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_MonomialProjGramSchmidtPCEBasis.hpp>
Inheritance diagram for Stokhos::MonomialProjGramSchmidtPCEBasis< ordinal_type, value_type >:
Public Member Functions | |
| MonomialProjGramSchmidtPCEBasis (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 ¶ms=Teuchos::ParameterList()) | |
| Constructor. More... | |
| virtual | ~MonomialProjGramSchmidtPCEBasis () |
| Destructor. More... | |
 Public Member Functions inherited from 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 ¶ms=Teuchos::ParameterList()) | |
| Constructor. More... | |
| virtual | ~GSReducedPCEBasisBase () |
| Destructor. More... | |
| 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... | |
| 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... | |
| 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... | |
Implementation of Stokhos::OrthogPolyBasis methods | |
| typedef Stokhos::CompletePolynomialBasisUtils< ordinal_type, value_type > | CPBUtils |
| typedef Teuchos::SerialDenseVector< ordinal_type, value_type > | SDV |
| typedef Teuchos::SerialDenseMatrix< ordinal_type, value_type > | SDM |
| std::string | name |
| Name of basis. More... | |
| virtual const std::string & | getName () const |
| Return string name of basis. More... | |
| 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_) |
Build the reduced basis, parameterized by total order max_p. More... | |
| MonomialProjGramSchmidtPCEBasis (const MonomialProjGramSchmidtPCEBasis &) | |
| MonomialProjGramSchmidtPCEBasis & | operator= (const MonomialProjGramSchmidtPCEBasis &b) |
Additional Inherited Members | |
| Protected Types inherited from Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type > | |
| 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 inherited from Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type > | |
| 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) |
| Protected Attributes inherited from Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type > | |
| 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 |
Detailed Description
template<typename ordinal_type, typename value_type>
class Stokhos::MonomialProjGramSchmidtPCEBasis< 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 59 of file Stokhos_MonomialProjGramSchmidtPCEBasis.hpp.
Member Typedef Documentation
◆ CPBUtils
template<typename ordinal_type , typename value_type >
|
protected |
Definition at line 116 of file Stokhos_MonomialProjGramSchmidtPCEBasis.hpp.
◆ SDV
template<typename ordinal_type , typename value_type >
|
protected |
Definition at line 117 of file Stokhos_MonomialProjGramSchmidtPCEBasis.hpp.
◆ SDM
template<typename ordinal_type , typename value_type >
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protected |
Definition at line 118 of file Stokhos_MonomialProjGramSchmidtPCEBasis.hpp.
Constructor & Destructor Documentation
◆ MonomialProjGramSchmidtPCEBasis() [1/2]
template<typename ordinal_type , typename value_type >
| Stokhos::MonomialProjGramSchmidtPCEBasis< ordinal_type, value_type >::MonomialProjGramSchmidtPCEBasis | ( | 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 47 of file Stokhos_MonomialProjGramSchmidtPCEBasisImp.hpp.
◆ ~MonomialProjGramSchmidtPCEBasis()
template<typename ordinal_type , typename value_type >
|
virtual |
Destructor.
Definition at line 60 of file Stokhos_MonomialProjGramSchmidtPCEBasisImp.hpp.
◆ MonomialProjGramSchmidtPCEBasis() [2/2]
template<typename ordinal_type , typename value_type >
|
private |
Member Function Documentation
◆ getName()
template<typename ordinal_type , typename value_type >
|
virtual |
Return string name of basis.
Implements Stokhos::OrthogPolyBasis< ordinal_type, value_type >.
Definition at line 67 of file Stokhos_MonomialProjGramSchmidtPCEBasisImp.hpp.
◆ buildReducedBasis()
template<typename ordinal_type , typename value_type >
|
protectedvirtual |
Build the reduced basis, parameterized by total order max_p.
Returns resulting size of reduced basis
Implements Stokhos::GSReducedPCEBasisBase< ordinal_type, value_type >.
Definition at line 75 of file Stokhos_MonomialProjGramSchmidtPCEBasisImp.hpp.
◆ operator=()
template<typename ordinal_type , typename value_type >
|
private |
Member Data Documentation
◆ name
template<typename ordinal_type , typename value_type >
|
protected |
Name of basis.
Definition at line 121 of file Stokhos_MonomialProjGramSchmidtPCEBasis.hpp.
The documentation for this class was generated from the following files:
