/usr/include/linbox/algorithms/matrix-inverse.h is in liblinbox-dev 1.1.6~rc0-4.1.
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/* File: matrix-inverse.h
* Author: Zhendong Wan
* draft date: 09-27-2003
*
* modified by Pascal Giorgi 1/07/04
* put the Field as template parameter
* and add Field F as a parameter
*/
#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 DenseMatrix>
static long matrixInverseIn(const Field& F, DenseMatrix& A) {
// check if A is a square matrix
linbox_check(A.rowdim() == A. coldim());
// PG 1/07/04
//typedef typename DenseMatrix::Field Field;
// step1 PLU Inplcae, actually, LPA = U.
std::vector<std::pair<int,int> > P;
P.reserve (A.rowdim());
typename DenseMatrix::RowIterator cur_r, tmp_r;
typename DenseMatrix::ColIterator cur_c, tmp_c;
typename DenseMatrix::Row::iterator cur_rp, tmp_rp;
typename DenseMatrix::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.
DenseMatrix tmp(A);
//2a compute inverse of PA, by solving upper-triangeular system, PA = U^{-1} L.
typename Field::Element Zero;
typename Field::Element N_one;
F.init(Zero,0);
F.init(N_one, -1);
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, Zero);
F.assign(*cur_cp, N_one); ++ 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() + (A.rowdim() - 1), tmp_r = tmp.rowBegin() + ( 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() + (A.rowdim() - 1), tmp_rp = tmp_r -> begin() + ( 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, BlasBlackbox<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
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