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doc: isl_union_*_foreach_*: specify header to include
[isl.git] / isl_mat.c
blob79be9389cc4220c52ac8760d7f70120e27dddac2
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 * Copyright 2014 Ecole Normale Superieure
4 *
5 * Use of this software is governed by the MIT license
6 *
7 * Written by Sven Verdoolaege, K.U.Leuven, Departement
8 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
9 * and Ecole Normale Superieure, 45 rue d'Ulm, 75230 Paris, France
10 */
11
12 #include <isl_ctx_private.h>
13 #include <isl_map_private.h>
14 #include <isl/space.h>
15 #include <isl_seq.h>
16 #include <isl_mat_private.h>
17 #include <isl_vec_private.h>
18 #include <isl_space_private.h>
19 #include <isl_val_private.h>
20 #include <isl/deprecated/mat_int.h>
21
22 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat)
23 {
24 return mat ? mat->ctx : NULL;
25 }
26
27 /* Return a hash value that digests "mat".
28 */
29 uint32_t isl_mat_get_hash(__isl_keep isl_mat *mat)
30 {
31 int i;
32 uint32_t hash;
33
34 if (!mat)
35 return 0;
36
37 hash = isl_hash_init();
38 isl_hash_byte(hash, mat->n_row & 0xFF);
39 isl_hash_byte(hash, mat->n_col & 0xFF);
40 for (i = 0; i < mat->n_row; ++i) {
41 uint32_t row_hash;
42
43 row_hash = isl_seq_get_hash(mat->row[i], mat->n_col);
44 isl_hash_hash(hash, row_hash);
45 }
46
47 return hash;
48 }
49
50 struct isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
51 unsigned n_row, unsigned n_col)
52 {
53 int i;
54 struct isl_mat *mat;
55
56 mat = isl_alloc_type(ctx, struct isl_mat);
57 if (!mat)
58 return NULL;
59
60 mat->row = NULL;
61 mat->block = isl_blk_alloc(ctx, n_row * n_col);
62 if (isl_blk_is_error(mat->block))
63 goto error;
64 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
65 if (n_row && !mat->row)
66 goto error;
67
68 for (i = 0; i < n_row; ++i)
69 mat->row[i] = mat->block.data + i * n_col;
70
71 mat->ctx = ctx;
72 isl_ctx_ref(ctx);
73 mat->ref = 1;
74 mat->n_row = n_row;
75 mat->n_col = n_col;
76 mat->max_col = n_col;
77 mat->flags = 0;
78
79 return mat;
80 error:
81 isl_blk_free(ctx, mat->block);
82 free(mat);
83 return NULL;
84 }
85
86 struct isl_mat *isl_mat_extend(struct isl_mat *mat,
87 unsigned n_row, unsigned n_col)
88 {
89 int i;
90 isl_int *old;
91 isl_int **row;
92
93 if (!mat)
94 return NULL;
95
96 if (mat->max_col >= n_col && mat->n_row >= n_row) {
97 if (mat->n_col < n_col)
98 mat->n_col = n_col;
99 return mat;
100 }
101
102 if (mat->max_col < n_col) {
103 struct isl_mat *new_mat;
104
105 if (n_row < mat->n_row)
106 n_row = mat->n_row;
107 new_mat = isl_mat_alloc(mat->ctx, n_row, n_col);
108 if (!new_mat)
109 goto error;
110 for (i = 0; i < mat->n_row; ++i)
111 isl_seq_cpy(new_mat->row[i], mat->row[i], mat->n_col);
112 isl_mat_free(mat);
113 return new_mat;
114 }
115
116 mat = isl_mat_cow(mat);
117 if (!mat)
118 goto error;
119
120 old = mat->block.data;
121 mat->block = isl_blk_extend(mat->ctx, mat->block, n_row * mat->max_col);
122 if (isl_blk_is_error(mat->block))
123 goto error;
124 row = isl_realloc_array(mat->ctx, mat->row, isl_int *, n_row);
125 if (n_row && !row)
126 goto error;
127 mat->row = row;
128
129 for (i = 0; i < mat->n_row; ++i)
130 mat->row[i] = mat->block.data + (mat->row[i] - old);
131 for (i = mat->n_row; i < n_row; ++i)
132 mat->row[i] = mat->block.data + i * mat->max_col;
133 mat->n_row = n_row;
134 if (mat->n_col < n_col)
135 mat->n_col = n_col;
136
137 return mat;
138 error:
139 isl_mat_free(mat);
140 return NULL;
141 }
142
143 __isl_give isl_mat *isl_mat_sub_alloc6(isl_ctx *ctx, isl_int **row,
144 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
145 {
146 int i;
147 struct isl_mat *mat;
148
149 mat = isl_alloc_type(ctx, struct isl_mat);
150 if (!mat)
151 return NULL;
152 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
153 if (n_row && !mat->row)
154 goto error;
155 for (i = 0; i < n_row; ++i)
156 mat->row[i] = row[first_row+i] + first_col;
157 mat->ctx = ctx;
158 isl_ctx_ref(ctx);
159 mat->ref = 1;
160 mat->n_row = n_row;
161 mat->n_col = n_col;
162 mat->block = isl_blk_empty();
163 mat->flags = ISL_MAT_BORROWED;
164 return mat;
165 error:
166 free(mat);
167 return NULL;
168 }
169
170 __isl_give isl_mat *isl_mat_sub_alloc(__isl_keep isl_mat *mat,
171 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
172 {
173 if (!mat)
174 return NULL;
175 return isl_mat_sub_alloc6(mat->ctx, mat->row, first_row, n_row,
176 first_col, n_col);
177 }
178
179 void isl_mat_sub_copy(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
180 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
181 {
182 int i;
183
184 for (i = 0; i < n_row; ++i)
185 isl_seq_cpy(dst[i]+dst_col, src[i]+src_col, n_col);
186 }
187
188 void isl_mat_sub_neg(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
189 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
190 {
191 int i;
192
193 for (i = 0; i < n_row; ++i)
194 isl_seq_neg(dst[i]+dst_col, src[i]+src_col, n_col);
195 }
196
197 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat)
198 {
199 if (!mat)
200 return NULL;
201
202 mat->ref++;
203 return mat;
204 }
205
206 __isl_give isl_mat *isl_mat_dup(__isl_keep isl_mat *mat)
207 {
208 int i;
209 struct isl_mat *mat2;
210
211 if (!mat)
212 return NULL;
213 mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
214 if (!mat2)
215 return NULL;
216 for (i = 0; i < mat->n_row; ++i)
217 isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);
218 return mat2;
219 }
220
221 __isl_give isl_mat *isl_mat_cow(__isl_take isl_mat *mat)
222 {
223 struct isl_mat *mat2;
224 if (!mat)
225 return NULL;
226
227 if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))
228 return mat;
229
230 mat2 = isl_mat_dup(mat);
231 isl_mat_free(mat);
232 return mat2;
233 }
234
235 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat)
236 {
237 if (!mat)
238 return NULL;
239
240 if (--mat->ref > 0)
241 return NULL;
242
243 if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))
244 isl_blk_free(mat->ctx, mat->block);
245 isl_ctx_deref(mat->ctx);
246 free(mat->row);
247 free(mat);
248
249 return NULL;
250 }
251
252 int isl_mat_rows(__isl_keep isl_mat *mat)
253 {
254 return mat ? mat->n_row : -1;
255 }
256
257 int isl_mat_cols(__isl_keep isl_mat *mat)
258 {
259 return mat ? mat->n_col : -1;
260 }
261
262 /* Check that "col" is a valid column position for "mat".
