Commit f6b6a931 authored by Timo Koch's avatar Timo Koch
Browse files

[test][math] Generalize invert cubic root test

parent 3d28631d
......@@ -33,6 +33,9 @@
#include <iostream>
#include <utility>
#include <algorithm>
#include <array>
#include <random>
#include <tuple>
#include <dune/common/float_cmp.hh>
#include <dune/common/fmatrix.hh>
......@@ -239,43 +242,96 @@ int main()
///// Dumux::invertCubicPolynomial ///////////////////////////////
//////////////////////////////////////////////////////////////////
const auto cubicCoefficientsFromRoots = [](auto x, auto y, auto z, double scale = 1.0){
const auto b = -(x + y + z);
const auto c = x*y + x*z + y*z;
const auto d = -x*y*z;
// scaling doesn't change the roots
return std::make_tuple(1.0*scale, b*scale, c*scale, d*scale);
};
const auto quadCoefficientsFromRoots = [](auto x, auto y, double scale = 1.0){
const auto b = -(x + y);
const auto c = x*y;
return std::make_tuple(1.0*scale, b*scale, c*scale);
};
const auto linearCoefficientsFromRoots = [](auto x, double scale = 1.0){
return std::make_tuple(1.0*scale, -x*scale);
};
std::mt19937 gen(std::random_device{}());
std::uniform_real_distribution<> dis(-10.0, 10.0);
auto threeRandomNumbers = [&]() mutable {
const auto x = dis(gen);
auto y = dis(gen); while (x == y) { y = dis(gen); }
auto z = dis(gen); while (x == z || y == z) { z = dis(gen); }
return std::make_tuple(x, y, z);
};
const auto checkRoots = [](const std::array<double, 3>& roots,
const std::array<double, 3>& ref,
int n)
{
for (int i = 0; i < n; i++)
{
using std::isfinite;
if (!isfinite(roots[i]))
DUNE_THROW(Dune::Exception, "Expecting finite root");
if (std::none_of(ref.begin(), ref.end(), [&](auto r){ return Dune::FloatCmp::eq(roots[i], r, 1e-10); }))
DUNE_THROW(Dune::Exception, "[invertCubicPolynomial] Root "
<< i << " of " << n << ": " << roots[i]
<< " does not match reference");
}
};
std::array<double, 3> roots{};
for (double scaling : {1.0, -1.0, 5.0})
{
for (int i = 0; i < 1000; ++i)
{
const auto [x, y, z] = threeRandomNumbers();
// test for three unique roots
{
const auto [a, b, c, d] = cubicCoefficientsFromRoots(x, y, z, scaling);
int numRoots = Dumux::invertCubicPolynomial(roots.data(), a, b, c, d);
if (numRoots != 3)
DUNE_THROW(Dune::Exception, "Expecting three roots! Got " << numRoots);
checkRoots(roots, {x, y, z}, numRoots);
}
// One corner case
// test for two unique roots
{
const auto [b, c, d] = quadCoefficientsFromRoots(x, z, scaling);
int numRoots = Dumux::invertCubicPolynomial(roots.data(), 0.0, b, c, d);
if (numRoots != 2)
DUNE_THROW(Dune::Exception, "Expecting two roots! Got " << numRoots);
checkRoots(roots, {x, z}, numRoots);
}
// test for one unique root
{
const auto [c, d] = linearCoefficientsFromRoots(x, scaling);
int numRoots = Dumux::invertCubicPolynomial(roots.data(), 0.0, 0.0, c, d);
if (numRoots != 1)
DUNE_THROW(Dune::Exception, "Expecting one root! Got " << numRoots);
checkRoots(roots, {x}, numRoots);
}
}
}
// Test one corner case (see MR!2594)
int nroots = Dumux::invertCubicPolynomial(roots.data(),
1.0,
-0.96165703943410097,
0.30826068470787077,
0.01340255221155587);
1.0, -0.96165703943410097, 0.30826068470787077, 0.01340255221155587
);
if (nroots != 1)
DUNE_THROW(Dune::Exception, "Expecting one root");
using std::isfinite;
if (!isfinite(roots[0]))
DUNE_THROW(Dune::Exception, "Expecting finite root");
if (!Dune::FloatCmp::eq(roots[0], -3.863448718244389e-02, 1e-14))
DUNE_THROW(Dune::Exception, "Root of cubic equation does not match reference");
// One simple case
std::array<double, 3> known_roots{-10.1, 0.001, 1000.77};
nroots = Dumux::invertCubicPolynomial(
roots.data(),
1.0,
-known_roots[0] - known_roots[1] - known_roots[2],
known_roots[0] * known_roots[1] + known_roots[0] * known_roots[2] + known_roots[1] * known_roots[2],
-known_roots[0] * known_roots[1] * known_roots[2]);
if (nroots != 3)
DUNE_THROW(Dune::Exception, "Expecting three roots");
for (int i = 0; i < 3; i++)
{
if (!isfinite(roots[i]))
DUNE_THROW(Dune::Exception, "Expecting finite root");
if (!Dune::FloatCmp::eq(roots[i], known_roots[i], 1e-10))
DUNE_THROW(Dune::Exception, "Root of cubic equation does not match reference");
}
return 0;
}
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