[tests][AnalyticalFunc] add example notebook.

tests/AnalyticalFunction/Outputs_PostProcessing_calib/totalsobol_Z.csv

 $X_1$,$X_2$
-9.993116948359226370e-01,3.945526636751626182e-01
-9.961447327121788486e-01,3.667186570442192428e-01
-9.947646363203489495e-01,3.647464239325610147e-01
-9.957567531711847275e-01,3.731759386892447572e-01
-9.938740724688709394e-01,3.496238556702422340e-01
-9.934295067779727040e-01,3.489816158549155500e-01
-1.000000000000000000e+00,2.733114696357644147e-01
-9.929163528111150105e-01,3.544359760567539208e-01
-9.927050241098982486e-01,3.584158152985525980e-01
-9.915077464334921542e-01,3.702678640580663316e-01
+9.366935781467614630e-01,1.296011206606640376e-01
+9.366778238387639677e-01,1.296333541870885453e-01
+9.366737110183974702e-01,1.296417560822205883e-01
+9.366715749203039509e-01,1.296461022957972054e-01
+9.366705838329740796e-01,1.296480821342860246e-01
+9.366707796164559507e-01,1.296475551494160605e-01
+9.366843916343090548e-01,1.296184596592687976e-01
+9.366660378655075059e-01,1.296580126549548295e-01
+9.366679119152595545e-01,1.296539068017917851e-01
+9.366689440746930329e-01,1.296517202892714382e-01

tests/AnalyticalFunction/AnalyticalFunction.py → tests/AnalyticalFunction/analytical_function.py

@@ -11,7 +11,7 @@ import scipy.stats as st
 import seaborn as sns
 
 
-def AnalyticalFunction(xx, t=None):
+def analytical_function(xx, t=None):
     """
     Analytical Non-Gaussian Function
 
@@ -68,56 +68,56 @@ if __name__ == "__main__":
     MCSize = 10000 #1000000
     ndim = 10
     sigma = 2
-    
+
     # -------------------------------------------------------------------------
     # ----------------------- Synthetic data generation -----------------------
     # -------------------------------------------------------------------------
     t = np.arange(0, 10, 1.) / 9
-    
+
     MAP = np.zeros((1, ndim))
     synthethicData = AnalyticalFunction(MAP, t=t)
-    
+
     # -------------------------------------------------------------------------
     # ---------------------- Generate Prior distribution ----------------------
     # -------------------------------------------------------------------------
-    
+
     xx = np.zeros((MCSize, ndim))
-    
+
     params = (-5,5)
-    
+
     for idxDim in range(ndim):
         lower, upper = params
         xx[:,idxDim] = stats.uniform(loc=lower, scale=upper-lower).rvs(size=MCSize)
-    
+
     # -------------------------------------------------------------------------
     # ------------- BME and Kullback-Leibler Divergence -----------------------
     # -------------------------------------------------------------------------
     Outputs = AnalyticalFunction(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)
-    
+
     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
     unif = np.random.rand(1, MCSize)[0]
-    
+
     # Reject the poorly performed prior
     accepted = normLikelihood >= unif
-    
+
     # Prior-based estimation of BME
     logBME = np.log(np.nanmean(Likelihoods))
     print('\nThe Naive MC-Estimation of BME is %.5f.'%(logBME))
-    
+
     # 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)
-    
+
     # -------------------------------------------------------------------------
     # ----------------- Save the arrays as .npy files -------------------------
     # -------------------------------------------------------------------------