?  search:
summary | log | graphiclog1 | graphiclog2 | commit | commitdiff | tree | refs | edit | fork
blame | history | raw | HEAD
isl_div.c: add missing include
[isl.git] / isl_mat.c
blob5cc25261b9f8d5f2959190224f1cb8ec86dd3f35
1 #include "isl_dim.h"
2 #include "isl_seq.h"
3 #include "isl_mat.h"
4 #include "isl_map_private.h"
5
6 struct isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
7 unsigned n_row, unsigned n_col)
8 {
9 int i;
10 struct isl_mat *mat;
11
12 mat = isl_alloc_type(ctx, struct isl_mat);
13 if (!mat)
14 return NULL;
15
16 mat->row = NULL;
17 mat->block = isl_blk_alloc(ctx, n_row * n_col);
18 if (isl_blk_is_error(mat->block))
19 goto error;
20 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
21 if (!mat->row)
22 goto error;
23
24 for (i = 0; i < n_row; ++i)
25 mat->row[i] = mat->block.data + i * n_col;
26
27 mat->ctx = ctx;
28 isl_ctx_ref(ctx);
29 mat->ref = 1;
30 mat->n_row = n_row;
31 mat->n_col = n_col;
32 mat->max_col = n_col;
33 mat->flags = 0;
34
35 return mat;
36 error:
37 isl_blk_free(ctx, mat->block);
38 free(mat);
39 return NULL;
40 }
41
42 struct isl_mat *isl_mat_extend(struct isl_mat *mat,
43 unsigned n_row, unsigned n_col)
44 {
45 int i;
46 isl_int *old;
47
48 if (!mat)
49 return NULL;
50
51 if (mat->max_col >= n_col && mat->n_row >= n_row) {
52 if (mat->n_col < n_col)
53 mat->n_col = n_col;
54 return mat;
55 }
56
57 if (mat->max_col < n_col) {
58 struct isl_mat *new_mat;
59
60 if (n_row < mat->n_row)
61 n_row = mat->n_row;
62 new_mat = isl_mat_alloc(mat->ctx, n_row, n_col);
63 if (!new_mat)
64 goto error;
65 for (i = 0; i < mat->n_row; ++i)
66 isl_seq_cpy(new_mat->row[i], mat->row[i], mat->n_col);
67 isl_mat_free(mat);
68 return new_mat;
69 }
70
71 mat = isl_mat_cow(mat);
72 if (!mat)
73 goto error;
74
75 assert(mat->ref == 1);
76 old = mat->block.data;
77 mat->block = isl_blk_extend(mat->ctx, mat->block, n_row * mat->max_col);
78 if (isl_blk_is_error(mat->block))
79 goto error;
80 mat->row = isl_realloc_array(mat->ctx, mat->row, isl_int *, n_row);
81 if (!mat->row)
82 goto error;
83
84 for (i = 0; i < mat->n_row; ++i)
85 mat->row[i] = mat->block.data + (mat->row[i] - old);
86 for (i = mat->n_row; i < n_row; ++i)
87 mat->row[i] = mat->block.data + i * mat->max_col;
88 mat->n_row = n_row;
89 if (mat->n_col < n_col)
90 mat->n_col = n_col;
91
92 return mat;
93 error:
94 isl_mat_free(mat);
95 return NULL;
96 }
97
98 struct isl_mat *isl_mat_sub_alloc(struct isl_ctx *ctx, isl_int **row,
99 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
100 {
101 int i;
102 struct isl_mat *mat;
103
104 mat = isl_alloc_type(ctx, struct isl_mat);
105 if (!mat)
106 return NULL;
107 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
108 if (!mat->row)
109 goto error;
110 for (i = 0; i < n_row; ++i)
111 mat->row[i] = row[first_row+i] + first_col;
112 mat->ctx = ctx;
113 isl_ctx_ref(ctx);
114 mat->ref = 1;
115 mat->n_row = n_row;
116 mat->n_col = n_col;
117 mat->block = isl_blk_empty();
118 mat->flags = ISL_MAT_BORROWED;
119 return mat;
120 error:
121 free(mat);
122 return NULL;
123 }
124
125 void isl_mat_sub_copy(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
126 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
