ConstrainedConjGrad.h
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@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 /* NOTE The functions of this file have been adapted from the GMM++ library */
11 
12 //========================================================================
13 //
14 // Copyright (C) 2002-2007 Yves Renard
15 //
16 // This file is a part of GETFEM++
17 //
18 // Getfem++ is free software; you can redistribute it and/or modify
19 // it under the terms of the GNU Lesser General Public License as
20 // published by the Free Software Foundation; version 2.1 of the License.
21 //
22 // This program is distributed in the hope that it will be useful,
23 // but WITHOUT ANY WARRANTY; without even the implied warranty of
24 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
25 // GNU Lesser General Public License for more details.
26 // You should have received a copy of the GNU Lesser General Public
27 // License along with this program; if not, write to the Free Software
28 // Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301,
29 // USA.
30 //
31 //========================================================================
32 
33 #include "../../../../Eigen/src/Core/util/NonMPL2.h"
34 
35 #ifndef EIGEN_CONSTRAINEDCG_H
36 #define EIGEN_CONSTRAINEDCG_H
37 
38 #include <Eigen/Core>
39 
40 namespace Eigen {
41 
42 namespace internal {
43 
50 template <typename CMatrix, typename CINVMatrix>
51 void pseudo_inverse(const CMatrix &C, CINVMatrix &CINV)
52 {
53  // optimisable : copie de la ligne, precalcul de C * trans(C).
54  typedef typename CMatrix::Scalar Scalar;
55  typedef typename CMatrix::Index Index;
56  // FIXME use sparse vectors ?
57  typedef Matrix<Scalar,Dynamic,1> TmpVec;
58 
59  Index rows = C.rows(), cols = C.cols();
60 
61  TmpVec d(rows), e(rows), l(cols), p(rows), q(rows), r(rows);
62  Scalar rho, rho_1, alpha;
63  d.setZero();
64 
65  CINV.startFill(); // FIXME estimate the number of non-zeros
66  for (Index i = 0; i < rows; ++i)
67  {
68  d[i] = 1.0;
69  rho = 1.0;
70  e.setZero();
71  r = d;
72  p = d;
73 
74  while (rho >= 1e-38)
75  { /* conjugate gradient to compute e */
76  /* which is the i-th row of inv(C * trans(C)) */
77  l = C.transpose() * p;
78  q = C * l;
79  alpha = rho / p.dot(q);
80  e += alpha * p;
81  r += -alpha * q;
82  rho_1 = rho;
83  rho = r.dot(r);
84  p = (rho/rho_1) * p + r;
85  }
86 
87  l = C.transpose() * e; // l is the i-th row of CINV
88  // FIXME add a generic "prune/filter" expression for both dense and sparse object to sparse
89  for (Index j=0; j<l.size(); ++j)
90  if (l[j]<1e-15)
91  CINV.fill(i,j) = l[j];
92 
93  d[i] = 0.0;
94  }
95  CINV.endFill();
96 }
97 
98 
99 
105 template<typename TMatrix, typename CMatrix,
106  typename VectorX, typename VectorB, typename VectorF>
107 void constrained_cg(const TMatrix& A, const CMatrix& C, VectorX& x,
108  const VectorB& b, const VectorF& f, IterationController &iter)
109 {
110  typedef typename TMatrix::Scalar Scalar;
111  typedef typename TMatrix::Index Index;
112  typedef Matrix<Scalar,Dynamic,1> TmpVec;
113 
114  Scalar rho = 1.0, rho_1, lambda, gamma;
115  Index xSize = x.size();
116  TmpVec p(xSize), q(xSize), q2(xSize),
117  r(xSize), old_z(xSize), z(xSize),
118  memox(xSize);
119  std::vector<bool> satured(C.rows());
120  p.setZero();
121  iter.setRhsNorm(sqrt(b.dot(b))); // gael vect_sp(PS, b, b)
122  if (iter.rhsNorm() == 0.0) iter.setRhsNorm(1.0);
123 
124  SparseMatrix<Scalar,RowMajor> CINV(C.rows(), C.cols());
125  pseudo_inverse(C, CINV);
126 
127  while(true)
128  {
129  // computation of residual
130  old_z = z;
131  memox = x;
132  r = b;
133  r += A * -x;
134  z = r;
135  bool transition = false;
136  for (Index i = 0; i < C.rows(); ++i)
137  {
138  Scalar al = C.row(i).dot(x) - f.coeff(i);
139  if (al >= -1.0E-15)
140  {
141  if (!satured[i])
142  {
143  satured[i] = true;
144  transition = true;
145  }
146  Scalar bb = CINV.row(i).dot(z);
147  if (bb > 0.0)
148  // FIXME: we should allow that: z += -bb * C.row(i);
149  for (typename CMatrix::InnerIterator it(C,i); it; ++it)
150  z.coeffRef(it.index()) -= bb*it.value();
151  }
152  else
153  satured[i] = false;
154  }
155 
156  // descent direction
157  rho_1 = rho;
158  rho = r.dot(z);
159 
160  if (iter.finished(rho)) break;
161 
162  if (iter.noiseLevel() > 0 && transition) std::cerr << "CCG: transition\n";
163  if (transition || iter.first()) gamma = 0.0;
164  else gamma = (std::max)(0.0, (rho - old_z.dot(z)) / rho_1);
165  p = z + gamma*p;
166 
167  ++iter;
168  // one dimensionnal optimization
169  q = A * p;
170  lambda = rho / q.dot(p);
171  for (Index i = 0; i < C.rows(); ++i)
172  {
173  if (!satured[i])
174  {
175  Scalar bb = C.row(i).dot(p) - f[i];
176  if (bb > 0.0)
177  lambda = (std::min)(lambda, (f.coeff(i)-C.row(i).dot(x)) / bb);
178  }
179  }
180  x += lambda * p;
181  memox -= x;
182  }
183 }
184 
185 } // end namespace internal
186 
187 } // end namespace Eigen
188 
189 #endif // EIGEN_CONSTRAINEDCG_H