263 */
264 static isl_stat check_col(__isl_keep isl_mat *mat, int col)
265 {
266 if (!mat)
267 return isl_stat_error;
268 if (col < 0 || col >= mat->n_col)
269 isl_die(isl_mat_get_ctx(mat), isl_error_invalid,
270 "column out of range", return isl_stat_error);
271 return isl_stat_ok;
272 }
273
274 /* Check that "row" is a valid row position for "mat".
275 */
276 static isl_stat check_row(__isl_keep isl_mat *mat, int row)
277 {
278 if (!mat)
279 return isl_stat_error;
280 if (row < 0 || row >= mat->n_row)
281 isl_die(isl_mat_get_ctx(mat), isl_error_invalid,
282 "row out of range", return isl_stat_error);
283 return isl_stat_ok;
284 }
285
286 /* Check that there are "n" columns starting at position "first" in "mat".
287 */
288 static isl_stat check_col_range(__isl_keep isl_mat *mat, unsigned first,
289 unsigned n)
290 {
291 if (!mat)
292 return isl_stat_error;
293 if (first + n > mat->n_col || first + n < first)
294 isl_die(isl_mat_get_ctx(mat), isl_error_invalid,
295 "column position or range out of bounds",
296 return isl_stat_error);
297 return isl_stat_ok;
298 }
299
300 /* Check that there are "n" rows starting at position "first" in "mat".
301 */
302 static isl_stat check_row_range(__isl_keep isl_mat *mat, unsigned first,
303 unsigned n)
304 {
305 if (!mat)
306 return isl_stat_error;
307 if (first + n > mat->n_row || first + n < first)
308 isl_die(isl_mat_get_ctx(mat), isl_error_invalid,
309 "row position or range out of bounds",
310 return isl_stat_error);
311 return isl_stat_ok;
312 }
313
314 int isl_mat_get_element(__isl_keep isl_mat *mat, int row, int col, isl_int *v)
315 {
316 if (check_row(mat, row) < 0)
317 return -1;
318 if (check_col(mat, col) < 0)
319 return -1;
320 isl_int_set(*v, mat->row[row][col]);
321 return 0;
322 }
323
324 /* Extract the element at row "row", oolumn "col" of "mat".
325 */
326 __isl_give isl_val *isl_mat_get_element_val(__isl_keep isl_mat *mat,
327 int row, int col)
328 {
329 isl_ctx *ctx;
330
331 if (check_row(mat, row) < 0)
332 return NULL;
333 if (check_col(mat, col) < 0)
334 return NULL;
335 ctx = isl_mat_get_ctx(mat);
336 return isl_val_int_from_isl_int(ctx, mat->row[row][col]);
337 }
338
339 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
340 int row, int col, isl_int v)
341 {
342 mat = isl_mat_cow(mat);
343 if (check_row(mat, row) < 0)
344 return isl_mat_free(mat);
345 if (check_col(mat, col) < 0)
346 return isl_mat_free(mat);
347 isl_int_set(mat->row[row][col], v);
348 return mat;
349 }
350
351 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
352 int row, int col, int v)
353 {
354 mat = isl_mat_cow(mat);
355 if (check_row(mat, row) < 0)
356 return isl_mat_free(mat);
357 if (check_col(mat, col) < 0)
358 return isl_mat_free(mat);
359 isl_int_set_si(mat->row[row][col], v);
360 return mat;
361 }
362
363 /* Replace the element at row "row", column "col" of "mat" by "v".
364 */
365 __isl_give isl_mat *isl_mat_set_element_val(__isl_take isl_mat *mat,
366 int row, int col, __isl_take isl_val *v)
367 {
368 if (!v)
369 return isl_mat_free(mat);
370 if (!isl_val_is_int(v))
371 isl_die(isl_val_get_ctx(v), isl_error_invalid,
372 "expecting integer value", goto error);
373 mat = isl_mat_set_element(mat, row, col, v->n);
374 isl_val_free(v);
375 return mat;
376 error:
377 isl_val_free(v);
378 return isl_mat_free(mat);
379 }
380
381 __isl_give isl_mat *isl_mat_diag(isl_ctx *ctx, unsigned n_row, isl_int d)
382 {
383 int i;
384 struct isl_mat *mat;
385
386 mat = isl_mat_alloc(ctx, n_row, n_row);
387 if (!mat)
388 return NULL;
389 for (i = 0; i < n_row; ++i) {
390 isl_seq_clr(mat->row[i], i);
391 isl_int_set(mat->row[i][i], d);
392 isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
393 }
394
395 return mat;
396 }
397
398 /* Create an "n_row" by "n_col" matrix with zero elements.
399 */
400 __isl_give isl_mat *isl_mat_zero(isl_ctx *ctx, unsigned n_row, unsigned n_col)
401 {
402 int i;
403 isl_mat *mat;
404
405 mat = isl_mat_alloc(ctx, n_row, n_col);
406 if (!mat)
407 return NULL;
408 for (i = 0; i < n_row; ++i)
409 isl_seq_clr(mat->row[i], n_col);
410
411 return mat;
412 }
413
414 __isl_give isl_mat *isl_mat_identity(isl_ctx *ctx, unsigned n_row)
415 {
416 if (!ctx)
417 return NULL;
418 return isl_mat_diag(ctx, n_row, ctx->one);
419 }
420
421 /* Is "mat" a (possibly scaled) identity matrix?
422 */
423 int isl_mat_is_scaled_identity(__isl_keep isl_mat *mat)
424 {
425 int i;
426
427 if (!mat)
428 return -1;
429 if (mat->n_row != mat->n_col)
430 return 0;
431
432 for (i = 0; i < mat->n_row; ++i) {
433 if (isl_seq_first_non_zero(mat->row[i], i) != -1)
434 return 0;
435 if (isl_int_ne(mat->row[0][0], mat->row[i][i]))
436 return 0;
437 if (isl_seq_first_non_zero(mat->row[i] + i + 1,
438 mat->n_col - (i + 1)) != -1)
439 return 0;
440 }
441
442 return 1;
443 }
444
445 __isl_give isl_vec *isl_mat_vec_product(__isl_take isl_mat *mat,
446 __isl_take isl_vec *vec)
447 {
448 int i;
449 struct isl_vec *prod;
450
451 if (!mat || !vec)
452 goto error;
453
454 isl_assert(mat->ctx, mat->n_col == vec->size, goto error);
455
456 prod = isl_vec_alloc(mat->ctx, mat->n_row);
457 if (!prod)
458 goto error;
459
460 for (i = 0; i < prod->size; ++i)
461 isl_seq_inner_product(mat->row[i], vec->el, vec->size,
462 &prod->block.data[i]);
463 isl_mat_free(mat);
464 isl_vec_free(vec);
465 return prod;
466 error:
467 isl_mat_free(mat);
468 isl_vec_free(vec);
469 return NULL;
470 }
471
472 __isl_give isl_vec *isl_mat_vec_inverse_product(__isl_take isl_mat *mat,
473 __isl_take isl_vec *vec)
474 {
475 struct isl_mat *vec_mat;
476 int i;
477
478 if (!mat || !vec)
479 goto error;
480 vec_mat = isl_mat_alloc(vec->ctx, vec->size, 1);
481 if (!vec_mat)
482 goto error;
483 for (i = 0; i < vec->size; ++i)
484 isl_int_set(vec_mat->row[i][0], vec->el[i]);
485 vec_mat = isl_mat_inverse_product(mat, vec_mat);
486 isl_vec_free(vec);
487 if (!vec_mat)
488 return NULL;
489 vec = isl_vec_alloc(vec_mat->ctx, vec_mat->n_row);
490 if (vec)
491 for (i = 0; i < vec->size; ++i)
492 isl_int_set(vec->el[i], vec_mat->row[i][0]);
493 isl_mat_free(vec_mat);
494 return vec;
495 error:
496 isl_mat_free(mat);
497 isl_vec_free(vec);
498 return NULL;
499 }
500
501 __isl_give isl_vec *isl_vec_mat_product(__isl_take isl_vec *vec,
502 __isl_take isl_mat *mat)
503 {
504 int i, j;
505 struct isl_vec *prod;
506
507 if (!mat || !vec)
508 goto error;
509
510 isl_assert(mat->ctx, mat->n_row == vec->size, goto error);
511
512 prod = isl_vec_alloc(mat->ctx, mat->n_col);
513 if (!prod)
514 goto error;
515
