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77 lines
2.7 KiB
C++
77 lines
2.7 KiB
C++
// Copyright Paul A. Bristow, 2019
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// Copyright Nick Thompson, 2019
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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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// This example requires C++11.
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#define BOOST_MATH_INSTRUMENT_OOURA // or -DBOOST_MATH_INSTRUMENT_OOURA etc for diagnostics.
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#include <boost/math/quadrature/ooura_fourier_integrals.hpp> //
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#include <boost/math/constants/constants.hpp> // For pi (including for multiprecision types, if used.)
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#include <cmath>
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#include <iostream>
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#include <limits>
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#include <iostream>
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int main()
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{
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std::cout.precision(std::numeric_limits<double>::max_digits10); // Show all potentially significant digits.
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using boost::math::quadrature::ooura_fourier_sin;
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using boost::math::constants::half_pi;
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// constexpr double double_tol = 10 * std::numeric_limits<double>::epsilon(); // Tolerance.
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//[ooura_fourier_integrals_example_1
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ooura_fourier_sin<double>integrator = ooura_fourier_sin<double>();
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// Use the default tolerance root_epsilon and eight levels for type double.
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auto f = [](double x)
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{ // Simple reciprocal function for sinc.
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return 1 / x;
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};
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double omega = 1;
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std::pair<double, double> result = integrator.integrate(f, omega);
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std::cout << "Integral = " << result.first << ", relative error estimate " << result.second << std::endl;
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//] [/ooura_fourier_integrals_example_1]
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//[ooura_fourier_integrals_example_2
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constexpr double expected = half_pi<double>();
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std::cout << "pi/2 = " << expected << ", difference " << result.first - expected << std::endl;
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//] [/ooura_fourier_integrals_example_2]
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} // int main()
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/*
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//[ooura_fourier_integrals_example_output_1
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integral = 1.5707963267948966, relative error estimate 1.2655356398390254e-11
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pi/2 = 1.5707963267948966, difference 0
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//] [/ooura_fourier_integrals_example_output_1]
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//[ooura_fourier_integrals_example_diagnostic_output_1
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ooura_fourier_sin with relative error goal 1.4901161193847656e-08 & 8 levels.
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h = 1.000000000000000, I_h = 1.571890732004545 = 0x1.92676e56d853500p+0, absolute error estimate = nan
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h = 0.500000000000000, I_h = 1.570793292491940 = 0x1.921f825c076f600p+0, absolute error estimate = 1.097439512605325e-03
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h = 0.250000000000000, I_h = 1.570796326814776 = 0x1.921fb54458acf00p+0, absolute error estimate = 3.034322835882008e-06
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h = 0.125000000000000, I_h = 1.570796326794897 = 0x1.921fb54442d1800p+0, absolute error estimate = 1.987898734512328e-11
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Integral = 1.570796326794897e+00, relative error estimate 1.265535639839025e-11
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pi/2 = 1.570796326794897e+00, difference 0.000000000000000e+00
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//] [/ooura_fourier_integrals_example_diagnostic_output_1]
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*/ |