Numerical Integration
[Auxiliary math functions]

Numerical integration routines. More...

Functions
double	itpp::quad (double(*f)(double), double a, double b, double tol)
double	itpp::quadl (double(*f)(double), double a, double b, double tol)

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Detailed Description

Numerical integration routines.

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Function Documentation

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.

References itpp::sum().

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.

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