127 {
128 int i;
129
130 for (i = 0; i < n_row; ++i)
131 isl_seq_cpy(dst[i]+dst_col, src[i]+src_col, n_col);
132 }
133
134 void isl_mat_sub_neg(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
135 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
136 {
137 int i;
138
139 for (i = 0; i < n_row; ++i)
140 isl_seq_neg(dst[i]+dst_col, src[i]+src_col, n_col);
141 }
142
143 struct isl_mat *isl_mat_copy(struct isl_mat *mat)
144 {
145 if (!mat)
146 return NULL;
147
148 mat->ref++;
149 return mat;
150 }
151
152 struct isl_mat *isl_mat_dup(struct isl_mat *mat)
153 {
154 int i;
155 struct isl_mat *mat2;
156
157 if (!mat)
158 return NULL;
159 mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
160 if (!mat2)
161 return NULL;
162 for (i = 0; i < mat->n_row; ++i)
163 isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);
164 return mat2;
165 }
166
167 struct isl_mat *isl_mat_cow(struct isl_mat *mat)
168 {
169 struct isl_mat *mat2;
170 if (!mat)
171 return NULL;
172
173 if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))
174 return mat;
175
176 mat2 = isl_mat_dup(mat);
177 isl_mat_free(mat);
178 return mat2;
179 }
180
181 void isl_mat_free(struct isl_mat *mat)
182 {
183 if (!mat)
184 return;
185
186 if (--mat->ref > 0)
187 return;
188
189 if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))
190 isl_blk_free(mat->ctx, mat->block);
191 isl_ctx_deref(mat->ctx);
192 free(mat->row);
193 free(mat);
194 }
195
196 struct isl_mat *isl_mat_identity(struct isl_ctx *ctx, unsigned n_row)
197 {
198 int i;
199 struct isl_mat *mat;
200
201 mat = isl_mat_alloc(ctx, n_row, n_row);
202 if (!mat)
203 return NULL;
204 for (i = 0; i < n_row; ++i) {
205 isl_seq_clr(mat->row[i], i);
206 isl_int_set_si(mat->row[i][i], 1);
207 isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
208 }
209
210 return mat;
211 }
212
213 struct isl_vec *isl_mat_vec_product(struct isl_mat *mat, struct isl_vec *vec)
214 {
215 int i;
216 struct isl_vec *prod;
217
218 if (!mat || !vec)
219 goto error;
220
221 isl_assert(ctx, mat->n_col == vec->size, goto error);
222
223 prod = isl_vec_alloc(mat->ctx, mat->n_row);
224 if (!prod)
225 goto error;
226
227 for (i = 0; i < prod->size; ++i)
228 isl_seq_inner_product(mat->row[i], vec->el, vec->size,
229 &prod->block.data[i]);
230 isl_mat_free(mat);
231 isl_vec_free(vec);
232 return prod;
233 error:
234 isl_mat_free(mat);
235 isl_vec_free(vec);
236 return NULL;
237 }
238
239 struct isl_vec *isl_vec_mat_product(struct isl_vec *vec, struct isl_mat *mat)
240 {
241 int i, j;
242 struct isl_vec *prod;
243
244 if (!mat || !vec)
245 goto error;
246
247 isl_assert(ctx, mat->n_row == vec->size, goto error);
248
249 prod = isl_vec_alloc(mat->ctx, mat->n_col);
250 if (!prod)
251 goto error;
252
253 for (i = 0; i < prod->size; ++i) {
254 isl_int_set_si(prod->el[i], 0);
255 for (j = 0; j < vec->size; ++j)
256 isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);
257 }
258 isl_mat_free(mat);
259 isl_vec_free(vec);
260 return prod;
261 error:
262 isl_mat_free(mat);
263 isl_vec_free(vec);
264 return NULL;
265 }
266
267 struct isl_mat *isl_mat_aff_direct_sum(struct isl_mat *left,
268 struct isl_mat *right)
269 {
270 int i;
