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Stokhos::MonomialProjGramSchmidtPCEBasis2< 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_MonomialProjGramSchmidtPCEBasis2.hpp>

Inheritance diagram for Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >:
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Public Member Functions

 MonomialProjGramSchmidtPCEBasis2 (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::ParameterList &params=Teuchos::ParameterList())
 Constructor.
 
virtual ~MonomialProjGramSchmidtPCEBasis2 ()
 Destructor.
 
- 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.
 

Implementation of Stokhos::ReducedPCEBasis methods

typedef Stokhos::CompletePolynomialBasisUtils< ordinal_type, value_type > CPBUtils
 
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.
 
Teuchos::RCP< const Stokhos::OrthogPolyBasis< ordinal_type, value_type > > pce_basis
 Original pce basis.
 
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::Array< Stokhos::MultiIndex< ordinal_type > > terms
 2-D array of basis terms
 
Teuchos::Array< ordinal_type > num_terms
 Number of terms up to each order.
 
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.
 
bool verbose
 Whether to print a bunch of stuff out.
 
value_type rank_threshold
 Rank threshold.
 
std::string orthogonalization_method
 Orthogonalization method.
 
Teuchos::BLAS< ordinal_type, value_type > blas
 
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 buildQ (ordinal_type max_p, value_type threshold, const Teuchos::Array< Stokhos::OrthogPolyApprox< ordinal_type, value_type > > &pce, const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &quad, Teuchos::Array< Stokhos::MultiIndex< ordinal_type > > &terms_, Teuchos::Array< ordinal_type > &num_terms_, Teuchos::SerialDenseMatrix< ordinal_type, value_type > &Qp_, Teuchos::SerialDenseMatrix< ordinal_type, value_type > &A_, Teuchos::SerialDenseMatrix< ordinal_type, value_type > &F_)
 Build the reduced basis, parameterized by total order max_p.
 
 MonomialProjGramSchmidtPCEBasis2 (const MonomialProjGramSchmidtPCEBasis2 &)
 
MonomialProjGramSchmidtPCEBasis2operator= (const MonomialProjGramSchmidtPCEBasis2 &b)
 

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 const std::string & getName () const
 Return string name of basis.
 
virtual void print (std::ostream &os) const
 Print basis to stream os.
 

Detailed Description

template<typename ordinal_type, typename value_type>
class Stokhos::MonomialProjGramSchmidtPCEBasis2< 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 non-orthogonal monomial basis.
Orthogonalize this basis using Gram-Schmidt, then build a quadrature rule using the simplex method.

Definition at line 69 of file Stokhos_MonomialProjGramSchmidtPCEBasis2.hpp.

Member Typedef Documentation

◆ CPBUtils

template<typename ordinal_type , typename value_type >
typedef Stokhos::CompletePolynomialBasisUtils<ordinal_type,value_type> Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::CPBUtils
protected

◆ SDV

template<typename ordinal_type , typename value_type >
typedef Teuchos::SerialDenseVector<ordinal_type,value_type> Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::SDV
protected

◆ SDM

template<typename ordinal_type , typename value_type >
typedef Teuchos::SerialDenseMatrix<ordinal_type,value_type> Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::SDM
protected

Constructor & Destructor Documentation

◆ MonomialProjGramSchmidtPCEBasis2() [1/2]

template<typename ordinal_type , typename value_type >
Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::MonomialProjGramSchmidtPCEBasis2 ( 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::ParameterList & params = Teuchos::ParameterList() )

Constructor.

Parameters
porder of the basis
pcepolynomial chaos expansions defining new measure
quadquadrature data for basis defining pce
Cijksparse triple product tensor for basis defining pce
sparse_toltolerance for dropping terms in sparse tensors

Definition at line 49 of file Stokhos_MonomialProjGramSchmidtPCEBasis2Imp.hpp.

◆ ~MonomialProjGramSchmidtPCEBasis2()

template<typename ordinal_type , typename value_type >
Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::~MonomialProjGramSchmidtPCEBasis2 ( )
virtual

Destructor.

Definition at line 287 of file Stokhos_MonomialProjGramSchmidtPCEBasis2Imp.hpp.

