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isl_mat.c: hermite_first_zero_col: exploit column echelon form
[isl.git] / isl_mat.c
blob20269befd76530a876344a51103b91cc554e4de5
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2010 INRIA Saclay
4 * Copyright 2014 Ecole Normale Superieure
5 *
6 * Use of this software is governed by the MIT license
7 *
8 * Written by Sven Verdoolaege, K.U.Leuven, Departement
9 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 * and INRIA Saclay - Ile-de-France, Parc Club Orsay Universite,
11 * ZAC des vignes, 4 rue Jacques Monod, 91893 Orsay, France
12 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
13 */
14
15 #include <isl_ctx_private.h>
16 #include <isl_map_private.h>
17 #include <isl/space.h>
18 #include <isl_seq.h>
19 #include <isl_mat_private.h>
20 #include <isl_vec_private.h>
21 #include <isl_space_private.h>
22 #include <isl_val_private.h>
23 #include <isl/deprecated/mat_int.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 int isl_mat_is_scaled_identity(__isl_keep isl_mat *mat)
427 {
428 int i;
429
430 if (!mat)
431 return -1;
432 if (mat->n_row != mat->n_col)
433 return 0;
434
435 for (i = 0; i < mat->n_row; ++i) {
436 if (isl_seq_first_non_zero(mat->row[i], i) != -1)
437 return 0;
438 if (isl_int_ne(mat->row[0][0], mat->row[i][i]))
439 return 0;
440 if (isl_seq_first_non_zero(mat->row[i] + i + 1,
441 mat->n_col - (i + 1)) != -1)
442 return 0;
443 }
444
445 return 1;
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 struct isl_mat *isl_mat_right_kernel(struct isl_mat *mat)
863 {
864 int i, 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 for (i = 0, rank = 0; rank < mat->n_col; ++rank) {
873 while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))
874 ++i;
875 if (i >= mat->n_row)
876 break;
877 }
878 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
879 if (!K)
880 goto error;
881 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
882 isl_mat_free(mat);
883 isl_mat_free(U);
884 return K;
885 error:
886 isl_mat_free(mat);
887 isl_mat_free(U);
888 return NULL;
889 }
890
891 __isl_give isl_mat *isl_mat_lin_to_aff(__isl_take isl_mat *mat)
892 {
893 int i;
894 struct isl_mat *mat2;
895
896 if (!mat)
897 return NULL;
898 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
899 if (!mat2)
900 goto error;
901 isl_int_set_si(mat2->row[0][0], 1);
902 isl_seq_clr(mat2->row[0]+1, mat->n_col);
903 for (i = 0; i < mat->n_row; ++i) {
904 isl_int_set_si(mat2->row[1+i][0], 0);
905 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
906 }
907 isl_mat_free(mat);
908 return mat2;
909 error:
910 isl_mat_free(mat);
911 return NULL;
912 }
913
914 /* Given two matrices M1 and M2, return the block matrix
915 *
916 * [ M1 0 ]
917 * [ 0 M2 ]
918 */
919 __isl_give isl_mat *isl_mat_diagonal(__isl_take isl_mat *mat1,
920 __isl_take isl_mat *mat2)
921 {
922 int i;
923 isl_mat *mat;
924
925 if (!mat1 || !mat2)
926 goto error;
927
928 mat = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
929 mat1->n_col + mat2->n_col);
930 if (!mat)
931 goto error;
932 for (i = 0; i < mat1->n_row; ++i) {
933 isl_seq_cpy(mat->row[i], mat1->row[i], mat1->n_col);
934 isl_seq_clr(mat->row[i] + mat1->n_col, mat2->n_col);
935 }
936 for (i = 0; i < mat2->n_row; ++i) {
937 isl_seq_clr(mat->row[mat1->n_row + i], mat1->n_col);
938 isl_seq_cpy(mat->row[mat1->n_row + i] + mat1->n_col,
939 mat2->row[i], mat2->n_col);
940 }
941 isl_mat_free(mat1);
942 isl_mat_free(mat2);
943 return mat;
944 error:
945 isl_mat_free(mat1);
946 isl_mat_free(mat2);
947 return NULL;
948 }
949
950 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
951 {
952 int i;
953
954 for (i = 0; i < n_row; ++i)
955 if (!isl_int_is_zero(row[i][col]))
956 return i;
957 return -1;
958 }
959
960 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
961 {
962 int i, min = row_first_non_zero(row, n_row, col);
963 if (min < 0)
964 return -1;
965 for (i = min + 1; i < n_row; ++i) {
966 if (isl_int_is_zero(row[i][col]))
967 continue;
