?  search:
summary | log | graphiclog1 | graphiclog2 | commit | commitdiff | tree | refs | edit | fork
blame | history | raw | HEAD
isl_space_drop_dims: take into account overflow when checking indices
[isl.git] / isl_mat.c
blob292264ce496e8d2c02c261d52aaa56fbb865c7aa
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 *
4 * Use of this software is governed by the MIT license
5 *
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
8 */
9
10 #include <isl_ctx_private.h>
11 #include <isl_map_private.h>
12 #include <isl/space.h>
13 #include <isl/seq.h>
14 #include <isl_mat_private.h>
15 #include <isl_space_private.h>
16 #include <isl_val_private.h>
17
18 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat)
19 {
20 return mat ? mat->ctx : NULL;
21 }
22
23 struct isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
24 unsigned n_row, unsigned n_col)
25 {
26 int i;
27 struct isl_mat *mat;
28
29 mat = isl_alloc_type(ctx, struct isl_mat);
30 if (!mat)
31 return NULL;
32
33 mat->row = NULL;
34 mat->block = isl_blk_alloc(ctx, n_row * n_col);
35 if (isl_blk_is_error(mat->block))
36 goto error;
37 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
38 if (n_row && !mat->row)
39 goto error;
40
41 for (i = 0; i < n_row; ++i)
42 mat->row[i] = mat->block.data + i * n_col;
43
44 mat->ctx = ctx;
45 isl_ctx_ref(ctx);
46 mat->ref = 1;
47 mat->n_row = n_row;
48 mat->n_col = n_col;
49 mat->max_col = n_col;
50 mat->flags = 0;
51
52 return mat;
53 error:
54 isl_blk_free(ctx, mat->block);
55 free(mat);
56 return NULL;
57 }
58
59 struct isl_mat *isl_mat_extend(struct isl_mat *mat,
60 unsigned n_row, unsigned n_col)
61 {
62 int i;
63 isl_int *old;
64 isl_int **row;
65
66 if (!mat)
67 return NULL;
68
69 if (mat->max_col >= n_col && mat->n_row >= n_row) {
70 if (mat->n_col < n_col)
71 mat->n_col = n_col;
72 return mat;
73 }
74
75 if (mat->max_col < n_col) {
76 struct isl_mat *new_mat;
77
78 if (n_row < mat->n_row)
79 n_row = mat->n_row;
80 new_mat = isl_mat_alloc(mat->ctx, n_row, n_col);
81 if (!new_mat)
82 goto error;
83 for (i = 0; i < mat->n_row; ++i)
84 isl_seq_cpy(new_mat->row[i], mat->row[i], mat->n_col);
85 isl_mat_free(mat);
86 return new_mat;
87 }
88
89 mat = isl_mat_cow(mat);
90 if (!mat)
91 goto error;
92
93 old = mat->block.data;
94 mat->block = isl_blk_extend(mat->ctx, mat->block, n_row * mat->max_col);
95 if (isl_blk_is_error(mat->block))
96 goto error;
97 row = isl_realloc_array(mat->ctx, mat->row, isl_int *, n_row);
98 if (n_row && !row)
99 goto error;
100 mat->row = row;
101
102 for (i = 0; i < mat->n_row; ++i)
103 mat->row[i] = mat->block.data + (mat->row[i] - old);
104 for (i = mat->n_row; i < n_row; ++i)
105 mat->row[i] = mat->block.data + i * mat->max_col;
106 mat->n_row = n_row;
107 if (mat->n_col < n_col)
108 mat->n_col = n_col;
109
110 return mat;
111 error:
112 isl_mat_free(mat);
113 return NULL;
114 }
115
116 __isl_give isl_mat *isl_mat_sub_alloc6(isl_ctx *ctx, isl_int **row,
117 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
118 {
119 int i;
120 struct isl_mat *mat;
121
122 mat = isl_alloc_type(ctx, struct isl_mat);
123 if (!mat)
124 return NULL;
125 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
126 if (n_row && !mat->row)
127 goto error;
128 for (i = 0; i < n_row; ++i)
129 mat->row[i] = row[first_row+i] + first_col;
130 mat->ctx = ctx;
131 isl_ctx_ref(ctx);
132 mat->ref = 1;
133 mat->n_row = n_row;
134 mat->n_col = n_col;
135 mat->block = isl_blk_empty();
136 mat->flags = ISL_MAT_BORROWED;
137 return mat;
138 error:
139 free(mat);
140 return NULL;
141 }
142
143 __isl_give isl_mat *isl_mat_sub_alloc(__isl_keep isl_mat *mat,
144 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
145 {
146 if (!mat)
147 return NULL;
148 return isl_mat_sub_alloc6(mat->ctx, mat->row, first_row, n_row,
149 first_col, n_col);
150 }
151
152 void isl_mat_sub_copy(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
153 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
154 {
155 int i;
156
157 for (i = 0; i < n_row; ++i)
158 isl_seq_cpy(dst[i]+dst_col, src[i]+src_col, n_col);
159 }
160
161 void isl_mat_sub_neg(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
162 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
163 {
164 int i;
165
166 for (i = 0; i < n_row; ++i)
167 isl_seq_neg(dst[i]+dst_col, src[i]+src_col, n_col);
168 }
169
170 struct isl_mat *isl_mat_copy(struct isl_mat *mat)
171 {
172 if (!mat)
173 return NULL;
174
175 mat->ref++;
176 return mat;
177 }
178
179 struct isl_mat *isl_mat_dup(struct isl_mat *mat)
180 {
181 int i;
182 struct isl_mat *mat2;
183
184 if (!mat)
185 return NULL;
186 mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
187 if (!mat2)
188 return NULL;
189 for (i = 0; i < mat->n_row; ++i)
190 isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);
191 return mat2;
192 }
193
194 struct isl_mat *isl_mat_cow(struct isl_mat *mat)
195 {
196 struct isl_mat *mat2;
197 if (!mat)
198 return NULL;
199
200 if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))
201 return mat;
202
203 mat2 = isl_mat_dup(mat);
204 isl_mat_free(mat);
205 return mat2;
206 }
207
208 void *isl_mat_free(struct isl_mat *mat)
209 {
210 if (!mat)
211 return NULL;
212
213 if (--mat->ref > 0)
214 return NULL;
215
216 if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))
217 isl_blk_free(mat->ctx, mat->block);
218 isl_ctx_deref(mat->ctx);
219 free(mat->row);
220 free(mat);
221
222 return NULL;
223 }
224
225 int isl_mat_rows(__isl_keep isl_mat *mat)
226 {
227 return mat ? mat->n_row : -1;
228 }
229
230 int isl_mat_cols(__isl_keep isl_mat *mat)
231 {
232 return mat ? mat->n_col : -1;
233 }
234
235 int isl_mat_get_element(__isl_keep isl_mat *mat, int row, int col, isl_int *v)
236 {
237 if (!mat)
238 return -1;
239 if (row < 0 || row >= mat->n_row)
240 isl_die(mat->ctx, isl_error_invalid, "row out of range",
241 return -1);
242 if (col < 0 || col >= mat->n_col)
243 isl_die(mat->ctx, isl_error_invalid, "column out of range",
244 return -1);
245 isl_int_set(*v, mat->row[row][col]);
246 return 0;
247 }
248
249 /* Extract the element at row "row", oolumn "col" of "mat".
