mirror of
https://github.com/vale981/arb
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109 lines
2.4 KiB
C
109 lines
2.4 KiB
C
/*
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Copyright (C) 2018 arbguest
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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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/*
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* Helper function to compute a lower bound of 1 - inf_norm(I - A*B).
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* Returns zero when this lower bound is zero.
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*/
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int _mag_err_complement(mag_t m,
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const arb_mat_t A, const arb_mat_t B, slong prec)
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{
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slong n;
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arb_mat_t I, E;
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mag_t err;
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n = arb_mat_nrows(A);
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arb_mat_init(I, n, n);
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arb_mat_one(I);
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arb_mat_init(E, n, n);
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arb_mat_mul(E, A, B, prec);
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arb_mat_sub(E, I, E, prec);
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mag_init(err);
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arb_mat_bound_inf_norm(err, E);
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mag_one(m);
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mag_sub_lower(m, m, err);
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mag_clear(err);
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arb_mat_clear(I);
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arb_mat_clear(E);
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return !mag_is_zero(m);
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}
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int arb_mat_solve_preapprox(arb_mat_t X, const arb_mat_t A,
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const arb_mat_t B, const arb_mat_t R, const arb_mat_t T, slong prec)
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{
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int result;
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slong m, n;
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mag_t d;
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result = 0;
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n = arb_mat_nrows(A);
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m = arb_mat_ncols(X);
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if (n == 0 || m == 0)
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return 1;
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/* Use Theorem 10.2 of Rump in Acta Numerica 2010 */
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mag_init(d);
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if (_mag_err_complement(d, R, A, prec))
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{
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arb_mat_t C;
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arb_mat_init(C, n, m);
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arb_mat_mul(C, A, T, prec);
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arb_mat_sub(C, C, B, prec);
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arb_mat_mul(C, R, C, prec);
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/* Each column gets its own error bound. */
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arb_mat_set(X, T);
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{
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slong i, j;
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mag_t e, err;
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mag_init(e);
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mag_init(err);
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for (j = 0; j < m; j++)
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{
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mag_zero(err);
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for (i = 0; i < n; i++)
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{
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arb_get_mag(e, arb_mat_entry(C, i, j));
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mag_max(err, err, e);
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}
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mag_div(err, err, d);
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for (i = 0; i < n; i++)
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{
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arb_add_error_mag(arb_mat_entry(X, i, j), err);
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}
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}
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mag_clear(e);
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mag_clear(err);
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}
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arb_mat_clear(C);
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result = 1;
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}
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mag_clear(d);
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return result;
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}
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