File: fmpz_mat.h

package info (click to toggle)
flint 2.5.2-19
  • links: PTS, VCS
  • area: main
  • in suites: buster
  • size: 30,308 kB
  • sloc: ansic: 289,367; cpp: 11,210; python: 1,280; sh: 649; makefile: 283
file content (419 lines) | stat: -rw-r--r-- 15,415 bytes parent folder | download | duplicates (4)
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
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
/*=============================================================================

    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 Fredrik Johansson

******************************************************************************/

#ifndef FMPZ_MAT_H
#define FMPZ_MAT_H

#ifdef FMPZ_MAT_INLINES_C
#define FMPZ_MAT_INLINE FLINT_DLL
#else
#define FMPZ_MAT_INLINE static __inline__
#endif

#undef ulong
#define ulong ulongxx /* interferes with system includes */
#include <stdio.h>
#undef ulong

#include <gmp.h>
#define ulong mp_limb_t
#include "flint.h"
#include "fmpz.h"
#include "nmod_mat.h"
#include "d_mat.h"
#include "mpf_mat.h"
#include "fmpz_poly.h"

#ifdef __cplusplus
 extern "C" {
#endif

typedef struct
{
    fmpz * entries;
    slong r;
    slong c;
    fmpz ** rows;
} fmpz_mat_struct;

typedef fmpz_mat_struct fmpz_mat_t[1];

/* Memory management  ********************************************************/

FMPZ_MAT_INLINE
fmpz * fmpz_mat_entry(const fmpz_mat_t mat, slong i, slong j)
{
   return mat->rows[i] + j;
}

FMPZ_MAT_INLINE
slong fmpz_mat_nrows(const fmpz_mat_t mat)
{
   return mat->r;
}

FMPZ_MAT_INLINE
slong fmpz_mat_ncols(const fmpz_mat_t mat)
{
   return mat->c;
}

FLINT_DLL void fmpz_mat_init(fmpz_mat_t mat, slong rows, slong cols);
FLINT_DLL void fmpz_mat_init_set(fmpz_mat_t mat, const fmpz_mat_t src);
FLINT_DLL void fmpz_mat_swap(fmpz_mat_t mat1, fmpz_mat_t mat2);
FLINT_DLL void fmpz_mat_set(fmpz_mat_t mat1, const fmpz_mat_t mat2);
FLINT_DLL void fmpz_mat_clear(fmpz_mat_t mat);

FLINT_DLL int fmpz_mat_equal(const fmpz_mat_t mat1, const fmpz_mat_t mat2);
FLINT_DLL int fmpz_mat_is_zero(const fmpz_mat_t mat);
FLINT_DLL int fmpz_mat_is_one(const fmpz_mat_t mat);

FMPZ_MAT_INLINE
int fmpz_mat_is_empty(const fmpz_mat_t mat)
{
    return (mat->r == 0) || (mat->c == 0);
}

FMPZ_MAT_INLINE
int fmpz_mat_is_square(const fmpz_mat_t mat)
{
    return (mat->r == mat->c);
}

FLINT_DLL void fmpz_mat_zero(fmpz_mat_t mat);
FLINT_DLL void fmpz_mat_one(fmpz_mat_t mat);

/* Windows and concatenation */

FLINT_DLL void fmpz_mat_window_init(fmpz_mat_t window, const fmpz_mat_t mat, slong r1,
    slong c1, slong r2, slong c2);

FLINT_DLL void fmpz_mat_window_clear(fmpz_mat_t window);

FLINT_DLL void fmpz_mat_concat_horizontal(fmpz_mat_t res,
                           const fmpz_mat_t mat1,  const fmpz_mat_t mat2);

FLINT_DLL void fmpz_mat_concat_vertical(fmpz_mat_t res,
                           const fmpz_mat_t mat1,  const fmpz_mat_t mat2);

/* Input and output  *********************************************************/

FLINT_DLL int fmpz_mat_fprint(FILE * file, const fmpz_mat_t mat);

