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// Copyright Paul A. Bristow, 2019
// Copyright Nick Thompson, 2019
// 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_MATH_INSTRUMENT_OOURA // or -DBOOST_MATH_INSTRUMENT_OOURA etc for diagnostic output.
#include <boost/math/quadrature/ooura_fourier_integrals.hpp> // For ooura_fourier_cos
#include <boost/math/constants/constants.hpp> // For pi (including for multiprecision types, if used.)
#include <cmath>
#include <iostream>
#include <limits>
#include <iostream>
int main()
{
try
{
std::cout.precision(std::numeric_limits<double>::max_digits10); // Show all potentially significant digits.
using boost::math::quadrature::ooura_fourier_cos;
using boost::math::constants::half_pi;
using boost::math::constants::e;
//[ooura_fourier_integrals_cosine_example_1
auto integrator = ooura_fourier_cos<double>();
// Use the default tolerance root_epsilon and eight levels for type double.
auto f = [](double x)
{ // More complex example function.
return 1 / (x * x + 1);
};
double omega = 1;
auto [result, relative_error] = integrator.integrate(f, omega);
std::cout << "Integral = " << result << ", relative error estimate " << relative_error << std::endl;
//] [/ooura_fourier_integrals_cosine_example_1]
//[ooura_fourier_integrals_cosine_example_2
constexpr double expected = half_pi<double>() / e<double>();
std::cout << "pi/(2e) = " << expected << ", difference " << result - expected << std::endl;
//] [/ooura_fourier_integrals_cosine_example_2]
}
catch (std::exception const & ex)
{
// Lacking try&catch blocks, the program will abort after any throw, whereas the
// message below from the thrown exception will give some helpful clues as to the cause of the problem.
std::cout << "\n""Message from thrown exception was:\n " << ex.what() << std::endl;
}
} // int main()
/*
//[ooura_fourier_integrals_example_cosine_output_1
``
Integral = 0.57786367489546109, relative error estimate 6.4177395404415149e-09
pi/(2e) = 0.57786367489546087, difference 2.2204460492503131e-16
``
//] [/ooura_fourier_integrals_example_cosine_output_1]
//[ooura_fourier_integrals_example_cosine_diagnostic_output_1
``
ooura_fourier_cos with relative error goal 1.4901161193847656e-08 & 8 levels.
epsilon for type = 2.2204460492503131e-16
h = 1.000000000000000, I_h = 0.588268622591776 = 0x1.2d318b7e96dbe00p-1, absolute error estimate = nan
h = 0.500000000000000, I_h = 0.577871642184837 = 0x1.27decab8f07b200p-1, absolute error estimate = 1.039698040693926e-02
h = 0.250000000000000, I_h = 0.577863671186883 = 0x1.27ddbf42969be00p-1, absolute error estimate = 7.970997954576120e-06
h = 0.125000000000000, I_h = 0.577863674895461 = 0x1.27ddbf6271dc000p-1, absolute error estimate = 3.708578555361441e-09
Integral = 5.778636748954611e-01, relative error estimate 6.417739540441515e-09
pi/(2e) = 5.778636748954609e-01, difference 2.220446049250313e-16
``
//] [/ooura_fourier_integrals_example_cosine_diagnostic_output_1]
*/
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