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// Copyright (c) 2014 Anton Bikineev
// 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)
//
// Computes test data for the derivatives of the
// various bessel functions. Results of derivatives
// are generated by the relations between the derivatives
// and Bessel functions, which actual implementation
// doesn't use. Results are printed to ~ 50 digits.
//
#include <fstream>
#include <boost/multiprecision/mpfr.hpp>
#include <boost/math/tools/test_data.hpp>
#include <boost/test/included/prg_exec_monitor.hpp>
#include <boost/math/special_functions/bessel.hpp>
using namespace boost::math::tools;
using namespace boost::math;
using namespace std;
using namespace boost::multiprecision;
template <class T>
T bessel_j_derivative_bare(T v, T x)
{
return (v / x) * boost::math::cyl_bessel_j(v, x) - boost::math::cyl_bessel_j(v+1, x);
}
template <class T>
T bessel_y_derivative_bare(T v, T x)
{
return (v / x) * boost::math::cyl_neumann(v, x) - boost::math::cyl_neumann(v+1, x);
}
template <class T>
T bessel_i_derivative_bare(T v, T x)
{
if ((x < 1) && (x > 0))
return (boost::math::cyl_bessel_i(v - 1, x) + boost::math::cyl_bessel_i(v + 1, x)) / 2;
if (x == 0)
throw std::domain_error("");
return (boost::math::cyl_bessel_i(v - 1, x) + boost::math::cyl_bessel_i(v + 1, x)) / 2;
}
template <class T>
T bessel_k_derivative_bare(T v, T x)
{
return (v / x) * boost::math::cyl_bessel_k(v, x) - boost::math::cyl_bessel_k(v+1, x);
}
template <class T>
T sph_bessel_j_derivative_bare(T v, T x)
{
if((v < 0) || (floor(v) != v))
throw std::domain_error("");
if(v == 0)
return -boost::math::sph_bessel(1, x);
return boost::math::sph_bessel(itrunc(v-1), x) - ((v + 1) / x) * boost::math::sph_bessel(itrunc(v), x);
}
template <class T>
T sph_bessel_y_derivative_bare(T v, T x)
{
if((v < 0) || (floor(v) != v))
throw std::domain_error("");
if(v == 0)
return -boost::math::sph_neumann(1, x);
return boost::math::sph_neumann(itrunc(v-1), x) - ((v + 1) / x) * boost::math::sph_neumann(itrunc(v), x);
}
enum
{
func_J = 0,
func_Y,
func_I,
func_K,
func_j,
func_y
};
int cpp_main(int argc, char*argv [])
{
typedef number<mpfr_float_backend<500> > bignum;
parameter_info<bignum> arg1, arg2;
test_data<bignum> data;
int functype = 0;
std::string letter = "J";
if(argc == 2)
{
if(std::strcmp(argv[1], "--Y") == 0)
{
functype = func_Y;
letter = "Y";
}
else if(std::strcmp(argv[1], "--I") == 0)
{
functype = func_I;
letter = "I";
}
else if(std::strcmp(argv[1], "--K") == 0)
{
functype = func_K;
letter = "K";
}
else if(std::strcmp(argv[1], "--j") == 0)
{
functype = func_j;
letter = "j";
}
else if(std::strcmp(argv[1], "--y") == 0)
{
functype = func_y;
letter = "y";
}
else
BOOST_MATH_ASSERT(0);
}
bool cont;
std::string line;
std::cout << "Welcome.\n"
"This program will generate spot tests for the Bessel " << letter << " function derivative\n\n";
do{
if(0 == get_user_parameter_info(arg1, "x"))
return 1;
if(0 == get_user_parameter_info(arg2, "v"))
return 1;
bignum (*fp)(bignum, bignum) = 0;
if(functype == func_J)
fp = bessel_j_derivative_bare;
else if(functype == func_I)
fp = bessel_i_derivative_bare;
else if(functype == func_K)
fp = bessel_k_derivative_bare;
else if(functype == func_Y)
fp = bessel_y_derivative_bare;
else if(functype == func_j)
fp = sph_bessel_j_derivative_bare;
else if(functype == func_y)
fp = sph_bessel_y_derivative_bare;
else
BOOST_MATH_ASSERT(0);
data.insert(fp, arg2, arg1);
std::cout << "Any more data [y/n]?";
std::getline(std::cin, line);
boost::algorithm::trim(line);
cont = (line == "y");
}while(cont);
std::cout << "Enter name of test data file [default=bessel_j_derivative_data.ipp]";
std::getline(std::cin, line);
boost::algorithm::trim(line);
if(line == "")
line = "bessel_j_derivative_data.ipp";
std::ofstream ofs(line.c_str());
line.erase(line.find('.'));
ofs << std::scientific << std::setprecision(50);
write_code(ofs, data, line.c_str());
return 0;
}
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