968 if (isl_int_abs_lt(row[i][col], row[min][col]))
969 min = i;
970 }
971 return min;
972 }
973
974 static isl_stat inv_exchange(__isl_keep isl_mat **left,
975 __isl_keep isl_mat **right, unsigned i, unsigned j)
976 {
977 *left = isl_mat_swap_rows(*left, i, j);
978 *right = isl_mat_swap_rows(*right, i, j);
979
980 if (!*left || !*right)
981 return isl_stat_error;
982 return isl_stat_ok;
983 }
984
985 static void inv_oppose(
986 struct isl_mat *left, struct isl_mat *right, unsigned row)
987 {
988 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
989 isl_seq_neg(right->row[row], right->row[row], right->n_col);
990 }
991
992 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
993 unsigned row, unsigned i, isl_int m)
994 {
995 isl_int_neg(m, m);
996 isl_seq_combine(left->row[i]+row,
997 left->ctx->one, left->row[i]+row,
998 m, left->row[row]+row,
999 left->n_col-row);
1000 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
1001 m, right->row[row], right->n_col);
1002 }
1003
1004 /* Compute inv(left)*right
1005 */
1006 __isl_give isl_mat *isl_mat_inverse_product(__isl_take isl_mat *left,
1007 __isl_take isl_mat *right)
1008 {
1009 int row;
1010 isl_int a, b;
1011
1012 if (!left || !right)
1013 goto error;
1014
1015 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
1016 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
1017
1018 if (left->n_row == 0) {
1019 isl_mat_free(left);
1020 return right;
1021 }
1022
1023 left = isl_mat_cow(left);
1024 right = isl_mat_cow(right);
1025 if (!left || !right)
1026 goto error;
1027
1028 isl_int_init(a);
1029 isl_int_init(b);
1030 for (row = 0; row < left->n_row; ++row) {
1031 int pivot, first, i, off;
1032 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
1033 if (pivot < 0) {
1034 isl_int_clear(a);
1035 isl_int_clear(b);
1036 isl_assert(left->ctx, pivot >= 0, goto error);
1037 }
1038 pivot += row;
1039 if (pivot != row)
1040 if (inv_exchange(&left, &right, pivot, row) < 0)
1041 goto error;
1042 if (isl_int_is_neg(left->row[row][row]))
1043 inv_oppose(left, right, row);
1044 first = row+1;
1045 while ((off = row_first_non_zero(left->row+first,
1046 left->n_row-first, row)) != -1) {
1047 first += off;
1048 isl_int_fdiv_q(a, left->row[first][row],
1049 left->row[row][row]);
1050 inv_subtract(left, right, row, first, a);
1051 if (!isl_int_is_zero(left->row[first][row])) {
1052 if (inv_exchange(&left, &right, row, first) < 0)
1053 goto error;
1054 } else {
1055 ++first;
1056 }
1057 }
1058 for (i = 0; i < row; ++i) {
1059 if (isl_int_is_zero(left->row[i][row]))
1060 continue;
1061 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
1062 isl_int_divexact(b, left->row[i][row], a);
1063 isl_int_divexact(a, left->row[row][row], a);
1064 isl_int_neg(b, b);
1065 isl_seq_combine(left->row[i] + i,
1066 a, left->row[i] + i,
1067 b, left->row[row] + i,
1068 left->n_col - i);
1069 isl_seq_combine(right->row[i], a, right->row[i],
1070 b, right->row[row], right->n_col);
1071 }
1072 }
1073 isl_int_clear(b);
1074
1075 isl_int_set(a, left->row[0][0]);
1076 for (row = 1; row < left->n_row; ++row)
1077 isl_int_lcm(a, a, left->row[row][row]);
1078 if (isl_int_is_zero(a)){
1079 isl_int_clear(a);
1080 isl_assert(left->ctx, 0, goto error);
1081 }
1082 for (row = 0; row < left->n_row; ++row) {
1083 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
1084 if (isl_int_is_one(left->row[row][row]))
1085 continue;
1086 isl_seq_scale(right->row[row], right->row[row],
1087 left->row[row][row], right->n_col);
1088 }
1089 isl_int_clear(a);
1090
1091 isl_mat_free(left);
1092 return right;
1093 error:
1094 isl_mat_free(left);
1095 isl_mat_free(right);
1096 return NULL;
1097 }
1098
1099 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
1100 {
1101 int i;
1102
1103 for (i = 0; i < mat->n_row; ++i)
1104 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
1105 }
1106
1107 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
1108 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
1109 {
1110 int i;
1111 isl_int tmp;
1112
1113 isl_int_init(tmp);
