--- /dev/null
+// 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)
+//
+// History:
+// XZ wrote the original of this file as part of the Google
+// Summer of Code 2006. JM modified it to fit into the
+// Boost.Math conceptual framework better, and to correctly
+// handle the p < 0 case.
+//
+
+#ifndef BOOST_MATH_ELLINT_RJ_HPP
+#define BOOST_MATH_ELLINT_RJ_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/math/special_functions/math_fwd.hpp>
+#include <boost/math/tools/config.hpp>
+#include <boost/math/policies/error_handling.hpp>
+#include <boost/math/special_functions/ellint_rc.hpp>
+#include <boost/math/special_functions/ellint_rf.hpp>
+
+// Carlson's elliptic integral of the third kind
+// R_J(x, y, z, p) = 1.5 * \int_{0}^{\infty} (t+p)^{-1} [(t+x)(t+y)(t+z)]^{-1/2} dt
+// Carlson, Numerische Mathematik, vol 33, 1 (1979)
+
+namespace boost { namespace math { namespace detail{
+
+template <typename T, typename Policy>
+T ellint_rj_imp(T x, T y, T z, T p, const Policy& pol)
+{
+ T value, u, lambda, alpha, beta, sigma, factor, tolerance;
+ T X, Y, Z, P, EA, EB, EC, E2, E3, S1, S2, S3;
+ unsigned long k;
+
+ BOOST_MATH_STD_USING
+ using namespace boost::math::tools;
+
+ static const char* function = "boost::math::ellint_rj<%1%>(%1%,%1%,%1%)";
+
+ if (x < 0)
+ {
+ return policies::raise_domain_error<T>(function,
+ "Argument x must be non-negative, but got x = %1%", x, pol);
+ }
+ if(y < 0)
+ {
+ return policies::raise_domain_error<T>(function,
+ "Argument y must be non-negative, but got y = %1%", y, pol);
+ }
+ if(z < 0)
+ {
+ return policies::raise_domain_error<T>(function,
+ "Argument z must be non-negative, but got z = %1%", z, pol);
+ }
+ if(p == 0)
+ {
+ return policies::raise_domain_error<T>(function,
+ "Argument p must not be zero, but got p = %1%", p, pol);
+ }
+ if (x + y == 0 || y + z == 0 || z + x == 0)
+ {
+ return policies::raise_domain_error<T>(function,
+ "At most one argument can be zero, "
+ "only possible result is %1%.", std::numeric_limits<T>::quiet_NaN(), pol);
+ }
+
+ // error scales as the 6th power of tolerance
+ tolerance = pow(T(1) * tools::epsilon<T>() / 3, T(1) / 6);
+
+ // for p < 0, the integral is singular, return Cauchy principal value
+ if (p < 0)
+ {
+ //
+ // We must ensure that (z - y) * (y - x) is positive.
+ // Since the integral is symmetrical in x, y and z
+ // we can just permute the values:
+ //
+ if(x > y)
+ std::swap(x, y);
+ if(y > z)
+ std::swap(y, z);
+ if(x > y)
+ std::swap(x, y);
+
+ T q = -p;
+ T pmy = (z - y) * (y - x) / (y + q); // p - y
+
+ BOOST_ASSERT(pmy >= 0);
+
+ p = pmy + y;
+ value = boost::math::ellint_rj(x, y, z, p, pol);
+ value *= pmy;
+ value -= 3 * boost::math::ellint_rf(x, y, z, pol);
+ value += 3 * sqrt((x * y * z) / (x * z + p * q)) * boost::math::ellint_rc(x * z + p * q, p * q, pol);
+ value /= (y + q);
+ return value;
+ }
+
+ // duplication
+ sigma = 0;
+ factor = 1;
+ k = 1;
+ do
+ {
+ u = (x + y + z + p + p) / 5;
+ X = (u - x) / u;
+ Y = (u - y) / u;
+ Z = (u - z) / u;
+ P = (u - p) / u;
+
+ if ((tools::max)(abs(X), abs(Y), abs(Z), abs(P)) < tolerance)
+ break;
+
+ T sx = sqrt(x);
+ T sy = sqrt(y);
+ T sz = sqrt(z);
+
+ lambda = sy * (sx + sz) + sz * sx;
+ alpha = p * (sx + sy + sz) + sx * sy * sz;
+ alpha *= alpha;
+ beta = p * (p + lambda) * (p + lambda);
+ sigma += factor * boost::math::ellint_rc(alpha, beta, pol);
+ factor /= 4;
+ x = (x + lambda) / 4;
+ y = (y + lambda) / 4;
+ z = (z + lambda) / 4;
+ p = (p + lambda) / 4;
+ ++k;
+ }
+ while(k < policies::get_max_series_iterations<Policy>());
+
+ // Check to see if we gave up too soon:
+ policies::check_series_iterations<T>(function, k, pol);
+
+ // Taylor series expansion to the 5th order
+ EA = X * Y + Y * Z + Z * X;
+ EB = X * Y * Z;
+ EC = P * P;
+ E2 = EA - 3 * EC;
+ E3 = EB + 2 * P * (EA - EC);
+ S1 = 1 + E2 * (E2 * T(9) / 88 - E3 * T(9) / 52 - T(3) / 14);
+ S2 = EB * (T(1) / 6 + P * (T(-6) / 22 + P * T(3) / 26));
+ S3 = P * ((EA - EC) / 3 - P * EA * T(3) / 22);
+ value = 3 * sigma + factor * (S1 + S2 + S3) / (u * sqrt(u));
+
+ return value;
+}
+
+} // namespace detail
+
+template <class T1, class T2, class T3, class T4, class Policy>
+inline typename tools::promote_args<T1, T2, T3, T4>::type
+ ellint_rj(T1 x, T2 y, T3 z, T4 p, const Policy& pol)
+{
+ typedef typename tools::promote_args<T1, T2, T3, T4>::type result_type;
+ typedef typename policies::evaluation<result_type, Policy>::type value_type;
+ return policies::checked_narrowing_cast<result_type, Policy>(
+ detail::ellint_rj_imp(
+ static_cast<value_type>(x),
+ static_cast<value_type>(y),
+ static_cast<value_type>(z),
+ static_cast<value_type>(p),
+ pol), "boost::math::ellint_rj<%1%>(%1%,%1%,%1%,%1%)");
+}
+
+template <class T1, class T2, class T3, class T4>
+inline typename tools::promote_args<T1, T2, T3, T4>::type
+ ellint_rj(T1 x, T2 y, T3 z, T4 p)
+{
+ return ellint_rj(x, y, z, p, policies::policy<>());
+}
+
+}} // namespaces
+
+#endif // BOOST_MATH_ELLINT_RJ_HPP
+
projects / rsem.git / blobdiff