?  search:
summary | log | graphiclog1 | graphiclog2 | commit | commitdiff | tree | refs | edit | fork
blame | history | raw | HEAD
hide undocumented *_solve_lp functions
[isl.git] / isl_mat.c
blobaa78c68007089985db9ef428e86b7ff77b6e6145
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_vec_private.h>
16 #include <isl_space_private.h>
17 #include <isl_val_private.h>
18
19 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat)
20 {
21 return mat ? mat->ctx : NULL;
22 }
23
24 struct isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
25 unsigned n_row, unsigned n_col)
26 {
27 int i;
28 struct isl_mat *mat;
29
30 mat = isl_alloc_type(ctx, struct isl_mat);
31 if (!mat)
32 return NULL;
33
34 mat->row = NULL;
35 mat->block = isl_blk_alloc(ctx, n_row * n_col);
36 if (isl_blk_is_error(mat->block))
37 goto error;
38 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
39 if (!mat->row)
40 goto error;
41
42 for (i = 0; i < n_row; ++i)
43 mat->row[i] = mat->block.data + i * n_col;
44
45 mat->ctx = ctx;
46 isl_ctx_ref(ctx);
47 mat->ref = 1;
48 mat->n_row = n_row;
49 mat->n_col = n_col;
50 mat->max_col = n_col;
51 mat->flags = 0;
52
53 return mat;
54 error:
55 isl_blk_free(ctx, mat->block);
56 free(mat);
57 return NULL;
58 }
59
60 struct isl_mat *isl_mat_extend(struct isl_mat *mat,
61 unsigned n_row, unsigned n_col)
62 {
63 int i;
64 isl_int *old;
65 isl_int **row;
66
67 if (!mat)
68 return NULL;
69
70 if (mat->max_col >= n_col && mat->n_row >= n_row) {
71 if (mat->n_col < n_col)
72 mat->n_col = n_col;
73 return mat;
74 }
75
76 if (mat->max_col < n_col) {
77 struct isl_mat *new_mat;
78
79 if (n_row < mat->n_row)
80 n_row = mat->n_row;
81 new_mat = isl_mat_alloc(mat->ctx, n_row, n_col);
82 if (!new_mat)
83 goto error;
84 for (i = 0; i < mat->n_row; ++i)
85 isl_seq_cpy(new_mat->row[i], mat->row[i], mat->n_col);
86 isl_mat_free(mat);
87 return new_mat;
88 }
89
90 mat = isl_mat_cow(mat);
91 if (!mat)
92 goto error;
93
94 old = mat->block.data;
95 mat->block = isl_blk_extend(mat->ctx, mat->block, n_row * mat->max_col);
96 if (isl_blk_is_error(mat->block))
97 goto error;
98 row = isl_realloc_array(mat->ctx, mat->row, isl_int *, n_row);
99 if (!row)
100 goto error;
101 mat->row = row;
102
103 for (i = 0; i < mat->n_row; ++i)
104 mat->row[i] = mat->block.data + (mat->row[i] - old);
105 for (i = mat->n_row; i < n_row; ++i)
106 mat->row[i] = mat->block.data + i * mat->max_col;
107 mat->n_row = n_row;
108 if (mat->n_col < n_col)
109 mat->n_col = n_col;
110
111 return mat;
112 error:
113 isl_mat_free(mat);
114 return NULL;
115 }
116
117 __isl_give isl_mat *isl_mat_sub_alloc6(isl_ctx *ctx, isl_int **row,
118 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
119 {
120 int i;
121 struct isl_mat *mat;
122
123 mat = isl_alloc_type(ctx, struct isl_mat);
124 if (!mat)
125 return NULL;
126 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
127 if (!mat->row)
128 goto error;
129 for (i = 0; i < n_row; ++i)
130 mat->row[i] = row[first_row+i] + first_col;
131 mat->ctx = ctx;
132 isl_ctx_ref(ctx);
133 mat->ref = 1;
134 mat->n_row = n_row;
135 mat->n_col = n_col;
136 mat->block = isl_blk_empty();
137 mat->flags = ISL_MAT_BORROWED;
138 return mat;
139 error:
140 free(mat);
141 return NULL;
142 }
143
144 __isl_give isl_mat *isl_mat_sub_alloc(__isl_keep isl_mat *mat,
145 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
146 {
147 if (!mat)
148 return NULL;
149 return isl_mat_sub_alloc6(mat->ctx, mat->row, first_row, n_row,
150 first_col, n_col);
151 }
152
153 void isl_mat_sub_copy(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
154 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
155 {
156 int i;
157
158 for (i = 0; i < n_row; ++i)
159 isl_seq_cpy(dst[i]+dst_col, src[i]+src_col, n_col);
160 }
161
162 void isl_mat_sub_neg(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
163 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
164 {
165 int i;
166
167 for (i = 0; i < n_row; ++i)
168 isl_seq_neg(dst[i]+dst_col, src[i]+src_col, n_col);
169 }
170
171 struct isl_mat *isl_mat_copy(struct isl_mat *mat)
172 {
173 if (!mat)
174 return NULL;
175
176 mat->ref++;
177 return mat;
178 }
179
180 struct isl_mat *isl_mat_dup(struct isl_mat *mat)
181 {
182 int i;
183 struct isl_mat *mat2;
184
185 if (!mat)
186 return NULL;
187 mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
188 if (!mat2)
189 return NULL;
190 for (i = 0; i < mat->n_row; ++i)
191 isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);
192 return mat2;
193 }
194
195 struct isl_mat *isl_mat_cow(struct isl_mat *mat)
196 {
197 struct isl_mat *mat2;
198 if (!mat)
199 return NULL;
200
201 if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))
202 return mat;
203
204 mat2 = isl_mat_dup(mat);
205 isl_mat_free(mat);
206 return mat2;
207 }
208
209 void *isl_mat_free(struct isl_mat *mat)
210 {
211 if (!mat)
212 return NULL;
213
214 if (--mat->ref > 0)
215 return NULL;
216
217 if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))
218 isl_blk_free(mat->ctx, mat->block);
219 isl_ctx_deref(mat->ctx);
220 free(mat->row);
221 free(mat);
222
223 return NULL;
224 }
225
226 int isl_mat_rows(__isl_keep isl_mat *mat)
227 {
228 return mat ? mat->n_row : -1;
229 }
230
231 int isl_mat_cols(__isl_keep isl_mat *mat)
232 {
233 return mat ? mat->n_col : -1;
234 }
235
236 int isl_mat_get_element(__isl_keep isl_mat *mat, int row, int col, isl_int *v)
237 {
238 if (!mat)
239 return -1;
240 if (row < 0 || row >= mat->n_row)
241 isl_die(mat->ctx, isl_error_invalid, "row out of range",
242 return -1);
243 if (col < 0 || col >= mat->n_col)
244 isl_die(mat->ctx, isl_error_invalid, "column out of range",
245 return -1);
246 isl_int_set(*v, mat->row[row][col]);
247 return 0;
248 }
249
250 /* Extract the element at row "row", oolumn "col" of "mat".
