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/*
Copyright (C) 2011 Fredrik Johansson
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "perm.h"
#include "nmod.h"
#include "nmod_mat.h"
slong
_nmod_mat_rref(nmod_mat_t A, slong * pivots_nonpivots, slong * P)
{
slong i, j, n, rank;
slong * pivots;
slong * nonpivots;
nmod_mat_t U, V;
n = A->c;
rank = nmod_mat_lu_with_pivots(P, pivots_nonpivots, A);
if (rank == 0)
return rank;
pivots = pivots_nonpivots;
nonpivots = pivots_nonpivots + rank;
/* Clear L. */
for (i = 0; i < A->r; i++)
for (j = 0; j < FLINT_MIN(i, rank); j++)
nmod_mat_entry(A, i, j) = UWORD(0);
if (rank != n)
{
/* We now reorder U to proper upper triangular form U | V
with U full-rank triangular, set V = U^(-1) V, and then
put the column back in the original order.
An improvement for some matrices would be to compress V by
discarding columns containing nothing but zeros. */
nmod_mat_init(U, rank, rank, A->mod.n);
nmod_mat_init(V, rank, n - rank, A->mod.n);
for (j = 0; j < rank; j++)
{
for (i = j; i < rank; i++)
nmod_mat_entry(U, j, i) = nmod_mat_entry(A, j, pivots[i]);
}
for (j = 0; j < rank; j++)
{
for (i = 0; i < n - rank; i++)
nmod_mat_entry(V, j, i) = nmod_mat_entry(A, j, nonpivots[i]);
}
nmod_mat_solve_triu(V, U, V, 0);
/* Write back the actual content */
for (j = 0; j < rank; j++)
{
for (i = 0; i < n - rank; i++)
nmod_mat_entry(A, j, nonpivots[i]) = nmod_mat_entry(V, j, i);
}
nmod_mat_clear(U);
nmod_mat_clear(V);
}
/* Clear pivot columns */
for (j = 0; j < rank; j++)
{
for (i = j; i < rank; i++)
nmod_mat_entry(A, j, pivots[i]) = (i == j);
}
return rank;
}
slong
nmod_mat_rref(nmod_mat_t A)
{
slong rank, * pivots_nonpivots, * P;
if (nmod_mat_is_empty(A))
return 0;
if (A->r == 1)
{
ulong c, cinv;
slong i, j;
slong r = 0;
for (i = 0; i < A->c; i++)
{
c = nmod_mat_entry(A, 0, i);
if (c != 0)
{
r = 1;
if (c == 1)
break;
cinv = nmod_inv(c, A->mod);
nmod_mat_set_entry(A, 0, i, 1);
for (j = i + 1;j < A->c; j++)
{
nmod_mat_set_entry(A, 0, j, nmod_mul(nmod_mat_get_entry(A, 0, j), cinv, A->mod));
}
break;
}
}
return r;
}
pivots_nonpivots = flint_malloc(sizeof(slong) * A->c);
P = _perm_init(nmod_mat_nrows(A));
rank = _nmod_mat_rref(A, pivots_nonpivots, P);
flint_free(pivots_nonpivots);
_perm_clear(P);
return rank;
}