/usr/include/linbox/algorithms/matrix-rank.h is in liblinbox-dev 1.1.6~rc0-4.1.
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/* File: matrix-rank.h
* Author: Zhendong Wan
* draft date: 09-27-2003
*/
#ifndef __LINBOX__MATRIX_RANK_H__
#define __LINBOX__MATRIX_RANK_H__
#include <linbox/util/debug.h>
#include <linbox/blackbox/dense.h>
#include <linbox/blackbox/sparse.h>
#include <linbox/solutions/rank.h>
#include <linbox/algorithms/matrix-hom.h>
#include <vector>
#include <algorithm>
#include <linbox/randiter/random-prime.h>
namespace LinBox
{
/** Compute the rank of an integer matrix in place over a finite field by Gaussian elimination.
*/
template<class _Ring, class _Field, class _RandomPrime = RandomPrimeIterator>
class MatrixRank {
public:
typedef _Ring Ring;
typedef _Field Field;
Ring r;
mutable _RandomPrime rp;
MatrixRank(const Ring& _r = Ring(), const _RandomPrime& _rp = _RandomPrime() ) : r(_r), rp (_rp) {}
~MatrixRank() {}
//compute the integer matrix A by modulo a random prime, Monto-Carlo
template<class IMatrix>
long rank(const IMatrix& A) const {
Field F (*rp);
DenseMatrix<Field>* Ap;
MatrixHom::map(Ap, A, F);
long result;
result = rankIn(*Ap);
delete Ap;
return result;
}
template <class Row>
long rank(const SparseMatrix<Ring, Row>& A) const {
Field F (*rp);
typename MatrixHomTrait<SparseMatrix<Ring, Row>, Field>::value_type* Ap;
MatrixHom::map (Ap, A, F);
long result;
result = rankIn (*Ap);
delete Ap;
return result;
}
template<class Field, class Row>
long rankIn(SparseMatrix<Field, Row>& A) const {
unsigned long result;
LinBox::rank(result, A, A.field());
return result;
}
// compute rank by Gauss Elimination
long rankIn(DenseMatrix<Field>& Ap) const {
typedef typename Field::Element Element;
Field F = Ap.field();
typename DenseMatrix<Field>::RowIterator cur_r, tmp_r;
typename DenseMatrix<Field>::ColIterator cur_c, tmp_c;
typename DenseMatrix<Field>::Row::iterator cur_rp, tmp_rp;
typename DenseMatrix<Field>::Col::iterator tmp_cp;
Element tmp_e;
std::vector<Element> tmp_v(Ap.coldim());
int offset_r = 0;
int offset_c = 0;
int r = 0;
for(cur_r = Ap. rowBegin(), cur_c = Ap. colBegin(); (cur_r != Ap. rowEnd())&&(cur_c != Ap.colEnd());) {
//try to find the pivot.
tmp_r = cur_r;
tmp_cp = cur_c -> begin() + offset_c;
while ((tmp_cp != cur_c -> end()) && F.isZero(*tmp_cp)) {
++ tmp_cp;
++ tmp_r;
}
// if no pivit found
if (tmp_cp == cur_c -> end()) {
++ offset_r;
++ cur_c;
continue;
}
//if swicth two row if nessary. Each row in dense matrix is stored in contiguous space
if (tmp_r != cur_r) {
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 != Ap.rowEnd(); ++ tmp_r) {
//see if need to update the row
if (!F.isZero(*(tmp_r -> begin() + offset_r ))) {
F.div (tmp_e, *(tmp_r -> begin() + offset_r), *(cur_r -> begin() + offset_r));
F.negin(tmp_e);
for ( cur_rp = cur_r ->begin() + offset_r,tmp_rp = tmp_r -> begin() + offset_r;
tmp_rp != tmp_r -> end(); ++ tmp_rp, ++ cur_rp )
F.axpyin ( *tmp_rp, *cur_rp, tmp_e);
}
}
++ cur_r;
++ cur_c;
++ offset_r;
++ offset_c;
++ r;
}
return r;
}
};
} // end namespace LinBox
#endif
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