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isl_set_project_out: always update dimension, even for empty sets
[isl.git] / isl_mat.c
blobc2c59e071a817c7de72a2dbc4dcf30cbc7b48ae6
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 *
4 * Use of this software is governed by the GNU LGPLv2.1 license
5 *
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
8 */
9
10 #include "isl_dim.h"
11 #include "isl_seq.h"
12 #include "isl_mat.h"
13 #include "isl_map_private.h"
14
15 struct isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
16 unsigned n_row, unsigned n_col)
17 {
18 int i;
19 struct isl_mat *mat;
20
21 mat = isl_alloc_type(ctx, struct isl_mat);
22 if (!mat)
23 return NULL;
24
25 mat->row = NULL;
26 mat->block = isl_blk_alloc(ctx, n_row * n_col);
27 if (isl_blk_is_error(mat->block))
28 goto error;
29 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
30 if (!mat->row)
31 goto error;
32
33 for (i = 0; i < n_row; ++i)
34 mat->row[i] = mat->block.data + i * n_col;
35
36 mat->ctx = ctx;
37 isl_ctx_ref(ctx);
38 mat->ref = 1;
39 mat->n_row = n_row;
40 mat->n_col = n_col;
41 mat->max_col = n_col;
42 mat->flags = 0;
43
44 return mat;
45 error:
46 isl_blk_free(ctx, mat->block);
47 free(mat);
48 return NULL;
49 }
50
51 struct isl_mat *isl_mat_extend(struct isl_mat *mat,
52 unsigned n_row, unsigned n_col)
53 {
54 int i;
55 isl_int *old;
56
57 if (!mat)
58 return NULL;
59
60 if (mat->max_col >= n_col && mat->n_row >= n_row) {
61 if (mat->n_col < n_col)
62 mat->n_col = n_col;
63 return mat;
64 }
65
66 if (mat->max_col < n_col) {
67 struct isl_mat *new_mat;
68
69 if (n_row < mat->n_row)
70 n_row = mat->n_row;
71 new_mat = isl_mat_alloc(mat->ctx, n_row, n_col);
72 if (!new_mat)
73 goto error;
74 for (i = 0; i < mat->n_row; ++i)
75 isl_seq_cpy(new_mat->row[i], mat->row[i], mat->n_col);
76 isl_mat_free(mat);
77 return new_mat;
78 }
79
80 mat = isl_mat_cow(mat);
81 if (!mat)
82 goto error;
83
84 assert(mat->ref == 1);
85 old = mat->block.data;
86 mat->block = isl_blk_extend(mat->ctx, mat->block, n_row * mat->max_col);
87 if (isl_blk_is_error(mat->block))
88 goto error;
89 mat->row = isl_realloc_array(mat->ctx, mat->row, isl_int *, n_row);
90 if (!mat->row)
91 goto error;
92
93 for (i = 0; i < mat->n_row; ++i)
94 mat->row[i] = mat->block.data + (mat->row[i] - old);
95 for (i = mat->n_row; i < n_row; ++i)
96 mat->row[i] = mat->block.data + i * mat->max_col;
97 mat->n_row = n_row;
98 if (mat->n_col < n_col)
99 mat->n_col = n_col;
100
101 return mat;
102 error:
103 isl_mat_free(mat);
104 return NULL;
105 }
106
107 struct isl_mat *isl_mat_sub_alloc(struct isl_ctx *ctx, isl_int **row,
108 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
109 {
110 int i;
111 struct isl_mat *mat;
112
113 mat = isl_alloc_type(ctx, struct isl_mat);
114 if (!mat)
115 return NULL;
116 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
117 if (!mat->row)
118 goto error;
119 for (i = 0; i < n_row; ++i)
120 mat->row[i] = row[first_row+i] + first_col;
121 mat->ctx = ctx;
122 isl_ctx_ref(ctx);
123 mat->ref = 1;
124 mat->n_row = n_row;
125 mat->n_col = n_col;
126 mat->block = isl_blk_empty();
127 mat->flags = ISL_MAT_BORROWED;
128 return mat;
129 error:
130 free(mat);
131 return NULL;
132 }
133
134 void isl_mat_sub_copy(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_cpy(dst[i]+dst_col, src[i]+src_col, n_col);
141 }
142
143 void isl_mat_sub_neg(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
