mirror of
https://github.com/vale981/arb
synced 2025-03-05 17:31:38 -05:00
138 lines
3.2 KiB
C
138 lines
3.2 KiB
C
/*
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Copyright (C) 2018 Fredrik Johansson
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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 it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "arb_mat.h"
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static void
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_arb_mat_det_cofactor_2x2(arb_t t, const arb_mat_t A, slong prec)
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{
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arb_mul (t, arb_mat_entry(A, 0, 0), arb_mat_entry(A, 1, 1), prec);
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arb_submul(t, arb_mat_entry(A, 0, 1), arb_mat_entry(A, 1, 0), prec);
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}
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static void
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_arb_mat_det_cofactor_3x3(arb_t t, const arb_mat_t A, slong prec)
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{
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arb_t a;
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arb_init(a);
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arb_mul (a, arb_mat_entry(A, 1, 0), arb_mat_entry(A, 2, 1), prec);
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arb_submul(a, arb_mat_entry(A, 1, 1), arb_mat_entry(A, 2, 0), prec);
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arb_mul (t, a, arb_mat_entry(A, 0, 2), prec);
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arb_mul (a, arb_mat_entry(A, 1, 2), arb_mat_entry(A, 2, 0), prec);
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arb_submul(a, arb_mat_entry(A, 1, 0), arb_mat_entry(A, 2, 2), prec);
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arb_addmul(t, a, arb_mat_entry(A, 0, 1), prec);
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arb_mul (a, arb_mat_entry(A, 1, 1), arb_mat_entry(A, 2, 2), prec);
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arb_submul(a, arb_mat_entry(A, 1, 2), arb_mat_entry(A, 2, 1), prec);
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arb_addmul(t, a, arb_mat_entry(A, 0, 0), prec);
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arb_clear(a);
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}
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int
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arb_mat_is_finite(const arb_mat_t A)
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{
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slong i, j, n, m;
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n = arb_mat_nrows(A);
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m = arb_mat_ncols(A);
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for (i = 0; i < n; i++)
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for (j = 0; j < m; j++)
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if (!arb_is_finite(arb_mat_entry(A, i, j)))
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return 0;
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return 1;
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}
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int
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arb_mat_is_triu(const arb_mat_t A)
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{
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slong i, j, n, m;
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n = arb_mat_nrows(A);
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m = arb_mat_ncols(A);
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for (i = 1; i < n; i++)
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for (j = 0; j < FLINT_MIN(i, m); j++)
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if (!arb_is_zero(arb_mat_entry(A, i, j)))
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return 0;
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return 1;
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}
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int
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arb_mat_is_tril(const arb_mat_t A)
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{
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slong i, j, n, m;
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n = arb_mat_nrows(A);
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m = arb_mat_ncols(A);
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for (i = 0; i < n; i++)
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for (j = i + 1; j < m; j++)
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if (!arb_is_zero(arb_mat_entry(A, i, j)))
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return 0;
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return 1;
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}
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void
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arb_mat_det(arb_t det, const arb_mat_t A, slong prec)
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{
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slong k, n;
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if (!arb_mat_is_square(A))
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{
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flint_printf("arb_mat_det: a square matrix is required!\n");
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flint_abort();
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}
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n = arb_mat_nrows(A);
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if (n == 0)
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{
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arb_one(det);
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}
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else if (n == 1)
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{
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arb_set_round(det, arb_mat_entry(A, 0, 0), prec);
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}
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else if (n == 2)
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{
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_arb_mat_det_cofactor_2x2(det, A, prec);
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}
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else if (!arb_mat_is_finite(A))
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{
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arb_indeterminate(det);
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}
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else if (arb_mat_is_tril(A) || arb_mat_is_triu(A))
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{
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arb_set(det, arb_mat_entry(A, 0, 0));
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for (k = 1; k < n; k++)
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arb_mul(det, det, arb_mat_entry(A, k, k), prec);
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}
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else if (n == 3)
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{
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_arb_mat_det_cofactor_3x3(det, A, prec);
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/* note: 4x4 performs worse than LU */
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}
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else
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{
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if (n <= 10 || prec > 10.0 * n)
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arb_mat_det_lu(det, A, prec);
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else
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arb_mat_det_precond(det, A, prec);
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}
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}
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