◆ MonomialProjGramSchmidtPCEBasis2() [2/2]

template<typename ordinal_type , typename value_type >
Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::MonomialProjGramSchmidtPCEBasis2 ( const MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type > & )
private

Member Function Documentation

◆ order()

template<typename ordinal_type , typename value_type >
ordinal_type Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::order ( ) const
virtual

◆ dimension()

template<typename ordinal_type , typename value_type >
ordinal_type Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::dimension ( ) const
virtual

Return dimension of basis.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

Definition at line 302 of file Stokhos_MonomialProjGramSchmidtPCEBasis2Imp.hpp.

◆ size()

template<typename ordinal_type , typename value_type >
ordinal_type Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::size ( ) const
virtual

Return total size of basis.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

Definition at line 310 of file Stokhos_MonomialProjGramSchmidtPCEBasis2Imp.hpp.

◆ norm_squared() [1/2]

template<typename ordinal_type , typename value_type >
const Teuchos::Array< value_type > & Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::norm_squared ( ) const
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 >.

Definition at line 318 of file Stokhos_MonomialProjGramSchmidtPCEBasis2Imp.hpp.

◆ norm_squared() [2/2]

template<typename ordinal_type , typename value_type >
const value_type & Stokhos::MonomialProjGramSchmidtPCEBasis2< 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 >.

Definition at line 326 of file Stokhos_MonomialProjGramSchmidtPCEBasis2Imp.hpp.

◆ computeTripleProductTensor()

template<typename ordinal_type , typename value_type >
Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::computeTripleProductTensor ( ) const
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 >.

Definition at line 334 of file Stokhos_MonomialProjGramSchmidtPCEBasis2Imp.hpp.

◆ computeLinearTripleProductTensor()

template<typename ordinal_type , typename value_type >
Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::computeLinearTripleProductTensor ( ) const
virtual

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

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

Definition at line 343 of file Stokhos_MonomialProjGramSchmidtPCEBasis2Imp.hpp.

◆ evaluateZero()

template<typename ordinal_type , typename value_type >
value_type Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::evaluateZero ( ordinal_type i) const
virtual

Evaluate basis polynomial i at zero.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

Definition at line 352 of file Stokhos_MonomialProjGramSchmidtPCEBasis2Imp.hpp.

◆ evaluateBases()

template<typename ordinal_type , typename value_type >
void Stokhos::MonomialProjGramSchmidtPCEBasis2< 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 >.

Definition at line 360 of file Stokhos_MonomialProjGramSchmidtPCEBasis2Imp.hpp.

◆ getName()

template<typename ordinal_type , typename value_type >
const std::string & Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::getName ( ) const
virtual

Return string name of basis.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

Definition at line 369 of file Stokhos_MonomialProjGramSchmidtPCEBasis2Imp.hpp.

◆ print()

template<typename ordinal_type , typename value_type >
void Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::print ( std::ostream & os) const
virtual

Print basis to stream os.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

Definition at line 377 of file Stokhos_MonomialProjGramSchmidtPCEBasis2Imp.hpp.

◆ transformToOriginalBasis()

template<typename ordinal_type , typename value_type >
void Stokhos::MonomialProjGramSchmidtPCEBasis2< 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 >.

Definition at line 391 of file Stokhos_MonomialProjGramSchmidtPCEBasis2Imp.hpp.

◆ transformFromOriginalBasis()

template<typename ordinal_type , typename value_type >
void Stokhos::MonomialProjGramSchmidtPCEBasis2< 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 >.

Definition at line 413 of file Stokhos_MonomialProjGramSchmidtPCEBasis2Imp.hpp.

◆ getReducedQuadrature()

template<typename ordinal_type , typename value_type >
Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::getReducedQuadrature ( ) const
virtual

Get reduced quadrature object.

Implements Stokhos::ReducedPCEBasis< ordinal_type, value_type >.

Definition at line 435 of file Stokhos_MonomialProjGramSchmidtPCEBasis2Imp.hpp.

◆ buildQ()

template<typename ordinal_type , typename value_type >
ordinal_type Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::buildQ ( ordinal_type max_p,
value_type threshold,
const Teuchos::Array< Stokhos::OrthogPolyApprox< ordinal_type, value_type > > & pce,
const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > & quad,
Teuchos::Array< Stokhos::MultiIndex< ordinal_type > > & terms_,
Teuchos::Array< ordinal_type > & num_terms_,
Teuchos::SerialDenseMatrix< ordinal_type, value_type > & Qp_,
Teuchos::SerialDenseMatrix< ordinal_type, value_type > & A_,
Teuchos::SerialDenseMatrix< ordinal_type, value_type > & F_ )
protected

Build the reduced basis, parameterized by total order max_p.

