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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"
void
acb_mat_solve_triu_classical(acb_mat_t X, const acb_mat_t U,
const acb_mat_t B, int unit, slong prec)
{
slong i, j, n, m;
acb_ptr tmp;
acb_t s;
n = U->r;
m = B->c;
acb_init(s);
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 = n - 1; j >= 0; j--)
{
acb_dot(s, acb_mat_entry(B, j, i), 1, U->rows[j] + j + 1, 1, tmp + j + 1, 1, n - j - 1, prec);
if (!unit)
acb_div(tmp + j, s, acb_mat_entry(U, j, j), 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);
}
void
acb_mat_solve_triu_recursive(acb_mat_t X,
const acb_mat_t U, const acb_mat_t B, int unit, slong prec)
{
acb_mat_t UA, UB, UD, XX, XY, BX, BY, T;
slong r, n, m;
n = U->r;
m = B->c;
r = n / 2;
if (n == 0 || m == 0)
return;
/*
Denoting inv(M) by M^, we have:
[A B]^ [X] == [A^ (X - B D^ Y)]
[0 D] [Y] == [ D^ Y ]
*/
acb_mat_window_init(UA, U, 0, 0, r, r);
acb_mat_window_init(UB, U, 0, r, r, n);
acb_mat_window_init(UD, U, 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_solve_triu(XY, UD, BY, unit, prec);
/* acb_mat_submul(XX, BX, UB, XY); */
acb_mat_init(T, UB->r, XY->c);
acb_mat_mul(T, UB, XY, prec);
acb_mat_sub(XX, BX, T, prec);
acb_mat_clear(T);
acb_mat_solve_triu(XX, UA, XX, unit, prec);
acb_mat_window_clear(UA);
acb_mat_window_clear(UB);
acb_mat_window_clear(UD);
acb_mat_window_clear(BX);
acb_mat_window_clear(BY);
acb_mat_window_clear(XX);
acb_mat_window_clear(XY);
}
void
acb_mat_solve_triu(acb_mat_t X, const acb_mat_t U,
const acb_mat_t B, int unit, slong prec)
{
if (B->r < 40 || B->c < 40)
acb_mat_solve_triu_classical(X, U, B, unit, prec);
else
acb_mat_solve_triu_recursive(X, U, B, unit, prec);
}
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