FLINT_DLL int fmpz_mat_fprint_pretty(FILE * file, const fmpz_mat_t mat);

FMPZ_MAT_INLINE
int fmpz_mat_print(const fmpz_mat_t mat)
{
    return fmpz_mat_fprint(stdout, mat);
}

FMPZ_MAT_INLINE
int fmpz_mat_print_pretty(const fmpz_mat_t mat)
{
    return fmpz_mat_fprint_pretty(stdout, mat);
}

FLINT_DLL int fmpz_mat_fread(FILE* file, fmpz_mat_t mat);

FMPZ_MAT_INLINE
int fmpz_mat_read(fmpz_mat_t mat)
{
    return fmpz_mat_fread(stdin, mat);
}

/* Random matrix generation  *************************************************/

FLINT_DLL void fmpz_mat_randbits(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits);
FLINT_DLL void fmpz_mat_randtest(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits);
FLINT_DLL void fmpz_mat_randtest_unsigned(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits);
FLINT_DLL void fmpz_mat_randintrel(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits);
FLINT_DLL void fmpz_mat_randsimdioph(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits, mp_bitcnt_t bits2);
FLINT_DLL void fmpz_mat_randntrulike(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits, ulong q);
FLINT_DLL void fmpz_mat_randntrulike2(fmpz_mat_t mat, flint_rand_t state, mp_bitcnt_t bits, ulong q);
FLINT_DLL void fmpz_mat_randajtai(fmpz_mat_t mat, flint_rand_t state, double alpha);
FLINT_DLL void fmpz_mat_randrank(fmpz_mat_t mat, flint_rand_t state, slong rank, mp_bitcnt_t bits);
FLINT_DLL void fmpz_mat_randdet(fmpz_mat_t mat, flint_rand_t state, const fmpz_t det);
FLINT_DLL void fmpz_mat_randops(fmpz_mat_t mat, flint_rand_t state, slong count);
FLINT_DLL int fmpz_mat_randpermdiag(fmpz_mat_t mat, flint_rand_t state, const fmpz * diag, slong n);

/* Norms */

FLINT_DLL slong fmpz_mat_max_bits(const fmpz_mat_t mat);

/* Transpose */

FLINT_DLL void fmpz_mat_transpose(fmpz_mat_t B, const fmpz_mat_t A);

/* Addition and subtraction */

FLINT_DLL void fmpz_mat_add(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B);
FLINT_DLL void fmpz_mat_sub(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B);
FLINT_DLL void fmpz_mat_neg(fmpz_mat_t B, const fmpz_mat_t A);

/* Scalar operations */
FLINT_DLL void fmpz_mat_scalar_mul_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t c);
FLINT_DLL void fmpz_mat_scalar_mul_si(fmpz_mat_t B, const fmpz_mat_t A, slong c);
FLINT_DLL void fmpz_mat_scalar_mul_ui(fmpz_mat_t B, const fmpz_mat_t A, ulong c);

FLINT_DLL void fmpz_mat_scalar_addmul_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t c);
FLINT_DLL void fmpz_mat_scalar_addmul_si(fmpz_mat_t B, const fmpz_mat_t A, slong c);
FLINT_DLL void fmpz_mat_scalar_addmul_ui(fmpz_mat_t B, const fmpz_mat_t A, ulong c);

FLINT_DLL void fmpz_mat_scalar_submul_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t c);
FLINT_DLL void fmpz_mat_scalar_submul_si(fmpz_mat_t B, const fmpz_mat_t A, slong c);
FLINT_DLL void fmpz_mat_scalar_submul_ui(fmpz_mat_t B, const fmpz_mat_t A, ulong c);

FLINT_DLL void fmpz_mat_scalar_addmul_nmod_mat_fmpz(fmpz_mat_t B, const nmod_mat_t A, const fmpz_t c);
FLINT_DLL void fmpz_mat_scalar_addmul_nmod_mat_ui(fmpz_mat_t B, const nmod_mat_t A, ulong c);

