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isl_mat_vec_product: add memory management annotations
[isl.git] / isl_mat.c
blob98873a45da31087685339c320cc08024150bf7d5
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2014 Ecole Normale Superieure
4 *
5 * Use of this software is governed by the MIT license
6 *
7 * Written by Sven Verdoolaege, K.U.Leuven, Departement
8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
9 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
10 */
11
12 #include <isl_ctx_private.h>
13 #include <isl_map_private.h>
14 #include <isl/space.h>
15 #include <isl_seq.h>
16 #include <isl_mat_private.h>
17 #include <isl_vec_private.h>
18 #include <isl_space_private.h>
19 #include <isl_val_private.h>
20 #include <isl/deprecated/mat_int.h>
21
22 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat)
23 {
24 return mat ? mat->ctx : NULL;
25 }
26
27 /* Return a hash value that digests "mat".
28 */
29 uint32_t isl_mat_get_hash(__isl_keep isl_mat *mat)
30 {
31 int i;
32 uint32_t hash;
33
34 if (!mat)
35 return 0;
36
37 hash = isl_hash_init();
38 isl_hash_byte(hash, mat->n_row & 0xFF);
39 isl_hash_byte(hash, mat->n_col & 0xFF);
40 for (i = 0; i < mat->n_row; ++i) {
41 uint32_t row_hash;
42
43 row_hash = isl_seq_get_hash(mat->row[i], mat->n_col);
44 isl_hash_hash(hash, row_hash);
45 }
46
47 return hash;
48 }
49
50 struct isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
51 unsigned n_row, unsigned n_col)
52 {
53 int i;
54 struct isl_mat *mat;
55
56 mat = isl_alloc_type(ctx, struct isl_mat);
57 if (!mat)
58 return NULL;
59
60 mat->row = NULL;
61 mat->block = isl_blk_alloc(ctx, n_row * n_col);
62 if (isl_blk_is_error(mat->block))
63 goto error;
64 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
65 if (n_row && !mat->row)
66 goto error;
67
68 for (i = 0; i < n_row; ++i)
69 mat->row[i] = mat->block.data + i * n_col;
70
71 mat->ctx = ctx;
72 isl_ctx_ref(ctx);
73 mat->ref = 1;
74 mat->n_row = n_row;
75 mat->n_col = n_col;
76 mat->max_col = n_col;
77 mat->flags = 0;
78
79 return mat;
80 error:
81 isl_blk_free(ctx, mat->block);
82 free(mat);
83 return NULL;
84 }
85
86 struct isl_mat *isl_mat_extend(struct isl_mat *mat,
87 unsigned n_row, unsigned n_col)
88 {
89 int i;
90 isl_int *old;
91 isl_int **row;
92
93 if (!mat)
94 return NULL;
95
96 if (mat->max_col >= n_col && mat->n_row >= n_row) {
97 if (mat->n_col < n_col)
98 mat->n_col = n_col;
99 return mat;
100 }
101
102 if (mat->max_col < n_col) {
103 struct isl_mat *new_mat;
104
105 if (n_row < mat->n_row)
106 n_row = mat->n_row;
107 new_mat = isl_mat_alloc(mat->ctx, n_row, n_col);
108 if (!new_mat)
109 goto error;
110 for (i = 0; i < mat->n_row; ++i)
111 isl_seq_cpy(new_mat->row[i], mat->row[i], mat->n_col);
112 isl_mat_free(mat);
113 return new_mat;
114 }
115
116 mat = isl_mat_cow(mat);
117 if (!mat)
118 goto error;
119
120 old = mat->block.data;
121 mat->block = isl_blk_extend(mat->ctx, mat->block, n_row * mat->max_col);
122 if (isl_blk_is_error(mat->block))
123 goto error;
124 row = isl_realloc_array(mat->ctx, mat->row, isl_int *, n_row);
125 if (n_row && !row)
126 goto error;
127 mat->row = row;
128
129 for (i = 0; i < mat->n_row; ++i)
130 mat->row[i] = mat->block.data + (mat->row[i] - old);
131 for (i = mat->n_row; i < n_row; ++i)
132 mat->row[i] = mat->block.data + i * mat->max_col;
133 mat->n_row = n_row;
134 if (mat->n_col < n_col)
135 mat->n_col = n_col;
136
137 return mat;
138 error:
139 isl_mat_free(mat);
140 return NULL;
141 }
142
143 __isl_give isl_mat *isl_mat_sub_alloc6(isl_ctx *ctx, isl_int **row,
144 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
145 {
146 int i;
147 struct isl_mat *mat;
148
149 mat = isl_alloc_type(ctx, struct isl_mat);
150 if (!mat)
151 return NULL;
152 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
153 if (n_row && !mat->row)
154 goto error;
155 for (i = 0; i < n_row; ++i)
156 mat->row[i] = row[first_row+i] + first_col;
157 mat->ctx = ctx;
158 isl_ctx_ref(ctx);
159 mat->ref = 1;
160 mat->n_row = n_row;
161 mat->n_col = n_col;
162 mat->block = isl_blk_empty();
163 mat->flags = ISL_MAT_BORROWED;
164 return mat;
165 error:
166 free(mat);
167 return NULL;
168 }
169
170 __isl_give isl_mat *isl_mat_sub_alloc(__isl_keep isl_mat *mat,
171 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
172 {
173 if (!mat)
174 return NULL;
175 return isl_mat_sub_alloc6(mat->ctx, mat->row, first_row, n_row,
176 first_col, n_col);
177 }
178
179 void isl_mat_sub_copy(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
180 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
181 {
182 int i;
183
184 for (i = 0; i < n_row; ++i)
185 isl_seq_cpy(dst[i]+dst_col, src[i]+src_col, n_col);
186 }
187
188 void isl_mat_sub_neg(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
189 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
190 {
191 int i;
192
193 for (i = 0; i < n_row; ++i)
194 isl_seq_neg(dst[i]+dst_col, src[i]+src_col, n_col);
195 }
196
197 struct isl_mat *isl_mat_copy(struct isl_mat *mat)
198 {
199 if (!mat)
200 return NULL;
201
202 mat->ref++;
203 return mat;
204 }
205
206 struct isl_mat *isl_mat_dup(struct isl_mat *mat)
207 {
208 int i;
209 struct isl_mat *mat2;
210
211 if (!mat)
212 return NULL;
213 mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
214 if (!mat2)
215 return NULL;
216 for (i = 0; i < mat->n_row; ++i)
217 isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);
218 return mat2;
219 }
220
221 struct isl_mat *isl_mat_cow(struct isl_mat *mat)
222 {
223 struct isl_mat *mat2;
224 if (!mat)
225 return NULL;
226
227 if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))
228 return mat;
229
230 mat2 = isl_mat_dup(mat);
231 isl_mat_free(mat);
232 return mat2;
233 }
234
235 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat)
236 {
237 if (!mat)
238 return NULL;
239
240 if (--mat->ref > 0)
241 return NULL;
242
243 if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))
244 isl_blk_free(mat->ctx, mat->block);
245 isl_ctx_deref(mat->ctx);
246 free(mat->row);
247 free(mat);
248
249 return NULL;
250 }
251
252 int isl_mat_rows(__isl_keep isl_mat *mat)
253 {
254 return mat ? mat->n_row : -1;
255 }
256
257 int isl_mat_cols(__isl_keep isl_mat *mat)
258 {
259 return mat ? mat->n_col : -1;
260 }
261
262 /* Check that "col" is a valid column position for "mat".
