Generates three-term recurrence using the Lanczos procedure applied to a polynomial chaos expansion in another basis. More...

#include <Stokhos_LanczosPCEBasis.hpp>

Inheritance diagram for Stokhos::LanczosPCEBasis< ordinal_type, value_type >:

[legend]

Public Member Functions
	LanczosPCEBasis (ordinal_type p, const Teuchos::RCP< const Stokhos::OrthogPolyApprox< ordinal_type, value_type > > &pce, const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &quad, bool normalize, bool limit_integration_order)
	Constructor. More...

	~LanczosPCEBasis ()
	Destructor. More...

value_type	getNewCoeffs (ordinal_type i) const
	Get new coefficients in this new basis. More...

void	transformCoeffsFromLanczos (const value_type in, value_type out) const
	Map expansion coefficients from this basis to original. More...

Public Member Functions inherited from Stokhos::RecurrenceBasis< ordinal_type, value_type >
virtual	~RecurrenceBasis ()
	Destructor. More...

virtual void	getRecurrenceCoefficients (Teuchos::Array< value_type > &alpha, Teuchos::Array< value_type > &beta, Teuchos::Array< value_type > &delta, Teuchos::Array< value_type > &gamma) const
	Return recurrence coefficients defined by above formula. More...

virtual void	evaluateBasesAndDerivatives (const value_type &point, Teuchos::Array< value_type > &vals, Teuchos::Array< value_type > &derivs) const
	Evaluate basis polynomials and their derivatives at given point `point`. More...

virtual void	setQuadZeroTol (value_type tol)
	Set tolerance for zero in quad point generation. More...

virtual ordinal_type	order () const
	Return order of basis (largest monomial degree ). More...

virtual ordinal_type	size () const
	Return total size of basis (given by order() + 1). More...

virtual const Teuchos::Array < value_type > &	norm_squared () const
	Return array storing norm-squared of each basis polynomial. More...

virtual const value_type &	norm_squared (ordinal_type i) const
	Return norm squared of basis polynomial `i`. More...

virtual Teuchos::RCP < Stokhos::Dense3Tensor < ordinal_type, value_type > >	computeTripleProductTensor () const
	Compute triple product tensor. More...

virtual Teuchos::RCP < Stokhos::Sparse3Tensor < ordinal_type, value_type > >	computeSparseTripleProductTensor (ordinal_type order) const
	Compute triple product tensor. More...

virtual Teuchos::RCP < Teuchos::SerialDenseMatrix < ordinal_type, value_type > >	computeDerivDoubleProductTensor () const
	Compute derivative double product tensor. More...

virtual void	evaluateBases (const value_type &point, Teuchos::Array< value_type > &basis_pts) const
	Evaluate each basis polynomial at given point `point`. More...

virtual value_type	evaluate (const value_type &point, ordinal_type order) const
	Evaluate basis polynomial given by order `order` at given point `point`. More...

virtual void	print (std::ostream &os) const
	Print basis to stream `os`. More...

virtual const std::string &	getName () const
	Return string name of basis. More...

virtual ordinal_type	quadDegreeOfExactness (ordinal_type n) const

virtual ordinal_type	coefficientGrowth (ordinal_type n) const
	Evaluate coefficient growth rule for Smolyak-type bases. More...

virtual ordinal_type	pointGrowth (ordinal_type n) const
	Evaluate point growth rule for Smolyak-type bases. More...

virtual LevelToOrderFnPtr	getSparseGridGrowthRule () const
	Get sparse grid level_to_order mapping function. More...

virtual void	setSparseGridGrowthRule (LevelToOrderFnPtr ptr)
	Set sparse grid rule. More...

Public Member Functions inherited from Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >
	OneDOrthogPolyBasis ()
	Default constructor. More...

virtual	~OneDOrthogPolyBasis ()
	Destructor. More...

virtual void	setSparseGridGrowthRule (LevelToOrderFnPtr ptr)=0
	Set sparse grid rule. More...

Protected Types
typedef WeightedVectorSpace < ordinal_type, value_type >	vectorspace_type

typedef DiagonalOperator < ordinal_type, value_type >	operator_type

typedef Stokhos::Lanczos < vectorspace_type, operator_type >	lanczos_type

typedef lanczos_type::matrix_type	matrix_type

typedef lanczos_type::vector_type	vector_type

Protected Member Functions
	LanczosPCEBasis (ordinal_type p, const LanczosPCEBasis &basis)
	Copy constructor with specified order. More...

