mirror of
https://github.com/saitohirga/WSJT-X.git
synced 2025-11-03 21:40:52 -05:00
631 lines
18 KiB
C++
631 lines
18 KiB
C++
// Copyright John Maddock 2006.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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#include <boost/math/tools/test_data.hpp>
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#include <boost/test/included/prg_exec_monitor.hpp>
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#include <boost/math/special_functions/ellint_rj.hpp>
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#include <boost/math/special_functions/ellint_rd.hpp>
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#include <fstream>
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#include <boost/math/tools/test_data.hpp>
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#include <boost/random.hpp>
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#include "mp_t.hpp"
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float extern_val;
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// confuse the compilers optimiser, and force a truncation to float precision:
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float truncate_to_float(float const * pf)
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{
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extern_val = *pf;
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return *pf;
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}
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//
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// Archived here is the original implementation of this
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// function by Xiaogang Zhang, we can use this to
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// generate special test cases for the new version:
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//
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template <typename T, typename Policy>
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T ellint_rj_old(T x, T y, T z, T p, const Policy& pol)
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{
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T value, u, lambda, alpha, beta, sigma, factor, tolerance;
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T X, Y, Z, P, EA, EB, EC, E2, E3, S1, S2, S3;
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unsigned long k;
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BOOST_MATH_STD_USING
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using namespace boost::math;
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static const char* function = "boost::math::ellint_rj<%1%>(%1%,%1%,%1%)";
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if(x < 0)
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{
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return policies::raise_domain_error<T>(function,
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"Argument x must be non-negative, but got x = %1%", x, pol);
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}
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if(y < 0)
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{
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return policies::raise_domain_error<T>(function,
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"Argument y must be non-negative, but got y = %1%", y, pol);
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}
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if(z < 0)
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{
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return policies::raise_domain_error<T>(function,
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"Argument z must be non-negative, but got z = %1%", z, pol);
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}
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if(p == 0)
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{
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return policies::raise_domain_error<T>(function,
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"Argument p must not be zero, but got p = %1%", p, pol);
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}
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if(x + y == 0 || y + z == 0 || z + x == 0)
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{
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return policies::raise_domain_error<T>(function,
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"At most one argument can be zero, "
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"only possible result is %1%.", std::numeric_limits<T>::quiet_NaN(), pol);
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}
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// error scales as the 6th power of tolerance
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tolerance = pow(T(1) * tools::epsilon<T>() / 3, T(1) / 6);
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// for p < 0, the integral is singular, return Cauchy principal value
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if(p < 0)
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{
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//
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// We must ensure that (z - y) * (y - x) is positive.
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// Since the integral is symmetrical in x, y and z
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// we can just permute the values:
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//
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if(x > y)
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std::swap(x, y);
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if(y > z)
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std::swap(y, z);
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if(x > y)
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std::swap(x, y);
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T q = -p;
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T pmy = (z - y) * (y - x) / (y + q); // p - y
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BOOST_ASSERT(pmy >= 0);
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p = pmy + y;
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value = ellint_rj_old(x, y, z, p, pol);
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value *= pmy;
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value -= 3 * boost::math::ellint_rf(x, y, z, pol);
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value += 3 * sqrt((x * y * z) / (x * z + p * q)) * boost::math::ellint_rc(x * z + p * q, p * q, pol);
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value /= (y + q);
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return value;
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}
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// duplication
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sigma = 0;
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factor = 1;
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k = 1;
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do
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{
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u = (x + y + z + p + p) / 5;
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X = (u - x) / u;
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Y = (u - y) / u;
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Z = (u - z) / u;
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P = (u - p) / u;
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if((tools::max)(abs(X), abs(Y), abs(Z), abs(P)) < tolerance)