251 */
252 __isl_give isl_val *isl_mat_get_element_val(__isl_keep isl_mat *mat,
253 int row, int col)
254 {
255 isl_ctx *ctx;
256
257 if (!mat)
258 return NULL;
259 ctx = isl_mat_get_ctx(mat);
260 if (row < 0 || row >= mat->n_row)
261 isl_die(ctx, isl_error_invalid, "row out of range",
262 return NULL);
263 if (col < 0 || col >= mat->n_col)
264 isl_die(ctx, isl_error_invalid, "column out of range",
265 return NULL);
266 return isl_val_int_from_isl_int(ctx, mat->row[row][col]);
267 }
268
269 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
270 int row, int col, isl_int v)
271 {
272 mat = isl_mat_cow(mat);
273 if (!mat)
274 return NULL;
275 if (row < 0 || row >= mat->n_row)
276 isl_die(mat->ctx, isl_error_invalid, "row out of range",
277 goto error);
278 if (col < 0 || col >= mat->n_col)
279 isl_die(mat->ctx, isl_error_invalid, "column out of range",
280 goto error);
281 isl_int_set(mat->row[row][col], v);
282 return mat;
283 error:
284 isl_mat_free(mat);
285 return NULL;
286 }
287
288 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
289 int row, int col, int v)
290 {
291 mat = isl_mat_cow(mat);
292 if (!mat)
293 return NULL;
294 if (row < 0 || row >= mat->n_row)
295 isl_die(mat->ctx, isl_error_invalid, "row out of range",
296 goto error);
297 if (col < 0 || col >= mat->n_col)
298 isl_die(mat->ctx, isl_error_invalid, "column out of range",
299 goto error);
300 isl_int_set_si(mat->row[row][col], v);
301 return mat;
302 error:
303 isl_mat_free(mat);
304 return NULL;
305 }
306
307 /* Replace the element at row "row", column "col" of "mat" by "v".
308 */
309 __isl_give isl_mat *isl_mat_set_element_val(__isl_take isl_mat *mat,
310 int row, int col, __isl_take isl_val *v)
311 {
312 if (!v)
313 return isl_mat_free(mat);
314 if (!isl_val_is_int(v))
315 isl_die(isl_val_get_ctx(v), isl_error_invalid,
316 "expecting integer value", goto error);
317 mat = isl_mat_set_element(mat, row, col, v->n);
318 isl_val_free(v);
319 return mat;
320 error:
321 isl_val_free(v);
322 return isl_mat_free(mat);
323 }
324
325 __isl_give isl_mat *isl_mat_diag(isl_ctx *ctx, unsigned n_row, isl_int d)
326 {
327 int i;
328 struct isl_mat *mat;
329
330 mat = isl_mat_alloc(ctx, n_row, n_row);
331 if (!mat)
332 return NULL;
333 for (i = 0; i < n_row; ++i) {
334 isl_seq_clr(mat->row[i], i);
335 isl_int_set(mat->row[i][i], d);
336 isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
337 }
338
339 return mat;
340 }
341
342 __isl_give isl_mat *isl_mat_identity(isl_ctx *ctx, unsigned n_row)
343 {
344 if (!ctx)
345 return NULL;
346 return isl_mat_diag(ctx, n_row, ctx->one);
347 }
348
349 struct isl_vec *isl_mat_vec_product(struct isl_mat *mat, struct isl_vec *vec)
350 {
351 int i;
352 struct isl_vec *prod;
353
354 if (!mat || !vec)
355 goto error;
356
357 isl_assert(mat->ctx, mat->n_col == vec->size, goto error);
358
359 prod = isl_vec_alloc(mat->ctx, mat->n_row);
360 if (!prod)
361 goto error;
362
363 for (i = 0; i < prod->size; ++i)
364 isl_seq_inner_product(mat->row[i], vec->el, vec->size,
365 &prod->block.data[i]);
366 isl_mat_free(mat);
367 isl_vec_free(vec);
368 return prod;
369 error:
370 isl_mat_free(mat);
371 isl_vec_free(vec);
372 return NULL;
373 }
374
375 __isl_give isl_vec *isl_mat_vec_inverse_product(__isl_take isl_mat *mat,
376 __isl_take isl_vec *vec)
377 {
378 struct isl_mat *vec_mat;
379 int i;
380
381 if (!mat || !vec)
382 goto error;
383 vec_mat = isl_mat_alloc(vec->ctx, vec->size, 1);
384 if (!vec_mat)
385 goto error;
386 for (i = 0; i < vec->size; ++i)
387 isl_int_set(vec_mat->row[i][0], vec->el[i]);
388 vec_mat = isl_mat_inverse_product(mat, vec_mat);
389 isl_vec_free(vec);
390 if (!vec_mat)
391 return NULL;
392 vec = isl_vec_alloc(vec_mat->ctx, vec_mat->n_row);
393 if (vec)
394 for (i = 0; i < vec->size; ++i)
395 isl_int_set(vec->el[i], vec_mat->row[i][0]);
396 isl_mat_free(vec_mat);
397 return vec;
398 error:
399 isl_mat_free(mat);
400 isl_vec_free(vec);
401 return NULL;
402 }
403
404 struct isl_vec *isl_vec_mat_product(struct isl_vec *vec, struct isl_mat *mat)
405 {
406 int i, j;
407 struct isl_vec *prod;
408
409 if (!mat || !vec)
410 goto error;
411
412 isl_assert(mat->ctx, mat->n_row == vec->size, goto error);
413
414 prod = isl_vec_alloc(mat->ctx, mat->n_col);
415 if (!prod)
416 goto error;
417
418 for (i = 0; i < prod->size; ++i) {
419 isl_int_set_si(prod->el[i], 0);
420 for (j = 0; j < vec->size; ++j)
421 isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);
422 }
423 isl_mat_free(mat);
424 isl_vec_free(vec);
425 return prod;
426 error:
427 isl_mat_free(mat);
428 isl_vec_free(vec);
429 return NULL;
430 }
431
432 struct isl_mat *isl_mat_aff_direct_sum(struct isl_mat *left,
433 struct isl_mat *right)
434 {
435 int i;
436 struct isl_mat *sum;
437
438 if (!left || !right)
439 goto error;
440
441 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
442 isl_assert(left->ctx, left->n_row >= 1, goto error);
443 isl_assert(left->ctx, left->n_col >= 1, goto error);
444 isl_assert(left->ctx, right->n_col >= 1, goto error);
445 isl_assert(left->ctx,
446 isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,
447 goto error);
448 isl_assert(left->ctx,
449 isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
450 goto error);
451
452 sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);
453 if (!sum)
454 goto error;
