42#ifndef STOKHOS_DISCRETIZEDSTIELTJESBASIS_HPP
43#define STOKHOS_DISCRETIZEDSTIELTJESBASIS_HPP
62 template <
typename ordinal_type,
typename value_type>
77 const std::string&
name,
const ordinal_type&
p,
78 value_type (*weightFn)(
const value_type&),
79 const value_type& leftEndPt,
80 const value_type& rightEndPt,
89 const ordinal_type& order2)
const;
101 virtual Teuchos::RCP<OneDOrthogPolyBasis<ordinal_type,value_type> >
cloneWithOrder(ordinal_type
p)
const;
111 Teuchos::Array<value_type>&
alpha,
112 Teuchos::Array<value_type>&
beta,
113 Teuchos::Array<value_type>&
delta,
114 Teuchos::Array<value_type>&
gamma)
const;
121 const Teuchos::Array<value_type>&
alpha,
122 const Teuchos::Array<value_type>&
beta)
const;
130 const Teuchos::Array<value_type>&
alpha,
131 const Teuchos::Array<value_type>&
beta)
const;
136 const Teuchos::Array<value_type>&
alpha,
137 const Teuchos::Array<value_type>&
beta)
const;
Generates three-term recurrence using the Discretized Stieltjes procedure.
value_type expectedValue_tJ_nsquared(const ordinal_type &order, const Teuchos::Array< value_type > &alpha, const Teuchos::Array< value_type > &beta) const
Approximates where = order.
const value_type leftEndPt_
Left end point of domain.
Teuchos::Array< value_type > quad_weights
Quadrature points for discretized stieltjes procedure.
~DiscretizedStieltjesBasis()
Destructor.
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.
Teuchos::Array< Teuchos::Array< value_type > > quad_values
Quadrature values for discretized stieltjes procedure.
Teuchos::Array< value_type > quad_points
Quadrature points for discretized stieltjes procedure.
value_type eval_inner_product(const ordinal_type &order1, const ordinal_type &order2) const
Evaluate inner product of two basis functions to test orthogonality.
value_type evaluateWeight(const value_type &x) const
Evaluates the scaled weight function.
value_type evaluateRecurrence(const value_type &point, ordinal_type order, const Teuchos::Array< value_type > &alpha, const Teuchos::Array< value_type > &beta) const
Evaluate 3-term recurrence formula using supplied coefficients.
value_type(* weightFn_)(const value_type &)
Weight function.
DiscretizedStieltjesBasis(const DiscretizedStieltjesBasis &)
value_type expectedValue_J_nsquared(const ordinal_type &order, const Teuchos::Array< value_type > &alpha, const Teuchos::Array< value_type > &beta) const
Approximates where = order.
DiscretizedStieltjesBasis & operator=(const DiscretizedStieltjesBasis &b)
const value_type rightEndPt_
Right end point of domain.
value_type scaleFactor
Scale for the weight.
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.
Implementation of OneDOrthogPolyBasis based on the general three-term recurrence relationship:
virtual ordinal_type order() const
Return order of basis (largest monomial degree ).
bool normalize
Normalize basis.
GrowthPolicy growth
Smolyak growth policy.
Teuchos::Array< value_type > alpha
Recurrence coefficients.
Teuchos::Array< value_type > beta
Recurrence coefficients.
ordinal_type p
Order of basis.
Teuchos::Array< value_type > gamma
Recurrence coefficients.
Teuchos::Array< value_type > delta
Recurrence coefficients.
std::string name
Name of basis.
Top-level namespace for Stokhos classes and functions.
GrowthPolicy
Enumerated type for determining Smolyak growth policies.