funct::GaussLegendreIntegrator Class Reference

#include <NumericalIntegration.h>

Public Member Functions
	GaussLegendreIntegrator ()
	GaussLegendreIntegrator (unsigned int samples, double epsilon)
template<typename F >
double	operator() (const F &f, double min, double max) const

Private Attributes
double	a0
double	b0
unsigned int	i
double	result
unsigned int	samples_
std::vector< double >	w
std::vector< double >	x

Detailed Description

Definition at line 42 of file NumericalIntegration.h.

Constructor & Destructor Documentation

funct::GaussLegendreIntegrator::GaussLegendreIntegrator ( )

inline

Definition at line 44 of file NumericalIntegration.h.

: samples_(0) {}

funct::GaussLegendreIntegrator::GaussLegendreIntegrator	(	unsigned int	samples,
		double	epsilon
	)

Definition at line 5 of file NumericalIntegration.cc.

References edm::errors::Configuration, funct::cos(), Exception, i, dqmiolumiharvest::j, funct::m, fireworks::p1, fireworks::p2, createTree::pp, w, and x.

                                                                                          : samples_(samples) {
  if (samples <= 0)
    throw edm::Exception(edm::errors::Configuration) << "gauss_legendre_integral: number of samples must be positive\n";
  if (epsilon <= 0)
    throw edm::Exception(edm::errors::Configuration)
        << "gauss_legendre_integral: numerical precision must be positive\n";

  x.resize(samples);
  w.resize(samples);
  const unsigned int m = (samples + 1) / 2;

  double z, zSqr, pp, p1, p2, p3;

  for (unsigned int i = 0; i < m; ++i) {
    z = std::cos(3.14159265358979323846 * (i + 0.75) / (samples + 0.5));
    zSqr = z * z;
    do {
      p1 = 1.0;
      p2 = 0.0;
      for (unsigned int j = 0; j < samples; ++j) {
        p3 = p2;
        p2 = p1;
        p1 = ((2.0 * j + 1.0) * z * p2 - j * p3) / (j + 1.0);
      }
      pp = samples * (z * p1 - p2) / (zSqr - 1.0);
      z -= p1 / pp;
    } while (std::fabs(p1 / pp) > epsilon);

    x[i] = -z;
    x[samples - i - 1] = z;
    w[i] = 2.0 / ((1.0 - zSqr) * pp * pp);
    w[samples - i - 1] = w[i];
  }
}

Member Function Documentation

template<typename F >

double funct::GaussLegendreIntegrator::operator() ( const F &  f, double  min, double  max  ) const

inline

Definition at line 47 of file NumericalIntegration.h.

References a0, b0, validate-o2o-wbm::f, i, SiStripPI::min, result, samples_, w, and x.

                                                                {
      a0 = 0.5 * (max + min);
      b0 = 0.5 * (max - min);
      result = 0.0;
      for (i = 0; i < samples_; ++i) {
        result += w[i] * f(a0 + b0 * x[i]);
      }

      return result * b0;
    }

Member Data Documentation

double funct::GaussLegendreIntegrator::a0

mutableprivate

Definition at line 61 of file NumericalIntegration.h.

Referenced by operator()().

double funct::GaussLegendreIntegrator::b0

mutableprivate

Definition at line 61 of file NumericalIntegration.h.

Referenced by operator()().

unsigned int funct::GaussLegendreIntegrator::i

mutableprivate

Definition at line 62 of file NumericalIntegration.h.

Referenced by GaussLegendreIntegrator(), and operator()().

double funct::GaussLegendreIntegrator::result

mutableprivate

Definition at line 61 of file NumericalIntegration.h.

Referenced by operator()().

unsigned int funct::GaussLegendreIntegrator::samples_

private

Definition at line 59 of file NumericalIntegration.h.

Referenced by operator()().

std::vector<double> funct::GaussLegendreIntegrator::w

private

Definition at line 60 of file NumericalIntegration.h.

Referenced by GaussLegendreIntegrator(), and operator()().

std::vector<double> funct::GaussLegendreIntegrator::x

private

Definition at line 60 of file NumericalIntegration.h.

Referenced by svgfig.Curve.Sample::__repr__(), svgfig.Ellipse::__repr__(), GaussLegendreIntegrator(), operator()(), geometryXMLparser.Alignable::pos(), ntupleDataFormat._HitObject::r(), and ntupleDataFormat._HitObject::r3D().