144 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
145 {
146 int i;
147
148 for (i = 0; i < n_row; ++i)
149 isl_seq_neg(dst[i]+dst_col, src[i]+src_col, n_col);
150 }
151
152 struct isl_mat *isl_mat_copy(struct isl_mat *mat)
153 {
154 if (!mat)
155 return NULL;
156
157 mat->ref++;
158 return mat;
159 }
160
161 struct isl_mat *isl_mat_dup(struct isl_mat *mat)
162 {
163 int i;
164 struct isl_mat *mat2;
165
166 if (!mat)
167 return NULL;
168 mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
169 if (!mat2)
170 return NULL;
171 for (i = 0; i < mat->n_row; ++i)
172 isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);
173 return mat2;
174 }
175
176 struct isl_mat *isl_mat_cow(struct isl_mat *mat)
177 {
178 struct isl_mat *mat2;
179 if (!mat)
180 return NULL;
181
182 if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))
183 return mat;
184
185 mat2 = isl_mat_dup(mat);
186 isl_mat_free(mat);
187 return mat2;
188 }
189
190 void isl_mat_free(struct isl_mat *mat)
191 {
192 if (!mat)
193 return;
194
195 if (--mat->ref > 0)
196 return;
197
198 if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))
199 isl_blk_free(mat->ctx, mat->block);
200 isl_ctx_deref(mat->ctx);
201 free(mat->row);
202 free(mat);
203 }
204
205 struct isl_mat *isl_mat_identity(struct isl_ctx *ctx, unsigned n_row)
206 {
207 int i;
208 struct isl_mat *mat;
209
210 mat = isl_mat_alloc(ctx, n_row, n_row);
211 if (!mat)
212 return NULL;
213 for (i = 0; i < n_row; ++i) {
214 isl_seq_clr(mat->row[i], i);
215 isl_int_set_si(mat->row[i][i], 1);
216 isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
217 }
218
219 return mat;
220 }
221
222 struct isl_vec *isl_mat_vec_product(struct isl_mat *mat, struct isl_vec *vec)
223 {
224 int i;
225 struct isl_vec *prod;
226
227 if (!mat || !vec)
228 goto error;
229
230 isl_assert(mat->ctx, mat->n_col == vec->size, goto error);
231
232 prod = isl_vec_alloc(mat->ctx, mat->n_row);
233 if (!prod)
234 goto error;
235
236 for (i = 0; i < prod->size; ++i)
237 isl_seq_inner_product(mat->row[i], vec->el, vec->size,
238 &prod->block.data[i]);
239 isl_mat_free(mat);
240 isl_vec_free(vec);
241 return prod;
242 error:
243 isl_mat_free(mat);
244 isl_vec_free(vec);
245 return NULL;
246 }
247
248 __isl_give isl_vec *isl_mat_vec_inverse_product(__isl_take isl_mat *mat,
249 __isl_take isl_vec *vec)
250 {
251 struct isl_mat *vec_mat;
252 int i;
253
254 if (!mat || !vec)
255 goto error;
256 vec_mat = isl_mat_alloc(vec->ctx, vec->size, 1);
257 if (!vec_mat)
258 goto error;
259 for (i = 0; i < vec->size; ++i)
260 isl_int_set(vec_mat->row[i][0], vec->el[i]);
261 vec_mat = isl_mat_inverse_product(mat, vec_mat);
262 isl_vec_free(vec);
263 if (!vec_mat)
264 return NULL;
265 vec = isl_vec_alloc(vec_mat->ctx, vec_mat->n_row);
266 if (vec)
267 for (i = 0; i < vec->size; ++i)
268 isl_int_set(vec->el[i], vec_mat->row[i][0]);
269 isl_mat_free(vec_mat);
270 return vec;
271 error:
272 isl_mat_free(mat);
273 isl_vec_free(vec);
274 return NULL;
275 }
276
277 struct isl_vec *isl_vec_mat_product(struct isl_vec *vec, struct isl_mat *mat)
278 {
279 int i, j;
280 struct isl_vec *prod;
281
282 if (!mat || !vec)
283 goto error;
284
285 isl_assert(mat->ctx, mat->n_row == vec->size, goto error);
286
287 prod = isl_vec_alloc(mat->ctx, mat->n_col);
288 if (!prod)
289 goto error;
290
291 for (i = 0; i < prod->size; ++i) {
292 isl_int_set_si(prod->el[i], 0);
293 for (j = 0; j < vec->size; ++j)
294 isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);
295 }
