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concepts::QuadratureRuleGaussJacobi Class Reference

Gauss Jacobi quadrature rule not including both endpoints. More...

#include <quadRule.hh>

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List of all members.

Public Member Functions

virtual const Real * abscissas () const
 Returns a pointer into the array of the abscissas.
virtual uint n () const
 Returns the number of points.
void printRule ()
 print weights and abscissas to stdout
 QuadratureRuleGaussJacobi (uint n)
 Constructor.
virtual const Real * weights () const
 Returns a pointer into the array of the weights.
virtual ~QuadratureRuleGaussJacobi ()

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.

Private Attributes

Quadrature< 4 > rule_

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 $x_i$ 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 126 of file quadRule.hh.

Constructor & Destructor Documentation

concepts::QuadratureRuleGaussJacobi::QuadratureRuleGaussJacobi ( uint  n) [inline]

Constructor.

Computes the quadrature points.

Parameters:
nNumber of points to be computed

Definition at line 131 of file quadRule.hh.

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virtual concepts::QuadratureRuleGaussJacobi::~QuadratureRuleGaussJacobi ( ) [virtual]

Member Function Documentation

virtual const Real* concepts::QuadratureRuleDynamic::abscissas ( ) const [inline, virtual, inherited]

Returns a pointer into the array of the abscissas.

Implements concepts::QuadratureRule.

Reimplemented in concepts::QuadratureRuleTrapeze.

Definition at line 53 of file quadRule.hh.

virtual std::ostream& concepts::QuadratureRuleGaussJacobi::info ( std::ostream &  os) const [protected, virtual]

Returns information in an output stream.

Reimplemented from concepts::OutputOperator.

virtual uint concepts::QuadratureRuleGaussJacobi::n ( ) const [inline, virtual]

Returns the number of points.

Implements concepts::QuadratureRule.

Definition at line 136 of file quadRule.hh.

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void concepts::QuadratureRule::printRule ( ) [inherited]

print weights and abscissas to stdout

virtual const Real* concepts::QuadratureRuleDynamic::weights ( ) const [inline, virtual, inherited]

Returns a pointer into the array of the weights.

Implements concepts::QuadratureRule.

Reimplemented in concepts::QuadratureRuleTrapeze.

Definition at line 54 of file quadRule.hh.

Member Data Documentation

const Real* concepts::QuadratureRuleDynamic::abscissas_ [protected, inherited]

Abscissas.

Definition at line 57 of file quadRule.hh.

Quadrature<4> concepts::QuadratureRuleGaussJacobi::rule_ [private]

Definition at line 140 of file quadRule.hh.

const Real* concepts::QuadratureRuleDynamic::weights_ [protected, inherited]

Weights.

Definition at line 59 of file quadRule.hh.

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