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isl_ast_graft.c: remove spurious include
[isl.git] / isl_mat.c
blob5290deabd403b0b32e94f4744487e9c9683b83a6
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/space.h>
12 #include <isl/seq.h>
13 #include <isl_mat_private.h>
14 #include "isl_map_private.h"
15 #include <isl_space_private.h>
16
17 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat)
18 {
19 return mat ? mat->ctx : NULL;
20 }
21
22 struct isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
23 unsigned n_row, unsigned n_col)
24 {
25 int i;
26 struct isl_mat *mat;
27
28 mat = isl_alloc_type(ctx, struct isl_mat);
29 if (!mat)
30 return NULL;
31
32 mat->row = NULL;
33 mat->block = isl_blk_alloc(ctx, n_row * n_col);
34 if (isl_blk_is_error(mat->block))
35 goto error;
36 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
37 if (!mat->row)
38 goto error;
39
40 for (i = 0; i < n_row; ++i)
41 mat->row[i] = mat->block.data + i * n_col;
42
43 mat->ctx = ctx;
44 isl_ctx_ref(ctx);
45 mat->ref = 1;
46 mat->n_row = n_row;
47 mat->n_col = n_col;
48 mat->max_col = n_col;
49 mat->flags = 0;
50
51 return mat;
52 error:
53 isl_blk_free(ctx, mat->block);
54 free(mat);
55 return NULL;
56 }
57
58 struct isl_mat *isl_mat_extend(struct isl_mat *mat,
59 unsigned n_row, unsigned n_col)
60 {
61 int i;
62 isl_int *old;
63 isl_int **row;
64
65 if (!mat)
66 return NULL;
67
68 if (mat->max_col >= n_col && mat->n_row >= n_row) {
69 if (mat->n_col < n_col)
70 mat->n_col = n_col;
71 return mat;
72 }
73
74 if (mat->max_col < n_col) {
75 struct isl_mat *new_mat;
76
77 if (n_row < mat->n_row)
78 n_row = mat->n_row;
79 new_mat = isl_mat_alloc(mat->ctx, n_row, n_col);
80 if (!new_mat)
81 goto error;
82 for (i = 0; i < mat->n_row; ++i)
83 isl_seq_cpy(new_mat->row[i], mat->row[i], mat->n_col);
84 isl_mat_free(mat);
85 return new_mat;
86 }
87
88 mat = isl_mat_cow(mat);
89 if (!mat)
90 goto error;
91
92 old = mat->block.data;
93 mat->block = isl_blk_extend(mat->ctx, mat->block, n_row * mat->max_col);
94 if (isl_blk_is_error(mat->block))
95 goto error;
96 row = isl_realloc_array(mat->ctx, mat->row, isl_int *, n_row);
97 if (!row)
98 goto error;
99 mat->row = row;
100
101 for (i = 0; i < mat->n_row; ++i)
102 mat->row[i] = mat->block.data + (mat->row[i] - old);
103 for (i = mat->n_row; i < n_row; ++i)
104 mat->row[i] = mat->block.data + i * mat->max_col;
105 mat->n_row = n_row;
106 if (mat->n_col < n_col)
107 mat->n_col = n_col;
108
109 return mat;
110 error:
111 isl_mat_free(mat);
112 return NULL;
113 }
114
115 __isl_give isl_mat *isl_mat_sub_alloc6(isl_ctx *ctx, isl_int **row,
116 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
117 {
118 int i;
119 struct isl_mat *mat;
120
121 mat = isl_alloc_type(ctx, struct isl_mat);
122 if (!mat)
123 return NULL;
124 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
125 if (!mat->row)
126 goto error;
127 for (i = 0; i < n_row; ++i)
128 mat->row[i] = row[first_row+i] + first_col;
129 mat->ctx = ctx;
130 isl_ctx_ref(ctx);
131 mat->ref = 1;
132 mat->n_row = n_row;
133 mat->n_col = n_col;
134 mat->block = isl_blk_empty();
135 mat->flags = ISL_MAT_BORROWED;
136 return mat;
137 error:
138 free(mat);
139 return NULL;
140 }
141
142 __isl_give isl_mat *isl_mat_sub_alloc(__isl_keep isl_mat *mat,
143 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
144 {
145 if (!mat)
146 return NULL;
147 return isl_mat_sub_alloc6(mat->ctx, mat->row, first_row, n_row,
148 first_col, n_col);
149 }
150
151 void isl_mat_sub_copy(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
152 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
153 {
154 int i;
155
156 for (i = 0; i < n_row; ++i)
157 isl_seq_cpy(dst[i]+dst_col, src[i]+src_col, n_col);
158 }
159
160 void isl_mat_sub_neg(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
161 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
162 {
163 int i;
164
165 for (i = 0; i < n_row; ++i)
166 isl_seq_neg(dst[i]+dst_col, src[i]+src_col, n_col);
167 }
168
169 struct isl_mat *isl_mat_copy(struct isl_mat *mat)
170 {
171 if (!mat)
172 return NULL;
173
174 mat->ref++;
175 return mat;
176 }
177
178 struct isl_mat *isl_mat_dup(struct isl_mat *mat)
179 {
180 int i;
181 struct isl_mat *mat2;
182
183 if (!mat)
184 return NULL;
185 mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
186 if (!mat2)
187 return NULL;
188 for (i = 0; i < mat->n_row; ++i)
189 isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);
190 return mat2;
191 }
192
193 struct isl_mat *isl_mat_cow(struct isl_mat *mat)
194 {
195 struct isl_mat *mat2;
196 if (!mat)
197 return NULL;
198
199 if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))
200 return mat;
201
202 mat2 = isl_mat_dup(mat);
203 isl_mat_free(mat);
204 return mat2;
205 }
206
207 void *isl_mat_free(struct isl_mat *mat)
208 {
209 if (!mat)
210 return NULL;
211
212 if (--mat->ref > 0)
213 return NULL;
214
215 if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))
216 isl_blk_free(mat->ctx, mat->block);
217 isl_ctx_deref(mat->ctx);
218 free(mat->row);
219 free(mat);
220
221 return NULL;
222 }
223
224 int isl_mat_rows(__isl_keep isl_mat *mat)
225 {
226 return mat ? mat->n_row : -1;
227 }
228
229 int isl_mat_cols(__isl_keep isl_mat *mat)
230 {
231 return mat ? mat->n_col : -1;
232 }
233
234 int isl_mat_get_element(__isl_keep isl_mat *mat, int row, int col, isl_int *v)
235 {
236 if (!mat)
