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Stokhos::MonomialGramSchmidtPCEBasis< 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_MonomialGramSchmidtPCEBasis.hpp>

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

 MonomialGramSchmidtPCEBasis (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 ~MonomialGramSchmidtPCEBasis ()
 Destructor.
 
- Public Member Functions inherited from Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >
 GSReducedPCEBasisBase (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 ~GSReducedPCEBasisBase ()
 Destructor.
 
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 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.
 
- 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::OrthogPolyBasis 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.
 
virtual const std::string & getName () const
 Return string name of basis.
 
virtual ordinal_type buildReducedBasis (ordinal_type max_p, value_type threshold, const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &A, const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &F, const Teuchos::Array< value_type > &weights, 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 > &Q_)
 Build the reduced basis, parameterized by total order max_p.
 
 MonomialGramSchmidtPCEBasis (const MonomialGramSchmidtPCEBasis &)
 
MonomialGramSchmidtPCEBasisoperator= (const MonomialGramSchmidtPCEBasis &b)
 

Additional Inherited Members

- Protected Types inherited from Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >
typedef Stokhos::CompletePolynomialBasisUtils< ordinal_type, value_type > CPBUtils
 
typedef Teuchos::SerialDenseVector< ordinal_type, value_type > SDV
 
typedef Teuchos::SerialDenseMatrix< ordinal_type, value_type > SDM
 
- Protected Member Functions inherited from Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >
void setup (ordinal_type p, const Teuchos::Array< Stokhos::OrthogPolyApprox< ordinal_type, value_type > > &pce, const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &quad)
 
- Protected Attributes inherited from Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >
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
 

Detailed Description

template<typename ordinal_type, typename value_type>
class Stokhos::MonomialGramSchmidtPCEBasis< 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 59 of file Stokhos_MonomialGramSchmidtPCEBasis.hpp.

Member Typedef Documentation

◆ CPBUtils

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

Definition at line 116 of file Stokhos_MonomialGramSchmidtPCEBasis.hpp.

◆ SDV

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

Definition at line 117 of file Stokhos_MonomialGramSchmidtPCEBasis.hpp.

◆ SDM

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

Definition at line 118 of file Stokhos_MonomialGramSchmidtPCEBasis.hpp.

Constructor & Destructor Documentation

◆ MonomialGramSchmidtPCEBasis() [1/2]

template<typename ordinal_type , typename value_type >
Stokhos::MonomialGramSchmidtPCEBasis< ordinal_type, value_type >::MonomialGramSchmidtPCEBasis ( 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 46 of file Stokhos_MonomialGramSchmidtPCEBasisImp.hpp.

◆ ~MonomialGramSchmidtPCEBasis()

template<typename ordinal_type , typename value_type >
Stokhos::MonomialGramSchmidtPCEBasis< ordinal_type, value_type >::~MonomialGramSchmidtPCEBasis
virtual

Destructor.

Definition at line 59 of file Stokhos_MonomialGramSchmidtPCEBasisImp.hpp.

◆ MonomialGramSchmidtPCEBasis() [2/2]

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

Member Function Documentation

◆ getName()

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

Return string name of basis.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

Definition at line 66 of file Stokhos_MonomialGramSchmidtPCEBasisImp.hpp.

◆ buildReducedBasis()

template<typename ordinal_type , typename value_type >
ordinal_type Stokhos::MonomialGramSchmidtPCEBasis< ordinal_type, value_type >::buildReducedBasis ( ordinal_type  max_p,
value_type  threshold,
const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &  A,
const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &  F,
const Teuchos::Array< value_type > &  weights,
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 > &  Q_ 
)
protectedvirtual

Build the reduced basis, parameterized by total order max_p.

Returns resulting size of reduced basis

Implements Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >.

Definition at line 74 of file Stokhos_MonomialGramSchmidtPCEBasisImp.hpp.

◆ operator=()

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

Member Data Documentation

◆ name

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

Name of basis.

Definition at line 121 of file Stokhos_MonomialGramSchmidtPCEBasis.hpp.


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