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

Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...

#include <Stokhos_ProductLanczosGramSchmidtPCEBasis.hpp>

Inheritance diagram for Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >:
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Collaboration diagram for Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >:
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Public Member Functions

 ProductLanczosGramSchmidtPCEBasis (ordinal_type p, const Teuchos::Array< Stokhos::OrthogPolyApprox< ordinal_type, value_type > > &pce, const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &quad, const Teuchos::RCP< const Stokhos::Sparse3Tensor< ordinal_type, value_type > > &Cijk, const Teuchos::ParameterList &params=Teuchos::ParameterList())
 Constructor.
 
virtual ~ProductLanczosGramSchmidtPCEBasis ()
 Destructor.
 
Implementation of Stokhos::OrthogPolyBasis methods
ordinal_type order () const
 Return order of basis.
 
ordinal_type dimension () const
 Return dimension of basis.
 
virtual ordinal_type size () const
 Return total size of basis.
 
virtual const Teuchos::Array< value_type > & norm_squared () const
 Return array storing norm-squared of each basis polynomial.
 
virtual const value_type & norm_squared (ordinal_type i) const
 Return norm squared of basis polynomial i.
 
virtual Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > computeTripleProductTensor () const
 Compute triple product tensor.
 
virtual Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > computeLinearTripleProductTensor () const
 Compute linear triple product tensor where k = 0,1,..,d.
 
virtual value_type evaluateZero (ordinal_type i) const
 Evaluate basis polynomial i at zero.
 
virtual void evaluateBases (const Teuchos::ArrayView< const value_type > &point, Teuchos::Array< value_type > &basis_vals) const
 Evaluate basis polynomials at given point point.
 
virtual void print (std::ostream &os) const
 Print basis to stream os.
 
virtual const std::string & getName () const
 Return string name of basis.
 
- Public Member Functions inherited from Stokhos::ReducedPCEBasis< ordinal_type, value_type >
 ReducedPCEBasis ()
 Default constructor.
 
virtual ~ReducedPCEBasis ()
 Destructor.
 
- 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.
 
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.
 
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.
 
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.
 

Implementation of Stokhos::ReducedPCEBasis methods

typedef Teuchos::SerialDenseVector< ordinal_type, value_type > SDV
 
typedef Teuchos::SerialDenseMatrix< ordinal_type, value_type > SDM
 
std::string name
 Name of basis.
 
Teuchos::ParameterList params
 Algorithm parameters.
 
ordinal_type pce_sz
 Size of original pce basis.
 
ordinal_type p
 Total order of basis.
 
ordinal_type d
 Total dimension of basis.
 
ordinal_type sz
 Total size of basis.
 
Teuchos::RCP< Stokhos::CompletePolynomialBasis< ordinal_type, value_type > > tensor_lanczos_basis
 Product Lanczos basis.
 
Teuchos::Array< value_type > norms
 Norms.
 
SDM Q
 Values of transformed basis at quadrature points.
 
SDM Qp
 Coefficients of transformed basis in original basis.
 
Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > reduced_quad
 Reduced quadrature object.
 
Stokhos::OrthogPolyApprox< ordinal_type, value_type > tmp_pce
 Temporary pce used in invariant subspace calculations.
 
virtual void transformToOriginalBasis (const value_type *in, value_type *out, ordinal_type ncol=1, bool transpose=false) const
 Transform coefficients to original basis from this basis.
 
virtual void transformFromOriginalBasis (const value_type *in, value_type *out, ordinal_type ncol=1, bool transpose=false) const
 Transform coefficients from original basis to this basis.
 
virtual Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > getReducedQuadrature () const
 Get reduced quadrature object.
 
ordinal_type isInvariant (const Stokhos::OrthogPolyApprox< ordinal_type, value_type > &pce) const
 

Detailed Description

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

Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions.

Given the PCE expansions, first build a an orthogonal basis for each compnent, then form the multivariate basis by a total-order tensor product. The resulting basis is not necessarily orthogonal with respect to the full measure.