296 isl_mat_free(mat);
297 isl_vec_free(vec);
298 return prod;
299 error:
300 isl_mat_free(mat);
301 isl_vec_free(vec);
302 return NULL;
303 }
304
305 struct isl_mat *isl_mat_aff_direct_sum(struct isl_mat *left,
306 struct isl_mat *right)
307 {
308 int i;
309 struct isl_mat *sum;
310
311 if (!left || !right)
312 goto error;
313
314 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
315 isl_assert(left->ctx, left->n_row >= 1, goto error);
316 isl_assert(left->ctx, left->n_col >= 1, goto error);
317 isl_assert(left->ctx, right->n_col >= 1, goto error);
318 isl_assert(left->ctx,
319 isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,
320 goto error);
321 isl_assert(left->ctx,
322 isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
323 goto error);
324
325 sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);
326 if (!sum)
327 goto error;
328 isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);
329 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
330 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
331
332 isl_seq_clr(sum->row[0]+1, sum->n_col-1);
333 for (i = 1; i < sum->n_row; ++i) {
334 isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);
335 isl_int_addmul(sum->row[i][0],
336 right->row[0][0], right->row[i][0]);
337 isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],
338 left->n_col-1);
339 isl_seq_scale(sum->row[i]+left->n_col,
340 right->row[i]+1, right->row[0][0],
341 right->n_col-1);
342 }
343
344 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
345 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
346 isl_mat_free(left);
347 isl_mat_free(right);
348 return sum;
349 error:
350 isl_mat_free(left);
351 isl_mat_free(right);
352 return NULL;
353 }
354
355 static void exchange(struct isl_mat *M, struct isl_mat **U,
356 struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
357 {
358 int r;
359 for (r = row; r < M->n_row; ++r)
360 isl_int_swap(M->row[r][i], M->row[r][j]);
361 if (U) {
362 for (r = 0; r < (*U)->n_row; ++r)
363 isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
364 }
365 if (Q)
366 isl_mat_swap_rows(*Q, i, j);
367 }
368
369 static void subtract(struct isl_mat *M, struct isl_mat **U,
370 struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)
371 {
372 int r;
373 for (r = row; r < M->n_row; ++r)
374 isl_int_submul(M->row[r][j], m, M->row[r][i]);
375 if (U) {
376 for (r = 0; r < (*U)->n_row; ++r)
377 isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);
378 }
379 if (Q) {
380 for (r = 0; r < (*Q)->n_col; ++r)
381 isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);
382 }
383 }
384
385 static void oppose(struct isl_mat *M, struct isl_mat **U,
386 struct isl_mat **Q, unsigned row, unsigned col)
387 {
388 int r;
389 for (r = row; r < M->n_row; ++r)
390 isl_int_neg(M->row[r][col], M->row[r][col]);
391 if (U) {
392 for (r = 0; r < (*U)->n_row; ++r)
393 isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);
394 }
395 if (Q)
396 isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);
397 }
398
399 /* Given matrix M, compute
400 *
401 * M U = H
402 * M = H Q
403 *
404 * with U and Q unimodular matrices and H a matrix in column echelon form
405 * such that on each echelon row the entries in the non-echelon column
406 * are non-negative (if neg == 0) or non-positive (if neg == 1)
407 * and stricly smaller (in absolute value) than the entries in the echelon
408 * column.
409 * If U or Q are NULL, then these matrices are not computed.
