mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
143 lines
3 KiB
C
143 lines
3 KiB
C
/*
|
|
Copyright (C) 2018 arbguest
|
|
|
|
This file is part of Arb.
|
|
|
|
Arb is free software: you can redistribute it and/or modify it under
|
|
the terms of the GNU Lesser General Public License (LGPL) as published
|
|
by the Free Software Foundation; either version 2.1 of the License, or
|
|
(at your option) any later version. See <http://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
#include "arb_mat.h"
|
|
|
|
int
|
|
_arb_mat_solve_c(arb_mat_t X, const arb_mat_t A, const arb_mat_t B, slong prec)
|
|
{
|
|
int result;
|
|
slong m, n;
|
|
arb_mat_t I, R;
|
|
|
|
n = arb_mat_nrows(A);
|
|
m = arb_mat_ncols(X);
|
|
|
|
if (n == 0 || m == 0)
|
|
return 1;
|
|
|
|
arb_mat_init(I, n, n);
|
|
arb_mat_init(R, n, n);
|
|
|
|
arb_mat_one(I);
|
|
result = arb_mat_approx_solve(R, A, I, prec);
|
|
if (result)
|
|
{
|
|
arb_mat_t RA, RB;
|
|
|
|
arb_mat_init(RA, n, n);
|
|
arb_mat_init(RB, n, m);
|
|
|
|
arb_mat_mul(RA, R, A, prec);
|
|
arb_mat_mul(RB, R, B, prec);
|
|
|
|
result = arb_mat_solve_lu(X, RA, RB, prec);
|
|
|
|
arb_mat_clear(RA);
|
|
arb_mat_clear(RB);
|
|
}
|
|
|
|
arb_mat_clear(I);
|
|
arb_mat_clear(R);
|
|
|
|
return result;
|
|
}
|
|
|
|
int
|
|
_arb_mat_solve_d(arb_mat_t X, const arb_mat_t A, const arb_mat_t B, slong prec)
|
|
{
|
|
int result;
|
|
slong m, n;
|
|
arb_mat_t I, R;
|
|
|
|
n = arb_mat_nrows(A);
|
|
m = arb_mat_ncols(X);
|
|
|
|
if (n == 0 || m == 0)
|
|
return 1;
|
|
|
|
arb_mat_init(I, n, n);
|
|
arb_mat_init(R, n, n);
|
|
|
|
arb_mat_one(I);
|
|
result = arb_mat_approx_solve(R, A, I, prec);
|
|
if (result)
|
|
{
|
|
arb_mat_t RA, RB, E;
|
|
mag_t d;
|
|
|
|
arb_mat_init(RA, n, n);
|
|
arb_mat_init(RB, n, m);
|
|
arb_mat_init(E, n, n);
|
|
mag_init(d);
|
|
|
|
arb_mat_mul(RA, R, A, prec);
|
|
arb_mat_mul(RB, R, B, prec);
|
|
arb_mat_sub(E, I, RA, prec);
|
|
arb_mat_bound_inf_norm(d, E);
|
|
|
|
if (mag_cmp_2exp_si(d, 0) < 0)
|
|
{
|
|
slong i, j;
|
|
mag_t e, err;
|
|
|
|
mag_init(e);
|
|
mag_init(err);
|
|
|
|
mag_geom_series(d, d, 1);
|
|
arb_mat_set(X, RB);
|
|
|
|
for (j = 0; j < m; j++)
|
|
{
|
|
mag_zero(err);
|
|
for (i = 0; i < n; i++)
|
|
{
|
|
arb_get_mag(e, arb_mat_entry(RB, i, j));
|
|
mag_max(err, err, e);
|
|
}
|
|
mag_mul(err, err, d);
|
|
for (i = 0; i < n; i++)
|
|
{
|
|
arb_add_error_mag(arb_mat_entry(X, i, j), err);
|
|
}
|
|
}
|
|
|
|
mag_clear(e);
|
|
mag_clear(err);
|
|
}
|
|
else
|
|
{
|
|
result = arb_mat_solve_lu(X, RA, RB, prec);
|
|
}
|
|
|
|
arb_mat_clear(RA);
|
|
arb_mat_clear(RB);
|
|
arb_mat_clear(E);
|
|
mag_clear(d);
|
|
}
|
|
|
|
arb_mat_clear(I);
|
|
arb_mat_clear(R);
|
|
|
|
return result;
|
|
}
|
|
|
|
int
|
|
arb_mat_solve_precond(arb_mat_t X, const arb_mat_t A, const arb_mat_t B, slong prec)
|
|
{
|
|
slong n = arb_mat_nrows(A);
|
|
slong m = arb_mat_ncols(B);
|
|
|
|
if (m < 0.1 * n + 1)
|
|
return _arb_mat_solve_c(X, A, B, prec);
|
|
else
|
|
return _arb_mat_solve_d(X, A, B, prec);
|
|
}
|