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Stokhos::GramSchmidtBasis< ordinal_type, value_type > Class Template Reference

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

#include <Stokhos_GramSchmidtBasis.hpp>

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Additional Inherited Members

- Public Member Functions inherited from Stokhos::OrthogPolyBasis< ordinal_type, value_type >
 OrthogPolyBasis ()
 Constructor.
 
virtual ~OrthogPolyBasis ()
 Destructor.
 
virtual ordinal_type order () const =0
 Return order of basis.
 
virtual ordinal_type dimension () const =0
 Return dimension of basis.
 
virtual ordinal_type size () const =0
 Return total size of basis.
 
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.
 
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.
 
virtual value_type evaluateZero (ordinal_type i) const =0
 Evaluate basis polynomial i at zero.
 
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.
 
virtual const std::string & getName () const =0
 Return string name of basis.
 

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.


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