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/*
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 "acb_mat.h"
static void
_acb_mat_det_cofactor_2x2(acb_t t, const acb_mat_t A, slong prec)
{
acb_mul (t, acb_mat_entry(A, 0, 0), acb_mat_entry(A, 1, 1), prec);
acb_submul(t, acb_mat_entry(A, 0, 1), acb_mat_entry(A, 1, 0), prec);
}
static void
_acb_mat_det_cofactor_3x3(acb_t t, const acb_mat_t A, slong prec)
{
acb_t a;
acb_init(a);
acb_mul (a, acb_mat_entry(A, 1, 0), acb_mat_entry(A, 2, 1), prec);
acb_submul(a, acb_mat_entry(A, 1, 1), acb_mat_entry(A, 2, 0), prec);
acb_mul (t, a, acb_mat_entry(A, 0, 2), prec);
acb_mul (a, acb_mat_entry(A, 1, 2), acb_mat_entry(A, 2, 0), prec);
acb_submul(a, acb_mat_entry(A, 1, 0), acb_mat_entry(A, 2, 2), prec);
acb_addmul(t, a, acb_mat_entry(A, 0, 1), prec);
acb_mul (a, acb_mat_entry(A, 1, 1), acb_mat_entry(A, 2, 2), prec);
acb_submul(a, acb_mat_entry(A, 1, 2), acb_mat_entry(A, 2, 1), prec);
acb_addmul(t, a, acb_mat_entry(A, 0, 0), prec);
acb_clear(a);
}
void
acb_mat_det(acb_t det, const acb_mat_t A, slong prec)
{
slong n;
if (!acb_mat_is_square(A))
{
flint_printf("acb_mat_det: a square matrix is required!\n");
flint_abort();
}
n = acb_mat_nrows(A);
if (n == 0)
{
acb_one(det);
}
else if (n == 1)
{
acb_set_round(det, acb_mat_entry(A, 0, 0), prec);
}
else if (n == 2)
{
_acb_mat_det_cofactor_2x2(det, A, prec);
}
else if (!acb_mat_is_finite(A))
{
acb_indeterminate(det);
}
else if (acb_mat_is_tril(A) || acb_mat_is_triu(A))
{
acb_mat_diag_prod(det, A, prec);
}
else if (n == 3)
{
_acb_mat_det_cofactor_3x3(det, A, prec);
/* note: 4x4 performs worse than LU */
}
else
{
if (n <= 14 || prec > 10.0 * n)
acb_mat_det_lu(det, A, prec);
else
acb_mat_det_precond(det, A, prec);
}
}
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