250 */
251 __isl_give isl_val *isl_mat_get_element_val(__isl_keep isl_mat *mat,
252 int row, int col)
253 {
254 isl_ctx *ctx;
255
256 if (!mat)
257 return NULL;
258 ctx = isl_mat_get_ctx(mat);
259 if (row < 0 || row >= mat->n_row)
260 isl_die(ctx, isl_error_invalid, "row out of range",
261 return NULL);
262 if (col < 0 || col >= mat->n_col)
263 isl_die(ctx, isl_error_invalid, "column out of range",
264 return NULL);
265 return isl_val_int_from_isl_int(ctx, mat->row[row][col]);
266 }
267
268 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
269 int row, int col, isl_int v)
270 {
271 mat = isl_mat_cow(mat);
272 if (!mat)
273 return NULL;
274 if (row < 0 || row >= mat->n_row)
275 isl_die(mat->ctx, isl_error_invalid, "row out of range",
276 goto error);
277 if (col < 0 || col >= mat->n_col)
278 isl_die(mat->ctx, isl_error_invalid, "column out of range",
279 goto error);
280 isl_int_set(mat->row[row][col], v);
281 return mat;
282 error:
283 isl_mat_free(mat);
284 return NULL;
285 }
286
287 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
288 int row, int col, int v)
289 {
290 mat = isl_mat_cow(mat);
291 if (!mat)
292 return NULL;
293 if (row < 0 || row >= mat->n_row)
294 isl_die(mat->ctx, isl_error_invalid, "row out of range",
295 goto error);
296 if (col < 0 || col >= mat->n_col)
297 isl_die(mat->ctx, isl_error_invalid, "column out of range",
298 goto error);
299 isl_int_set_si(mat->row[row][col], v);
300 return mat;
301 error:
302 isl_mat_free(mat);
303 return NULL;
304 }
305
306 /* Replace the element at row "row", column "col" of "mat" by "v".
307 */
308 __isl_give isl_mat *isl_mat_set_element_val(__isl_take isl_mat *mat,
309 int row, int col, __isl_take isl_val *v)
310 {
311 if (!v)
312 return isl_mat_free(mat);
313 if (!isl_val_is_int(v))
314 isl_die(isl_val_get_ctx(v), isl_error_invalid,
315 "expecting integer value", goto error);
316 mat = isl_mat_set_element(mat, row, col, v->n);
317 isl_val_free(v);
318 return mat;
319 error:
320 isl_val_free(v);
321 return isl_mat_free(mat);
322 }
323
324 __isl_give isl_mat *isl_mat_diag(isl_ctx *ctx, unsigned n_row, isl_int d)
325 {
326 int i;
327 struct isl_mat *mat;
328
329 mat = isl_mat_alloc(ctx, n_row, n_row);
330 if (!mat)
331 return NULL;
332 for (i = 0; i < n_row; ++i) {
333 isl_seq_clr(mat->row[i], i);
334 isl_int_set(mat->row[i][i], d);
335 isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
336 }
337
338 return mat;
339 }
340
341 __isl_give isl_mat *isl_mat_identity(isl_ctx *ctx, unsigned n_row)
342 {
343 if (!ctx)
344 return NULL;
345 return isl_mat_diag(ctx, n_row, ctx->one);
346 }
347
348 struct isl_vec *isl_mat_vec_product(struct isl_mat *mat, struct isl_vec *vec)
349 {
350 int i;
351 struct isl_vec *prod;
352
353 if (!mat || !vec)
354 goto error;
355
356 isl_assert(mat->ctx, mat->n_col == vec->size, goto error);
357
358 prod = isl_vec_alloc(mat->ctx, mat->n_row);
359 if (!prod)
360 goto error;
361
362 for (i = 0; i < prod->size; ++i)
363 isl_seq_inner_product(mat->row[i], vec->el, vec->size,
364 &prod->block.data[i]);
365 isl_mat_free(mat);
366 isl_vec_free(vec);
367 return prod;
368 error:
369 isl_mat_free(mat);
370 isl_vec_free(vec);
371 return NULL;
372 }
373
374 __isl_give isl_vec *isl_mat_vec_inverse_product(__isl_take isl_mat *mat,
375 __isl_take isl_vec *vec)
376 {
377 struct isl_mat *vec_mat;
378 int i;
379
380 if (!mat || !vec)
381 goto error;
382 vec_mat = isl_mat_alloc(vec->ctx, vec->size, 1);
383 if (!vec_mat)
384 goto error;
385 for (i = 0; i < vec->size; ++i)
386 isl_int_set(vec_mat->row[i][0], vec->el[i]);
387 vec_mat = isl_mat_inverse_product(mat, vec_mat);
388 isl_vec_free(vec);
389 if (!vec_mat)
390 return NULL;
391 vec = isl_vec_alloc(vec_mat->ctx, vec_mat->n_row);
392 if (vec)
393 for (i = 0; i < vec->size; ++i)
394 isl_int_set(vec->el[i], vec_mat->row[i][0]);
395 isl_mat_free(vec_mat);
396 return vec;
397 error:
398 isl_mat_free(mat);
399 isl_vec_free(vec);
400 return NULL;
401 }
402
403 struct isl_vec *isl_vec_mat_product(struct isl_vec *vec, struct isl_mat *mat)
404 {
405 int i, j;
406 struct isl_vec *prod;
407
408 if (!mat || !vec)
409 goto error;
410
411 isl_assert(mat->ctx, mat->n_row == vec->size, goto error);
412
413 prod = isl_vec_alloc(mat->ctx, mat->n_col);
414 if (!prod)
415 goto error;
416
417 for (i = 0; i < prod->size; ++i) {
418 isl_int_set_si(prod->el[i], 0);
419 for (j = 0; j < vec->size; ++j)
420 isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);
421 }
422 isl_mat_free(mat);
423 isl_vec_free(vec);
424 return prod;
425 error:
426 isl_mat_free(mat);
427 isl_vec_free(vec);
428 return NULL;
429 }
430
431 struct isl_mat *isl_mat_aff_direct_sum(struct isl_mat *left,
432 struct isl_mat *right)
433 {
434 int i;
435 struct isl_mat *sum;
436
437 if (!left || !right)
438 goto error;
439
440 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
441 isl_assert(left->ctx, left->n_row >= 1, goto error);
442 isl_assert(left->ctx, left->n_col >= 1, goto error);
443 isl_assert(left->ctx, right->n_col >= 1, goto error);
444 isl_assert(left->ctx,
445 isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,
446 goto error);
447 isl_assert(left->ctx,
448 isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
449 goto error);
450
451 sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);
452 if (!sum)
453 goto error;
