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

#include <Stokhos_LanczosProjPCEBasis.hpp>

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

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Collaboration diagram for Stokhos::LanczosProjPCEBasis< ordinal_type, value_type >:

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Public Member Functions
	LanczosProjPCEBasis (ordinal_type p, const Teuchos::RCP< const Stokhos::OrthogPolyApprox< ordinal_type, value_type > > &pce, const Teuchos::RCP< const Stokhos::Sparse3Tensor< ordinal_type, value_type > > &Cijk, bool normalize, bool limit_integration_order=false)
	Constructor.
	~LanczosProjPCEBasis ()
	Destructor.
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.
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.
value_type	getNewCoeffs (ordinal_type i) const
	Get new coefficients in this new basis.
void	transformCoeffsFromLanczos (const value_type in, value_type out) const
	Map expansion coefficients from this basis to original.
Public Member Functions inherited from Stokhos::RecurrenceBasis< ordinal_type, value_type >
virtual	~RecurrenceBasis ()
	Destructor.
virtual ordinal_type	order () const
	Return order of basis (largest monomial degree ).
virtual ordinal_type	size () const
	Return total size of basis (given by order() + 1).
virtual const Teuchos::Array< value_type > &	norm_squared () const
	Return array storing norm-squared of each basis polynomial.
virtual const value_type &	norm_squared (ordinal_type i) const
	Return norm squared of basis polynomial `i`.
virtual Teuchos::RCP< Stokhos::Dense3Tensor< ordinal_type, value_type > >	computeTripleProductTensor () const
	Compute triple product tensor.
virtual Teuchos::RCP< Stokhos::Sparse3Tensor< ordinal_type, value_type > >	computeSparseTripleProductTensor (ordinal_type order) const
	Compute triple product tensor.
virtual Teuchos::RCP< Teuchos::SerialDenseMatrix< ordinal_type, value_type > >	computeDerivDoubleProductTensor () const
	Compute derivative double product tensor.
virtual void	evaluateBases (const value_type &point, Teuchos::Array< value_type > &basis_pts) const
	Evaluate each basis polynomial at given point `point`.
virtual value_type	evaluate (const value_type &point, ordinal_type order) const
	Evaluate basis polynomial given by order `order` at given point `point`.
virtual void	print (std::ostream &os) const
	Print basis to stream `os`.
virtual const std::string &	getName () const
	Return string name of basis.
virtual ordinal_type	quadDegreeOfExactness (ordinal_type n) const
virtual ordinal_type	coefficientGrowth (ordinal_type n) const
	Evaluate coefficient growth rule for Smolyak-type bases.
virtual ordinal_type	pointGrowth (ordinal_type n) const
	Evaluate point growth rule for Smolyak-type bases.
virtual LevelToOrderFnPtr	getSparseGridGrowthRule () const
	Get sparse grid level_to_order mapping function.
virtual void	setSparseGridGrowthRule (LevelToOrderFnPtr ptr)
	Set sparse grid rule.
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.
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`.
virtual void	setQuadZeroTol (value_type tol)
	Set tolerance for zero in quad point generation.
Public Member Functions inherited from Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type >
	OneDOrthogPolyBasis ()
	Default constructor.
virtual	~OneDOrthogPolyBasis ()
	Destructor.
virtual void	setSparseGridGrowthRule (LevelToOrderFnPtr ptr)=0
	Set sparse grid rule.

Implementation of Stokhos::RecurrenceBasis methods
typedef WeightedVectorSpace< ordinal_type, value_type >	vectorspace_type
typedef DenseOperator< 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
Teuchos::RCP< const Stokhos::OrthogPolyApprox< ordinal_type, value_type > >	pce
	PCE Lanczos procedure is based on.
bool	limit_integration_order
	Flag indicating whether to limit the integration order.
ordinal_type	pce_sz
	Size of PC expansion.
Teuchos::Array< value_type >	pce_norms
	Basis norms.
matrix_type	Cijk_matrix
	Triple-product matrix used in generating lanczos vectors.
vector_type	weights
	Weighting vector used in inner-products.
vector_type	u0
	Initial Lanczos vector.
matrix_type	lanczos_vecs
	Lanczos vectors.
vector_type	new_pce
	Projection of pce in new basis.
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.
virtual void	setup ()
	Setup basis after computing recurrence coefficients.
	LanczosProjPCEBasis (ordinal_type p, const LanczosProjPCEBasis &basis)
	Copy constructor with specified order.

