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Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type > Class Template Reference

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>

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List of all members.

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.
virtual ~GSReducedPCEBasisBase ()
 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 (ordinal_type order) const
 Compute triple product tensor.
virtual value_type evaluateZero (ordinal_type i) const
 Evaluate basis polynomial i at zero.
virtual void evaluateBases (const Teuchos::Array< 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.
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.

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< Teuchos::Array< 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.

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< Teuchos::Array
< 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::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.


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:
porder of the basis
pcepolynomial chaos expansions defining new measure
quadquadrature data for basis defining pce
Cijksparse triple product tensor for basis defining pce
sparse_toltolerance for dropping terms in sparse tensors

Member Function Documentation

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< Teuchos::Array< ordinal_type > > &  terms_,
Teuchos::Array< ordinal_type > &  num_terms_,
Teuchos::SerialDenseMatrix< ordinal_type, value_type > &  Qp_,
Teuchos::SerialDenseMatrix< ordinal_type, value_type > &  Q_ 
) [protected, pure 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 >
Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >::computeTripleProductTensor ( ordinal_type  order) 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 $i,j=0,\dots,P$ where $P$ is size()-1 and $k=0,\dots,p$ where $p$ is the supplied order.

Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.

template<typename ordinal_type , typename value_type >
void Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >::evaluateBases ( const Teuchos::Array< 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::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 >.


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