454 isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);
455 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
456 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
457
458 isl_seq_clr(sum->row[0]+1, sum->n_col-1);
459 for (i = 1; i < sum->n_row; ++i) {
460 isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);
461 isl_int_addmul(sum->row[i][0],
462 right->row[0][0], right->row[i][0]);
463 isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],
464 left->n_col-1);
465 isl_seq_scale(sum->row[i]+left->n_col,
466 right->row[i]+1, right->row[0][0],
467 right->n_col-1);
468 }
469
470 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
471 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
472 isl_mat_free(left);
473 isl_mat_free(right);
474 return sum;
475 error:
476 isl_mat_free(left);
477 isl_mat_free(right);
478 return NULL;
479 }
480
481 static void exchange(struct isl_mat *M, struct isl_mat **U,
482 struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
483 {
484 int r;
485 for (r = row; r < M->n_row; ++r)
486 isl_int_swap(M->row[r][i], M->row[r][j]);
487 if (U) {
488 for (r = 0; r < (*U)->n_row; ++r)
489 isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
490 }
491 if (Q)
492 isl_mat_swap_rows(*Q, i, j);
493 }
494
495 static void subtract(struct isl_mat *M, struct isl_mat **U,
496 struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)
497 {
498 int r;
499 for (r = row; r < M->n_row; ++r)
500 isl_int_submul(M->row[r][j], m, M->row[r][i]);
501 if (U) {
502 for (r = 0; r < (*U)->n_row; ++r)
503 isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);
504 }
505 if (Q) {
506 for (r = 0; r < (*Q)->n_col; ++r)
507 isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);
508 }
509 }
510
511 static void oppose(struct isl_mat *M, struct isl_mat **U,
512 struct isl_mat **Q, unsigned row, unsigned col)
513 {
514 int r;
515 for (r = row; r < M->n_row; ++r)
516 isl_int_neg(M->row[r][col], M->row[r][col]);
517 if (U) {
518 for (r = 0; r < (*U)->n_row; ++r)
519 isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);
520 }
521 if (Q)
522 isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);
523 }
524
525 /* Given matrix M, compute
526 *
527 * M U = H
528 * M = H Q
529 *
530 * with U and Q unimodular matrices and H a matrix in column echelon form
531 * such that on each echelon row the entries in the non-echelon column
532 * are non-negative (if neg == 0) or non-positive (if neg == 1)
533 * and stricly smaller (in absolute value) than the entries in the echelon
534 * column.
535 * If U or Q are NULL, then these matrices are not computed.
536 */
537 struct isl_mat *isl_mat_left_hermite(struct isl_mat *M, int neg,
538 struct isl_mat **U, struct isl_mat **Q)
539 {
540 isl_int c;
541 int row, col;
542
543 if (U)
544 *U = NULL;
545 if (Q)
546 *Q = NULL;
547 if (!M)
548 goto error;
549 M = isl_mat_cow(M);
550 if (!M)
551 goto error;
552 if (U) {
553 *U = isl_mat_identity(M->ctx, M->n_col);
554 if (!*U)
555 goto error;
556 }
557 if (Q) {
558 *Q = isl_mat_identity(M->ctx, M->n_col);
559 if (!*Q)
560 goto error;
561 }
562
563 col = 0;
564 isl_int_init(c);
565 for (row = 0; row < M->n_row; ++row) {
566 int first, i, off;
567 first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);
568 if (first == -1)
569 continue;
570 first += col;
571 if (first != col)
572 exchange(M, U, Q, row, first, col);
573 if (isl_int_is_neg(M->row[row][col]))
574 oppose(M, U, Q, row, col);
575 first = col+1;
576 while ((off = isl_seq_first_non_zero(M->row[row]+first,
577 M->n_col-first)) != -1) {
578 first += off;
579 isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);
580 subtract(M, U, Q, row, col, first, c);
581 if (!isl_int_is_zero(M->row[row][first]))
582 exchange(M, U, Q, row, first, col);
583 else
584 ++first;
585 }
586 for (i = 0; i < col; ++i) {
587 if (isl_int_is_zero(M->row[row][i]))
588 continue;
589 if (neg)
590 isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);
591 else
592 isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);
593 if (isl_int_is_zero(c))
594 continue;
595 subtract(M, U, Q, row, col, i, c);
596 }
597 ++col;
598 }
599 isl_int_clear(c);
600
601 return M;
602 error:
603 if (Q) {
604 isl_mat_free(*Q);
605 *Q = NULL;
606 }
607 if (U) {
608 isl_mat_free(*U);
609 *U = NULL;
610 }
611 isl_mat_free(M);
612 return NULL;
613 }
614
615 struct isl_mat *isl_mat_right_kernel(struct isl_mat *mat)
616 {
617 int i, rank;
618 struct isl_mat *U = NULL;
619 struct isl_mat *K;
620
621 mat = isl_mat_left_hermite(mat, 0, &U, NULL);
622 if (!mat || !U)
623 goto error;
624
625 for (i = 0, rank = 0; rank < mat->n_col; ++rank) {
626 while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))
627 ++i;
628 if (i >= mat->n_row)
629 break;
630 }
631 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
632 if (!K)
633 goto error;
634 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
635 isl_mat_free(mat);
636 isl_mat_free(U);
637 return K;
638 error:
639 isl_mat_free(mat);
640 isl_mat_free(U);
641 return NULL;
642 }
643
644 struct isl_mat *isl_mat_lin_to_aff(struct isl_mat *mat)
645 {
646 int i;
647 struct isl_mat *mat2;
648
649 if (!mat)
650 return NULL;
651 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
652 if (!mat2)
653 goto error;
654 isl_int_set_si(mat2->row[0][0], 1);
655 isl_seq_clr(mat2->row[0]+1, mat->n_col);