237 return -1;
238 if (row < 0 || row >= mat->n_row)
239 isl_die(mat->ctx, isl_error_invalid, "row out of range",
240 return -1);
241 if (col < 0 || col >= mat->n_col)
242 isl_die(mat->ctx, isl_error_invalid, "column out of range",
243 return -1);
244 isl_int_set(*v, mat->row[row][col]);
245 return 0;
246 }
247
248 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
249 int row, int col, isl_int v)
250 {
251 mat = isl_mat_cow(mat);
252 if (!mat)
253 return NULL;
254 if (row < 0 || row >= mat->n_row)
255 isl_die(mat->ctx, isl_error_invalid, "row out of range",
256 goto error);
257 if (col < 0 || col >= mat->n_col)
258 isl_die(mat->ctx, isl_error_invalid, "column out of range",
259 goto error);
260 isl_int_set(mat->row[row][col], v);
261 return mat;
262 error:
263 isl_mat_free(mat);
264 return NULL;
265 }
266
267 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
268 int row, int col, int v)
269 {
270 mat = isl_mat_cow(mat);
271 if (!mat)
272 return NULL;
273 if (row < 0 || row >= mat->n_row)
274 isl_die(mat->ctx, isl_error_invalid, "row out of range",
275 goto error);
276 if (col < 0 || col >= mat->n_col)
277 isl_die(mat->ctx, isl_error_invalid, "column out of range",
278 goto error);
279 isl_int_set_si(mat->row[row][col], v);
280 return mat;
281 error:
282 isl_mat_free(mat);
283 return NULL;
284 }
285
286 __isl_give isl_mat *isl_mat_diag(isl_ctx *ctx, unsigned n_row, isl_int d)
287 {
288 int i;
289 struct isl_mat *mat;
290
291 mat = isl_mat_alloc(ctx, n_row, n_row);
292 if (!mat)
293 return NULL;
294 for (i = 0; i < n_row; ++i) {
295 isl_seq_clr(mat->row[i], i);
296 isl_int_set(mat->row[i][i], d);
297 isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
298 }
299
300 return mat;
301 }
302
303 __isl_give isl_mat *isl_mat_identity(isl_ctx *ctx, unsigned n_row)
304 {
305 if (!ctx)
306 return NULL;
307 return isl_mat_diag(ctx, n_row, ctx->one);
308 }
309
310 struct isl_vec *isl_mat_vec_product(struct isl_mat *mat, struct isl_vec *vec)
311 {
312 int i;
313 struct isl_vec *prod;
314
315 if (!mat || !vec)
316 goto error;
317
318 isl_assert(mat->ctx, mat->n_col == vec->size, goto error);
319
320 prod = isl_vec_alloc(mat->ctx, mat->n_row);
321 if (!prod)
322 goto error;
323
324 for (i = 0; i < prod->size; ++i)
325 isl_seq_inner_product(mat->row[i], vec->el, vec->size,
326 &prod->block.data[i]);
327 isl_mat_free(mat);
328 isl_vec_free(vec);
329 return prod;
330 error:
331 isl_mat_free(mat);
332 isl_vec_free(vec);
333 return NULL;
334 }
335
336 __isl_give isl_vec *isl_mat_vec_inverse_product(__isl_take isl_mat *mat,
337 __isl_take isl_vec *vec)
338 {
339 struct isl_mat *vec_mat;
340 int i;
341
342 if (!mat || !vec)
343 goto error;
344 vec_mat = isl_mat_alloc(vec->ctx, vec->size, 1);
345 if (!vec_mat)
346 goto error;
347 for (i = 0; i < vec->size; ++i)
348 isl_int_set(vec_mat->row[i][0], vec->el[i]);
349 vec_mat = isl_mat_inverse_product(mat, vec_mat);
350 isl_vec_free(vec);
351 if (!vec_mat)
352 return NULL;
353 vec = isl_vec_alloc(vec_mat->ctx, vec_mat->n_row);
354 if (vec)
355 for (i = 0; i < vec->size; ++i)
356 isl_int_set(vec->el[i], vec_mat->row[i][0]);
357 isl_mat_free(vec_mat);
358 return vec;
359 error:
360 isl_mat_free(mat);
361 isl_vec_free(vec);
362 return NULL;
363 }
364
365 struct isl_vec *isl_vec_mat_product(struct isl_vec *vec, struct isl_mat *mat)
366 {
367 int i, j;
368 struct isl_vec *prod;
369
370 if (!mat || !vec)
371 goto error;
372
373 isl_assert(mat->ctx, mat->n_row == vec->size, goto error);
374
375 prod = isl_vec_alloc(mat->ctx, mat->n_col);
376 if (!prod)
377 goto error;
378
379 for (i = 0; i < prod->size; ++i) {
380 isl_int_set_si(prod->el[i], 0);
381 for (j = 0; j < vec->size; ++j)
382 isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);
383 }
384 isl_mat_free(mat);
385 isl_vec_free(vec);
386 return prod;
387 error:
388 isl_mat_free(mat);
389 isl_vec_free(vec);
390 return NULL;
391 }
392
393 struct isl_mat *isl_mat_aff_direct_sum(struct isl_mat *left,
394 struct isl_mat *right)
395 {
396 int i;
397 struct isl_mat *sum;
398
399 if (!left || !right)
400 goto error;
401
402 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
403 isl_assert(left->ctx, left->n_row >= 1, goto error);
404 isl_assert(left->ctx, left->n_col >= 1, goto error);
405 isl_assert(left->ctx, right->n_col >= 1, goto error);
406 isl_assert(left->ctx,
407 isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,
408 goto error);
409 isl_assert(left->ctx,
410 isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
411 goto error);
412
413 sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);
414 if (!sum)
415 goto error;
416 isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);
417 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
418 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
419
420 isl_seq_clr(sum->row[0]+1, sum->n_col-1);
421 for (i = 1; i < sum->n_row; ++i) {
422 isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);
423 isl_int_addmul(sum->row[i][0],
424 right->row[0][0], right->row[i][0]);
425 isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],
426 left->n_col-1);
427 isl_seq_scale(sum->row[i]+left->n_col,
428 right->row[i]+1, right->row[0][0],
429 right->n_col-1);
430 }
431
432 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
433 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
434 isl_mat_free(left);
435 isl_mat_free(right);
