mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
88 lines
2.3 KiB
C
88 lines
2.3 KiB
C
/*
|
|
Copyright (C) 2018 Fredrik Johansson
|
|
|
|
This file is part of Arb.
|
|
|
|
Arb 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 "arb_mat.h"
|
|
|
|
static void
|
|
_arb_mat_det_cofactor_2x2(arb_t t, const arb_mat_t A, slong prec)
|
|
{
|
|
arb_mul (t, arb_mat_entry(A, 0, 0), arb_mat_entry(A, 1, 1), prec);
|
|
arb_submul(t, arb_mat_entry(A, 0, 1), arb_mat_entry(A, 1, 0), prec);
|
|
}
|
|
|
|
static void
|
|
_arb_mat_det_cofactor_3x3(arb_t t, const arb_mat_t A, slong prec)
|
|
{
|
|
arb_t a;
|
|
arb_init(a);
|
|
|
|
arb_mul (a, arb_mat_entry(A, 1, 0), arb_mat_entry(A, 2, 1), prec);
|
|
arb_submul(a, arb_mat_entry(A, 1, 1), arb_mat_entry(A, 2, 0), prec);
|
|
arb_mul (t, a, arb_mat_entry(A, 0, 2), prec);
|
|
|
|
arb_mul (a, arb_mat_entry(A, 1, 2), arb_mat_entry(A, 2, 0), prec);
|
|
arb_submul(a, arb_mat_entry(A, 1, 0), arb_mat_entry(A, 2, 2), prec);
|
|
arb_addmul(t, a, arb_mat_entry(A, 0, 1), prec);
|
|
|
|
arb_mul (a, arb_mat_entry(A, 1, 1), arb_mat_entry(A, 2, 2), prec);
|
|
arb_submul(a, arb_mat_entry(A, 1, 2), arb_mat_entry(A, 2, 1), prec);
|
|
arb_addmul(t, a, arb_mat_entry(A, 0, 0), prec);
|
|
|
|
arb_clear(a);
|
|
}
|
|
|
|
void
|
|
arb_mat_det(arb_t det, const arb_mat_t A, slong prec)
|
|
{
|
|
slong n;
|
|
|
|
if (!arb_mat_is_square(A))
|
|
{
|
|
flint_printf("arb_mat_det: a square matrix is required!\n");
|
|
flint_abort();
|
|
}
|
|
|
|
n = arb_mat_nrows(A);
|
|
|
|
if (n == 0)
|
|
{
|
|
arb_one(det);
|
|
}
|
|
else if (n == 1)
|
|
{
|
|
arb_set_round(det, arb_mat_entry(A, 0, 0), prec);
|
|
}
|
|
else if (n == 2)
|
|
{
|
|
_arb_mat_det_cofactor_2x2(det, A, prec);
|
|
}
|
|
else if (!arb_mat_is_finite(A))
|
|
{
|
|
arb_indeterminate(det);
|
|
}
|
|
else if (arb_mat_is_tril(A) || arb_mat_is_triu(A))
|
|
{
|
|
arb_mat_diag_prod(det, A, prec);
|
|
}
|
|
else if (n == 3)
|
|
{
|
|
_arb_mat_det_cofactor_3x3(det, A, prec);
|
|
/* note: 4x4 performs worse than LU */
|
|
}
|
|
else
|
|
{
|
|
if (n <= 10 || prec > 10.0 * n)
|
|
arb_mat_det_lu(det, A, prec);
|
|
else
|
|
arb_mat_det_precond(det, A, prec);
|
|
}
|
|
}
|
|
|