656 for (i = 0; i < mat->n_row; ++i) {
657 isl_int_set_si(mat2->row[1+i][0], 0);
658 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
659 }
660 isl_mat_free(mat);
661 return mat2;
662 error:
663 isl_mat_free(mat);
664 return NULL;
665 }
666
667 /* Given two matrices M1 and M2, return the block matrix
668 *
669 * [ M1 0 ]
670 * [ 0 M2 ]
671 */
672 __isl_give isl_mat *isl_mat_diagonal(__isl_take isl_mat *mat1,
673 __isl_take isl_mat *mat2)
674 {
675 int i;
676 isl_mat *mat;
677
678 if (!mat1 || !mat2)
679 goto error;
680
681 mat = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
682 mat1->n_col + mat2->n_col);
683 if (!mat)
684 goto error;
685 for (i = 0; i < mat1->n_row; ++i) {
686 isl_seq_cpy(mat->row[i], mat1->row[i], mat1->n_col);
687 isl_seq_clr(mat->row[i] + mat1->n_col, mat2->n_col);
688 }
689 for (i = 0; i < mat2->n_row; ++i) {
690 isl_seq_clr(mat->row[mat1->n_row + i], mat1->n_col);
691 isl_seq_cpy(mat->row[mat1->n_row + i] + mat1->n_col,
692 mat2->row[i], mat2->n_col);
693 }
694 isl_mat_free(mat1);
695 isl_mat_free(mat2);
696 return mat;
697 error:
698 isl_mat_free(mat1);
699 isl_mat_free(mat2);
700 return NULL;
701 }
702
703 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
704 {
705 int i;
706
707 for (i = 0; i < n_row; ++i)
708 if (!isl_int_is_zero(row[i][col]))
709 return i;
710 return -1;
711 }
712
713 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
714 {
715 int i, min = row_first_non_zero(row, n_row, col);
716 if (min < 0)
717 return -1;
718 for (i = min + 1; i < n_row; ++i) {
719 if (isl_int_is_zero(row[i][col]))
720 continue;
721 if (isl_int_abs_lt(row[i][col], row[min][col]))
722 min = i;
723 }
724 return min;
725 }
726
727 static void inv_exchange(struct isl_mat *left, struct isl_mat *right,
728 unsigned i, unsigned j)
729 {
730 left = isl_mat_swap_rows(left, i, j);
731 right = isl_mat_swap_rows(right, i, j);
732 }
733
734 static void inv_oppose(
735 struct isl_mat *left, struct isl_mat *right, unsigned row)
736 {
737 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
738 isl_seq_neg(right->row[row], right->row[row], right->n_col);
739 }
740
741 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
742 unsigned row, unsigned i, isl_int m)
743 {
744 isl_int_neg(m, m);
745 isl_seq_combine(left->row[i]+row,
746 left->ctx->one, left->row[i]+row,
747 m, left->row[row]+row,
748 left->n_col-row);
749 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
750 m, right->row[row], right->n_col);
751 }
752
753 /* Compute inv(left)*right
754 */
755 struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
756 struct isl_mat *right)
757 {
758 int row;
759 isl_int a, b;
760
761 if (!left || !right)
762 goto error;
763
764 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
765 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
766
767 if (left->n_row == 0) {
768 isl_mat_free(left);
769 return right;
770 }
771
772 left = isl_mat_cow(left);
773 right = isl_mat_cow(right);
774 if (!left || !right)
775 goto error;
776
777 isl_int_init(a);
778 isl_int_init(b);
779 for (row = 0; row < left->n_row; ++row) {
780 int pivot, first, i, off;
781 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
782 if (pivot < 0) {
783 isl_int_clear(a);
784 isl_int_clear(b);
785 isl_assert(left->ctx, pivot >= 0, goto error);
786 }
787 pivot += row;
788 if (pivot != row)
789 inv_exchange(left, right, pivot, row);
790 if (isl_int_is_neg(left->row[row][row]))
791 inv_oppose(left, right, row);
792 first = row+1;
793 while ((off = row_first_non_zero(left->row+first,
794 left->n_row-first, row)) != -1) {
795 first += off;
796 isl_int_fdiv_q(a, left->row[first][row],
797 left->row[row][row]);
798 inv_subtract(left, right, row, first, a);
799 if (!isl_int_is_zero(left->row[first][row]))
800 inv_exchange(left, right, row, first);
801 else
802 ++first;
803 }
804 for (i = 0; i < row; ++i) {
805 if (isl_int_is_zero(left->row[i][row]))
806 continue;
807 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
808 isl_int_divexact(b, left->row[i][row], a);
809 isl_int_divexact(a, left->row[row][row], a);
810 isl_int_neg(b, b);
811 isl_seq_combine(left->row[i] + i,
812 a, left->row[i] + i,
813 b, left->row[row] + i,
814 left->n_col - i);
815 isl_seq_combine(right->row[i], a, right->row[i],
816 b, right->row[row], right->n_col);
817 }
818 }
819 isl_int_clear(b);
820
821 isl_int_set(a, left->row[0][0]);
822 for (row = 1; row < left->n_row; ++row)
823 isl_int_lcm(a, a, left->row[row][row]);
824 if (isl_int_is_zero(a)){
825 isl_int_clear(a);
826 isl_assert(left->ctx, 0, goto error);
827 }
828 for (row = 0; row < left->n_row; ++row) {
829 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
830 if (isl_int_is_one(left->row[row][row]))
831 continue;
832 isl_seq_scale(right->row[row], right->row[row],
833 left->row[row][row], right->n_col);
834 }
835 isl_int_clear(a);
836
837 isl_mat_free(left);
838 return right;
839 error:
840 isl_mat_free(left);
841 isl_mat_free(right);
842 return NULL;
843 }
844
845 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
846 {
847 int i;
848
849 for (i = 0; i < mat->n_row; ++i)
850 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
851 }
852
853 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
854 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
855 {
856 int i;
857 isl_int tmp;
858
859 isl_int_init(tmp);