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break;
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T sx = sqrt(x);
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T sy = sqrt(y);
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T sz = sqrt(z);
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lambda = sy * (sx + sz) + sz * sx;
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alpha = p * (sx + sy + sz) + sx * sy * sz;
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alpha *= alpha;
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beta = p * (p + lambda) * (p + lambda);
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sigma += factor * boost::math::ellint_rc(alpha, beta, pol);
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factor /= 4;
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x = (x + lambda) / 4;
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y = (y + lambda) / 4;
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z = (z + lambda) / 4;
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p = (p + lambda) / 4;
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++k;
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} while(k < policies::get_max_series_iterations<Policy>());
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// Check to see if we gave up too soon:
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policies::check_series_iterations<T>(function, k, pol);
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// Taylor series expansion to the 5th order
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EA = X * Y + Y * Z + Z * X;
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EB = X * Y * Z;
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EC = P * P;
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E2 = EA - 3 * EC;
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E3 = EB + 2 * P * (EA - EC);
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S1 = 1 + E2 * (E2 * T(9) / 88 - E3 * T(9) / 52 - T(3) / 14);
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S2 = EB * (T(1) / 6 + P * (T(-6) / 22 + P * T(3) / 26));
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S3 = P * ((EA - EC) / 3 - P * EA * T(3) / 22);
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value = 3 * sigma + factor * (S1 + S2 + S3) / (u * sqrt(u));
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return value;
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}
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template <typename T, typename Policy>
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T ellint_rd_imp_old(T x, T y, T z, const Policy& pol)
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{
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T value, u, lambda, sigma, factor, tolerance;
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T X, Y, Z, EA, EB, EC, ED, EE, S1, S2;
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unsigned long k;
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BOOST_MATH_STD_USING
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using namespace boost::math;
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static const char* function = "boost::math::ellint_rd<%1%>(%1%,%1%,%1%)";
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if(x < 0)
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{
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return policies::raise_domain_error<T>(function,
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"Argument x must be >= 0, but got %1%", x, pol);
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}
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if(y < 0)
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{
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return policies::raise_domain_error<T>(function,
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"Argument y must be >= 0, but got %1%", y, pol);
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}
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if(z <= 0)
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{
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return policies::raise_domain_error<T>(function,
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"Argument z must be > 0, but got %1%", z, pol);
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}
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if(x + y == 0)
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{
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return policies::raise_domain_error<T>(function,
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"At most one argument can be zero, but got, x + y = %1%", x + y, pol);
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}
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// error scales as the 6th power of tolerance
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tolerance = pow(tools::epsilon<T>() / 3, T(1) / 6);
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// duplication
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sigma = 0;
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factor = 1;
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k = 1;
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do
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{
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u = (x + y + z + z + z) / 5;
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X = (u - x) / u;
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Y = (u - y) / u;
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Z = (u - z) / u;
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if((tools::max)(abs(X), abs(Y), abs(Z)) < tolerance)
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break;
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T sx = sqrt(x);
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T sy = sqrt(y);
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T sz = sqrt(z);
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lambda = sy * (sx + sz) + sz * sx; //sqrt(x * y) + sqrt(y * z) + sqrt(z * x);
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sigma += factor / (sz * (z + lambda));
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factor /= 4;
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x = (x + lambda) / 4;
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y = (y + lambda) / 4;
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z = (z + lambda) / 4;
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++k;
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} while(k < policies::get_max_series_iterations<Policy>());
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// Check to see if we gave up too soon:
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policies::check_series_iterations<T>(function, k, pol);
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// Taylor series expansion to the 5th order
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EA = X * Y;
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EB = Z * Z;
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EC = EA - EB;
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ED = EA - 6 * EB;
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EE = ED + EC + EC;
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S1 = ED * (ED * T(9) / 88 - Z * EE * T(9) / 52 - T(3) / 14);
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S2 = Z * (EE / 6 + Z * (-EC * T(9) / 22 + Z * EA * T(3) / 26));
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value = 3 * sigma + factor * (1 + S1 + S2) / (u * sqrt(u));
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return value;