263 */
264 static isl_stat check_col(__isl_keep isl_mat *mat, int col)
265 {
266 if (!mat)
267 return isl_stat_error;
268 if (col < 0 || col >= mat->n_col)
269 isl_die(isl_mat_get_ctx(mat), isl_error_invalid,
270 "column out of range", return isl_stat_error);
271 return isl_stat_ok;
272 }
273
274 int isl_mat_get_element(__isl_keep isl_mat *mat, int row, int col, isl_int *v)
275 {
276 if (!mat)
277 return -1;
278 if (row < 0 || row >= mat->n_row)
279 isl_die(mat->ctx, isl_error_invalid, "row out of range",
280 return -1);
281 if (check_col(mat, col) < 0)
282 return -1;
283 isl_int_set(*v, mat->row[row][col]);
284 return 0;
285 }
286
287 /* Extract the element at row "row", oolumn "col" of "mat".
288 */
289 __isl_give isl_val *isl_mat_get_element_val(__isl_keep isl_mat *mat,
290 int row, int col)
291 {
292 isl_ctx *ctx;
293
294 if (!mat)
295 return NULL;
296 ctx = isl_mat_get_ctx(mat);
297 if (row < 0 || row >= mat->n_row)
298 isl_die(ctx, isl_error_invalid, "row out of range",
299 return NULL);
300 if (check_col(mat, col) < 0)
301 return NULL;
302 return isl_val_int_from_isl_int(ctx, mat->row[row][col]);
303 }
304
305 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
306 int row, int col, isl_int v)
307 {
308 mat = isl_mat_cow(mat);
309 if (!mat)
310 return NULL;
311 if (row < 0 || row >= mat->n_row)
312 isl_die(mat->ctx, isl_error_invalid, "row out of range",
313 goto error);
314 if (check_col(mat, col) < 0)
315 return isl_mat_free(mat);
316 isl_int_set(mat->row[row][col], v);
317 return mat;
318 error:
319 isl_mat_free(mat);
320 return NULL;
321 }
322
323 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
324 int row, int col, int v)
325 {
326 mat = isl_mat_cow(mat);
327 if (!mat)
328 return NULL;
329 if (row < 0 || row >= mat->n_row)
330 isl_die(mat->ctx, isl_error_invalid, "row out of range",
331 goto error);
332 if (check_col(mat, col) < 0)
333 return isl_mat_free(mat);
334 isl_int_set_si(mat->row[row][col], v);
335 return mat;
336 error:
337 isl_mat_free(mat);
338 return NULL;
339 }
340
341 /* Replace the element at row "row", column "col" of "mat" by "v".
342 */
343 __isl_give isl_mat *isl_mat_set_element_val(__isl_take isl_mat *mat,
344 int row, int col, __isl_take isl_val *v)
345 {
346 if (!v)
347 return isl_mat_free(mat);
348 if (!isl_val_is_int(v))
349 isl_die(isl_val_get_ctx(v), isl_error_invalid,
350 "expecting integer value", goto error);
351 mat = isl_mat_set_element(mat, row, col, v->n);
352 isl_val_free(v);
353 return mat;
354 error:
355 isl_val_free(v);
356 return isl_mat_free(mat);
357 }
358
359 __isl_give isl_mat *isl_mat_diag(isl_ctx *ctx, unsigned n_row, isl_int d)
360 {
361 int i;
362 struct isl_mat *mat;
363
364 mat = isl_mat_alloc(ctx, n_row, n_row);
365 if (!mat)
366 return NULL;
367 for (i = 0; i < n_row; ++i) {
368 isl_seq_clr(mat->row[i], i);
369 isl_int_set(mat->row[i][i], d);
370 isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
371 }
372
373 return mat;
374 }
375
376 /* Create an "n_row" by "n_col" matrix with zero elements.
377 */
378 __isl_give isl_mat *isl_mat_zero(isl_ctx *ctx, unsigned n_row, unsigned n_col)
379 {
380 int i;
381 isl_mat *mat;
382
383 mat = isl_mat_alloc(ctx, n_row, n_col);
384 if (!mat)
385 return NULL;
386 for (i = 0; i < n_row; ++i)
387 isl_seq_clr(mat->row[i], n_col);
388
389 return mat;
390 }
391
392 __isl_give isl_mat *isl_mat_identity(isl_ctx *ctx, unsigned n_row)
393 {
394 if (!ctx)
395 return NULL;
396 return isl_mat_diag(ctx, n_row, ctx->one);
397 }
398
399 /* Is "mat" a (possibly scaled) identity matrix?