860 for (i = 0; i < mat->n_row; ++i) {
861 isl_int_mul(tmp, m1, mat->row[i][src1]);
862 isl_int_addmul(tmp, m2, mat->row[i][src2]);
863 isl_int_set(mat->row[i][dst], tmp);
864 }
865 isl_int_clear(tmp);
866 }
867
868 struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
869 {
870 struct isl_mat *inv;
871 int row;
872 isl_int a, b;
873
874 mat = isl_mat_cow(mat);
875 if (!mat)
876 return NULL;
877
878 inv = isl_mat_identity(mat->ctx, mat->n_col);
879 inv = isl_mat_cow(inv);
880 if (!inv)
881 goto error;
882
883 isl_int_init(a);
884 isl_int_init(b);
885 for (row = 0; row < mat->n_row; ++row) {
886 int pivot, first, i, off;
887 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
888 if (pivot < 0) {
889 isl_int_clear(a);
890 isl_int_clear(b);
891 isl_assert(mat->ctx, pivot >= 0, goto error);
892 }
893 pivot += row;
894 if (pivot != row)
895 exchange(mat, &inv, NULL, row, pivot, row);
896 if (isl_int_is_neg(mat->row[row][row]))
897 oppose(mat, &inv, NULL, row, row);
898 first = row+1;
899 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
900 mat->n_col-first)) != -1) {
901 first += off;
902 isl_int_fdiv_q(a, mat->row[row][first],
903 mat->row[row][row]);
904 subtract(mat, &inv, NULL, row, row, first, a);
905 if (!isl_int_is_zero(mat->row[row][first]))
906 exchange(mat, &inv, NULL, row, row, first);
907 else
908 ++first;
909 }
910 for (i = 0; i < row; ++i) {
911 if (isl_int_is_zero(mat->row[row][i]))
912 continue;
913 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
914 isl_int_divexact(b, mat->row[row][i], a);
915 isl_int_divexact(a, mat->row[row][row], a);
916 isl_int_neg(a, a);
917 isl_mat_col_combine(mat, i, a, i, b, row);
918 isl_mat_col_combine(inv, i, a, i, b, row);
919 }
920 }
921 isl_int_clear(b);
922
923 isl_int_set(a, mat->row[0][0]);
924 for (row = 1; row < mat->n_row; ++row)
925 isl_int_lcm(a, a, mat->row[row][row]);
926 if (isl_int_is_zero(a)){
927 isl_int_clear(a);
928 goto error;
929 }
930 for (row = 0; row < mat->n_row; ++row) {
931 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
932 if (isl_int_is_one(mat->row[row][row]))
933 continue;
934 isl_mat_col_scale(inv, row, mat->row[row][row]);
935 }
936 isl_int_clear(a);
937
938 isl_mat_free(mat);
939
940 return inv;
941 error:
942 isl_mat_free(mat);
943 isl_mat_free(inv);
944 return NULL;
945 }
946
947 struct isl_mat *isl_mat_transpose(struct isl_mat *mat)
948 {
949 struct isl_mat *transpose = NULL;
950 int i, j;
951
952 if (!mat)
953 return NULL;
954
955 if (mat->n_col == mat->n_row) {
956 mat = isl_mat_cow(mat);
957 if (!mat)
958 return NULL;
959 for (i = 0; i < mat->n_row; ++i)
960 for (j = i + 1; j < mat->n_col; ++j)
961 isl_int_swap(mat->row[i][j], mat->row[j][i]);
962 return mat;
963 }
964 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
965 if (!transpose)
966 goto error;
967 for (i = 0; i < mat->n_row; ++i)
968 for (j = 0; j < mat->n_col; ++j)
969 isl_int_set(transpose->row[j][i], mat->row[i][j]);
970 isl_mat_free(mat);
971 return transpose;
972 error:
973 isl_mat_free(mat);
974 return NULL;
975 }
976
977 struct isl_mat *isl_mat_swap_cols(struct isl_mat *mat, unsigned i, unsigned j)
978 {
979 int r;
980
981 mat = isl_mat_cow(mat);
982 if (!mat)
983 return NULL;
984 isl_assert(mat->ctx, i < mat->n_col, goto error);
985 isl_assert(mat->ctx, j < mat->n_col, goto error);
986
987 for (r = 0; r < mat->n_row; ++r)
988 isl_int_swap(mat->row[r][i], mat->row[r][j]);
989 return mat;
990 error:
991 isl_mat_free(mat);
992 return NULL;
993 }
994
995 struct isl_mat *isl_mat_swap_rows(struct isl_mat *mat, unsigned i, unsigned j)
996 {
997 isl_int *t;
998
999 if (!mat)
1000 return NULL;
1001 mat = isl_mat_cow(mat);
1002 if (!mat)
1003 return NULL;
1004 t = mat->row[i];
1005 mat->row[i] = mat->row[j];
1006 mat->row[j] = t;
1007 return mat;
1008 }
1009
1010 __isl_give isl_mat *isl_mat_product(__isl_take isl_mat *left,
1011 __isl_take isl_mat *right)
1012 {
1013 int i, j, k;
1014 struct isl_mat *prod;
1015
1016 if (!left || !right)
1017 goto error;
1018 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
1019 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
1020 if (!prod)
1021 goto error;
1022 if (left->n_col == 0) {
1023 for (i = 0; i < prod->n_row; ++i)
1024 isl_seq_clr(prod->row[i], prod->n_col);
1025 isl_mat_free(left);
1026 isl_mat_free(right);
1027 return prod;
1028 }
1029 for (i = 0; i < prod->n_row; ++i) {
1030 for (j = 0; j < prod->n_col; ++j) {
1031 isl_int_mul(prod->row[i][j],
1032 left->row[i][0], right->row[0][j]);
1033 for (k = 1; k < left->n_col; ++k)
1034 isl_int_addmul(prod->row[i][j],
1035 left->row[i][k], right->row[k][j]);
1036 }
1037 }
1038 isl_mat_free(left);
1039 isl_mat_free(right);
1040 return prod;
1041 error:
1042 isl_mat_free(left);
1043 isl_mat_free(right);
1044 return NULL;
1045 }
1046
1047 /* Replace the variables x in the rows q by x' given by x = M x',
1048 * with M the matrix mat.
1049 *
1050 * If the number of new variables is greater than the original
1051 * number of variables, then the rows q have already been
1052 * preextended. If the new number is smaller, then the coefficients
1053 * of the divs, which are not changed, need to be shifted down.
1054 * The row q may be the equalities, the inequalities or the
1055 * div expressions. In the latter case, has_div is true and
1056 * we need to take into account the extra denominator column.