516 for (i = 0; i < prod->size; ++i) {
517 isl_int_set_si(prod->el[i], 0);
518 for (j = 0; j < vec->size; ++j)
519 isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);
520 }
521 isl_mat_free(mat);
522 isl_vec_free(vec);
523 return prod;
524 error:
525 isl_mat_free(mat);
526 isl_vec_free(vec);
527 return NULL;
528 }
529
530 __isl_give isl_mat *isl_mat_aff_direct_sum(__isl_take isl_mat *left,
531 __isl_take isl_mat *right)
532 {
533 int i;
534 struct isl_mat *sum;
535
536 if (!left || !right)
537 goto error;
538
539 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
540 isl_assert(left->ctx, left->n_row >= 1, goto error);
541 isl_assert(left->ctx, left->n_col >= 1, goto error);
542 isl_assert(left->ctx, right->n_col >= 1, goto error);
543 isl_assert(left->ctx,
544 isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,
545 goto error);
546 isl_assert(left->ctx,
547 isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
548 goto error);
549
550 sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);
551 if (!sum)
552 goto error;
553 isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);
554 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
555 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
556
557 isl_seq_clr(sum->row[0]+1, sum->n_col-1);
558 for (i = 1; i < sum->n_row; ++i) {
559 isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);
560 isl_int_addmul(sum->row[i][0],
561 right->row[0][0], right->row[i][0]);
562 isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],
563 left->n_col-1);
564 isl_seq_scale(sum->row[i]+left->n_col,
565 right->row[i]+1, right->row[0][0],
566 right->n_col-1);
567 }
568
569 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
570 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
571 isl_mat_free(left);
572 isl_mat_free(right);
573 return sum;
574 error:
575 isl_mat_free(left);
576 isl_mat_free(right);
577 return NULL;
578 }
579
580 static void exchange(struct isl_mat *M, struct isl_mat **U,
581 struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
582 {
583 int r;
584 for (r = row; r < M->n_row; ++r)
585 isl_int_swap(M->row[r][i], M->row[r][j]);
586 if (U) {
587 for (r = 0; r < (*U)->n_row; ++r)
588 isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
589 }
590 if (Q)
591 isl_mat_swap_rows(*Q, i, j);
592 }
593
594 static void subtract(struct isl_mat *M, struct isl_mat **U,
595 struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)
596 {
597 int r;
598 for (r = row; r < M->n_row; ++r)
599 isl_int_submul(M->row[r][j], m, M->row[r][i]);
600 if (U) {
601 for (r = 0; r < (*U)->n_row; ++r)
602 isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);
603 }
604 if (Q) {
605 for (r = 0; r < (*Q)->n_col; ++r)
606 isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);
607 }
608 }
609
610 static void oppose(struct isl_mat *M, struct isl_mat **U,
611 struct isl_mat **Q, unsigned row, unsigned col)
612 {
613 int r;
614 for (r = row; r < M->n_row; ++r)
615 isl_int_neg(M->row[r][col], M->row[r][col]);
616 if (U) {
617 for (r = 0; r < (*U)->n_row; ++r)
618 isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);
619 }
620 if (Q)
621 isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);
622 }
623
624 /* Given matrix M, compute
625 *
626 * M U = H
627 * M = H Q
628 *
629 * with U and Q unimodular matrices and H a matrix in column echelon form
630 * such that on each echelon row the entries in the non-echelon column
631 * are non-negative (if neg == 0) or non-positive (if neg == 1)
632 * and strictly smaller (in absolute value) than the entries in the echelon
633 * column.
634 * If U or Q are NULL, then these matrices are not computed.
635 */
636 __isl_give isl_mat *isl_mat_left_hermite(__isl_take isl_mat *M, int neg,
637 __isl_give isl_mat **U, __isl_give isl_mat **Q)
638 {
639 isl_int c;
640 int row, col;
641
642 if (U)
643 *U = NULL;
644 if (Q)
645 *Q = NULL;
646 if (!M)
647 goto error;
648 M = isl_mat_cow(M);
649 if (!M)
650 goto error;
651 if (U) {
652 *U = isl_mat_identity(M->ctx, M->n_col);
653 if (!*U)
654 goto error;
655 }
656 if (Q) {
657 *Q = isl_mat_identity(M->ctx, M->n_col);
658 if (!*Q)
659 goto error;
660 }
661
662 col = 0;
663 isl_int_init(c);
664 for (row = 0; row < M->n_row; ++row) {
665 int first, i, off;
666 first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);
667 if (first == -1)
668 continue;
669 first += col;
670 if (first != col)
671 exchange(M, U, Q, row, first, col);
672 if (isl_int_is_neg(M->row[row][col]))
673 oppose(M, U, Q, row, col);
674 first = col+1;
675 while ((off = isl_seq_first_non_zero(M->row[row]+first,
676 M->n_col-first)) != -1) {
677 first += off;
678 isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);
679 subtract(M, U, Q, row, col, first, c);
680 if (!isl_int_is_zero(M->row[row][first]))
681 exchange(M, U, Q, row, first, col);
682 else
683 ++first;
684 }
685 for (i = 0; i < col; ++i) {
686 if (isl_int_is_zero(M->row[row][i]))
687 continue;
688 if (neg)
689 isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);
690 else
691 isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);
692 if (isl_int_is_zero(c))
693 continue;
694 subtract(M, U, Q, row, col, i, c);
695 }
696 ++col;
697 }
698 isl_int_clear(c);
699
700 return M;
701 error:
702 if (Q) {
703 isl_mat_free(*Q);
704 *Q = NULL;
705 }
706 if (U) {
707 isl_mat_free(*U);
708 *U = NULL;
709 }
710 isl_mat_free(M);
711 return NULL;
712 }
713
714 /* Use row "row" of "mat" to eliminate column "col" from all other rows.
715 */
716 static __isl_give isl_mat *eliminate(__isl_take isl_mat *mat, int row, int col)
717 {
718 int k, nr, nc;
719 isl_ctx *ctx;
720
721 if (!mat)
722 return NULL;
723
724 ctx = isl_mat_get_ctx(mat);
725 nr = isl_mat_rows(mat);
726 nc = isl_mat_cols(mat);
727
728 for (k = 0; k < nr; ++k) {
729 if (k == row)
730 continue;
731 if (isl_int_is_zero(mat->row[k][col]))
732 continue;
733 mat = isl_mat_cow(mat);
734 if (!mat)
735 return NULL;
736 isl_seq_elim(mat->row[k], mat->row[row], col, nc, NULL);
737 isl_seq_normalize(ctx, mat->row[k], nc);
738 }
739
740 return mat;
741 }
742
743 /* Perform Gaussian elimination on the rows of "mat", but start
744 * from the final row and the final column.
745 * Any zero rows that result from the elimination are removed.
746 *
747 * In particular, for each column from last to first,
748 * look for the last row with a non-zero coefficient in that column,
749 * move it last (but before other rows moved last in previous steps) and
750 * use it to eliminate the column from the other rows.
