mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
113 lines
2.9 KiB
C
113 lines
2.9 KiB
C
/*
|
|
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 "arb_mat.h"
|
|
|
|
static void
|
|
arb_approx_div(arb_t z, const arb_t x, const arb_t y, slong prec)
|
|
{
|
|
arf_div(arb_midref(z), arb_midref(x), arb_midref(y), prec, ARB_RND);
|
|
}
|
|
|
|
void
|
|
arb_mat_approx_solve_tril_classical(arb_mat_t X,
|
|
const arb_mat_t L, const arb_mat_t B, int unit, slong prec)
|
|
{
|
|
slong i, j, n, m;
|
|
arb_ptr tmp;
|
|
arb_t s;
|
|
|
|
n = L->r;
|
|
m = B->c;
|
|
|
|
arb_init(s);
|
|
tmp = flint_malloc(sizeof(arb_struct) * n);
|
|
|
|
for (i = 0; i < m; i++)
|
|
{
|
|
for (j = 0; j < n; j++)
|
|
tmp[j] = *arb_mat_entry(X, j, i);
|
|
|
|
for (j = 0; j < n; j++)
|
|
{
|
|
arb_approx_dot(s, arb_mat_entry(B, j, i), 1, L->rows[j], 1, tmp, 1, j, prec);
|
|
|
|
if (!unit)
|
|
arb_approx_div(tmp + j, s, arb_mat_entry(L, j, j), prec);
|
|
else
|
|
arb_swap(tmp + j, s);
|
|
}
|
|
|
|
for (j = 0; j < n; j++)
|
|
*arb_mat_entry(X, j, i) = tmp[j];
|
|
}
|
|
|
|
flint_free(tmp);
|
|
arb_clear(s);
|
|
}
|
|
|
|
void
|
|
arb_mat_approx_solve_tril_recursive(arb_mat_t X,
|
|
const arb_mat_t L, const arb_mat_t B, int unit, slong prec)
|
|
{
|
|
arb_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)]
|
|
*/
|
|
arb_mat_window_init(LA, L, 0, 0, r, r);
|
|
arb_mat_window_init(LC, L, r, 0, n, r);
|
|
arb_mat_window_init(LD, L, r, r, n, n);
|
|
arb_mat_window_init(BX, B, 0, 0, r, m);
|
|
arb_mat_window_init(BY, B, r, 0, n, m);
|
|
arb_mat_window_init(XX, X, 0, 0, r, m);
|
|
arb_mat_window_init(XY, X, r, 0, n, m);
|
|
|
|
arb_mat_approx_solve_tril(XX, LA, BX, unit, prec);
|
|
|
|
/* arb_mat_submul(XY, BY, LC, XX); */
|
|
arb_mat_init(T, LC->r, BX->c);
|
|
arb_mat_approx_mul(T, LC, XX, prec);
|
|
arb_mat_sub(XY, BY, T, prec);
|
|
arb_mat_get_mid(XY, XY);
|
|
arb_mat_clear(T);
|
|
|
|
arb_mat_approx_solve_tril(XY, LD, XY, unit, prec);
|
|
|
|
arb_mat_window_clear(LA);
|
|
arb_mat_window_clear(LC);
|
|
arb_mat_window_clear(LD);
|
|
arb_mat_window_clear(BX);
|
|
arb_mat_window_clear(BY);
|
|
arb_mat_window_clear(XX);
|
|
arb_mat_window_clear(XY);
|
|
}
|
|
|
|
void
|
|
arb_mat_approx_solve_tril(arb_mat_t X, const arb_mat_t L,
|
|
const arb_mat_t B, int unit, slong prec)
|
|
{
|
|
if (B->r < 40 || B->c < 40)
|
|
arb_mat_approx_solve_tril_classical(X, L, B, unit, prec);
|
|
else
|
|
arb_mat_approx_solve_tril_recursive(X, L, B, unit, prec);
|
|
}
|