mirror of
https://github.com/boostorg/math.git
synced 2026-07-22 13:34:12 +00:00
Matt Borland
77 lines
2.9 KiB
C++
77 lines
2.9 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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//
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// Module build check for the Gauss-Legendre quadrature component. It consumes
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// <boost/math/quadrature/gauss.hpp> through import boost.math and exercises the
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// public gauss<Real, Points>::integrate entry point. Expected values are the
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// mathematically-exact integrals and known-good results taken from
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// gauss_quadrature_test.cpp (double/float paths only).
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#ifndef BOOST_MATH_BUILD_MODULE
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#include <boost/math/quadrature/gauss.hpp>
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#else
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import boost.math;
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#endif
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#ifndef BOOST_MATH_BUILD_MODULE
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#include <cmath>
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#endif
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#include "math_unit_test.hpp"
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using boost::math::quadrature::gauss;
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template <class Real>
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void test_spots(const char* type_name)
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{
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std::cout << "Testing gauss quadrature for type " << type_name << std::endl;
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using std::exp;
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using std::sqrt;
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using std::cos;
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const Real pi {boost::math::constants::pi<Real>()};
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// A Gauss rule integrates polynomials of degree <= 2N-1 exactly, so a
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// 7-point rule reproduces linear and quadratic integrands to rounding.
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// Integral of 5x + 7 over [0, 1] is 9.5; the L1 norm matches on a positive
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// integrand.
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auto linear = [](const Real& x) { return 5 * x + 7; };
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Real L1 {};
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Real Q {gauss<Real, 7>::integrate(linear, static_cast<Real>(0), static_cast<Real>(1), &L1)};
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CHECK_ULP_CLOSE(static_cast<Real>(9.5), Q, 32);
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CHECK_ULP_CLOSE(static_cast<Real>(9.5), L1, 32);
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// Swapping the limits negates the result.
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Q = gauss<Real, 7>::integrate(linear, static_cast<Real>(1), static_cast<Real>(0));
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CHECK_ULP_CLOSE(static_cast<Real>(-9.5), Q, 32);
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// Integral of 5x^2 + 7x + 12 over [0, 1] is 103/6.
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auto quadratic = [](const Real& x) { return 5 * x * x + 7 * x + 12; };
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Q = gauss<Real, 7>::integrate(quadratic, static_cast<Real>(0), static_cast<Real>(1), &L1);
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CHECK_ULP_CLOSE(static_cast<Real>(103) / 6, Q, 32);
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CHECK_ULP_CLOSE(static_cast<Real>(103) / 6, L1, 32);
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// Smooth analytic integrand: exp(t) cos(t) over [0, pi/2] is (e^(pi/2) - 1)/2.
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auto smooth = [](const Real& t) { return exp(t) * cos(t); };
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Q = gauss<Real, 7>::integrate(smooth, static_cast<Real>(0), pi / 2);
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const Real smooth_expected {(exp(pi / 2) - 1) / 2};
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CHECK_ABSOLUTE_ERROR(smooth_expected, Q, static_cast<Real>(1e-5));
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// Area of the quarter unit circle: integral of sqrt(1 - t^2) over [0, 1] is pi/4.
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auto circle = [](const Real& t) { return sqrt(1 - t * t); };
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Q = gauss<Real, 7>::integrate(circle, static_cast<Real>(0), static_cast<Real>(1));
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CHECK_ABSOLUTE_ERROR(pi / 4, Q, static_cast<Real>(3.5e-3));
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}
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int main()
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{
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test_spots<double>("double");
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test_spots<float>("float");
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return boost::math::test::report_errors();
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}
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