gsGaussRule< T > Class Template Reference

Detailed Description

template<class T>
class gismo::gsGaussRule< T >

Class that represents the (tensor) Gauss-Legendre quadrature rule.

Inheritance diagram for gsGaussRule< T >:

Collaboration diagram for gsGaussRule< T >:

Public Member Functions
index_t	dim () const
	Dimension of the rule.
	gsGaussRule ()
	Default empty constructor.
	gsGaussRule (gsVector< index_t > const &numNodes, const unsigned digits=0)
	Initialize a tensor-product Gauss quadrature rule with numNodes (direction-wise)
	gsGaussRule (index_t numNodes, const unsigned digits=0)
	Initialize a 1D Gauss quadrature rule with numNodes.
	gsGaussRule (const gsBasis< T > &basis, const T quA, const index_t quB, short_t fixDir=-1)
	gsGaussRule (const gsBasis< T > &basis, const gsOptionList &options, short_t fixDir=-1)
virtual void	mapTo (const gsVector< T > &lower, const gsVector< T > &upper, gsMatrix< T > &nodes, gsVector< T > &weights) const
	Maps quadrature rule (i.e., points and weights) from the reference domain to an element. More...
virtual void	mapTo (T startVal, T endVal, gsMatrix< T > &nodes, gsVector< T > &weights) const
	Maps a univariate quadrature rule (i.e., points and weights) from the reference interval to an arbitrary interval.
void	mapToAll (const std::vector< T > &breaks, gsMatrix< T > &nodes, gsVector< T > &weights) const
	Maps a univariate quadrature rule (i.e., points and weights) from the reference interval to a number of intervals, implied by the breaks.
index_t	numNodes () const
	Number of nodes in the currently kept rule.
const gsMatrix< T > &	referenceNodes () const
	Returns reference nodes for the currently kept rule. More...
const gsVector< T > &	referenceWeights () const
	Returns reference weights for the currently kept rule. More...
void	setNodes (gsVector< index_t > const &numNodes, unsigned digits=0)
	Initialize quadrature rule with numNodes number of quadrature points per integration variable. More...
void	setNodes (index_t numNodes, unsigned digits=0)
	Initialize a univariate quadrature rule with numNodes quadrature points. More...

Static Public Member Functions
static uPtr	make (gsVector< index_t > const &numNodes, const unsigned digits=0)
	Make function returning a smart pointer.

Protected Member Functions
void	computeTensorProductRule (const std::vector< gsVector< T > > &nodes, const std::vector< gsVector< T > > &weights)
	Computes the tensor product rule from coordinate-wise 1D nodes and weights.

Protected Attributes
gsMatrix< T >	m_nodes
	Reference quadrature nodes (on the interval [-1,1]).
gsVector< T >	m_weights
	Reference quadrature weights (corresponding to interval [-1,1]).

Static Private Member Functions
static void	computeReference (index_t n, gsVector< T > &x, gsVector< T > &w, unsigned digits=0)
	Computes the Gauss quadrature rule with n nodes in the interval [-1,1]. More...
static bool	lookupReference (index_t n, gsVector< T > &x, gsVector< T > &w)
	Look up function for the Gauss quadrature rule in the interval [-1,1]. More...

Constructor & Destructor Documentation

gsGaussRule	(	const gsBasis< T > &	basis,
		const T	quA,
		const index_t	quB,
		short_t	fixDir = -1
	)

Initialize a tensor-product Gauss quadrature rule for basis using quA *deg_i + quB nodes (direction-wise)

gsGaussRule	(	const gsBasis< T > &	basis,
		const gsOptionList &	options,
		short_t	fixDir = -1
	)

Initialize a tensor-product Gauss quadrature rule for basis using quA *deg_i + quB nodes (direction-wise). Values of quA and quB are taken from the options

Member Function Documentation

void computeReference ( index_t  n, gsVector< T > &  x, gsVector< T > &  w, unsigned  digits = 0  )

staticprivate

Computes the Gauss quadrature rule with n nodes in the interval [-1,1].

This function is called by setNodes(), if lookupReference() (which is called first) returned false.

bool lookupReference ( index_t  n, gsVector< T > &  x, gsVector< T > &  w  )

staticprivate

Look up function for the Gauss quadrature rule in the interval [-1,1].

When the member function setNodes() is called, it will first try to look up the corresponding Gauss rule. If this look up was not successful, the function computeReference() will be called.

Returns

true if the look up was successful

void mapTo ( const gsVector< T > &  lower, const gsVector< T > &  upper, gsMatrix< T > &  nodes, gsVector< T > &  weights  ) const

inlinevirtualinherited

Maps quadrature rule (i.e., points and weights) from the reference domain to an element.

The currently kept rule (which is initialized on the reference hypercube [-1,1]^d by calling setNodes()) is mapped to the d-dimensional hypercube specified by lower and upper.
For example, for d=2, the square [a,b]x[c,d] is defined by lower = [a,c], upper = [b,d].

Parameters

[in]	lower	vector of length d, defining the coordinates of the lower corner of the hypercube.
[in]	upper	vector of length d, defining the coordinates of the upper corner of the hypercube.
[in,out]	nodes	will be overwritten with the coordinates of the quadrature nodes. Size of the matrix nodes = d x n, where d is the dimension of the element, and n is the number of quadrature points.
[in,out]	weights	will be overwritten with the corresponding Gauss quadrature weights. Length of the vector weights = number of quadrature nodes.

Reimplemented in gsPatchRule< T >, and gsOverIntegrateRule< T >.

const gsMatrix<T>& referenceNodes ( ) const

inlineinherited

Returns reference nodes for the currently kept rule.

Returns

v Vector of length d = dim(), where each entry v_i of v is again a vector. v_i contains the reference quadrature points for the i-th coordinate direction.

const gsVector<T>& referenceWeights ( ) const

inlineinherited

Returns reference weights for the currently kept rule.

Returns

v Vector of length d = dim(), where each entry v_i of v is again a vector. v_i contains the reference quadrature weights for the i-th coordinate direction.

void setNodes ( gsVector< index_t > const &  , unsigned  = 0  )

virtual

Initialize quadrature rule with numNodes number of quadrature points per integration variable.

The call of this function initializes the quadrature rule for further use, i.e., the quadrature points and weights on the reference cube are set up and stored. The dimension d of the reference cube is specified by the length of the vector numNodes.

Example: numNodes = [2,5] corresponds to quadrature in 2D where two quadrature points are used for the first coordinate and five quadrature points for the second coordinate. In this case, 2*5 = 10 quadrature nodes and weights are set up.

---

Parameters
numNodes vector of length digits containing numbers of nodes to be used (per integration variable).
digits accuracy of nodes and weights. If 0, the quadrature rule will use precomputed tables if possible. If greater then 0, it will force to compute it everytime.

Reimplemented from gsQuadRule< T >.

void setNodes ( index_t  numNodes, unsigned  digits = 0  )

inlineinherited

Initialize a univariate quadrature rule with numNodes quadrature points.

Parameters

numNodes	quadrature point
digits	accuracy of nodes and weights. If 0, the quadrature rule will use precomputed tables if possible. If greater then 0, it will force to compute it everytime.