436 return sum;
437 error:
438 isl_mat_free(left);
439 isl_mat_free(right);
440 return NULL;
441 }
442
443 static void exchange(struct isl_mat *M, struct isl_mat **U,
444 struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
445 {
446 int r;
447 for (r = row; r < M->n_row; ++r)
448 isl_int_swap(M->row[r][i], M->row[r][j]);
449 if (U) {
450 for (r = 0; r < (*U)->n_row; ++r)
451 isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
452 }
453 if (Q)
454 isl_mat_swap_rows(*Q, i, j);
455 }
456
457 static void subtract(struct isl_mat *M, struct isl_mat **U,
458 struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)
459 {
460 int r;
461 for (r = row; r < M->n_row; ++r)
462 isl_int_submul(M->row[r][j], m, M->row[r][i]);
463 if (U) {
464 for (r = 0; r < (*U)->n_row; ++r)
465 isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);
466 }
467 if (Q) {
468 for (r = 0; r < (*Q)->n_col; ++r)
469 isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);
470 }
471 }
472
473 static void oppose(struct isl_mat *M, struct isl_mat **U,
474 struct isl_mat **Q, unsigned row, unsigned col)
475 {
476 int r;
477 for (r = row; r < M->n_row; ++r)
478 isl_int_neg(M->row[r][col], M->row[r][col]);
479 if (U) {
480 for (r = 0; r < (*U)->n_row; ++r)
481 isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);
482 }
483 if (Q)
484 isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);
485 }
486
487 /* Given matrix M, compute
488 *
489 * M U = H
490 * M = H Q
491 *
492 * with U and Q unimodular matrices and H a matrix in column echelon form
493 * such that on each echelon row the entries in the non-echelon column
494 * are non-negative (if neg == 0) or non-positive (if neg == 1)
495 * and stricly smaller (in absolute value) than the entries in the echelon
496 * column.
497 * If U or Q are NULL, then these matrices are not computed.
498 */
499 struct isl_mat *isl_mat_left_hermite(struct isl_mat *M, int neg,
500 struct isl_mat **U, struct isl_mat **Q)
501 {
502 isl_int c;
503 int row, col;
504
505 if (U)
506 *U = NULL;
507 if (Q)
508 *Q = NULL;
509 if (!M)
510 goto error;
511 M = isl_mat_cow(M);
512 if (!M)
513 goto error;
514 if (U) {
515 *U = isl_mat_identity(M->ctx, M->n_col);
516 if (!*U)
517 goto error;
518 }
519 if (Q) {
520 *Q = isl_mat_identity(M->ctx, M->n_col);
521 if (!*Q)
522 goto error;
523 }
524
525 col = 0;
526 isl_int_init(c);
527 for (row = 0; row < M->n_row; ++row) {
528 int first, i, off;
529 first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);
530 if (first == -1)
531 continue;
532 first += col;
533 if (first != col)
534 exchange(M, U, Q, row, first, col);
535 if (isl_int_is_neg(M->row[row][col]))
536 oppose(M, U, Q, row, col);
537 first = col+1;
538 while ((off = isl_seq_first_non_zero(M->row[row]+first,
539 M->n_col-first)) != -1) {
540 first += off;
541 isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);
542 subtract(M, U, Q, row, col, first, c);
543 if (!isl_int_is_zero(M->row[row][first]))
544 exchange(M, U, Q, row, first, col);
545 else
546 ++first;
547 }
548 for (i = 0; i < col; ++i) {
549 if (isl_int_is_zero(M->row[row][i]))
550 continue;
551 if (neg)
552 isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);
553 else
554 isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);
555 if (isl_int_is_zero(c))
556 continue;
557 subtract(M, U, Q, row, col, i, c);
558 }
559 ++col;
560 }
561 isl_int_clear(c);
562
563 return M;
564 error:
565 if (Q) {
566 isl_mat_free(*Q);
567 *Q = NULL;
568 }
569 if (U) {
570 isl_mat_free(*U);
571 *U = NULL;
572 }
573 isl_mat_free(M);
574 return NULL;
575 }
576
577 struct isl_mat *isl_mat_right_kernel(struct isl_mat *mat)
578 {
579 int i, rank;
580 struct isl_mat *U = NULL;
581 struct isl_mat *K;
582
583 mat = isl_mat_left_hermite(mat, 0, &U, NULL);
584 if (!mat || !U)
585 goto error;
586
587 for (i = 0, rank = 0; rank < mat->n_col; ++rank) {
588 while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))
589 ++i;
590 if (i >= mat->n_row)
591 break;
592 }
593 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
594 if (!K)
595 goto error;
596 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
597 isl_mat_free(mat);
598 isl_mat_free(U);
599 return K;
600 error:
601 isl_mat_free(mat);
602 isl_mat_free(U);
603 return NULL;
604 }
605
606 struct isl_mat *isl_mat_lin_to_aff(struct isl_mat *mat)
607 {
608 int i;
609 struct isl_mat *mat2;
610
611 if (!mat)
612 return NULL;
613 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
614 if (!mat2)
615 goto error;
616 isl_int_set_si(mat2->row[0][0], 1);
617 isl_seq_clr(mat2->row[0]+1, mat->n_col);
618 for (i = 0; i < mat->n_row; ++i) {
619 isl_int_set_si(mat2->row[1+i][0], 0);
620 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
621 }
622 isl_mat_free(mat);
623 return mat2;
624 error:
625 isl_mat_free(mat);
626 return NULL;
627 }
628
629 /* Given two matrices M1 and M2, return the block matrix
630 *
631 * [ M1 0 ]
632 * [ 0 M2 ]
633 */
634 __isl_give isl_mat *isl_mat_diagonal(__isl_take isl_mat *mat1,
635 __isl_take isl_mat *mat2)
636 {
637 int i;
638 isl_mat *mat;
639
640 if (!mat1 || !mat2)
641 goto error;
642
643 mat = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
644 mat1->n_col + mat2->n_col);
645 if (!mat)
646 goto error;
647 for (i = 0; i < mat1->n_row; ++i) {
648 isl_seq_cpy(mat->row[i], mat1->row[i], mat1->n_col);
649 isl_seq_clr(mat->row[i] + mat1->n_col, mat2->n_col);