455 isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);
456 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
457 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
458
459 isl_seq_clr(sum->row[0]+1, sum->n_col-1);
460 for (i = 1; i < sum->n_row; ++i) {
461 isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);
462 isl_int_addmul(sum->row[i][0],
463 right->row[0][0], right->row[i][0]);
464 isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],
465 left->n_col-1);
466 isl_seq_scale(sum->row[i]+left->n_col,
467 right->row[i]+1, right->row[0][0],
468 right->n_col-1);
469 }
470
471 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
472 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
473 isl_mat_free(left);
474 isl_mat_free(right);
475 return sum;
476 error:
477 isl_mat_free(left);
478 isl_mat_free(right);
479 return NULL;
480 }
481
482 static void exchange(struct isl_mat *M, struct isl_mat **U,
483 struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
484 {
485 int r;
486 for (r = row; r < M->n_row; ++r)
487 isl_int_swap(M->row[r][i], M->row[r][j]);
488 if (U) {
489 for (r = 0; r < (*U)->n_row; ++r)
490 isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
491 }
492 if (Q)
493 isl_mat_swap_rows(*Q, i, j);
494 }
495
496 static void subtract(struct isl_mat *M, struct isl_mat **U,
497 struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)
498 {
499 int r;
500 for (r = row; r < M->n_row; ++r)
501 isl_int_submul(M->row[r][j], m, M->row[r][i]);
502 if (U) {
503 for (r = 0; r < (*U)->n_row; ++r)
504 isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);
505 }
506 if (Q) {
507 for (r = 0; r < (*Q)->n_col; ++r)
508 isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);
509 }
510 }
511
512 static void oppose(struct isl_mat *M, struct isl_mat **U,
513 struct isl_mat **Q, unsigned row, unsigned col)
514 {
515 int r;
516 for (r = row; r < M->n_row; ++r)
517 isl_int_neg(M->row[r][col], M->row[r][col]);
518 if (U) {
519 for (r = 0; r < (*U)->n_row; ++r)
520 isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);
521 }
522 if (Q)
523 isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);
524 }
525
526 /* Given matrix M, compute
527 *
528 * M U = H
529 * M = H Q
530 *
531 * with U and Q unimodular matrices and H a matrix in column echelon form
532 * such that on each echelon row the entries in the non-echelon column
533 * are non-negative (if neg == 0) or non-positive (if neg == 1)
534 * and stricly smaller (in absolute value) than the entries in the echelon
535 * column.
536 * If U or Q are NULL, then these matrices are not computed.
537 */
538 struct isl_mat *isl_mat_left_hermite(struct isl_mat *M, int neg,
539 struct isl_mat **U, struct isl_mat **Q)
540 {
541 isl_int c;
542 int row, col;
543
544 if (U)
545 *U = NULL;
546 if (Q)
547 *Q = NULL;
548 if (!M)
549 goto error;
550 M = isl_mat_cow(M);
551 if (!M)
552 goto error;
553 if (U) {
554 *U = isl_mat_identity(M->ctx, M->n_col);
555 if (!*U)
556 goto error;
557 }
558 if (Q) {
559 *Q = isl_mat_identity(M->ctx, M->n_col);
560 if (!*Q)
561 goto error;
562 }
563
564 col = 0;
565 isl_int_init(c);
566 for (row = 0; row < M->n_row; ++row) {
567 int first, i, off;
568 first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);
569 if (first == -1)
570 continue;
571 first += col;
572 if (first != col)
573 exchange(M, U, Q, row, first, col);
574 if (isl_int_is_neg(M->row[row][col]))
575 oppose(M, U, Q, row, col);
576 first = col+1;
577 while ((off = isl_seq_first_non_zero(M->row[row]+first,
578 M->n_col-first)) != -1) {
579 first += off;
580 isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);
581 subtract(M, U, Q, row, col, first, c);
582 if (!isl_int_is_zero(M->row[row][first]))
583 exchange(M, U, Q, row, first, col);
584 else
585 ++first;
586 }
587 for (i = 0; i < col; ++i) {
588 if (isl_int_is_zero(M->row[row][i]))
589 continue;
590 if (neg)
591 isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);
592 else
593 isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);
594 if (isl_int_is_zero(c))
595 continue;
596 subtract(M, U, Q, row, col, i, c);
597 }
598 ++col;
599 }
600 isl_int_clear(c);
601
602 return M;
603 error:
604 if (Q) {
605 isl_mat_free(*Q);
606 *Q = NULL;
607 }
608 if (U) {
609 isl_mat_free(*U);
610 *U = NULL;
611 }
612 isl_mat_free(M);
613 return NULL;
614 }
615
616 struct isl_mat *isl_mat_right_kernel(struct isl_mat *mat)
617 {
618 int i, rank;
619 struct isl_mat *U = NULL;
620 struct isl_mat *K;
621
622 mat = isl_mat_left_hermite(mat, 0, &U, NULL);
623 if (!mat || !U)
624 goto error;
625
626 for (i = 0, rank = 0; rank < mat->n_col; ++rank) {
627 while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))
628 ++i;
629 if (i >= mat->n_row)
630 break;
631 }
632 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
633 if (!K)
634 goto error;
635 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
636 isl_mat_free(mat);
637 isl_mat_free(U);
638 return K;
639 error:
640 isl_mat_free(mat);
641 isl_mat_free(U);
642 return NULL;
643 }
644
645 struct isl_mat *isl_mat_lin_to_aff(struct isl_mat *mat)
646 {
647 int i;
648 struct isl_mat *mat2;
649
650 if (!mat)
651 return NULL;
652 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
653 if (!mat2)
654 goto error;
655 isl_int_set_si(mat2->row[0][0], 1);
656 isl_seq_clr(mat2->row[0]+1, mat->n_col);
