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_ProductLanczosPCEBasis.hpp>

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

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

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Public Member Functions
	ProductLanczosPCEBasis (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::RCP< const Stokhos::Sparse3Tensor< ordinal_type, value_type > > &Cijk, const Teuchos::ParameterList &params=Teuchos::ParameterList())
	Constructor.
virtual	~ProductLanczosPCEBasis ()
	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.
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 const std::string &	getName () const
	Return string name of basis.
Implementation of Stokhos::ProductBasis methods
virtual const MultiIndex< ordinal_type > &	term (ordinal_type i) const
	Get orders of each coordinate polynomial given an index `i`.
virtual ordinal_type	index (const MultiIndex< ordinal_type > &term) const
	Get index of the multivariate polynomial given orders of each coordinate.
Teuchos::Array< Teuchos::RCP< const OneDOrthogPolyBasis< ordinal_type, value_type > > >	getCoordinateBases () const
	Return coordinate bases.
virtual MultiIndex< ordinal_type >	getMaxOrders () const
	Return maximum order allowable for each coordinate basis.
Public Member Functions inherited from Stokhos::ProductBasis< ordinal_type, value_type >
	ProductBasis ()
	Constructor.
virtual	~ProductBasis ()
	Destructor.
Public Member Functions inherited from Stokhos::OrthogPolyBasis< ordinal_type, value_type >
	OrthogPolyBasis ()
	Constructor.
virtual	~OrthogPolyBasis ()
	Destructor.
Public Member Functions inherited from Stokhos::ReducedPCEBasis< ordinal_type, value_type >
	ReducedPCEBasis ()
	Default constructor.
virtual	~ReducedPCEBasis ()
	Destructor.

Implementation of Stokhos::ReducedPCEBasis methods
typedef Teuchos::SerialDenseVector< ordinal_type, value_type >	SDV
typedef Teuchos::SerialDenseMatrix< ordinal_type, value_type >	SDM
std::string	name
	Name of basis.
Teuchos::ParameterList	params
	Algorithm parameters.
Teuchos::RCP< Stokhos::CompletePolynomialBasis< ordinal_type, value_type > >	tensor_lanczos_basis
	Product Lanczos basis.
SDM	Phi
	Values of transformed basis at quadrature points.
SDM	A
	Transition matrix from reduced basis to original.
SDM	Ainv
	Projection matrix from original matrix to reduced.
Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > >	reduced_quad
	Reduced quadrature object.
Stokhos::OrthogPolyApprox< ordinal_type, value_type >	tmp_pce
	Temporary pce used in invariant subspace calculations.
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	isInvariant (const Stokhos::OrthogPolyApprox< ordinal_type, value_type > &pce) const

Detailed Description

template<typename ordinal_type, typename value_type>
class Stokhos::ProductLanczosPCEBasis< 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 an orthogonal basis for each compnent, then form the multivariate basis by a total-order tensor product. The resulting basis is not necessarily orthogonal with respect to the full measure.

Constructor & Destructor Documentation

◆ ProductLanczosPCEBasis()

template<typename ordinal_type, typename value_type>

Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >::ProductLanczosPCEBasis	(	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::RCP< const Stokhos::Sparse3Tensor< ordinal_type, value_type > > &	Cijk,
		const Teuchos::ParameterList &	params = Teuchos::ParameterList() )

Constructor.

Parameters

p	order of the basis
pce	polynomial chaos expansions defining new measure
Cijk	sparse triple product tensor for basis defining pce

References A, Ainv, Stokhos::QuadratureFactory< ordinal_type, value_type >::create(), name, params, Phi, reduced_quad, Stokhos::ProductContainer< coeff_type >::size(), and tensor_lanczos_basis.

Member Function Documentation

◆ computeLinearTripleProductTensor()

template<typename ordinal_type, typename value_type>

Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >::computeLinearTripleProductTensor ( ) const

virtual

Compute linear triple product tensor where k = 0,1,..,d.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

References tensor_lanczos_basis.

◆ computeTripleProductTensor()

template<typename ordinal_type, typename value_type>

Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >::computeTripleProductTensor ( ) const

virtual

Compute triple product tensor.

The 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 and $i,j,k=0,\dots,P$ where is size()-1.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

References tensor_lanczos_basis.

◆ dimension()

template<typename ordinal_type, typename value_type>

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

virtual

Return dimension of basis.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

References tensor_lanczos_basis.

◆ evaluateBases()

template<typename ordinal_type, typename value_type>

void Stokhos::ProductLanczosPCEBasis< 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 >.

References tensor_lanczos_basis.