Returns resulting size of reduced basis

Definition at line 180 of file Stokhos_MonomialProjGramSchmidtPCEBasis2Imp.hpp.

◆ operator=()

template<typename ordinal_type , typename value_type >
MonomialProjGramSchmidtPCEBasis2 & Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::operator= ( const MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type > & b)
private

Member Data Documentation

◆ name

template<typename ordinal_type , typename value_type >
std::string Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::name
protected

Name of basis.

Definition at line 204 of file Stokhos_MonomialProjGramSchmidtPCEBasis2.hpp.

◆ params

template<typename ordinal_type , typename value_type >
Teuchos::ParameterList Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::params
protected

Algorithm parameters.

Definition at line 207 of file Stokhos_MonomialProjGramSchmidtPCEBasis2.hpp.

◆ pce_basis

template<typename ordinal_type , typename value_type >
Teuchos::RCP<const Stokhos::OrthogPolyBasis<ordinal_type,value_type> > Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::pce_basis
protected

Original pce basis.

Definition at line 210 of file Stokhos_MonomialProjGramSchmidtPCEBasis2.hpp.

◆ pce_sz

template<typename ordinal_type , typename value_type >
ordinal_type Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::pce_sz
protected

Size of original pce basis.

Definition at line 213 of file Stokhos_MonomialProjGramSchmidtPCEBasis2.hpp.

◆ p

template<typename ordinal_type , typename value_type >
ordinal_type Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::p
protected

Total order of basis.

Definition at line 216 of file Stokhos_MonomialProjGramSchmidtPCEBasis2.hpp.

◆ d

template<typename ordinal_type , typename value_type >
ordinal_type Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::d
protected

Total dimension of basis.

Definition at line 219 of file Stokhos_MonomialProjGramSchmidtPCEBasis2.hpp.

◆ sz

template<typename ordinal_type , typename value_type >
ordinal_type Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::sz
protected

Total size of basis.

Definition at line 222 of file Stokhos_MonomialProjGramSchmidtPCEBasis2.hpp.

◆ terms

template<typename ordinal_type , typename value_type >
Teuchos::Array< Stokhos::MultiIndex<ordinal_type> > Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::terms
protected

2-D array of basis terms

Definition at line 225 of file Stokhos_MonomialProjGramSchmidtPCEBasis2.hpp.

◆ num_terms

template<typename ordinal_type , typename value_type >
Teuchos::Array<ordinal_type> Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::num_terms
protected

Number of terms up to each order.

Definition at line 228 of file Stokhos_MonomialProjGramSchmidtPCEBasis2.hpp.

◆ norms

template<typename ordinal_type , typename value_type >
Teuchos::Array<value_type> Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::norms
protected

Norms.

Definition at line 231 of file Stokhos_MonomialProjGramSchmidtPCEBasis2.hpp.

◆ Q

template<typename ordinal_type , typename value_type >
SDM Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::Q
protected

Values of transformed basis at quadrature points.

Definition at line 234 of file Stokhos_MonomialProjGramSchmidtPCEBasis2.hpp.

◆ Qp

template<typename ordinal_type , typename value_type >
SDM Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::Qp
protected

Coefficients of transformed basis in original basis.

Definition at line 237 of file Stokhos_MonomialProjGramSchmidtPCEBasis2.hpp.

◆ reduced_quad

template<typename ordinal_type , typename value_type >
Teuchos::RCP<const Stokhos::Quadrature<ordinal_type, value_type> > Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::reduced_quad
protected

Reduced quadrature object.

Definition at line 240 of file Stokhos_MonomialProjGramSchmidtPCEBasis2.hpp.

◆ verbose

template<typename ordinal_type , typename value_type >
bool Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::verbose
protected

Whether to print a bunch of stuff out.

Definition at line 243 of file Stokhos_MonomialProjGramSchmidtPCEBasis2.hpp.

◆ rank_threshold

template<typename ordinal_type , typename value_type >
value_type Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::rank_threshold
protected

Rank threshold.

Definition at line 246 of file Stokhos_MonomialProjGramSchmidtPCEBasis2.hpp.

◆ orthogonalization_method

template<typename ordinal_type , typename value_type >
std::string Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::orthogonalization_method
protected

Orthogonalization method.

Definition at line 249 of file Stokhos_MonomialProjGramSchmidtPCEBasis2.hpp.

◆ blas

template<typename ordinal_type , typename value_type >
Teuchos::BLAS<ordinal_type,value_type> Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::blas
protected

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