Additional Inherited Members
typedef OneDOrthogPolyBasis< ordinal_type, value_type >::LevelToOrderFnPtr	LevelToOrderFnPtr
	Function pointer needed for level_to_order mappings.
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.
	RecurrenceBasis (const std::string &name, ordinal_type p, bool normalize, GrowthPolicy growth=SLOW_GROWTH)
	Constructor to be called by derived classes.
	RecurrenceBasis (ordinal_type p, const RecurrenceBasis &basis)
	Copy constructor with specified order.
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.
std::string	name
	Name of basis.
ordinal_type	p
	Order of basis.
bool	normalize
	Normalize basis.
GrowthPolicy	growth
	Smolyak growth policy.
value_type	quad_zero_tol
	Tolerance for quadrature points near zero.
LevelToOrderFnPtr	sparse_grid_growth_rule
	Sparse grid growth rule (as determined by Pecos).
Teuchos::Array< value_type >	alpha
	Recurrence $\alpha$ coefficients.
Teuchos::Array< value_type >	beta
	Recurrence $\beta$ coefficients.
Teuchos::Array< value_type >	delta
	Recurrence $\delta$ coefficients.
Teuchos::Array< value_type >	gamma
	Recurrence $\gamma$ coefficients.
Teuchos::Array< value_type >	norms
	Norms.

Detailed Description

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

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

Constructor & Destructor Documentation

◆ LanczosProjPCEBasis()

template<typename ordinal_type, typename value_type>

Stokhos::LanczosProjPCEBasis< ordinal_type, value_type >::LanczosProjPCEBasis	(	ordinal_type	p,
		const Teuchos::RCP< const Stokhos::OrthogPolyApprox< ordinal_type, value_type > > &	pce,
		const Teuchos::RCP< const Stokhos::Sparse3Tensor< ordinal_type, value_type > > &	Cijk,
		bool	normalize,
		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

References Cijk_matrix, lanczos_vecs, limit_integration_order, new_pce, Stokhos::RecurrenceBasis< ordinal_type, value_type >::norm_squared(), Stokhos::RecurrenceBasis< ordinal_type, value_type >::normalize, Stokhos::RecurrenceBasis< ordinal_type, value_type >::p, pce, pce_norms, pce_sz, Stokhos::RecurrenceBasis< ordinal_type, value_type >::RecurrenceBasis(), setup(), Stokhos::RecurrenceBasis< ordinal_type, value_type >::size(), u0, and weights.

Referenced by LanczosProjPCEBasis().

Member Function Documentation

◆ cloneWithOrder()

template<typename ordinal_type, typename value_type>

Teuchos::RCP< Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type > > Stokhos::LanczosProjPCEBasis< 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 >.

References Stokhos::RecurrenceBasis< ordinal_type, value_type >::p.

◆ computeRecurrenceCoefficients()

template<typename ordinal_type, typename value_type>

bool Stokhos::LanczosProjPCEBasis< 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 >.

References Stokhos::RecurrenceBasis< ordinal_type, value_type >::alpha, Stokhos::RecurrenceBasis< ordinal_type, value_type >::beta, Cijk_matrix, Stokhos::Lanczos< vectorspace_type, operator_type >::compute(), Stokhos::Lanczos< vectorspace_type, operator_type >::computeNormalized(), Stokhos::RecurrenceBasis< ordinal_type, value_type >::delta, Stokhos::RecurrenceBasis< ordinal_type, value_type >::gamma, lanczos_vecs, Stokhos::RecurrenceBasis< ordinal_type, value_type >::normalize, Stokhos::RecurrenceBasis< ordinal_type, value_type >::p, pce_sz, u0, and weights.

◆ getQuadPoints()

template<typename ordinal_type, typename value_type>

void Stokhos::LanczosProjPCEBasis< 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