GaussLegendre Class Reference

Gauss-Legendre quadrature. More...

#include <gauss.h>

Inheritance diagram for GaussLegendre:

Collaboration diagram for GaussLegendre:

Public Member Functions
void	scaled_nodes_and_weights (int points, Complex x1, Complex x2, Complex *xs, Complex *ws) const
	Get Gauss-Legendre quadrature points and weights in interval. More...
template<class Functor , class... Data>
Complex	quad (Functor f, Bspline const &bspline, int points, int iknot, Complex x1, Complex x2, Data... data) const
	Gauss-Legendre integrator. More...
template<class ClassPtr , class Functor , class... Data>
Complex	quadMFP (ClassPtr ptr, Functor f, Bspline const &bspline, int points, int iknot, Complex x1, Complex x2, Data... data) const
	Gauss-Legendre integrator. More...

Additional Inherited Members
Static Public Member Functions inherited from GaussLegendreData
static void	gauss_nodes_and_weights (int points, const Real *&vx, const Real *&vw)
	Retrieve Gauss-Legendre data. More...
static void	precompute_nodes_and_weights (int points)
	Precalculate nodes and weights so that the retrieval is fast and thread-safe. More...

Detailed Description

This class's purpose is aid in fixed-order Gauss-Legendre quadrature. It is constructed above a B-spline environment, which is passed to the constructor. The functions "p_points" and "p_weights" return evaluation nodes and weights, respectively, and the functions "quad" do the fixed-order quadrature itself. Every call to p_points or p_weights resuts in call to gauss_nodes_and_weights, which uses GSL to get the requested data. The computed nodes and weights are stored in a cache table to allow faster subsequent computations.

Member Function Documentation

quad()

template<class Functor , class... Data>

Complex GaussLegendre::quad ( Functor  f, Bspline const &  bspline, int  points, int  iknot, Complex  x1, Complex  x2, Data...  data  ) const

inline

Integrate the given function.

Parameters

f	Function of type (void (*) (unsigned, complex*, complex*, data...)), where the first parameter is number of points to evaluate, the second parameter is pointer to an array of double complex values at which to evaluate, the third is pointer to an array into which the data will be written (responsibility for memory management is on callers side) and finally the fourth (and further) parameter is any other data to be suplied to the function.
data	Data to pass to the function.
points	Gauss-Legendre points count.
iknot	Knot index.
x1	Left integration boundary.
x2	Right integration boundary.

It must be

t[iknot] <= x1 <= t[iknot+1]
t[iknot] <= x2 <= t[iknot+1]

quadMFP()

template<class ClassPtr , class Functor , class... Data>

Complex GaussLegendre::quadMFP ( ClassPtr  ptr, Functor  f, Bspline const &  bspline, int  points, int  iknot, Complex  x1, Complex  x2, Data...  data  ) const

inline

This is a variant of the other quad function that can be used together with the pointer-to-member-function arguments. A typical usage woud be

Class A { ... };
A a;
result = quad (&a, &a::integrand, ...);

scaled_nodes_and_weights()

void GaussLegendre::scaled_nodes_and_weights	(	int	points,
		Complex	x1,
		Complex	x2,
		Complex *	xs,
		Complex *	ws
	)		const

Map Gauss-Legendre points provided by gauss_nodes_and_weights to a complex interval \( (x_1,x_2) \).

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The documentation for this class was generated from the following files:

• src/gauss.h
• src/gauss.cpp