Top-level namespace for Stokhos classes and functions. More...

Namespaces
namespace	KL
	Namespace for analytic KL expansions.
Classes
class	HouseTriDiagPCEBasis
	Generates three-term recurrence using the Lanczos procedure applied to a polynomial chaos expansion in another basis. More...
class	MonoProjPCEBasis
	Generates three-term recurrence using the Lanczos procedure applied to a polynomial chaos expansion in another basis. More...
class	DynamicStorage
	Dynamically allocated storage class. More...
class	DynamicStridedStorage
	Dynamically allocated storage class with striding. More...
class	DynamicThreadedStorage
	Dynamically allocated storage class with striding. More...
struct	IsScalarType2
	Base template specification for IsScalarType. More...
struct	IsScalarType2< float >
struct	IsScalarType2< double >
struct	IsScalarType2< int >
struct	IsScalarType2< long >
struct	DynArrayTraits
	Dynamic array allocation class that works for any type. More...
class	LocalStorage
	Statically allocated storage class. More...
struct	StaticArrayTraits
	Static array allocation class. More...
class	StaticFixedStorage
	Statically allocated storage class. More...
class	StaticStorage
	Statically allocated storage class. More...
class	AbstractPreconditionerFactory
	An abstract class to represent a generic preconditioner factory. More...
class	AdaptivityManager
class	AlgebraicOrthogPolyExpansion
	Orthogonal polynomial expansions limited to algebraic operations. More...
class	AnisoSparseGridQuadrature
	Defines quadrature for a tensor product basis by anisotropic Smolyak sparse grids. More...
class	ApproxGaussSeidelPreconditioner
	A stochastic preconditioner based on applying one iteration of approximate Gauss-Seidel. More...
class	ApproxJacobiPreconditioner
	A stochastic preconditioner based on applying two iterations of approximate Jacobi. More...
class	ApproxSchurComplementPreconditioner
	A stochastic preconditioner based on applying the approximate Schur complement preconditioner as defined by Sousedik, Ghanem, and Phipps, Numerical Linear Algebra and Applications, 2012. More...
class	BasisFactory
	Factory for building multivariate orthogonal polynomial bases. More...
class	BasisInteractionGraph
class	BlockDiagonalOperator
	An Epetra operator representing the block stochastic Galerkin operator. More...
class	BlockPreconditioner
class	CGDivisionExpansionStrategy
	Strategy interface for computing PCE of a/b using only b[0]. More...
class	ClenshawCurtisLegendreBasis
	Legendre polynomial basis using Clenshaw-Curtis quadrature points. More...
class	CompletePolynomialBasis
	Multivariate orthogonal polynomial basis generated from a total-order complete-polynomial tensor product of univariate polynomials. More...
class	ConstantOrthogPolyExpansion
	Orthogonal polynomial expansion class for constant (size 1) expansions. More...
struct	make_tuple_N
struct	make_tuple_N< 1, array_type >
struct	make_tuple_N< 2, array_type >
struct	make_tuple_N< 3, array_type >
struct	make_tuple_N< 4, array_type >
class	Dense3Tensor
	Data structure storing a dense 3-tensor C(i,j,k). More...
class	DenseDirectDivisionExpansionStrategy
	Strategy interface for computing PCE of a/b using only b[0]. More...
class	DerivBasis
	Abstract base class for multivariate orthogonal polynomials that support computing double and triple products involving derivatives of the basis polynomials. More...
class	DerivOrthogPolyExpansion
	Othogonal polynomial expansions based on derivative calculations. More...
class	DiagEpetraOp
	An Epetra operator representing the block stochastic Galerkin operator. More...
class	DiagPreconditioner
class	DiscretizedStieltjesBasis
	Generates three-term recurrence using the Discretized Stieltjes procedure. More...
class	DivisionExpansionStrategy
	Strategy interface for computing PCE of a/b. More...
struct	IsScalarType
	Base template specification for IsScalarType. More...
struct	IsScalarType< float >
struct	IsScalarType< double >
struct	IsScalarType< int >
struct	IsScalarType< long >
struct	ds_array
	Dynamic array allocation class that works for any type. More...
struct	ds_array< T, true >
	Dynamic array allocation class that is specialized for scalar i.e., fundamental or built-in types (float, double, etc...). More...
class	EpetraMultiVectorOperator
	An adaptor that supplies the operator interface to a multi-vector. More...
class	EpetraMultiVectorOperatorOrthogPoly
