mirror of
https://github.com/saitohirga/WSJT-X.git
synced 2025-11-03 21:40:52 -05:00
255 lines
9.7 KiB
C++
255 lines
9.7 KiB
C++
|
// Copyright John Maddock 2014
|
||
|
|
|
||
|
|
// 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)
|
||
|
|
|
||
|
|
#define BOOST_TEST_MAIN
|
||
|
|
#include <boost/test/unit_test.hpp> // Boost.Test
|
||
|
|
#include <boost/test/results_collector.hpp>
|
||
|
|
#include <boost/test/unit_test.hpp>
|
||
|
|
#include <boost/test/floating_point_comparison.hpp>
|
||
|
|
#include <boost/tuple/tuple.hpp>
|
||
|
|
#include <boost/fusion/include/tuple.hpp>
|
||
|
|
#include <boost/fusion/include/std_pair.hpp>
|
||
|
|
#ifndef BOOST_NO_CXX11_HDR_TUPLE
|
||
|
|
#include <tuple>
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#include <iostream>
|
||
|
|
#include <iomanip>
|
||
|
|
using std::cout;
|
||
|
|
using std::endl;
|
||
|
|
using std::setprecision;
|
||
|
|
|
||
|
|
#include <boost/math/tools/roots.hpp>
|
||
|
|
|
||
|
|
//
|
||
|
|
// We'll use cbrt as an example:
|
||
|
|
//
|
||
|
|
struct cbtr_functor_1
|
||
|
|
{
|
||
|
|
cbtr_functor_1(double x) : m_target(x) {}
|
||
|
|
double operator()(double x)
|
||
|
|
{
|
||
|
|
return x * x * x - m_target;
|
||
|
|
}
|
||
|
|
private:
|
||
|
|
double m_target;
|
||
|
|
};
|
||
|
|
|
||
|
|
struct cbtr_functor_2a
|
||
|
|
{
|
||
|
|
cbtr_functor_2a(double x) : m_target(x) {}
|
||
|
|
std::pair<double, double> operator()(double x)
|
||
|
|
{
|
||
|
|
return std::make_pair(x * x * x - m_target, 3 * x * x);
|
||
|
|
}
|
||
|
|
private:
|
||
|
|
double m_target;
|
||
|
|
};
|
||
|
|
#ifndef BOOST_NO_CXX11_HDR_TUPLE
|
||
|
|
struct cbtr_functor_2b
|
||
|
|
{
|
||
|
|
cbtr_functor_2b(double x) : m_target(x) {}
|
||
|
|
std::tuple<double, double> operator()(double x)
|
||
|
|
{
|
||
|
|
return std::tuple<double, double>(x * x * x - m_target, 3 * x * x);
|
||
|
|
}
|
||
|
|
private:
|
||
|
|
double m_target;
|
||
|
|
};
|
||
|
|
#endif
|
||
|
|
struct cbtr_functor_2c
|
||
|
|
{
|
||
|
|
cbtr_functor_2c(double x) : m_target(x) {}
|
||
|
|
boost::tuple<double, double> operator()(double x)
|
||
|
|
{
|
||
|
|
return boost::tuple<double, double>(x * x * x - m_target, 3 * x * x);
|
||
|
|
}
|
||
|
|
private:
|
||
|
|
double m_target;
|
||
|
|
};
|
||
|
|
struct cbtr_functor_2d
|
||
|
|
{
|
||
|
|
cbtr_functor_2d(double x) : m_target(x) {}
|
||
|
|
boost::fusion::tuple<double, double> operator()(double x)
|
||
|
|
{
|
||
|
|
return boost::fusion::tuple<double, double>(x * x * x - m_target, 3 * x * x);
|
||
|
|
}
|
||
|
|
private:
|
||
|
|
double m_target;
|
||
|
|
};
|
||
|
|
|
||
|
|
#ifndef BOOST_NO_CXX11_HDR_TUPLE
|
||
|
|
struct cbtr_functor_3b
|
||
|
|
{
|
||
|
|
cbtr_functor_3b(double x) : m_target(x) {}
|
||
|
|
std::tuple<double, double, double> operator()(double x)
|
||
|
|
{
|
||
|
|
return std::tuple<double, double, double>(x * x * x - m_target, 3 * x * x, 6 * x);
|
||
|
|
}
|
||
|
|
private:
|
||
|
|
double m_target;
|
||
|
|
};
|
||
|
|
#endif
|
||
|
|
struct cbtr_functor_3c
|
||
|
|
{
|
||
|
|
cbtr_functor_3c(double x) : m_target(x) {}
|
||
|
|
boost::tuple<double, double, double> operator()(double x)
|
||
|
|
{
|
||
|
|
return boost::tuple<double, double, double>(x * x * x - m_target, 3 * x * x, 6 * x);
|
||
|
|
}
|
||
|
|
private:
|
||
|
|
double m_target;
|
||
|
|
};
|
||
|
|
struct cbtr_functor_3d
|
||
|
|
{
|
||
|
|
