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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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