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> 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> 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