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

#include <Stokhos_HouseTriDiagPCEBasis.hpp>

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

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Public Member Functions
	HouseTriDiagPCEBasis (ordinal_type p, const Stokhos::OrthogPolyApprox< ordinal_type, value_type > &pce, const Stokhos::Sparse3Tensor< ordinal_type, value_type > &Cijk, bool limit_integration_order=false)
	Constructor. More...

	~HouseTriDiagPCEBasis ()
	Destructor. More...

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

void	transformCoeffsFromHouse (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 Teuchos::SerialDenseMatrix < ordinal_type, value_type >	matrix_type

typedef Teuchos::SerialDenseVector < ordinal_type, value_type >	vector_type

Protected Attributes
Teuchos::LAPACK< ordinal_type, value_type >	lapack
	LAPACK routines. More...

Teuchos::BLAS< ordinal_type, value_type >	blas
	BLAS routines. More...

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

ordinal_type	pce_sz
	Size of PC expansion. More...

Teuchos::Array< value_type >	pce_norms
	Basis norms. More...

Teuchos::Array< value_type >	a
	Stores full set of alpha coefficients. More...

Teuchos::Array< value_type >	b
	Stores full set of beta coefficients. More...

matrix_type	basis_vecs
	Basis vectors. 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
	HouseTriDiagPCEBasis (const HouseTriDiagPCEBasis &)

HouseTriDiagPCEBasis &	operator= (const HouseTriDiagPCEBasis &b)

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

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...

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...

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...

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

Detailed Description

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

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

Definition at line 63 of file Stokhos_HouseTriDiagPCEBasis.hpp.

Member Typedef Documentation

template<typename ordinal_type, typename value_type>

typedef Teuchos::SerialDenseMatrix<ordinal_type,value_type> Stokhos::HouseTriDiagPCEBasis< ordinal_type, value_type >::matrix_type

protected

Definition at line 141 of file Stokhos_HouseTriDiagPCEBasis.hpp.

template<typename ordinal_type, typename value_type>

typedef Teuchos::SerialDenseVector<ordinal_type,value_type> Stokhos::HouseTriDiagPCEBasis< ordinal_type, value_type >::vector_type

protected

Definition at line 142 of file Stokhos_HouseTriDiagPCEBasis.hpp.

Constructor & Destructor Documentation

template<typename ordinal_type, typename value_type>

Stokhos::HouseTriDiagPCEBasis< ordinal_type, value_type >::HouseTriDiagPCEBasis	(	ordinal_type	p,
		const Stokhos::OrthogPolyApprox< ordinal_type, value_type > &	pce,
		const Stokhos::Sparse3Tensor< ordinal_type, value_type > &	Cijk,
		bool	limit_integration_order = `false`
	)

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_HouseTriDiagPCEBasisImp.hpp.

template<typename ordinal_type , typename value_type >

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

Destructor.

Definition at line 151 of file Stokhos_HouseTriDiagPCEBasisImp.hpp.

template<typename ordinal_type, typename value_type>

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

private

template<typename ordinal_type, typename value_type>

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

private

Copy constructor with specified order.

Definition at line 250 of file Stokhos_HouseTriDiagPCEBasisImp.hpp.

Member Function Documentation

template<typename ordinal_type, typename value_type>

void Stokhos::HouseTriDiagPCEBasis< 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 158 of file Stokhos_HouseTriDiagPCEBasisImp.hpp.

template<typename ordinal_type, typename value_type >

Teuchos::RCP< Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type > > Stokhos::HouseTriDiagPCEBasis< 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 198 of file Stokhos_HouseTriDiagPCEBasisImp.hpp.

template<typename ordinal_type, typename value_type >

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

Get new coefficients in this new basis.

Definition at line 208 of file Stokhos_HouseTriDiagPCEBasisImp.hpp.

template<typename ordinal_type , typename value_type>

void Stokhos::HouseTriDiagPCEBasis< ordinal_type, value_type >::transformCoeffsFromHouse	(	const value_type *	in,
		value_type *	out
	)		const

Map expansion coefficients from this basis to original.

Definition at line 216 of file Stokhos_HouseTriDiagPCEBasisImp.hpp.

template<typename ordinal_type, typename value_type>

bool Stokhos::HouseTriDiagPCEBasis< 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

protectedvirtual

Compute recurrence coefficients.

Implements Stokhos::RecurrenceBasis< ordinal_type, value_type >.

Definition at line 228 of file Stokhos_HouseTriDiagPCEBasisImp.hpp.

template<typename ordinal_type, typename value_type>

HouseTriDiagPCEBasis& Stokhos::HouseTriDiagPCEBasis< ordinal_type, value_type >::operator= ( const HouseTriDiagPCEBasis< ordinal_type, value_type > & b )