;"/>
+ <defs>
+ <path d="M 0 5
+C 1.326016 5 2.597899 4.473168 3.535534 3.535534
+C 4.473168 2.597899 5 1.326016 5 0
+C 5 -1.326016 4.473168 -2.597899 3.535534 -3.535534
+C 2.597899 -4.473168 1.326016 -5 0 -5
+C -1.326016 -5 -2.597899 -4.473168 -3.535534 -3.535534
+C -4.473168 -2.597899 -5 -1.326016 -5 0
+C -5 1.326016 -4.473168 2.597899 -3.535534 3.535534
+C -2.597899 4.473168 -1.326016 5 0 5
+z
+" id="mc9b7777a7d" style="stroke:#1f77b4;"/>
+ </defs>
+ <g clip-path="url(#p94371e9dc2)">
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="141.185112" xlink:href="#mc9b7777a7d" y="863.753392"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="228.146151" xlink:href="#mc9b7777a7d" y="863.754197"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="315.10719" xlink:href="#mc9b7777a7d" y="863.748938"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="402.068229" xlink:href="#mc9b7777a7d" y="863.752282"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="489.029268" xlink:href="#mc9b7777a7d" y="863.78749"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="575.990307" xlink:href="#mc9b7777a7d" y="863.859182"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="662.951346" xlink:href="#mc9b7777a7d" y="863.942932"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="749.912385" xlink:href="#mc9b7777a7d" y="864.009331"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="836.873424" xlink:href="#mc9b7777a7d" y="864.025767"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="923.834463" xlink:href="#mc9b7777a7d" y="864.179979"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1010.795502" xlink:href="#mc9b7777a7d" y="864.18095"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1097.756541" xlink:href="#mc9b7777a7d" y="864.180769"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1184.71758" xlink:href="#mc9b7777a7d" y="864.176712"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1271.678619" xlink:href="#mc9b7777a7d" y="852.525037"/>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1358.639658" xlink:href="#mc9b7777a7d" y="213.524338"/>
+ </g>
+ </g>
+ <g id="line2d_42">
+ <path clip-path="url(#p94371e9dc2)" d="M 141.185112 406.833728
+L 228.146151 406.096964
+L 315.10719 405.131781
+L 402.068229 404.938001
+L 489.029268 407.444677
+L 575.990307 414.056994
+L 662.951346 420.361906
+L 749.912385 419.748476
+L 836.873424 348.463325
+L 923.834463 73.490041
+L 1010.795502 309.723051
+L 1097.756541 459.777606
+L 1184.71758 405.396197
+L 1271.678619 398.605104
+L 1358.639658 730.095369
+" style="fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:2;"/>
+ <defs>
+ <path d="M 0 5
+C 1.326016 5 2.597899 4.473168 3.535534 3.535534
+C 4.473168 2.597899 5 1.326016 5 0
+C 5 -1.326016 4.473168 -2.597899 3.535534 -3.535534
+C 2.597899 -4.473168 1.326016 -5 0 -5
+C -1.326016 -5 -2.597899 -4.473168 -3.535534 -3.535534
+C -4.473168 -2.597899 -5 -1.326016 -5 0
+C -5 1.326016 -4.473168 2.597899 -3.535534 3.535534
+C -2.597899 4.473168 -1.326016 5 0 5
+z
+" id="m23e02272bc" style="stroke:#ff7f0e;"/>
+ </defs>
+ <g clip-path="url(#p94371e9dc2)">
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="141.185112" xlink:href="#m23e02272bc" y="406.833728"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="228.146151" xlink:href="#m23e02272bc" y="406.096964"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="315.10719" xlink:href="#m23e02272bc" y="405.131781"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="402.068229" xlink:href="#m23e02272bc" y="404.938001"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="489.029268" xlink:href="#m23e02272bc" y="407.444677"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="575.990307" xlink:href="#m23e02272bc" y="414.056994"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="662.951346" xlink:href="#m23e02272bc" y="420.361906"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="749.912385" xlink:href="#m23e02272bc" y="419.748476"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="836.873424" xlink:href="#m23e02272bc" y="348.463325"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="923.834463" xlink:href="#m23e02272bc" y="73.490041"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1010.795502" xlink:href="#m23e02272bc" y="309.723051"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1097.756541" xlink:href="#m23e02272bc" y="459.777606"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1184.71758" xlink:href="#m23e02272bc" y="405.396197"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1271.678619" xlink:href="#m23e02272bc" y="398.605104"/>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1358.639658" xlink:href="#m23e02272bc" y="730.095369"/>
+ </g>
+ </g>
+ <g id="line2d_43">
+ <path clip-path="url(#p94371e9dc2)" d="M 141.185112 404.025334
+L 228.146151 404.761294
+L 315.10719 405.731735
+L 402.068229 405.922171
+L 489.029268 403.380288
+L 575.990307 396.696279
+L 662.951346 390.307617
+L 749.912385 390.854648
+L 836.873424 462.123362
+L 923.834463 736.942435
+L 1010.795502 500.708453
+L 1097.756541 350.654079
+L 1184.71758 405.039545
+L 1271.678619 423.482313
+L 1358.639658 730.992748
+" style="fill:none;stroke:#2ca02c;stroke-linecap:square;stroke-width:2;"/>
+ <defs>
+ <path d="M 0 5
+C 1.326016 5 2.597899 4.473168 3.535534 3.535534
+C 4.473168 2.597899 5 1.326016 5 0
+C 5 -1.326016 4.473168 -2.597899 3.535534 -3.535534
+C 2.597899 -4.473168 1.326016 -5 0 -5
+C -1.326016 -5 -2.597899 -4.473168 -3.535534 -3.535534
+C -4.473168 -2.597899 -5 -1.326016 -5 0
+C -5 1.326016 -4.473168 2.597899 -3.535534 3.535534
+C -2.597899 4.473168 -1.326016 5 0 5
+z
+" id="m10d8549d92" style="stroke:#2ca02c;"/>
+ </defs>
+ <g clip-path="url(#p94371e9dc2)">
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="141.185112" xlink:href="#m10d8549d92" y="404.025334"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="228.146151" xlink:href="#m10d8549d92" y="404.761294"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="315.10719" xlink:href="#m10d8549d92" y="405.731735"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="402.068229" xlink:href="#m10d8549d92" y="405.922171"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="489.029268" xlink:href="#m10d8549d92" y="403.380288"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="575.990307" xlink:href="#m10d8549d92" y="396.696279"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="662.951346" xlink:href="#m10d8549d92" y="390.307617"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="749.912385" xlink:href="#m10d8549d92" y="390.854648"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="836.873424" xlink:href="#m10d8549d92" y="462.123362"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="923.834463" xlink:href="#m10d8549d92" y="736.942435"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1010.795502" xlink:href="#m10d8549d92" y="500.708453"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1097.756541" xlink:href="#m10d8549d92" y="350.654079"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1184.71758" xlink:href="#m10d8549d92" y="405.039545"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1271.678619" xlink:href="#m10d8549d92" y="423.482313"/>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1358.639658" xlink:href="#m10d8549d92" y="730.992748"/>
+ </g>
+ </g>
+ <g id="patch_3">
+ <path d="M 80.312385 903.715495
+L 80.312385 33.955495
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:3;"/>
+ </g>
+ <g id="patch_4">
+ <path d="M 1419.512385 903.715495
+L 1419.512385 33.955495
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:3;"/>
+ </g>
+ <g id="patch_5">
+ <path d="M 80.312385 903.715495
+L 1419.512385 903.715495
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:3;"/>
+ </g>
+ <g id="patch_6">
+ <path d="M 80.312385 33.955495
+L 1419.512385 33.955495
+" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:3;"/>
+ </g>
+ <g id="text_23">
+ <!-- Data generated by: linear -->
+ <g transform="translate(595.947281 27.955495)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 333 4352
+L 333 4185
+C 774 4185 845 4185 845 3898
+L 845 453
+C 845 166 774 166 333 166
+L 333 0
+L 2368 0
+C 3398 0 4224 943 4224 2140
+C 4224 3344 3411 4352 2368 4352
+L 333 4352
+z
+M 1523 166
+C 1267 166 1254 198 1254 414
+L 1254 3936
+C 1254 4153 1267 4185 1523 4185
+L 2240 4185
+C 2771 4185 3750 3873 3750 2140
+C 3750 1242 3488 879 3366 707
+C 3213 510 2848 166 2240 166
+L 1523 166
+z
+" id="CMR17-44" transform="scale(0.015625)"/>
+ <path d="M 1869 4345
+L 1869 4179
+C 2246 4179 2304 4141 2304 3843
+L 2304 2371
+C 2278 2403 2016 2816 1498 2816
+C 845 2816 211 2228 211 1376
+C 211 529 806 -64 1434 -64
+C 1978 -64 2259 361 2291 406
+L 2291 -64
+L 3066 -13
+L 3066 154
+C 2688 154 2630 193 2630 503
+L 2630 4416
+L 1869 4345
+z
+M 2291 762
+C 2291 568 2176 393 2029 264
+C 1811 70 1594 38 1472 38
+C 1286 38 621 135 621 1369
+C 621 2636 1363 2713 1530 2713
+C 1824 2713 2061 2545 2208 2313
+C 2291 2177 2291 2157 2291 2041
+L 2291 762
+z
+" id="CMR17-64" transform="scale(0.015625)"/>
+ <path d="M 960 4416
+L 198 4345
+L 198 4179
+C 576 4179 634 4141 634 3843
+L 634 -13
+L 749 -13
+L 934 445
+C 1120 141 1395 -64 1766 -64
+C 2406 -64 3053 503 3053 1382
+C 3053 2209 2477 2816 1830 2816
+C 1434 2816 1152 2603 960 2351
+L 960 4416
+z
+M 973 2022
+C 973 2138 973 2157 1062 2293
+C 1312 2681 1670 2713 1792 2713
+C 1984 2713 2643 2610 2643 1388
+C 2643 109 1888 38 1734 38
+C 1536 38 1248 115 1043 490
+C 973 613 973 626 973 742
+L 973 2022
+z
+" id="CMR17-62" transform="scale(0.015625)"/>
+ <path d="M 2496 2183
+C 2656 2579 2944 2585 3034 2585
+L 3034 2752
+C 2912 2745 2752 2739 2630 2739
+C 2496 2739 2285 2739 2157 2752
+L 2157 2585
+C 2400 2566 2406 2384 2406 2332
+C 2406 2268 2394 2235 2362 2158
+L 1664 409
+L 902 2300
+C 870 2378 870 2423 870 2430
+C 870 2572 1018 2585 1171 2585
+L 1171 2752
+C 1018 2739 742 2739 582 2739
+C 410 2739 205 2739 64 2752
+L 64 2585
+C 410 2585 448 2553 531 2345
+L 1485 -31
+C 1197 -795 1030 -1242 627 -1242
+C 557 -1242 397 -1223 282 -1106
+C 429 -1093 493 -1002 493 -892
+C 493 -782 416 -685 288 -685
+C 147 -685 77 -782 77 -899
+C 77 -1158 339 -1344 627 -1344
+C 998 -1344 1229 -983 1357 -659
+L 2496 2183
+z
+" id="CMR17-79" transform="scale(0.015625)"/>
+ <path d="M 1062 2489
+C 1062 2649 934 2752 800 2752
+C 672 2752 538 2649 538 2489
+C 538 2329 666 2227 800 2227
+C 928 2227 1062 2329 1062 2489
+z
+M 1062 262
+C 1062 422 934 524 800 524
+C 672 524 538 422 538 262
+C 538 102 666 0 800 0
+C 928 0 1062 102 1062 262
+z
+" id="CMR17-3a" transform="scale(0.015625)"/>
+ <path d="M 979 4416
+L 218 4345
+L 218 4179
+C 595 4179 653 4141 653 3835
+L 653 439
+C 653 198 627 166 218 166
+L 218 0
+C 371 12 653 12 813 12
+C 979 12 1261 12 1414 0
+L 1414 166
+C 1005 166 979 191 979 439
+L 979 4416
+z
+" id="CMR17-6c" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-44"/>
+ <use transform="translate(70.393556 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(116.084033 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(151.364801 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(227.131244 0)scale(0.996264)" xlink:href="#CMR17-67"/>
+ <use transform="translate(272.821721 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(313.307382 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(364.202752 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(404.688412 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ <use transform="translate(439.96918 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(485.659657 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(520.940425 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(561.426085 0)scale(0.996264)" xlink:href="#CMR17-64"/>
+ <use transform="translate(642.397421 0)scale(0.996264)" xlink:href="#CMR17-62"/>
+ <use transform="translate(690.690337 0)scale(0.996264)" xlink:href="#CMR17-79"/>
+ <use transform="translate(738.983253 0)scale(0.996264)" xlink:href="#CMR17-3a"/>
+ <use transform="translate(804.339972 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(829.211031 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(854.082089 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(904.977459 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(945.463119 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(991.153596 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ <g id="legend_1">
+ <g id="patch_7">
+ <path d="M 1165.006183 183.395846
+L 1398.512385 183.395846
+Q 1404.512385 183.395846 1404.512385 177.395846
+L 1404.512385 54.955495
+Q 1404.512385 48.955495 1398.512385 48.955495
+L 1165.006183 48.955495
+Q 1159.006183 48.955495 1159.006183 54.955495
+L 1159.006183 177.395846
+Q 1159.006183 183.395846 1165.006183 183.395846
+z
+" style="fill:#ffffff;opacity:0.8;stroke:#cccccc;stroke-linejoin:miter;"/>
+ </g>
+ <g id="line2d_44">
+ <path d="M 1171.006183 71.455495
+L 1231.006183 71.455495
+" style="fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:2;"/>
+ </g>
+ <g id="line2d_45">
+ <g>
+ <use style="fill:#1f77b4;stroke:#1f77b4;" x="1201.006183" xlink:href="#mc9b7777a7d" y="71.455495"/>
+ </g>
+ </g>
+ <g id="text_24">
+ <!-- linear -->
+ <g transform="translate(1255.006183 81.955495)scale(0.3 -0.3)">
+ <use transform="scale(0.996264)" xlink:href="#CMR17-6c"/>
+ <use transform="translate(24.871058 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(49.742117 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(100.637487 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(141.123147 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(186.813624 0)scale(0.996264)" xlink:href="#CMR17-72"/>
+ </g>
+ </g>
+ <g id="line2d_46">
+ <path d="M 1171.006183 113.268946
+L 1231.006183 113.268946
+" style="fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:2;"/>
+ </g>
+ <g id="line2d_47">
+ <g>
+ <use style="fill:#ff7f0e;stroke:#ff7f0e;" x="1201.006183" xlink:href="#m23e02272bc" y="113.268946"/>
+ </g>
+ </g>
+ <g id="text_25">
+ <!-- exponential -->
+ <g transform="translate(1255.006183 123.768946)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 1664 1491
+C 1856 1740 2074 2022 2253 2233
+C 2464 2476 2707 2579 2989 2585
+L 2989 2752
+C 2880 2745 2656 2739 2541 2739
+C 2368 2739 2170 2739 2022 2752
+L 2022 2585
+C 2112 2572 2163 2508 2163 2419
+C 2163 2304 2099 2233 2067 2188
+L 1594 1587
+L 1030 2323
+C 973 2393 973 2406 973 2438
+C 973 2515 1037 2579 1146 2585
+L 1146 2752
+C 992 2739 717 2739 557 2739
+C 384 2739 179 2739 38 2752
+L 38 2585
+C 384 2585 461 2560 614 2368
+L 1350 1414
+C 1363 1401 1395 1363 1395 1344
+C 1395 1318 838 633 768 544
+C 480 198 179 172 6 166
+L 6 0
+C 115 6 339 12 454 12
+C 582 12 864 12 979 0
+L 979 166
+C 941 172 838 185 838 332
+C 838 448 890 518 947 595
+L 1478 1248
+L 2035 524
+C 2086 454 2163 358 2163 313
+C 2163 224 2086 172 1984 166
+L 1984 0
+C 2138 12 2413 12 2573 12
+C 2746 12 2950 12 3091 0
+L 3091 166
+C 2771 166 2675 179 2522 377
+L 1664 1491
+z
+" id="CMR17-78" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-78"/>
+ <use transform="translate(88.778576 0)scale(0.996264)" xlink:href="#CMR17-70"/>
+ <use transform="translate(142.276385 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(187.966862 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(238.862232 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ <use transform="translate(279.347892 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(327.640808 0)scale(0.996264)" xlink:href="#CMR17-74"/>
+ <use transform="translate(362.921576 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(387.792634 0)scale(0.996264)" xlink:href="#CMR17-61"/>
+ <use transform="translate(433.483111 0)scale(0.996264)" xlink:href="#CMR17-6c"/>
+ </g>
+ </g>
+ <g id="line2d_48">
+ <path d="M 1171.006183 155.082396
+L 1231.006183 155.082396
+" style="fill:none;stroke:#2ca02c;stroke-linecap:square;stroke-width:2;"/>
+ </g>
+ <g id="line2d_49">
+ <g>
+ <use style="fill:#2ca02c;stroke:#2ca02c;" x="1201.006183" xlink:href="#m10d8549d92" y="155.082396"/>
+ </g>
+ </g>
+ <g id="text_26">
+ <!-- cosine -->
+ <g transform="translate(1255.006183 165.582396)scale(0.3 -0.3)">
+ <defs>
+ <path d="M 2234 2240
+C 2112 2240 1933 2240 1933 2015
+C 1933 1836 2080 1785 2163 1785
+C 2208 1785 2394 1804 2394 2028
+C 2394 2476 1958 2816 1466 2816
+C 787 2816 211 2201 211 1379
+C 211 521 813 -64 1466 -64
+C 2259 -64 2458 676 2458 747
+C 2458 773 2451 792 2406 792
+C 2362 792 2355 786 2330 702
+C 2163 180 1798 51 1523 51
+C 1114 51 621 431 621 1385
+C 621 2358 1094 2700 1472 2700
+C 1722 2700 2093 2582 2234 2240
+z
+" id="CMR17-63" transform="scale(0.015625)"/>
+ </defs>
+ <use transform="scale(0.996264)" xlink:href="#CMR17-63"/>
+ <use transform="translate(40.48566 0)scale(0.996264)" xlink:href="#CMR17-6f"/>
+ <use transform="translate(86.176138 0)scale(0.996264)" xlink:href="#CMR17-73"/>
+ <use transform="translate(121.977475 0)scale(0.996264)" xlink:href="#CMR17-69"/>
+ <use transform="translate(146.848534 0)scale(0.996264)" xlink:href="#CMR17-6e"/>
+ <use transform="translate(197.743903 0)scale(0.996264)" xlink:href="#CMR17-65"/>
+ </g>
+ </g>
+ </g>
+ </g>
+ </g>
+ <defs>
+ <clipPath id="p94371e9dc2">
+ <rect height="869.76" width="1339.2" x="80.312385" y="33.955495"/>
+ </clipPath>
+ </defs>
+</svg>
diff --git a/examples/model-comparison/reference/model_weights_ref.pkl b/examples/model-comparison/reference/model_weights_ref.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..99e095e5466bef739e82ab1609012ba4bacb0e30
Binary files /dev/null and b/examples/model-comparison/reference/model_weights_ref.pkl differ
diff --git a/examples/model-comparison/test_model_comparison.py b/examples/model-comparison/test_model_comparison.py
new file mode 100644
index 0000000000000000000000000000000000000000..d5f523871d99b5115437c2f66e8a1ce2a845f503
--- /dev/null
+++ b/examples/model-comparison/test_model_comparison.py
@@ -0,0 +1,279 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+This test shows the multi-model comparison.
+
+You will see how to:
+ Perform a multi-model comparison
+
+Author: Farid Mohammadi, M.Sc.
+E-Mail: farid.mohammadi@iws.uni-stuttgart.de
+Department of Hydromechanics and Modelling of Hydrosystems (LH2)
+Institute for Modelling Hydraulic and Environmental Systems (IWS),
+University of Stuttgart, www.iws.uni-stuttgart.de/lh2/
+Pfaffenwaldring 61
+70569 Stuttgart
+
+Created on Wed Oct 10 2021
+
+"""
+
+import numpy as np
+import scipy.io as io
+import pandas as pd
+import joblib
+import sys
+sys.path.append("../../src/bayesvalidrox/")
+
+from pylink.pylink import PyLinkForwardModel
+from surrogate_models.inputs import Input
+from surrogate_models.surrogate_models import MetaModel
+from post_processing.post_processing import PostProcessing
+from bayes_inference.bayes_inference import BayesInference
+from bayes_inference.bayes_model_comparison import BayesModelComparison
+from bayes_inference.discrepancy import Discrepancy
+
+if __name__ == "__main__":
+
+ # Read data
+ sigma = 0.6
+ data = {
+ 'x [m]': np.linspace(0.25, 4.75, 15),
+ 'Z': io.loadmat('data/synth_data.mat')['d'].reshape(1, -1)[0]
+ }
+
+ # =====================================================
+ # ============ COMPUTATIONAL MODELS ================
+ # =====================================================
+ # Define the models options
+ # ---------- Linear model -------------
+ myL2Model = PyLinkForwardModel()
+
+ myL2Model.link_type = 'Function'
+ myL2Model.py_file = 'L2_model'
+ myL2Model.name = 'linear'
+ myL2Model.Output.names = ['Z']
+ myL2Model.observations = data
+
+ # -- Nonlinear exponential model -------
+ myNL2Model = PyLinkForwardModel()
+
+ myNL2Model.link_type = 'Function'
+ myNL2Model.py_file = 'NL2_model'
+ myNL2Model.name = 'exponential'
+ myNL2Model.Output.names = ['Z']
+ myNL2Model.observations = data
+
+ # ------ Nonlinear cosine model ---------
+ # Data generating process
+ myNL4Model = PyLinkForwardModel()
+
+ myNL4Model.link_type = 'Function'
+ myNL4Model.py_file = 'NL4_model'
+ myNL4Model.name = 'cosine'
+ myNL4Model.Output.names = ['Z']
+ myNL4Model.observations = data
+
+ # =====================================================
+ # ========= PROBABILISTIC INPUT MODEL ==============
+ # =====================================================
+ # Define model inputs
+ n_sample = 10000
+ # ---------- Linear model -------------
+ L2_Inputs = Input()
+ L2_prior_mean = np.array([1, 0])
+ L2_prior_cov = np.array(
+ [[0.04, -0.007],
+ [-0.007, 0.04]]
+ )
+ L2_input_params = np.random.multivariate_normal(
+ L2_prior_mean, L2_prior_cov, size=n_sample
+ )
+
+ for i in range(L2_input_params.shape[1]):
+ L2_Inputs.add_marginals()
+ L2_Inputs.Marginals[i].name = f'$X_{i+1}$'
+ L2_Inputs.Marginals[i].input_data = L2_input_params[:, i]
+
+ # ------ Nonlinear exponential model ---------
+ NL2_Inputs = Input()
+ NL2_prior_mean = np.array([0.4, -0.3])
+ NL2_prior_cov = np.array(
+ [[0.003, -0.0001],
+ [-0.0001, 0.03]]
+ )
+ NL2_input_params = np.random.multivariate_normal(
+ NL2_prior_mean, NL2_prior_cov, size=n_sample
+ )
+
+ for i in range(NL2_input_params.shape[1]):
+ NL2_Inputs.add_marginals()
+ NL2_Inputs.Marginals[i].name = f'$X_{i+1}$'
+ NL2_Inputs.Marginals[i].input_data = NL2_input_params[:, i]
+
+ # ------ Nonlinear cosine model ---------
+ NL4_Inputs = Input()
+ NL4_prior_mean = np.array([2.6, 0.5, -2.8, 2.3])
+ NL4_prior_cov = np.array(
+ [[0.46, -0.07, 0.24, -0.14],
+ [-0.07, 0.04, -0.05, 0.02],
+ [0.24, -0.05, 0.30, -0.16],
+ [-0.14, 0.02, -0.16, 0.30]]
+ )
+ NL4_input_params = np.random.multivariate_normal(
+ NL4_prior_mean, NL4_prior_cov, size=n_sample
+ )
+
+ for i in range(NL4_input_params.shape[1]):
+ NL4_Inputs.add_marginals()
+ NL4_Inputs.Marginals[i].name = f'$X_{i+1}$'
+ NL4_Inputs.Marginals[i].input_data = NL4_input_params[:, i]
+
+ # =====================================================
+ # ====== POLYNOMIAL CHAOS EXPANSION METAMODELS ======
+ # =====================================================
+ # Define meta-model options
+ # ---------- Linear model -------------
+ L2_MetaModelOpts = MetaModel(L2_Inputs)
+
+ # Select if you want to preserve the spatial/temporal depencencies
+ # L2_MetaModelOpts.dim_red_method = 'PCA'
+ # MetaModelOpts.var_pca_threshold = 99.999
+ # MetaModelOpts.n_pca_components = 10 #3, 10
+
+ # Select your metamodel method
+ L2_MetaModelOpts.meta_model_type = 'aPCE'
+
+ # ------------------------------------------------
+ # ------------- PCE Specification ----------------
+ # ------------------------------------------------
+ # Select the sparse least-square minimization method for
+ # the PCE coefficients calculation:
+ # 1)OLS: Ordinary Least Square 2)BRR: Bayesian Ridge Regression
+ # 3)LARS: Least angle regression 4)ARD: Bayesian ARD Regression
+ # 5)FastARD: Fast Bayesian ARD Regression
+ # 6)VBL: Variational Bayesian Learning
+ # 7)EBL: Emperical Bayesian Learning
+ L2_MetaModelOpts.pce_reg_method = 'FastARD'
+
+ # Specify the max degree to be compared by the adaptive algorithm:
+ # The degree with the lowest Leave-One-Out cross-validation (LOO)
+ # error (or the highest score=1-LOO)estimator is chosen as the final
+ # metamodel. pce_deg accepts degree as a scalar or a range.
+ L2_MetaModelOpts.pce_deg = np.arange(1, 12)
+
+ # q-quasi-norm 0<q<1 (default=1)
+ L2_MetaModelOpts.pce_q_norm = 1.0
+
+ # ------------------------------------------------
+ # ------ Experimental Design Configuration -------
+ # ------------------------------------------------
+ L2_MetaModelOpts.add_ExpDesign()
+
+ # One-shot (normal) or Sequential Adaptive (sequential) Design
+ L2_MetaModelOpts.ExpDesign.method = 'normal'
+ L2_MetaModelOpts.ExpDesign.n_init_samples = 100
+
+ # Sampling methods
+ # 1) random 2) latin_hypercube 3) sobol 4) halton 5) hammersley
+ # 6) chebyshev(FT) 7) grid(FT) 8)user
+ L2_MetaModelOpts.ExpDesign.sampling_method = 'latin_hypercube'
+
+ # ------ Nonlinear cosine model ---------
+ NL2_MetaModelOpts = L2_MetaModelOpts.copy_meta_model_opts(NL2_Inputs)
+
+ # ------ Nonlinear cosine model ---------
+ NL4_MetaModelOpts = L2_MetaModelOpts.copy_meta_model_opts(NL4_Inputs)
+
+ # >>>>>> Train the Surrogates <<<<<<<<<<<
+ L2_MetaModel = L2_MetaModelOpts.create_metamodel(myL2Model)
+ NL2_MetaModel = NL2_MetaModelOpts.create_metamodel(myNL2Model)
+ NL4_MetaModel = NL4_MetaModelOpts.create_metamodel(myNL4Model)
+
+ # =====================================================
+ # ========= POST PROCESSING OF METAMODELS ===========
+ # =====================================================
+ # ---------- Linear model -------------
+ L2_PostPCE = PostProcessing(L2_MetaModel, name=myL2Model.name)
+
+ # Plot to check validation visually.
+ L2_PostPCE.valid_metamodel(n_samples=3)
+
+ # Plot moments
+ L2_PostPCE.plot_moments()
+
+ # Compute and print RMSE error
+ L2_PostPCE.check_accuracy(n_samples=3000)
+
+ # Plot the sobol indices
+ sobol_cell, total_sobol = L2_PostPCE.sobol_indices()
+
+ # ---------- Linear model -------------
+ NL2_PostPCE = PostProcessing(NL2_MetaModel, name=myNL2Model.name)
+
+ # Plot to check validation visually.
+ NL2_PostPCE.valid_metamodel(n_samples=3)
+
+ # Plot moments
+ NL2_PostPCE.plot_moments()
+
+ # Compute and print RMSE error
+ NL2_PostPCE.check_accuracy(n_samples=3000)
+
+ # Plot the sobol indices
+ sobol_cell, total_sobol = NL2_PostPCE.sobol_indices()
+
+ # ------ Nonlinear cosine model ---------
+ NL4_PostPCE = PostProcessing(NL4_MetaModel, name=myNL4Model.name)
+
+ # Plot to check validation visually.
+ NL4_PostPCE.valid_metamodel(n_samples=3)
+
+ # Plot moments
+ NL4_PostPCE.plot_moments()
+
+ # Compute and print RMSE error
+ NL4_PostPCE.check_accuracy(n_samples=3000)
+
+ # Plot the sobol indices
+ sobol_cell, total_sobol = NL4_PostPCE.sobol_indices()
+
+ # =====================================================
+ # ========= BAYESIAN MULTIMODEL COMPARISON ===========
+ # =====================================================
+ # ----- Define the discrepancy model -------
+ sigma = np.ones(15) * np.array(sigma).flatten()
+ DiscrepancyOpts = Discrepancy('')
+ DiscrepancyOpts.type = 'Gaussian'
+ DiscrepancyOpts.parameters = pd.DataFrame(sigma**2, columns=['Z'])
+
+ # ----- Define the options model -------
+ meta_models = {
+ "linear": L2_MetaModel,
+ "exponential": NL4_MetaModel,
+ "cosine": NL4_MetaModel
+ }
+
+ # BME Bootstrap optuions
+ opts_bootstrap = {
+ "bootstrap": True,
+ "n_samples": 10000,
+ "Discrepancy": DiscrepancyOpts,
+ "emulator": True,
+ "plot_post_pred": False
+ }
+
+ # Run model comparison
+ BayesOpts = BayesModelComparison(
+ justifiability=True,
+ n_bootstarp=1000,
+ just_n_meas=2
+ )
+ output_dict = BayesOpts.create_model_comparison(
+ meta_models,
+ opts_bootstrap
+ )
+
+ # Save the results
+ with open('model_comparison_output_dict.pkl', 'wb') as output:
+ joblib.dump(output_dict, output, 2)
diff --git a/examples/pollution/data/MeasuredData_valid.npy b/examples/pollution/data/MeasuredData_valid.npy
new file mode 100644
index 0000000000000000000000000000000000000000..e9fdbcaf5e6bee00097d2a8c8d5e32a210c439b9
Binary files /dev/null and b/examples/pollution/data/MeasuredData_valid.npy differ
diff --git a/examples/pollution/pollution.py b/examples/pollution/pollution.py
index f05c2d45ed99083fd6ceed9fb671957d6351120b..09a5ffff46daab07f9629213f37ceb071feafcff 100644
--- a/examples/pollution/pollution.py
+++ b/examples/pollution/pollution.py
@@ -9,94 +9,96 @@ import numpy as np
import scipy.stats as stats
import seaborn as sns
+
def pollution(xx, s=None, t=None):
"""
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- %
- % ENVIRONMENTAL MODEL FUNCTION
- %
- % Authors: Sonja Surjanovic, Simon Fraser University
- % Derek Bingham, Simon Fraser University
- % Questions/Comments: Please email Derek Bingham at dbingham@stat.sfu.ca.
- %
- % Copyright 2013. Derek Bingham, Simon Fraser University.
- %
- % THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY
- % FOR THE USE OF THIS SOFTWARE. If software is modified to produce
- % derivative works, such modified software should be clearly marked.
- % Additionally, this program is free software; you can redistribute it
- % and/or modify it under the terms of the GNU General Public License as
- % published by the Free Software Foundation; version 2.0 of the License.
- % Accordingly, this program is distributed in the hope that it will be
- % useful, but WITHOUT ANY WARRANTY; without even the implied warranty
- % of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
- % General Public License for more details.
- %
- % For function details and reference information, see:
- % http://www.sfu.ca/~ssurjano/
- %
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- %
- % OUTPUT AND INPUTS:
- %
- % y = row vector of scaled concentrations of the pollutant at the
- % space-time vectors (s, t)
- % Its structure is:
- % y(s_1, t_1), y(s_1, t_2), ..., y(s_1, t_dt), y(s_2, t_1), ...,
- % y(s_2,t_dt), ..., y(s_ds, t_1), ..., y(s_ds, t_dt)
- % xx = [M, D, L, tau]
- % s = vector of locations (optional), with default value
- % [0.5, 1, 1.5, 2, 2.5]
- % t = vector of times (optional), with default value
- % [0.3, 0.6, ..., 50.7, 60]
- %
- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
- """
- MCSize = xx.shape[0]
-
+ ENVIRONMENTAL MODEL FUNCTION
+
+ Authors: Sonja Surjanovic, Simon Fraser University
+ Derek Bingham, Simon Fraser University
+ Questions/Comments: Please email Derek Bingham at dbingham@stat.sfu.ca.
+
+ Copyright 2013. Derek Bingham, Simon Fraser University.
+
+ THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY
+ FOR THE USE OF THIS SOFTWARE. If software is modified to produce
+ derivative works, such modified software should be clearly marked.
+ Additionally, this program is free software; you can redistribute it
+ and/or modify it under the terms of the GNU General Public License as
+ published by the Free Software Foundation; version 2.0 of the License.
+ Accordingly, this program is distributed in the hope that it will be
+ useful, but WITHOUT ANY WARRANTY; without even the implied warranty
+ of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ General Public License for more details.
+
+ For function details and reference information, see:
+ http://www.sfu.ca/~ssurjano/
+
+ Parameters
+ ----------
+ xx : array of shape (n_samples, n_params)
+ [M, D, L, tau].
+ s : array, optional
+ Vector of locations. The default is None, which mean np.array([3.0]).
+ t : array, optional
+ Vector of time steps. The default is None, which means
+ [40+5*i for i in range(21)].
+
+ Returns
+ -------
+ output : TYPE
+ DESCRIPTION.
+ """
+ n_samples = xx.shape[0]
- if t is None: t = np.array([40+5*i for i in range(21)])
+ if t is None:
+ t = np.array([40+5*i for i in range(21)])
- if s is None: s = np.array([3.0])#np.array([0.5, 1, 1.5, 2, 2.5])
+ if s is None:
+ s = np.array([3.0]) # np.array([0.5, 1, 1.5, 2, 2.5])
- ds = len(s);
- dt = len(t);
- dY = ds * dt;
+ ds = len(s)
+ dt = len(t)
+ dY = ds * dt
Y = np.zeros((ds, dt))
- Output = np.zeros((MCSize, dY))
+ output = np.zeros((n_samples, dY))
- for idx in range(MCSize):
+ for idx in range(n_samples):
M, D, L, tau = xx[idx]
# Create matrix Y, where each row corresponds to si and each column
# corresponds to tj.
- for ii in range(ds): #1:ds)
+ for ii in range(ds):
si = s[ii]
- for jj in range(dt): #1:dt)
+ for jj in range(dt):
tj = t[jj]
term1a = M / np.sqrt(4*np.pi*D*tj)
term1b = np.exp(-si**2 / (4*D*tj))
- term1 = term1a * term1b;
+ term1 = term1a * term1b
- term2 = 0;
+ term2 = 0
if tau < tj:
term2a = M / np.sqrt(4*np.pi*D*(tj-tau))
term2b = np.exp(-(si-L)**2 / (4*D*(tj-tau)))
- term2 = term2a * term2b;
+ term2 = term2a * term2b
C = term1 + term2
Y[ii, jj] = np.sqrt(4*np.pi) * C
# Convert the matrix into a vector (by rows).
Yrow = Y.T
- Output[idx] = Yrow.flatten('F')
+ output[idx] = Yrow.flatten('F')
+
+ # Prepare output dict using standard bayesvalidrox format
+ output = {'x_values': t, 'C': output[0]}
+
+ return output
- return np.vstack((t, Output))
if __name__ == "__main__":
- MCSize = 500000 #500000
+ MCSize = 500000
validSize = 100
ndim = 4
sigma_noise = 0.15
@@ -106,41 +108,49 @@ if __name__ == "__main__":
# ----------------------- Synthetic data generation -----------------------
# -------------------------------------------------------------------------
MAP = np.array([[10, 0.07, 1.0, 30.16]])
- outputMAP = Pollution(MAP)
+ output_MAP = pollution(MAP, s=np.array([3])) # Calibration
+ # output_MAP = pollution(MAP, s=np.array([6])) # Validation
- synthethicData = outputMAP[1] + np.random.normal(0,sigma_noise,outputMAP[1].shape)
+ # Noise
+ noise = np.random.normal(0, sigma_noise, len(output_MAP['C']))
+ synthethicData = output_MAP['C'] + noise
import matplotlib.pyplot as plt
- plt.scatter(outputMAP[0], synthethicData, ls='-', marker='*', label='Obs. Data')
+ plt.scatter(output_MAP['C'], synthethicData,
+ ls='-', marker='*', label='Obs. Data')
plt.legend(loc='best')
plt.show()
- np.save("data/MeasuredData.npy", synthethicData)
+ np.save("data/MeasuredData_valid.npy", synthethicData)
# -------------------------------------------------------------------------
# ---------------------- Generate Prior distribution ----------------------
# -------------------------------------------------------------------------
- validSet = np.zeros((validSize, ndim))
+ valid_set = np.zeros((validSize, ndim))
xx = np.zeros((MCSize, ndim))
params = [(7, 13), (0.02, 0.12), (0.01, 3), (30.01, 30.295)]
for idxDim in range(ndim):
lower, upper = params[idxDim]
- xx[:,idxDim] = stats.uniform(loc=lower, scale=upper-lower).rvs(size=MCSize)
- validSet[:,idxDim] = stats.uniform(loc=lower, scale=upper-lower).rvs(size=validSize)
+ xx[:, idxDim] = stats.uniform(loc=lower, scale=upper-lower).rvs(
+ size=MCSize)
+ valid_set[:, idxDim] = stats.uniform(loc=lower, scale=upper-lower).rvs(
+ size=validSize)
# run validation set
- validOutputs = Pollution(validSet)
+ valid_outputs = pollution(valid_set)
# -------------------------------------------------------------------------
# ------------- BME and Kullback-Leibler Divergence -----------------------
# -------------------------------------------------------------------------
- Outputs = pollution(xx)
+ outputs = pollution(xx)
cov_matrix = np.diag(np.repeat(sigma_error**2, synthethicData.shape))
- Likelihoods = stats.multivariate_normal.pdf(Outputs[1:], mean=synthethicData, cov=cov_matrix)
+ Likelihoods = stats.multivariate_normal.pdf(
+ outputs[1:], mean=synthethicData, cov=cov_matrix)
- sns.kdeplot(np.log(Likelihoods[Likelihoods>0]), shade=True, color="g", label='Ref. Likelihood')
+ sns.kdeplot(np.log(Likelihoods[Likelihoods > 0]),
+ shade=True, color="g", label='Ref. Likelihood')
normLikelihood = Likelihoods / np.nanmax(Likelihoods)
# Random numbers between 0 and 1
@@ -151,26 +161,24 @@ if __name__ == "__main__":
# Prior-based estimation of BME
logBME = np.log(np.nanmean(Likelihoods))
- print('\nThe Naive MC-Estimation of BME is %.5f.'%(logBME))
+ print(f'\nThe Naive MC-Estimation of BME is {logBME:.5f}.')
# Posterior-based expectation of likelihoods
postExpLikelihoods = np.mean(np.log(Likelihoods[accepted]))
# Calculate Kullback-Leibler Divergence
KLD = postExpLikelihoods - logBME
- print("The Kullback-Leibler divergence estimation is %.5f."%KLD)
+ print("The Kullback-Leibler divergence estimation is {KLD:.5f}.")
# -------------------------------------------------------------------------
# ----------------- Save the arrays as .npy files -------------------------
# -------------------------------------------------------------------------
np.save("data/ParamSets.npy", xx)
np.save("data/refBME_KLD.npy", (logBME, KLD))
- np.save("data/mean.npy", np.mean(Outputs[1:],axis=0))
- np.save("data/std.npy", np.std(Outputs[1:],axis=0))
+ np.save("data/mean.npy", np.mean(outputs['C'], axis=0))
+ np.save("data/std.npy", np.std(outputs['C'], axis=0))
np.save("data/validLikelihoods.npy", Likelihoods)
# Save validation set
- np.save("data/validSet.npy", validSet)
- np.save("data/validSetOutput.npy", validOutputs[1:])
-
-
+ np.save("data/validSet.npy", valid_set)
+ np.save("data/validSetOutput.npy", valid_outputs['C'])
diff --git a/examples/pollution/test_pollution.py b/examples/pollution/test_pollution.py
index 14ad29f11a7657c3866008c58fee4de29cd131c8..f2de52e2caf0196d8d05a2035950e2f28ff8fc70 100644
--- a/examples/pollution/test_pollution.py
+++ b/examples/pollution/test_pollution.py
@@ -21,7 +21,6 @@ import numpy as np
import pandas as pd
import joblib
-
# import bayesvalidrox
# Add BayesValidRox path
import sys
@@ -88,13 +87,13 @@ if __name__ == "__main__":
# time of the second spill
Inputs.add_marginals()
Inputs.Marginals[3].name = '$\\tau$'
- Inputs.Marginals[3].dist_type = 'unif'
+ Inputs.Marginals[3].dist_type = 'uniform'
Inputs.Marginals[3].parameters = [30.01, 30.295]
# =====================================================
# ====== POLYNOMIAL CHAOS EXPANSION METAMODELS ======
# =====================================================
- MetaModelOpts = MetaModel(Inputs)
+ MetaModelOpts = MetaModel(Inputs, Model)
# Select if you want to preserve the spatial/temporal depencencies
# MetaModelOpts.dim_red_method = 'PCA'
@@ -114,15 +113,22 @@ if __name__ == "__main__":
# 1)OLS: Ordinary Least Square 2)BRR: Bayesian Ridge Regression
# 3)LARS: Least angle regression 4)ARD: Bayesian ARD Regression
# 5)FastARD: Fast Bayesian ARD Regression
- # 6)VBL: Variational Bayesian Learning
- # 7)EBL: Emperical Bayesian Learning
- MetaModelOpts.pce_reg_method = 'FastARD'
+ # 6)BCS: Bayesian Compressive Sensing
+ # 7)OMP: Orthogonal Matching Pursuit
+ # 8)VBL: Variational Bayesian Learning
+ # 9)EBL: Emperical Bayesian Learning
+ MetaModelOpts.pce_reg_method = 'BCS'
+
+ # Bootstraping
+ # 1) normal 2) fast
+ MetaModelOpts.bootstrap_method = 'fast'
+ MetaModelOpts.n_bootstrap_itrs = 100
# Specify the max degree to be compared by the adaptive algorithm:
# The degree with the lowest Leave-One-Out cross-validation (LOO)
# error (or the highest score=1-LOO)estimator is chosen as the final
# metamodel. pce_deg accepts degree as a scalar or a range.
- MetaModelOpts.pce_deg = np.arange(6)
+ MetaModelOpts.pce_deg = 8
# q-quasi-norm 0<q<1 (default=1)
# MetaModelOpts.pce_q_norm = 0.75
@@ -135,7 +141,7 @@ if __name__ == "__main__":
# One-shot (normal) or Sequential Adaptive (sequential) Design
MetaModelOpts.ExpDesign.method = 'normal'
- MetaModelOpts.ExpDesign.n_init_samples = 150 # 5*ndim
+ MetaModelOpts.ExpDesign.n_init_samples = 150
# Sampling methods
# 1) random 2) latin_hypercube 3) sobol 4) halton 5) hammersley 6) korobov
@@ -209,7 +215,7 @@ if __name__ == "__main__":
# >>>>>>>>>>>>>>>>>>>>>> Build Surrogate <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
# Adaptive sparse arbitrary polynomial chaos expansion
- PCEModel = MetaModelOpts.create_metamodel(Model)
+ PCEModel = MetaModelOpts.create_metamodel()
# =====================================================
# ========= POST PROCESSING OF METAMODELS ===========
@@ -229,7 +235,7 @@ if __name__ == "__main__":
# Plot the sobol indices
if MetaModelOpts.meta_model_type != 'GPE':
- sobol_cell, total_sobol = PostPCE.sobol_indices()
+ total_sobol = PostPCE.sobol_indices()
# Compute and print RMSE error
valid_out_dict = dict()
diff --git a/examples/pollution/test_valid_pollution.py b/examples/pollution/test_valid_pollution.py
new file mode 100644
index 0000000000000000000000000000000000000000..e2aacbe5d2186c38287e552ae588332150dd519b
--- /dev/null
+++ b/examples/pollution/test_valid_pollution.py
@@ -0,0 +1,302 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+This test shows a surrogate-assisted Bayesian calibration of a time dependent
+ pollution function. Here, the noise will be jointly inferred with the input
+ parameters.
+
+Author: Farid Mohammadi, M.Sc.
+E-Mail: farid.mohammadi@iws.uni-stuttgart.de
+Department of Hydromechanics and Modelling of Hydrosystems (LH2)
+Institute for Modelling Hydraulic and Environmental Systems (IWS), University
+of Stuttgart, www.iws.uni-stuttgart.de/lh2/
+Pfaffenwaldring 61
+70569 Stuttgart
+
+Created on Fri Aug 9 2019
+
+"""
+
+import numpy as np
+import joblib
+
+# import bayesvalidrox
+# Add BayesValidRox path
+import sys
+sys.path.append("../../src/bayesvalidrox/")
+
+from pylink.pylink import PyLinkForwardModel
+from surrogate_models.inputs import Input
+from surrogate_models.surrogate_models import MetaModel
+from post_processing.post_processing import PostProcessing
+from bayes_inference.bayes_inference import BayesInference
+from bayes_inference.discrepancy import Discrepancy
+
+if __name__ == "__main__":
+
+ # =====================================================
+ # ============= COMPUTATIONAL MODEL ================
+ # =====================================================
+ Model = PyLinkForwardModel()
+
+ # Define model options
+ Model.link_type = 'Function'
+ Model.py_file = 'pollution'
+ Model.name = 'pollution'
+
+ Model.Output.names = ['C']
+
+ # Synthetic data for Bayesian inversion.
+ # MAP = (10, 0.07, 1.0, 30.16)
+ Model.observations = {}
+ Model.observations['Time [s]'] = [40+5*i for i in range(21)]
+ Model.observations['C'] = np.load("data/MeasuredData.npy")
+
+ # For Checking with the MonteCarlo refrence
+ Model.mc_reference = {}
+ Model.mc_reference['Time [s]'] = [40+5*i for i in range(21)]
+ Model.mc_reference['mean'] = np.load("data/mean.npy")
+ Model.mc_reference['std'] = np.load("data/std.npy")
+
+ # =====================================================
+ # ========= PROBABILISTIC INPUT MODEL ==============
+ # =====================================================
+ # Define the uncertain parameters with their mean and
+ # standard deviation
+ Inputs = Input()
+
+ # mass of pollutant spilled at each location
+ Inputs.add_marginals()
+ Inputs.Marginals[0].name = 'M'
+ Inputs.Marginals[0].dist_type = 'uniform'
+ Inputs.Marginals[0].parameters = [7, 13]
+
+ # diffusion rate in the channel
+ Inputs.add_marginals()
+ Inputs.Marginals[1].name = 'D'
+ Inputs.Marginals[1].dist_type = 'uniform'
+ Inputs.Marginals[1].parameters = [0.02, 0.12]
+
+ # location of the second spill
+ Inputs.add_marginals()
+ Inputs.Marginals[2].name = 'L'
+ Inputs.Marginals[2].dist_type = 'uniform'
+ Inputs.Marginals[2].parameters = [0.01, 3]
+
+ # time of the second spill
+ Inputs.add_marginals()
+ Inputs.Marginals[3].name = '$\\tau$'
+ Inputs.Marginals[3].dist_type = 'uniform'
+ Inputs.Marginals[3].parameters = [30.01, 30.295]
+
+ # =====================================================
+ # ====== POLYNOMIAL CHAOS EXPANSION METAMODELS ======
+ # =====================================================
+ MetaModelOpts = MetaModel(Inputs, Model)
+
+ # Select if you want to preserve the spatial/temporal depencencies
+ MetaModelOpts.dim_red_method = 'PCA'
+ MetaModelOpts.var_pca_threshold = 99.999
+ # MetaModelOpts.n_pca_components = 5
+
+ # Select your metamodel method
+ # 1) PCE (Polynomial Chaos Expansion) 2) aPCE (arbitrary PCE)
+ # 3) GPE (Gaussian Process Emulator)
+ MetaModelOpts.meta_model_type = 'aPCE'
+
+ # ------------------------------------------------
+ # ------------- PCE Specification ----------------
+ # ------------------------------------------------
+ # Select the sparse least-square minimization method for
+ # the PCE coefficients calculation:
+ # 1)OLS: Ordinary Least Square 2)BRR: Bayesian Ridge Regression
+ # 3)LARS: Least angle regression 4)ARD: Bayesian ARD Regression
+ # 5)FastARD: Fast Bayesian ARD Regression
+ # 6)BCS: Bayesian Compressive Sensing
+ # 7)OMP: Orthogonal Matching Pursuit
+ # 8)VBL: Variational Bayesian Learning
+ # 9)EBL: Emperical Bayesian Learning
+ MetaModelOpts.pce_reg_method = 'FastARD'
+
+ # Bootstraping
+ # 1) normal 2) fast
+ MetaModelOpts.bootstrap_method = 'fast'
+ MetaModelOpts.n_bootstrap_itrs = 100
+
+ # Specify the max degree to be compared by the adaptive algorithm:
+ # The degree with the lowest Leave-One-Out cross-validation (LOO)
+ # error (or the highest score=1-LOO)estimator is chosen as the final
+ # metamodel. pce_deg accepts degree as a scalar or a range.