	A container class storing an orthogonal polynomial whose coefficients are vectors, operators, or in general any type that would have an expensive copy constructor. More...
class	EpetraMultiVectorOrthogPoly
	A container class storing an orthogonal polynomial whose coefficients are vectors, operators, or in general any type that would have an expensive copy constructor. More...
class	EpetraOperatorOrthogPoly
	A container class storing an orthogonal polynomial whose coefficients are vectors, operators, or in general any type that would have an expensive copy constructor. More...
class	EpetraSparse3Tensor
class	EpetraVectorOrthogPoly
	A container class storing an orthogonal polynomial whose coefficients are vectors, operators, or in general any type that would have an expensive copy constructor. More...
class	ExpansionFactory
	Factory for building multivariate expansion strategies. More...
class	ForUQTKOrthogPolyExpansion
class	FullyAssembledOperator
	An Epetra operator representing the block stochastic Galerkin operator generated by fully assembling the matrix. More...
class	FullyAssembledPreconditioner
	A stochastic preconditioner based on applying a preconditioner to the fully assembled operator. More...
class	GMRESDivisionExpansionStrategy
	Strategy interface for computing PCE of a/b using only b[0]. More...
class	GramSchmidtBasis
	Transforms a non-orthogonal multivariate basis to an orthogonal one using the Gram-Schmit procedure. More...
class	GSPreconditioner
class	GSReducedPCEBasisBase
	Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...
class	HermiteBasis
	Hermite polynomial basis. More...
class	IfpackPreconditionerFactory
	A factory for building Ifpack preconditioners. More...
class	InterlacedOperator
	An Epetra operator representing the block stochastic Galerkin operator generated by fully assembling the matrix. The ordering of this operator is interlaced. That means that all stochastic degrees of freedom associated with a deterministic degree of freedom are interlaced. The result is a large sparse matrix that is composed of small (relatively) dense blocks. More...
class	InversePreconditioner
class	JacobiBasis
	Jacobi polynomial basis. More...
class	JacobiPreconditioner
class	KLMatrixFreeOperator
	An Epetra operator representing the block stochastic Galerkin operator. More...
class	KLReducedMatrixFreeOperator
	An Epetra operator representing the block stochastic Galerkin operator. More...
class	KroneckerProductPreconditioner
	An Epetra operator representing applying the mean in a block stochastic Galerkin expansion. More...
class	WeightedVectorSpace
class	Lanczos
	Applies Lanczos procedure to a given matrix. More...
class	DiagonalOperator
class	LanczosPCEBasis
	Generates three-term recurrence using the Lanczos procedure applied to a polynomial chaos expansion in another basis. More...
class	DenseOperator
class	LanczosProjPCEBasis
	Generates three-term recurrence using the Lanczos procedure applied to a polynomial chaos expansion in another basis. More...
class	LegendreBasis
	Legendre polynomial basis. More...
class	MatrixFreeOperator
	An Epetra operator representing the block stochastic Galerkin operator. More...
class	MeanBasedDivisionExpansionStrategy
	Strategy interface for computing PCE of a/b using only b[0]. More...
class	MeanBasedPreconditioner
	A stochastic preconditioner based on applying the inverse of the mean. More...
class	MLPreconditionerFactory
	A factory for building ML preconditioners. More...
class	MonomialGramSchmidtPCEBasis
	Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...
class	MonomialProjGramSchmidtPCEBasis
	Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...
class	MonomialProjGramSchmidtPCEBasis2
	Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...
class	MPBlockDiagonalPreconditioner
	A multi-point preconditioner based on applying the inverse of the diagonal. More...
class	MPInverseModelEvaluator
	Nonlinear, inverse multi-point ModelEvaluator. More...
class	MPMeanBasedPreconditioner
	A multi-point preconditioner based on applying the inverse of the mean. More...
class	MPModelEvaluator
	Multi-point model evaluator. More...
class	MPModelEvaluatorAdapter
	ModelEvaluator adapter that implements the multi-point evaluations through sampling. More...
class	MPPreconditioner
	An abstract class to represent a generic stochastic Galerkin preconditioner as an Epetra_Operator. More...
class	MPPreconditionerFactory
	Factory for generating stochastic Galerkin preconditioners. More...