Constructor & Destructor Documentation

◆ ProductLanczosGramSchmidtPCEBasis()

template<typename ordinal_type , typename value_type >
Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >::ProductLanczosGramSchmidtPCEBasis ( ordinal_type  p,
const Teuchos::Array< Stokhos::OrthogPolyApprox< ordinal_type, value_type > > &  pce,
const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &  quad,
const Teuchos::RCP< const Stokhos::Sparse3Tensor< ordinal_type, value_type > > &  Cijk,
const Teuchos::ParameterList &  params = Teuchos::ParameterList() 
)

Member Function Documentation

◆ computeLinearTripleProductTensor()

template<typename ordinal_type , typename value_type >
Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >::computeLinearTripleProductTensor
virtual

Compute linear triple product tensor where k = 0,1,..,d.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

◆ computeTripleProductTensor()

template<typename ordinal_type , typename value_type >
Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >::computeTripleProductTensor
virtual

Compute triple product tensor.

The $(i,j,k)$ entry of the tensor $C_{ijk}$ is given by $C_{ijk} = \langle\Psi_i\Psi_j\Psi_k\rangle$ where $\Psi_l$ represents basis polynomial $l$ and $i,j,k=0,\dots,P$ where $P$ is size()-1.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

◆ dimension()

template<typename ordinal_type , typename value_type >
ordinal_type Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >::dimension
virtual

Return dimension of basis.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

◆ evaluateBases()

template<typename ordinal_type , typename value_type >
void Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >::evaluateBases ( const Teuchos::ArrayView< const value_type > &  point,
Teuchos::Array< value_type > &  basis_vals 
) const
virtual

Evaluate basis polynomials at given point point.

Size of returned array is given by size(), and coefficients are ordered from order 0 up to size size()-1.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

◆ evaluateZero()

template<typename ordinal_type , typename value_type >
value_type Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >::evaluateZero ( ordinal_type  i) const
virtual

Evaluate basis polynomial i at zero.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

◆ getName()

template<typename ordinal_type , typename value_type >
const std::string & Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >::getName
virtual

Return string name of basis.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

◆ getReducedQuadrature()

template<typename ordinal_type , typename value_type >
Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >::getReducedQuadrature
virtual

Get reduced quadrature object.

Implements Stokhos::ReducedPCEBasis< ordinal_type, value_type >.

◆ norm_squared() [1/2]

template<typename ordinal_type , typename value_type >
const Teuchos::Array< value_type > & Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >::norm_squared
virtual

Return array storing norm-squared of each basis polynomial.

Entry $l$ of returned array is given by $\langle\Psi_l^2\rangle$ for $l=0,\dots,P$ where $P$ is size()-1.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

◆ norm_squared() [2/2]

template<typename ordinal_type , typename value_type >
const value_type & Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >::norm_squared ( ordinal_type  i) const
virtual

Return norm squared of basis polynomial i.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

◆ order()

template<typename ordinal_type , typename value_type >
ordinal_type Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >::order
virtual

Return order of basis.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

◆ print()

template<typename ordinal_type , typename value_type >
void Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >::print ( std::ostream &  os) const
virtual

Print basis to stream os.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

◆ size()

template<typename ordinal_type , typename value_type >
ordinal_type Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >::size
virtual

Return total size of basis.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

◆ transformFromOriginalBasis()

template<typename ordinal_type , typename value_type >
void Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >::transformFromOriginalBasis ( const value_type *  in,
value_type *  out,
ordinal_type  ncol = 1,
bool  transpose = false 
) const
virtual

Transform coefficients from original basis to this basis.

Implements Stokhos::ReducedPCEBasis< ordinal_type, value_type >.

◆ transformToOriginalBasis()

template<typename ordinal_type , typename value_type >
void Stokhos::ProductLanczosGramSchmidtPCEBasis< ordinal_type, value_type >::transformToOriginalBasis ( const value_type *  in,
value_type *  out,
ordinal_type  ncol = 1,
bool  transpose = false 
) const
virtual

Transform coefficients to original basis from this basis.

Implements Stokhos::ReducedPCEBasis< ordinal_type, value_type >.


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