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isl_map_simplify.c: eliminate_divs_eq: isl_basic_map_offset
[isl.git] / isl_mat.c
blobbc20a16fe93ed9233b246af4b3b457b0e5c5c8a5
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2014 Ecole Normale Superieure
5 * Copyright 2017 Sven Verdoolaege
6 *
7 * Use of this software is governed by the MIT license
8 *
9 * Written by Sven Verdoolaege, K.U.Leuven, Departement
10 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
11 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
12 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
13 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
14 */
15
16 #include <isl_ctx_private.h>
17 #include <isl_map_private.h>
18 #include <isl/space.h>
19 #include <isl_seq.h>
20 #include <isl_mat_private.h>
21 #include <isl_vec_private.h>
22 #include <isl_space_private.h>
23 #include <isl_val_private.h>
24
25 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat)
26 {
27 return mat ? mat->ctx : NULL;
28 }
29
30 /* Return a hash value that digests "mat".
31 */
32 uint32_t isl_mat_get_hash(__isl_keep isl_mat *mat)
33 {
34 int i;
35 uint32_t hash;
36
37 if (!mat)
38 return 0;
39
40 hash = isl_hash_init();
41 isl_hash_byte(hash, mat->n_row & 0xFF);
42 isl_hash_byte(hash, mat->n_col & 0xFF);
43 for (i = 0; i < mat->n_row; ++i) {
44 uint32_t row_hash;
45
46 row_hash = isl_seq_get_hash(mat->row[i], mat->n_col);
47 isl_hash_hash(hash, row_hash);
48 }
49
50 return hash;
51 }
52
53 struct isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
54 unsigned n_row, unsigned n_col)
55 {
56 int i;
57 struct isl_mat *mat;
58
59 mat = isl_alloc_type(ctx, struct isl_mat);
60 if (!mat)
61 return NULL;
62
63 mat->row = NULL;
64 mat->block = isl_blk_alloc(ctx, n_row * n_col);
65 if (isl_blk_is_error(mat->block))
66 goto error;
67 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
68 if (n_row && !mat->row)
69 goto error;
70
71 for (i = 0; i < n_row; ++i)
72 mat->row[i] = mat->block.data + i * n_col;
73
74 mat->ctx = ctx;
75 isl_ctx_ref(ctx);
76 mat->ref = 1;
77 mat->n_row = n_row;
78 mat->n_col = n_col;
79 mat->max_col = n_col;
80 mat->flags = 0;
81
82 return mat;
83 error:
84 isl_blk_free(ctx, mat->block);
85 free(mat);
86 return NULL;
87 }
88
89 struct isl_mat *isl_mat_extend(struct isl_mat *mat,
90 unsigned n_row, unsigned n_col)
91 {
92 int i;
93 isl_int *old;
94 isl_int **row;
95
96 if (!mat)
97 return NULL;
98
99 if (mat->max_col >= n_col && mat->n_row >= n_row) {
100 if (mat->n_col < n_col)
101 mat->n_col = n_col;
102 return mat;
103 }
104
105 if (mat->max_col < n_col) {
106 struct isl_mat *new_mat;
107
108 if (n_row < mat->n_row)
109 n_row = mat->n_row;
110 new_mat = isl_mat_alloc(mat->ctx, n_row, n_col);
111 if (!new_mat)
112 goto error;
113 for (i = 0; i < mat->n_row; ++i)
114 isl_seq_cpy(new_mat->row[i], mat->row[i], mat->n_col);
115 isl_mat_free(mat);
116 return new_mat;
117 }
118
119 mat = isl_mat_cow(mat);
120 if (!mat)
121 goto error;
122
123 old = mat->block.data;
124 mat->block = isl_blk_extend(mat->ctx, mat->block, n_row * mat->max_col);
125 if (isl_blk_is_error(mat->block))
126 goto error;
127 row = isl_realloc_array(mat->ctx, mat->row, isl_int *, n_row);
128 if (n_row && !row)
129 goto error;
130 mat->row = row;
131
132 for (i = 0; i < mat->n_row; ++i)
133 mat->row[i] = mat->block.data + (mat->row[i] - old);
134 for (i = mat->n_row; i < n_row; ++i)
135 mat->row[i] = mat->block.data + i * mat->max_col;
136 mat->n_row = n_row;
137 if (mat->n_col < n_col)
138 mat->n_col = n_col;
139
140 return mat;
141 error:
142 isl_mat_free(mat);
143 return NULL;
144 }
145
146 __isl_give isl_mat *isl_mat_sub_alloc6(isl_ctx *ctx, isl_int **row,
147 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
148 {
149 int i;
150 struct isl_mat *mat;
151
152 mat = isl_alloc_type(ctx, struct isl_mat);
153 if (!mat)
154 return NULL;
155 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
156 if (n_row && !mat->row)
157 goto error;
158 for (i = 0; i < n_row; ++i)
159 mat->row[i] = row[first_row+i] + first_col;
160 mat->ctx = ctx;
161 isl_ctx_ref(ctx);
162 mat->ref = 1;
163 mat->n_row = n_row;
164 mat->n_col = n_col;
165 mat->block = isl_blk_empty();
166 mat->flags = ISL_MAT_BORROWED;
167 return mat;
168 error:
169 free(mat);
170 return NULL;
171 }
172
173 __isl_give isl_mat *isl_mat_sub_alloc(__isl_keep isl_mat *mat,
174 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
175 {
176 if (!mat)
177 return NULL;
178 return isl_mat_sub_alloc6(mat->ctx, mat->row, first_row, n_row,
179 first_col, n_col);
180 }
181
182 void isl_mat_sub_copy(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
183 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
184 {
185 int i;
186
187 for (i = 0; i < n_row; ++i)
188 isl_seq_cpy(dst[i]+dst_col, src[i]+src_col, n_col);
189 }
190
191 void isl_mat_sub_neg(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
192 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
193 {
194 int i;
195
196 for (i = 0; i < n_row; ++i)
197 isl_seq_neg(dst[i]+dst_col, src[i]+src_col, n_col);
198 }
199
200 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat)
201 {
202 if (!mat)
203 return NULL;
204
205 mat->ref++;
206 return mat;
207 }
208
209 __isl_give isl_mat *isl_mat_dup(__isl_keep isl_mat *mat)
210 {
211 int i;
212 struct isl_mat *mat2;
213
214 if (!mat)
215 return NULL;
216 mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
217 if (!mat2)
218 return NULL;
219 for (i = 0; i < mat->n_row; ++i)
220 isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);
221 return mat2;
222 }
223
224 __isl_give isl_mat *isl_mat_cow(__isl_take isl_mat *mat)
225 {
226 struct isl_mat *mat2;
227 if (!mat)
228 return NULL;
229
230 if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))
231 return mat;
232
233 mat2 = isl_mat_dup(mat);
234 isl_mat_free(mat);
235 return mat2;
236 }
237
238 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat)
239 {
240 if (!mat)
241 return NULL;
242
243 if (--mat->ref > 0)
244 return NULL;
245
246 if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))
247 isl_blk_free(mat->ctx, mat->block);
248 isl_ctx_deref(mat->ctx);
249 free(mat->row);
250 free(mat);
251
252 return NULL;
253 }
254
255 int isl_mat_rows(__isl_keep isl_mat *mat)
256 {
257 return mat ? mat->n_row : -1;
258 }
259
260 int isl_mat_cols(__isl_keep isl_mat *mat)
261 {
262 return mat ? mat->n_col : -1;
263 }
264
265 /* Check that "col" is a valid column position for "mat".
266 */
267 static isl_stat check_col(__isl_keep isl_mat *mat, int col)
268 {
269 if (!mat)
270 return isl_stat_error;
271 if (col < 0 || col >= mat->n_col)
272 isl_die(isl_mat_get_ctx(mat), isl_error_invalid,
273 "column out of range", return isl_stat_error);
274 return isl_stat_ok;
275 }
276
277 /* Check that "row" is a valid row position for "mat".
278 */
279 static isl_stat check_row(__isl_keep isl_mat *mat, int row)
280 {
281 if (!mat)
282 return isl_stat_error;
283 if (row < 0 || row >= mat->n_row)
284 isl_die(isl_mat_get_ctx(mat), isl_error_invalid,
285 "row out of range", return isl_stat_error);
286 return isl_stat_ok;
287 }
288
289 /* Check that there are "n" columns starting at position "first" in "mat".