class	OneDOrthogPolyBasis
	Abstract base class for 1-D orthogonal polynomials. More...
class	Operator
class	OrthogonalizationFactory
	Encapsulate various orthogonalization (ie QR) methods. More...
class	OrthogPolyApprox
	Class to store coefficients of a projection onto an orthogonal polynomial basis. More...
class	OrthogPolyBasis
	Abstract base class for multivariate orthogonal polynomials. More...
class	OrthogPolyExpansion
	Abstract base class for orthogonal polynomial-based expansions. More...
class	OrthogPolyExpansionBase
	Base class for consolidating common expansion implementations. More...
class	ParallelData
class	PCECovarianceOp
	An Epetra operator representing the covariance operator of a polynomial chaos expansion. More...
class	PecosOneDOrthogPolyBasis
	Implementation of OneDOrthogPolyBasis via Pecos. More...
class	PreconditionerFactory
	An class for building preconditioners. More...
class	ProductBasis
	Abstract base class for multivariate orthogonal polynomials generated from tensor products of univariate polynomials. More...
class	CompletePolynomialBasisUtils
	Utilities for indexing a multi-variate complete polynomial basis. More...
class	ProductContainerTraits
	Base traits definition for ProductContainer. More...
class	ProductContainer
	A product (in the mathematical sense) container class whose coefficients are vectors, operators, or in general any type that would have an expensive copy constructor. More...
class	ProductEpetraMultiVector
	A container class storing products of Epetra_MultiVector's. More...
class	ProductEpetraMultiVectorOperator
	A container class for products of Epetra_Vector's. More...
class	ProductEpetraOperator
	A container class for products of Epetra_Vector's. More...
class	ProductEpetraVector
	A container class for products of Epetra_Vector's. More...
class	ProductLanczosGramSchmidtPCEBasis
	Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...
class	ProductLanczosPCEBasis
	Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...
class	QuadOrthogPolyExpansion
	Orthogonal polynomial expansions based on numerical quadrature. More...
class	Quadrature
	Abstract base class for quadrature methods. More...
class	QuadratureFactory
	Factory for building multivariate quadrature strategies. More...
class	RecurrenceBasis
	Implementation of OneDOrthogPolyBasis based on the general three-term recurrence relationship: $\gamma_{k+1}\psi_{k+1}(x) = (\delta_k x - \alpha_k)\psi_k(x) - \beta_k\psi_{k-1}(x)$ for $k=0,\dots,P$ where $\psi_{-1}(x) = 0$ , $\psi_{0}(x) = 1/\gamma_0$ , and $\beta_{0} = (1,1) = \int d\lambda$ . More...
class	ReducedBasisFactory
	Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...
class	ReducedPCEBasis
	Abstract base class for reduced basis strategies built from polynomial chaos expansions in some other basis. More...
class	ReducedQuadratureFactory
	Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions. More...
class	ResponseStatisticModelEvaluator
	ModelEvaluator providing statistic response functions. More...
class	RysBasis
	Rys polynomial basis. More...
class	SchurPreconditioner
class	SGInverseModelEvaluator
	Nonlinear, inverse stochastic Galerkin ModelEvaluator. More...
class	SGModelEvaluator
	Nonlinear, stochastic Galerkin ModelEvaluator. More...
class	SGModelEvaluator_Adaptive
	Nonlinear, stochastic Galerkin ModelEvaluator that constructs an adapted Jacobian. More...
class	SGModelEvaluator_Interlaced
	Nonlinear, stochastic Galerkin ModelEvaluator that constructs a interlaced Jacobian. More...
class	SGOperator
	An abstract class to represent a generic stochastic Galerkin operator as an Epetra_Operator. More...
class	SGOperatorFactory
	Factory for generating stochastic Galerkin preconditioners. More...
class	SGPreconditioner
	An abstract class to represent a generic stochastic Galerkin preconditioner as an Epetra_Operator. More...
class	SGPreconditionerFactory
	Factory for generating stochastic Galerkin preconditioners. More...
class	SGQuadModelEvaluator
	ModelEvaluator adaptor that implements the stochastic Galerkin residual and Jacobian computations using quadrature. More...
class	SGQuadMPModelEvaluator
	ModelEvaluator adaptor that implements the stochastic Galerkin residual and Jacobian computations using quadrature. More...
class	Sparse3Tensor
	Data structure storing a sparse 3-tensor C(i,j,k) in a a compressed format. More...
struct	SparseArray
	Container for a "sparse" array. More...
class	SparseArrayIterator
