mirror of
https://github.com/vale981/arb
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63 lines
1.5 KiB
C
63 lines
1.5 KiB
C
/*
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Copyright 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 "acb_mat.h"
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void
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acb_mat_eig_global_enclosure(mag_t eps, const acb_mat_t A, acb_srcptr E, const acb_mat_t R, slong prec)
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{
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acb_mat_t Y, R1, R2;
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slong i, j, n;
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mag_t r1, r2;
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n = acb_mat_nrows(A);
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acb_mat_init(Y, n, n);
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acb_mat_init(R1, n, n);
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acb_mat_init(R2, n, n);
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mag_init(r1);
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mag_init(r2);
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/* Y ~= inv(R) */
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acb_mat_one(R1);
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acb_mat_approx_solve(Y, R, R1, prec);
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/* R2 = Y*R - I */
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acb_mat_mul(R2, Y, R, prec);
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for (i = 0; i < n; i++)
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acb_sub_ui(acb_mat_entry(R2, i, i), acb_mat_entry(R2, i, i), 1, prec);
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acb_mat_bound_inf_norm(r2, R2);
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if (mag_cmp_2exp_si(r2, 0) < 0)
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{
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/* R1 = Y*(AR - RD) */
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acb_mat_mul(R2, A, R, prec);
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for (i = 0; i < n; i++)
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for (j = 0; j < n; j++)
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acb_submul(acb_mat_entry(R2, i, j), acb_mat_entry(R, i, j), E + j, prec);
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acb_mat_mul(R1, Y, R2, prec);
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acb_mat_bound_inf_norm(r1, R1);
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mag_geom_series(r2, r2, 0);
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mag_mul(eps, r1, r2);
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}
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else
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{
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mag_inf(eps);
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}
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acb_mat_clear(R1);
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acb_mat_clear(R2);
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acb_mat_clear(Y);
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mag_clear(r1);
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mag_clear(r2);
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}
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