657 for (i = 0; i < mat->n_row; ++i) {
658 isl_int_set_si(mat2->row[1+i][0], 0);
659 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
660 }
661 isl_mat_free(mat);
662 return mat2;
663 error:
664 isl_mat_free(mat);
665 return NULL;
666 }
667
668 /* Given two matrices M1 and M2, return the block matrix
669 *
670 * [ M1 0 ]
671 * [ 0 M2 ]
672 */
673 __isl_give isl_mat *isl_mat_diagonal(__isl_take isl_mat *mat1,
674 __isl_take isl_mat *mat2)
675 {
676 int i;
677 isl_mat *mat;
678
679 if (!mat1 || !mat2)
680 goto error;
681
682 mat = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
683 mat1->n_col + mat2->n_col);
684 if (!mat)
685 goto error;
686 for (i = 0; i < mat1->n_row; ++i) {
687 isl_seq_cpy(mat->row[i], mat1->row[i], mat1->n_col);
688 isl_seq_clr(mat->row[i] + mat1->n_col, mat2->n_col);
689 }
690 for (i = 0; i < mat2->n_row; ++i) {
691 isl_seq_clr(mat->row[mat1->n_row + i], mat1->n_col);
692 isl_seq_cpy(mat->row[mat1->n_row + i] + mat1->n_col,
693 mat2->row[i], mat2->n_col);
694 }
695 isl_mat_free(mat1);
696 isl_mat_free(mat2);
697 return mat;
698 error:
699 isl_mat_free(mat1);
700 isl_mat_free(mat2);
701 return NULL;
702 }
703
704 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
705 {
706 int i;
707
708 for (i = 0; i < n_row; ++i)
709 if (!isl_int_is_zero(row[i][col]))
710 return i;
711 return -1;
712 }
713
714 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
715 {
716 int i, min = row_first_non_zero(row, n_row, col);
717 if (min < 0)
718 return -1;
719 for (i = min + 1; i < n_row; ++i) {
720 if (isl_int_is_zero(row[i][col]))
721 continue;
722 if (isl_int_abs_lt(row[i][col], row[min][col]))
723 min = i;
724 }
725 return min;
726 }
727
728 static void inv_exchange(struct isl_mat *left, struct isl_mat *right,
729 unsigned i, unsigned j)
730 {
731 left = isl_mat_swap_rows(left, i, j);
732 right = isl_mat_swap_rows(right, i, j);
733 }
734
735 static void inv_oppose(
736 struct isl_mat *left, struct isl_mat *right, unsigned row)
737 {
738 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
739 isl_seq_neg(right->row[row], right->row[row], right->n_col);
740 }
741
742 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
743 unsigned row, unsigned i, isl_int m)
744 {
745 isl_int_neg(m, m);
746 isl_seq_combine(left->row[i]+row,
747 left->ctx->one, left->row[i]+row,
748 m, left->row[row]+row,
749 left->n_col-row);
750 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
751 m, right->row[row], right->n_col);
752 }
753
754 /* Compute inv(left)*right
755 */
756 struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
757 struct isl_mat *right)
758 {
759 int row;
760 isl_int a, b;
761
762 if (!left || !right)
763 goto error;
764
765 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
766 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
767
768 if (left->n_row == 0) {
769 isl_mat_free(left);
770 return right;
771 }
772
773 left = isl_mat_cow(left);
774 right = isl_mat_cow(right);
775 if (!left || !right)
776 goto error;
777
778 isl_int_init(a);
779 isl_int_init(b);
780 for (row = 0; row < left->n_row; ++row) {
781 int pivot, first, i, off;
782 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
783 if (pivot < 0) {
784 isl_int_clear(a);
785 isl_int_clear(b);
786 isl_assert(left->ctx, pivot >= 0, goto error);
787 }
788 pivot += row;
789 if (pivot != row)
790 inv_exchange(left, right, pivot, row);
791 if (isl_int_is_neg(left->row[row][row]))
792 inv_oppose(left, right, row);
793 first = row+1;
794 while ((off = row_first_non_zero(left->row+first,
795 left->n_row-first, row)) != -1) {
796 first += off;
797 isl_int_fdiv_q(a, left->row[first][row],
798 left->row[row][row]);
799 inv_subtract(left, right, row, first, a);
800 if (!isl_int_is_zero(left->row[first][row]))
801 inv_exchange(left, right, row, first);
802 else
803 ++first;
804 }
805 for (i = 0; i < row; ++i) {
806 if (isl_int_is_zero(left->row[i][row]))
807 continue;
808 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
809 isl_int_divexact(b, left->row[i][row], a);
810 isl_int_divexact(a, left->row[row][row], a);
811 isl_int_neg(b, b);
812 isl_seq_combine(left->row[i] + i,
813 a, left->row[i] + i,
814 b, left->row[row] + i,
815 left->n_col - i);
816 isl_seq_combine(right->row[i], a, right->row[i],
817 b, right->row[row], right->n_col);
818 }
819 }
820 isl_int_clear(b);
821
822 isl_int_set(a, left->row[0][0]);
823 for (row = 1; row < left->n_row; ++row)
824 isl_int_lcm(a, a, left->row[row][row]);
825 if (isl_int_is_zero(a)){
826 isl_int_clear(a);
827 isl_assert(left->ctx, 0, goto error);
828 }
829 for (row = 0; row < left->n_row; ++row) {
830 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
831 if (isl_int_is_one(left->row[row][row]))
832 continue;
833 isl_seq_scale(right->row[row], right->row[row],
834 left->row[row][row], right->n_col);
835 }
836 isl_int_clear(a);
837
838 isl_mat_free(left);
839 return right;
840 error:
841 isl_mat_free(left);
842 isl_mat_free(right);
843 return NULL;
844 }
845
846 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
847 {
848 int i;
849
850 for (i = 0; i < mat->n_row; ++i)
851 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
852 }
853
854 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
855 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
856 {
857 int i;
858 isl_int tmp;
859
860 isl_int_init(tmp);
861 for (i = 0; i < mat->n_row; ++i) {