	Bi-directional iterator for traversing a sparse array. More...
class	SparseArrayReverseIterator
	Bi-directional reverse iterator for traversing a sparse array. More...
class	SparseGridQuadrature
	Defines quadrature for a tensor product basis by Smolyak sparse grids. More...
class	SPDDenseDirectDivisionExpansionStrategy
	Strategy interface for computing PCE of a/b using only b[0]. More...
class	StandardStorage
class	StaticFixedStandardStorage
	Statically allocated storage class. More...
class	StaticStandardStorage
	Statically allocated storage class. More...
class	StieltjesBasis
	Generates three-term recurrence using the Discretized Stieltjes procedure applied to a functional mapping another basis. More...
class	StieltjesGramSchmidtBuilder
	Class for building a reduced-dimension basis and quadrature from a given set of polynomial chaos expansions. First generates 1-D orthogonal bases using the discretized Stieltjes procedure, forms their tensor product, and then orthogonalizes using Gram-Schmidt. More...
class	StieltjesPCEBasis
	Generates three-term recurrence using the Discretized Stieltjes procedure applied to a polynomial chaos expansion in another basis. More...
class	TensorProductQuadrature
	Defines quadrature for a tensor product basis by tensor products of 1-D quadrature rules. More...
class	UserDefinedQuadrature
class	VectorOrthogPoly
	A container class storing an orthogonal polynomial whose coefficients are vectors, operators, or in general any type that would have an expensive copy constructor. More...
class	EpetraVectorCloner
	Cloner for Epetra_Vector coefficients. More...
class	EpetraMultiVectorCloner
	Cloner for Epetra_MultiVector coefficients. More...
class	EpetraOperatorCloner
	Cloner for Epetra_Operator coefficients. More...
class	EpetraCrsMatrixCloner
	Cloner for Epetra_CrsMatrix coefficients. More...
class	ProductContainerTraits< Epetra_Vector >
	Specialization of ProductContainerTraits to Epetra_Vector coefficients. More...
class	ProductContainerTraits< Epetra_MultiVector >
	Specialization of ProductContainerTraits to Epetra_MultiVector coefficients. More...
class	ProductContainerTraits< Epetra_CrsMatrix >
	Specialization of ProductContainerTraits to Epetra_CrsMatrix coefficients. More...
class	ProductContainerTraits< Epetra_Operator >
	Specialization of ProductContainerTraits to Epetra_Operator coefficients. More...
Functions
template<typename ordinal_type , typename value_type >
std::ostream &	operator<< (std::ostream &os, const Dense3Tensor< ordinal_type, value_type > &Cijk)
template<typename ordinal_type , typename value_type >
std::ostream &	operator<< (std::ostream &os, const OneDOrthogPolyBasis< ordinal_type, value_type > &b)
	Print basis to stream `os`.
template<typename ordinal_type , typename value_type , typename node_type >
std::ostream &	operator<< (std::ostream &os, const OrthogPolyApprox< ordinal_type, value_type, node_type > &a)
	Prints the array of coefficients (more compact than print())
template<typename ordinal_type , typename value_type >
std::ostream &	operator<< (std::ostream &os, const OrthogPolyBasis< ordinal_type, value_type > &b)
	Print basis to stream `os`.
Teuchos::RCP< const EpetraExt::MultiComm >	buildMultiComm (const Epetra_Comm &globalComm, int num_global_stochastic_blocks, int num_spatial_procs=-1)
Teuchos::RCP< const Epetra_Comm >	getSpatialComm (const Teuchos::RCP< const EpetraExt::MultiComm > &globalMultiComm)
Teuchos::RCP< const Epetra_Comm >	getStochasticComm (const Teuchos::RCP< const EpetraExt::MultiComm > &globalMultiComm)
template<typename coeff_type >
std::ostream &	operator<< (std::ostream &os, const ProductContainer< coeff_type > &vec)
template<typename ordinal_type , typename value_type >
std::ostream &	operator<< (std::ostream &os, const Quadrature< ordinal_type, value_type > &quad)
	Print quadrature object to stream.
template<typename ordinal_type , typename scalar_type >
void	print_matlab (std::ostream &os, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A)
template<typename ordinal_type , typename scalar_type >
void	QR_CGS (ordinal_type k, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R)
	Compute thin QR using classical Gram-Schmidt.
template<typename ordinal_type , typename scalar_type >
void	QR_MGS (ordinal_type k, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R)
	Compute thin QR using modified Gram-Schmidt.
template<typename ordinal_type , typename scalar_type >
