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// (C) Copyright John Maddock 2018.
// 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)
#define BOOST_TEST_MODULE test_recurrences
#include <boost/config.hpp>
#ifndef BOOST_NO_CXX11_HDR_TUPLE
#include <boost/multiprecision/cpp_bin_float.hpp>
#include <boost/math/tools/recurrence.hpp>
#include <boost/math/special_functions/bessel.hpp>
#include <boost/test/included/unit_test.hpp>
#include <boost/test/floating_point_comparison.hpp>
//#include <boost/test/tools/floating_point_comparison.hpp>
#include <boost/math/concepts/real_concept.hpp>
#ifdef BOOST_MSVC
#pragma warning(disable:4127)
#endif
template <class T>
struct bessel_jy_recurrence
{
bessel_jy_recurrence(T v, T z) : v(v), z(z) {}
boost::math::tuple<T, T, T> operator()(int k)const
{
return boost::math::tuple<T, T, T>(T(1), -2 * (v + k) / z, T(1));
}
T v, z;
};
template <class T>
struct bessel_ik_recurrence
{
bessel_ik_recurrence(T v, T z) : v(v), z(z) {}
boost::math::tuple<T, T, T> operator()(int k)const
{
return boost::math::tuple<T, T, T>(T(1), -2 * (v + k) / z, T(-1));
}
T v, z;
};
template <class T>
void test_spots(T, const char* name)
{
std::cout << "Running tests for type " << name << std::endl;
T tol = boost::math::tools::epsilon<T>() * 5;
if ((std::numeric_limits<T>::digits > 53) || (std::numeric_limits<T>::digits == 0))
tol *= 5;
//
// Test forward recurrence on Y_v(x):
//
{
T v = 22.25;
T x = 4.125;
bessel_jy_recurrence<T> coef(v, x);
T prev;
T first = boost::math::cyl_neumann(v - 1, x);
T second = boost::math::cyl_neumann(v, x);
T sixth = boost::math::tools::apply_recurrence_relation_forward(coef, 6, first, second, (int*)0, &prev);
T expected1 = boost::math::cyl_neumann(v + 6, x);
T expected2 = boost::math::cyl_neumann(v + 5, x);
BOOST_CHECK_CLOSE_FRACTION(sixth, expected1, tol);
BOOST_CHECK_CLOSE_FRACTION(prev, expected2, tol);
boost::math::tools::forward_recurrence_iterator< bessel_jy_recurrence<T> > it(coef, first, second);
for (unsigned i = 0; i < 15; ++i)
{
expected1 = boost::math::cyl_neumann(v + i, x);
T found = *it;
BOOST_CHECK_CLOSE_FRACTION(found, expected1, tol);
++it;
}
if (std::numeric_limits<T>::max_exponent > 300)
{
//
// This calculates the ratio Y_v(x)/Y_v+1(x) from the recurrence relations
// which are only transiently stable since Y_v is not minimal as v->-INF
// but only as v->0. We have to be sure that v is sufficiently large that
// convergence is complete before we reach the origin.
//
v = 102.75;
boost::uintmax_t max_iter = 200;
T ratio = boost::math::tools::function_ratio_from_forwards_recurrence(bessel_jy_recurrence<T>(v, x), boost::math::tools::epsilon<T>(), max_iter);
first = boost::math::cyl_neumann(v, x);
second = boost::math::cyl_neumann(v + 1, x);
BOOST_CHECK_CLOSE_FRACTION(ratio, first / second, tol);
boost::math::tools::forward_recurrence_iterator< bessel_jy_recurrence<T> > it2(bessel_jy_recurrence<T>(v, x), boost::math::cyl_neumann(v, x));
for (unsigned i = 0; i < 15; ++i)
{
expected1 = boost::math::cyl_neumann(v + i, x);
T found = *it2;
BOOST_CHECK_CLOSE_FRACTION(found, expected1, tol);
++it2;
}
}
}
//
// Test backward recurrence on J_v(x):
//
{
if ((std::numeric_limits<T>::digits > 53) || !std::numeric_limits<T>::is_specialized)
tol *= 5;
T v = 22.25;
T x = 4.125;
bessel_jy_recurrence<T> coef(v, x);
T prev;
T first = boost::math::cyl_bessel_j(v + 1, x);
T second = boost::math::cyl_bessel_j(v, x);
T sixth = boost::math::tools::apply_recurrence_relation_backward(coef, 6, first, second, (int*)0, &prev);
T expected1 = boost::math::cyl_bessel_j(v - 6, x);
T expected2 = boost::math::cyl_bessel_j(v - 5, x);
BOOST_CHECK_CLOSE_FRACTION(sixth, expected1, tol);
BOOST_CHECK_CLOSE_FRACTION(prev, expected2, tol);
boost::math::tools::backward_recurrence_iterator< bessel_jy_recurrence<T> > it(coef, first, second);
for (unsigned i = 0; i < 15; ++i)
{
expected1 = boost::math::cyl_bessel_j(v - i, x);
T found = *it;
BOOST_CHECK_CLOSE_FRACTION(found, expected1, tol);
++it;
}
boost::uintmax_t max_iter = 200;
T ratio = boost::math::tools::function_ratio_from_backwards_recurrence(bessel_jy_recurrence<T>(v, x), boost::math::tools::epsilon<T>(), max_iter);
first = boost::math::cyl_bessel_j(v, x);
second = boost::math::cyl_bessel_j(v - 1, x);
BOOST_CHECK_CLOSE_FRACTION(ratio, first / second, tol);
boost::math::tools::backward_recurrence_iterator< bessel_jy_recurrence<T> > it2(bessel_jy_recurrence<T>(v, x), boost::math::cyl_bessel_j(v, x));
//boost::math::tools::backward_recurrence_iterator< bessel_jy_recurrence<T> > it3(bessel_jy_recurrence<T>(v, x), boost::math::cyl_neumann(v+1, x), boost::math::cyl_neumann(v, x));
for (unsigned i = 0; i < 15; ++i)
{
expected1 = boost::math::cyl_bessel_j(v - i, x);
T found = *it2;
BOOST_CHECK_CLOSE_FRACTION(found, expected1, tol);
++it2;
}
}
}
BOOST_AUTO_TEST_CASE( test_main )
{
BOOST_MATH_CONTROL_FP;
#if !defined(TEST) || TEST == 1
test_spots(0.0F, "float");
test_spots(0.0, "double");
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_spots(0.0L, "long double");
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
test_spots(boost::math::concepts::real_concept(0.1), "real_concept");
#endif
#endif
#endif
#if !defined(TEST) || TEST == 2 || TEST == 3
test_spots(boost::multiprecision::cpp_bin_float_quad(), "cpp_bin_float_quad");
#endif
}
#else
int main() { return 0; }
#endif
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