271 struct isl_mat *sum;
272
273 if (!left || !right)
274 goto error;
275
276 isl_assert(ctx, left->n_row == right->n_row, goto error);
277 isl_assert(ctx, left->n_row >= 1, goto error);
278 isl_assert(ctx, left->n_col >= 1, goto error);
279 isl_assert(ctx, right->n_col >= 1, goto error);
280 isl_assert(ctx,
281 isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,
282 goto error);
283 isl_assert(ctx,
284 isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
285 goto error);
286
287 sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);
288 if (!sum)
289 goto error;
290 isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);
291 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
292 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
293
294 isl_seq_clr(sum->row[0]+1, sum->n_col-1);
295 for (i = 1; i < sum->n_row; ++i) {
296 isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);
297 isl_int_addmul(sum->row[i][0],
298 right->row[0][0], right->row[i][0]);
299 isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],
300 left->n_col-1);
301 isl_seq_scale(sum->row[i]+left->n_col,
302 right->row[i]+1, right->row[0][0],
303 right->n_col-1);
304 }
305
306 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
307 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
308 isl_mat_free(left);
309 isl_mat_free(right);
310 return sum;
311 error:
312 isl_mat_free(left);
313 isl_mat_free(right);
314 return NULL;
315 }
316
317 static void exchange(struct isl_mat *M, struct isl_mat **U,
318 struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
319 {
320 int r;
321 for (r = row; r < M->n_row; ++r)
322 isl_int_swap(M->row[r][i], M->row[r][j]);
323 if (U) {
324 for (r = 0; r < (*U)->n_row; ++r)
325 isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
326 }
327 if (Q)
328 isl_mat_swap_rows(*Q, i, j);
329 }
330
331 static void subtract(struct isl_mat *M, struct isl_mat **U,
332 struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)
333 {
334 int r;
335 for (r = row; r < M->n_row; ++r)
336 isl_int_submul(M->row[r][j], m, M->row[r][i]);
337 if (U) {
338 for (r = 0; r < (*U)->n_row; ++r)
339 isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);
340 }
341 if (Q) {
342 for (r = 0; r < (*Q)->n_col; ++r)
343 isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);
344 }
345 }
346
347 static void oppose(struct isl_mat *M, struct isl_mat **U,
348 struct isl_mat **Q, unsigned row, unsigned col)
349 {
350 int r;
351 for (r = row; r < M->n_row; ++r)
352 isl_int_neg(M->row[r][col], M->row[r][col]);
353 if (U) {
354 for (r = 0; r < (*U)->n_row; ++r)
355 isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);
356 }
357 if (Q)
358 isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);
359 }
360
361 /* Given matrix M, compute
362 *
363 * M U = H
364 * M = H Q
365 *
366 * with U and Q unimodular matrices and H a matrix in column echelon form
367 * such that on each echelon row the entries in the non-echelon column
368 * are non-negative (if neg == 0) or non-positive (if neg == 1)
369 * and stricly smaller (in absolute value) than the entries in the echelon
370 * column.
371 * If U or Q are NULL, then these matrices are not computed.
