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/*
Copyright (C) 2022, 2025 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 "gr.h"
#include "gr_mat.h"
int
gr_mat_rank_fflu(slong * rank, const gr_mat_t A, gr_ctx_t ctx)
{
slong n, m;
slong * P;
int status;
gr_mat_t T;
gr_ptr den;
n = gr_mat_nrows(A, ctx);
m = gr_mat_ncols(A, ctx);
if (n == 0 || m == 0)
{
*rank = 0;
return GR_SUCCESS;
}
else
{
GR_TMP_INIT(den, ctx);
gr_mat_init(T, n, m, ctx);
P = _perm_init(n);
status = gr_mat_fflu(rank, P, T, den, A, 0, ctx);
gr_mat_clear(T, ctx);
_perm_clear(P);
GR_TMP_CLEAR(den, ctx);
if (status != GR_SUCCESS)
status |= GR_UNABLE;
return status;
}
}
int
gr_mat_rank_lu(slong * rank, const gr_mat_t A, gr_ctx_t ctx)
{
slong n, m;
slong * P;
int status;
gr_mat_t T;
n = gr_mat_nrows(A, ctx);
m = gr_mat_ncols(A, ctx);
if (n == 0 || m == 0)
{
*rank = 0;
return GR_SUCCESS;
}
else
{
gr_mat_init(T, n, m, ctx);
P = _perm_init(n);
status = gr_mat_lu(rank, P, T, A, 0, ctx);
gr_mat_clear(T, ctx);
_perm_clear(P);
if (status != GR_SUCCESS)
status |= GR_UNABLE;
return status;
}
}
int
gr_mat_rank(slong * rank, const gr_mat_t A, gr_ctx_t ctx)
{
truth_t dom;
/* Sensible definition over any ring. */
if (gr_mat_nrows(A, ctx) == 0 || gr_mat_ncols(A, ctx) == 0)
{
*rank = 0;
return GR_SUCCESS;
}
dom = gr_ctx_is_field(ctx);
/* Prefer standard LU only over finite fields */
/* Prefer FFLU over non-finite fields as it often results in
smaller coefficients. TODO: this choice surely wants
tuning, e.g. when we have fast matrix multiplication.
For example, ca_mat currently uses LU for number fields. */
if (dom == T_TRUE && gr_ctx_is_finite(ctx) == T_TRUE)
return gr_mat_rank_lu(rank, A, ctx);
if (dom != T_TRUE)
dom = gr_ctx_is_integral_domain(ctx);
if (dom == T_TRUE)
return gr_mat_rank_fflu(rank, A, ctx);
/* There are ways to generalize the notation of rank to
non-integral domains, but we do not currently implement them;
for now we define the rank as undefined. */
if (dom == T_FALSE)
return GR_DOMAIN;
return GR_UNABLE;
}