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}
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template <typename T, typename Policy>
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T ellint_rf_imp_old(T x, T y, T z, const Policy& pol)
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{
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T value, X, Y, Z, E2, E3, u, lambda, tolerance;
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unsigned long k;
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BOOST_MATH_STD_USING
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using namespace boost::math;
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static const char* function = "boost::math::ellint_rf<%1%>(%1%,%1%,%1%)";
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if(x < 0 || y < 0 || z < 0)
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{
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return policies::raise_domain_error<T>(function,
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"domain error, all arguments must be non-negative, "
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"only sensible result is %1%.",
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std::numeric_limits<T>::quiet_NaN(), pol);
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}
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if(x + y == 0 || y + z == 0 || z + x == 0)
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{
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return policies::raise_domain_error<T>(function,
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"domain error, at most one argument can be zero, "
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"only sensible result is %1%.",
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std::numeric_limits<T>::quiet_NaN(), pol);
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}
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// Carlson scales error as the 6th power of tolerance,
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// but this seems not to work for types larger than
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// 80-bit reals, this heuristic seems to work OK:
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if(policies::digits<T, Policy>() > 64)
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{
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tolerance = pow(tools::epsilon<T>(), T(1) / 4.25f);
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BOOST_MATH_INSTRUMENT_VARIABLE(tolerance);
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}
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else
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{
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tolerance = pow(4 * tools::epsilon<T>(), T(1) / 6);
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BOOST_MATH_INSTRUMENT_VARIABLE(tolerance);
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}
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// duplication
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k = 1;
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do
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{
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u = (x + y + z) / 3;
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X = (u - x) / u;
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Y = (u - y) / u;
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Z = (u - z) / u;
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// Termination condition:
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if((tools::max)(abs(X), abs(Y), abs(Z)) < tolerance)
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break;
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T sx = sqrt(x);
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T sy = sqrt(y);
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T sz = sqrt(z);
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lambda = sy * (sx + sz) + sz * sx;
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x = (x + lambda) / 4;
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y = (y + lambda) / 4;
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z = (z + lambda) / 4;
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++k;
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} while(k < policies::get_max_series_iterations<Policy>());
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// Check to see if we gave up too soon:
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policies::check_series_iterations<T>(function, k, pol);
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BOOST_MATH_INSTRUMENT_VARIABLE(k);
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// Taylor series expansion to the 5th order
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E2 = X * Y - Z * Z;
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E3 = X * Y * Z;
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value = (1 + E2*(E2 / 24 - E3*T(3) / 44 - T(0.1)) + E3 / 14) / sqrt(u);
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BOOST_MATH_INSTRUMENT_VARIABLE(value);
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return value;
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rj_data_4e(mp_t n)
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{
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mp_t result = ellint_rj_old(n, n, n, n, boost::math::policies::policy<>());
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return boost::math::make_tuple(n, n, n, result);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t> generate_rj_data_3e(mp_t x, mp_t p)
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{
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mp_t r = ellint_rj_old(x, x, x, p, boost::math::policies::policy<>());
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return boost::math::make_tuple(x, x, x, p, r);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t> generate_rj_data_2e_1(mp_t x, mp_t y, mp_t p)
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{
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mp_t r = ellint_rj_old(x, x, y, p, boost::math::policies::policy<>());
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return boost::math::make_tuple(x, x, y, p, r);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t> generate_rj_data_2e_2(mp_t x, mp_t y, mp_t p)
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{
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mp_t r = ellint_rj_old(x, y, x, p, boost::math::policies::policy<>());
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return boost::math::make_tuple(x, y, x, p, r);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t> generate_rj_data_2e_3(mp_t x, mp_t y, mp_t p)
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{
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mp_t r = ellint_rj_old(y, x, x, p, boost::math::policies::policy<>());
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return boost::math::make_tuple(y, x, x, p, r);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t> generate_rj_data_2e_4(mp_t x, mp_t y, mp_t p)
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{
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mp_t r = ellint_rj_old(x, y, p, p, boost::math::policies::policy<>());
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return boost::math::make_tuple(x, y, p, p, r);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rd_data_2e_1(mp_t x, mp_t y)
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{
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mp_t r = ellint_rd_imp_old(x, y, y, boost::math::policies::policy<>());