+ MetaModelOpts.pce_deg = 6
+
+ # q-quasi-norm 0<q<1 (default=1)
+ # MetaModelOpts.pce_q_norm = 0.75
+
+ # Print summary of the regression results
+ # MetaModelOpts.verbose = True
+
+ # ------ Experimental Design --------
+ MetaModelOpts.add_ExpDesign()
+
+ # One-shot (normal) or Sequential Adaptive (sequential) Design
+ MetaModelOpts.ExpDesign.method = 'normal'
+ MetaModelOpts.ExpDesign.n_init_samples = 150
+
+ # Sampling methods
+ # 1) random 2) latin_hypercube 3) sobol 4) halton 5) hammersley 6) korobov
+ # 7) chebyshev(FT) 8) grid(FT) 9) nested_grid(FT) 10)user
+ MetaModelOpts.ExpDesign.sampling_method = 'latin_hypercube'
+
+ # Provide the experimental design object with a hdf5 file
+ # MetaModelOpts.ExpDesign.hdf5_file = 'ExpDesign_AnalyticFunc.hdf5'
+
+ # >>>>>>>>>>>>>>>>>>>>>> Build Surrogate <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
+ # Adaptive sparse arbitrary polynomial chaos expansion
+ PCEModel = MetaModelOpts.create_metamodel()
+
+ # Save PCE models
+ with open(f"PCEModel_{Model.name}.pkl", "wb") as output:
+ joblib.dump(PCEModel, output, 2)
+
+ # Load the objects
+ # with open(f"PCEModel_{Model.name}.pkl", "rb") as input:
+ # PCEModel = joblib.load(input)
+
+ # =====================================================
+ # ========= POST PROCESSING OF METAMODELS ===========
+ # =====================================================
+ PostPCE = PostProcessing(PCEModel)
+
+ # Plot to check validation visually.
+ PostPCE.valid_metamodel(n_samples=3)
+
+ # Compute the moments and compare with the Monte-Carlo reference
+ PostPCE.plot_moments()
+
+ # Plot the sobol indices
+ if MetaModelOpts.meta_model_type != 'GPE':
+ total_sobol = PostPCE.sobol_indices()
+
+ # Compute and print RMSE error
+ valid_samples = np.load("data/validSet.npy")
+ valid_out_dict = dict()
+ valid_out_dict['Time [s]'] = [40+5*i for i in range(21)]
+ valid_out_dict['C'] = np.load("data/validSetOutput.npy")
+ PostPCE.check_accuracy(samples=valid_samples,
+ outputs=valid_out_dict)
+
+ # =====================================================
+ # ======== BAYESIAN INFERENCE (CALIBRATION) ==========
+ # =====================================================
+ BayesOpts = BayesInference(PCEModel)
+ BayesOpts.emulator = True
+
+ # Select the inference method
+ BayesOpts.inference_method = "MCMC"
+ # Set the MCMC parameters
+ BayesOpts.mcmc_params = {
+ 'n_steps': 1e5,
+ 'n_walkers': 30,
+ 'multiprocessing': False,
+ 'verbose': False
+ }
+
+ BayesOpts.plot_post_pred = True
+
+ # ----- Define the discrepancy model -------
+ # Let us infer the sigma2
+ DiscOutputOpts = Input()
+ # # OutputName = 'Z'
+ DiscOutputOpts.add_marginals()
+ DiscOutputOpts.Marginals[0].name = '$\\sigma^2_{\\epsilon}$'
+ DiscOutputOpts.Marginals[0].dist_type = 'uniform'
+ DiscOutputOpts.Marginals[0].parameters = [0.0, 0.1]
+ BayesOpts.Discrepancy = Discrepancy(DiscOutputOpts)
+
+ # Start the inference
+ BayesCalib = BayesOpts.create_inference()
+
+ # Save class objects
+ with open(f'Bayes_{Model.name}.pkl', 'wb') as output:
+ joblib.dump(BayesCalib, output, 2)
+
+ # Load the objects
+ # with open(f"Bayes_{Model.name}.pkl", "rb") as input:
+ # BayesCalib = joblib.load(input)
+
+ # =====================================================
+ # =========== BAYESIAN MODEL VALIDATION ==============
+ # =====================================================
+ # ------- Model definition --------
+ ValidModel = PyLinkForwardModel()
+
+ # Define model options
+ ValidModel.link_type = 'Function'
+ ValidModel.py_file = 'pollution'
+ ValidModel.func_args = {'s': np.array([6])}
+ ValidModel.name = 'pollution-valid'
+
+ ValidModel.Output.names = ['C']
+
+ # Synthetic data for Bayesian inversion.
+ # MAP = (10, 0.07, 1.0, 30.16)
+ ValidModel.observations_valid = {}
+ ValidModel.observations_valid['Time [s]'] = [40+5*i for i in range(21)]
+ ValidModel.observations_valid['C'] = np.load("data/MeasuredData_valid.npy")
+
+ # ------- Input definition --------
+ ValidInputs = Input()
+
+ ValidInputs.add_marginals()
+ ValidInputs.Marginals[0].name = "M"
+ ValidInputs.Marginals[0].input_data = BayesCalib.posterior_df['M']
+
+ ValidInputs.add_marginals()
+ ValidInputs.Marginals[1].name = "D"
+ ValidInputs.Marginals[1].input_data = BayesCalib.posterior_df['D']
+
+ ValidInputs.add_marginals()
+ ValidInputs.Marginals[2].name = "L"
+ ValidInputs.Marginals[2].input_data = BayesCalib.posterior_df['L']
+
+ ValidInputs.add_marginals()
+ ValidInputs.Marginals[3].name = "$\\tau$"
+ ValidInputs.Marginals[3].input_data = BayesCalib.posterior_df['$\\tau$']
+
+ MetaModelOpts_valid = MetaModelOpts.copy_meta_model_opts(
+ ValidInputs, ValidModel)
+ ValidMetaModel = MetaModelOpts_valid.create_metamodel()
+
+ # Save PCE models
+ with open(f"PCEModel_{ValidModel.name}.pkl", "wb") as output:
+ joblib.dump(ValidMetaModel, output, 2)
+
+ # Load the objects
+ # with open(f"PCEModel_{ValidModel.name}.pkl", "rb") as input:
+ # ValidPCEModel = joblib.load(input)
+
+ # ------- Baysian inference definition --------
+ BayesOptsValid = BayesInference(ValidMetaModel)
+
+ BayesOptsValid.name = "Valid"
+ BayesOptsValid.emulator = True
+
+ # Bootstrap for BME and BF
+ BayesOptsValid.bootstrap = True
+ BayesOptsValid.n_bootstrap_itrs = 10
+
+ # ----- Define the discrepancy model -------
+ DiscrepancyOpts = Discrepancy("")
+ DiscrepancyOpts.type = "Gaussian"
+ DiscrepancyOpts.parameters = {
+ "C": np.ones(21) * np.mean(
+ BayesCalib.posterior_df['$\\sigma^2_{\\epsilon}$'].values)
+ }
+ BayesOptsValid.Discrepancy = DiscrepancyOpts
+
+ # ----- Strat Bayesian inference -------
+ BayesValid = BayesOptsValid.create_inference()
+
+ # Save class objects
+ with open(f"Bayes_{ValidModel.name}.pkl", "wb") as output:
+ joblib.dump(BayesValid, output, 2)
diff --git a/setup.cfg b/setup.cfg
index 4c713af00ba223618b8a8d734c5645056c8ebfc7..78940cfb54d78b867d8d4447ee25162b9adfed91 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -1,6 +1,6 @@
[metadata]
name = bayesvalidrox
-version = 0.0.4
+version = 0.0.5
author = Farid Mohammadi
author_email = farid.mohammadi@iws.uni-stuttgart.de
description = An open-source, object-oriented Python package for surrogate-assisted Bayesain Validation of computational models.
@@ -25,6 +25,7 @@ install_requires =
joblib==1.0.1
matplotlib==3.4.2
seaborn==0.11.1
+ scipy==1.7.3
scikit-learn==0.24.2
tqdm==4.61.1
chaospy==4.3.3
diff --git a/src/bayesvalidrox/__init__.py b/src/bayesvalidrox/__init__.py
index 20621c5144fb115aff93bc525979970b51e371ab..55c14687472fe6ff00a2438f31b9ba9ecd2992cd 100644
--- a/src/bayesvalidrox/__init__.py
+++ b/src/bayesvalidrox/__init__.py
@@ -1,11 +1,13 @@
# -*- coding: utf-8 -*-
-__version__ = "0.0.4"
+__version__ = "0.0.5"
from .pylink.pylink import PyLinkForwardModel
from .surrogate_models.surrogate_models import MetaModel
+from .surrogate_models.meta_model_engine import MetaModelEngine
from .surrogate_models.inputs import Input
from .post_processing.post_processing import PostProcessing
from .bayes_inference.bayes_inference import BayesInference
+from .bayes_inference.bayes_model_comparison import BayesModelComparison
from .bayes_inference.discrepancy import Discrepancy
__all__ = [
@@ -14,6 +16,8 @@ __all__ = [
"Input",
"Discrepancy",
"MetaModel",
+ "MetaModelEngine",
"PostProcessing",
- "BayesInference"
+ "BayesInference",
+ "BayesModelComparison"
]
diff --git a/src/bayesvalidrox/bayes_inference/bayes_inference.py b/src/bayesvalidrox/bayes_inference/bayes_inference.py
index 0b9965edf4507cfba385abdd3d89c4201e7a37f0..c8073ba76ebeb3249646e17b7f395f8a2472e2f6 100644
--- a/src/bayesvalidrox/bayes_inference/bayes_inference.py
+++ b/src/bayesvalidrox/bayes_inference/bayes_inference.py
@@ -8,7 +8,7 @@ import pandas as pd
from tqdm import tqdm
from scipy import stats
import scipy.linalg as spla
-
+import joblib
import seaborn as sns
import corner
import h5py
@@ -101,6 +101,8 @@ class BayesInference:
User defined perturbed data. The default is `[]`.
bootstrap_noise : float, optional
A noise level to perturb the data set. The default is `0.05`.
+ just_analysis : bool, optional
+ Justifiability analysis. The default is False.
valid_metrics : list, optional
List of the validation metrics. The following metrics are supported:
@@ -119,19 +121,19 @@ class BayesInference:
is `'mean'`.
corner_title_fmt : str, optional
Title format for the posterior distribution plot with python
- package `corner`. The default is `'.3e'`.
+ package `corner`. The default is `'.2e'`.
"""
def __init__(self, MetaModel, discrepancy=None, emulator=True,
name='Calib', bootstrap=False, req_outputs=None,
- selected_indices=None, samples=None, n_samples=500000,
+ selected_indices=None, samples=None, n_samples=100000,
measured_data=None, inference_method='rejection',
mcmc_params=None, bayes_loocv=False, n_bootstrap_itrs=1,
- perturbed_data=[], bootstrap_noise=0.05,
+ perturbed_data=[], bootstrap_noise=0.05, just_analysis=False,
valid_metrics=['BME'], plot_post_pred=True,
plot_map_pred=False, max_a_posteriori='mean',
- corner_title_fmt='.3e'):
+ corner_title_fmt='.2e'):
self.MetaModel = MetaModel
self.Discrepancy = discrepancy
@@ -149,6 +151,7 @@ class BayesInference:
self.bayes_loocv = bayes_loocv
self.n_bootstrap_itrs = n_bootstrap_itrs
self.bootstrap_noise = bootstrap_noise
+ self.just_analysis = just_analysis
self.valid_metrics = valid_metrics
self.plot_post_pred = plot_post_pred
self.plot_map_pred = plot_map_pred
@@ -261,7 +264,7 @@ class BayesInference:
pass
# ---------------- Bootstrap & TOM --------------------
- if self.bootstrap or self.bayes_loocv:
+ if self.bootstrap or self.bayes_loocv or self.just_analysis:
if len(self.perturbed_data) == 0:
# zero mean noise Adding some noise to the observation function
self.perturbed_data = self._perturb_data(
@@ -322,6 +325,7 @@ class BayesInference:
self.__model_prior_pred = self._eval_model(
samples=self.samples, key='PriorPred'
)
+ surrError = None
# Start the likelihood-BME computations for the perturbed data
for itr_idx, data in tqdm(
@@ -337,12 +341,12 @@ class BayesInference:
model_evals = self.__model_prior_pred
# Leave one out
- if self.bayes_loocv:
+ if self.bayes_loocv or self.just_analysis:
self.selected_indices = np.nonzero(data)[0]
# Prepare data dataframe
nobs = list(self.measured_data.count().values[1:])
- numbers = list(map(sum, zip([0] + nobs, nobs)))
+ numbers = list(np.cumsum(nobs))
indices = list(zip([0] + numbers, numbers))
data_dict = {
output_names[i]: data[j:k] for i, (j, k) in
@@ -369,11 +373,11 @@ class BayesInference:
dtype=np.float128))
)
- # TODO: BME correction when using Emulator
- # if self.emulator:
- # BME_Corr[itr_idx] = self._corr_factor_BME(
- # data, total_sigma2, posterior
- # )
+ # BME correction when using Emulator
+ if self.emulator:
+ BME_Corr[itr_idx] = self.__corr_factor_BME(
+ data_dict, total_sigma2, log_BME[itr_idx]
+ )
# Rejection Step
if 'kld' in list(map(str.lower, self.valid_metrics)) and\
@@ -418,8 +422,10 @@ class BayesInference:
# BME (log), KLD, infEntropy (Size: 1,n_bootstrap_itr)
self.log_BME = log_BME
- # TODO: BMECorrFactor (log) (Size: 1,n_bootstrap_itr)
- # if self.emulator: self.BMECorrFactor = BME_Corr
+
+ # BMECorrFactor (log) (Size: 1,n_bootstrap_itr)
+ if self.emulator:
+ self.log_BME_corr_factor = BME_Corr
if 'kld' in list(map(str.lower, self.valid_metrics)):
self.KLD = KLD
@@ -428,7 +434,7 @@ class BayesInference:
# BME = BME + BMECorrFactor
if self.emulator:
- self.log_BME = self.log_BME # + self.BMECorrFactor
+ self.log_BME += self.log_BME_corr_factor
# ---------------- Parameter Bayesian inference ----------------
if self.inference_method.lower() == 'mcmc':
@@ -520,6 +526,7 @@ class BayesInference:
for xi in range(yi):
ax = axes[yi, xi]
ax.set_xlim(MetaModel.bound_tuples[xi])
+ plt.close()
# Turn off gridlines
for ax in figPosterior.axes:
@@ -539,7 +546,8 @@ class BayesInference:
self._plot_max_a_posteriori()
# -------- Plot log_BME dist --------
- if self.bootstrap and self.n_bootstrap_itrs > 1:
+ if self.bootstrap:
+
# Computing the TOM performance
self.log_BME_tom = stats.chi2.rvs(
self.n_tot_measurement, size=self.log_BME.shape[0]
@@ -677,8 +685,8 @@ class BayesInference:
Returns
-------
- model_outputs : TYPE
- DESCRIPTION.
+ model_outputs : dict
+ Model outputs.
"""
MetaModel = self.MetaModel
@@ -813,17 +821,22 @@ class BayesInference:
# Add the std of the PCE is chosen as emulator.
if self.emulator:
if std is not None:
- std_pce = std[out]
- else:
- std_pce = np.mean(
- self._std_pce_prior_pred[out], axis=0)
- # Expected value of variance (Assump: i.i.d stds)
- tot_sigma2s += std_pce**2
+ tot_sigma2s += std[out]**2
+
+ # Covariance Matrix
+ covMatrix = np.diag(tot_sigma2s)
+
+ # Select the data points to compare
+ try:
+ indices = self.selected_indices[out]
+ except:
+ indices = list(range(nout))
+ covMatrix = np.diag(covMatrix[indices, indices])
# If sigma2 is not given, use given total_sigma2s
if sigma2 is None:
logLik += stats.multivariate_normal.logpdf(
- outputs[out], data, np.diag(tot_sigma2s))
+ outputs[out][:, indices], data[indices], covMatrix)
continue
# Loop over each run/sample and calculate logLikelihood
@@ -858,11 +871,11 @@ class BayesInference:
# covMatrix = np.diag(sigma2 * total_sigma2s)
# Select the data points to compare
- if self.selected_indices is not None:
+ try:
indices = self.selected_indices[out]
- covMatrix = np.diag(covMatrix[indices, indices])
- else:
+ except:
indices = list(range(nout))
+ covMatrix = np.diag(covMatrix[indices, indices])
# Compute loglikelihood
logliks[s_idx] = self._logpdf(
@@ -873,7 +886,7 @@ class BayesInference:
return logLik
# -------------------------------------------------------------------------
- def _corr_factor_BME(self, Data, total_sigma2s, posterior):
+ def _corr_factor_BME_old(self, Data, total_sigma2s, posterior):
"""
Calculates the correction factor for BMEs.
"""
@@ -916,78 +929,90 @@ class BayesInference:
TotalPCEstdOutputRS= np.concatenate([stdOutputRS[x] for x in stdOutputRS], 1)
logweight = 0
- for i,sample in enumerate(Samples):
+ for i, sample in enumerate(Samples):
# Compute likelilhood output vs RS
covMatrix = np.diag(TotalPCEstdOutputRS[i]**2)
logLik = self._logpdf(TotalOutputs[i], TotalPCEOutputs[i], covMatrix)
# Compute posterior likelihood of the collocation points
- logpostLik = np.log(postDist.pdf(sample[:,None]))[0]
+ logpostLik = np.log(postDist.pdf(sample[:, None]))[0]
if logpostLik != -np.inf:
logweight += logLik + logpostLik
return logweight
-# # Initialization
-# covMatrix=np.zeros((NofMeasurements, NofMeasurements), float)
-# BME_RM_Model_Weight = np.zeros((SampleSize))
-# BME_RM_Data_Weight = np.zeros((SampleSize))
-# BME_Corr = np.zeros((1))
-
-
-# # Deviation Computations
-# RM_Model_Deviation = np.zeros((SampleSize,NofMeasurements))
-# RM_Data_Deviation = np.zeros((SampleSize,NofMeasurements))
-# for i in range(SampleSize):
-# RM_Model_Deviation[i] = TotalOutputs[i][:NofMeasurements] - TotalPCEOutputs[i, :] # Reduce model- Full Model
-# RM_Data_Deviation[i] = Observations - TotalPCEOutputs[i, :] # Reduce model- Measurement Data
-
-
-# # Initialization of Co-Variance Matrix
-# # For BME_RM_ModelWeight
-# if NofMeasurements == 1:
-# RM_Model_Error = np.zeros((NofMeasurements, NofMeasurements), float)
-# np.fill_diagonal(RM_Model_Error, np.cov(RM_Model_Deviation.T))
-# else:
-# RM_Model_Error = np.cov(RM_Model_Deviation.T)
-
-
-# # Computation of Weight according to the deviations
-# for i in range(SampleSize):
-# # For BME_RM_DataWeight
-# try:
-# var = Sigma[i]
-# if len(var)==1:
-# np.fill_diagonal(covMatrix, var)
-# else:
-# row,col = np.diag_indices(covMatrix.shape[0])
-# covMatrix[row,col] = np.hstack((np.repeat(var[0], NofMeasurements*0.5),np.repeat(var[1], NofMeasurements*0.5)))
-
-# except:
-# var = Sigma
-
-# np.fill_diagonal(covMatrix, var)
-
-# # Add the std of the PCE is emulator is chosen.
-# # if self.emulator:
-# # covMatrix_PCE = np.zeros((NofMeasurements, NofMeasurements), float)
-# # stdPCE = np.empty((SampleSize,0))
-# # for outputType in OutputType:
-# # stdPCE = np.hstack((stdPCE, stdOutputRS[outputType]))
-# #
-# # stdPCE = np.mean(stdPCE, axis=1)
-# # np.fill_diagonal(covMatrix_PCE, stdPCE**2)
-# #
-# # covMatrix = covMatrix + covMatrix_PCE
-
-# # Calculate the denomitor
-# denom1 = (np.sqrt(2*np.pi)) ** NofMeasurements
-# denom2 = (((2*np.pi)**(NofMeasurements/2)) * np.sqrt(np.linalg.det(covMatrix)))
-
-# BME_RM_Model_Weight[i] = (np.exp(-0.5 * np.dot(np.dot(RM_Model_Deviation[i], np.linalg.pinv(RM_Model_Error)), RM_Model_Deviation[i])))/denom1
-# BME_RM_Data_Weight[i] = (np.exp(-0.5 * np.dot(np.dot(RM_Data_Deviation[i], np.linalg.pinv(covMatrix)), RM_Data_Deviation[i][:,np.newaxis])))/denom2
-
-# for i in range(SampleSize):
-# BME_Corr[0] += BME_RM_Model_Weight[i] * BME_RM_Data_Weight[i] / np.nansum(BME_RM_Data_Weight)
-
-# return np.log(BME_Corr[0])
+
+ # -------------------------------------------------------------------------
+ def __corr_factor_BME(self, obs_data, total_sigma2s, logBME):
+ """
+ Calculates the correction factor for BMEs.
+ """
+ MetaModel = self.MetaModel
+ samples = MetaModel.ExpDesign.X
+ model_outputs = MetaModel.ExpDesign.Y
+ Model = MetaModel.ModelObj
+ n_samples = samples.shape[0]
+
+ # Extract the requested model outputs for likelihood calulation
+ output_names = Model.Output.names
+
+ # Evaluate MetaModel on the experimental design and ValidSet
+ OutputRS, stdOutputRS = MetaModel.eval_metamodel(samples=samples)
+
+ logLik_data = np.zeros((n_samples))
+ logLik_model = np.zeros((n_samples))
+ # Loop over the outputs
+ for idx, out in enumerate(output_names):
+
+ # (Meta)Model Output
+ nsamples, nout = model_outputs[out].shape
+
+ # Prepare data and remove NaN
+ try:
+ data = obs_data[out].values[~np.isnan(obs_data[out])]
+ except AttributeError:
+ data = obs_data[out][~np.isnan(obs_data[out])]
+
+ # Prepare sigma2s
+ non_nan_indices = ~np.isnan(total_sigma2s[out])
+ tot_sigma2s = total_sigma2s[out][non_nan_indices][:nout]
+
+ # Covariance Matrix
+ covMatrix_data = np.diag(tot_sigma2s)
+
+ for i, sample in enumerate(samples):
+
+ # Simulation run
+ y_m = model_outputs[out][i]
+
+ # Surrogate prediction
+ y_m_hat = OutputRS[out][i]
+
+ # CovMatrix with the surrogate error
+ covMatrix = np.eye(len(y_m)) * 1/(2*np.pi)
+
+ # Select the data points to compare
+ try:
+ indices = self.selected_indices[out]
+ except:
+ indices = list(range(nout))
+ covMatrix = np.diag(covMatrix[indices, indices])
+ covMatrix_data = np.diag(covMatrix_data[indices, indices])
+
+ # Compute likelilhood output vs data
+ logLik_data[i] += self._logpdf(
+ y_m_hat[indices], data[indices],
+ covMatrix_data
+ )
+
+ # Compute likelilhood output vs surrogate
+ logLik_model[i] += self._logpdf(
+ y_m_hat[indices], y_m[indices],
+ covMatrix
+ )
+
+ # Weight
+ logLik_data -= logBME
+ weights = np.mean(np.exp(logLik_model+logLik_data))
+
+ return np.log(weights)
# -------------------------------------------------------------------------
def _rejection_sampling(self):
@@ -1015,7 +1040,12 @@ class BayesInference:
samples = np.hstack((samples, sigma2_prior))
# Take the first column of Likelihoods (Observation data without noise)
- likelihoods = np.exp(self.log_likes[:, 0], dtype=np.float128)
+ if self.just_analysis or self.bayes_loocv:
+ index = self.n_tot_measurement-1
+ likelihoods = np.exp(self.log_likes[:, index], dtype=np.float128)
+ else:
+ likelihoods = np.exp(self.log_likes[:, 0], dtype=np.float128)
+
n_samples = len(likelihoods)
norm_ikelihoods = likelihoods / np.max(likelihoods)
@@ -1354,7 +1384,8 @@ class BayesInference:
x_key = list(self.measured_data)[0]
# --- Read prior and posterior predictive ---
- if self.inference_method == 'rejection':
+ if self.inference_method == 'rejection' and \
+ self.name.lower() != 'valid':
# --- Prior ---
# Load posterior predictive
f = h5py.File(
@@ -1438,9 +1469,9 @@ class BayesInference:
f = h5py.File(f"{out_dir}/postPredictive.hdf5", 'r+')
try:
- x_coords = np.array(f["x_values"])
- except:
x_coords = np.array(f[f"x_values/{out_name}"])
+ except:
+ x_coords = np.array(f["x_values"])
mu = np.mean(np.array(f[f"EDY/{out_name}"]), axis=0)
std = np.std(np.array(f[f"EDY/{out_name}"]), axis=0)
diff --git a/src/bayesvalidrox/bayes_inference/bayes_model_comparison.py b/src/bayesvalidrox/bayes_inference/bayes_model_comparison.py
new file mode 100644
index 0000000000000000000000000000000000000000..4d829f61a118b7544298e469272fc05f5d0f0b7f
--- /dev/null
+++ b/src/bayesvalidrox/bayes_inference/bayes_model_comparison.py
@@ -0,0 +1,658 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Sat Aug 24 16:04:06 2019
+
+@author: farid
+"""
+import numpy as np
+import os
+from scipy import stats
+import seaborn as sns
+import matplotlib.patches as patches
+import matplotlib.colors as mcolors
+import matplotlib.pylab as plt
+from .bayes_inference import BayesInference
+
+# Load the mplstyle
+plt.style.use(os.path.join(os.path.split(__file__)[0],
+ '../', 'bayesvalidrox.mplstyle'))
+
+
+class BayesModelComparison:
+ """
+ A class to perform Bayesian Analysis.
+
+
+ Attributes
+ ----------
+ justifiability : bool, optional
+ Whether to perform the justifiability analysis. The default is
+ `True`.
+ perturbed_data : array of shape (n_bootstrap_itrs, n_obs), optional
+ User defined perturbed data. The default is `None`.
+ n_bootstarp : int
+ Number of bootstrap iteration. The default is `1000`.
+ data_noise_level : float
+ A noise level to perturb the data set. The default is `0.01`.
+ just_n_meas : int
+ Number of measurements considered for visualization of the
+ justifiability results.
+
+ """
+
+ def __init__(self, justifiability=True, perturbed_data=None,
+ n_bootstarp=1000, data_noise_level=0.01, just_n_meas=2):
+
+ self.justifiability = justifiability
+ self.perturbed_data = perturbed_data
+ self.n_bootstarp = n_bootstarp
+ self.data_noise_level = data_noise_level
+ self.just_n_meas = just_n_meas
+
+ # --------------------------------------------------------------------------
+ def create_model_comparison(self, model_dict, opts_dict):
+ """
+ Starts the two-stage model comparison.
+ Stage I: Compare models using Bayes factors.
+ Stage II: Compare models via justifiability analysis.
+
+ Parameters
+ ----------
+ model_dict : dict
+ A dictionary including the metamodels.
+ opts_dict : dict
+ A dictionary given the `BayesInference` options.
+
+ Example:
+
+ >>> opts_bootstrap = {
+ "bootstrap": True,
+ "n_samples": 10000,
+ "Discrepancy": DiscrepancyOpts,
+ "emulator": True,
+ "plot_post_pred": True
+ }
+
+ Returns
+ -------
+ output : dict
+ A dictionary containing the objects and the model weights for the
+ comparison using Bayes factors and justifiability analysis.
+
+ """
+
+ # Bayes factor
+ bayes_dict_bf, model_weights_dict_bf = self.compare_models(
+ model_dict, opts_dict
+ )
+
+ output = {
+ 'Bayes objects BF': bayes_dict_bf,
+ 'Model weights BF': model_weights_dict_bf
+ }
+
+ # Justifiability analysis
+ if self.justifiability:
+ bayes_dict_ja, model_weights_dict_ja = self.compare_models(
+ model_dict, opts_dict, justifiability=True
+ )
+
+ output['Bayes objects JA'] = bayes_dict_ja
+ output['Model weights JA'] = model_weights_dict_ja
+
+ return output
+
+ # --------------------------------------------------------------------------
+ def compare_models(self, model_dict, opts_dict, justifiability=False):
+ """
+ Passes the options to instantiates the BayesInference class for each
+ model and passes the options from `opts_dict`. Then, it starts the
+ computations.
+ It also creates a folder and saves the diagrams, e.g., Bayes factor
+ plot, confusion matrix, etc.
+
+ Parameters
+ ----------
+ model_dict : dict
+ A dictionary including the metamodels.
+ opts_dict : dict
+ A dictionary given the `BayesInference` options.
+ justifiability : bool, optional
+ Whether to perform the justifiability analysis. The default is
+ `False`.
+
+ Returns
+ -------
+ bayes_dict : dict
+ A dictionary with `BayesInference` objects.
+ model_weights_dict : dict
+ A dictionary containing the model weights.
+
+ """
+
+ if not isinstance(model_dict, dict):
+ raise Exception("To run model comparsion, you need to pass a "
+ "dictionary of models.")
+
+ # Extract model names
+ self.model_names = [*model_dict]
+
+ # Compute total number of the measurement points
+ MetaModel = list(model_dict.items())[0][1]
+ MetaModel.ModelObj.read_observation()
+ self.n_meas = MetaModel.ModelObj.n_obs
+
+ # ----- Generate data -----
+ # Find n_bootstrap
+ if self.perturbed_data is None:
+ n_bootstarp = self.n_bootstarp
+ else:
+ n_bootstarp = self.perturbed_data.shape[0]
+
+ # Create dataset
+ justData = self.generate_dataset(
+ model_dict, justifiability, n_bootstarp=n_bootstarp)
+
+ # Run create Interface for each model
+ bayes_dict = {}
+ for model in model_dict.keys():
+ print("-"*20)
+ print("Bayesian inference of {}.\n".format(model))
+
+ BayesOpts = BayesInference(model_dict[model])
+
+ # Set BayesInference options
+ for key, value in opts_dict.items():
+ if key in BayesOpts.__dict__.keys():
+ if key == "Discrepancy" and isinstance(value, dict):
+ setattr(BayesOpts, key, value[model])
+ else:
+ setattr(BayesOpts, key, value)
+
+ # Pass justifiability data as perturbed data
+ BayesOpts.perturbed_data = justData
+ BayesOpts.just_analysis = justifiability
+
+ bayes_dict[model] = BayesOpts.create_inference()
+ print("-"*20)
+
+ # Compute model weights
+ BME_Dict = dict()
+ for modelName, bayesObj in bayes_dict.items():
+ BME_Dict[modelName] = np.exp(bayesObj.log_BME, dtype=np.float128)
+
+ # BME correction in BayesInference class
+ model_weights = self.cal_model_weight(
+ BME_Dict, justifiability, n_bootstarp=n_bootstarp)
+
+ # Plot model weights
+ if justifiability:
+ model_names = self.model_names
+ model_names.insert(0, 'Observation')
+
+ # Split the model weights and save in a dict
+ list_ModelWeights = np.split(
+ model_weights, model_weights.shape[1]/self.n_meas, axis=1)
+ model_weights_dict = {key: weights for key, weights in
+ zip(model_names, list_ModelWeights)}
+
+ self.plot_just_analysis(model_weights_dict)
+ else:
+ # Create box plot for model weights
+ self.plot_model_weights(model_weights, 'model_weights')
+
+ # Create kde plot for bayes factors
+ self.plot_bayes_factor(BME_Dict, 'kde_plot')
+
+ # Store model weights in a dict
+ model_weights_dict = {key: weights for key, weights in
+ zip(self.model_names, model_weights)}
+
+ return bayes_dict, model_weights_dict
+
+ # -------------------------------------------------------------------------
+ def generate_dataset(self, model_dict, justifiability=False,
+ n_bootstarp=1):
+ """
+ Generates the perturbed data set for the Bayes factor calculations and
+ the data set for the justifiability analysis.
+
+ Parameters
+ ----------
+ model_dict : dict
+ A dictionary including the metamodels.
+ bool, optional
+ Whether to perform the justifiability analysis. The default is
+ `False`.
+ n_bootstarp : int, optional
+ Number of bootstrap iterations. The default is `1`.
+
+ Returns
+ -------
+ all_just_data: array
+ Created data set.
+
+ """
+ # Compute some variables
+ all_just_data = []
+ metaModel = list(model_dict.items())[0][1]
+ out_names = metaModel.ModelObj.Output.names
+
+ # Perturb observations for Bayes Factor
+ if self.perturbed_data is None:
+ self.perturbed_data = self.__perturb_data(
+ metaModel.ModelObj.observations, out_names, n_bootstarp,
+ noise_level=self.data_noise_level)
+
+ # Only for Bayes Factor
+ if not justifiability:
+ return self.perturbed_data
+
+ # Evaluate metamodel
+ runs = {}
+ for key, metaModel in model_dict.items():
+ y_hat, _ = metaModel.eval_metamodel(nsamples=n_bootstarp)
+ runs[key] = y_hat
+
+ # Generate data
+ for i in range(n_bootstarp):
+ y_data = self.perturbed_data[i].reshape(1, -1)
+ justData = np.tril(np.repeat(y_data, y_data.shape[1], axis=0))
+ # Use surrogate runs for data-generating process
+ for key, metaModel in model_dict.items():
+ model_data = np.array(
+ [runs[key][out][i] for out in out_names]).reshape(y_data.shape)
+ justData = np.vstack((
+ justData,
+ np.tril(np.repeat(model_data, model_data.shape[1], axis=0))
+ ))
+ # Save in a list
+ all_just_data.append(justData)
+
+ # Squeeze the array
+ all_just_data = np.array(all_just_data).transpose(1, 0, 2).reshape(
+ -1, np.array(all_just_data).shape[2]
+ )
+
+ return all_just_data
+
+ # -------------------------------------------------------------------------
+ def __perturb_data(self, data, output_names, n_bootstrap, noise_level):
+ """
+ Returns an array with n_bootstrap_itrs rowsof perturbed data.
+ The first row includes the original observation data.
+ If `self.bayes_loocv` is True, a 2d-array will be returned with
+ repeated rows and zero diagonal entries.
+
+ Parameters
+ ----------
+ data : pandas DataFrame
+ Observation data.
+ output_names : list
+ List of the output names.
+
+ Returns
+ -------
+ final_data : array
+ Perturbed data set.
+
+ """
+ obs_data = data[output_names].values
+ n_measurement, n_outs = obs_data.shape
+ n_tot_measurement = obs_data[~np.isnan(obs_data)].shape[0]
+ final_data = np.zeros(
+ (n_bootstrap, n_tot_measurement)
+ )
+ final_data[0] = obs_data.T[~np.isnan(obs_data.T)]
+ for itrIdx in range(1, n_bootstrap):
+ data = np.zeros((n_measurement, n_outs))
+ for idx in range(len(output_names)):
+ std = np.nanstd(obs_data[:, idx])
+ if std == 0:
+ std = 0.001
+ noise = std * noise_level
+ data[:, idx] = np.add(
+ obs_data[:, idx],
+ np.random.normal(0, 1, obs_data.shape[0]) * noise,
+ )
+
+ final_data[itrIdx] = data.T[~np.isnan(data.T)]
+
+ return final_data
+
+ # -------------------------------------------------------------------------
+ def cal_model_weight(self, BME_Dict, justifiability=False, n_bootstarp=1):
+ """
+ Normalize the BME (Asumption: Model Prior weights are equal for models)
+
+ Parameters
+ ----------
+ BME_Dict : dict
+ A dictionary containing the BME values.
+
+ Returns
+ -------
+ model_weights : array
+ Model weights.
+
+ """
+ # Stack the BME values for all models
+ all_BME = np.vstack(list(BME_Dict.values()))
+
+ if justifiability:
+ # Compute expected log_BME for justifiabiliy analysis
+ all_BME = all_BME.reshape(
+ all_BME.shape[0], -1, n_bootstarp).mean(axis=2)
+
+ # Model weights
+ model_weights = np.divide(all_BME, np.nansum(all_BME, axis=0))
+
+ return model_weights
+
+ # -------------------------------------------------------------------------
+ def plot_just_analysis(self, model_weights_dict):
+ """
+ Visualizes the confusion matrix and the model wights for the
+ justifiability analysis.
+
+ Parameters
+ ----------
+ model_weights_dict : dict
+ Model weights.
+
+ Returns
+ -------
+ None.
+
+ """
+
+ directory = 'Outputs_Comparison/'
+ os.makedirs(directory, exist_ok=True)
+ Color = [*mcolors.TABLEAU_COLORS]
+ names = [*model_weights_dict]
+
+ model_names = [model.replace('_', '$-$') for model in self.model_names]
+ for name in names:
+ fig, ax = plt.subplots()
+ for i, model in enumerate(model_names[1:]):
+ plt.plot(list(range(1, self.n_meas+1)),
+ model_weights_dict[name][i],
+ color=Color[i], marker='o',
+ ms=10, linewidth=2, label=model
+ )
+
+ plt.title(f"Data generated by: {name.replace('_', '$-$')}")
+ plt.ylabel("Weights")
+ plt.xlabel("No. of measurement points")
+ ax.set_xticks(list(range(1, self.n_meas+1)))
+ plt.legend(loc="best")
+ fig.savefig(
+ f'{directory}modelWeights_{name}.svg', bbox_inches='tight'
+ )
+ plt.close()
+
+ # Confusion matrix for some measurement points
+ epsilon = 1 if self.just_n_meas != 1 else 0
+ for index in range(0, self.n_meas+epsilon, self.just_n_meas):
+ weights = np.array(
+ [model_weights_dict[key][:, index] for key in model_weights_dict]
+ )
+ g = sns.heatmap(
+ weights.T, annot=True, cmap='Blues', xticklabels=model_names,
+ yticklabels=model_names[1:], annot_kws={"size": 24}
+ )
+
+ # x axis on top
+ g.xaxis.tick_top()
+ g.xaxis.set_label_position('top')
+ g.set_xlabel(r"\textbf{Data generated by:}", labelpad=15)
+ g.set_ylabel(r"\textbf{Model weight for:}", labelpad=15)
+ g.figure.savefig(
+ f"{directory}confusionMatrix_ND_{index+1}.pdf",
+ bbox_inches='tight'
+ )
+ plt.close()
+
+ # -------------------------------------------------------------------------
+ def plot_model_weights(self, model_weights, plot_name):
+ """
+ Visualizes the model weights resulting from BMS via the observation
+ data.
+
+ Parameters
+ ----------
+ model_weights : array
+ Model weights.
+ plot_name : str
+ Plot name.
+
+ Returns
+ -------
+ None.
+
+ """
+ font_size = 40
+ # mkdir for plots
+ directory = 'Outputs_Comparison/'
+ os.makedirs(directory, exist_ok=True)
+
+ # Create figure
+ fig, ax = plt.subplots()
+
+ # Filter data using np.isnan
+ mask = ~np.isnan(model_weights.T)
+ filtered_data = [d[m] for d, m in zip(model_weights, mask.T)]
+
+ # Create the boxplot
+ bp = ax.boxplot(filtered_data, patch_artist=True, showfliers=False)
+
+ # change outline color, fill color and linewidth of the boxes
+ for box in bp['boxes']:
+ # change outline color
+ box.set(color='#7570b3', linewidth=4)
+ # change fill color
+ box.set(facecolor='#1b9e77')
+
+ # change color and linewidth of the whiskers
+ for whisker in bp['whiskers']:
+ whisker.set(color='#7570b3', linewidth=2)
+
+ # change color and linewidth of the caps
+ for cap in bp['caps']:
+ cap.set(color='#7570b3', linewidth=2)
+
+ # change color and linewidth of the medians
+ for median in bp['medians']:
+ median.set(color='#b2df8a', linewidth=2)
+
+ # change the style of fliers and their fill
+ # for flier in bp['fliers']:
+ # flier.set(marker='o', color='#e7298a', alpha=0.75)
+
+ # Custom x-axis labels
+ model_names = [model.replace('_', '$-$') for model in self.model_names]
+ ax.set_xticklabels(model_names)
+
+ ax.set_ylabel('Weight', fontsize=font_size)
+
+ # Title
+ plt.title('Posterior Model Weights')
+
+ # Set y lim
+ ax.set_ylim((-0.05, 1.05))
+
+ # Set size of the ticks
+ for t in ax.get_xticklabels():
+ t.set_fontsize(font_size)
+ for t in ax.get_yticklabels():
+ t.set_fontsize(font_size)
+
+ # Save the figure
+ fig.savefig(
+ f'./{directory}{plot_name}.pdf', bbox_inches='tight'
+ )
+
+ plt.close()
+
+ # -------------------------------------------------------------------------
+ def plot_bayes_factor(self, BME_Dict, plot_name=''):
+ """
+ Plots the Bayes factor distibutions in a :math:`N_m \\times N_m`
+ matrix, where :math:`N_m` is the number of the models.
+
+ Parameters
+ ----------
+ BME_Dict : dict
+ A dictionary containing the BME values of the models.
+ plot_name : str, optional
+ Plot name. The default is ''.
+
+ Returns
+ -------
+ None.
+
+ """
+
+ font_size = 40
+
+ # mkdir for plots
+ directory = 'Outputs_Comparison/'
+ os.makedirs(directory, exist_ok=True)
+
+ Colors = ["blue", "green", "gray", "brown"]
+
+ model_names = list(BME_Dict.keys())
+ nModels = len(model_names)
+
+ # Plots
+ fig, axes = plt.subplots(
+ nrows=nModels, ncols=nModels, sharex=True, sharey=True
+ )
+
+ for i, key_i in enumerate(model_names):
+
+ for j, key_j in enumerate(model_names):
+ ax = axes[i, j]
+ # Set size of the ticks
+ for t in ax.get_xticklabels():
+ t.set_fontsize(font_size)
+ for t in ax.get_yticklabels():
+ t.set_fontsize(font_size)
+
+ if j != i:
+
+ # Null hypothesis: key_j is the better model
+ BayesFactor = np.log10(
+ np.divide(BME_Dict[key_i], BME_Dict[key_j])
+ )
+
+ # sns.kdeplot(BayesFactor, ax=ax, color=Colors[i], shade=True)
+ # sns.histplot(BayesFactor, ax=ax, stat="probability",
+ # kde=True, element='step',
+ # color=Colors[j])
+
+ # taken from seaborn's source code (utils.py and
+ # distributions.py)
+ def seaborn_kde_support(data, bw, gridsize, cut, clip):
+ if clip is None:
+ clip = (-np.inf, np.inf)
+ support_min = max(data.min() - bw * cut, clip[0])
+ support_max = min(data.max() + bw * cut, clip[1])
+ return np.linspace(support_min, support_max, gridsize)
+
+ kde_estim = stats.gaussian_kde(
+ BayesFactor, bw_method='scott'
+ )
+
+ # manual linearization of data
+ # linearized = np.linspace(
+ # quotient.min(), quotient.max(), num=500)
+
+ # or better: mimic seaborn's internal stuff
+ bw = kde_estim.scotts_factor() * np.std(BayesFactor)
+ linearized = seaborn_kde_support(
+ BayesFactor, bw, 100, 3, None)
+
+ # computes values of the estimated function on the
+ # estimated linearized inputs
+ Z = kde_estim.evaluate(linearized)
+
+ # https://stackoverflow.com/questions/29661574/normalize-
+ # numpy-array-columns-in-python
+ def normalize(x):
+ return (x - x.min(0)) / x.ptp(0)
+
+ # normalize so it is between 0;1
+ Z2 = normalize(Z)
+ ax.plot(linearized, Z2, "-", color=Colors[i], linewidth=4)
+ ax.fill_between(
+ linearized, 0, Z2, color=Colors[i], alpha=0.25
+ )
+
+ # Draw BF significant levels according to Jeffreys 1961
+ # Strong evidence for both models
+ ax.axvline(
+ x=np.log10(3), ymin=0, linewidth=4, color='dimgrey'
+ )
+ # Strong evidence for one model
+ ax.axvline(
+ x=np.log10(10), ymin=0, linewidth=4, color='orange'
+ )
+ # Decisive evidence for one model
+ ax.axvline(
+ x=np.log10(100), ymin=0, linewidth=4, color='r'
+ )
+
+ # legend
+ BF_label = key_i.replace('_', '$-$') + \
+ '/' + key_j.replace('_', '$-$')
+ legend_elements = [
+ patches.Patch(facecolor=Colors[i], edgecolor=Colors[i],
+ label=f'BF({BF_label})')
+ ]
+ ax.legend(
+ loc='upper left', handles=legend_elements,
+ fontsize=font_size-(nModels+1)*5
+ )
+
+ elif j == i:
+ # build a rectangle in axes coords
+ left, width = 0, 1
+ bottom, height = 0, 1
+
+ # axes coordinates are 0,0 is bottom left and 1,1 is upper
+ # right
+ p = patches.Rectangle(
+ (left, bottom), width, height, color='white',
+ fill=True, transform=ax.transAxes, clip_on=False
+ )
+ ax.grid(False)
+ ax.add_patch(p)
+ # ax.text(0.5*(left+right), 0.5*(bottom+top), key_i,
+ fsize = font_size+20 if nModels < 4 else font_size
+ ax.text(0.5, 0.5, key_i.replace('_', '$-$'),
+ horizontalalignment='center',
+ verticalalignment='center',
+ fontsize=fsize, color=Colors[i],
+ transform=ax.transAxes)
+
+ # Defining custom 'ylim' values.
+ custom_ylim = (0, 1.05)
+
+ # Setting the values for all axes.
+ plt.setp(axes, ylim=custom_ylim)
+
+ # set labels
+ for i in range(nModels):
+ axes[-1, i].set_xlabel('log$_{10}$(BF)', fontsize=font_size)
+ axes[i, 0].set_ylabel('Probability', fontsize=font_size)
+
+ # Adjust subplots
+ plt.subplots_adjust(wspace=0.2, hspace=0.1)
+
+ plt.savefig(
+ f'./{directory}Bayes_Factor{plot_name}.pdf', bbox_inches='tight'
+ )
+
+ plt.close()
diff --git a/src/bayesvalidrox/bayes_inference/mcmc.py b/src/bayesvalidrox/bayes_inference/mcmc.py
index 8a7a44b8fadb327959ee9c4320bb7490617ffc9d..6b9ca94823fb7064baa2f0588d0f97fb4c9d1d44 100755
--- a/src/bayesvalidrox/bayes_inference/mcmc.py
+++ b/src/bayesvalidrox/bayes_inference/mcmc.py
@@ -569,28 +569,20 @@ class MCMC:
mean_pred, std_pred = MetaModel.eval_metamodel(samples=theta)
else:
# Evaluate the origModel
-
- # Prepare the function
mean_pred, std_pred = dict(), dict()
- output_names = Model.Output.names
- try:
- filename = Model.py_file
- function = getattr(__import__(filename), filename)
+ model_outs, _ = Model.run_model_parallel(
+ theta, prevRun_No=self.counter,
+ key_str='_MCMC', mp=False, verbose=False)
- # Run function for theta
- model_outs = function(theta.reshape(1, -1))
- except:
- model_outs, _ = Model.run_model_parallel(
- theta[0], prevRun_No=self.counter,
- key_str='_MCMC', mp=False)
# Save outputs in respective dicts
- for varIdx, var in enumerate(output_names):
+ for varIdx, var in enumerate(Model.Output.names):
mean_pred[var] = model_outs[var]
std_pred[var] = np.zeros((mean_pred[var].shape))
# Remove the folder
- shutil.rmtree(f"{Model.Name}_MCMC_{self.counter+1}")
+ if Model.link_type.lower() != 'function':
+ shutil.rmtree(f"{Model.name}_MCMC_{self.counter+1}")
# Add one to the counter
self.counter += 1
diff --git a/src/bayesvalidrox/post_processing/adaptPlot.py b/src/bayesvalidrox/post_processing/adaptPlot.py
deleted file mode 100755
index c67bdeea9e9f8f2692e5732beb9bc38ac3eb05f7..0000000000000000000000000000000000000000
--- a/src/bayesvalidrox/post_processing/adaptPlot.py
+++ /dev/null
@@ -1,103 +0,0 @@
-#!/usr/bin/env python3
-# -*- coding: utf-8 -*-
-"""
-Created on Thu Aug 13 13:46:24 2020
-
-@author: farid
-"""
-
-import numpy as np
-import os
-from sklearn.metrics import mean_squared_error, r2_score
-from itertools import cycle
-from matplotlib.backends.backend_pdf import PdfPages
-import matplotlib.pyplot as plt
-plt.rcParams.update({'font.size': 24})
-plt.rc('figure', figsize = (24, 16))
-plt.rc('font', family='serif', serif='Arial')
-plt.rc('axes', grid = True)
-plt.rc('text', usetex=True)
-plt.rc('xtick', labelsize=24)
-plt.rc('ytick', labelsize=24)
-plt.rc('axes', labelsize=24)
-plt.rc('axes', linewidth=2)
-plt.rc('axes', grid=True)
-plt.rc('grid', linestyle="-")
-plt.rc('savefig', dpi=1000)
-
-def adaptPlot(PCEModel, Y_Val, Y_PC_Val, Y_PC_Val_std, x_values=[], plotED=False, SaveFig=True):
-
- NrofSamples = PCEModel.ExpDesign.n_new_samples
- initNSamples = PCEModel.ExpDesign.n_init_samples
- itrNr = 1 + (PCEModel.ExpDesign.X.shape[0] - initNSamples)//NrofSamples
-
- oldEDY = PCEModel.ExpDesign.Y
-
- if SaveFig:
- newpath = (r'adaptivePlots')
- if not os.path.exists(newpath): os.makedirs(newpath)
-
- # create a PdfPages object
- pdf = PdfPages('./'+newpath+'/Model_vs_PCEModel'+'_itr_'+str(itrNr)+'.pdf')
-
- # List of markers and colors
- color = cycle((['b', 'g', 'r', 'y', 'k']))
- marker = cycle(('x', 'd', '+', 'o', '*'))
-
- OutNames = list(Y_Val.keys())
- x_axis = 'Time [s]'
- if len(OutNames) == 1: OutNames.insert(0, x_axis)
- try:
- x_values = Y_Val[OutNames[0]]
- except:
- x_values = x_values
-
- fig = plt.figure(figsize=(24, 16))
-
- # Plot the model vs PCE model
- for keyIdx, key in enumerate(OutNames[1:]):
-
- Y_PC_Val_ = Y_PC_Val[key]
- Y_PC_Val_std_ = Y_PC_Val_std[key]
- Y_Val_ = Y_Val[key]
- old_EDY = oldEDY[key]
-
- for idx in range(NrofSamples):
- Color = next(color)
- Marker = next(marker)
-
- plt.plot(x_values, Y_Val_[idx,:], color=Color, marker=Marker, lw=2.0, label='$Y_{%s}^{M}$'%(idx+itrNr))
-
- plt.plot(x_values, Y_PC_Val_[idx,:], color=Color, marker=Marker, lw=2.0, linestyle='--', label='$Y_{%s}^{PCE}$'%(idx+itrNr))
- plt.fill_between(x_values, Y_PC_Val_[idx,:]-1.96*Y_PC_Val_std_[idx,:],
- Y_PC_Val_[idx,:]+1.96*Y_PC_Val_std_[idx,:], color=Color,alpha=0.15)
-
- if plotED:
- for output in old_EDY:
- plt.plot(x_values, output, color='grey', alpha=0.1)
-
- # Calculate the RMSE
- RMSE = mean_squared_error(Y_PC_Val_, Y_Val_, squared=False)
- R2 = r2_score(Y_PC_Val_.reshape(-1,1), Y_Val_.reshape(-1,1))
-
- plt.ylabel(key)
- plt.xlabel(x_axis)
- plt.title(key)
-
- ax = fig.axes[0]
- ax.legend(loc='best', frameon=True)
- fig.canvas.draw()
- ax.text(0.65, 0.85, 'RMSE = '+ str(round(RMSE, 3)) + '\n' + r'$R^2$ = '+ str(round(R2, 3)),
- transform=ax.transAxes, color='black', bbox=dict(facecolor='none', edgecolor='black',
- boxstyle='round,pad=1'))
-
- plt.grid()
-
- if SaveFig:
- # save the current figure
- pdf.savefig(fig, bbox_inches='tight')
-
- # Destroy the current plot
- plt.clf()
-
- pdf.close()
\ No newline at end of file
diff --git a/src/bayesvalidrox/post_processing/post_processing.py b/src/bayesvalidrox/post_processing/post_processing.py
index 63ead63fa397d1ce219978193887cccdccbdb96a..3c90b56ffaf1fd099f0971daff7cbe5947639d36 100644
--- a/src/bayesvalidrox/post_processing/post_processing.py
+++ b/src/bayesvalidrox/post_processing/post_processing.py
@@ -9,7 +9,6 @@ import pandas as pd
import scipy.stats as stats
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error, r2_score
-from statsmodels.graphics.gofplots import qqplot
from matplotlib.backends.backend_pdf import PdfPages
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker
@@ -73,7 +72,7 @@ class PostProcessing:
x_values_orig = self.MetaModel.ExpDesign.x_values
# Compute the moments with the PCEModel object
- self._compute_pce_moments()
+ self.pce_means, self.pce_stds = self.compute_pce_moments()
# Get the variables
out_names = Model.Output.names
@@ -158,7 +157,8 @@ class PostProcessing:
return self.pce_means, self.pce_stds
# -------------------------------------------------------------------------
- def valid_metamodel(self, n_samples=1, samples=None, x_axis='Time [s]'):
+ def valid_metamodel(self, n_samples=1, samples=None, model_out_dict=None,
+ x_axis='Time [s]'):
"""
Evaluates and plots the meta model and the PCEModel outputs for the
given number of samples or the given samples.
