pqc/external/flint-2.4.3/fmpz_mat/charpoly.c
2014-05-24 23:16:06 +02:00

125 lines
3.4 KiB
C

/*=============================================================================
This file is part of FLINT.
FLINT 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.
FLINT 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 FLINT; 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 "fmpz_mat.h"
/*
Assumes that \code{mat} is an $n \times n$ matrix and sets \code{(cp,n+1)}
to its characteristic polynomial.
Employs a division-free algorithm using $O(n^4)$ ring operations.
*/
void _fmpz_mat_charpoly(fmpz *cp, const fmpz_mat_t mat)
{
const slong n = mat->r;
if (n == 0)
{
fmpz_one(cp);
}
else if (n == 1)
{
fmpz_neg(cp + 0, fmpz_mat_entry(mat, 0, 0));
fmpz_one(cp + 1);
}
else
{
slong i, j, k, t;
fmpz *a, *A, *s;
a = _fmpz_vec_init(n * n);
A = a + (n - 1) * n;
_fmpz_vec_zero(cp, n + 1);
fmpz_neg(cp + 0, fmpz_mat_entry(mat, 0, 0));
for (t = 1; t < n; t++)
{
for (i = 0; i <= t; i++)
{
fmpz_set(a + 0 * n + i, fmpz_mat_entry(mat, i, t));
}
fmpz_set(A + 0, fmpz_mat_entry(mat, t, t));
for (k = 1; k < t; k++)
{
for (i = 0; i <= t; i++)
{
s = a + k * n + i;
fmpz_zero(s);
for (j = 0; j <= t; j++)
{
fmpz_addmul(s, fmpz_mat_entry(mat, i, j), a + (k - 1) * n + j);
}
}
fmpz_set(A + k, a + k * n + t);
}
fmpz_zero(A + t);
for (j = 0; j <= t; j++)
{
fmpz_addmul(A + t, fmpz_mat_entry(mat, t, j), a + (t - 1) * n + j);
}
for (k = 0; k <= t; k++)
{
for (j = 0; j < k; j++)
{
fmpz_submul(cp + k, A + j, cp + (k - j - 1));
}
fmpz_sub(cp + k, cp + k, A + k);
}
}
/* Shift all coefficients up by one */
for (i = n; i > 0; i--)
{
fmpz_swap(cp + i, cp + (i - 1));
}
fmpz_one(cp + 0);
_fmpz_poly_reverse(cp, cp, n + 1, n + 1);
_fmpz_vec_clear(a, n * n);
}
}
void fmpz_mat_charpoly(fmpz_poly_t cp, const fmpz_mat_t mat)
{
if (mat->r != mat->c)
{
flint_printf("Exception (fmpz_mat_charpoly). Non-square matrix.\n");
abort();
}
fmpz_poly_fit_length(cp, mat->r + 1);
_fmpz_poly_set_length(cp, mat->r + 1);
_fmpz_mat_charpoly(cp->coeffs, mat);
}