751 */
752 __isl_give isl_mat *isl_mat_reverse_gauss(__isl_take isl_mat *mat)
753 {
754 int k, row, last, nr, nc;
755
756 if (!mat)
757 return NULL;
758
759 nr = isl_mat_rows(mat);
760 nc = isl_mat_cols(mat);
761
762 last = nc - 1;
763 for (row = nr - 1; row >= 0; --row) {
764 for (; last >= 0; --last) {
765 for (k = row; k >= 0; --k)
766 if (!isl_int_is_zero(mat->row[k][last]))
767 break;
768 if (k >= 0)
769 break;
770 }
771 if (last < 0)
772 break;
773 if (k != row)
774 mat = isl_mat_swap_rows(mat, k, row);
775 if (!mat)
776 return NULL;
777 if (isl_int_is_neg(mat->row[row][last]))
778 mat = isl_mat_row_neg(mat, row);
779 mat = eliminate(mat, row, last);
780 if (!mat)
781 return NULL;
782 }
783 mat = isl_mat_drop_rows(mat, 0, row + 1);
784
785 return mat;
786 }
787
788 /* Negate the lexicographically negative rows of "mat" such that
789 * all rows in the result are lexicographically non-negative.
790 */
791 __isl_give isl_mat *isl_mat_lexnonneg_rows(__isl_take isl_mat *mat)
792 {
793 int i, nr, nc;
794
795 if (!mat)
796 return NULL;
797
798 nr = isl_mat_rows(mat);
799 nc = isl_mat_cols(mat);
800
801 for (i = 0; i < nr; ++i) {
802 int pos;
803
804 pos = isl_seq_first_non_zero(mat->row[i], nc);
805 if (pos < 0)
806 continue;
807 if (isl_int_is_nonneg(mat->row[i][pos]))
808 continue;
809 mat = isl_mat_row_neg(mat, i);
810 if (!mat)
811 return NULL;
812 }
813
814 return mat;
815 }
816
817 struct isl_mat *isl_mat_right_kernel(struct isl_mat *mat)
818 {
819 int i, rank;
820 struct isl_mat *U = NULL;
821 struct isl_mat *K;
822
823 mat = isl_mat_left_hermite(mat, 0, &U, NULL);
824 if (!mat || !U)
825 goto error;
826
827 for (i = 0, rank = 0; rank < mat->n_col; ++rank) {
828 while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))
829 ++i;
830 if (i >= mat->n_row)
831 break;
832 }
833 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
834 if (!K)
835 goto error;
836 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
837 isl_mat_free(mat);
838 isl_mat_free(U);
839 return K;
840 error:
841 isl_mat_free(mat);
842 isl_mat_free(U);
843 return NULL;
844 }
845
846 __isl_give isl_mat *isl_mat_lin_to_aff(__isl_take isl_mat *mat)
847 {
848 int i;
849 struct isl_mat *mat2;
850
851 if (!mat)
852 return NULL;
853 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
854 if (!mat2)
855 goto error;
856 isl_int_set_si(mat2->row[0][0], 1);
857 isl_seq_clr(mat2->row[0]+1, mat->n_col);
858 for (i = 0; i < mat->n_row; ++i) {
859 isl_int_set_si(mat2->row[1+i][0], 0);
860 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
861 }
862 isl_mat_free(mat);
863 return mat2;
864 error:
865 isl_mat_free(mat);
866 return NULL;
867 }
868
869 /* Given two matrices M1 and M2, return the block matrix
870 *
871 * [ M1 0 ]
872 * [ 0 M2 ]
873 */
874 __isl_give isl_mat *isl_mat_diagonal(__isl_take isl_mat *mat1,
875 __isl_take isl_mat *mat2)
876 {
877 int i;
878 isl_mat *mat;
879
880 if (!mat1 || !mat2)
881 goto error;
882
883 mat = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
884 mat1->n_col + mat2->n_col);
885 if (!mat)
886 goto error;
887 for (i = 0; i < mat1->n_row; ++i) {
888 isl_seq_cpy(mat->row[i], mat1->row[i], mat1->n_col);
889 isl_seq_clr(mat->row[i] + mat1->n_col, mat2->n_col);
890 }
891 for (i = 0; i < mat2->n_row; ++i) {
892 isl_seq_clr(mat->row[mat1->n_row + i], mat1->n_col);
893 isl_seq_cpy(mat->row[mat1->n_row + i] + mat1->n_col,
894 mat2->row[i], mat2->n_col);
895 }
896 isl_mat_free(mat1);
897 isl_mat_free(mat2);
898 return mat;
899 error:
900 isl_mat_free(mat1);
901 isl_mat_free(mat2);
902 return NULL;
903 }
904
905 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
906 {
907 int i;
908
909 for (i = 0; i < n_row; ++i)
910 if (!isl_int_is_zero(row[i][col]))
911 return i;
912 return -1;
913 }
914
915 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
916 {
917 int i, min = row_first_non_zero(row, n_row, col);
918 if (min < 0)
919 return -1;
920 for (i = min + 1; i < n_row; ++i) {
921 if (isl_int_is_zero(row[i][col]))
922 continue;
923 if (isl_int_abs_lt(row[i][col], row[min][col]))
924 min = i;
925 }
926 return min;
927 }
928
929 static isl_stat inv_exchange(__isl_keep isl_mat **left,
930 __isl_keep isl_mat **right, unsigned i, unsigned j)
931 {
932 *left = isl_mat_swap_rows(*left, i, j);
933 *right = isl_mat_swap_rows(*right, i, j);
934
935 if (!*left || !*right)
936 return isl_stat_error;
937 return isl_stat_ok;
938 }
939
940 static void inv_oppose(
941 struct isl_mat *left, struct isl_mat *right, unsigned row)
942 {
943 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
944 isl_seq_neg(right->row[row], right->row[row], right->n_col);
945 }
946
947 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
948 unsigned row, unsigned i, isl_int m)
949 {
950 isl_int_neg(m, m);
951 isl_seq_combine(left->row[i]+row,
952 left->ctx->one, left->row[i]+row,
953 m, left->row[row]+row,
954 left->n_col-row);
955 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
956 m, right->row[row], right->n_col);
957 }
958
959 /* Compute inv(left)*right
960 */
961 __isl_give isl_mat *isl_mat_inverse_product(__isl_take isl_mat *left,
962 __isl_take isl_mat *right)
963 {
964 int row;
965 isl_int a, b;
966
967 if (!left || !right)
968 goto error;
969
970 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
971 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
972
973 if (left->n_row == 0) {
974 isl_mat_free(left);
975 return right;
976 }
977
978 left = isl_mat_cow(left);
979 right = isl_mat_cow(right);
980 if (!left || !right)
981 goto error;
982
983 isl_int_init(a);
984 isl_int_init(b);
985 for (row = 0; row < left->n_row; ++row) {
986 int pivot, first, i, off;
987 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
988 if (pivot < 0) {
989 isl_int_clear(a);
990 isl_int_clear(b);
991 isl_assert(left->ctx, pivot >= 0, goto error);
992 }
993 pivot += row;
994 if (pivot != row)
995 if (inv_exchange(&left, &right, pivot, row) < 0)
996 goto error;
997 if (isl_int_is_neg(left->row[row][row]))
998 inv_oppose(left, right, row);
999 first = row+1;
1000 while ((off = row_first_non_zero(left->row+first,