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return boost::math::make_tuple(x, y, y, r);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rd_data_2e_2(mp_t x, mp_t y)
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{
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mp_t r = ellint_rd_imp_old(x, x, y, boost::math::policies::policy<>());
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return boost::math::make_tuple(x, x, y, r);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rd_data_2e_3(mp_t x)
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{
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mp_t r = ellint_rd_imp_old(mp_t(0), x, x, boost::math::policies::policy<>());
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return boost::math::make_tuple(0, x, x, r);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rd_data_3e(mp_t x)
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{
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mp_t r = ellint_rd_imp_old(x, x, x, boost::math::policies::policy<>());
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return boost::math::make_tuple(x, x, x, r);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rd_data_0xy(mp_t x, mp_t y)
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{
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mp_t r = ellint_rd_imp_old(mp_t(0), x, y, boost::math::policies::policy<>());
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return boost::math::make_tuple(mp_t(0), x, y, r);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rf_data_xxx(mp_t x)
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{
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mp_t r = ellint_rf_imp_old(x, x, x, boost::math::policies::policy<>());
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return boost::math::make_tuple(x, x, x, r);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rf_data_xyy(mp_t x, mp_t y)
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{
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mp_t r = ellint_rf_imp_old(x, y, y, boost::math::policies::policy<>());
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return boost::math::make_tuple(x, y, y, r);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rf_data_xxy(mp_t x, mp_t y)
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{
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mp_t r = ellint_rf_imp_old(x, x, y, boost::math::policies::policy<>());
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return boost::math::make_tuple(x, x, y, r);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rf_data_xyx(mp_t x, mp_t y)
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{
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mp_t r = ellint_rf_imp_old(x, y, x, boost::math::policies::policy<>());
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return boost::math::make_tuple(x, y, x, r);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rf_data_0yy(mp_t y)
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{
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mp_t r = ellint_rf_imp_old(mp_t(0), y, y, boost::math::policies::policy<>());
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return boost::math::make_tuple(mp_t(0), y, y, r);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rf_data_xy0(mp_t x, mp_t y)
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{
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mp_t r = ellint_rf_imp_old(x, y, mp_t(0), boost::math::policies::policy<>());
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return boost::math::make_tuple(x, y, mp_t(0), r);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rf_data(mp_t n)
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{
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static boost::mt19937 r;
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boost::uniform_real<float> ur(0, 1);
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boost::uniform_int<int> ui(-100, 100);
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float x = ur(r);
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x = ldexp(x, ui(r));
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mp_t xr(truncate_to_float(&x));
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float y = ur(r);
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y = ldexp(y, ui(r));
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mp_t yr(truncate_to_float(&y));
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float z = ur(r);
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z = ldexp(z, ui(r));
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mp_t zr(truncate_to_float(&z));
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mp_t result = boost::math::ellint_rf(xr, yr, zr);
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return boost::math::make_tuple(xr, yr, zr, result);
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}
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boost::math::tuple<mp_t, mp_t, mp_t> generate_rc_data(mp_t n)
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{
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static boost::mt19937 r;
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boost::uniform_real<float> ur(0, 1);
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boost::uniform_int<int> ui(-100, 100);
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float x = ur(r);
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x = ldexp(x, ui(r));
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mp_t xr(truncate_to_float(&x));
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float y = ur(r);
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y = ldexp(y, ui(r));
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mp_t yr(truncate_to_float(&y));
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mp_t result = boost::math::ellint_rc(xr, yr);
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return boost::math::make_tuple(xr, yr, result);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t, mp_t> generate_rj_data(mp_t n)
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{
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static boost::mt19937 r;
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boost::uniform_real<float> ur(0, 1);
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boost::uniform_real<float> nur(-1, 1);
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boost::uniform_int<int> ui(-100, 100);
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float x = ur(r);
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x = ldexp(x, ui(r));
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mp_t xr(truncate_to_float(&x));
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float y = ur(r);
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y = ldexp(y, ui(r));
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mp_t yr(truncate_to_float(&y));
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float z = ur(r);
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z = ldexp(z, ui(r));
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mp_t zr(truncate_to_float(&z));
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float p = nur(r);
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p = ldexp(p, ui(r));
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mp_t pr(truncate_to_float(&p));
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boost::math::ellint_rj(x, y, z, p);
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mp_t result = boost::math::ellint_rj(xr, yr, zr, pr);
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return boost::math::make_tuple(xr, yr, zr, pr, result);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rd_data(mp_t n)
