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isl_tab_basic_set_non_trivial_lexmin: extract out update_outer_levels
[isl.git] / isl_mat.c
blob9ce38d8d49f28f9693aae5ebe3d071c5eacf88ff
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 #include <isl/deprecated/mat_int.h>
25
26 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat)
27 {
28 return mat ? mat->ctx : NULL;
29 }
30
31 /* Return a hash value that digests "mat".
32 */
33 uint32_t isl_mat_get_hash(__isl_keep isl_mat *mat)
34 {
35 int i;
36 uint32_t hash;
37
38 if (!mat)
39 return 0;
40
41 hash = isl_hash_init();
42 isl_hash_byte(hash, mat->n_row & 0xFF);
43 isl_hash_byte(hash, mat->n_col & 0xFF);
44 for (i = 0; i < mat->n_row; ++i) {
45 uint32_t row_hash;
46
47 row_hash = isl_seq_get_hash(mat->row[i], mat->n_col);
48 isl_hash_hash(hash, row_hash);
49 }
50
51 return hash;
52 }
53
54 struct isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
55 unsigned n_row, unsigned n_col)
56 {
57 int i;
58 struct isl_mat *mat;
59
60 mat = isl_alloc_type(ctx, struct isl_mat);
61 if (!mat)
62 return NULL;
63
64 mat->row = NULL;
65 mat->block = isl_blk_alloc(ctx, n_row * n_col);
66 if (isl_blk_is_error(mat->block))
67 goto error;
68 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
69 if (n_row && !mat->row)
70 goto error;
71
72 for (i = 0; i < n_row; ++i)
73 mat->row[i] = mat->block.data + i * n_col;
74
75 mat->ctx = ctx;
76 isl_ctx_ref(ctx);
77 mat->ref = 1;
78 mat->n_row = n_row;
79 mat->n_col = n_col;
80 mat->max_col = n_col;
81 mat->flags = 0;
82
83 return mat;
84 error:
85 isl_blk_free(ctx, mat->block);
86 free(mat);
87 return NULL;
88 }
89
90 struct isl_mat *isl_mat_extend(struct isl_mat *mat,
91 unsigned n_row, unsigned n_col)
92 {
93 int i;
94 isl_int *old;
95 isl_int **row;
96
97 if (!mat)
98 return NULL;
99
100 if (mat->max_col >= n_col && mat->n_row >= n_row) {
101 if (mat->n_col < n_col)
102 mat->n_col = n_col;
103 return mat;
104 }
105
106 if (mat->max_col < n_col) {
107 struct isl_mat *new_mat;
108
109 if (n_row < mat->n_row)
110 n_row = mat->n_row;
111 new_mat = isl_mat_alloc(mat->ctx, n_row, n_col);
112 if (!new_mat)
113 goto error;
114 for (i = 0; i < mat->n_row; ++i)
115 isl_seq_cpy(new_mat->row[i], mat->row[i], mat->n_col);
116 isl_mat_free(mat);
117 return new_mat;
118 }
119
120 mat = isl_mat_cow(mat);
121 if (!mat)
122 goto error;
123
124 old = mat->block.data;
125 mat->block = isl_blk_extend(mat->ctx, mat->block, n_row * mat->max_col);
126 if (isl_blk_is_error(mat->block))
127 goto error;
128 row = isl_realloc_array(mat->ctx, mat->row, isl_int *, n_row);
129 if (n_row && !row)
130 goto error;
131 mat->row = row;
132
133 for (i = 0; i < mat->n_row; ++i)
134 mat->row[i] = mat->block.data + (mat->row[i] - old);
135 for (i = mat->n_row; i < n_row; ++i)
136 mat->row[i] = mat->block.data + i * mat->max_col;
137 mat->n_row = n_row;
138 if (mat->n_col < n_col)
139 mat->n_col = n_col;
140
141 return mat;
142 error:
143 isl_mat_free(mat);
144 return NULL;
145 }
146
147 __isl_give isl_mat *isl_mat_sub_alloc6(isl_ctx *ctx, isl_int **row,
148 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
149 {
150 int i;
151 struct isl_mat *mat;
152
153 mat = isl_alloc_type(ctx, struct isl_mat);
154 if (!mat)
155 return NULL;
156 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
157 if (n_row && !mat->row)
158 goto error;
159 for (i = 0; i < n_row; ++i)
160 mat->row[i] = row[first_row+i] + first_col;
161 mat->ctx = ctx;
162 isl_ctx_ref(ctx);
163 mat->ref = 1;
164 mat->n_row = n_row;
165 mat->n_col = n_col;
166 mat->block = isl_blk_empty();
167 mat->flags = ISL_MAT_BORROWED;
168 return mat;
169 error:
170 free(mat);
171 return NULL;
172 }
173
174 __isl_give isl_mat *isl_mat_sub_alloc(__isl_keep isl_mat *mat,
175 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
176 {
177 if (!mat)
178 return NULL;
179 return isl_mat_sub_alloc6(mat->ctx, mat->row, first_row, n_row,
180 first_col, n_col);
181 }
182
183 void isl_mat_sub_copy(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
184 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
185 {
186 int i;
187
188 for (i = 0; i < n_row; ++i)
189 isl_seq_cpy(dst[i]+dst_col, src[i]+src_col, n_col);
190 }
191
192 void isl_mat_sub_neg(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
193 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
194 {
195 int i;
196
197 for (i = 0; i < n_row; ++i)
198 isl_seq_neg(dst[i]+dst_col, src[i]+src_col, n_col);
199 }
200
201 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat)
202 {
203 if (!mat)
204 return NULL;
205
206 mat->ref++;
207 return mat;
208 }
209
210 __isl_give isl_mat *isl_mat_dup(__isl_keep isl_mat *mat)
211 {
212 int i;
213 struct isl_mat *mat2;
214
215 if (!mat)
216 return NULL;
217 mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
218 if (!mat2)
219 return NULL;
220 for (i = 0; i < mat->n_row; ++i)
221 isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);
222 return mat2;
223 }
224
225 __isl_give isl_mat *isl_mat_cow(__isl_take isl_mat *mat)
226 {
227 struct isl_mat *mat2;
228 if (!mat)
229 return NULL;
230
231 if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))
232 return mat;
233
234 mat2 = isl_mat_dup(mat);
235 isl_mat_free(mat);
236 return mat2;
237 }
238
239 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat)
240 {
241 if (!mat)
242 return NULL;
243
244 if (--mat->ref > 0)
245 return NULL;
246
247 if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))
248 isl_blk_free(mat->ctx, mat->block);
249 isl_ctx_deref(mat->ctx);
250 free(mat->row);
251 free(mat);
252
253 return NULL;
254 }
255
256 int isl_mat_rows(__isl_keep isl_mat *mat)
257 {
258 return mat ? mat->n_row : -1;
259 }
260
261 int isl_mat_cols(__isl_keep isl_mat *mat)
262 {
263 return mat ? mat->n_col : -1;
264 }
265
266 /* Check that "col" is a valid column position for "mat".
267 */
268 static isl_stat check_col(__isl_keep isl_mat *mat, int col)
269 {
270 if (!mat)
271 return isl_stat_error;
272 if (col < 0 || col >= mat->n_col)
273 isl_die(isl_mat_get_ctx(mat), isl_error_invalid,
274 "column out of range", return isl_stat_error);
275 return isl_stat_ok;
276 }
277
278 /* Check that "row" is a valid row position for "mat".
279 */
280 static isl_stat check_row(__isl_keep isl_mat *mat, int row)
281 {
282 if (!mat)
283 return isl_stat_error;
284 if (row < 0 || row >= mat->n_row)
285 isl_die(isl_mat_get_ctx(mat), isl_error_invalid,
286 "row out of range", return isl_stat_error);
287 return isl_stat_ok;
288 }
289
290 /* Check that there are "n" columns starting at position "first" in "mat".
291 */
292 static isl_stat check_col_range(__isl_keep isl_mat *mat, unsigned first,
293 unsigned n)
294 {
295 if (!mat)
296 return isl_stat_error;
297 if (first + n > mat->n_col || first + n < first)
298 isl_die(isl_mat_get_ctx(mat), isl_error_invalid,
299 "column position or range out of bounds",
300 return isl_stat_error);
301 return isl_stat_ok;
302 }
303
304 /* Check that there are "n" rows starting at position "first" in "mat".
