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7c7b1cab02
The Newton-Raphson method has an option to log convergence via `BOOST_MATH_INSTRUMENT`. However, too much information was give about some things which were not super helpful, and too little about residuals. In addition, remove buffer flushes as they slow down the process dramatically.
227 lines
9.2 KiB
C++
227 lines
9.2 KiB
C++
// Copyright John Maddock 2014
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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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#define BOOST_TEST_MAIN
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#include <boost/test/unit_test.hpp> // Boost.Test
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#include <boost/test/results_collector.hpp>
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#include <boost/test/unit_test.hpp>
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#include <boost/test/tools/floating_point_comparison.hpp>
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#include <boost/tuple/tuple.hpp>
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#include <boost/fusion/include/tuple.hpp>
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#include <boost/fusion/include/std_pair.hpp>
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#include <boost/math/tools/toms748_solve.hpp>
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#include <tuple>
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#include <iostream>
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#include <iomanip>
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using std::cout;
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using std::endl;
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using std::setprecision;
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#include <boost/math/tools/roots.hpp>
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//
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// We'll use cbrt as an example:
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//
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struct cbtr_functor_1
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{
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cbtr_functor_1(double x) : m_target(x) {}
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double operator()(double x)
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{
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return x * x * x - m_target;
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}
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private:
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double m_target;
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};
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struct cbtr_functor_2a
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{
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cbtr_functor_2a(double x) : m_target(x) {}
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std::pair<double, double> operator()(double x)
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{
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return std::make_pair(x * x * x - m_target, 3 * x * x);
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}
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private:
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double m_target;
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};
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struct cbtr_functor_2b
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{
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cbtr_functor_2b(double x) : m_target(x) {}
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std::tuple<double, double> operator()(double x)
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{
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return std::tuple<double, double>(x * x * x - m_target, 3 * x * x);
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}
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private:
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double m_target;
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};
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struct cbtr_functor_2c
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{
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cbtr_functor_2c(double x) : m_target(x) {}
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boost::tuple<double, double> operator()(double x)
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{
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return boost::tuple<double, double>(x * x * x - m_target, 3 * x * x);
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}
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private:
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double m_target;
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};
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struct cbtr_functor_2d
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{
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cbtr_functor_2d(double x) : m_target(x) {}
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boost::fusion::tuple<double, double> operator()(double x)
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{
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return boost::fusion::tuple<double, double>(x * x * x - m_target, 3 * x * x);
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}
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private:
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double m_target;
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};
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struct cbtr_functor_3b
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{
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cbtr_functor_3b(double x) : m_target(x) {}
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std::tuple<double, double, double> operator()(double x)
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{
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return std::tuple<double, double, double>(x * x * x - m_target, 3 * x * x, 6 * x);
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}
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private:
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double m_target;
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};
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struct cbtr_functor_3c
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{
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cbtr_functor_3c(double x) : m_target(x) {}
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boost::tuple<double, double, double> operator()(double x)
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{
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return boost::tuple<double, double, double>(x * x * x - m_target, 3 * x * x, 6 * x);
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}
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private:
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double m_target;
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};
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struct cbtr_functor_3d
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{
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cbtr_functor_3d(double x) : m_target(x) {}
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boost::fusion::tuple<double, double, double> operator()(double x)
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{
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return boost::fusion::tuple<double, double, double>(x * x * x - m_target, 3 * x * x, 6 * x);
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}
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private:
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double m_target;
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};
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BOOST_AUTO_TEST_CASE( test_main )
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{
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double x = 27;
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double expected = 3;
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double result;
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double tolerance = std::numeric_limits<double>::epsilon() * 5;
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std::pair<double, double> p;
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//
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// Start by trying the unary functors, bisect first:
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//
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cbtr_functor_1 f1(x);
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boost::math::tools::eps_tolerance<double> t(std::numeric_limits<double>::digits - 1);
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p = boost::math::tools::bisect(f1, 0.0, x, t);
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result = (p.first + p.second) / 2;
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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//
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// bracket_and_solve_root:
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//
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boost::uintmax_t max_iter = boost::math::policies::get_max_root_iterations<boost::math::policies::policy<> >();
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p = boost::math::tools::bracket_and_solve_root(f1, x, 2.0, true, t, max_iter);
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result = (p.first + p.second) / 2;
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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//
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// toms748_solve:
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//
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max_iter = boost::math::policies::get_max_root_iterations<boost::math::policies::policy<> >();
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p = boost::math::tools::toms748_solve(f1, 0.0, x, t, max_iter);
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result = (p.first + p.second) / 2;
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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//
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// Now try again with C++11 lambda's
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//
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p = boost::math::tools::bisect([x](double z){ return z * z * z - x; }, 0.0, x, t);
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result = (p.first + p.second) / 2;
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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//
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// bracket_and_solve_root:
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//
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max_iter = boost::math::policies::get_max_root_iterations<boost::math::policies::policy<> >();
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p = boost::math::tools::bracket_and_solve_root([x](double z){ return z * z * z - x; }, x, 2.0, true, t, max_iter);
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result = (p.first + p.second) / 2;
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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//
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// toms748_solve:
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//
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max_iter = boost::math::policies::get_max_root_iterations<boost::math::policies::policy<> >();
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p = boost::math::tools::toms748_solve([x](double z){ return z * z * z - x; }, 0.0, x, t, max_iter);
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result = (p.first + p.second) / 2;
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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cbtr_functor_2a f2(x);
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cbtr_functor_2b f3(x);
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cbtr_functor_2c f4(x);
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cbtr_functor_2d f5(x);
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//
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// Binary Functors - newton_raphson_iterate - test each possible tuple type:
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//
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result = boost::math::tools::newton_raphson_iterate(f2, x, 0.0, x, std::numeric_limits<double>::digits - 1);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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result = boost::math::tools::newton_raphson_iterate(f3, x, 0.0, x, std::numeric_limits<double>::digits - 1);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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result = boost::math::tools::newton_raphson_iterate(f4, x, 0.0, x, std::numeric_limits<double>::digits - 1);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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result = boost::math::tools::newton_raphson_iterate(f5, x, 0.0, x, std::numeric_limits<double>::digits - 1);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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//
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// And again but with lambdas:
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//
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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);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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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);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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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);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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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);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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cbtr_functor_3b f6(x);
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cbtr_functor_3c f7(x);
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cbtr_functor_3d f8(x);
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//
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// Ternary functors:
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//
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result = boost::math::tools::halley_iterate(f6, x, 0.0, x, std::numeric_limits<double>::digits - 1);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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result = boost::math::tools::halley_iterate(f7, x, 0.0, x, std::numeric_limits<double>::digits - 1);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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result = boost::math::tools::halley_iterate(f8, x, 0.0, x, std::numeric_limits<double>::digits - 1);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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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);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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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);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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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);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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result = boost::math::tools::schroder_iterate(f6, x, 0.0, x, std::numeric_limits<double>::digits - 1);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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result = boost::math::tools::schroder_iterate(f7, x, 0.0, x, std::numeric_limits<double>::digits - 1);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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result = boost::math::tools::schroder_iterate(f8, x, 0.0, x, std::numeric_limits<double>::digits - 1);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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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);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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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);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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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);
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BOOST_CHECK_CLOSE_FRACTION(expected, result, tolerance);
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} // BOOST_AUTO_TEST_CASE( test_main )
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