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Scaling.h
1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2012 Desire NUENTSA WAKAM <desire.nuentsa_wakam@inria.fr
5//
6// This Source Code Form is subject to the terms of the Mozilla
7// Public License v. 2.0. If a copy of the MPL was not distributed
8// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10#ifndef EIGEN_ITERSCALING_H
11#define EIGEN_ITERSCALING_H
12
13namespace Eigen {
14
47template<typename _MatrixType>
49{
50 public:
51 typedef _MatrixType MatrixType;
52 typedef typename MatrixType::Scalar Scalar;
53 typedef typename MatrixType::Index Index;
54
55 public:
56 IterScaling() { init(); }
57
58 IterScaling(const MatrixType& matrix)
59 {
60 init();
61 compute(matrix);
62 }
63
64 ~IterScaling() { }
65
73 void compute (const MatrixType& mat)
74 {
75 using std::abs;
76 int m = mat.rows();
77 int n = mat.cols();
78 eigen_assert((m>0 && m == n) && "Please give a non - empty matrix");
79 m_left.resize(m);
80 m_right.resize(n);
81 m_left.setOnes();
82 m_right.setOnes();
83 m_matrix = mat;
84 VectorXd Dr, Dc, DrRes, DcRes; // Temporary Left and right scaling vectors
85 Dr.resize(m); Dc.resize(n);
86 DrRes.resize(m); DcRes.resize(n);
87 double EpsRow = 1.0, EpsCol = 1.0;
88 int its = 0;
89 do
90 { // Iterate until the infinite norm of each row and column is approximately 1
91 // Get the maximum value in each row and column
92 Dr.setZero(); Dc.setZero();
93 for (int k=0; k<m_matrix.outerSize(); ++k)
94 {
95 for (typename MatrixType::InnerIterator it(m_matrix, k); it; ++it)
96 {
97 if ( Dr(it.row()) < abs(it.value()) )
98 Dr(it.row()) = abs(it.value());
99
100 if ( Dc(it.col()) < abs(it.value()) )
101 Dc(it.col()) = abs(it.value());
102 }
103 }
104 for (int i = 0; i < m; ++i)
105 {
106 Dr(i) = std::sqrt(Dr(i));
107 Dc(i) = std::sqrt(Dc(i));
108 }
109 // Save the scaling factors
110 for (int i = 0; i < m; ++i)
111 {
112 m_left(i) /= Dr(i);
113 m_right(i) /= Dc(i);
114 }
115 // Scale the rows and the columns of the matrix
116 DrRes.setZero(); DcRes.setZero();
117 for (int k=0; k<m_matrix.outerSize(); ++k)
118 {
119 for (typename MatrixType::InnerIterator it(m_matrix, k); it; ++it)
120 {
121 it.valueRef() = it.value()/( Dr(it.row()) * Dc(it.col()) );
122 // Accumulate the norms of the row and column vectors
123 if ( DrRes(it.row()) < abs(it.value()) )
124 DrRes(it.row()) = abs(it.value());
125
126 if ( DcRes(it.col()) < abs(it.value()) )
127 DcRes(it.col()) = abs(it.value());
128 }
129 }
130 DrRes.array() = (1-DrRes.array()).abs();
131 EpsRow = DrRes.maxCoeff();
132 DcRes.array() = (1-DcRes.array()).abs();
133 EpsCol = DcRes.maxCoeff();
134 its++;
135 }while ( (EpsRow >m_tol || EpsCol > m_tol) && (its < m_maxits) );
136 m_isInitialized = true;
137 }
143 void computeRef (MatrixType& mat)
144 {
145 compute (mat);
146 mat = m_matrix;
147 }
150 VectorXd& LeftScaling()
151 {
152 return m_left;
153 }
154
157 VectorXd& RightScaling()
158 {
159 return m_right;
160 }
161
164 void setTolerance(double tol)
165 {
166 m_tol = tol;
167 }
168
169 protected:
170
171 void init()
172 {
173 m_tol = 1e-10;
174 m_maxits = 5;
175 m_isInitialized = false;
176 }
177
178 MatrixType m_matrix;
179 mutable ComputationInfo m_info;
180 bool m_isInitialized;
181 VectorXd m_left; // Left scaling vector
182 VectorXd m_right; // m_right scaling vector
183 double m_tol;
184 int m_maxits; // Maximum number of iterations allowed
185};
186}
187#endif
iterative scaling algorithm to equilibrate rows and column norms in matrices
Definition: Scaling.h:49
void compute(const MatrixType &mat)
Definition: Scaling.h:73
void setTolerance(double tol)
Definition: Scaling.h:164
VectorXd & LeftScaling()
Definition: Scaling.h:150
VectorXd & RightScaling()
Definition: Scaling.h:157
void computeRef(MatrixType &mat)
Definition: Scaling.h:143
Namespace containing all symbols from the Eigen library.
Definition: AdolcForward:45