1114 for (i = 0; i < mat->n_row; ++i) {
1115 isl_int_mul(tmp, m1, mat->row[i][src1]);
1116 isl_int_addmul(tmp, m2, mat->row[i][src2]);
1117 isl_int_set(mat->row[i][dst], tmp);
1118 }
1119 isl_int_clear(tmp);
1120 }
1121
1122 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat)
1123 {
1124 struct isl_mat *inv;
1125 int row;
1126 isl_int a, b;
1127
1128 mat = isl_mat_cow(mat);
1129 if (!mat)
1130 return NULL;
1131
1132 inv = isl_mat_identity(mat->ctx, mat->n_col);
1133 inv = isl_mat_cow(inv);
1134 if (!inv)
1135 goto error;
1136
1137 isl_int_init(a);
1138 isl_int_init(b);
1139 for (row = 0; row < mat->n_row; ++row) {
1140 int pivot, first, i, off;
1141 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
1142 if (pivot < 0) {
1143 isl_int_clear(a);
1144 isl_int_clear(b);
1145 isl_assert(mat->ctx, pivot >= 0, goto error);
1146 }
1147 pivot += row;
1148 if (pivot != row)
1149 exchange(mat, &inv, NULL, row, pivot, row);
1150 if (isl_int_is_neg(mat->row[row][row]))
1151 oppose(mat, &inv, NULL, row, row);
1152 first = row+1;
1153 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
1154 mat->n_col-first)) != -1) {
1155 first += off;
1156 isl_int_fdiv_q(a, mat->row[row][first],
1157 mat->row[row][row]);
1158 subtract(mat, &inv, NULL, row, row, first, a);
1159 if (!isl_int_is_zero(mat->row[row][first]))
1160 exchange(mat, &inv, NULL, row, row, first);
1161 else
1162 ++first;
1163 }
1164 for (i = 0; i < row; ++i) {
1165 if (isl_int_is_zero(mat->row[row][i]))
1166 continue;
1167 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
1168 isl_int_divexact(b, mat->row[row][i], a);
1169 isl_int_divexact(a, mat->row[row][row], a);
1170 isl_int_neg(a, a);
1171 isl_mat_col_combine(mat, i, a, i, b, row);
1172 isl_mat_col_combine(inv, i, a, i, b, row);
1173 }
1174 }
1175 isl_int_clear(b);
1176
1177 isl_int_set(a, mat->row[0][0]);
1178 for (row = 1; row < mat->n_row; ++row)
1179 isl_int_lcm(a, a, mat->row[row][row]);
1180 if (isl_int_is_zero(a)){
1181 isl_int_clear(a);
1182 goto error;
1183 }
1184 for (row = 0; row < mat->n_row; ++row) {
1185 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
1186 if (isl_int_is_one(mat->row[row][row]))
1187 continue;
1188 isl_mat_col_scale(inv, row, mat->row[row][row]);
1189 }
1190 isl_int_clear(a);
1191
1192 isl_mat_free(mat);
1193
1194 return inv;
1195 error:
1196 isl_mat_free(mat);
1197 isl_mat_free(inv);
1198 return NULL;
1199 }
1200
1201 __isl_give isl_mat *isl_mat_transpose(__isl_take isl_mat *mat)
1202 {
1203 struct isl_mat *transpose = NULL;
1204 int i, j;
1205
1206 if (!mat)
1207 return NULL;
1208
1209 if (mat->n_col == mat->n_row) {
1210 mat = isl_mat_cow(mat);
1211 if (!mat)
1212 return NULL;
1213 for (i = 0; i < mat->n_row; ++i)
1214 for (j = i + 1; j < mat->n_col; ++j)
1215 isl_int_swap(mat->row[i][j], mat->row[j][i]);
1216 return mat;
1217 }
1218 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
1219 if (!transpose)
1220 goto error;
1221 for (i = 0; i < mat->n_row; ++i)
1222 for (j = 0; j < mat->n_col; ++j)
1223 isl_int_set(transpose->row[j][i], mat->row[i][j]);
1224 isl_mat_free(mat);
1225 return transpose;
1226 error:
1227 isl_mat_free(mat);
1228 return NULL;
1229 }
1230
1231 __isl_give isl_mat *isl_mat_swap_cols(__isl_take isl_mat *mat,
1232 unsigned i, unsigned j)
1233 {
1234 int r;
1235
1236 mat = isl_mat_cow(mat);
1237 if (check_col_range(mat, i, 1) < 0 ||
1238 check_col_range(mat, j, 1) < 0)
1239 return isl_mat_free(mat);
1240
1241 for (r = 0; r < mat->n_row; ++r)
1242 isl_int_swap(mat->row[r][i], mat->row[r][j]);
1243 return mat;
1244 }
1245
1246 __isl_give isl_mat *isl_mat_swap_rows(__isl_take isl_mat *mat,
1247 unsigned i, unsigned j)
1248 {
1249 isl_int *t;
1250
1251 if (!mat)
1252 return NULL;
1253 mat = isl_mat_cow(mat);
1254 if (check_row_range(mat, i, 1) < 0 ||
1255 check_row_range(mat, j, 1) < 0)
1256 return isl_mat_free(mat);
1257
1258 t = mat->row[i];
1259 mat->row[i] = mat->row[j];
1260 mat->row[j] = t;
1261 return mat;
1262 }
1263
1264 /* Calculate the product of two matrices.