1001 left->n_row-first, row)) != -1) {
1002 first += off;
1003 isl_int_fdiv_q(a, left->row[first][row],
1004 left->row[row][row]);
1005 inv_subtract(left, right, row, first, a);
1006 if (!isl_int_is_zero(left->row[first][row])) {
1007 if (inv_exchange(&left, &right, row, first) < 0)
1008 goto error;
1009 } else {
1010 ++first;
1011 }
1012 }
1013 for (i = 0; i < row; ++i) {
1014 if (isl_int_is_zero(left->row[i][row]))
1015 continue;
1016 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
1017 isl_int_divexact(b, left->row[i][row], a);
1018 isl_int_divexact(a, left->row[row][row], a);
1019 isl_int_neg(b, b);
1020 isl_seq_combine(left->row[i] + i,
1021 a, left->row[i] + i,
1022 b, left->row[row] + i,
1023 left->n_col - i);
1024 isl_seq_combine(right->row[i], a, right->row[i],
1025 b, right->row[row], right->n_col);
1026 }
1027 }
1028 isl_int_clear(b);
1029
1030 isl_int_set(a, left->row[0][0]);
1031 for (row = 1; row < left->n_row; ++row)
1032 isl_int_lcm(a, a, left->row[row][row]);
1033 if (isl_int_is_zero(a)){
1034 isl_int_clear(a);
1035 isl_assert(left->ctx, 0, goto error);
1036 }
1037 for (row = 0; row < left->n_row; ++row) {
1038 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
1039 if (isl_int_is_one(left->row[row][row]))
1040 continue;
1041 isl_seq_scale(right->row[row], right->row[row],
1042 left->row[row][row], right->n_col);
1043 }
1044 isl_int_clear(a);
1045
1046 isl_mat_free(left);
1047 return right;
1048 error:
1049 isl_mat_free(left);
1050 isl_mat_free(right);
1051 return NULL;
1052 }
1053
1054 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
1055 {
1056 int i;
1057
1058 for (i = 0; i < mat->n_row; ++i)
1059 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
1060 }
1061
1062 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
1063 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
1064 {
1065 int i;
1066 isl_int tmp;
1067
1068 isl_int_init(tmp);
1069 for (i = 0; i < mat->n_row; ++i) {
1070 isl_int_mul(tmp, m1, mat->row[i][src1]);
1071 isl_int_addmul(tmp, m2, mat->row[i][src2]);
1072 isl_int_set(mat->row[i][dst], tmp);
1073 }
1074 isl_int_clear(tmp);
1075 }
1076
1077 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat)
1078 {
1079 struct isl_mat *inv;
1080 int row;
1081 isl_int a, b;
1082
1083 mat = isl_mat_cow(mat);
1084 if (!mat)
1085 return NULL;
1086
1087 inv = isl_mat_identity(mat->ctx, mat->n_col);
1088 inv = isl_mat_cow(inv);
1089 if (!inv)
1090 goto error;
1091
1092 isl_int_init(a);
1093 isl_int_init(b);
1094 for (row = 0; row < mat->n_row; ++row) {
1095 int pivot, first, i, off;
1096 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
1097 if (pivot < 0) {
1098 isl_int_clear(a);
1099 isl_int_clear(b);
1100 isl_assert(mat->ctx, pivot >= 0, goto error);
1101 }
1102 pivot += row;
1103 if (pivot != row)
1104 exchange(mat, &inv, NULL, row, pivot, row);
1105 if (isl_int_is_neg(mat->row[row][row]))
1106 oppose(mat, &inv, NULL, row, row);
1107 first = row+1;
1108 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
1109 mat->n_col-first)) != -1) {
1110 first += off;
1111 isl_int_fdiv_q(a, mat->row[row][first],
1112 mat->row[row][row]);
1113 subtract(mat, &inv, NULL, row, row, first, a);
1114 if (!isl_int_is_zero(mat->row[row][first]))
1115 exchange(mat, &inv, NULL, row, row, first);
1116 else
1117 ++first;
1118 }
1119 for (i = 0; i < row; ++i) {
1120 if (isl_int_is_zero(mat->row[row][i]))
1121 continue;
1122 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
1123 isl_int_divexact(b, mat->row[row][i], a);
1124 isl_int_divexact(a, mat->row[row][row], a);
1125 isl_int_neg(a, a);
1126 isl_mat_col_combine(mat, i, a, i, b, row);
1127 isl_mat_col_combine(inv, i, a, i, b, row);
1128 }
1129 }
1130 isl_int_clear(b);
1131
1132 isl_int_set(a, mat->row[0][0]);
1133 for (row = 1; row < mat->n_row; ++row)
1134 isl_int_lcm(a, a, mat->row[row][row]);
1135 if (isl_int_is_zero(a)){
1136 isl_int_clear(a);
1137 goto error;
1138 }
1139 for (row = 0; row < mat->n_row; ++row) {
1140 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
1141 if (isl_int_is_one(mat->row[row][row]))
1142 continue;
1143 isl_mat_col_scale(inv, row, mat->row[row][row]);
1144 }
1145 isl_int_clear(a);
1146
1147 isl_mat_free(mat);
1148
1149 return inv;
1150 error:
1151 isl_mat_free(mat);
1152 isl_mat_free(inv);
1153 return NULL;
1154 }
1155
1156 __isl_give isl_mat *isl_mat_transpose(__isl_take isl_mat *mat)
1157 {
1158 struct isl_mat *transpose = NULL;
1159 int i, j;
1160
1161 if (!mat)
1162 return NULL;
1163
1164 if (mat->n_col == mat->n_row) {
1165 mat = isl_mat_cow(mat);
1166 if (!mat)
1167 return NULL;
1168 for (i = 0; i < mat->n_row; ++i)
1169 for (j = i + 1; j < mat->n_col; ++j)
1170 isl_int_swap(mat->row[i][j], mat->row[j][i]);
1171 return mat;
1172 }
1173 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
1174 if (!transpose)
1175 goto error;
1176 for (i = 0; i < mat->n_row; ++i)
1177 for (j = 0; j < mat->n_col; ++j)
1178 isl_int_set(transpose->row[j][i], mat->row[i][j]);
1179 isl_mat_free(mat);
1180 return transpose;
1181 error:
1182 isl_mat_free(mat);
1183 return NULL;
1184 }
1185
1186 __isl_give isl_mat *isl_mat_swap_cols(__isl_take isl_mat *mat,
1187 unsigned i, unsigned j)
1188 {
1189 int r;
1190
1191 mat = isl_mat_cow(mat);
1192 if (check_col_range(mat, i, 1) < 0 ||
1193 check_col_range(mat, j, 1) < 0)
1194 return isl_mat_free(mat);
1195
1196 for (r = 0; r < mat->n_row; ++r)
1197 isl_int_swap(mat->row[r][i], mat->row[r][j]);
1198 return mat;
1199 }
1200
1201 __isl_give isl_mat *isl_mat_swap_rows(__isl_take isl_mat *mat,
1202 unsigned i, unsigned j)
1203 {
1204 isl_int *t;
1205
1206 if (!mat)
1207 return NULL;
1208 mat = isl_mat_cow(mat);
1209 if (check_row_range(mat, i, 1) < 0 ||
1210 check_row_range(mat, j, 1) < 0)
1211 return isl_mat_free(mat);
1212
1213 t = mat->row[i];
1214 mat->row[i] = mat->row[j];
1215 mat->row[j] = t;
1216 return mat;
1217 }
1218
1219 /* Calculate the product of two matrices.
1220 *
1221 * This function is optimized for operand matrices that contain many zeros and
1222 * skips multiplications where we know one of the operands is zero.