410 */
411 struct isl_mat *isl_mat_left_hermite(struct isl_mat *M, int neg,
412 struct isl_mat **U, struct isl_mat **Q)
413 {
414 isl_int c;
415 int row, col;
416
417 if (U)
418 *U = NULL;
419 if (Q)
420 *Q = NULL;
421 if (!M)
422 goto error;
423 M = isl_mat_cow(M);
424 if (!M)
425 goto error;
426 if (U) {
427 *U = isl_mat_identity(M->ctx, M->n_col);
428 if (!*U)
429 goto error;
430 }
431 if (Q) {
432 *Q = isl_mat_identity(M->ctx, M->n_col);
433 if (!*Q)
434 goto error;
435 }
436
437 col = 0;
438 isl_int_init(c);
439 for (row = 0; row < M->n_row; ++row) {
440 int first, i, off;
441 first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);
442 if (first == -1)
443 continue;
444 first += col;
445 if (first != col)
446 exchange(M, U, Q, row, first, col);
447 if (isl_int_is_neg(M->row[row][col]))
448 oppose(M, U, Q, row, col);
449 first = col+1;
450 while ((off = isl_seq_first_non_zero(M->row[row]+first,
451 M->n_col-first)) != -1) {
452 first += off;
453 isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);
454 subtract(M, U, Q, row, col, first, c);
455 if (!isl_int_is_zero(M->row[row][first]))
456 exchange(M, U, Q, row, first, col);
457 else
458 ++first;
459 }
460 for (i = 0; i < col; ++i) {
461 if (isl_int_is_zero(M->row[row][i]))
462 continue;
463 if (neg)
464 isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);
465 else
466 isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);
467 if (isl_int_is_zero(c))
468 continue;
469 subtract(M, U, Q, row, col, i, c);
470 }
471 ++col;
472 }
473 isl_int_clear(c);
474
475 return M;
476 error:
477 if (Q) {
478 isl_mat_free(*Q);
479 *Q = NULL;
480 }
481 if (U) {
482 isl_mat_free(*U);
483 *U = NULL;
484 }
485 return NULL;
486 }
487
488 struct isl_mat *isl_mat_right_kernel(struct isl_mat *mat)
489 {
490 int i, rank;
491 struct isl_mat *U = NULL;
492 struct isl_mat *K;
493
494 mat = isl_mat_left_hermite(mat, 0, &U, NULL);
495 if (!mat || !U)
496 goto error;
497
498 for (i = 0, rank = 0; rank < mat->n_col; ++rank) {
499 while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))
500 ++i;
501 if (i >= mat->n_row)
502 break;
503 }
504 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
505 if (!K)
506 goto error;
507 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
508 isl_mat_free(mat);
509 isl_mat_free(U);
510 return K;
511 error:
512 isl_mat_free(mat);
513 isl_mat_free(U);
514 return NULL;
515 }
516
517 struct isl_mat *isl_mat_lin_to_aff(struct isl_mat *mat)
518 {
519 int i;
520 struct isl_mat *mat2;
521
522 if (!mat)
523 return NULL;
524 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
525 if (!mat2)
526 return NULL;
527 isl_int_set_si(mat2->row[0][0], 1);
528 isl_seq_clr(mat2->row[0]+1, mat->n_col);
529 for (i = 0; i < mat->n_row; ++i) {
530 isl_int_set_si(mat2->row[1+i][0], 0);
531 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
532 }
533 isl_mat_free(mat);
534 return mat2;
535 }
536
537 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
538 {
539 int i;
540
541 for (i = 0; i < n_row; ++i)
542 if (!isl_int_is_zero(row[i][col]))
543 return i;
544 return -1;
545 }
546
547 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
548 {
549 int i, min = row_first_non_zero(row, n_row, col);
550 if (min < 0)
551 return -1;
552 for (i = min + 1; i < n_row; ++i) {
553 if (isl_int_is_zero(row[i][col]))
554 continue;
555 if (isl_int_abs_lt(row[i][col], row[min][col]))
556 min = i;
557 }
558 return min;
559 }
560
561 static void inv_exchange(struct isl_mat *left, struct isl_mat *right,
562 unsigned i, unsigned j)
563 {
564 left = isl_mat_swap_rows(left, i, j);
565 right = isl_mat_swap_rows(right, i, j);
566 }
567
568 static void inv_oppose(
569 struct isl_mat *left, struct isl_mat *right, unsigned row)
570 {