290 */
291 static isl_stat check_col_range(__isl_keep isl_mat *mat, unsigned first,
292 unsigned n)
293 {
294 if (!mat)
295 return isl_stat_error;
296 if (first + n > mat->n_col || first + n < first)
297 isl_die(isl_mat_get_ctx(mat), isl_error_invalid,
298 "column position or range out of bounds",
299 return isl_stat_error);
300 return isl_stat_ok;
301 }
302
303 /* Check that there are "n" rows starting at position "first" in "mat".
304 */
305 static isl_stat check_row_range(__isl_keep isl_mat *mat, unsigned first,
306 unsigned n)
307 {
308 if (!mat)
309 return isl_stat_error;
310 if (first + n > mat->n_row || first + n < first)
311 isl_die(isl_mat_get_ctx(mat), isl_error_invalid,
312 "row position or range out of bounds",
313 return isl_stat_error);
314 return isl_stat_ok;
315 }
316
317 int isl_mat_get_element(__isl_keep isl_mat *mat, int row, int col, isl_int *v)
318 {
319 if (check_row(mat, row) < 0)
320 return -1;
321 if (check_col(mat, col) < 0)
322 return -1;
323 isl_int_set(*v, mat->row[row][col]);
324 return 0;
325 }
326
327 /* Extract the element at row "row", oolumn "col" of "mat".
328 */
329 __isl_give isl_val *isl_mat_get_element_val(__isl_keep isl_mat *mat,
330 int row, int col)
331 {
332 isl_ctx *ctx;
333
334 if (check_row(mat, row) < 0)
335 return NULL;
336 if (check_col(mat, col) < 0)
337 return NULL;
338 ctx = isl_mat_get_ctx(mat);
339 return isl_val_int_from_isl_int(ctx, mat->row[row][col]);
340 }
341
342 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
343 int row, int col, isl_int v)
344 {
345 mat = isl_mat_cow(mat);
346 if (check_row(mat, row) < 0)
347 return isl_mat_free(mat);
348 if (check_col(mat, col) < 0)
349 return isl_mat_free(mat);
350 isl_int_set(mat->row[row][col], v);
351 return mat;
352 }
353
354 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
355 int row, int col, int v)
356 {
357 mat = isl_mat_cow(mat);
358 if (check_row(mat, row) < 0)
359 return isl_mat_free(mat);
360 if (check_col(mat, col) < 0)
361 return isl_mat_free(mat);
362 isl_int_set_si(mat->row[row][col], v);
363 return mat;
364 }
365
366 /* Replace the element at row "row", column "col" of "mat" by "v".
367 */
368 __isl_give isl_mat *isl_mat_set_element_val(__isl_take isl_mat *mat,
369 int row, int col, __isl_take isl_val *v)
370 {
371 if (!v)
372 return isl_mat_free(mat);
373 if (!isl_val_is_int(v))
374 isl_die(isl_val_get_ctx(v), isl_error_invalid,
375 "expecting integer value", goto error);
376 mat = isl_mat_set_element(mat, row, col, v->n);
377 isl_val_free(v);
378 return mat;
379 error:
380 isl_val_free(v);
381 return isl_mat_free(mat);
382 }
383
384 __isl_give isl_mat *isl_mat_diag(isl_ctx *ctx, unsigned n_row, isl_int d)
385 {
386 int i;
387 struct isl_mat *mat;
388
389 mat = isl_mat_alloc(ctx, n_row, n_row);
390 if (!mat)
391 return NULL;
392 for (i = 0; i < n_row; ++i) {
393 isl_seq_clr(mat->row[i], i);
394 isl_int_set(mat->row[i][i], d);
395 isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
396 }
397
398 return mat;
399 }
400
401 /* Create an "n_row" by "n_col" matrix with zero elements.
402 */
403 __isl_give isl_mat *isl_mat_zero(isl_ctx *ctx, unsigned n_row, unsigned n_col)
404 {
405 int i;
406 isl_mat *mat;
407
408 mat = isl_mat_alloc(ctx, n_row, n_col);
409 if (!mat)
410 return NULL;
411 for (i = 0; i < n_row; ++i)
412 isl_seq_clr(mat->row[i], n_col);
413
414 return mat;
415 }
416
417 __isl_give isl_mat *isl_mat_identity(isl_ctx *ctx, unsigned n_row)
418 {
419 if (!ctx)
420 return NULL;
421 return isl_mat_diag(ctx, n_row, ctx->one);
422 }
423
424 /* Is "mat" a (possibly scaled) identity matrix?
425 */
426 isl_bool isl_mat_is_scaled_identity(__isl_keep isl_mat *mat)
427 {
428 int i;
429
430 if (!mat)
431 return isl_bool_error;
432 if (mat->n_row != mat->n_col)
433 return isl_bool_false;
434
435 for (i = 0; i < mat->n_row; ++i) {
436 if (isl_seq_first_non_zero(mat->row[i], i) != -1)
437 return isl_bool_false;
438 if (isl_int_ne(mat->row[0][0], mat->row[i][i]))
439 return isl_bool_false;
440 if (isl_seq_first_non_zero(mat->row[i] + i + 1,
441 mat->n_col - (i + 1)) != -1)
442 return isl_bool_false;
443 }
444
445 return isl_bool_true;
446 }
447
448 __isl_give isl_vec *isl_mat_vec_product(__isl_take isl_mat *mat,
449 __isl_take isl_vec *vec)
450 {
451 int i;
452 struct isl_vec *prod;
453
454 if (!mat || !vec)
455 goto error;
456
457 isl_assert(mat->ctx, mat->n_col == vec->size, goto error);
458
459 prod = isl_vec_alloc(mat->ctx, mat->n_row);
460 if (!prod)
461 goto error;
462
463 for (i = 0; i < prod->size; ++i)
464 isl_seq_inner_product(mat->row[i], vec->el, vec->size,
465 &prod->block.data[i]);
466 isl_mat_free(mat);
467 isl_vec_free(vec);
468 return prod;
469 error:
470 isl_mat_free(mat);
471 isl_vec_free(vec);
472 return NULL;
473 }
474
475 __isl_give isl_vec *isl_mat_vec_inverse_product(__isl_take isl_mat *mat,
476 __isl_take isl_vec *vec)
477 {
478 struct isl_mat *vec_mat;
479 int i;
480
481 if (!mat || !vec)
482 goto error;
483 vec_mat = isl_mat_alloc(vec->ctx, vec->size, 1);
484 if (!vec_mat)
485 goto error;
486 for (i = 0; i < vec->size; ++i)
487 isl_int_set(vec_mat->row[i][0], vec->el[i]);
488 vec_mat = isl_mat_inverse_product(mat, vec_mat);
489 isl_vec_free(vec);
490 if (!vec_mat)
491 return NULL;
492 vec = isl_vec_alloc(vec_mat->ctx, vec_mat->n_row);
493 if (vec)
494 for (i = 0; i < vec->size; ++i)
495 isl_int_set(vec->el[i], vec_mat->row[i][0]);
496 isl_mat_free(vec_mat);
497 return vec;
498 error:
499 isl_mat_free(mat);
500 isl_vec_free(vec);
501 return NULL;
502 }
503
504 __isl_give isl_vec *isl_vec_mat_product(__isl_take isl_vec *vec,
505 __isl_take isl_mat *mat)
506 {
507 int i, j;
508 struct isl_vec *prod;
509
510 if (!mat || !vec)
511 goto error;
512
513 isl_assert(mat->ctx, mat->n_row == vec->size, goto error);
514
515 prod = isl_vec_alloc(mat->ctx, mat->n_col);
516 if (!prod)
517 goto error;
518
519 for (i = 0; i < prod->size; ++i) {
520 isl_int_set_si(prod->el[i], 0);
521 for (j = 0; j < vec->size; ++j)
522 isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);
523 }
524 isl_mat_free(mat);
525 isl_vec_free(vec);
526 return prod;
527 error:
528 isl_mat_free(mat);
529 isl_vec_free(vec);
530 return NULL;
531 }
532
533 __isl_give isl_mat *isl_mat_aff_direct_sum(__isl_take isl_mat *left,
534 __isl_take isl_mat *right)
535 {
536 int i;
537 struct isl_mat *sum;
538
539 if (!left || !right)
540 goto error;
541
542 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
543 isl_assert(left->ctx, left->n_row >= 1, goto error);
544 isl_assert(left->ctx, left->n_col >= 1, goto error);
545 isl_assert(left->ctx, right->n_col >= 1, goto error);
546 isl_assert(left->ctx,
547 isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,
548 goto error);
549 isl_assert(left->ctx,
550 isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
551 goto error);
552
553 sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);
554 if (!sum)
555 goto error;
556 isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);