305 */
306 static isl_stat check_row_range(__isl_keep isl_mat *mat, unsigned first,
307 unsigned n)
308 {
309 if (!mat)
310 return isl_stat_error;
311 if (first + n > mat->n_row || first + n < first)
312 isl_die(isl_mat_get_ctx(mat), isl_error_invalid,
313 "row position or range out of bounds",
314 return isl_stat_error);
315 return isl_stat_ok;
316 }
317
318 int isl_mat_get_element(__isl_keep isl_mat *mat, int row, int col, isl_int *v)
319 {
320 if (check_row(mat, row) < 0)
321 return -1;
322 if (check_col(mat, col) < 0)
323 return -1;
324 isl_int_set(*v, mat->row[row][col]);
325 return 0;
326 }
327
328 /* Extract the element at row "row", oolumn "col" of "mat".
329 */
330 __isl_give isl_val *isl_mat_get_element_val(__isl_keep isl_mat *mat,
331 int row, int col)
332 {
333 isl_ctx *ctx;
334
335 if (check_row(mat, row) < 0)
336 return NULL;
337 if (check_col(mat, col) < 0)
338 return NULL;
339 ctx = isl_mat_get_ctx(mat);
340 return isl_val_int_from_isl_int(ctx, mat->row[row][col]);
341 }
342
343 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
344 int row, int col, isl_int v)
345 {
346 mat = isl_mat_cow(mat);
347 if (check_row(mat, row) < 0)
348 return isl_mat_free(mat);
349 if (check_col(mat, col) < 0)
350 return isl_mat_free(mat);
351 isl_int_set(mat->row[row][col], v);
352 return mat;
353 }
354
355 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
356 int row, int col, int v)
357 {
358 mat = isl_mat_cow(mat);
359 if (check_row(mat, row) < 0)
360 return isl_mat_free(mat);
361 if (check_col(mat, col) < 0)
362 return isl_mat_free(mat);
363 isl_int_set_si(mat->row[row][col], v);
364 return mat;
365 }
366
367 /* Replace the element at row "row", column "col" of "mat" by "v".
368 */
369 __isl_give isl_mat *isl_mat_set_element_val(__isl_take isl_mat *mat,
370 int row, int col, __isl_take isl_val *v)
371 {
372 if (!v)
373 return isl_mat_free(mat);
374 if (!isl_val_is_int(v))
375 isl_die(isl_val_get_ctx(v), isl_error_invalid,
376 "expecting integer value", goto error);
377 mat = isl_mat_set_element(mat, row, col, v->n);
378 isl_val_free(v);
379 return mat;
380 error:
381 isl_val_free(v);
382 return isl_mat_free(mat);
383 }
384
385 __isl_give isl_mat *isl_mat_diag(isl_ctx *ctx, unsigned n_row, isl_int d)
386 {
387 int i;
388 struct isl_mat *mat;
389
390 mat = isl_mat_alloc(ctx, n_row, n_row);
391 if (!mat)
392 return NULL;
393 for (i = 0; i < n_row; ++i) {
394 isl_seq_clr(mat->row[i], i);
395 isl_int_set(mat->row[i][i], d);
396 isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
397 }
398
399 return mat;
400 }
401
402 /* Create an "n_row" by "n_col" matrix with zero elements.
403 */
404 __isl_give isl_mat *isl_mat_zero(isl_ctx *ctx, unsigned n_row, unsigned n_col)
405 {
406 int i;
407 isl_mat *mat;
408
409 mat = isl_mat_alloc(ctx, n_row, n_col);
410 if (!mat)
411 return NULL;
412 for (i = 0; i < n_row; ++i)
413 isl_seq_clr(mat->row[i], n_col);
414
415 return mat;
416 }
417
418 __isl_give isl_mat *isl_mat_identity(isl_ctx *ctx, unsigned n_row)
419 {
420 if (!ctx)
421 return NULL;
422 return isl_mat_diag(ctx, n_row, ctx->one);
423 }
424
425 /* Is "mat" a (possibly scaled) identity matrix?
426 */
427 int isl_mat_is_scaled_identity(__isl_keep isl_mat *mat)
428 {
429 int i;
430
431 if (!mat)
432 return -1;
433 if (mat->n_row != mat->n_col)
434 return 0;
435
436 for (i = 0; i < mat->n_row; ++i) {
437 if (isl_seq_first_non_zero(mat->row[i], i) != -1)
438 return 0;
439 if (isl_int_ne(mat->row[0][0], mat->row[i][i]))
440 return 0;
441 if (isl_seq_first_non_zero(mat->row[i] + i + 1,
442 mat->n_col - (i + 1)) != -1)
443 return 0;
444 }
445
446 return 1;
447 }
448
449 __isl_give isl_vec *isl_mat_vec_product(__isl_take isl_mat *mat,
450 __isl_take isl_vec *vec)
451 {
452 int i;
453 struct isl_vec *prod;
454
455 if (!mat || !vec)
456 goto error;
457
458 isl_assert(mat->ctx, mat->n_col == vec->size, goto error);
459
460 prod = isl_vec_alloc(mat->ctx, mat->n_row);
461 if (!prod)
462 goto error;
463
464 for (i = 0; i < prod->size; ++i)
465 isl_seq_inner_product(mat->row[i], vec->el, vec->size,
466 &prod->block.data[i]);
467 isl_mat_free(mat);
468 isl_vec_free(vec);
469 return prod;
470 error:
471 isl_mat_free(mat);
472 isl_vec_free(vec);
473 return NULL;
474 }
475
476 __isl_give isl_vec *isl_mat_vec_inverse_product(__isl_take isl_mat *mat,
477 __isl_take isl_vec *vec)
478 {
479 struct isl_mat *vec_mat;
480 int i;
481
482 if (!mat || !vec)
483 goto error;
484 vec_mat = isl_mat_alloc(vec->ctx, vec->size, 1);
485 if (!vec_mat)
486 goto error;
487 for (i = 0; i < vec->size; ++i)
488 isl_int_set(vec_mat->row[i][0], vec->el[i]);
489 vec_mat = isl_mat_inverse_product(mat, vec_mat);
490 isl_vec_free(vec);
491 if (!vec_mat)
492 return NULL;
493 vec = isl_vec_alloc(vec_mat->ctx, vec_mat->n_row);
494 if (vec)
495 for (i = 0; i < vec->size; ++i)
496 isl_int_set(vec->el[i], vec_mat->row[i][0]);
497 isl_mat_free(vec_mat);
498 return vec;
499 error:
500 isl_mat_free(mat);
501 isl_vec_free(vec);
502 return NULL;
503 }
504
505 __isl_give isl_vec *isl_vec_mat_product(__isl_take isl_vec *vec,
506 __isl_take isl_mat *mat)
507 {
508 int i, j;
509 struct isl_vec *prod;
510
511 if (!mat || !vec)
512 goto error;
513
514 isl_assert(mat->ctx, mat->n_row == vec->size, goto error);
515
516 prod = isl_vec_alloc(mat->ctx, mat->n_col);
517 if (!prod)
518 goto error;
519
520 for (i = 0; i < prod->size; ++i) {
521 isl_int_set_si(prod->el[i], 0);
522 for (j = 0; j < vec->size; ++j)
523 isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);
524 }
525 isl_mat_free(mat);
526 isl_vec_free(vec);
527 return prod;
528 error:
529 isl_mat_free(mat);
530 isl_vec_free(vec);
531 return NULL;
532 }
533
534 __isl_give isl_mat *isl_mat_aff_direct_sum(__isl_take isl_mat *left,
535 __isl_take isl_mat *right)
536 {
537 int i;
538 struct isl_mat *sum;
539
540 if (!left || !right)
541 goto error;
542
543 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
544 isl_assert(left->ctx, left->n_row >= 1, goto error);
545 isl_assert(left->ctx, left->n_col >= 1, goto error);
546 isl_assert(left->ctx, right->n_col >= 1, goto error);
547 isl_assert(left->ctx,
548 isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,
549 goto error);
550 isl_assert(left->ctx,
551 isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
552 goto error);
553
554 sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);
555 if (!sum)
556 goto error;
557 isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);
558 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
559 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
560
561 isl_seq_clr(sum->row[0]+1, sum->n_col-1);
562 for (i = 1; i < sum->n_row; ++i) {
563 isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);
564 isl_int_addmul(sum->row[i][0],
565 right->row[0][0], right->row[i][0]);
566 isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],
567 left->n_col-1);
568 isl_seq_scale(sum->row[i]+left->n_col,
569 right->row[i]+1, right->row[0][0],
570 right->n_col-1);
571 }
572
573 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
574 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
575 isl_mat_free(left);
576 isl_mat_free(right);
577 return sum;
578 error:
579 isl_mat_free(left);
580 isl_mat_free(right);
581 return NULL;
582 }
583
584 static void exchange(struct isl_mat *M, struct isl_mat **U,
585 struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
586 {
587 int r;
588 for (r = row; r < M->n_row; ++r)
589 isl_int_swap(M->row[r][i], M->row[r][j]);
590 if (U) {
591 for (r = 0; r < (*U)->n_row; ++r)
592 isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
593 }
594 if (Q)
595 isl_mat_swap_rows(*Q, i, j);
596 }
597
598 static void subtract(struct isl_mat *M, struct isl_mat **U,
599 struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)
600 {
601 int r;
602 for (r = row; r < M->n_row; ++r)
603 isl_int_submul(M->row[r][j], m, M->row[r][i]);
604 if (U) {
605 for (r = 0; r < (*U)->n_row; ++r)
606 isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);
607 }
608 if (Q) {
609 for (r = 0; r < (*Q)->n_col; ++r)
610 isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);
611 }
612 }
613
614 static void oppose(struct isl_mat *M, struct isl_mat **U,
615 struct isl_mat **Q, unsigned row, unsigned col)
616 {
617 int r;
618 for (r = row; r < M->n_row; ++r)
619 isl_int_neg(M->row[r][col], M->row[r][col]);
620 if (U) {
621 for (r = 0; r < (*U)->n_row; ++r)
622 isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);
623 }
624 if (Q)
625 isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);
626 }
627
628 /* Given matrix M, compute
629 *
630 * M U = H
631 * M = H Q
632 *
633 * with U and Q unimodular matrices and H a matrix in column echelon form
634 * such that on each echelon row the entries in the non-echelon column
635 * are non-negative (if neg == 0) or non-positive (if neg == 1)
636 * and strictly smaller (in absolute value) than the entries in the echelon
637 * column.
