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101 lines
3.3 KiB
101 lines
3.3 KiB
// Copyright (c) 2006 Xiaogang Zhang |
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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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#ifndef BOOST_MATH_BESSEL_I0_HPP |
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#define BOOST_MATH_BESSEL_I0_HPP |
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#ifdef _MSC_VER |
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#pragma once |
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#endif |
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#include <boost/math/tools/rational.hpp> |
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#include <boost/assert.hpp> |
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// Modified Bessel function of the first kind of order zero |
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// minimax rational approximations on intervals, see |
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// Blair and Edwards, Chalk River Report AECL-4928, 1974 |
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namespace boost { namespace math { namespace detail{ |
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template <typename T> |
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T bessel_i0(T x) |
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{ |
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static const T P1[] = { |
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static_cast<T>(-2.2335582639474375249e+15L), |
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static_cast<T>(-5.5050369673018427753e+14L), |
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static_cast<T>(-3.2940087627407749166e+13L), |
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static_cast<T>(-8.4925101247114157499e+11L), |
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static_cast<T>(-1.1912746104985237192e+10L), |
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static_cast<T>(-1.0313066708737980747e+08L), |
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static_cast<T>(-5.9545626019847898221e+05L), |
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static_cast<T>(-2.4125195876041896775e+03L), |
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static_cast<T>(-7.0935347449210549190e+00L), |
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static_cast<T>(-1.5453977791786851041e-02L), |
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static_cast<T>(-2.5172644670688975051e-05L), |
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static_cast<T>(-3.0517226450451067446e-08L), |
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static_cast<T>(-2.6843448573468483278e-11L), |
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static_cast<T>(-1.5982226675653184646e-14L), |
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static_cast<T>(-5.2487866627945699800e-18L), |
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}; |
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static const T Q1[] = { |
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static_cast<T>(-2.2335582639474375245e+15L), |
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static_cast<T>(7.8858692566751002988e+12L), |
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static_cast<T>(-1.2207067397808979846e+10L), |
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static_cast<T>(1.0377081058062166144e+07L), |
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static_cast<T>(-4.8527560179962773045e+03L), |
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static_cast<T>(1.0L), |
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}; |
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static const T P2[] = { |
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static_cast<T>(-2.2210262233306573296e-04L), |
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static_cast<T>(1.3067392038106924055e-02L), |
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static_cast<T>(-4.4700805721174453923e-01L), |
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static_cast<T>(5.5674518371240761397e+00L), |
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static_cast<T>(-2.3517945679239481621e+01L), |
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static_cast<T>(3.1611322818701131207e+01L), |
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static_cast<T>(-9.6090021968656180000e+00L), |
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}; |
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static const T Q2[] = { |
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static_cast<T>(-5.5194330231005480228e-04L), |
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static_cast<T>(3.2547697594819615062e-02L), |
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static_cast<T>(-1.1151759188741312645e+00L), |
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static_cast<T>(1.3982595353892851542e+01L), |
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static_cast<T>(-6.0228002066743340583e+01L), |
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static_cast<T>(8.5539563258012929600e+01L), |
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static_cast<T>(-3.1446690275135491500e+01L), |
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static_cast<T>(1.0L), |
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}; |
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T value, factor, r; |
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BOOST_MATH_STD_USING |
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using namespace boost::math::tools; |
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if (x < 0) |
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{ |
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x = -x; // even function |
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} |
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if (x == 0) |
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{ |
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return static_cast<T>(1); |
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} |
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if (x <= 15) // x in (0, 15] |
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{ |
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T y = x * x; |
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value = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y); |
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} |
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else // x in (15, \infty) |
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{ |
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T y = 1 / x - T(1) / 15; |
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r = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y); |
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factor = exp(x) / sqrt(x); |
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value = factor * r; |
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} |
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return value; |
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} |
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}}} // namespaces |
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#endif // BOOST_MATH_BESSEL_I0_HPP |
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