557 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
558 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
559
560 isl_seq_clr(sum->row[0]+1, sum->n_col-1);
561 for (i = 1; i < sum->n_row; ++i) {
562 isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);
563 isl_int_addmul(sum->row[i][0],
564 right->row[0][0], right->row[i][0]);
565 isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],
566 left->n_col-1);
567 isl_seq_scale(sum->row[i]+left->n_col,
568 right->row[i]+1, right->row[0][0],
569 right->n_col-1);
570 }
571
572 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
573 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
574 isl_mat_free(left);
575 isl_mat_free(right);
576 return sum;
577 error:
578 isl_mat_free(left);
579 isl_mat_free(right);
580 return NULL;
581 }
582
583 static void exchange(struct isl_mat *M, struct isl_mat **U,
584 struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
585 {
586 int r;
587 for (r = row; r < M->n_row; ++r)
588 isl_int_swap(M->row[r][i], M->row[r][j]);
589 if (U) {
590 for (r = 0; r < (*U)->n_row; ++r)
591 isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
592 }
593 if (Q)
594 isl_mat_swap_rows(*Q, i, j);
595 }
596
597 static void subtract(struct isl_mat *M, struct isl_mat **U,
598 struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)
599 {
600 int r;
601 for (r = row; r < M->n_row; ++r)
602 isl_int_submul(M->row[r][j], m, M->row[r][i]);
603 if (U) {
604 for (r = 0; r < (*U)->n_row; ++r)
605 isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);
606 }
607 if (Q) {
608 for (r = 0; r < (*Q)->n_col; ++r)
609 isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);
610 }
611 }
612
613 static void oppose(struct isl_mat *M, struct isl_mat **U,
614 struct isl_mat **Q, unsigned row, unsigned col)
615 {
616 int r;
617 for (r = row; r < M->n_row; ++r)
618 isl_int_neg(M->row[r][col], M->row[r][col]);
619 if (U) {
620 for (r = 0; r < (*U)->n_row; ++r)
621 isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);
622 }
623 if (Q)
624 isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);
625 }
626
627 /* Given matrix M, compute
628 *
629 * M U = H
630 * M = H Q
631 *
632 * with U and Q unimodular matrices and H a matrix in column echelon form
633 * such that on each echelon row the entries in the non-echelon column
634 * are non-negative (if neg == 0) or non-positive (if neg == 1)
635 * and strictly smaller (in absolute value) than the entries in the echelon
636 * column.
637 * If U or Q are NULL, then these matrices are not computed.
638 */
639 __isl_give isl_mat *isl_mat_left_hermite(__isl_take isl_mat *M, int neg,
640 __isl_give isl_mat **U, __isl_give isl_mat **Q)
641 {
642 isl_int c;
643 int row, col;
644
645 if (U)
646 *U = NULL;
647 if (Q)
648 *Q = NULL;
649 if (!M)
650 goto error;
651 M = isl_mat_cow(M);
652 if (!M)
653 goto error;
654 if (U) {
655 *U = isl_mat_identity(M->ctx, M->n_col);
656 if (!*U)
657 goto error;
658 }
659 if (Q) {
660 *Q = isl_mat_identity(M->ctx, M->n_col);
661 if (!*Q)
662 goto error;
663 }
664
665 col = 0;
666 isl_int_init(c);
667 for (row = 0; row < M->n_row; ++row) {
668 int first, i, off;
669 first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);
670 if (first == -1)
671 continue;
672 first += col;
673 if (first != col)
674 exchange(M, U, Q, row, first, col);
675 if (isl_int_is_neg(M->row[row][col]))
676 oppose(M, U, Q, row, col);
677 first = col+1;
678 while ((off = isl_seq_first_non_zero(M->row[row]+first,
679 M->n_col-first)) != -1) {
680 first += off;
681 isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);
682 subtract(M, U, Q, row, col, first, c);
683 if (!isl_int_is_zero(M->row[row][first]))
684 exchange(M, U, Q, row, first, col);
685 else
686 ++first;
687 }
688 for (i = 0; i < col; ++i) {
689 if (isl_int_is_zero(M->row[row][i]))
690 continue;
691 if (neg)
692 isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);
693 else
694 isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);
695 if (isl_int_is_zero(c))
696 continue;
697 subtract(M, U, Q, row, col, i, c);
698 }
699 ++col;
700 }
701 isl_int_clear(c);
702
703 return M;
704 error:
705 if (Q) {
706 isl_mat_free(*Q);
707 *Q = NULL;
708 }
709 if (U) {
710 isl_mat_free(*U);
711 *U = NULL;
712 }
713 isl_mat_free(M);
714 return NULL;
715 }
716
717 /* Use row "row" of "mat" to eliminate column "col" from all other rows.
718 */
719 static __isl_give isl_mat *eliminate(__isl_take isl_mat *mat, int row, int col)
720 {
721 int k, nr, nc;
722 isl_ctx *ctx;
723
724 if (!mat)
725 return NULL;
726
727 ctx = isl_mat_get_ctx(mat);
728 nr = isl_mat_rows(mat);
729 nc = isl_mat_cols(mat);
730
731 for (k = 0; k < nr; ++k) {
732 if (k == row)
733 continue;
734 if (isl_int_is_zero(mat->row[k][col]))
735 continue;
736 mat = isl_mat_cow(mat);
737 if (!mat)
738 return NULL;
739 isl_seq_elim(mat->row[k], mat->row[row], col, nc, NULL);
740 isl_seq_normalize(ctx, mat->row[k], nc);
741 }
742
743 return mat;
744 }
745
746 /* Perform Gaussian elimination on the rows of "mat", but start
747 * from the final row and the final column.
748 * Any zero rows that result from the elimination are removed.
749 *
750 * In particular, for each column from last to first,
751 * look for the last row with a non-zero coefficient in that column,
752 * move it last (but before other rows moved last in previous steps) and
753 * use it to eliminate the column from the other rows.
754 */
755 __isl_give isl_mat *isl_mat_reverse_gauss(__isl_take isl_mat *mat)
756 {
757 int k, row, last, nr, nc;
758
759 if (!mat)
760 return NULL;
761
762 nr = isl_mat_rows(mat);
763 nc = isl_mat_cols(mat);
764
765 last = nc - 1;
766 for (row = nr - 1; row >= 0; --row) {
767 for (; last >= 0; --last) {
768 for (k = row; k >= 0; --k)
769 if (!isl_int_is_zero(mat->row[k][last]))
770 break;
771 if (k >= 0)
772 break;
773 }
774 if (last < 0)
775 break;
776 if (k != row)
777 mat = isl_mat_swap_rows(mat, k, row);
778 if (!mat)
779 return NULL;
780 if (isl_int_is_neg(mat->row[row][last]))
781 mat = isl_mat_row_neg(mat, row);
782 mat = eliminate(mat, row, last);
783 if (!mat)
784 return NULL;
785 }
786 mat = isl_mat_drop_rows(mat, 0, row + 1);
787
788 return mat;
789 }
790
791 /* Negate the lexicographically negative rows of "mat" such that
792 * all rows in the result are lexicographically non-negative.
793 */
794 __isl_give isl_mat *isl_mat_lexnonneg_rows(__isl_take isl_mat *mat)
795 {
796 int i, nr, nc;
797
798 if (!mat)
799 return NULL;
800
801 nr = isl_mat_rows(mat);
802 nc = isl_mat_cols(mat);
803
804 for (i = 0; i < nr; ++i) {
805 int pos;
806
807 pos = isl_seq_first_non_zero(mat->row[i], nc);
808 if (pos < 0)
809 continue;
810 if (isl_int_is_nonneg(mat->row[i][pos]))
811 continue;
812 mat = isl_mat_row_neg(mat, i);
813 if (!mat)
814 return NULL;
815 }
816
817 return mat;
818 }
819
820 /* Given a matrix "H" is column echelon form, what is the first
821 * zero column? That is how many initial columns are non-zero?