638 * If U or Q are NULL, then these matrices are not computed.
639 */
640 __isl_give isl_mat *isl_mat_left_hermite(__isl_take isl_mat *M, int neg,
641 __isl_give isl_mat **U, __isl_give isl_mat **Q)
642 {
643 isl_int c;
644 int row, col;
645
646 if (U)
647 *U = NULL;
648 if (Q)
649 *Q = NULL;
650 if (!M)
651 goto error;
652 M = isl_mat_cow(M);
653 if (!M)
654 goto error;
655 if (U) {
656 *U = isl_mat_identity(M->ctx, M->n_col);
657 if (!*U)
658 goto error;
659 }
660 if (Q) {
661 *Q = isl_mat_identity(M->ctx, M->n_col);
662 if (!*Q)
663 goto error;
664 }
665
666 col = 0;
667 isl_int_init(c);
668 for (row = 0; row < M->n_row; ++row) {
669 int first, i, off;
670 first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);
671 if (first == -1)
672 continue;
673 first += col;
674 if (first != col)
675 exchange(M, U, Q, row, first, col);
676 if (isl_int_is_neg(M->row[row][col]))
677 oppose(M, U, Q, row, col);
678 first = col+1;
679 while ((off = isl_seq_first_non_zero(M->row[row]+first,
680 M->n_col-first)) != -1) {
681 first += off;
682 isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);
683 subtract(M, U, Q, row, col, first, c);
684 if (!isl_int_is_zero(M->row[row][first]))
685 exchange(M, U, Q, row, first, col);
686 else
687 ++first;
688 }
689 for (i = 0; i < col; ++i) {
690 if (isl_int_is_zero(M->row[row][i]))
691 continue;
692 if (neg)
693 isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);
694 else
695 isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);
696 if (isl_int_is_zero(c))
697 continue;
698 subtract(M, U, Q, row, col, i, c);
699 }
700 ++col;
701 }
702 isl_int_clear(c);
703
704 return M;
705 error:
706 if (Q) {
707 isl_mat_free(*Q);
708 *Q = NULL;
709 }
710 if (U) {
711 isl_mat_free(*U);
712 *U = NULL;
713 }
714 isl_mat_free(M);
715 return NULL;
716 }
717
718 /* Use row "row" of "mat" to eliminate column "col" from all other rows.
719 */
720 static __isl_give isl_mat *eliminate(__isl_take isl_mat *mat, int row, int col)
721 {
722 int k, nr, nc;
723 isl_ctx *ctx;
724
725 if (!mat)
726 return NULL;
727
728 ctx = isl_mat_get_ctx(mat);
729 nr = isl_mat_rows(mat);
730 nc = isl_mat_cols(mat);
731
732 for (k = 0; k < nr; ++k) {
733 if (k == row)
734 continue;
735 if (isl_int_is_zero(mat->row[k][col]))
736 continue;
737 mat = isl_mat_cow(mat);
738 if (!mat)
739 return NULL;
740 isl_seq_elim(mat->row[k], mat->row[row], col, nc, NULL);
741 isl_seq_normalize(ctx, mat->row[k], nc);
742 }
743
744 return mat;
745 }
746
747 /* Perform Gaussian elimination on the rows of "mat", but start
748 * from the final row and the final column.
749 * Any zero rows that result from the elimination are removed.
750 *
751 * In particular, for each column from last to first,
752 * look for the last row with a non-zero coefficient in that column,
753 * move it last (but before other rows moved last in previous steps) and
754 * use it to eliminate the column from the other rows.
755 */
756 __isl_give isl_mat *isl_mat_reverse_gauss(__isl_take isl_mat *mat)
757 {
758 int k, row, last, nr, nc;
759
760 if (!mat)
761 return NULL;
762
763 nr = isl_mat_rows(mat);
764 nc = isl_mat_cols(mat);
765
766 last = nc - 1;
767 for (row = nr - 1; row >= 0; --row) {
768 for (; last >= 0; --last) {
769 for (k = row; k >= 0; --k)
770 if (!isl_int_is_zero(mat->row[k][last]))
771 break;
772 if (k >= 0)
773 break;
774 }
775 if (last < 0)
776 break;
777 if (k != row)
778 mat = isl_mat_swap_rows(mat, k, row);
779 if (!mat)
780 return NULL;
781 if (isl_int_is_neg(mat->row[row][last]))
782 mat = isl_mat_row_neg(mat, row);
783 mat = eliminate(mat, row, last);
784 if (!mat)
785 return NULL;
786 }
787 mat = isl_mat_drop_rows(mat, 0, row + 1);
788
789 return mat;
790 }
791
792 /* Negate the lexicographically negative rows of "mat" such that
793 * all rows in the result are lexicographically non-negative.
794 */
795 __isl_give isl_mat *isl_mat_lexnonneg_rows(__isl_take isl_mat *mat)
796 {
797 int i, nr, nc;
798
799 if (!mat)
800 return NULL;
801
802 nr = isl_mat_rows(mat);
803 nc = isl_mat_cols(mat);
804
805 for (i = 0; i < nr; ++i) {
806 int pos;
807
808 pos = isl_seq_first_non_zero(mat->row[i], nc);
809 if (pos < 0)
810 continue;
811 if (isl_int_is_nonneg(mat->row[i][pos]))
812 continue;
813 mat = isl_mat_row_neg(mat, i);
814 if (!mat)
815 return NULL;
816 }
817
818 return mat;
819 }
820
821 /* Given a matrix "H" is column echelon form, what is the first
822 * zero column? That is how many initial columns are non-zero?
823 * Start looking at column "first_col" and only consider
824 * the columns to be of size "n_row".
825 * "H" is assumed to be non-NULL.
826 *
827 * Since "H" is in column echelon form, the first non-zero entry
828 * in a column is always in a later position compared to the previous column.
