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///////////////////////////////////////////////////////////////////////////////
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// Copyright 2014 Anton Bikineev
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// Copyright 2014 Christopher Kormanyos
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// Copyright 2014 John Maddock
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// Copyright 2014 Paul Bristow
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// Distributed under the Boost
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// 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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//
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#ifndef BOOST_MATH_HYPERGEOMETRIC_PADE_HPP
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#define BOOST_MATH_HYPERGEOMETRIC_PADE_HPP
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namespace boost{ namespace math{ namespace detail{
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// Luke: C ---------- SUBROUTINE R1F1P(CP, Z, A, B, N) ----------
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// Luke: C ----- PADE APPROXIMATION OF 1F1( 1 ; CP ; -Z ) -------
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template <class T, class Policy>
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inline T hypergeometric_1F1_pade(const T& cp, const T& zp, const Policy& )
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{
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BOOST_MATH_STD_USING
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static const T one = T(1);
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// Luke: C ------------- INITIALIZATION -------------
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const T z = -zp;
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const T zz = z * z;
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T b0 = one;
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T a0 = one;
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T xi1 = one;
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T ct1 = cp + one;
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T cp1 = cp - one;
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T b1 = one + (z / ct1);
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T a1 = b1 - (z / cp);
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const unsigned max_iterations = boost::math::policies::get_max_series_iterations<Policy>();
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T b2 = T(0), a2 = T(0);
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T result = T(0), prev_result;
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for (unsigned k = 1; k < max_iterations; ++k)
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{
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// Luke: C ----- CALCULATION OF THE MULTIPLIERS -----
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// Luke: C ----------- FOR THE RECURSION ------------
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const T ct2 = ct1 * ct1;
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const T g1 = one + ((cp1 / (ct2 + ct1 + ct1)) * z);
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const T g2 = ((xi1 / (ct2 - one)) * ((xi1 + cp1) / ct2)) * zz;
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// Luke: C ------- THE RECURRENCE RELATIONS ---------
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// Luke: C ------------ ARE AS FOLLOWS --------------
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b2 = (g1 * b1) + (g2 * b0);
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a2 = (g1 * a1) + (g2 * a0);
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prev_result = result;
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result = a2 / b2;
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// condition for interruption
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if ((fabs(result) * boost::math::tools::epsilon<T>()) > fabs(result - prev_result))
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break;
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b0 = b1; b1 = b2;
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a0 = a1; a1 = a2;
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ct1 += 2;
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xi1 += 1;
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}
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return a2 / b2;
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}
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// Luke: C -------- SUBROUTINE R2F1P(BP, CP, Z, A, B, N) --------
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// Luke: C ---- PADE APPROXIMATION OF 2F1( 1 , BP; CP ; -Z ) ----
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template <class T, class Policy>
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inline T hypergeometric_2F1_pade(const T& bp, const T& cp, const T& zp, const Policy& pol)
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{
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BOOST_MATH_STD_USING
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static const T one = T(1);
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// Luke: C ---------- INITIALIZATION -----------
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const T z = -zp;
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const T zz = z * z;
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T b0 = one;
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T a0 = one;
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T xi1 = one;
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T ct1 = cp;
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const T b1c1 = (cp - one) * (bp - one);
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T b1 = one + ((z / (cp + one)) * (bp + one));
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T a1 = b1 - ((bp / cp) * z);
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const unsigned max_iterations = boost::math::policies::get_max_series_iterations<Policy>();
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T b2 = T(0), a2 = T(0);
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T result = T(0), prev_result = a1 / b1;
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for (unsigned k = 1; k < max_iterations; ++k)
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{
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// Luke: C ----- CALCULATION OF THE MULTIPLIERS -----
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// Luke: C ----------- FOR THE RECURSION ------------
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const T ct2 = ct1 + xi1;
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const T ct3 = ct2 * ct2;
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const T g2 = (((((ct1 / ct3) * (bp - ct1)) / (ct3 - one)) * xi1) * (bp + xi1)) * zz;
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++xi1;
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const T g1 = one + (((((xi1 + xi1) * ct1) + b1c1) / (ct3 + ct2 + ct2)) * z);
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// Luke: C ------- THE RECURRENCE RELATIONS ---------
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// Luke: C ------------ ARE AS FOLLOWS --------------
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b2 = (g1 * b1) + (g2 * b0);
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a2 = (g1 * a1) + (g2 * a0);
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prev_result = result;
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result = a2 / b2;
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// condition for interruption
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if ((fabs(result) * boost::math::tools::epsilon<T>()) > fabs(result - prev_result))
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break;
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b0 = b1; b1 = b2;
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a0 = a1; a1 = a2;
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++ct1;
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}
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return a2 / b2;
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}
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} } } // namespaces
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#endif // BOOST_MATH_HYPERGEOMETRIC_PADE_HPP
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