822 * Start looking at column "first_col" and only consider
823 * the columns to be of size "n_row".
824 * "H" is assumed to be non-NULL.
825 *
826 * Since "H" is in column echelon form, the first non-zero entry
827 * in a column is always in a later position compared to the previous column.
828 */
829 static int hermite_first_zero_col(__isl_keep isl_mat *H, int first_col,
830 int n_row)
831 {
832 int row, col;
833
834 for (col = first_col, row = 0; col < H->n_col; ++col) {
835 for (; row < n_row; ++row)
836 if (!isl_int_is_zero(H->row[row][col]))
837 break;
838 if (row == n_row)
839 return col;
840 }
841
842 return H->n_col;
843 }
844
845 /* Return the rank of "mat", or -1 in case of error.
846 */
847 int isl_mat_rank(__isl_keep isl_mat *mat)
848 {
849 int rank;
850 isl_mat *H;
851
852 H = isl_mat_left_hermite(isl_mat_copy(mat), 0, NULL, NULL);
853 if (!H)
854 return -1;
855
856 rank = hermite_first_zero_col(H, 0, H->n_row);
857 isl_mat_free(H);
858
859 return rank;
860 }
861
862 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat)
863 {
864 int rank;
865 struct isl_mat *U = NULL;
866 struct isl_mat *K;
867
868 mat = isl_mat_left_hermite(mat, 0, &U, NULL);
869 if (!mat || !U)
870 goto error;
871
872 rank = hermite_first_zero_col(mat, 0, mat->n_row);
873 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
874 if (!K)
875 goto error;
876 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
877 isl_mat_free(mat);
878 isl_mat_free(U);
879 return K;
880 error:
881 isl_mat_free(mat);
882 isl_mat_free(U);
883 return NULL;
884 }
885
886 __isl_give isl_mat *isl_mat_lin_to_aff(__isl_take isl_mat *mat)
887 {
888 int i;
889 struct isl_mat *mat2;
890
891 if (!mat)
892 return NULL;
893 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
894 if (!mat2)
895 goto error;
896 isl_int_set_si(mat2->row[0][0], 1);
897 isl_seq_clr(mat2->row[0]+1, mat->n_col);
898 for (i = 0; i < mat->n_row; ++i) {
899 isl_int_set_si(mat2->row[1+i][0], 0);
900 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
901 }
902 isl_mat_free(mat);
903 return mat2;
904 error:
905 isl_mat_free(mat);
906 return NULL;
907 }
908
909 /* Given two matrices M1 and M2, return the block matrix
910 *
911 * [ M1 0 ]
912 * [ 0 M2 ]
913 */
914 __isl_give isl_mat *isl_mat_diagonal(__isl_take isl_mat *mat1,
915 __isl_take isl_mat *mat2)
916 {
917 int i;
918 isl_mat *mat;
919
920 if (!mat1 || !mat2)
921 goto error;
922
923 mat = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
924 mat1->n_col + mat2->n_col);
925 if (!mat)
926 goto error;
927 for (i = 0; i < mat1->n_row; ++i) {
928 isl_seq_cpy(mat->row[i], mat1->row[i], mat1->n_col);
929 isl_seq_clr(mat->row[i] + mat1->n_col, mat2->n_col);
930 }
931 for (i = 0; i < mat2->n_row; ++i) {
932 isl_seq_clr(mat->row[mat1->n_row + i], mat1->n_col);
933 isl_seq_cpy(mat->row[mat1->n_row + i] + mat1->n_col,
934 mat2->row[i], mat2->n_col);
935 }
936 isl_mat_free(mat1);
937 isl_mat_free(mat2);
938 return mat;
939 error:
940 isl_mat_free(mat1);
941 isl_mat_free(mat2);
942 return NULL;
943 }
944
945 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
946 {
947 int i;
948
949 for (i = 0; i < n_row; ++i)
950 if (!isl_int_is_zero(row[i][col]))
951 return i;
952 return -1;
953 }
954
955 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
956 {
957 int i, min = row_first_non_zero(row, n_row, col);
958 if (min < 0)
959 return -1;
960 for (i = min + 1; i < n_row; ++i) {
961 if (isl_int_is_zero(row[i][col]))
962 continue;
963 if (isl_int_abs_lt(row[i][col], row[min][col]))
964 min = i;
965 }
966 return min;
967 }
968
969 static isl_stat inv_exchange(__isl_keep isl_mat **left,
970 __isl_keep isl_mat **right, unsigned i, unsigned j)
971 {
972 *left = isl_mat_swap_rows(*left, i, j);
973 *right = isl_mat_swap_rows(*right, i, j);
974
975 if (!*left || !*right)
976 return isl_stat_error;
977 return isl_stat_ok;
978 }
979
980 static void inv_oppose(
981 struct isl_mat *left, struct isl_mat *right, unsigned row)
982 {
983 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
984 isl_seq_neg(right->row[row], right->row[row], right->n_col);
985 }
986
987 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
988 unsigned row, unsigned i, isl_int m)
989 {
990 isl_int_neg(m, m);
991 isl_seq_combine(left->row[i]+row,
992 left->ctx->one, left->row[i]+row,
993 m, left->row[row]+row,
994 left->n_col-row);
995 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
996 m, right->row[row], right->n_col);
997 }
998
999 /* Compute inv(left)*right
1000 */
1001 __isl_give isl_mat *isl_mat_inverse_product(__isl_take isl_mat *left,
1002 __isl_take isl_mat *right)
1003 {
1004 int row;
1005 isl_int a, b;
1006
1007 if (!left || !right)
1008 goto error;
1009
1010 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
1011 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
1012
1013 if (left->n_row == 0) {
1014 isl_mat_free(left);
1015 return right;
1016 }
1017
1018 left = isl_mat_cow(left);
1019 right = isl_mat_cow(right);
1020 if (!left || !right)
1021 goto error;
1022
1023 isl_int_init(a);
1024 isl_int_init(b);
1025 for (row = 0; row < left->n_row; ++row) {
1026 int pivot, first, i, off;
1027 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
1028 if (pivot < 0) {
1029 isl_int_clear(a);
1030 isl_int_clear(b);
1031 isl_assert(left->ctx, pivot >= 0, goto error);
1032 }
1033 pivot += row;
1034 if (pivot != row)
1035 if (inv_exchange(&left, &right, pivot, row) < 0)
1036 goto error;
1037 if (isl_int_is_neg(left->row[row][row]))
1038 inv_oppose(left, right, row);
1039 first = row+1;
1040 while ((off = row_first_non_zero(left->row+first,
1041 left->n_row-first, row)) != -1) {
1042 first += off;
1043 isl_int_fdiv_q(a, left->row[first][row],
1044 left->row[row][row]);
1045 inv_subtract(left, right, row, first, a);
1046 if (!isl_int_is_zero(left->row[first][row])) {
1047 if (inv_exchange(&left, &right, row, first) < 0)
1048 goto error;
1049 } else {
1050 ++first;
1051 }
1052 }
1053 for (i = 0; i < row; ++i) {
1054 if (isl_int_is_zero(left->row[i][row]))
1055 continue;
1056 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
1057 isl_int_divexact(b, left->row[i][row], a);
1058 isl_int_divexact(a, left->row[row][row], a);
1059 isl_int_neg(b, b);
1060 isl_seq_combine(left->row[i] + i,
1061 a, left->row[i] + i,
1062 b, left->row[row] + i,
1063 left->n_col - i);
1064 isl_seq_combine(right->row[i], a, right->row[i],
1065 b, right->row[row], right->n_col);
1066 }
1067 }
1068 isl_int_clear(b);
1069
1070 isl_int_set(a, left->row[0][0]);
1071 for (row = 1; row < left->n_row; ++row)
1072 isl_int_lcm(a, a, left->row[row][row]);
1073 if (isl_int_is_zero(a)){
1074 isl_int_clear(a);
1075 isl_assert(left->ctx, 0, goto error);
1076 }
1077 for (row = 0; row < left->n_row; ++row) {
1078 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
1079 if (isl_int_is_one(left->row[row][row]))
1080 continue;
1081 isl_seq_scale(right->row[row], right->row[row],
1082 left->row[row][row], right->n_col);
1083 }
1084 isl_int_clear(a);
1085
1086 isl_mat_free(left);
1087 return right;
1088 error:
1089 isl_mat_free(left);
1090 isl_mat_free(right);
1091 return NULL;
1092 }
