Generates three-term recurrence using the Discretized Stieltjes procedure applied to a functional mapping another basis. More...

#include <Stokhos_StieltjesBasis.hpp>

Inheritance diagram for Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >:

[legend]

Public Member Functions
	StieltjesBasis (ordinal_type p, const Teuchos::RCP< const func_type > &func, const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &quad, bool use_pce_quad_points, bool normalize=false)
	Constructor. More...

	~StieltjesBasis ()
	Destructor. 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 Member Functions
void	stieltjes (ordinal_type nstart, ordinal_type nfinish, const Teuchos::Array< value_type > &weights, const Teuchos::Array< value_type > &points, Teuchos::Array< value_type > &a, Teuchos::Array< value_type > &b, Teuchos::Array< value_type > &nrm, Teuchos::Array< Teuchos::Array< value_type > > &phi_vals) const
	Compute 3-term recurrence using Stieljtes procedure. More...

void	integrateBasisSquared (ordinal_type k, const Teuchos::Array< value_type > &a, const Teuchos::Array< value_type > &b, const Teuchos::Array< value_type > &weights, const Teuchos::Array< value_type > &points, Teuchos::Array< Teuchos::Array< value_type > > &phi_vals, value_type &val1, value_type &val2) const
	Compute $\int\psi^2_k(t) d\lambda(t)$ and $\int t\psi^2_k(t) d\lambda(t)$ . More...

void	evaluateRecurrence (ordinal_type k, const Teuchos::Array< value_type > &a, const Teuchos::Array< value_type > &b, const Teuchos::Array< value_type > &points, Teuchos::Array< Teuchos::Array< value_type > > &values) const
	Evaluate polynomials via 3-term recurrence. More...

	StieltjesBasis (ordinal_type p, const StieltjesBasis &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 func_type >	func
	PC expansion. More...

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

const Teuchos::Array < value_type > &	pce_weights
	PCE quadrature weights. More...

const Teuchos::Array < Teuchos::Array< value_type > > &	basis_values
	Values of PCE basis functions at quadrature points. More...

Teuchos::Array< value_type >	func_vals
	Values of func at quadrature points. More...

Teuchos::Array< Teuchos::Array < value_type > >	phi_vals
	Values of generated polynomials at PCE quadrature points. More...

bool	use_pce_quad_points
	Use underlying pce's quadrature data. 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
	StieltjesBasis (const StieltjesBasis &)

StieltjesBasis &	operator= (const StieltjesBasis &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, typename func_type>
class Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >

Generates three-term recurrence using the Discretized Stieltjes procedure applied to a functional mapping another basis.

Definition at line 58 of file Stokhos_StieltjesBasis.hpp.

Constructor & Destructor Documentation

template<typename ordinal_type , typename value_type , typename func_type >

Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >::StieltjesBasis	(	ordinal_type	p,
		const Teuchos::RCP< const func_type > &	func,
		const Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > &	quad,
		bool	use_pce_quad_points,
		bool	normalize = `false`
	)

Constructor.

Parameters

p	order of the basis
func	mapping defining new density function
quad	quadrature data for basis of PC expansion
use_pce_quad_points	whether to use quad to define quadrature points for the new basis, or whether to use the Golub-Welsch system.
normalize	whether polynomials should be given unit norm

Definition at line 47 of file Stokhos_StieltjesBasisImp.hpp.

template<typename ordinal_type , typename value_type , typename func_type >

Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >::~StieltjesBasis ( )

Destructor.

Definition at line 68 of file Stokhos_StieltjesBasisImp.hpp.

template<typename ordinal_type , typename value_type , typename func_type >

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

protected

Copy constructor with specified order.

Definition at line 258 of file Stokhos_StieltjesBasisImp.hpp.

template<typename ordinal_type , typename value_type , typename func_type >

Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >::StieltjesBasis ( const StieltjesBasis< ordinal_type, value_type, func_type > & )

private

Member Function Documentation

template<typename ordinal_type , typename value_type , typename func_type >

void Stokhos::StieltjesBasis< ordinal_type, value_type, func_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 75 of file Stokhos_StieltjesBasisImp.hpp.

template<typename ordinal_type , typename value_type , typename func_type >

Teuchos::RCP< Stokhos::OneDOrthogPolyBasis< ordinal_type, value_type > > Stokhos::StieltjesBasis< ordinal_type, value_type, func_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 251 of file Stokhos_StieltjesBasisImp.hpp.

template<typename ordinal_type , typename value_type , typename func_type >

bool Stokhos::StieltjesBasis< ordinal_type, value_type, func_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 122 of file Stokhos_StieltjesBasisImp.hpp.

template<typename ordinal_type , typename value_type , typename func_type >

void Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >::setup ( )

protectedvirtual

Setup basis after computing recurrence coefficients.