@@ -169,6 +169,8 @@ class PostProcessing:
Number of samples to be evaluated. The default is 1.
samples : array of shape (n_samples, n_params), optional
Samples to be evaluated. The default is None.
+ model_out_dict: dict
+ The model runs using the samples provided.
x_axis : str, optional
Label of x axis. The default is `'Time [s]'`.
@@ -189,7 +191,10 @@ class PostProcessing:
# Extract x_values
x_values = MetaModel.ExpDesign.x_values
- self.model_out_dict = self._eval_model(samples, key_str='valid')
+ if model_out_dict is not None:
+ self.model_out_dict = model_out_dict
+ else:
+ self.model_out_dict = self._eval_model(samples, key_str='valid')
self.pce_out_mean, self.pce_out_std = MetaModel.eval_metamodel(samples)
try:
@@ -278,7 +283,7 @@ class PostProcessing:
self.MetaModel.rmse = self.rmse
self.MetaModel.valid_error = self.valid_error
- return self.rmse, self.valid_error
+ return
# -------------------------------------------------------------------------
def plot_seq_design_diagnostics(self, ref_BME_KLD=None, save_fig=True):
@@ -334,14 +339,14 @@ class PostProcessing:
# Extract the values from dict
sorted_seq_opt = {}
# Number of replications
- n_reps = PCEModel.ExpDesign.nReprications
+ n_reps = PCEModel.ExpDesign.n_replication
# Get the list of utility function names
# Handle if only one UtilityFunction is provided
- if not isinstance(PCEModel.ExpDesign.UtilityFunction, list):
- util_funcs = [PCEModel.ExpDesign.UtilityFunction]
+ if not isinstance(PCEModel.ExpDesign.util_func, list):
+ util_funcs = [PCEModel.ExpDesign.util_func]
else:
- util_funcs = PCEModel.ExpDesign.UtilityFunction
+ util_funcs = PCEModel.ExpDesign.util_func
for util in util_funcs:
sortedSeq = {}
@@ -393,12 +398,12 @@ class PostProcessing:
if ref_BME_KLD is not None:
if plot == 'BME':
refValue = ref_BME_KLD[0]
- plot_label = r'$BME/BME^{Ref.}$'
+ plot_label = r'BME/BME$^{Ref.}$'
if plot == 'KLD':
refValue = ref_BME_KLD[1]
- plot_label = '$D_{KL}[p(\theta|y_*),p(\theta)]'\
- ' / D_{KL}^{Ref.}[p(\theta|y_*), '\
- 'p(\theta)]$'
+ plot_label = '$D_{KL}[p(\\theta|y_*),p(\\theta)]'\
+ ' / D_{KL}^{Ref.}[p(\\theta|y_*), '\
+ 'p(\\theta)]$'
# Difference between BME/KLD and the ref. values
all_errors = np.divide(all_errors,
@@ -442,7 +447,8 @@ class PostProcessing:
# Destroy the current plot
plt.clf()
# Save arrays into files
- f = open(f'./{newpath}/Seq{plot}.txt', 'w')
+ plot_name = plot.replace(' ', '_')
+ f = open(f'./{newpath}/seq_{plot_name}.txt', 'w')
f.write(str(sorted_seq_opt))
f.close()
else:
@@ -461,12 +467,12 @@ class PostProcessing:
if ref_BME_KLD is not None:
if plot == 'BME':
refValue = ref_BME_KLD[0]
- plot_label = r'$BME/BME^{Ref.}$'
+ plot_label = r'BME/BME$^{Ref.}$'
if plot == 'KLD':
refValue = ref_BME_KLD[1]
- plot_label = '$D_{KL}[p(\theta|y_*),p(\theta)]'\
- ' / D_{KL}^{Ref.}[p(\theta|y_*), '\
- 'p(\theta)]$'
+ plot_label = '$D_{KL}[p(\\theta|y_*),p(\\theta)]'\
+ ' / D_{KL}^{Ref.}[p(\\theta|y_*), '\
+ 'p(\\theta)]$'
# Difference between BME/KLD and the ref. values
values = np.divide(seq_values,
@@ -497,13 +503,9 @@ class PostProcessing:
seq_values = np.nan_to_num(seq_values)
# Plot the error evolution for each output
- for i in range(seq_values.shape[1]):
- plt.semilogy(x_idx, seq_values[:, i], ls='--',
- lw=2, marker=markers[idx],
- color=colors[idx], alpha=0.15)
-
- plt.semilogy(x_idx, seq_values, marker=markers[idx],
- ls='--', lw=2, color=colors[idx],
+ plt.semilogy(x_idx, seq_values.mean(axis=1),
+ marker=markers[idx], ls='--', lw=2,
+ color=colors[idx],
label=name.split("_rep", 1)[0])
# Set the major and minor locators
@@ -528,7 +530,8 @@ class PostProcessing:
plt.clf()
# ---------------- Saving arrays into files ---------------
- np.save(f'./{newpath}/Seq{plot}.npy', seq_values)
+ plot_name = plot.replace(' ', '_')
+ np.save(f'./{newpath}/seq_{plot_name}.npy', seq_values)
# Close the pdf
pdf.close()
@@ -575,173 +578,204 @@ class PostProcessing:
coeffs_dict = PCEModel.coeffs_dict
n_params = PCEModel.n_params
max_order = np.max(PCEModel.pce_deg)
- self.sobol_cell = {}
- self.total_sobol = {}
+ sobol_cell_b = {}
+ total_sobol_b = {}
+ cov_Z_p_q = np.zeros((n_params))
- for Output in PCEModel.ModelObj.Output.names:
+ for b_i in range(PCEModel.n_bootstrap_itrs):
- n_meas_points = len(coeffs_dict[Output])
+ sobol_cell_, total_sobol_ = {}, {}
- # Initialize the (cell) array containing the (total) Sobol indices.
- sobol_array = dict.fromkeys(range(1, max_order+1), [])
- sobol_cell_array = dict.fromkeys(range(1, max_order+1), [])
+ for output in PCEModel.ModelObj.Output.names:
- for i_order in range(1, max_order+1):
- n_comb = math.comb(n_params, i_order)
+ n_meas_points = len(coeffs_dict[f'b_{b_i+1}'][output])
- sobol_cell_array[i_order] = np.zeros((n_comb, n_meas_points))
+ # Initialize the (cell) array containing the (total) Sobol indices.
+ sobol_array = dict.fromkeys(range(1, max_order+1), [])
+ sobol_cell_array = dict.fromkeys(range(1, max_order+1), [])
- total_sobol_array = np.zeros((n_params, n_meas_points))
+ for i_order in range(1, max_order+1):
+ n_comb = math.comb(n_params, i_order)
- # Initialize the cell to store the names of the variables
- TotalVariance = np.zeros((n_meas_points))
+ sobol_cell_array[i_order] = np.zeros((n_comb, n_meas_points))
- # Loop over all measurement points and calculate sobol indices
- for pIdx in range(n_meas_points):
+ total_sobol_array = np.zeros((n_params, n_meas_points))
- # Extract the basis indices (alpha) and coefficients
- Basis = basis_dict[Output][f'y_{pIdx+1}']
+ # Initialize the cell to store the names of the variables
+ TotalVariance = np.zeros((n_meas_points))
+ # Loop over all measurement points and calculate sobol indices
+ for pIdx in range(n_meas_points):
- try:
- clf_poly = PCEModel.clf_poly[Output][f'y_{pIdx+1}']
- PCECoeffs = clf_poly.coef_
- except:
- PCECoeffs = coeffs_dict[Output][f'y_{pIdx+1}']
+ # Extract the basis indices (alpha) and coefficients
+ Basis = basis_dict[f'b_{b_i+1}'][output][f'y_{pIdx+1}']
- # Compute total variance
- TotalVariance[pIdx] = np.sum(np.square(PCECoeffs[1:]))
+ try:
+ clf_poly = PCEModel.clf_poly[f'b_{b_i+1}'][output][f'y_{pIdx+1}']
+ PCECoeffs = clf_poly.coef_
+ except:
+ PCECoeffs = coeffs_dict[f'b_{b_i+1}'][output][f'y_{pIdx+1}']
- nzidx = np.where(PCECoeffs != 0)[0]
- # Set all the Sobol indices equal to zero in the presence of a
- # null output.
- if len(nzidx) == 0:
- # This is buggy.
- for i_order in range(1, max_order+1):
- sobol_cell_array[i_order][:, pIdx] = 0
+ # Compute total variance
+ TotalVariance[pIdx] = np.sum(np.square(PCECoeffs[1:]))
- # Otherwise compute them by summing well-chosen coefficients
- else:
- nz_basis = Basis[nzidx]
- for i_order in range(1, max_order+1):
- idx = np.where(np.sum(nz_basis > 0, axis=1) == i_order)
- subbasis = nz_basis[idx]
- Z = np.array(list(combinations(range(n_params), i_order)))
+ nzidx = np.where(PCECoeffs != 0)[0]
+ # Set all the Sobol indices equal to zero in the presence of a
+ # null output.
+ if len(nzidx) == 0:
+ # This is buggy.
+ for i_order in range(1, max_order+1):
+ sobol_cell_array[i_order][:, pIdx] = 0
+
+ # Otherwise compute them by summing well-chosen coefficients
+ else:
+ nz_basis = Basis[nzidx]
+ for i_order in range(1, max_order+1):
+ idx = np.where(np.sum(nz_basis > 0, axis=1) == i_order)
+ subbasis = nz_basis[idx]
+ Z = np.array(list(combinations(range(n_params), i_order)))
+
+ for q in range(Z.shape[0]):
+ Zq = Z[q]
+ subsubbasis = subbasis[:, Zq]
+ subidx = np.prod(subsubbasis, axis=1) > 0
+ sum_ind = nzidx[idx[0][subidx]]
+ if TotalVariance[pIdx] == 0.0:
+ sobol_cell_array[i_order][q, pIdx] = 0.0
+ else:
+ sobol = np.sum(np.square(PCECoeffs[sum_ind]))
+ sobol /= TotalVariance[pIdx]
+ sobol_cell_array[i_order][q, pIdx] = sobol
+
+ # Compute the TOTAL Sobol indices.
+ for ParIdx in range(n_params):
+ idx = nz_basis[:, ParIdx] > 0
+ sum_ind = nzidx[idx]
- for q in range(Z.shape[0]):
- Zq = Z[q]
- subsubbasis = subbasis[:, Zq]
- subidx = np.prod(subsubbasis, axis=1) > 0
- sum_ind = nzidx[idx[0][subidx]]
if TotalVariance[pIdx] == 0.0:
- sobol_cell_array[i_order][q, pIdx] = 0.0
+ total_sobol_array[ParIdx, pIdx] = 0.0
else:
sobol = np.sum(np.square(PCECoeffs[sum_ind]))
sobol /= TotalVariance[pIdx]
- sobol_cell_array[i_order][q, pIdx] = sobol
-
- # Compute the TOTAL Sobol indices.
- for ParIdx in range(n_params):
- idx = nz_basis[:, ParIdx] > 0
- sum_ind = nzidx[idx]
+ total_sobol_array[ParIdx, pIdx] = sobol
+
+ # ----- if PCA selected: Compute covariance -----
+ if PCEModel.dim_red_method.lower() == 'pca':
+ # Extract the basis indices (alpha) and coefficients for
+ # next component
+ if pIdx < n_meas_points-1:
+ nextBasis = basis_dict[f'b_{b_i+1}'][output][f'y_{pIdx+2}']
+ if PCEModel.bootstrap_method != 'fast' or b_i == 0:
+ clf_poly = PCEModel.clf_poly[f'b_{b_i+1}'][output][f'y_{pIdx+2}']
+ nextPCECoeffs = clf_poly.coef_
+ else:
+ nextPCECoeffs = coeffs_dict[f'b_{b_i+1}'][output][f'y_{pIdx+2}']
+
+ # Choose the common non-zero basis
+ mask = (Basis[:, None] == nextBasis).all(-1).any(-1)
+ n_mask = (nextBasis[:, None] == Basis).all(-1).any(-1)
+
+ # Compute the covariance in Eq 17.
+ for ParIdx in range(n_params):
+ idx = (mask) & (Basis[:, ParIdx] > 0)
+ n_idx = (n_mask) & (nextBasis[:, ParIdx] > 0)
+ try:
+ cov_Z_p_q[ParIdx] += np.sum(np.dot(
+ PCECoeffs[idx], nextPCECoeffs[n_idx])
+ )
+ except:
+ pass
+
+ # Compute the sobol indices according to Ref. 2
+ if PCEModel.dim_red_method.lower() == 'pca':
+ n_c_points = PCEModel.ExpDesign.Y[output].shape[1]
+ PCA = PCEModel.pca[f'b_{b_i+1}'][output]
+ compPCA = PCA.components_
+ nComp = compPCA.shape[0]
+ var_Z_p = PCA.explained_variance_
- if TotalVariance[pIdx] == 0.0:
- total_sobol_array[ParIdx, pIdx] = 0.0
- else:
- sobol = np.sum(np.square(PCECoeffs[sum_ind]))
- sobol /= TotalVariance[pIdx]
- total_sobol_array[ParIdx, pIdx] = sobol
+ # Extract the sobol index of the components
+ for i_order in range(1, max_order+1):
+ n_comb = math.comb(n_params, i_order)
+ sobol_array[i_order] = np.zeros((n_comb, n_c_points))
+ Z = np.array(list(combinations(range(n_params), i_order)))
- # ----- if PCA selected: Compute covariance -----
- if PCEModel.dim_red_method.lower() == 'pca':
- cov_Z_p_q = np.zeros((n_params))
- # Extract the basis indices (alpha) and coefficients for
- # next component
- if pIdx < n_meas_points-1:
- nextBasis = basis_dict[Output][f'y_{pIdx+2}']
-
- try:
- clf_poly = PCEModel.clf_poly[Output][f'y_{pIdx+2}']
- nextPCECoeffs = clf_poly.coef_
- except:
- nextPCECoeffs = coeffs_dict[Output][f'y_{pIdx+2}']
-
- # Choose the common non-zero basis
- mask = (Basis[:, None] == nextBasis).all(-1).any(-1)
- similar_basis = Basis[mask]
- # Compute the TOTAL Sobol indices.
- for ParIdx in range(n_params):
- idx = similar_basis[:, ParIdx] > 0
- try:
- sum_is = nzidx[idx]
- cov_Z_p_q[ParIdx] = np.sum(PCECoeffs[sum_ind] *
- nextPCECoeffs[sum_is])
- except:
- cov_Z_p_q[ParIdx] = 0.0
-
- # Compute the sobol indices according to Ref. 2
- if PCEModel.dim_red_method.lower() == 'pca':
- n_c_points = PCEModel.ExpDesign.Y[Output].shape[1]
- PCA = PCEModel.pca[Output]
- compPCA = PCA.components_
- nComp = compPCA.shape[0]
- var_Z_p = PCA.explained_variance_
-
- # Extract the sobol index of the components
- for i_order in range(1, max_order+1):
- n_comb = math.comb(n_params, i_order)
- sobol_array[i_order] = np.zeros((n_comb, n_c_points))
- Z = np.array(list(combinations(range(n_params), i_order)))
+ # Loop over parameters
+ for q in range(Z.shape[0]):
+ S_Z_i = sobol_cell_array[i_order][q]
+
+ for tIdx in range(n_c_points):
+ var_Y_t = np.var(
+ PCEModel.ExpDesign.Y[output][:, tIdx])
+ if var_Y_t == 0.0:
+ term1, term2 = 0.0, 0.0
+ else:
+ # Eq. 17
+ term1 = 0.0
+ for i in range(nComp):
+ a = S_Z_i[i] * var_Z_p[i]
+ a *= compPCA[i, tIdx]**2
+ term1 += a
+
+ # TODO: Term 2
+ # term2 = 0.0
+ # for i in range(nComp-1):
+ # term2 += cov_Z_p_q[q] * compPCA[i, tIdx]
+ # term2 *= compPCA[i+1, tIdx]
+ # term2 *= 2
+
+ sobol_array[i_order][q, tIdx] = term1 #+ term2
+
+ # Devide over total output variance Eq. 18
+ sobol_array[i_order][q, tIdx] /= var_Y_t
- for q in range(Z.shape[0]):
- S_Z_i = sobol_cell_array[i_order][q]
+ # Compute the TOTAL Sobol indices.
+ total_sobol = np.zeros((n_params, n_c_points))
+ for ParIdx in range(n_params):
+ S_Z_i = total_sobol_array[ParIdx]
for tIdx in range(n_c_points):
- var_Y_t = np.var(PCEModel.ExpDesign.Y[Output][:, tIdx])
+ var_Y_t = np.var(PCEModel.ExpDesign.Y[output][:, tIdx])
if var_Y_t == 0.0:
term1, term2 = 0.0, 0.0
else:
- term1 = np.sum([S_Z_i[i]*(var_Z_p[i]*(compPCA[i, tIdx]**2)/var_Y_t) for i in range(nComp)])
+ term1 = 0
+ for i in range(nComp):
+ term1 += S_Z_i[i] * var_Z_p[i] * \
+ (compPCA[i, tIdx]**2)
# Term 2
- # cov_Z_p_q = np.ones((nComp))# TODO: from coeffs
- Phi_t_p = compPCA[:nComp-1]
- Phi_t_q = compPCA
- term2 = 2 * np.sum([cov_Z_p_q[ParIdx] * Phi_t_p[i,tIdx] * Phi_t_q[i,tIdx]/var_Y_t for i in range(nComp-1)])
-
- sobol_array[i_order][q, tIdx] = term1 #+ term2
-
- # Compute the TOTAL Sobol indices.
- total_sobol = np.zeros((n_params, n_c_points))
- for ParIdx in range(n_params):
- S_Z_i = total_sobol_array[ParIdx]
-
- for tIdx in range(n_c_points):
- var_Y_t = np.var(PCEModel.ExpDesign.Y[Output][:, tIdx])
- if var_Y_t == 0.0:
- term1, term2 = 0.0, 0.0
- else:
- term1 = 0
- for i in range(nComp):
- term1 += S_Z_i[i] * var_Z_p[i] * \
- (compPCA[i, tIdx]**2) / var_Y_t
-
- # Term 2
- # cov_Z_p_q = np.ones((nComp))# TODO: from coeffs
- Phi_t_p = compPCA[:nComp-1]
- Phi_t_q = compPCA
- term2 = 0
- for i in range(nComp-1):
- term2 += cov_Z_p_q[ParIdx] * Phi_t_p[i, tIdx] \
- * Phi_t_q[i, tIdx] / var_Y_t
- term2 *= 2
-
- total_sobol[ParIdx, tIdx] = term1 + term2
-
- self.sobol_cell[Output] = sobol_array
- self.total_sobol[Output] = total_sobol
- else:
- self.sobol_cell[Output] = sobol_cell_array
- self.total_sobol[Output] = total_sobol_array
+ term2 = 0
+ for i in range(nComp-1):
+ term2 += cov_Z_p_q[ParIdx] * compPCA[i, tIdx] \
+ * compPCA[i+1, tIdx]
+ term2 *= 2
+
+ total_sobol[ParIdx, tIdx] = term1 #+ term2
+
+ # Devide over total output variance Eq. 18
+ total_sobol[ParIdx, tIdx] /= var_Y_t
+
+ sobol_cell_[output] = sobol_array
+ total_sobol_[output] = total_sobol
+ else:
+ sobol_cell_[output] = sobol_cell_array
+ total_sobol_[output] = total_sobol_array
+
+ # Save for each bootsrtap iteration
+ sobol_cell_b[b_i] = sobol_cell_
+ total_sobol_b[b_i] = total_sobol_
+
+ # Average total sobol indices
+ total_sobol_all = {}
+ for i in sorted(total_sobol_b):
+ for k, v in total_sobol_b[i].items():
+ if k not in total_sobol_all:
+ total_sobol_all[k] = [None] * len(total_sobol_b)
+ total_sobol_all[k][i] = v
+
+ self.total_sobol = {}
+ for output in PCEModel.ModelObj.Output.names:
+ self.total_sobol[output] = np.mean(total_sobol_all[output], axis=0)
# ---------------- Plot -----------------------
par_names = PCEModel.ExpDesign.par_names
@@ -761,14 +795,18 @@ class PostProcessing:
fig = plt.figure()
- for outIdx, Output in enumerate(PCEModel.ModelObj.Output.names):
+ for outIdx, output in enumerate(PCEModel.ModelObj.Output.names):
# Extract total Sobol indices
- total_sobol = self.total_sobol[Output]
+ total_sobol = self.total_sobol[output]
+
+ # Compute quantiles
+ q_5 = np.quantile(total_sobol_all[output], q=0.05, axis=0)
+ q_97_5 = np.quantile(total_sobol_all[output], q=0.975, axis=0)
# Extract a list of x values
if type(x_values_orig) is dict:
- x = x_values_orig[Output]
+ x = x_values_orig[output]
else:
x = x_values_orig
@@ -780,24 +818,25 @@ class PostProcessing:
df = pd.DataFrame({**dict1, **dict2})
df.plot(x=xlabel, y=par_names, kind="bar", ax=ax, rot=0,
- colormap='Dark2')
+ colormap='Dark2', yerr=q_97_5-q_5)
ax.set_ylabel('Total Sobol indices, $S^T$')
else:
for i, sobolIndices in enumerate(total_sobol):
plt.plot(x, sobolIndices, label=par_names[i],
marker='x', lw=2.5)
+ plt.fill_between(x, q_5[i], q_97_5[i], alpha=0.15)
plt.ylabel('Total Sobol indices, $S^T$')
plt.xlabel(xlabel)
- plt.title(f'Sensitivity analysis of {Output}')
+ plt.title(f'Sensitivity analysis of {output}')
if plot_type != 'bar':
plt.legend(loc='best', frameon=True)
# Save indices
np.savetxt(f'./{newpath}{name}totalsobol_' +
- Output.replace('/', '_') + '.csv',
+ output.replace('/', '_') + '.csv',
total_sobol.T, delimiter=',',
header=','.join(par_names), comments='')
@@ -810,7 +849,7 @@ class PostProcessing:
pdf.close()
- return self.sobol_cell, self.total_sobol
+ return self.total_sobol
# -------------------------------------------------------------------------
def check_reg_quality(self, n_samples=1000, samples=None, save_fig=True):
@@ -856,32 +895,34 @@ class PostProcessing:
y_pce_val_ = y_pce_val[key]
y_val_ = y_val[key]
+ residuals = y_val_ - y_pce_val_
# ------ Residuals vs. predicting variables ------
# Check the assumptions of linearity and independence
fig1 = plt.figure()
- plt.title(key+": Residuals vs. Predicting variables")
- residuals = y_val_ - y_pce_val_
- plt.scatter(x=y_val_, y=residuals, color='blue', edgecolor='k')
- plt.grid(True)
- xmin, xmax = min(y_val_), max(y_val_)
- plt.hlines(y=0, xmin=xmin*0.9, xmax=xmax*1.1, color='red', lw=3,
- linestyle='--')
- plt.xlabel(key)
- plt.ylabel('Residuals')
- plt.show()
+ for i, par in enumerate(MetaModel.ExpDesign.par_names):
+ plt.title(f"{key}: Residuals vs. {par}")
+ plt.scatter(
+ x=samples[:, i], y=residuals, color='blue', edgecolor='k')
+ plt.grid(True)
+ xmin, xmax = min(samples[:, i]), max(samples[:, i])
+ plt.hlines(y=0, xmin=xmin*0.9, xmax=xmax*1.1, color='red',
+ lw=3, linestyle='--')
+ plt.xlabel(par)
+ plt.ylabel('Residuals')
+ plt.show()
- if save_fig:
- # save the current figure
- fig1.savefig(f'./{newpath}/Residuals_vs_PredVariables.pdf',
- bbox_inches='tight')
- # Destroy the current plot
- plt.clf()
+ if save_fig:
+ # save the current figure
+ fig1.savefig(f'./{newpath}/Residuals_vs_Par_{i+1}.pdf',
+ bbox_inches='tight')
+ # Destroy the current plot
+ plt.clf()
# ------ Fitted vs. residuals ------
# Check the assumptions of linearity and independence
fig2 = plt.figure()
- plt.title(key+": Residuals vs. predicting variables")
+ plt.title(f"{key}: Residuals vs. fitted values")
plt.scatter(x=y_pce_val_, y=residuals, color='blue', edgecolor='k')
plt.grid(True)
xmin, xmax = min(y_val_), max(y_val_)
@@ -929,19 +970,19 @@ class PostProcessing:
# ------ Q-Q plot of the normalized residuals ------
plt.figure()
- fig4 = qqplot(resid_pearson, line='45', fit='True')
+ stats.probplot(residuals[:, 0], plot=plt)
plt.xticks()
plt.yticks()
plt.xlabel("Theoretical quantiles")
plt.ylabel("Sample quantiles")
- plt.title(key+": Q-Q plot of normalized residuals")
+ plt.title(f"{key}: Q-Q plot of normalized residuals")
plt.grid(True)
plt.show()
if save_fig:
# save the current figure
- fig4.savefig(f'./{newpath}/QQPlot_NormResiduals.pdf',
- bbox_inches='tight')
+ plt.savefig(f'./{newpath}/QQPlot_NormResiduals.pdf',
+ bbox_inches='tight')
# Destroy the current plot
plt.clf()
@@ -1041,58 +1082,93 @@ class PostProcessing:
return
# -------------------------------------------------------------------------
- def _compute_pce_moments(self):
+ def compute_pce_moments(self):
"""
Computes the first two moments using the PCE-based meta-model.
Returns
-------
- None.
+ pce_means: dict
+ The first moments (mean) of outpust.
+ pce_means: dict
+ The first moments (mean) of outpust.
"""
MetaModel = self.MetaModel
- self.pce_means = {}
- self.pce_stds = {}
-
- for Outkey, ValuesDict in MetaModel.coeffs_dict.items():
-
- pce_mean = np.zeros((len(ValuesDict)))
- pce_var = np.zeros((len(ValuesDict)))
-
- for Inkey, InIdxValues in ValuesDict.items():
- idx = int(Inkey.split('_')[1]) - 1
- coeffs = MetaModel.coeffs_dict[Outkey][Inkey]
-
- # Mean = c_0
- if coeffs[0] != 0:
- pce_mean[idx] = coeffs[0]
+ outputs = MetaModel.ModelObj.Output.names
+ pce_means_b = {}
+ pce_stds_b = {}
+
+ # Loop over bootstrap iterations
+ for b_i in range(MetaModel.n_bootstrap_itrs):
+ # Loop over the metamodels
+ coeffs_dicts = MetaModel.coeffs_dict[f'b_{b_i+1}'].items()
+ means = {}
+ stds = {}
+ for output, coef_dict in coeffs_dicts:
+
+ pce_mean = np.zeros((len(coef_dict)))
+ pce_var = np.zeros((len(coef_dict)))
+
+ for index, values in coef_dict.items():
+ idx = int(index.split('_')[1]) - 1
+ coeffs = MetaModel.coeffs_dict[f'b_{b_i+1}'][output][index]
+
+ # Mean = c_0
+ if coeffs[0] != 0:
+ pce_mean[idx] = coeffs[0]
+ else:
+ clf_poly = MetaModel.clf_poly[f'b_{b_i+1}'][output]
+ pce_mean[idx] = clf_poly[index].intercept_
+ # Var = sum(coeffs[1:]**2)
+ pce_var[idx] = np.sum(np.square(coeffs[1:]))
+
+ # Save predictions for each output
+ if MetaModel.dim_red_method.lower() == 'pca':
+ PCA = MetaModel.pca[f'b_{b_i+1}'][output]
+ means[output] = PCA.inverse_transform(pce_mean)
+ stds[output] = np.sqrt(np.dot(pce_var,
+ PCA.components_**2))
else:
- pce_mean[idx] = MetaModel.clf_poly[Outkey][Inkey].intercept_
-
- # Var = sum(coeffs[1:]**2)
- pce_var[idx] = np.sum(np.square(coeffs[1:]))
-
- # Back transformation if PCA is selected.
- if MetaModel.dim_red_method.lower() == 'pca':
- PCA = MetaModel.pca[Outkey]
- self.pce_means[Outkey] = PCA.mean_
- self.pce_means[Outkey] += np.dot(pce_mean, PCA.components_)
- self.pce_stds[Outkey] = np.sqrt(np.dot(pce_var,
- PCA.components_**2))
- else:
- self.pce_means[Outkey] = pce_mean
- self.pce_stds[Outkey] = np.sqrt(pce_var)
+ means[output] = pce_mean
+ stds[output] = np.sqrt(pce_var)
+
+ # Save predictions for each bootstrap iteration
+ pce_means_b[b_i] = means
+ pce_stds_b[b_i] = stds
+
+ # Change the order of nesting
+ mean_all = {}
+ for i in sorted(pce_means_b):
+ for k, v in pce_means_b[i].items():
+ if k not in mean_all:
+ mean_all[k] = [None] * len(pce_means_b)
+ mean_all[k][i] = v
+ std_all = {}
+ for i in sorted(pce_stds_b):
+ for k, v in pce_stds_b[i].items():
+ if k not in std_all:
+ std_all[k] = [None] * len(pce_stds_b)
+ std_all[k][i] = v
+
+ # Back transformation if PCA is selected.
+ pce_means, pce_stds = {}, {}
+ for output in outputs:
+ pce_means[output] = np.mean(mean_all[output], axis=0)
+ pce_stds[output] = np.mean(std_all[output], axis=0)
# Print a report table
- print("\n>>>>> Moments of {} <<<<<".format(Outkey))
+ print("\n>>>>> Moments of {} <<<<<".format(output))
print("\nIndex | Mean | Std. deviation")
print('-'*35)
print('\n'.join(f'{i+1} | {k:.3e} | {j:.3e}' for i, (k, j)
- in enumerate(zip(self.pce_means[Outkey],
- self.pce_stds[Outkey]))))
+ in enumerate(zip(pce_means[output],
+ pce_stds[output]))))
print('-'*40)
+ return pce_means, pce_stds
+
# -------------------------------------------------------------------------
def _get_sample(self, n_samples=None):
"""
@@ -1106,8 +1182,10 @@ class PostProcessing:
"""
if n_samples is None:
n_samples = self.n_samples
- PCEModel = self.MetaModel
- self.samples = PCEModel.ExpDesign.generate_samples(n_samples, 'random')
+ MetaModel = self.MetaModel
+ self.samples = MetaModel.ExpDesign.generate_samples(
+ n_samples,
+ sampling_method='random')
return self.samples
# -------------------------------------------------------------------------
@@ -1194,7 +1272,7 @@ class PostProcessing:
# the total number of explanatory variables in the model
# (not including the constant term)
length_list = []
- for key, value in PCEModel.coeffs_dict[key].items():
+ for key, value in PCEModel.coeffs_dict['b_1'][key].items():
length_list.append(len(value))
n_predictors = min(length_list)
n_samples = x_val.shape[0]
@@ -1265,7 +1343,7 @@ class PostProcessing:
y_val = self.model_out_dict[key]
try:
x = self.model_out_dict['x_values'][key]
- except IndexError:
+ except (TypeError, IndexError):
x = x_values
for idx in range(y_val.shape[0]):
@@ -1288,7 +1366,7 @@ class PostProcessing:
y_val[idx].reshape(-1, 1))
plt.annotate(f'RMSE = {rmse:.3f}\n $R^2$ = {R2:.3f}',
- xy=(0.2, 0.75), xycoords='axes fraction')
+ xy=(0.85, 0.1), xycoords='axes fraction')
plt.ylabel(key)
plt.xlabel(x_axis)
diff --git a/src/bayesvalidrox/pylink/pylink.py b/src/bayesvalidrox/pylink/pylink.py
index 62b169c8aa5b3082676aaf9b18e0bbf77ecea36e..7af4a14b8f8acb62c21862d5df4a527dc7fe57b9 100644
--- a/src/bayesvalidrox/pylink/pylink.py
+++ b/src/bayesvalidrox/pylink/pylink.py
@@ -10,6 +10,7 @@ import time
import zipfile
import pandas as pd
import multiprocessing
+from functools import partial
import tqdm
@@ -36,6 +37,8 @@ class PyLinkForwardModel(object):
must be simillar. This function must recieve the parameters in an array
of shape `(n_samples, n_params)` and returns a dictionary with the
x_values and output arrays for given output names.
+ func_args : dict
+ Additional arguments for the python file. The default is `{}`.
shell_command : str
Shell command to be executed for the `'pylink'` wrapper.
input_file : str or list
@@ -108,16 +111,17 @@ class PyLinkForwardModel(object):
file_names: list = None
def __init__(self, link_type='pylink', name=None, py_file=None,
- shell_command='', input_file=None, input_template=None,
- aux_file=None, exe_path='', output_file_names=[],
- output_names=[], output_parser='', multi_process=True,
- n_cpus=None, meas_file=None, meas_file_valid=None,
- mc_ref_file=None, obs_dict={}, obs_dict_valid={},
- mc_ref_dict={}):
+ func_args={}, shell_command='', input_file=None,
+ input_template=None, aux_file=None, exe_path='',
+ output_file_names=[], output_names=[], output_parser='',
+ multi_process=True, n_cpus=None, meas_file=None,
+ meas_file_valid=None, mc_ref_file=None, obs_dict={},
+ obs_dict_valid={}, mc_ref_dict={}):
self.link_type = link_type
self.name = name
self.shell_command = shell_command
self.py_file = py_file
+ self.func_args = func_args
self.input_file = input_file
self.input_template = input_template
self.aux_file = aux_file
@@ -207,17 +211,16 @@ class PyLinkForwardModel(object):
None
"""
- if self.mc_ref_file is None and not bool(self.mc_reference):
- return
+ if self.mc_ref_file is None and \
+ isinstance(self.mc_reference, pd.DataFrame):
+ return self.mc_reference
elif isinstance(self.mc_reference, dict) and bool(self.mc_reference):
self.mc_reference = pd.DataFrame.from_dict(self.mc_reference)
elif self.mc_ref_file is not None:
file_path = os.path.join(os.getcwd(), self.mc_ref_file)
self.mc_reference = pd.read_csv(file_path, delimiter=',')
else:
- raise Exception("Please provide the MC reference data as a "
- "dictionary via mc_reference attribute or pass the"
- " csv-file path to mc_ref_file attribute")
+ self.mc_reference = None
return self.mc_reference
# -------------------------------------------------------------------------
@@ -402,7 +405,7 @@ class PyLinkForwardModel(object):
# -------------------------------------------------------------------------
def run_model_parallel(self, c_points, prevRun_No=0, key_str='',
- mp=True):
+ mp=True, verbose=True):
"""
Runs model simulations. If mp is true (default), then the simulations
are started in parallel.
@@ -418,6 +421,8 @@ class PyLinkForwardModel(object):
A descriptive string for validation runs. The default is `''`.
mp : bool, optional
Multiprocessing. The default is `True`.
+ verbose: bool, optional
+ Verbosity. The default is `True`.
Returns
-------
@@ -448,35 +453,47 @@ class PyLinkForwardModel(object):
n_cpus = self.n_cpus
# Run forward model
- if n_c_points == 1:
+ if n_c_points == 1 or not mp:
if self.link_type.lower() == 'function':
- group_results = Function(c_points)[np.newaxis]
+ group_results = Function(c_points, **self.func_args)
else:
group_results = self.run_forwardmodel(
- c_points, prevRun_No+1, key_str
- )[np.newaxis]
+ (c_points[0], prevRun_No, key_str)
+ )
- elif self.multi_process:
+ elif self.multi_process or mp:
with multiprocessing.Pool(n_cpus) as p:
- desc = f'Running forward model {key_str}'
+
if self.link_type.lower() == 'function':
- imap_var = p.imap(Function, c_points[:, np.newaxis])
+ imap_var = p.imap(partial(Function, **self.func_args),
+ c_points[:, np.newaxis])
else:
args = zip(c_points,
[prevRun_No+i for i in range(n_c_points)],
[key_str]*n_c_points)
imap_var = p.imap(self.run_forwardmodel, args)
- group_results = list(tqdm.tqdm(imap_var, total=n_c_points,
- desc=desc))
+ if verbose:
+ desc = f'Running forward model {key_str}'
+ group_results = list(tqdm.tqdm(imap_var, total=n_c_points,
+ desc=desc))
+ else:
+ group_results = list(imap_var)
# Check for NaN
- for varIdx, var in enumerate(self.Output.names):
- Outputs = np.asarray([item[varIdx+1] for item in group_results],
- dtype=np.float64)
+ for var_i, var in enumerate(self.Output.names):
+ # If results are given as one dictionary
+ if isinstance(group_results, dict):
+ Outputs = np.asarray(group_results[var])
+ # If results are given as list of dictionaries
+ elif isinstance(group_results, list):
+ Outputs = np.asarray([item[var] for item in group_results],
+ dtype=np.float64)
NaN_idx = np.unique(np.argwhere(np.isnan(Outputs))[:, 0])
new_c_points = np.delete(c_points, NaN_idx, axis=0)
- all_outputs[var] = np.delete(Outputs, NaN_idx, axis=0)
+ all_outputs[var] = np.atleast_2d(
+ np.delete(Outputs, NaN_idx, axis=0)
+ )
# Print the collocation points whose simulations crashed
if len(NaN_idx) != 0:
@@ -488,7 +505,10 @@ class PyLinkForwardModel(object):
print('*'*20)
# Save time steps or x-values
- all_outputs["x_values"] = group_results[0][0]
+ if isinstance(group_results, dict):
+ all_outputs["x_values"] = group_results["x_values"]
+ elif any(isinstance(i, dict) for i in group_results):
+ all_outputs["x_values"] = group_results[0]["x_values"]
# Store simulations in a hdf5 file
self._store_simulations(
diff --git a/src/bayesvalidrox/surrogate_models/adaptPlot.py b/src/bayesvalidrox/surrogate_models/adaptPlot.py
new file mode 100755
index 0000000000000000000000000000000000000000..102f0373c1086ba4420ada2fb2fc723b78bbd53f
--- /dev/null
+++ b/src/bayesvalidrox/surrogate_models/adaptPlot.py
@@ -0,0 +1,109 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Thu Aug 13 13:46:24 2020
+
+@author: farid
+"""
+import os
+from sklearn.metrics import mean_squared_error, r2_score
+from itertools import cycle
+from matplotlib.backends.backend_pdf import PdfPages
+import matplotlib.pyplot as plt
+
+
+def adaptPlot(PCEModel, Y_Val, Y_PC_Val, Y_PC_Val_std, x_values=[],
+ plotED=False, SaveFig=True):
+
+ NrofSamples = PCEModel.ExpDesign.n_new_samples
+ initNSamples = PCEModel.ExpDesign.n_init_samples
+ itrNr = 1 + (PCEModel.ExpDesign.X.shape[0] - initNSamples)//NrofSamples
+
+ oldEDY = PCEModel.ExpDesign.Y
+
+ if SaveFig:
+ newpath = 'adaptivePlots'
+ os.makedirs(newpath, exist_ok=True)
+
+ # create a PdfPages object
+ pdf = PdfPages(f'./{newpath}/Model_vs_PCEModel_itr_{itrNr}.pdf')
+
+ # List of markers and colors
+ color = cycle((['b', 'g', 'r', 'y', 'k']))
+ marker = cycle(('x', 'd', '+', 'o', '*'))
+
+ OutNames = list(Y_Val.keys())
+ x_axis = 'Time [s]'
+
+ if len(OutNames) == 1:
+ OutNames.insert(0, x_axis)
+ try:
+ x_values = Y_Val['x_values']
+ except KeyError:
+ x_values = x_values
+
+ fig = plt.figure(figsize=(24, 16))
+
+ # Plot the model vs PCE model
+ for keyIdx, key in enumerate(PCEModel.ModelObj.Output.names):
+ Y_PC_Val_ = Y_PC_Val[key]
+ Y_PC_Val_std_ = Y_PC_Val_std[key]
+ Y_Val_ = Y_Val[key]
+ if Y_Val_.ndim == 1:
+ Y_Val_ = Y_Val_.reshape(1, -1)
+ old_EDY = oldEDY[key]
+ if isinstance(x_values, dict):
+ x = x_values[key]
+ else:
+ x = x_values
+
+ for idx, y in enumerate(Y_Val_):
+ Color = next(color)
+ Marker = next(marker)
+
+ plt.plot(
+ x, y, color=Color, marker=Marker,
+ lw=2.0, label='$Y_{%s}^{M}$'%(idx+itrNr)
+ )
+
+ plt.plot(
+ x, Y_PC_Val_[idx], color=Color, marker=Marker,
+ lw=2.0, linestyle='--', label='$Y_{%s}^{PCE}$'%(idx+itrNr)
+ )
+ plt.fill_between(
+ x, Y_PC_Val_[idx]-1.96*Y_PC_Val_std_[idx],
+ Y_PC_Val_[idx]+1.96*Y_PC_Val_std_[idx], color=Color,
+ alpha=0.15
+ )
+
+ if plotED:
+ for output in old_EDY:
+ plt.plot(x, output, color='grey', alpha=0.1)
+
+ # Calculate the RMSE
+ RMSE = mean_squared_error(Y_PC_Val_, Y_Val_, squared=False)
+ R2 = r2_score(Y_PC_Val_.reshape(-1, 1), Y_Val_.reshape(-1, 1))
+
+ plt.ylabel(key)
+ plt.xlabel(x_axis)
+ plt.title(key)
+
+ ax = fig.axes[0]
+ ax.legend(loc='best', frameon=True)
+ fig.canvas.draw()
+ ax.text(0.65, 0.85,
+ f'RMSE = {round(RMSE, 3)}\n$R^2$ = {round(R2, 3)}',
+ transform=ax.transAxes, color='black',
+ bbox=dict(facecolor='none',
+ edgecolor='black',
+ boxstyle='round,pad=1')
+ )
+ plt.grid()
+
+ if SaveFig:
+ # save the current figure
+ pdf.savefig(fig, bbox_inches='tight')
+
+ # Destroy the current plot
+ plt.clf()
+ pdf.close()
diff --git a/src/bayesvalidrox/surrogate_models/exp_designs.py b/src/bayesvalidrox/surrogate_models/exp_designs.py
index 71a37736c7557ff316bd8eaebaec615faef529cd..a078aec9c19c5a85a637ba50d02c48459ceea6d3 100644
--- a/src/bayesvalidrox/surrogate_models/exp_designs.py
+++ b/src/bayesvalidrox/surrogate_models/exp_designs.py
@@ -35,10 +35,8 @@ class ExpDesigns:
* sobol
* halton
* hammersley
- * korobov
* chebyshev(FT)
* grid(FT)
- * nested_grid(FT)
* user
hdf5_file : str
Name of the hdf5 file that contains the experimental design.
@@ -166,17 +164,12 @@ class ExpDesigns:
"""
try:
samples = chaospy.generate_samples(
- int(n_samples), domain=self.JDist, rule=sampling_method
+ int(n_samples), domain=self.origJDist, rule=sampling_method
)
except:
- samples = self.JDist.resample(int(n_samples))
+ samples = self.random_sampler(int(n_samples)).T
- # Transform samples to the original space
- if transform:
- tr_samples = self.transform(samples.T)
- return samples.T, tr_samples
- else:
- return samples.T
+ return samples.T
# -------------------------------------------------------------------------
def generate_ED(self, n_samples, sampling_method='random', transform=False,
@@ -261,8 +254,14 @@ class ExpDesigns:
# Transform samples to the original space
if transform:
- tr_samples = self.transform(samples)
- return samples, tr_samples
+ tr_samples = self.transform(
+ samples,
+ method=sampling_method
+ )
+ if sampling_method == 'user' or not self.apce:
+ return samples, tr_samples
+ else:
+ return tr_samples, samples
else:
return samples
@@ -322,8 +321,10 @@ class ExpDesigns:
self.polycoeffs = {}
for parIdx in tqdm(range(ndim), ascii=True,
desc="Computing orth. polynomial coeffs"):
- poly_coeffs = apoly_construction(self.raw_data[parIdx],
- max_deg)
+ poly_coeffs = apoly_construction(
+ self.raw_data[parIdx],
+ max_deg
+ )
self.polycoeffs[f'p_{parIdx+1}'] = poly_coeffs
# Extract moments
@@ -412,9 +413,10 @@ class ExpDesigns:
elif 'lognorm' in dist_type.lower():
polytype = 'hermite'
- Mu = np.log(params[0]**2/np.sqrt(params[0]**2 + params[1]**2))
- Sigma = np.sqrt(np.log(1 + params[1]**2 / params[0]**2))
- dist = chaospy.LogNormal(mu=Mu, sigma=Sigma)
+ mu = np.log(params[0]**2/np.sqrt(params[0]**2 + params[1]**2))
+ sigma = np.sqrt(np.log(1 + params[1]**2 / params[0]**2))
+ dist = chaospy.LogNormal(mu, sigma)
+ # dist = chaospy.LogNormal(mu=params[0], sigma=params[1])
elif 'expon' in dist_type.lower():
polytype = 'arbitrary'
@@ -467,12 +469,36 @@ class ExpDesigns:
"""
samples = np.zeros((n_samples, self.ndim))
-
- for idxPa in range(self.ndim):
- # input_data given
- sample_size = len(self.raw_data[idxPa])
- randIdx = np.random.randint(0, sample_size, n_samples)
- samples[:, idxPa] = self.raw_data[idxPa, randIdx]
+ sample_size = self.raw_data.shape[1]
+
+ # Use a combination of raw data
+ if n_samples < sample_size:
+ for pa_idx in range(self.ndim):
+ # draw random indices
+ rand_idx = np.random.randint(0, sample_size, n_samples)
+ # store the raw data with given random indices
+ samples[:, pa_idx] = self.raw_data[pa_idx, rand_idx]
+ else:
+ try:
+ samples = self.JDist.resample(int(n_samples)).T
+ except AttributeError:
+ samples = self.JDist.sample(int(n_samples)).T
+ # Check if all samples are in the bound_tuples
+ for idx, param_set in enumerate(samples):
+ if not self._check_ranges(param_set, self.bound_tuples):
+ try:
+ proposed_sample = chaospy.generate_samples(
+ 1, domain=self.JDist, rule='random').T[0]
+ except:
+ proposed_sample = self.JDist.resample(1).T[0]
+ while not self._check_ranges(proposed_sample,
+ self.bound_tuples):
+ try:
+ proposed_sample = chaospy.generate_samples(
+ 1, domain=self.JDist, rule='random').T[0]
+ except:
+ proposed_sample = self.JDist.resample(1).T[0]
+ samples[idx] = proposed_sample
return samples
@@ -552,7 +578,7 @@ class ExpDesigns:
return opt_col_points
# -------------------------------------------------------------------------
- def transform(self, X, params=None):
+ def transform(self, X, params=None, method=None):
"""
Transform the samples via either a Rosenblatt or an isoprobabilistic
transformation.
