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Jacobi polynomials: Tests and derivatives [CI SKIP]

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NAThompson
2019-08-06 09:53:58 -04:00
parent b5114e1c75
commit 09d3ee47cf
3 changed files with 133 additions and 0 deletions
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1
test/Jamfile.v2
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@@ -939,6 +939,7 @@ test-suite misc :
[ run test_vector_barycentric_rational.cpp ../../test/build//boost_unit_test_framework : : : [ requires cxx11_smart_ptr cxx11_defaulted_functions cxx11_auto_declarations cxx11_unified_initialization_syntax ] [ check-target-builds ../../multiprecision/config//has_eigen : : <build>no ] ]
[ run test_cubic_b_spline.cpp ../../test/build//boost_unit_test_framework : : : [ requires cxx11_smart_ptr cxx11_defaulted_functions ] <debug-symbols>off <toolset>msvc:<cxxflags>/bigobj release ]
[ run cardinal_b_spline_test.cpp : : : [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
[ run jacobi_test.cpp : : : [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] [ check-target-builds ../config//has_float128 "GCC libquadmath and __float128 support" : <linkflags>-lquadmath ] ]
[ run whittaker_shannon_test.cpp : : : [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]
[ run cardinal_quadratic_b_spline_test.cpp : : : [ requires cxx11_auto_declarations cxx11_constexpr cxx11_smart_ptr cxx11_defaulted_functions ] ]
[ run catmull_rom_test.cpp ../../test/build//boost_unit_test_framework : : : <define>TEST=1 [ requires cxx11_hdr_array cxx11_hdr_initializer_list ] : catmull_rom_test_1 ]

118
test/jacobi_test.cpp Normal file
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@@ -0,0 +1,118 @@
/*
* Copyright Nick Thompson, 2019
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
*/
#include "math_unit_test.hpp"
#include <numeric>
#include <utility>
#include <random>
#include <cmath>
#include <boost/math/special_functions/jacobi.hpp>
#ifdef BOOST_HAS_FLOAT128
#include <boost/multiprecision/float128.hpp>
using boost::multiprecision::float128;
#endif
using std::abs;
using boost::math::jacobi;
using boost::math::jacobi_derivative;
template<typename Real>
void test_to_quadratic()
{
Real h = 1/Real(8);
for (Real alpha = -1 + h; alpha < 2; alpha += h) {
for (Real beta = -1 + h; beta < 2; beta += h) {
for (Real x = -1; x < 1; x += h) {
Real expected = 1;
Real computed = jacobi(0, alpha, beta, x);
CHECK_ULP_CLOSE(expected, computed, 0);
expected = (alpha + 1) + (alpha + beta +2)*(x-1)/2;
computed = jacobi(1, alpha, beta, x);
CHECK_ULP_CLOSE(expected, computed, 0);
expected = (alpha + 1)*(alpha+2)/2 + (alpha + 2)*(alpha + beta + 3)*(x-1)/2 + (alpha + beta + 3)*(alpha + beta + 4)*(x-1)*(x-1)/8;
computed = jacobi(2, alpha, beta, x);
CHECK_ULP_CLOSE(expected, computed, 1);
}
}
}
}
template<typename Real>
void test_symmetry()
{
Real h = 1/Real(4);
for (Real alpha = -1 + h; alpha < 2; alpha += h) {
for (Real beta = -1 + h; beta < 2; beta += h) {
for (Real x = -1; x < 1; x += h) {
for (size_t n = 0; n < 20; n += 2)
{
Real expected = jacobi(n, beta, alpha , -x);
Real computed = jacobi(n, alpha, beta, x);
CHECK_ULP_CLOSE(expected, computed, 0);
expected = jacobi(n+1, beta, alpha, -x);
computed = -jacobi(n+1, alpha, beta, x);
CHECK_ULP_CLOSE(expected, computed, 0);
}
}
}
}
}
template<typename Real>
void test_derivative()
{
Real h = 1/Real(4);
for (Real alpha = -1 + h; alpha < 2; alpha += h) {
for (Real beta = -1 + h; beta < 2; beta += h) {
for (Real x = -1; x < 1; x += h) {
Real expected = 0;
Real computed = jacobi_derivative(0, alpha, beta, x, 1);
CHECK_ULP_CLOSE(expected, computed, 0);
expected = (alpha + beta + 2)/2;
computed = jacobi_derivative(1, alpha, beta, x, 1);
CHECK_ULP_CLOSE(expected, computed, 0);
expected = (alpha + 2)*(alpha + beta + 3)/2 + (alpha + beta + 3)*(alpha + beta + 4)*(x-1)/4;
computed = jacobi_derivative(2, alpha, beta, x, 1);
CHECK_ULP_CLOSE(expected, computed, 0);
expected = (alpha + beta + 3)*(alpha + beta + 4)/4;
computed = jacobi_derivative(2, alpha, beta, x, 2);
CHECK_ULP_CLOSE(expected, computed, 0);
}
}
}
}
int main()
{
test_to_quadratic<float>();
test_to_quadratic<double>();
test_to_quadratic<long double>();
test_symmetry<float>();
test_symmetry<double>();
test_symmetry<long double>();
test_derivative<float>();
test_derivative<double>();
test_derivative<long double>();
#ifdef BOOST_HAS_FLOAT128
test_to_quadratic<boost::multiprecision::float128>();
test_symmetry<boost::multiprecision::float128>();
test_derivative<boost::multiprecision::float128>();
#endif
return boost::math::test::report_errors();
}