1265 *
1266 * This function is optimized for operand matrices that contain many zeros and
1267 * skips multiplications where we know one of the operands is zero.
1268 */
1269 __isl_give isl_mat *isl_mat_product(__isl_take isl_mat *left,
1270 __isl_take isl_mat *right)
1271 {
1272 int i, j, k;
1273 struct isl_mat *prod;
1274
1275 if (!left || !right)
1276 goto error;
1277 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
1278 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
1279 if (!prod)
1280 goto error;
1281 if (left->n_col == 0) {
1282 for (i = 0; i < prod->n_row; ++i)
1283 isl_seq_clr(prod->row[i], prod->n_col);
1284 isl_mat_free(left);
1285 isl_mat_free(right);
1286 return prod;
1287 }
1288 for (i = 0; i < prod->n_row; ++i) {
1289 for (j = 0; j < prod->n_col; ++j)
1290 isl_int_mul(prod->row[i][j],
1291 left->row[i][0], right->row[0][j]);
1292 for (k = 1; k < left->n_col; ++k) {
1293 if (isl_int_is_zero(left->row[i][k]))
1294 continue;
1295 for (j = 0; j < prod->n_col; ++j)
1296 isl_int_addmul(prod->row[i][j],
1297 left->row[i][k], right->row[k][j]);
1298 }
1299 }
1300 isl_mat_free(left);
1301 isl_mat_free(right);
1302 return prod;
1303 error:
1304 isl_mat_free(left);
1305 isl_mat_free(right);
1306 return NULL;
1307 }
1308
1309 /* Replace the variables x in the rows q by x' given by x = M x',
1310 * with M the matrix mat.
1311 *
1312 * If the number of new variables is greater than the original
1313 * number of variables, then the rows q have already been
1314 * preextended. If the new number is smaller, then the coefficients
1315 * of the divs, which are not changed, need to be shifted down.
1316 * The row q may be the equalities, the inequalities or the
1317 * div expressions. In the latter case, has_div is true and
1318 * we need to take into account the extra denominator column.
1319 */
1320 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
1321 unsigned n_div, int has_div, struct isl_mat *mat)
1322 {
1323 int i;
1324 struct isl_mat *t;
1325 int e;
1326
1327 if (mat->n_col >= mat->n_row)
1328 e = 0;
1329 else
1330 e = mat->n_row - mat->n_col;
1331 if (has_div)
1332 for (i = 0; i < n; ++i)
1333 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
1334 t = isl_mat_sub_alloc6(mat->ctx, q, 0, n, has_div, mat->n_row);
1335 t = isl_mat_product(t, mat);
1336 if (!t)
1337 return -1;
1338 for (i = 0; i < n; ++i) {
1339 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
1340 isl_seq_cpy(q[i] + has_div + t->n_col,
1341 q[i] + has_div + t->n_col + e, n_div);
1342 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
1343 }
1344 isl_mat_free(t);
1345 return 0;
1346 }
1347
1348 /* Replace the variables x in bset by x' given by x = M x', with
1349 * M the matrix mat.
1350 *
1351 * If there are fewer variables x' then there are x, then we perform
1352 * the transformation in place, which means that, in principle,
1353 * this frees up some extra variables as the number
1354 * of columns remains constant, but we would have to extend
1355 * the div array too as the number of rows in this array is assumed
1356 * to be equal to extra.
1357 */
1358 __isl_give isl_basic_set *isl_basic_set_preimage(
1359 __isl_take isl_basic_set *bset, __isl_take isl_mat *mat)
1360 {
1361 struct isl_ctx *ctx;
1362
1363 if (!bset || !mat)
1364 goto error;
1365
1366 ctx = bset->ctx;
1367 bset = isl_basic_set_cow(bset);
1368 if (!bset)
1369 goto error;
1370
1371 isl_assert(ctx, bset->dim->nparam == 0, goto error);
1372 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
1373 isl_assert(ctx, mat->n_col > 0, goto error);
1374
1375 if (mat->n_col > mat->n_row) {
1376 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0, 0, 0);
1377 if (!bset)
1378 goto error;
1379 } else if (mat->n_col < mat->n_row) {
1380 bset->dim = isl_space_cow(bset->dim);
1381 if (!bset->dim)
1382 goto error;
1383 bset->dim->n_out -= mat->n_row - mat->n_col;
1384 }
1385
1386 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
1387 isl_mat_copy(mat)) < 0)
1388 goto error;
1389
1390 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
1391 isl_mat_copy(mat)) < 0)
1392 goto error;
1393
1394 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
1395 goto error2;
1396
1397 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
1398 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
1399 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1400 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1401 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
1402
1403 bset = isl_basic_set_simplify(bset);
1404 bset = isl_basic_set_finalize(bset);
1405
1406 return bset;
1407 error:
1408 isl_mat_free(mat);
1409 error2:
1410 isl_basic_set_free(bset);
1411 return NULL;
1412 }
1413
1414 __isl_give isl_set *isl_set_preimage(
1415 __isl_take isl_set *set, __isl_take isl_mat *mat)
1416 {
1417 int i;
1418
1419 set = isl_set_cow(set);
1420 if (!set)
1421 goto error;
1422
1423 for (i = 0; i < set->n; ++i) {
1424 set->p[i] = isl_basic_set_preimage(set->p[i],
1425 isl_mat_copy(mat));
1426 if (!set->p[i])
1427 goto error;
1428 }
1429 if (mat->n_col != mat->n_row) {
1430 set->dim = isl_space_cow(set->dim);
1431 if (!set->dim)
1432 goto error;
1433 set->dim->n_out += mat->n_col;
1434 set->dim->n_out -= mat->n_row;
1435 }
1436 isl_mat_free(mat);
1437 ISL_F_CLR(set, ISL_SET_NORMALIZED);
1438 return set;
1439 error:
1440 isl_set_free(set);
1441 isl_mat_free(mat);
1442 return NULL;
1443 }
1444
1445 /* Replace the variables x starting at "first_col" in the rows "rows"
1446 * of some coefficient matrix by x' with x = M x' with M the matrix mat.