400 */
401 int isl_mat_is_scaled_identity(__isl_keep isl_mat *mat)
402 {
403 int i;
404
405 if (!mat)
406 return -1;
407 if (mat->n_row != mat->n_col)
408 return 0;
409
410 for (i = 0; i < mat->n_row; ++i) {
411 if (isl_seq_first_non_zero(mat->row[i], i) != -1)
412 return 0;
413 if (isl_int_ne(mat->row[0][0], mat->row[i][i]))
414 return 0;
415 if (isl_seq_first_non_zero(mat->row[i] + i + 1,
416 mat->n_col - (i + 1)) != -1)
417 return 0;
418 }
419
420 return 1;
421 }
422
423 __isl_give isl_vec *isl_mat_vec_product(__isl_take isl_mat *mat,
424 __isl_take isl_vec *vec)
425 {
426 int i;
427 struct isl_vec *prod;
428
429 if (!mat || !vec)
430 goto error;
431
432 isl_assert(mat->ctx, mat->n_col == vec->size, goto error);
433
434 prod = isl_vec_alloc(mat->ctx, mat->n_row);
435 if (!prod)
436 goto error;
437
438 for (i = 0; i < prod->size; ++i)
439 isl_seq_inner_product(mat->row[i], vec->el, vec->size,
440 &prod->block.data[i]);
441 isl_mat_free(mat);
442 isl_vec_free(vec);
443 return prod;
444 error:
445 isl_mat_free(mat);
446 isl_vec_free(vec);
447 return NULL;
448 }
449
450 __isl_give isl_vec *isl_mat_vec_inverse_product(__isl_take isl_mat *mat,
451 __isl_take isl_vec *vec)
452 {
453 struct isl_mat *vec_mat;
454 int i;
455
456 if (!mat || !vec)
457 goto error;
458 vec_mat = isl_mat_alloc(vec->ctx, vec->size, 1);
459 if (!vec_mat)
460 goto error;
461 for (i = 0; i < vec->size; ++i)
462 isl_int_set(vec_mat->row[i][0], vec->el[i]);
463 vec_mat = isl_mat_inverse_product(mat, vec_mat);
464 isl_vec_free(vec);
465 if (!vec_mat)
466 return NULL;
467 vec = isl_vec_alloc(vec_mat->ctx, vec_mat->n_row);
468 if (vec)
469 for (i = 0; i < vec->size; ++i)
470 isl_int_set(vec->el[i], vec_mat->row[i][0]);
471 isl_mat_free(vec_mat);
472 return vec;
473 error:
474 isl_mat_free(mat);
475 isl_vec_free(vec);
476 return NULL;
477 }
478
479 struct isl_vec *isl_vec_mat_product(struct isl_vec *vec, struct isl_mat *mat)
480 {
481 int i, j;
482 struct isl_vec *prod;
483
484 if (!mat || !vec)
485 goto error;
486
487 isl_assert(mat->ctx, mat->n_row == vec->size, goto error);
488
489 prod = isl_vec_alloc(mat->ctx, mat->n_col);
490 if (!prod)
491 goto error;
492
493 for (i = 0; i < prod->size; ++i) {
494 isl_int_set_si(prod->el[i], 0);
495 for (j = 0; j < vec->size; ++j)
496 isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);
497 }
498 isl_mat_free(mat);
499 isl_vec_free(vec);
500 return prod;
501 error:
502 isl_mat_free(mat);
503 isl_vec_free(vec);
504 return NULL;
505 }
506
507 struct isl_mat *isl_mat_aff_direct_sum(struct isl_mat *left,
508 struct isl_mat *right)
509 {
510 int i;
511 struct isl_mat *sum;
512
513 if (!left || !right)
514 goto error;
515
516 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
517 isl_assert(left->ctx, left->n_row >= 1, goto error);
518 isl_assert(left->ctx, left->n_col >= 1, goto error);
519 isl_assert(left->ctx, right->n_col >= 1, goto error);
520 isl_assert(left->ctx,
521 isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,
522 goto error);
523 isl_assert(left->ctx,
524 isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
525 goto error);
526
527 sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);
528 if (!sum)
529 goto error;
530 isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);
531 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
532 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
533
534 isl_seq_clr(sum->row[0]+1, sum->n_col-1);
535 for (i = 1; i < sum->n_row; ++i) {
536 isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);
537 isl_int_addmul(sum->row[i][0],
538 right->row[0][0], right->row[i][0]);
539 isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],
540 left->n_col-1);
541 isl_seq_scale(sum->row[i]+left->n_col,
542 right->row[i]+1, right->row[0][0],
543 right->n_col-1);
544 }
545
546 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
547 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
548 isl_mat_free(left);
549 isl_mat_free(right);
550 return sum;
551 error:
552 isl_mat_free(left);
553 isl_mat_free(right);
554 return NULL;
555 }
556
557 static void exchange(struct isl_mat *M, struct isl_mat **U,
558 struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
559 {
560 int r;
561 for (r = row; r < M->n_row; ++r)
562 isl_int_swap(M->row[r][i], M->row[r][j]);
563 if (U) {
564 for (r = 0; r < (*U)->n_row; ++r)
565 isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
566 }
567 if (Q)
568 isl_mat_swap_rows(*Q, i, j);
569 }
570
571 static void subtract(struct isl_mat *M, struct isl_mat **U,
572 struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)
573 {
574 int r;
575 for (r = row; r < M->n_row; ++r)
576 isl_int_submul(M->row[r][j], m, M->row[r][i]);
577 if (U) {
578 for (r = 0; r < (*U)->n_row; ++r)
579 isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);
580 }
581 if (Q) {
582 for (r = 0; r < (*Q)->n_col; ++r)
583 isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);
584 }
585 }
586
587 static void oppose(struct isl_mat *M, struct isl_mat **U,
588 struct isl_mat **Q, unsigned row, unsigned col)
589 {
590 int r;
591 for (r = row; r < M->n_row; ++r)
592 isl_int_neg(M->row[r][col], M->row[r][col]);
593 if (U) {
594 for (r = 0; r < (*U)->n_row; ++r)
595 isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);
596 }
597 if (Q)
598 isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);
599 }
600
601 /* Given matrix M, compute
602 *
603 * M U = H
604 * M = H Q
605 *
606 * with U and Q unimodular matrices and H a matrix in column echelon form
607 * such that on each echelon row the entries in the non-echelon column
608 * are non-negative (if neg == 0) or non-positive (if neg == 1)
609 * and strictly smaller (in absolute value) than the entries in the echelon
610 * column.
611 * If U or Q are NULL, then these matrices are not computed.
612 */
613 struct isl_mat *isl_mat_left_hermite(struct isl_mat *M, int neg,
614 struct isl_mat **U, struct isl_mat **Q)
615 {
616 isl_int c;
617 int row, col;
618
619 if (U)
620 *U = NULL;
621 if (Q)
622 *Q = NULL;
623 if (!M)
624 goto error;
625 M = isl_mat_cow(M);
626 if (!M)
627 goto error;
628 if (U) {
629 *U = isl_mat_identity(M->ctx, M->n_col);
630 if (!*U)
631 goto error;
632 }
633 if (Q) {
634 *Q = isl_mat_identity(M->ctx, M->n_col);
635 if (!*Q)
636 goto error;
637 }
638
639 col = 0;
640 isl_int_init(c);
641 for (row = 0; row < M->n_row; ++row) {
642 int first, i, off;
643 first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);
644 if (first == -1)
645 continue;
646 first += col;
647 if (first != col)
648 exchange(M, U, Q, row, first, col);
