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

An operator for building pseudo-spectral coefficients using a sparse Smolyak construction. More...

#include <Stokhos_SmolyakPseudoSpectralOperator.hpp>

Inheritance diagram for Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >:
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Collaboration diagram for Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >:
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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
typedef TensorProductPseudoSpectralOperator< ordinal_type, value_type > operator_type
typedef Teuchos::Array< Teuchos::RCP< operator_type > > operator_set_type
Public Types inherited from Stokhos::PseudoSpectralOperator< ordinal_t, value_t, point_compare_type >
typedef ordinal_t ordinal_type
typedef value_t value_type
typedef TensorProductElement< ordinal_type, value_type > point_type
typedef std::map< point_type, std::pair< value_type, ordinal_type >, point_compare_type > point_set_type
typedef Teuchos::Array< point_type > point_map_type
typedef point_map_type::iterator iterator
typedef point_map_type::const_iterator const_iterator
typedef point_set_type::iterator set_iterator
typedef point_set_type::const_iterator const_set_iterator

Public Member Functions

template<typename coeff_compare_type>
 SmolyakPseudoSpectralOperator (const SmolyakBasis< ordinal_type, value_type, coeff_compare_type > &smolyak_basis, bool use_smolyak_apply=true, bool use_pst=true, const point_compare_type &point_compare=point_compare_type())
 Constructor.
virtual ~SmolyakPseudoSpectralOperator ()
 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_type & point (ordinal_type n) const
 Get point for given index.
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.
Public Member Functions inherited from Stokhos::PseudoSpectralOperator< ordinal_t, value_t, point_compare_type >
 PseudoSpectralOperator ()
 Constructor.
virtual ~PseudoSpectralOperator ()
 Destructor.

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 transformQP2PCE_smolyak (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
 Transform values at quadrature points to PCE coefficients using Smolyak formula.
void transformPCE2QP_smolyak (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
 Transform PCE coefficients to values at quadrature points using Smolyak formula.
void gather (const Teuchos::Array< ordinal_type > &map, const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &input, bool trans, Teuchos::SerialDenseMatrix< ordinal_type, value_type > &result) const
void scatter (const Teuchos::Array< ordinal_type > &map, const Teuchos::SerialDenseMatrix< ordinal_type, value_type > &input, bool trans, Teuchos::SerialDenseMatrix< ordinal_type, value_type > &result) const

Protected Attributes

bool use_smolyak
 Use Smolyak apply method.
ordinal_type coeff_sz
 Number of coefficients.
point_set_type points
 Smolyak sparse grid.
point_map_type point_map
 Map index to sparse grid term.
Teuchos::Array< value_type > smolyak_coeffs
 Smolyak coefficients.
operator_set_type operators
 Tensor pseudospectral operators.
Teuchos::Array< Teuchos::Array< ordinal_type > > gather_maps
 Gather maps for each operator for Smolyak apply.
Teuchos::Array< Teuchos::Array< ordinal_type > > scatter_maps
 Scatter maps for each operator for Smolyak apply.
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::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::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >

An operator for building pseudo-spectral coefficients using a sparse Smolyak construction.

Constructor & Destructor Documentation

◆ SmolyakPseudoSpectralOperator()

template<typename ordinal_type, typename value_type, typename point_compare_type>
template<typename coeff_compare_type>
Stokhos::SmolyakPseudoSpectralOperator< ordinal_type, value_type, point_compare_type >::SmolyakPseudoSpectralOperator ( const SmolyakBasis< ordinal_type, value_type, coeff_compare_type > & smolyak_basis,
bool use_smolyak_apply = true,
bool use_pst = true,
const point_compare_type & point_compare = point_compare_type() )

Constructor.

References coeff_sz, Stokhos::SmolyakBasis< ordinal_type, value_type, coeff_compare_type >::dimension(), Stokhos::SmolyakBasis< ordinal_type, value_type, coeff_compare_type >::evaluateBases(), gather_maps, Stokhos::SmolyakBasis< ordinal_type, value_type, coeff_compare_type >::getCoordinateBases(), Stokhos::SmolyakBasis< ordinal_type, value_type, coeff_compare_type >::getNumSmolyakTerms(), Stokhos::SmolyakBasis< ordinal_type, value_type, coeff_compare_type >::getSmolyakCoefficient(), Stokhos::SmolyakBasis< ordinal_type, value_type, coeff_compare_type >::getTensorProductBasis(), Stokhos::SmolyakBasis< ordinal_type, value_type, coeff_compare_type >::index(), Stokhos::SmolyakBasis< ordinal_type, value_type, coeff_compare_type >::norm_squared(), operators, pce2qp, point(), point_map, points, qp2pce, scatter_maps, Stokhos::SmolyakBasis< ordinal_type, value_type, coeff_compare_type >::size(), smolyak_coeffs, and use_smolyak.

Member Function Documentation

◆ apply_direct()

template<typename ordinal_type, typename value_type, typename point_compare_type>
void Stokhos::SmolyakPseudoSpectralOperator< ordinal_type, value_type, point_compare_type >::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
protected

Apply transformation operator using direct method.

References blas.

Referenced by transformPCE2QP(), and transformQP2PCE().

◆ begin() [1/2]

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
iterator Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::begin ( )
inlinevirtual

Iterator to begining of point set.

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

References point_map.

◆ begin() [2/2]

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
const_iterator Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::begin ( ) const
inlinevirtual

Iterator to begining of point set.

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

References point_map.

◆ coeff_size()

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
ordinal_type Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::coeff_size ( ) const
inlinevirtual

Number of coefficients.