1057 */
1058 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
1059 unsigned n_div, int has_div, struct isl_mat *mat)
1060 {
1061 int i;
1062 struct isl_mat *t;
1063 int e;
1064
1065 if (mat->n_col >= mat->n_row)
1066 e = 0;
1067 else
1068 e = mat->n_row - mat->n_col;
1069 if (has_div)
1070 for (i = 0; i < n; ++i)
1071 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
1072 t = isl_mat_sub_alloc6(mat->ctx, q, 0, n, has_div, mat->n_row);
1073 t = isl_mat_product(t, mat);
1074 if (!t)
1075 return -1;
1076 for (i = 0; i < n; ++i) {
1077 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
1078 isl_seq_cpy(q[i] + has_div + t->n_col,
1079 q[i] + has_div + t->n_col + e, n_div);
1080 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
1081 }
1082 isl_mat_free(t);
1083 return 0;
1084 }
1085
1086 /* Replace the variables x in bset by x' given by x = M x', with
1087 * M the matrix mat.
1088 *
1089 * If there are fewer variables x' then there are x, then we perform
1090 * the transformation in place, which that, in principle,
1091 * this frees up some extra variables as the number
1092 * of columns remains constant, but we would have to extend
1093 * the div array too as the number of rows in this array is assumed
1094 * to be equal to extra.
1095 */
1096 struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
1097 struct isl_mat *mat)
1098 {
1099 struct isl_ctx *ctx;
1100
1101 if (!bset || !mat)
1102 goto error;
1103
1104 ctx = bset->ctx;
1105 bset = isl_basic_set_cow(bset);
1106 if (!bset)
1107 goto error;
1108
1109 isl_assert(ctx, bset->dim->nparam == 0, goto error);
1110 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
1111 isl_assert(ctx, mat->n_col > 0, goto error);
1112
1113 if (mat->n_col > mat->n_row) {
1114 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0, 0, 0);
1115 if (!bset)
1116 goto error;
1117 } else if (mat->n_col < mat->n_row) {
1118 bset->dim = isl_space_cow(bset->dim);
1119 if (!bset->dim)
1120 goto error;
1121 bset->dim->n_out -= mat->n_row - mat->n_col;
1122 }
1123
1124 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
1125 isl_mat_copy(mat)) < 0)
1126 goto error;
1127
1128 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
1129 isl_mat_copy(mat)) < 0)
1130 goto error;
1131
1132 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
1133 goto error2;
1134
1135 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
1136 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
1137 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1138 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1139 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
1140
1141 bset = isl_basic_set_simplify(bset);
1142 bset = isl_basic_set_finalize(bset);
1143
1144 return bset;
1145 error:
1146 isl_mat_free(mat);
1147 error2:
1148 isl_basic_set_free(bset);
1149 return NULL;
1150 }
1151
1152 struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
1153 {
1154 struct isl_ctx *ctx;
1155 int i;
1156
1157 set = isl_set_cow(set);
1158 if (!set)
1159 return NULL;
1160
1161 ctx = set->ctx;
1162 for (i = 0; i < set->n; ++i) {
1163 set->p[i] = isl_basic_set_preimage(set->p[i],
1164 isl_mat_copy(mat));
1165 if (!set->p[i])
1166 goto error;
1167 }
1168 if (mat->n_col != mat->n_row) {
1169 set->dim = isl_space_cow(set->dim);
1170 if (!set->dim)
1171 goto error;
1172 set->dim->n_out += mat->n_col;
1173 set->dim->n_out -= mat->n_row;
1174 }
1175 isl_mat_free(mat);
1176 ISL_F_CLR(set, ISL_SET_NORMALIZED);
1177 return set;
1178 error:
1179 isl_set_free(set);
1180 isl_mat_free(mat);
1181 return NULL;
1182 }
1183
1184 /* Replace the variables x starting at pos in the rows q
1185 * by x' with x = M x' with M the matrix mat.
1186 * That is, replace the corresponding coefficients c by c M.
1187 */
1188 static int transform(isl_ctx *ctx, isl_int **q, unsigned n,
1189 unsigned pos, __isl_take isl_mat *mat)
1190 {
1191 int i;
1192 isl_mat *t;
1193
1194 t = isl_mat_sub_alloc6(ctx, q, 0, n, pos, mat->n_row);
1195 t = isl_mat_product(t, mat);
1196 if (!t)
1197 return -1;
1198 for (i = 0; i < n; ++i)
1199 isl_seq_swp_or_cpy(q[i] + pos, t->row[i], t->n_col);
1200 isl_mat_free(t);
1201 return 0;
1202 }
1203
1204 /* Replace the variables x of type "type" starting at "first" in "bset"
1205 * by x' with x = M x' with M the matrix trans.
1206 * That is, replace the corresponding coefficients c by c M.
1207 *
1208 * The transformation matrix should be a square matrix.
