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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Collaboration 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. More...

virtual	~MonomialProjGramSchmidtPCEBasis2 ()
	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. More...

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. More...

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`. More...

virtual const std::string &	getName () const
	Return string name of basis.

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

Implementation of Stokhos::ReducedPCEBasis methods
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.

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 Member Functions
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`. More...

Protected Attributes
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::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.

Constructor & Destructor Documentation

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

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

Member Function Documentation

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

Referenced by Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >::MonomialProjGramSchmidtPCEBasis2().

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 >.

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 >.

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 >.

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

Stokhos_MonomialProjGramSchmidtPCEBasis2.hpp
Stokhos_MonomialProjGramSchmidtPCEBasis2Imp.hpp

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Detailed Description

template<typename ordinal_type, typename value_type> class Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >

Constructor & Destructor Documentation

Member Function Documentation

template<typename ordinal_type, typename value_type>
class Stokhos::MonomialProjGramSchmidtPCEBasis2< ordinal_type, value_type >