/usr/include/linbox/algorithms/matrix-inverse.h is in liblinbox-dev 1.4.2-3.
This file is owned by root:root, with mode 0o644.
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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 | /* Copyright (C) 2003 LinBox
* Written by Zhendong Wan
*
* modified by Pascal Giorgi 1/07/04
* put the Field as template parameter
* and add Field F as a parameter
*
* ========LICENCE========
* This file is part of the library LinBox.
*
* LinBox 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; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library 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 library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
* ========LICENCE========
*/
#ifndef __LINBOX_matrix_inverse_H
#define __LINBOX_matrix_inverse_H
#include "linbox/util/debug.h"
#include "linbox/util/error.h"
#include <vector>
#include <algorithm>
namespace LinBox
{
class MatrixInverse {
public:
/** \brief compute the inverse of a dense matrix, by Gaussian elimination.
* The matrix should support ColIterator and RowIterator.
* It returns 0, if an inverse is found, and
* returns 1, otherwise.
*/
template<class Field, class AnyDenseMatrix>
static long matrixInverseIn(const Field& F, AnyDenseMatrix& A)
{
// check if A is a square matrix
linbox_check(A.rowdim() == A. coldim());
// PG 1/07/04
//typedef typename AnyDenseMatrix::Field Field;
// step1 PLU Inplcae, actually, LPA = U.
// XXX Permutation
std::vector<std::pair<int,int> > P;
P.reserve (A.rowdim());
typename AnyDenseMatrix::RowIterator cur_r, tmp_r;
typename AnyDenseMatrix::ColIterator cur_c, tmp_c;
typename AnyDenseMatrix::Row::iterator cur_rp, tmp_rp;
typename AnyDenseMatrix::Col::iterator cur_cp, tmp_cp;
std::vector<typename Field::Element> tmp_v (A.rowdim());
typename Field::Element tmp_e;
// PG 1/07/04
//const Field F = A. field();
int offset = 0;
cur_r = A. rowBegin();
cur_c = A. colBegin();
for( ; cur_r != A. rowEnd(); ++ cur_r, ++ cur_c, ++ offset) {
//for(cur_r = A. rowBegin(), cur_c = A. colBegin(); cur_r != A. rowEnd(); ++ cur_r, ++ cur_c, ++ offset)
//try to find the pivot.
tmp_r = cur_r;
tmp_cp = cur_c -> begin() + offset;
while ((tmp_cp != cur_c -> end()) && F.isZero(*tmp_cp)) {
++ tmp_cp;
++ tmp_r;
}
if (tmp_cp == cur_c -> end()) return 1;
//if swicth two row if nessary. Each row in dense matrix is stored in contiguous space
if (tmp_r != cur_r) {
P.push_back(std::pair<int,int>(offset, (int)(tmp_cp - cur_c -> begin()) ) );
std::copy (tmp_r -> begin(), tmp_r -> end(), tmp_v.begin());
std::copy (cur_r -> begin(), cur_r -> end(), tmp_r -> begin());
std::copy (tmp_v.begin(), tmp_v.end(), cur_r -> begin());
}
// continue gauss elimination
for(tmp_r = cur_r + 1; tmp_r != A.rowEnd(); ++ tmp_r) {
//see if need to update the row
if (!F.isZero(*(tmp_r -> begin() + offset ))) {
F.div (tmp_e, *(tmp_r -> begin() + offset), *(cur_r -> begin() + offset));
F.negin(tmp_e);
for ( cur_rp = cur_r ->begin(),tmp_rp = tmp_r -> begin();
tmp_rp != tmp_r -> end(); ++ tmp_rp, ++ cur_rp )
F.axpyin ( *tmp_rp, *cur_rp, tmp_e);
F.assign(*(tmp_r -> begin() + offset), tmp_e);
}
}
}
//second compute inverse of A.
AnyDenseMatrix tmp(A);
//2a compute inverse of PA, by solving upper-triangeular system, PA = U^{-1} L.
offset = 0;
for(cur_c = A.colBegin();cur_c != A. colEnd(); ++ cur_c, ++ offset) {
for (cur_cp = cur_c -> begin();
cur_cp != cur_c -> begin() + offset; ++ cur_cp)
F.assign (*cur_cp, F.zero);
F.assign(*cur_cp, F.mOne); ++ cur_cp;
for (; cur_cp != cur_c -> end(); ++ cur_cp)
F.negin(*cur_cp);
//matrix is indexed by 0, instead of 1.
for (cur_cp = cur_c -> begin() + (ptrdiff_t)(A.rowdim() - 1),
tmp_r = tmp.rowBegin() + ( (int)A.rowdim() - 1);
cur_cp != cur_c -> begin() - 1;
-- cur_cp, -- tmp_r) {
F.assign (tmp_e, *cur_cp);
for(tmp_cp = cur_c -> begin() + (ptrdiff_t) (A.rowdim() - 1), tmp_rp = tmp_r -> begin() + (ptrdiff_t) ( A.rowdim() -1);
tmp_cp != cur_cp; -- tmp_cp, -- tmp_rp)
F.axpyin(tmp_e, *tmp_cp, *tmp_rp);
F. div(*cur_cp, tmp_e, *tmp_rp);
F.negin(*cur_cp);
}
}
// 2b, compute inverse of A, A^{-1} = (PA)^{-1} P
std::vector<std::pair<int, int> >::reverse_iterator v_p;
for(v_p = P.rbegin(); v_p != P.rend(); ++ v_p) {
cur_c = A.colBegin() + v_p -> first;
tmp_c = A.colBegin() + v_p -> second;
std::copy (cur_c -> begin(), cur_c -> end(), tmp_v.begin());
std::copy (tmp_c -> begin(), tmp_c -> end(), cur_c -> begin());
std::copy (tmp_v.begin(), tmp_v.end(), tmp_c -> begin());
}
return 0;
}
};
template<>
inline long MatrixInverse::matrixInverseIn(const MultiModDouble& F, BlasMatrix<MultiModDouble>& A) {
throw LinboxError("LinBox ERROR: use of MultiModDouble with too large moduli is not allowed at this time\n");
return 0;
}
} // namespace LinBox
#endif //__LINBOX_matrix_inverse_H
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