mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
114 lines
3 KiB
C
114 lines
3 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) 2016 Arb authors
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******************************************************************************/
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#include "arb_mat.h"
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int
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_arb_mat_cholesky_banachiewicz(arb_mat_t A, slong prec)
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{
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slong n, i, j, k;
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n = arb_mat_nrows(A);
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for (i = 0; i < n; i++)
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{
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for (j = 0; j < i; j++)
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{
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for (k = 0; k < j; k++)
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{
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arb_submul(arb_mat_entry(A, i, j),
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arb_mat_entry(A, i, k),
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arb_mat_entry(A, j, k), prec);
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}
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arb_div(arb_mat_entry(A, i, j),
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arb_mat_entry(A, i, j),
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arb_mat_entry(A, j, j), prec);
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}
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for (k = 0; k < i; k++)
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{
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arb_submul(arb_mat_entry(A, i, i),
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arb_mat_entry(A, i, k),
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arb_mat_entry(A, i, k), prec);
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}
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if (!arb_is_positive(arb_mat_entry(A, i, i)))
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return 0;
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arb_sqrt(arb_mat_entry(A, i, i),
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arb_mat_entry(A, i, i), prec);
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}
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return 1;
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}
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int
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arb_mat_cho(arb_mat_t L, const arb_mat_t A, slong prec)
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{
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slong n;
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if (!arb_mat_is_square(A))
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{
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flint_printf("arb_mat_cho: a square matrix is required\n");
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abort();
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}
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if (arb_mat_nrows(L) != arb_mat_nrows(A) ||
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arb_mat_ncols(L) != arb_mat_ncols(A))
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{
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flint_printf("arb_mat_cho: incompatible dimensions\n");
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abort();
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}
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if (arb_mat_is_empty(A))
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return 1;
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n = arb_mat_nrows(A);
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if (n == 1)
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{
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if (arb_is_positive(arb_mat_entry(A, 0, 0)))
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{
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arb_sqrt(arb_mat_entry(L, 0, 0), arb_mat_entry(A, 0, 0), prec);
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return 1;
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}
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else
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{
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return 0;
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}
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}
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arb_mat_set(L, A);
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if (!_arb_mat_cholesky_banachiewicz(L, prec))
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return 0;
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/* set the strictly upper triangular region of L to zero */
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{
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slong i, j;
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for (i = 0; i < n; i++)
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for (j = i+1; j < n; j++)
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arb_zero(arb_mat_entry(L, i, j));
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}
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return 1;
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}
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