829 */
830 static int hermite_first_zero_col(__isl_keep isl_mat *H, int first_col,
831 int n_row)
832 {
833 int row, col;
834
835 for (col = first_col, row = 0; col < H->n_col; ++col) {
836 for (; row < n_row; ++row)
837 if (!isl_int_is_zero(H->row[row][col]))
838 break;
839 if (row == n_row)
840 return col;
841 }
842
843 return H->n_col;
844 }
845
846 /* Return the rank of "mat", or -1 in case of error.
847 */
848 int isl_mat_rank(__isl_keep isl_mat *mat)
849 {
850 int rank;
851 isl_mat *H;
852
853 H = isl_mat_left_hermite(isl_mat_copy(mat), 0, NULL, NULL);
854 if (!H)
855 return -1;
856
857 rank = hermite_first_zero_col(H, 0, H->n_row);
858 isl_mat_free(H);
859
860 return rank;
861 }
862
863 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat)
864 {
865 int rank;
866 struct isl_mat *U = NULL;
867 struct isl_mat *K;
868
869 mat = isl_mat_left_hermite(mat, 0, &U, NULL);
870 if (!mat || !U)
871 goto error;
872
873 rank = hermite_first_zero_col(mat, 0, mat->n_row);
874 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
875 if (!K)
876 goto error;
877 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
878 isl_mat_free(mat);
879 isl_mat_free(U);
880 return K;
881 error:
882 isl_mat_free(mat);
883 isl_mat_free(U);
884 return NULL;
885 }
886
887 __isl_give isl_mat *isl_mat_lin_to_aff(__isl_take isl_mat *mat)
888 {
889 int i;
890 struct isl_mat *mat2;
891
892 if (!mat)
893 return NULL;
894 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
895 if (!mat2)
896 goto error;
897 isl_int_set_si(mat2->row[0][0], 1);
898 isl_seq_clr(mat2->row[0]+1, mat->n_col);
899 for (i = 0; i < mat->n_row; ++i) {
900 isl_int_set_si(mat2->row[1+i][0], 0);
901 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
902 }
903 isl_mat_free(mat);
904 return mat2;
905 error:
906 isl_mat_free(mat);
907 return NULL;
908 }
909
910 /* Given two matrices M1 and M2, return the block matrix
911 *
912 * [ M1 0 ]
913 * [ 0 M2 ]
914 */
915 __isl_give isl_mat *isl_mat_diagonal(__isl_take isl_mat *mat1,
916 __isl_take isl_mat *mat2)
917 {
918 int i;
919 isl_mat *mat;
920
921 if (!mat1 || !mat2)
922 goto error;
923
924 mat = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
925 mat1->n_col + mat2->n_col);
926 if (!mat)
927 goto error;
928 for (i = 0; i < mat1->n_row; ++i) {
929 isl_seq_cpy(mat->row[i], mat1->row[i], mat1->n_col);
930 isl_seq_clr(mat->row[i] + mat1->n_col, mat2->n_col);
931 }
932 for (i = 0; i < mat2->n_row; ++i) {
933 isl_seq_clr(mat->row[mat1->n_row + i], mat1->n_col);
934 isl_seq_cpy(mat->row[mat1->n_row + i] + mat1->n_col,
935 mat2->row[i], mat2->n_col);
936 }
937 isl_mat_free(mat1);
938 isl_mat_free(mat2);
939 return mat;
940 error:
941 isl_mat_free(mat1);
942 isl_mat_free(mat2);
943 return NULL;
944 }
945
946 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
947 {
948 int i;
949
950 for (i = 0; i < n_row; ++i)
951 if (!isl_int_is_zero(row[i][col]))
952 return i;
953 return -1;
954 }
955
956 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
957 {
958 int i, min = row_first_non_zero(row, n_row, col);
959 if (min < 0)
960 return -1;
961 for (i = min + 1; i < n_row; ++i) {
962 if (isl_int_is_zero(row[i][col]))
963 continue;
964 if (isl_int_abs_lt(row[i][col], row[min][col]))
965 min = i;
966 }
967 return min;
968 }
969
970 static isl_stat inv_exchange(__isl_keep isl_mat **left,
971 __isl_keep isl_mat **right, unsigned i, unsigned j)
972 {
973 *left = isl_mat_swap_rows(*left, i, j);
974 *right = isl_mat_swap_rows(*right, i, j);
975
976 if (!*left || !*right)
977 return isl_stat_error;
978 return isl_stat_ok;
979 }
980
981 static void inv_oppose(
982 struct isl_mat *left, struct isl_mat *right, unsigned row)
983 {
984 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
985 isl_seq_neg(right->row[row], right->row[row], right->n_col);
986 }
987
988 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
989 unsigned row, unsigned i, isl_int m)
990 {
991 isl_int_neg(m, m);
992 isl_seq_combine(left->row[i]+row,
993 left->ctx->one, left->row[i]+row,
994 m, left->row[row]+row,
995 left->n_col-row);
996 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
997 m, right->row[row], right->n_col);
998 }
999
1000 /* Compute inv(left)*right
1001 */
1002 __isl_give isl_mat *isl_mat_inverse_product(__isl_take isl_mat *left,
1003 __isl_take isl_mat *right)
1004 {
1005 int row;
1006 isl_int a, b;
1007
1008 if (!left || !right)
1009 goto error;
1010
1011 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
1012 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
1013
1014 if (left->n_row == 0) {
1015 isl_mat_free(left);
1016 return right;
1017 }
1018
1019 left = isl_mat_cow(left);
1020 right = isl_mat_cow(right);
1021 if (!left || !right)
1022 goto error;
1023
1024 isl_int_init(a);
1025 isl_int_init(b);
1026 for (row = 0; row < left->n_row; ++row) {
1027 int pivot, first, i, off;
1028 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
1029 if (pivot < 0) {
1030 isl_int_clear(a);
1031 isl_int_clear(b);
1032 isl_assert(left->ctx, pivot >= 0, goto error);
1033 }
1034 pivot += row;
1035 if (pivot != row)
1036 if (inv_exchange(&left, &right, pivot, row) < 0)
1037 goto error;
1038 if (isl_int_is_neg(left->row[row][row]))
1039 inv_oppose(left, right, row);
1040 first = row+1;
1041 while ((off = row_first_non_zero(left->row+first,
1042 left->n_row-first, row)) != -1) {
1043 first += off;
1044 isl_int_fdiv_q(a, left->row[first][row],
1045 left->row[row][row]);
1046 inv_subtract(left, right, row, first, a);
1047 if (!isl_int_is_zero(left->row[first][row])) {
1048 if (inv_exchange(&left, &right, row, first) < 0)
1049 goto error;
1050 } else {
1051 ++first;
1052 }
1053 }
1054 for (i = 0; i < row; ++i) {
1055 if (isl_int_is_zero(left->row[i][row]))
1056 continue;
1057 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
1058 isl_int_divexact(b, left->row[i][row], a);
1059 isl_int_divexact(a, left->row[row][row], a);
1060 isl_int_neg(b, b);
1061 isl_seq_combine(left->row[i] + i,
1062 a, left->row[i] + i,
1063 b, left->row[row] + i,
1064 left->n_col - i);
1065 isl_seq_combine(right->row[i], a, right->row[i],
1066 b, right->row[row], right->n_col);
1067 }
1068 }
1069 isl_int_clear(b);
1070
1071 isl_int_set(a, left->row[0][0]);
1072 for (row = 1; row < left->n_row; ++row)
1073 isl_int_lcm(a, a, left->row[row][row]);
1074 if (isl_int_is_zero(a)){
1075 isl_int_clear(a);
1076 isl_assert(left->ctx, 0, goto error);
1077 }
1078 for (row = 0; row < left->n_row; ++row) {
1079 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
1080 if (isl_int_is_one(left->row[row][row]))
1081 continue;
1082 isl_seq_scale(right->row[row], right->row[row],
1083 left->row[row][row], right->n_col);
1084 }
1085 isl_int_clear(a);
1086
1087 isl_mat_free(left);
1088 return right;
1089 error:
1090 isl_mat_free(left);
1091 isl_mat_free(right);
1092 return NULL;
1093 }
1094
1095 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
1096 {
1097 int i;
1098
1099 for (i = 0; i < mat->n_row; ++i)