@@ -561,6 +587,8 @@ class ExpDesigns:
----------
X : array of shape (n_samples,n_params)
Samples to be transformed.
+ method : string
+ If transformation method is 'user' transform X, else just pass X.
Returns
-------
@@ -570,7 +598,11 @@ class ExpDesigns:
"""
if self.InputObj.Rosenblatt:
self.origJDist, _ = self.build_dist(False)
- tr_X = self.origJDist.inv(self.JDist.fwd(X.T)).T
+ if method == 'user':
+ tr_X = self.JDist.inv(self.origJDist.fwd(X.T)).T
+ else:
+ # Inverse to original spcace -- generate sample ED
+ tr_X = self.origJDist.inv(self.JDist.fwd(X.T)).T
else:
# Transform samples via an isoprobabilistic transformation
n_samples, n_params = X.shape
@@ -675,3 +707,31 @@ class ExpDesigns:
return sel_dist, params[sel_dist]
else:
return None, None
+
+ # -------------------------------------------------------------------------
+ def _check_ranges(self, theta, ranges):
+ """
+ This function checks if theta lies in the given ranges.
+
+ Parameters
+ ----------
+ theta : array
+ Proposed parameter set.
+ ranges : nested list
+ List of the praremeter ranges.
+
+ Returns
+ -------
+ c : bool
+ If it lies in the given range, it return True else False.
+
+ """
+ c = True
+ # traverse in the list1
+ for i, bounds in enumerate(ranges):
+ x = theta[i]
+ # condition check
+ if x < bounds[0] or x > bounds[1]:
+ c = False
+ return c
+ return c
diff --git a/src/bayesvalidrox/surrogate_models/exploration.py b/src/bayesvalidrox/surrogate_models/exploration.py
index d2e90c362cf2e11e7e90de9f1026758c1a9c3101..cb3ccfcd4a15e26b2292973167d01efedd5a9a62 100644
--- a/src/bayesvalidrox/surrogate_models/exploration.py
+++ b/src/bayesvalidrox/surrogate_models/exploration.py
@@ -223,7 +223,6 @@ class Exploration:
self.all_candidates = all_candidates
# initialization
- new_samples = np.empty((0, ndim))
min_intersite_dist = np.zeros((n_candidate))
min_projected_dist = np.zeros((n_candidate))
@@ -232,10 +231,9 @@ class Exploration:
# find candidate that is farthest away from any existing sample
maxMinDistance = 0
- new_samples = np.vstack((old_ED_X, new_samples))
# find min distorted distance from all other samples
euclidean_dist = self._build_dist_matrix_point(
- new_samples, candidate, do_sqrt=True
+ old_ED_X, candidate, do_sqrt=True
)
min_euclidean_dist = np.min(euclidean_dist)
min_intersite_dist[i] = min_euclidean_dist
@@ -246,8 +244,8 @@ class Exploration:
maxMinDistance = min_euclidean_dist
# Projected distance
- projected_dist = distance.cdist(
- new_samples, [candidate], 'chebyshev'
+ projected_dist = self._build_dist_matrix_point(
+ old_ED_X, candidate, 'chebyshev'
)
min_projected_dist[i] = np.min(projected_dist)
@@ -338,7 +336,8 @@ class Exploration:
return self.areas, self.all_candidates
# -------------------------------------------------------------------------
- def _build_dist_matrix_point(self, samples, point, do_sqrt=False):
+ def _build_dist_matrix_point(self, samples, point, method='euclidean',
+ do_sqrt=False):
"""
Calculates the intersite distance of all points in samples from point.
@@ -348,6 +347,8 @@ class Exploration:
The old experimental design.
point : array
A candidate point.
+ method : str
+ Distance method.
do_sqrt : bool, optional
Whether to return distances or squared distances. The default is
`False`.
@@ -358,7 +359,7 @@ class Exploration:
Distances.
"""
- distances = distance.cdist(samples, np.array([point]), 'euclidean')
+ distances = distance.cdist(samples, np.array([point]), method)
# do square root?
if do_sqrt:
diff --git a/src/bayesvalidrox/surrogate_models/meta_model_engine.py b/src/bayesvalidrox/surrogate_models/meta_model_engine.py
new file mode 100644
index 0000000000000000000000000000000000000000..2df2dee5390ae4e6dc7eb88343c2469dbd88aad6
--- /dev/null
+++ b/src/bayesvalidrox/surrogate_models/meta_model_engine.py
@@ -0,0 +1,2146 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Fri Jan 28 09:21:18 2022
+
+@author: farid
+"""
+import numpy as np
+from scipy import stats, signal, linalg, sparse
+from scipy.spatial import distance
+from copy import deepcopy, copy
+from tqdm import tqdm
+import scipy.optimize as opt
+from sklearn.metrics import mean_squared_error
+import multiprocessing
+import matplotlib.pyplot as plt
+import sys
+import os
+import gc
+import seaborn as sns
+from joblib import Parallel, delayed
+from .exploration import Exploration
+
+
+class MetaModelEngine():
+ """ Sequential experimental design
+ This class provieds method for trainig the meta-model in an iterative
+ manners.
+ The main method to execute the task is `train_seq_design`, which
+ recieves a model object and returns the trained metamodel.
+ """
+
+ def __init__(self, meta_model_opts):
+ self.MetaModel = meta_model_opts
+
+ # -------------------------------------------------------------------------
+ def run(self):
+
+ Model = self.MetaModel.ModelObj
+ self.MetaModel.n_params = len(self.MetaModel.input_obj.Marginals)
+ self.MetaModel.ExpDesignFlag = 'normal'
+ # --- Prepare pce degree ---
+ if self.MetaModel.meta_model_type.lower() == 'pce':
+ if type(self.MetaModel.pce_deg) is not np.ndarray:
+ self.MetaModel.pce_deg = np.array(self.MetaModel.pce_deg)
+
+ if self.MetaModel.ExpDesign.method == 'normal':
+ self.MetaModel.ExpDesignFlag = 'normal'
+ self.MetaModel.train_norm_design(verbose=True)
+
+ elif self.MetaModel.ExpDesign.method == 'sequential':
+ self.train_seq_design()
+ else:
+ raise Exception("The method for experimental design you requested"
+ " has not been implemented yet.")
+
+ # Zip the model run directories
+ if self.MetaModel.ModelObj.link_type.lower() == 'pylink' and\
+ self.MetaModel.ExpDesign.sampling_method.lower() != 'user':
+ Model.zip_subdirs(Model.name, f'{Model.name}_')
+
+ # -------------------------------------------------------------------------
+ def train_seq_design(self):
+ """
+ Starts the adaptive sequential design for refining the surrogate model
+ by selecting training points in a sequential manner.
+
+ Returns
+ -------
+ MetaModel : object
+ Meta model object.
+
+ """
+ Model = self.MetaModel.ModelObj
+ # MetaModel = self.MetaModel
+ self.Model = Model
+
+ # Initialization
+ self.MetaModel.SeqModifiedLOO = {}
+ self.MetaModel.seqValidError = {}
+ self.MetaModel.SeqBME = {}
+ self.MetaModel.SeqKLD = {}
+ self.MetaModel.SeqDistHellinger = {}
+ self.MetaModel.seqRMSEMean = {}
+ self.MetaModel.seqRMSEStd = {}
+ self.MetaModel.seqMinDist = []
+
+ # Determine the metamodel type
+ if self.MetaModel.meta_model_type.lower() != 'gpe':
+ pce = True
+ else:
+ pce = False
+ mc_ref = True if bool(Model.mc_reference) else False
+ if mc_ref:
+ Model.read_mc_reference()
+
+ if not hasattr(self.MetaModel, 'valid_samples'):
+ self.MetaModel.valid_samples = []
+ self.MetaModel.valid_model_runs = []
+ self.MetaModel.valid_likelihoods = []
+
+ # Get the parameters
+ max_n_samples = self.MetaModel.ExpDesign.n_max_samples
+ mod_LOO_threshold = self.MetaModel.ExpDesign.mod_LOO_threshold
+ n_canddidate = self.MetaModel.ExpDesign.n_canddidate
+ post_snapshot = self.MetaModel.ExpDesign.post_snapshot
+ n_replication = self.MetaModel.ExpDesign.n_replication
+ util_func = self.MetaModel.ExpDesign.util_func
+ output_name = Model.Output.names
+ validError = None
+ # Handle if only one UtilityFunctions is provided
+ if not isinstance(util_func, list):
+ util_func = [self.MetaModel.ExpDesign.util_func]
+
+ # Read observations or MCReference
+ if len(Model.observations) != 0 or Model.meas_file is not None:
+ self.observations = Model.read_observation()
+ obs_data = self.observations
+ else:
+ obs_data = []
+ TotalSigma2 = {}
+ # TODO: ---------- Initial self.MetaModel ----------
+ # self.MetaModel.train_norm_design(parallel=False, verbose=True)
+ self.MetaModel.train_norm_design(verbose=True)
+ initMetaModel = deepcopy(self.MetaModel)
+
+ # Validation error if validation set is provided.
+ if self.MetaModel.valid_model_runs:
+ init_rmse, init_valid_error = self.__validError(initMetaModel)
+ init_valid_error = list(init_valid_error.values())
+ else:
+ init_rmse = None
+
+ # Check if discrepancy is provided
+ if len(obs_data) != 0 and hasattr(self.MetaModel, 'Discrepancy'):
+ TotalSigma2 = self.MetaModel.Discrepancy.parameters
+
+ # Calculate the initial BME
+ out = self.__BME_Calculator(
+ initMetaModel, obs_data, TotalSigma2, init_rmse)
+ init_BME, init_KLD, init_post, init_likes, init_dist_hellinger = out
+ print(f"\nInitial BME: {init_BME:.2f}")
+ print(f"Initial KLD: {init_KLD:.2f}")
+
+ # Posterior snapshot (initial)
+ if post_snapshot:
+ parNames = self.MetaModel.ExpDesign.par_names
+ print('Posterior snapshot (initial) is being plotted...')
+ self.__posteriorPlot(init_post, parNames, 'SeqPosterior_init')
+
+ # Check the convergence of the Mean & Std
+ if mc_ref and pce:
+ init_rmse_mean, init_rmse_std = self.__error_Mean_Std()
+ print(f"Initial Mean and Std error: {init_rmse_mean:.2f},"
+ f" {init_rmse_std:.2f}")
+
+ # Read the initial experimental design
+ Xinit = initMetaModel.ExpDesign.X
+ init_n_samples = len(initMetaModel.ExpDesign.X)
+ initYprev = initMetaModel.ModelOutputDict
+ initLCerror = initMetaModel.LCerror
+ n_itrs = max_n_samples - init_n_samples
+
+ # Read the initial ModifiedLOO
+ if pce:
+ Scores_all, varExpDesignY = [], []
+ for out_name in output_name:
+ y = self.MetaModel.ExpDesign.Y[out_name]
+ Scores_all.append(list(
+ self.MetaModel.score_dict['b_1'][out_name].values()))
+ if self.MetaModel.dim_red_method.lower() == 'pca':
+ pca = self.MetaModel.pca['b_1'][out_name]
+ components = pca.transform(y)
+ varExpDesignY.append(np.var(components, axis=0))
+ else:
+ varExpDesignY.append(np.var(y, axis=0))
+
+ Scores = [item for sublist in Scores_all for item in sublist]
+ weights = [item for sublist in varExpDesignY for item in sublist]
+ init_mod_LOO = [np.average([1-score for score in Scores],
+ weights=weights)]
+
+ prevMetaModel_dict = {}
+ # Replicate the sequential design
+ for repIdx in range(n_replication):
+ print(f'\n>>>> Replication: {repIdx+1}<<<<')
+
+ # To avoid changes ub original aPCE object
+ self.MetaModel.ExpDesign.X = Xinit
+ self.MetaModel.ExpDesign.Y = initYprev
+ self.MetaModel.LCerror = initLCerror
+
+ for util_f in util_func:
+ print(f'\n>>>> Utility Function: {util_f} <<<<')
+ # To avoid changes ub original aPCE object
+ self.MetaModel.ExpDesign.X = Xinit
+ self.MetaModel.ExpDesign.Y = initYprev
+ self.MetaModel.LCerror = initLCerror
+
+ # Set the experimental design
+ Xprev = Xinit
+ total_n_samples = init_n_samples
+ Yprev = initYprev
+
+ Xfull = []
+ Yfull = []
+
+ # Store the initial ModifiedLOO
+ if pce:
+ print("\nInitial ModifiedLOO:", init_mod_LOO)
+ SeqModifiedLOO = np.array(init_mod_LOO)
+
+ if len(self.MetaModel.valid_model_runs) != 0:
+ SeqValidError = np.array(init_valid_error)
+
+ # Check if data is provided
+ if len(obs_data) != 0:
+ SeqBME = np.array([init_BME])
+ SeqKLD = np.array([init_KLD])
+ SeqDistHellinger = np.array([init_dist_hellinger])
+
+ if mc_ref and pce:
+ seqRMSEMean = np.array([init_rmse_mean])
+ seqRMSEStd = np.array([init_rmse_std])
+
+ # ------- Start Sequential Experimental Design -------
+ postcnt = 1
+ for itr_no in range(1, n_itrs+1):
+ print(f'\n>>>> Iteration number {itr_no} <<<<')
+
+ # Save the metamodel prediction before updating
+ prevMetaModel_dict[itr_no] = deepcopy(self.MetaModel)
+ if itr_no > 1:
+ pc_model = prevMetaModel_dict[itr_no-1]
+ self._y_hat_prev, _ = pc_model.eval_metamodel(
+ samples=Xfull[-1].reshape(1, -1))
+ del prevMetaModel_dict[itr_no-1]
+
+ # Optimal Bayesian Design
+ self.MetaModel.ExpDesignFlag = 'sequential'
+ Xnew, updatedPrior = self.opt_SeqDesign(TotalSigma2,
+ n_canddidate,
+ util_f)
+ S = np.min(distance.cdist(Xinit, Xnew, 'euclidean'))
+ self.MetaModel.seqMinDist.append(S)
+ print(f"\nmin Dist from OldExpDesign: {S:2f}")
+ print("\n")
+
+ # Evaluate the full model response at the new sample
+ Ynew, _ = Model.run_model_parallel(
+ Xnew, prevRun_No=total_n_samples
+ )
+ total_n_samples += Xnew.shape[0]
+
+ # ------ Plot the surrogate model vs Origninal Model ------
+ if hasattr(self.MetaModel, 'adapt_verbose') and \
+ self.MetaModel.adapt_verbose:
+ from .adaptPlot import adaptPlot
+ y_hat, std_hat = self.MetaModel.eval_metamodel(
+ samples=Xnew
+ )
+ adaptPlot(
+ self.MetaModel, Ynew, y_hat, std_hat,
+ plotED=False
+ )
+
+ # -------- Retrain the surrogate model -------
+ # Extend new experimental design
+ Xfull = np.vstack((Xprev, Xnew))
+
+ # Updating experimental design Y
+ for out_name in output_name:
+ Yfull = np.vstack((Yprev[out_name], Ynew[out_name]))
+ self.MetaModel.ModelOutputDict[out_name] = Yfull
+
+ # Pass new design to the metamodel object
+ self.MetaModel.ExpDesign.sampling_method = 'user'
+ self.MetaModel.ExpDesign.X = Xfull
+ self.MetaModel.ExpDesign.Y = self.MetaModel.ModelOutputDict
+
+ # Save the Experimental Design for next iteration
+ Xprev = Xfull
+ Yprev = self.MetaModel.ModelOutputDict
+
+ # Pass the new prior as the input
+ self.MetaModel.input_obj.poly_coeffs_flag = False
+ if updatedPrior is not None:
+ self.MetaModel.input_obj.poly_coeffs_flag = True
+ print("updatedPrior:", updatedPrior.shape)
+ # Arbitrary polynomial chaos
+ for i in range(updatedPrior.shape[1]):
+ self.MetaModel.input_obj.Marginals[i].dist_type = None
+ x = updatedPrior[:, i]
+ self.MetaModel.input_obj.Marginals[i].raw_data = x
+
+ # Train the surrogate model for new ExpDesign
+ self.MetaModel.train_norm_design(parallel=False)
+
+ # -------- Evaluate the retrained surrogate model -------
+ # Extract Modified LOO from Output
+ if pce:
+ Scores_all, varExpDesignY = [], []
+ for out_name in output_name:
+ y = self.MetaModel.ExpDesign.Y[out_name]
+ Scores_all.append(list(
+ self.MetaModel.score_dict['b_1'][out_name].values()))
+ if self.MetaModel.dim_red_method.lower() == 'pca':
+ pca = self.MetaModel.pca['b_1'][out_name]
+ components = pca.transform(y)
+ varExpDesignY.append(np.var(components,
+ axis=0))
+ else:
+ varExpDesignY.append(np.var(y, axis=0))
+ Scores = [item for sublist in Scores_all for item
+ in sublist]
+ weights = [item for sublist in varExpDesignY for item
+ in sublist]
+ ModifiedLOO = [np.average(
+ [1-score for score in Scores], weights=weights)]
+
+ print('\n')
+ print(f"Updated ModifiedLOO {util_f}:\n", ModifiedLOO)
+ print('\n')
+
+ # Compute the validation error
+ if self.MetaModel.valid_model_runs:
+ rmse, validError = self.__validError(self.MetaModel)
+ ValidError = list(validError.values())
+ else:
+ rmse = None
+
+ # Store updated ModifiedLOO
+ if pce:
+ SeqModifiedLOO = np.vstack(
+ (SeqModifiedLOO, ModifiedLOO))
+ if len(self.MetaModel.valid_model_runs) != 0:
+ SeqValidError = np.vstack(
+ (SeqValidError, ValidError))
+ # -------- Caclulation of BME as accuracy metric -------
+ # Check if data is provided
+ if len(obs_data) != 0:
+ # Calculate the initial BME
+ out = self.__BME_Calculator(self.MetaModel, obs_data,
+ TotalSigma2, rmse)
+ BME, KLD, Posterior, likes, DistHellinger = out
+ print('\n')
+ print(f"Updated BME: {BME:.2f}")
+ print(f"Updated KLD: {KLD:.2f}")
+ print('\n')
+
+ # Plot some snapshots of the posterior
+ step_snapshot = self.MetaModel.ExpDesign.step_snapshot
+ if post_snapshot and postcnt % step_snapshot == 0:
+ parNames = self.MetaModel.ExpDesign.par_names
+ print('Posterior snapshot is being plotted...')
+ self.__posteriorPlot(Posterior, parNames,
+ f'SeqPosterior_{postcnt}')
+ postcnt += 1
+
+ # Check the convergence of the Mean&Std
+ if mc_ref and pce:
+ print('\n')
+ RMSE_Mean, RMSE_std = self.__error_Mean_Std()
+ print(f"Updated Mean and Std error: {RMSE_Mean:.2f}, "
+ f"{RMSE_std:.2f}")
+ print('\n')
+
+ # Store the updated BME & KLD
+ # Check if data is provided
+ if len(obs_data) != 0:
+ SeqBME = np.vstack((SeqBME, BME))
+ SeqKLD = np.vstack((SeqKLD, KLD))
+ SeqDistHellinger = np.vstack((SeqDistHellinger,
+ DistHellinger))
+ if mc_ref and pce:
+ seqRMSEMean = np.vstack((seqRMSEMean, RMSE_Mean))
+ seqRMSEStd = np.vstack((seqRMSEStd, RMSE_std))
+
+ if pce and any(LOO < mod_LOO_threshold
+ for LOO in ModifiedLOO):
+ break
+
+ # Clean up
+ if len(obs_data) != 0:
+ del out
+ print()
+ print('-'*50)
+ print()
+
+ # Store updated ModifiedLOO and BME in dictonary
+ strKey = f'{util_f}_rep_{repIdx+1}'
+ if pce:
+ self.MetaModel.SeqModifiedLOO[strKey] = SeqModifiedLOO
+ if len(self.MetaModel.valid_model_runs) != 0:
+ self.MetaModel.seqValidError[strKey] = SeqValidError
+
+ # Check if data is provided
+ if len(obs_data) != 0:
+ self.MetaModel.SeqBME[strKey] = SeqBME
+ self.MetaModel.SeqKLD[strKey] = SeqKLD
+ if hasattr(self.MetaModel, 'valid_likelihoods') and \
+ self.MetaModel.valid_likelihoods:
+ self.MetaModel.SeqDistHellinger[strKey] = SeqDistHellinger
+ if mc_ref and pce:
+ self.MetaModel.seqRMSEMean[strKey] = seqRMSEMean
+ self.MetaModel.seqRMSEStd[strKey] = seqRMSEStd
+
+ # return self.MetaModel
+
+ # -------------------------------------------------------------------------
+ def util_VarBasedDesign(self, X_can, index, util_func='Entropy'):
+ """
+ Computes the exploitation scores based on:
+ active learning MacKay(ALM) and active learning Cohn (ALC)
+ Paper: Sequential Design with Mutual Information for Computer
+ Experiments (MICE): Emulation of a Tsunami Model by Beck and Guillas
+ (2016)
+
+ Parameters
+ ----------
+ X_can : array of shape (n_samples, n_params)
+ Candidate samples.
+ index : int
+ Model output index.
+ UtilMethod : string, optional
+ Exploitation utility function. The default is 'Entropy'.
+
+ Returns
+ -------
+ float
+ Score.
+
+ """
+ MetaModel = self.MetaModel
+ ED_X = MetaModel.ExpDesign.X
+ out_dict_y = MetaModel.ExpDesign.Y
+ out_names = MetaModel.ModelObj.Output.names
+
+ # Run the Metamodel for the candidate
+ X_can = X_can.reshape(1, -1)
+ Y_PC_can, std_PC_can = MetaModel.eval_metamodel(samples=X_can)
+
+ if util_func.lower() == 'alm':
+ # ----- Entropy/MMSE/active learning MacKay(ALM) -----
+ # Compute perdiction variance of the old model
+ canPredVar = {key: std_PC_can[key]**2 for key in out_names}
+
+ varPCE = np.zeros((len(out_names), X_can.shape[0]))
+ for KeyIdx, key in enumerate(out_names):
+ varPCE[KeyIdx] = np.max(canPredVar[key], axis=1)
+ score = np.max(varPCE, axis=0)
+
+ elif util_func.lower() == 'eigf':
+ # ----- Expected Improvement for Global fit -----
+ # Find closest EDX to the candidate
+ distances = distance.cdist(ED_X, X_can, 'euclidean')
+ index = np.argmin(distances)
+
+ # Compute perdiction error and variance of the old model
+ predError = {key: Y_PC_can[key] for key in out_names}
+ canPredVar = {key: std_PC_can[key]**2 for key in out_names}
+
+ # Compute perdiction error and variance of the old model
+ # Eq (5) from Liu et al.(2018)
+ EIGF_PCE = np.zeros((len(out_names), X_can.shape[0]))
+ for KeyIdx, key in enumerate(out_names):
+ residual = predError[key] - out_dict_y[key][int(index)]
+ var = canPredVar[key]
+ EIGF_PCE[KeyIdx] = np.max(residual**2 + var, axis=1)
+ score = np.max(EIGF_PCE, axis=0)
+
+ return -1 * score # -1 is for minimization instead of maximization
+
+ # -------------------------------------------------------------------------
+ def util_BayesianActiveDesign(self, y_hat, std, sigma2Dict, var='DKL'):
+ """
+ Computes scores based on Bayesian active design criterion (var).
+
+ It is based on the following paper:
+ Oladyshkin, Sergey, Farid Mohammadi, Ilja Kroeker, and Wolfgang Nowak.
+ "Bayesian3 active learning for the gaussian process emulator using
+ information theory." Entropy 22, no. 8 (2020): 890.
+
+ Parameters
+ ----------
+ X_can : array of shape (n_samples, n_params)
+ Candidate samples.
+ sigma2Dict : dict
+ A dictionary containing the measurement errors (sigma^2).
+ var : string, optional
+ BAL design criterion. The default is 'DKL'.
+
+ Returns
+ -------
+ float
+ Score.
+
+ """
+
+ # Get the data
+ obs_data = self.observations
+ n_obs = self.Model.n_obs
+ mc_size = 10000
+
+ # Sample a distribution for a normal dist
+ # with Y_mean_can as the mean and Y_std_can as std.
+ Y_MC, std_MC = {}, {}
+ logPriorLikelihoods = np.zeros((mc_size))
+ for key in list(y_hat):
+ cov = np.diag(std[key]**2)
+ rv = stats.multivariate_normal(mean=y_hat[key], cov=cov)
+ Y_MC[key] = rv.rvs(size=mc_size)
+ logPriorLikelihoods += rv.logpdf(Y_MC[key])
+ std_MC[key] = np.zeros((mc_size, y_hat[key].shape[0]))
+
+ # Likelihood computation (Comparison of data and simulation
+ # results via PCE with candidate design)
+ likelihoods = self.__normpdf(Y_MC, std_MC, obs_data, sigma2Dict)
+
+ # Rejection Step
+ # Random numbers between 0 and 1
+ unif = np.random.rand(1, mc_size)[0]
+
+ # Reject the poorly performed prior
+ accepted = (likelihoods/np.max(likelihoods)) >= unif
+
+ # Prior-based estimation of BME
+ logBME = np.log(np.nanmean(likelihoods), dtype=np.float128)
+
+ # Posterior-based expectation of likelihoods
+ postLikelihoods = likelihoods[accepted]
+ postExpLikelihoods = np.mean(np.log(postLikelihoods))
+
+ # Posterior-based expectation of prior densities
+ postExpPrior = np.mean(logPriorLikelihoods[accepted])
+
+ # Utility function Eq.2 in Ref. (2)
+ # Posterior covariance matrix after observing data y
+ # Kullback-Leibler Divergence (Sergey's paper)
+ if var == 'DKL':
+
+ # TODO: Calculate the correction factor for BME
+ # BMECorrFactor = self.BME_Corr_Weight(PCE_SparseBayes_can,
+ # ObservationData, sigma2Dict)
+ # BME += BMECorrFactor
+ # Haun et al implementation
+ # U_J_d = np.mean(np.log(Likelihoods[Likelihoods!=0])- logBME)
+ U_J_d = postExpLikelihoods - logBME
+
+ # Marginal log likelihood
+ elif var == 'BME':
+ U_J_d = np.nanmean(likelihoods)
+
+ # Entropy-based information gain
+ elif var == 'infEntropy':
+ logBME = np.log(np.nanmean(likelihoods))
+ infEntropy = logBME - postExpPrior - postExpLikelihoods
+ U_J_d = infEntropy * -1 # -1 for minimization
+
+ # Bayesian information criterion
+ elif var == 'BIC':
+ coeffs = self.MetaModel.coeffs_dict.values()
+ nModelParams = max(len(v) for val in coeffs for v in val.values())
+ maxL = np.nanmax(likelihoods)
+ U_J_d = -2 * np.log(maxL) + np.log(n_obs) * nModelParams
+
+ # Akaike information criterion
+ elif var == 'AIC':
+ coeffs = self.MetaModel.coeffs_dict.values()
+ nModelParams = max(len(v) for val in coeffs for v in val.values())
+ maxlogL = np.log(np.nanmax(likelihoods))
+ AIC = -2 * maxlogL + 2 * nModelParams
+ # 2 * nModelParams * (nModelParams+1) / (n_obs-nModelParams-1)
+ penTerm = 0
+ U_J_d = 1*(AIC + penTerm)
+
+ # Deviance information criterion
+ elif var == 'DIC':
+ # D_theta_bar = np.mean(-2 * Likelihoods)
+ N_star_p = 0.5 * np.var(np.log(likelihoods[likelihoods != 0]))
+ Likelihoods_theta_mean = self.__normpdf(
+ y_hat, std, obs_data, sigma2Dict
+ )
+ DIC = -2 * np.log(Likelihoods_theta_mean) + 2 * N_star_p
+
+ U_J_d = DIC
+
+ else:
+ print('The algorithm you requested has not been implemented yet!')
+
+ # Handle inf and NaN (replace by zero)
+ if np.isnan(U_J_d) or U_J_d == -np.inf or U_J_d == np.inf:
+ U_J_d = 0.0
+
+ # Clear memory
+ del likelihoods
+ del Y_MC
+ del std_MC
+
+ return -1 * U_J_d # -1 is for minimization instead of maximization
+
+ # -------------------------------------------------------------------------
+ def update_metamodel(self, MetaModel, output, y_hat_can, univ_p_val, index,
+ new_pca=False):
+ BasisIndices = MetaModel.basis_dict[output]["y_"+str(index+1)]
+ clf_poly = MetaModel.clf_poly[output]["y_"+str(index+1)]
+ Mn = clf_poly.coef_
+ Sn = clf_poly.sigma_
+ beta = clf_poly.alpha_
+ active = clf_poly.active_
+ Psi = self.MetaModel.create_psi(BasisIndices, univ_p_val)
+
+ Sn_new_inv = np.linalg.inv(Sn)
+ Sn_new_inv += beta * np.dot(Psi[:, active].T, Psi[:, active])
+ Sn_new = np.linalg.inv(Sn_new_inv)
+
+ Mn_new = np.dot(Sn_new_inv, Mn[active]).reshape(-1, 1)
+ Mn_new += beta * np.dot(Psi[:, active].T, y_hat_can)
+ Mn_new = np.dot(Sn_new, Mn_new).flatten()
+
+ # Compute the old and new moments of PCEs
+ mean_old = Mn[0]
+ mean_new = Mn_new[0]
+ std_old = np.sqrt(np.sum(np.square(Mn[1:])))
+ std_new = np.sqrt(np.sum(np.square(Mn_new[1:])))
+
+ # Back transformation if PCA is selected.
+ if MetaModel.dim_red_method.lower() == 'pca':
+ old_pca = MetaModel.pca[output]
+ mean_old = old_pca.mean_[index]
+ mean_old += np.sum(mean_old * old_pca.components_[:, index])
+ std_old = np.sqrt(np.sum(std_old**2 *
+ old_pca.components_[:, index]**2))
+ mean_new = new_pca.mean_[index]
+ mean_new += np.sum(mean_new * new_pca.components_[:, index])
+ std_new = np.sqrt(np.sum(std_new**2 *
+ new_pca.components_[:, index]**2))
+ # print(f"mean_old: {mean_old:.2f} mean_new: {mean_new:.2f}")
+ # print(f"std_old: {std_old:.2f} std_new: {std_new:.2f}")
+ # Store the old and new moments of PCEs
+ results = {
+ 'mean_old': mean_old,
+ 'mean_new': mean_new,
+ 'std_old': std_old,
+ 'std_new': std_new
+ }
+ return results
+
+ # -------------------------------------------------------------------------
+ def util_BayesianDesign_old(self, X_can, X_MC, sigma2Dict, var='DKL'):
+ """
+ Computes scores based on Bayesian sequential design criterion (var).
+
+ Parameters
+ ----------
+ X_can : array of shape (n_samples, n_params)
+ Candidate samples.
+ sigma2Dict : dict
+ A dictionary containing the measurement errors (sigma^2).
+ var : string, optional
+ Bayesian design criterion. The default is 'DKL'.
+
+ Returns
+ -------
+ float
+ Score.
+
+ """
+
+ # To avoid changes ub original aPCE object
+ Model = self.Model
+ MetaModel = deepcopy(self.MetaModel)
+ old_EDY = MetaModel.ExpDesign.Y
+
+ # Evaluate the PCE metamodels using the candidate design
+ Y_PC_can, Y_std_can = self.MetaModel.eval_metamodel(
+ samples=np.array([X_can])
+ )
+
+ # Generate y from posterior predictive
+ m_size = 100
+ y_hat_samples = {}
+ for idx, key in enumerate(Model.Output.names):
+ means, stds = Y_PC_can[key][0], Y_std_can[key][0]
+ y_hat_samples[key] = np.random.multivariate_normal(
+ means, np.diag(stds), m_size)
+
+ # Create the SparseBayes-based PCE metamodel:
+ MetaModel.input_obj.poly_coeffs_flag = False
+ univ_p_val = self.MetaModel.univ_basis_vals(X_can)
+ G_n_m_all = np.zeros((m_size, len(Model.Output.names), Model.n_obs))
+
+ for i in range(m_size):
+ for idx, key in enumerate(Model.Output.names):
+ if MetaModel.dim_red_method.lower() == 'pca':
+ # Equal number of components
+ new_outputs = np.vstack(
+ (old_EDY[key], y_hat_samples[key][i])
+ )
+ new_pca, _ = MetaModel.pca_transformation(new_outputs)
+ target = new_pca.transform(
+ y_hat_samples[key][i].reshape(1, -1)
+ )[0]
+ else:
+ new_pca, target = False, y_hat_samples[key][i]
+
+ for j in range(len(target)):
+
+ # Update surrogate
+ result = self.update_metamodel(
+ MetaModel, key, target[j], univ_p_val, j, new_pca)
+
+ # Compute Expected Information Gain (Eq. 39)
+ G_n_m = np.log(result['std_old']/result['std_new']) - 1./2
+ G_n_m += result['std_new']**2 / (2*result['std_old']**2)
+ G_n_m += (result['mean_new'] - result['mean_old'])**2 /\
+ (2*result['std_old']**2)
+
+ G_n_m_all[i, idx, j] = G_n_m
+
+ U_J_d = G_n_m_all.mean(axis=(1, 2)).mean()
+ return -1 * U_J_d
+
+ # -------------------------------------------------------------------------
+ def util_BayesianDesign(self, X_can, X_MC, sigma2Dict, var='DKL'):
+ """
+ Computes scores based on Bayesian sequential design criterion (var).
+
+ Parameters
+ ----------
+ X_can : array of shape (n_samples, n_params)
+ Candidate samples.
+ sigma2Dict : dict
+ A dictionary containing the measurement errors (sigma^2).
+ var : string, optional
+ Bayesian design criterion. The default is 'DKL'.
+
+ Returns
+ -------
+ float
+ Score.
+
+ """
+
+ # To avoid changes ub original aPCE object
+ MetaModel = self.MetaModel
+ out_names = MetaModel.ModelObj.Output.names
+ if X_can.ndim == 1:
+ X_can = X_can.reshape(1, -1)
+
+ # Compute the mean and std based on the MetaModel
+ # pce_means, pce_stds = self._compute_pce_moments(MetaModel)
+ if var == 'ALC':
+ Y_MC, Y_MC_std = MetaModel.eval_metamodel(samples=X_MC)
+
+ # Old Experimental design
+ oldExpDesignX = MetaModel.ExpDesign.X
+ oldExpDesignY = MetaModel.ExpDesign.Y
+
+ # Evaluate the PCE metamodels at that location ???
+ Y_PC_can, Y_std_can = MetaModel.eval_metamodel(samples=X_can)
+ PCE_Model_can = deepcopy(MetaModel)
+ # Add the candidate to the ExpDesign
+ NewExpDesignX = np.vstack((oldExpDesignX, X_can))
+
+ NewExpDesignY = {}
+ for key in oldExpDesignY.keys():
+ NewExpDesignY[key] = np.vstack(
+ (oldExpDesignY[key], Y_PC_can[key])
+ )
+
+ PCE_Model_can.ExpDesign.sampling_method = 'user'
+ PCE_Model_can.ExpDesign.X = NewExpDesignX
+ PCE_Model_can.ModelOutputDict = NewExpDesignY
+ PCE_Model_can.ExpDesign.Y = NewExpDesignY
+
+ # Train the model for the observed data using x_can
+ PCE_Model_can.input_obj.poly_coeffs_flag = False
+ PCE_Model_can.train_norm_design(parallel=False)
+
+ # Set the ExpDesign to its original values
+ PCE_Model_can.ExpDesign.X = oldExpDesignX
+ PCE_Model_can.ModelOutputDict = oldExpDesignY
+ PCE_Model_can.ExpDesign.Y = oldExpDesignY
+
+ if var.lower() == 'mi':
+ # Mutual information based on Krause et al
+ # Adapted from Beck & Guillas (MICE) paper
+ _, std_PC_can = PCE_Model_can.eval_metamodel(samples=X_can)
+ std_can = {key: std_PC_can[key] for key in out_names}
+
+ std_old = {key: Y_std_can[key] for key in out_names}
+
+ varPCE = np.zeros((len(out_names)))
+ for i, key in enumerate(out_names):
+ varPCE[i] = np.mean(std_old[key]**2/std_can[key]**2)
+ score = np.mean(varPCE)
+
+ return -1 * score
+
+ elif var.lower() == 'alc':
+ # Active learning based on Gramyc and Lee
+ # Adaptive design and analysis of supercomputer experiments Techno-
+ # metrics, 51 (2009), pp. 130–145.
+
+ # Evaluate the MetaModel at the given samples
+ Y_MC_can, Y_MC_std_can = PCE_Model_can.eval_metamodel(samples=X_MC)
+
+ # Compute the score
+ score = []
+ for i, key in enumerate(out_names):
+ pce_var = Y_MC_std_can[key]**2
+ pce_var_can = Y_MC_std[key]**2
+ score.append(np.mean(pce_var-pce_var_can, axis=0))
+ score = np.mean(score)
+
+ return -1 * score
+
+ # ---------- Inner MC simulation for computing Utility Value ----------
+ # Estimation of the integral via Monte Varlo integration
+ MCsize = X_MC.shape[0]
+ ESS = 0
+
+ while ((ESS > MCsize) or (ESS < 1)):
+
+ # Enriching Monte Carlo samples if need be
+ if ESS != 0:
+ X_MC = self.MetaModel.ExpDesign.generate_samples(
+ MCsize, 'random'
+ )
+
+ # Evaluate the MetaModel at the given samples
+ Y_MC, std_MC = PCE_Model_can.eval_metamodel(samples=X_MC)
+
+ # Likelihood computation (Comparison of data and simulation
+ # results via PCE with candidate design)
+ likelihoods = self.__normpdf(
+ Y_MC, std_MC, self.observations, sigma2Dict
+ )
+
+ # Check the Effective Sample Size (1<ESS<MCsize)
+ ESS = 1 / np.sum(np.square(likelihoods/np.sum(likelihoods)))
+
+ # Enlarge sample size if it doesn't fulfill the criteria
+ if ((ESS > MCsize) or (ESS < 1)):
+ print("--- increasing MC size---")
+ MCsize *= 10
+ ESS = 0
+
+ # Rejection Step
+ # Random numbers between 0 and 1
+ unif = np.random.rand(1, MCsize)[0]
+
+ # Reject the poorly performed prior
+ accepted = (likelihoods/np.max(likelihoods)) >= unif
+
+ # -------------------- Utility functions --------------------
+ # Utility function Eq.2 in Ref. (2)
+ # Kullback-Leibler Divergence (Sergey's paper)
+ if var == 'DKL':
+
+ # Prior-based estimation of BME
+ logBME = np.log(np.nanmean(likelihoods, dtype=np.float128))
+
+ # Posterior-based expectation of likelihoods
+ postLikelihoods = likelihoods[accepted]
+ postExpLikelihoods = np.mean(np.log(postLikelihoods))
+
+ # Haun et al implementation
+ U_J_d = np.mean(np.log(likelihoods[likelihoods != 0]) - logBME)
+
+ # U_J_d = np.sum(G_n_m_all)
+ # Ryan et al (2014) implementation
+ # importanceWeights = Likelihoods[Likelihoods!=0]/np.sum(Likelihoods[Likelihoods!=0])
+ # U_J_d = np.mean(importanceWeights*np.log(Likelihoods[Likelihoods!=0])) - logBME
+
+ # U_J_d = postExpLikelihoods - logBME
+
+ # Marginal likelihood
+ elif var == 'BME':
+
+ # Prior-based estimation of BME
+ logBME = np.log(np.nanmean(likelihoods))
+ U_J_d = logBME
+
+ # Bayes risk likelihood
+ elif var == 'BayesRisk':
+
+ U_J_d = -1 * np.var(likelihoods)
+
+ # Entropy-based information gain
+ elif var == 'infEntropy':
+ # Prior-based estimation of BME
+ logBME = np.log(np.nanmean(likelihoods))
+
+ # Posterior-based expectation of likelihoods
+ postLikelihoods = likelihoods[accepted]
+ postLikelihoods /= np.nansum(likelihoods[accepted])
+ postExpLikelihoods = np.mean(np.log(postLikelihoods))
+
+ # Posterior-based expectation of prior densities
+ postExpPrior = np.mean(logPriorLikelihoods[accepted])
+
+ infEntropy = logBME - postExpPrior - postExpLikelihoods
+
+ U_J_d = infEntropy * -1 # -1 for minimization
+
+ # D-Posterior-precision
+ elif var == 'DPP':
+ X_Posterior = X_MC[accepted]
+ # covariance of the posterior parameters
+ U_J_d = -np.log(np.linalg.det(np.cov(X_Posterior)))
+
+ # A-Posterior-precision
+ elif var == 'APP':
+ X_Posterior = X_MC[accepted]
+ # trace of the posterior parameters
+ U_J_d = -np.log(np.trace(np.cov(X_Posterior)))
+
+ else:
+ print('The algorithm you requested has not been implemented yet!')
+
+ # Clear memory
+ del likelihoods
+ del Y_MC
+ del std_MC
+
+ return -1 * U_J_d # -1 is for minimization instead of maximization
+
+ # -------------------------------------------------------------------------
+ def subdomain(self, Bounds, n_new_samples):
+ """
+ Divides a domain defined by Bounds into sub domains.
+
+ Parameters
+ ----------
+ Bounds : list of tuples
+ List of lower and upper bounds.
+ n_new_samples : TYPE
+ DESCRIPTION.
+
+ Returns
+ -------
+ Subdomains : TYPE
+ DESCRIPTION.
+
+ """
+ n_params = self.MetaModel.n_params
+ n_subdomains = n_new_samples + 1
+ LinSpace = np.zeros((n_params, n_subdomains))
+
+ for i in range(n_params):
+ LinSpace[i] = np.linspace(start=Bounds[i][0], stop=Bounds[i][1],
+ num=n_subdomains)
+ Subdomains = []
+ for k in range(n_subdomains-1):
+ mylist = []
+ for i in range(n_params):
+ mylist.append((LinSpace[i, k+0], LinSpace[i, k+1]))
+ Subdomains.append(tuple(mylist))
+
+ return Subdomains
+
+ # -------------------------------------------------------------------------
+ def run_util_func(self, method, candidates, index, sigma2Dict=None,
+ var=None, X_MC=None):
+ """
+ Runs the utility function based on the given method.
+
+ Parameters
+ ----------
+ method : string
+ Exploitation method: `VarOptDesign`, `BayesActDesign` and
+ `BayesOptDesign`.
+ candidates : array of shape (n_samples, n_params)
+ All candidate parameter sets.
+ index : int
+ ExpDesign index.
+ sigma2Dict : dict, optional
+ A dictionary containing the measurement errors (sigma^2). The
+ default is None.
+ var : string, optional
+ Utility function. The default is None.
+ X_MC : TYPE, optional
+ DESCRIPTION. The default is None.
+
+ Returns
+ -------
+ index : TYPE
+ DESCRIPTION.
+ List
+ Scores.
+
+ """
+
+ if method.lower() == 'varoptdesign':
+ # U_J_d = self.util_VarBasedDesign(candidates, index, var)
+ U_J_d = np.zeros((candidates.shape[0]))
+ for idx, X_can in tqdm(enumerate(candidates), ascii=True,
+ desc="varoptdesign"):
+ U_J_d[idx] = self.util_VarBasedDesign(X_can, index, var)
+
+ elif method.lower() == 'bayesactdesign':
+ NCandidate = candidates.shape[0]
+ U_J_d = np.zeros((NCandidate))
+ # Evaluate all candidates
+ y_can, std_can = self.MetaModel.eval_metamodel(samples=candidates)
+ # loop through candidates
+ for idx, X_can in tqdm(enumerate(candidates), ascii=True,
+ desc="BAL Design"):
+ y_hat = {key: items[idx] for key, items in y_can.items()}
+ std = {key: items[idx] for key, items in std_can.items()}
+ U_J_d[idx] = self.util_BayesianActiveDesign(
+ y_hat, std, sigma2Dict, var)
+
+ elif method.lower() == 'bayesoptdesign':
+ NCandidate = candidates.shape[0]
+ U_J_d = np.zeros((NCandidate))
+ for idx, X_can in tqdm(enumerate(candidates), ascii=True,
+ desc="OptBayesianDesign"):
+ U_J_d[idx] = self.util_BayesianDesign(X_can, X_MC, sigma2Dict,
+ var)
+ return (index, -1 * U_J_d)
+
+ # -------------------------------------------------------------------------
+ def dual_annealing(self, method, Bounds, sigma2Dict, var, Run_No,
+ verbose=False):
+ """
+ Exploration algorithim to find the optimum parameter space.
+
+ Parameters
+ ----------
+ method : string
+ Exploitation method: `VarOptDesign`, `BayesActDesign` and
+ `BayesOptDesign`.
+ Bounds : list of tuples
+ List of lower and upper boundaries of parameters.
+ sigma2Dict : dict
+ A dictionary containing the measurement errors (sigma^2).
+ Run_No : int
+ Run number.
+ verbose : bool, optional
+ Print out a summary. The default is False.
+
+ Returns
+ -------
+ Run_No : int
+ Run number.
+ array
+ Optimial candidate.
+
+ """
+
+ Model = self.Model
+ max_func_itr = self.MetaModel.ExpDesign.max_func_itr
+
+ if method == 'VarOptDesign':
+ Res_Global = opt.dual_annealing(self.util_VarBasedDesign,
+ bounds=Bounds,
+ args=(Model, var),
+ maxfun=max_func_itr)
+
+ elif method == 'BayesOptDesign':
+ Res_Global = opt.dual_annealing(self.util_BayesianDesign,
+ bounds=Bounds,
+ args=(Model, sigma2Dict, var),
+ maxfun=max_func_itr)
+
+ if verbose:
+ print(f"global minimum: xmin = {Res_Global.x}, "
+ f"f(xmin) = {Res_Global.fun:.6f}, nfev = {Res_Global.nfev}")
+
+ return (Run_No, Res_Global.x)
+
+ # -------------------------------------------------------------------------
+ def tradoff_weights(self, tradeoff_scheme, old_EDX, old_EDY):
+ """
+ Calculates weights for exploration scores based on the requested
+ scheme: `None`, `equal`, `epsilon-decreasing` and `adaptive`.
+
+ `None`: No exploration.
+ `equal`: Same weights for exploration and exploitation scores.
+ `epsilon-decreasing`: Start with more exploration and increase the
+ influence of exploitation along the way with a exponential decay
+ function
+ `adaptive`: An adaptive method based on:
+ Liu, Haitao, Jianfei Cai, and Yew-Soon Ong. "An adaptive sampling
+ approach for Kriging metamodeling by maximizing expected prediction
+ error." Computers & Chemical Engineering 106 (2017): 171-182.
+
+ Parameters
+ ----------
+ tradeoff_scheme : string
+ Trade-off scheme for exloration and exploitation scores.
+ old_EDX : array (n_samples, n_params)
+ Old experimental design (training points).
+ old_EDY : dict
+ Old model responses (targets).
+
+ Returns
+ -------
+ exploration_weight : float
+ Exploration weight.
+ exploitation_weight: float
+ Exploitation weight.
+
+ """
+ if tradeoff_scheme is None:
+ exploration_weight = 0
+
+ elif tradeoff_scheme == 'equal':
+ exploration_weight = 0.5
+
+ elif tradeoff_scheme == 'epsilon-decreasing':
+ # epsilon-decreasing scheme
+ # Start with more exploration and increase the influence of
+ # exploitation along the way with a exponential decay function
+ initNSamples = self.MetaModel.ExpDesign.n_init_samples
+ n_max_samples = self.MetaModel.ExpDesign.n_max_samples
+
+ itrNumber = (self.MetaModel.ExpDesign.X.shape[0] - initNSamples)
+ itrNumber //= self.MetaModel.ExpDesign.n_new_samples
+
+ tau2 = -(n_max_samples-initNSamples-1) / np.log(1e-8)
+ exploration_weight = signal.exponential(n_max_samples-initNSamples,
+ 0, tau2, False)[itrNumber]
+
+ elif tradeoff_scheme == 'adaptive':
+
+ # Extract itrNumber
+ initNSamples = self.MetaModel.ExpDesign.n_init_samples
+ n_max_samples = self.MetaModel.ExpDesign.n_max_samples
+ itrNumber = (self.MetaModel.ExpDesign.X.shape[0] - initNSamples)
+ itrNumber //= self.MetaModel.ExpDesign.n_new_samples
+
+ if itrNumber == 0:
+ exploration_weight = 0.5
+ else:
+ # New adaptive trade-off according to Liu et al. (2017)
+ # Mean squared error for last design point
+ last_EDX = old_EDX[-1].reshape(1, -1)
+ lastPCEY, _ = self.MetaModel.eval_metamodel(samples=last_EDX)
+ pce_y = np.array(list(lastPCEY.values()))[:, 0]
+ y = np.array(list(old_EDY.values()))[:, -1, :]
+ mseError = mean_squared_error(pce_y, y)
+
+ # Mean squared CV - error for last design point
+ pce_y_prev = np.array(list(self._y_hat_prev.values()))[:, 0]
+ mseCVError = mean_squared_error(pce_y_prev, y)
+
+ exploration_weight = min([0.5*mseError/mseCVError, 1])
+
+ # Exploitation weight
+ exploitation_weight = 1 - exploration_weight
+
+ return exploration_weight, exploitation_weight
+
+ # -------------------------------------------------------------------------
+ def opt_SeqDesign(self, sigma2, n_candidates=5, var='DKL'):
+ """
+ Runs optimal sequential design.
