44#ifndef STOKHOS_STIELTJESPCEBASIS_HPP
45#define STOKHOS_STIELTJESPCEBASIS_HPP
47#include "Teuchos_RCP.hpp"
48#include "Teuchos_Array.hpp"
55#include "Teuchos_SerialDenseMatrix.hpp"
63 template <
typename ordinal_type,
typename value_type>
96 Teuchos::Array<value_type>& points,
97 Teuchos::Array<value_type>& weights,
98 Teuchos::Array< Teuchos::Array<value_type> >& values)
const;
110 virtual Teuchos::RCP<OneDOrthogPolyBasis<ordinal_type,value_type> >
cloneWithOrder(ordinal_type
p)
const;
116 value_type *out)
const;
126 Teuchos::Array<value_type>&
alpha,
127 Teuchos::Array<value_type>&
beta,
128 Teuchos::Array<value_type>&
delta,
129 Teuchos::Array<value_type>&
gamma)
const;
132 virtual void setup();
138 ordinal_type nfinish,
139 const Teuchos::Array<value_type>& weights,
140 const Teuchos::Array<value_type>& points,
141 Teuchos::Array<value_type>& a,
142 Teuchos::Array<value_type>& b,
143 Teuchos::Array<value_type>& nrm,
144 Teuchos::Array< Teuchos::Array<value_type> >&
phi_vals)
const;
152 const Teuchos::Array<value_type>& a,
153 const Teuchos::Array<value_type>& b,
154 const Teuchos::Array<value_type>& weights,
155 const Teuchos::Array<value_type>& points,
156 Teuchos::Array< Teuchos::Array<value_type> >&
phi_vals,
157 value_type& val1, value_type& val2)
const;
166 const Teuchos::Array<value_type>& a,
167 const Teuchos::Array<value_type>& b,
168 const Teuchos::Array<value_type>& weights,
169 const Teuchos::Array<value_type>& points,
170 Teuchos::Array< Teuchos::Array<value_type> >&
phi_vals,
171 value_type& val1, value_type& val2)
const;
175 const Teuchos::Array<value_type>& a,
176 const Teuchos::Array<value_type>& b,
177 const Teuchos::Array<value_type>& points,
178 Teuchos::Array< Teuchos::Array<value_type> >& values)
const;
194 Teuchos::RCP<const Stokhos::OrthogPolyApprox<ordinal_type, value_type> >
pce;
197 Teuchos::RCP<const Stokhos::Quadrature<ordinal_type, value_type> >
quad;
209 mutable Teuchos::Array< Teuchos::Array<value_type> >
phi_vals;
221 Teuchos::RCP<const Stokhos::OrthogPolyBasis<ordinal_type, value_type> >
basis;
227 Teuchos::RCP<const Cijk_type>
Cijk;
Class to store coefficients of a projection onto an orthogonal polynomial basis.
Abstract base class for quadrature methods.
Implementation of OneDOrthogPolyBasis based on the general three-term recurrence relationship:
bool normalize
Normalize basis.
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.
Data structure storing a sparse 3-tensor C(i,j,k) in a a compressed format.
Generates three-term recurrence using the Discretized Stieltjes procedure applied to a polynomial cha...
Teuchos::RCP< const Stokhos::Quadrature< ordinal_type, value_type > > quad
Quadrature object.
Teuchos::SerialDenseMatrix< ordinal_type, value_type > fromStieltjesMat
Matrix mapping coefficients in Stieltjes basis back to original basis.
Stokhos::Sparse3Tensor< ordinal_type, value_type > Cijk_type
Short-hand for triple product.
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.
Teuchos::Array< Teuchos::Array< value_type > > phi_vals
Values of generated polynomials at PCE quadrature points.
StieltjesPCEBasis(const StieltjesPCEBasis &)
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.
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 and .
Teuchos::Array< value_type > pce_vals
Values of PCE at quadrature points.
bool use_pce_quad_points
Use underlying pce's quadrature data.
Teuchos::RCP< const Cijk_type > Cijk
Triple product tensor (needed for integral projection method)
Teuchos::RCP< const Stokhos::OrthogPolyApprox< ordinal_type, value_type > > pce
PC expansion.
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.
const Teuchos::Array< Teuchos::Array< value_type > > & basis_values
Values of PCE basis functions at quadrature points.
Teuchos::RCP< const Stokhos::OrthogPolyBasis< ordinal_type, value_type > > basis
PCE basis (needed for integral projection method)
bool project_integrals
Project Stieltjes integrals to original PCE basis.
StieltjesPCEBasis & operator=(const StieltjesPCEBasis &b)
void integrateBasisSquaredProj(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 and by projecting onto original PCE basis.
virtual void setup()
Setup basis after computing recurrence coefficients.
const Teuchos::Array< value_type > & pce_weights
PCE quadrature weights.
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.
StieltjesPCEBasis(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 use_pce_quad_points, bool normalize=false, bool project_integrals=false, const Teuchos::RCP< const Stokhos::Sparse3Tensor< ordinal_type, value_type > > &Cijk=Teuchos::null)
Constructor.
~StieltjesPCEBasis()
Destructor.
void transformCoeffsFromStieltjes(const value_type *in, value_type *out) const
Map expansion coefficients from this basis to original.
Teuchos::Array< value_type > phi_pce_coeffs
Array store PC expansion of generated orthogonal polynomials.
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.
Top-level namespace for Stokhos classes and functions.