649 if (isl_int_is_neg(M->row[row][col]))
650 oppose(M, U, Q, row, col);
651 first = col+1;
652 while ((off = isl_seq_first_non_zero(M->row[row]+first,
653 M->n_col-first)) != -1) {
654 first += off;
655 isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);
656 subtract(M, U, Q, row, col, first, c);
657 if (!isl_int_is_zero(M->row[row][first]))
658 exchange(M, U, Q, row, first, col);
659 else
660 ++first;
661 }
662 for (i = 0; i < col; ++i) {
663 if (isl_int_is_zero(M->row[row][i]))
664 continue;
665 if (neg)
666 isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);
667 else
668 isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);
669 if (isl_int_is_zero(c))
670 continue;
671 subtract(M, U, Q, row, col, i, c);
672 }
673 ++col;
674 }
675 isl_int_clear(c);
676
677 return M;
678 error:
679 if (Q) {
680 isl_mat_free(*Q);
681 *Q = NULL;
682 }
683 if (U) {
684 isl_mat_free(*U);
685 *U = NULL;
686 }
687 isl_mat_free(M);
688 return NULL;
689 }
690
691 struct isl_mat *isl_mat_right_kernel(struct isl_mat *mat)
692 {
693 int i, rank;
694 struct isl_mat *U = NULL;
695 struct isl_mat *K;
696
697 mat = isl_mat_left_hermite(mat, 0, &U, NULL);
698 if (!mat || !U)
699 goto error;
700
701 for (i = 0, rank = 0; rank < mat->n_col; ++rank) {
702 while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))
703 ++i;
704 if (i >= mat->n_row)
705 break;
706 }
707 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
708 if (!K)
709 goto error;
710 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
711 isl_mat_free(mat);
712 isl_mat_free(U);
713 return K;
714 error:
715 isl_mat_free(mat);
716 isl_mat_free(U);
717 return NULL;
718 }
719
720 struct isl_mat *isl_mat_lin_to_aff(struct isl_mat *mat)
721 {
722 int i;
723 struct isl_mat *mat2;
724
725 if (!mat)
726 return NULL;
727 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
728 if (!mat2)
729 goto error;
730 isl_int_set_si(mat2->row[0][0], 1);
731 isl_seq_clr(mat2->row[0]+1, mat->n_col);
732 for (i = 0; i < mat->n_row; ++i) {
733 isl_int_set_si(mat2->row[1+i][0], 0);
734 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
735 }
736 isl_mat_free(mat);
737 return mat2;
738 error:
739 isl_mat_free(mat);
740 return NULL;
741 }
742
743 /* Given two matrices M1 and M2, return the block matrix
744 *
745 * [ M1 0 ]
746 * [ 0 M2 ]
747 */
748 __isl_give isl_mat *isl_mat_diagonal(__isl_take isl_mat *mat1,
749 __isl_take isl_mat *mat2)
750 {
751 int i;
752 isl_mat *mat;
753
754 if (!mat1 || !mat2)
755 goto error;
756
757 mat = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
758 mat1->n_col + mat2->n_col);
759 if (!mat)
760 goto error;
761 for (i = 0; i < mat1->n_row; ++i) {
762 isl_seq_cpy(mat->row[i], mat1->row[i], mat1->n_col);
763 isl_seq_clr(mat->row[i] + mat1->n_col, mat2->n_col);
764 }
765 for (i = 0; i < mat2->n_row; ++i) {
766 isl_seq_clr(mat->row[mat1->n_row + i], mat1->n_col);
767 isl_seq_cpy(mat->row[mat1->n_row + i] + mat1->n_col,
768 mat2->row[i], mat2->n_col);
769 }
770 isl_mat_free(mat1);
771 isl_mat_free(mat2);
772 return mat;
773 error:
774 isl_mat_free(mat1);
775 isl_mat_free(mat2);
776 return NULL;
777 }
778
779 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
780 {
781 int i;
782
783 for (i = 0; i < n_row; ++i)
784 if (!isl_int_is_zero(row[i][col]))
785 return i;
786 return -1;
787 }
788
789 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
790 {
791 int i, min = row_first_non_zero(row, n_row, col);
792 if (min < 0)
793 return -1;
794 for (i = min + 1; i < n_row; ++i) {
795 if (isl_int_is_zero(row[i][col]))
796 continue;
797 if (isl_int_abs_lt(row[i][col], row[min][col]))
798 min = i;
799 }
800 return min;
801 }
802
803 static isl_stat inv_exchange(__isl_keep isl_mat **left,
804 __isl_keep isl_mat **right, unsigned i, unsigned j)
805 {
806 *left = isl_mat_swap_rows(*left, i, j);
807 *right = isl_mat_swap_rows(*right, i, j);
808
809 if (!*left || !*right)
810 return isl_stat_error;
811 return isl_stat_ok;
812 }
813
814 static void inv_oppose(
815 struct isl_mat *left, struct isl_mat *right, unsigned row)
816 {
817 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
818 isl_seq_neg(right->row[row], right->row[row], right->n_col);
819 }
820
821 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
822 unsigned row, unsigned i, isl_int m)
823 {
824 isl_int_neg(m, m);
825 isl_seq_combine(left->row[i]+row,
826 left->ctx->one, left->row[i]+row,
827 m, left->row[row]+row,
828 left->n_col-row);
829 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
830 m, right->row[row], right->n_col);
831 }
832
833 /* Compute inv(left)*right
834 */
835 struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
836 struct isl_mat *right)
837 {
838 int row;
839 isl_int a, b;
840
841 if (!left || !right)
842 goto error;
843
844 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
845 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
846
847 if (left->n_row == 0) {
848 isl_mat_free(left);
849 return right;
850 }
851
852 left = isl_mat_cow(left);
853 right = isl_mat_cow(right);
854 if (!left || !right)
855 goto error;
856
857 isl_int_init(a);
858 isl_int_init(b);
859 for (row = 0; row < left->n_row; ++row) {
860 int pivot, first, i, off;
861 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
862 if (pivot < 0) {
863 isl_int_clear(a);
864 isl_int_clear(b);
865 isl_assert(left->ctx, pivot >= 0, goto error);
866 }
867 pivot += row;
868 if (pivot != row)
869 if (inv_exchange(&left, &right, pivot, row) < 0)
870 goto error;
871 if (isl_int_is_neg(left->row[row][row]))
872 inv_oppose(left, right, row);
873 first = row+1;
874 while ((off = row_first_non_zero(left->row+first,
875 left->n_row-first, row)) != -1) {
876 first += off;
877 isl_int_fdiv_q(a, left->row[first][row],
878 left->row[row][row]);
879 inv_subtract(left, right, row, first, a);
880 if (!isl_int_is_zero(left->row[first][row])) {
881 if (inv_exchange(&left, &right, row, first) < 0)
882 goto error;
883 } else {
884 ++first;
885 }
886 }
887 for (i = 0; i < row; ++i) {
888 if (isl_int_is_zero(left->row[i][row]))
889 continue;
890 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
891 isl_int_divexact(b, left->row[i][row], a);
892 isl_int_divexact(a, left->row[row][row], a);
893 isl_int_neg(b, b);
894 isl_seq_combine(left->row[i] + i,
895 a, left->row[i] + i,
896 b, left->row[row] + i,
897 left->n_col - i);
898 isl_seq_combine(right->row[i], a, right->row[i],
899 b, right->row[row], right->n_col);
900 }
901 }
902 isl_int_clear(b);
903
904 isl_int_set(a, left->row[0][0]);
905 for (row = 1; row < left->n_row; ++row)
906 isl_int_lcm(a, a, left->row[row][row]);
907 if (isl_int_is_zero(a)){