cbtr_functor_3d(double x) : m_target(x) {}
|
||
|
|
boost::fusion::tuple<double, double, double> operator()(double x)
|
||
|
|
{
|
||
|
|
return boost::fusion::tuple<double, double, double>(x * x * x - m_target, 3 * x * x, 6 * x);
|
||
|
|
}
|
||
|
|
private:
|
||
|
|
double m_target;
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
BOOST_AUTO_TEST_CASE( test_main )
|
||
|
|
{
|
||
|
|
double x = 27;
|
||
|
|
double expected = 3;
|
||
|
|
double result;
|
||
|
|
double tolerance = std::numeric_limits<double>::epsilon() * 5;
|
||
|
|
std::pair<double, double> p;
|
||
|
|
//
|
||
|
|
// Start by trying the unary functors, bisect first:
|
||
|
|
//
|
||
|
|
cbtr_functor_1 f1(x);
|
||
|
|
boost::math::tools::eps_tolerance<double> t(std::numeric_limits<double>::digits - 1);
|
||
|
|
p = boost::math::tools::bisect(f1, 0.0, x, t);
|
||
|
|
result = (p.first + p.second) / 2;
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
//
|
||
|
|
// bracket_and_solve_root:
|
||
|
|
//
|
||
|
|
boost::uintmax_t max_iter = boost::math::policies::get_max_root_iterations<boost::math::policies::policy<> >();
|
||
|
|
p = boost::math::tools::bracket_and_solve_root(f1, x, 2.0, true, t, max_iter);
|
||
|
|
result = (p.first + p.second) / 2;
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
//
|
||
|
|
// toms748_solve:
|
||
|
|
//
|
||
|
|
max_iter = boost::math::policies::get_max_root_iterations<boost::math::policies::policy<> >();
|
||
|
|
p = boost::math::tools::toms748_solve(f1, 0.0, x, t, max_iter);
|
||
|
|
result = (p.first + p.second) / 2;
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
|
||
|
|
#ifndef BOOST_NO_CXX11_LAMBDAS
|
||
|
|
//
|
||
|
|
// Now try again with C++11 lambda's
|
||
|
|
//
|
||
|
|
p = boost::math::tools::bisect([x](double z){ return z * z * z - x; }, 0.0, x, t);
|
||
|
|
result = (p.first + p.second) / 2;
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
//
|
||
|
|
// bracket_and_solve_root:
|
||
|
|
//
|
||
|
|
max_iter = boost::math::policies::get_max_root_iterations<boost::math::policies::policy<> >();
|
||
|
|
p = boost::math::tools::bracket_and_solve_root([x](double z){ return z * z * z - x; }, x, 2.0, true, t, max_iter);
|
||
|
|
result = (p.first + p.second) / 2;
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
//
|
||
|
|
// toms748_solve:
|
||
|
|
//
|
||
|
|
max_iter = boost::math::policies::get_max_root_iterations<boost::math::policies::policy<> >();
|
||
|
|
p = boost::math::tools::toms748_solve([x](double z){ return z * z * z - x; }, 0.0, x, t, max_iter);
|
||
|
|
result = (p.first + p.second) / 2;
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
#endif
|
||
|
|
|
||
|
|
cbtr_functor_2a f2(x);
|
||
|
|
#ifndef BOOST_NO_CXX11_HDR_TUPLE
|
||
|
|
cbtr_functor_2b f3(x);
|
||
|
|
#endif
|
||
|
|
cbtr_functor_2c f4(x);
|
||
|
|
cbtr_functor_2d f5(x);
|
||
|
|
|
||
|
|
//
|
||
|
|
// Binary Functors - newton_raphson_iterate - test each possible tuple type:
|
||
|
|
//
|
||
|
|
#ifndef BOOST_NO_CXX11_HDR_TUPLE
|
||
|
|
result = boost::math::tools::newton_raphson_iterate(f2, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
result = boost::math::tools::newton_raphson_iterate(f3, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
#endif
|
||
|
|
result = boost::math::tools::newton_raphson_iterate(f4, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