void	QR_MGS2 (ordinal_type k, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R)
	Compute thin QR using modified Gram-Schmidt with reorthogonalization.
template<typename ordinal_type , typename scalar_type >
void	QR_Householder (ordinal_type k, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R)
	Compute thin QR using Householder reflections.
template<typename ordinal_type , typename scalar_type >
void	CPQR_Householder (const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R, Teuchos::Array< ordinal_type > &piv)
	Compute column-pivoted QR using Householder reflections.
template<typename ordinal_type , typename scalar_type >
void	CPQR_Householder3 (const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R, Teuchos::Array< ordinal_type > &piv)
	Compute column-pivoted QR using Householder reflections.
template<typename ordinal_type , typename scalar_type >
ordinal_type	CPQR_Householder_threshold (const scalar_type &rank_threshold, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R, Teuchos::Array< ordinal_type > &piv)
	Compute column-pivoted QR using Householder reflections.
template<typename ordinal_type , typename scalar_type >
ordinal_type	CPQR_MGS_threshold (const scalar_type &rank_threshold, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R, Teuchos::Array< ordinal_type > &piv)
	Compute column-pivoted QR using modified Gram-Schmidt.
template<typename ordinal_type , typename scalar_type >
ordinal_type	CPQR_MGS_reorthog_threshold (const scalar_type &rank_threshold, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R, Teuchos::Array< ordinal_type > &piv)
	Compute column-pivoted QR using modified Gram-Schmidt and reorthogonalization.
template<typename ordinal_type , typename scalar_type >
scalar_type	cond_R (const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R)
	Compute condition number of upper-triangular R.
template<typename ordinal_type , typename scalar_type >
scalar_type	weightedQROrthogonalizationError (const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, const Teuchos::Array< scalar_type > &w)
	Compute weighted QR orthogonalization error.
template<typename ordinal_type , typename scalar_type >
scalar_type	QROrthogonalizationError (const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q)
	Compute QR orthogonalization error.
template<typename ordinal_type , typename scalar_type >
scalar_type	residualQRError (const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R)
	Compute QR residual error.
template<typename ordinal_type , typename scalar_type >
scalar_type	residualCPQRError (const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R, const Teuchos::Array< ordinal_type > &piv)
	Compute column-pivoted QR residual error.
template<typename ordinal_type , typename scalar_type >
void	svd (const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, Teuchos::Array< scalar_type > &s, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &U, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Vt)
	Compute SVD of matrix.
template<typename ordinal_type , typename scalar_type >
ordinal_type	svd_threshold (const scalar_type &rank_threshold, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, Teuchos::Array< scalar_type > &s, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &U, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Vt)
template<typename ordinal_type , typename value_type >
Teuchos::RCP< Epetra_CrsGraph >	sparse3Tensor2CrsGraph (const Stokhos::OrthogPolyBasis< ordinal_type, value_type > &basis, const Stokhos::Sparse3Tensor< ordinal_type, value_type > &Cijk, const Epetra_Comm &comm)
	Build an Epetra_CrsGraph from a sparse 3 tensor.
template<typename ordinal_type , typename value_type >
Teuchos::RCP< Epetra_CrsGraph >	sparse3Tensor2CrsGraph (const Stokhos::Sparse3Tensor< ordinal_type, value_type > &Cijk, const Epetra_BlockMap &map)
	Build an Epetra_CrsGraph from a sparse 3 tensor.
template<typename ordinal_type , typename value_type >
void	sparse3Tensor2MatrixMarket (const Stokhos::OrthogPolyBasis< ordinal_type, value_type > &basis, const Stokhos::Sparse3Tensor< ordinal_type, value_type > &Cijk, const Epetra_Comm &comm, const std::string &file)
template<typename ordinal_type , typename value_type >
void	sparse3Tensor2MatrixMarket (const Stokhos::Sparse3Tensor< ordinal_type, value_type > &Cijk, const Epetra_BlockMap &map, const std::string &file)
template<typename coeff_type >
std::ostream &	operator<< (std::ostream &os, const VectorOrthogPoly< coeff_type > &vec)

