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lll_original.c
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/*
Copyright (C) 2014 Abhinav Baid
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 2.1 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "fmpz_mat.h"
#include "fmpq_mat.h"
void
fmpz_mat_lll_original(fmpz_mat_t A, const fmpq_t delta, const fmpq_t eta)
{
slong i, j, k, l, m, n;
fmpz_t r, one;
fmpq_t chi, nu, xi, half, rat;
fmpq_mat_t R, mu;
if (A->r == 0)
{
return;
}
m = A->r;
n = A->c;
fmpq_mat_init(R, m, m);
fmpq_mat_init(mu, m, m);
fmpz_init(r);
fmpz_init_set_ui(one, 1);
fmpq_init(chi);
fmpq_init(nu);
fmpq_init(xi);
fmpq_init(half);
fmpq_init(rat);
fmpq_set_si(half, 1, 2);
/* compute the rational GSO */
for (i = 0; i < m; i++)
{
_fmpz_vec_dot(fmpq_mat_entry_num(mu, i, i), A->rows[i], A->rows[i], n);
for (j = 0; j <= i - 1; j++)
{
_fmpz_vec_dot(fmpq_mat_entry_num(R, i, j), A->rows[i], A->rows[j],
n);
for (k = 0; k <= j - 1; k++)
{
fmpq_submul(fmpq_mat_entry(R, i, j), fmpq_mat_entry(mu, j, k),
fmpq_mat_entry(R, i, k));
}
fmpq_div(fmpq_mat_entry(mu, i, j), fmpq_mat_entry(R, i, j),
fmpq_mat_entry(mu, j, j));
fmpq_submul(fmpq_mat_entry(mu, i, i), fmpq_mat_entry(mu, i, j),
fmpq_mat_entry(R, i, j));
}
}
/* index k counts the current number of LLL-reduced rows */
k = 1;
while (k < m)
{
/* size reduce row k against row k - 1 */
fmpq_abs(rat, fmpq_mat_entry(mu, k, k - 1));
if (fmpq_cmp(rat, eta) > 0)
{
/* determine reduction coefficient */
fmpq_sub(rat, fmpq_mat_entry(mu, k, k - 1), half);
fmpz_cdiv_q(r, fmpq_numref(rat), fmpq_denref(rat));
/* perform reduction */
for (i = 0; i < n; i++)
fmpz_submul(fmpz_mat_entry(A, k, i), r,
fmpz_mat_entry(A, k - 1, i));
/* update mu */
fmpq_set_fmpz_frac(rat, r, one);
for (j = 0; j <= k - 2; j++)
fmpq_submul(fmpq_mat_entry(mu, k, j), rat,
fmpq_mat_entry(mu, k - 1, j));
fmpq_sub(fmpq_mat_entry(mu, k, k - 1),
fmpq_mat_entry(mu, k, k - 1), rat);
}
/* check exchange condition */
fmpq_set(rat, delta);
fmpq_submul(rat, fmpq_mat_entry(mu, k, k - 1),
fmpq_mat_entry(mu, k, k - 1));
fmpq_mul(rat, rat, fmpq_mat_entry(mu, k - 1, k - 1));
if (fmpq_cmp(fmpq_mat_entry(mu, k, k), rat) >= 0)
{
for (l = k - 2; l >= 0; l--)
{
/* size reduce row k against row l */
fmpq_abs(rat, fmpq_mat_entry(mu, k, l));
if (fmpq_cmp(rat, eta) > 0)
{
fmpq_sub(rat, fmpq_mat_entry(mu, k, l), half);
fmpz_cdiv_q(r, fmpq_numref(rat), fmpq_denref(rat));
for (i = 0; i < n; i++)
fmpz_submul(fmpz_mat_entry(A, k, i), r,
fmpz_mat_entry(A, l, i));
fmpq_set_fmpz_frac(rat, r, one);
for (j = 0; j <= l - 1; j++)
fmpq_submul(fmpq_mat_entry(mu, k, j), rat,
fmpq_mat_entry(mu, l, j));
fmpq_sub(fmpq_mat_entry(mu, k, l),
fmpq_mat_entry(mu, k, l), rat);
}
}
/* increment LLL-reduced index */
k++;
}
else
{
fmpq_set(nu, fmpq_mat_entry(mu, k, k - 1));
fmpq_mul(chi, fmpq_mat_entry(mu, k - 1, k - 1), nu);
fmpq_mul(chi, chi, nu);
fmpq_add(chi, chi, fmpq_mat_entry(mu, k, k));
fmpq_mul(fmpq_mat_entry(mu, k, k - 1),
fmpq_mat_entry(mu, k, k - 1), fmpq_mat_entry(mu, k - 1,
k - 1));
fmpq_div(fmpq_mat_entry(mu, k, k - 1),
fmpq_mat_entry(mu, k, k - 1), chi);
fmpq_mul(fmpq_mat_entry(mu, k, k), fmpq_mat_entry(mu, k, k),
fmpq_mat_entry(mu, k - 1, k - 1));
fmpq_div(fmpq_mat_entry(mu, k, k), fmpq_mat_entry(mu, k, k), chi);
fmpq_set(fmpq_mat_entry(mu, k - 1, k - 1), chi);
/* swap row k - 1 and row k */
fmpz_mat_swap_rows(A, NULL, k - 1, k);
/* update mu */
for (j = 0; j <= k - 2; j++)
{
fmpq_swap(fmpq_mat_entry(mu, k - 1, j),
fmpq_mat_entry(mu, k, j));
}
for (i = k + 1; i < m; i++)
{
fmpq_set(xi, fmpq_mat_entry(mu, i, k));
fmpq_set(fmpq_mat_entry(mu, i, k),
fmpq_mat_entry(mu, i, k - 1));
fmpq_submul(fmpq_mat_entry(mu, i, k), nu, xi);
fmpq_mul(fmpq_mat_entry(mu, i, k - 1),
fmpq_mat_entry(mu, k, k - 1), fmpq_mat_entry(mu, i,
k));
fmpq_add(fmpq_mat_entry(mu, i, k - 1),
fmpq_mat_entry(mu, i, k - 1), xi);
}
/* decrement LLL-reduced index */
if (k > 1)
k--;
}
}
fmpz_clear(r);
fmpz_clear(one);
fmpq_clear(chi);
fmpq_clear(nu);
fmpq_clear(xi);
fmpq_clear(half);
fmpq_clear(rat);
fmpq_mat_clear(R);
fmpq_mat_clear(mu);
}