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

   1 /*
   2  * Copyright Nick Thompson, 2017
   3  * Use, modification and distribution are subject to the
   4  * Boost Software License, Version 1.0. (See accompanying file
   5  * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
   6  *
   7  * This example shows to to numerically integrate a periodic function using the adaptive_trapezoidal routine provided by boost.
   8  */
   9
  10 #include <iostream>
  11 #include <cmath>
  12 #include <limits>
  13 #include <boost/math/quadrature/trapezoidal.hpp>
  14
  15 int main()
  16 {
  17     using boost::math::constants::two_pi;
  18     using boost::math::constants::third;
  19     using boost::math::quadrature::trapezoidal;
  20     // This function has an analytic form for its integral over a period: 2pi/3.
  21     auto f = [](double x) { return 1/(5 - 4*cos(x)); };
  22
  23     double Q = trapezoidal(f, (double) 0, two_pi<double>());
  24
  25     std::cout << std::setprecision(std::numeric_limits<double>::digits10);
  26     std::cout << "The adaptive trapezoidal rule gives the integral of our function as " << Q << "\n";
  27     std::cout << "The exact result is                                                 " << two_pi<double>()*third<double>() << "\n";
  28
  29 }