862 isl_int_mul(tmp, m1, mat->row[i][src1]);
863 isl_int_addmul(tmp, m2, mat->row[i][src2]);
864 isl_int_set(mat->row[i][dst], tmp);
865 }
866 isl_int_clear(tmp);
867 }
868
869 struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
870 {
871 struct isl_mat *inv;
872 int row;
873 isl_int a, b;
874
875 mat = isl_mat_cow(mat);
876 if (!mat)
877 return NULL;
878
879 inv = isl_mat_identity(mat->ctx, mat->n_col);
880 inv = isl_mat_cow(inv);
881 if (!inv)
882 goto error;
883
884 isl_int_init(a);
885 isl_int_init(b);
886 for (row = 0; row < mat->n_row; ++row) {
887 int pivot, first, i, off;
888 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
889 if (pivot < 0) {
890 isl_int_clear(a);
891 isl_int_clear(b);
892 isl_assert(mat->ctx, pivot >= 0, goto error);
893 }
894 pivot += row;
895 if (pivot != row)
896 exchange(mat, &inv, NULL, row, pivot, row);
897 if (isl_int_is_neg(mat->row[row][row]))
898 oppose(mat, &inv, NULL, row, row);
899 first = row+1;
900 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
901 mat->n_col-first)) != -1) {
902 first += off;
903 isl_int_fdiv_q(a, mat->row[row][first],
904 mat->row[row][row]);
905 subtract(mat, &inv, NULL, row, row, first, a);
906 if (!isl_int_is_zero(mat->row[row][first]))
907 exchange(mat, &inv, NULL, row, row, first);
908 else
909 ++first;
910 }
911 for (i = 0; i < row; ++i) {
912 if (isl_int_is_zero(mat->row[row][i]))
913 continue;
914 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
915 isl_int_divexact(b, mat->row[row][i], a);
916 isl_int_divexact(a, mat->row[row][row], a);
917 isl_int_neg(a, a);
918 isl_mat_col_combine(mat, i, a, i, b, row);
919 isl_mat_col_combine(inv, i, a, i, b, row);
920 }
921 }
922 isl_int_clear(b);
923
924 isl_int_set(a, mat->row[0][0]);
925 for (row = 1; row < mat->n_row; ++row)
926 isl_int_lcm(a, a, mat->row[row][row]);
927 if (isl_int_is_zero(a)){
928 isl_int_clear(a);
929 goto error;
930 }
931 for (row = 0; row < mat->n_row; ++row) {
932 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
933 if (isl_int_is_one(mat->row[row][row]))
934 continue;
935 isl_mat_col_scale(inv, row, mat->row[row][row]);
936 }
937 isl_int_clear(a);
938
939 isl_mat_free(mat);
940
941 return inv;
942 error:
943 isl_mat_free(mat);
944 isl_mat_free(inv);
945 return NULL;
946 }
947
948 struct isl_mat *isl_mat_transpose(struct isl_mat *mat)
949 {
950 struct isl_mat *transpose = NULL;
951 int i, j;
952
953 if (!mat)
954 return NULL;
955
956 if (mat->n_col == mat->n_row) {
957 mat = isl_mat_cow(mat);
958 if (!mat)
959 return NULL;
960 for (i = 0; i < mat->n_row; ++i)
961 for (j = i + 1; j < mat->n_col; ++j)
962 isl_int_swap(mat->row[i][j], mat->row[j][i]);
963 return mat;
964 }
965 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
966 if (!transpose)
967 goto error;
968 for (i = 0; i < mat->n_row; ++i)
969 for (j = 0; j < mat->n_col; ++j)
970 isl_int_set(transpose->row[j][i], mat->row[i][j]);
971 isl_mat_free(mat);
972 return transpose;
973 error:
974 isl_mat_free(mat);
975 return NULL;
976 }
977
978 struct isl_mat *isl_mat_swap_cols(struct isl_mat *mat, unsigned i, unsigned j)
979 {
980 int r;
981
982 mat = isl_mat_cow(mat);
983 if (!mat)
984 return NULL;
985 isl_assert(mat->ctx, i < mat->n_col, goto error);
986 isl_assert(mat->ctx, j < mat->n_col, goto error);
987
988 for (r = 0; r < mat->n_row; ++r)
989 isl_int_swap(mat->row[r][i], mat->row[r][j]);
990 return mat;
991 error:
992 isl_mat_free(mat);
993 return NULL;
994 }
995
996 struct isl_mat *isl_mat_swap_rows(struct isl_mat *mat, unsigned i, unsigned j)
997 {
998 isl_int *t;
999
1000 if (!mat)
1001 return NULL;
1002 mat = isl_mat_cow(mat);
1003 if (!mat)
1004 return NULL;
1005 t = mat->row[i];
1006 mat->row[i] = mat->row[j];
1007 mat->row[j] = t;
1008 return mat;
1009 }
1010
1011 __isl_give isl_mat *isl_mat_product(__isl_take isl_mat *left,
1012 __isl_take isl_mat *right)
1013 {
1014 int i, j, k;
1015 struct isl_mat *prod;
1016
1017 if (!left || !right)
1018 goto error;
1019 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
1020 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
1021 if (!prod)
1022 goto error;
1023 if (left->n_col == 0) {
1024 for (i = 0; i < prod->n_row; ++i)
1025 isl_seq_clr(prod->row[i], prod->n_col);
1026 isl_mat_free(left);
1027 isl_mat_free(right);
1028 return prod;
1029 }
1030 for (i = 0; i < prod->n_row; ++i) {
1031 for (j = 0; j < prod->n_col; ++j) {
1032 isl_int_mul(prod->row[i][j],
1033 left->row[i][0], right->row[0][j]);
1034 for (k = 1; k < left->n_col; ++k)
1035 isl_int_addmul(prod->row[i][j],
1036 left->row[i][k], right->row[k][j]);
1037 }
1038 }
1039 isl_mat_free(left);
1040 isl_mat_free(right);
1041 return prod;
1042 error:
1043 isl_mat_free(left);
1044 isl_mat_free(right);
1045 return NULL;
1046 }
1047
1048 /* Replace the variables x in the rows q by x' given by x = M x',
1049 * with M the matrix mat.
1050 *
1051 * If the number of new variables is greater than the original
1052 * number of variables, then the rows q have already been
1053 * preextended. If the new number is smaller, then the coefficients
1054 * of the divs, which are not changed, need to be shifted down.
1055 * The row q may be the equalities, the inequalities or the
1056 * div expressions. In the latter case, has_div is true and
1057 * we need to take into account the extra denominator column.
