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/*
Copyright (C) 2011 Fredrik Johansson
Copyright (C) 2013 Mike Hansen
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/>.
*/
#ifdef T
#include "templates.h"
slong
TEMPLATE(T, mat_nullspace) (TEMPLATE(T, mat_t) X, const TEMPLATE(T, mat_t) A,
const TEMPLATE(T, ctx_t) ctx)
{
slong i, j, k, m, n, rank, nullity;
slong *p;
slong *pivots;
slong *nonpivots;
TEMPLATE(T, mat_t) tmp;
m = A->r;
n = A->c;
p = flint_malloc(sizeof(slong) * FLINT_MAX(m, n));
TEMPLATE(T, mat_init_set) (tmp, A, ctx);
rank = TEMPLATE(T, mat_rref) (tmp, tmp, ctx);
nullity = n - rank;
TEMPLATE(T, mat_zero) (X, ctx);
if (rank == 0)
{
for (i = 0; i < nullity; i++)
TEMPLATE(T, one) (TEMPLATE(T, mat_entry) (X, i, i), ctx);
}
else if (nullity)
{
pivots = p; /* length = rank */
nonpivots = p + rank; /* length = nullity */
for (i = j = k = 0; i < rank; i++)
{
while (TEMPLATE(T, is_zero)
(TEMPLATE(T, mat_entry) (tmp, i, j), ctx))
{
nonpivots[k] = j;
k++;
j++;
}
pivots[i] = j;
j++;
}
while (k < nullity)
{
nonpivots[k] = j;
k++;
j++;
}
for (i = 0; i < nullity; i++)
{
for (j = 0; j < rank; j++)
{
TEMPLATE(T, neg) (TEMPLATE(T, mat_entry) (X, pivots[j], i),
TEMPLATE(T, mat_entry) (tmp, j,
nonpivots[i]), ctx);
}
TEMPLATE(T, one) (TEMPLATE(T, mat_entry) (X, nonpivots[i], i),
ctx);
}
}
flint_free(p);
TEMPLATE(T, mat_clear) (tmp, ctx);
return nullity;
}
#endif