Quadrature.hpp File Reference

Templates for the quadrature of functions that do not depend on any grid functions. More...

#include "gaussweights.hpp"

Include dependency graph for Quadrature.hpp:


Functions
template<typename T, class Integrand>
T	Midpoint_Integrate (Integrand &integrand, int index, double *xi, int n_points)
	The auxiliary recursive function for Midpoint_Integrate.
template<typename T, class Integrand>
T	Midpoint_Integrate (Integrand &integrand, double *xi, int n_points=1)
	Integration of a scalar function using the summation midpoint rule.
template<typename T, class Integrand>
T	Midpoint_Integrate (Integrand &integrand, int index, double *xi, int n_points[])
	The auxiliary recursive function for Midpoint_Integrate.
template<typename T, class Integrand>
T	Midpoint_Integrate (Integrand &integrand, double *xi, int n_points[])
	The quadrature routine.
template<typename T, class Integrand>
T	Trapezoidal_Integrate (Integrand &integrand, int index, double *xi, int n_points)
	The auxiliary recursive function.
template<typename T, class Integrand>
T	Trapezoidal_Integrate (Integrand &integrand, double *xi, int n_points=1)
	Integration of a scalar function using the summation trapezoidal rule.
template<typename T, class Integrand>
T	Gauss_Integrate (Integrand &integrand, int index, double *xi, int n_points)
	The auxiliary recursive function.
template<typename T, class Integrand>
T	Gauss_Integrate (Integrand &integrand, double *xi, int n_points=1)
	Integration of a scalar function using the Gaussian quadrature.

Detailed Description

Templates for the quadrature of functions that do not depend on any grid functions.

The integral to compute:

$\int_\Omega f (x) dx, where \ \Omega = [0, 1]^d.$

All the quadrature procedures are implemented as templates depending on the class 'Integrand' that specifies 'f'. If possible, 'f' should be implemented as an inline function. The class should contain the following fields:

dim as an integer: the dimensionality of 'x',
T f (double * xi) - the function 'f'.

Date:: Nov. 22, 2005 - created

Function Documentation

template<typename T, class Integrand>

T Gauss_Integrate	(	Integrand &	integrand,
		double *	xi,
		int	n_points = `1`
	)			`[inline]`

Integration of a scalar function using the Gaussian quadrature.

Parameters:

`[in]`	integrand	The integrand
`[in]`	xi	A buffer for the coordinates
`[in]`	n_points	Number of the gaussian points in every direction

template<typename T, class Integrand>

T Gauss_Integrate	(	Integrand &	integrand,
		int	index,
		double *	xi,
		int	n_points
	)			`[inline]`

The auxiliary recursive function.

Parameters:

`[in]`	integrand	The integrand
`[in]`	index	Number of the index
`[in]`	xi	The coordinates
`[in]`	n_points	Number of the gaussian points in every direction - 1

template<typename T, class Integrand>

T Midpoint_Integrate	(	Integrand &	integrand,
		double *	xi,
		int	n_points[]
	)			`[inline]`

The quadrature routine.

Parameters:

`[in]`	integrand	The integrand
`[in]`	xi	A buffer for the coordinates
`[in]`	n_points	Array of numbers of the points in every direction

template<typename T, class Integrand>

T Midpoint_Integrate	(	Integrand &	integrand,
		int	index,
		double *	xi,
		int	n_points[]
	)			`[inline]`

The auxiliary recursive function for Midpoint_Integrate.

Parameters:

`[in]`	integrand	The integrand
`[in]`	index	Number of the index
`[in]`	xi	The coordinates
`[in]`	n_points	Array of numbers of the points in every direction

template<typename T, class Integrand>

T Midpoint_Integrate	(	Integrand &	integrand,
		double *	xi,
		int	n_points = `1`
	)			`[inline]`

Integration of a scalar function using the summation midpoint rule.

Parameters:

`[in]`	integrand	The integrand
`[in]`	xi	A buffer for the coordinates
`[in]`	n_points	Number of the points in every direction

template<typename T, class Integrand>

T Midpoint_Integrate	(	Integrand &	integrand,
		int	index,
		double *	xi,
		int	n_points
	)			`[inline]`

The auxiliary recursive function for Midpoint_Integrate.

Parameters:

`[in]`	integrand	The integrand
`[in]`	index	Number of the index
`[in]`	xi	The coordinates
`[in]`	n_points	Number of the points in every direction

template<typename T, class Integrand>

T Trapezoidal_Integrate	(	Integrand &	integrand,
		double *	xi,
		int	n_points = `1`
	)			`[inline]`

Integration of a scalar function using the summation trapezoidal rule.

Parameters:

`[in]`	integrand	The integrand
`[in]`	xi	A buffer for the coordinates
`[in]`	n_points	Number of the points in every direction

template<typename T, class Integrand>

T Trapezoidal_Integrate	(	Integrand &	integrand,
		int	index,
		double *	xi,
		int	n_points
	)			`[inline]`

The auxiliary recursive function.

Parameters:

`[in]`	integrand	The integrand
`[in]`	index	Number of the index
`[in]`	xi	The coordinates
`[in]`	n_points	Number of the points in every direction - 1

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