mirror of
https://github.com/vale981/arb
synced 2025-03-06 01:41:39 -05:00
109 lines
3.1 KiB
C
109 lines
3.1 KiB
C
/*=============================================================================
|
|
|
|
This file is part of ARB.
|
|
|
|
ARB is free software; you can redistribute it and/or modify
|
|
it under the terms of the GNU General Public License as published by
|
|
the Free Software Foundation; either version 2 of the License, or
|
|
(at your option) any later version.
|
|
|
|
ARB is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
GNU General Public License for more details.
|
|
|
|
You should have received a copy of the GNU General Public License
|
|
along with ARB; if not, write to the Free Software
|
|
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
|
|
|
=============================================================================*/
|
|
/******************************************************************************
|
|
|
|
Copyright (C) 2012 Sebastian Pancratz
|
|
|
|
******************************************************************************/
|
|
|
|
#include "acb_mat.h"
|
|
|
|
void _acb_mat_charpoly(acb_ptr cp, const acb_mat_t mat, slong prec)
|
|
{
|
|
const slong n = mat->r;
|
|
|
|
if (n == 0)
|
|
{
|
|
acb_one(cp);
|
|
}
|
|
else if (n == 1)
|
|
{
|
|
acb_neg(cp + 0, acb_mat_entry(mat, 0, 0));
|
|
acb_one(cp + 1);
|
|
}
|
|
else
|
|
{
|
|
slong i, j, k, t;
|
|
acb_ptr a, A, s;
|
|
|
|
a = _acb_vec_init(n * n);
|
|
A = a + (n - 1) * n;
|
|
|
|
_acb_vec_zero(cp, n + 1);
|
|
acb_neg(cp + 0, acb_mat_entry(mat, 0, 0));
|
|
|
|
for (t = 1; t < n; t++)
|
|
{
|
|
for (i = 0; i <= t; i++)
|
|
{
|
|
acb_set(a + 0 * n + i, acb_mat_entry(mat, i, t));
|
|
}
|
|
|
|
acb_set(A + 0, acb_mat_entry(mat, t, t));
|
|
|
|
for (k = 1; k < t; k++)
|
|
{
|
|
for (i = 0; i <= t; i++)
|
|
{
|
|
s = a + k * n + i;
|
|
acb_zero(s);
|
|
for (j = 0; j <= t; j++)
|
|
acb_addmul(s, acb_mat_entry(mat, i, j), a + (k - 1) * n + j, prec);
|
|
}
|
|
|
|
acb_set(A + k, a + k * n + t);
|
|
}
|
|
|
|
acb_zero(A + t);
|
|
for (j = 0; j <= t; j++)
|
|
acb_addmul(A + t, acb_mat_entry(mat, t, j), a + (t - 1) * n + j, prec);
|
|
|
|
for (k = 0; k <= t; k++)
|
|
{
|
|
for (j = 0; j < k; j++)
|
|
acb_submul(cp + k, A + j, cp + (k - j - 1), prec);
|
|
|
|
acb_sub(cp + k, cp + k, A + k, prec);
|
|
}
|
|
}
|
|
|
|
/* Shift all coefficients up by one */
|
|
for (i = n; i > 0; i--)
|
|
acb_swap(cp + i, cp + (i - 1));
|
|
|
|
acb_one(cp + 0);
|
|
_acb_poly_reverse(cp, cp, n + 1, n + 1);
|
|
_acb_vec_clear(a, n * n);
|
|
}
|
|
}
|
|
|
|
void acb_mat_charpoly(acb_poly_t cp, const acb_mat_t mat, slong prec)
|
|
{
|
|
if (mat->r != mat->c)
|
|
{
|
|
flint_printf("Exception (acb_mat_charpoly). Non-square matrix.\n");
|
|
abort();
|
|
}
|
|
|
|
acb_poly_fit_length(cp, mat->r + 1);
|
|
_acb_poly_set_length(cp, mat->r + 1);
|
|
_acb_mat_charpoly(cp->coeffs, mat, prec);
|
|
}
|
|
|