1100 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
1101 }
1102
1103 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
1104 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
1105 {
1106 int i;
1107 isl_int tmp;
1108
1109 isl_int_init(tmp);
1110 for (i = 0; i < mat->n_row; ++i) {
1111 isl_int_mul(tmp, m1, mat->row[i][src1]);
1112 isl_int_addmul(tmp, m2, mat->row[i][src2]);
1113 isl_int_set(mat->row[i][dst], tmp);
1114 }
1115 isl_int_clear(tmp);
1116 }
1117
1118 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat)
1119 {
1120 struct isl_mat *inv;
1121 int row;
1122 isl_int a, b;
1123
1124 mat = isl_mat_cow(mat);
1125 if (!mat)
1126 return NULL;
1127
1128 inv = isl_mat_identity(mat->ctx, mat->n_col);
1129 inv = isl_mat_cow(inv);
1130 if (!inv)
1131 goto error;
1132
1133 isl_int_init(a);
1134 isl_int_init(b);
1135 for (row = 0; row < mat->n_row; ++row) {
1136 int pivot, first, i, off;
1137 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
1138 if (pivot < 0) {
1139 isl_int_clear(a);
1140 isl_int_clear(b);
1141 isl_assert(mat->ctx, pivot >= 0, goto error);
1142 }
1143 pivot += row;
1144 if (pivot != row)
1145 exchange(mat, &inv, NULL, row, pivot, row);
1146 if (isl_int_is_neg(mat->row[row][row]))
1147 oppose(mat, &inv, NULL, row, row);
1148 first = row+1;
1149 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
1150 mat->n_col-first)) != -1) {
1151 first += off;
1152 isl_int_fdiv_q(a, mat->row[row][first],
1153 mat->row[row][row]);
1154 subtract(mat, &inv, NULL, row, row, first, a);
1155 if (!isl_int_is_zero(mat->row[row][first]))
1156 exchange(mat, &inv, NULL, row, row, first);
1157 else
1158 ++first;
1159 }
1160 for (i = 0; i < row; ++i) {
1161 if (isl_int_is_zero(mat->row[row][i]))
1162 continue;
1163 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
1164 isl_int_divexact(b, mat->row[row][i], a);
1165 isl_int_divexact(a, mat->row[row][row], a);
1166 isl_int_neg(a, a);
1167 isl_mat_col_combine(mat, i, a, i, b, row);
1168 isl_mat_col_combine(inv, i, a, i, b, row);
1169 }
1170 }
1171 isl_int_clear(b);
1172
1173 isl_int_set(a, mat->row[0][0]);
1174 for (row = 1; row < mat->n_row; ++row)
1175 isl_int_lcm(a, a, mat->row[row][row]);
1176 if (isl_int_is_zero(a)){
1177 isl_int_clear(a);
1178 goto error;
1179 }
1180 for (row = 0; row < mat->n_row; ++row) {
1181 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
1182 if (isl_int_is_one(mat->row[row][row]))
1183 continue;
1184 isl_mat_col_scale(inv, row, mat->row[row][row]);
1185 }
1186 isl_int_clear(a);
1187
1188 isl_mat_free(mat);
1189
1190 return inv;
1191 error:
1192 isl_mat_free(mat);
1193 isl_mat_free(inv);
1194 return NULL;
1195 }
1196
1197 __isl_give isl_mat *isl_mat_transpose(__isl_take isl_mat *mat)
1198 {
1199 struct isl_mat *transpose = NULL;
1200 int i, j;
1201
1202 if (!mat)
1203 return NULL;
1204
1205 if (mat->n_col == mat->n_row) {
1206 mat = isl_mat_cow(mat);
1207 if (!mat)
1208 return NULL;
1209 for (i = 0; i < mat->n_row; ++i)
1210 for (j = i + 1; j < mat->n_col; ++j)
1211 isl_int_swap(mat->row[i][j], mat->row[j][i]);
1212 return mat;
1213 }
1214 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
1215 if (!transpose)
1216 goto error;
1217 for (i = 0; i < mat->n_row; ++i)
1218 for (j = 0; j < mat->n_col; ++j)
1219 isl_int_set(transpose->row[j][i], mat->row[i][j]);
1220 isl_mat_free(mat);
1221 return transpose;
1222 error:
1223 isl_mat_free(mat);
1224 return NULL;
1225 }
1226
1227 __isl_give isl_mat *isl_mat_swap_cols(__isl_take isl_mat *mat,
1228 unsigned i, unsigned j)
1229 {
1230 int r;
1231
1232 mat = isl_mat_cow(mat);
1233 if (check_col_range(mat, i, 1) < 0 ||
1234 check_col_range(mat, j, 1) < 0)
1235 return isl_mat_free(mat);
1236
1237 for (r = 0; r < mat->n_row; ++r)
1238 isl_int_swap(mat->row[r][i], mat->row[r][j]);
1239 return mat;
1240 }
1241
1242 __isl_give isl_mat *isl_mat_swap_rows(__isl_take isl_mat *mat,
1243 unsigned i, unsigned j)
1244 {
1245 isl_int *t;
1246
1247 if (!mat)
1248 return NULL;
1249 mat = isl_mat_cow(mat);
1250 if (check_row_range(mat, i, 1) < 0 ||
1251 check_row_range(mat, j, 1) < 0)
1252 return isl_mat_free(mat);
1253
1254 t = mat->row[i];
1255 mat->row[i] = mat->row[j];
1256 mat->row[j] = t;
1257 return mat;
1258 }
1259
1260 /* Calculate the product of two matrices.
1261 *
1262 * This function is optimized for operand matrices that contain many zeros and
1263 * skips multiplications where we know one of the operands is zero.
1264 */
1265 __isl_give isl_mat *isl_mat_product(__isl_take isl_mat *left,
1266 __isl_take isl_mat *right)
1267 {
1268 int i, j, k;
1269 struct isl_mat *prod;
1270
1271 if (!left || !right)
1272 goto error;
1273 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
1274 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
1275 if (!prod)
1276 goto error;
1277 if (left->n_col == 0) {
1278 for (i = 0; i < prod->n_row; ++i)
1279 isl_seq_clr(prod->row[i], prod->n_col);
1280 isl_mat_free(left);
1281 isl_mat_free(right);
1282 return prod;
1283 }
1284 for (i = 0; i < prod->n_row; ++i) {
1285 for (j = 0; j < prod->n_col; ++j)
1286 isl_int_mul(prod->row[i][j],
1287 left->row[i][0], right->row[0][j]);
1288 for (k = 1; k < left->n_col; ++k) {
1289 if (isl_int_is_zero(left->row[i][k]))
1290 continue;
1291 for (j = 0; j < prod->n_col; ++j)
1292 isl_int_addmul(prod->row[i][j],
1293 left->row[i][k], right->row[k][j]);
1294 }
1295 }
1296 isl_mat_free(left);
1297 isl_mat_free(right);
1298 return prod;
1299 error:
1300 isl_mat_free(left);
1301 isl_mat_free(right);
1302 return NULL;
1303 }
1304
1305 /* Replace the variables x in the rows q by x' given by x = M x',
1306 * with M the matrix mat.
1307 *
1308 * If the number of new variables is greater than the original
1309 * number of variables, then the rows q have already been
1310 * preextended. If the new number is smaller, then the coefficients
1311 * of the divs, which are not changed, need to be shifted down.
1312 * The row q may be the equalities, the inequalities or the
1313 * div expressions. In the latter case, has_div is true and
1314 * we need to take into account the extra denominator column.
1315 */
1316 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
1317 unsigned n_div, int has_div, struct isl_mat *mat)
1318 {
1319 int i;
1320 struct isl_mat *t;
1321 int e;
1322
1323 if (mat->n_col >= mat->n_row)
1324 e = 0;
1325 else
1326 e = mat->n_row - mat->n_col;
1327 if (has_div)
1328 for (i = 0; i < n; ++i)
1329 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
1330 t = isl_mat_sub_alloc6(mat->ctx, q, 0, n, has_div, mat->n_row);
1331 t = isl_mat_product(t, mat);
1332 if (!t)
1333 return -1;
1334 for (i = 0; i < n; ++i) {
1335 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
1336 isl_seq_cpy(q[i] + has_div + t->n_col,
1337 q[i] + has_div + t->n_col + e, n_div);
1338 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
1339 }
1340 isl_mat_free(t);
1341 return 0;
1342 }
1343
1344 /* Replace the variables x in bset by x' given by x = M x', with
1345 * M the matrix mat.