1058 */
1059 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
1060 unsigned n_div, int has_div, struct isl_mat *mat)
1061 {
1062 int i;
1063 struct isl_mat *t;
1064 int e;
1065
1066 if (mat->n_col >= mat->n_row)
1067 e = 0;
1068 else
1069 e = mat->n_row - mat->n_col;
1070 if (has_div)
1071 for (i = 0; i < n; ++i)
1072 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
1073 t = isl_mat_sub_alloc6(mat->ctx, q, 0, n, has_div, mat->n_row);
1074 t = isl_mat_product(t, mat);
1075 if (!t)
1076 return -1;
1077 for (i = 0; i < n; ++i) {
1078 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
1079 isl_seq_cpy(q[i] + has_div + t->n_col,
1080 q[i] + has_div + t->n_col + e, n_div);
1081 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
1082 }
1083 isl_mat_free(t);
1084 return 0;
1085 }
1086
1087 /* Replace the variables x in bset by x' given by x = M x', with
1088 * M the matrix mat.
1089 *
1090 * If there are fewer variables x' then there are x, then we perform
1091 * the transformation in place, which that, in principle,
1092 * this frees up some extra variables as the number
1093 * of columns remains constant, but we would have to extend
1094 * the div array too as the number of rows in this array is assumed
1095 * to be equal to extra.
1096 */
1097 struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
1098 struct isl_mat *mat)
1099 {
1100 struct isl_ctx *ctx;
1101
1102 if (!bset || !mat)
1103 goto error;
1104
1105 ctx = bset->ctx;
1106 bset = isl_basic_set_cow(bset);
1107 if (!bset)
1108 goto error;
1109
1110 isl_assert(ctx, bset->dim->nparam == 0, goto error);
1111 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
1112 isl_assert(ctx, mat->n_col > 0, goto error);
1113
1114 if (mat->n_col > mat->n_row) {
1115 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0, 0, 0);
1116 if (!bset)
1117 goto error;
1118 } else if (mat->n_col < mat->n_row) {
1119 bset->dim = isl_space_cow(bset->dim);
1120 if (!bset->dim)
1121 goto error;
1122 bset->dim->n_out -= mat->n_row - mat->n_col;
1123 }
1124
1125 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
1126 isl_mat_copy(mat)) < 0)
1127 goto error;
1128
1129 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
1130 isl_mat_copy(mat)) < 0)
1131 goto error;
1132
1133 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
1134 goto error2;
1135
1136 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
1137 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
1138 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1139 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1140 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
1141
1142 bset = isl_basic_set_simplify(bset);
1143 bset = isl_basic_set_finalize(bset);
1144
1145 return bset;
1146 error:
1147 isl_mat_free(mat);
1148 error2:
1149 isl_basic_set_free(bset);
1150 return NULL;
1151 }
1152
1153 struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
1154 {
1155 struct isl_ctx *ctx;
1156 int i;
1157
1158 set = isl_set_cow(set);
1159 if (!set)
1160 return NULL;
1161
1162 ctx = set->ctx;
1163 for (i = 0; i < set->n; ++i) {
1164 set->p[i] = isl_basic_set_preimage(set->p[i],
1165 isl_mat_copy(mat));
1166 if (!set->p[i])
1167 goto error;
1168 }
1169 if (mat->n_col != mat->n_row) {
1170 set->dim = isl_space_cow(set->dim);
1171 if (!set->dim)
1172 goto error;
1173 set->dim->n_out += mat->n_col;
1174 set->dim->n_out -= mat->n_row;
1175 }
1176 isl_mat_free(mat);
1177 ISL_F_CLR(set, ISL_SET_NORMALIZED);
1178 return set;
1179 error:
1180 isl_set_free(set);
1181 isl_mat_free(mat);
1182 return NULL;
1183 }
1184
1185 /* Replace the variables x starting at pos in the rows q
1186 * by x' with x = M x' with M the matrix mat.
1187 * That is, replace the corresponding coefficients c by c M.
1188 */
1189 static int transform(isl_ctx *ctx, isl_int **q, unsigned n,
1190 unsigned pos, __isl_take isl_mat *mat)
1191 {
1192 int i;
1193 isl_mat *t;
1194
1195 t = isl_mat_sub_alloc6(ctx, q, 0, n, pos, mat->n_row);
1196 t = isl_mat_product(t, mat);
1197 if (!t)
1198 return -1;
1199 for (i = 0; i < n; ++i)
1200 isl_seq_swp_or_cpy(q[i] + pos, t->row[i], t->n_col);
1201 isl_mat_free(t);
1202 return 0;
1203 }
1204
1205 /* Replace the variables x of type "type" starting at "first" in "bset"
1206 * by x' with x = M x' with M the matrix trans.
1207 * That is, replace the corresponding coefficients c by c M.
1208 *
1209 * The transformation matrix should be a square matrix.
