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_MonomialProjGramSchmidtPCEBasis.hpp>

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

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Collaboration diagram for Stokhos::MonomialProjGramSchmidtPCEBasis< ordinal_type, value_type >:

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Public Member Functions
	MonomialProjGramSchmidtPCEBasis (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	~MonomialProjGramSchmidtPCEBasis ()
	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.
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 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.
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::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`.

Additional Inherited Members
typedef Stokhos::CompletePolynomialBasisUtils< ordinal_type, value_type >	CPBUtils
typedef Teuchos::SerialDenseVector< ordinal_type, value_type >	SDV
typedef Teuchos::SerialDenseMatrix< ordinal_type, value_type >	SDM
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)
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::MonomialProjGramSchmidtPCEBasis< 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.

Constructor & Destructor Documentation

◆ MonomialProjGramSchmidtPCEBasis()

template<typename ordinal_type, typename value_type>

Stokhos::MonomialProjGramSchmidtPCEBasis< ordinal_type, value_type >::MonomialProjGramSchmidtPCEBasis	(	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

p	order of the basis
pce	polynomial chaos expansions defining new measure
quad	quadrature data for basis defining pce
Cijk	sparse triple product tensor for basis defining pce
sparse_tol	tolerance for dropping terms in sparse tensors

References Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >::GSReducedPCEBasisBase(), name, and Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >::params.

Member Function Documentation

◆ buildReducedBasis()

template<typename ordinal_type, typename value_type>

ordinal_type Stokhos::MonomialProjGramSchmidtPCEBasis< 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 >.

References Stokhos::CompletePolynomialBasisUtils< ordinal_type, value_type >::compute_terms(), Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >::d, Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >::orthogonalization_method, Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >::pce_basis, Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >::pce_sz, Stokhos::ProductContainer< coeff_type >::size(), and Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >::verbose.

◆ getName()

template<typename ordinal_type, typename value_type>

const std::string & Stokhos::MonomialProjGramSchmidtPCEBasis< ordinal_type, value_type >::getName ( ) const

virtual

Return string name of basis.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

References name.

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

Stokhos_MonomialProjGramSchmidtPCEBasis.hpp
Stokhos_MonomialProjGramSchmidtPCEBasisImp.hpp

Public Member Functions

Implementation of Stokhos::OrthogPolyBasis methods

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ MonomialProjGramSchmidtPCEBasis()

Member Function Documentation

◆ buildReducedBasis()

◆ getName()