projects / ceph.git / blame
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| 92f5a8d4 TL |
1 | // Copyright Paul A. Bristow, 2019 |
| 2 | // Copyright Nick Thompson, 2019 | |
| 3 | ||
| 4 | // Use, modification and distribution are subject to the | |
| 5 | // Boost Software License, Version 1.0. | |
| 6 | // (See accompanying file LICENSE_1_0.txt | |
| 7 | // or copy at http://www.boost.org/LICENSE_1_0.txt) | |
| 8 | ||
| 9 | #ifdef BOOST_NO_CXX11_LAMBDAS | |
| 10 | # error "This example requires a C++11 compiler that supports lambdas. Try C++11 or later." | |
| 11 | #endif | |
| 12 | ||
| 13 | //#define BOOST_MATH_INSTRUMENT_OOURA // or -DBOOST_MATH_INSTRUMENT_OOURA etc for diagnostics. | |
| 14 | ||
| 15 | #include <boost/math/quadrature/ooura_fourier_integrals.hpp> | |
| 16 | #include <boost/math/constants/constants.hpp> // For pi (including for multiprecision types, if used.) | |
| 17 | ||
| 18 | #include <cmath> | |
| 19 | #include <iostream> | |
| 20 | #include <limits> | |
| 21 | #include <iostream> | |
| 22 | ||
| 23 | int main() | |
| 24 | { | |
| 25 | try | |
| 26 | { | |
| 27 | std::cout.precision(std::numeric_limits<double>::max_digits10); // Show all potentially significant digits. | |
| 28 | ||
| 29 | using boost::math::quadrature::ooura_fourier_sin; | |
| 30 | using boost::math::constants::half_pi; | |
| 31 | ||
| 32 | //[ooura_fourier_integrals_example_1 | |
| 33 | ooura_fourier_sin<double>integrator = ooura_fourier_sin<double>(); | |
| 34 | // Use the default tolerance root_epsilon and eight levels for type double. | |
| 35 | ||
| 36 | auto f = [](double x) | |
| 37 | { // Simple reciprocal function for sinc. | |
| 38 | return 1 / x; | |
| 39 | }; | |
| 40 | ||
| 41 | double omega = 1; | |
| 42 | std::pair<double, double> result = integrator.integrate(f, omega); | |
| 43 | std::cout << "Integral = " << result.first << ", relative error estimate " << result.second << std::endl; | |
| 44 | ||
| 45 | //] [/ooura_fourier_integrals_example_1] | |
| 46 | ||
| 47 | //[ooura_fourier_integrals_example_2 | |
| 48 | ||
| 49 | constexpr double expected = half_pi<double>(); | |
| 50 | std::cout << "pi/2 = " << expected << ", difference " << result.first - expected << std::endl; | |
| 51 | //] [/ooura_fourier_integrals_example_2] | |
| 52 | } | |
| 53 | catch (std::exception const & ex) | |
| 54 | { | |
| 55 | // Lacking try&catch blocks, the program will abort after any throw, whereas the | |
| 56 | // message below from the thrown exception will give some helpful clues as to the cause of the problem. | |
| 57 | std::cout << "\n""Message from thrown exception was:\n " << ex.what() << std::endl; | |
| 58 | } | |
| 59 | } // int main() | |
| 60 | ||
| 61 | /* | |
| 62 | ||
| 63 | //[ooura_fourier_integrals_example_output_1 | |
| 64 | ||
| 65 | integral = 1.5707963267948966, relative error estimate 1.2655356398390254e-11 | |
| 66 | pi/2 = 1.5707963267948966, difference 0 | |
| 67 | ||
| 68 | //] [/ooura_fourier_integrals_example_output_1] | |
| 69 | ||
| 70 | ||
| 71 | //[ooura_fourier_integrals_example_diagnostic_output_1 | |
| 72 | ||
| 73 | ooura_fourier_sin with relative error goal 1.4901161193847656e-08 & 8 levels. | |
| 74 | h = 1.000000000000000, I_h = 1.571890732004545 = 0x1.92676e56d853500p+0, absolute error estimate = nan | |
| 75 | h = 0.500000000000000, I_h = 1.570793292491940 = 0x1.921f825c076f600p+0, absolute error estimate = 1.097439512605325e-03 | |
| 76 | h = 0.250000000000000, I_h = 1.570796326814776 = 0x1.921fb54458acf00p+0, absolute error estimate = 3.034322835882008e-06 | |
| 77 | h = 0.125000000000000, I_h = 1.570796326794897 = 0x1.921fb54442d1800p+0, absolute error estimate = 1.987898734512328e-11 | |
| 78 | Integral = 1.570796326794897e+00, relative error estimate 1.265535639839025e-11 | |
| 79 | pi/2 = 1.570796326794897e+00, difference 0.000000000000000e+00 | |
| 80 | ||
| 81 | //] [/ooura_fourier_integrals_example_diagnostic_output_1] | |
| 82 | ||
| 83 | */ |