Detailed Description

Top-level namespace for Stokhos classes and functions.

Function Documentation

template<typename ordinal_type , typename scalar_type >

void Stokhos::CPQR_Householder	(	const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R,
		Teuchos::Array< ordinal_type > &	piv
	)

Compute column-pivoted QR using Householder reflections.

For A an m-by-n matrix with m >= n, computes A*P = Q*R with R n-by-n upper triangular and Q m-by-n with orthogonal columns (often called the economy size QR) and P an m-by-n permutation matrix. For n >= m, computes A*P = Q*R with R m-by-n upper trapezoidal and Q m-by-m upper trapezoidal (R = [R_1 R_2] with R_1 upper triangular and R_2 rectangular). For k = min(m,n), both cases are handled with Q m-by-k and R k-by-n.

The QR factorization is computed by the corresponding LAPACK function.

template<typename ordinal_type , typename scalar_type >

void Stokhos::CPQR_Householder3	(	const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R,
		Teuchos::Array< ordinal_type > &	piv
	)

Compute column-pivoted QR using Householder reflections.

For A an m-by-n matrix with m >= n, computes A*P = Q*R with R n-by-n upper triangular and Q m-by-n with orthogonal columns (often called the economy size QR) and P an m-by-n permutation matrix. For n >= m, computes A*P = Q*R with R m-by-n upper trapezoidal and Q m-by-m upper trapezoidal (R = [R_1 R_2] with R_1 upper triangular and R_2 rectangular). For k = min(m,n), both cases are handled with Q m-by-k and R k-by-n.

The QR factorization is computed by the corresponding LAPACK function. This version uses the BLAS3-rich xGEQP3.

template<typename ordinal_type , typename scalar_type >

ordinal_type Stokhos::CPQR_Householder_threshold	(	const scalar_type &	rank_threshold,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		const Teuchos::Array< scalar_type > &	w,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R,
		Teuchos::Array< ordinal_type > &	piv
	)

Compute column-pivoted QR using Householder reflections.

For A an m-by-n matrix, computes A*P = Q*R with R k-by-k upper triangular, Q m-by-k with orthonormal columns, and P an n-by-k permutation matrix. Here k <= min(m,n) is determined by a rank threshold tau provided by the user. The resulting R will have cond(R) <= 1/tau. P is returned in the pivot array piv and the rank k returned by the function. Only the first k entries of piv will be set. As with LAPACK, the user can require columns of A to be included in P by setting the corresponding entries of piv to be nonzero on input.

If make_R_square is false then R is k-by-n.

This ultimately uses the LAPACK column-pivoted QR function which does a full QR factorization. This then extracts the parts of Q, R, and P determined by the threshold as described above. As such, this function requires the weight vector to be 1 (Note the weight vector will be ignored if it is size 0).

template<typename ordinal_type , typename scalar_type >

ordinal_type Stokhos::CPQR_MGS_reorthog_threshold	(	const scalar_type &	rank_threshold,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		const Teuchos::Array< scalar_type > &	w,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R,
		Teuchos::Array< ordinal_type > &	piv
	)

Compute column-pivoted QR using modified Gram-Schmidt and reorthogonalization.

For A an m-by-n matrix, computes A*P = Q*R with R k-by-k upper triangular, Q m-by-k with orthonormal columns, and P an n-by-k permutation matrix. Here k <= min(m,n) is determined by a rank threshold tau provided by the user. The resulting R will have cond(R) <= 1/tau. P is returned in the pivot array piv and the rank k returned by the function. Only the first k entries of piv will be set. As with LAPACK, the user can require columns of A to be included in P by setting the corresponding entries of piv to be nonzero on input. The orthogonality of Q is determined by the weight vector w, defining a weighted inner-product.

template<typename ordinal_type , typename scalar_type >

ordinal_type Stokhos::CPQR_MGS_threshold	(	const scalar_type &	rank_threshold,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		const Teuchos::Array< scalar_type > &	w,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R,
		Teuchos::Array< ordinal_type > &	piv
	)

Compute column-pivoted QR using modified Gram-Schmidt.

For A an m-by-n matrix, computes A*P = Q*R with R k-by-k upper triangular, Q m-by-k with orthonormal columns, and P an n-by-k permutation matrix. Here k <= min(m,n) is determined by a rank threshold tau provided by the user. The resulting R will have cond(R) <= 1/tau. P is returned in the pivot array piv and the rank k returned by the function. Only the first k entries of piv will be set. As with LAPACK, the user can require columns of A to be included in P by setting the corresponding entries of piv to be nonzero on input. The orthogonality of Q is determined by the weight vector w, defining a weighted inner-product.

template<typename ordinal_type , typename scalar_type >

void Stokhos::QR_CGS	(	ordinal_type	k,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		const Teuchos::Array< scalar_type > &	w,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R
	)

Compute thin QR using classical Gram-Schmidt.

