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/*
Copyright (C) 2015 Arb authors
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"
void
arb_mat_sqr_classical(arb_mat_t B, const arb_mat_t A, slong prec)
{
slong n, i, j, k;
arb_t p, s;
n = arb_mat_nrows(A);
if (arb_mat_ncols(A) != n || arb_mat_nrows(B) != n || arb_mat_ncols(B) != n)
{
flint_printf("arb_mat_sqr: incompatible dimensions\n");
flint_abort();
}
if (n == 0)
return;
if (n == 1)
{
arb_mul(arb_mat_entry(B, 0, 0),
arb_mat_entry(A, 0, 0),
arb_mat_entry(A, 0, 0), prec);
return;
}
if (A == B)
{
arb_mat_t T;
arb_mat_init(T, n, n);
arb_mat_sqr_classical(T, A, prec);
arb_mat_swap(T, B);
arb_mat_clear(T);
return;
}
arb_init(p);
arb_init(s);
/* contribution of diagonal of A to diagonal of B */
for (i = 0; i < n; i++)
{
arb_mul(arb_mat_entry(B, i, i),
arb_mat_entry(A, i, i),
arb_mat_entry(A, i, i), prec);
}
for (i = 0; i < n; i++)
{
for (j = 0; j < i; j++)
{
/* contribution of off-diagonal of A to diagonal of B */
arb_mul(p, arb_mat_entry(A, i, j), arb_mat_entry(A, j, i), prec);
arb_add(arb_mat_entry(B, i, i), arb_mat_entry(B, i, i), p, prec);
arb_add(arb_mat_entry(B, j, j), arb_mat_entry(B, j, j), p, prec);
/* contribution of diagonal of A to off-diagonal of B */
arb_add(s, arb_mat_entry(A, i, i), arb_mat_entry(A, j, j), prec);
arb_mul(arb_mat_entry(B, i, j), arb_mat_entry(A, i, j), s, prec);
arb_mul(arb_mat_entry(B, j, i), arb_mat_entry(A, j, i), s, prec);
}
}
/* contribution of off-diagonal of A to off-diagonal of B */
if (n > 2)
{
for (i = 0; i < n; i++)
{
for (j = 0; j < n; j++)
{
for (k = 0; k < n; k++)
{
if (i != j && j != k && k != i)
{
arb_addmul(arb_mat_entry(B, i, j),
arb_mat_entry(A, i, k),
arb_mat_entry(A, k, j), prec);
}
}
}
}
}
arb_clear(p);
arb_clear(s);
}
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