372 */
373 struct isl_mat *isl_mat_left_hermite(struct isl_mat *M, int neg,
374 struct isl_mat **U, struct isl_mat **Q)
375 {
376 isl_int c;
377 int row, col;
378
379 if (U)
380 *U = NULL;
381 if (Q)
382 *Q = NULL;
383 if (!M)
384 goto error;
385 M = isl_mat_cow(M);
386 if (!M)
387 goto error;
388 if (U) {
389 *U = isl_mat_identity(M->ctx, M->n_col);
390 if (!*U)
391 goto error;
392 }
393 if (Q) {
394 *Q = isl_mat_identity(M->ctx, M->n_col);
395 if (!*Q)
396 goto error;
397 }
398
399 col = 0;
400 isl_int_init(c);
401 for (row = 0; row < M->n_row; ++row) {
402 int first, i, off;
403 first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);
404 if (first == -1)
405 continue;
406 first += col;
407 if (first != col)
408 exchange(M, U, Q, row, first, col);
409 if (isl_int_is_neg(M->row[row][col]))
410 oppose(M, U, Q, row, col);
411 first = col+1;
412 while ((off = isl_seq_first_non_zero(M->row[row]+first,
413 M->n_col-first)) != -1) {
414 first += off;
415 isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);
416 subtract(M, U, Q, row, col, first, c);
417 if (!isl_int_is_zero(M->row[row][first]))
418 exchange(M, U, Q, row, first, col);
419 else
420 ++first;
421 }
422 for (i = 0; i < col; ++i) {
423 if (isl_int_is_zero(M->row[row][i]))
424 continue;
425 if (neg)
426 isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);
427 else
428 isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);
429 if (isl_int_is_zero(c))
430 continue;
431 subtract(M, U, Q, row, col, i, c);
432 }
433 ++col;
434 }
435 isl_int_clear(c);
436
437 return M;
438 error:
439 if (Q) {
440 isl_mat_free(*Q);
441 *Q = NULL;
442 }
443 if (U) {
444 isl_mat_free(*U);
445 *U = NULL;
446 }
447 return NULL;
448 }
449
450 struct isl_mat *isl_mat_right_kernel(struct isl_mat *mat)
451 {
452 int i, rank;
453 struct isl_mat *U = NULL;
454 struct isl_mat *K;
455
456 mat = isl_mat_left_hermite(mat, 0, &U, NULL);
457 if (!mat || !U)
458 goto error;
459
460 for (i = 0, rank = 0; rank < mat->n_col; ++rank) {
461 while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))
462 ++i;
463 if (i >= mat->n_row)
464 break;
465 }
466 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
467 if (!K)
468 goto error;
469 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
470 isl_mat_free(mat);
471 isl_mat_free(U);
472 return K;
473 error:
474 isl_mat_free(mat);
475 isl_mat_free(U);
476 return NULL;
477 }
478
479 struct isl_mat *isl_mat_lin_to_aff(struct isl_mat *mat)
480 {
481 int i;
482 struct isl_mat *mat2;
483
484 if (!mat)
485 return NULL;
486 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
487 if (!mat2)
488 return NULL;
489 isl_int_set_si(mat2->row[0][0], 1);
490 isl_seq_clr(mat2->row[0]+1, mat->n_col);
491 for (i = 0; i < mat->n_row; ++i) {
492 isl_int_set_si(mat2->row[1+i][0], 0);
493 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
494 }
495 isl_mat_free(mat);
496 return mat2;
497 }
498
499 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
500 {
501 int i;
502
503 for (i = 0; i < n_row; ++i)
504 if (!isl_int_is_zero(row[i][col]))
505 return i;
506 return -1;
507 }
508
509 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
510 {
511 int i, min = row_first_non_zero(row, n_row, col);
512 if (min < 0)
513 return -1;
514 for (i = min + 1; i < n_row; ++i) {
515 if (isl_int_is_zero(row[i][col]))
516 continue;
517 if (isl_int_abs_lt(row[i][col], row[min][col]))
518 min = i;
519 }
520 return min;
521 }
522
523 static void inv_exchange(struct isl_mat *left, struct isl_mat *right,
524 unsigned i, unsigned j)
525 {
526 left = isl_mat_swap_rows(left, i, j);
527 right = isl_mat_swap_rows(right, i, j);
528 }
529
530 static void inv_oppose(
531 struct isl_mat *left, struct isl_mat *right, unsigned row)
532 {
533 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
534 isl_seq_neg(right->row[row], right->row[row], right->n_col);
535 }
536
537 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
