99 lines
2.6 KiB
C
99 lines
2.6 KiB
C
|
/*=============================================================================
|
||
|
|
|
||
|
|
This file is part of FLINT.
|
||
|
|
|
||
|
|
FLINT is free software; you can redistribute it and/or modify
|
||
|
|
it under the terms of the GNU General Public License as published by
|
||
|
|
the Free Software Foundation; either version 2 of the License, or
|
||
|
|
(at your option) any later version.
|
||
|
|
|
||
|
|
FLINT 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 General Public License for more details.
|
||
|
|
|
||
|
|
You should have received a copy of the GNU General Public License
|
||
|
|
along with FLINT; if not, write to the Free Software
|
||
|
|
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||
|
|
|
||
|
|
=============================================================================*/
|
||
|
|
/******************************************************************************
|
||
|
|
|
||
|
|
Copyright (C) 2011 Fredrik Johansson
|
||
|
|
Copyright (C) 2012 Lina Kulakova
|
||
|
|
|
||
|
|
******************************************************************************/
|
||
|
|
|
||
|
|
#include "fmpz_mat.h"
|
||
|
|
|
||
|
|
#define E(j,k) fmpz_mat_entry(A,j,k)
|
||
|
|
|
||
|
|
slong
|
||
|
|
fmpz_mat_rref_mod(slong * perm, fmpz_mat_t A, const fmpz_t p)
|
||
|
|
{
|
||
|
|
fmpz_t t, inv;
|
||
|
|
slong m, n, j, k, rank, r, pivot_row, pivot_col;
|
||
|
|
|
||
|
|
if (fmpz_mat_is_empty(A))
|
||
|
|
{
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
m = A->r;
|
||
|
|
n = A->c;
|
||
|
|
rank = pivot_row = pivot_col = 0;
|
||
|
|
|
||
|
|
fmpz_init(t);
|
||
|
|
fmpz_init(inv);
|
||
|
|
|
||
|
|
while (pivot_row < m && pivot_col < n)
|
||
|
|
{
|
||
|
|
r = fmpz_mat_find_pivot_any(A, pivot_row, m, pivot_col);
|
||
|
|
|
||
|
|
if (r == -1)
|
||
|
|
{
|
||
|
|
pivot_col++;
|
||
|
|
continue;
|
||
|
|
}
|
||
|
|
else if (r != pivot_row)
|
||
|
|
{
|
||
|
|
fmpz_mat_swap_rows(A, perm, pivot_row, r);
|
||
|
|
}
|
||
|
|
rank++;
|
||
|
|
|
||
|
|
fmpz_invmod(inv, E(pivot_row, pivot_col), p);
|
||
|
|
|
||
|
|
/* pivot row */
|
||
|
|
for (k = pivot_col + 1; k < n; k++)
|
||
|
|
{
|
||
|
|
fmpz_mul(E(pivot_row, k), E(pivot_row, k), inv);
|
||
|
|
fmpz_mod(E(pivot_row, k), E(pivot_row, k), p);
|
||
|
|
}
|
||
|
|
fmpz_one(E(pivot_row, pivot_col));
|
||
|
|
|
||
|
|
/* other rows */
|
||
|
|
for (j = 0; j < m; j++)
|
||
|
|
{
|
||
|
|
if (j == pivot_row)
|
||
|
|
continue;
|
||
|
|
|
||
|
|
for (k = pivot_col + 1; k < n; k++)
|
||
|
|
{
|
||
|
|
fmpz_mul(t, E(j, pivot_col), E(pivot_row, k));
|
||
|
|
fmpz_sub(E(j, k), E(j, k), t);
|
||
|
|
fmpz_mod(E(j, k), E(j, k), p);
|
||
|
|
}
|
||
|
|
|
||
|
|
fmpz_zero(E(j, pivot_col));
|
||
|
|
}
|
||
|
|
|
||
|
|
pivot_row++;
|
||
|
|
pivot_col++;
|
||
|
|
}
|
||
|
|
|
||
|
|
fmpz_clear(inv);
|
||
|
|
fmpz_clear(t);
|
||
|
|
|
||
|
|
return rank;
|
||
|
|
}
|