Protected Member Functions inherited from Stokhos::RecurrenceBasis< ordinal_type, value_type >
	RecurrenceBasis (const std::string &name, ordinal_type p, bool normalize, GrowthPolicy growth=SLOW_GROWTH)
	Constructor to be called by derived classes. More...

	RecurrenceBasis (ordinal_type p, const RecurrenceBasis &basis)
	Copy constructor with specified order. More...

void	normalizeRecurrenceCoefficients (Teuchos::Array< value_type > &alpha, Teuchos::Array< value_type > &beta, Teuchos::Array< value_type > &delta, Teuchos::Array< value_type > &gamma) const
	Normalize coefficients. More...

Protected Attributes
Teuchos::RCP< const Stokhos::OrthogPolyApprox < ordinal_type, value_type > >	pce
	PCE Lanczos procedure is based on. More...

Teuchos::RCP< const Stokhos::Quadrature < ordinal_type, value_type > >	quad
	Quadrature object. More...

bool	limit_integration_order
	Flag indicating whether to limit the integration order. More...

ordinal_type	nqp
	Number of quadrature points. More...

vector_type	pce_weights
	Quadrature weights. More...

vector_type	pce_vals
	Values of PCE at quadrature points. More...

vector_type	u0
	Initial Lanczos vector. More...

matrix_type	lanczos_vecs
	Lanczos vectors. More...

matrix_type	fromStieltjesMat
	Matrix mapping coefficients in Stieltjes basis back to original basis. More...

vector_type	new_pce
	Projection of pce in new basis. More...

Protected Attributes inherited from Stokhos::RecurrenceBasis< ordinal_type, value_type >
std::string	name
	Name of basis. More...

ordinal_type	p
	Order of basis. More...

bool	normalize
	Normalize basis. More...

GrowthPolicy	growth
	Smolyak growth policy. More...

value_type	quad_zero_tol
	Tolerance for quadrature points near zero. More...

LevelToOrderFnPtr	sparse_grid_growth_rule
	Sparse grid growth rule (as determined by Pecos) More...

Teuchos::Array< value_type >	alpha
	Recurrence $\alpha$ coefficients. More...

Teuchos::Array< value_type >	beta
	Recurrence $\beta$ coefficients. More...

Teuchos::Array< value_type >	delta
	Recurrence $\delta$ coefficients. More...

Teuchos::Array< value_type >	gamma
	Recurrence $\gamma$ coefficients. More...

Teuchos::Array< value_type >	norms
	Norms. More...

Private Member Functions
	LanczosPCEBasis (const LanczosPCEBasis &)

LanczosPCEBasis &	operator= (const LanczosPCEBasis &b)

Implementation of Stokhos::OneDOrthogPolyBasis methods
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. More...

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. More...

Implementation of Stokhos::RecurrenceBasis methods
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. More...

virtual void	setup ()
	Setup basis after computing recurrence coefficients. More...

Additional Inherited Members
Public Types inherited from Stokhos::RecurrenceBasis< ordinal_type, value_type >
typedef OneDOrthogPolyBasis < ordinal_type, value_type > ::LevelToOrderFnPtr	LevelToOrderFnPtr
	Function pointer needed for level_to_order mappings. More...

Public Types inherited from Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >
typedef int(*	LevelToOrderFnPtr )(int level, int growth)
	Function pointer needed for level_to_order mappings. More...

Detailed Description

template<typename ordinal_type, typename value_type>
class Stokhos::LanczosPCEBasis< ordinal_type, value_type >

Generates three-term recurrence using the Lanczos procedure applied to a polynomial chaos expansion in another basis.

Definition at line 84 of file Stokhos_LanczosPCEBasis.hpp.