1093
1094 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
1095 {
1096 int i;
1097
1098 for (i = 0; i < mat->n_row; ++i)
1099 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
1100 }
1101
1102 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
1103 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
1104 {
1105 int i;
1106 isl_int tmp;
1107
1108 isl_int_init(tmp);
1109 for (i = 0; i < mat->n_row; ++i) {
1110 isl_int_mul(tmp, m1, mat->row[i][src1]);
1111 isl_int_addmul(tmp, m2, mat->row[i][src2]);
1112 isl_int_set(mat->row[i][dst], tmp);
1113 }
1114 isl_int_clear(tmp);
1115 }
1116
1117 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat)
1118 {
1119 struct isl_mat *inv;
1120 int row;
1121 isl_int a, b;
1122
1123 mat = isl_mat_cow(mat);
1124 if (!mat)
1125 return NULL;
1126
1127 inv = isl_mat_identity(mat->ctx, mat->n_col);
1128 inv = isl_mat_cow(inv);
1129 if (!inv)
1130 goto error;
1131
1132 isl_int_init(a);
1133 isl_int_init(b);
1134 for (row = 0; row < mat->n_row; ++row) {
1135 int pivot, first, i, off;
1136 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
1137 if (pivot < 0) {
1138 isl_int_clear(a);
1139 isl_int_clear(b);
1140 isl_assert(mat->ctx, pivot >= 0, goto error);
1141 }
1142 pivot += row;
1143 if (pivot != row)
1144 exchange(mat, &inv, NULL, row, pivot, row);
1145 if (isl_int_is_neg(mat->row[row][row]))
1146 oppose(mat, &inv, NULL, row, row);
1147 first = row+1;
1148 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
1149 mat->n_col-first)) != -1) {
1150 first += off;
1151 isl_int_fdiv_q(a, mat->row[row][first],
1152 mat->row[row][row]);
1153 subtract(mat, &inv, NULL, row, row, first, a);
1154 if (!isl_int_is_zero(mat->row[row][first]))
1155 exchange(mat, &inv, NULL, row, row, first);
1156 else
1157 ++first;
1158 }
1159 for (i = 0; i < row; ++i) {
1160 if (isl_int_is_zero(mat->row[row][i]))
1161 continue;
1162 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
1163 isl_int_divexact(b, mat->row[row][i], a);
1164 isl_int_divexact(a, mat->row[row][row], a);
1165 isl_int_neg(a, a);
1166 isl_mat_col_combine(mat, i, a, i, b, row);
1167 isl_mat_col_combine(inv, i, a, i, b, row);
1168 }
1169 }
1170 isl_int_clear(b);
1171
1172 isl_int_set(a, mat->row[0][0]);
1173 for (row = 1; row < mat->n_row; ++row)
1174 isl_int_lcm(a, a, mat->row[row][row]);
1175 if (isl_int_is_zero(a)){
1176 isl_int_clear(a);
1177 goto error;
1178 }
1179 for (row = 0; row < mat->n_row; ++row) {
1180 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
1181 if (isl_int_is_one(mat->row[row][row]))
1182 continue;
1183 isl_mat_col_scale(inv, row, mat->row[row][row]);
1184 }
1185 isl_int_clear(a);
1186
1187 isl_mat_free(mat);
1188
1189 return inv;
1190 error:
1191 isl_mat_free(mat);
1192 isl_mat_free(inv);
1193 return NULL;
1194 }
1195
1196 __isl_give isl_mat *isl_mat_transpose(__isl_take isl_mat *mat)
1197 {
1198 struct isl_mat *transpose = NULL;
1199 int i, j;
1200
1201 if (!mat)
1202 return NULL;
1203
1204 if (mat->n_col == mat->n_row) {
1205 mat = isl_mat_cow(mat);
1206 if (!mat)
1207 return NULL;
1208 for (i = 0; i < mat->n_row; ++i)
1209 for (j = i + 1; j < mat->n_col; ++j)
1210 isl_int_swap(mat->row[i][j], mat->row[j][i]);
1211 return mat;
1212 }
1213 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
1214 if (!transpose)
1215 goto error;
1216 for (i = 0; i < mat->n_row; ++i)
1217 for (j = 0; j < mat->n_col; ++j)
1218 isl_int_set(transpose->row[j][i], mat->row[i][j]);
1219 isl_mat_free(mat);
1220 return transpose;
1221 error:
1222 isl_mat_free(mat);
1223 return NULL;
1224 }
1225
1226 __isl_give isl_mat *isl_mat_swap_cols(__isl_take isl_mat *mat,
1227 unsigned i, unsigned j)
1228 {
1229 int r;
1230
1231 mat = isl_mat_cow(mat);
1232 if (check_col_range(mat, i, 1) < 0 ||
1233 check_col_range(mat, j, 1) < 0)
1234 return isl_mat_free(mat);
1235
1236 for (r = 0; r < mat->n_row; ++r)
1237 isl_int_swap(mat->row[r][i], mat->row[r][j]);
1238 return mat;
1239 }
1240
1241 __isl_give isl_mat *isl_mat_swap_rows(__isl_take isl_mat *mat,
1242 unsigned i, unsigned j)
1243 {
1244 isl_int *t;
1245
1246 if (!mat)
1247 return NULL;
1248 mat = isl_mat_cow(mat);
1249 if (check_row_range(mat, i, 1) < 0 ||
1250 check_row_range(mat, j, 1) < 0)
1251 return isl_mat_free(mat);
1252
1253 t = mat->row[i];
1254 mat->row[i] = mat->row[j];
1255 mat->row[j] = t;
1256 return mat;
1257 }
1258
1259 /* Calculate the product of two matrices.
1260 *
1261 * This function is optimized for operand matrices that contain many zeros and
1262 * skips multiplications where we know one of the operands is zero.
1263 */
1264 __isl_give isl_mat *isl_mat_product(__isl_take isl_mat *left,
1265 __isl_take isl_mat *right)
1266 {
1267 int i, j, k;
1268 struct isl_mat *prod;
1269
1270 if (!left || !right)
1271 goto error;
1272 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
1273 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
1274 if (!prod)
1275 goto error;
1276 if (left->n_col == 0) {
1277 for (i = 0; i < prod->n_row; ++i)
1278 isl_seq_clr(prod->row[i], prod->n_col);
1279 isl_mat_free(left);
1280 isl_mat_free(right);
1281 return prod;
1282 }
1283 for (i = 0; i < prod->n_row; ++i) {
1284 for (j = 0; j < prod->n_col; ++j)
1285 isl_int_mul(prod->row[i][j],
1286 left->row[i][0], right->row[0][j]);
1287 for (k = 1; k < left->n_col; ++k) {
1288 if (isl_int_is_zero(left->row[i][k]))
1289 continue;
1290 for (j = 0; j < prod->n_col; ++j)
1291 isl_int_addmul(prod->row[i][j],
1292 left->row[i][k], right->row[k][j]);
1293 }
1294 }
1295 isl_mat_free(left);
1296 isl_mat_free(right);
1297 return prod;
1298 error:
1299 isl_mat_free(left);
1300 isl_mat_free(right);
1301 return NULL;
1302 }
1303
1304 /* Replace the variables x in the rows q by x' given by x = M x',
1305 * with M the matrix mat.
1306 *
1307 * If the number of new variables is greater than the original
1308 * number of variables, then the rows q have already been
1309 * preextended. If the new number is smaller, then the coefficients
1310 * of the divs, which are not changed, need to be shifted down.
1311 * The row q may be the equalities, the inequalities or the
1312 * div expressions. In the latter case, has_div is true and
1313 * we need to take into account the extra denominator column.
1314 */
1315 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
1316 unsigned n_div, int has_div, struct isl_mat *mat)
1317 {
1318 int i;
1319 struct isl_mat *t;
1320 int e;
1321
1322 if (mat->n_col >= mat->n_row)
1323 e = 0;
1324 else
1325 e = mat->n_row - mat->n_col;
1326 if (has_div)
1327 for (i = 0; i < n; ++i)
1328 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
1329 t = isl_mat_sub_alloc6(mat->ctx, q, 0, n, has_div, mat->n_row);
1330 t = isl_mat_product(t, mat);
1331 if (!t)
1332 return -1;
1333 for (i = 0; i < n; ++i) {
1334 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
1335 isl_seq_cpy(q[i] + has_div + t->n_col,
1336 q[i] + has_div + t->n_col + e, n_div);
1337 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
1338 }
1339 isl_mat_free(t);
1340 return 0;
1341 }
1342
1343 /* Replace the variables x in bset by x' given by x = M x', with
1344 * M the matrix mat.