538 unsigned row, unsigned i, isl_int m)
539 {
540 isl_int_neg(m, m);
541 isl_seq_combine(left->row[i]+row,
542 left->ctx->one, left->row[i]+row,
543 m, left->row[row]+row,
544 left->n_col-row);
545 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
546 m, right->row[row], right->n_col);
547 }
548
549 /* Compute inv(left)*right
550 */
551 struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
552 struct isl_mat *right)
553 {
554 int row;
555 isl_int a, b;
556
557 if (!left || !right)
558 goto error;
559
560 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
561 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
562
563 if (left->n_row == 0) {
564 isl_mat_free(left);
565 return right;
566 }
567
568 left = isl_mat_cow(left);
569 right = isl_mat_cow(right);
570 if (!left || !right)
571 goto error;
572
573 isl_int_init(a);
574 isl_int_init(b);
575 for (row = 0; row < left->n_row; ++row) {
576 int pivot, first, i, off;
577 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
578 if (pivot < 0) {
579 isl_int_clear(a);
580 isl_int_clear(b);
581 isl_assert(ctx, pivot >= 0, goto error);
582 }
583 pivot += row;
584 if (pivot != row)
585 inv_exchange(left, right, pivot, row);
586 if (isl_int_is_neg(left->row[row][row]))
587 inv_oppose(left, right, row);
588 first = row+1;
589 while ((off = row_first_non_zero(left->row+first,
590 left->n_row-first, row)) != -1) {
591 first += off;
592 isl_int_fdiv_q(a, left->row[first][row],
593 left->row[row][row]);
594 inv_subtract(left, right, row, first, a);
595 if (!isl_int_is_zero(left->row[first][row]))
596 inv_exchange(left, right, row, first);
597 else
598 ++first;
599 }
600 for (i = 0; i < row; ++i) {
601 if (isl_int_is_zero(left->row[i][row]))
602 continue;
603 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
604 isl_int_divexact(b, left->row[i][row], a);
605 isl_int_divexact(a, left->row[row][row], a);
606 isl_int_neg(a, a);
607 isl_seq_combine(left->row[i]+row,
608 a, left->row[i]+row,
609 b, left->row[row]+row,
610 left->n_col-row);
611 isl_seq_combine(right->row[i], a, right->row[i],
612 b, right->row[row], right->n_col);
613 }
614 }
615 isl_int_clear(b);
616
617 isl_int_set(a, left->row[0][0]);
618 for (row = 1; row < left->n_row; ++row)
619 isl_int_lcm(a, a, left->row[row][row]);
620 if (isl_int_is_zero(a)){
621 isl_int_clear(a);
622 isl_assert(ctx, 0, goto error);
623 }
624 for (row = 0; row < left->n_row; ++row) {
625 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
626 if (isl_int_is_one(left->row[row][row]))
627 continue;
628 isl_seq_scale(right->row[row], right->row[row],
629 left->row[row][row], right->n_col);
630 }
631 isl_int_clear(a);
632
633 isl_mat_free(left);
634 return right;
635 error:
636 isl_mat_free(left);
637 isl_mat_free(right);
638 return NULL;
639 }
640
641 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
642 {
643 int i;
644
645 for (i = 0; i < mat->n_row; ++i)
646 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
647 }
648
649 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
650 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
651 {
652 int i;
653 isl_int tmp;
654
655 isl_int_init(tmp);
656 for (i = 0; i < mat->n_row; ++i) {
657 isl_int_mul(tmp, m1, mat->row[i][src1]);
658 isl_int_addmul(tmp, m2, mat->row[i][src2]);
659 isl_int_set(mat->row[i][dst], tmp);
660 }
661 isl_int_clear(tmp);
662 }
663
664 struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
665 {
666 struct isl_mat *inv;
667 int row;
668 isl_int a, b;
669
670 mat = isl_mat_cow(mat);
671 if (!mat)
672 return NULL;
673
674 inv = isl_mat_identity(mat->ctx, mat->n_col);
675 inv = isl_mat_cow(inv);
676 if (!inv)
677 goto error;
678
679 isl_int_init(a);
680 isl_int_init(b);
681 for (row = 0; row < mat->n_row; ++row) {
682 int pivot, first, i, off;
683 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
684 if (pivot < 0) {
685 isl_int_clear(a);
686 isl_int_clear(b);