1223 */
1224 __isl_give isl_mat *isl_mat_product(__isl_take isl_mat *left,
1225 __isl_take isl_mat *right)
1226 {
1227 int i, j, k;
1228 struct isl_mat *prod;
1229
1230 if (!left || !right)
1231 goto error;
1232 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
1233 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
1234 if (!prod)
1235 goto error;
1236 if (left->n_col == 0) {
1237 for (i = 0; i < prod->n_row; ++i)
1238 isl_seq_clr(prod->row[i], prod->n_col);
1239 isl_mat_free(left);
1240 isl_mat_free(right);
1241 return prod;
1242 }
1243 for (i = 0; i < prod->n_row; ++i) {
1244 for (j = 0; j < prod->n_col; ++j)
1245 isl_int_mul(prod->row[i][j],
1246 left->row[i][0], right->row[0][j]);
1247 for (k = 1; k < left->n_col; ++k) {
1248 if (isl_int_is_zero(left->row[i][k]))
1249 continue;
1250 for (j = 0; j < prod->n_col; ++j)
1251 isl_int_addmul(prod->row[i][j],
1252 left->row[i][k], right->row[k][j]);
1253 }
1254 }
1255 isl_mat_free(left);
1256 isl_mat_free(right);
1257 return prod;
1258 error:
1259 isl_mat_free(left);
1260 isl_mat_free(right);
1261 return NULL;
1262 }
1263
1264 /* Replace the variables x in the rows q by x' given by x = M x',
1265 * with M the matrix mat.
1266 *
1267 * If the number of new variables is greater than the original
1268 * number of variables, then the rows q have already been
1269 * preextended. If the new number is smaller, then the coefficients
1270 * of the divs, which are not changed, need to be shifted down.
1271 * The row q may be the equalities, the inequalities or the
1272 * div expressions. In the latter case, has_div is true and
1273 * we need to take into account the extra denominator column.
1274 */
1275 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
1276 unsigned n_div, int has_div, struct isl_mat *mat)
1277 {
1278 int i;
1279 struct isl_mat *t;
1280 int e;
1281
1282 if (mat->n_col >= mat->n_row)
1283 e = 0;
1284 else
1285 e = mat->n_row - mat->n_col;
1286 if (has_div)
1287 for (i = 0; i < n; ++i)
1288 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
1289 t = isl_mat_sub_alloc6(mat->ctx, q, 0, n, has_div, mat->n_row);
1290 t = isl_mat_product(t, mat);
1291 if (!t)
1292 return -1;
1293 for (i = 0; i < n; ++i) {
1294 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
1295 isl_seq_cpy(q[i] + has_div + t->n_col,
1296 q[i] + has_div + t->n_col + e, n_div);
1297 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
1298 }
1299 isl_mat_free(t);
1300 return 0;
1301 }
1302
1303 /* Replace the variables x in bset by x' given by x = M x', with
1304 * M the matrix mat.
1305 *
1306 * If there are fewer variables x' then there are x, then we perform
1307 * the transformation in place, which means that, in principle,
1308 * this frees up some extra variables as the number
1309 * of columns remains constant, but we would have to extend
1310 * the div array too as the number of rows in this array is assumed
1311 * to be equal to extra.
1312 */
1313 __isl_give isl_basic_set *isl_basic_set_preimage(
1314 __isl_take isl_basic_set *bset, __isl_take isl_mat *mat)
1315 {
1316 struct isl_ctx *ctx;
1317
1318 if (!bset || !mat)
1319 goto error;
1320
1321 ctx = bset->ctx;
1322 bset = isl_basic_set_cow(bset);
1323 if (!bset)
1324 goto error;
1325
1326 isl_assert(ctx, bset->dim->nparam == 0, goto error);
1327 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
1328 isl_assert(ctx, mat->n_col > 0, goto error);
1329
1330 if (mat->n_col > mat->n_row) {
1331 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0, 0, 0);
1332 if (!bset)
1333 goto error;
1334 } else if (mat->n_col < mat->n_row) {
1335 bset->dim = isl_space_cow(bset->dim);
1336 if (!bset->dim)
1337 goto error;
1338 bset->dim->n_out -= mat->n_row - mat->n_col;
1339 }
1340
1341 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
1342 isl_mat_copy(mat)) < 0)
1343 goto error;
1344
1345 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
1346 isl_mat_copy(mat)) < 0)
1347 goto error;
1348
1349 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
1350 goto error2;
1351
1352 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
1353 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
1354 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1355 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1356 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
1357
1358 bset = isl_basic_set_simplify(bset);
1359 bset = isl_basic_set_finalize(bset);
1360
1361 return bset;
1362 error:
1363 isl_mat_free(mat);
1364 error2:
1365 isl_basic_set_free(bset);
1366 return NULL;
1367 }
1368
1369 __isl_give isl_set *isl_set_preimage(
1370 __isl_take isl_set *set, __isl_take isl_mat *mat)
1371 {
1372 int i;
1373
1374 set = isl_set_cow(set);
1375 if (!set)
1376 goto error;
1377
1378 for (i = 0; i < set->n; ++i) {
1379 set->p[i] = isl_basic_set_preimage(set->p[i],
1380 isl_mat_copy(mat));
1381 if (!set->p[i])
1382 goto error;
1383 }
1384 if (mat->n_col != mat->n_row) {
1385 set->dim = isl_space_cow(set->dim);
1386 if (!set->dim)
1387 goto error;
1388 set->dim->n_out += mat->n_col;
1389 set->dim->n_out -= mat->n_row;
1390 }
1391 isl_mat_free(mat);
1392 ISL_F_CLR(set, ISL_SET_NORMALIZED);
1393 return set;
1394 error:
1395 isl_set_free(set);
1396 isl_mat_free(mat);
1397 return NULL;
1398 }
1399
1400 /* Replace the variables x starting at "first_col" in the rows "rows"
1401 * of some coefficient matrix by x' with x = M x' with M the matrix mat.
1402 * That is, replace the corresponding coefficients c by c M.
1403 */
1404 isl_stat isl_mat_sub_transform(isl_int **row, unsigned n_row,
1405 unsigned first_col, __isl_take isl_mat *mat)
1406 {
1407 int i;
1408 isl_ctx *ctx;
1409 isl_mat *t;
1410
1411 if (!mat)
1412 return isl_stat_error;
1413 ctx = isl_mat_get_ctx(mat);
1414 t = isl_mat_sub_alloc6(ctx, row, 0, n_row, first_col, mat->n_row);
1415 t = isl_mat_product(t, mat);
1416 if (!t)
1417 return isl_stat_error;
1418 for (i = 0; i < n_row; ++i)
1419 isl_seq_swp_or_cpy(row[i] + first_col, t->row[i], t->n_col);
1420 isl_mat_free(t);
1421 return isl_stat_ok;
1422 }
1423