+
+ Parameters
+ ----------
+ sigma2 : dict, optional
+ A dictionary containing the measurement errors (sigma^2). The
+ default is None.
+ n_candidates : int, optional
+ Number of candidate samples. The default is 5.
+ var : string, optional
+ Utility function. The default is None.
+
+ Raises
+ ------
+ NameError
+ Wrong utility function.
+
+ Returns
+ -------
+ Xnew : array (n_samples, n_params)
+ Selected new training point(s).
+ """
+
+ # Initialization
+ MetaModel = self.MetaModel
+ Bounds = MetaModel.bound_tuples
+ n_new_samples = MetaModel.ExpDesign.n_new_samples
+ explore_method = MetaModel.ExpDesign.explore_method
+ exploit_method = MetaModel.ExpDesign.exploit_method
+ n_cand_groups = MetaModel.ExpDesign.n_cand_groups
+ tradeoff_scheme = MetaModel.ExpDesign.tradeoff_scheme
+
+ old_EDX = MetaModel.ExpDesign.X
+ old_EDY = MetaModel.ExpDesign.Y.copy()
+ ndim = MetaModel.ExpDesign.X.shape[1]
+ OutputNames = MetaModel.ModelObj.Output.names
+
+ # -----------------------------------------
+ # ----------- CUSTOMIZED METHODS ----------
+ # -----------------------------------------
+ # Utility function exploit_method provided by user
+ if exploit_method.lower() == 'user':
+
+ Xnew, filteredSamples = MetaModel.ExpDesign.ExploitFunction(self)
+
+ print("\n")
+ print("\nXnew:\n", Xnew)
+
+ return Xnew, filteredSamples
+
+ # -----------------------------------------
+ # ---------- EXPLORATION METHODS ----------
+ # -----------------------------------------
+ if explore_method == 'dual annealing':
+ # ------- EXPLORATION: OPTIMIZATION -------
+ import time
+ start_time = time.time()
+
+ # Divide the domain to subdomains
+ args = []
+ subdomains = self.subdomain(Bounds, n_new_samples)
+ for i in range(n_new_samples):
+ args.append((exploit_method, subdomains[i], sigma2, var, i))
+
+ # Multiprocessing
+ pool = multiprocessing.Pool(multiprocessing.cpu_count())
+
+ # With Pool.starmap_async()
+ results = pool.starmap_async(self.dual_annealing, args).get()
+
+ # Close the pool
+ pool.close()
+
+ Xnew = np.array([results[i][1] for i in range(n_new_samples)])
+
+ print("\nXnew:\n", Xnew)
+
+ elapsed_time = time.time() - start_time
+ print("\n")
+ print(f"elapsed_time: {round(elapsed_time,2)} sec.")
+ print('-'*20)
+
+ elif explore_method == 'LOOCV':
+ # -----------------------------------------------------------------
+ # TODO: LOOCV model construnction based on Feng et al. (2020)
+ # 'LOOCV':
+ # Initilize the ExploitScore array
+
+ # Generate random samples
+ allCandidates = MetaModel.ExpDesign.generate_samples(n_candidates,
+ 'random')
+
+ # Construct error model based on LCerror
+ errorModel = MetaModel.create_ModelError(old_EDX, self.LCerror)
+ self.errorModel.append(copy(errorModel))
+
+ # Evaluate the error models for allCandidates
+ eLCAllCands, _ = errorModel.eval_errormodel(allCandidates)
+ # Select the maximum as the representative error
+ eLCAllCands = np.dstack(eLCAllCands.values())
+ eLCAllCandidates = np.max(eLCAllCands, axis=1)[:, 0]
+
+ # Normalize the error w.r.t the maximum error
+ scoreExploration = eLCAllCandidates / np.sum(eLCAllCandidates)
+
+ else:
+ # ------- EXPLORATION: SPACE-FILLING DESIGN -------
+ # Generate candidate samples from Exploration class
+ explore = Exploration(MetaModel, n_candidates)
+ explore.w = 100 # * ndim #500
+ # Select criterion (mc-intersite-proj-th, mc-intersite-proj)
+ explore.mc_criterion = 'mc-intersite-proj'
+ allCandidates, scoreExploration = explore.get_exploration_samples()
+
+ # Temp: ---- Plot all candidates -----
+ if ndim == 2:
+ def plotter(points, allCandidates, Method,
+ scoreExploration=None):
+ if Method == 'Voronoi':
+ from scipy.spatial import Voronoi, voronoi_plot_2d
+ vor = Voronoi(points)
+ fig = voronoi_plot_2d(vor)
+ ax1 = fig.axes[0]
+ else:
+ fig = plt.figure()
+ ax1 = fig.add_subplot(111)
+ ax1.scatter(points[:, 0], points[:, 1], s=10, c='r',
+ marker="s", label='Old Design Points')
+ ax1.scatter(allCandidates[:, 0], allCandidates[:, 1], s=10,
+ c='b', marker="o", label='Design candidates')
+ for i in range(points.shape[0]):
+ txt = 'p'+str(i+1)
+ ax1.annotate(txt, (points[i, 0], points[i, 1]))
+ if scoreExploration is not None:
+ for i in range(allCandidates.shape[0]):
+ txt = str(round(scoreExploration[i], 5))
+ ax1.annotate(txt, (allCandidates[i, 0],
+ allCandidates[i, 1]))
+
+ plt.xlim(self.bound_tuples[0])
+ plt.ylim(self.bound_tuples[1])
+ # plt.show()
+ plt.legend(loc='upper left')
+
+ # -----------------------------------------
+ # --------- EXPLOITATION METHODS ----------
+ # -----------------------------------------
+ if exploit_method == 'BayesOptDesign' or\
+ exploit_method == 'BayesActDesign':
+
+ # ------- Calculate Exoploration weight -------
+ # Compute exploration weight based on trade off scheme
+ explore_w, exploit_w = self.tradoff_weights(tradeoff_scheme,
+ old_EDX,
+ old_EDY)
+ print(f"\n Exploration weight={explore_w:0.3f} "
+ f"Exploitation weight={exploit_w:0.3f}\n")
+
+ # ------- EXPLOITATION: BayesOptDesign & ActiveLearning -------
+ if explore_w != 1.0:
+
+ # Create a sample pool for rejection sampling
+ MCsize = 15000
+ X_MC = MetaModel.ExpDesign.generate_samples(MCsize, 'random')
+ candidates = MetaModel.ExpDesign.generate_samples(
+ MetaModel.ExpDesign.max_func_itr, 'latin_hypercube')
+
+ # Split the candidates in groups for multiprocessing
+ split_cand = np.array_split(
+ candidates, n_cand_groups, axis=0
+ )
+
+ results = Parallel(n_jobs=-1, backend='multiprocessing')(
+ delayed(self.run_util_func)(
+ exploit_method, split_cand[i], i, sigma2, var, X_MC)
+ for i in range(n_cand_groups))
+ # out = map(self.run_util_func,
+ # [exploit_method]*n_cand_groups,
+ # split_cand,
+ # range(n_cand_groups),
+ # [sigma2] * n_cand_groups,
+ # [var] * n_cand_groups,
+ # [X_MC] * n_cand_groups
+ # )
+ # results = list(out)
+
+ # Retrieve the results and append them
+ U_J_d = np.concatenate([results[NofE][1] for NofE in
+ range(n_cand_groups)])
+
+ # Check if all scores are inf
+ if np.isinf(U_J_d).all() or np.isnan(U_J_d).all():
+ U_J_d = np.ones(len(U_J_d))
+
+ # Get the expected value (mean) of the Utility score
+ # for each cell
+ if explore_method == 'Voronoi':
+ U_J_d = np.mean(U_J_d.reshape(-1, n_candidates), axis=1)
+
+ # create surrogate model for U_J_d
+ # from sklearn.preprocessing import MinMaxScaler
+ # # Take care of inf entries
+ # good_indices = [i for i, arr in enumerate(U_J_d)
+ # if np.isfinite(arr).all()]
+ # scaler = MinMaxScaler()
+ # X_S = scaler.fit_transform(candidates[good_indices])
+ # gp = MetaModel.gaussian_process_emulator(
+ # X_S, U_J_d[good_indices], autoSelect=False
+ # )
+ # U_J_d = gp.predict(scaler.transform(allCandidates))
+
+ # Normalize U_J_d
+ norm_U_J_d = U_J_d / np.sum(U_J_d)
+ else:
+ norm_U_J_d = np.zeros((len(scoreExploration)))
+
+ # ------- Calculate Total score -------
+ # ------- Trade off between EXPLORATION & EXPLOITATION -------
+ # Total score
+ totalScore = exploit_w * norm_U_J_d
+ totalScore += explore_w * scoreExploration
+
+ # temp: Plot
+ # dim = self.ExpDesign.X.shape[1]
+ # if dim == 2:
+ # plotter(self.ExpDesign.X, allCandidates, explore_method)
+
+ # ------- Select the best candidate -------
+ # find an optimal point subset to add to the initial design by
+ # maximization of the utility score and taking care of NaN values
+ temp = totalScore.copy()
+ temp[np.isnan(totalScore)] = -np.inf
+ sorted_idxtotalScore = np.argsort(temp)[::-1]
+ bestIdx = sorted_idxtotalScore[:n_new_samples]
+
+ # select the requested number of samples
+ if explore_method == 'Voronoi':
+ Xnew = np.zeros((n_new_samples, ndim))
+ for i, idx in enumerate(bestIdx):
+ X_can = explore.closestPoints[idx]
+
+ # Calculate the maxmin score for the region of interest
+ newSamples, maxminScore = explore.get_mc_samples(X_can)
+
+ # select the requested number of samples
+ Xnew[i] = newSamples[np.argmax(maxminScore)]
+ else:
+ Xnew = allCandidates[sorted_idxtotalScore[:n_new_samples]]
+
+ elif exploit_method == 'VarOptDesign':
+ # ------- EXPLOITATION: VarOptDesign -------
+ UtilMethod = var
+
+ # ------- Calculate Exoploration weight -------
+ # Compute exploration weight based on trade off scheme
+ explore_w, exploit_w = self.tradoff_weights(tradeoff_scheme,
+ old_EDX,
+ old_EDY)
+ print(f"\nweightExploration={explore_w:0.3f} "
+ f"weightExploitation={exploit_w:0.3f}")
+
+ # Generate candidate samples from Exploration class
+ nMeasurement = old_EDY[OutputNames[0]].shape[1]
+
+ # Find sensitive region
+ if UtilMethod == 'LOOCV':
+ LCerror = MetaModel.LCerror
+ allModifiedLOO = np.zeros((len(old_EDX), len(OutputNames),
+ nMeasurement))
+ for y_idx, y_key in enumerate(OutputNames):
+ for idx, key in enumerate(LCerror[y_key].keys()):
+ allModifiedLOO[:, y_idx, idx] = abs(
+ LCerror[y_key][key])
+
+ ExploitScore = np.max(np.max(allModifiedLOO, axis=1), axis=1)
+
+ elif UtilMethod in ['EIGF', 'ALM']:
+ # ----- All other in ['EIGF', 'ALM'] -----
+ # Initilize the ExploitScore array
+ ExploitScore = np.zeros((len(old_EDX), len(OutputNames)))
+
+ # Split the candidates in groups for multiprocessing
+ if explore_method != 'Voronoi':
+ split_cand = np.array_split(allCandidates,
+ n_cand_groups,
+ axis=0)
+ goodSampleIdx = range(n_cand_groups)
+ else:
+ # Find indices of the Vornoi cells with samples
+ goodSampleIdx = []
+ for idx in range(len(explore.closest_points)):
+ if len(explore.closest_points[idx]) != 0:
+ goodSampleIdx.append(idx)
+ split_cand = explore.closest_points
+
+ # Split the candidates in groups for multiprocessing
+ args = []
+ for index in goodSampleIdx:
+ args.append((exploit_method, split_cand[index], index,
+ sigma2, var))
+
+ # Multiprocessing
+ pool = multiprocessing.Pool(multiprocessing.cpu_count())
+ # With Pool.starmap_async()
+ results = pool.starmap_async(self.run_util_func, args).get()
+
+ # Close the pool
+ pool.close()
+ # out = map(self.run_util_func,
+ # [exploit_method]*len(goodSampleIdx),
+ # split_cand,
+ # range(len(goodSampleIdx)),
+ # [sigma2] * len(goodSampleIdx),
+ # [var] * len(goodSampleIdx)
+ # )
+ # results = list(out)
+
+ # Retrieve the results and append them
+ if explore_method == 'Voronoi':
+ ExploitScore = [np.mean(results[k][1]) for k in
+ range(len(goodSampleIdx))]
+ else:
+ ExploitScore = np.concatenate(
+ [results[k][1] for k in range(len(goodSampleIdx))])
+
+ else:
+ raise NameError('The requested utility function is not '
+ 'available.')
+
+ # print("ExploitScore:\n", ExploitScore)
+
+ # find an optimal point subset to add to the initial design by
+ # maximization of the utility score and taking care of NaN values
+ # Total score
+ # Normalize U_J_d
+ ExploitScore = ExploitScore / np.sum(ExploitScore)
+ totalScore = exploit_w * ExploitScore
+ totalScore += explore_w * scoreExploration
+
+ temp = totalScore.copy()
+ sorted_idxtotalScore = np.argsort(temp, axis=0)[::-1]
+ bestIdx = sorted_idxtotalScore[:n_new_samples]
+
+ Xnew = np.zeros((n_new_samples, ndim))
+ if explore_method != 'Voronoi':
+ Xnew = allCandidates[bestIdx]
+ else:
+ for i, idx in enumerate(bestIdx.flatten()):
+ X_can = explore.closest_points[idx]
+ # plotter(self.ExpDesign.X, X_can, explore_method,
+ # scoreExploration=None)
+
+ # Calculate the maxmin score for the region of interest
+ newSamples, maxminScore = explore.get_mc_samples(X_can)
+
+ # select the requested number of samples
+ Xnew[i] = newSamples[np.argmax(maxminScore)]
+
+ elif exploit_method == 'alphabetic':
+ # ------- EXPLOITATION: ALPHABETIC -------
+ Xnew = self.util_AlphOptDesign(allCandidates, var)
+
+ elif exploit_method == 'Space-filling':
+ # ------- EXPLOITATION: SPACE-FILLING -------
+ totalScore = scoreExploration
+
+ # ------- Select the best candidate -------
+ # find an optimal point subset to add to the initial design by
+ # maximization of the utility score and taking care of NaN values
+ temp = totalScore.copy()
+ temp[np.isnan(totalScore)] = -np.inf
+ sorted_idxtotalScore = np.argsort(temp)[::-1]
+
+ # select the requested number of samples
+ Xnew = allCandidates[sorted_idxtotalScore[:n_new_samples]]
+
+ else:
+ raise NameError('The requested design method is not available.')
+
+ print("\n")
+ print("\nRun No. {}:".format(old_EDX.shape[0]+1))
+ print("Xnew:\n", Xnew)
+
+ return Xnew, None
+
+ # -------------------------------------------------------------------------
+ def util_AlphOptDesign(self, candidates, var='D-Opt'):
+ """
+ Enriches the Experimental design with the requested alphabetic
+ criterion based on exploring the space with number of sampling points.
+
+ Ref: Hadigol, M., & Doostan, A. (2018). Least squares polynomial chaos
+ expansion: A review of sampling strategies., Computer Methods in
+ Applied Mechanics and Engineering, 332, 382-407.
+
+ Arguments
+ ---------
+ NCandidate : int
+ Number of candidate points to be searched
+
+ var : string
+ Alphabetic optimality criterion
+
+ Returns
+ -------
+ X_new : array of shape (1, n_params)
+ The new sampling location in the input space.
+ """
+ MetaModelOrig = self
+ Model = self.Model
+ n_new_samples = MetaModelOrig.ExpDesign.n_new_samples
+ NCandidate = candidates.shape[0]
+
+ # TODO: Loop over outputs
+ OutputName = Model.Output.names[0]
+
+ # To avoid changes ub original aPCE object
+ MetaModel = deepcopy(MetaModelOrig)
+
+ # Old Experimental design
+ oldExpDesignX = MetaModel.ExpDesign.X
+
+ # TODO: Only one psi can be selected.
+ # Suggestion: Go for the one with the highest LOO error
+ Scores = list(MetaModel.score_dict[OutputName].values())
+ ModifiedLOO = [1-score for score in Scores]
+ outIdx = np.argmax(ModifiedLOO)
+
+ # Initialize Phi to save the criterion's values
+ Phi = np.zeros((NCandidate))
+
+ BasisIndices = MetaModelOrig.basis_dict[OutputName]["y_"+str(outIdx+1)]
+ P = len(BasisIndices)
+
+ # ------ Old Psi ------------
+ univ_p_val = MetaModelOrig.univ_basis_vals(oldExpDesignX)
+ Psi = MetaModelOrig.create_psi(BasisIndices, univ_p_val)
+
+ # ------ New candidates (Psi_c) ------------
+ # Assemble Psi_c
+ univ_p_val_c = self.univ_basis_vals(candidates)
+ Psi_c = self.create_psi(BasisIndices, univ_p_val_c)
+
+ for idx in range(NCandidate):
+
+ # Include the new row to the original Psi
+ Psi_cand = np.vstack((Psi, Psi_c[idx]))
+
+ # Information matrix
+ PsiTPsi = np.dot(Psi_cand.T, Psi_cand)
+ M = PsiTPsi / (len(oldExpDesignX)+1)
+
+ if np.linalg.cond(PsiTPsi) > 1e-12 \
+ and np.linalg.cond(PsiTPsi) < 1 / sys.float_info.epsilon:
+ # faster
+ invM = linalg.solve(M, sparse.eye(PsiTPsi.shape[0]).toarray())
+ else:
+ # stabler
+ invM = np.linalg.pinv(M)
+
+ # ---------- Calculate optimality criterion ----------
+ # Optimality criteria according to Section 4.5.1 in Ref.
+
+ # D-Opt
+ if var == 'D-Opt':
+ Phi[idx] = (np.linalg.det(invM)) ** (1/P)
+
+ # A-Opt
+ elif var == 'A-Opt':
+ Phi[idx] = np.trace(invM)
+
+ # K-Opt
+ elif var == 'K-Opt':
+ Phi[idx] = np.linalg.cond(M)
+
+ else:
+ raise Exception('The optimality criterion you requested has '
+ 'not been implemented yet!')
+
+ # find an optimal point subset to add to the initial design
+ # by minimization of the Phi
+ sorted_idxtotalScore = np.argsort(Phi)
+
+ # select the requested number of samples
+ Xnew = candidates[sorted_idxtotalScore[:n_new_samples]]
+
+ return Xnew
+
+ # -------------------------------------------------------------------------
+ def __normpdf(self, y_hat_pce, std_pce, obs_data, total_sigma2s,
+ rmse=None):
+
+ Model = self.Model
+ likelihoods = 1.0
+
+ # Loop over the outputs
+ for idx, out in enumerate(Model.Output.names):
+
+ # (Meta)Model Output
+ nsamples, nout = y_hat_pce[out].shape
+
+ # Prepare data and remove NaN
+ try:
+ data = obs_data[out].values[~np.isnan(obs_data[out])]
+ except AttributeError:
+ data = obs_data[out][~np.isnan(obs_data[out])]
+
+ # Prepare sigma2s
+ non_nan_indices = ~np.isnan(total_sigma2s[out])
+ tot_sigma2s = total_sigma2s[out][non_nan_indices][:nout].values
+
+ # Surrogate error if valid dataset is given.
+ if rmse is not None:
+ tot_sigma2s += rmse[out]**2
+ else:
+ tot_sigma2s += np.mean(std_pce[out])**2
+
+ likelihoods *= stats.multivariate_normal.pdf(
+ y_hat_pce[out], data, np.diag(tot_sigma2s),
+ allow_singular=True)
+
+ self.Likelihoods = likelihoods
+
+ return likelihoods
+
+ # -------------------------------------------------------------------------
+ def __corr_factor_BME(self, obs_data, total_sigma2s, logBME):
+ """
+ Calculates the correction factor for BMEs.
+ """
+ MetaModel = self.MetaModel
+ samples = MetaModel.ExpDesign.X # valid_samples
+ model_outputs = MetaModel.ExpDesign.Y # valid_model_runs
+ Model = MetaModel.ModelObj
+ n_samples = samples.shape[0]
+
+ # Extract the requested model outputs for likelihood calulation
+ output_names = Model.Output.names
+
+ # TODO: Evaluate MetaModel on the experimental design and ValidSet
+ OutputRS, stdOutputRS = MetaModel.eval_metamodel(samples=samples)
+
+ logLik_data = np.zeros((n_samples))
+ logLik_model = np.zeros((n_samples))
+ # Loop over the outputs
+ for idx, out in enumerate(output_names):
+
+ # (Meta)Model Output
+ nsamples, nout = model_outputs[out].shape
+
+ # Prepare data and remove NaN
+ try:
+ data = obs_data[out].values[~np.isnan(obs_data[out])]
+ except AttributeError:
+ data = obs_data[out][~np.isnan(obs_data[out])]
+
+ # Prepare sigma2s
+ non_nan_indices = ~np.isnan(total_sigma2s[out])
+ tot_sigma2s = total_sigma2s[out][non_nan_indices][:nout]
+
+ # Covariance Matrix
+ covMatrix_data = np.diag(tot_sigma2s)
+
+ for i, sample in enumerate(samples):
+
+ # Simulation run
+ y_m = model_outputs[out][i]
+
+ # Surrogate prediction
+ y_m_hat = OutputRS[out][i]
+
+ # CovMatrix with the surrogate error
+ # covMatrix = np.diag(stdOutputRS[out][i]**2)
+ covMatrix = np.diag((y_m-y_m_hat)**2)
+ covMatrix = np.diag(
+ np.mean((model_outputs[out]-OutputRS[out]), axis=0)**2
+ )
+
+ # Compute likelilhood output vs data
+ logLik_data[i] += self.__logpdf(
+ y_m_hat, data, covMatrix_data
+ )
+
+ # Compute likelilhood output vs surrogate
+ logLik_model[i] += self.__logpdf(y_m_hat, y_m, covMatrix)
+
+ # Weight
+ logLik_data -= logBME
+ weights = np.exp(logLik_model+logLik_data)
+
+ return np.log(np.mean(weights))
+
+ # -------------------------------------------------------------------------
+ def __logpdf(self, x, mean, cov):
+ """
+ computes the likelihood based on a multivariate normal distribution.
+
+ Parameters
+ ----------
+ x : TYPE
+ DESCRIPTION.
+ mean : array_like
+ Observation data.
+ cov : 2d array
+ Covariance matrix of the distribution.
+
+ Returns
+ -------
+ log_lik : float
+ Log likelihood.
+
+ """
+ n = len(mean)
+ L = linalg.cholesky(cov, lower=True)
+ beta = np.sum(np.log(np.diag(L)))
+ dev = x - mean
+ alpha = dev.dot(linalg.cho_solve((L, True), dev))
+ log_lik = -0.5 * alpha - beta - n / 2. * np.log(2 * np.pi)
+
+ return log_lik
+
+ # -------------------------------------------------------------------------
+ def __posteriorPlot(self, posterior, par_names, key):
+
+ # Initialization
+ newpath = (r'Outputs_SeqPosteriorComparison/posterior')
+ os.makedirs(newpath, exist_ok=True)
+
+ bound_tuples = self.MetaModel.bound_tuples
+ n_params = len(par_names)
+ font_size = 40
+ if n_params == 2:
+
+ figPosterior, ax = plt.subplots(figsize=(15, 15))
+
+ sns.kdeplot(x=posterior[:, 0], y=posterior[:, 1],
+ fill=True, ax=ax, cmap=plt.cm.jet,
+ clip=bound_tuples)
+ # Axis labels
+ plt.xlabel(par_names[0], fontsize=font_size)
+ plt.ylabel(par_names[1], fontsize=font_size)
+
+ # Set axis limit
+ plt.xlim(bound_tuples[0])
+ plt.ylim(bound_tuples[1])
+
+ # Increase font size
+ plt.xticks(fontsize=font_size)
+ plt.yticks(fontsize=font_size)
+
+ # Switch off the grids
+ plt.grid(False)
+
+ else:
+ import corner
+ figPosterior = corner.corner(posterior, labels=par_names,
+ title_fmt='.2e', show_titles=True,
+ title_kwargs={"fontsize": 12})
+
+ figPosterior.savefig(f'./{newpath}/{key}.pdf', bbox_inches='tight')
+ plt.close()
+
+ # Save the posterior as .npy
+ np.save(f'./{newpath}/{key}.npy', posterior)
+
+ return figPosterior
+
+ # -------------------------------------------------------------------------
+ def __hellinger_distance(self, P, Q):
+ """
+ Hellinger distance between two continuous distributions.
+
+ The maximum distance 1 is achieved when P assigns probability zero to
+ every set to which Q assigns a positive probability, and vice versa.
+ 0 (identical) and 1 (maximally different)
+
+ Parameters
+ ----------
+ P : array
+ Reference likelihood.
+ Q : array
+ Estimated likelihood.
+
+ Returns
+ -------
+ float
+ Hellinger distance of two distributions.
+
+ """
+ mu1 = P.mean()
+ Sigma1 = np.std(P)
+
+ mu2 = Q.mean()
+ Sigma2 = np.std(Q)
+
+ term1 = np.sqrt(2*Sigma1*Sigma2 / (Sigma1**2 + Sigma2**2))
+
+ term2 = np.exp(-.25 * (mu1 - mu2)**2 / (Sigma1**2 + Sigma2**2))
+
+ H_squared = 1 - term1 * term2
+
+ return np.sqrt(H_squared)
+
+ # -------------------------------------------------------------------------
+ def __BME_Calculator(self, MetaModel, obs_data, sigma2Dict, rmse=None):
+ """
+ This function computes the Bayesian model evidence (BME) via Monte
+ Carlo integration.
+
+ """
+ # Initializations
+ if hasattr(MetaModel, 'valid_likelihoods'):
+ valid_likelihoods = MetaModel.valid_likelihoods
+ else:
+ valid_likelihoods = []
+
+ post_snapshot = MetaModel.ExpDesign.post_snapshot
+ if post_snapshot or len(valid_likelihoods) != 0:
+ newpath = (r'Outputs_SeqPosteriorComparison/likelihood_vs_ref')
+ os.makedirs(newpath, exist_ok=True)
+
+ SamplingMethod = 'random'
+ MCsize = 10000
+ ESS = 0
+
+ # Estimation of the integral via Monte Varlo integration
+ while (ESS > MCsize) or (ESS < 1):
+
+ # Generate samples for Monte Carlo simulation
+ X_MC = MetaModel.ExpDesign.generate_samples(
+ MCsize, SamplingMethod
+ )
+
+ # Monte Carlo simulation for the candidate design
+ Y_MC, std_MC = MetaModel.eval_metamodel(samples=X_MC)
+
+ # Likelihood computation (Comparison of data and
+ # simulation results via PCE with candidate design)
+ Likelihoods = self.__normpdf(
+ Y_MC, std_MC, obs_data, sigma2Dict, rmse
+ )
+
+ # Check the Effective Sample Size (1000<ESS<MCsize)
+ ESS = 1 / np.sum(np.square(Likelihoods/np.sum(Likelihoods)))
+
+ # Enlarge sample size if it doesn't fulfill the criteria
+ if (ESS > MCsize) or (ESS < 1):
+ print(f'ESS={ESS} MC size should be larger.')
+ MCsize *= 10
+ ESS = 0
+
+ # Rejection Step
+ # Random numbers between 0 and 1
+ unif = np.random.rand(1, MCsize)[0]
+
+ # Reject the poorly performed prior
+ accepted = (Likelihoods/np.max(Likelihoods)) >= unif
+ X_Posterior = X_MC[accepted]
+
+ # ------------------------------------------------------------
+ # --- Kullback-Leibler Divergence & Information Entropy ------
+ # ------------------------------------------------------------
+ # Prior-based estimation of BME
+ logBME = np.log(np.nanmean(Likelihoods))
+
+ # TODO: Correction factor
+ # log_weight = self.__corr_factor_BME(obs_data, sigma2Dict, logBME)
+
+ # Posterior-based expectation of likelihoods
+ postExpLikelihoods = np.mean(np.log(Likelihoods[accepted]))
+
+ # Posterior-based expectation of prior densities
+ postExpPrior = np.mean(
+ np.log(MetaModel.ExpDesign.JDist.pdf(X_Posterior.T))
+ )
+
+ # Calculate Kullback-Leibler Divergence
+ # KLD = np.mean(np.log(Likelihoods[Likelihoods!=0])- logBME)
+ KLD = postExpLikelihoods - logBME
+
+ # Information Entropy based on Entropy paper Eq. 38
+ infEntropy = logBME - postExpPrior - postExpLikelihoods
+
+ # If post_snapshot is True, plot likelihood vs refrence
+ if post_snapshot or valid_likelihoods:
+ # Hellinger distance
+ ref_like = np.log(valid_likelihoods[valid_likelihoods > 0])
+ est_like = np.log(Likelihoods[Likelihoods > 0])
+ distHellinger = self.__hellinger_distance(ref_like, est_like)
+
+ idx = len([name for name in os.listdir(newpath) if 'Likelihoods_'
+ in name and os.path.isfile(os.path.join(newpath, name))])
+ fig, ax = plt.subplots()
+ try:
+ sns.kdeplot(np.log(valid_likelihoods[valid_likelihoods > 0]),
+ shade=True, color="g", label='Ref. Likelihood')
+ sns.kdeplot(np.log(Likelihoods[Likelihoods > 0]), shade=True,
+ color="b", label='Likelihood with PCE')
+ except:
+ pass
+
+ text = f"Hellinger Dist.={distHellinger:.3f}\n logBME={logBME:.3f}"
+ "\n DKL={KLD:.3f}"
+
+ plt.text(0.05, 0.75, text, bbox=dict(facecolor='wheat',
+ edgecolor='black',
+ boxstyle='round,pad=1'),
+ transform=ax.transAxes)
+
+ fig.savefig(f'./{newpath}/Likelihoods_{idx}.pdf',
+ bbox_inches='tight')
+ plt.close()
+
+ else:
+ distHellinger = 0.0
+
+ # Bayesian inference with Emulator only for 2D problem
+ if post_snapshot and MetaModel.n_params == 2 and not idx % 5:
+ from bayes_inference.bayes_inference import BayesInference
+ from bayes_inference.discrepancy import Discrepancy
+ import pandas as pd
+ BayesOpts = BayesInference(MetaModel)
+ BayesOpts.emulator = True
+ BayesOpts.plot_post_pred = False
+
+ # Select the inference method
+ import emcee
+ BayesOpts.inference_method = "MCMC"
+ # Set the MCMC parameters passed to self.mcmc_params
+ BayesOpts.mcmc_params = {
+ 'n_steps': 1e5,
+ 'n_walkers': 30,
+ 'moves': emcee.moves.KDEMove(),
+ 'verbose': False
+ }
+
+ # ----- Define the discrepancy model -------
+ obs_data = pd.DataFrame(obs_data, columns=self.Model.Output.names)
+ BayesOpts.measurement_error = obs_data
+
+ # # -- (Option B) --
+ DiscrepancyOpts = Discrepancy('')
+ DiscrepancyOpts.type = 'Gaussian'
+ DiscrepancyOpts.parameters = obs_data**2
+ BayesOpts.Discrepancy = DiscrepancyOpts
+ # Start the calibration/inference
+ Bayes_PCE = BayesOpts.create_inference()
+ X_Posterior = Bayes_PCE.posterior_df.values
+
+ return (logBME, KLD, X_Posterior, Likelihoods, distHellinger)
+
+ # -------------------------------------------------------------------------
+ def __validError(self, MetaModel):
+
+ # MetaModel = self.MetaModel
+ Model = MetaModel.ModelObj
+ OutputName = Model.Output.names
+
+ # Extract the original model with the generated samples
+ valid_samples = MetaModel.valid_samples
+ valid_model_runs = MetaModel.valid_model_runs
+
+ # Run the PCE model with the generated samples
+ valid_PCE_runs, _ = MetaModel.eval_metamodel(samples=valid_samples)
+
+ rms_error = {}
+ valid_error = {}
+ # Loop over the keys and compute RMSE error.
+ for key in OutputName:
+ rms_error[key] = mean_squared_error(
+ valid_model_runs[key], valid_PCE_runs[key],
+ multioutput='raw_values',
+ sample_weight=None,
+ squared=False)
+ # Validation error
+ valid_error[key] = (rms_error[key]**2)
+ valid_error[key] /= np.var(valid_model_runs[key], ddof=1, axis=0)
+
+ # Print a report table
+ print("\n>>>>> Updated Errors of {} <<<<<".format(key))
+ print("\nIndex | RMSE | Validation Error")
+ print('-'*35)
+ print('\n'.join(f'{i+1} | {k:.3e} | {j:.3e}' for i, (k, j)
+ in enumerate(zip(rms_error[key],
+ valid_error[key]))))
+
+ return rms_error, valid_error
+
+ # -------------------------------------------------------------------------
+ def __error_Mean_Std(self):
+
+ MetaModel = self.MetaModel
+ # Extract the mean and std provided by user
+ df_MCReference = MetaModel.ModelObj.mc_reference
+
+ # Compute the mean and std based on the MetaModel
+ pce_means, pce_stds = self._compute_pce_moments(MetaModel)
+
+ # Compute the root mean squared error
+ for output in MetaModel.ModelObj.Output.names:
+
+ # Compute the error between mean and std of MetaModel and OrigModel
+ RMSE_Mean = mean_squared_error(
+ df_MCReference['mean'], pce_means[output], squared=False
+ )
+ RMSE_std = mean_squared_error(
+ df_MCReference['std'], pce_means[output], squared=False
+ )
+
+ return RMSE_Mean, RMSE_std
+
+ # -------------------------------------------------------------------------
+ def _compute_pce_moments(self, MetaModel):
+ """
+ Computes the first two moments using the PCE-based meta-model.
+
+ Returns
+ -------
+ pce_means: dict
+ The first moment (mean) of the surrogate.
+ pce_stds: dict
+ The second moment (standard deviation) of the surrogate.
+
+ """
+ outputs = MetaModel.ModelObj.Output.names
+ pce_means_b = {}
+ pce_stds_b = {}
+
+ # Loop over bootstrap iterations
+ for b_i in range(MetaModel.n_bootstrap_itrs):
+ # Loop over the metamodels
+ coeffs_dicts = MetaModel.coeffs_dict[f'b_{b_i+1}'].items()
+ means = {}
+ stds = {}
+ for output, coef_dict in coeffs_dicts:
+
+ pce_mean = np.zeros((len(coef_dict)))
+ pce_var = np.zeros((len(coef_dict)))
+
+ for index, values in coef_dict.items():
+ idx = int(index.split('_')[1]) - 1
+ coeffs = MetaModel.coeffs_dict[f'b_{b_i+1}'][output][index]
+
+ # Mean = c_0
+ if coeffs[0] != 0:
+ pce_mean[idx] = coeffs[0]
+ else:
+ clf_poly = MetaModel.clf_poly[f'b_{b_i+1}'][output]
+ pce_mean[idx] = clf_poly[index].intercept_
+ # Var = sum(coeffs[1:]**2)
+ pce_var[idx] = np.sum(np.square(coeffs[1:]))
+
+ # Save predictions for each output
+ if MetaModel.dim_red_method.lower() == 'pca':
+ PCA = MetaModel.pca[f'b_{b_i+1}'][output]
+ means[output] = PCA.inverse_transform(pce_mean)
+ stds[output] = PCA.inverse_transform(np.sqrt(pce_var))
+ else:
+ means[output] = pce_mean
+ stds[output] = np.sqrt(pce_var)
+
+ # Save predictions for each bootstrap iteration
+ pce_means_b[b_i] = means
+ pce_stds_b[b_i] = stds
+
+ # Change the order of nesting
+ mean_all = {}
+ for i in sorted(pce_means_b):
+ for k, v in pce_means_b[i].items():
+ if k not in mean_all:
+ mean_all[k] = [None] * len(pce_means_b)
+ mean_all[k][i] = v
+ std_all = {}
+ for i in sorted(pce_stds_b):
+ for k, v in pce_stds_b[i].items():
+ if k not in std_all:
+ std_all[k] = [None] * len(pce_stds_b)
+ std_all[k][i] = v
+
+ # Back transformation if PCA is selected.
+ pce_means, pce_stds = {}, {}
+ for output in outputs:
+ pce_means[output] = np.mean(mean_all[output], axis=0)
+ pce_stds[output] = np.mean(std_all[output], axis=0)
+
+ return pce_means, pce_stds
diff --git a/src/bayesvalidrox/surrogate_models/orthogonal_matching_pursuit.py b/src/bayesvalidrox/surrogate_models/orthogonal_matching_pursuit.py
new file mode 100644
index 0000000000000000000000000000000000000000..d4f99b8a19bb5dbdf41f093bd454c80c63a321bb
--- /dev/null
+++ b/src/bayesvalidrox/surrogate_models/orthogonal_matching_pursuit.py
@@ -0,0 +1,366 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Fri Jul 15 14:08:59 2022
+
+@author: farid
+"""
+import numpy as np
+from sklearn.base import RegressorMixin
+from sklearn.linear_model._base import LinearModel
+from sklearn.utils import check_X_y
+
+
+def corr(x, y):
+ return abs(x.dot(y))/np.sqrt((x**2).sum())
+
+
+class OrthogonalMatchingPursuit(LinearModel, RegressorMixin):
+ '''
+ Regression with Orthogonal Matching Pursuit [1].
+
+ Parameters
+ ----------
+ fit_intercept : boolean, optional (DEFAULT = True)
+ whether to calculate the intercept for this model. If set
+ to false, no intercept will be used in calculations
+ (e.g. data is expected to be already centered).
+
+ copy_X : boolean, optional (DEFAULT = True)
+ If True, X will be copied; else, it may be overwritten.
+
+ verbose : boolean, optional (DEFAULT = FALSE)
+ Verbose mode when fitting the model
+
+ Attributes
+ ----------
+ coef_ : array, shape = (n_features)
+ Coefficients of the regression model (mean of posterior distribution)
+
+ active_ : array, dtype = np.bool, shape = (n_features)
+ True for non-zero coefficients, False otherwise
+
+ References
+ ----------
+ [1] Pati, Y., Rezaiifar, R., Krishnaprasad, P. (1993). Orthogonal matching
+ pursuit: recursive function approximation with application to wavelet
+ decomposition. Proceedings of 27th Asilomar Conference on Signals,
+ Systems and Computers, 40-44.
+ '''
+
+ def __init__(self, fit_intercept=True, normalize=False, copy_X=True,
+ verbose=False):
+ self.fit_intercept = fit_intercept
+ self.normalize = normalize
+ self.copy_X = copy_X
+ self.verbose = verbose
+
+ def _preprocess_data(self, X, y):
+ """Center and scale data.
+ Centers data to have mean zero along axis 0. If fit_intercept=False or
+ if the X is a sparse matrix, no centering is done, but normalization
+ can still be applied. The function returns the statistics necessary to
+ reconstruct the input data, which are X_offset, y_offset, X_scale, such
+ that the output
+ X = (X - X_offset) / X_scale
+ X_scale is the L2 norm of X - X_offset.
+ """
+
+ if self.copy_X:
+ X = X.copy(order='K')
+
+ y = np.asarray(y, dtype=X.dtype)
+
+ if self.fit_intercept:
+ X_offset = np.average(X, axis=0)
+ X -= X_offset
+ if self.normalize:
+ X_scale = np.ones(X.shape[1], dtype=X.dtype)
+ std = np.sqrt(np.sum(X**2, axis=0)/(len(X)-1))
+ X_scale[std != 0] = std[std != 0]
+ X /= X_scale
+ else:
+ X_scale = np.ones(X.shape[1], dtype=X.dtype)
+ y_offset = np.mean(y)
+ y = y - y_offset
+ else:
+ X_offset = np.zeros(X.shape[1], dtype=X.dtype)
+ X_scale = np.ones(X.shape[1], dtype=X.dtype)
+ if y.ndim == 1:
+ y_offset = X.dtype.type(0)
+ else:
+ y_offset = np.zeros(y.shape[1], dtype=X.dtype)
+
+ return X, y, X_offset, y_offset, X_scale
+
+ def fit(self, X, y):
+ '''
+ Fits Regression with Orthogonal Matching Pursuit Algorithm.
+
+ Parameters
+ -----------
+ X: {array-like, sparse matrix} of size (n_samples, n_features)
+ Training data, matrix of explanatory variables
+
+ y: array-like of size [n_samples, n_features]
+ Target values
+
+ Returns
+ -------
+ self : object
+ Returns self.
+ '''
+ X, y = check_X_y(X, y, dtype=np.float64, y_numeric=True)
+ n_samples, n_features = X.shape
+
+ X, y, X_mean, y_mean, X_std = self._preprocess_data(X, y)
+ self._x_mean_ = X_mean
+ self._y_mean = y_mean
+ self._x_std = X_std
+
+ # Normalize columns of Psi, so that each column has norm = 1
+ norm_X = np.linalg.norm(X, axis=0)
+ X_norm = X/norm_X
+
+ # Initialize residual vector to full model response and normalize
+ R = y
+ norm_y = np.sqrt(np.dot(y, y))
+ r = y/norm_y
+
+ # Check for constant regressors
+ const_indices = np.where(~np.diff(X, axis=0).any(axis=0))[0]
+ bool_const = not const_indices
+
+ # Start regression using OPM algorithm
+ precision = 0 # Set precision criterion to precision of program
+ early_stop = True
+ cond_early = True # Initialize condition for early stop
+ ind = []
+ iindx = [] # index of selected columns
+ indtot = np.arange(n_features) # Full index set for remaining columns
+ kmax = min(n_samples, n_features) # Maximum number of iterations
+ LOO = np.PINF * np.ones(kmax) # Store LOO error at each iteration
+ LOOmin = np.PINF # Initialize minimum value of LOO
+ coeff = np.zeros((n_features, kmax))
+ count = 0
+ k = 0.1 # Percentage of iteration history for early stop
+
+ # Begin iteration over regressors set (Matrix X)
+ while (np.linalg.norm(R) > precision) and (count <= kmax-1) and \
+ ((cond_early or early_stop) ^ ~cond_early):
+
+ # Update index set of columns yet to select
+ if count != 0:
+ indtot = np.delete(indtot, iindx)
+
+ # Find column of X that is most correlated with residual
+ h = abs(np.dot(r, X_norm))
+ iindx = np.argmax(h[indtot])
+ indx = indtot[iindx]
+
+ # initialize with the constant regressor, if it exists in the basis
+ if (count == 0) and bool_const:
+ # overwrite values for iindx and indx
+ iindx = const_indices[0]
+ indx = indtot[iindx]
+
+ # Invert the information matrix at the first iteration, later only
+ # update its value on the basis of the previously inverted one,
+ if count == 0:
+ M = 1 / np.dot(X[:, indx], X[:, indx])
+ else:
+ x = np.dot(X[:, ind].T, X[:, indx])
+ r = np.dot(X[:, indx], X[:, indx])
+ M = self.blockwise_inverse(M, x, x.T, r)
+
+ # Add newly found index to the selected indexes set
+ ind.append(indx)
+
+ # Select regressors subset (Projection subspace)
+ Xpro = X[:, ind]
+
+ # Obtain coefficient by performing OLS
+ TT = np.dot(y, Xpro)
+ beta = np.dot(M, TT)
+ coeff[ind, count] = beta
+
+ # Compute LOO error
+ LOO[count] = self.loo_error(Xpro, M, y, beta)
+
+ # Compute new residual due to new projection
+ R = y - np.dot(Xpro, beta)
+
+ # Normalize residual
+ norm_R = np.sqrt(np.dot(R, R))
+ r = R / norm_R
+
+ # Update counters and early-stop criterions
+ countinf = max(0, int(count-k*kmax))
+ LOOmin = min(LOOmin, LOO[count])
+
+ if count == 0:
+ cond_early = (LOO[0] <= LOOmin)
+ else:
+ cond_early = (min(LOO[countinf:count+1]) <= LOOmin)
+
+ if self.verbose:
+ print(f'Iteration: {count+1}, mod. LOOCV error : '
+ f'{LOO[count]:.2e}')
+
+ # Update counter
+ count += 1
+
+ # Select projection with smallest cross-validation error
+ countmin = np.argmin(LOO[:-1])
+ self.coef_ = coeff[:, countmin]
+ self.active = coeff[:, countmin] != 0.0
+
+ # set intercept_
+ if self.fit_intercept:
+ self.coef_ = self.coef_ / X_std
+ self.intercept_ = y_mean - np.dot(X_mean, self.coef_.T)
+ else:
+ self.intercept_ = 0.
+
+ return self
+
+ def predict(self, X):
+ '''
+ Computes predictive distribution for test set.
+
+ Parameters
+ -----------
+ X: {array-like, sparse} (n_samples_test, n_features)
+ Test data, matrix of explanatory variables
+
+ Returns
+ -------
+ y_hat: numpy array of size (n_samples_test,)
+ Estimated values of targets on test set (i.e. mean of
+ predictive distribution)
+ '''
+
+ y_hat = np.dot(X, self.coef_) + self.intercept_
+
+ return y_hat
+
+ def loo_error(self, psi, inv_inf_matrix, y, coeffs):
+ """
+ Calculates the corrected LOO error for regression on regressor
+ matrix `psi` that generated the coefficients based on [1] and [2].
+
+ [1] Blatman, G., 2009. Adaptive sparse polynomial chaos expansions for
+ uncertainty propagation and sensitivity analysis (Doctoral
+ dissertation, Clermont-Ferrand 2).
+
+ [2] Blatman, G. and Sudret, B., 2011. Adaptive sparse polynomial chaos
+ expansion based on least angle regression. Journal of computational
+ Physics, 230(6), pp.2345-2367.
+
+ Parameters
+ ----------
+ psi : array of shape (n_samples, n_feature)
+ Orthogonal bases evaluated at the samples.
+ inv_inf_matrix : array
+ Inverse of the information matrix.
+ y : array of shape (n_samples, )
+ Targets.
+ coeffs : array
+ Computed regresssor cofficients.
+
+ Returns
+ -------
+ loo_error : float
+ Modified LOOCV error.
+
+ """
+
+ # NrEvaluation (Size of experimental design)
+ N, P = psi.shape
+
+ # h factor (the full matrix is not calculated explicitly,
+ # only the trace is, to save memory)
+ PsiM = np.dot(psi, inv_inf_matrix)
+
+ h = np.sum(np.multiply(PsiM, psi), axis=1, dtype=np.float128)
+
+ # ------ Calculate Error Loocv for each measurement point ----
+ # Residuals
+ residual = np.dot(psi, coeffs) - y
+
+ # Variance
+ varY = np.var(y)
+
+ if varY == 0:
+ norm_emp_error = 0
+ loo_error = 0
+ else:
+ norm_emp_error = np.mean(residual**2)/varY
+
+ loo_error = np.mean(np.square(residual / (1-h))) / varY
+
+ # if there are NaNs, just return an infinite LOO error (this
+ # happens, e.g., when a strongly underdetermined problem is solved)
+ if np.isnan(loo_error):
+ loo_error = np.inf
+
+ # Corrected Error for over-determined system
+ tr_M = np.trace(np.atleast_2d(inv_inf_matrix))
+ if tr_M < 0 or abs(tr_M) > 1e6:
+ tr_M = np.trace(np.linalg.pinv(np.dot(psi.T, psi)))
+
+ # Over-determined system of Equation
+ if N > P:
+ T_factor = N/(N-P) * (1 + tr_M)
+
+ # Under-determined system of Equation
+ else:
+ T_factor = np.inf
+
+ loo_error *= T_factor
+
+ return loo_error
+
+ def blockwise_inverse(self, Ainv, B, C, D):
+ """
+ non-singular square matrix M defined as M = [[A B]; [C D]] .
+ B, C and D can have any dimension, provided their combination defines
+ a square matrix M.
+
+ Parameters
+ ----------
+ Ainv : float or array
+ inverse of the square-submatrix A.
+ B : float or array
+ Information matrix with all new regressor.
+ C : float or array
+ Transpose of B.
+ D : float or array
+ Information matrix with all selected regressors.
+
+ Returns
+ -------
+ M : array
+ Inverse of the information matrix.
+
+ """
+ if np.isscalar(D):
+ # Inverse of D
+ Dinv = 1/D
+ # Schur complement
+ SCinv = 1/(D - np.dot(C, np.dot(Ainv, B[:, None])))[0]
+ else:
+ # Inverse of D
+ Dinv = np.linalg.solve(D, np.eye(D.shape))
+ # Schur complement
+ SCinv = np.linalg.solve((D - C*Ainv*B), np.eye(D.shape))
+
+ T1 = np.dot(Ainv, np.dot(B[:, None], SCinv))
+ T2 = np.dot(C, Ainv)
+
+ # Assemble the inverse matrix
+ M = np.vstack((
+ np.hstack((Ainv+T1*T2, -T1)),
+ np.hstack((-(SCinv)*T2, SCinv))
+ ))
+ return M
diff --git a/src/bayesvalidrox/surrogate_models/reg_fast_ard.py b/src/bayesvalidrox/surrogate_models/reg_fast_ard.py
index 2d9eaca8a3b0880c4cfc88a9d32316e03a208c95..44073da8e78642ba3b3914f6ce55a2d01986b1f1 100755
--- a/src/bayesvalidrox/surrogate_models/reg_fast_ard.py
+++ b/src/bayesvalidrox/surrogate_models/reg_fast_ard.py
@@ -17,14 +17,14 @@ from scipy.linalg import pinvh
def update_precisions(Q,S,q,s,A,active,tol,n_samples,clf_bias):
'''
- Selects one feature to be added/recomputed/deleted to model based on
+ Selects one feature to be added/recomputed/deleted to model based on
effect it will have on value of log marginal likelihood.
