42 #ifndef STOKHOS_LANCZOSPROJPCEBASIS_HPP 43 #define STOKHOS_LANCZOSPROJPCEBASIS_HPP 45 #include "Teuchos_RCP.hpp" 46 #include "Teuchos_Array.hpp" 47 #include "Teuchos_SerialDenseVector.hpp" 48 #include "Teuchos_SerialDenseMatrix.hpp" 57 template <
typename ord_type,
typename val_type>
62 typedef Teuchos::SerialDenseMatrix<ordinal_type, value_type>
matrix_type;
63 typedef Teuchos::SerialDenseVector<ordinal_type, value_type>
vector_type;
69 v.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS,
value_type(1),
83 template <
typename ordinal_type,
typename value_type>
110 Teuchos::Array<value_type>& points,
111 Teuchos::Array<value_type>&
weights,
112 Teuchos::Array< Teuchos::Array<value_type> >& values)
const;
143 Teuchos::Array<value_type>&
alpha,
144 Teuchos::Array<value_type>&
beta,
145 Teuchos::Array<value_type>&
delta,
146 Teuchos::Array<value_type>&
gamma)
const;
149 virtual void setup();
173 Teuchos::RCP< const Stokhos::OrthogPolyApprox<ordinal_type, value_type> >
pce;
Teuchos::Array< value_type > delta
Recurrence coefficients.
matrix_type Cijk_matrix
Triple-product matrix used in generating lanczos vectors.
virtual bool computeRecurrenceCoefficients(ordinal_type n, Teuchos::Array< value_type > &alpha, Teuchos::Array< value_type > &beta, Teuchos::Array< value_type > &delta, Teuchos::Array< value_type > &gamma) const
Compute recurrence coefficients.
value_type getNewCoeffs(ordinal_type i) const
Get new coefficients in this new basis.
virtual void setup()
Setup basis after computing recurrence coefficients.
Implementation of OneDOrthogPolyBasis based on the general three-term recurrence relationship: for ...
virtual Teuchos::RCP< OneDOrthogPolyBasis< ordinal_type, value_type > > cloneWithOrder(ordinal_type p) const
Clone this object with the option of building a higher order basis.
DenseOperator< ordinal_type, value_type > operator_type
Data structure storing a sparse 3-tensor C(i,j,k) in a a compressed format.
~LanczosProjPCEBasis()
Destructor.
void transformCoeffsFromLanczos(const value_type *in, value_type *out) const
Map expansion coefficients from this basis to original.
lanczos_type::matrix_type matrix_type
Stokhos::Lanczos< vectorspace_type, operator_type > lanczos_type
Teuchos::Array< value_type > beta
Recurrence coefficients.
Teuchos::RCP< const Stokhos::OrthogPolyApprox< ordinal_type, value_type > > pce
PCE Lanczos procedure is based on.
Teuchos::Array< value_type > alpha
Recurrence coefficients.
LanczosProjPCEBasis & operator=(const LanczosProjPCEBasis &b)
Teuchos::SerialDenseVector< ordinal_type, value_type > vector_type
Teuchos::SerialDenseVector< ordinal_type, value_type > vector_type
Teuchos::Array< value_type > pce_norms
Basis norms.
vector_type u0
Initial Lanczos vector.
Teuchos::SerialDenseMatrix< ordinal_type, value_type > matrix_type
Top-level namespace for Stokhos classes and functions.
virtual void getQuadPoints(ordinal_type quad_order, Teuchos::Array< value_type > &points, Teuchos::Array< value_type > &weights, Teuchos::Array< Teuchos::Array< value_type > > &values) const
Get Gauss quadrature points, weights, and values of basis at points.
vector_type weights
Weighting vector used in inner-products.
LanczosProjPCEBasis(ordinal_type p, const Teuchos::RCP< const Stokhos::OrthogPolyApprox< ordinal_type, value_type > > &pce, const Teuchos::RCP< const Stokhos::Sparse3Tensor< ordinal_type, value_type > > &Cijk, bool normalize, bool limit_integration_order=false)
Constructor.
void apply(const vector_type &u, vector_type &v) const
bool limit_integration_order
Flag indicating whether to limit the integration order.
Applies Lanczos procedure to a given matrix.
vector_type new_pce
Projection of pce in new basis.
Teuchos::SerialDenseMatrix< ordinal_type, value_type > matrix_type
DenseOperator(const matrix_type &A_)
ordinal_type p
Order of basis.
ordinal_type pce_sz
Size of PC expansion.
Teuchos::Array< value_type > gamma
Recurrence coefficients.
matrix_type lanczos_vecs
Lanczos vectors.
bool normalize
Normalize basis.
WeightedVectorSpace< ordinal_type, value_type > vectorspace_type
Generates three-term recurrence using the Lanczos procedure applied to a polynomial chaos expansion i...
lanczos_type::vector_type vector_type