571 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
572 isl_seq_neg(right->row[row], right->row[row], right->n_col);
573 }
574
575 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
576 unsigned row, unsigned i, isl_int m)
577 {
578 isl_int_neg(m, m);
579 isl_seq_combine(left->row[i]+row,
580 left->ctx->one, left->row[i]+row,
581 m, left->row[row]+row,
582 left->n_col-row);
583 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
584 m, right->row[row], right->n_col);
585 }
586
587 /* Compute inv(left)*right
588 */
589 struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
590 struct isl_mat *right)
591 {
592 int row;
593 isl_int a, b;
594
595 if (!left || !right)
596 goto error;
597
598 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
599 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
600
601 if (left->n_row == 0) {
602 isl_mat_free(left);
603 return right;
604 }
605
606 left = isl_mat_cow(left);
607 right = isl_mat_cow(right);
608 if (!left || !right)
609 goto error;
610
611 isl_int_init(a);
612 isl_int_init(b);
613 for (row = 0; row < left->n_row; ++row) {
614 int pivot, first, i, off;
615 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
616 if (pivot < 0) {
617 isl_int_clear(a);
618 isl_int_clear(b);
619 isl_assert(left->ctx, pivot >= 0, goto error);
620 }
621 pivot += row;
622 if (pivot != row)
623 inv_exchange(left, right, pivot, row);
624 if (isl_int_is_neg(left->row[row][row]))
625 inv_oppose(left, right, row);
626 first = row+1;
627 while ((off = row_first_non_zero(left->row+first,
628 left->n_row-first, row)) != -1) {
629 first += off;
630 isl_int_fdiv_q(a, left->row[first][row],
631 left->row[row][row]);
632 inv_subtract(left, right, row, first, a);
633 if (!isl_int_is_zero(left->row[first][row]))
634 inv_exchange(left, right, row, first);
635 else
636 ++first;
637 }
638 for (i = 0; i < row; ++i) {
639 if (isl_int_is_zero(left->row[i][row]))
640 continue;
641 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
642 isl_int_divexact(b, left->row[i][row], a);
643 isl_int_divexact(a, left->row[row][row], a);
644 isl_int_neg(b, b);
645 isl_seq_combine(left->row[i] + i,
646 a, left->row[i] + i,
647 b, left->row[row] + i,
648 left->n_col - i);
649 isl_seq_combine(right->row[i], a, right->row[i],
650 b, right->row[row], right->n_col);
651 }
652 }
653 isl_int_clear(b);
654
655 isl_int_set(a, left->row[0][0]);
656 for (row = 1; row < left->n_row; ++row)
657 isl_int_lcm(a, a, left->row[row][row]);
658 if (isl_int_is_zero(a)){
659 isl_int_clear(a);
660 isl_assert(left->ctx, 0, goto error);
661 }
662 for (row = 0; row < left->n_row; ++row) {
663 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
664 if (isl_int_is_one(left->row[row][row]))
665 continue;
666 isl_seq_scale(right->row[row], right->row[row],
667 left->row[row][row], right->n_col);
668 }
669 isl_int_clear(a);
670
671 isl_mat_free(left);
672 return right;
673 error:
674 isl_mat_free(left);
675 isl_mat_free(right);
676 return NULL;
677 }
678
679 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
680 {
681 int i;
682
683 for (i = 0; i < mat->n_row; ++i)
684 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
685 }
686
687 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
688 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
689 {
690 int i;
691 isl_int tmp;
692
693 isl_int_init(tmp);
694 for (i = 0; i < mat->n_row; ++i) {
695 isl_int_mul(tmp, m1, mat->row[i][src1]);
696 isl_int_addmul(tmp, m2, mat->row[i][src2]);
697 isl_int_set(mat->row[i][dst], tmp);
698 }
699 isl_int_clear(tmp);
700 }
701
702 struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
703 {
704 struct isl_mat *inv;
705 int row;
706 isl_int a, b;
707
708 mat = isl_mat_cow(mat);
709 if (!mat)
710 return NULL;
711
