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- /*
- * 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<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();
- }
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