mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
113 lines
2.6 KiB
C
113 lines
2.6 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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_apply_permutation(slong * AP, arb_mat_t A, slong * P,
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slong n, slong offset)
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{
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if (n != 0)
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{
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arb_ptr * Atmp;
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slong * APtmp;
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slong i;
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Atmp = flint_malloc(sizeof(arb_ptr) * n);
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APtmp = flint_malloc(sizeof(slong) * n);
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for (i = 0; i < n; i++) Atmp[i] = A->rows[P[i] + offset];
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for (i = 0; i < n; i++) A->rows[i + offset] = Atmp[i];
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for (i = 0; i < n; i++) APtmp[i] = AP[P[i] + offset];
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for (i = 0; i < n; i++) AP[i + offset] = APtmp[i];
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flint_free(Atmp);
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flint_free(APtmp);
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}
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}
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int
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arb_mat_lu_recursive(slong * P, arb_mat_t LU, const arb_mat_t A, slong prec)
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{
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slong i, m, n, r1, r2, n1;
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arb_mat_t A0, A1, A00, A01, A10, A11;
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slong * P1;
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m = A->r;
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n = A->c;
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if (m <= 1 || n <= 1)
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{
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return arb_mat_lu_classical(P, LU, A, prec);
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}
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if (LU != A)
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arb_mat_set(LU, A);
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n1 = n / 2;
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for (i = 0; i < m; i++)
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P[i] = i;
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P1 = flint_malloc(sizeof(slong) * m);
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arb_mat_window_init(A0, LU, 0, 0, m, n1);
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arb_mat_window_init(A1, LU, 0, n1, m, n);
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r1 = arb_mat_lu(P1, A0, A0, prec);
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if (!r1)
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{
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flint_free(P1);
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arb_mat_window_clear(A0);
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arb_mat_window_clear(A1);
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return 0;
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}
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/* r1 = rank of A0 */
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r1 = FLINT_MIN(m, n1);
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_apply_permutation(P, LU, P1, m, 0);
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arb_mat_window_init(A00, LU, 0, 0, r1, r1);
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arb_mat_window_init(A10, LU, r1, 0, m, r1);
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arb_mat_window_init(A01, LU, 0, n1, r1, n);
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arb_mat_window_init(A11, LU, r1, n1, m, n);
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arb_mat_solve_tril(A01, A00, A01, 1, prec);
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{
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/* arb_mat_submul(A11, A11, A10, A01, prec); */
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arb_mat_t T;
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arb_mat_init(T, A10->r, A01->c);
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arb_mat_mul(T, A10, A01, prec);
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arb_mat_sub(A11, A11, T, prec);
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arb_mat_clear(T);
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}
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r2 = arb_mat_lu(P1, A11, A11, prec);
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if (!r2)
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r1 = r2 = 0;
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else
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_apply_permutation(P, LU, P1, m - r1, r1);
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flint_free(P1);
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arb_mat_window_clear(A00);
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arb_mat_window_clear(A01);
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arb_mat_window_clear(A10);
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arb_mat_window_clear(A11);
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arb_mat_window_clear(A0);
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arb_mat_window_clear(A1);
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return r1 && r2;
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}
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