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

References coeff_sz.

◆ end() [1/2]

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
iterator Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::end ( )
inlinevirtual

Iterator to end of point set.

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

References point_map.

◆ end() [2/2]

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
const_iterator Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::end ( ) const
inlinevirtual

Iterator to end of point set.

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

References point_map.

◆ index()

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
ordinal_type Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::index ( const point_type & point) const
inlinevirtual

Get point index for given point.

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

References point(), and points.

◆ point()

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
const point_type & Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::point ( ordinal_type n) const
inlinevirtual

Get point for given index.

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

References point_map.

Referenced by index(), and SmolyakPseudoSpectralOperator().

◆ point_size()

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
ordinal_type Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::point_size ( ) const
inlinevirtual

Number of points.

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

References points.

◆ set_begin() [1/2]

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
set_iterator Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::set_begin ( )
inlinevirtual

Iterator to begining of point set.

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

References points.

◆ set_begin() [2/2]

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
const_set_iterator Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::set_begin ( ) const
inlinevirtual

Iterator to begining of point set.

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

References points.

◆ set_end() [1/2]

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
set_iterator Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::set_end ( )
inlinevirtual

Iterator to end of point set.

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

References points.

◆ set_end() [2/2]

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
const_set_iterator Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::set_end ( ) const
inlinevirtual

Iterator to end of point set.

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

References points.

◆ transformPCE2QP()

template<typename ordinal_type, typename value_type, typename point_compare_type>
void Stokhos::SmolyakPseudoSpectralOperator< ordinal_type, value_type, 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
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 >.

References apply_direct(), and pce2qp.

◆ transformPCE2QP_smolyak()

template<typename ordinal_type, typename value_type, typename point_compare_type>
void Stokhos::SmolyakPseudoSpectralOperator< ordinal_type, value_type, point_compare_type >::transformPCE2QP_smolyak ( 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
protected

Transform PCE coefficients to values at quadrature points using Smolyak formula.

References gather_maps, operators, scatter_maps, and smolyak_coeffs.

◆ transformQP2PCE()

template<typename ordinal_type, typename value_type, typename point_compare_type>
void Stokhos::SmolyakPseudoSpectralOperator< ordinal_type, value_type, 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
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 >.

References apply_direct(), qp2pce, transformQP2PCE_smolyak(), and use_smolyak.

◆ transformQP2PCE_smolyak()

template<typename ordinal_type, typename value_type, typename point_compare_type>
void Stokhos::SmolyakPseudoSpectralOperator< ordinal_type, value_type, point_compare_type >::transformQP2PCE_smolyak ( 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
protected

Transform values at quadrature points to PCE coefficients using Smolyak formula.

References gather_maps, operators, scatter_maps, and smolyak_coeffs.

Referenced by transformQP2PCE().

Member Data Documentation

◆ blas

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
Teuchos::BLAS<ordinal_type,value_type> Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::blas
protected

BLAS wrappers.

Referenced by apply_direct().

◆ coeff_sz

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
ordinal_type Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::coeff_sz
protected

Number of coefficients.

Referenced by coeff_size(), and SmolyakPseudoSpectralOperator().

◆ gather_maps

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
Teuchos::Array< Teuchos::Array<ordinal_type> > Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::gather_maps
protected

Gather maps for each operator for Smolyak apply.

Referenced by SmolyakPseudoSpectralOperator(), transformPCE2QP_smolyak(), and transformQP2PCE_smolyak().

◆ operators

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
operator_set_type Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::operators
protected

Tensor pseudospectral operators.

Referenced by SmolyakPseudoSpectralOperator(), transformPCE2QP_smolyak(), and transformQP2PCE_smolyak().

◆ pce2qp

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
Teuchos::SerialDenseMatrix<ordinal_type,value_type> Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::pce2qp
protected

Matrix mapping coefficients to points.

Referenced by SmolyakPseudoSpectralOperator(), and transformPCE2QP().

◆ point_map

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
point_map_type Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::point_map
protected

Map index to sparse grid term.

Referenced by begin(), begin(), end(), end(), point(), and SmolyakPseudoSpectralOperator().

◆ points

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
point_set_type Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::points
protected

Smolyak sparse grid.

Referenced by index(), point_size(), set_begin(), set_begin(), set_end(), set_end(), and SmolyakPseudoSpectralOperator().

◆ qp2pce

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
Teuchos::SerialDenseMatrix<ordinal_type,value_type> Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::qp2pce
protected

Matrix mapping points to coefficients.

Referenced by SmolyakPseudoSpectralOperator(), and transformQP2PCE().

◆ scatter_maps

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
Teuchos::Array< Teuchos::Array<ordinal_type> > Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::scatter_maps
protected

Scatter maps for each operator for Smolyak apply.

Referenced by SmolyakPseudoSpectralOperator(), transformPCE2QP_smolyak(), and transformQP2PCE_smolyak().

◆ smolyak_coeffs

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
Teuchos::Array<value_type> Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::smolyak_coeffs
protected

Smolyak coefficients.

Referenced by SmolyakPseudoSpectralOperator(), transformPCE2QP_smolyak(), and transformQP2PCE_smolyak().

◆ use_smolyak

template<typename ordinal_t, typename value_t, typename point_compare_type = typename DefaultPointCompare<ordinal_t,value_t>::type>
bool Stokhos::SmolyakPseudoSpectralOperator< ordinal_t, value_t, point_compare_type >::use_smolyak
protected

Use Smolyak apply method.

Referenced by SmolyakPseudoSpectralOperator(), and transformQP2PCE().

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