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Stokhos_LanczosProjPCEBasis.hpp
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41
42#ifndef STOKHOS_LANCZOSPROJPCEBASIS_HPP
43#define STOKHOS_LANCZOSPROJPCEBASIS_HPP
44
45#include "Teuchos_RCP.hpp"
46#include "Teuchos_Array.hpp"
47#include "Teuchos_SerialDenseVector.hpp"
48#include "Teuchos_SerialDenseMatrix.hpp"
49
53#include "Stokhos_Lanczos.hpp"
54
55namespace Stokhos {
56
57 template <typename ord_type, typename val_type>
59 public:
60 typedef ord_type ordinal_type;
61 typedef val_type value_type;
62 typedef Teuchos::SerialDenseMatrix<ordinal_type, value_type> matrix_type;
63 typedef Teuchos::SerialDenseVector<ordinal_type, value_type> vector_type;
64
65 DenseOperator(const matrix_type& A_): A(A_) {}
66
67 void
68 apply(const vector_type& u, vector_type& v) const {
69 v.multiply(Teuchos::NO_TRANS, Teuchos::NO_TRANS, value_type(1),
70 A, u, value_type(0));
71 }
72
73 protected:
74
75 const matrix_type& A;
76
77 };
78
83 template <typename ordinal_type, typename value_type>
85 public RecurrenceBasis<ordinal_type, value_type> {
86 public:
87
89
95 ordinal_type p,
97 const Teuchos::RCP< const Stokhos::Sparse3Tensor<ordinal_type, value_type> >& Cijk,
98 bool normalize,
99 bool limit_integration_order = false);
100
103
105
106
108 virtual void
109 getQuadPoints(ordinal_type quad_order,
110 Teuchos::Array<value_type>& points,
111 Teuchos::Array<value_type>& weights,
112 Teuchos::Array< Teuchos::Array<value_type> >& values) const;
113
124 virtual Teuchos::RCP<OneDOrthogPolyBasis<ordinal_type,value_type> > cloneWithOrder(ordinal_type p) const;
125
127
129 value_type getNewCoeffs(ordinal_type i) const;
130
132 void transformCoeffsFromLanczos(const value_type *in,
133 value_type *out) const;
134
135 protected:
136
138
139
141 virtual bool
142 computeRecurrenceCoefficients(ordinal_type n,
143 Teuchos::Array<value_type>& alpha,
144 Teuchos::Array<value_type>& beta,
145 Teuchos::Array<value_type>& delta,
146 Teuchos::Array<value_type>& gamma) const;
147
149 virtual void setup();
150
152
154 LanczosProjPCEBasis(ordinal_type p, const LanczosProjPCEBasis& basis);
155
156 private:
157
158 // Prohibit copying
160
161 // Prohibit Assignment
163
164 protected:
165
171
173 Teuchos::RCP< const Stokhos::OrthogPolyApprox<ordinal_type, value_type> > pce;
174
177
179 ordinal_type pce_sz;
180
182 Teuchos::Array<value_type> pce_norms;
183
186
189
192
195
198
199 }; // class LanczosProjPCEBasis
200
201} // Namespace Stokhos
202
203// Include template definitions
205
206#endif
DenseOperator(const matrix_type &A_)
void apply(const vector_type &u, vector_type &v) const
Teuchos::SerialDenseMatrix< ordinal_type, value_type > matrix_type
Teuchos::SerialDenseVector< ordinal_type, value_type > vector_type
Generates three-term recurrence using the Lanczos procedure applied to a polynomial chaos expansion i...
virtual void setup()
Setup basis after computing recurrence coefficients.
WeightedVectorSpace< ordinal_type, value_type > vectorspace_type
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.
vector_type weights
Weighting vector used in inner-products.
Stokhos::Lanczos< vectorspace_type, operator_type > lanczos_type
matrix_type Cijk_matrix
Triple-product matrix used in generating lanczos vectors.
LanczosProjPCEBasis & operator=(const LanczosProjPCEBasis &b)
void transformCoeffsFromLanczos(const value_type *in, value_type *out) const
Map expansion coefficients from this basis to original.
Teuchos::RCP< const Stokhos::OrthogPolyApprox< ordinal_type, value_type > > pce
PCE Lanczos procedure is based on.
matrix_type lanczos_vecs
Lanczos vectors.
Teuchos::Array< value_type > pce_norms
Basis norms.
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.
DenseOperator< ordinal_type, value_type > operator_type
vector_type new_pce
Projection of pce in new basis.
ordinal_type pce_sz
Size of PC expansion.
LanczosProjPCEBasis(const LanczosProjPCEBasis &)
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.
bool limit_integration_order
Flag indicating whether to limit the integration order.
vector_type u0
Initial Lanczos vector.
value_type getNewCoeffs(ordinal_type i) const
Get new coefficients in this new basis.
Applies Lanczos procedure to a given matrix.
Teuchos::SerialDenseVector< ordinal_type, value_type > vector_type
Teuchos::SerialDenseMatrix< ordinal_type, value_type > matrix_type
Class to store coefficients of a projection onto an orthogonal polynomial basis.
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.
Top-level namespace for Stokhos classes and functions.