1424 void isl_mat_print_internal(__isl_keep isl_mat *mat, FILE *out, int indent)
1425 {
1426 int i, j;
1427
1428 if (!mat) {
1429 fprintf(out, "%*snull mat\n", indent, "");
1430 return;
1431 }
1432
1433 if (mat->n_row == 0)
1434 fprintf(out, "%*s[]\n", indent, "");
1435
1436 for (i = 0; i < mat->n_row; ++i) {
1437 if (!i)
1438 fprintf(out, "%*s[[", indent, "");
1439 else
1440 fprintf(out, "%*s[", indent+1, "");
1441 for (j = 0; j < mat->n_col; ++j) {
1442 if (j)
1443 fprintf(out, ",");
1444 isl_int_print(out, mat->row[i][j], 0);
1445 }
1446 if (i == mat->n_row-1)
1447 fprintf(out, "]]\n");
1448 else
1449 fprintf(out, "]\n");
1450 }
1451 }
1452
1453 void isl_mat_dump(__isl_keep isl_mat *mat)
1454 {
1455 isl_mat_print_internal(mat, stderr, 0);
1456 }
1457
1458 __isl_give isl_mat *isl_mat_drop_cols(__isl_take isl_mat *mat,
1459 unsigned col, unsigned n)
1460 {
1461 int r;
1462
1463 if (n == 0)
1464 return mat;
1465
1466 mat = isl_mat_cow(mat);
1467 if (check_col_range(mat, col, n) < 0)
1468 return isl_mat_free(mat);
1469
1470 if (col != mat->n_col-n) {
1471 for (r = 0; r < mat->n_row; ++r)
1472 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1473 mat->n_col - col - n);
1474 }
1475 mat->n_col -= n;
1476 return mat;
1477 }
1478
1479 __isl_give isl_mat *isl_mat_drop_rows(__isl_take isl_mat *mat,
1480 unsigned row, unsigned n)
1481 {
1482 int r;
1483
1484 mat = isl_mat_cow(mat);
1485 if (check_row_range(mat, row, n) < 0)
1486 return isl_mat_free(mat);
1487
1488 for (r = row; r+n < mat->n_row; ++r)
1489 mat->row[r] = mat->row[r+n];
1490
1491 mat->n_row -= n;
1492 return mat;
1493 }
1494
1495 __isl_give isl_mat *isl_mat_insert_cols(__isl_take isl_mat *mat,
1496 unsigned col, unsigned n)
1497 {
1498 isl_mat *ext;
1499
1500 if (check_col_range(mat, col, 0) < 0)
1501 return isl_mat_free(mat);
1502 if (n == 0)
1503 return mat;
1504
1505 ext = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col + n);
1506 if (!ext)
1507 goto error;
1508
1509 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row, 0, 0, col);
1510 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row,
1511 col + n, col, mat->n_col - col);
1512
1513 isl_mat_free(mat);
1514 return ext;
1515 error:
1516 isl_mat_free(mat);
1517 return NULL;
1518 }
1519
1520 __isl_give isl_mat *isl_mat_insert_zero_cols(__isl_take isl_mat *mat,
1521 unsigned first, unsigned n)
1522 {
1523 int i;
1524
1525 if (!mat)
1526 return NULL;
1527 mat = isl_mat_insert_cols(mat, first, n);
1528 if (!mat)
1529 return NULL;
1530
1531 for (i = 0; i < mat->n_row; ++i)
1532 isl_seq_clr(mat->row[i] + first, n);
1533
1534 return mat;
1535 }
1536
1537 __isl_give isl_mat *isl_mat_add_zero_cols(__isl_take isl_mat *mat, unsigned n)
1538 {
1539 if (!mat)
1540 return NULL;
1541
1542 return isl_mat_insert_zero_cols(mat, mat->n_col, n);
1543 }
1544
1545 __isl_give isl_mat *isl_mat_insert_rows(__isl_take isl_mat *mat,
1546 unsigned row, unsigned n)
1547 {
1548 isl_mat *ext;
1549
1550 if (check_row_range(mat, row, 0) < 0)
1551 return isl_mat_free(mat);
1552 if (n == 0)
1553 return mat;
1554
1555 ext = isl_mat_alloc(mat->ctx, mat->n_row + n, mat->n_col);
1556 if (!ext)
1557 goto error;
1558
1559 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, row, 0, 0, mat->n_col);
1560 isl_mat_sub_copy(mat->ctx, ext->row + row + n, mat->row + row,
1561 mat->n_row - row, 0, 0, mat->n_col);
1562
1563 isl_mat_free(mat);
1564 return ext;
1565 error:
1566 isl_mat_free(mat);
1567 return NULL;
1568 }
1569
1570 __isl_give isl_mat *isl_mat_add_rows(__isl_take isl_mat *mat, unsigned n)
1571 {
1572 if (!mat)
1573 return NULL;
1574
1575 return isl_mat_insert_rows(mat, mat->n_row, n);
1576 }
1577
1578 __isl_give isl_mat *isl_mat_insert_zero_rows(__isl_take isl_mat *mat,
1579 unsigned row, unsigned n)
1580 {
1581 int i;
1582
1583 mat = isl_mat_insert_rows(mat, row, n);
1584 if (!mat)
1585 return NULL;
1586
1587 for (i = 0; i < n; ++i)
1588 isl_seq_clr(mat->row[row + i], mat->n_col);
1589
1590 return mat;
1591 }
1592
1593 __isl_give isl_mat *isl_mat_add_zero_rows(__isl_take isl_mat *mat, unsigned n)
1594 {
1595 if (!mat)
1596 return NULL;
1597
1598 return isl_mat_insert_zero_rows(mat, mat->n_row, n);
1599 }
1600
1601 void isl_mat_col_submul(struct isl_mat *mat,
1602 int dst_col, isl_int f, int src_col)
1603 {
1604 int i;
1605
1606 for (i = 0; i < mat->n_row; ++i)
1607 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1608 }
1609
1610 void isl_mat_col_add(__isl_keep isl_mat *mat, int dst_col, int src_col)
1611 {
1612 int i;
1613
1614 if (!mat)
1615 return;
1616
1617 for (i = 0; i < mat->n_row; ++i)
1618 isl_int_add(mat->row[i][dst_col],
1619 mat->row[i][dst_col], mat->row[i][src_col]);
1620 }
1621
1622 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1623 {
1624 int i;
1625
1626 for (i = 0; i < mat->n_row; ++i)
1627 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1628 }
1629
1630 /* Add "f" times column "src_col" to column "dst_col" of "mat" and
1631 * return the result.
1632 */
1633 __isl_give isl_mat *isl_mat_col_addmul(__isl_take isl_mat *mat, int dst_col,
1634 isl_int f, int src_col)
1635 {
1636 int i;
1637
1638 if (check_col(mat, dst_col) < 0 || check_col(mat, src_col) < 0)
1639 return isl_mat_free(mat);
1640
1641 for (i = 0; i < mat->n_row; ++i) {
1642 if (isl_int_is_zero(mat->row[i][src_col]))
1643 continue;
1644 mat = isl_mat_cow(mat);
1645 if (!mat)
1646 return NULL;
1647 isl_int_addmul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1648 }
1649
1650 return mat;
1651 }
1652
1653 /* Negate column "col" of "mat" and return the result.
1654 */
1655 __isl_give isl_mat *isl_mat_col_neg(__isl_take isl_mat *mat, int col)
1656 {
1657 int i;
1658
1659 if (check_col(mat, col) < 0)
1660 return isl_mat_free(mat);
1661
1662 for (i = 0; i < mat->n_row; ++i) {
1663 if (isl_int_is_zero(mat->row[i][col]))
1664 continue;
1665 mat = isl_mat_cow(mat);
1666 if (!mat)
1667 return NULL;
1668 isl_int_neg(mat->row[i][col], mat->row[i][col]);
1669 }
1670
1671 return mat;
1672 }
1673
1674 /* Negate row "row" of "mat" and return the result.