1447 * That is, replace the corresponding coefficients c by c M.
1448 */
1449 isl_stat isl_mat_sub_transform(isl_int **row, unsigned n_row,
1450 unsigned first_col, __isl_take isl_mat *mat)
1451 {
1452 int i;
1453 isl_ctx *ctx;
1454 isl_mat *t;
1455
1456 if (!mat)
1457 return isl_stat_error;
1458 ctx = isl_mat_get_ctx(mat);
1459 t = isl_mat_sub_alloc6(ctx, row, 0, n_row, first_col, mat->n_row);
1460 t = isl_mat_product(t, mat);
1461 if (!t)
1462 return isl_stat_error;
1463 for (i = 0; i < n_row; ++i)
1464 isl_seq_swp_or_cpy(row[i] + first_col, t->row[i], t->n_col);
1465 isl_mat_free(t);
1466 return isl_stat_ok;
1467 }
1468
1469 void isl_mat_print_internal(__isl_keep isl_mat *mat, FILE *out, int indent)
1470 {
1471 int i, j;
1472
1473 if (!mat) {
1474 fprintf(out, "%*snull mat\n", indent, "");
1475 return;
1476 }
1477
1478 if (mat->n_row == 0)
1479 fprintf(out, "%*s[]\n", indent, "");
1480
1481 for (i = 0; i < mat->n_row; ++i) {
1482 if (!i)
1483 fprintf(out, "%*s[[", indent, "");
1484 else
1485 fprintf(out, "%*s[", indent+1, "");
1486 for (j = 0; j < mat->n_col; ++j) {
1487 if (j)
1488 fprintf(out, ",");
1489 isl_int_print(out, mat->row[i][j], 0);
1490 }
1491 if (i == mat->n_row-1)
1492 fprintf(out, "]]\n");
1493 else
1494 fprintf(out, "]\n");
1495 }
1496 }
1497
1498 void isl_mat_dump(__isl_keep isl_mat *mat)
1499 {
1500 isl_mat_print_internal(mat, stderr, 0);
1501 }
1502
1503 __isl_give isl_mat *isl_mat_drop_cols(__isl_take isl_mat *mat,
1504 unsigned col, unsigned n)
1505 {
1506 int r;
1507
1508 if (n == 0)
1509 return mat;
1510
1511 mat = isl_mat_cow(mat);
1512 if (check_col_range(mat, col, n) < 0)
1513 return isl_mat_free(mat);
1514
1515 if (col != mat->n_col-n) {
1516 for (r = 0; r < mat->n_row; ++r)
1517 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1518 mat->n_col - col - n);
1519 }
1520 mat->n_col -= n;
1521 return mat;
1522 }
1523
1524 __isl_give isl_mat *isl_mat_drop_rows(__isl_take isl_mat *mat,
1525 unsigned row, unsigned n)
1526 {
1527 int r;
1528
1529 mat = isl_mat_cow(mat);
1530 if (check_row_range(mat, row, n) < 0)
1531 return isl_mat_free(mat);
1532
1533 for (r = row; r+n < mat->n_row; ++r)
1534 mat->row[r] = mat->row[r+n];
1535
1536 mat->n_row -= n;
1537 return mat;
1538 }
1539
1540 __isl_give isl_mat *isl_mat_insert_cols(__isl_take isl_mat *mat,
1541 unsigned col, unsigned n)
1542 {
1543 isl_mat *ext;
1544
1545 if (check_col_range(mat, col, 0) < 0)
1546 return isl_mat_free(mat);
1547 if (n == 0)
1548 return mat;
1549
1550 ext = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col + n);
1551 if (!ext)
1552 goto error;
1553
1554 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row, 0, 0, col);
1555 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row,
1556 col + n, col, mat->n_col - col);
1557
1558 isl_mat_free(mat);
1559 return ext;
1560 error:
1561 isl_mat_free(mat);
1562 return NULL;
1563 }
1564
1565 __isl_give isl_mat *isl_mat_insert_zero_cols(__isl_take isl_mat *mat,
1566 unsigned first, unsigned n)
1567 {
1568 int i;
1569
1570 if (!mat)
1571 return NULL;
1572 mat = isl_mat_insert_cols(mat, first, n);
