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