For A an m-by-n matrix computes A = Q*R with R k-by-k upper triangular, Q m-by-k with orthogonal columns, k <= min(m,n).

template<typename ordinal_type , typename scalar_type >

void Stokhos::QR_Householder	(	ordinal_type	k,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		const Teuchos::Array< scalar_type > &	w,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R
	)

Compute thin QR using Householder reflections.

For A an m-by-n matrix computes A = Q*R with R k-by-k upper triangular, Q m-by-k with orthogonal columns, k <= min(m,n).

The QR factorization is computed by the corresponding LAPACK function.

template<typename ordinal_type , typename scalar_type >

void Stokhos::QR_MGS	(	ordinal_type	k,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		const Teuchos::Array< scalar_type > &	w,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R
	)

Compute thin QR using modified Gram-Schmidt.

For A an m-by-n matrix computes A = Q*R with R k-by-k upper triangular, Q m-by-k with orthogonal columns, k <= min(m,n).

template<typename ordinal_type , typename scalar_type >

void Stokhos::QR_MGS2	(	ordinal_type	k,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		const Teuchos::Array< scalar_type > &	w,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R
	)

Compute thin QR using modified Gram-Schmidt with reorthogonalization.

For A an m-by-n matrix computes A = Q*R with R k-by-k upper triangular, Q m-by-k with orthogonal columns, k <= min(m,n).

template<typename ordinal_type , typename scalar_type >

scalar_type Stokhos::QROrthogonalizationError ( const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > & Q )

Compute QR orthogonalization error.

Computes ||Q^T*Q-I||_infinity for Q coming from a QR factorization.

template<typename ordinal_type , typename scalar_type >

scalar_type Stokhos::residualCPQRError	(	const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R,
		const Teuchos::Array< ordinal_type > &	piv
	)

Compute column-pivoted QR residual error.

Computes ||Q*R-A*P||_infinity for Q,R coming from a column-pivoted QR factorization.

Works with thin or full QR, weighted or not.

template<typename ordinal_type , typename scalar_type >

scalar_type Stokhos::residualQRError	(	const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	R
	)

Compute QR residual error.

Computes ||Q*R-A||_infinity for Q,R coming from QR factorization.

Works with thin or full QR, weighted or not.

template<typename ordinal_type , typename value_type >

Teuchos::RCP<Epetra_CrsGraph> Stokhos::sparse3Tensor2CrsGraph	(	const Stokhos::OrthogPolyBasis< ordinal_type, value_type > &	basis,
		const Stokhos::Sparse3Tensor< ordinal_type, value_type > &	Cijk,
		const Epetra_Comm &	comm
	)

Build an Epetra_CrsGraph from a sparse 3 tensor.

Builds a sparse graph from a sparse 3 tensor by summing over the third index. This graph then represents the sparsity pattern of the stochastic part of the block stochastic Galerkin operator. Redistributing the graph should then provide a suitable parallel distribution for block stochastic Galerkin linear solves.

template<typename ordinal_type , typename value_type >

Teuchos::RCP<Epetra_CrsGraph> Stokhos::sparse3Tensor2CrsGraph	(	const Stokhos::Sparse3Tensor< ordinal_type, value_type > &	Cijk,
		const Epetra_BlockMap &	map
	)

Build an Epetra_CrsGraph from a sparse 3 tensor.

Builds a sparse graph from a sparse 3 tensor by summing over the third index. This graph then represents the sparsity pattern of the stochastic part of the block stochastic Galerkin operator. Redistributing the graph should then provide a suitable parallel distribution for block stochastic Galerkin linear solves.

template<typename ordinal_type , typename scalar_type >

void Stokhos::svd	(	const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	A,
		Teuchos::Array< scalar_type > &	s,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	U,
		Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Vt
	)

Compute SVD of matrix.

The SVD is computed by the corresponding LAPACK function.

template<typename ordinal_type , typename scalar_type >

scalar_type Stokhos::weightedQROrthogonalizationError	(	const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &	Q,
		const Teuchos::Array< scalar_type > &	w
	)

Compute weighted QR orthogonalization error.

Computes ||Q^T*W*Q-I||_infinity for Q coming from a weighted QR factorization.

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