1345 *
1346 * If there are fewer variables x' then there are x, then we perform
1347 * the transformation in place, which means that, in principle,
1348 * this frees up some extra variables as the number
1349 * of columns remains constant, but we would have to extend
1350 * the div array too as the number of rows in this array is assumed
1351 * to be equal to extra.
1352 */
1353 __isl_give isl_basic_set *isl_basic_set_preimage(
1354 __isl_take isl_basic_set *bset, __isl_take isl_mat *mat)
1355 {
1356 struct isl_ctx *ctx;
1357
1358 if (!bset || !mat)
1359 goto error;
1360
1361 ctx = bset->ctx;
1362 bset = isl_basic_set_cow(bset);
1363 if (isl_basic_set_check_no_params(bset) < 0)
1364 goto error;
1365
1366 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
1367 isl_assert(ctx, mat->n_col > 0, goto error);
1368
1369 if (mat->n_col > mat->n_row) {
1370 bset = isl_basic_set_add_dims(bset, isl_dim_set,
1371 mat->n_col - mat->n_row);
1372 if (!bset)
1373 goto error;
1374 } else if (mat->n_col < mat->n_row) {
1375 bset->dim = isl_space_cow(bset->dim);
1376 if (!bset->dim)
1377 goto error;
1378 bset->dim->n_out -= mat->n_row - mat->n_col;
1379 }
1380
1381 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
1382 isl_mat_copy(mat)) < 0)
1383 goto error;
1384
1385 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
1386 isl_mat_copy(mat)) < 0)
1387 goto error;
1388
1389 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
1390 goto error2;
1391
1392 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
1393 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
1394 ISL_F_CLR(bset, ISL_BASIC_SET_SORTED);
1395 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1396 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
1397
1398 bset = isl_basic_set_simplify(bset);
1399 bset = isl_basic_set_finalize(bset);
1400
1401 return bset;
1402 error:
1403 isl_mat_free(mat);
1404 error2:
1405 isl_basic_set_free(bset);
1406 return NULL;
1407 }
1408
1409 __isl_give isl_set *isl_set_preimage(
1410 __isl_take isl_set *set, __isl_take isl_mat *mat)
1411 {
1412 int i;
1413
1414 set = isl_set_cow(set);
1415 if (!set)
1416 goto error;
1417
1418 for (i = 0; i < set->n; ++i) {
1419 set->p[i] = isl_basic_set_preimage(set->p[i],
1420 isl_mat_copy(mat));
1421 if (!set->p[i])
1422 goto error;
1423 }
1424 if (mat->n_col != mat->n_row) {
1425 set->dim = isl_space_cow(set->dim);
1426 if (!set->dim)
1427 goto error;
1428 set->dim->n_out += mat->n_col;
1429 set->dim->n_out -= mat->n_row;
1430 }
1431 isl_mat_free(mat);
1432 ISL_F_CLR(set, ISL_SET_NORMALIZED);
1433 return set;
1434 error:
1435 isl_set_free(set);
1436 isl_mat_free(mat);
1437 return NULL;
1438 }
1439
1440 /* Replace the variables x starting at "first_col" in the rows "rows"
1441 * of some coefficient matrix by x' with x = M x' with M the matrix mat.
1442 * That is, replace the corresponding coefficients c by c M.
1443 */
1444 isl_stat isl_mat_sub_transform(isl_int **row, unsigned n_row,
1445 unsigned first_col, __isl_take isl_mat *mat)
1446 {
1447 int i;
1448 isl_ctx *ctx;
1449 isl_mat *t;
1450
1451 if (!mat)
1452 return isl_stat_error;
1453 ctx = isl_mat_get_ctx(mat);
1454 t = isl_mat_sub_alloc6(ctx, row, 0, n_row, first_col, mat->n_row);
1455 t = isl_mat_product(t, mat);
1456 if (!t)
1457 return isl_stat_error;
1458 for (i = 0; i < n_row; ++i)
1459 isl_seq_swp_or_cpy(row[i] + first_col, t->row[i], t->n_col);
1460 isl_mat_free(t);
1461 return isl_stat_ok;
1462 }
1463
1464 void isl_mat_print_internal(__isl_keep isl_mat *mat, FILE *out, int indent)
1465 {
1466 int i, j;
1467
1468 if (!mat) {
1469 fprintf(out, "%*snull mat\n", indent, "");
1470 return;
1471 }
1472
1473 if (mat->n_row == 0)
1474 fprintf(out, "%*s[]\n", indent, "");
1475
1476 for (i = 0; i < mat->n_row; ++i) {
1477 if (!i)
1478 fprintf(out, "%*s[[", indent, "");
1479 else
1480 fprintf(out, "%*s[", indent+1, "");
1481 for (j = 0; j < mat->n_col; ++j) {
1482 if (j)
1483 fprintf(out, ",");
1484 isl_int_print(out, mat->row[i][j], 0);
1485 }
1486 if (i == mat->n_row-1)
1487 fprintf(out, "]]\n");
1488 else
1489 fprintf(out, "]\n");
1490 }
1491 }
1492
1493 void isl_mat_dump(__isl_keep isl_mat *mat)
1494 {
1495 isl_mat_print_internal(mat, stderr, 0);
1496 }
1497
1498 __isl_give isl_mat *isl_mat_drop_cols(__isl_take isl_mat *mat,
1499 unsigned col, unsigned n)
1500 {
1501 int r;
1502
1503 if (n == 0)
1504 return mat;
1505
1506 mat = isl_mat_cow(mat);
1507 if (check_col_range(mat, col, n) < 0)
1508 return isl_mat_free(mat);
1509
1510 if (col != mat->n_col-n) {
1511 for (r = 0; r < mat->n_row; ++r)
1512 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1513 mat->n_col - col - n);
1514 }
1515 mat->n_col -= n;
1516 return mat;
1517 }
1518
1519 __isl_give isl_mat *isl_mat_drop_rows(__isl_take isl_mat *mat,
1520 unsigned row, unsigned n)
1521 {
1522 int r;
1523
1524 mat = isl_mat_cow(mat);
1525 if (check_row_range(mat, row, n) < 0)
1526 return isl_mat_free(mat);
1527
1528 for (r = row; r+n < mat->n_row; ++r)
1529 mat->row[r] = mat->row[r+n];
1530
1531 mat->n_row -= n;
1532 return mat;
1533 }
1534
1535 __isl_give isl_mat *isl_mat_insert_cols(__isl_take isl_mat *mat,
1536 unsigned col, unsigned n)
1537 {
1538 isl_mat *ext;
1539
1540 if (check_col_range(mat, col, 0) < 0)
1541 return isl_mat_free(mat);
1542 if (n == 0)
1543 return mat;
1544
1545 ext = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col + n);
1546 if (!ext)
1547 goto error;
1548
1549 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row, 0, 0, col);
1550 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row,
1551 col + n, col, mat->n_col - col);
1552
1553 isl_mat_free(mat);
1554 return ext;
1555 error:
1556 isl_mat_free(mat);
1557 return NULL;
1558 }
1559
1560 __isl_give isl_mat *isl_mat_insert_zero_cols(__isl_take isl_mat *mat,
1561 unsigned first, unsigned n)
1562 {
1563 int i;
1564
1565 if (!mat)
1566 return NULL;
1567 mat = isl_mat_insert_cols(mat, first, n);
1568 if (!mat)
1569 return NULL;
1570
1571 for (i = 0; i < mat->n_row; ++i)
1572 isl_seq_clr(mat->row[i] + first, n);
1573
1574 return mat;
1575 }
1576
1577 __isl_give isl_mat *isl_mat_add_zero_cols(__isl_take isl_mat *mat, unsigned n)
1578 {
