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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| 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...
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virtual | ~MonomialProjGramSchmidtPCEBasis () |
| Destructor. More...
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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. More...
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virtual | ~GSReducedPCEBasisBase () |
| Destructor. More...
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ordinal_type | order () const |
| Return order of basis. More...
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ordinal_type | dimension () const |
| Return dimension of basis. More...
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virtual ordinal_type | size () const |
| Return total size of basis. More...
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virtual const Teuchos::Array< value_type > & | norm_squared () const |
| Return array storing norm-squared of each basis polynomial. More...
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virtual const value_type & | norm_squared (ordinal_type i) const |
| Return norm squared of basis polynomial i . More...
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virtual Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > > | computeTripleProductTensor () const |
| Compute triple product tensor. More...
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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. More...
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virtual value_type | evaluateZero (ordinal_type i) const |
| Evaluate basis polynomial i at zero. More...
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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 . More...
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virtual void | print (std::ostream &os) const |
| Print basis to stream os . More...
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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. More...
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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. More...
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virtual Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > | getReducedQuadrature () const |
| Get reduced quadrature object. More...
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| ReducedPCEBasis () |
| Default constructor. More...
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virtual | ~ReducedPCEBasis () |
| Destructor. More...
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| OrthogPolyBasis () |
| Constructor. More...
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virtual | ~OrthogPolyBasis () |
| Destructor. More...
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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 . More...
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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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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.
template<typename ordinal_type , typename value_type >
ordinal_type Stokhos::MonomialProjGramSchmidtPCEBasis< 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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protectedvirtual |