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Stokhos_OrthogonalizationFactory.hpp
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41
42#ifndef STOKHOS_ORTHOGONALIZATION_FACTORY_HPP
43#define STOKHOS_ORTHOGONALIZATION_FACTORY_HPP
44
45#include <string>
46#include "Teuchos_Array.hpp"
47#include "Teuchos_SerialDenseMatrix.hpp"
48#include "Stokhos_SDMUtils.hpp"
49
50namespace Stokhos {
51
55 template <typename ordinal_type, typename value_type>
57 public:
58
60
64
67
68 typedef Teuchos::SerialDenseMatrix<ordinal_type,value_type> SDM;
69
71 static ordinal_type
72 createOrthogonalBasis(const std::string& method, value_type threshold,
73 bool verbose, const SDM& A,
74 const Teuchos::Array<value_type>& w,
75 SDM& Q, SDM& R,
76 Teuchos::Array<ordinal_type>& piv) {
77
78 ordinal_type m = A.numRows();
79 ordinal_type n = A.numCols();
80 ordinal_type rank = std::min(m,n);
81
82 if (method == "SVD") { // A = U*diag(sigma)*V^T, Q = U, R = sigma*V^T
83 Teuchos::Array<value_type> sigma;
84 SDM Vt;
85 rank = svd_threshold(threshold, A, sigma, Q, Vt);
86 R.reshape(rank, Vt.numCols());
87 for (ordinal_type j=0; j<Vt.numCols(); j++)
88 for (ordinal_type i=0; i<rank; i++)
89 R(i,j) = sigma[i]*Vt(i,j);
90 piv.resize(n);
91 for (int i=0; i<n; i++)
92 piv[i] = i;
93
94 if (verbose) {
95 // std::cout << "diag(sigma) = [ ";
96 // for (ordinal_type i=0; i<rank; i++)
97 // std::cout << sigma[i] << " ";
98 // std::cout << "]" << std::endl;
99
100 std::cout << "rank = " << rank << std::endl;
101 }
102 }
103
104 else { // All QR-based methods
105
106 if (method == "Householder")
107 rank = CPQR_Householder_threshold(threshold, A, w, Q, R, piv);
108
109 else if (method == "Householder without Pivoting") {
110 QR_Householder(rank, A, w, Q, R);
111 piv.resize(n);
112 for (int i=0; i<n; i++)
113 piv[i] = i;
114 }
115
116 else if (method == "Modified Gram-Schmidt")
117 rank = CPQR_MGS_threshold(threshold, A, w, Q, R, piv);
118
119 else if (method == "Modified Gram-Schmidt with Reorthogonalization")
120 rank = CPQR_MGS_reorthog_threshold(threshold, A, w, Q, R, piv);
121
122 else if (method == "Modified Gram-Schmidt without Pivoting") {
123 QR_MGS(rank, A, w, Q, R);
124 piv.resize(n);
125 for (int i=0; i<n; i++)
126 piv[i] = i;
127 }
128
129 else if (method == "Modified Gram-Schmidt without Pivoting with Reorthogonalization") {
130 QR_MGS2(rank, A, w, Q, R);
131 piv.resize(n);
132 for (int i=0; i<n; i++)
133 piv[i] = i;
134 }
135
136 else
137 TEUCHOS_TEST_FOR_EXCEPTION(
138 true, std::logic_error,
139 "Invalid orthogonalization method " << method);
140
141 if (verbose) {
142 // std::cout << "piv = [";
143 // for (ordinal_type i=0; i<rank; i++)
144 // std::cout << piv[i] << " ";
145 // std::cout << "]" << std::endl;
146
147 // std::cout << "diag(R) = [ ";
148 // for (ordinal_type i=0; i<rank; i++)
149 // std::cout << R(i,i) << " ";
150 // std::cout << "]" << std::endl;
151
152 std::cout << "rank = " << rank << std::endl;
153
154 // Check A*P = Q*R
155 std::cout << "||A*P-Q*R||_infty = "
156 << Stokhos::residualCPQRError(A,Q,R,piv) << std::endl;
157
158 // Check Q^T*diag(w)*Q = I
159 std::cout << "||I - Q^T*diag(w)**Q||_infty = "
160 << weightedQROrthogonalizationError(Q,w) << std::endl;
161 }
162 }
163
164 return rank;
165 }
166
167 private:
168
169 // Prohibit copying
171
172 // Prohibit Assignment
174
175 }; // class OrthogonalizationFactory
176
177} // Namespace Stokhos
178
179#endif
Encapsulate various orthogonalization (ie QR) methods.
Teuchos::SerialDenseMatrix< ordinal_type, value_type > SDM
OrthogonalizationFactory(const OrthogonalizationFactory &)
static ordinal_type createOrthogonalBasis(const std::string &method, value_type threshold, bool verbose, const SDM &A, const Teuchos::Array< value_type > &w, SDM &Q, SDM &R, Teuchos::Array< ordinal_type > &piv)
Create orthogonal basis via the method indicated by method.
OrthogonalizationFactory & operator=(const OrthogonalizationFactory &)
Top-level namespace for Stokhos classes and functions.
ordinal_type CPQR_MGS_threshold(const scalar_type &rank_threshold, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R, Teuchos::Array< ordinal_type > &piv)
Compute column-pivoted QR using modified Gram-Schmidt.
ordinal_type CPQR_MGS_reorthog_threshold(const scalar_type &rank_threshold, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R, Teuchos::Array< ordinal_type > &piv)
Compute column-pivoted QR using modified Gram-Schmidt and reorthogonalization.
ordinal_type CPQR_Householder_threshold(const scalar_type &rank_threshold, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R, Teuchos::Array< ordinal_type > &piv)
Compute column-pivoted QR using Householder reflections.
ordinal_type svd_threshold(const scalar_type &rank_threshold, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, Teuchos::Array< scalar_type > &s, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &U, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Vt)
scalar_type residualCPQRError(const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R, const Teuchos::Array< ordinal_type > &piv)
Compute column-pivoted QR residual error.
void QR_MGS(ordinal_type k, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R)
Compute thin QR using modified Gram-Schmidt.
void QR_MGS2(ordinal_type k, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R)
Compute thin QR using modified Gram-Schmidt with reorthogonalization.
void QR_Householder(ordinal_type k, const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &A, const Teuchos::Array< scalar_type > &w, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &R)
Compute thin QR using Householder reflections.
scalar_type weightedQROrthogonalizationError(const Teuchos::SerialDenseMatrix< ordinal_type, scalar_type > &Q, const Teuchos::Array< scalar_type > &w)
Compute weighted QR orthogonalization error.