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 /* NOTE The functions of this file have been adapted from the GMM++ library */
7
8 //========================================================================
9 //
10 // Copyright (C) 2002-2007 Yves Renard
11 //
12 // This file is a part of GETFEM++
13 //
14 // Getfem++ is free software; you can redistribute it and/or modify
15 // it under the terms of the GNU Lesser General Public License as
16 // published by the Free Software Foundation; version 2.1 of the License.
17 //
18 // This program is distributed in the hope that it will be useful,
19 // but WITHOUT ANY WARRANTY; without even the implied warranty of
20 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
21 // GNU Lesser General Public License for more details.
22 // You should have received a copy of the GNU Lesser General Public
23 // License along with this program; if not, write to the Free Software
24 // Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301,
25 // USA.
26 //
27 //========================================================================
28
29 #include "../../../../Eigen/src/Core/util/NonMPL2.h"
30
31 #ifndef EIGEN_CONSTRAINEDCG_H
32 #define EIGEN_CONSTRAINEDCG_H
33
34 #include <Eigen/Core>
35
36 namespace Eigen {
37
38 namespace internal {
39
40 /** \ingroup IterativeSolvers_Module
41 * Compute the pseudo inverse of the non-square matrix C such that
42 * \f$ CINV = (C * C^T)^{-1} * C \f$ based on a conjugate gradient method.
43 *
44 * This function is internally used by constrained_cg.
45 */
46 template <typename CMatrix, typename CINVMatrix>
pseudo_inverse(const CMatrix & C,CINVMatrix & CINV)47 void pseudo_inverse(const CMatrix &C, CINVMatrix &CINV)
48 {
49 // optimisable : copie de la ligne, precalcul de C * trans(C).
50 typedef typename CMatrix::Scalar Scalar;
51 typedef typename CMatrix::Index Index;
52 // FIXME use sparse vectors ?
53 typedef Matrix<Scalar,Dynamic,1> TmpVec;
54
55 Index rows = C.rows(), cols = C.cols();
56
57 TmpVec d(rows), e(rows), l(cols), p(rows), q(rows), r(rows);
58 Scalar rho, rho_1, alpha;
59 d.setZero();
60
61 typedef Triplet<double> T;
62 std::vector<T> tripletList;
63
64 for (Index i = 0; i < rows; ++i)
65 {
66 d[i] = 1.0;
67 rho = 1.0;
68 e.setZero();
69 r = d;
70 p = d;
71
72 while (rho >= 1e-38)
73 { /* conjugate gradient to compute e */
74 /* which is the i-th row of inv(C * trans(C)) */
75 l = C.transpose() * p;
76 q = C * l;
77 alpha = rho / p.dot(q);
78 e += alpha * p;
79 r += -alpha * q;
80 rho_1 = rho;
81 rho = r.dot(r);
82 p = (rho/rho_1) * p + r;
83 }
84
85 l = C.transpose() * e; // l is the i-th row of CINV
86 // FIXME add a generic "prune/filter" expression for both dense and sparse object to sparse
87 for (Index j=0; j<l.size(); ++j)
88 if (l[j]<1e-15)
89 tripletList.push_back(T(i,j,l(j)));
90
91
92 d[i] = 0.0;
93 }
94 CINV.setFromTriplets(tripletList.begin(), tripletList.end());
95 }
96
97
98
99 /** \ingroup IterativeSolvers_Module
100 * Constrained conjugate gradient
101 *
102 * Computes the minimum of \f$ 1/2((Ax).x) - bx \f$ under the contraint \f$ Cx \le f \f$
103 */
104 template<typename TMatrix, typename CMatrix,
105 typename VectorX, typename VectorB, typename VectorF>
constrained_cg(const TMatrix & A,const CMatrix & C,VectorX & x,const VectorB & b,const VectorF & f,IterationController & iter)106 void constrained_cg(const TMatrix& A, const CMatrix& C, VectorX& x,
107 const VectorB& b, const VectorF& f, IterationController &iter)
108 {
109 using std::sqrt;
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
190