forked from SPancratz/flint2
-
Notifications
You must be signed in to change notification settings - Fork 0
/
nmod_mat.h
215 lines (150 loc) · 6.59 KB
/
nmod_mat.h
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
/*=============================================================================
This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
FLINT is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2010 William Hart
Copyright (C) 2010,2011 Fredrik Johansson
******************************************************************************/
#ifndef NMOD_MAT_H
#define NMOD_MAT_H
#undef ulong /* interferes with system includes */
#include <stdlib.h>
#define ulong unsigned long
#include <gmp.h>
#include "flint.h"
#include "longlong.h"
#include "ulong_extras.h"
#include "nmod_vec.h"
#ifdef __cplusplus
extern "C" {
#endif
typedef struct
{
mp_limb_t * entries;
long r;
long c;
mp_limb_t ** rows;
nmod_t mod;
}
nmod_mat_struct;
/* nmod_mat_t allows reference-like semantics for nmod_mat_struct */
typedef nmod_mat_struct nmod_mat_t[1];
#define nmod_mat_entry(mat,i,j) ((mat)->rows[(i)][(j)])
#define nmod_mat_nrows(mat) ((mat)->r)
#define nmod_mat_ncols(mat) ((mat)->c)
static __inline__
void
_nmod_mat_set_mod(nmod_mat_t mat, mp_limb_t n)
{
mat->mod.n = n;
mat->mod.ninv = n_preinvert_limb(n);
count_leading_zeros(mat->mod.norm, n);
}
/* Memory management */
void nmod_mat_init(nmod_mat_t mat, long rows, long cols, mp_limb_t n);
void nmod_mat_init_set(nmod_mat_t mat, const nmod_mat_t src);
void nmod_mat_clear(nmod_mat_t mat);
void nmod_mat_window_init(nmod_mat_t window, const nmod_mat_t mat, long r1, long c1, long r2, long c2);
void nmod_mat_window_clear(nmod_mat_t window);
/* Random matrix generation */
void nmod_mat_randtest(nmod_mat_t mat, flint_rand_t state);
void nmod_mat_randfull(nmod_mat_t mat, flint_rand_t state);
int nmod_mat_randpermdiag(nmod_mat_t mat, flint_rand_t state,
mp_srcptr diag, long n);
void nmod_mat_randrank(nmod_mat_t, flint_rand_t state, long rank);
void nmod_mat_randops(nmod_mat_t mat, long count, flint_rand_t state);
void nmod_mat_randtril(nmod_mat_t mat, flint_rand_t state, int unit);
void nmod_mat_randtriu(nmod_mat_t mat, flint_rand_t state, int unit);
void nmod_mat_print_pretty(const nmod_mat_t mat);
int nmod_mat_equal(const nmod_mat_t mat1, const nmod_mat_t mat2);
void nmod_mat_zero(nmod_mat_t mat);
int nmod_mat_is_zero(const nmod_mat_t mat);
static __inline__ int
nmod_mat_is_empty(const nmod_mat_t mat)
{
return (mat->r == 0) || (mat->c == 0);
}
static __inline__ int
nmod_mat_is_square(const nmod_mat_t mat)
{
return (mat->r == mat->c);
}
void nmod_mat_set(nmod_mat_t B, const nmod_mat_t A);
void nmod_mat_transpose(nmod_mat_t B, const nmod_mat_t A);
/* Addition and subtraction */
void nmod_mat_add(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B);
void nmod_mat_sub(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B);
void nmod_mat_neg(nmod_mat_t B, const nmod_mat_t A);
/* Matrix-scalar arithmetic */
void nmod_mat_scalar_mul(nmod_mat_t B, const nmod_mat_t A, mp_limb_t c);
/* Matrix multiplication */
void nmod_mat_mul(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B);
void nmod_mat_mul_classical(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B);
void nmod_mat_mul_strassen(nmod_mat_t C, const nmod_mat_t A, const nmod_mat_t B);
void
_nmod_mat_mul_classical(nmod_mat_t D, const nmod_mat_t C,
const nmod_mat_t A, const nmod_mat_t B, int op);
void nmod_mat_addmul(nmod_mat_t D, const nmod_mat_t C,
const nmod_mat_t A, const nmod_mat_t B);
void nmod_mat_submul(nmod_mat_t D, const nmod_mat_t C,
const nmod_mat_t A, const nmod_mat_t B);
/* Trace */
mp_limb_t nmod_mat_trace(const nmod_mat_t mat);
/* Determinant */
mp_limb_t _nmod_mat_det(nmod_mat_t A);
mp_limb_t nmod_mat_det(const nmod_mat_t A);
/* Rank */
long nmod_mat_rank(const nmod_mat_t A);
/* Inverse */
int nmod_mat_inv(nmod_mat_t B, const nmod_mat_t A);
/* Triangular solving */
void nmod_mat_solve_tril(nmod_mat_t X, const nmod_mat_t L, const nmod_mat_t B, int unit);
void nmod_mat_solve_tril_recursive(nmod_mat_t X, const nmod_mat_t L, const nmod_mat_t B, int unit);
void nmod_mat_solve_tril_classical(nmod_mat_t X, const nmod_mat_t L, const nmod_mat_t B, int unit);
void nmod_mat_solve_triu(nmod_mat_t X, const nmod_mat_t U, const nmod_mat_t B, int unit);
void nmod_mat_solve_triu_recursive(nmod_mat_t X, const nmod_mat_t U, const nmod_mat_t B, int unit);
void nmod_mat_solve_triu_classical(nmod_mat_t X, const nmod_mat_t U, const nmod_mat_t B, int unit);
/* LU decomposition */
long nmod_mat_lu(long * P, nmod_mat_t A, int rank_check);
long nmod_mat_lu_classical(long * P, nmod_mat_t A, int rank_check);
long nmod_mat_lu_recursive(long * P, nmod_mat_t A, int rank_check);
/* Nonsingular solving */
int nmod_mat_solve(nmod_mat_t X, const nmod_mat_t A, const nmod_mat_t B);
int nmod_mat_solve_vec(mp_ptr x, const nmod_mat_t A, mp_srcptr b);
/* Reduced row echelon form */
long nmod_mat_rref(nmod_mat_t A);
/* Nullspace */
long nmod_mat_nullspace(nmod_mat_t X, const nmod_mat_t A);
/* Tuning parameters *********************************************************/
/* Size at which pre-transposing becomes faster in classical multiplication */
#define NMOD_MAT_MUL_TRANSPOSE_CUTOFF 20
/* Strassen multiplication */
#define NMOD_MAT_MUL_STRASSEN_CUTOFF 256
/* Cutoff between classical and recursive triangular solving */
#define NMOD_MAT_SOLVE_TRI_ROWS_CUTOFF 64
#define NMOD_MAT_SOLVE_TRI_COLS_CUTOFF 64
/* Cutoff between classical and recursive LU decomposition */
#define NMOD_MAT_LU_RECURSIVE_CUTOFF 4
/*
Suggested initial modulus size for multimodular algorithms. This should
be chosen so that we get the most number of bits per cycle
in matrix multiplication. On x86-64 it appears to be optimal to use
moduli giving nlimbs = 2. This should hold both in the classical
range and in Strassen blocks.
*/
#define NMOD_MAT_OPTIMAL_MODULUS_BITS (FLINT_BITS-5)
#ifdef __cplusplus
}
#endif
#endif