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/*
Copyright (C) 2022 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 "gr_vec.h"
#include "gr_mat.h"
static void
_gr_mat_swap_rows(gr_mat_t mat, slong * perm, slong r, slong s, gr_ctx_t ctx)
{
if (r != s)
{
gr_ptr u;
slong t;
if (perm != NULL)
{
t = perm[s];
perm[s] = perm[r];
perm[r] = t;
}
u = mat->rows[s];
mat->rows[s] = mat->rows[r];
mat->rows[r] = u;
}
}
int
gr_mat_lu_classical(slong * res_rank, slong * P, gr_mat_t LU, const gr_mat_t A, int rank_check, gr_ctx_t ctx)
{
gr_ptr d, e;
gr_ptr * a;
slong i, j, m, n, r, rank, row, col, sz;
int status = GR_SUCCESS;
int pivot_status;
if (gr_mat_is_empty(A, ctx) == T_TRUE)
{
*res_rank = 0;
return GR_SUCCESS;
}
GR_TMP_INIT2(d, e, ctx);
m = gr_mat_nrows(A, ctx);
n = gr_mat_ncols(A, ctx);
sz = ctx->sizeof_elem;
status |= gr_mat_set(LU, A, ctx);
a = LU->rows;
rank = row = col = 0;
for (i = 0; i < m; i++)
P[i] = i;
while (row < m && col < n)
{
pivot_status = gr_mat_find_nonzero_pivot(&r, LU, row, m, col, ctx);
/* We don't know whether there is a nonzero pivot element,
so we can't determine the rank. */
if (pivot_status == GR_UNABLE)
{
status = GR_UNABLE;
break;
}
/* There is certainly no nonzero pivot element. */
if (pivot_status == GR_DOMAIN)
{
/* We proved that the matrix is rank-deficient,
accomplishing the goal. */
if (rank_check)
{
status = GR_SUCCESS;
rank = 0;
break;
}
/* Continue with next column. */
col++;
continue;
}
rank++;
if (r != row)
_gr_mat_swap_rows(LU, P, row, r, ctx);
/* Must be able to invert pivot element. */
status |= gr_inv(d, GR_ENTRY(a[row], col, sz), ctx);
if (status != GR_SUCCESS)
break;
for (j = row + 1; j < m; j++)
{
status |= gr_mul(e, GR_ENTRY(a[j], col, sz), d, ctx);
status |= gr_neg(e, e, ctx);
if (n - col - 1 > 0)
status |= _gr_vec_addmul_scalar(GR_ENTRY(a[j], col + 1, sz), GR_ENTRY(a[row], col + 1, sz), n - col - 1, e, ctx);
status |= gr_zero(GR_ENTRY(a[j], col, sz), ctx);
status |= gr_neg(GR_ENTRY(a[j], rank - 1, sz), e, ctx);
}
row++;
col++;
}
GR_TMP_CLEAR2(d, e, ctx);
*res_rank = rank;
return status;
}