1573 if (!mat)
1574 return NULL;
1575
1576 for (i = 0; i < mat->n_row; ++i)
1577 isl_seq_clr(mat->row[i] + first, n);
1578
1579 return mat;
1580 }
1581
1582 __isl_give isl_mat *isl_mat_add_zero_cols(__isl_take isl_mat *mat, unsigned n)
1583 {
1584 if (!mat)
1585 return NULL;
1586
1587 return isl_mat_insert_zero_cols(mat, mat->n_col, n);
1588 }
1589
1590 __isl_give isl_mat *isl_mat_insert_rows(__isl_take isl_mat *mat,
1591 unsigned row, unsigned n)
1592 {
1593 isl_mat *ext;
1594
1595 if (check_row_range(mat, row, 0) < 0)
1596 return isl_mat_free(mat);
1597 if (n == 0)
1598 return mat;
1599
1600 ext = isl_mat_alloc(mat->ctx, mat->n_row + n, mat->n_col);
1601 if (!ext)
1602 goto error;
1603
1604 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, row, 0, 0, mat->n_col);
1605 isl_mat_sub_copy(mat->ctx, ext->row + row + n, mat->row + row,
1606 mat->n_row - row, 0, 0, mat->n_col);
1607
1608 isl_mat_free(mat);
1609 return ext;
1610 error:
1611 isl_mat_free(mat);
1612 return NULL;
1613 }
1614
1615 __isl_give isl_mat *isl_mat_add_rows(__isl_take isl_mat *mat, unsigned n)
1616 {
1617 if (!mat)
1618 return NULL;
1619
1620 return isl_mat_insert_rows(mat, mat->n_row, n);
1621 }
1622
1623 __isl_give isl_mat *isl_mat_insert_zero_rows(__isl_take isl_mat *mat,
1624 unsigned row, unsigned n)
1625 {
1626 int i;
1627
1628 mat = isl_mat_insert_rows(mat, row, n);
1629 if (!mat)
1630 return NULL;
1631
1632 for (i = 0; i < n; ++i)
1633 isl_seq_clr(mat->row[row + i], mat->n_col);
1634
1635 return mat;
1636 }
1637
1638 __isl_give isl_mat *isl_mat_add_zero_rows(__isl_take isl_mat *mat, unsigned n)
1639 {
1640 if (!mat)
1641 return NULL;
1642
1643 return isl_mat_insert_zero_rows(mat, mat->n_row, n);
1644 }
1645
1646 void isl_mat_col_submul(struct isl_mat *mat,
1647 int dst_col, isl_int f, int src_col)
1648 {
1649 int i;
1650
1651 for (i = 0; i < mat->n_row; ++i)
1652 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1653 }
1654
1655 void isl_mat_col_add(__isl_keep isl_mat *mat, int dst_col, int src_col)
1656 {
1657 int i;
1658
1659 if (!mat)
1660 return;
1661
1662 for (i = 0; i < mat->n_row; ++i)
1663 isl_int_add(mat->row[i][dst_col],
1664 mat->row[i][dst_col], mat->row[i][src_col]);
1665 }
1666
1667 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1668 {
1669 int i;
1670
1671 for (i = 0; i < mat->n_row; ++i)
1672 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1673 }
1674
1675 /* Add "f" times column "src_col" to column "dst_col" of "mat" and
1676 * return the result.
1677 */
1678 __isl_give isl_mat *isl_mat_col_addmul(__isl_take isl_mat *mat, int dst_col,
1679 isl_int f, int src_col)
1680 {
1681 int i;
1682
1683 if (check_col(mat, dst_col) < 0 || check_col(mat, src_col) < 0)
1684 return isl_mat_free(mat);
1685
1686 for (i = 0; i < mat->n_row; ++i) {
1687 if (isl_int_is_zero(mat->row[i][src_col]))
1688 continue;
1689 mat = isl_mat_cow(mat);
1690 if (!mat)
1691 return NULL;
1692 isl_int_addmul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1693 }
1694
1695 return mat;
1696 }
1697
1698 /* Negate column "col" of "mat" and return the result.