650 }
651 for (i = 0; i < mat2->n_row; ++i) {
652 isl_seq_clr(mat->row[mat1->n_row + i], mat1->n_col);
653 isl_seq_cpy(mat->row[mat1->n_row + i] + mat1->n_col,
654 mat2->row[i], mat2->n_col);
655 }
656 isl_mat_free(mat1);
657 isl_mat_free(mat2);
658 return mat;
659 error:
660 isl_mat_free(mat1);
661 isl_mat_free(mat2);
662 return NULL;
663 }
664
665 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
666 {
667 int i;
668
669 for (i = 0; i < n_row; ++i)
670 if (!isl_int_is_zero(row[i][col]))
671 return i;
672 return -1;
673 }
674
675 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
676 {
677 int i, min = row_first_non_zero(row, n_row, col);
678 if (min < 0)
679 return -1;
680 for (i = min + 1; i < n_row; ++i) {
681 if (isl_int_is_zero(row[i][col]))
682 continue;
683 if (isl_int_abs_lt(row[i][col], row[min][col]))
684 min = i;
685 }
686 return min;
687 }
688
689 static void inv_exchange(struct isl_mat *left, struct isl_mat *right,
690 unsigned i, unsigned j)
691 {
692 left = isl_mat_swap_rows(left, i, j);
693 right = isl_mat_swap_rows(right, i, j);
694 }
695
696 static void inv_oppose(
697 struct isl_mat *left, struct isl_mat *right, unsigned row)
698 {
699 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
700 isl_seq_neg(right->row[row], right->row[row], right->n_col);
701 }
702
703 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
704 unsigned row, unsigned i, isl_int m)
705 {
706 isl_int_neg(m, m);
707 isl_seq_combine(left->row[i]+row,
708 left->ctx->one, left->row[i]+row,
709 m, left->row[row]+row,
710 left->n_col-row);
711 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
712 m, right->row[row], right->n_col);
713 }
714
715 /* Compute inv(left)*right
716 */
717 struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
718 struct isl_mat *right)
719 {
720 int row;
721 isl_int a, b;
722
723 if (!left || !right)
724 goto error;
725
726 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
727 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
728
729 if (left->n_row == 0) {
730 isl_mat_free(left);
731 return right;
732 }
733
734 left = isl_mat_cow(left);
735 right = isl_mat_cow(right);
736 if (!left || !right)
737 goto error;
738
739 isl_int_init(a);
740 isl_int_init(b);
741 for (row = 0; row < left->n_row; ++row) {
742 int pivot, first, i, off;
743 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
744 if (pivot < 0) {
745 isl_int_clear(a);
746 isl_int_clear(b);
747 isl_assert(left->ctx, pivot >= 0, goto error);
748 }
749 pivot += row;
750 if (pivot != row)
751 inv_exchange(left, right, pivot, row);
752 if (isl_int_is_neg(left->row[row][row]))
753 inv_oppose(left, right, row);
754 first = row+1;
755 while ((off = row_first_non_zero(left->row+first,
756 left->n_row-first, row)) != -1) {
757 first += off;
758 isl_int_fdiv_q(a, left->row[first][row],
759 left->row[row][row]);
760 inv_subtract(left, right, row, first, a);
761 if (!isl_int_is_zero(left->row[first][row]))
762 inv_exchange(left, right, row, first);
763 else
764 ++first;
765 }
766 for (i = 0; i < row; ++i) {
767 if (isl_int_is_zero(left->row[i][row]))
768 continue;
769 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
770 isl_int_divexact(b, left->row[i][row], a);
771 isl_int_divexact(a, left->row[row][row], a);
772 isl_int_neg(b, b);
773 isl_seq_combine(left->row[i] + i,
774 a, left->row[i] + i,
775 b, left->row[row] + i,
776 left->n_col - i);
777 isl_seq_combine(right->row[i], a, right->row[i],
778 b, right->row[row], right->n_col);
779 }
780 }
781 isl_int_clear(b);
782
783 isl_int_set(a, left->row[0][0]);
784 for (row = 1; row < left->n_row; ++row)
785 isl_int_lcm(a, a, left->row[row][row]);
786 if (isl_int_is_zero(a)){
787 isl_int_clear(a);
788 isl_assert(left->ctx, 0, goto error);
789 }
790 for (row = 0; row < left->n_row; ++row) {
791 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
792 if (isl_int_is_one(left->row[row][row]))
793 continue;
794 isl_seq_scale(right->row[row], right->row[row],
795 left->row[row][row], right->n_col);
796 }
797 isl_int_clear(a);
798
799 isl_mat_free(left);
800 return right;
801 error:
802 isl_mat_free(left);
803 isl_mat_free(right);
804 return NULL;
805 }
806
807 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
808 {
809 int i;
810
811 for (i = 0; i < mat->n_row; ++i)
812 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
813 }
814
815 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
816 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
817 {
818 int i;
819 isl_int tmp;
820
821 isl_int_init(tmp);
822 for (i = 0; i < mat->n_row; ++i) {
823 isl_int_mul(tmp, m1, mat->row[i][src1]);
824 isl_int_addmul(tmp, m2, mat->row[i][src2]);
825 isl_int_set(mat->row[i][dst], tmp);
826 }
827 isl_int_clear(tmp);
828 }
829
830 struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
831 {
832 struct isl_mat *inv;
833 int row;
834 isl_int a, b;
835
836 mat = isl_mat_cow(mat);
837 if (!mat)
838 return NULL;
839
840 inv = isl_mat_identity(mat->ctx, mat->n_col);
841 inv = isl_mat_cow(inv);
842 if (!inv)
843 goto error;
844
845 isl_int_init(a);
846 isl_int_init(b);
847 for (row = 0; row < mat->n_row; ++row) {
848 int pivot, first, i, off;
849 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
850 if (pivot < 0) {
851 isl_int_clear(a);
852 isl_int_clear(b);
853 isl_assert(mat->ctx, pivot >= 0, goto error);
854 }
855 pivot += row;
856 if (pivot != row)