result = boost::math::tools::newton_raphson_iterate(f5, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
//
|
||
|
|
// And again but with lambdas:
|
||
|
|
//
|
||
|
|
#ifndef BOOST_NO_CXX11_LAMBDAS
|
||
|
|
result = boost::math::tools::newton_raphson_iterate([x](double z){ return std::make_pair(z * z * z - x, 3 * z * z); }, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
#ifndef BOOST_NO_CXX11_HDR_TUPLE
|
||
|
|
result = boost::math::tools::newton_raphson_iterate([x](double z){ return std::make_tuple(z * z * z - x, 3 * z * z); }, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
#endif
|
||
|
|
result = boost::math::tools::newton_raphson_iterate([x](double z){ return boost::tuple<double, double>(z * z * z - x, 3 * z * z); }, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
result = boost::math::tools::newton_raphson_iterate([x](double z){ return boost::fusion::tuple<double, double>(z * z * z - x, 3 * z * z); }, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#ifndef BOOST_NO_CXX11_HDR_TUPLE
|
||
|
|
cbtr_functor_3b f6(x);
|
||
|
|
#endif
|
||
|
|
cbtr_functor_3c f7(x);
|
||
|
|
cbtr_functor_3d f8(x);
|
||
|
|
|
||
|
|
//
|
||
|
|
// Ternary functors:
|
||
|
|
//
|
||
|
|
#ifndef BOOST_NO_CXX11_HDR_TUPLE
|
||
|
|
result = boost::math::tools::halley_iterate(f6, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
#endif
|
||
|
|
result = boost::math::tools::halley_iterate(f7, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
result = boost::math::tools::halley_iterate(f8, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
#ifndef BOOST_NO_CXX11_LAMBDAS
|
||
|
|
#ifndef BOOST_NO_CXX11_HDR_TUPLE
|
||
|
|
result = boost::math::tools::halley_iterate([x](double z){ return std::make_tuple(z * z * z - x, 3 * z * z, 6 * z); }, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
#endif
|
||
|
|
result = boost::math::tools::halley_iterate([x](double z){ return boost::tuple<double, double, double>(z * z * z - x, 3 * z * z, 6 * z); }, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
result = boost::math::tools::halley_iterate([x](double z){ return boost::fusion::tuple<double, double, double>(z * z * z - x, 3 * z * z, 6 * z); }, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
#endif
|
||
|
|
#ifndef BOOST_NO_CXX11_HDR_TUPLE
|
||
|
|
result = boost::math::tools::schroder_iterate(f6, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
#endif
|
||
|
|
result = boost::math::tools::schroder_iterate(f7, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
result = boost::math::tools::schroder_iterate(f8, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
#ifndef BOOST_NO_CXX11_LAMBDAS
|
||
|
|
#ifndef BOOST_NO_CXX11_HDR_TUPLE
|
||
|
|
result = boost::math::tools::schroder_iterate([x](double z){ return std::make_tuple(z * z * z - x, 3 * z * z, 6 * z); }, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
#endif
|
||
|
|
result = boost::math::tools::schroder_iterate([x](double z){ return boost::tuple<double, double, double>(z * z * z - x, 3 * z * z, 6 * z); }, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
result = boost::math::tools::schroder_iterate([x](double z){ return boost::fusion::tuple<double, double, double>(z * z * z - x, 3 * z * z, 6 * z); }, x, 0.0, x, std::numeric_limits<double>::digits - 1);
|
||
|
|
BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
|
||
|
|
#endif
|
||
|
|
} // BOOST_AUTO_TEST_CASE( test_main )
|
||
|
|
|