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Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type > Class Template Reference

Class to store coefficients of a projection onto an orthogonal polynomial basis. More...

#include <Stokhos_OrthogPolyApprox.hpp>

Public Types

typedef storage_type::reference reference
typedef storage_type::const_reference const_reference
typedef storage_type::pointer pointer
typedef storage_type::const_pointer const_pointer

Public Member Functions

 OrthogPolyApprox (const Teuchos::RCP< const Stokhos::OrthogPolyBasis< ordinal_type, value_type > > &basis=Teuchos::null, ordinal_type sz=0, const value_type *vals=NULL)
 Constructor with supplied size sz.
 OrthogPolyApprox (const OrthogPolyApprox &x)
 Copy constructor.
 ~OrthogPolyApprox ()
 Destructor.
OrthogPolyApprox & operator= (const OrthogPolyApprox &x)
 Assignment operator (deep copy).
OrthogPolyApprox & operator= (const value_type &v)
 Assignment operator with scalar.
void init (const value_type &v)
 Initialize coefficients to value.
void init (const value_type *v)
 Initialize coefficients to an array of values.
template<typename S>
void init (const OrthogPolyApprox< ordinal_type, value_type, S > &v)
 Initialize coefficients from an OrthogPolyApprox with different storage.
void load (value_type *v)
 Load coefficients to an array of values.
template<typename S>
void load (OrthogPolyApprox< ordinal_type, value_type, S > &v)
 Load coefficients into an OrthogPolyApprox with different storage.
Teuchos::RCP< const Stokhos::OrthogPolyBasis< ordinal_type, value_type > > basis () const
 Return basis.
void reset (const Teuchos::RCP< const Stokhos::OrthogPolyBasis< ordinal_type, value_type > > &new_basis, ordinal_type sz=0)
 Reset to a new basis.
void resize (ordinal_type sz)
 Resize coefficient array (coefficients are preserved).
ordinal_type size () const
 Return size.
pointer coeff ()
 Return coefficient array.
const_pointer coeff () const
 Return coefficient array.
reference operator[] (ordinal_type i)
 Array access.
const_reference operator[] (ordinal_type i) const
 Array access.
reference term (ordinal_type dimension, ordinal_type order)
 Get coefficient term for given dimension and order.
const_reference term (ordinal_type dimension, ordinal_type order) const
 Get coefficient term for given dimension and order.
const MultiIndex< ordinal_type > & order (ordinal_type term) const
 Get orders for a given term.
value_type evaluate (const Teuchos::Array< value_type > &point) const
 Evaluate polynomial approximation at a point.
value_type evaluate (const Teuchos::Array< value_type > &point, const Teuchos::Array< value_type > &basis_vals) const
 Evaluate polynomial approximation at a point with supplied basis values.
value_type mean () const
 Compute mean of expansion.
value_type standard_deviation () const
 Compute standard deviation of expansion.
value_type two_norm () const
 Compute the two-norm of expansion.
value_type two_norm_squared () const
 Compute the squared two-norm of expansion.
value_type inner_product (const OrthogPolyApprox &b) const
 Compute the L2 inner product of 2 PCEs.
std::ostream & print (std::ostream &os) const
 Print approximation in basis.

Protected Attributes

Teuchos::RCP< const Stokhos::OrthogPolyBasis< ordinal_type, value_type > > basis_
 Basis expansion is relative to.
storage_type coeff_
 OrthogPolyApprox coefficients.

Detailed Description

template<typename ordinal_type, typename value_type, typename storage_type = Stokhos::StandardStorage<ordinal_type, value_type>>
class Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >

Class to store coefficients of a projection onto an orthogonal polynomial basis.

Constructor & Destructor Documentation

◆ OrthogPolyApprox() [1/2]

template<typename ordinal_type, typename value_type, typename storage_type>
Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::OrthogPolyApprox ( const Teuchos::RCP< const Stokhos::OrthogPolyBasis< ordinal_type, value_type > > & basis = Teuchos::null,
ordinal_type sz = 0,
const value_type * vals = NULL )

Constructor with supplied size sz.

Normally sz should equal the basis size, however this is not enforced since other situations can arise, e.g., using a size of 1 for a constant expansion. If sz = 0, it is computed from the basis size (and is 1 if basis is null).

References basis_, and coeff_.

Referenced by init(), load(), operator=(), and OrthogPolyApprox().

◆ OrthogPolyApprox() [2/2]

template<typename ordinal_type, typename value_type, typename storage_type = Stokhos::StandardStorage<ordinal_type, value_type>>
Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::OrthogPolyApprox ( const OrthogPolyApprox< ordinal_type, value_type, storage_type > & x)

Copy constructor.

References OrthogPolyApprox().

Member Function Documentation

◆ basis()

template<typename ordinal_type, typename value_type, typename storage_type>
Teuchos::RCP< const Stokhos::OrthogPolyBasis< ordinal_type, value_type > > Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::basis ( ) const

Return basis.

Referenced by Stokhos::HouseTriDiagPCEBasis< ordinal_type, value_type >::HouseTriDiagPCEBasis().