857 exchange(mat, &inv, NULL, row, pivot, row);
858 if (isl_int_is_neg(mat->row[row][row]))
859 oppose(mat, &inv, NULL, row, row);
860 first = row+1;
861 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
862 mat->n_col-first)) != -1) {
863 first += off;
864 isl_int_fdiv_q(a, mat->row[row][first],
865 mat->row[row][row]);
866 subtract(mat, &inv, NULL, row, row, first, a);
867 if (!isl_int_is_zero(mat->row[row][first]))
868 exchange(mat, &inv, NULL, row, row, first);
869 else
870 ++first;
871 }
872 for (i = 0; i < row; ++i) {
873 if (isl_int_is_zero(mat->row[row][i]))
874 continue;
875 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
876 isl_int_divexact(b, mat->row[row][i], a);
877 isl_int_divexact(a, mat->row[row][row], a);
878 isl_int_neg(a, a);
879 isl_mat_col_combine(mat, i, a, i, b, row);
880 isl_mat_col_combine(inv, i, a, i, b, row);
881 }
882 }
883 isl_int_clear(b);
884
885 isl_int_set(a, mat->row[0][0]);
886 for (row = 1; row < mat->n_row; ++row)
887 isl_int_lcm(a, a, mat->row[row][row]);
888 if (isl_int_is_zero(a)){
889 isl_int_clear(a);
890 goto error;
891 }
892 for (row = 0; row < mat->n_row; ++row) {
893 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
894 if (isl_int_is_one(mat->row[row][row]))
895 continue;
896 isl_mat_col_scale(inv, row, mat->row[row][row]);
897 }
898 isl_int_clear(a);
899
900 isl_mat_free(mat);
901
902 return inv;
903 error:
904 isl_mat_free(mat);
905 isl_mat_free(inv);
906 return NULL;
907 }
908
909 struct isl_mat *isl_mat_transpose(struct isl_mat *mat)
910 {
911 struct isl_mat *transpose = NULL;
912 int i, j;
913
914 if (!mat)
915 return NULL;
916
917 if (mat->n_col == mat->n_row) {
918 mat = isl_mat_cow(mat);
919 if (!mat)
920 return NULL;
921 for (i = 0; i < mat->n_row; ++i)
922 for (j = i + 1; j < mat->n_col; ++j)
923 isl_int_swap(mat->row[i][j], mat->row[j][i]);
924 return mat;
925 }
926 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
927 if (!transpose)
928 goto error;
929 for (i = 0; i < mat->n_row; ++i)
930 for (j = 0; j < mat->n_col; ++j)
931 isl_int_set(transpose->row[j][i], mat->row[i][j]);
932 isl_mat_free(mat);
933 return transpose;
934 error:
935 isl_mat_free(mat);
936 return NULL;
937 }
938
939 struct isl_mat *isl_mat_swap_cols(struct isl_mat *mat, unsigned i, unsigned j)
940 {
941 int r;
942
943 mat = isl_mat_cow(mat);
944 if (!mat)
945 return NULL;
946 isl_assert(mat->ctx, i < mat->n_col, goto error);
947 isl_assert(mat->ctx, j < mat->n_col, goto error);
948
949 for (r = 0; r < mat->n_row; ++r)
950 isl_int_swap(mat->row[r][i], mat->row[r][j]);
951 return mat;
952 error:
953 isl_mat_free(mat);
954 return NULL;
955 }
956
957 struct isl_mat *isl_mat_swap_rows(struct isl_mat *mat, unsigned i, unsigned j)
958 {
959 isl_int *t;
960
961 if (!mat)
962 return NULL;
963 mat = isl_mat_cow(mat);
964 if (!mat)
965 return NULL;
966 t = mat->row[i];
967 mat->row[i] = mat->row[j];
968 mat->row[j] = t;
969 return mat;
970 }
971
972 __isl_give isl_mat *isl_mat_product(__isl_take isl_mat *left,
973 __isl_take isl_mat *right)
974 {
975 int i, j, k;
976 struct isl_mat *prod;
977
978 if (!left || !right)
979 goto error;
980 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
981 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
982 if (!prod)
983 goto error;
984 if (left->n_col == 0) {
985 for (i = 0; i < prod->n_row; ++i)
986 isl_seq_clr(prod->row[i], prod->n_col);
987 isl_mat_free(left);
988 isl_mat_free(right);
989 return prod;
990 }
991 for (i = 0; i < prod->n_row; ++i) {
992 for (j = 0; j < prod->n_col; ++j) {
993 isl_int_mul(prod->row[i][j],
994 left->row[i][0], right->row[0][j]);
995 for (k = 1; k < left->n_col; ++k)
996 isl_int_addmul(prod->row[i][j],
997 left->row[i][k], right->row[k][j]);
998 }
999 }
1000 isl_mat_free(left);
1001 isl_mat_free(right);
1002 return prod;
1003 error:
1004 isl_mat_free(left);
1005 isl_mat_free(right);
1006 return NULL;
1007 }
1008
1009 /* Replace the variables x in the rows q by x' given by x = M x',
1010 * with M the matrix mat.
1011 *
1012 * If the number of new variables is greater than the original
1013 * number of variables, then the rows q have already been
1014 * preextended. If the new number is smaller, then the coefficients
1015 * of the divs, which are not changed, need to be shifted down.
1016 * The row q may be the equalities, the inequalities or the
1017 * div expressions. In the latter case, has_div is true and
1018 * we need to take into account the extra denominator column.
1019 */
1020 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
1021 unsigned n_div, int has_div, struct isl_mat *mat)
1022 {
1023 int i;
1024 struct isl_mat *t;
1025 int e;
1026
1027 if (mat->n_col >= mat->n_row)
1028 e = 0;
1029 else
1030 e = mat->n_row - mat->n_col;
1031 if (has_div)
1032 for (i = 0; i < n; ++i)
1033 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
1034 t = isl_mat_sub_alloc6(mat->ctx, q, 0, n, has_div, mat->n_row);
1035 t = isl_mat_product(t, mat);
1036 if (!t)
1037 return -1;
1038 for (i = 0; i < n; ++i) {
1039 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
1040 isl_seq_cpy(q[i] + has_div + t->n_col,
1041 q[i] + has_div + t->n_col + e, n_div);
1042 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
1043 }
1044 isl_mat_free(t);
1045 return 0;
1046 }
1047
1048 /* Replace the variables x in bset by x' given by x = M x', with
1049 * M the matrix mat.