Member Typedef Documentation

template<typename ordinal_type, typename value_type>

typedef WeightedVectorSpace<ordinal_type,value_type> Stokhos::LanczosPCEBasis< ordinal_type, value_type >::vectorspace_type

protected

Definition at line 166 of file Stokhos_LanczosPCEBasis.hpp.

template<typename ordinal_type, typename value_type>

typedef DiagonalOperator<ordinal_type,value_type> Stokhos::LanczosPCEBasis< ordinal_type, value_type >::operator_type

protected

Definition at line 167 of file Stokhos_LanczosPCEBasis.hpp.

template<typename ordinal_type, typename value_type>

typedef Stokhos::Lanczos<vectorspace_type, operator_type> Stokhos::LanczosPCEBasis< ordinal_type, value_type >::lanczos_type

protected

Definition at line 168 of file Stokhos_LanczosPCEBasis.hpp.

template<typename ordinal_type, typename value_type>

typedef lanczos_type::matrix_type Stokhos::LanczosPCEBasis< ordinal_type, value_type >::matrix_type

protected

Definition at line 169 of file Stokhos_LanczosPCEBasis.hpp.

template<typename ordinal_type, typename value_type>

typedef lanczos_type::vector_type Stokhos::LanczosPCEBasis< ordinal_type, value_type >::vector_type

protected

Definition at line 170 of file Stokhos_LanczosPCEBasis.hpp.

Constructor & Destructor Documentation

template<typename ordinal_type, typename value_type>

Stokhos::LanczosPCEBasis< ordinal_type, value_type >::LanczosPCEBasis	(	ordinal_type	p,
		const Teuchos::RCP< const Stokhos::OrthogPolyApprox< ordinal_type, value_type > > &	pce,
		const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &	quad,
		bool	normalize,
		bool	limit_integration_order
	)

Constructor.

Parameters

p	order of the basis
pce	polynomial chaos expansion defining new density function
quad	quadrature data for basis of PC expansion

Definition at line 48 of file Stokhos_LanczosPCEBasisImp.hpp.

template<typename ordinal_type , typename value_type >

Stokhos::LanczosPCEBasis< ordinal_type, value_type >::~LanczosPCEBasis ( )

Destructor.

Definition at line 84 of file Stokhos_LanczosPCEBasisImp.hpp.

template<typename ordinal_type, typename value_type>

Stokhos::LanczosPCEBasis< ordinal_type, value_type >::LanczosPCEBasis	(	ordinal_type	p,
		const LanczosPCEBasis< ordinal_type, value_type > &	basis
	)

protected

Copy constructor with specified order.

Definition at line 230 of file Stokhos_LanczosPCEBasisImp.hpp.

template<typename ordinal_type, typename value_type>

Stokhos::LanczosPCEBasis< ordinal_type, value_type >::LanczosPCEBasis ( const LanczosPCEBasis< ordinal_type, value_type > & )

private

Member Function Documentation

template<typename ordinal_type, typename value_type>

void Stokhos::LanczosPCEBasis< ordinal_type, value_type >::getQuadPoints	(	ordinal_type	quad_order,
		Teuchos::Array< value_type > &	points,
		Teuchos::Array< value_type > &	weights,
		Teuchos::Array< Teuchos::Array< value_type > > &	values
	)		const

virtual

Get Gauss quadrature points, weights, and values of basis at points.

Reimplemented from Stokhos::RecurrenceBasis< ordinal_type, value_type >.

Definition at line 91 of file Stokhos_LanczosPCEBasisImp.hpp.

template<typename ordinal_type, typename value_type >

Teuchos::RCP< Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type > > Stokhos::LanczosPCEBasis< ordinal_type, value_type >::cloneWithOrder ( ordinal_type p ) const

virtual

Clone this object with the option of building a higher order basis.

This method is following the Prototype pattern (see Design Pattern's textbook). The slight variation is that it allows the order of the polynomial to be modified, otherwise an exact copy is formed. The use case for this is creating basis functions for column indices in a spatially varying adaptive refinement context.

Implements Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >.

Definition at line 131 of file Stokhos_LanczosPCEBasisImp.hpp.

template<typename ordinal_type, typename value_type >

value_type Stokhos::LanczosPCEBasis< ordinal_type, value_type >::getNewCoeffs ( ordinal_type i ) const

Get new coefficients in this new basis.

Definition at line 140 of file Stokhos_LanczosPCEBasisImp.hpp.

template<typename ordinal_type , typename value_type>

void Stokhos::LanczosPCEBasis< ordinal_type, value_type >::transformCoeffsFromLanczos	(	const value_type *	in,
		value_type *	out
	)		const

Map expansion coefficients from this basis to original.

Definition at line 148 of file Stokhos_LanczosPCEBasisImp.hpp.

template<typename ordinal_type, typename value_type>

bool Stokhos::LanczosPCEBasis< ordinal_type, value_type >::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