908 isl_int_clear(a);
909 isl_assert(left->ctx, 0, goto error);
910 }
911 for (row = 0; row < left->n_row; ++row) {
912 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
913 if (isl_int_is_one(left->row[row][row]))
914 continue;
915 isl_seq_scale(right->row[row], right->row[row],
916 left->row[row][row], right->n_col);
917 }
918 isl_int_clear(a);
919
920 isl_mat_free(left);
921 return right;
922 error:
923 isl_mat_free(left);
924 isl_mat_free(right);
925 return NULL;
926 }
927
928 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
929 {
930 int i;
931
932 for (i = 0; i < mat->n_row; ++i)
933 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
934 }
935
936 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
937 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
938 {
939 int i;
940 isl_int tmp;
941
942 isl_int_init(tmp);
943 for (i = 0; i < mat->n_row; ++i) {
944 isl_int_mul(tmp, m1, mat->row[i][src1]);
945 isl_int_addmul(tmp, m2, mat->row[i][src2]);
946 isl_int_set(mat->row[i][dst], tmp);
947 }
948 isl_int_clear(tmp);
949 }
950
951 struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
952 {
953 struct isl_mat *inv;
954 int row;
955 isl_int a, b;
956
957 mat = isl_mat_cow(mat);
958 if (!mat)
959 return NULL;
960
961 inv = isl_mat_identity(mat->ctx, mat->n_col);
962 inv = isl_mat_cow(inv);
963 if (!inv)
964 goto error;
965
966 isl_int_init(a);
967 isl_int_init(b);
968 for (row = 0; row < mat->n_row; ++row) {
969 int pivot, first, i, off;
970 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
971 if (pivot < 0) {
972 isl_int_clear(a);
973 isl_int_clear(b);
974 isl_assert(mat->ctx, pivot >= 0, goto error);
975 }
976 pivot += row;
977 if (pivot != row)
978 exchange(mat, &inv, NULL, row, pivot, row);
979 if (isl_int_is_neg(mat->row[row][row]))
980 oppose(mat, &inv, NULL, row, row);
981 first = row+1;
982 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
983 mat->n_col-first)) != -1) {
984 first += off;
985 isl_int_fdiv_q(a, mat->row[row][first],
986 mat->row[row][row]);
987 subtract(mat, &inv, NULL, row, row, first, a);
988 if (!isl_int_is_zero(mat->row[row][first]))
989 exchange(mat, &inv, NULL, row, row, first);
990 else
991 ++first;
992 }
993 for (i = 0; i < row; ++i) {
994 if (isl_int_is_zero(mat->row[row][i]))
995 continue;
996 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
997 isl_int_divexact(b, mat->row[row][i], a);
998 isl_int_divexact(a, mat->row[row][row], a);
999 isl_int_neg(a, a);
1000 isl_mat_col_combine(mat, i, a, i, b, row);
1001 isl_mat_col_combine(inv, i, a, i, b, row);
1002 }
1003 }
1004 isl_int_clear(b);
1005
1006 isl_int_set(a, mat->row[0][0]);
1007 for (row = 1; row < mat->n_row; ++row)
1008 isl_int_lcm(a, a, mat->row[row][row]);
1009 if (isl_int_is_zero(a)){
1010 isl_int_clear(a);
1011 goto error;
1012 }
1013 for (row = 0; row < mat->n_row; ++row) {
1014 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
1015 if (isl_int_is_one(mat->row[row][row]))
1016 continue;
1017 isl_mat_col_scale(inv, row, mat->row[row][row]);
1018 }
1019 isl_int_clear(a);
1020
1021 isl_mat_free(mat);
1022
1023 return inv;
1024 error:
1025 isl_mat_free(mat);
1026 isl_mat_free(inv);
1027 return NULL;
1028 }
1029
1030 struct isl_mat *isl_mat_transpose(struct isl_mat *mat)
1031 {
1032 struct isl_mat *transpose = NULL;
1033 int i, j;
1034
1035 if (!mat)
1036 return NULL;
1037
1038 if (mat->n_col == mat->n_row) {
1039 mat = isl_mat_cow(mat);
1040 if (!mat)
1041 return NULL;
1042 for (i = 0; i < mat->n_row; ++i)
1043 for (j = i + 1; j < mat->n_col; ++j)
1044 isl_int_swap(mat->row[i][j], mat->row[j][i]);
1045 return mat;
1046 }
1047 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
1048 if (!transpose)
1049 goto error;
1050 for (i = 0; i < mat->n_row; ++i)
1051 for (j = 0; j < mat->n_col; ++j)
1052 isl_int_set(transpose->row[j][i], mat->row[i][j]);
1053 isl_mat_free(mat);
1054 return transpose;
1055 error:
1056 isl_mat_free(mat);
1057 return NULL;
1058 }
1059
1060 struct isl_mat *isl_mat_swap_cols(struct isl_mat *mat, unsigned i, unsigned j)
1061 {
1062 int r;
1063
1064 mat = isl_mat_cow(mat);
1065 if (!mat)
1066 return NULL;
1067 isl_assert(mat->ctx, i < mat->n_col, goto error);
1068 isl_assert(mat->ctx, j < mat->n_col, goto error);
1069
1070 for (r = 0; r < mat->n_row; ++r)
1071 isl_int_swap(mat->row[r][i], mat->row[r][j]);
1072 return mat;
1073 error:
1074 isl_mat_free(mat);
1075 return NULL;
1076 }
1077
1078 struct isl_mat *isl_mat_swap_rows(struct isl_mat *mat, unsigned i, unsigned j)
1079 {
1080 isl_int *t;
1081
1082 if (!mat)
1083 return NULL;
1084 mat = isl_mat_cow(mat);
1085 if (!mat)
1086 return NULL;
1087 t = mat->row[i];
1088 mat->row[i] = mat->row[j];
1089 mat->row[j] = t;
1090 return mat;
1091 }
1092
1093 /* Calculate the product of two matrices.
1094 *
1095 * This function is optimized for operand matrices that contain many zeros and
1096 * skips multiplications where we know one of the operands is zero.
1097 */
1098 __isl_give isl_mat *isl_mat_product(__isl_take isl_mat *left,
1099 __isl_take isl_mat *right)
1100 {
1101 int i, j, k;
1102 struct isl_mat *prod;
1103
1104 if (!left || !right)
1105 goto error;
1106 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
1107 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
1108 if (!prod)
1109 goto error;
1110 if (left->n_col == 0) {
1111 for (i = 0; i < prod->n_row; ++i)
1112 isl_seq_clr(prod->row[i], prod->n_col);
1113 isl_mat_free(left);
1114 isl_mat_free(right);
1115 return prod;
1116 }
1117 for (i = 0; i < prod->n_row; ++i) {
1118 for (j = 0; j < prod->n_col; ++j)
1119 isl_int_mul(prod->row[i][j],
1120 left->row[i][0], right->row[0][j]);
1121 for (k = 1; k < left->n_col; ++k) {
1122 if (isl_int_is_zero(left->row[i][k]))
1123 continue;
1124 for (j = 0; j < prod->n_col; ++j)
1125 isl_int_addmul(prod->row[i][j],
1126 left->row[i][k], right->row[k][j]);
1127 }
1128 }
1129 isl_mat_free(left);
1130 isl_mat_free(right);
1131 return prod;
1132 error:
1133 isl_mat_free(left);
1134 isl_mat_free(right);
1135 return NULL;
1136 }
1137
1138 /* Replace the variables x in the rows q by x' given by x = M x',
1139 * with M the matrix mat.
1140 *
1141 * If the number of new variables is greater than the original
1142 * number of variables, then the rows q have already been
1143 * preextended. If the new number is smaller, then the coefficients
1144 * of the divs, which are not changed, need to be shifted down.
1145 * The row q may be the equalities, the inequalities or the
1146 * div expressions. In the latter case, has_div is true and
1147 * we need to take into account the extra denominator column.