1050 *
1051 * If there are fewer variables x' then there are x, then we perform
1052 * the transformation in place, which that, in principle,
1053 * this frees up some extra variables as the number
1054 * of columns remains constant, but we would have to extend
1055 * the div array too as the number of rows in this array is assumed
1056 * to be equal to extra.
1057 */
1058 struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
1059 struct isl_mat *mat)
1060 {
1061 struct isl_ctx *ctx;
1062
1063 if (!bset || !mat)
1064 goto error;
1065
1066 ctx = bset->ctx;
1067 bset = isl_basic_set_cow(bset);
1068 if (!bset)
1069 goto error;
1070
1071 isl_assert(ctx, bset->dim->nparam == 0, goto error);
1072 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
1073 isl_assert(ctx, mat->n_col > 0, goto error);
1074
1075 if (mat->n_col > mat->n_row) {
1076 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0, 0, 0);
1077 if (!bset)
1078 goto error;
1079 } else if (mat->n_col < mat->n_row) {
1080 bset->dim = isl_space_cow(bset->dim);
1081 if (!bset->dim)
1082 goto error;
1083 bset->dim->n_out -= mat->n_row - mat->n_col;
1084 }
1085
1086 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
1087 isl_mat_copy(mat)) < 0)
1088 goto error;
1089
1090 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
1091 isl_mat_copy(mat)) < 0)
1092 goto error;
1093
1094 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
1095 goto error2;
1096
1097 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
1098 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
1099 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1100 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1101 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
1102
1103 bset = isl_basic_set_simplify(bset);
1104 bset = isl_basic_set_finalize(bset);
1105
1106 return bset;
1107 error:
1108 isl_mat_free(mat);
1109 error2:
1110 isl_basic_set_free(bset);
1111 return NULL;
1112 }
1113
1114 struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
1115 {
1116 struct isl_ctx *ctx;
1117 int i;
1118
1119 set = isl_set_cow(set);
1120 if (!set)
1121 return NULL;
1122
1123 ctx = set->ctx;
1124 for (i = 0; i < set->n; ++i) {
1125 set->p[i] = isl_basic_set_preimage(set->p[i],
1126 isl_mat_copy(mat));
1127 if (!set->p[i])
1128 goto error;
1129 }
1130 if (mat->n_col != mat->n_row) {
1131 set->dim = isl_space_cow(set->dim);
1132 if (!set->dim)
1133 goto error;
1134 set->dim->n_out += mat->n_col;
1135 set->dim->n_out -= mat->n_row;
1136 }
1137 isl_mat_free(mat);
1138 ISL_F_CLR(set, ISL_SET_NORMALIZED);
1139 return set;
1140 error:
1141 isl_set_free(set);
1142 isl_mat_free(mat);
1143 return NULL;
1144 }
1145
1146 /* Replace the variables x starting at pos in the rows q
1147 * by x' with x = M x' with M the matrix mat.
1148 * That is, replace the corresponding coefficients c by c M.
1149 */
1150 static int transform(isl_ctx *ctx, isl_int **q, unsigned n,
1151 unsigned pos, __isl_take isl_mat *mat)
1152 {
1153 int i;
1154 isl_mat *t;
1155
1156 t = isl_mat_sub_alloc6(ctx, q, 0, n, pos, mat->n_row);
1157 t = isl_mat_product(t, mat);
1158 if (!t)
1159 return -1;
1160 for (i = 0; i < n; ++i)
1161 isl_seq_swp_or_cpy(q[i] + pos, t->row[i], t->n_col);
1162 isl_mat_free(t);
1163 return 0;
1164 }
1165
1166 /* Replace the variables x of type "type" starting at "first" in "bset"
1167 * by x' with x = M x' with M the matrix trans.
1168 * That is, replace the corresponding coefficients c by c M.
1169 *
1170 * The transformation matrix should be a square matrix.
1171 */
1172 __isl_give isl_basic_set *isl_basic_set_transform_dims(
1173 __isl_take isl_basic_set *bset, enum isl_dim_type type, unsigned first,
1174 __isl_take isl_mat *trans)
1175 {
1176 isl_ctx *ctx;
1177 unsigned pos;
1178
1179 bset = isl_basic_set_cow(bset);
1180 if (!bset || !trans)
1181 goto error;
1182
1183 ctx = isl_basic_set_get_ctx(bset);
1184 if (trans->n_row != trans->n_col)
1185 isl_die(trans->ctx, isl_error_invalid,
1186 "expecting square transformation matrix", goto error);
1187 if (first + trans->n_row > isl_basic_set_dim(bset, type))
1188 isl_die(trans->ctx, isl_error_invalid,
1189 "oversized transformation matrix", goto error);
1190
1191 pos = isl_basic_set_offset(bset, type) + first;
1192
1193 if (transform(ctx, bset->eq, bset->n_eq, pos, isl_mat_copy(trans)) < 0)
1194 goto error;
1195 if (transform(ctx, bset->ineq, bset->n_ineq, pos,
1196 isl_mat_copy(trans)) < 0)
1197 goto error;
1198 if (transform(ctx, bset->div, bset->n_div, 1 + pos,
1199 isl_mat_copy(trans)) < 0)
1200 goto error;
1201
1202 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1203 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1204
1205 isl_mat_free(trans);
1206 return bset;
1207 error:
1208 isl_mat_free(trans);
1209 isl_basic_set_free(bset);
1210 return NULL;
1211 }
1212
1213 void isl_mat_print_internal(__isl_keep isl_mat *mat, FILE *out, int indent)
1214 {
1215 int i, j;
1216
1217 if (!mat) {
1218 fprintf(out, "%*snull mat\n", indent, "");
1219 return;
1220 }
1221
1222 if (mat->n_row == 0)
