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/*
Copyright (C) 2020 Fredrik Johansson
This file is part of Calcium.
Calcium 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 "ca_mat.h"
int
ca_mat_right_kernel(ca_mat_t X, const ca_mat_t A, ca_ctx_t ctx)
{
slong i, j, k, m, n, rank, nullity;
slong *p;
slong *pivots;
slong *nonpivots;
ca_mat_t tmp;
int success;
m = ca_mat_nrows(A);
n = ca_mat_ncols(A);
p = flint_malloc(sizeof(slong) * FLINT_MAX(m, n));
ca_mat_init(tmp, m, n, ctx);
success = ca_mat_rref(&rank, tmp, A, ctx);
nullity = n - rank;
if (!success)
goto cleanup;
ca_mat_clear(X, ctx);
ca_mat_init(X, n, nullity, ctx);
success = 1;
if (rank == 0)
{
for (i = 0; i < nullity; i++)
ca_one(ca_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 (1)
{
/* Todo: this should not be T_UNKNOWN. Should we save
the pivot data in the lu algorithm? */
truth_t is_zero = ca_check_is_zero(ca_mat_entry(tmp, i, j), ctx);
if (is_zero == T_FALSE)
{
break;
}
else if (is_zero == T_TRUE)
{
nonpivots[k] = j;
k++;
j++;
}
else
{
success = 0;
goto cleanup;
}
}
pivots[i] = j;
j++;
}
while (k < n - rank)
{
nonpivots[k] = j;
k++;
j++;
}
for (i = 0; i < nullity; i++)
{
for (j = 0; j < rank; j++)
ca_neg(ca_mat_entry(X, pivots[j], i), ca_mat_entry(tmp, j, nonpivots[i]), ctx);
ca_one(ca_mat_entry(X, nonpivots[i], i), ctx);
}
}
cleanup:
flint_free(p);
ca_mat_clear(tmp, ctx);
return success;
}
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