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/*
Copyright (C) 2018 Fredrik Johansson
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 "acb_mat.h"
static void
acb_approx_mul(acb_t res, const acb_t x, const acb_t y, slong prec)
{
arf_complex_mul(arb_midref(acb_realref(res)), arb_midref(acb_imagref(res)),
arb_midref(acb_realref(x)), arb_midref(acb_imagref(x)),
arb_midref(acb_realref(y)), arb_midref(acb_imagref(y)), prec, ARB_RND);
}
/* note: the tmp variable t should have zero radius */
static void
acb_approx_div(acb_t z, const acb_t x, const acb_t y, acb_t t, slong prec)
{
arf_set(arb_midref(acb_realref(t)), arb_midref(acb_realref(y)));
arf_set(arb_midref(acb_imagref(t)), arb_midref(acb_imagref(y)));
acb_inv(t, t, prec);
mag_zero(arb_radref(acb_realref(t)));
mag_zero(arb_radref(acb_imagref(t)));
acb_approx_mul(z, x, t, prec);
}
void
acb_mat_approx_solve_tril_classical(acb_mat_t X,
const acb_mat_t L, const acb_mat_t B, int unit, slong prec)
{
slong i, j, n, m;
acb_ptr tmp;
acb_t s, t;
n = L->r;
m = B->c;
acb_init(s);
acb_init(t);
tmp = flint_malloc(sizeof(acb_struct) * n);
for (i = 0; i < m; i++)
{
for (j = 0; j < n; j++)
tmp[j] = *acb_mat_entry(X, j, i);
for (j = 0; j < n; j++)
{
acb_approx_dot(s, acb_mat_entry(B, j, i), 1, L->rows[j], 1, tmp, 1, j, prec);
if (!unit)
acb_approx_div(tmp + j, s, acb_mat_entry(L, j, j), t, prec);
else
acb_swap(tmp + j, s);
}
for (j = 0; j < n; j++)
*acb_mat_entry(X, j, i) = tmp[j];
}
flint_free(tmp);
acb_clear(s);
acb_clear(t);
}
void
acb_mat_approx_solve_tril_recursive(acb_mat_t X,
const acb_mat_t L, const acb_mat_t B, int unit, slong prec)
{
acb_mat_t LA, LC, LD, XX, XY, BX, BY, T;
slong r, n, m;
n = L->r;
m = B->c;
r = n / 2;
if (n == 0 || m == 0)
return;
/*
Denoting inv(M) by M^, we have:
[A 0]^ [X] == [A^ 0 ] [X] == [A^ X]
[C D] [Y] == [-D^ C A^ D^] [Y] == [D^ (Y - C A^ X)]
*/
acb_mat_window_init(LA, L, 0, 0, r, r);
acb_mat_window_init(LC, L, r, 0, n, r);
acb_mat_window_init(LD, L, r, r, n, n);
acb_mat_window_init(BX, B, 0, 0, r, m);
acb_mat_window_init(BY, B, r, 0, n, m);
acb_mat_window_init(XX, X, 0, 0, r, m);
acb_mat_window_init(XY, X, r, 0, n, m);
acb_mat_approx_solve_tril(XX, LA, BX, unit, prec);
/* acb_mat_submul(XY, BY, LC, XX); */
acb_mat_init(T, LC->r, BX->c);
acb_mat_approx_mul(T, LC, XX, prec);
acb_mat_sub(XY, BY, T, prec);
acb_mat_get_mid(XY, XY);
acb_mat_clear(T);
acb_mat_approx_solve_tril(XY, LD, XY, unit, prec);
acb_mat_window_clear(LA);
acb_mat_window_clear(LC);
acb_mat_window_clear(LD);
acb_mat_window_clear(BX);
acb_mat_window_clear(BY);
acb_mat_window_clear(XX);
acb_mat_window_clear(XY);
}
void
acb_mat_approx_solve_tril(acb_mat_t X, const acb_mat_t L,
const acb_mat_t B, int unit, slong prec)
{
if (B->r < 40 || B->c < 40)
acb_mat_approx_solve_tril_classical(X, L, B, unit, prec);
else
acb_mat_approx_solve_tril_recursive(X, L, B, unit, prec);
}
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