FLINT_DLL void fmpz_mat_scalar_divexact_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t c);
FLINT_DLL void fmpz_mat_scalar_divexact_si(fmpz_mat_t B, const fmpz_mat_t A, slong c);
FLINT_DLL void fmpz_mat_scalar_divexact_ui(fmpz_mat_t B, const fmpz_mat_t A, ulong c);

FLINT_DLL void fmpz_mat_scalar_mul_2exp(fmpz_mat_t B, const fmpz_mat_t A, ulong exp);
FLINT_DLL void fmpz_mat_scalar_tdiv_q_2exp(fmpz_mat_t B, const fmpz_mat_t A, ulong exp);

FLINT_DLL void fmpz_mat_scalar_mod_fmpz(fmpz_mat_t B, const fmpz_mat_t A, const fmpz_t m);

/* Multiplication */

FLINT_DLL void fmpz_mat_mul(fmpz_mat_t C, const fmpz_mat_t A, const fmpz_mat_t B);

FLINT_DLL void fmpz_mat_mul_classical(fmpz_mat_t C, const fmpz_mat_t A,
    const fmpz_mat_t B);

FLINT_DLL void fmpz_mat_mul_classical_inline(fmpz_mat_t C, const fmpz_mat_t A,
    const fmpz_mat_t B);

FLINT_DLL void _fmpz_mat_mul_multi_mod(fmpz_mat_t C, const fmpz_mat_t A,
    const fmpz_mat_t B, mp_bitcnt_t bits);

FLINT_DLL void fmpz_mat_mul_multi_mod(fmpz_mat_t C, const fmpz_mat_t A,
    const fmpz_mat_t B);

FLINT_DLL void fmpz_mat_sqr_bodrato(fmpz_mat_t B, const fmpz_mat_t A);

FLINT_DLL void fmpz_mat_sqr(fmpz_mat_t B, const fmpz_mat_t A);

FLINT_DLL void fmpz_mat_pow(fmpz_mat_t B, const fmpz_mat_t A, ulong exp);

/* Content */

FLINT_DLL void fmpz_mat_content(fmpz_t ret, const fmpz_mat_t A);

/* Permutations */

FMPZ_MAT_INLINE
void fmpz_mat_swap_rows(fmpz_mat_t mat, slong * perm, slong r, slong s)
{
    if (r != s)
    {
        fmpz * u;
        slong t;

        if (perm)
        {
            t = perm[s];
            perm[s] = perm[r];
            perm[r] = t;
        }

        u = mat->rows[s];
        mat->rows[s] = mat->rows[r];
        mat->rows[r] = u;
    }
}

/* Gaussian elimination *****************************************************/

FLINT_DLL slong fmpz_mat_find_pivot_any(const fmpz_mat_t mat,
                                    slong start_row, slong end_row, slong c);

FLINT_DLL slong fmpz_mat_fflu(fmpz_mat_t B, fmpz_t den, slong * perm,
                            const fmpz_mat_t A, int rank_check);

FLINT_DLL slong fmpz_mat_rref(fmpz_mat_t B, fmpz_t den, const fmpz_mat_t A);
FLINT_DLL slong fmpz_mat_rref_fflu(fmpz_mat_t B, fmpz_t den, const fmpz_mat_t A);
FLINT_DLL slong fmpz_mat_rref_mul(fmpz_mat_t B, fmpz_t den, const fmpz_mat_t A);
FLINT_DLL int fmpz_mat_is_in_rref_with_rank(const fmpz_mat_t A, const fmpz_t den,
        slong rank);

/* Modular gaussian elimination *********************************************/

FLINT_DLL slong fmpz_mat_rref_mod(slong * perm, fmpz_mat_t A, const fmpz_t p);

/* Trace ********************************************************************/

FLINT_DLL void fmpz_mat_trace(fmpz_t trace, const fmpz_mat_t mat);

/* Determinant **************************************************************/

FLINT_DLL void fmpz_mat_det(fmpz_t det, const fmpz_mat_t A);

