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
/*=============================================================================
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This file is part of ARB.
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ARB is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2012 Sebastian Pancratz
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******************************************************************************/
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#include "arb_mat.h"
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void _arb_mat_charpoly(arb_ptr cp, const arb_mat_t mat, slong prec)
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{
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const slong n = mat->r;
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if (n == 0)
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{
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arb_one(cp);
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}
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else if (n == 1)
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{
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arb_neg(cp + 0, arb_mat_entry(mat, 0, 0));
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arb_one(cp + 1);
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}
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else
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{
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slong i, j, k, t;
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arb_ptr a, A, s;
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a = _arb_vec_init(n * n);
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A = a + (n - 1) * n;
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_arb_vec_zero(cp, n + 1);
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arb_neg(cp + 0, arb_mat_entry(mat, 0, 0));
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for (t = 1; t < n; t++)
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{
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for (i = 0; i <= t; i++)
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{
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arb_set(a + 0 * n + i, arb_mat_entry(mat, i, t));
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}
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arb_set(A + 0, arb_mat_entry(mat, t, t));
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for (k = 1; k < t; k++)
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{
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for (i = 0; i <= t; i++)
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{
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s = a + k * n + i;
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arb_zero(s);
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for (j = 0; j <= t; j++)
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arb_addmul(s, arb_mat_entry(mat, i, j), a + (k - 1) * n + j, prec);
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}
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arb_set(A + k, a + k * n + t);
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}
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arb_zero(A + t);
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for (j = 0; j <= t; j++)
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arb_addmul(A + t, arb_mat_entry(mat, t, j), a + (t - 1) * n + j, prec);
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for (k = 0; k <= t; k++)
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{
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for (j = 0; j < k; j++)
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arb_submul(cp + k, A + j, cp + (k - j - 1), prec);
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arb_sub(cp + k, cp + k, A + k, prec);
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}
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}
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/* Shift all coefficients up by one */
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for (i = n; i > 0; i--)
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arb_swap(cp + i, cp + (i - 1));
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arb_one(cp + 0);
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_arb_poly_reverse(cp, cp, n + 1, n + 1);
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_arb_vec_clear(a, n * n);
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}
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}
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void arb_mat_charpoly(arb_poly_t cp, const arb_mat_t mat, slong prec)
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{
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if (mat->r != mat->c)
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{
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flint_printf("Exception (arb_mat_charpoly). Non-square matrix.\n");
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abort();
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}
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arb_poly_fit_length(cp, mat->r + 1);
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_arb_poly_set_length(cp, mat->r + 1);
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_arb_mat_charpoly(cp->coeffs, mat, prec);
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}
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