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

Definition at line 149 of file Stokhos_StieltjesBasisImp.hpp.

template<typename ordinal_type , typename value_type , typename func_type >

void Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >::stieltjes	(	ordinal_type	nstart,
		ordinal_type	nfinish,
		const Teuchos::Array< value_type > &	weights,
		const Teuchos::Array< value_type > &	points,
		Teuchos::Array< value_type > &	a,
		Teuchos::Array< value_type > &	b,
		Teuchos::Array< value_type > &	nrm,
		Teuchos::Array< Teuchos::Array< value_type > > &	phi_vals
	)		const

protected

Compute 3-term recurrence using Stieljtes procedure.

Definition at line 168 of file Stokhos_StieltjesBasisImp.hpp.

template<typename ordinal_type , typename value_type , typename func_type >

void Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >::integrateBasisSquared	(	ordinal_type	k,
		const Teuchos::Array< value_type > &	a,
		const Teuchos::Array< value_type > &	b,
		const Teuchos::Array< value_type > &	weights,
		const Teuchos::Array< value_type > &	points,
		Teuchos::Array< Teuchos::Array< value_type > > &	phi_vals,
		value_type &	val1,
		value_type &	val2
	)		const

protected

Compute $\int\psi^2_k(t) d\lambda(t)$ and $\int t\psi^2_k(t) d\lambda(t)$ .

Definition at line 208 of file Stokhos_StieltjesBasisImp.hpp.

template<typename ordinal_type , typename value_type , typename func_type >

void Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >::evaluateRecurrence	(	ordinal_type	k,
		const Teuchos::Array< value_type > &	a,
		const Teuchos::Array< value_type > &	b,
		const Teuchos::Array< value_type > &	points,
		Teuchos::Array< Teuchos::Array< value_type > > &	values
	)		const

protected

Evaluate polynomials via 3-term recurrence.

Definition at line 229 of file Stokhos_StieltjesBasisImp.hpp.

template<typename ordinal_type , typename value_type , typename func_type >

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

private

Member Data Documentation

template<typename ordinal_type , typename value_type , typename func_type >

Teuchos::RCP<const func_type> Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >::func

protected

PC expansion.

Definition at line 168 of file Stokhos_StieltjesBasis.hpp.

template<typename ordinal_type , typename value_type , typename func_type >

Teuchos::RCP<const Stokhos::Quadrature<ordinal_type, value_type> > Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >::quad

protected

Quadrature object.

Definition at line 171 of file Stokhos_StieltjesBasis.hpp.

template<typename ordinal_type , typename value_type , typename func_type >

const Teuchos::Array<value_type>& Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >::pce_weights

protected

PCE quadrature weights.

Definition at line 174 of file Stokhos_StieltjesBasis.hpp.

template<typename ordinal_type , typename value_type , typename func_type >

const Teuchos::Array< Teuchos::Array<value_type> >& Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >::basis_values

protected

Values of PCE basis functions at quadrature points.

Definition at line 177 of file Stokhos_StieltjesBasis.hpp.

template<typename ordinal_type , typename value_type , typename func_type >

Teuchos::Array<value_type> Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >::func_vals

mutableprotected

Values of func at quadrature points.

Definition at line 180 of file Stokhos_StieltjesBasis.hpp.

template<typename ordinal_type , typename value_type , typename func_type >

Teuchos::Array< Teuchos::Array<value_type> > Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >::phi_vals

mutableprotected

Values of generated polynomials at PCE quadrature points.

Definition at line 183 of file Stokhos_StieltjesBasis.hpp.

template<typename ordinal_type , typename value_type , typename func_type >

bool Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >::use_pce_quad_points

protected

Use underlying pce's quadrature data.

Definition at line 186 of file Stokhos_StieltjesBasis.hpp.

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

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Implementation of Stokhos::OneDOrthogPolyBasis methods

Implementation of Stokhos::RecurrenceBasis methods

Additional Inherited Members

Detailed Description

template<typename ordinal_type, typename value_type, typename func_type> class Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<typename ordinal_type, typename value_type, typename func_type>
class Stokhos::StieltjesBasis< ordinal_type, value_type, func_type >