687 goto error;
688 }
689 pivot += row;
690 if (pivot != row)
691 exchange(mat, &inv, NULL, row, pivot, row);
692 if (isl_int_is_neg(mat->row[row][row]))
693 oppose(mat, &inv, NULL, row, row);
694 first = row+1;
695 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
696 mat->n_col-first)) != -1) {
697 first += off;
698 isl_int_fdiv_q(a, mat->row[row][first],
699 mat->row[row][row]);
700 subtract(mat, &inv, NULL, row, row, first, a);
701 if (!isl_int_is_zero(mat->row[row][first]))
702 exchange(mat, &inv, NULL, row, row, first);
703 else
704 ++first;
705 }
706 for (i = 0; i < row; ++i) {
707 if (isl_int_is_zero(mat->row[row][i]))
708 continue;
709 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
710 isl_int_divexact(b, mat->row[row][i], a);
711 isl_int_divexact(a, mat->row[row][row], a);
712 isl_int_neg(a, a);
713 isl_mat_col_combine(mat, i, a, i, b, row);
714 isl_mat_col_combine(inv, i, a, i, b, row);
715 }
716 }
717 isl_int_clear(b);
718
719 isl_int_set(a, mat->row[0][0]);
720 for (row = 1; row < mat->n_row; ++row)
721 isl_int_lcm(a, a, mat->row[row][row]);
722 if (isl_int_is_zero(a)){
723 isl_int_clear(a);
724 goto error;
725 }
726 for (row = 0; row < mat->n_row; ++row) {
727 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
728 if (isl_int_is_one(mat->row[row][row]))
729 continue;
730 isl_mat_col_scale(inv, row, mat->row[row][row]);
731 }
732 isl_int_clear(a);
733
734 isl_mat_free(mat);
735
736 return inv;
737 error:
738 isl_mat_free(mat);
739 return NULL;
740 }
741
742 struct isl_mat *isl_mat_transpose(struct isl_mat *mat)
743 {
744 struct isl_mat *transpose = NULL;
745 int i, j;
746
747 if (mat->n_col == mat->n_row) {
748 mat = isl_mat_cow(mat);
749 if (!mat)
750 return NULL;
751 for (i = 0; i < mat->n_row; ++i)
752 for (j = i + 1; j < mat->n_col; ++j)
753 isl_int_swap(mat->row[i][j], mat->row[j][i]);
754 return mat;
755 }
756 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
757 if (!transpose)
758 goto error;
759 for (i = 0; i < mat->n_row; ++i)
760 for (j = 0; j < mat->n_col; ++j)
761 isl_int_set(transpose->row[j][i], mat->row[i][j]);
762 isl_mat_free(mat);
763 return transpose;
764 error:
765 isl_mat_free(mat);
766 return NULL;
767 }
768
769 struct isl_mat *isl_mat_swap_cols(struct isl_mat *mat, unsigned i, unsigned j)
770 {
771 int r;
772
773 mat = isl_mat_cow(mat);
774 if (!mat)
775 return NULL;
776 isl_assert(ctx, i < mat->n_col, goto error);
777 isl_assert(ctx, j < mat->n_col, goto error);
778
779 for (r = 0; r < mat->n_row; ++r)
780 isl_int_swap(mat->row[r][i], mat->row[r][j]);
781 return mat;
782 error:
783 isl_mat_free(mat);
784 return NULL;
785 }
786
787 struct isl_mat *isl_mat_swap_rows(struct isl_mat *mat, unsigned i, unsigned j)
788 {
789 isl_int *t;
790
791 if (!mat)
792 return NULL;
793 mat = isl_mat_cow(mat);
794 if (!mat)
795 return NULL;
796 t = mat->row[i];
797 mat->row[i] = mat->row[j];
798 mat->row[j] = t;
799 return mat;
800 }
801
802 struct isl_mat *isl_mat_product(struct isl_mat *left, struct isl_mat *right)
803 {
804 int i, j, k;
805 struct isl_mat *prod;
806
807 if (!left || !right)
808 goto error;
809 isl_assert(ctx, left->n_col == right->n_row, goto error);
810 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
811 if (!prod)
812 goto error;
813 if (left->n_col == 0) {
814 for (i = 0; i < prod->n_row; ++i)
815 isl_seq_clr(prod->row[i], prod->n_col);
816 return prod;
817 }
818 for (i = 0; i < prod->n_row; ++i) {
819 for (j = 0; j < prod->n_col; ++j) {
820 isl_int_mul(prod->row[i][j],
821 left->row[i][0], right->row[0][j]);
822 for (k = 1; k < left->n_col; ++k)
823 isl_int_addmul(prod->row[i][j],
824 left->row[i][k], right->row[k][j]);
825 }
826 }
827 isl_mat_free(left);
828 isl_mat_free(right);
829 return prod;
830 error:
831 isl_mat_free(left);
832 isl_mat_free(right);
833 return NULL;
834 }
835
836 /* Replace the variables x in the rows q by x' given by x = M x',
837 * with M the matrix mat.