1209 */
1210 __isl_give isl_basic_set *isl_basic_set_transform_dims(
1211 __isl_take isl_basic_set *bset, enum isl_dim_type type, unsigned first,
1212 __isl_take isl_mat *trans)
1213 {
1214 isl_ctx *ctx;
1215 unsigned pos;
1216
1217 bset = isl_basic_set_cow(bset);
1218 if (!bset || !trans)
1219 goto error;
1220
1221 ctx = isl_basic_set_get_ctx(bset);
1222 if (trans->n_row != trans->n_col)
1223 isl_die(trans->ctx, isl_error_invalid,
1224 "expecting square transformation matrix", goto error);
1225 if (first + trans->n_row > isl_basic_set_dim(bset, type))
1226 isl_die(trans->ctx, isl_error_invalid,
1227 "oversized transformation matrix", goto error);
1228
1229 pos = isl_basic_set_offset(bset, type) + first;
1230
1231 if (transform(ctx, bset->eq, bset->n_eq, pos, isl_mat_copy(trans)) < 0)
1232 goto error;
1233 if (transform(ctx, bset->ineq, bset->n_ineq, pos,
1234 isl_mat_copy(trans)) < 0)
1235 goto error;
1236 if (transform(ctx, bset->div, bset->n_div, 1 + pos,
1237 isl_mat_copy(trans)) < 0)
1238 goto error;
1239
1240 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1241 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1242
1243 isl_mat_free(trans);
1244 return bset;
1245 error:
1246 isl_mat_free(trans);
1247 isl_basic_set_free(bset);
1248 return NULL;
1249 }
1250
1251 void isl_mat_print_internal(__isl_keep isl_mat *mat, FILE *out, int indent)
1252 {
1253 int i, j;
1254
1255 if (!mat) {
1256 fprintf(out, "%*snull mat\n", indent, "");
1257 return;
1258 }
1259
1260 if (mat->n_row == 0)
1261 fprintf(out, "%*s[]\n", indent, "");
1262
1263 for (i = 0; i < mat->n_row; ++i) {
1264 if (!i)
1265 fprintf(out, "%*s[[", indent, "");
1266 else
1267 fprintf(out, "%*s[", indent+1, "");
1268 for (j = 0; j < mat->n_col; ++j) {
1269 if (j)
1270 fprintf(out, ",");
1271 isl_int_print(out, mat->row[i][j], 0);
1272 }
1273 if (i == mat->n_row-1)
1274 fprintf(out, "]]\n");
1275 else
1276 fprintf(out, "]\n");
1277 }
1278 }
1279
1280 void isl_mat_dump(__isl_keep isl_mat *mat)
1281 {
1282 isl_mat_print_internal(mat, stderr, 0);
1283 }
1284
1285 struct isl_mat *isl_mat_drop_cols(struct isl_mat *mat, unsigned col, unsigned n)
1286 {
1287 int r;
1288
1289 if (n == 0)
1290 return mat;
1291
1292 mat = isl_mat_cow(mat);
1293 if (!mat)
1294 return NULL;
1295
1296 if (col != mat->n_col-n) {
1297 for (r = 0; r < mat->n_row; ++r)
1298 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1299 mat->n_col - col - n);
1300 }
1301 mat->n_col -= n;
1302 return mat;
1303 }
1304
1305 struct isl_mat *isl_mat_drop_rows(struct isl_mat *mat, unsigned row, unsigned n)
1306 {
1307 int r;
1308
1309 mat = isl_mat_cow(mat);
1310 if (!mat)
1311 return NULL;
1312
1313 for (r = row; r+n < mat->n_row; ++r)
1314 mat->row[r] = mat->row[r+n];
1315
1316 mat->n_row -= n;
1317 return mat;
1318 }
1319
1320 __isl_give isl_mat *isl_mat_insert_cols(__isl_take isl_mat *mat,
1321 unsigned col, unsigned n)
1322 {
1323 isl_mat *ext;
1324
1325 if (!mat)
1326 return NULL;
1327 if (n == 0)
1328 return mat;
1329
1330 ext = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col + n);
1331 if (!ext)
1332 goto error;
1333
1334 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row, 0, 0, col);
1335 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row,
1336 col + n, col, mat->n_col - col);
1337
1338 isl_mat_free(mat);
1339 return ext;
1340 error:
1341 isl_mat_free(mat);
1342 return NULL;
1343 }
1344
1345 __isl_give isl_mat *isl_mat_insert_zero_cols(__isl_take isl_mat *mat,
1346 unsigned first, unsigned n)
1347 {
1348 int i;
1349
1350 if (!mat)
1351 return NULL;
1352 mat = isl_mat_insert_cols(mat, first, n);
1353 if (!mat)
1354 return NULL;
1355
1356 for (i = 0; i < mat->n_row; ++i)
1357 isl_seq_clr(mat->row[i] + first, n);
1358
1359 return mat;
1360 }
1361
1362 __isl_give isl_mat *isl_mat_add_zero_cols(__isl_take isl_mat *mat, unsigned n)
1363 {
1364 if (!mat)
1365 return NULL;
1366
1367 return isl_mat_insert_zero_cols(mat, mat->n_col, n);
1368 }
1369
1370 __isl_give isl_mat *isl_mat_insert_rows(__isl_take isl_mat *mat,
1371 unsigned row, unsigned n)
1372 {
1373 isl_mat *ext;
1374
1375 if (!mat)
1376 return NULL;
1377 if (n == 0)
1378 return mat;
1379
1380 ext = isl_mat_alloc(mat->ctx, mat->n_row + n, mat->n_col);
1381 if (!ext)
1382 goto error;
1383
1384 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, row, 0, 0, mat->n_col);
1385 isl_mat_sub_copy(mat->ctx, ext->row + row + n, mat->row + row,
1386 mat->n_row - row, 0, 0, mat->n_col);
1387
1388 isl_mat_free(mat);
1389 return ext;
1390 error:
1391 isl_mat_free(mat);
1392 return NULL;
1393 }
1394
1395 __isl_give isl_mat *isl_mat_add_rows(__isl_take isl_mat *mat, unsigned n)
1396 {
1397 if (!mat)
1398 return NULL;
1399
1400 return isl_mat_insert_rows(mat, mat->n_row, n);
1401 }
1402
1403 __isl_give isl_mat *isl_mat_insert_zero_rows(__isl_take isl_mat *mat,
1404 unsigned row, unsigned n)
1405 {
1406 int i;
1407
1408 mat = isl_mat_insert_rows(mat, row, n);
1409 if (!mat)
1410 return NULL;
1411
1412 for (i = 0; i < n; ++i)
1413 isl_seq_clr(mat->row[row + i], mat->n_col);
1414
1415 return mat;
1416 }
1417
1418 __isl_give isl_mat *isl_mat_add_zero_rows(__isl_take isl_mat *mat, unsigned n)
1419 {
1420 if (!mat)
1421 return NULL;
1422
1423 return isl_mat_insert_zero_rows(mat, mat->n_row, n);
1424 }
1425
1426 void isl_mat_col_submul(struct isl_mat *mat,
1427 int dst_col, isl_int f, int src_col)
1428 {
1429 int i;
1430
1431 for (i = 0; i < mat->n_row; ++i)
1432 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1433 }
1434
1435 void isl_mat_col_add(__isl_keep isl_mat *mat, int dst_col, int src_col)
1436 {
1437 int i;
1438
1439 if (!mat)
1440 return;
1441
1442 for (i = 0; i < mat->n_row; ++i)
1443 isl_int_add(mat->row[i][dst_col],
1444 mat->row[i][dst_col], mat->row[i][src_col]);
1445 }
1446
1447 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1448 {