◆ coeff() [1/2]

template<typename ordinal_type, typename value_type, typename storage_type>
Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::pointer Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::coeff ( )

Return coefficient array.

Referenced by Stokhos::PseudoSpectralOrthogPolyExpansion< ordinal_type, value_type, point_compare_type, node_type >::binary_op(), Stokhos::PseudoSpectralOrthogPolyExpansion< ordinal_type, value_type, point_compare_type, node_type >::binary_op(), Stokhos::PseudoSpectralOrthogPolyExpansion< ordinal_type, value_type, point_compare_type, node_type >::binary_op(), Stokhos::QuadOrthogPolyExpansion< ordinal_type, value_type, node_type >::binary_op(), Stokhos::QuadOrthogPolyExpansion< ordinal_type, value_type, node_type >::binary_op(), Stokhos::QuadOrthogPolyExpansion< ordinal_type, value_type, node_type >::binary_op(), Stokhos::StieltjesGramSchmidtBuilder< ordinal_type, value_type >::computeReducedPCEs(), init(), load(), Stokhos::PseudoSpectralOrthogPolyExpansion< ordinal_type, value_type, point_compare_type, node_type >::unary_op(), and Stokhos::QuadOrthogPolyExpansion< ordinal_type, value_type, node_type >::unary_op().

◆ coeff() [2/2]

template<typename ordinal_type, typename value_type, typename storage_type>
Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::const_pointer Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::coeff ( ) const

Return coefficient array.

References coeff_.

◆ evaluate() [1/2]

template<typename ordinal_type, typename value_type, typename storage_type>
value_type Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::evaluate ( const Teuchos::Array< value_type > & point) const

Evaluate polynomial approximation at a point.

References basis_, and evaluate().

Referenced by evaluate(), and Stokhos::MonoProjPCEBasis< ordinal_type, value_type >::MonoProjPCEBasis().

◆ evaluate() [2/2]

template<typename ordinal_type, typename value_type, typename storage_type>
value_type Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::evaluate ( const Teuchos::Array< value_type > & point,
const Teuchos::Array< value_type > & basis_vals ) const

Evaluate polynomial approximation at a point with supplied basis values.

References coeff_.

◆ init() [1/3]

template<typename ordinal_type, typename value_type, typename storage_type = Stokhos::StandardStorage<ordinal_type, value_type>>
template<typename S>
void Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::init ( const OrthogPolyApprox< ordinal_type, value_type, S > & v)
inline

Initialize coefficients from an OrthogPolyApprox with different storage.

References coeff(), coeff_, and OrthogPolyApprox().

◆ init() [2/3]

template<typename ordinal_type, typename value_type, typename storage_type>
void Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::init ( const value_type & v)

Initialize coefficients to value.

Referenced by Stokhos::OrthogPolyApprox< OrdinalType, ValueType >::init(), and operator=().

◆ init() [3/3]

template<typename ordinal_type, typename value_type, typename storage_type>
void Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::init ( const value_type * v)

Initialize coefficients to an array of values.

References coeff_.

◆ inner_product()

template<typename ordinal_type, typename value_type, typename storage_type = Stokhos::StandardStorage<ordinal_type, value_type>>
value_type Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::inner_product ( const OrthogPolyApprox< ordinal_type, value_type, storage_type > & b) const

Compute the L2 inner product of 2 PCEs.

References basis_, coeff_, and Stokhos::ProductContainer< coeff_type >::coeff_.

◆ load()

template<typename ordinal_type, typename value_type, typename storage_type = Stokhos::StandardStorage<ordinal_type, value_type>>
template<typename S>
void Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::load ( OrthogPolyApprox< ordinal_type, value_type, S > & v)
inline

Load coefficients into an OrthogPolyApprox with different storage.

References coeff(), coeff_, and OrthogPolyApprox().

◆ mean()

template<typename ordinal_type, typename value_type, typename storage_type>
value_type Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::mean ( ) const

Compute mean of expansion.

References coeff_.

◆ operator=()

template<typename ordinal_type, typename value_type, typename storage_type = Stokhos::StandardStorage<ordinal_type, value_type>>
OrthogPolyApprox & Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::operator= ( const OrthogPolyApprox< ordinal_type, value_type, storage_type > & x)

Assignment operator (deep copy).

References init(), operator=(), and OrthogPolyApprox().

Referenced by operator=().

◆ operator[]() [1/2]

template<typename ordinal_type, typename value_type, typename storage_type>
Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::reference Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::operator[] ( ordinal_type i)

Array access.

References coeff_.

◆ operator[]() [2/2]

template<typename ordinal_type, typename value_type, typename storage_type>
Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::const_reference Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::operator[] ( ordinal_type i) const

Array access.

References coeff_.

◆ order()

template<typename ordinal_type, typename value_type, typename storage_type>
const Stokhos::MultiIndex< ordinal_type > & Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::order ( ordinal_type term) const

Get orders for a given term.

References basis_.

◆ print()

template<typename ordinal_type, typename value_type, typename storage_type>
std::ostream & Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::print ( std::ostream & os) const

Print approximation in basis.