1223 fprintf(out, "%*s[]\n", indent, "");
1224
1225 for (i = 0; i < mat->n_row; ++i) {
1226 if (!i)
1227 fprintf(out, "%*s[[", indent, "");
1228 else
1229 fprintf(out, "%*s[", indent+1, "");
1230 for (j = 0; j < mat->n_col; ++j) {
1231 if (j)
1232 fprintf(out, ",");
1233 isl_int_print(out, mat->row[i][j], 0);
1234 }
1235 if (i == mat->n_row-1)
1236 fprintf(out, "]]\n");
1237 else
1238 fprintf(out, "]\n");
1239 }
1240 }
1241
1242 void isl_mat_dump(__isl_keep isl_mat *mat)
1243 {
1244 isl_mat_print_internal(mat, stderr, 0);
1245 }
1246
1247 struct isl_mat *isl_mat_drop_cols(struct isl_mat *mat, unsigned col, unsigned n)
1248 {
1249 int r;
1250
1251 if (n == 0)
1252 return mat;
1253
1254 mat = isl_mat_cow(mat);
1255 if (!mat)
1256 return NULL;
1257
1258 if (col != mat->n_col-n) {
1259 for (r = 0; r < mat->n_row; ++r)
1260 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1261 mat->n_col - col - n);
1262 }
1263 mat->n_col -= n;
1264 return mat;
1265 }
1266
1267 struct isl_mat *isl_mat_drop_rows(struct isl_mat *mat, unsigned row, unsigned n)
1268 {
1269 int r;
1270
1271 mat = isl_mat_cow(mat);
1272 if (!mat)
1273 return NULL;
1274
1275 for (r = row; r+n < mat->n_row; ++r)
1276 mat->row[r] = mat->row[r+n];
1277
1278 mat->n_row -= n;
1279 return mat;
1280 }
1281
1282 __isl_give isl_mat *isl_mat_insert_cols(__isl_take isl_mat *mat,
1283 unsigned col, unsigned n)
1284 {
1285 isl_mat *ext;
1286
1287 if (!mat)
1288 return NULL;
1289 if (n == 0)
1290 return mat;
1291
1292 ext = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col + n);
1293 if (!ext)
1294 goto error;
1295
1296 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row, 0, 0, col);
1297 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row,
1298 col + n, col, mat->n_col - col);
1299
1300 isl_mat_free(mat);
1301 return ext;
1302 error:
1303 isl_mat_free(mat);
1304 return NULL;
1305 }
1306
1307 __isl_give isl_mat *isl_mat_insert_zero_cols(__isl_take isl_mat *mat,
1308 unsigned first, unsigned n)
1309 {
1310 int i;
1311
1312 if (!mat)
1313 return NULL;
1314 mat = isl_mat_insert_cols(mat, first, n);
1315 if (!mat)
1316 return NULL;
1317
1318 for (i = 0; i < mat->n_row; ++i)
1319 isl_seq_clr(mat->row[i] + first, n);
1320
1321 return mat;
1322 }
1323
1324 __isl_give isl_mat *isl_mat_add_zero_cols(__isl_take isl_mat *mat, unsigned n)
1325 {
1326 if (!mat)
1327 return NULL;
1328
1329 return isl_mat_insert_zero_cols(mat, mat->n_col, n);
1330 }
1331
1332 __isl_give isl_mat *isl_mat_insert_rows(__isl_take isl_mat *mat,
1333 unsigned row, unsigned n)
1334 {
1335 isl_mat *ext;
1336
1337 if (!mat)
1338 return NULL;
1339 if (n == 0)
1340 return mat;
1341
1342 ext = isl_mat_alloc(mat->ctx, mat->n_row + n, mat->n_col);
1343 if (!ext)
1344 goto error;
1345
1346 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, row, 0, 0, mat->n_col);
1347 isl_mat_sub_copy(mat->ctx, ext->row + row + n, mat->row + row,
1348 mat->n_row - row, 0, 0, mat->n_col);
1349
1350 isl_mat_free(mat);
1351 return ext;
1352 error:
1353 isl_mat_free(mat);
1354 return NULL;
1355 }
1356
1357 __isl_give isl_mat *isl_mat_add_rows(__isl_take isl_mat *mat, unsigned n)
1358 {
1359 if (!mat)
1360 return NULL;
1361
1362 return isl_mat_insert_rows(mat, mat->n_row, n);
1363 }
1364
1365 __isl_give isl_mat *isl_mat_insert_zero_rows(__isl_take isl_mat *mat,
1366 unsigned row, unsigned n)
1367 {
1368 int i;
1369
1370 mat = isl_mat_insert_rows(mat, row, n);
1371 if (!mat)
1372 return NULL;
1373
1374 for (i = 0; i < n; ++i)
1375 isl_seq_clr(mat->row[row + i], mat->n_col);
1376
1377 return mat;
1378 }
1379
1380 __isl_give isl_mat *isl_mat_add_zero_rows(__isl_take isl_mat *mat, unsigned n)
1381 {
1382 if (!mat)
1383 return NULL;
1384
1385 return isl_mat_insert_zero_rows(mat, mat->n_row, n);
1386 }
1387
1388 void isl_mat_col_submul(struct isl_mat *mat,
1389 int dst_col, isl_int f, int src_col)
1390 {
1391 int i;
1392
1393 for (i = 0; i < mat->n_row; ++i)
1394 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1395 }
1396
1397 void isl_mat_col_add(__isl_keep isl_mat *mat, int dst_col, int src_col)
1398 {
1399 int i;
1400
1401 if (!mat)
1402 return;
1403
1404 for (i = 0; i < mat->n_row; ++i)
1405 isl_int_add(mat->row[i][dst_col],
1406 mat->row[i][dst_col], mat->row[i][src_col]);
1407 }
1408
1409 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1410 {
1411 int i;
1412
1413 for (i = 0; i < mat->n_row; ++i)
1414 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1415 }
1416
1417 struct isl_mat *isl_mat_unimodular_complete(struct isl_mat *M, int row)
1418 {
1419 int r;
1420 struct isl_mat *H = NULL, *Q = NULL;
1421
1422 if (!M)
1423 return NULL;
1424
1425 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1426 M->n_row = row;
1427 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1428 M->n_row = M->n_col;
1429 if (!H)
1430 goto error;
1431 for (r = 0; r < row; ++r)
1432 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1433 for (r = row; r < M->n_row; ++r)
1434 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1435 isl_mat_free(H);
1436 isl_mat_free(Q);
1437 return M;