FLINT_DLL void fmpz_mat_det_cofactor(fmpz_t det, const fmpz_mat_t A);
FLINT_DLL void _fmpz_mat_det_cofactor_2x2(fmpz_t det, fmpz ** const x);
FLINT_DLL void _fmpz_mat_det_cofactor_3x3(fmpz_t det, fmpz ** const x);
FLINT_DLL void _fmpz_mat_det_cofactor_4x4(fmpz_t det, fmpz ** const x);

FLINT_DLL void fmpz_mat_det_bareiss(fmpz_t det, const fmpz_mat_t A);

FLINT_DLL void fmpz_mat_det_modular(fmpz_t det, const fmpz_mat_t A, int proved);

FLINT_DLL void fmpz_mat_det_modular_accelerated(fmpz_t det,
    const fmpz_mat_t A, int proved);

FLINT_DLL void fmpz_mat_det_modular_given_divisor(fmpz_t det, const fmpz_mat_t A,
        const fmpz_t d, int proved);

FLINT_DLL void fmpz_mat_det_bound(fmpz_t bound, const fmpz_mat_t A);
FLINT_DLL void fmpz_mat_det_divisor(fmpz_t d, const fmpz_mat_t A);

/* Characteristic polynomial ************************************************/

FLINT_DLL void _fmpz_mat_charpoly(fmpz *cp, const fmpz_mat_t mat);
FLINT_DLL void fmpz_mat_charpoly(fmpz_poly_t cp, const fmpz_mat_t mat);

/* Rank *********************************************************************/

FLINT_DLL slong fmpz_mat_rank(const fmpz_mat_t A);

/* Nonsingular solving ******************************************************/

FLINT_DLL void fmpz_mat_solve_bound(fmpz_t N, fmpz_t D,
        const fmpz_mat_t A, const fmpz_mat_t B);

FLINT_DLL int fmpz_mat_solve(fmpz_mat_t X, fmpz_t den,
        const fmpz_mat_t A, const fmpz_mat_t B);

FLINT_DLL int fmpz_mat_solve_cramer(fmpz_mat_t X, fmpz_t den,
        const fmpz_mat_t A, const fmpz_mat_t B);

FLINT_DLL int fmpz_mat_solve_fflu(fmpz_mat_t X, fmpz_t den,
        const fmpz_mat_t A, const fmpz_mat_t B);

FLINT_DLL void fmpz_mat_solve_fflu_precomp(fmpz_mat_t X, const slong * perm,
        const fmpz_mat_t FFLU, const fmpz_mat_t B);

FLINT_DLL int fmpz_mat_solve_dixon(fmpz_mat_t X, fmpz_t mod,
        const fmpz_mat_t A, const fmpz_mat_t B);

/* Nullspace ****************************************************************/

FLINT_DLL slong fmpz_mat_nullspace(fmpz_mat_t res, const fmpz_mat_t mat);

/* Inverse ******************************************************************/

FLINT_DLL int fmpz_mat_inv(fmpz_mat_t B, fmpz_t den, const fmpz_mat_t A);

/* Modular reduction and reconstruction *************************************/

FLINT_DLL void fmpz_mat_set_nmod_mat(fmpz_mat_t A, const nmod_mat_t Amod);

FLINT_DLL void fmpz_mat_set_nmod_mat_unsigned(fmpz_mat_t A, const nmod_mat_t Amod);

FLINT_DLL void fmpz_mat_get_nmod_mat(nmod_mat_t Amod, const fmpz_mat_t A);

FLINT_DLL void fmpz_mat_CRT_ui(fmpz_mat_t res, const fmpz_mat_t mat1,
                        const fmpz_t m1, const nmod_mat_t mat2, int sign);

FLINT_DLL void fmpz_mat_multi_mod_ui_precomp(nmod_mat_t * residues, slong nres, 
    const fmpz_mat_t mat, const fmpz_comb_t comb, fmpz_comb_temp_t temp);

FLINT_DLL void fmpz_mat_multi_mod_ui(nmod_mat_t * residues, slong nres, const fmpz_mat_t mat);