1699 */
1700 __isl_give isl_mat *isl_mat_col_neg(__isl_take isl_mat *mat, int col)
1701 {
1702 int i;
1703
1704 if (check_col(mat, col) < 0)
1705 return isl_mat_free(mat);
1706
1707 for (i = 0; i < mat->n_row; ++i) {
1708 if (isl_int_is_zero(mat->row[i][col]))
1709 continue;
1710 mat = isl_mat_cow(mat);
1711 if (!mat)
1712 return NULL;
1713 isl_int_neg(mat->row[i][col], mat->row[i][col]);
1714 }
1715
1716 return mat;
1717 }
1718
1719 /* Negate row "row" of "mat" and return the result.
1720 */
1721 __isl_give isl_mat *isl_mat_row_neg(__isl_take isl_mat *mat, int row)
1722 {
1723 if (check_row(mat, row) < 0)
1724 return isl_mat_free(mat);
1725 if (isl_seq_first_non_zero(mat->row[row], mat->n_col) == -1)
1726 return mat;
1727 mat = isl_mat_cow(mat);
1728 if (!mat)
1729 return NULL;
1730 isl_seq_neg(mat->row[row], mat->row[row], mat->n_col);
1731 return mat;
1732 }
1733
1734 __isl_give isl_mat *isl_mat_unimodular_complete(__isl_take isl_mat *M, int row)
1735 {
1736 int r;
1737 struct isl_mat *H = NULL, *Q = NULL;
1738
1739 if (!M)
1740 return NULL;
1741
1742 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1743 M->n_row = row;
1744 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1745 M->n_row = M->n_col;
1746 if (!H)
1747 goto error;
1748 for (r = 0; r < row; ++r)
1749 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1750 for (r = row; r < M->n_row; ++r)
1751 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1752 isl_mat_free(H);
1753 isl_mat_free(Q);
1754 return M;
1755 error:
1756 isl_mat_free(H);
1757 isl_mat_free(Q);
1758 isl_mat_free(M);
1759 return NULL;
1760 }
1761
1762 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1763 __isl_take isl_mat *bot)
1764 {
1765 struct isl_mat *mat;
1766
1767 if (!top || !bot)
1768 goto error;
1769
1770 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1771 if (top->n_row == 0) {
1772 isl_mat_free(top);
1773 return bot;
1774 }
1775 if (bot->n_row == 0) {
1776 isl_mat_free(bot);
1777 return top;
1778 }
1779
1780 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1781 if (!mat)
1782 goto error;
1783 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1784 0, 0, mat->n_col);
1785 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1786 0, 0, mat->n_col);
1787 isl_mat_free(top);
1788 isl_mat_free(bot);
1789 return mat;
1790 error:
1791 isl_mat_free(top);
1792 isl_mat_free(bot);
1793 return NULL;
1794 }
1795
1796 isl_bool isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
1797 {
1798 int i;
1799
1800 if (!mat1 || !mat2)
1801 return isl_bool_error;
1802
1803 if (mat1->n_row != mat2->n_row)
1804 return isl_bool_false;
1805
1806 if (mat1->n_col != mat2->n_col)
1807 return isl_bool_false;
1808
1809 for (i = 0; i < mat1->n_row; ++i)
1810 if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
1811 return isl_bool_false;
1812
1813 return isl_bool_true;
1814 }
1815
1816 __isl_give isl_mat *isl_mat_from_row_vec(__isl_take isl_vec *vec)
1817 {
1818 struct isl_mat *mat;
1819
1820 if (!vec)
1821 return NULL;
1822 mat = isl_mat_alloc(vec->ctx, 1, vec->size);
1823 if (!mat)
1824 goto error;
1825
1826 isl_seq_cpy(mat->row[0], vec->el, vec->size);
1827
1828 isl_vec_free(vec);
1829 return mat;
1830 error:
1831 isl_vec_free(vec);
1832 return NULL;
1833 }
1834
1835 /* Return a copy of row "row" of "mat" as an isl_vec.
1836 */
1837 __isl_give isl_vec *isl_mat_get_row(__isl_keep isl_mat *mat, unsigned row)
1838 {
1839 isl_vec *v;
1840
1841 if (!mat)
1842 return NULL;
1843 if (row >= mat->n_row)
1844 isl_die(mat->ctx, isl_error_invalid, "row out of range",
1845 return NULL);
1846
1847 v = isl_vec_alloc(isl_mat_get_ctx(mat), mat->n_col);
1848 if (!v)
1849 return NULL;
1850 isl_seq_cpy(v->el, mat->row[row], mat->n_col);
1851
1852 return v;
1853 }
1854
1855 __isl_give isl_mat *isl_mat_vec_concat(__isl_take isl_mat *top,
1856 __isl_take isl_vec *bot)
1857 {
1858 return isl_mat_concat(top, isl_mat_from_row_vec(bot));
1859 }
1860
1861 __isl_give isl_mat *isl_mat_move_cols(__isl_take isl_mat *mat,
1862 unsigned dst_col, unsigned src_col, unsigned n)
1863 {
1864 isl_mat *res;
1865
1866 if (!mat)
1867 return NULL;
1868 if (n == 0 || dst_col == src_col)
1869 return mat;
1870
1871 res = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
1872 if (!res)
1873 goto error;
1874
1875 if (dst_col < src_col) {
1876 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1877 0, 0, dst_col);
1878 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1879 dst_col, src_col, n);
1880 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1881 dst_col + n, dst_col, src_col - dst_col);
1882 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1883 src_col + n, src_col + n,
1884 res->n_col - src_col - n);
1885 } else {
1886 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1887 0, 0, src_col);
1888 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1889 src_col, src_col + n, dst_col - src_col);
1890 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1891 dst_col, src_col, n);
1892 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1893 dst_col + n, dst_col + n,
1894 res->n_col - dst_col - n);
1895 }
1896 isl_mat_free(mat);
1897
1898 return res;
1899 error:
1900 isl_mat_free(mat);
1901 return NULL;
1902 }
1903
1904 /* Return the gcd of the elements in row "row" of "mat" in *gcd.