1210 */
1211 __isl_give isl_basic_set *isl_basic_set_transform_dims(
1212 __isl_take isl_basic_set *bset, enum isl_dim_type type, unsigned first,
1213 __isl_take isl_mat *trans)
1214 {
1215 isl_ctx *ctx;
1216 unsigned pos;
1217
1218 bset = isl_basic_set_cow(bset);
1219 if (!bset || !trans)
1220 goto error;
1221
1222 ctx = isl_basic_set_get_ctx(bset);
1223 if (trans->n_row != trans->n_col)
1224 isl_die(trans->ctx, isl_error_invalid,
1225 "expecting square transformation matrix", goto error);
1226 if (first + trans->n_row > isl_basic_set_dim(bset, type))
1227 isl_die(trans->ctx, isl_error_invalid,
1228 "oversized transformation matrix", goto error);
1229
1230 pos = isl_basic_set_offset(bset, type) + first;
1231
1232 if (transform(ctx, bset->eq, bset->n_eq, pos, isl_mat_copy(trans)) < 0)
1233 goto error;
1234 if (transform(ctx, bset->ineq, bset->n_ineq, pos,
1235 isl_mat_copy(trans)) < 0)
1236 goto error;
1237 if (transform(ctx, bset->div, bset->n_div, 1 + pos,
1238 isl_mat_copy(trans)) < 0)
1239 goto error;
1240
1241 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1242 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1243
1244 isl_mat_free(trans);
1245 return bset;
1246 error:
1247 isl_mat_free(trans);
1248 isl_basic_set_free(bset);
1249 return NULL;
1250 }
1251
1252 void isl_mat_print_internal(__isl_keep isl_mat *mat, FILE *out, int indent)
1253 {
1254 int i, j;
1255
1256 if (!mat) {
1257 fprintf(out, "%*snull mat\n", indent, "");
1258 return;
1259 }
1260
1261 if (mat->n_row == 0)
1262 fprintf(out, "%*s[]\n", indent, "");
1263
1264 for (i = 0; i < mat->n_row; ++i) {
1265 if (!i)
1266 fprintf(out, "%*s[[", indent, "");
1267 else
1268 fprintf(out, "%*s[", indent+1, "");
1269 for (j = 0; j < mat->n_col; ++j) {
1270 if (j)
1271 fprintf(out, ",");
1272 isl_int_print(out, mat->row[i][j], 0);
1273 }
1274 if (i == mat->n_row-1)
1275 fprintf(out, "]]\n");
1276 else
1277 fprintf(out, "]\n");
1278 }
1279 }
1280
1281 void isl_mat_dump(__isl_keep isl_mat *mat)
1282 {
1283 isl_mat_print_internal(mat, stderr, 0);
1284 }
1285
1286 struct isl_mat *isl_mat_drop_cols(struct isl_mat *mat, unsigned col, unsigned n)
1287 {
1288 int r;
1289
1290 if (n == 0)
1291 return mat;
1292
1293 mat = isl_mat_cow(mat);
1294 if (!mat)
1295 return NULL;
1296
1297 if (col != mat->n_col-n) {
1298 for (r = 0; r < mat->n_row; ++r)
1299 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1300 mat->n_col - col - n);
1301 }
1302 mat->n_col -= n;
1303 return mat;
1304 }
1305
1306 struct isl_mat *isl_mat_drop_rows(struct isl_mat *mat, unsigned row, unsigned n)
1307 {
1308 int r;
1309
1310 mat = isl_mat_cow(mat);
1311 if (!mat)
1312 return NULL;
1313
1314 for (r = row; r+n < mat->n_row; ++r)
1315 mat->row[r] = mat->row[r+n];
1316
1317 mat->n_row -= n;
1318 return mat;
1319 }
1320
1321 __isl_give isl_mat *isl_mat_insert_cols(__isl_take isl_mat *mat,
1322 unsigned col, unsigned n)
1323 {
1324 isl_mat *ext;
1325
1326 if (!mat)
1327 return NULL;
1328 if (n == 0)
1329 return mat;
1330
1331 ext = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col + n);
1332 if (!ext)
1333 goto error;
1334
1335 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row, 0, 0, col);
1336 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row,
1337 col + n, col, mat->n_col - col);
1338
1339 isl_mat_free(mat);
1340 return ext;
1341 error:
1342 isl_mat_free(mat);
1343 return NULL;
1344 }
1345
1346 __isl_give isl_mat *isl_mat_insert_zero_cols(__isl_take isl_mat *mat,
1347 unsigned first, unsigned n)
1348 {
1349 int i;
1350
1351 if (!mat)
1352 return NULL;
1353 mat = isl_mat_insert_cols(mat, first, n);
1354 if (!mat)
1355 return NULL;
1356
1357 for (i = 0; i < mat->n_row; ++i)
1358 isl_seq_clr(mat->row[i] + first, n);
1359
1360 return mat;
1361 }
1362
1363 __isl_give isl_mat *isl_mat_add_zero_cols(__isl_take isl_mat *mat, unsigned n)
1364 {
1365 if (!mat)
1366 return NULL;
1367
1368 return isl_mat_insert_zero_cols(mat, mat->n_col, n);
1369 }
1370
1371 __isl_give isl_mat *isl_mat_insert_rows(__isl_take isl_mat *mat,
1372 unsigned row, unsigned n)
1373 {
1374 isl_mat *ext;
1375
1376 if (!mat)
1377 return NULL;
1378 if (n == 0)
1379 return mat;
1380
1381 ext = isl_mat_alloc(mat->ctx, mat->n_row + n, mat->n_col);
1382 if (!ext)
1383 goto error;
1384
1385 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, row, 0, 0, mat->n_col);
1386 isl_mat_sub_copy(mat->ctx, ext->row + row + n, mat->row + row,
1387 mat->n_row - row, 0, 0, mat->n_col);
1388
1389 isl_mat_free(mat);
1390 return ext;
1391 error:
1392 isl_mat_free(mat);
1393 return NULL;
1394 }
1395
1396 __isl_give isl_mat *isl_mat_add_rows(__isl_take isl_mat *mat, unsigned n)
1397 {
1398 if (!mat)
1399 return NULL;
1400
1401 return isl_mat_insert_rows(mat, mat->n_row, n);
1402 }
1403
1404 __isl_give isl_mat *isl_mat_insert_zero_rows(__isl_take isl_mat *mat,
1405 unsigned row, unsigned n)
1406 {
1407 int i;
1408
1409 mat = isl_mat_insert_rows(mat, row, n);
1410 if (!mat)
1411 return NULL;
1412
1413 for (i = 0; i < n; ++i)
1414 isl_seq_clr(mat->row[row + i], mat->n_col);
1415
1416 return mat;
1417 }
1418
1419 __isl_give isl_mat *isl_mat_add_zero_rows(__isl_take isl_mat *mat, unsigned n)
1420 {
1421 if (!mat)
1422 return NULL;
1423
1424 return isl_mat_insert_zero_rows(mat, mat->n_row, n);
1425 }
1426
1427 void isl_mat_col_submul(struct isl_mat *mat,
1428 int dst_col, isl_int f, int src_col)
1429 {
1430 int i;
1431
1432 for (i = 0; i < mat->n_row; ++i)
1433 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1434 }
1435
1436 void isl_mat_col_add(__isl_keep isl_mat *mat, int dst_col, int src_col)
1437 {
1438 int i;
1439
1440 if (!mat)
1441 return;
1442
1443 for (i = 0; i < mat->n_row; ++i)
1444 isl_int_add(mat->row[i][dst_col],
1445 mat->row[i][dst_col], mat->row[i][src_col]);
1446 }
1447
1448 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1449 {