'''
# initialise vector holding changes in log marginal likelihood
deltaL = np.zeros(Q.shape[0])
# identify features that can be added , recomputed and deleted in model
- theta = q**2 - s
+ theta = q**2 - s
add = (theta > 0) * (active == False)
recompute = (theta > 0) * (active == True)
delete = ~(add + recompute)
@@ -40,7 +40,7 @@ def update_precisions(Q,S,q,s,A,active,tol,n_samples,clf_bias):
Anew = s[recompute]**2/ ( theta[recompute] + np.finfo(np.float32).eps)
delta_alpha = (1./Anew - 1./Arec)
- # compute change in log marginal likelihood
+ # compute change in log marginal likelihood
deltaL[add] = ( Qadd**2 - Sadd ) / Sadd + np.log(Sadd/Qadd**2 )
deltaL[recompute] = Qrec**2 / (Srec + 1. / delta_alpha) - np.log(1 + Srec*delta_alpha)
deltaL[delete] = Qdel**2 / (Sdel - Adel) - np.log(1 - Sdel / Adel)
@@ -56,7 +56,7 @@ def update_precisions(Q,S,q,s,A,active,tol,n_samples,clf_bias):
no_delta = np.sum( abs( Anew - Arec ) > tol ) == 0
# if same_features: print(abs( Anew - Arec ))
# print("same_features = {} no_delta = {}".format(same_features,no_delta))
- # check convergence: if no features to add or delete and small change in
+ # check convergence: if no features to add or delete and small change in
# precision for current features then terminate
converged = False
if same_features and no_delta:
@@ -71,7 +71,7 @@ def update_precisions(Q,S,q,s,A,active,tol,n_samples,clf_bias):
else:
# at least two active features
if active[feature_index] == True and np.sum(active) >= 2:
- # do not remove bias term in classification
+ # do not remove bias term in classification
# (in regression it is factored in through centering)
if not (feature_index == 0 and clf_bias):
active[feature_index] = False
@@ -82,7 +82,7 @@ def update_precisions(Q,S,q,s,A,active,tol,n_samples,clf_bias):
class RegressionFastARD(LinearModel, RegressorMixin):
'''
- Regression with Automatic Relevance Determination (Fast Version uses
+ Regression with Automatic Relevance Determination (Fast Version uses
Sparse Bayesian Learning)
https://github.com/AmazaspShumik/sklearn-bayes/blob/master/skbayes/rvm_ard_models/fast_rvm.py
@@ -143,7 +143,7 @@ class RegressionFastARD(LinearModel, RegressorMixin):
(http://www.miketipping.com/abstracts.htm#Faul:NIPS01)
'''
- def __init__(self, n_iter=300, start=None, tol=1e-3, fit_intercept=True,
+ def __init__(self, n_iter=300, start=None, tol=1e-3, fit_intercept=True,
normalize=False, copy_X=True, compute_score=False, verbose=False):
self.n_iter = n_iter
self.start = start
@@ -230,8 +230,10 @@ class RegressionFastARD(LinearModel, RegressorMixin):
# check that variance is non zero !!!
if var_y == 0:
beta = 1e-2
+ self.var_y = True
else:
beta = 1. / np.var(y)
+ self.var_y = False
A = np.PINF * np.ones(n_features)
active = np.zeros(n_features, dtype=np.bool)
@@ -262,6 +264,13 @@ class RegressionFastARD(LinearModel, RegressorMixin):
warning_flag = 0
scores_ = []
for i in range(self.n_iter):
+ # Handle variance zero
+ if self.var_y:
+ A[0] = y_mean
+ active[0] = True
+ converged = True
+ break
+
XXa = XX[active, :][:, active]
XYa = XY[active]
Aa = A[active]
@@ -381,11 +390,15 @@ class RegressionFastARD(LinearModel, RegressorMixin):
y_hat = np.dot(X, self.coef_) + self.intercept_
if return_std:
+ # Handle the zero variance case
+ if self.var_y:
+ return y_hat, np.zeros_like(y_hat)
+
if self.normalize:
- x = (X - self._x_mean_) / self._x_std
+ X -= self._x_mean_[self.active_]
+ X /= self._x_std[self.active_]
var_hat = 1./self.alpha_
- var_hat += np.sum(np.dot(x[:, self.active_], self.sigma_) *
- x[:, self.active_], axis=1)
+ var_hat += np.sum(X.dot(self.sigma_) * X, axis=1)
std_hat = np.sqrt(var_hat)
return y_hat, std_hat
else:
diff --git a/src/bayesvalidrox/surrogate_models/reg_fast_laplace.py b/src/bayesvalidrox/surrogate_models/reg_fast_laplace.py
index 92909fd00a14db10b1793a28e737f254ec3d4a54..bdff324ede818a42d226e9aa55aaf01666ca8fc8 100644
--- a/src/bayesvalidrox/surrogate_models/reg_fast_laplace.py
+++ b/src/bayesvalidrox/surrogate_models/reg_fast_laplace.py
@@ -3,411 +3,450 @@
import numpy as np
from sklearn.utils import as_float_array
from sklearn.model_selection import KFold
-import warnings
-warnings.filterwarnings("ignore")
-import sys
-import matplotlib.pyplot as plt
+
class RegressionFastLaplace():
'''
- Sparse regression with Bayesian Compressive Sensing as described in Alg. 1
+ Sparse regression with Bayesian Compressive Sensing as described in Alg. 1
(Fast Laplace) of Ref.[1], which updated formulas from [2].
sigma2: noise precision (sigma^2)
nu fixed to 0
-
+
uqlab/lib/uq_regression/BCS/uq_bsc.m
-
+
Parameters
----------
n_iter: int, optional (DEFAULT = 1000)
Maximum number of iterations
-
+
tol: float, optional (DEFAULT = 1e-7)
- If absolute change in precision parameter for weights is below threshold
- algorithm terminates.
-
+ If absolute change in precision parameter for weights is below
+ threshold algorithm terminates.
+
fit_intercept : boolean, optional (DEFAULT = True)
whether to calculate the intercept for this model. If set
to false, no intercept will be used in calculations
(e.g. data is expected to be already centered).
-
+
copy_X : boolean, optional (DEFAULT = True)
If True, X will be copied; else, it may be overwritten.
-
+
verbose : boolean, optional (DEFAULT = FALSE)
Verbose mode when fitting the model
-
-
+
Attributes
----------
coef_ : array, shape = (n_features)
Coefficients of the regression model (mean of posterior distribution)
-
+
alpha_ : float
estimated precision of the noise
-
+
active_ : array, dtype = np.bool, shape = (n_features)
True for non-zero coefficients, False otherwise
-
+
lambda_ : array, shape = (n_features)
estimated precisions of the coefficients
-
+
sigma_ : array, shape = (n_features, n_features)
estimated covariance matrix of the weights, computed only
- for non-zero coefficients
-
+ for non-zero coefficients
+
References
----------
- [1] Babacan, S. D., Molina, R., & Katsaggelos, A. K. (2009). Bayesian
- compressive sensing using Laplace priors. IEEE Transactions on image
+ [1] Babacan, S. D., Molina, R., & Katsaggelos, A. K. (2009). Bayesian
+ compressive sensing using Laplace priors. IEEE Transactions on image
processing, 19(1), 53-63.
- [2] Fast marginal likelihood maximisation for sparse Bayesian models
+ [2] Fast marginal likelihood maximisation for sparse Bayesian models
(Tipping & Faul 2003).
(http://www.miketipping.com/papers/met-fastsbl.pdf)
'''
-
- def __init__(self, n_iter=1000, n_Kfold=10, tol=1e-7, fit_intercept=False,
- copy_X=True, verbose=True):
- self.n_iter = n_iter
- self.n_Kfold = n_Kfold
- self.tol = tol
- self.fit_intercept = fit_intercept
- self.copy_X = copy_X
- self.verbose = verbose
-
-
- def _center_data(self, X,y):
+
+ def __init__(self, n_iter=1000, n_Kfold=10, tol=1e-7, fit_intercept=False,
+ bias_term=True, copy_X=True, verbose=False):
+ self.n_iter = n_iter
+ self.n_Kfold = n_Kfold
+ self.tol = tol
+ self.fit_intercept = fit_intercept
+ self.bias_term = bias_term
+ self.copy_X = copy_X
+ self.verbose = verbose
+
+ def _center_data(self, X, y):
''' Centers data'''
- X = as_float_array(X,self.copy_X)
+ X = as_float_array(X, self.copy_X)
+
# normalisation should be done in preprocessing!
- X_std = np.ones(X.shape[1], dtype = X.dtype)
+ X_std = np.ones(X.shape[1], dtype=X.dtype)
if self.fit_intercept:
- X_mean = np.average(X,axis = 0)
- y_mean = np.average(y,axis = 0)
- X -= X_mean
- y = y - y_mean
+ X_mean = np.average(X, axis=0)
+ y_mean = np.average(y, axis=0)
+ X -= X_mean
+ y -= y_mean
else:
- X_mean = np.zeros(X.shape[1],dtype = X.dtype)
+ X_mean = np.zeros(X.shape[1], dtype=X.dtype)
y_mean = 0. if y.ndim == 1 else np.zeros(y.shape[1], dtype=X.dtype)
- return X,y, X_mean, y_mean, X_std
-
- def fit(self, X,Y):
+ return X, y, X_mean, y_mean, X_std
+
+ def fit(self, X, y):
k_fold = KFold(n_splits=self.n_Kfold)
- varY = np.var(Y,ddof=1) if np.var(Y,ddof=1)!=0 else 1.0
- sigma2s = len(Y)*varY*10**np.linspace(-16,-1,self.n_Kfold)
+ varY = np.var(y, ddof=1) if np.var(y, ddof=1) != 0 else 1.0
+ sigma2s = len(y)*varY*(10**np.linspace(-16, -1, self.n_Kfold))
- errors = np.zeros((len(sigma2s),self.n_Kfold))
+ errors = np.zeros((len(sigma2s), self.n_Kfold))
for s, sigma2 in enumerate(sigma2s):
- for k, (train, test) in enumerate(k_fold.split(X, Y)):
- self.fit_(X[train], Y[train], sigma2)
- errors[s,k] = np.linalg.norm(Y[test] - self.predict(X[test]))**2/len(test)
+ for k, (train, test) in enumerate(k_fold.split(X, y)):
+ self.fit_(X[train], y[train], sigma2)
+ errors[s, k] = np.linalg.norm(
+ y[test] - self.predict(X[test])
+ )**2/len(test)
- KfCVerror = np.sum(errors,axis=1)/self.n_Kfold/varY
+ KfCVerror = np.sum(errors, axis=1)/self.n_Kfold/varY
i_minCV = np.argmin(KfCVerror)
-
+
self.kfoldCVerror = np.min(KfCVerror)
-
- return self.fit_(X, Y, sigma2s[i_minCV])
- def fit_(self, X, Y, sigma2):
-
- N,P = X.shape
+ return self.fit_(X, y, sigma2s[i_minCV])
+
+ def fit_(self, X, y, sigma2):
+
+ N, P = X.shape
# n_samples, n_features = X.shape
-
- X, y, X_mean, y_mean, X_std = self._center_data(X, Y)
+
+ X, y, X_mean, y_mean, X_std = self._center_data(X, y)
self._x_mean_ = X_mean
- self._y_mean = y_mean
- self._x_std = X_std
-
+ self._y_mean = y_mean
+ self._x_std = X_std
+
+ # check that variance is non zero !!!
+ if np.var(y) == 0:
+ self.var_y = True
+ else:
+ self.var_y = False
beta = 1./sigma2
-
+
# precompute X'*Y , X'*X for faster iterations & allocate memory for
- # sparsity & quality vectors X=Psi, y=Y
- PsiTY = np.dot(X.T,y) #XY
- PsiTPsi = np.dot(X.T,X) #XX
- XXd = np.diag(PsiTPsi)
-
+ # sparsity & quality vectors X=Psi
+ PsiTY = np.dot(X.T, y)
+ PsiTPsi = np.dot(X.T, X)
+ XXd = np.diag(PsiTPsi)
+
# initialize with constant regressor, or if that one does not exist,
# with the one that has the largest correlation with Y
- ind_global_to_local = np.zeros(P , dtype = np.int32)#np.bool) #active
-
+ ind_global_to_local = np.zeros(P, dtype=np.int32)
+
# identify constant regressors
- constidx = np.where(~np.diff(X,axis=0).all(axis=0))[0]
-
- if constidx.size != 0:
- ind_start = constidx[0]
- ind_global_to_local[ind_start] = True
+ constidx = np.where(~np.diff(X, axis=0).all(axis=0))[0]
+
+ if self.bias_term and constidx.size != 0:
+ ind_start = constidx[0]
+ ind_global_to_local[ind_start] = True
else:
- # start from a single basis vector with largest projection on targets
- proj = np.divide(np.square(PsiTY) , XXd)
+ # start from a single basis vector with largest projection on
+ # targets
+ proj = np.divide(np.square(PsiTY), XXd)
ind_start = np.argmax(proj)
ind_global_to_local[ind_start] = True
-
num_active = 1
active_indices = [ind_start]
deleted_indices = []
bcs_path = [ind_start]
gamma = np.zeros(P)
- # for the initial value of gamma(ind_start), use the RVM formula
+ # for the initial value of gamma(ind_start), use the RVM formula
# gamma = (q^2 - s) / (s^2)
# and the fact that initially s = S = beta*Psi_i'*Psi_i and q = Q =
# beta*Psi_i'*Y
- gamma[ind_start] = (np.square(PsiTY[ind_start]) - sigma2 * PsiTPsi[ind_start,ind_start]) / \
- (np.square(PsiTPsi[ind_start, ind_start]))
-
- Sigma = 1. / (beta * PsiTPsi[ind_start,ind_start] + 1./gamma[ind_start])
-
+ gamma[ind_start] = np.square(PsiTY[ind_start])
+ gamma[ind_start] -= sigma2 * PsiTPsi[ind_start, ind_start]
+ gamma[ind_start] /= np.square(PsiTPsi[ind_start, ind_start])
+
+ Sigma = 1. / (beta * PsiTPsi[ind_start, ind_start]
+ + 1./gamma[ind_start])
+
mu = Sigma * PsiTY[ind_start] * beta
- tmp1 = beta * PsiTPsi[ind_start,:]
- S = beta * np.diag(PsiTPsi).T - Sigma * np.square(tmp1)
+ tmp1 = beta * PsiTPsi[ind_start]
+ S = beta * np.diag(PsiTPsi).T - Sigma * np.square(tmp1)
Q = beta * PsiTY.T - mu*(tmp1)
-
- tmp2 = np.ones(P) # alternative computation for the initial s,q
- q0tilde = PsiTY[ind_start];
- s0tilde = PsiTPsi[ind_start, ind_start];
+
+ tmp2 = np.ones(P) # alternative computation for the initial s,q
+ q0tilde = PsiTY[ind_start]
+ s0tilde = PsiTPsi[ind_start, ind_start]
tmp2[ind_start] = s0tilde / (q0tilde**2) / beta
- s = np.divide(S,tmp2)
- q = np.divide(Q,tmp2)
- Lambda = 2*(num_active - 1) / np.sum(gamma) # initialize lambda as well
-
+ s = np.divide(S, tmp2)
+ q = np.divide(Q, tmp2)
+ Lambda = 2*(num_active - 1) / np.sum(gamma)
+
Delta_L_max = []
for i in range(self.n_iter):
-
+ # Handle variance zero
+ if self.var_y:
+ mu = np.mean(y)
+ break
+
if self.verbose:
- print(' lambda = {0:.3e}\n'.format(Lambda))
-
+ print(' lambda = {0:.6e}\n'.format(Lambda))
+
# Calculate the potential updated value of each gamma[i]
- if Lambda == 0.0: # RVM
- gamma_potential = np.multiply(((np.square(q) - s) > Lambda), \
- np.divide(np.square(q) - s, np.square(s)))
+ if Lambda == 0.0: # RVM
+ gamma_potential = np.multiply((
+ (q**2 - s) > Lambda),
+ np.divide(q**2 - s, s**2)
+ )
else:
- a = Lambda * np.square(s)
- b = np.square(s) + 2*Lambda*s
- c = Lambda + s - np.square(q) # <-- important decision boundary
- gamma_potential = np.multiply((c < 0) ,
- np.divide(-b + np.sqrt(np.square(b) - 4*np.multiply(a,c)),2*a))
-
- l_gamma = - np.log(np.absolute(1 + np.multiply(gamma,s))) \
- + np.divide(np.multiply(np.square(q), gamma),(1 + np.multiply(gamma,s))) \
- - Lambda*gamma # omitted the factor 1/2
-
+ a = Lambda * s**2
+ b = s**2 + 2*Lambda*s
+ c = Lambda + s - q**2
+ gamma_potential = np.multiply(
+ (c < 0), np.divide(
+ -b + np.sqrt(b**2 - 4*np.multiply(a, c)), 2*a)
+ )
+
+ l_gamma = - np.log(np.absolute(1 + np.multiply(gamma, s)))
+ l_gamma += np.divide(np.multiply(q**2, gamma),
+ (1 + np.multiply(gamma, s)))
+ l_gamma -= Lambda*gamma # omitted the factor 1/2
+
# Contribution of each updated gamma(i) to L(gamma)
- l_gamma_potential = - np.log(np.absolute(1 + np.multiply(gamma_potential,s))) \
- + np.divide(np.multiply(np.square(q), gamma_potential),(1 + np.multiply(gamma_potential,s))) \
- - Lambda*gamma_potential # omitted the factor 1/2
-
+ l_gamma_potential = - np.log(
+ np.absolute(1 + np.multiply(gamma_potential, s))
+ )
+ l_gamma_potential += np.divide(
+ np.multiply(q**2, gamma_potential),
+ (1 + np.multiply(gamma_potential, s))
+ )
+ # omitted the factor 1/2
+ l_gamma_potential -= Lambda*gamma_potential
+
# Check how L(gamma) would change if we replaced gamma(i) by the
# updated gamma_potential(i), for each i separately
Delta_L_potential = l_gamma_potential - l_gamma
+
# deleted indices should not be chosen again
- if len(deleted_indices)!=0:
- Delta_L_potential[deleted_indices] = -np.inf * np.ones(len(deleted_indices))
-
+ if len(deleted_indices) != 0:
+ values = -np.inf * np.ones(len(deleted_indices))
+ Delta_L_potential[deleted_indices] = values
+
Delta_L_max.append(np.nanmax(Delta_L_potential))
ind_L_max = np.nanargmax(Delta_L_potential)
-
-
- # in case there is only 1 regressor in the model and it would now be
- # deleted
+
+ # in case there is only 1 regressor in the model and it would now
+ # be deleted
if len(active_indices) == 1 and ind_L_max == active_indices[0] \
- and gamma_potential[ind_L_max] == 0.0:
+ and gamma_potential[ind_L_max] == 0.0:
Delta_L_potential[ind_L_max] = -np.inf
Delta_L_max[i] = np.max(Delta_L_potential)
ind_L_max = np.argmax(Delta_L_potential)
# If L did not change significantly anymore, break
if Delta_L_max[i] <= 0.0 or\
- ( i > 0 and \
- all(np.absolute(Delta_L_max[i-1:]) \
- < sum(Delta_L_max)*self.tol)) or \
- ( i > 0 and all(np.diff(bcs_path)[i-1:]==0.0)):
+ (i > 0 and all(np.absolute(Delta_L_max[i-1:])
+ < sum(Delta_L_max)*self.tol)) or \
+ (i > 0 and all(np.diff(bcs_path)[i-1:] == 0.0)):
if self.verbose:
- print('Increase in L: {0:.3e} (eta = {1:.3e})\
- -- break\n'.format(Delta_L_max[i],self.tol))
+ print('Increase in L: {0:.6e} (eta = {1:.3e})\
+ -- break\n'.format(Delta_L_max[i], self.tol))
break
# Print information
if self.verbose:
- print(' Delta L = {0:.3e} \n'.format(Delta_L_max[i]))
-
- what_changed = int(gamma[ind_L_max]==0.0) - int(gamma_potential[ind_L_max]==0.0)
+ print(' Delta L = {0:.6e} \n'.format(Delta_L_max[i]))
+
+ what_changed = int(gamma[ind_L_max] == 0.0)
+ what_changed -= int(gamma_potential[ind_L_max] == 0.0)
# Print information
if self.verbose:
if what_changed < 0:
- print('{} - Remove regressor #{}..\n'.format(i+1,ind_L_max+1))
+ print(f'{i+1} - Remove regressor #{ind_L_max+1}..\n')
elif what_changed == 0:
- print('{} - Recompute regressor #{}..\n'.format(i+1,ind_L_max+1))
+ print(f'{i+1} - Recompute regressor #{ind_L_max+1}..\n')
else:
- print('{} - Add regressor #{}..\n'.format(i+1,ind_L_max+1))
-
+ print(f'{i+1} - Add regressor #{ind_L_max+1}..\n')
+
# --- Update all quantities ----
if what_changed == 1:
# adding a regressor
# update gamma
gamma[ind_L_max] = gamma_potential[ind_L_max]
-
+
Sigma_ii = 1.0 / (1.0/gamma[ind_L_max] + S[ind_L_max])
try:
- x_i = np.matmul(Sigma, PsiTPsi[active_indices,ind_L_max].reshape(-1,1))
- except:
- x_i = Sigma * PsiTPsi[active_indices,ind_L_max]
+ x_i = np.matmul(
+ Sigma, PsiTPsi[active_indices, ind_L_max].reshape(-1, 1)
+ )
+ except ValueError:
+ x_i = Sigma * PsiTPsi[active_indices, ind_L_max]
tmp_1 = - (beta * Sigma_ii) * x_i
- Sigma = np.vstack((np.hstack(((beta**2 * Sigma_ii) * np.dot(x_i,x_i.T) + Sigma , tmp_1))\
- , np.append(tmp_1.T,Sigma_ii)))
+ Sigma = np.vstack(
+ (np.hstack(((beta**2 * Sigma_ii) * np.dot(x_i, x_i.T)
+ + Sigma, tmp_1)), np.append(tmp_1.T, Sigma_ii))
+ )
mu_i = Sigma_ii * Q[ind_L_max]
mu = np.vstack((mu - (beta * mu_i) * x_i, mu_i))
-
- tmp2 = beta * (PsiTPsi[:,ind_L_max] - beta * \
- np.squeeze(np.matmul(PsiTPsi[:,active_indices],x_i))).T # row vector
+
+ tmp2_1 = PsiTPsi[:, ind_L_max] - beta * np.squeeze(
+ np.matmul(PsiTPsi[:, active_indices], x_i)
+ )
+ if i == 0:
+ tmp2_1[0] /= 2
+ tmp2 = beta * tmp2_1.T
S = S - Sigma_ii * np.square(tmp2)
Q = Q - mu_i * tmp2
-
+
num_active += 1
- ind_global_to_local[ind_L_max] = num_active # local index
+ ind_global_to_local[ind_L_max] = num_active
active_indices.append(ind_L_max)
bcs_path.append(ind_L_max)
-
+
elif what_changed == 0:
# recomputation
- if not ind_global_to_local[ind_L_max]: # zero if regressor has not been chosen yet
+ # zero if regressor has not been chosen yet
+ if not ind_global_to_local[ind_L_max]:
raise Exception('cannot recompute index{0} -- not yet\
part of the model!'.format(ind_L_max))
-
+ Sigma = np.atleast_2d(Sigma)
+ mu = np.atleast_2d(mu)
gamma_i_new = gamma_potential[ind_L_max]
gamma_i_old = gamma[ind_L_max]
# update gamma
gamma[ind_L_max] = gamma_potential[ind_L_max]
-
+
# index of regressor in Sigma
local_ind = ind_global_to_local[ind_L_max]-1
- kappa_i = 1.0 / (Sigma[local_ind, local_ind] + 1.0 / (1.0/gamma_i_new - 1.0/gamma_i_old))
- Sigma_i_col = Sigma[:,local_ind] # column of interest in Sigma
-
+ kappa_i = (1.0/gamma_i_new - 1.0/gamma_i_old)
+ kappa_i = 1.0 / kappa_i
+ kappa_i += Sigma[local_ind, local_ind]
+ kappa_i = 1 / kappa_i
+ Sigma_i_col = Sigma[:, local_ind]
+
Sigma = Sigma - kappa_i * (Sigma_i_col * Sigma_i_col.T)
mu_i = mu[local_ind]
- mu = mu - (kappa_i * mu_i) * Sigma_i_col[:,None]
-
- tmp1 = beta * np.dot(Sigma_i_col.reshape(1,-1),PsiTPsi[active_indices])[0] # row vector
+ mu = mu - (kappa_i * mu_i) * Sigma_i_col[:, None]
+
+ tmp1 = beta * np.dot(
+ Sigma_i_col.reshape(1, -1), PsiTPsi[active_indices])[0]
S = S + kappa_i * np.square(tmp1)
Q = Q + (kappa_i * mu_i) * tmp1
# no change in active_indices or ind_global_to_local
- bcs_path.append(ind_L_max+ 0.1)
-
+ bcs_path.append(ind_L_max + 0.1)
+
elif what_changed == -1:
gamma[ind_L_max] = 0
-
+
# index of regressor in Sigma
local_ind = ind_global_to_local[ind_L_max]-1
-
- Sigma_ii_inv = 1. / Sigma[local_ind,local_ind]
- Sigma_i_col = Sigma[:,local_ind] # column to be deleted in Sigma
-
- Sigma = Sigma - Sigma_ii_inv * (Sigma_i_col * Sigma_i_col.T);
-
- Sigma = np.delete(np.delete(Sigma, local_ind, axis=0), local_ind, axis=1)
-
- mu = mu - (mu[local_ind] * Sigma_ii_inv) * Sigma_i_col[:,None]
+
+ Sigma_ii_inv = 1. / Sigma[local_ind, local_ind]
+ Sigma_i_col = Sigma[:, local_ind]
+
+ Sigma = Sigma - Sigma_ii_inv * (Sigma_i_col * Sigma_i_col.T)
+
+ Sigma = np.delete(
+ np.delete(Sigma, local_ind, axis=0), local_ind, axis=1)
+
+ mu = mu - (mu[local_ind] * Sigma_ii_inv) * Sigma_i_col[:, None]
mu = np.delete(mu, local_ind, axis=0)
-
- tmp1 = beta * np.dot(Sigma_i_col,PsiTPsi[active_indices]) # row vector
+
+ tmp1 = beta * np.dot(Sigma_i_col, PsiTPsi[active_indices])
S = S + Sigma_ii_inv * np.square(tmp1)
Q = Q + (mu_i * Sigma_ii_inv) * tmp1
-
+
num_active -= 1
ind_global_to_local[ind_L_max] = 0.0
- ind_global_to_local[ind_global_to_local > local_ind] = ind_global_to_local[ind_global_to_local > local_ind] - 1
+ v = ind_global_to_local[ind_global_to_local > local_ind] - 1
+ ind_global_to_local[ind_global_to_local > local_ind] = v
del active_indices[local_ind]
- deleted_indices.append(ind_L_max) # mark this index as deleted
+ deleted_indices.append(ind_L_max)
# and therefore ineligible
bcs_path.append(-ind_L_max)
-
- # same for all three cases
- tmp3 = 1 - np.multiply(gamma,S)
- s = np.divide(S,tmp3)
- q = np.divide(Q,tmp3)
-
+
+ # same for all three cases
+ tmp3 = 1 - np.multiply(gamma, S)
+ s = np.divide(S, tmp3)
+ q = np.divide(Q, tmp3)
+
# Update lambda
Lambda = 2*(num_active - 1) / np.sum(gamma)
-
- # Prepare the result object
- self.coef_ = np.zeros(P)
+
+ # Prepare the result object
+ self.coef_ = np.zeros(P)
self.coef_[active_indices] = np.squeeze(mu)
- self.sigma_ = Sigma
- self.active_ = active_indices
- self.gamma = gamma
- self.Lambda = Lambda
- self.beta = beta
- self.bcs_path = bcs_path
+ self.sigma_ = Sigma
+ self.active_ = active_indices
+ self.gamma = gamma
+ self.Lambda = Lambda
+ self.beta = beta
+ self.bcs_path = bcs_path
+
+ # set intercept_
+ if self.fit_intercept:
+ self.coef_ = self.coef_ / X_std
+ self.intercept_ = y_mean - np.dot(X_mean, self.coef_.T)
+ else:
+ self.intercept_ = 0.
return self
-
-
- def predict(self,X, return_std=False):
+
+ def predict(self, X, return_std=False):
'''
Computes predictive distribution for test set.
Predictive distribution for each data point is one dimensional
Gaussian and therefore is characterised by mean and variance based on
Ref.[1] Section 3.3.2.
-
+
Parameters
-----------
X: {array-like, sparse} (n_samples_test, n_features)
Test data, matrix of explanatory variables
-
+
Returns
-------
: list of length two [y_hat, var_hat]
-
+
y_hat: numpy array of size (n_samples_test,)
- Estimated values of targets on test set (i.e. mean of predictive
- distribution)
-
- var_hat: numpy array of size (n_samples_test,)
+ Estimated values of targets on test set (i.e. mean of
+ predictive distribution)
+
+ var_hat: numpy array of size (n_samples_test,)
Variance of predictive distribution
-
+
References
----------
- [1] Bishop, C. M. (2006). Pattern recognition and machine learning. springer.
+ [1] Bishop, C. M. (2006). Pattern recognition and machine learning.
+ springer.
'''
- x = (X - self._x_mean_) / self._x_std
- y_hat = np.dot(x,self.coef_) + self._y_mean
-
+ y_hat = np.dot(X, self.coef_) + self.intercept_
+
if return_std:
- var_hat = 1./self.beta
- var_hat += np.sum( np.dot(x[:,self.active_],self.sigma_) * x[:,self.active_], axis = 1)
+ # Handle the zero variance case
+ if self.var_y:
+ return y_hat, np.zeros_like(y_hat)
+
+ var_hat = 1./self.beta
+ var_hat += np.sum(X.dot(self.sigma_) * X, axis=1)
std_hat = np.sqrt(var_hat)
return y_hat, std_hat
else:
return y_hat
+
# l2norm = 0.0
# for idx in range(10):
# sigma2 = np.genfromtxt('./test/sigma2_{0}.csv'.format(idx+1), delimiter=',')
# Psi_train = np.genfromtxt('./test/Psi_train_{0}.csv'.format(idx+1), delimiter=',')
# Y_train = np.genfromtxt('./test/Y_train_{0}.csv'.format(idx+1))
-# coeffs_fold = np.genfromtxt('./test/coeffs_fold_{0}.csv'.format(idx+1))
# Psi_test = np.genfromtxt('./test/Psi_test_{0}.csv'.format(idx+1), delimiter=',')
# Y_test = np.genfromtxt('./test/Y_test_{0}.csv'.format(idx+1))
-
+
# clf = RegressionFastLaplace(verbose=True)
# clf.fit_(Psi_train, Y_train, sigma2)
+# coeffs_fold = np.genfromtxt('./test/coeffs_fold_{0}.csv'.format(idx+1))
# print("coeffs error: {0:.4g}".format(np.linalg.norm(clf.coef_ - coeffs_fold)))
# l2norm += np.linalg.norm(Y_test - clf.predict(Psi_test))**2/len(Y_test)
# print("l2norm error: {0:.4g}".format(l2norm))
-
-# import sys
-# sys.exit()
-
-# Psi = np.genfromtxt('../tests/AnalyticalFunction/Psi.csv', delimiter=',')
-# Y = np.genfromtxt('../tests/AnalyticalFunction/Y.csv')
-
-# clf = RegressionFastLaplace(verbose=True)
-# best = clf.fit_(Psi, Y,7.608010186983984e-11)
-# y_hat, std = best.predict(Psi[:2], return_std=True)
diff --git a/src/bayesvalidrox/surrogate_models/sequential_design.py b/src/bayesvalidrox/surrogate_models/sequential_design.py
index bc3a9089a75c061aac9737e9c43a3732cb970956..fc81dcd4529ca0708dfba47385aef4415992eb3e 100644
--- a/src/bayesvalidrox/surrogate_models/sequential_design.py
+++ b/src/bayesvalidrox/surrogate_models/sequential_design.py
@@ -9,15 +9,17 @@ import numpy as np
from scipy import stats, signal, linalg, sparse
from scipy.spatial import distance
from copy import deepcopy, copy
-import tqdm
+from tqdm import tqdm
import scipy.optimize as opt
from sklearn.metrics import mean_squared_error
import multiprocessing
import matplotlib.pyplot as plt
import sys
import os
+import gc
import seaborn as sns
-
+from joblib import Parallel, delayed
+import resource
from .exploration import Exploration
@@ -26,15 +28,11 @@ class SeqDesign():
This class provieds method for trainig the meta-model in an iterative
manners.
The main method to execute the task is `train_seq_design`, which
- recieves a model object and returns the trained metamodel.
+ recieves a model object and returns the trained metamodel.
"""
- def __init__(self, MetaModel):
- self.MetaModel = MetaModel
- self.Model = MetaModel.ModelObj
-
# -------------------------------------------------------------------------
- def train_seq_design(self, Model):
+ def train_seq_design(self, MetaModel):
"""
Starts the adaptive sequential design for refining the surrogate model
by selecting training points in a sequential manner.
@@ -46,15 +44,16 @@ class SeqDesign():
Returns
-------
- PCEModel : object
+ MetaModel : object
Meta model object.
"""
- MetaModel = self.MetaModel
- self.Model = MetaModel.ModelObj
+ # MetaModel = self
+ Model = MetaModel.ModelObj
+ self.MetaModel = MetaModel
+ self.Model = Model
# Initialization
- errorIncreases = False
MetaModel.SeqModifiedLOO = {}
MetaModel.seqValidError = {}
MetaModel.SeqBME = {}
@@ -64,7 +63,7 @@ class SeqDesign():
MetaModel.seqRMSEStd = {}
MetaModel.seqMinDist = []
pce = True if MetaModel.meta_model_type.lower() != 'gpe' else False
- mc_ref = True if hasattr(Model, 'MCReference') else False
+ mc_ref = True if bool(Model.mc_reference) else False
if mc_ref:
Model.read_mc_reference()
@@ -79,67 +78,69 @@ class SeqDesign():
n_canddidate = MetaModel.ExpDesign.n_canddidate
post_snapshot = MetaModel.ExpDesign.post_snapshot
n_replication = MetaModel.ExpDesign.n_replication
-
+ util_func = MetaModel.ExpDesign.util_func
+ output_name = Model.Output.names
+ validError = None
# Handle if only one UtilityFunctions is provided
- if not isinstance(MetaModel.ExpDesign.util_func, list):
+ if not isinstance(util_func, list):
util_func = [MetaModel.ExpDesign.util_func]
# Read observations or MCReference
- if len(Model.observations) != 0:
- self.observations = self.Model.read_observation()
- # ---------- Initial PCEModel ----------
- PCEModel = MetaModel.train_norm_design(Model)
- initPCEModel = deepcopy(PCEModel)
-
- # TODO: Loop over outputs
- OutputName = Model.Output.names
-
- # Estimation of the integral via Monte Varlo integration
- obs_data = self.observations
+ if len(Model.observations) != 0 or Model.meas_file is not None:
+ self.observations = Model.read_observation()
+ obs_data = self.observations
+ else:
+ obs_data = []
+ TotalSigma2 = {}
+ # ---------- Initial MetaModel ----------
+ initMetaModel = deepcopy(MetaModel)
+
+ # Validation error if validation set is provided.
+ if len(MetaModel.valid_model_runs) != 0:
+ init_rmse, init_valid_error = self.__validError(initMetaModel)
+ init_valid_error = list(init_valid_error.values())
+ else:
+ init_rmse = None
- # Check if data is provided
- TotalSigma2 = np.empty((0, 1))
- if len(obs_data) != 0 and hasattr(PCEModel, 'Discrepancy'):
- # ------ Prepare diagonal enteries for co-variance matrix ---------
- for keyIdx, key in enumerate(Model.Output.names):
- # optSigma = 'B'
- sigma2 = np.array(PCEModel.Discrepancy.parameters[key])
- TotalSigma2 = np.append(TotalSigma2, sigma2)
+ # Check if discrepancy is provided
+ if len(obs_data) != 0 and hasattr(MetaModel, 'Discrepancy'):
+ TotalSigma2 = MetaModel.Discrepancy.parameters
# Calculate the initial BME
- out = self.__BME_Calculator(initPCEModel, obs_data, TotalSigma2)
- initBME, initKLD, initPosterior, initDistHellinger = out
- print("\nInitial BME:", initBME)
- print("Initial KLD:", initKLD)
+ out = self.__BME_Calculator(
+ initMetaModel, obs_data, TotalSigma2, init_rmse)
+ init_BME, init_KLD, init_post, init_likes, init_dist_hellinger = out
+ print(f"\nInitial BME: {init_BME:.2f}")
+ print(f"Initial KLD: {init_KLD:.2f}")
# Posterior snapshot (initial)
if post_snapshot:
- MAP = PCEModel.ExpDesign.max_a_post
- parNames = PCEModel.ExpDesign.par_names
+ parNames = MetaModel.ExpDesign.par_names
print('Posterior snapshot (initial) is being plotted...')
- self.__posteriorPlot(initPosterior, MAP, parNames,
- 'SeqPosterior_init')
+ self.__posteriorPlot(init_post, parNames, 'SeqPosterior_init')
# Check the convergence of the Mean & Std
if mc_ref and pce:
- initRMSEMean, initRMSEStd = self.__error_Mean_Std()
- print(f"Initial Mean and Std error: {initRMSEMean}, {initRMSEStd}")
+ init_rmse_mean, init_rmse_std = self.__error_Mean_Std()
+ print(f"Initial Mean and Std error: {init_rmse_mean},"
+ f" {init_rmse_std}")
# Read the initial experimental design
- Xinit = initPCEModel.ExpDesign.X
- initTotalNSamples = len(PCEModel.ExpDesign.X)
- initYprev = initPCEModel.ModelOutputDict
- initLCerror = initPCEModel.LCerror
+ Xinit = initMetaModel.ExpDesign.X
+ init_n_samples = len(MetaModel.ExpDesign.X)
+ initYprev = initMetaModel.ModelOutputDict
+ initLCerror = initMetaModel.LCerror
+ n_itrs = max_n_samples - init_n_samples
# Read the initial ModifiedLOO
if pce:
Scores_all, varExpDesignY = [], []
- for OutName in OutputName:
- y = initPCEModel.ExpDesign.Y[OutName]
+ for out_name in output_name:
+ y = initMetaModel.ExpDesign.Y[out_name]
Scores_all.append(list(
- initPCEModel.score_dict[OutName].values()))
- if PCEModel.dim_red_method.lower() == 'pca':
- pca = PCEModel.pca[OutName]
+ initMetaModel.score_dict['b_1'][out_name].values()))
+ if MetaModel.dim_red_method.lower() == 'pca':
+ pca = MetaModel.pca['b_1'][out_name]
components = pca.transform(y)
varExpDesignY.append(np.var(components, axis=0))
else:
@@ -147,35 +148,29 @@ class SeqDesign():
Scores = [item for sublist in Scores_all for item in sublist]
weights = [item for sublist in varExpDesignY for item in sublist]
- initModifiedLOO = [np.average([1-score for score in Scores],
- weights=weights)]
-
- if len(PCEModel.valid_model_runs) != 0:
- initValidError = self.__validError()
- initValidError = list(initValidError.values())
- print("\nInitial ValidError:", initValidError)
+ init_mod_LOO = [np.average([1-score for score in Scores],
+ weights=weights)]
+ prevMetaModel_dict = {}
# Replicate the sequential design
for repIdx in range(n_replication):
- print(f'>>>> Replication: {repIdx+1}<<<<')
+ print(f'\n>>>> Replication: {repIdx+1}<<<<')
# To avoid changes ub original aPCE object
- # PCEModel = copy.deepcopy(initPCEModel)
- PCEModel.ExpDesign.X = Xinit
- PCEModel.ExpDesign.Y = initYprev
- PCEModel.LCerror = initLCerror
+ MetaModel.ExpDesign.X = Xinit
+ MetaModel.ExpDesign.Y = initYprev
+ MetaModel.LCerror = initLCerror
for util_f in util_func:
- print(f'>>>> UtilityFunction: {util_f} <<<<')
+ print(f'\n>>>> Utility Function: {util_f} <<<<')
# To avoid changes ub original aPCE object
- # PCEModel = copy.deepcopy(initPCEModel)
- PCEModel.ExpDesign.X = Xinit
- PCEModel.ExpDesign.Y = initYprev
- PCEModel.LCerror = initLCerror
+ MetaModel.ExpDesign.X = Xinit
+ MetaModel.ExpDesign.Y = initYprev
+ MetaModel.LCerror = initLCerror
# Set the experimental design
Xprev = Xinit
- total_n_samples = initTotalNSamples
+ total_n_samples = init_n_samples
Yprev = initYprev
Xfull = []
@@ -183,105 +178,101 @@ class SeqDesign():
# Store the initial ModifiedLOO
if pce:
- print("\nInitial ModifiedLOO:", initModifiedLOO)
- ModifiedLOO = initModifiedLOO
- SeqModifiedLOO = np.array(ModifiedLOO)
+ print("\nInitial ModifiedLOO:", init_mod_LOO)
+ SeqModifiedLOO = np.array(init_mod_LOO)
- if len(PCEModel.valid_model_runs) != 0:
- ValidError = initValidError
- SeqValidError = np.array(ValidError)
+ if len(MetaModel.valid_model_runs) != 0:
+ SeqValidError = np.array(init_valid_error)
# Check if data is provided
if len(obs_data) != 0:
- SeqBME = np.array([initBME])
- SeqKLD = np.array([initKLD])
- SeqDistHellinger = np.array([initDistHellinger])
+ SeqBME = np.array([init_BME])
+ SeqKLD = np.array([init_KLD])
+ SeqDistHellinger = np.array([init_dist_hellinger])
if mc_ref and pce:
- seqRMSEMean = np.array([initRMSEMean])
- seqRMSEStd = np.array([initRMSEStd])
+ seqRMSEMean = np.array([init_rmse_mean])
+ seqRMSEStd = np.array([init_rmse_std])
- # Start Sequential Experimental Design
+ # ------- Start Sequential Experimental Design -------
postcnt = 1
- itrNr = 1
- while total_n_samples < max_n_samples:
+ for itr_no in range(1, n_itrs+1):
+ print(f'\n>>>> Iteration number {itr_no} <<<<')
+
+ # Save the metamodel prediction before updating
+ prevMetaModel_dict[itr_no] = deepcopy(MetaModel)
+ if itr_no > 1:
+ pc_model = prevMetaModel_dict[itr_no-1]
+ self._y_hat_prev, _ = pc_model.eval_metamodel(
+ samples=Xfull[-1].reshape(1, -1))
# Optimal Bayesian Design
- PCEModel.ExpDesignFlag = 'sequential'
+ m_1 = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss/1024
+ MetaModel.ExpDesignFlag = 'sequential'
Xnew, updatedPrior = self.opt_SeqDesign(TotalSigma2,
n_canddidate,
util_f)
-
+ m_2 = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss/1024
S = np.min(distance.cdist(Xinit, Xnew, 'euclidean'))
- PCEModel.seqMinDist.append(S)
- print("\nmin Dist from OldExpDesign:", S)
+ MetaModel.seqMinDist.append(S)
+ print(f"\nmin Dist from OldExpDesign: {S:2f}")
print("\n")
- # Evaluate the full model response at the new sample:
+ # Evaluate the full model response at the new sample
Ynew, _ = Model.run_model_parallel(
Xnew, prevRun_No=total_n_samples
)
total_n_samples += Xnew.shape[0]
-
# ------ Plot the surrogate model vs Origninal Model ------
- if hasattr(PCEModel, 'adapt_verbose') and \
- PCEModel.adapt_verbose:
- from post_processing.adaptPlot import adaptPlot
- y_hat, std_hat = PCEModel.eval_metamodel(samples=Xnew)
- adaptPlot(PCEModel, Ynew, y_hat, std_hat, plotED=False)
+ if hasattr(MetaModel, 'adapt_verbose') and \
+ MetaModel.adapt_verbose:
+ from .adaptPlot import adaptPlot
+ y_hat, std_hat = MetaModel.eval_metamodel(samples=Xnew)
+ adaptPlot(MetaModel, Ynew, y_hat, std_hat, plotED=False)
# -------- Retrain the surrogate model -------
# Extend new experimental design
Xfull = np.vstack((Xprev, Xnew))
- # Updating existing key's value
- for OutIdx in range(len(OutputName)):
- OutName = OutputName[OutIdx]
- try:
- Yfull = np.vstack((Yprev[OutName], Ynew[OutName]))
- except:
- Yfull = np.vstack((Yprev[OutName], Ynew))
+ # Updating experimental design Y
+ for out_name in output_name:
+ Yfull = np.vstack((Yprev[out_name], Ynew[out_name]))
+ MetaModel.ModelOutputDict[out_name] = Yfull
- PCEModel.ModelOutputDict[OutName] = Yfull
+ # Pass new design to the metamodel object
+ MetaModel.ExpDesign.sampling_method = 'user'
+ MetaModel.ExpDesign.X = Xfull
+ MetaModel.ExpDesign.Y = MetaModel.ModelOutputDict
- PCEModel.ExpDesign.sampling_method = 'user'
- PCEModel.ExpDesign.X = Xfull
- PCEModel.ExpDesign.Y = PCEModel.ModelOutputDict
-
- # save the Experimental Design for next iteration
+ # Save the Experimental Design for next iteration
Xprev = Xfull
- Yprev = PCEModel.ModelOutputDict
+ Yprev = MetaModel.ModelOutputDict
# Pass the new prior as the input
- PCEModel.input_obj.poly_coeffs_flag = False
+ MetaModel.input_obj.poly_coeffs_flag = False
if updatedPrior is not None:
- PCEModel.input_obj.poly_coeffs_flag = True
+ MetaModel.input_obj.poly_coeffs_flag = True
print("updatedPrior:", updatedPrior.shape)
# Arbitrary polynomial chaos
for i in range(updatedPrior.shape[1]):
- PCEModel.Inputs.Marginals[i].dist_type = None
+ MetaModel.input_obj.Marginals[i].dist_type = None
x = updatedPrior[:, i]
- PCEModel.Inputs.Marginals[i].raw_data = x
-
- prevPCEModel = PCEModel
- PCEModel = PCEModel.train_norm_design(Model)
+ MetaModel.input_obj.Marginals[i].raw_data = x
- # -------- Evaluate the retrain surrogate model -------
- # Compute the validation error
- if len(PCEModel.valid_model_runs) != 0:
- validError = self.__validError()
- ValidError = list(validError.values())
- print("\nUpdated ValidError:", ValidError)
+ # Train the surrogate model for new ExpDesign
+ MetaModel.train_norm_design(parallel=False)
+ m_3 = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss/1024
+ # -------- Evaluate the retrained surrogate model -------
# Extract Modified LOO from Output
if pce:
Scores_all, varExpDesignY = [], []
- for OutName in OutputName:
- y = initPCEModel.ExpDesign.Y[OutName]
+ for out_name in output_name:
+ y = MetaModel.ExpDesign.Y[out_name]
Scores_all.append(list(
- PCEModel.score_dict[OutName].values()))
- if PCEModel.dim_red_method.lower() == 'pca':
- pca = PCEModel.pca[OutName]
+ MetaModel.score_dict['b_1'][out_name].values()))
+ if MetaModel.dim_red_method.lower() == 'pca':
+ pca = MetaModel.pca['b_1'][out_name]
components = pca.transform(y)
varExpDesignY.append(np.var(components,
axis=0))
@@ -296,64 +287,51 @@ class SeqDesign():
print('\n')
print(f"Updated ModifiedLOO {util_f}:\n", ModifiedLOO)
- print("Xfull:", Xfull.shape)
print('\n')
- # check the direction of the error (on average):
- # if it increases consistently stop the iterations
- n_checks = 3
- if itrNr > n_checks * PCEModel.ExpDesign.n_new_samples:
- # ss<0 error increasing
- ss = np.sign(SeqModifiedLOO - ModifiedLOO)
- errorIncreases = np.sum(np.mean(ss[-2:], axis=1)) <= \
- -1*n_checks
-
- # If error is increasing in the last n_check iteration,
- # stop the search and return the previous PCEModel
- if errorIncreases:
- print("Warning: The modified error is increasing "
- "compared to the last {n_checks} iterations.")
- PCEModel = prevPCEModel
- break
+ # Compute the validation error
+ if len(MetaModel.valid_model_runs) != 0:
+ rmse, validError = self.__validError(MetaModel)
+ ValidError = list(validError.values())
else:
- prevPCEModel = PCEModel
+ rmse = None
# Store updated ModifiedLOO
if pce:
SeqModifiedLOO = np.vstack(
(SeqModifiedLOO, ModifiedLOO))
- if len(PCEModel.valid_model_runs) != 0:
+ if len(MetaModel.valid_model_runs) != 0:
SeqValidError = np.vstack(
(SeqValidError, ValidError))
-
+ m_4 = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss/1024
# -------- Caclulation of BME as accuracy metric -------
# Check if data is provided
if len(obs_data) != 0:
# Calculate the initial BME
- out = self.__BME_Calculator(PCEModel, obs_data,
- TotalSigma2)
- BME, KLD, Posterior, DistHellinger = out
+ out = self.__BME_Calculator(MetaModel, obs_data,
+ TotalSigma2, rmse)
+ BME, KLD, Posterior, likes, DistHellinger = out
print('\n')
- print("Updated BME:", BME)
- print("Updated KLD:", KLD)
+ print(f"Updated BME: {BME:.2f}")
+ print(f"Updated KLD: {KLD:.2f}")
print('\n')
# Plot some snapshots of the posterior
- step_snapshot = PCEModel.ExpDesign.step_snapshot
+ step_snapshot = MetaModel.ExpDesign.step_snapshot
if post_snapshot and postcnt % step_snapshot == 0:
- MAP = PCEModel.ExpDesign.max_a_post
- parNames = PCEModel.ExpDesign.par_names
+ parNames = MetaModel.ExpDesign.par_names
print('Posterior snapshot is being plotted...')