1675 */
1676 __isl_give isl_mat *isl_mat_row_neg(__isl_take isl_mat *mat, int row)
1677 {
1678 if (check_row(mat, row) < 0)
1679 return isl_mat_free(mat);
1680 if (isl_seq_first_non_zero(mat->row[row], mat->n_col) == -1)
1681 return mat;
1682 mat = isl_mat_cow(mat);
1683 if (!mat)
1684 return NULL;
1685 isl_seq_neg(mat->row[row], mat->row[row], mat->n_col);
1686 return mat;
1687 }
1688
1689 __isl_give isl_mat *isl_mat_unimodular_complete(__isl_take isl_mat *M, int row)
1690 {
1691 int r;
1692 struct isl_mat *H = NULL, *Q = NULL;
1693
1694 if (!M)
1695 return NULL;
1696
1697 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1698 M->n_row = row;
1699 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1700 M->n_row = M->n_col;
1701 if (!H)
1702 goto error;
1703 for (r = 0; r < row; ++r)
1704 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1705 for (r = row; r < M->n_row; ++r)
1706 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1707 isl_mat_free(H);
1708 isl_mat_free(Q);
1709 return M;
1710 error:
1711 isl_mat_free(H);
1712 isl_mat_free(Q);
1713 isl_mat_free(M);
1714 return NULL;
1715 }
1716
1717 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1718 __isl_take isl_mat *bot)
1719 {
1720 struct isl_mat *mat;
1721
1722 if (!top || !bot)
1723 goto error;
1724
1725 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1726 if (top->n_row == 0) {
1727 isl_mat_free(top);
1728 return bot;
1729 }
1730 if (bot->n_row == 0) {
1731 isl_mat_free(bot);
1732 return top;
1733 }
1734
1735 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1736 if (!mat)
1737 goto error;
1738 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1739 0, 0, mat->n_col);
1740 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1741 0, 0, mat->n_col);
1742 isl_mat_free(top);
1743 isl_mat_free(bot);
1744 return mat;
1745 error:
1746 isl_mat_free(top);
1747 isl_mat_free(bot);
1748 return NULL;
1749 }
1750
1751 isl_bool isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
1752 {
1753 int i;
1754
1755 if (!mat1 || !mat2)
1756 return isl_bool_error;
1757
1758 if (mat1->n_row != mat2->n_row)
1759 return isl_bool_false;
1760
1761 if (mat1->n_col != mat2->n_col)
1762 return isl_bool_false;
1763
1764 for (i = 0; i < mat1->n_row; ++i)
1765 if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
1766 return isl_bool_false;
1767
1768 return isl_bool_true;
1769 }
1770
1771 __isl_give isl_mat *isl_mat_from_row_vec(__isl_take isl_vec *vec)
1772 {
1773 struct isl_mat *mat;
1774
1775 if (!vec)
1776 return NULL;
1777 mat = isl_mat_alloc(vec->ctx, 1, vec->size);
1778 if (!mat)
1779 goto error;
1780
1781 isl_seq_cpy(mat->row[0], vec->el, vec->size);
1782
1783 isl_vec_free(vec);
1784 return mat;
1785 error:
1786 isl_vec_free(vec);
1787 return NULL;
1788 }
1789
1790 /* Return a copy of row "row" of "mat" as an isl_vec.
1791 */
1792 __isl_give isl_vec *isl_mat_get_row(__isl_keep isl_mat *mat, unsigned row)
1793 {
1794 isl_vec *v;
1795
1796 if (!mat)
1797 return NULL;
1798 if (row >= mat->n_row)
1799 isl_die(mat->ctx, isl_error_invalid, "row out of range",
1800 return NULL);
1801
1802 v = isl_vec_alloc(isl_mat_get_ctx(mat), mat->n_col);
1803 if (!v)
1804 return NULL;
1805 isl_seq_cpy(v->el, mat->row[row], mat->n_col);
1806
1807 return v;
1808 }
1809
1810 __isl_give isl_mat *isl_mat_vec_concat(__isl_take isl_mat *top,
1811 __isl_take isl_vec *bot)
1812 {
1813 return isl_mat_concat(top, isl_mat_from_row_vec(bot));
1814 }
1815
1816 __isl_give isl_mat *isl_mat_move_cols(__isl_take isl_mat *mat,
1817 unsigned dst_col, unsigned src_col, unsigned n)
1818 {
1819 isl_mat *res;
1820
1821 if (!mat)
1822 return NULL;
1823 if (n == 0 || dst_col == src_col)
1824 return mat;
1825
1826 res = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
1827 if (!res)
1828 goto error;
1829
1830 if (dst_col < src_col) {
1831 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1832 0, 0, dst_col);
1833 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1834 dst_col, src_col, n);
1835 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1836 dst_col + n, dst_col, src_col - dst_col);
1837 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1838 src_col + n, src_col + n,
1839 res->n_col - src_col - n);
1840 } else {
1841 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1842 0, 0, src_col);
1843 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1844 src_col, src_col + n, dst_col - src_col);
1845 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1846 dst_col, src_col, n);
1847 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1848 dst_col + n, dst_col + n,
1849 res->n_col - dst_col - n);
1850 }
1851 isl_mat_free(mat);
1852
1853 return res;
1854 error:
1855 isl_mat_free(mat);
1856 return NULL;
1857 }
1858
1859 /* Return the gcd of the elements in row "row" of "mat" in *gcd.
1860 * Return isl_stat_ok on success and isl_stat_error on failure.
1861 */
1862 isl_stat isl_mat_row_gcd(__isl_keep isl_mat *mat, int row, isl_int *gcd)
1863 {
1864 if (check_row(mat, row) < 0)
1865 return isl_stat_error;
1866
1867 isl_seq_gcd(mat->row[row], mat->n_col, gcd);
1868
1869 return isl_stat_ok;
1870 }
1871
1872 void isl_mat_gcd(__isl_keep isl_mat *mat, isl_int *gcd)
1873 {
1874 int i;
1875 isl_int g;
1876
1877 isl_int_set_si(*gcd, 0);
1878 if (!mat)
1879 return;
1880
1881 isl_int_init(g);
1882 for (i = 0; i < mat->n_row; ++i) {
1883 isl_seq_gcd(mat->row[i], mat->n_col, &g);
1884 isl_int_gcd(*gcd, *gcd, g);
1885 }
1886 isl_int_clear(g);
1887 }
1888
1889 /* Return the result of scaling "mat" by a factor of "m".
1890 */
1891 __isl_give isl_mat *isl_mat_scale(__isl_take isl_mat *mat, isl_int m)
1892 {
1893 int i;
1894
1895 if (isl_int_is_one(m))
1896 return mat;
1897
1898 mat = isl_mat_cow(mat);
1899 if (!mat)
1900 return NULL;
1901
1902 for (i = 0; i < mat->n_row; ++i)
1903 isl_seq_scale(mat->row[i], mat->row[i], m, mat->n_col);
1904
1905 return mat;
1906 }
1907
1908 __isl_give isl_mat *isl_mat_scale_down(__isl_take isl_mat *mat, isl_int m)
1909 {
1910 int i;
1911
1912 if (isl_int_is_one(m))
1913 return mat;
1914
1915 mat = isl_mat_cow(mat);
1916 if (!mat)
1917 return NULL;
1918
1919 for (i = 0; i < mat->n_row; ++i)
1920 isl_seq_scale_down(mat->row[i], mat->row[i], m, mat->n_col);
1921
1922 return mat;
1923 }
1924
1925 __isl_give isl_mat *isl_mat_scale_down_row(__isl_take isl_mat *mat, int row,
1926 isl_int m)
1927 {
1928 if (isl_int_is_one(m))
1929 return mat;
1930
1931 mat = isl_mat_cow(mat);
1932 if (!mat)
1933 return NULL;
1934
1935 isl_seq_scale_down(mat->row[row], mat->row[row], m, mat->n_col);
1936
1937 return mat;
1938 }
1939
1940 __isl_give isl_mat *isl_mat_normalize(__isl_take isl_mat *mat)
1941 {
1942 isl_int gcd;
1943
1944 if (!mat)
1945 return NULL;
1946
1947 isl_int_init(gcd);
1948 isl_mat_gcd(mat, &gcd);
1949 mat = isl_mat_scale_down(mat, gcd);
1950 isl_int_clear(gcd);
1951
1952 return mat;
1953 }
1954
1955 __isl_give isl_mat *isl_mat_normalize_row(__isl_take isl_mat *mat, int row)
1956 {
1957 mat = isl_mat_cow(mat);
1958 if (!mat)
1959 return NULL;
1960
1961 isl_seq_normalize(mat->ctx, mat->row[row], mat->n_col);
1962
1963 return mat;
1964 }
1965
1966 /* Number of initial non-zero columns.
1967 */
1968 int isl_mat_initial_non_zero_cols(__isl_keep isl_mat *mat)
1969 {
1970 int i;
1971
1972 if (!mat)
1973 return -1;
1974
1975 for (i = 0; i < mat->n_col; ++i)
1976 if (row_first_non_zero(mat->row, mat->n_row, i) < 0)
1977 break;
1978
1979 return i;
1980 }
Integer set library