1579 if (!mat)
1580 return NULL;
1581
1582 return isl_mat_insert_zero_cols(mat, mat->n_col, n);
1583 }
1584
1585 __isl_give isl_mat *isl_mat_insert_rows(__isl_take isl_mat *mat,
1586 unsigned row, unsigned n)
1587 {
1588 isl_mat *ext;
1589
1590 if (check_row_range(mat, row, 0) < 0)
1591 return isl_mat_free(mat);
1592 if (n == 0)
1593 return mat;
1594
1595 ext = isl_mat_alloc(mat->ctx, mat->n_row + n, mat->n_col);
1596 if (!ext)
1597 goto error;
1598
1599 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, row, 0, 0, mat->n_col);
1600 isl_mat_sub_copy(mat->ctx, ext->row + row + n, mat->row + row,
1601 mat->n_row - row, 0, 0, mat->n_col);
1602
1603 isl_mat_free(mat);
1604 return ext;
1605 error:
1606 isl_mat_free(mat);
1607 return NULL;
1608 }
1609
1610 __isl_give isl_mat *isl_mat_add_rows(__isl_take isl_mat *mat, unsigned n)
1611 {
1612 if (!mat)
1613 return NULL;
1614
1615 return isl_mat_insert_rows(mat, mat->n_row, n);
1616 }
1617
1618 __isl_give isl_mat *isl_mat_insert_zero_rows(__isl_take isl_mat *mat,
1619 unsigned row, unsigned n)
1620 {
1621 int i;
1622
1623 mat = isl_mat_insert_rows(mat, row, n);
1624 if (!mat)
1625 return NULL;
1626
1627 for (i = 0; i < n; ++i)
1628 isl_seq_clr(mat->row[row + i], mat->n_col);
1629
1630 return mat;
1631 }
1632
1633 __isl_give isl_mat *isl_mat_add_zero_rows(__isl_take isl_mat *mat, unsigned n)
1634 {
1635 if (!mat)
1636 return NULL;
1637
1638 return isl_mat_insert_zero_rows(mat, mat->n_row, n);
1639 }
1640
1641 void isl_mat_col_submul(struct isl_mat *mat,
1642 int dst_col, isl_int f, int src_col)
1643 {
1644 int i;
1645
1646 for (i = 0; i < mat->n_row; ++i)
1647 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1648 }
1649
1650 void isl_mat_col_add(__isl_keep isl_mat *mat, int dst_col, int src_col)
1651 {
1652 int i;
1653
1654 if (!mat)
1655 return;
1656
1657 for (i = 0; i < mat->n_row; ++i)
1658 isl_int_add(mat->row[i][dst_col],
1659 mat->row[i][dst_col], mat->row[i][src_col]);
1660 }
1661
1662 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1663 {
1664 int i;
1665
1666 for (i = 0; i < mat->n_row; ++i)
1667 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1668 }
1669
1670 /* Add "f" times column "src_col" to column "dst_col" of "mat" and
1671 * return the result.
1672 */
1673 __isl_give isl_mat *isl_mat_col_addmul(__isl_take isl_mat *mat, int dst_col,
1674 isl_int f, int src_col)
1675 {
1676 int i;
1677
1678 if (check_col(mat, dst_col) < 0 || check_col(mat, src_col) < 0)
1679 return isl_mat_free(mat);
1680
1681 for (i = 0; i < mat->n_row; ++i) {
1682 if (isl_int_is_zero(mat->row[i][src_col]))
1683 continue;
1684 mat = isl_mat_cow(mat);
1685 if (!mat)
1686 return NULL;
1687 isl_int_addmul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1688 }
1689
1690 return mat;
1691 }
1692
1693 /* Negate column "col" of "mat" and return the result.
1694 */
1695 __isl_give isl_mat *isl_mat_col_neg(__isl_take isl_mat *mat, int col)
1696 {
1697 int i;
1698
1699 if (check_col(mat, col) < 0)
1700 return isl_mat_free(mat);
1701
1702 for (i = 0; i < mat->n_row; ++i) {
1703 if (isl_int_is_zero(mat->row[i][col]))
1704 continue;
1705 mat = isl_mat_cow(mat);
1706 if (!mat)
1707 return NULL;
1708 isl_int_neg(mat->row[i][col], mat->row[i][col]);
1709 }
1710
1711 return mat;
1712 }
1713
1714 /* Negate row "row" of "mat" and return the result.
1715 */
1716 __isl_give isl_mat *isl_mat_row_neg(__isl_take isl_mat *mat, int row)
1717 {
1718 if (check_row(mat, row) < 0)
1719 return isl_mat_free(mat);
1720 if (isl_seq_first_non_zero(mat->row[row], mat->n_col) == -1)
1721 return mat;
1722 mat = isl_mat_cow(mat);
1723 if (!mat)
1724 return NULL;
1725 isl_seq_neg(mat->row[row], mat->row[row], mat->n_col);
1726 return mat;
1727 }
1728
1729 __isl_give isl_mat *isl_mat_unimodular_complete(__isl_take isl_mat *M, int row)
1730 {
1731 int r;
1732 struct isl_mat *H = NULL, *Q = NULL;
1733
1734 if (!M)
1735 return NULL;
1736
1737 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1738 M->n_row = row;
1739 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1740 M->n_row = M->n_col;
1741 if (!H)
1742 goto error;
1743 for (r = 0; r < row; ++r)
1744 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1745 for (r = row; r < M->n_row; ++r)
1746 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1747 isl_mat_free(H);
1748 isl_mat_free(Q);
1749 return M;
1750 error:
1751 isl_mat_free(H);
1752 isl_mat_free(Q);
1753 isl_mat_free(M);
1754 return NULL;
1755 }
1756
1757 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1758 __isl_take isl_mat *bot)
1759 {
1760 struct isl_mat *mat;
1761
1762 if (!top || !bot)
1763 goto error;
1764
1765 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1766 if (top->n_row == 0) {
1767 isl_mat_free(top);
1768 return bot;
1769 }
1770 if (bot->n_row == 0) {
1771 isl_mat_free(bot);
1772 return top;
1773 }
1774
1775 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1776 if (!mat)
1777 goto error;
1778 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1779 0, 0, mat->n_col);
1780 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1781 0, 0, mat->n_col);
1782 isl_mat_free(top);
1783 isl_mat_free(bot);
1784 return mat;
1785 error:
1786 isl_mat_free(top);
1787 isl_mat_free(bot);
1788 return NULL;
1789 }
1790
1791 isl_bool isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
1792 {
1793 int i;
1794
1795 if (!mat1 || !mat2)
1796 return isl_bool_error;
1797
1798 if (mat1->n_row != mat2->n_row)
1799 return isl_bool_false;
1800
1801 if (mat1->n_col != mat2->n_col)
1802 return isl_bool_false;
1803
1804 for (i = 0; i < mat1->n_row; ++i)
1805 if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
1806 return isl_bool_false;
1807
1808 return isl_bool_true;
1809 }
1810
1811 __isl_give isl_mat *isl_mat_from_row_vec(__isl_take isl_vec *vec)
1812 {
1813 struct isl_mat *mat;
1814
1815 if (!vec)
1816 return NULL;
1817 mat = isl_mat_alloc(vec->ctx, 1, vec->size);
1818 if (!mat)
1819 goto error;
1820
1821 isl_seq_cpy(mat->row[0], vec->el, vec->size);
1822
1823 isl_vec_free(vec);
1824 return mat;
1825 error:
1826 isl_vec_free(vec);
1827 return NULL;
1828 }
1829
1830 /* Return a copy of row "row" of "mat" as an isl_vec.
