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_GSReducedPCEBasisBase.hpp>

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

[legend]

Public Member Functions
	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...

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...

virtual const std::string &	getName () const =0
	Return string name of basis. 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 Member Functions
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)

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_)=0
	Build the reduced basis, parameterized by total order `max_p`. More...

Protected Attributes
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
	GSReducedPCEBasisBase (const GSReducedPCEBasisBase &)

GSReducedPCEBasisBase &	operator= (const GSReducedPCEBasisBase &b)

Implementation of Stokhos::OrthogPolyBasis methods
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...

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. 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...

Detailed Description

template<typename ordinal_type, typename value_type>
class Stokhos::GSReducedPCEBasisBase< 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_GSReducedPCEBasisBase.hpp.

Member Typedef Documentation

template<typename ordinal_type , typename value_type >

typedef Stokhos::CompletePolynomialBasisUtils<ordinal_type,value_type> Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >::CPBUtils

protected

Definition at line 201 of file Stokhos_GSReducedPCEBasisBase.hpp.

template<typename ordinal_type , typename value_type >

typedef Teuchos::SerialDenseVector<ordinal_type,value_type> Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >::SDV

protected

Definition at line 202 of file Stokhos_GSReducedPCEBasisBase.hpp.

template<typename ordinal_type , typename value_type >

typedef Teuchos::SerialDenseMatrix<ordinal_type,value_type> Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >::SDM

protected

Definition at line 203 of file Stokhos_GSReducedPCEBasisBase.hpp.

Constructor & Destructor Documentation

template<typename ordinal_type , typename value_type >

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.

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 46 of file Stokhos_GSReducedPCEBasisBaseImp.hpp.

template<typename ordinal_type , typename value_type >

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

virtual

Destructor.

Definition at line 143 of file Stokhos_GSReducedPCEBasisBaseImp.hpp.

template<typename ordinal_type , typename value_type >

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

private

Member Function Documentation

template<typename ordinal_type , typename value_type >

ordinal_type Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >::order ( ) const

virtual

Return order of basis.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

Definition at line 150 of file Stokhos_GSReducedPCEBasisBaseImp.hpp.

template<typename ordinal_type , typename value_type >

ordinal_type Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >::dimension ( ) const

virtual

Return dimension of basis.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

Definition at line 158 of file Stokhos_GSReducedPCEBasisBaseImp.hpp.

template<typename ordinal_type , typename value_type >

ordinal_type Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >::size ( ) const

virtual

Return total size of basis.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

Definition at line 166 of file Stokhos_GSReducedPCEBasisBaseImp.hpp.

template<typename ordinal_type , typename value_type >

const Teuchos::Array< value_type > & Stokhos::GSReducedPCEBasisBase< 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 174 of file Stokhos_GSReducedPCEBasisBaseImp.hpp.

template<typename ordinal_type , typename value_type >

const value_type & Stokhos::GSReducedPCEBasisBase< 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 182 of file Stokhos_GSReducedPCEBasisBaseImp.hpp.

template<typename ordinal_type , typename value_type >

Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > Stokhos::GSReducedPCEBasisBase< 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 190 of file Stokhos_GSReducedPCEBasisBaseImp.hpp.

template<typename ordinal_type , typename value_type >

Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > Stokhos::GSReducedPCEBasisBase< 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 199 of file Stokhos_GSReducedPCEBasisBaseImp.hpp.

template<typename ordinal_type , typename value_type >

value_type Stokhos::GSReducedPCEBasisBase< 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 208 of file Stokhos_GSReducedPCEBasisBaseImp.hpp.

template<typename ordinal_type , typename value_type >

void Stokhos::GSReducedPCEBasisBase< 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 216 of file Stokhos_GSReducedPCEBasisBaseImp.hpp.

template<typename ordinal_type , typename value_type >

void Stokhos::GSReducedPCEBasisBase< 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 225 of file Stokhos_GSReducedPCEBasisBaseImp.hpp.

template<typename ordinal_type , typename value_type >

void Stokhos::GSReducedPCEBasisBase< 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 239 of file Stokhos_GSReducedPCEBasisBaseImp.hpp.

template<typename ordinal_type , typename value_type >

void Stokhos::GSReducedPCEBasisBase< 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 261 of file Stokhos_GSReducedPCEBasisBaseImp.hpp.

template<typename ordinal_type , typename value_type >

Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >::getReducedQuadrature ( ) const

virtual

Get reduced quadrature object.

Implements Stokhos::ReducedPCEBasis< ordinal_type, value_type >.

Definition at line 283 of file Stokhos_GSReducedPCEBasisBaseImp.hpp.

template<typename ordinal_type , typename value_type >

void Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >::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

Definition at line 66 of file Stokhos_GSReducedPCEBasisBaseImp.hpp.

template<typename ordinal_type , typename value_type >

virtual ordinal_type Stokhos::GSReducedPCEBasisBase< 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_
	)

protectedpure virtual

Build the reduced basis, parameterized by total order max_p.

Returns resulting size of reduced basis

Implemented in Stokhos::MonomialGramSchmidtPCEBasis< ordinal_type, value_type >, and Stokhos::MonomialProjGramSchmidtPCEBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type >

GSReducedPCEBasisBase& Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >::operator= ( const GSReducedPCEBasisBase< ordinal_type, value_type > & b )