File size: 5,324 Bytes
a42735d |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 |
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
/* NOTE The functions of this file have been adapted from the GMM++ library */
//========================================================================
//
// Copyright (C) 2002-2007 Yves Renard
//
// This file is a part of GETFEM++
//
// Getfem++ is free software; you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; version 2.1 of the License.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
// You should have received a copy of the GNU Lesser General Public
// License along with this program; if not, write to the Free Software
// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301,
// USA.
//
//========================================================================
#include "../../../../Eigen/src/Core/util/NonMPL2.h"
#ifndef EIGEN_CONSTRAINEDCG_H
#define EIGEN_CONSTRAINEDCG_H
#include "../../../../Eigen/Core"
namespace Eigen {
namespace internal {
/** \ingroup IterativeLinearSolvers_Module
* Compute the pseudo inverse of the non-square matrix C such that
* \f$ CINV = (C * C^T)^{-1} * C \f$ based on a conjugate gradient method.
*
* This function is internally used by constrained_cg.
*/
template <typename CMatrix, typename CINVMatrix>
void pseudo_inverse(const CMatrix &C, CINVMatrix &CINV)
{
// optimisable : copie de la ligne, precalcul de C * trans(C).
typedef typename CMatrix::Scalar Scalar;
typedef typename CMatrix::Index Index;
// FIXME use sparse vectors ?
typedef Matrix<Scalar,Dynamic,1> TmpVec;
Index rows = C.rows(), cols = C.cols();
TmpVec d(rows), e(rows), l(cols), p(rows), q(rows), r(rows);
Scalar rho, rho_1, alpha;
d.setZero();
typedef Triplet<double> T;
std::vector<T> tripletList;
for (Index i = 0; i < rows; ++i)
{
d[i] = 1.0;
rho = 1.0;
e.setZero();
r = d;
p = d;
while (rho >= 1e-38)
{ /* conjugate gradient to compute e */
/* which is the i-th row of inv(C * trans(C)) */
l = C.transpose() * p;
q = C * l;
alpha = rho / p.dot(q);
e += alpha * p;
r += -alpha * q;
rho_1 = rho;
rho = r.dot(r);
p = (rho/rho_1) * p + r;
}
l = C.transpose() * e; // l is the i-th row of CINV
// FIXME add a generic "prune/filter" expression for both dense and sparse object to sparse
for (Index j=0; j<l.size(); ++j)
if (l[j]<1e-15)
tripletList.push_back(T(i,j,l(j)));
d[i] = 0.0;
}
CINV.setFromTriplets(tripletList.begin(), tripletList.end());
}
/** \ingroup IterativeLinearSolvers_Module
* Constrained conjugate gradient
*
* Computes the minimum of \f$ 1/2((Ax).x) - bx \f$ under the constraint \f$ Cx \le f \f$
*/
template<typename TMatrix, typename CMatrix,
typename VectorX, typename VectorB, typename VectorF>
void constrained_cg(const TMatrix& A, const CMatrix& C, VectorX& x,
const VectorB& b, const VectorF& f, IterationController &iter)
{
using std::sqrt;
typedef typename TMatrix::Scalar Scalar;
typedef typename TMatrix::Index Index;
typedef Matrix<Scalar,Dynamic,1> TmpVec;
Scalar rho = 1.0, rho_1, lambda, gamma;
Index xSize = x.size();
TmpVec p(xSize), q(xSize), q2(xSize),
r(xSize), old_z(xSize), z(xSize),
memox(xSize);
std::vector<bool> satured(C.rows());
p.setZero();
iter.setRhsNorm(sqrt(b.dot(b))); // gael vect_sp(PS, b, b)
if (iter.rhsNorm() == 0.0) iter.setRhsNorm(1.0);
SparseMatrix<Scalar,RowMajor> CINV(C.rows(), C.cols());
pseudo_inverse(C, CINV);
while(true)
{
// computation of residual
old_z = z;
memox = x;
r = b;
r += A * -x;
z = r;
bool transition = false;
for (Index i = 0; i < C.rows(); ++i)
{
Scalar al = C.row(i).dot(x) - f.coeff(i);
if (al >= -1.0E-15)
{
if (!satured[i])
{
satured[i] = true;
transition = true;
}
Scalar bb = CINV.row(i).dot(z);
if (bb > 0.0)
// FIXME: we should allow that: z += -bb * C.row(i);
for (typename CMatrix::InnerIterator it(C,i); it; ++it)
z.coeffRef(it.index()) -= bb*it.value();
}
else
satured[i] = false;
}
// descent direction
rho_1 = rho;
rho = r.dot(z);
if (iter.finished(rho)) break;
if (transition || iter.first()) gamma = 0.0;
else gamma = (std::max)(0.0, (rho - old_z.dot(z)) / rho_1);
p = z + gamma*p;
++iter;
// one dimensionnal optimization
q = A * p;
lambda = rho / q.dot(p);
for (Index i = 0; i < C.rows(); ++i)
{
if (!satured[i])
{
Scalar bb = C.row(i).dot(p) - f[i];
if (bb > 0.0)
lambda = (std::min)(lambda, (f.coeff(i)-C.row(i).dot(x)) / bb);
}
}
x += lambda * p;
memox -= x;
}
}
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_CONSTRAINEDCG_H
|