- self.__posteriorPlot(Posterior, MAP, parNames,
- 'SeqPosterior_{postcnt}')
+ self.__posteriorPlot(Posterior, parNames,
+ f'SeqPosterior_{postcnt}')
postcnt += 1
+ m_5 = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss/1024
# Check the convergence of the Mean&Std
if mc_ref and pce:
print('\n')
RMSE_Mean, RMSE_std = self.__error_Mean_Std()
- print(f"Updated Mean and Std error: {RMSE_Mean}, "
- f"{RMSE_std}")
+ print(f"Updated Mean and Std error: {RMSE_Mean:.2f}, "
+ f"{RMSE_std:.2f}")
print('\n')
# Store the updated BME & KLD
@@ -370,25 +348,40 @@ class SeqDesign():
if pce and any(LOO < mod_LOO_threshold
for LOO in ModifiedLOO):
break
- itrNr += 1
+
+ print(f"Memory itr {itr_no}: I: {m_2-m_1:.2f} MB")
+ print(f"Memory itr {itr_no}: II: {m_3-m_2:.2f} MB")
+ print(f"Memory itr {itr_no}: III: {m_4-m_3:.2f} MB")
+ print(f"Memory itr {itr_no}: IV: {m_5-m_4:.2f} MB")
+ m_6 = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss/1024
+ print(f"Memory itr {itr_no}: total: {m_6:.2f} MB")
+
+ # Clean up
+ if len(obs_data) != 0:
+ del out
+ gc.collect()
+ print()
+ print('-'*50)
+ print()
+
# Store updated ModifiedLOO and BME in dictonary
strKey = f'{util_f}_rep_{repIdx+1}'
if pce:
- PCEModel.SeqModifiedLOO[strKey] = SeqModifiedLOO
- if len(PCEModel.valid_model_runs) != 0:
- PCEModel.seqValidError[strKey] = SeqValidError
+ MetaModel.SeqModifiedLOO[strKey] = SeqModifiedLOO
+ if len(MetaModel.valid_model_runs) != 0:
+ MetaModel.seqValidError[strKey] = SeqValidError
# Check if data is provided
if len(obs_data) != 0:
- PCEModel.SeqBME[strKey] = SeqBME
- PCEModel.SeqKLD[strKey] = SeqKLD
- if len(PCEModel.valid_likelihoods) != 0:
- PCEModel.SeqDistHellinger[strKey] = SeqDistHellinger
+ MetaModel.SeqBME[strKey] = SeqBME
+ MetaModel.SeqKLD[strKey] = SeqKLD
+ if len(MetaModel.valid_likelihoods) != 0:
+ MetaModel.SeqDistHellinger[strKey] = SeqDistHellinger
if mc_ref and pce:
- PCEModel.seqRMSEMean[strKey] = seqRMSEMean
- PCEModel.seqRMSEStd[strKey] = seqRMSEStd
+ MetaModel.seqRMSEMean[strKey] = seqRMSEMean
+ MetaModel.seqRMSEStd[strKey] = seqRMSEStd
- return PCEModel
+ return MetaModel
# -------------------------------------------------------------------------
def util_VarBasedDesign(self, X_can, index, util_func='Entropy'):
@@ -414,13 +407,18 @@ class SeqDesign():
Score.
"""
- out_dict_y = self.MetaModel.ExpDesign.Y
- out_names = self.MetaModel.ModelObj.Output.names
+ MetaModel = self.MetaModel
+ ED_X = MetaModel.ExpDesign.X
+ out_dict_y = MetaModel.ExpDesign.Y
+ out_names = MetaModel.ModelObj.Output.names
+
+ # Run the Metamodel for the candidate
+ X_can = X_can.reshape(1, -1)
+ Y_PC_can, std_PC_can = MetaModel.eval_metamodel(samples=X_can)
- if util_func == 'Entropy':
+ if util_func.lower() == 'alm':
# ----- Entropy/MMSE/active learning MacKay(ALM) -----
# Compute perdiction variance of the old model
- Y_PC_can, std_PC_can = self.MetaModel.eval_metamodel(samples=X_can)
canPredVar = {key: std_PC_can[key]**2 for key in out_names}
varPCE = np.zeros((len(out_names), X_can.shape[0]))
@@ -428,14 +426,18 @@ class SeqDesign():
varPCE[KeyIdx] = np.max(canPredVar[key], axis=1)
score = np.max(varPCE, axis=0)
- elif util_func == 'EIGF':
+ elif util_func.lower() == 'eigf':
# ----- Expected Improvement for Global fit -----
- # Eq (5) from Liu et al.(2018)
+ # Find closest EDX to the candidate
+ distances = distance.cdist(ED_X, X_can, 'euclidean')
+ index = np.argmin(distances)
+
# Compute perdiction error and variance of the old model
- Y_PC_can, std_PC_can = self.eval_metamodel(samples=X_can)
predError = {key: Y_PC_can[key] for key in out_names}
canPredVar = {key: std_PC_can[key]**2 for key in out_names}
+ # Compute perdiction error and variance of the old model
+ # Eq (5) from Liu et al.(2018)
EIGF_PCE = np.zeros((len(out_names), X_can.shape[0]))
for KeyIdx, key in enumerate(out_names):
residual = predError[key] - out_dict_y[key][int(index)]
@@ -472,11 +474,13 @@ class SeqDesign():
"""
# Evaluate the PCE metamodels at that location ???
- Y_mean_can, Y_std_can = self.eval_metamodel(samples=np.array([X_can]))
+ Y_mean_can, Y_std_can = self.MetaModel.eval_metamodel(
+ samples=np.array([X_can])
+ )
# Get the data
obs_data = self.observations
- nObs = self.Model.n_obs
+ n_obs = self.Model.n_obs
# TODO: Analytical DKL
# Sample a distribution for a normal dist
# with Y_mean_can as the mean and Y_std_can as std.
@@ -530,9 +534,9 @@ class SeqDesign():
# cov = np.zeros((means.shape[0], means.shape[0]), float)
# np.fill_diagonal(cov, stds**2)
- Y_MC[key] = np.zeros((MCsize, nObs))
- logsamples = np.zeros((MCsize, nObs))
- for i in range(nObs):
+ Y_MC[key] = np.zeros((MCsize, n_obs))
+ logsamples = np.zeros((MCsize, n_obs))
+ for i in range(n_obs):
NormalDensity = stats.norm(means[i], stds[i])
Y_MC[key][:, i] = NormalDensity.rvs(MCsize)
logsamples[:, i] = NormalDensity.logpdf(Y_MC[key][:, i])
@@ -597,7 +601,7 @@ class SeqDesign():
coeffs = self.MetaModel.coeffs_dict.values()
nModelParams = max(len(v) for val in coeffs for v in val.values())
maxL = np.nanmax(likelihoods)
- U_J_d = -2 * np.log(maxL) + np.log(nObs) * nModelParams
+ U_J_d = -2 * np.log(maxL) + np.log(n_obs) * nModelParams
# Akaike information criterion
elif var == 'AIC':
@@ -605,7 +609,7 @@ class SeqDesign():
nModelParams = max(len(v) for val in coeffs for v in val.values())
maxlogL = np.log(np.nanmax(likelihoods))
AIC = -2 * maxlogL + 2 * nModelParams
- # 2 * nModelParams * (nModelParams+1) / (nObs-nModelParams-1)
+ # 2 * nModelParams * (nModelParams+1) / (n_obs-nModelParams-1)
penTerm = 0
U_J_d = 1*(AIC + penTerm)
@@ -613,8 +617,9 @@ class SeqDesign():
elif var == 'DIC':
# D_theta_bar = np.mean(-2 * Likelihoods)
N_star_p = 0.5 * np.var(np.log(likelihoods[likelihoods != 0]))
- Likelihoods_theta_mean = self.__normpdf(Y_mean_can, Y_std_can,
- obs_data, sigma2Dict)
+ Likelihoods_theta_mean = self.__normpdf(
+ Y_mean_can, Y_std_can, obs_data, sigma2Dict
+ )
DIC = -2 * np.log(Likelihoods_theta_mean) + 2 * N_star_p
U_J_d = DIC
@@ -626,8 +631,136 @@ class SeqDesign():
if np.isnan(U_J_d) or U_J_d == -np.inf or U_J_d == np.inf:
U_J_d = 0.0
+ # Clear memory
+ del likelihoods
+ del Y_MC
+ del std_MC
+ gc.collect(generation=2)
+
return -1 * U_J_d # -1 is for minimization instead of maximization
+ # -------------------------------------------------------------------------
+ def update_metamodel(self, MetaModel, output, y_hat_can, univ_p_val, index,
+ new_pca=False):
+ BasisIndices = MetaModel.basis_dict[output]["y_"+str(index+1)]
+ clf_poly = MetaModel.clf_poly[output]["y_"+str(index+1)]
+ Mn = clf_poly.coef_
+ Sn = clf_poly.sigma_
+ beta = clf_poly.alpha_
+ active = clf_poly.active_
+ Psi = self.MetaModel.create_psi(BasisIndices, univ_p_val)
+
+ Sn_new_inv = np.linalg.inv(Sn)
+ Sn_new_inv += beta * np.dot(Psi[:, active].T, Psi[:, active])
+ Sn_new = np.linalg.inv(Sn_new_inv)
+
+ Mn_new = np.dot(Sn_new_inv, Mn[active]).reshape(-1, 1)
+ Mn_new += beta * np.dot(Psi[:, active].T, y_hat_can)
+ Mn_new = np.dot(Sn_new, Mn_new).flatten()
+
+ # Compute the old and new moments of PCEs
+ mean_old = Mn[0]
+ mean_new = Mn_new[0]
+ std_old = np.sqrt(np.sum(np.square(Mn[1:])))
+ std_new = np.sqrt(np.sum(np.square(Mn_new[1:])))
+
+ # Back transformation if PCA is selected.
+ if MetaModel.dim_red_method.lower() == 'pca':
+ old_pca = MetaModel.pca[output]
+ mean_old = old_pca.mean_[index]
+ mean_old += np.sum(mean_old * old_pca.components_[:, index])
+ std_old = np.sqrt(np.sum(std_old**2 *
+ old_pca.components_[:, index]**2))
+ mean_new = new_pca.mean_[index]
+ mean_new += np.sum(mean_new * new_pca.components_[:, index])
+ std_new = np.sqrt(np.sum(std_new**2 *
+ new_pca.components_[:, index]**2))
+ # print(f"mean_old: {mean_old:.2f} mean_new: {mean_new:.2f}")
+ # print(f"std_old: {std_old:.2f} std_new: {std_new:.2f}")
+ # Store the old and new moments of PCEs
+ results = {
+ 'mean_old': mean_old,
+ 'mean_new': mean_new,
+ 'std_old': std_old,
+ 'std_new': std_new
+ }
+ return results
+
+ # -------------------------------------------------------------------------
+ def util_BayesianDesign_old(self, X_can, X_MC, sigma2Dict, var='DKL'):
+ """
+ Computes scores based on Bayesian sequential design criterion (var).
+
+ Parameters
+ ----------
+ X_can : array of shape (n_samples, n_params)
+ Candidate samples.
+ sigma2Dict : dict
+ A dictionary containing the measurement errors (sigma^2).
+ var : string, optional
+ Bayesian design criterion. The default is 'DKL'.
+
+ Returns
+ -------
+ float
+ Score.
+
+ """
+
+ # To avoid changes ub original aPCE object
+ Model = self.Model
+ MetaModel = deepcopy(self.MetaModel)
+ old_EDY = MetaModel.ExpDesign.Y
+
+ # Evaluate the PCE metamodels using the candidate design
+ Y_PC_can, Y_std_can = self.MetaModel.eval_metamodel(
+ samples=np.array([X_can])
+ )
+
+ # Generate y from posterior predictive
+ m_size = 100
+ y_hat_samples = {}
+ for idx, key in enumerate(Model.Output.names):
+ means, stds = Y_PC_can[key][0], Y_std_can[key][0]
+ y_hat_samples[key] = np.random.multivariate_normal(
+ means, np.diag(stds), m_size)
+
+ # Create the SparseBayes-based PCE metamodel:
+ MetaModel.input_obj.poly_coeffs_flag = False
+ univ_p_val = self.MetaModel.univ_basis_vals(X_can)
+ G_n_m_all = np.zeros((m_size, len(Model.Output.names), Model.n_obs))
+
+ for i in range(m_size):
+ for idx, key in enumerate(Model.Output.names):
+ if MetaModel.dim_red_method.lower() == 'pca':
+ # Equal number of components
+ new_outputs = np.vstack(
+ (old_EDY[key], y_hat_samples[key][i])
+ )
+ new_pca, _ = MetaModel.pca_transformation(new_outputs)
+ target = new_pca.transform(
+ y_hat_samples[key][i].reshape(1, -1)
+ )[0]
+ else:
+ new_pca, target = False, y_hat_samples[key][i]
+
+ for j in range(len(target)):
+
+ # Update surrogate
+ result = self.update_metamodel(
+ MetaModel, key, target[j], univ_p_val, j, new_pca)
+
+ # Compute Expected Information Gain (Eq. 39)
+ G_n_m = np.log(result['std_old']/result['std_new']) - 1./2
+ G_n_m += result['std_new']**2 / (2*result['std_old']**2)
+ G_n_m += (result['mean_new'] - result['mean_old'])**2 /\
+ (2*result['std_old']**2)
+
+ G_n_m_all[i, idx, j] = G_n_m
+
+ U_J_d = G_n_m_all.mean(axis=(1, 2)).mean()
+ return -1 * U_J_d
+
# -------------------------------------------------------------------------
def util_BayesianDesign(self, X_can, X_MC, sigma2Dict, var='DKL'):
"""
@@ -651,14 +784,22 @@ class SeqDesign():
# To avoid changes ub original aPCE object
Model = self.Model
- PCEModel = deepcopy(self.MetaModel)
+ MetaModel = deepcopy(self.MetaModel)
+ out_names = MetaModel.ModelObj.Output.names
+ if X_can.ndim == 1:
+ X_can = X_can.reshape(1, -1)
+
+ # Compute the mean and std based on the MetaModel
+ # pce_means, pce_stds = self._compute_pce_moments(MetaModel)
+ if var == 'ALC':
+ Y_MC, Y_MC_std = MetaModel.eval_metamodel(samples=X_MC)
# Old Experimental design
- oldExpDesignX = PCEModel.ExpDesign.X
- oldExpDesignY = PCEModel.ExpDesign.Y
+ oldExpDesignX = MetaModel.ExpDesign.X
+ oldExpDesignY = MetaModel.ExpDesign.Y
# Evaluate the PCE metamodels at that location ???
- Y_PC_can, _ = self.MetaModel.eval_metamodel(samples=np.array([X_can]))
+ Y_PC_can, Y_std_can = MetaModel.eval_metamodel(samples=X_can)
# Add all suggestion as new ExpDesign
NewExpDesignX = np.vstack((oldExpDesignX, X_can))
@@ -671,55 +812,47 @@ class SeqDesign():
except:
NewExpDesignY[key] = oldExpDesignY[key]
- PCEModel.ExpDesign.sampling_method = 'user'
- PCEModel.ExpDesign.X = NewExpDesignX
- PCEModel.ExpDesign.Y = NewExpDesignY
+ MetaModel.ExpDesign.sampling_method = 'user'
+ MetaModel.ExpDesign.X = NewExpDesignX
+ MetaModel.ExpDesign.Y = NewExpDesignY
- # Create the SparseBayes-based PCE metamodel:
- PCEModel.Inputs.__poly_coeffs_flag = False
- univ_p_val = self.MetaModel.univ_basis_vals(X_can)
- G_n_m_all = np.zeros((len(Model.Output.names), Model.nObs))
+ # Train the model for the observed data using x_can
+ MetaModel.input_obj.poly_coeffs_flag = False
+ MetaModel.train_norm_design(parallel=False)
+ PCE_Model_can = MetaModel
- for idx, key in enumerate(Model.Output.names):
- for i in range(Model.nObs):
- BasisIndices = PCEModel.basis_dict[key]["y_"+str(i+1)]
- clf_poly = PCEModel.clf_poly[key]["y_"+str(i+1)]
- Mn = clf_poly.coef_
- Sn = clf_poly.sigma_
- beta = clf_poly.alpha_
- active = clf_poly.active_
- Psi = self.MetaModel.create_psi(BasisIndices, univ_p_val)
-
- Sn_new_inv = np.linalg.inv(Sn)
- Sn_new_inv += beta * np.dot(Psi[:, active].T, Psi[:, active])
- Sn_new = np.linalg.inv(Sn_new_inv)
-
- Mn_new = np.dot(Sn_new_inv, Mn[active]).reshape(-1, 1)
- Mn_new += beta * np.dot(Psi[:, active].T, Y_PC_can[key][0, i])
- Mn_new = np.dot(Sn_new, Mn_new).flatten()
-
- # Compute new moments
- mean_old = Mn[0]
- mean_new = Mn_new[0]
- std_old = np.sqrt(np.sum(np.square(Mn[1:])))
- std_new = np.sqrt(np.sum(np.square(Mn_new[1:])))
-
- G_n_m = np.log(std_old/std_new) - 1./2
- G_n_m += std_new**2 / (2*std_new**2)
- G_n_m += (mean_new - mean_old)**2 / (2*std_old**2)
-
- G_n_m_all[idx, i] = G_n_m
-
- clf_poly.coef_[active] = Mn_new
- clf_poly.sigma_ = Sn_new
- PCEModel.clf_poly[key]["y_"+str(i+1)] = clf_poly
-
- # return np.sum(G_n_m_all)
- # PCEModel.train_norm_design(Model, verbose=True)
- PCE_SparseBayes_can = PCEModel
+ if var.lower() == 'mi':
+ # Mutual information based on Krause et al
+ # Adapted from Beck & Guillas (MICE) paper
+ _, std_PC_can = PCE_Model_can.eval_metamodel(samples=X_can)
+ std_can = {key: std_PC_can[key] for key in out_names}
- # Get the data
- obs_data = self.observations
+ std_old = {key: Y_std_can[key] for key in out_names}
+
+ varPCE = np.zeros((len(out_names)))
+ for i, key in enumerate(out_names):
+ varPCE[i] = np.mean(std_old[key]**2/std_can[key]**2)
+ score = np.mean(varPCE)
+
+ return -1 * score
+
+ elif var.lower() == 'alc':
+ # Active learning based on Gramyc and Lee
+ # Adaptive design and analysis of supercomputer experiments Techno-
+ # metrics, 51 (2009), pp. 130–145.
+
+ # Evaluate the MetaModel at the given samples
+ Y_MC_can, Y_MC_std_can = PCE_Model_can.eval_metamodel(samples=X_MC)
+
+ # Compute the score
+ score = []
+ for i, key in enumerate(out_names):
+ pce_var = Y_MC_std_can[key]**2
+ pce_var_can = Y_MC_std[key]**2
+ score.append(np.mean(pce_var-pce_var_can, axis=0))
+ score = np.mean(score)
+
+ return -1 * score
# ---------- Inner MC simulation for computing Utility Value ----------
# Estimation of the integral via Monte Varlo integration
@@ -730,21 +863,25 @@ class SeqDesign():
# Enriching Monte Carlo samples if need be
if ESS != 0:
- X_MC = self.MetaModel.ExpDesign.generate_samples(MCsize,
- 'random')
+ X_MC = self.MetaModel.ExpDesign.generate_samples(
+ MCsize, 'random'
+ )
- # Evaluate the PCEModel at the given samples
- Y_MC, std_MC = PCE_SparseBayes_can.eval_metamodel(samples=X_MC)
+ # Evaluate the MetaModel at the given samples
+ Y_MC, std_MC = PCE_Model_can.eval_metamodel(samples=X_MC)
# Likelihood computation (Comparison of data and simulation
# results via PCE with candidate design)
- likelihoods = self.__normpdf(Y_MC, std_MC, obs_data, sigma2Dict)
+ likelihoods = self.__normpdf(
+ Y_MC, std_MC, self.observations, sigma2Dict
+ )
# Check the Effective Sample Size (1<ESS<MCsize)
ESS = 1 / np.sum(np.square(likelihoods/np.sum(likelihoods)))
# Enlarge sample size if it doesn't fulfill the criteria
if ((ESS > MCsize) or (ESS < 1)):
+ print("--- increasing MC size---")
MCsize *= 10
ESS = 0
@@ -761,16 +898,16 @@ class SeqDesign():
if var == 'DKL':
# Prior-based estimation of BME
- logBME = np.log(np.nanmean(likelihoods))
+ logBME = np.log(np.nanmean(likelihoods, dtype=np.float128))
# Posterior-based expectation of likelihoods
postLikelihoods = likelihoods[accepted]
postExpLikelihoods = np.mean(np.log(postLikelihoods))
# Haun et al implementation
- U_J_d = np.mean(np.log(likelihoods[likelihoods != 0])- logBME)
+ U_J_d = np.mean(np.log(likelihoods[likelihoods != 0]) - logBME)
- U_J_d = np.sum(G_n_m_all)
+ # U_J_d = np.sum(G_n_m_all)
# Ryan et al (2014) implementation
# importanceWeights = Likelihoods[Likelihoods!=0]/np.sum(Likelihoods[Likelihoods!=0])
# U_J_d = np.mean(importanceWeights*np.log(Likelihoods[Likelihoods!=0])) - logBME
@@ -820,6 +957,12 @@ class SeqDesign():
else:
print('The algorithm you requested has not been implemented yet!')
+ # Clear memory
+ del likelihoods
+ del Y_MC
+ del std_MC
+ gc.collect(generation=2)
+
return -1 * U_J_d # -1 is for minimization instead of maximization
# -------------------------------------------------------------------------
@@ -883,13 +1026,17 @@ class SeqDesign():
-------
index : TYPE
DESCRIPTION.
- TYPE
- DESCRIPTION.
+ List
+ Scores.
"""
if method.lower() == 'varoptdesign':
- U_J_d = self.util_VarBasedDesign(candidates, index, var)
+ # U_J_d = self.util_VarBasedDesign(candidates, index, var)
+ U_J_d = np.zeros((candidates.shape[0]))
+ for idx, X_can in tqdm(enumerate(candidates), ascii=True,
+ desc="varoptdesign"):
+ U_J_d[idx] = self.util_VarBasedDesign(X_can, index, var)
elif method.lower() == 'bayesactdesign':
NCandidate = candidates.shape[0]
@@ -1000,7 +1147,7 @@ class SeqDesign():
# epsilon-decreasing scheme
# Start with more exploration and increase the influence of
# exploitation along the way with a exponential decay function
- initNSamples = self.MetaModel.ExpDesign.initNrSamples
+ initNSamples = self.MetaModel.ExpDesign.n_init_samples
n_max_samples = self.MetaModel.ExpDesign.n_max_samples
itrNumber = (self.MetaModel.ExpDesign.X.shape[0] - initNSamples)
@@ -1013,52 +1160,27 @@ class SeqDesign():
elif tradeoff_scheme == 'adaptive':
# Extract itrNumber
- initNSamples = self.MetaModel.ExpDesign.initNrSamples
+ initNSamples = self.MetaModel.ExpDesign.n_init_samples
n_max_samples = self.MetaModel.ExpDesign.n_max_samples
- itrNumber = (self.ExpDesign.X.shape[0] - initNSamples)
- itrNumber //= self.ExpDesign.n_new_samples
+ itrNumber = (self.MetaModel.ExpDesign.X.shape[0] - initNSamples)
+ itrNumber //= self.MetaModel.ExpDesign.n_new_samples
if itrNumber == 0:
exploration_weight = 0.5
else:
- # # Extract the model errors from the last and next to last
- # # iterations
- # errorModel_i , errorModel_i_1 = self.errorModel[itrNumber],
- # self.errorModel[itrNumber-1]
-
- # # Evaluate the error models for all selected samples so far
- # eLCAllCands_i, _ = errorModel_i.eval_errormodel(OldExpDesign)
- # eLCAllCands_i_1, _ = errorModel_i_1.eval_errormodel(OldExpDesign)
-
- # # Local improvement of LC error at last selected design
- # sl_i = np.max(np.dstack(eLCAllCands_i.values())[-1])
- # sl_i_1 = np.max(np.dstack(eLCAllCands_i_1.values())[-1])
-
- # p = sl_i**2 / sl_i_1**2
-
- # # Global improvement of LC error at OldExpDesign
- # sg_i = np.max(np.dstack(eLCAllCands_i.values()),axis=1)
- # sg_i_1 = np.max(np.dstack(eLCAllCands_i_1.values()),axis=1)
-
- # q = np.sum(np.square(sg_i)) / np.sum(np.square(sg_i_1))
-
- # weightExploration = min([0.5*p/q, 1])
-
- # TODO: New adaptive trade-off according to Liu et al. (2017)
+ # New adaptive trade-off according to Liu et al. (2017)
# Mean squared error for last design point
last_EDX = old_EDX[-1].reshape(1, -1)
lastPCEY, _ = self.MetaModel.eval_metamodel(samples=last_EDX)
pce_y = np.array(list(lastPCEY.values()))[:, 0]
- y = np.array(list(old_EDY.values())[1:])[:, -1, :]
+ y = np.array(list(old_EDY.values()))[:, -1, :]
mseError = mean_squared_error(pce_y, y)
# Mean squared CV - error for last design point
- error = []
- for V in self.MetaModel.LCerror.values():
- for v in V.values():
- error.append(v[-1])
- mseCVError = np.mean(np.square(error))
- exploration_weight = 0.99 * min([0.5*mseError/mseCVError, 1])
+ pce_y_prev = np.array(list(self._y_hat_prev.values()))[:, 0]
+ mseCVError = mean_squared_error(pce_y_prev, y)
+
+ exploration_weight = min([0.5*mseError/mseCVError, 1])
# Exploitation weight
exploitation_weight = 1 - exploration_weight
@@ -1092,18 +1214,18 @@ class SeqDesign():
"""
# Initialization
- PCEModel = self.MetaModel
- Bounds = PCEModel.bound_tuples
- n_new_samples = PCEModel.ExpDesign.n_new_samples
- explore_method = PCEModel.ExpDesign.explore_method
- exploit_method = PCEModel.ExpDesign.exploit_method
- n_cand_groups = PCEModel.ExpDesign.n_cand_groups
- tradeoff_scheme = PCEModel.ExpDesign.tradeoff_scheme
-
- old_EDX = PCEModel.ExpDesign.X
- old_EDY = PCEModel.ExpDesign.Y.copy()
- ndim = PCEModel.ExpDesign.X.shape[1]
- OutputNames = PCEModel.ModelObj.Output.names
+ MetaModel = self.MetaModel
+ Bounds = MetaModel.bound_tuples
+ n_new_samples = MetaModel.ExpDesign.n_new_samples
+ explore_method = MetaModel.ExpDesign.explore_method
+ exploit_method = MetaModel.ExpDesign.exploit_method
+ n_cand_groups = MetaModel.ExpDesign.n_cand_groups
+ tradeoff_scheme = MetaModel.ExpDesign.tradeoff_scheme
+
+ old_EDX = MetaModel.ExpDesign.X
+ old_EDY = MetaModel.ExpDesign.Y.copy()
+ ndim = MetaModel.ExpDesign.X.shape[1]
+ OutputNames = MetaModel.ModelObj.Output.names
# -----------------------------------------
# ----------- CUSTOMIZED METHODS ----------
@@ -1111,7 +1233,7 @@ class SeqDesign():
# Utility function exploit_method provided by user
if exploit_method.lower() == 'user':
- Xnew, filteredSamples = PCEModel.ExpDesign.ExploitFunction(self)
+ Xnew, filteredSamples = MetaModel.ExpDesign.ExploitFunction(self)
print("\n")
print("\nXnew:\n", Xnew)
@@ -1157,11 +1279,11 @@ class SeqDesign():
# Initilize the ExploitScore array
# Generate random samples
- allCandidates = PCEModel.ExpDesign.generate_samples(n_candidates,
+ allCandidates = MetaModel.ExpDesign.generate_samples(n_candidates,
'random')
# Construct error model based on LCerror
- errorModel = PCEModel.create_ModelError(old_EDX, self.LCerror)
+ errorModel = MetaModel.create_ModelError(old_EDX, self.LCerror)
self.errorModel.append(copy(errorModel))
# Evaluate the error models for allCandidates
@@ -1176,7 +1298,7 @@ class SeqDesign():
else:
# ------- EXPLORATION: SPACE-FILLING DESIGN -------
# Generate candidate samples from Exploration class
- explore = Exploration(PCEModel, n_candidates)
+ explore = Exploration(MetaModel, n_candidates)
explore.w = 100 # * ndim #500
# Select criterion (mc-intersite-proj-th, mc-intersite-proj)
explore.mc_criterion = 'mc-intersite-proj'
@@ -1223,42 +1345,62 @@ class SeqDesign():
explore_w, exploit_w = self.tradoff_weights(tradeoff_scheme,
old_EDX,
old_EDY)
- print(f"\nweightExploration={explore_w:0.3f} "
- f"weightExploitation={exploit_w:0.3f}")
+ print(f"\n Exploration weight={explore_w:0.3f} "
+ f"Exploitation weight={exploit_w:0.3f}\n")
# ------- EXPLOITATION: BayesOptDesign & ActiveLearning -------
if explore_w != 1.0:
# Create a sample pool for rejection sampling
MCsize = 15000
- X_MC = PCEModel.ExpDesign.generate_samples(MCsize, 'random')
-
- # Multiprocessing
- pool = multiprocessing.Pool(multiprocessing.cpu_count())
+ X_MC = MetaModel.ExpDesign.generate_samples(MCsize, 'random')
+ candidates = MetaModel.ExpDesign.generate_samples(
+ MetaModel.ExpDesign.max_func_itr, 'latin_hypercube')
# Split the candidates in groups for multiprocessing
- split_cand = np.array_split(allCandidates,
- n_cand_groups, axis=0)
- args = []
- for i in range(n_cand_groups):
- args.append((exploit_method, split_cand[i], i, sigma2, var,
- X_MC))
-
- # With Pool.starmap_async()
- results = pool.starmap_async(self.run_util_func, args).get()
-
- # Close the pool
- pool.close()
+ split_cand = np.array_split(
+ candidates, n_cand_groups, axis=0
+ )
+
+ results = Parallel(n_jobs=-1, backend='threading')(
+ delayed(self.run_util_func)(
+ exploit_method, split_cand[i], i, sigma2, var, X_MC)
+ for i in range(n_cand_groups))
+ # out = map(self.run_util_func,
+ # [exploit_method]*n_cand_groups,
+ # split_cand,
+ # range(n_cand_groups),
+ # [sigma2] * n_cand_groups,
+ # [var] * n_cand_groups,
+ # [X_MC] * n_cand_groups
+ # )
+ # results = list(out)
# Retrieve the results and append them
U_J_d = np.concatenate([results[NofE][1] for NofE in
range(n_cand_groups)])
+ # Check if all scores are inf
+ if np.isinf(U_J_d).all() or np.isnan(U_J_d).all():
+ U_J_d = np.ones(len(U_J_d))
+
# Get the expected value (mean) of the Utility score
# for each cell
if explore_method == 'Voronoi':
U_J_d = np.mean(U_J_d.reshape(-1, n_candidates), axis=1)
+ # create surrogate model for U_J_d
+ from sklearn.preprocessing import MinMaxScaler
+ # Take care of inf entries
+ good_indices = [i for i, arr in enumerate(U_J_d)
+ if np.isfinite(arr).all()]
+ scaler = MinMaxScaler()
+ X_S = scaler.fit_transform(candidates[good_indices])
+ gp = MetaModel.gaussian_process_emulator(
+ X_S, U_J_d[good_indices], autoSelect=True
+ )
+ U_J_d = gp.predict(scaler.transform(allCandidates))
+
# Normalize U_J_d
norm_U_J_d = U_J_d / np.sum(U_J_d)
print("norm_U_J_d:\n", norm_U_J_d)
@@ -1315,7 +1457,7 @@ class SeqDesign():
# Find sensitive region
if UtilMethod == 'LOOCV':
- LCerror = PCEModel.LCerror
+ LCerror = MetaModel.LCerror
allModifiedLOO = np.zeros((len(old_EDX), len(OutputNames),
nMeasurement))
for y_idx, y_key in enumerate(OutputNames):
@@ -1325,8 +1467,8 @@ class SeqDesign():
ExploitScore = np.max(np.max(allModifiedLOO, axis=1), axis=1)
- elif UtilMethod in ['EIGF', 'Entropy']:
- # ----- All other in ['EIGF', 'Entropy', 'ALM'] -----
+ elif UtilMethod in ['EIGF', 'ALM']:
+ # ----- All other in ['EIGF', 'ALM'] -----
# Initilize the ExploitScore array
ExploitScore = np.zeros((len(old_EDX), len(OutputNames)))
@@ -1357,6 +1499,14 @@ class SeqDesign():
# Close the pool
pool.close()
+ # out = map(self.run_util_func,
+ # [exploit_method]*len(goodSampleIdx),
+ # split_cand,
+ # range(len(goodSampleIdx)),
+ # [sigma2] * len(goodSampleIdx),
+ # [var] * len(goodSampleIdx)
+ # )
+ # results = list(out)
# Retrieve the results and append them
if explore_method == 'Voronoi':
@@ -1423,6 +1573,7 @@ class SeqDesign():
print("\n")
print("\nRun No. {}:".format(old_EDX.shape[0]+1))
print("Xnew:\n", Xnew)
+ gc.collect()
return Xnew, None
@@ -1449,35 +1600,35 @@ class SeqDesign():
X_new : array of shape (1, n_params)
The new sampling location in the input space.
"""
- PCEModelOrig = self.PCEModel
- Model = self.ModelObj
- n_new_samples = PCEModelOrig.ExpDesign.n_new_samples
+ MetaModelOrig = self
+ Model = self.Model
+ n_new_samples = MetaModelOrig.ExpDesign.n_new_samples
NCandidate = candidates.shape[0]
# TODO: Loop over outputs
OutputName = Model.Output.names[0]
# To avoid changes ub original aPCE object
- PCEModel = deepcopy(PCEModelOrig)
+ MetaModel = deepcopy(MetaModelOrig)
# Old Experimental design
- oldExpDesignX = PCEModel.ExpDesign.X
+ oldExpDesignX = MetaModel.ExpDesign.X
# TODO: Only one psi can be selected.
# Suggestion: Go for the one with the highest LOO error
- Scores = list(PCEModel.score_dict[OutputName].values())
+ Scores = list(MetaModel.score_dict[OutputName].values())
ModifiedLOO = [1-score for score in Scores]
outIdx = np.argmax(ModifiedLOO)
# Initialize Phi to save the criterion's values
Phi = np.zeros((NCandidate))
- BasisIndices = PCEModelOrig.basis_dict[OutputName]["y_"+str(outIdx+1)]
+ BasisIndices = MetaModelOrig.basis_dict[OutputName]["y_"+str(outIdx+1)]
P = len(BasisIndices)
# ------ Old Psi ------------
- univ_p_val = PCEModelOrig.univ_basis_vals(oldExpDesignX)
- Psi = PCEModelOrig.create_psi(BasisIndices, univ_p_val)
+ univ_p_val = MetaModelOrig.univ_basis_vals(oldExpDesignX)
+ Psi = MetaModelOrig.create_psi(BasisIndices, univ_p_val)
# ------ New candidates (Psi_c) ------------
# Assemble Psi_c
@@ -1530,119 +1681,178 @@ class SeqDesign():
return Xnew
# -------------------------------------------------------------------------
- def __normpdf(self, PCEOutputs, std_PC_MC, obs_data, Sigma2s):
+ def __normpdf(self, y_hat_pce, std_pce, obs_data, total_sigma2s,
+ rmse=None):
+
+ Model = self.Model
+ likelihoods = 1.0
+
+ # Loop over the outputs
+ for idx, out in enumerate(Model.Output.names):
+
+ # (Meta)Model Output
+ nsamples, nout = y_hat_pce[out].shape
+
+ # Prepare data and remove NaN
+ try:
+ data = obs_data[out].values[~np.isnan(obs_data[out])]
+ except AttributeError:
+ data = obs_data[out][~np.isnan(obs_data[out])]
- output_names = self.Model.Output.names
+ # Prepare sigma2s
+ non_nan_indices = ~np.isnan(total_sigma2s[out])
+ tot_sigma2s = total_sigma2s[out][non_nan_indices][:nout].values
- SampleSize, index = PCEOutputs[output_names[0]].shape
+ # Surrogate error if valid dataset is given.
+ if rmse is not None:
+ tot_sigma2s += rmse[out]**2
- # Flatten the ObservationData
- TotalData = obs_data[output_names].to_numpy().flatten('F')
+ likelihoods *= stats.multivariate_normal.pdf(
+ y_hat_pce[out], data, np.diag(tot_sigma2s),
+ allow_singular=True)
+ self.Likelihoods = likelihoods
- # Remove NaN
- TotalData = TotalData[~np.isnan(TotalData)]
- Sigma2s = Sigma2s[~np.isnan(Sigma2s)]
+ return likelihoods
- # Flatten the Output
- TotalOutputs = np.empty((SampleSize, 0))
- for idx, key in enumerate(output_names):
- TotalOutputs = np.hstack((TotalOutputs, PCEOutputs[key]))
+ # -------------------------------------------------------------------------
+ def __corr_factor_BME(self, obs_data, total_sigma2s, logBME):
+ """
+ Calculates the correction factor for BMEs.
+ """
+ MetaModel = self.MetaModel
+ samples = MetaModel.ExpDesign.X # valid_samples
+ model_outputs = MetaModel.ExpDesign.Y # valid_model_runs
+ Model = MetaModel.ModelObj
+ n_samples = samples.shape[0]
- # Covariance Matrix
- covMatrix = np.zeros((Sigma2s.shape[0], Sigma2s.shape[0]), float)
- np.fill_diagonal(covMatrix, Sigma2s)
+ # Extract the requested model outputs for likelihood calulation
+ output_names = Model.Output.names
- # Add the std of the PCE.
- covMatrix_PCE = np.zeros((Sigma2s.shape[0], Sigma2s.shape[0]), float)
- stdPCE = np.empty((SampleSize, 0))
- for idx, key in enumerate(output_names):
- stdPCE = np.hstack((stdPCE, std_PC_MC[key]))
+ # TODO: Evaluate MetaModel on the experimental design and ValidSet
+ OutputRS, stdOutputRS = MetaModel.eval_metamodel(samples=samples)
- # Expected value of variance (Assump: i.i.d stds)
- varPCE = np.mean(stdPCE**2, axis=0)
- # # varPCE = np.var(stdPCE, axis=1)
- np.fill_diagonal(covMatrix_PCE, varPCE)
+ logLik_data = np.zeros((n_samples))
+ logLik_model = np.zeros((n_samples))
+ # Loop over the outputs
+ for idx, out in enumerate(output_names):
- # Aggregate the cov matrices
- covMatrix += covMatrix_PCE
+ # (Meta)Model Output
+ nsamples, nout = model_outputs[out].shape
- # Compute likelihood
- self.Likelihoods = stats.multivariate_normal.pdf(TotalOutputs,
- mean=TotalData,
- cov=covMatrix,
- allow_singular=True)
- return self.Likelihoods
+ # Prepare data and remove NaN
+ try:
+ data = obs_data[out].values[~np.isnan(obs_data[out])]
+ except AttributeError:
+ data = obs_data[out][~np.isnan(obs_data[out])]
+
+ # Prepare sigma2s
+ non_nan_indices = ~np.isnan(total_sigma2s[out])
+ tot_sigma2s = total_sigma2s[out][non_nan_indices][:nout]
+
+ # Covariance Matrix
+ covMatrix_data = np.diag(tot_sigma2s)
+
+ for i, sample in enumerate(samples):
+
+ # Simulation run
+ y_m = model_outputs[out][i]
+
+ # Surrogate prediction
+ y_m_hat = OutputRS[out][i]
+
+ # CovMatrix with the surrogate error
+ # covMatrix = np.diag(stdOutputRS[out][i]**2)
+ covMatrix = np.diag((y_m-y_m_hat)**2)
+ covMatrix = np.diag(
+ np.mean((model_outputs[out]-OutputRS[out]), axis=0)**2
+ )
+
+ # Compute likelilhood output vs data
+ logLik_data[i] += self.__logpdf(
+ y_m_hat, data, covMatrix_data
+ )
+
+ # Compute likelilhood output vs surrogate
+ logLik_model[i] += self.__logpdf(y_m_hat, y_m, covMatrix)
+
+ # Weight
+ logLik_data -= logBME
+ weights = np.exp(logLik_model+logLik_data)
+
+ return np.log(np.mean(weights))
# -------------------------------------------------------------------------
- def __posteriorPlot(self, Posterior, MAP, parNames, key, figsize=(10, 10)):
+ def __logpdf(self, x, mean, cov):
+ """
+ computes the likelihood based on a multivariate normal distribution.
- # Initialization
- newpath = (r'Outputs_SeqPosteriorComparison')
- if not os.path.exists(newpath):
- os.makedirs(newpath)
+ Parameters
+ ----------
+ x : TYPE
+ DESCRIPTION.
+ mean : array_like
+ Observation data.
+ cov : 2d array
+ Covariance matrix of the distribution.
+
+ Returns
+ -------
+ log_lik : float
+ Log likelihood.
+
+ """
+ n = len(mean)
+ L = linalg.cholesky(cov, lower=True)
+ beta = np.sum(np.log(np.diag(L)))
+ dev = x - mean
+ alpha = dev.dot(linalg.cho_solve((L, True), dev))
+ log_lik = -0.5 * alpha - beta - n / 2. * np.log(2 * np.pi)
- lw = 3.
- bound_tuples = self.bound_tuples
- n_params = len(MAP)
+ return log_lik
- # This is the true mean of the second mode that we used above:
- value1 = MAP
+ # -------------------------------------------------------------------------
+ def __posteriorPlot(self, posterior, par_names, key):
- # This is the empirical mean of the sample:
- value2 = np.mean(Posterior, axis=0)
+ # Initialization
+ newpath = (r'Outputs_SeqPosteriorComparison/posterior')
+ os.makedirs(newpath, exist_ok=True)
+ bound_tuples = self.MetaModel.bound_tuples
+ n_params = len(par_names)
+ font_size = 40
if n_params == 2:
- figPosterior, ax = plt.subplots()
- plt.hist2d(Posterior[:, 0], Posterior[:, 1], bins=(200, 200),
- range=np.array([bound_tuples[0], bound_tuples[1]]),
- cmap=plt.cm.jet)
+ figPosterior, ax = plt.subplots(figsize=(15, 15))
- plt.xlabel(parNames[0])
- plt.ylabel(parNames[1])
+ sns.kdeplot(x=posterior[:, 0], y=posterior[:, 1],
+ fill=True, ax=ax, cmap=plt.cm.jet,
+ clip=bound_tuples)
+ # Axis labels
+ plt.xlabel(par_names[0], fontsize=font_size)
+ plt.ylabel(par_names[1], fontsize=font_size)
+ # Set axis limit
plt.xlim(bound_tuples[0])
plt.ylim(bound_tuples[1])
- ax.axvline(value1[0], color="g", lw=lw)
- ax.axhline(value1[1], color="g", lw=lw)
- ax.plot(value1[0], value1[1], "sg", lw=lw+1)
+ # Increase font size
+ plt.xticks(fontsize=font_size)
+ plt.yticks(fontsize=font_size)
- ax.axvline(value2[0], ls='--', color="r", lw=lw)
- ax.axhline(value2[1], ls='--', color="r", lw=lw)
- ax.plot(value2[0], value2[1], "sr", lw=lw+1)
+ # Switch off the grids
+ plt.grid(False)
else:
import corner
- figPosterior = corner.corner(Posterior, labels=parNames,
+ figPosterior = corner.corner(posterior, labels=par_names,
title_fmt='.2e', show_titles=True,
title_kwargs={"fontsize": 12})
- # Extract the axes
- axes = np.array(figPosterior.axes).reshape((n_params, n_params))
-
- # Loop over the diagonal
- for i in range(n_params):
- ax = axes[i, i]
- ax.axvline(value1[i], color="g")
- ax.axvline(value2[i], ls='--', color="r")
-
- # Loop over the histograms
- for yi in range(n_params):
- for xi in range(yi):
- ax = axes[yi, xi]
- ax.axvline(value1[xi], color="g")
- ax.axvline(value2[xi], ls='--', color="r")
- ax.axhline(value1[yi], color="g")
- ax.axhline(value2[yi], ls='--', color="r")
- ax.plot(value1[xi], value1[yi], "sg")
- ax.plot(value2[xi], value2[yi], "sr")
-
- figPosterior.savefig(f'./{newpath}/{key}.svg', bbox_inches='tight')
+ figPosterior.savefig(f'./{newpath}/{key}.pdf', bbox_inches='tight')
plt.close()
# Save the posterior as .npy
- np.save(f'./{newpath}/{key}.npy', Posterior)
+ np.save(f'./{newpath}/{key}.npy', posterior)
return figPosterior
@@ -1683,50 +1893,51 @@ class SeqDesign():
return np.sqrt(H_squared)
# -------------------------------------------------------------------------
- def __BME_Calculator(self, PCEModel, obs_data, sigma2Dict):
+ def __BME_Calculator(self, MetaModel, obs_data, sigma2Dict, rmse=None):
"""
This function computes the Bayesian model evidence (BME) via Monte
Carlo integration.
"""
# Initializations
- valid_likelihoods = PCEModel.valid_likelihoods
+ valid_likelihoods = MetaModel.valid_likelihoods
- post_snapshot = PCEModel.ExpDesign.post_snapshot
+ post_snapshot = MetaModel.ExpDesign.post_snapshot
if post_snapshot or len(valid_likelihoods) != 0:
- newpath = (r'Outputs_SeqPosteriorComparison')
- if not os.path.exists(newpath):
- os.makedirs(newpath)
+ newpath = (r'Outputs_SeqPosteriorComparison/likelihood_vs_ref')
+ os.makedirs(newpath, exist_ok=True)
SamplingMethod = 'random'
- MCsize = 100000
+ MCsize = 10000
ESS = 0
# Estimation of the integral via Monte Varlo integration
- while ((ESS > MCsize) or (ESS < 1)):
+ while (ESS > MCsize) or (ESS < 1):
# Generate samples for Monte Carlo simulation
- if len(valid_likelihoods) == 0:
- X_MC = PCEModel.ExpDesign.generate_samples(MCsize,
- SamplingMethod)
- else:
- X_MC = PCEModel.valid_samples
- MCsize = X_MC.shape[0]
+ X_MC = MetaModel.ExpDesign.generate_samples(
+ MCsize, SamplingMethod
+ )
# Monte Carlo simulation for the candidate design
- Y_MC, std_MC = PCEModel.eval_metamodel(samples=X_MC)
+ m_1 = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss/1024
+ Y_MC, std_MC = MetaModel.eval_metamodel(samples=X_MC)
+ m_2 = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss/1024
+ print(f"\nMemory eval_metamodel in BME: {m_2-m_1:.2f} MB")
# Likelihood computation (Comparison of data and
# simulation results via PCE with candidate design)
- Likelihoods = self.__normpdf(Y_MC, std_MC, obs_data, sigma2Dict)
+ Likelihoods = self.__normpdf(
+ Y_MC, std_MC, obs_data, sigma2Dict, rmse
+ )
# Check the Effective Sample Size (1000<ESS<MCsize)
ESS = 1 / np.sum(np.square(Likelihoods/np.sum(Likelihoods)))
# Enlarge sample size if it doesn't fulfill the criteria
- if ((ESS > MCsize) or (ESS < 1)):
- print('ESS={0} MC size should be larger.'.format(ESS))
- MCsize = MCsize * 10
+ if (ESS > MCsize) or (ESS < 1):
+ print(f'ESS={ESS} MC size should be larger.')
