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Stokhos_StieltjesPCEBasis.hpp
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43
44#ifndef STOKHOS_STIELTJESPCEBASIS_HPP
45#define STOKHOS_STIELTJESPCEBASIS_HPP
46
47#include "Teuchos_RCP.hpp"
48#include "Teuchos_Array.hpp"
49
54
55#include "Teuchos_SerialDenseMatrix.hpp"
56
57namespace Stokhos {
58
63 template <typename ordinal_type, typename value_type>
65 public RecurrenceBasis<ordinal_type, value_type> {
66 public:
67
69
79 ordinal_type p,
81 const Teuchos::RCP<const Stokhos::Quadrature<ordinal_type, value_type> >& quad,
83 bool normalize = false,
84 bool project_integrals = false,
85 const Teuchos::RCP<const Stokhos::Sparse3Tensor<ordinal_type, value_type> >& Cijk = Teuchos::null);
86
89
91
92
94 virtual void
95 getQuadPoints(ordinal_type quad_order,
96 Teuchos::Array<value_type>& points,
97 Teuchos::Array<value_type>& weights,
98 Teuchos::Array< Teuchos::Array<value_type> >& values) const;
99
110 virtual Teuchos::RCP<OneDOrthogPolyBasis<ordinal_type,value_type> > cloneWithOrder(ordinal_type p) const;
111
113
115 void transformCoeffsFromStieltjes(const value_type *in,
116 value_type *out) const;
117
118 protected:
119
121
122
124 virtual bool
125 computeRecurrenceCoefficients(ordinal_type n,
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;
130
132 virtual void setup();
133
135
137 void stieltjes(ordinal_type nstart,
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;
145
151 ordinal_type k,
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;
158
165 ordinal_type k,
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;
172
174 void evaluateRecurrence(ordinal_type k,
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;
179
181 StieltjesPCEBasis(ordinal_type p, const StieltjesPCEBasis& basis);
182
183 private:
184
185 // Prohibit copying
187
188 // Prohibit Assignment
190
191 protected:
192
194 Teuchos::RCP<const Stokhos::OrthogPolyApprox<ordinal_type, value_type> > pce;
195
197 Teuchos::RCP<const Stokhos::Quadrature<ordinal_type, value_type> > quad;
198
200 const Teuchos::Array<value_type>& pce_weights;
201
203 const Teuchos::Array< Teuchos::Array<value_type> >& basis_values;
204
206 mutable Teuchos::Array<value_type> pce_vals;
207
209 mutable Teuchos::Array< Teuchos::Array<value_type> > phi_vals;
210
213
215 Teuchos::SerialDenseMatrix<ordinal_type, value_type> fromStieltjesMat;
216
219
221 Teuchos::RCP<const Stokhos::OrthogPolyBasis<ordinal_type, value_type> > basis;
222
225
227 Teuchos::RCP<const Cijk_type> Cijk;
228
230 mutable Teuchos::Array<value_type> phi_pce_coeffs;
231
232 }; // class StieltjesPCEBasis
233
234} // Namespace Stokhos
235
236// Include template definitions
238
239#endif
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:
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.
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.