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/*
Copyright (C) 2014 Alex J. Best
Copyright (C) 2017 Tommy Hofmann
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 "fmpz.h"
#include "fmpz_mat.h"
/*
This is the algorithm of Kannan, Bachem, "Polynomial algorithms for computing
the Smith and Hermite normal forms of an integer matrix", Siam J. Comput.,
Vol. 8, No. 4, pp. 499-507.
*/
void
fmpz_mat_hnf_minors_transform(fmpz_mat_t H, fmpz_mat_t U, const fmpz_mat_t A)
{
slong j, j2, i, k, l, m, n;
fmpz_t u, v, d, r2d, r1d, q, b;
m = fmpz_mat_nrows(A);
n = fmpz_mat_ncols(A);
fmpz_init(u);
fmpz_init(v);
fmpz_init(d);
fmpz_init(r1d);
fmpz_init(r2d);
fmpz_init(q);
fmpz_init(b);
fmpz_mat_set(H, A);
fmpz_mat_one(U);
/* put the kth principal minor in HNF */
for (k = 0, l = m - 1; k < n; k++)
{
for (j = 0; j < k; j++)
{
if (fmpz_is_zero(fmpz_mat_entry(H, k, j)))
{
continue;
}
fmpz_xgcd(d, u, v, fmpz_mat_entry(H, j, j),
fmpz_mat_entry(H, k, j));
if (fmpz_cmpabs(d, fmpz_mat_entry(H, j, j)) == 0)
{
fmpz_divexact(b, fmpz_mat_entry(H, k, j), fmpz_mat_entry(H, j, j));
for (j2 = j; j2 < n; j2++)
{
fmpz_submul(fmpz_mat_entry(H, k, j2), b, fmpz_mat_entry(H, j, j2));
}
for (j2 = 0; j2 < m; j2++)
{
fmpz_submul(fmpz_mat_entry(U, k, j2), b, fmpz_mat_entry(U, j, j2));
}
continue;
}
fmpz_divexact(r1d, fmpz_mat_entry(H, j, j), d);
fmpz_divexact(r2d, fmpz_mat_entry(H, k, j), d);
for (j2 = j; j2 < n; j2++)
{
fmpz_mul(b, u, fmpz_mat_entry(H, j, j2));
fmpz_addmul(b, v, fmpz_mat_entry(H, k, j2));
fmpz_mul(fmpz_mat_entry(H, k, j2), r1d,
fmpz_mat_entry(H, k, j2));
fmpz_submul(fmpz_mat_entry(H, k, j2), r2d,
fmpz_mat_entry(H, j, j2));
fmpz_set(fmpz_mat_entry(H, j, j2), b);
}
for (j2 = 0; j2 < m; j2++)
{
fmpz_mul(b, u, fmpz_mat_entry(U, j, j2));
fmpz_addmul(b, v, fmpz_mat_entry(U, k, j2));
fmpz_mul(fmpz_mat_entry(U, k, j2), r1d,
fmpz_mat_entry(U, k, j2));
fmpz_submul(fmpz_mat_entry(U, k, j2), r2d,
fmpz_mat_entry(U, j, j2));
fmpz_set(fmpz_mat_entry(U, j, j2), b);
}
}
/* if H_k,k is zero we swap row k for some other row (starting with the
last) */
if (fmpz_is_zero(fmpz_mat_entry(H, k, k)))
{
fmpz_mat_swap_rows(H, NULL, k, l);
fmpz_mat_swap_rows(U, NULL, k, l);
l--;
k--;
continue;
}
/* ensure H_k,k is positive */
if (fmpz_sgn(fmpz_mat_entry(H, k, k)) < 0)
{
for (j = k; j < n; j++)
{
fmpz_neg(fmpz_mat_entry(H, k, j), fmpz_mat_entry(H, k, j));
}
for (j = 0; j < m; j++)
{
fmpz_neg(fmpz_mat_entry(U, k, j), fmpz_mat_entry(U, k, j));
}
}
/* reduce above diagonal elements of each row i */
for (i = k - 1; i >= 0; i--)
{
for (j = i + 1; j <= k; j++)
{
fmpz_fdiv_q(q, fmpz_mat_entry(H, i, j),
fmpz_mat_entry(H, j, j));
if (fmpz_is_zero(q))
{
continue;
}
for (j2 = j; j2 < n; j2++)
{
fmpz_submul(fmpz_mat_entry(H, i, j2), q,
fmpz_mat_entry(H, j, j2));
}
for (j2 = 0; j2 < m; j2++)
{
fmpz_submul(fmpz_mat_entry(U, i, j2), q,
fmpz_mat_entry(U, j, j2));
}
}
}
l = m - 1;
}
/* reduce final rows */
for (k = n; k < m; k++)
{
for (j = 0; j < n; j++)
{
fmpz_xgcd(d, u, v, fmpz_mat_entry(H, j, j),
fmpz_mat_entry(H, k, j));
if (fmpz_cmpabs(d, fmpz_mat_entry(H, j, j)) == 0)
{
fmpz_divexact(b, fmpz_mat_entry(H, k, j), fmpz_mat_entry(H, j, j));
for (j2 = j; j2 < n; j2++)
{
fmpz_submul(fmpz_mat_entry(H, k, j2), b, fmpz_mat_entry(H, j, j2));
}
for (j2 = 0; j2 < m; j2++)
{
fmpz_submul(fmpz_mat_entry(U, k, j2), b, fmpz_mat_entry(U, j, j2));
}
continue;
}
fmpz_divexact(r1d, fmpz_mat_entry(H, j, j), d);
fmpz_divexact(r2d, fmpz_mat_entry(H, k, j), d);
for (j2 = j; j2 < n; j2++)
{
fmpz_mul(b, u, fmpz_mat_entry(H, j, j2));
fmpz_addmul(b, v, fmpz_mat_entry(H, k, j2));
fmpz_mul(fmpz_mat_entry(H, k, j2), r1d,
fmpz_mat_entry(H, k, j2));
fmpz_submul(fmpz_mat_entry(H, k, j2), r2d,
fmpz_mat_entry(H, j, j2));
fmpz_set(fmpz_mat_entry(H, j, j2), b);
}
for (j2 = 0; j2 < m; j2++)
{
fmpz_mul(b, u, fmpz_mat_entry(U, j, j2));
fmpz_addmul(b, v, fmpz_mat_entry(U, k, j2));
fmpz_mul(fmpz_mat_entry(U, k, j2), r1d,
fmpz_mat_entry(U, k, j2));
fmpz_submul(fmpz_mat_entry(U, k, j2), r2d,
fmpz_mat_entry(U, j, j2));
fmpz_set(fmpz_mat_entry(U, j, j2), b);
}
}
/* reduce above diagonal elements of each row i */
for (i = n - 1; i >= 0; i--)
{
for (j = i + 1; j < n; j++)
{
fmpz_fdiv_q(q, fmpz_mat_entry(H, i, j),
fmpz_mat_entry(H, j, j));
if (fmpz_is_zero(q))
{
continue;
}
for (j2 = j; j2 < n; j2++)
{
fmpz_submul(fmpz_mat_entry(H, i, j2), q,
fmpz_mat_entry(H, j, j2));
}
for (j2 = 0; j2 < m; j2++)
{
fmpz_submul(fmpz_mat_entry(U, i, j2), q,
fmpz_mat_entry(U, j, j2));
}
}
}
}
fmpz_clear(b);
fmpz_clear(q);
fmpz_clear(r2d);
fmpz_clear(r1d);
fmpz_clear(d);
fmpz_clear(v);
fmpz_clear(u);
}