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{
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static boost::mt19937 r;
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boost::uniform_real<float> ur(0, 1);
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boost::uniform_int<int> ui(-100, 100);
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float x = ur(r);
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x = ldexp(x, ui(r));
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mp_t xr(truncate_to_float(&x));
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float y = ur(r);
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y = ldexp(y, ui(r));
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mp_t yr(truncate_to_float(&y));
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float z = ur(r);
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z = ldexp(z, ui(r));
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mp_t zr(truncate_to_float(&z));
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mp_t result = boost::math::ellint_rd(xr, yr, zr);
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return boost::math::make_tuple(xr, yr, zr, result);
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}
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mp_t rg_imp(mp_t x, mp_t y, mp_t z)
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{
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using std::swap;
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// If z is zero permute so the call to RD is valid:
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if(z == 0)
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swap(x, z);
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return (z * ellint_rf_imp_old(x, y, z, boost::math::policies::policy<>())
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- (x - z) * (y - z) * ellint_rd_imp_old(x, y, z, boost::math::policies::policy<>()) / 3
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+ sqrt(x * y / z)) / 2;
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_data(mp_t n)
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{
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static boost::mt19937 r;
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boost::uniform_real<float> ur(0, 1);
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boost::uniform_int<int> ui(-100, 100);
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float x = ur(r);
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x = ldexp(x, ui(r));
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mp_t xr(truncate_to_float(&x));
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float y = ur(r);
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y = ldexp(y, ui(r));
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mp_t yr(truncate_to_float(&y));
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float z = ur(r);
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z = ldexp(z, ui(r));
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mp_t zr(truncate_to_float(&z));
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mp_t result = rg_imp(xr, yr, zr);
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return boost::math::make_tuple(xr, yr, zr, result);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_xxx(mp_t x)
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{
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mp_t result = rg_imp(x, x, x);
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return boost::math::make_tuple(x, x, x, result);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_xyy(mp_t x, mp_t y)
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{
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mp_t result = rg_imp(x, y, y);
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return boost::math::make_tuple(x, y, y, result);
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}
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|
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_xxy(mp_t x, mp_t y)
|
|
{
|
|
mp_t result = rg_imp(x, x, y);
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|
return boost::math::make_tuple(x, x, y, result);
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}
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_xyx(mp_t x, mp_t y)
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|
{
|
|
mp_t result = rg_imp(x, y, x);
|
|
return boost::math::make_tuple(x, y, x, result);
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|
}
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|
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_0xx(mp_t x)
|
|
{
|
|
mp_t result = rg_imp(mp_t(0), x, x);
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|
return boost::math::make_tuple(mp_t(0), x, x, result);
|
|
}
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|
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boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_x0x(mp_t x)
|
|
{
|
|
mp_t result = rg_imp(x, mp_t(0), x);
|
|
return boost::math::make_tuple(x, mp_t(0), x, result);
|
|
}
|
|
|
|
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_xx0(mp_t x)
|
|
{
|
|
mp_t result = rg_imp(x, x, mp_t(0));
|
|
return boost::math::make_tuple(x, x, mp_t(0), result);
|
|
}
|
|
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|
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_00x(mp_t x)
|
|
{
|
|
mp_t result = sqrt(x) / 2;
|
|
return boost::math::make_tuple(mp_t(0), mp_t(0), x, result);
|
|
}
|
|
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|
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_0x0(mp_t x)
|
|
{
|
|
mp_t result = sqrt(x) / 2;
|
|
return boost::math::make_tuple(mp_t(0), x, mp_t(0), result);
|
|
}
|
|
|
|
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_x00(mp_t x)
|
|
{
|
|
mp_t result = sqrt(x) / 2;
|
|
return boost::math::make_tuple(x, mp_t(0), mp_t(0), result);
|
|
}
|
|
|
|
boost::math::tuple<mp_t, mp_t, mp_t, mp_t> generate_rg_xy0(mp_t x, mp_t y)
|
|
{
|
|
mp_t result = rg_imp(x, y, mp_t(0));
|
|
return boost::math::make_tuple(x, y, mp_t(0), result);
|
|
}
|
|
|
|
int cpp_main(int argc, char*argv[])
|
|
{
|
|
using namespace boost::math::tools;
|
|
|
|
parameter_info<mp_t> arg1, arg2, arg3;
|
|
test_data<mp_t> data;
|
|
|
|
bool cont;
|
|
std::string line;
|
|
|
|
if(argc < 1)
|
|
return 1;
|
|
|
|
do{
|
|
#if 0
|
|
int count;
|
|
std::cout << "Number of points: ";
|
|
std::cin >> count;
|
|
|
|
arg1 = make_periodic_param(mp_t(0), mp_t(1), count);
|
|
arg1.type |= dummy_param;
|
|
|
|
//
|
|
// Change this next line to get the R variant you want:
|
|
//
|
|
data.insert(&generate_rd_data, arg1);
|
|
|
|
std::cout << "Any more data [y/n]?";
|
|
std::getline(std::cin, line);
|
|
boost::algorithm::trim(line);
|
|
cont = (line == "y");
|
|
#else
|
|
get_user_parameter_info(arg1, "x");
|
|
get_user_parameter_info(arg2, "y");
|
|
//get_user_parameter_info(arg3, "p");
|
|
arg1.type |= dummy_param;
|
|
arg2.type |= dummy_param;
|
|
//arg3.type |= dummy_param;
|
|
data.insert(generate_rd_data_0xy, arg1, arg2);
|
|
|
|
std::cout << "Any more data [y/n]?";
|
|
std::getline(std::cin, line);
|
|
boost::algorithm::trim(line);
|
|
cont = (line == "y");
|
|
#endif
|
|
}while(cont);
|
|
|
|
std::cout << "Enter name of test data file [default=ellint_rf_data.ipp]";
|
|
std::getline(std::cin, line);
|
|
boost::algorithm::trim(line);
|
|
if(line == "")
|
|
line = "ellint_rf_data.ipp";
|
|
std::ofstream ofs(line.c_str());
|
|
line.erase(line.find('.'));
|
|
ofs << std::scientific << std::setprecision(40);
|
|
write_code(ofs, data, line.c_str());
|
|
|
|
return 0;
|
|
}
|
|
|
|
|