1905 * Return isl_stat_ok on success and isl_stat_error on failure.
1906 */
1907 isl_stat isl_mat_row_gcd(__isl_keep isl_mat *mat, int row, isl_int *gcd)
1908 {
1909 if (check_row(mat, row) < 0)
1910 return isl_stat_error;
1911
1912 isl_seq_gcd(mat->row[row], mat->n_col, gcd);
1913
1914 return isl_stat_ok;
1915 }
1916
1917 void isl_mat_gcd(__isl_keep isl_mat *mat, isl_int *gcd)
1918 {
1919 int i;
1920 isl_int g;
1921
1922 isl_int_set_si(*gcd, 0);
1923 if (!mat)
1924 return;
1925
1926 isl_int_init(g);
1927 for (i = 0; i < mat->n_row; ++i) {
1928 isl_seq_gcd(mat->row[i], mat->n_col, &g);
1929 isl_int_gcd(*gcd, *gcd, g);
1930 }
1931 isl_int_clear(g);
1932 }
1933
1934 /* Return the result of scaling "mat" by a factor of "m".
1935 */
1936 __isl_give isl_mat *isl_mat_scale(__isl_take isl_mat *mat, isl_int m)
1937 {
1938 int i;
1939
1940 if (isl_int_is_one(m))
1941 return mat;
1942
1943 mat = isl_mat_cow(mat);
1944 if (!mat)
1945 return NULL;
1946
1947 for (i = 0; i < mat->n_row; ++i)
1948 isl_seq_scale(mat->row[i], mat->row[i], m, mat->n_col);
1949
1950 return mat;
1951 }
1952
1953 __isl_give isl_mat *isl_mat_scale_down(__isl_take isl_mat *mat, isl_int m)
1954 {
1955 int i;
1956
1957 if (isl_int_is_one(m))
1958 return mat;
1959
1960 mat = isl_mat_cow(mat);
1961 if (!mat)
1962 return NULL;
1963
1964 for (i = 0; i < mat->n_row; ++i)
1965 isl_seq_scale_down(mat->row[i], mat->row[i], m, mat->n_col);
1966
1967 return mat;
1968 }
1969
1970 __isl_give isl_mat *isl_mat_scale_down_row(__isl_take isl_mat *mat, int row,
1971 isl_int m)
1972 {
1973 if (isl_int_is_one(m))
1974 return mat;
1975
1976 mat = isl_mat_cow(mat);
1977 if (!mat)
1978 return NULL;
1979
1980 isl_seq_scale_down(mat->row[row], mat->row[row], m, mat->n_col);
1981
1982 return mat;
1983 }
1984
1985 __isl_give isl_mat *isl_mat_normalize(__isl_take isl_mat *mat)
1986 {
1987 isl_int gcd;
1988
1989 if (!mat)
1990 return NULL;
1991
1992 isl_int_init(gcd);
1993 isl_mat_gcd(mat, &gcd);
1994 mat = isl_mat_scale_down(mat, gcd);
1995 isl_int_clear(gcd);
1996
1997 return mat;
1998 }
1999
2000 __isl_give isl_mat *isl_mat_normalize_row(__isl_take isl_mat *mat, int row)
2001 {
2002 mat = isl_mat_cow(mat);
2003 if (!mat)
2004 return NULL;
2005
2006 isl_seq_normalize(mat->ctx, mat->row[row], mat->n_col);
2007
2008 return mat;
2009 }
2010
2011 /* Number of initial non-zero columns.
2012 */
2013 int isl_mat_initial_non_zero_cols(__isl_keep isl_mat *mat)
2014 {
2015 int i;
2016
2017 if (!mat)
2018 return -1;
2019
2020 for (i = 0; i < mat->n_col; ++i)
2021 if (row_first_non_zero(mat->row, mat->n_row, i) < 0)
2022 break;
2023
2024 return i;
2025 }
Integer set library