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 >:

[legend]

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. More...

virtual	~MonomialGramSchmidtPCEBasis ()
	Destructor. More...

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. More...

virtual	~GSReducedPCEBasisBase ()
	Destructor. More...

ordinal_type	order () const
	Return order of basis. More...

ordinal_type	dimension () const
	Return dimension of basis. More...

virtual ordinal_type	size () const
	Return total size of basis. More...

virtual const Teuchos::Array < value_type > &	norm_squared () const
	Return array storing norm-squared of each basis polynomial. More...

virtual const value_type &	norm_squared (ordinal_type i) const
	Return norm squared of basis polynomial `i`. More...

virtual Teuchos::RCP < Stokhos::Sparse3Tensor < ordinal_type, value_type > >	computeTripleProductTensor () const
	Compute triple product tensor. More...

virtual Teuchos::RCP < Stokhos::Sparse3Tensor < ordinal_type, value_type > >	computeLinearTripleProductTensor () const
	Compute linear triple product tensor where k = 0,1,..,d. More...

virtual value_type	evaluateZero (ordinal_type i) const
	Evaluate basis polynomial `i` at zero. More...

virtual void	evaluateBases (const Teuchos::ArrayView< const value_type > &point, Teuchos::Array< value_type > &basis_vals) const
	Evaluate basis polynomials at given point `point`. More...

virtual void	print (std::ostream &os) const
	Print basis to stream `os`. More...

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. More...

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. More...

virtual Teuchos::RCP< const Stokhos::Quadrature < ordinal_type, value_type > >	getReducedQuadrature () const
	Get reduced quadrature object. More...

Public Member Functions inherited from Stokhos::ReducedPCEBasis< ordinal_type, value_type >
	ReducedPCEBasis ()
	Default constructor. More...

virtual	~ReducedPCEBasis ()
	Destructor. More...

Public Member Functions inherited from Stokhos::OrthogPolyBasis< ordinal_type, value_type >
	OrthogPolyBasis ()
	Constructor. More...

virtual	~OrthogPolyBasis ()
	Destructor. More...

Protected Types
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 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
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`. More...

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
std::string	name
	Name of basis. More...

Protected Attributes inherited from Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >
std::string	name
	Name of basis. More...

Teuchos::ParameterList	params
	Algorithm parameters. More...

Teuchos::RCP< const Stokhos::OrthogPolyBasis < ordinal_type, value_type > >	pce_basis
	Original pce basis. More...

ordinal_type	pce_sz
	Size of original pce basis. More...

ordinal_type	p
	Total order of basis. More...

ordinal_type	d
	Total dimension of basis. More...

ordinal_type	sz
	Total size of basis. More...

Teuchos::Array < Stokhos::MultiIndex < ordinal_type > >	terms
	2-D array of basis terms More...

Teuchos::Array< ordinal_type >	num_terms
	Number of terms up to each order. More...

Teuchos::Array< value_type >	norms
	Norms. More...

SDM	Q
	Values of transformed basis at quadrature points. More...

SDM	Qp
	Coefficients of transformed basis in original basis. More...

Teuchos::RCP< const Stokhos::Quadrature < ordinal_type, value_type > >	reduced_quad
	Reduced quadrature object. More...

bool	verbose
	Whether to print a bunch of stuff out. More...

value_type	rank_threshold
	Rank threshold. More...

std::string	orthogonalization_method
	Orthogonalization method. More...

Teuchos::BLAS< ordinal_type, value_type >	blas

Private Member Functions
	MonomialGramSchmidtPCEBasis (const MonomialGramSchmidtPCEBasis &)

MonomialGramSchmidtPCEBasis &	operator= (const MonomialGramSchmidtPCEBasis &b)

Implementation of Stokhos::OrthogPolyBasis methods
virtual const std::string &	getName () const
	Return string name of basis. More...

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 27 of file Stokhos_MonomialGramSchmidtPCEBasis.hpp.

Member Typedef Documentation

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 84 of file Stokhos_MonomialGramSchmidtPCEBasis.hpp.

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 85 of file Stokhos_MonomialGramSchmidtPCEBasis.hpp.

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 86 of file Stokhos_MonomialGramSchmidtPCEBasis.hpp.

Constructor & Destructor Documentation

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

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

Definition at line 15 of file Stokhos_MonomialGramSchmidtPCEBasisImp.hpp.

template<typename ordinal_type , typename value_type >

Stokhos::MonomialGramSchmidtPCEBasis< ordinal_type, value_type >::~MonomialGramSchmidtPCEBasis ( )

virtual

Destructor.

Definition at line 28 of file Stokhos_MonomialGramSchmidtPCEBasisImp.hpp.

template<typename ordinal_type , typename value_type >

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

private

Member Function Documentation

template<typename ordinal_type , typename value_type >

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

virtual

Return string name of basis.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

Definition at line 35 of file Stokhos_MonomialGramSchmidtPCEBasisImp.hpp.

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 43 of file Stokhos_MonomialGramSchmidtPCEBasisImp.hpp.

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

template<typename ordinal_type , typename value_type >

std::string Stokhos::MonomialGramSchmidtPCEBasis< ordinal_type, value_type >::name

protected

Name of basis.

Definition at line 89 of file Stokhos_MonomialGramSchmidtPCEBasis.hpp.

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

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Private Member Functions

Implementation of Stokhos::OrthogPolyBasis methods

Detailed Description

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

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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