1831 */
1832 __isl_give isl_vec *isl_mat_get_row(__isl_keep isl_mat *mat, unsigned row)
1833 {
1834 isl_vec *v;
1835
1836 if (!mat)
1837 return NULL;
1838 if (row >= mat->n_row)
1839 isl_die(mat->ctx, isl_error_invalid, "row out of range",
1840 return NULL);
1841
1842 v = isl_vec_alloc(isl_mat_get_ctx(mat), mat->n_col);
1843 if (!v)
1844 return NULL;
1845 isl_seq_cpy(v->el, mat->row[row], mat->n_col);
1846
1847 return v;
1848 }
1849
1850 __isl_give isl_mat *isl_mat_vec_concat(__isl_take isl_mat *top,
1851 __isl_take isl_vec *bot)
1852 {
1853 return isl_mat_concat(top, isl_mat_from_row_vec(bot));
1854 }
1855
1856 __isl_give isl_mat *isl_mat_move_cols(__isl_take isl_mat *mat,
1857 unsigned dst_col, unsigned src_col, unsigned n)
1858 {
1859 isl_mat *res;
1860
1861 if (!mat)
1862 return NULL;
1863 if (n == 0 || dst_col == src_col)
1864 return mat;
1865
1866 res = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
1867 if (!res)
1868 goto error;
1869
1870 if (dst_col < src_col) {
1871 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1872 0, 0, dst_col);
1873 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1874 dst_col, src_col, n);
1875 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1876 dst_col + n, dst_col, src_col - dst_col);
1877 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1878 src_col + n, src_col + n,
1879 res->n_col - src_col - n);
1880 } else {
1881 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1882 0, 0, src_col);
1883 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1884 src_col, src_col + n, dst_col - src_col);
1885 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1886 dst_col, src_col, n);
1887 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1888 dst_col + n, dst_col + n,
1889 res->n_col - dst_col - n);
1890 }
1891 isl_mat_free(mat);
1892
1893 return res;
1894 error:
1895 isl_mat_free(mat);
1896 return NULL;
1897 }
1898
1899 /* Return the gcd of the elements in row "row" of "mat" in *gcd.
1900 * Return isl_stat_ok on success and isl_stat_error on failure.
1901 */
1902 isl_stat isl_mat_row_gcd(__isl_keep isl_mat *mat, int row, isl_int *gcd)
1903 {
1904 if (check_row(mat, row) < 0)
1905 return isl_stat_error;
1906
1907 isl_seq_gcd(mat->row[row], mat->n_col, gcd);
1908
1909 return isl_stat_ok;
1910 }
1911
1912 void isl_mat_gcd(__isl_keep isl_mat *mat, isl_int *gcd)
1913 {
1914 int i;
1915 isl_int g;
1916
1917 isl_int_set_si(*gcd, 0);
1918 if (!mat)
1919 return;
1920
1921 isl_int_init(g);
1922 for (i = 0; i < mat->n_row; ++i) {
1923 isl_seq_gcd(mat->row[i], mat->n_col, &g);
1924 isl_int_gcd(*gcd, *gcd, g);
1925 }
1926 isl_int_clear(g);
1927 }
1928
1929 /* Return the result of scaling "mat" by a factor of "m".
1930 */
1931 __isl_give isl_mat *isl_mat_scale(__isl_take isl_mat *mat, isl_int m)
1932 {
1933 int i;
1934
1935 if (isl_int_is_one(m))
1936 return mat;
1937
1938 mat = isl_mat_cow(mat);
1939 if (!mat)
1940 return NULL;
1941
1942 for (i = 0; i < mat->n_row; ++i)
1943 isl_seq_scale(mat->row[i], mat->row[i], m, mat->n_col);
1944
1945 return mat;
1946 }
1947
1948 __isl_give isl_mat *isl_mat_scale_down(__isl_take isl_mat *mat, isl_int m)
1949 {
1950 int i;
1951
1952 if (isl_int_is_one(m))
1953 return mat;
1954
1955 mat = isl_mat_cow(mat);
1956 if (!mat)
1957 return NULL;
1958
1959 for (i = 0; i < mat->n_row; ++i)
1960 isl_seq_scale_down(mat->row[i], mat->row[i], m, mat->n_col);
1961
1962 return mat;
1963 }
1964
1965 __isl_give isl_mat *isl_mat_scale_down_row(__isl_take isl_mat *mat, int row,
1966 isl_int m)
1967 {
1968 if (isl_int_is_one(m))
1969 return mat;
1970
1971 mat = isl_mat_cow(mat);
1972 if (!mat)
1973 return NULL;
1974
1975 isl_seq_scale_down(mat->row[row], mat->row[row], m, mat->n_col);
1976
1977 return mat;
1978 }
1979
1980 __isl_give isl_mat *isl_mat_normalize(__isl_take isl_mat *mat)
1981 {
1982 isl_int gcd;
1983
1984 if (!mat)
1985 return NULL;
1986
1987 isl_int_init(gcd);
1988 isl_mat_gcd(mat, &gcd);
1989 mat = isl_mat_scale_down(mat, gcd);
1990 isl_int_clear(gcd);
1991
1992 return mat;
1993 }
1994
1995 __isl_give isl_mat *isl_mat_normalize_row(__isl_take isl_mat *mat, int row)
1996 {
1997 mat = isl_mat_cow(mat);
1998 if (!mat)
1999 return NULL;
2000
2001 isl_seq_normalize(mat->ctx, mat->row[row], mat->n_col);
2002
2003 return mat;
2004 }
2005
2006 /* Number of initial non-zero columns.
2007 */
2008 int isl_mat_initial_non_zero_cols(__isl_keep isl_mat *mat)
2009 {
2010 int i;
2011
2012 if (!mat)
2013 return -1;
2014
2015 for (i = 0; i < mat->n_col; ++i)
2016 if (row_first_non_zero(mat->row, mat->n_row, i) < 0)
2017 break;
2018
2019 return i;
2020 }
2021
2022 /* Return a basis for the space spanned by the rows of "mat".
2023 * Any basis will do, so simply perform Gaussian elimination and
2024 * remove the empty rows.
2025 */
2026 __isl_give isl_mat *isl_mat_row_basis(__isl_take isl_mat *mat)
2027 {
2028 return isl_mat_reverse_gauss(mat);
2029 }
2030
2031 /* Return rows that extend a basis of "mat1" to one
2032 * that covers both "mat1" and "mat2".
2033 * The Hermite normal form of the concatenation of the two matrices is
2034 *
2035 * [ Q1 ]
2036 * [ M1 ] = [ H1 0 0 ] [ Q2 ]
2037 * [ M2 ] = [ H2 H3 0 ] [ Q3 ]
2038 *
2039 * The number of columns in H1 and H3 determine the number of rows
2040 * in Q1 and Q2. Q1 is a basis for M1, while Q2 extends this basis
2041 * to also cover M2.
2042 */
2043 __isl_give isl_mat *isl_mat_row_basis_extension(
2044 __isl_take isl_mat *mat1, __isl_take isl_mat *mat2)
2045 {
2046 int n_row;
2047 int r1, r, n1;
2048 isl_mat *H, *Q;
2049
2050 n1 = isl_mat_rows(mat1);
2051 H = isl_mat_concat(mat1, mat2);
2052 H = isl_mat_left_hermite(H, 0, NULL, &Q);
2053 if (!H || !Q)
2054 goto error;
2055
2056 r1 = hermite_first_zero_col(H, 0, n1);
2057 r = hermite_first_zero_col(H, r1, H->n_row);
2058 n_row = isl_mat_rows(Q);
2059 Q = isl_mat_drop_rows(Q, r, n_row - r);
2060 Q = isl_mat_drop_rows(Q, 0, r1);
2061
2062 isl_mat_free(H);
2063 return Q;
2064 error:
2065 isl_mat_free(H);
2066 isl_mat_free(Q);
2067 return NULL;
2068 }
2069
2070 /* Are the rows of "mat1" linearly independent of those of "mat2"?
2071 * That is, is there no linear dependence among the combined rows
2072 * that is not already present in either "mat1" or "mat2"?
2073 * In other words, is the rank of "mat1" and "mat2" combined equal
2074 * to the sum of the ranks of "mat1" and "mat2"?
2075 */
2076 isl_bool isl_mat_has_linearly_independent_rows(__isl_keep isl_mat *mat1,
2077 __isl_keep isl_mat *mat2)
2078 {
2079 int r1, r2, r;
2080 isl_mat *mat;
2081
2082 r1 = isl_mat_rank(mat1);
2083 if (r1 < 0)
2084 return isl_bool_error;
2085 if (r1 == 0)
2086 return isl_bool_true;
2087 r2 = isl_mat_rank(mat2);
2088 if (r2 < 0)
2089 return isl_bool_error;
2090 if (r2 == 0)
2091 return isl_bool_true;
2092
2093 mat = isl_mat_concat(isl_mat_copy(mat1), isl_mat_copy(mat2));
2094 r = isl_mat_rank(mat);
2095 isl_mat_free(mat);
2096 if (r < 0)
2097 return isl_bool_error;
2098 return r == r1 + r2;
2099 }
Integer set library