References basis_, coeff_, Stokhos::MultiIndex< ordinal_t >::size(), and Stokhos::ProductContainer< coeff_type >::size().

◆ reset()

template<typename ordinal_type, typename value_type, typename storage_type>
void Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::reset ( const Teuchos::RCP< const Stokhos::OrthogPolyBasis< ordinal_type, value_type > > & new_basis,
ordinal_type sz = 0 )

Reset to a new basis.

This resizes array to fit new basis. Coefficients are preserved.

◆ resize()

template<typename ordinal_type, typename value_type, typename storage_type>
void Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::resize ( ordinal_type sz)

Resize coefficient array (coefficients are preserved).

Referenced by Stokhos::PseudoSpectralOrthogPolyExpansion< ordinal_type, value_type, point_compare_type, node_type >::binary_op(), Stokhos::PseudoSpectralOrthogPolyExpansion< ordinal_type, value_type, point_compare_type, node_type >::binary_op(), Stokhos::PseudoSpectralOrthogPolyExpansion< ordinal_type, value_type, point_compare_type, node_type >::binary_op(), Stokhos::QuadOrthogPolyExpansion< ordinal_type, value_type, node_type >::binary_op(), Stokhos::QuadOrthogPolyExpansion< ordinal_type, value_type, node_type >::binary_op(), Stokhos::QuadOrthogPolyExpansion< ordinal_type, value_type, node_type >::binary_op(), Stokhos::PseudoSpectralOrthogPolyExpansion< ordinal_type, value_type, point_compare_type, node_type >::unary_op(), and Stokhos::QuadOrthogPolyExpansion< ordinal_type, value_type, node_type >::unary_op().

◆ size()

template<typename ordinal_type, typename value_type, typename storage_type>
ordinal_type Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::size ( ) const

Return size.

Referenced by Stokhos::PseudoSpectralOrthogPolyExpansion< ordinal_type, value_type, point_compare_type, node_type >::binary_op(), Stokhos::PseudoSpectralOrthogPolyExpansion< ordinal_type, value_type, point_compare_type, node_type >::binary_op(), Stokhos::PseudoSpectralOrthogPolyExpansion< ordinal_type, value_type, point_compare_type, node_type >::binary_op(), Stokhos::QuadOrthogPolyExpansion< ordinal_type, value_type, node_type >::binary_op(), Stokhos::QuadOrthogPolyExpansion< ordinal_type, value_type, node_type >::binary_op(), Stokhos::QuadOrthogPolyExpansion< ordinal_type, value_type, node_type >::binary_op(), Stokhos::PseudoSpectralOrthogPolyExpansion< ordinal_type, value_type, point_compare_type, node_type >::unary_op(), and Stokhos::QuadOrthogPolyExpansion< ordinal_type, value_type, node_type >::unary_op().

◆ standard_deviation()

template<typename ordinal_type, typename value_type, typename storage_type>
value_type Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::standard_deviation ( ) const

Compute standard deviation of expansion.

References basis_, and coeff_.

◆ term() [1/2]

template<typename ordinal_type, typename value_type, typename storage_type>
Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::reference Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::term ( ordinal_type dimension,
ordinal_type order )

Get coefficient term for given dimension and order.

References basis_, and coeff_.

Referenced by Stokhos::StieltjesGramSchmidtBuilder< ordinal_type, value_type >::computeReducedPCEs().

◆ term() [2/2]

template<typename ordinal_type, typename value_type, typename storage_type>
Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::const_reference Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::term ( ordinal_type dimension,
ordinal_type order ) const

Get coefficient term for given dimension and order.

References basis_, and coeff_.

◆ two_norm()

template<typename ordinal_type, typename value_type, typename storage_type>
value_type Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::two_norm ( ) const

Compute the two-norm of expansion.

References two_norm_squared().

◆ two_norm_squared()

template<typename ordinal_type, typename value_type, typename storage_type>
value_type Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::two_norm_squared ( ) const

Compute the squared two-norm of expansion.

References basis_, and coeff_.

Referenced by two_norm().

Member Data Documentation

◆ basis_

template<typename ordinal_type, typename value_type, typename storage_type = Stokhos::StandardStorage<ordinal_type, value_type>>
Teuchos::RCP<const Stokhos::OrthogPolyBasis<ordinal_type, value_type> > Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::basis_
protected

Basis expansion is relative to.

Referenced by evaluate(), inner_product(), order(), OrthogPolyApprox(), print(), standard_deviation(), term(), term(), and two_norm_squared().

◆ coeff_

template<typename ordinal_type, typename value_type, typename storage_type = Stokhos::StandardStorage<ordinal_type, value_type>>
storage_type Stokhos::OrthogPolyApprox< ordinal_type, value_type, storage_type >::coeff_
protected

OrthogPolyApprox coefficients.

Referenced by coeff(), evaluate(), init(), init(), inner_product(), load(), mean(), operator[](), operator[](), OrthogPolyApprox(), print(), standard_deviation(), term(), term(), and two_norm_squared().

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