FLINT_DLL void fmpz_mat_multi_CRT_ui_precomp(fmpz_mat_t mat,
    nmod_mat_t * const residues, slong nres,
    const fmpz_comb_t comb, fmpz_comb_temp_t temp, int sign);

FLINT_DLL void fmpz_mat_multi_CRT_ui(fmpz_mat_t mat, nmod_mat_t * const residues,
    slong nres, int sign);

/* HNF and SNF **************************************************************/

FLINT_DLL void fmpz_mat_hnf(fmpz_mat_t H, const fmpz_mat_t A);
FLINT_DLL void fmpz_mat_hnf_transform(fmpz_mat_t H, fmpz_mat_t U, const fmpz_mat_t A);
FLINT_DLL void fmpz_mat_hnf_classical(fmpz_mat_t H, const fmpz_mat_t A);
FLINT_DLL void fmpz_mat_hnf_xgcd(fmpz_mat_t H, const fmpz_mat_t A);
FLINT_DLL void fmpz_mat_hnf_minors(fmpz_mat_t H, const fmpz_mat_t A);
FLINT_DLL void fmpz_mat_hnf_modular(fmpz_mat_t H, const fmpz_mat_t A, const fmpz_t D);
FLINT_DLL int fmpz_mat_hnf_pernet_stein(fmpz_mat_t H, const fmpz_mat_t A, flint_rand_t state);
FLINT_DLL int fmpz_mat_is_in_hnf(const fmpz_mat_t A);

FLINT_DLL void fmpz_mat_snf(fmpz_mat_t S, const fmpz_mat_t A);
FLINT_DLL void fmpz_mat_snf_diagonal(fmpz_mat_t S, const fmpz_mat_t A);
FLINT_DLL void fmpz_mat_snf_kannan_bachem(fmpz_mat_t S, const fmpz_mat_t A);
FLINT_DLL void fmpz_mat_snf_iliopoulos(fmpz_mat_t S, const fmpz_mat_t A,
        const fmpz_t mod);
FLINT_DLL int fmpz_mat_is_in_snf(const fmpz_mat_t A);

/* Special matrices **********************************************************/

FLINT_DLL int fmpz_mat_is_hadamard(const fmpz_mat_t A);

FLINT_DLL int fmpz_mat_hadamard(fmpz_mat_t A);

/* Gram matrix **************************************************************/

FLINT_DLL void fmpz_mat_gram(fmpz_mat_t B, const fmpz_mat_t A);

/* Conversions **************************************************************/

FLINT_DLL int fmpz_mat_get_d_mat(d_mat_t B, const fmpz_mat_t A);

FLINT_DLL int fmpz_mat_get_d_mat_transpose(d_mat_t B, const fmpz_mat_t A);

FLINT_DLL void fmpz_mat_get_mpf_mat(mpf_mat_t B, const fmpz_mat_t A);

/* Cholesky Decomposition ****************************************************/

FLINT_DLL void fmpz_mat_chol_d(d_mat_t R, const fmpz_mat_t A);

/* LLL ***********************************************************************/

FLINT_DLL int fmpz_mat_is_reduced(const fmpz_mat_t A, double delta, double eta);

FLINT_DLL int fmpz_mat_is_reduced_gram(const fmpz_mat_t A, double delta, double eta);

FLINT_DLL int fmpz_mat_is_reduced_with_removal(const fmpz_mat_t A, double delta, double eta, const fmpz_t gs_B, int newd);

FLINT_DLL int fmpz_mat_is_reduced_gram_with_removal(const fmpz_mat_t A, double delta, double eta, const fmpz_t gs_B, int newd);

/* Classical LLL *************************************************************/

FLINT_DLL void fmpz_mat_lll_original(fmpz_mat_t A, const fmpq_t delta, const fmpq_t eta);

/* Modified LLL **************************************************************/

FLINT_DLL void fmpz_mat_lll_storjohann(fmpz_mat_t A, const fmpq_t delta, const fmpq_t eta);

#ifdef __cplusplus
}
#endif

#endif