838 *
839 * If the number of new variables is greater than the original
840 * number of variables, then the rows q have already been
841 * preextended. If the new number is smaller, then the coefficients
842 * of the divs, which are not changed, need to be shifted down.
843 * The row q may be the equalities, the inequalities or the
844 * div expressions. In the latter case, has_div is true and
845 * we need to take into account the extra denominator column.
846 */
847 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
848 unsigned n_div, int has_div, struct isl_mat *mat)
849 {
850 int i;
851 struct isl_mat *t;
852 int e;
853
854 if (mat->n_col >= mat->n_row)
855 e = 0;
856 else
857 e = mat->n_row - mat->n_col;
858 if (has_div)
859 for (i = 0; i < n; ++i)
860 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
861 t = isl_mat_sub_alloc(mat->ctx, q, 0, n, has_div, mat->n_row);
862 t = isl_mat_product(t, mat);
863 if (!t)
864 return -1;
865 for (i = 0; i < n; ++i) {
866 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
867 isl_seq_cpy(q[i] + has_div + t->n_col,
868 q[i] + has_div + t->n_col + e, n_div);
869 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
870 }
871 isl_mat_free(t);
872 return 0;
873 }
874
875 /* Replace the variables x in bset by x' given by x = M x', with
876 * M the matrix mat.
877 *
878 * If there are fewer variables x' then there are x, then we perform
879 * the transformation in place, which that, in principle,
880 * this frees up some extra variables as the number
881 * of columns remains constant, but we would have to extend
882 * the div array too as the number of rows in this array is assumed
883 * to be equal to extra.
884 */
885 struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
886 struct isl_mat *mat)
887 {
888 struct isl_ctx *ctx;
889
890 if (!bset || !mat)
891 goto error;
892
893 ctx = bset->ctx;
894 bset = isl_basic_set_cow(bset);
895 if (!bset)
896 goto error;
897
898 isl_assert(ctx, bset->dim->nparam == 0, goto error);
899 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
900
901 if (mat->n_col > mat->n_row)
902 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0,
903 0, 0);
904 else if (mat->n_col < mat->n_row) {
905 bset->dim = isl_dim_cow(bset->dim);
906 if (!bset->dim)
907 goto error;
908 bset->dim->n_out -= mat->n_row - mat->n_col;
909 }
910
911 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
912 isl_mat_copy(mat)) < 0)
913 goto error;
914
915 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
916 isl_mat_copy(mat)) < 0)
917 goto error;
918
919 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
920 goto error2;
921
922 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
923 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
924 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
925 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
926 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
927
928 bset = isl_basic_set_simplify(bset);
929 bset = isl_basic_set_finalize(bset);
930
931 return bset;
932 error:
933 isl_mat_free(mat);
934 error2:
935 isl_basic_set_free(bset);
936 return NULL;