1450 int i;
1451
1452 for (i = 0; i < mat->n_row; ++i)
1453 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1454 }
1455
1456 struct isl_mat *isl_mat_unimodular_complete(struct isl_mat *M, int row)
1457 {
1458 int r;
1459 struct isl_mat *H = NULL, *Q = NULL;
1460
1461 if (!M)
1462 return NULL;
1463
1464 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1465 M->n_row = row;
1466 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1467 M->n_row = M->n_col;
1468 if (!H)
1469 goto error;
1470 for (r = 0; r < row; ++r)
1471 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1472 for (r = row; r < M->n_row; ++r)
1473 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1474 isl_mat_free(H);
1475 isl_mat_free(Q);
1476 return M;
1477 error:
1478 isl_mat_free(H);
1479 isl_mat_free(Q);
1480 isl_mat_free(M);
1481 return NULL;
1482 }
1483
1484 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1485 __isl_take isl_mat *bot)
1486 {
1487 struct isl_mat *mat;
1488
1489 if (!top || !bot)
1490 goto error;
1491
1492 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1493 if (top->n_row == 0) {
1494 isl_mat_free(top);
1495 return bot;
1496 }
1497 if (bot->n_row == 0) {
1498 isl_mat_free(bot);
1499 return top;
1500 }
1501
1502 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1503 if (!mat)
1504 goto error;
1505 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1506 0, 0, mat->n_col);
1507 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1508 0, 0, mat->n_col);
1509 isl_mat_free(top);
1510 isl_mat_free(bot);
1511 return mat;
1512 error:
1513 isl_mat_free(top);
1514 isl_mat_free(bot);
1515 return NULL;
1516 }
1517
1518 int isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
1519 {
1520 int i;
1521
1522 if (!mat1 || !mat2)
1523 return -1;
1524
1525 if (mat1->n_row != mat2->n_row)
1526 return 0;
1527
1528 if (mat1->n_col != mat2->n_col)
1529 return 0;
1530
1531 for (i = 0; i < mat1->n_row; ++i)
1532 if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
1533 return 0;
1534
1535 return 1;
1536 }
1537
1538 __isl_give isl_mat *isl_mat_from_row_vec(__isl_take isl_vec *vec)
1539 {
1540 struct isl_mat *mat;
1541
1542 if (!vec)
1543 return NULL;
1544 mat = isl_mat_alloc(vec->ctx, 1, vec->size);
1545 if (!mat)
1546 goto error;
1547
1548 isl_seq_cpy(mat->row[0], vec->el, vec->size);
1549
1550 isl_vec_free(vec);
1551 return mat;
1552 error:
1553 isl_vec_free(vec);
1554 return NULL;
1555 }
1556
1557 __isl_give isl_mat *isl_mat_vec_concat(__isl_take isl_mat *top,
1558 __isl_take isl_vec *bot)
1559 {
1560 return isl_mat_concat(top, isl_mat_from_row_vec(bot));
1561 }
1562
1563 __isl_give isl_mat *isl_mat_move_cols(__isl_take isl_mat *mat,
1564 unsigned dst_col, unsigned src_col, unsigned n)
1565 {
1566 isl_mat *res;
1567
1568 if (!mat)
1569 return NULL;
1570 if (n == 0 || dst_col == src_col)
1571 return mat;
1572
1573 res = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
1574 if (!res)
1575 goto error;
1576
1577 if (dst_col < src_col) {
1578 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1579 0, 0, dst_col);
1580 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1581 dst_col, src_col, n);
1582 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1583 dst_col + n, dst_col, src_col - dst_col);
1584 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1585 src_col + n, src_col + n,
1586 res->n_col - src_col - n);
1587 } else {
1588 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1589 0, 0, src_col);
1590 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1591 src_col, src_col + n, dst_col - src_col);
1592 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1593 dst_col, src_col, n);
1594 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1595 dst_col + n, dst_col + n,
1596 res->n_col - dst_col - n);
1597 }
1598 isl_mat_free(mat);
1599
1600 return res;
1601 error:
1602 isl_mat_free(mat);
1603 return NULL;
1604 }
1605
1606 void isl_mat_gcd(__isl_keep isl_mat *mat, isl_int *gcd)
1607 {
1608 int i;
1609 isl_int g;
1610
1611 isl_int_set_si(*gcd, 0);
1612 if (!mat)
1613 return;
1614
1615 isl_int_init(g);
1616 for (i = 0; i < mat->n_row; ++i) {
1617 isl_seq_gcd(mat->row[i], mat->n_col, &g);
1618 isl_int_gcd(*gcd, *gcd, g);
1619 }
1620 isl_int_clear(g);
1621 }
1622
1623 __isl_give isl_mat *isl_mat_scale_down(__isl_take isl_mat *mat, isl_int m)
1624 {
1625 int i;
1626
1627 if (isl_int_is_one(m))
1628 return mat;
1629
1630 mat = isl_mat_cow(mat);
1631 if (!mat)
1632 return NULL;
1633
1634 for (i = 0; i < mat->n_row; ++i)
1635 isl_seq_scale_down(mat->row[i], mat->row[i], m, mat->n_col);
1636
1637 return mat;
1638 }
1639
1640 __isl_give isl_mat *isl_mat_scale_down_row(__isl_take isl_mat *mat, int row,
1641 isl_int m)
1642 {
1643 if (isl_int_is_one(m))
1644 return mat;
1645
1646 mat = isl_mat_cow(mat);
1647 if (!mat)
1648 return NULL;
1649
1650 isl_seq_scale_down(mat->row[row], mat->row[row], m, mat->n_col);
1651
1652 return mat;
1653 }
1654
1655 __isl_give isl_mat *isl_mat_normalize(__isl_take isl_mat *mat)
1656 {
1657 isl_int gcd;
1658
1659 if (!mat)
1660 return NULL;
1661
1662 isl_int_init(gcd);
1663 isl_mat_gcd(mat, &gcd);
1664 mat = isl_mat_scale_down(mat, gcd);
1665 isl_int_clear(gcd);
1666
1667 return mat;
1668 }
1669
1670 __isl_give isl_mat *isl_mat_normalize_row(__isl_take isl_mat *mat, int row)
1671 {
1672 mat = isl_mat_cow(mat);
1673 if (!mat)
1674 return NULL;
1675
1676 isl_seq_normalize(mat->ctx, mat->row[row], mat->n_col);
1677
1678 return mat;
1679 }
1680
1681 /* Number of initial non-zero columns.
1682 */
1683 int isl_mat_initial_non_zero_cols(__isl_keep isl_mat *mat)
1684 {
1685 int i;
1686
1687 if (!mat)
1688 return -1;
1689
1690 for (i = 0; i < mat->n_col; ++i)
1691 if (row_first_non_zero(mat->row, mat->n_row, i) < 0)
1692 break;
1693
1694 return i;
1695 }
Integer set library