Home | Doxygen Documentation | Tutorials | Developer Tools (restricted)
Public Member Functions | Protected Member Functions | Protected Attributes | Private Attributes
concepts::QuadratureRuleGaussLobatto Class Reference

Gauss Lobatto quadrature rule including both endpoints. More...

#include <quadRule.hh>

Inheritance diagram for concepts::QuadratureRuleGaussLobatto:
Inheritance graph
[legend]
Collaboration diagram for concepts::QuadratureRuleGaussLobatto:
Collaboration graph
[legend]

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
 QuadratureRuleGaussLobatto (uint n)
 Constructor.
virtual const Real * weights () const
 Returns a pointer into the array of the weights.
virtual ~QuadratureRuleGaussLobatto ()

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< 0 > rule_

Detailed Description

Gauss Lobatto quadrature rule 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 2.

The abscissas $x_i$ are the zeros of $(1-x^2) P_{p-1}^{(1,1)}(x)$ and the weights are $w_i = 2/(p(p+1) (P_p^{(0,0)}(x_i))^2)$.

The computations and the storage of the values are done by the class Quadrature with template parameter 0. 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 85 of file quadRule.hh.

Constructor & Destructor Documentation

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

Constructor.

Computes the quadrature points.

Parameters:
nNumber of points to be computed

Definition at line 91 of file quadRule.hh.

Here is the call graph for this function:

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

Returns information in an output stream.

Reimplemented from concepts::OutputOperator.

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

Returns the number of points.

Implements concepts::QuadratureRule.

Definition at line 96 of file quadRule.hh.

Here is the call graph for this function:

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<0> concepts::QuadratureRuleGaussLobatto::rule_ [private]

Definition at line 100 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:
Home | Doxygen Documentation | Tutorials | Developer Tools (restricted)