◆ evaluateZero()

template<typename ordinal_type, typename value_type>

value_type Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >::evaluateZero ( ordinal_type i ) const

virtual

Evaluate basis polynomial i at zero.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

References tensor_lanczos_basis.

◆ getCoordinateBases()

template<typename ordinal_type, typename value_type>

Teuchos::Array< Teuchos::RCP< const Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type > > > Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >::getCoordinateBases ( ) const

virtual

Return coordinate bases.

Array is of size dimension().

Implements Stokhos::ProductBasis< ordinal_type, value_type >.

References tensor_lanczos_basis.

◆ getMaxOrders()

template<typename ordinal_type, typename value_type>

Stokhos::MultiIndex< ordinal_type > Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >::getMaxOrders ( ) const

virtual

Return maximum order allowable for each coordinate basis.

Implements Stokhos::ProductBasis< ordinal_type, value_type >.

References tensor_lanczos_basis.

◆ getName()

template<typename ordinal_type, typename value_type>

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

virtual

Return string name of basis.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

References name.

◆ getReducedQuadrature()

template<typename ordinal_type, typename value_type>

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

virtual

Get reduced quadrature object.

Implements Stokhos::ReducedPCEBasis< ordinal_type, value_type >.

References reduced_quad.

◆ index()

template<typename ordinal_type, typename value_type>

ordinal_type Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >::index ( const MultiIndex< ordinal_type > & term ) const

virtual

Get index of the multivariate polynomial given orders of each coordinate.

Given the array term storing $i_1,\dots,\i_d$ , returns the index such that $\Psi_i(x) = \psi_{i_1}(x_1)\dots\psi_{i_d}(x_d)$ .

Implements Stokhos::ProductBasis< ordinal_type, value_type >.

References tensor_lanczos_basis, and term().

◆ norm_squared() [1/2]

template<typename ordinal_type, typename value_type>

const Teuchos::Array< value_type > & Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >::norm_squared ( ) const

virtual

Return array storing norm-squared of each basis polynomial.

Entry of returned array is given by $\langle\Psi_l^2\rangle$ for $l=0,\dots,P$ where is size()-1.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

References tensor_lanczos_basis.

◆ norm_squared() [2/2]

template<typename ordinal_type, typename value_type>

const value_type & Stokhos::ProductLanczosPCEBasis< 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 >.

References tensor_lanczos_basis.

◆ order()

template<typename ordinal_type, typename value_type>

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

virtual

Return order of basis.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

References tensor_lanczos_basis.

◆ print()

template<typename ordinal_type, typename value_type>

void Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >::print ( std::ostream & os ) const

virtual

Print basis to stream os.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

References tensor_lanczos_basis.

◆ size()

template<typename ordinal_type, typename value_type>

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

virtual

Return total size of basis.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

References tensor_lanczos_basis.

◆ term()

template<typename ordinal_type, typename value_type>

const Stokhos::MultiIndex< ordinal_type > & Stokhos::ProductLanczosPCEBasis< ordinal_type, value_type >::term ( ordinal_type i ) const

virtual

Get orders of each coordinate polynomial given an index i.

The returned array is of size , where is the dimension of the basis, and entry is given by where $\Psi_i(x) = \psi_{i_1}(x_1)\dots\psi_{i_d}(x_d)$ .

Implements Stokhos::ProductBasis< ordinal_type, value_type >.

References tensor_lanczos_basis.

Referenced by index().

◆ transformFromOriginalBasis()

template<typename ordinal_type, typename value_type>

void Stokhos::ProductLanczosPCEBasis< 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 >.

References A, and Ainv.

◆ transformToOriginalBasis()

template<typename ordinal_type, typename value_type>

void Stokhos::ProductLanczosPCEBasis< 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 >.

References A.

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

Stokhos_ProductLanczosPCEBasis.hpp
Stokhos_ProductLanczosPCEBasisImp.hpp

Public Member Functions

Implementation of Stokhos::ReducedPCEBasis methods

Detailed Description

Constructor & Destructor Documentation

◆ ProductLanczosPCEBasis()

Member Function Documentation

◆ computeLinearTripleProductTensor()

◆ computeTripleProductTensor()

◆ dimension()

◆ evaluateBases()

◆ evaluateZero()

◆ getCoordinateBases()

◆ getMaxOrders()

◆ getName()

◆ getReducedQuadrature()

◆ index()

◆ norm_squared() [1/2]

◆ norm_squared() [2/2]

◆ order()

◆ print()

◆ size()

◆ term()

◆ transformFromOriginalBasis()

◆ transformToOriginalBasis()