1148 */
1149 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
1150 unsigned n_div, int has_div, struct isl_mat *mat)
1151 {
1152 int i;
1153 struct isl_mat *t;
1154 int e;
1155
1156 if (mat->n_col >= mat->n_row)
1157 e = 0;
1158 else
1159 e = mat->n_row - mat->n_col;
1160 if (has_div)
1161 for (i = 0; i < n; ++i)
1162 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
1163 t = isl_mat_sub_alloc6(mat->ctx, q, 0, n, has_div, mat->n_row);
1164 t = isl_mat_product(t, mat);
1165 if (!t)
1166 return -1;
1167 for (i = 0; i < n; ++i) {
1168 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
1169 isl_seq_cpy(q[i] + has_div + t->n_col,
1170 q[i] + has_div + t->n_col + e, n_div);
1171 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
1172 }
1173 isl_mat_free(t);
1174 return 0;
1175 }
1176
1177 /* Replace the variables x in bset by x' given by x = M x', with
1178 * M the matrix mat.
1179 *
1180 * If there are fewer variables x' then there are x, then we perform
1181 * the transformation in place, which means that, in principle,
1182 * this frees up some extra variables as the number
1183 * of columns remains constant, but we would have to extend
1184 * the div array too as the number of rows in this array is assumed
1185 * to be equal to extra.
1186 */
1187 struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
1188 struct isl_mat *mat)
1189 {
1190 struct isl_ctx *ctx;
1191
1192 if (!bset || !mat)
1193 goto error;
1194
1195 ctx = bset->ctx;
1196 bset = isl_basic_set_cow(bset);
1197 if (!bset)
1198 goto error;
1199
1200 isl_assert(ctx, bset->dim->nparam == 0, goto error);
1201 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
1202 isl_assert(ctx, mat->n_col > 0, goto error);
1203
1204 if (mat->n_col > mat->n_row) {
1205 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0, 0, 0);
1206 if (!bset)
1207 goto error;
1208 } else if (mat->n_col < mat->n_row) {
1209 bset->dim = isl_space_cow(bset->dim);
1210 if (!bset->dim)
1211 goto error;
1212 bset->dim->n_out -= mat->n_row - mat->n_col;
1213 }
1214
1215 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
1216 isl_mat_copy(mat)) < 0)
1217 goto error;
1218
1219 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
1220 isl_mat_copy(mat)) < 0)
1221 goto error;
1222
1223 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
1224 goto error2;
1225
1226 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
1227 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
1228 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1229 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1230 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
1231
1232 bset = isl_basic_set_simplify(bset);
1233 bset = isl_basic_set_finalize(bset);
1234
1235 return bset;
1236 error:
1237 isl_mat_free(mat);
1238 error2:
1239 isl_basic_set_free(bset);
1240 return NULL;
1241 }
1242
1243 struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
1244 {
1245 int i;
1246
1247 set = isl_set_cow(set);
1248 if (!set)
1249 goto error;
1250
1251 for (i = 0; i < set->n; ++i) {
1252 set->p[i] = isl_basic_set_preimage(set->p[i],
1253 isl_mat_copy(mat));
1254 if (!set->p[i])
1255 goto error;
1256 }
1257 if (mat->n_col != mat->n_row) {
1258 set->dim = isl_space_cow(set->dim);
1259 if (!set->dim)
1260 goto error;
1261 set->dim->n_out += mat->n_col;
1262 set->dim->n_out -= mat->n_row;
1263 }
1264 isl_mat_free(mat);
1265 ISL_F_CLR(set, ISL_SET_NORMALIZED);
1266 return set;
1267 error:
1268 isl_set_free(set);
1269 isl_mat_free(mat);
1270 return NULL;
1271 }
1272
1273 /* Replace the variables x starting at "first_col" in the rows "rows"
1274 * of some coefficient matrix by x' with x = M x' with M the matrix mat.
1275 * That is, replace the corresponding coefficients c by c M.
1276 */
1277 isl_stat isl_mat_sub_transform(isl_int **row, unsigned n_row,
1278 unsigned first_col, __isl_take isl_mat *mat)
1279 {
1280 int i;
1281 isl_ctx *ctx;
1282 isl_mat *t;
1283
1284 if (!mat)
1285 return isl_stat_error;
1286 ctx = isl_mat_get_ctx(mat);
1287 t = isl_mat_sub_alloc6(ctx, row, 0, n_row, first_col, mat->n_row);
1288 t = isl_mat_product(t, mat);
1289 if (!t)
1290 return isl_stat_error;
1291 for (i = 0; i < n_row; ++i)
1292 isl_seq_swp_or_cpy(row[i] + first_col, t->row[i], t->n_col);
1293 isl_mat_free(t);
1294 return isl_stat_ok;
1295 }
1296
1297 void isl_mat_print_internal(__isl_keep isl_mat *mat, FILE *out, int indent)
1298 {
1299 int i, j;
1300
1301 if (!mat) {
1302 fprintf(out, "%*snull mat\n", indent, "");
1303 return;
1304 }
1305
1306 if (mat->n_row == 0)
1307 fprintf(out, "%*s[]\n", indent, "");
1308
1309 for (i = 0; i < mat->n_row; ++i) {
1310 if (!i)
1311 fprintf(out, "%*s[[", indent, "");
1312 else
1313 fprintf(out, "%*s[", indent+1, "");
1314 for (j = 0; j < mat->n_col; ++j) {
1315 if (j)
1316 fprintf(out, ",");
1317 isl_int_print(out, mat->row[i][j], 0);
1318 }
1319 if (i == mat->n_row-1)
1320 fprintf(out, "]]\n");
1321 else
1322 fprintf(out, "]\n");
1323 }
1324 }
1325
1326 void isl_mat_dump(__isl_keep isl_mat *mat)
1327 {
1328 isl_mat_print_internal(mat, stderr, 0);
1329 }
1330
1331 struct isl_mat *isl_mat_drop_cols(struct isl_mat *mat, unsigned col, unsigned n)
1332 {
1333 int r;
1334
1335 if (n == 0)
1336 return mat;
1337
1338 mat = isl_mat_cow(mat);
1339 if (!mat)
1340 return NULL;
1341
1342 if (col != mat->n_col-n) {
1343 for (r = 0; r < mat->n_row; ++r)
1344 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1345 mat->n_col - col - n);
1346 }
1347 mat->n_col -= n;
1348 return mat;
1349 }
1350
1351 struct isl_mat *isl_mat_drop_rows(struct isl_mat *mat, unsigned row, unsigned n)
1352 {
1353 int r;
1354
1355 mat = isl_mat_cow(mat);
1356 if (!mat)
1357 return NULL;
1358
1359 for (r = row; r+n < mat->n_row; ++r)
1360 mat->row[r] = mat->row[r+n];
1361
1362 mat->n_row -= n;
1363 return mat;
1364 }
1365
1366 __isl_give isl_mat *isl_mat_insert_cols(__isl_take isl_mat *mat,
1367 unsigned col, unsigned n)
1368 {
1369 isl_mat *ext;
1370
1371 if (!mat)
1372 return NULL;
1373 if (n == 0)
1374 return mat;
1375
1376 ext = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col + n);
1377 if (!ext)
1378 goto error;
1379
1380 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row, 0, 0, col);
1381 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row,