1346 *
1347 * If there are fewer variables x' then there are x, then we perform
1348 * the transformation in place, which means that, in principle,
1349 * this frees up some extra variables as the number
1350 * of columns remains constant, but we would have to extend
1351 * the div array too as the number of rows in this array is assumed
1352 * to be equal to extra.
1353 */
1354 __isl_give isl_basic_set *isl_basic_set_preimage(
1355 __isl_take isl_basic_set *bset, __isl_take isl_mat *mat)
1356 {
1357 struct isl_ctx *ctx;
1358
1359 if (!bset || !mat)
1360 goto error;
1361
1362 ctx = bset->ctx;
1363 bset = isl_basic_set_cow(bset);
1364 if (!bset)
1365 goto error;
1366
1367 isl_assert(ctx, bset->dim->nparam == 0, goto error);
1368 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
1369 isl_assert(ctx, mat->n_col > 0, goto error);
1370
1371 if (mat->n_col > mat->n_row) {
1372 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0, 0, 0);
1373 if (!bset)
1374 goto error;
1375 } else if (mat->n_col < mat->n_row) {
1376 bset->dim = isl_space_cow(bset->dim);
1377 if (!bset->dim)
1378 goto error;
1379 bset->dim->n_out -= mat->n_row - mat->n_col;
1380 }
1381
1382 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
1383 isl_mat_copy(mat)) < 0)
1384 goto error;
1385
1386 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
1387 isl_mat_copy(mat)) < 0)
1388 goto error;
1389
1390 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
1391 goto error2;
1392
1393 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
1394 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
1395 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1396 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1397 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
1398
1399 bset = isl_basic_set_simplify(bset);
1400 bset = isl_basic_set_finalize(bset);
1401
1402 return bset;
1403 error:
1404 isl_mat_free(mat);
1405 error2:
1406 isl_basic_set_free(bset);
1407 return NULL;
1408 }
1409
1410 __isl_give isl_set *isl_set_preimage(
1411 __isl_take isl_set *set, __isl_take isl_mat *mat)
1412 {
1413 int i;
1414
1415 set = isl_set_cow(set);
1416 if (!set)
1417 goto error;
1418
1419 for (i = 0; i < set->n; ++i) {
1420 set->p[i] = isl_basic_set_preimage(set->p[i],
1421 isl_mat_copy(mat));
1422 if (!set->p[i])
1423 goto error;
1424 }
1425 if (mat->n_col != mat->n_row) {
1426 set->dim = isl_space_cow(set->dim);
1427 if (!set->dim)
1428 goto error;
1429 set->dim->n_out += mat->n_col;
1430 set->dim->n_out -= mat->n_row;
1431 }
1432 isl_mat_free(mat);
1433 ISL_F_CLR(set, ISL_SET_NORMALIZED);
1434 return set;
1435 error:
1436 isl_set_free(set);
1437 isl_mat_free(mat);
1438 return NULL;
1439 }
1440
1441 /* Replace the variables x starting at "first_col" in the rows "rows"
1442 * of some coefficient matrix by x' with x = M x' with M the matrix mat.
1443 * That is, replace the corresponding coefficients c by c M.
1444 */
1445 isl_stat isl_mat_sub_transform(isl_int **row, unsigned n_row,
1446 unsigned first_col, __isl_take isl_mat *mat)
1447 {
1448 int i;
1449 isl_ctx *ctx;
1450 isl_mat *t;
1451
1452 if (!mat)
1453 return isl_stat_error;
1454 ctx = isl_mat_get_ctx(mat);
1455 t = isl_mat_sub_alloc6(ctx, row, 0, n_row, first_col, mat->n_row);
1456 t = isl_mat_product(t, mat);
1457 if (!t)
1458 return isl_stat_error;
1459 for (i = 0; i < n_row; ++i)
1460 isl_seq_swp_or_cpy(row[i] + first_col, t->row[i], t->n_col);
1461 isl_mat_free(t);
1462 return isl_stat_ok;
1463 }
1464
1465 void isl_mat_print_internal(__isl_keep isl_mat *mat, FILE *out, int indent)
1466 {
1467 int i, j;
1468
1469 if (!mat) {
1470 fprintf(out, "%*snull mat\n", indent, "");
1471 return;
1472 }
1473
1474 if (mat->n_row == 0)
1475 fprintf(out, "%*s[]\n", indent, "");
1476
1477 for (i = 0; i < mat->n_row; ++i) {
1478 if (!i)
1479 fprintf(out, "%*s[[", indent, "");
1480 else
1481 fprintf(out, "%*s[", indent+1, "");
1482 for (j = 0; j < mat->n_col; ++j) {
1483 if (j)
1484 fprintf(out, ",");
1485 isl_int_print(out, mat->row[i][j], 0);
1486 }
1487 if (i == mat->n_row-1)
1488 fprintf(out, "]]\n");
1489 else
1490 fprintf(out, "]\n");
1491 }
1492 }
1493
1494 void isl_mat_dump(__isl_keep isl_mat *mat)
1495 {
1496 isl_mat_print_internal(mat, stderr, 0);
1497 }
1498
1499 __isl_give isl_mat *isl_mat_drop_cols(__isl_take isl_mat *mat,
1500 unsigned col, unsigned n)
1501 {
1502 int r;
1503
1504 if (n == 0)
1505 return mat;
1506
1507 mat = isl_mat_cow(mat);
1508 if (check_col_range(mat, col, n) < 0)
1509 return isl_mat_free(mat);
1510
1511 if (col != mat->n_col-n) {
1512 for (r = 0; r < mat->n_row; ++r)
1513 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1514 mat->n_col - col - n);
1515 }
1516 mat->n_col -= n;
1517 return mat;
1518 }
1519
1520 __isl_give isl_mat *isl_mat_drop_rows(__isl_take isl_mat *mat,
1521 unsigned row, unsigned n)
1522 {
1523 int r;
1524
1525 mat = isl_mat_cow(mat);
1526 if (check_row_range(mat, row, n) < 0)
1527 return isl_mat_free(mat);
1528
1529 for (r = row; r+n < mat->n_row; ++r)
1530 mat->row[r] = mat->row[r+n];
1531
1532 mat->n_row -= n;
1533 return mat;
1534 }
1535
1536 __isl_give isl_mat *isl_mat_insert_cols(__isl_take isl_mat *mat,
1537 unsigned col, unsigned n)
1538 {
1539 isl_mat *ext;
1540
1541 if (check_col_range(mat, col, 0) < 0)
1542 return isl_mat_free(mat);
1543 if (n == 0)
1544 return mat;
1545
1546 ext = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col + n);
1547 if (!ext)
1548 goto error;
1549
1550 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row, 0, 0, col);
1551 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row,
1552 col + n, col, mat->n_col - col);
1553
1554 isl_mat_free(mat);
1555 return ext;
1556 error:
1557 isl_mat_free(mat);
1558 return NULL;
1559 }
1560
1561 __isl_give isl_mat *isl_mat_insert_zero_cols(__isl_take isl_mat *mat,
1562 unsigned first, unsigned n)
1563 {
1564 int i;
1565
1566 if (!mat)
1567 return NULL;
1568 mat = isl_mat_insert_cols(mat, first, n);
1569 if (!mat)
1570 return NULL;
1571
1572 for (i = 0; i < mat->n_row; ++i)
1573 isl_seq_clr(mat->row[i] + first, n);
1574
1575 return mat;
1576 }
1577
1578 __isl_give isl_mat *isl_mat_add_zero_cols(__isl_take isl_mat *mat, unsigned n)
