1 /*
2 Copyright (C) 2011 Fredrik Johansson
3 Copyright (C) 2013 Mike Hansen
4
5 This file is part of FLINT.
6
7 FLINT is free software: you can redistribute it and/or modify it under
8 the terms of the GNU Lesser General Public License (LGPL) as published
9 by the Free Software Foundation; either version 2.1 of the License, or
10 (at your option) any later version. See <http://www.gnu.org/licenses/>.
11 */
12
13 #ifdef T
14
15 #include "templates.h"
16
17 slong
TEMPLATE(T,mat_nullspace)18 TEMPLATE(T, mat_nullspace) (TEMPLATE(T, mat_t) X, const TEMPLATE(T, mat_t) A,
19 const TEMPLATE(T, ctx_t) ctx)
20 {
21 slong i, j, k, m, n, rank, nullity;
22 slong *p;
23 slong *pivots;
24 slong *nonpivots;
25 TEMPLATE(T, mat_t) tmp;
26
27 m = A->r;
28 n = A->c;
29
30 p = flint_malloc(sizeof(slong) * FLINT_MAX(m, n));
31
32 TEMPLATE(T, mat_init_set) (tmp, A, ctx);
33 rank = TEMPLATE(T, mat_rref) (tmp, ctx);
34 nullity = n - rank;
35
36 TEMPLATE(T, mat_zero) (X, ctx);
37
38 if (rank == 0)
39 {
40 for (i = 0; i < nullity; i++)
41 TEMPLATE(T, one) (TEMPLATE(T, mat_entry) (X, i, i), ctx);
42 }
43 else if (nullity)
44 {
45 pivots = p; /* length = rank */
46 nonpivots = p + rank; /* length = nullity */
47
48 for (i = j = k = 0; i < rank; i++)
49 {
50 while (TEMPLATE(T, is_zero)
51 (TEMPLATE(T, mat_entry) (tmp, i, j), ctx))
52 {
53 nonpivots[k] = j;
54 k++;
55 j++;
56 }
57 pivots[i] = j;
58 j++;
59 }
60 while (k < nullity)
61 {
62 nonpivots[k] = j;
63 k++;
64 j++;
65 }
66
67 for (i = 0; i < nullity; i++)
68 {
69 for (j = 0; j < rank; j++)
70 {
71 TEMPLATE(T, neg) (TEMPLATE(T, mat_entry) (X, pivots[j], i),
72 TEMPLATE(T, mat_entry) (tmp, j,
73 nonpivots[i]), ctx);
74 }
75
76 TEMPLATE(T, one) (TEMPLATE(T, mat_entry) (X, nonpivots[i], i),
77 ctx);
78 }
79 }
80
81 flint_free(p);
82 TEMPLATE(T, mat_clear) (tmp, ctx);
83
84 return nullity;
85 }
86
87 #endif
88