1382 col + n, col, mat->n_col - col);
1383
1384 isl_mat_free(mat);
1385 return ext;
1386 error:
1387 isl_mat_free(mat);
1388 return NULL;
1389 }
1390
1391 __isl_give isl_mat *isl_mat_insert_zero_cols(__isl_take isl_mat *mat,
1392 unsigned first, unsigned n)
1393 {
1394 int i;
1395
1396 if (!mat)
1397 return NULL;
1398 mat = isl_mat_insert_cols(mat, first, n);
1399 if (!mat)
1400 return NULL;
1401
1402 for (i = 0; i < mat->n_row; ++i)
1403 isl_seq_clr(mat->row[i] + first, n);
1404
1405 return mat;
1406 }
1407
1408 __isl_give isl_mat *isl_mat_add_zero_cols(__isl_take isl_mat *mat, unsigned n)
1409 {
1410 if (!mat)
1411 return NULL;
1412
1413 return isl_mat_insert_zero_cols(mat, mat->n_col, n);
1414 }
1415
1416 __isl_give isl_mat *isl_mat_insert_rows(__isl_take isl_mat *mat,
1417 unsigned row, unsigned n)
1418 {
1419 isl_mat *ext;
1420
1421 if (!mat)
1422 return NULL;
1423 if (n == 0)
1424 return mat;
1425
1426 ext = isl_mat_alloc(mat->ctx, mat->n_row + n, mat->n_col);
1427 if (!ext)
1428 goto error;
1429
1430 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, row, 0, 0, mat->n_col);
1431 isl_mat_sub_copy(mat->ctx, ext->row + row + n, mat->row + row,
1432 mat->n_row - row, 0, 0, mat->n_col);
1433
1434 isl_mat_free(mat);
1435 return ext;
1436 error:
1437 isl_mat_free(mat);
1438 return NULL;
1439 }
1440
1441 __isl_give isl_mat *isl_mat_add_rows(__isl_take isl_mat *mat, unsigned n)
1442 {
1443 if (!mat)
1444 return NULL;
1445
1446 return isl_mat_insert_rows(mat, mat->n_row, n);
1447 }
1448
1449 __isl_give isl_mat *isl_mat_insert_zero_rows(__isl_take isl_mat *mat,
1450 unsigned row, unsigned n)
1451 {
1452 int i;
1453
1454 mat = isl_mat_insert_rows(mat, row, n);
1455 if (!mat)
1456 return NULL;
1457
1458 for (i = 0; i < n; ++i)
1459 isl_seq_clr(mat->row[row + i], mat->n_col);
1460
1461 return mat;
1462 }
1463
1464 __isl_give isl_mat *isl_mat_add_zero_rows(__isl_take isl_mat *mat, unsigned n)
1465 {
1466 if (!mat)
1467 return NULL;
1468
1469 return isl_mat_insert_zero_rows(mat, mat->n_row, n);
1470 }
1471
1472 void isl_mat_col_submul(struct isl_mat *mat,
1473 int dst_col, isl_int f, int src_col)
1474 {
1475 int i;
1476
1477 for (i = 0; i < mat->n_row; ++i)
1478 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1479 }
1480
1481 void isl_mat_col_add(__isl_keep isl_mat *mat, int dst_col, int src_col)
1482 {
1483 int i;
1484
1485 if (!mat)
1486 return;
1487
1488 for (i = 0; i < mat->n_row; ++i)
1489 isl_int_add(mat->row[i][dst_col],
1490 mat->row[i][dst_col], mat->row[i][src_col]);
1491 }
1492
1493 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1494 {
1495 int i;
1496
1497 for (i = 0; i < mat->n_row; ++i)
1498 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1499 }
1500
1501 /* Add "f" times column "src_col" to column "dst_col" of "mat" and
1502 * return the result.
1503 */
1504 __isl_give isl_mat *isl_mat_col_addmul(__isl_take isl_mat *mat, int dst_col,
1505 isl_int f, int src_col)
1506 {
1507 int i;
1508
1509 if (check_col(mat, dst_col) < 0 || check_col(mat, src_col) < 0)
1510 return isl_mat_free(mat);
1511
1512 for (i = 0; i < mat->n_row; ++i) {
1513 if (isl_int_is_zero(mat->row[i][src_col]))
1514 continue;
1515 mat = isl_mat_cow(mat);
1516 if (!mat)
1517 return NULL;
1518 isl_int_addmul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1519 }
1520
1521 return mat;
1522 }
1523
1524 /* Negate column "col" of "mat" and return the result.
1525 */
1526 __isl_give isl_mat *isl_mat_col_neg(__isl_take isl_mat *mat, int col)
1527 {
1528 int i;
1529
1530 if (check_col(mat, col) < 0)
1531 return isl_mat_free(mat);
1532
1533 for (i = 0; i < mat->n_row; ++i) {
1534 if (isl_int_is_zero(mat->row[i][col]))
1535 continue;
1536 mat = isl_mat_cow(mat);
1537 if (!mat)
1538 return NULL;
1539 isl_int_neg(mat->row[i][col], mat->row[i][col]);
1540 }
1541
1542 return mat;
1543 }
1544
1545 struct isl_mat *isl_mat_unimodular_complete(struct isl_mat *M, int row)
1546 {
1547 int r;
1548 struct isl_mat *H = NULL, *Q = NULL;
1549
1550 if (!M)
1551 return NULL;
1552
1553 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1554 M->n_row = row;
1555 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1556 M->n_row = M->n_col;
1557 if (!H)
1558 goto error;
1559 for (r = 0; r < row; ++r)
1560 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1561 for (r = row; r < M->n_row; ++r)
1562 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1563 isl_mat_free(H);
1564 isl_mat_free(Q);
1565 return M;
1566 error:
1567 isl_mat_free(H);
1568 isl_mat_free(Q);
1569 isl_mat_free(M);
1570 return NULL;
1571 }
1572
1573 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1574 __isl_take isl_mat *bot)
1575 {
1576 struct isl_mat *mat;
1577
1578 if (!top || !bot)
1579 goto error;
1580
1581 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1582 if (top->n_row == 0) {
1583 isl_mat_free(top);
1584 return bot;
1585 }
1586 if (bot->n_row == 0) {
1587 isl_mat_free(bot);
1588 return top;
1589 }
1590
1591 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1592 if (!mat)
1593 goto error;
1594 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1595 0, 0, mat->n_col);
1596 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1597 0, 0, mat->n_col);
1598 isl_mat_free(top);
1599 isl_mat_free(bot);
1600 return mat;
1601 error:
1602 isl_mat_free(top);
1603 isl_mat_free(bot);
1604 return NULL;
1605 }
1606
1607 isl_bool isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
1608 {
1609 int i;
1610
1611 if (!mat1 || !mat2)
1612 return isl_bool_error;
1613
1614 if (mat1->n_row != mat2->n_row)
1615 return isl_bool_false;
1616
1617 if (mat1->n_col != mat2->n_col)
1618 return isl_bool_false;
1619
1620 for (i = 0; i < mat1->n_row; ++i)
1621 if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
1622 return isl_bool_false;
1623
1624 return isl_bool_true;
1625 }
1626
1627 __isl_give isl_mat *isl_mat_from_row_vec(__isl_take isl_vec *vec)
1628 {
1629 struct isl_mat *mat;
1630
1631 if (!vec)
1632 return NULL;
1633 mat = isl_mat_alloc(vec->ctx, 1, vec->size);
1634 if (!mat)
1635 goto error;
1636
1637 isl_seq_cpy(mat->row[0], vec->el, vec->size);
1638
1639 isl_vec_free(vec);
1640 return mat;
1641 error:
1642 isl_vec_free(vec);
1643 return NULL;
1644 }
1645
1646 /* Return a copy of row "row" of "mat" as an isl_vec.