1449 int i;
1450
1451 for (i = 0; i < mat->n_row; ++i)
1452 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1453 }
1454
1455 struct isl_mat *isl_mat_unimodular_complete(struct isl_mat *M, int row)
1456 {
1457 int r;
1458 struct isl_mat *H = NULL, *Q = NULL;
1459
1460 if (!M)
1461 return NULL;
1462
1463 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1464 M->n_row = row;
1465 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1466 M->n_row = M->n_col;
1467 if (!H)
1468 goto error;
1469 for (r = 0; r < row; ++r)
1470 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1471 for (r = row; r < M->n_row; ++r)
1472 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1473 isl_mat_free(H);
1474 isl_mat_free(Q);
1475 return M;
1476 error:
1477 isl_mat_free(H);
1478 isl_mat_free(Q);
1479 isl_mat_free(M);
1480 return NULL;
1481 }
1482
1483 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1484 __isl_take isl_mat *bot)
1485 {
1486 struct isl_mat *mat;
1487
1488 if (!top || !bot)
1489 goto error;
1490
1491 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1492 if (top->n_row == 0) {
1493 isl_mat_free(top);
1494 return bot;
1495 }
1496 if (bot->n_row == 0) {
1497 isl_mat_free(bot);
1498 return top;
1499 }
1500
1501 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1502 if (!mat)
1503 goto error;
1504 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1505 0, 0, mat->n_col);
1506 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1507 0, 0, mat->n_col);
1508 isl_mat_free(top);
1509 isl_mat_free(bot);
1510 return mat;
1511 error:
1512 isl_mat_free(top);
1513 isl_mat_free(bot);
1514 return NULL;
1515 }
1516
1517 int isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
1518 {
1519 int i;
1520
1521 if (!mat1 || !mat2)
1522 return -1;
1523
1524 if (mat1->n_row != mat2->n_row)
1525 return 0;
1526
1527 if (mat1->n_col != mat2->n_col)
1528 return 0;
1529
1530 for (i = 0; i < mat1->n_row; ++i)
1531 if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
1532 return 0;
1533
1534 return 1;
1535 }
1536
1537 __isl_give isl_mat *isl_mat_from_row_vec(__isl_take isl_vec *vec)
1538 {
1539 struct isl_mat *mat;
1540
1541 if (!vec)
1542 return NULL;
1543 mat = isl_mat_alloc(vec->ctx, 1, vec->size);
1544 if (!mat)
1545 goto error;
1546
1547 isl_seq_cpy(mat->row[0], vec->el, vec->size);
1548
1549 isl_vec_free(vec);
1550 return mat;
1551 error:
1552 isl_vec_free(vec);
1553 return NULL;
1554 }
1555
1556 __isl_give isl_mat *isl_mat_vec_concat(__isl_take isl_mat *top,
1557 __isl_take isl_vec *bot)
1558 {
1559 return isl_mat_concat(top, isl_mat_from_row_vec(bot));
1560 }
1561
1562 __isl_give isl_mat *isl_mat_move_cols(__isl_take isl_mat *mat,
1563 unsigned dst_col, unsigned src_col, unsigned n)
1564 {
1565 isl_mat *res;
1566
1567 if (!mat)
1568 return NULL;
1569 if (n == 0 || dst_col == src_col)
1570 return mat;
1571
1572 res = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
1573 if (!res)
1574 goto error;
1575
1576 if (dst_col < src_col) {
1577 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1578 0, 0, dst_col);
1579 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1580 dst_col, src_col, n);
1581 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1582 dst_col + n, dst_col, src_col - dst_col);
1583 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1584 src_col + n, src_col + n,
1585 res->n_col - src_col - n);
1586 } else {
1587 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1588 0, 0, src_col);
1589 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1590 src_col, src_col + n, dst_col - src_col);
1591 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1592 dst_col, src_col, n);
1593 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1594 dst_col + n, dst_col + n,
1595 res->n_col - dst_col - n);
1596 }
1597 isl_mat_free(mat);
1598
1599 return res;
1600 error:
1601 isl_mat_free(mat);
1602 return NULL;
1603 }
1604
1605 void isl_mat_gcd(__isl_keep isl_mat *mat, isl_int *gcd)
1606 {
1607 int i;
1608 isl_int g;
1609
1610 isl_int_set_si(*gcd, 0);
1611 if (!mat)
1612 return;
1613
1614 isl_int_init(g);
1615 for (i = 0; i < mat->n_row; ++i) {
1616 isl_seq_gcd(mat->row[i], mat->n_col, &g);
1617 isl_int_gcd(*gcd, *gcd, g);
1618 }
1619 isl_int_clear(g);
1620 }
1621
1622 __isl_give isl_mat *isl_mat_scale_down(__isl_take isl_mat *mat, isl_int m)
1623 {
1624 int i;
1625
1626 if (isl_int_is_one(m))
1627 return mat;
1628
1629 mat = isl_mat_cow(mat);
1630 if (!mat)
1631 return NULL;
1632
1633 for (i = 0; i < mat->n_row; ++i)
1634 isl_seq_scale_down(mat->row[i], mat->row[i], m, mat->n_col);
1635
1636 return mat;
1637 }
1638
1639 __isl_give isl_mat *isl_mat_scale_down_row(__isl_take isl_mat *mat, int row,
1640 isl_int m)
1641 {
1642 if (isl_int_is_one(m))
1643 return mat;
1644
1645 mat = isl_mat_cow(mat);
1646 if (!mat)
1647 return NULL;
1648
1649 isl_seq_scale_down(mat->row[row], mat->row[row], m, mat->n_col);
1650
1651 return mat;
1652 }
1653
1654 __isl_give isl_mat *isl_mat_normalize(__isl_take isl_mat *mat)
1655 {
1656 isl_int gcd;
1657
1658 if (!mat)
1659 return NULL;
1660
1661 isl_int_init(gcd);
1662 isl_mat_gcd(mat, &gcd);
1663 mat = isl_mat_scale_down(mat, gcd);
1664 isl_int_clear(gcd);
1665
1666 return mat;
1667 }
1668
1669 __isl_give isl_mat *isl_mat_normalize_row(__isl_take isl_mat *mat, int row)
1670 {
1671 mat = isl_mat_cow(mat);
1672 if (!mat)
1673 return NULL;
1674
1675 isl_seq_normalize(mat->ctx, mat->row[row], mat->n_col);
1676
1677 return mat;
1678 }
1679
1680 /* Number of initial non-zero columns.
1681 */
1682 int isl_mat_initial_non_zero_cols(__isl_keep isl_mat *mat)
1683 {
1684 int i;
1685
1686 if (!mat)
1687 return -1;
1688
1689 for (i = 0; i < mat->n_col; ++i)
1690 if (row_first_non_zero(mat->row, mat->n_row, i) < 0)
1691 break;
1692
1693 return i;
1694 }
Integer set library