#include <quadRule.hh>

Inheritance diagram for concepts::QuadratureRule1dGaussJacobi:

Public Member Functions
	QuadratureRule1dGaussJacobi (uint n)

virtual uint	n () const
	Returns the number of points.

virtual const Real *	abscissas () const
	Returns a pointer into the array of the abscissas.

virtual const Real *	weights () const
	Returns a pointer into the array of the weights.

virtual void	printRule ()
	print weights and abscissas to stdout

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.

Protected Attributes
const Real *	abscissas_
	Abscissas.

const Real *	weights_
	Weights.

Detailed Description

Gauss Jacobi quadrature rule not including both endpoints.

$\int_{-1}^1 f(x) \, dx \approx \sum_{i=0}^p w_i f(x_i)$

is exact for $f \in P_{2p+1}$ and n = p+1 points. n must be greater or equal to 1.

The abscissas are the zeros of $P_{p+1}^{(0,0)}(x)$ and the weights are

$w_i = \frac{2}{1-x_i^2} \left( \frac{d}{dx} \left. P^{(0,0)}_{p+1}(x) \right|_{x=x_i} \right)^{-2}.$

The computations and the storage of the values are done by the class Quadrature with template parameter 4. The difference between this class and Quadrature is that it is in a class hierarchy of quadrature rules. This has advantages when dynamically switching quadrature rules is needed. On the other hand, this class returns the values via a virtual function call abscissas() and weights() should therefore not be called to often (inside loops etc.).

See also: Quadrature

Author: Philipp Frauenfelder, 2004

Definition at line 135 of file quadRule.hh.

Constructor & Destructor Documentation

◆ QuadratureRule1dGaussJacobi()

concepts::QuadratureRule1dGaussJacobi::QuadratureRule1dGaussJacobi ( uint n )

inline

Constructor. Computes the quadrature points.

Parameters

n	Number of points to be computed

Definition at line 140 of file quadRule.hh.

Member Function Documentation

◆ abscissas()

virtual const Real * concepts::QuadratureRule1dDynamic::abscissas ( ) const

inlinevirtualinherited

Returns a pointer into the array of the abscissas.

Implements concepts::QuadratureRule1d.

Reimplemented in concepts::QuadratureRule1dTrapeze.

Definition at line 62 of file quadRule.hh.

◆ info()

virtual std::ostream & concepts::QuadratureRule1dGaussJacobi::info ( std::ostream & os ) const

protectedvirtual

Returns information in an output stream.

Reimplemented from concepts::OutputOperator.

◆ n()

virtual uint concepts::QuadratureRule1dGaussJacobi::n ( ) const

inlinevirtual

Returns the number of points.

Implements concepts::QuadratureRule1d.

Definition at line 145 of file quadRule.hh.

◆ printRule()

virtual void concepts::QuadratureRule1d::printRule ( )

virtualinherited

print weights and abscissas to stdout

Reimplemented in concepts::AdaptiveQuadratureRule1d< ruleType >.

◆ weights()

virtual const Real * concepts::QuadratureRule1dDynamic::weights ( ) const

inlinevirtualinherited

Returns a pointer into the array of the weights.

Implements concepts::QuadratureRule1d.

Reimplemented in concepts::QuadratureRule1dTrapeze.

Definition at line 63 of file quadRule.hh.

Member Data Documentation

◆ abscissas_

const Real* concepts::QuadratureRule1dDynamic::abscissas_

protectedinherited

Abscissas.

Definition at line 66 of file quadRule.hh.

◆ weights_

const Real* concepts::QuadratureRule1dDynamic::weights_

protectedinherited

Weights.

Definition at line 68 of file quadRule.hh.

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

integration/quadRule.hh

Class documentation of Concepts

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ QuadratureRule1dGaussJacobi()

Member Function Documentation

◆ abscissas()

◆ info()

◆ n()

◆ printRule()

◆ weights()

Member Data Documentation

◆ abscissas_

◆ weights_