ceph/src/boost/libs/math/example/ooura_fourier_integrals_cosine_example.cpp

   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 //#define BOOST_MATH_INSTRUMENT_OOURA // or -DBOOST_MATH_INSTRUMENT_OOURA etc for diagnostic output.
  10
  11 #include <boost/math/quadrature/ooura_fourier_integrals.hpp> // For ooura_fourier_cos
  12 #include <boost/math/constants/constants.hpp>  // For pi (including for multiprecision types, if used.)
  13
  14 #include <cmath>
  15 #include <iostream>
  16 #include <limits>
  17 #include <iostream>
  18
  19 int main()
  20 {
  21   try
  22   {
  23   std::cout.precision(std::numeric_limits<double>::max_digits10); // Show all potentially significant digits.
  24
  25   using boost::math::quadrature::ooura_fourier_cos;
  26   using boost::math::constants::half_pi;
  27   using boost::math::constants::e;
  28
  29  //[ooura_fourier_integrals_cosine_example_1
  30   auto integrator = ooura_fourier_cos<double>();
  31   // Use the default tolerance root_epsilon and eight levels for type double.
  32
  33   auto f = [](double x)
  34   { // More complex example function.
  35     return 1 / (x * x + 1);
  36   };
  37
  38   double omega = 1;
  39
  40   auto [result, relative_error] = integrator.integrate(f, omega);
  41   std::cout << "Integral = " << result << ", relative error estimate " << relative_error << std::endl;
  42
  43   //] [/ooura_fourier_integrals_cosine_example_1]
  44
  45   //[ooura_fourier_integrals_cosine_example_2
  46
  47   constexpr double expected = half_pi<double>() / e<double>();
  48   std::cout << "pi/(2e) =  " << expected << ", difference " << result - expected << std::endl;
  49   //] [/ooura_fourier_integrals_cosine_example_2]
  50   }
  51   catch (std::exception const & ex)
  52   {
  53     // Lacking try&catch blocks, the program will abort after any throw, whereas the
  54     // message below from the thrown exception will give some helpful clues as to the cause of the problem.
  55     std::cout << "\n""Message from thrown exception was:\n   " << ex.what() << std::endl;
  56   }
  57
  58 } // int main()
  59
  60 /*
  61
  62 //[ooura_fourier_integrals_example_cosine_output_1
  63 ``
  64 Integral = 0.57786367489546109, relative error estimate 6.4177395404415149e-09
  65 pi/(2e) =  0.57786367489546087, difference 2.2204460492503131e-16
  66 ``
  67 //] [/ooura_fourier_integrals_example_cosine_output_1]
  68
  69
  70 //[ooura_fourier_integrals_example_cosine_diagnostic_output_1
  71 ``
  72 ooura_fourier_cos with relative error goal 1.4901161193847656e-08 & 8 levels.
  73 epsilon for type = 2.2204460492503131e-16
  74 h = 1.000000000000000, I_h = 0.588268622591776 = 0x1.2d318b7e96dbe00p-1, absolute error estimate = nan
  75 h = 0.500000000000000, I_h = 0.577871642184837 = 0x1.27decab8f07b200p-1, absolute error estimate = 1.039698040693926e-02
  76 h = 0.250000000000000, I_h = 0.577863671186883 = 0x1.27ddbf42969be00p-1, absolute error estimate = 7.970997954576120e-06
  77 h = 0.125000000000000, I_h = 0.577863674895461 = 0x1.27ddbf6271dc000p-1, absolute error estimate = 3.708578555361441e-09
  78 Integral = 5.778636748954611e-01, relative error estimate 6.417739540441515e-09
  79 pi/(2e)  = 5.778636748954609e-01, difference 2.220446049250313e-16
  80 ``
  81 //] [/ooura_fourier_integrals_example_cosine_diagnostic_output_1]
  82
  83 */