Transforms a non-orthogonal multivariate basis to an orthogonal one using the Gram-Schmit procedure. More...

#include <Stokhos_GramSchmidtBasis.hpp>

Inheritance diagram for Stokhos::GramSchmidtBasis< ordinal_type, value_type >:

Additional Inherited Members
Public Member Functions inherited from Stokhos::OrthogPolyBasis< ordinal_type, value_type >
	OrthogPolyBasis ()
	Constructor. More...

virtual	~OrthogPolyBasis ()
	Destructor. More...

virtual ordinal_type	order () const =0
	Return order of basis. More...

virtual ordinal_type	dimension () const =0
	Return dimension of basis. More...

virtual ordinal_type	size () const =0
	Return total size of basis. More...

virtual const Teuchos::Array < value_type > &	norm_squared () const =0
	Return array storing norm-squared of each basis polynomial. More...

virtual const value_type &	norm_squared (ordinal_type i) const =0
	Return norm squared of basis polynomial `i`. More...

virtual Teuchos::RCP < Stokhos::Sparse3Tensor < ordinal_type, value_type > >	computeTripleProductTensor () const =0
	Compute triple product tensor. More...

virtual Teuchos::RCP < Stokhos::Sparse3Tensor < ordinal_type, value_type > >	computeLinearTripleProductTensor () const =0
	Compute linear triple product tensor where k = 0,1. More...

virtual value_type	evaluateZero (ordinal_type i) const =0
	Evaluate basis polynomial `i` at zero. More...

virtual void	evaluateBases (const Teuchos::ArrayView< const value_type > &point, Teuchos::Array< value_type > &basis_vals) const =0
	Evaluate basis polynomials at given point `point`. More...

virtual void	print (std::ostream &os) const =0
	Print basis to stream `os`. More...

virtual const std::string &	getName () const =0
	Return string name of basis. More...

Detailed Description

template<typename ordinal_type, typename value_type>
class Stokhos::GramSchmidtBasis< ordinal_type, value_type >

Transforms a non-orthogonal multivariate basis to an orthogonal one using the Gram-Schmit procedure.

Given a basis $\{\Psi_i\}$ with an inner product defined by

$(\Psi_i,\Psi_j) = \sum_{k=0}^Q w_k\Psi_i(x_k)\Psi_j(x_k)$

where $\{x_k\}$ and $\{w_k\}$ are a set of $Q$ quadrature points and weights, this class generates a new basis $\{\tilde{\Psi}_i\}$ that satisfies $(\Psi_i,\Psi_j) = \delta_{ij}$ .

NOTE: Currently on the classical Gram-Schmidt algorithm is implemented.

Definition at line 38 of file Stokhos_GramSchmidtBasis.hpp.

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

Stokhos_GramSchmidtBasis.hpp

Additional Inherited Members

Detailed Description

template<typename ordinal_type, typename value_type> class Stokhos::GramSchmidtBasis< ordinal_type, value_type >

template<typename ordinal_type, typename value_type>
class Stokhos::GramSchmidtBasis< ordinal_type, value_type >