1647 */
1648 __isl_give isl_vec *isl_mat_get_row(__isl_keep isl_mat *mat, unsigned row)
1649 {
1650 isl_vec *v;
1651
1652 if (!mat)
1653 return NULL;
1654 if (row >= mat->n_row)
1655 isl_die(mat->ctx, isl_error_invalid, "row out of range",
1656 return NULL);
1657
1658 v = isl_vec_alloc(isl_mat_get_ctx(mat), mat->n_col);
1659 if (!v)
1660 return NULL;
1661 isl_seq_cpy(v->el, mat->row[row], mat->n_col);
1662
1663 return v;
1664 }
1665
1666 __isl_give isl_mat *isl_mat_vec_concat(__isl_take isl_mat *top,
1667 __isl_take isl_vec *bot)
1668 {
1669 return isl_mat_concat(top, isl_mat_from_row_vec(bot));
1670 }
1671
1672 __isl_give isl_mat *isl_mat_move_cols(__isl_take isl_mat *mat,
1673 unsigned dst_col, unsigned src_col, unsigned n)
1674 {
1675 isl_mat *res;
1676
1677 if (!mat)
1678 return NULL;
1679 if (n == 0 || dst_col == src_col)
1680 return mat;
1681
1682 res = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
1683 if (!res)
1684 goto error;
1685
1686 if (dst_col < src_col) {
1687 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1688 0, 0, dst_col);
1689 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1690 dst_col, src_col, n);
1691 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1692 dst_col + n, dst_col, src_col - dst_col);
1693 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1694 src_col + n, src_col + n,
1695 res->n_col - src_col - n);
1696 } else {
1697 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1698 0, 0, src_col);
1699 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1700 src_col, src_col + n, dst_col - src_col);
1701 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1702 dst_col, src_col, n);
1703 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1704 dst_col + n, dst_col + n,
1705 res->n_col - dst_col - n);
1706 }
1707 isl_mat_free(mat);
1708
1709 return res;
1710 error:
1711 isl_mat_free(mat);
1712 return NULL;
1713 }
1714
1715 /* Return the gcd of the elements in row "row" of "mat" in *gcd.
1716 * Return isl_stat_ok on success and isl_stat_error on failure.
1717 */
1718 isl_stat isl_mat_row_gcd(__isl_keep isl_mat *mat, int row, isl_int *gcd)
1719 {
1720 if (!mat)
1721 return isl_stat_error;
1722
1723 if (row < 0 || row >= mat->n_row)
1724 isl_die(isl_mat_get_ctx(mat), isl_error_invalid,
1725 "row out of range", return isl_stat_error);
1726 isl_seq_gcd(mat->row[row], mat->n_col, gcd);
1727
1728 return isl_stat_ok;
1729 }
1730
1731 void isl_mat_gcd(__isl_keep isl_mat *mat, isl_int *gcd)
1732 {
1733 int i;
1734 isl_int g;
1735
1736 isl_int_set_si(*gcd, 0);
1737 if (!mat)
1738 return;
1739
1740 isl_int_init(g);
1741 for (i = 0; i < mat->n_row; ++i) {
1742 isl_seq_gcd(mat->row[i], mat->n_col, &g);
1743 isl_int_gcd(*gcd, *gcd, g);
1744 }
1745 isl_int_clear(g);
1746 }
1747
1748 /* Return the result of scaling "mat" by a factor of "m".
1749 */
1750 __isl_give isl_mat *isl_mat_scale(__isl_take isl_mat *mat, isl_int m)
1751 {
1752 int i;
1753
1754 if (isl_int_is_one(m))
1755 return mat;
1756
1757 mat = isl_mat_cow(mat);
1758 if (!mat)
1759 return NULL;
1760
1761 for (i = 0; i < mat->n_row; ++i)
1762 isl_seq_scale(mat->row[i], mat->row[i], m, mat->n_col);
1763
1764 return mat;
1765 }
1766
1767 __isl_give isl_mat *isl_mat_scale_down(__isl_take isl_mat *mat, isl_int m)
1768 {
1769 int i;
1770
1771 if (isl_int_is_one(m))
1772 return mat;
1773
1774 mat = isl_mat_cow(mat);
1775 if (!mat)
1776 return NULL;
1777
1778 for (i = 0; i < mat->n_row; ++i)
1779 isl_seq_scale_down(mat->row[i], mat->row[i], m, mat->n_col);
1780
1781 return mat;
1782 }
1783
1784 __isl_give isl_mat *isl_mat_scale_down_row(__isl_take isl_mat *mat, int row,
1785 isl_int m)
1786 {
1787 if (isl_int_is_one(m))
1788 return mat;
1789
1790 mat = isl_mat_cow(mat);
1791 if (!mat)
1792 return NULL;
1793
1794 isl_seq_scale_down(mat->row[row], mat->row[row], m, mat->n_col);
1795
1796 return mat;
1797 }
1798
1799 __isl_give isl_mat *isl_mat_normalize(__isl_take isl_mat *mat)
1800 {
1801 isl_int gcd;
1802
1803 if (!mat)
1804 return NULL;
1805
1806 isl_int_init(gcd);
1807 isl_mat_gcd(mat, &gcd);
1808 mat = isl_mat_scale_down(mat, gcd);
1809 isl_int_clear(gcd);
1810
1811 return mat;
1812 }
1813
1814 __isl_give isl_mat *isl_mat_normalize_row(__isl_take isl_mat *mat, int row)
1815 {
1816 mat = isl_mat_cow(mat);
1817 if (!mat)
1818 return NULL;
1819
1820 isl_seq_normalize(mat->ctx, mat->row[row], mat->n_col);
1821
1822 return mat;
1823 }
1824
1825 /* Number of initial non-zero columns.
1826 */
1827 int isl_mat_initial_non_zero_cols(__isl_keep isl_mat *mat)
1828 {
1829 int i;
1830
1831 if (!mat)
1832 return -1;
1833
1834 for (i = 0; i < mat->n_col; ++i)
1835 if (row_first_non_zero(mat->row, mat->n_row, i) < 0)
1836 break;
1837
1838 return i;
1839 }
Integer set library