Generate a basis from a given set of PCE expansions that is orthogonal with respect to the product measure induced by these expansions.
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| MonomialGramSchmidtPCEBasis (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.
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virtual | ~MonomialGramSchmidtPCEBasis () |
| Destructor.
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| 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.
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virtual | ~GSReducedPCEBasisBase () |
| Destructor.
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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.
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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.
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virtual Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > | getReducedQuadrature () const |
| Get reduced quadrature object.
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ordinal_type | order () const |
| Return order of basis.
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ordinal_type | dimension () const |
| Return dimension of basis.
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virtual ordinal_type | size () const |
| Return total size of basis.
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virtual const Teuchos::Array< value_type > & | norm_squared () const |
| Return array storing norm-squared of each basis polynomial.
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virtual const value_type & | norm_squared (ordinal_type i) const |
| Return norm squared of basis polynomial i .
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virtual Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > | computeTripleProductTensor () const |
| Compute triple product tensor.
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virtual Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > | computeLinearTripleProductTensor () const |
| Compute linear triple product tensor where k = 0,1,..,d.
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virtual value_type | evaluateZero (ordinal_type i) const |
| Evaluate basis polynomial i at zero.
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virtual void | evaluateBases (const Teuchos::ArrayView< const value_type > &point, Teuchos::Array< value_type > &basis_vals) const |
| Evaluate basis polynomials at given point point .
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virtual void | print (std::ostream &os) const |
| Print basis to stream os .
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| ReducedPCEBasis () |
| Default constructor.
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virtual | ~ReducedPCEBasis () |
| Destructor.
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| OrthogPolyBasis () |
| Constructor.
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virtual | ~OrthogPolyBasis () |
| Destructor.
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typedef Stokhos::CompletePolynomialBasisUtils< ordinal_type, value_type > | CPBUtils |
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typedef Teuchos::SerialDenseVector< ordinal_type, value_type > | SDV |
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typedef Teuchos::SerialDenseMatrix< ordinal_type, value_type > | SDM |
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std::string | name |
| Name of basis.
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virtual const std::string & | getName () const |
| Return string name of basis.
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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 .
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| MonomialGramSchmidtPCEBasis (const MonomialGramSchmidtPCEBasis &) |
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MonomialGramSchmidtPCEBasis & | operator= (const MonomialGramSchmidtPCEBasis &b) |
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typedef Stokhos::CompletePolynomialBasisUtils< ordinal_type, value_type > | CPBUtils |
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typedef Teuchos::SerialDenseVector< ordinal_type, value_type > | SDV |
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typedef Teuchos::SerialDenseMatrix< ordinal_type, value_type > | SDM |
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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) |
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std::string | name |
| Name of basis.
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Teuchos::ParameterList | params |
| Algorithm parameters.
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Teuchos::RCP< const Stokhos::OrthogPolyBasis< ordinal_type, value_type > > | pce_basis |
| Original pce basis.
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ordinal_type | pce_sz |
| Size of original pce basis.
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ordinal_type | p |
| Total order of basis.
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ordinal_type | d |
| Total dimension of basis.
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ordinal_type | sz |
| Total size of basis.
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Teuchos::Array< Stokhos::MultiIndex< ordinal_type > > | terms |
| 2-D array of basis terms
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Teuchos::Array< ordinal_type > | num_terms |
| Number of terms up to each order.
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Teuchos::Array< value_type > | norms |
| Norms.
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SDM | Q |
| Values of transformed basis at quadrature points.
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SDM | Qp |
| Coefficients of transformed basis in original basis.
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Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > | reduced_quad |
| Reduced quadrature object.
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bool | verbose |
| Whether to print a bunch of stuff out.
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value_type | rank_threshold |
| Rank threshold.
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std::string | orthogonalization_method |
| Orthogonalization method.
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Teuchos::BLAS< ordinal_type, value_type > | blas |
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template<typename ordinal_type, typename value_type>
class Stokhos::MonomialGramSchmidtPCEBasis< 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_MonomialGramSchmidtPCEBasis.hpp.
template<typename ordinal_type , typename value_type >
ordinal_type Stokhos::MonomialGramSchmidtPCEBasis< ordinal_type, value_type >::buildReducedBasis |
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ordinal_type | max_p, |
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value_type | threshold, |
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const Teuchos::SerialDenseMatrix< ordinal_type, value_type > & | A, |
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const Teuchos::SerialDenseMatrix< ordinal_type, value_type > & | F, |
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const Teuchos::Array< value_type > & | weights, |
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Teuchos::Array< Stokhos::MultiIndex< ordinal_type > > & | terms_, |
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Teuchos::Array< ordinal_type > & | num_terms_, |
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Teuchos::SerialDenseMatrix< ordinal_type, value_type > & | Qp_, |
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Teuchos::SerialDenseMatrix< ordinal_type, value_type > & | Q_ ) |
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