JQuadrature.cc

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#include <string>
#include <iostream>
#include <iomanip>
#include <cmath>

#include "JTools/JQuadrature.hh"

#include "JMath/JPolynome.hh"
#include "JMath/JGauss.hh"

#include "Jeep/JParser.hh"
#include "Jeep/JMessage.hh"


namespace GAUSS_LEGENDRE {

  using namespace JPP;

  const int    numberOfPoints = 10;
  const double epsilon        = 1.0e-12;

  const double xmin = -5.0;
  const double xmax = +3.0;

  /**
   * Function.
   */
  const JPolynome f1(1.0, 2.0, 3.0);

  /**
   * Integral.
   */
  const JPolynome F1 = f1.getIntegral();
}

namespace GAUSS_LAGUERRE {

  using namespace JPP;

  const int    numberOfPoints = 10;
  const double a              = 1.0;
  const double epsilon        = 1.0e-12;

  const double xmin =  0.0;
  const double xmax = +1.0e10;  // approximation of infinity

  /**
   * Function.
   */
  inline double f1(const double x)
  {
    return sin(x);
  }

  /**
   * Integral.
   */
  inline double F1(const double x)
  {
    // integral of sin(x) * x^1 * exp(-x)

    return -0.5 * exp(-x) * (x*sin(x) + (x + 1.0)*cos(x));
  }
}

namespace GAUSS_HERMITE {

  using namespace JPP;

  const int    numberOfPoints = 10;
  const double epsilon        = 1.0e-12;

  const double sigma[] = { 4.0, 0.5 };
  
  const double xmin = -3.0 * sigma[0];
  const double xmax = +3.0 * sigma[0];

  /**
   * Function.
   */
  const JGauss f1(0.0, sigma[0]);

  /**
   * Integral.
   */
  const JGauss F1(0.0, hypot(sigma[0], sigma[1]));
}


/**
 * \file
 *
 * Example program to test JTOOLS::JQuadrature.
 * \author mdejong
 */
int main(int argc, char **argv)
{
  using namespace std;
  using namespace JPP;

  double    precision;
  int       debug;

  try {

    JParser<> zap("Example program to test JTOOLS::JQuadrature.");

    zap['e'] = make_field(precision)      = 1.0e-4;
    zap['d'] = make_field(debug)          = 3;

    zap(argc, argv);
  }
  catch(const exception &error) {
    FATAL(error.what() << endl);
  }

  {
    using namespace GAUSS_LEGENDRE;
          
    double V = F1(xmax) - F1(xmin);

    JGaussLegendre engine(numberOfPoints, epsilon);

    const double x0 = 0.5 * (xmax + xmin);
    const double x1 = 0.5 * (xmax - xmin);

    double W = 0.0;

    for (JGaussLegendre::const_iterator i = engine.begin(); i != engine.end(); ++i) {

      const double x = x0 + i->getX() * x1;
     
      W += f1(x) * i->getY() * x1;
    }

    DEBUG("integral analytical " << FIXED(9,5) << V << endl);
    DEBUG("integral numerical  " << FIXED(9,5) << W << endl);

    ASSERT(fabs(V - W) <= precision, "Test Gauss-Legendre integration.");
  }
  {
    using namespace GAUSS_LAGUERRE;

    const double V = F1(xmax) - F1(xmin);

    JGaussLaguerre engine(numberOfPoints, a, epsilon);

    double W = 0.0;

    for (JGaussLaguerre::const_iterator i = engine.begin(); i != engine.end(); ++i) {

      const double x = i->getX();
     
      W += f1(x) * i->getY();
    }

    DEBUG("integral analytical " << FIXED(9,5) << V << endl);
    DEBUG("integral numerical  " << FIXED(9,5) << W << endl);

    ASSERT(fabs(V - W) <= precision, "Test Gauss-Laguerre integration.");
  }
  {
    using namespace GAUSS_HERMITE;

    JGaussHermite engine(numberOfPoints, epsilon);

    for (double x = xmin; x <= xmax; x += 0.05*(xmax - xmin)) {

      const double V = F1(x);
      
      double W = 0.0;

      for (JGaussHermite::const_iterator i = engine.begin(); i != engine.end(); ++i) {

        const double u = i->getX() * sigma[1] * sqrt(2.0);
        const double v = i->getY() / sqrt(PI);
     
        W += f1(x + u) * v;
      }

      DEBUG(FIXED(7,3) << x << ' ' << FIXED(9,5) << V << ' ' << FIXED(9,5) << W << endl);

      ASSERT(fabs(V - W) <= precision * V, "Test Gauss-Hermite integration.");
    }
  }

  return 0;
}