+ MCsize *= 10
ESS = 0
# Rejection Step
@@ -1743,33 +1954,42 @@ class SeqDesign():
# Prior-based estimation of BME
logBME = np.log(np.nanmean(Likelihoods))
+ # TODO: Correction factor
+ # log_weight = self.__corr_factor_BME(obs_data, sigma2Dict, logBME)
+
# Posterior-based expectation of likelihoods
postExpLikelihoods = np.mean(np.log(Likelihoods[accepted]))
# Posterior-based expectation of prior densities
- # postExpPrior = np.mean([log_prior(sample) for sample in X_Posterior])
+ postExpPrior = np.mean(
+ np.log(MetaModel.ExpDesign.JDist.pdf(X_Posterior.T))
+ )
# Calculate Kullback-Leibler Divergence
# KLD = np.mean(np.log(Likelihoods[Likelihoods!=0])- logBME)
KLD = postExpLikelihoods - logBME
# Information Entropy based on Entropy paper Eq. 38
- # infEntropy = logBME - postExpPrior - postExpLikelihoods
+ infEntropy = logBME - postExpPrior - postExpLikelihoods
# If post_snapshot is True, plot likelihood vs refrence
if post_snapshot or len(valid_likelihoods) != 0:
- idx = len([name for name in os.listdir(newpath) if 'Likelihoods_'
- in name and os.path.isfile(os.path.join(newpath, name))])
- fig, ax = plt.subplots()
- sns.kdeplot(np.log(valid_likelihoods[valid_likelihoods > 0]),
- shade=True, color="g", label='Ref. Likelihood')
- sns.kdeplot(np.log(Likelihoods[Likelihoods > 0]), shade=True,
- color="b", label='Likelihood with PCE')
-
# Hellinger distance
ref_like = np.log(valid_likelihoods[valid_likelihoods > 0])
est_like = np.log(Likelihoods[Likelihoods > 0])
distHellinger = self.__hellinger_distance(ref_like, est_like)
+
+ idx = len([name for name in os.listdir(newpath) if 'Likelihoods_'
+ in name and os.path.isfile(os.path.join(newpath, name))])
+ fig, ax = plt.subplots()
+ try:
+ sns.kdeplot(np.log(valid_likelihoods[valid_likelihoods > 0]),
+ shade=True, color="g", label='Ref. Likelihood')
+ sns.kdeplot(np.log(Likelihoods[Likelihoods > 0]), shade=True,
+ color="b", label='Likelihood with PCE')
+ except:
+ pass
+
text = f"Hellinger Dist.={distHellinger:.3f}\n logBME={logBME:.3f}"
"\n DKL={KLD:.3f}"
@@ -1778,82 +1998,190 @@ class SeqDesign():
boxstyle='round,pad=1'),
transform=ax.transAxes)
- fig.savefig(f'./{newpath}/Likelihoods_{idx}.svg',
+ fig.savefig(f'./{newpath}/Likelihoods_{idx}.pdf',
bbox_inches='tight')
plt.close()
else:
distHellinger = 0.0
- return (logBME, KLD, X_Posterior, distHellinger)
+ # Bayesian inference with Emulator only for 2D problem
+ if post_snapshot and MetaModel.n_params == 2 and not idx % 5:
+ from bayes_inference.bayes_inference import BayesInference
+ from bayes_inference.discrepancy import Discrepancy
+ import pandas as pd
+ BayesOpts = BayesInference(MetaModel)
+ BayesOpts.emulator = True
+ BayesOpts.plot_post_pred = False
+
+ # Select the inference method
+ import emcee
+ BayesOpts.inference_method = "MCMC"
+ # Set the MCMC parameters passed to self.mcmc_params
+ BayesOpts.mcmc_params = {
+ 'n_steps': 1e5,
+ 'n_walkers': 30,
+ 'moves': emcee.moves.KDEMove(),
+ 'verbose': False
+ }
+
+ # ----- Define the discrepancy model -------
+ obs_data = pd.DataFrame(obs_data, columns=self.Model.Output.names)
+ BayesOpts.measurement_error = obs_data
+
+ # # -- (Option B) --
+ DiscrepancyOpts = Discrepancy('')
+ DiscrepancyOpts.type = 'Gaussian'
+ DiscrepancyOpts.parameters = obs_data**2
+ BayesOpts.Discrepancy = DiscrepancyOpts
+ # Start the calibration/inference
+ Bayes_PCE = BayesOpts.create_inference()
+ X_Posterior = Bayes_PCE.posterior_df.values
+
+ # Clean up
+ del Y_MC, std_MC
+ gc.collect()
+
+ return (logBME, KLD, X_Posterior, Likelihoods, distHellinger)
# -------------------------------------------------------------------------
- def __validError(self):
+ def __validError(self, MetaModel):
- PCEModel = self.MetaModel
- Model = self.Model
+ # MetaModel = self.MetaModel
+ Model = MetaModel.ModelObj
OutputName = Model.Output.names
- # Generate random samples
- Samples = PCEModel.valid_samples
-
# Extract the original model with the generated samples
- ModelOutputs = PCEModel.valid_model_runs
+ valid_samples = MetaModel.valid_samples
+ valid_model_runs = MetaModel.valid_model_runs
# Run the PCE model with the generated samples
- PCEOutputs, PCEOutputs_std = PCEModel.eval_metamodel(samples=Samples)
+ m_1 = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss/1024
+ valid_PCE_runs, valid_PCE_std = MetaModel.eval_metamodel(samples=valid_samples)
+ m_2 = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss/1024
+ print(f"\nMemory eval_metamodel: {m_2-m_1:.2f} MB")
- validError_dict = {}
+ rms_error = {}
+ valid_error = {}
# Loop over the keys and compute RMSE error.
for key in OutputName:
- weight = np.mean(np.square(PCEOutputs_std[key]), axis=0)
- if all(weight == 0):
- weight = 'variance_weighted'
- validError_dict[key] = mean_squared_error(ModelOutputs[key],
- PCEOutputs[key])
- validError_dict[key] /= np.var(ModelOutputs[key], ddof=1)
-
- return validError_dict
+ rms_error[key] = mean_squared_error(
+ valid_model_runs[key], valid_PCE_runs[key],
+ multioutput='raw_values',
+ sample_weight=None,
+ squared=False)
+
+ # Validation error
+ valid_error[key] = (rms_error[key]**2)
+ valid_error[key] /= np.var(valid_model_runs[key], ddof=1, axis=0)
+
+ # Print a report table
+ print("\n>>>>> Updated Errors of {} <<<<<".format(key))
+ print("\nIndex | RMSE | Validation Error")
+ print('-'*35)
+ print('\n'.join(f'{i+1} | {k:.3e} | {j:.3e}' for i, (k, j)
+ in enumerate(zip(rms_error[key],
+ valid_error[key]))))
+
+ return rms_error, valid_error
# -------------------------------------------------------------------------
def __error_Mean_Std(self):
- PCEModel = self.MetaModel
+ MetaModel = self.MetaModel
# Extract the mean and std provided by user
- df_MCReference = PCEModel.ModelObj.MCReference
-
- # Compute the mean and std based on the PCEModel
- PCEMeans = dict()
- PCEStds = dict()
- for Outkey, ValuesDict in PCEModel.coeffs_dict.items():
- PCEMean = np.zeros((len(ValuesDict)))
- PCEStd = np.zeros((len(ValuesDict)))
-
- for Inkey, InIdxValues in ValuesDict.items():
- idx = int(Inkey.split('_')[1]) - 1
- coeffs = PCEModel.coeffs_dict[Outkey][Inkey]
-
- # Mean = c_0
- if coeffs[0] != 0:
- PCEMean[idx] = coeffs[0]
- else:
- PCEMean[idx] = PCEModel.clf_poly[Outkey][Inkey].intercept_
+ df_MCReference = MetaModel.ModelObj.mc_reference
- # Std = sqrt(sum(coeffs[1:]**2))
- PCEStd[idx] = np.sqrt(np.sum(np.square(coeffs[1:])))
+ # Compute the mean and std based on the MetaModel
+ pce_means, pce_stds = self._compute_pce_moments(MetaModel)
- if PCEModel.dim_red_method.lower() == 'pca':
- PCA = PCEModel.pca[Outkey]
- PCEMean = PCA.mean_ + np.dot(PCEMean, PCA.components_)
- PCEStd = np.dot(PCEStd, PCA.components_)
+ # Compute the root mean squared error
+ for output in MetaModel.ModelObj.Output.names:
- # Compute the error between mean and std of PCEModel and OrigModel
- RMSE_Mean = mean_squared_error(df_MCReference['mean'], PCEMean,
- squared=False)
- RMSE_std = mean_squared_error(df_MCReference['std'], PCEStd,
- squared=False)
-
- PCEMeans[Outkey] = PCEMean
- PCEStds[Outkey] = PCEStd
+ # Compute the error between mean and std of MetaModel and OrigModel
+ RMSE_Mean = mean_squared_error(
+ df_MCReference['mean'], pce_means[output], squared=False
+ )
+ RMSE_std = mean_squared_error(
+ df_MCReference['std'], pce_means[output], squared=False
+ )
return RMSE_Mean, RMSE_std
+
+ # -------------------------------------------------------------------------
+ def _compute_pce_moments(self, MetaModel):
+ """
+ Computes the first two moments using the PCE-based meta-model.
+
+ Returns
+ -------
+ pce_means: dict
+ The first moment (mean) of the surrogate.
+ pce_stds: dict
+ The second moment (standard deviation) of the surrogate.
+
+ """
+ outputs = MetaModel.ModelObj.Output.names
+ pce_means_b = {}
+ pce_stds_b = {}
+
+ # Loop over bootstrap iterations
+ for b_i in range(MetaModel.n_bootstrap_itrs):
+ # Loop over the metamodels
+ coeffs_dicts = MetaModel.coeffs_dict[f'b_{b_i+1}'].items()
+ means = {}
+ stds = {}
+ for output, coef_dict in coeffs_dicts:
+
+ pce_mean = np.zeros((len(coef_dict)))
+ pce_var = np.zeros((len(coef_dict)))
+
+ for index, values in coef_dict.items():
+ idx = int(index.split('_')[1]) - 1
+ coeffs = MetaModel.coeffs_dict[f'b_{b_i+1}'][output][index]
+
+ # Mean = c_0
+ if coeffs[0] != 0:
+ pce_mean[idx] = coeffs[0]
+ else:
+ clf_poly = MetaModel.clf_poly[f'b_{b_i+1}'][output]
+ pce_mean[idx] = clf_poly[index].intercept_
+ # Var = sum(coeffs[1:]**2)
+ pce_var[idx] = np.sum(np.square(coeffs[1:]))
+
+ # Save predictions for each output
+ if MetaModel.dim_red_method.lower() == 'pca':
+ PCA = MetaModel.pca[f'b_{b_i+1}'][output]
+ means[output] = PCA.mean_ + np.dot(
+ pce_mean, PCA.components_)
+ stds[output] = np.sqrt(np.dot(pce_var,
+ PCA.components_**2))
+ else:
+ means[output] = pce_mean
+ stds[output] = np.sqrt(pce_var)
+
+ # Save predictions for each bootstrap iteration
+ pce_means_b[b_i] = means
+ pce_stds_b[b_i] = stds
+
+ # Change the order of nesting
+ mean_all = {}
+ for i in sorted(pce_means_b):
+ for k, v in pce_means_b[i].items():
+ if k not in mean_all:
+ mean_all[k] = [None] * len(pce_means_b)
+ mean_all[k][i] = v
+ std_all = {}
+ for i in sorted(pce_stds_b):
+ for k, v in pce_stds_b[i].items():
+ if k not in std_all:
+ std_all[k] = [None] * len(pce_stds_b)
+ std_all[k][i] = v
+
+ # Back transformation if PCA is selected.
+ pce_means, pce_stds = {}, {}
+ for output in outputs:
+ pce_means[output] = np.mean(mean_all[output], axis=0)
+ pce_stds[output] = np.mean(std_all[output], axis=0)
+
+ return pce_means, pce_stds
diff --git a/src/bayesvalidrox/surrogate_models/surrogate_models.py b/src/bayesvalidrox/surrogate_models/surrogate_models.py
index c751d9b5761ae41dcf008659ff8d112a65ff1632..c51ea8c6679aaeec685da069154e8f460c7c4450 100644
--- a/src/bayesvalidrox/surrogate_models/surrogate_models.py
+++ b/src/bayesvalidrox/surrogate_models/surrogate_models.py
@@ -14,14 +14,15 @@ import sklearn.linear_model as lm
from sklearn.gaussian_process import GaussianProcessRegressor
import sklearn.gaussian_process.kernels as kernels
import os
-import sys
from joblib import Parallel, delayed
+import copy
from .exp_designs import ExpDesigns
from .glexindex import glexindex
from .eval_rec_rule import eval_univ_basis
from .reg_fast_ard import RegressionFastARD
from .reg_fast_laplace import RegressionFastLaplace
+from .orthogonal_matching_pursuit import OrthogonalMatchingPursuit
from .bayes_linear import VBLinearRegression, EBLinearRegression
warnings.filterwarnings("ignore")
# Load the mplstyle
@@ -29,7 +30,7 @@ plt.style.use(os.path.join(os.path.split(__file__)[0],
'../', 'bayesvalidrox.mplstyle'))
-class MetaModel:
+class MetaModel():
"""
Meta (surrogate) model
@@ -57,6 +58,12 @@ class MetaModel:
6. VBL: Variational Bayesian Learning
7. EBL: Emperical Bayesian Learning
Default is `OLS`.
+ bootstrap_method : str
+ Bootstraping method. Options are `'normal'` and `'fast'`. The default
+ is `'fast'`. It means that in each iteration except the first one, only
+ the coefficent are recalculated with the ordinary least square method.
+ n_bootstrap_itrs : int
+ Number of iterations for the bootstrap sampling. The default is `1`.
pce_deg : int or list of int
Polynomial degree(s). If a list is given, an adaptive algorithm is used
to find the best degree with the lowest Leave-One-Out cross-validation
@@ -91,36 +98,35 @@ class MetaModel:
"""
- def __init__(self, input_obj, meta_model_type='PCE', pce_reg_method='OLS',
- pce_deg=1, pce_q_norm=1.0, dim_red_method='no',
- verbose=False):
+ def __init__(self, input_obj, model_obj, meta_model_type='PCE',
+ pce_reg_method='OLS', bootstrap_method='fast',
+ n_bootstrap_itrs=1, pce_deg=1, pce_q_norm=1.0,
+ dim_red_method='no', verbose=False):
self.input_obj = input_obj
+ self.ModelObj = model_obj
self.meta_model_type = meta_model_type
self.pce_reg_method = pce_reg_method
+ self.bootstrap_method = bootstrap_method
+ self.n_bootstrap_itrs = n_bootstrap_itrs
self.pce_deg = pce_deg
self.pce_q_norm = pce_q_norm
self.dim_red_method = dim_red_method
self.verbose = False
# -------------------------------------------------------------------------
- def create_metamodel(self, Model):
+ def create_metamodel(self):
"""
Starts the training of the meta-model for the model objects containg
the given computational model.
- Parameters
- ----------
- Model : obj
- Model object.
-
Returns
-------
metamodel : obj
The meta model object.
"""
- self.ModelObj = Model
+ Model = self.ModelObj
self.n_params = len(self.input_obj.Marginals)
self.ExpDesignFlag = 'normal'
# --- Prepare pce degree ---
@@ -129,34 +135,35 @@ class MetaModel:
self.pce_deg = np.array(self.pce_deg)
if self.ExpDesign.method == 'sequential':
- from .sequential_design import SeqDesign
- seq_design = SeqDesign(self)
- metamodel = seq_design.train_seq_design(Model)
+ raise Exception(
+ "Please use MetaModelEngine class for the sequential design!"
+ )
elif self.ExpDesign.method == 'normal':
self.ExpDesignFlag = 'normal'
- metamodel = self.train_norm_design(Model)
+ self.train_norm_design(Model, verbose=True)
else:
raise Exception("The method for experimental design you requested"
" has not been implemented yet.")
# Zip the model run directories
- if self.ModelObj.link_type.lower() == 'pylink':
+ if self.ModelObj.link_type.lower() == 'pylink' and\
+ self.ExpDesign.sampling_method.lower() != 'user':
Model.zip_subdirs(Model.name, f'{Model.name}_')
- return metamodel
+ return self
# -------------------------------------------------------------------------
- def train_norm_design(self, Model, verbose=False):
+ def train_norm_design(self, parallel=True, verbose=False):
"""
This function loops over the outputs and each time step/point and fits
the meta model.
Parameters
----------
- Model : obj
- Model object.
+ parallel : bool
+ The parallel computation of coefficents. The default is True.
verbose : bool, optional
Flag for a sequential design in silent mode. The default is False.
@@ -166,29 +173,33 @@ class MetaModel:
Meta-model object.
"""
-
+ Model = self.ModelObj
# Get the collocation points to run the forward model
CollocationPoints, OutputDict = self.generate_ExpDesign(Model)
# Initialize the nested dictionaries
- self.deg_dict = self.auto_vivification()
- self.q_norm_dict = self.auto_vivification()
- self.coeffs_dict = self.auto_vivification()
- self.basis_dict = self.auto_vivification()
- self.score_dict = self.auto_vivification()
- self.clf_poly = self.auto_vivification()
- self.gp_poly = self.auto_vivification()
- self.pca = self.auto_vivification()
- self.LCerror = self.auto_vivification()
- self.x_scaler = {}
-
- # Define the DegreeArray
- nSamples, ndim = CollocationPoints.shape
- self.DegreeArray = self.__select_degree(ndim, nSamples)
+ if self.meta_model_type.lower() == 'gpe':
+ self.gp_poly = self.auto_vivification()
+ self.x_scaler = self.auto_vivification()
+ self.LCerror = self.auto_vivification()
+ else:
+ self.deg_dict = self.auto_vivification()
+ self.q_norm_dict = self.auto_vivification()
+ self.coeffs_dict = self.auto_vivification()
+ self.basis_dict = self.auto_vivification()
+ self.score_dict = self.auto_vivification()
+ self.clf_poly = self.auto_vivification()
+ self.LCerror = self.auto_vivification()
+ if self.dim_red_method.lower() == 'pca':
+ self.pca = self.auto_vivification()
+
+ # Define an array containing the degrees
+ n_samples, ndim = CollocationPoints.shape
+ self.deg_array = self.__select_degree(ndim, n_samples)
# Generate all basis indices
self.allBasisIndices = self.auto_vivification()
- for deg in self.DegreeArray:
+ for deg in self.deg_array:
keys = self.allBasisIndices.keys()
if deg not in np.fromiter(keys, dtype=float):
# Generate the polynomial basis indices
@@ -199,65 +210,183 @@ class MetaModel:
# Evaluate the univariate polynomials on ExpDesign
if self.meta_model_type.lower() != 'gpe':
- self.univ_p_val = self.univ_basis_vals(CollocationPoints)
+ univ_p_val = self.univ_basis_vals(CollocationPoints)
if 'x_values' in OutputDict:
self.ExpDesign.x_values = OutputDict['x_values']
del OutputDict['x_values']
# --- Loop through data points and fit the surrogate ---
- if not verbose:
+ if verbose:
print(f"\n>>>> Training the {self.meta_model_type} metamodel "
"started. <<<<<<\n")
- items = tqdm(OutputDict.items(), desc="Fitting regression")
- else:
- items = OutputDict.items()
- # For loop over the components/outputs
- for key, Output in items:
+ # --- Bootstrap sampling ---
+ # Correct number of bootstrap if PCA transformation is required.
+ if self.dim_red_method.lower() == 'pca' and self.n_bootstrap_itrs == 1:
+ self.n_bootstrap_itrs = 100
- # Dimensionality reduction with PCA, if specified
- if self.dim_red_method.lower() == 'pca':
- self.pca[key], target = self.pca_transformation(Output)
+ # Check if fast version (update coeffs with OLS) is selected.
+ if self.bootstrap_method.lower() == 'fast':
+ fast_bootstrap = True
+ first_out = {}
+ n_comp_dict = {}
+ else:
+ fast_bootstrap = False
+
+ # Prepare tqdm iteration maessage
+ if verbose and self.n_bootstrap_itrs > 1:
+ enum_obj = tqdm(range(self.n_bootstrap_itrs),
+ total=self.n_bootstrap_itrs,
+ desc="Boostraping the metamodel",
+ ascii=True)
+ else:
+ enum_obj = range(self.n_bootstrap_itrs)
+
+ # Loop over the bootstrap iterations
+ for b_i in enum_obj:
+ if b_i > 0:
+ b_indices = np.random.randint(n_samples, size=n_samples)
else:
- target = Output
+ b_indices = np.arange(len(CollocationPoints))
- # Parallel fit regression
- if self.meta_model_type.lower() == 'gpe':
- # Prepare the input matrix
- scaler = MinMaxScaler()
- X_S = scaler.fit_transform(CollocationPoints)
+ X_train_b = CollocationPoints[b_indices]
- self.x_scaler[key] = scaler
+ if verbose and self.n_bootstrap_itrs == 1:
+ items = tqdm(OutputDict.items(), desc="Fitting regression")
+ else:
+ items = OutputDict.items()
+
+ # For loop over the components/outputs
+ for key, Output in items:
+
+ # Dimensionality reduction with PCA, if specified
+ if self.dim_red_method.lower() == 'pca':
+
+ # Use the stored n_comp for fast bootsrtrapping
+ if fast_bootstrap and b_i > 0:
+ self.n_pca_components = n_comp_dict[key]
+
+ # Start transformation
+ pca, target, n_comp = self.pca_transformation(
+ Output[b_indices], verbose=False
+ )
+ self.pca[f'b_{b_i+1}'][key] = pca
+ # Store the number of components for fast bootsrtrapping
+ if fast_bootstrap and b_i == 0:
+ n_comp_dict[key] = n_comp
+ else:
+ target = Output[b_indices]
- out = Parallel(n_jobs=-1, prefer='threads')(
- delayed(self.gaussian_process_emulator)(X_S, target[:, idx])
- for idx in range(target.shape[1]))
+ # Parallel fit regression
+ if self.meta_model_type.lower() == 'gpe':
+ # Prepare the input matrix
+ scaler = MinMaxScaler()
+ X_S = scaler.fit_transform(X_train_b)
+
+ self.x_scaler[f'b_{b_i+1}'][key] = scaler
+ if parallel:
+ out = Parallel(n_jobs=-1, backend='multiprocessing')(
+ delayed(self.gaussian_process_emulator)(
+ X_S, target[:, idx]) for idx in
+ range(target.shape[1]))
+ else:
+ results = map(self.gaussian_process_emulator,
+ [X_train_b]*target.shape[1],
+ [target[:, idx] for idx in
+ range(target.shape[1])]
+ )
+ out = list(results)
+
+ for idx in range(target.shape[1]):
+ self.gp_poly[f'b_{b_i+1}'][key][f"y_{idx+1}"] = out[idx]
- for idx in range(target.shape[1]):
- self.gp_poly[key][f"y_{idx+1}"] = out[idx]
+ else:
+ self.univ_p_val = univ_p_val[b_indices]
+ if parallel and (not fast_bootstrap or b_i == 0):
+ out = Parallel(n_jobs=-1, backend='multiprocessing')(
+ delayed(self.adaptive_regression)(X_train_b,
+ target[:, idx],
+ idx)
+ for idx in range(target.shape[1]))
+ elif not parallel and (not fast_bootstrap or b_i == 0):
+ results = map(self.adaptive_regression,
+ [X_train_b]*target.shape[1],
+ [target[:, idx] for idx in
+ range(target.shape[1])],
+ range(target.shape[1]))
+ out = list(results)
+
+ # Store the first out dictionary
+ if fast_bootstrap and b_i == 0:
+ first_out[key] = copy.deepcopy(out)
+
+ if b_i > 0 and fast_bootstrap:
+
+ # fast bootstrap
+ out = self.update_pce_coeffs(
+ X_train_b, target, first_out[key])
+
+ for i in range(target.shape[1]):
+ # Create a dict to pass the variables
+ self.deg_dict[f'b_{b_i+1}'][key][f"y_{i+1}"] = out[i]['degree']
+ self.q_norm_dict[f'b_{b_i+1}'][key][f"y_{i+1}"] = out[i]['qnorm']
+ self.coeffs_dict[f'b_{b_i+1}'][key][f"y_{i+1}"] = out[i]['coeffs']
+ self.basis_dict[f'b_{b_i+1}'][key][f"y_{i+1}"] = out[i]['multi_indices']
+ self.score_dict[f'b_{b_i+1}'][key][f"y_{i+1}"] = out[i]['LOOCVScore']
+ self.clf_poly[f'b_{b_i+1}'][key][f"y_{i+1}"] = out[i]['clf_poly']
+ #self.LCerror[f'b_{b_i+1}'][key][f"y_{i+1}"] = out[i]['LCerror']
- else:
- out = Parallel(n_jobs=-1, prefer='threads')(
- delayed(self.adaptive_regression)(CollocationPoints,
- target[:, idx], idx)
- for idx in range(target.shape[1]))
-
- for i in range(target.shape[1]):
- # Create a dict to pass the variables
- self.deg_dict[key][f"y_{i+1}"] = out[i]['degree']
- self.q_norm_dict[key][f"y_{i+1}"] = out[i]['qnorm']
- self.coeffs_dict[key][f"y_{i+1}"] = out[i]['coeffs']
- self.basis_dict[key][f"y_{i+1}"] = out[i]['multi_indices']
- self.score_dict[key][f"y_{i+1}"] = out[i]['LOOCVScore']
- self.clf_poly[key][f"y_{i+1}"] = out[i]['clf_poly']
- self.LCerror[key][f"y_{i+1}"] = out[i]['LCerror']
-
- if not verbose:
+ if verbose:
print(f"\n>>>> Training the {self.meta_model_type} metamodel"
" sucessfully completed. <<<<<<\n")
- return self
+ # -------------------------------------------------------------------------
+ def update_pce_coeffs(self, X, y, out_dict):
+ """
+ Updates the PCE coefficents using only the ordinary least square method
+ for the fast version of the bootsrtrapping.
+
+ Parameters
+ ----------
+ X : array of shape (n_samples, n_params)
+ Training set.
+ y : array of shape (n_samples, n_outs)
+ The (transformed) model responses.
+ out_dict : dict
+ The training output dictionary of the first iteration, i.e.
+ the surrogate model for the original experimental design.
+
+ Returns
+ -------
+ final_out_dict : dict
+ The updated training output dictionary.
+
+ """
+ # Make a copy
+ final_out_dict = copy.deepcopy(out_dict)
+
+ # Loop over the points
+ for i in range(y.shape[1]):
+
+ # Extract nonzero basis indices
+ nnz_idx = np.nonzero(out_dict[i]['coeffs'])[0]
+ if len(nnz_idx) != 0:
+ basis_indices = out_dict[i]['multi_indices']
+
+ # Evaluate the multivariate polynomials on CollocationPoints
+ psi = self.create_psi(basis_indices, self.univ_p_val)
+
+ # Calulate the cofficients of surrogate model
+ updated_out = self.fit(
+ psi, y[:, i], basis_indices, reg_method='OLS',
+ sparsity=False
+ )
+
+ # Update coeffs in out_dict
+ final_out_dict[i]['coeffs'][nnz_idx] = updated_out['coeffs']
+
+ return final_out_dict
# -------------------------------------------------------------------------
def create_basis_indices(self, degree, q_norm):
@@ -466,8 +595,10 @@ class MetaModel:
# check that the variables have consistent sizes
if n_params != basis_indices.shape[1]:
- raise ValueError("The shapes of basis_indices and univ_p_val don't"
- " match!!")
+ raise ValueError(
+ f"The shapes of basis_indices ({basis_indices.shape[1]}) and "
+ f"univ_p_val ({n_params}) don't match!!"
+ )
# Preallocate the Psi matrix for performance
psi = np.ones((n_samples, n_terms))
@@ -476,15 +607,14 @@ class MetaModel:
aa = np.where(basis_indices[:, m] > 0)[0]
try:
basisIdx = basis_indices[aa, m]
- bb = np.reshape(univ_p_val[:, m, basisIdx], psi[:, aa].shape)
+ bb = univ_p_val[:, m, basisIdx].reshape(psi[:, aa].shape)
psi[:, aa] = np.multiply(psi[:, aa], bb)
except ValueError as err:
raise err
-
return psi
# -------------------------------------------------------------------------
- def fit(self, X, y, basis_indices, reg_method=None):
+ def fit(self, X, y, basis_indices, reg_method=None, sparsity=True):
"""
Fit regression using the regression method provided.
@@ -509,10 +639,8 @@ class MetaModel:
if reg_method is None:
reg_method = self.pce_reg_method
- # Check if BasisIndices is a sparse matrix
- sparsity = sp.sparse.issparse(basis_indices)
+ bias_term = self.dim_red_method.lower() != 'pca'
- clf_poly = []
compute_score = True if self.verbose else False
# inverse of the observed variance of the data
@@ -522,97 +650,70 @@ class MetaModel:
Lambda = 1e-6
# Bayes sparse adaptive aPCE
- if reg_method.lower() != 'ols':
- if reg_method.lower() == 'brr' or np.var(y) == 0:
- clf_poly = lm.BayesianRidge(n_iter=1000, tol=1e-7,
- fit_intercept=True,
- normalize=True,
- compute_score=compute_score,
- alpha_1=1e-04, alpha_2=1e-04,
- lambda_1=Lambda, lambda_2=Lambda)
- clf_poly.converged = True
-
- elif reg_method.lower() == 'ard':
- clf_poly = lm.ARDRegression(fit_intercept=True,
- normalize=True,
- compute_score=compute_score,
- n_iter=1000, tol=0.0001,
- alpha_1=1e-3, alpha_2=1e-3,
- lambda_1=Lambda, lambda_2=Lambda)
-
- elif reg_method.lower() == 'fastard':
- clf_poly = RegressionFastARD(fit_intercept=True,
- normalize=True,
- compute_score=compute_score,
- n_iter=300, tol=1e-10)
-
- elif reg_method.lower() == 'bcs':
- clf_poly = RegressionFastLaplace(fit_intercept=False,
- n_iter=1000, tol=1e-7)
-
- elif reg_method.lower() == 'lars':
- clf_poly = lm.LassoLarsCV(fit_intercept=False)
-
- elif reg_method.lower() == 'sgdr':
- clf_poly = lm.SGDRegressor(fit_intercept=False,
- max_iter=5000, tol=1e-7)
-
- elif reg_method.lower() == 'omp':
- clf_poly = lm.OrthogonalMatchingPursuitCV(fit_intercept=False,
- max_iter=10)
-
- elif reg_method.lower() == 'vbl':
- clf_poly = VBLinearRegression(fit_intercept=False)
-
- elif reg_method.lower() == 'ebl':
- clf_poly = EBLinearRegression(optimizer='em')
-
- # Fit
- clf_poly.fit(X, y)
-
- # Select the nonzero entries of coefficients
- # The first column must be kept (For mean calculations)
+ if reg_method.lower() == 'ols':
+ clf_poly = lm.LinearRegression(fit_intercept=False)
+ elif reg_method.lower() == 'brr':
+ clf_poly = lm.BayesianRidge(n_iter=1000, tol=1e-7,
+ fit_intercept=False,
+ normalize=True,
+ compute_score=compute_score,
+ alpha_1=1e-04, alpha_2=1e-04,
+ lambda_1=Lambda, lambda_2=Lambda)
+ clf_poly.converged = True
+
+ elif reg_method.lower() == 'ard':
+ clf_poly = lm.ARDRegression(fit_intercept=False,
+ normalize=True,
+ compute_score=compute_score,
+ n_iter=1000, tol=0.0001,
+ alpha_1=1e-3, alpha_2=1e-3,
+ lambda_1=Lambda, lambda_2=Lambda)
+
+ elif reg_method.lower() == 'fastard':
+ clf_poly = RegressionFastARD(fit_intercept=False,
+ normalize=True,
+ compute_score=compute_score,
+ n_iter=300, tol=1e-10)
+
+ elif reg_method.lower() == 'bcs':
+ clf_poly = RegressionFastLaplace(fit_intercept=False,
+ bias_term=bias_term,
+ n_iter=1000, tol=1e-7)
+
+ elif reg_method.lower() == 'lars':
+ clf_poly = lm.LassoLarsCV(fit_intercept=False)
+
+ elif reg_method.lower() == 'sgdr':
+ clf_poly = lm.SGDRegressor(fit_intercept=False,
+ max_iter=5000, tol=1e-7)
+
+ elif reg_method.lower() == 'omp':
+ clf_poly = OrthogonalMatchingPursuit(fit_intercept=False)
+
+ elif reg_method.lower() == 'vbl':
+ clf_poly = VBLinearRegression(fit_intercept=False)
+
+ elif reg_method.lower() == 'ebl':
+ clf_poly = EBLinearRegression(optimizer='em')
+
+ # Fit
+ clf_poly.fit(X, y)
+
+ # Select the nonzero entries of coefficients
+ if sparsity:
nnz_idx = np.nonzero(clf_poly.coef_)[0]
-
- if len(nnz_idx) == 0 or nnz_idx[0] != 0:
- nnz_idx = np.insert(np.nonzero(clf_poly.coef_)[0], 0, 0)
- # Remove the zero entries for Bases and PSI if need be
- if sparsity:
- sparse_basis_indices = basis_indices.toarray()[nnz_idx]
- else:
- sparse_basis_indices = basis_indices[nnz_idx]
- sparse_X = X[:, nnz_idx]
-
- # Store the coefficients of the regression model
- clf_poly.fit(sparse_X, y)
- coeffs = clf_poly.coef_
- else:
- # This is for the case where all outputs are zero, thereby
- # all coefficients are zero
- if sparsity:
- sparse_basis_indices = basis_indices.toarray()
- else:
- sparse_basis_indices = basis_indices
- sparse_X = X
- coeffs = clf_poly.coef_
-
- # Ordinary least square method (OLS)
else:
- if sparsity:
- sparse_basis_indices = basis_indices.toarray()
- else:
- sparse_basis_indices = basis_indices
- sparse_X = X
+ nnz_idx = np.arange(clf_poly.coef_.shape[0])
- X_T_X = np.dot(sparse_X.T, sparse_X)
+ # This is for the case where all outputs are zero, thereby
+ # all coefficients are zero
+ if (y == 0).all():
+ nnz_idx = np.insert(np.nonzero(clf_poly.coef_)[0], 0, 0)
- if np.linalg.cond(X_T_X) > 1e-12 and \
- np.linalg.cond(X_T_X) < 1 / sys.float_info.epsilon:
- # faster
- coeffs = sp.linalg.solve(X_T_X, np.dot(sparse_X.T, y))
- else:
- # stabler
- coeffs = np.dot(np.dot(np.linalg.pinv(X_T_X), sparse_X.T), y)
+ sparse_basis_indices = basis_indices[nnz_idx]
+ sparse_X = X[:, nnz_idx]
+ coeffs = clf_poly.coef_[nnz_idx]
+ clf_poly.coef_ = coeffs
# Create a dict to pass the outputs
return_out_dict = dict()
@@ -647,7 +748,7 @@ class MetaModel:
"""
- NrSamples, n_params = ED_X.shape
+ n_samples, n_params = ED_X.shape
# Initialization
qAllCoeffs, AllCoeffs = {}, {}
qAllIndices_Sparse, AllIndices_Sparse = {}, {}
@@ -656,8 +757,8 @@ class MetaModel:
qAllLCerror, AllLCerror = {}, {}
# Extract degree array and qnorm array
- DegreeArray = np.array([*self.allBasisIndices], dtype=int)
- qnorm = [*self.allBasisIndices[str(int(DegreeArray[0]))]]
+ deg_array = np.array([*self.allBasisIndices], dtype=int)
+ qnorm = [*self.allBasisIndices[str(int(deg_array[0]))]]
# Some options for EarlyStop
errorIncreases = False
@@ -675,10 +776,10 @@ class MetaModel:
# polynomial degree until the highest accuracy is reached
# =====================================================================
# For each degree check all q-norms and choose the best one
- scores = -np.inf * np.ones(DegreeArray.shape[0])
+ scores = -np.inf * np.ones(deg_array.shape[0])
qNormScores = -np.inf * np.ones(nqnorms)
- for degIdx, deg in enumerate(DegreeArray):
+ for degIdx, deg in enumerate(deg_array):
for qidx, q in enumerate(qnorm):
@@ -758,7 +859,7 @@ class MetaModel:
LOOCVScore = np.nanmax(scores)
P = AllnTerms[str(best_deg)]
LCerror = AllLCerror[str(best_deg)]
- degree = DegreeArray[np.nanargmax(scores)]
+ degree = deg_array[np.nanargmax(scores)]
qnorm = float(qnorm[best_q])
# ------------------ Print out Summary of results ------------------
@@ -769,7 +870,7 @@ class MetaModel:
print(f'Output variable {varIdx+1}:')
print('The estimation of PCE coefficients converged at polynomial '
- f'degree {DegreeArray[best_deg-1]} with '
+ f'degree {deg_array[best_deg-1]} with '
f'{len(BasisIndices_Sparse)} terms (Sparsity index = '
f'{round(len(BasisIndices_Sparse)/P, 3)}).')
@@ -782,7 +883,7 @@ class MetaModel:
print('='*50)
print("scores:\n", scores)
- print("Best score's degree:", self.DegreeArray[best_deg-1])
+ print("Best score's degree:", self.deg_array[best_deg-1])
print("NO. of terms:", len(basis_indices))
print("Sparsity index:", round(len(basis_indices)/P, 3))
print("Best Indices:\n", basis_indices)
@@ -844,7 +945,7 @@ class MetaModel:
Returns
-------
- Q_2 : float
+ R_2 : float
LOOCV Validation score (1-LOOCV erro).
residual : array of shape (n_samples,)
Residual values (y - predicted targets).
@@ -866,8 +967,8 @@ class MetaModel:
# Build the projection matrix
PsiTPsi = np.dot(psi_sparse.T, psi_sparse)
- if np.linalg.cond(PsiTPsi) > 1e-12 and \
- np.linalg.cond(PsiTPsi) < 1/sys.float_info.epsilon:
+ if np.linalg.cond(PsiTPsi) > 1e-12: #and \
+ # np.linalg.cond(PsiTPsi) < 1/sys.float_info.epsilon:
# faster
M = sp.linalg.solve(PsiTPsi,
sp.sparse.eye(PsiTPsi.shape[0]).toarray())
@@ -883,56 +984,57 @@ class MetaModel:
# ------ Calculate Error Loocv for each measurement point ----
# Residuals
- if isinstance(clf, list):
- residual = np.dot(psi, coeffs) - y
- else:
+ try:
residual = clf.predict(psi) - y
+ except:
+ residual = np.dot(psi, coeffs) - y
# Variance
- varY = np.var(y)
+ var_y = np.var(y)
- if varY == 0:
- normEmpErr = 0
- ErrLoo = 0
+ if var_y == 0:
+ norm_emp_error = 0
+ loo_error = 0
LCerror = np.zeros((y.shape))
+ return 1-loo_error, LCerror
else:
- normEmpErr = np.mean(residual**2)/varY
+ norm_emp_error = np.mean(residual**2)/var_y
# LCerror = np.divide(residual, (1-h))
- LCerror = residual / (1-h)[:, np.newaxis]
- ErrLoo = np.mean(np.square(LCerror)) / varY
+ LCerror = residual / (1-h)
+ loo_error = np.mean(np.square(LCerror)) / var_y
# if there are NaNs, just return an infinite LOO error (this
# happens, e.g., when a strongly underdetermined problem is solved)
- if np.isnan(ErrLoo):
- ErrLoo = np.inf
+ if np.isnan(loo_error):
+ loo_error = np.inf
# Corrected Error for over-determined system
- trM = np.trace(M)
- if trM < 0 or abs(trM) > 1e6:
- trM = np.trace(np.linalg.pinv(np.dot(psi.T, psi)))
+ tr_M = np.trace(M)
+ if tr_M < 0 or abs(tr_M) > 1e6:
+ tr_M = np.trace(np.linalg.pinv(np.dot(psi.T, psi)))
# Over-determined system of Equation
if N > P:
- T_factor = N/(N-P) * (1 + trM)
+ T_factor = N/(N-P) * (1 + tr_M)
# Under-determined system of Equation
else:
T_factor = np.inf
- CorrectedErrLoo = ErrLoo * T_factor
+ corrected_loo_error = loo_error * T_factor
- Q_2 = 1 - CorrectedErrLoo
+ R_2 = 1 - corrected_loo_error
- return Q_2, residual
+ return R_2, LCerror
# -------------------------------------------------------------------------
- def pca_transformation(self, Output):
+ def pca_transformation(self, target, verbose=False):
"""
Transforms the targets (outputs) via Principal Component Analysis
Parameters
----------
- Output : array of shape (n_samples,)
+ target : array of shape (n_samples,)
Target values.
Returns
@@ -941,6 +1043,8 @@ class MetaModel:
Fitted sklearnPCA object.
OutputMatrix : array of shape (n_samples,)
Transformed target values.
+ n_pca_components : int
+ Number of selected principal components.
"""
# Transform via Principal Component Analysis
@@ -948,14 +1052,14 @@ class MetaModel:
var_pca_threshold = self.var_pca_threshold
else:
var_pca_threshold = 100.0
- n_samples, n_features = Output.shape
+ n_samples, n_features = target.shape
if hasattr(self, 'n_pca_components'):
n_pca_components = self.n_pca_components
else:
# Instantiate and fit sklearnPCA object
covar_matrix = sklearnPCA(n_components=None)
- covar_matrix.fit(Output)
+ covar_matrix.fit(target)
var = np.cumsum(np.round(covar_matrix.explained_variance_ratio_,
decimals=5)*100)
# Find the number of components to explain self.varPCAThreshold of
@@ -968,19 +1072,19 @@ class MetaModel:
n_pca_components = min(n_samples, n_features, n_components)
# Print out a report
- print()
- print('-' * 50)
- print(f"PCA transformation is performed with {n_pca_components}"
- " components.")
- print('-' * 50)
- print()
+ if verbose:
+ print()
+ print('-' * 50)
+ print(f"PCA transformation is performed with {n_pca_components}"
+ " components.")
+ print('-' * 50)
+ print()
# Fit and transform with the selected number of components
- pca = sklearnPCA(n_components=n_pca_components,
- svd_solver='randomized')
- OutputMatrix = pca.fit_transform(Output)
+ pca = sklearnPCA(n_components=n_pca_components, svd_solver='arpack')
+ scaled_target = pca.fit_transform(target)
- return pca, OutputMatrix
+ return pca, scaled_target, n_pca_components
# -------------------------------------------------------------------------
def gaussian_process_emulator(self, X, y, nug_term=None, autoSelect=False,
@@ -1080,75 +1184,118 @@ class MetaModel:
std_pred : dict
Standard deviatioon of the predictions.
"""
- if self.meta_model_type.lower() == 'gpe':
- model_dict = self.gp_poly
- else:
- model_dict = self.coeffs_dict
+ outputs = self.ModelObj.Output.names
+ # Generate or transform (if need be) samples
if samples is None:
- if nsamples is None:
- self.n_samples = 100000
- else:
- self.n_samples = nsamples
-
- samples = self.ExpDesign.generate_samples(self.n_samples,
- sampling_method)
- else:
- self.samples = samples
- self.n_samples = len(samples)
-
- # Transform samples
- samples = self.ExpDesign.transform(samples)
-
+ # Generate
+ samples = self.ExpDesign.generate_samples(
+ nsamples,
+ sampling_method
+ )
+
+ # Transform samples to the independent space
+ samples = self.ExpDesign.transform(
+ samples,
+ method='user'
+ )
+ # print(samples)
+
+ # Compute univariate bases for the given samples
if self.meta_model_type.lower() != 'gpe':
- univ_p_val = self.univ_basis_vals(samples,
- n_max=np.max(self.pce_deg))
+ univ_p_val = self.univ_basis_vals(
+ samples,
+ n_max=np.max(self.pce_deg)
+ )
- mean_pred = {}
- std_pred = {}
-
- # Loop over outputs
- for ouput, values in model_dict.items():
-
- mean = np.zeros((len(samples), len(values)))
- std = np.zeros((len(samples), len(values)))
- idx = 0
- for in_key, InIdxValues in values.items():
-
- # Perdiction with GPE
- if self.meta_model_type.lower() == 'gpe':
- X_T = self.x_scaler[ouput].transform(samples)
- gp = self.gp_poly[ouput][in_key]
- y_mean, y_std = gp.predict(X_T, return_std=True)
+ mean_pred_b = {}
+ std_pred_b = {}
+ # Loop over bootstrap iterations
+ for b_i in range(self.n_bootstrap_itrs):
+ # Extract model dictionary
+ if self.meta_model_type.lower() == 'gpe':
+ model_dict = self.gp_poly[f'b_{b_i+1}']
+ else:
+ model_dict = self.coeffs_dict[f'b_{b_i+1}']
+
+ # Loop over outputs
+ mean_pred = {}
+ std_pred = {}
+ for output, values in model_dict.items():
+
+ mean = np.empty((len(samples), len(values)))
+ std = np.empty((len(samples), len(values)))
+ idx = 0
+ for in_key, InIdxValues in values.items():
+
+ # Perdiction with GPE
+ if self.meta_model_type.lower() == 'gpe':
+ X_T = self.x_scaler[f'b_{b_i+1}'][output].transform(samples)
+ gp = self.gp_poly[f'b_{b_i+1}'][output][in_key]
+ y_mean, y_std = gp.predict(X_T, return_std=True)
+
+ else:
+ # Perdiction with PCE
+ # Assemble Psi matrix
+ basis = self.basis_dict[f'b_{b_i+1}'][output][in_key]
+ psi = self.create_psi(basis, univ_p_val)
+
+ # Perdiction
+ if self.bootstrap_method != 'fast' or b_i == 0:
+ # with error bar, i.e. use clf_poly
+ clf_poly = self.clf_poly[f'b_{b_i+1}'][output][in_key]
+ try:
+ y_mean, y_std = clf_poly.predict(
+ psi, return_std=True
+ )
+ except TypeError:
+ y_mean = clf_poly.predict(psi)
+ y_std = np.zeros_like(y_mean)
+ else:
+ # without error bar
+ coeffs = self.coeffs_dict[f'b_{b_i+1}'][output][in_key]
+ y_mean = np.dot(psi, coeffs)
+ y_std = np.zeros_like(y_mean)
+
+ mean[:, idx] = y_mean
+ std[:, idx] = y_std
+ idx += 1
+
+ # Save predictions for each output
+ if self.dim_red_method.lower() == 'pca':
+ PCA = self.pca[f'b_{b_i+1}'][output]
+ mean_pred[output] = PCA.inverse_transform(mean)
+ std_pred[output] = np.zeros(mean.shape)
else:
- # Perdiction with PCE or pcekriging
- # Assemble Psi matrix
- psi = self.create_psi(self.basis_dict[ouput][in_key],
- univ_p_val)
- # Perdiction
- try:
- # with error bar
- clf_poly = self.clf_poly[ouput][in_key]
- y_mean, y_std = clf_poly.predict(psi, return_std=True)
-
- except:
- # without error bar
- coeffs = self.coeffs_dict[ouput][in_key]
- y_mean = np.dot(psi, coeffs)
- y_std = np.zeros_like(y_mean)
-
- mean[:, idx] = y_mean
- std[:, idx] = y_std
- idx += 1
-
- if self.dim_red_method.lower() == 'pca':
- PCA = self.pca[ouput]
- mean_pred[ouput] = PCA.mean_ + np.dot(mean, PCA.components_)
- std_pred[ouput] = np.sqrt(np.dot(std**2, PCA.components_**2))
+ mean_pred[output] = mean
+ std_pred[output] = std
+
+ # Save predictions for each bootstrap iteration
+ mean_pred_b[b_i] = mean_pred
+ std_pred_b[b_i] = std_pred
+
+ # Change the order of nesting
+ mean_pred_all = {}
+ for i in sorted(mean_pred_b):
+ for k, v in mean_pred_b[i].items():
+ if k not in mean_pred_all:
+ mean_pred_all[k] = [None] * len(mean_pred_b)
+ mean_pred_all[k][i] = v
+
+ # Compute the moments of predictions over the predictions
+ for output in outputs:
+ # Only use bootstraps with finite values
+ finite_rows = np.isfinite(
+ mean_pred_all[output]).all(axis=2).all(axis=1)
+ outs = np.asarray(mean_pred_all[output])[finite_rows]
+ # Compute mean
+ mean_pred[output] = np.mean(outs, axis=0)
+ # Compute standard deviation
+ if self.n_bootstrap_itrs > 1:
+ std_pred[output] = np.std(outs, axis=0)
else:
- mean_pred[ouput] = mean
- std_pred[ouput] = std
+ std_pred[output] = std_pred_b[b_i][output]
if return_samples:
return mean_pred, std_pred, samples
@@ -1177,7 +1324,7 @@ class MetaModel:
"""
Model = self.ModelObj
- outputNames = Model.Output.Names
+ outputNames = Model.Output.names
self.errorRegMethod = 'GPE'
self.errorclf_poly = self.auto_vivification()
self.errorScale = self.auto_vivification()
@@ -1269,28 +1416,57 @@ class MetaModel:
return value
# -------------------------------------------------------------------------
- def __select_degree(self, ndim, nSamples):
+ def copy_meta_model_opts(self, InputObj, ModelObj):
+ """
+ This method is a convinient function to copy the metamodel options.
+
+ Parameters
+ ----------
+ InputObj : object
+ The input object.
+ ModelObj : object
+ The Model object.
+
+ Returns
+ -------
+ new_MetaModelOpts : object
+ The copied object.
+
+ """
+ new_MetaModelOpts = copy.deepcopy(self)
+ new_MetaModelOpts.ModelObj = ModelObj
+ new_MetaModelOpts.input_obj = InputObj
+ new_MetaModelOpts.ExpDesign.meta_Model = 'aPCE'
+ new_MetaModelOpts.ExpDesign.InputObj = InputObj
+ new_MetaModelOpts.ExpDesign.ndim = len(InputObj.Marginals)
+ new_MetaModelOpts.n_params = len(InputObj.Marginals)
+ new_MetaModelOpts.ExpDesign.hdf5_file = None
+
+ return new_MetaModelOpts
+
+ # -------------------------------------------------------------------------
+ def __select_degree(self, ndim, n_samples):
"""
Selects degree based on the number of samples and parameters in the
sequential design.
Parameters
----------
- ndim : TYPE
- DESCRIPTION.
- nSamples : TYPE
- DESCRIPTION.
+ ndim : int
+ Dimension of the parameter space.
+ n_samples : int
+ Number of samples.
Returns
-------
- TYPE
- DESCRIPTION.
+ deg_array: array
+ Array containing the arrays.
"""
- # Define the DegreeArray
+ # Define the deg_array
max_deg = np.max(self.pce_deg)
min_Deg = np.min(self.pce_deg)
- nitr = nSamples - self.ExpDesign.n_init_samples
+ nitr = n_samples - self.ExpDesign.n_init_samples
# Check q-norm
if not np.isscalar(self.pce_q_norm):
@@ -1306,15 +1482,16 @@ class MetaModel:
return n_combo
if self.ExpDesignFlag != 'sequential':
- degNew = max_deg
+ deg_new = max_deg
else:
d = nitr if nitr != 0 and self.n_params > 5 else 1
- min_index = np.argmin(abs(M_uptoMax(max_deg)-ndim*nSamples*d))
- degNew = range(1, max_deg+1)[min_index]
+ min_index = np.argmin(abs(M_uptoMax(max_deg)-ndim*n_samples*d))
+ deg_new = max_deg
+ # deg_new = range(1, max_deg+1)[min_index]
- if degNew > min_Deg and self.pce_reg_method.lower() != 'fastard':
- DegreeArray = np.arange(min_Deg, degNew+1)
+ if deg_new > min_Deg and self.pce_reg_method.lower() != 'fastard':
+ deg_array = np.arange(min_Deg, deg_new+1)
else:
- DegreeArray = np.array([degNew])
+ deg_array = np.array([deg_new])
- return DegreeArray
+ return deg_array