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Stokhos::TensorProductPseudoSpectralOperator< ordinal_t, value_t, point_compare_type > Class Template Reference

An operator for building pseudo-spectral coefficients using tensor-product quadrature. More...

#include <Stokhos_TensorProductPseudoSpectralOperator.hpp>

Inheritance diagram for Stokhos::TensorProductPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >:
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List of all members.

Public Types

typedef ordinal_t ordinal_type
typedef value_t value_type
typedef PseudoSpectralOperator
< ordinal_type, value_type,
point_compare_type > 
base_type
typedef base_type::point_type point_type
typedef base_type::point_set_type point_set_type
typedef base_type::point_map_type point_map_type
typedef base_type::iterator iterator
typedef base_type::const_iterator const_iterator
typedef base_type::set_iterator set_iterator
typedef
base_type::const_set_iterator 
const_set_iterator
typedef MultiIndex< ordinal_type > multiindex_type

Public Member Functions

 TensorProductPseudoSpectralOperator (const ProductBasis< ordinal_type, value_type > &product_basis, bool use_pst_=false, multiindex_type multiindex=multiindex_type(), const point_compare_type &point_compare=point_compare_type())
 Constructor.
virtual ~TensorProductPseudoSpectralOperator ()
 Destructor.
ordinal_type point_size () const
 Number of points.
ordinal_type coeff_size () const
 Number of coefficients.
iterator begin ()
 Iterator to begining of point set.
iterator end ()
 Iterator to end of point set.
const_iterator begin () const
 Iterator to begining of point set.
const_iterator end () const
 Iterator to end of point set.
set_iterator set_begin ()
 Iterator to begining of point set.
set_iterator set_end ()
 Iterator to end of point set.
const_set_iterator set_begin () const
 Iterator to begining of point set.
const_set_iterator set_end () const
 Iterator to end of point set.
ordinal_type index (const point_type &point) const
 Get point index for given point.
const point_typepoint (ordinal_type n) const
 Get point for given index.
virtual void transformQP2PCE (const value_type &alpha, const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &input, Teuchos::SerialDenseMatrix< ordinal_type, value_type > &result, const value_type &beta, bool trans=false) const
 Transform values at quadrature points to PCE coefficients.
virtual void transformPCE2QP (const value_type &alpha, const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &input, Teuchos::SerialDenseMatrix< ordinal_type, value_type > &result, const value_type &beta, bool trans=false) const
 Transform PCE coefficients to quadrature values.

Protected Member Functions

void apply_direct (const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &A, const value_type &alpha, const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &input, Teuchos::SerialDenseMatrix< ordinal_type, value_type > &result, const value_type &beta, bool trans) const
 Apply transformation operator using direct method.
void apply_pst (const Teuchos::Array< Teuchos::SerialDenseMatrix< ordinal_type, value_type > > &Ak, const value_type &alpha, const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &input, Teuchos::SerialDenseMatrix< ordinal_type, value_type > &result, const value_type &beta, bool trans, bool reorder_input, bool reorder_result) const
 Apply tranformation operator using PST method.

Protected Attributes

bool use_pst
 Use partial-summation-transformation.
ordinal_type coeff_sz
 Number of coefficients.
ordinal_type dim
 Dimension.
point_set_type points
 Quadrature points.
point_map_type point_map
 Map index to point term.
bool reorder
 Do we need to reorder coefficients for PST.
Teuchos::Array< ordinal_type > perm
 Permutation array when reordering for PST.
Teuchos::SerialDenseMatrix
< ordinal_type, value_type > 
qp2pce
 Matrix mapping points to coefficients.
Teuchos::SerialDenseMatrix
< ordinal_type, value_type > 
pce2qp
 Matrix mapping coefficients to points.
Teuchos::Array
< Teuchos::SerialDenseMatrix
< ordinal_type, value_type > > 
qp2pce_k
 Matrix mapping points to coefficients for each dimension for PST.
Teuchos::Array
< Teuchos::SerialDenseMatrix
< ordinal_type, value_type > > 
pce2qp_k
 Matrix mapping coefficients to points for each dimension for PST.
Teuchos::BLAS< ordinal_type,
value_type > 
blas
 BLAS wrappers.

Detailed Description

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
class Stokhos::TensorProductPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >

An operator for building pseudo-spectral coefficients using tensor-product quadrature.


Member Function Documentation

template<typename ordinal_t , typename value_t , typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
void Stokhos::TensorProductPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::apply_pst ( const Teuchos::Array< Teuchos::SerialDenseMatrix< ordinal_type, value_type > > &  Ak,
const value_type &  alpha,
const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &  input,
Teuchos::SerialDenseMatrix< ordinal_type, value_type > &  result,
const value_type &  beta,
bool  trans,
bool  reorder_input,
bool  reorder_result 
) const [inline, protected]

Apply tranformation operator using PST method.

For k=1,...,d, let A_k be the m_k-by-n_k quadrature operator for dimension k and A = A_1 ... A_d be m--n where m = m_1...m_d and n = n_1...n_d. For any two matrices B and C and vector x, (B C)x = vec( C*X*B^T ) = vec( C*(B*X^T)^T ) where x = vec(X), and the vec() operator makes a vector out of a matrix by stacking columns. Applying this formula recursively to A yields the simple algorithm for computing y = A*x (x is n-by-1 and y is m-by-1): X = x; for k=1:d n = n / n_k; X = reshape(X, n, n_k); X = A_k*X'; n = n * m_k; end y = reshape(X, m, 1);

When x has p columns, it is somehwat more complicated because the standard transpose above isn't correct. Instead the transpose needs to be applied to each p block in X.

The strategy here for dealing with transposed input and result is to transpose them when copying to/from the temporary buffers used in the algorithm.

template<typename ordinal_t , typename value_t , typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
virtual void Stokhos::TensorProductPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::transformPCE2QP ( const value_type &  alpha,
const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &  input,
Teuchos::SerialDenseMatrix< ordinal_type, value_type > &  result,
const value_type &  beta,
bool  trans = false 
) const [inline, virtual]

Transform PCE coefficients to quadrature values.

input is a vector storing polynomial chaos coefficients and result will contain the resulting values at the quadrature points. input and result can have multiple columns for vector-valued functions and set trans to true if these (multi-) vectors are layed out in a transposed fashion.

Implements Stokhos::PseudoSpectralOperator< ordinal_t, value_t, point_compare_type >.

template<typename ordinal_t , typename value_t , typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
virtual void Stokhos::TensorProductPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::transformQP2PCE ( const value_type &  alpha,
const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &  input,
Teuchos::SerialDenseMatrix< ordinal_type, value_type > &  result,
const value_type &  beta,
bool  trans = false 
) const [inline, virtual]

Transform values at quadrature points to PCE coefficients.

input is a vector storing values of a function at the quadrature points, and result will contain the resulting polynomial chaos coefficients. input and result can have multiple columns for vector-valued functions and set trans to true if these (multi-) vectors are layed out in a transposed fashion.

Implements Stokhos::PseudoSpectralOperator< ordinal_t, value_t, point_compare_type >.


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