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/*
Copyright (C) 2016 Arb authors
This file is part of FLINT.
FLINT 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 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "arb.h"
#include "arb_mat.h"
void
arb_mat_inv_ldl_precomp(arb_mat_t X, const arb_mat_t L, slong prec)
{
slong n;
if (arb_mat_nrows(X) != arb_mat_nrows(L) ||
arb_mat_ncols(X) != arb_mat_ncols(L))
{
flint_throw(FLINT_ERROR, "arb_mat_inv_ldl_precomp: incompatible dimensions\n");
}
if (arb_mat_is_empty(L))
return;
n = arb_mat_nrows(L);
if (n == 1)
{
arb_inv(arb_mat_entry(X, 0, 0), arb_mat_entry(L, 0, 0), prec);
return;
}
if (X == L)
{
flint_throw(FLINT_ERROR, "arb_mat_inv_ldl_precomp: unsupported aliasing\n");
}
/* invert a 2x2 or larger matrix given its L * D * L^T decomposition */
{
slong i, j, k;
arb_struct *s;
s = _arb_vec_init(n);
for (i = 0; i < n; i++)
{
arb_inv(s + i, arb_mat_entry(L, i, i), prec);
}
arb_mat_zero(X);
for (j = n-1; j >= 0; j--)
{
for (i = j; i >= 0; i--)
{
if (i == j)
{
arb_set(arb_mat_entry(X, i, j), s + i);
}
else
{
arb_zero(arb_mat_entry(X, i, j));
}
for (k = i + 1; k < n; k++)
{
arb_submul(arb_mat_entry(X, i, j),
arb_mat_entry(L, k, i),
arb_mat_entry(X, k, j), prec);
}
arb_set(arb_mat_entry(X, j, i),
arb_mat_entry(X, i, j));
}
}
_arb_vec_clear(s, n);
}
}