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/*
Copyright (C) 2020 Fredrik Johansson
This file is part of Calcium.
Calcium 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 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "ca_mat.h"
int
ca_mat_lu_classical(slong * res_rank, slong * P, ca_mat_t LU, const ca_mat_t A, int rank_check, ca_ctx_t ctx)
{
ca_t d, e;
ca_ptr * a;
slong i, j, m, n, r, rank, row, col;
int success;
truth_t found_pivot;
if (ca_mat_is_empty(A))
{
*res_rank = 0;
return 1;
}
m = ca_mat_nrows(A);
n = ca_mat_ncols(A);
ca_mat_set(LU, A, ctx);
a = LU->rows;
rank = row = col = 0;
for (i = 0; i < m; i++)
P[i] = i;
ca_init(d, ctx);
ca_init(e, ctx);
success = 1;
while (row < m && col < n)
{
found_pivot = ca_mat_find_pivot(&r, LU, row, m, col, ctx);
if (found_pivot == T_UNKNOWN)
{
success = 0;
break;
}
if (found_pivot == T_FALSE)
{
if (rank_check)
{
rank = 0;
break;
}
col++;
continue;
}
rank++;
if (r != row)
_ca_mat_swap_rows(LU, P, row, r);
ca_inv(d, a[row] + col, ctx);
for (j = row + 1; j < m; j++)
{
ca_mul(e, a[j] + col, d, ctx);
ca_neg(e, e, ctx);
_ca_vec_scalar_addmul_ca(a[j] + col + 1, a[row] + col + 1, n - col - 1, e, ctx);
ca_zero(a[j] + col, ctx);
ca_neg(a[j] + rank - 1, e, ctx);
}
row++;
col++;
}
ca_clear(d, ctx);
ca_clear(e, ctx);
*res_rank = rank;
return success;
}
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