e7e915816f
# Please enter a commit message to explain why this merge is necessary, # especially if it merges an updated upstream into a topic branch. # # Lines starting with '#' will be ignored, and an empty message aborts # the commit.
111 lines
3.9 KiB
C++
111 lines
3.9 KiB
C++
// Copyright Nick Thompson 2017.
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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 <iostream>
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#include <string>
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#include <boost/math/constants/constants.hpp>
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#include <boost/multiprecision/cpp_bin_float.hpp>
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#include <boost/multiprecision/cpp_dec_float.hpp>
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#include <boost/math/special_functions/legendre_stieltjes.hpp>
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using boost::math::legendre_p;
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using boost::math::legendre_p_zeros;
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using boost::math::legendre_p_prime;
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using boost::math::legendre_stieltjes;
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using boost::multiprecision::cpp_bin_float_quad;
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using boost::multiprecision::cpp_bin_float_100;
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using boost::multiprecision::cpp_dec_float_100;
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template<class Real>
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void gauss_kronrod_rule(size_t order)
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{
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std::cout << std::setprecision(std::numeric_limits<Real>::digits10);
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std::cout << std::fixed;
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auto gauss_nodes = boost::math::legendre_p_zeros<Real>(order);
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auto E = legendre_stieltjes<Real>(order + 1);
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std::vector<Real> gauss_weights(gauss_nodes.size(), std::numeric_limits<Real>::quiet_NaN());
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std::vector<Real> gauss_kronrod_weights(gauss_nodes.size(), std::numeric_limits<Real>::quiet_NaN());
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for (size_t i = 0; i < gauss_nodes.size(); ++i)
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{
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Real node = gauss_nodes[i];
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Real lp = legendre_p_prime<Real>(order, node);
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gauss_weights[i] = 2/( (1-node*node)*lp*lp);
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// P_n(x) = (2n)!/(2^n (n!)^2) pi_n(x), where pi_n is the monic Legendre polynomial.
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gauss_kronrod_weights[i] = gauss_weights[i] + static_cast<Real>(2)/(static_cast<Real>(order+1)*legendre_p_prime(order, node)*E(node));
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}
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std::cout << "static const std::vector<Real> gauss_nodes {\n";
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for (auto const & node : gauss_nodes)
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{
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std::cout << " boost::lexical_cast<Real>(\"" << node << "\"),\n";
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}
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std::cout << "};\n\n";
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std::cout << "static const std::vector<Real> gauss_weights {\n";
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for (auto const & weight : gauss_weights)
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{
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std::cout << " boost::lexical_cast<Real>(\"" << weight << "\"),\n";
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}
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std::cout << "};\n\n";
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std::cout << "static const std::vector<Real> gauss_kronrod_weights {\n";
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for (auto const & weight : gauss_kronrod_weights)
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{
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std::cout << " boost::lexical_cast<Real>(\"" << weight << "\"),\n";
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}
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std::cout << "};\n\n";
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auto kronrod_nodes = E.zeros();
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std::vector<Real> kronrod_weights(kronrod_nodes.size());
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for (size_t i = 0; i < kronrod_weights.size(); ++i)
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{
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Real node = kronrod_nodes[i];
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kronrod_weights[i] = static_cast<Real>(2)/(static_cast<Real>(order+1)*legendre_p(order, node)*E.prime(node));
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}
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std::cout << "static const std::vector<Real> kronrod_nodes {\n";
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for (auto node : kronrod_nodes)
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{
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std::cout << " boost::lexical_cast<Real>(\"" << node << "\"),\n";
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}
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std::cout << "};\n\n";
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std::cout << "static const std::vector<Real> kronrod_weights {\n";
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for (auto const & weight : kronrod_weights)
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{
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std::cout << " boost::lexical_cast<Real>(\"" << weight << "\"),\n";
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}
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std::cout << "};\n\n";
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}
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int main()
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{
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//std::cout << "Gauss-Kronrod 7-15 Rule:\n";
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//gauss_kronrod_rule<cpp_dec_float_100>(7);
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//std::cout << "\n\nGauss-Kronrod 10-21 Rule:\n";
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//gauss_kronrod_rule<cpp_dec_float_100>(10);
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std::cout << "\n\nGauss-Kronrod 15-31 Rule:\n";
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gauss_kronrod_rule<cpp_dec_float_100>(15);
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/*
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std::cout << "\n\nGauss-Kronrod 20-41 Rule:\n";
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gauss_kronrod_rule<cpp_dec_float_100>(20);
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std::cout << "\n\nGauss-Kronrod 25-51 Rule:\n";
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gauss_kronrod_rule<cpp_dec_float_100>(25);
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std::cout << "\n\nGauss-Kronrod 30-61 Rule:\n";
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gauss_kronrod_rule<cpp_dec_float_100>(30);
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std::cout << "\n\nGauss-Kronrod 35-71 Rule:\n";
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gauss_kronrod_rule<cpp_dec_float_100>(35);
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std::cout << "\n\nGauss-Kronrod 40-81 Rule:\n";
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gauss_kronrod_rule<cpp_dec_float_100>(40);*/
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}
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