937 }
938
939 struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
940 {
941 struct isl_ctx *ctx;
942 int i;
943
944 set = isl_set_cow(set);
945 if (!set)
946 return NULL;
947
948 ctx = set->ctx;
949 for (i = 0; i < set->n; ++i) {
950 set->p[i] = isl_basic_set_preimage(set->p[i],
951 isl_mat_copy(mat));
952 if (!set->p[i])
953 goto error;
954 }
955 if (mat->n_col != mat->n_row) {
956 set->dim = isl_dim_cow(set->dim);
957 if (!set->dim)
958 goto error;
959 set->dim->n_out += mat->n_col;
960 set->dim->n_out -= mat->n_row;
961 }
962 isl_mat_free(mat);
963 ISL_F_CLR(set, ISL_SET_NORMALIZED);
964 return set;
965 error:
966 isl_set_free(set);
967 isl_mat_free(mat);
968 return NULL;
969 }
970
971 void isl_mat_dump(struct isl_mat *mat, FILE *out, int indent)
972 {
973 int i, j;
974
975 if (!mat) {
976 fprintf(out, "%*snull mat\n", indent, "");
977 return;
978 }
979
980 if (mat->n_row == 0)
981 fprintf(out, "%*s[]\n", indent, "");
982
983 for (i = 0; i < mat->n_row; ++i) {
984 if (!i)
985 fprintf(out, "%*s[[", indent, "");
986 else
987 fprintf(out, "%*s[", indent+1, "");
988 for (j = 0; j < mat->n_col; ++j) {
989 if (j)
990 fprintf(out, ",");
991 isl_int_print(out, mat->row[i][j], 0);
992 }
993 if (i == mat->n_row-1)
994 fprintf(out, "]]\n");
995 else
996 fprintf(out, "]\n");
997 }
998 }
999
1000 struct isl_mat *isl_mat_drop_cols(struct isl_mat *mat, unsigned col, unsigned n)
1001 {
1002 int r;
1003
1004 mat = isl_mat_cow(mat);
1005 if (!mat)
1006 return NULL;
1007
1008 if (col != mat->n_col-n) {
1009 for (r = 0; r < mat->n_row; ++r)
1010 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1011 mat->n_col - col - n);
1012 }
1013 mat->n_col -= n;
1014 return mat;
1015 }
1016
1017 struct isl_mat *isl_mat_drop_rows(struct isl_mat *mat, unsigned row, unsigned n)
1018 {
1019 int r;
1020
1021 mat = isl_mat_cow(mat);
1022 if (!mat)
1023 return NULL;
1024
1025 for (r = row; r+n < mat->n_row; ++r)
1026 mat->row[r] = mat->row[r+n];
1027
1028 mat->n_row -= n;
1029 return mat;
1030 }
1031
1032 void isl_mat_col_submul(struct isl_mat *mat,
1033 int dst_col, isl_int f, int src_col)
1034 {
1035 int i;
1036
1037 for (i = 0; i < mat->n_row; ++i)
1038 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1039 }
1040
1041 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1042 {
1043 int i;
1044
1045 for (i = 0; i < mat->n_row; ++i)
1046 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1047 }
1048
1049 struct isl_mat *isl_mat_unimodular_complete(struct isl_mat *M, int row)
1050 {
1051 int r;
1052 struct isl_mat *H = NULL, *Q = NULL;
1053
1054 isl_assert(ctx, M->n_row == M->n_col, goto error);
1055 M->n_row = row;
1056 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1057 M->n_row = M->n_col;
1058 if (!H)
1059 goto error;
1060 for (r = 0; r < row; ++r)
1061 isl_assert(ctx, isl_int_is_one(H->row[r][r]), goto error);
1062 for (r = row; r < M->n_row; ++r)
1063 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1064 isl_mat_free(H);
1065 isl_mat_free(Q);
1066 return M;
1067 error:
1068 isl_mat_free(H);
1069 isl_mat_free(Q);
1070 isl_mat_free(M);
1071 return NULL;
1072 }
Integer set library