1438 error:
1439 isl_mat_free(H);
1440 isl_mat_free(Q);
1441 isl_mat_free(M);
1442 return NULL;
1443 }
1444
1445 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1446 __isl_take isl_mat *bot)
1447 {
1448 struct isl_mat *mat;
1449
1450 if (!top || !bot)
1451 goto error;
1452
1453 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1454 if (top->n_row == 0) {
1455 isl_mat_free(top);
1456 return bot;
1457 }
1458 if (bot->n_row == 0) {
1459 isl_mat_free(bot);
1460 return top;
1461 }
1462
1463 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1464 if (!mat)
1465 goto error;
1466 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1467 0, 0, mat->n_col);
1468 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1469 0, 0, mat->n_col);
1470 isl_mat_free(top);
1471 isl_mat_free(bot);
1472 return mat;
1473 error:
1474 isl_mat_free(top);
1475 isl_mat_free(bot);
1476 return NULL;
1477 }
1478
1479 int isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
1480 {
1481 int i;
1482
1483 if (!mat1 || !mat2)
1484 return -1;
1485
1486 if (mat1->n_row != mat2->n_row)
1487 return 0;
1488
1489 if (mat1->n_col != mat2->n_col)
1490 return 0;
1491
1492 for (i = 0; i < mat1->n_row; ++i)
1493 if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
1494 return 0;
1495
1496 return 1;
1497 }
1498
1499 __isl_give isl_mat *isl_mat_from_row_vec(__isl_take isl_vec *vec)
1500 {
1501 struct isl_mat *mat;
1502
1503 if (!vec)
1504 return NULL;
1505 mat = isl_mat_alloc(vec->ctx, 1, vec->size);
1506 if (!mat)
1507 goto error;
1508
1509 isl_seq_cpy(mat->row[0], vec->el, vec->size);
1510
1511 isl_vec_free(vec);
1512 return mat;
1513 error:
1514 isl_vec_free(vec);
1515 return NULL;
1516 }
1517
1518 __isl_give isl_mat *isl_mat_vec_concat(__isl_take isl_mat *top,
1519 __isl_take isl_vec *bot)
1520 {
1521 return isl_mat_concat(top, isl_mat_from_row_vec(bot));
1522 }
1523
1524 __isl_give isl_mat *isl_mat_move_cols(__isl_take isl_mat *mat,
1525 unsigned dst_col, unsigned src_col, unsigned n)
1526 {
1527 isl_mat *res;
1528
1529 if (!mat)
1530 return NULL;
1531 if (n == 0 || dst_col == src_col)
1532 return mat;
1533
1534 res = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
1535 if (!res)
1536 goto error;
1537
1538 if (dst_col < src_col) {
1539 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1540 0, 0, dst_col);
1541 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1542 dst_col, src_col, n);
1543 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1544 dst_col + n, dst_col, src_col - dst_col);
1545 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1546 src_col + n, src_col + n,
1547 res->n_col - src_col - n);
1548 } else {
1549 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1550 0, 0, src_col);
1551 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1552 src_col, src_col + n, dst_col - src_col);
1553 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1554 dst_col, src_col, n);
1555 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1556 dst_col + n, dst_col + n,
1557 res->n_col - dst_col - n);
1558 }
1559 isl_mat_free(mat);
1560
1561 return res;
1562 error:
1563 isl_mat_free(mat);
1564 return NULL;
1565 }
1566
1567 void isl_mat_gcd(__isl_keep isl_mat *mat, isl_int *gcd)
1568 {
1569 int i;
1570 isl_int g;
1571
1572 isl_int_set_si(*gcd, 0);
1573 if (!mat)
1574 return;
1575
1576 isl_int_init(g);
1577 for (i = 0; i < mat->n_row; ++i) {
1578 isl_seq_gcd(mat->row[i], mat->n_col, &g);
1579 isl_int_gcd(*gcd, *gcd, g);
1580 }
1581 isl_int_clear(g);
1582 }
1583
1584 __isl_give isl_mat *isl_mat_scale_down(__isl_take isl_mat *mat, isl_int m)
1585 {
1586 int i;
1587
1588 if (isl_int_is_one(m))
1589 return mat;
1590
1591 mat = isl_mat_cow(mat);
1592 if (!mat)
1593 return NULL;
1594
1595 for (i = 0; i < mat->n_row; ++i)
1596 isl_seq_scale_down(mat->row[i], mat->row[i], m, mat->n_col);
1597
1598 return mat;
1599 }
1600
1601 __isl_give isl_mat *isl_mat_scale_down_row(__isl_take isl_mat *mat, int row,
1602 isl_int m)
1603 {
1604 if (isl_int_is_one(m))
1605 return mat;
1606
1607 mat = isl_mat_cow(mat);
1608 if (!mat)
1609 return NULL;
1610
1611 isl_seq_scale_down(mat->row[row], mat->row[row], m, mat->n_col);
1612
1613 return mat;
1614 }
1615
1616 __isl_give isl_mat *isl_mat_normalize(__isl_take isl_mat *mat)
1617 {
1618 isl_int gcd;
1619
1620 if (!mat)
1621 return NULL;
1622
1623 isl_int_init(gcd);
1624 isl_mat_gcd(mat, &gcd);
1625 mat = isl_mat_scale_down(mat, gcd);
1626 isl_int_clear(gcd);
1627
1628 return mat;
1629 }
1630
1631 __isl_give isl_mat *isl_mat_normalize_row(__isl_take isl_mat *mat, int row)
1632 {
1633 mat = isl_mat_cow(mat);
1634 if (!mat)
1635 return NULL;
1636
1637 isl_seq_normalize(mat->ctx, mat->row[row], mat->n_col);
1638
1639 return mat;
1640 }
1641
1642 /* Number of initial non-zero columns.
1643 */
1644 int isl_mat_initial_non_zero_cols(__isl_keep isl_mat *mat)
1645 {
1646 int i;
1647
1648 if (!mat)
1649 return -1;
1650
1651 for (i = 0; i < mat->n_col; ++i)
1652 if (row_first_non_zero(mat->row, mat->n_row, i) < 0)
1653 break;
1654
1655 return i;
1656 }
Integer set library