Numerical Integration

Numerical integration routines. More...

Functions
template<typename Ftn >
double	itpp::quad (Ftn f, double a, double b, double tol=std::numeric_limits< double >::epsilon())
ITPP_EXPORT double	itpp::quad (double(*f)(double), double a, double b, double tol=std::numeric_limits< double >::epsilon())
template<typename Ftn >
double	itpp::quadl (Ftn f, double a, double b, double tol=std::numeric_limits< double >::epsilon())
ITPP_EXPORT double	itpp::quadl (double(*f)(double), double a, double b, double tol=std::numeric_limits< double >::epsilon())

Detailed Description

Numerical integration routines.

Function Documentation

template<typename Ftn >

double itpp::quad	(	Ftn	f,
		double	a,
		double	b,
		double	tol = std::numeric_limits<double>::epsilon()
	)

1-dimensional numerical Simpson quadrature integration

Calculate the 1-dimensional integral

Uses an adaptive Simpson quadrature method. See [Gander] for more details. The integrand is specified as a templated function object.

Example:

#include "itpp/itbase.h"

struct Integrand_Functor
{
double operator()(const double x) const
{
  return x*log(x);
}
};

int main()
{
double res = quad(Integrand_Functor(), 1.5, 3.5);
  cout << "res = " << res << endl;

  return 0;
}

References:

[Gander] Gander, W. and W. Gautschi, "Adaptive Quadrature - Revisited", BIT, Vol. 40, 2000, pp. 84-101. This document is also available at http://www.inf.ethz.ch/personal/gander.

Definition at line 162 of file integration.h.

References itpp::sum().

Referenced by itpp::EXIT::apriori_mutual_info().

ITPP_EXPORT double itpp::quad	(	double(*)(double)	f,
		double	a,
		double	b,
		double	tol = std::numeric_limits< double >::epsilon()
	)

1-dimensional numerical Simpson quadrature integration

Calculate the 1-dimensional integral

Uses an adaptive Simpson quadrature method. See [Gander] for more details. The integrand is specified as a function:

double f(double) 

Example:

#include "itpp/itbase.h"

double f(const double x)
{
  return x*log(x);
}

int main()
{
  double res = quad( f, 1.5, 3.5);
  cout << "res = " << res << endl;

  return 0;
}

References:

[Gander] Gander, W. and W. Gautschi, "Adaptive Quadrature - Revisited", BIT, Vol. 40, 2000, pp. 84-101. This document is also available at http://www.inf.ethz.ch/personal/gander.

template<typename Ftn >

double itpp::quadl	(	Ftn	f,
		double	a,
		double	b,
		double	tol = std::numeric_limits<double>::epsilon()
	)

1-dimensional numerical adaptive Lobatto quadrature integration

Calculate the 1-dimensional integral

Uses an adaptive Lobatto quadrature method. See [Gander] for more details. The integrand is specified as a templated function object.

Example:

#include "itpp/itbase.h"

struct Integrand_Functor
{
double operator()(const double x) const
{
  return x*log(x);
}
};

int main()
{
  double res = quadl(Integrand_Functor(), 1.5, 3.5);
  cout << "res = " << res << endl;

  return 0;
}

References:

[Gander] Gander, W. and W. Gautschi, "Adaptive Quadrature - Revisited", BIT, Vol. 40, 2000, pp. 84-101. This document is also available at http:// www.inf.ethz.ch/personal/gander.

Definition at line 264 of file integration.h.

References itpp::abs(), itpp::sign(), and itpp::sqrt().

ITPP_EXPORT double itpp::quadl	(	double(*)(double)	f,
		double	a,
		double	b,
		double	tol = std::numeric_limits< double >::epsilon()
	)

1-dimensional numerical adaptive Lobatto quadrature integration

Calculate the 1-dimensional integral

Uses an adaptive Lobatto quadrature method. See [Gander] for more details. The integrand is specified as a function:

double f(double) 

Example:

#include "itpp/itbase.h"

double f(const double x)
{
  return x*log(x);
}

int main()
{
  double res = quadl( f, 1.5, 3.5);
  cout << "res = " << res << endl;

  return 0;
}

References:

[Gander] Gander, W. and W. Gautschi, "Adaptive Quadrature - Revisited", BIT, Vol. 40, 2000, pp. 84-101. This document is also available at http:// www.inf.ethz.ch/personal/gander.