concepts::QuadratureRule1dGaussJacobi Class Reference
Gauss Jacobi quadrature rule not including both endpoints. More...
#include <quadRule.hh>
Public Member Functions | |
| virtual const Real * | abscissas () const |
| Returns a pointer into the array of the abscissas. More... | |
| virtual uint | n () const |
| Returns the number of points. More... | |
| virtual void | printRule () |
| print weights and abscissas to stdout More... | |
| QuadratureRule1dGaussJacobi (uint n) | |
| Constructor. More... | |
| virtual const Real * | weights () const |
| Returns a pointer into the array of the weights. More... | |
| virtual | ~QuadratureRule1dGaussJacobi () |
Protected Member Functions | |
| virtual std::ostream & | info (std::ostream &os) const |
| Returns information in an output stream. More... | |
Protected Attributes | |
| const Real * | abscissas_ |
| Abscissas. More... | |
| const Real * | weights_ |
| Weights. More... | |
Private Attributes | |
| Quadrature< 4 > | rule_ |
Detailed Description
Gauss Jacobi quadrature rule not including both endpoints.
![\[ \int_{-1}^1 f(x) \, dx \approx \sum_{i=0}^p w_i f(x_i) \]](form_615.png)
is exact for 
and n = p+1 points. n must be greater or equal to 1.
The abscissas 
are the zeros of 
and the weights are
![\[w_i = \frac{2}{1-x_i^2} \left( \frac{d}{dx} \left. P^{(0,0)}_{p+1}(x) \right|_{x=x_i} \right)^{-2}.\]](form_633.png)
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
Definition at line 135 of file quadRule.hh.
Constructor & Destructor Documentation
◆ QuadratureRule1dGaussJacobi()
|
inline |
Constructor.
Computes the quadrature points.
- Parameters
-
n Number of points to be computed
Definition at line 140 of file quadRule.hh.
◆ ~QuadratureRule1dGaussJacobi()
|
virtual |
Member Function Documentation
◆ abscissas()
|
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()
|
protectedvirtual |
Returns information in an output stream.
Reimplemented from concepts::OutputOperator.
◆ n()
|
inlinevirtual |
Returns the number of points.
Implements concepts::QuadratureRule1d.
Definition at line 145 of file quadRule.hh.
◆ printRule()
|
virtualinherited |
print weights and abscissas to stdout
Reimplemented in concepts::AdaptiveQuadratureRule1d< ruleType >.
◆ weights()
|
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_
|
protectedinherited |
Abscissas.
Definition at line 66 of file quadRule.hh.
◆ rule_
|
private |
Definition at line 149 of file quadRule.hh.
◆ 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