1579 {
1580 if (!mat)
1581 return NULL;
1582
1583 return isl_mat_insert_zero_cols(mat, mat->n_col, n);
1584 }
1585
1586 __isl_give isl_mat *isl_mat_insert_rows(__isl_take isl_mat *mat,
1587 unsigned row, unsigned n)
1588 {
1589 isl_mat *ext;
1590
1591 if (check_row_range(mat, row, 0) < 0)
1592 return isl_mat_free(mat);
1593 if (n == 0)
1594 return mat;
1595
1596 ext = isl_mat_alloc(mat->ctx, mat->n_row + n, mat->n_col);
1597 if (!ext)
1598 goto error;
1599
1600 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, row, 0, 0, mat->n_col);
1601 isl_mat_sub_copy(mat->ctx, ext->row + row + n, mat->row + row,
1602 mat->n_row - row, 0, 0, mat->n_col);
1603
1604 isl_mat_free(mat);
1605 return ext;
1606 error:
1607 isl_mat_free(mat);
1608 return NULL;
1609 }
1610
1611 __isl_give isl_mat *isl_mat_add_rows(__isl_take isl_mat *mat, unsigned n)
1612 {
1613 if (!mat)
1614 return NULL;
1615
1616 return isl_mat_insert_rows(mat, mat->n_row, n);
1617 }
1618
1619 __isl_give isl_mat *isl_mat_insert_zero_rows(__isl_take isl_mat *mat,
1620 unsigned row, unsigned n)
1621 {
1622 int i;
1623
1624 mat = isl_mat_insert_rows(mat, row, n);
1625 if (!mat)
1626 return NULL;
1627
1628 for (i = 0; i < n; ++i)
1629 isl_seq_clr(mat->row[row + i], mat->n_col);
1630
1631 return mat;
1632 }
1633
1634 __isl_give isl_mat *isl_mat_add_zero_rows(__isl_take isl_mat *mat, unsigned n)
1635 {
1636 if (!mat)
1637 return NULL;
1638
1639 return isl_mat_insert_zero_rows(mat, mat->n_row, n);
1640 }
1641
1642 void isl_mat_col_submul(struct isl_mat *mat,
1643 int dst_col, isl_int f, int src_col)
1644 {
1645 int i;
1646
1647 for (i = 0; i < mat->n_row; ++i)
1648 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1649 }
1650
1651 void isl_mat_col_add(__isl_keep isl_mat *mat, int dst_col, int src_col)
1652 {
1653 int i;
1654
1655 if (!mat)
1656 return;
1657
1658 for (i = 0; i < mat->n_row; ++i)
1659 isl_int_add(mat->row[i][dst_col],
1660 mat->row[i][dst_col], mat->row[i][src_col]);
1661 }
1662
1663 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1664 {
1665 int i;
1666
1667 for (i = 0; i < mat->n_row; ++i)
1668 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1669 }
1670
1671 /* Add "f" times column "src_col" to column "dst_col" of "mat" and
1672 * return the result.
1673 */
1674 __isl_give isl_mat *isl_mat_col_addmul(__isl_take isl_mat *mat, int dst_col,
1675 isl_int f, int src_col)
1676 {
1677 int i;
1678
1679 if (check_col(mat, dst_col) < 0 || check_col(mat, src_col) < 0)
1680 return isl_mat_free(mat);
1681
1682 for (i = 0; i < mat->n_row; ++i) {
1683 if (isl_int_is_zero(mat->row[i][src_col]))
1684 continue;
1685 mat = isl_mat_cow(mat);
1686 if (!mat)
1687 return NULL;
1688 isl_int_addmul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1689 }
1690
1691 return mat;
1692 }
1693
1694 /* Negate column "col" of "mat" and return the result.
1695 */
1696 __isl_give isl_mat *isl_mat_col_neg(__isl_take isl_mat *mat, int col)
1697 {
1698 int i;
1699
1700 if (check_col(mat, col) < 0)
1701 return isl_mat_free(mat);
1702
1703 for (i = 0; i < mat->n_row; ++i) {
1704 if (isl_int_is_zero(mat->row[i][col]))
1705 continue;
1706 mat = isl_mat_cow(mat);
1707 if (!mat)
1708 return NULL;
1709 isl_int_neg(mat->row[i][col], mat->row[i][col]);
1710 }
1711
1712 return mat;
1713 }
1714
1715 /* Negate row "row" of "mat" and return the result.
1716 */
1717 __isl_give isl_mat *isl_mat_row_neg(__isl_take isl_mat *mat, int row)
1718 {
1719 if (check_row(mat, row) < 0)
1720 return isl_mat_free(mat);
1721 if (isl_seq_first_non_zero(mat->row[row], mat->n_col) == -1)
1722 return mat;
1723 mat = isl_mat_cow(mat);
1724 if (!mat)
1725 return NULL;
1726 isl_seq_neg(mat->row[row], mat->row[row], mat->n_col);
1727 return mat;
1728 }
1729
1730 __isl_give isl_mat *isl_mat_unimodular_complete(__isl_take isl_mat *M, int row)
1731 {
1732 int r;
1733 struct isl_mat *H = NULL, *Q = NULL;
1734
1735 if (!M)
1736 return NULL;
1737
1738 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1739 M->n_row = row;
1740 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1741 M->n_row = M->n_col;
1742 if (!H)
1743 goto error;
1744 for (r = 0; r < row; ++r)
1745 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1746 for (r = row; r < M->n_row; ++r)
1747 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1748 isl_mat_free(H);
1749 isl_mat_free(Q);
1750 return M;
1751 error:
1752 isl_mat_free(H);
1753 isl_mat_free(Q);
1754 isl_mat_free(M);
1755 return NULL;
1756 }
1757
1758 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1759 __isl_take isl_mat *bot)
1760 {
1761 struct isl_mat *mat;
1762
1763 if (!top || !bot)
1764 goto error;
1765
1766 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1767 if (top->n_row == 0) {
1768 isl_mat_free(top);
1769 return bot;
1770 }
1771 if (bot->n_row == 0) {
1772 isl_mat_free(bot);
1773 return top;
1774 }
1775
1776 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1777 if (!mat)
1778 goto error;
1779 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1780 0, 0, mat->n_col);
1781 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1782 0, 0, mat->n_col);
1783 isl_mat_free(top);
1784 isl_mat_free(bot);
1785 return mat;
1786 error:
1787 isl_mat_free(top);
1788 isl_mat_free(bot);
1789 return NULL;
1790 }
1791
1792 isl_bool isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
1793 {
1794 int i;
1795
1796 if (!mat1 || !mat2)
1797 return isl_bool_error;
1798
1799 if (mat1->n_row != mat2->n_row)
1800 return isl_bool_false;
1801
1802 if (mat1->n_col != mat2->n_col)
1803 return isl_bool_false;
1804
1805 for (i = 0; i < mat1->n_row; ++i)
1806 if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
1807 return isl_bool_false;
1808
1809 return isl_bool_true;
1810 }
1811
1812 __isl_give isl_mat *isl_mat_from_row_vec(__isl_take isl_vec *vec)
1813 {
1814 struct isl_mat *mat;
1815
1816 if (!vec)
1817 return NULL;
1818 mat = isl_mat_alloc(vec->ctx, 1, vec->size);
1819 if (!mat)
1820 goto error;
1821
1822 isl_seq_cpy(mat->row[0], vec->el, vec->size);
1823
1824 isl_vec_free(vec);
1825 return mat;
1826 error:
1827 isl_vec_free(vec);
1828 return NULL;
1829 }
1830
1831 /* Return a copy of row "row" of "mat" as an isl_vec.
