// Copyright (c) 2006 Xiaogang Zhang | |
// 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) | |
#ifndef BOOST_MATH_BESSEL_K1_HPP | |
#define BOOST_MATH_BESSEL_K1_HPP | |
#ifdef _MSC_VER | |
#pragma once | |
#endif | |
#include <boost/math/tools/rational.hpp> | |
#include <boost/math/policies/error_handling.hpp> | |
#include <boost/assert.hpp> | |
// Modified Bessel function of the second kind of order one | |
// minimax rational approximations on intervals, see | |
// Russon and Blair, Chalk River Report AECL-3461, 1969 | |
namespace boost { namespace math { namespace detail{ | |
template <typename T, typename Policy> | |
T bessel_k1(T x, const Policy& pol) | |
{ | |
static const T P1[] = { | |
static_cast<T>(-2.2149374878243304548e+06L), | |
static_cast<T>(7.1938920065420586101e+05L), | |
static_cast<T>(1.7733324035147015630e+05L), | |
static_cast<T>(7.1885382604084798576e+03L), | |
static_cast<T>(9.9991373567429309922e+01L), | |
static_cast<T>(4.8127070456878442310e-01L) | |
}; | |
static const T Q1[] = { | |
static_cast<T>(-2.2149374878243304548e+06L), | |
static_cast<T>(3.7264298672067697862e+04L), | |
static_cast<T>(-2.8143915754538725829e+02L), | |
static_cast<T>(1.0L) | |
}; | |
static const T P2[] = { | |
static_cast<T>(0.0L), | |
static_cast<T>(-1.3531161492785421328e+06L), | |
static_cast<T>(-1.4758069205414222471e+05L), | |
static_cast<T>(-4.5051623763436087023e+03L), | |
static_cast<T>(-5.3103913335180275253e+01L), | |
static_cast<T>(-2.2795590826955002390e-01L) | |
}; | |
static const T Q2[] = { | |
static_cast<T>(-2.7062322985570842656e+06L), | |
static_cast<T>(4.3117653211351080007e+04L), | |
static_cast<T>(-3.0507151578787595807e+02L), | |
static_cast<T>(1.0L) | |
}; | |
static const T P3[] = { | |
static_cast<T>(2.2196792496874548962e+00L), | |
static_cast<T>(4.4137176114230414036e+01L), | |
static_cast<T>(3.4122953486801312910e+02L), | |
static_cast<T>(1.3319486433183221990e+03L), | |
static_cast<T>(2.8590657697910288226e+03L), | |
static_cast<T>(3.4540675585544584407e+03L), | |
static_cast<T>(2.3123742209168871550e+03L), | |
static_cast<T>(8.1094256146537402173e+02L), | |
static_cast<T>(1.3182609918569941308e+02L), | |
static_cast<T>(7.5584584631176030810e+00L), | |
static_cast<T>(6.4257745859173138767e-02L) | |
}; | |
static const T Q3[] = { | |
static_cast<T>(1.7710478032601086579e+00L), | |
static_cast<T>(3.4552228452758912848e+01L), | |
static_cast<T>(2.5951223655579051357e+02L), | |
static_cast<T>(9.6929165726802648634e+02L), | |
static_cast<T>(1.9448440788918006154e+03L), | |
static_cast<T>(2.1181000487171943810e+03L), | |
static_cast<T>(1.2082692316002348638e+03L), | |
static_cast<T>(3.3031020088765390854e+02L), | |
static_cast<T>(3.6001069306861518855e+01L), | |
static_cast<T>(1.0L) | |
}; | |
T value, factor, r, r1, r2; | |
BOOST_MATH_STD_USING | |
using namespace boost::math::tools; | |
static const char* function = "boost::math::bessel_k1<%1%>(%1%,%1%)"; | |
if (x < 0) | |
{ | |
return policies::raise_domain_error<T>(function, | |
"Got x = %1%, but argument x must be non-negative, complex number result not supported.", x, pol); | |
} | |
if (x == 0) | |
{ | |
return policies::raise_overflow_error<T>(function, 0, pol); | |
} | |
if (x <= 1) // x in (0, 1] | |
{ | |
T y = x * x; | |
r1 = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y); | |
r2 = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y); | |
factor = log(x); | |
value = (r1 + factor * r2) / x; | |
} | |
else // x in (1, \infty) | |
{ | |
T y = 1 / x; | |
r = evaluate_polynomial(P3, y) / evaluate_polynomial(Q3, y); | |
factor = exp(-x) / sqrt(x); | |
value = factor * r; | |
} | |
return value; | |
} | |
}}} // namespaces | |
#endif // BOOST_MATH_BESSEL_K1_HPP | |