1832 */
1833 __isl_give isl_vec *isl_mat_get_row(__isl_keep isl_mat *mat, unsigned row)
1834 {
1835 isl_vec *v;
1836
1837 if (!mat)
1838 return NULL;
1839 if (row >= mat->n_row)
1840 isl_die(mat->ctx, isl_error_invalid, "row out of range",
1841 return NULL);
1842
1843 v = isl_vec_alloc(isl_mat_get_ctx(mat), mat->n_col);
1844 if (!v)
1845 return NULL;
1846 isl_seq_cpy(v->el, mat->row[row], mat->n_col);
1847
1848 return v;
1849 }
1850
1851 __isl_give isl_mat *isl_mat_vec_concat(__isl_take isl_mat *top,
1852 __isl_take isl_vec *bot)
1853 {
1854 return isl_mat_concat(top, isl_mat_from_row_vec(bot));
1855 }
1856
1857 __isl_give isl_mat *isl_mat_move_cols(__isl_take isl_mat *mat,
1858 unsigned dst_col, unsigned src_col, unsigned n)
1859 {
1860 isl_mat *res;
1861
1862 if (!mat)
1863 return NULL;
1864 if (n == 0 || dst_col == src_col)
1865 return mat;
1866
1867 res = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
1868 if (!res)
1869 goto error;
1870
1871 if (dst_col < src_col) {
1872 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1873 0, 0, dst_col);
1874 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1875 dst_col, src_col, n);
1876 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1877 dst_col + n, dst_col, src_col - dst_col);
1878 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1879 src_col + n, src_col + n,
1880 res->n_col - src_col - n);
1881 } else {
1882 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1883 0, 0, src_col);
1884 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1885 src_col, src_col + n, dst_col - src_col);
1886 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1887 dst_col, src_col, n);
1888 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1889 dst_col + n, dst_col + n,
1890 res->n_col - dst_col - n);
1891 }
1892 isl_mat_free(mat);
1893
1894 return res;
1895 error:
1896 isl_mat_free(mat);
1897 return NULL;
1898 }
1899
1900 /* Return the gcd of the elements in row "row" of "mat" in *gcd.
1901 * Return isl_stat_ok on success and isl_stat_error on failure.
1902 */
1903 isl_stat isl_mat_row_gcd(__isl_keep isl_mat *mat, int row, isl_int *gcd)
1904 {
1905 if (check_row(mat, row) < 0)
1906 return isl_stat_error;
1907
1908 isl_seq_gcd(mat->row[row], mat->n_col, gcd);
1909
1910 return isl_stat_ok;
1911 }
1912
1913 void isl_mat_gcd(__isl_keep isl_mat *mat, isl_int *gcd)
1914 {
1915 int i;
1916 isl_int g;
1917
1918 isl_int_set_si(*gcd, 0);
1919 if (!mat)
1920 return;
1921
1922 isl_int_init(g);
1923 for (i = 0; i < mat->n_row; ++i) {
1924 isl_seq_gcd(mat->row[i], mat->n_col, &g);
1925 isl_int_gcd(*gcd, *gcd, g);
1926 }
1927 isl_int_clear(g);
1928 }
1929
1930 /* Return the result of scaling "mat" by a factor of "m".
1931 */
1932 __isl_give isl_mat *isl_mat_scale(__isl_take isl_mat *mat, isl_int m)
1933 {
1934 int i;
1935
1936 if (isl_int_is_one(m))
1937 return mat;
1938
1939 mat = isl_mat_cow(mat);
1940 if (!mat)
1941 return NULL;
1942
1943 for (i = 0; i < mat->n_row; ++i)
1944 isl_seq_scale(mat->row[i], mat->row[i], m, mat->n_col);
1945
1946 return mat;
1947 }
1948
1949 __isl_give isl_mat *isl_mat_scale_down(__isl_take isl_mat *mat, isl_int m)
1950 {
1951 int i;
1952
1953 if (isl_int_is_one(m))
1954 return mat;
1955
1956 mat = isl_mat_cow(mat);
1957 if (!mat)
1958 return NULL;
1959
1960 for (i = 0; i < mat->n_row; ++i)
1961 isl_seq_scale_down(mat->row[i], mat->row[i], m, mat->n_col);
1962
1963 return mat;
1964 }
1965
1966 __isl_give isl_mat *isl_mat_scale_down_row(__isl_take isl_mat *mat, int row,
1967 isl_int m)
1968 {
1969 if (isl_int_is_one(m))
1970 return mat;
1971
1972 mat = isl_mat_cow(mat);
1973 if (!mat)
1974 return NULL;
1975
1976 isl_seq_scale_down(mat->row[row], mat->row[row], m, mat->n_col);
1977
1978 return mat;
1979 }
1980
1981 __isl_give isl_mat *isl_mat_normalize(__isl_take isl_mat *mat)
1982 {
1983 isl_int gcd;
1984
1985 if (!mat)
1986 return NULL;
1987
1988 isl_int_init(gcd);
1989 isl_mat_gcd(mat, &gcd);
1990 mat = isl_mat_scale_down(mat, gcd);
1991 isl_int_clear(gcd);
1992
1993 return mat;
1994 }
1995
1996 __isl_give isl_mat *isl_mat_normalize_row(__isl_take isl_mat *mat, int row)
1997 {
1998 mat = isl_mat_cow(mat);
1999 if (!mat)
2000 return NULL;
2001
2002 isl_seq_normalize(mat->ctx, mat->row[row], mat->n_col);
2003
2004 return mat;
2005 }
2006
2007 /* Number of initial non-zero columns.
2008 */
2009 int isl_mat_initial_non_zero_cols(__isl_keep isl_mat *mat)
2010 {
2011 int i;
2012
2013 if (!mat)
2014 return -1;
2015
2016 for (i = 0; i < mat->n_col; ++i)
2017 if (row_first_non_zero(mat->row, mat->n_row, i) < 0)
2018 break;
2019
2020 return i;
2021 }
2022
2023 /* Return a basis for the space spanned by the rows of "mat".
2024 * Any basis will do, so simply perform Gaussian elimination and
2025 * remove the empty rows.
2026 */
2027 __isl_give isl_mat *isl_mat_row_basis(__isl_take isl_mat *mat)
2028 {
2029 return isl_mat_reverse_gauss(mat);
2030 }
2031
2032 /* Return rows that extend a basis of "mat1" to one
2033 * that covers both "mat1" and "mat2".
2034 * The Hermite normal form of the concatenation of the two matrices is
2035 *
2036 * [ Q1 ]
2037 * [ M1 ] = [ H1 0 0 ] [ Q2 ]
2038 * [ M2 ] = [ H2 H3 0 ] [ Q3 ]
2039 *
2040 * The number of columns in H1 and H3 determine the number of rows
2041 * in Q1 and Q2. Q1 is a basis for M1, while Q2 extends this basis
2042 * to also cover M2.
2043 */
2044 __isl_give isl_mat *isl_mat_row_basis_extension(
2045 __isl_take isl_mat *mat1, __isl_take isl_mat *mat2)
2046 {
2047 int n_row;
2048 int r1, r, n1;
2049 isl_mat *H, *Q;
2050
2051 n1 = isl_mat_rows(mat1);
2052 H = isl_mat_concat(mat1, mat2);
2053 H = isl_mat_left_hermite(H, 0, NULL, &Q);
2054 if (!H || !Q)
2055 goto error;
2056
2057 r1 = hermite_first_zero_col(H, 0, n1);
2058 r = hermite_first_zero_col(H, r1, H->n_row);
2059 n_row = isl_mat_rows(Q);
2060 Q = isl_mat_drop_rows(Q, r, n_row - r);
2061 Q = isl_mat_drop_rows(Q, 0, r1);
2062
2063 isl_mat_free(H);
2064 return Q;
2065 error:
2066 isl_mat_free(H);
2067 isl_mat_free(Q);
2068 return NULL;
2069 }
2070
2071 /* Are the rows of "mat1" linearly independent of those of "mat2"?
2072 * That is, is there no linear dependence among the combined rows
2073 * that is not already present in either "mat1" or "mat2"?
2074 * In other words, is the rank of "mat1" and "mat2" combined equal
2075 * to the sum of the ranks of "mat1" and "mat2"?
2076 */
2077 isl_bool isl_mat_has_linearly_independent_rows(__isl_keep isl_mat *mat1,
2078 __isl_keep isl_mat *mat2)
2079 {
2080 int r1, r2, r;
2081 isl_mat *mat;
2082
2083 r1 = isl_mat_rank(mat1);
2084 if (r1 < 0)
2085 return isl_bool_error;
2086 if (r1 == 0)
2087 return isl_bool_true;
2088 r2 = isl_mat_rank(mat2);
2089 if (r2 < 0)
2090 return isl_bool_error;
2091 if (r2 == 0)
2092 return isl_bool_true;
2093
2094 mat = isl_mat_concat(isl_mat_copy(mat1), isl_mat_copy(mat2));
2095 r = isl_mat_rank(mat);
2096 isl_mat_free(mat);
2097 if (r < 0)
2098 return isl_bool_error;
2099 return r == r1 + r2;
2100 }
Integer set library