712 inv = isl_mat_identity(mat->ctx, mat->n_col);
713 inv = isl_mat_cow(inv);
714 if (!inv)
715 goto error;
716
717 isl_int_init(a);
718 isl_int_init(b);
719 for (row = 0; row < mat->n_row; ++row) {
720 int pivot, first, i, off;
721 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
722 if (pivot < 0) {
723 isl_int_clear(a);
724 isl_int_clear(b);
725 isl_assert(mat->ctx, pivot >= 0, goto error);
726 }
727 pivot += row;
728 if (pivot != row)
729 exchange(mat, &inv, NULL, row, pivot, row);
730 if (isl_int_is_neg(mat->row[row][row]))
731 oppose(mat, &inv, NULL, row, row);
732 first = row+1;
733 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
734 mat->n_col-first)) != -1) {
735 first += off;
736 isl_int_fdiv_q(a, mat->row[row][first],
737 mat->row[row][row]);
738 subtract(mat, &inv, NULL, row, row, first, a);
739 if (!isl_int_is_zero(mat->row[row][first]))
740 exchange(mat, &inv, NULL, row, row, first);
741 else
742 ++first;
743 }
744 for (i = 0; i < row; ++i) {
745 if (isl_int_is_zero(mat->row[row][i]))
746 continue;
747 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
748 isl_int_divexact(b, mat->row[row][i], a);
749 isl_int_divexact(a, mat->row[row][row], a);
750 isl_int_neg(a, a);
751 isl_mat_col_combine(mat, i, a, i, b, row);
752 isl_mat_col_combine(inv, i, a, i, b, row);
753 }
754 }
755 isl_int_clear(b);
756
757 isl_int_set(a, mat->row[0][0]);
758 for (row = 1; row < mat->n_row; ++row)
759 isl_int_lcm(a, a, mat->row[row][row]);
760 if (isl_int_is_zero(a)){
761 isl_int_clear(a);
762 goto error;
763 }
764 for (row = 0; row < mat->n_row; ++row) {
765 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
766 if (isl_int_is_one(mat->row[row][row]))
767 continue;
768 isl_mat_col_scale(inv, row, mat->row[row][row]);
769 }
770 isl_int_clear(a);
771
772 isl_mat_free(mat);
773
774 return inv;
775 error:
776 isl_mat_free(mat);
777 return NULL;
778 }
779
780 struct isl_mat *isl_mat_transpose(struct isl_mat *mat)
781 {
782 struct isl_mat *transpose = NULL;
783 int i, j;
784
785 if (mat->n_col == mat->n_row) {
786 mat = isl_mat_cow(mat);
787 if (!mat)
788 return NULL;
789 for (i = 0; i < mat->n_row; ++i)
790 for (j = i + 1; j < mat->n_col; ++j)
791 isl_int_swap(mat->row[i][j], mat->row[j][i]);
792 return mat;
793 }
794 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
795 if (!transpose)
796 goto error;
797 for (i = 0; i < mat->n_row; ++i)
798 for (j = 0; j < mat->n_col; ++j)
799 isl_int_set(transpose->row[j][i], mat->row[i][j]);
800 isl_mat_free(mat);
801 return transpose;
802 error:
803 isl_mat_free(mat);
804 return NULL;
805 }
806
807 struct isl_mat *isl_mat_swap_cols(struct isl_mat *mat, unsigned i, unsigned j)
808 {
809 int r;
810
811 mat = isl_mat_cow(mat);
812 if (!mat)
813 return NULL;
814 isl_assert(mat->ctx, i < mat->n_col, goto error);
815 isl_assert(mat->ctx, j < mat->n_col, goto error);
816
817 for (r = 0; r < mat->n_row; ++r)
818 isl_int_swap(mat->row[r][i], mat->row[r][j]);
819 return mat;
820 error:
821 isl_mat_free(mat);
822 return NULL;
823 }
824
825 struct isl_mat *isl_mat_swap_rows(struct isl_mat *mat, unsigned i, unsigned j)
826 {
827 isl_int *t;
828
829 if (!mat)
830 return NULL;
831 mat = isl_mat_cow(mat);
832 if (!mat)
833 return NULL;
834 t = mat->row[i];
835 mat->row[i] = mat->row[j];
836 mat->row[j] = t;
837 return mat;
838 }
839
840 struct isl_mat *isl_mat_product(struct isl_mat *left, struct isl_mat *right)
841 {
842 int i, j, k;
843 struct isl_mat *prod;
844
845 if (!left || !right)
846 goto error;
847 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
848 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
849 if (!prod)
850 goto error;
851 if (left->n_col == 0) {
852 for (i = 0; i < prod->n_row; ++i)
853 isl_seq_clr(prod->row[i], prod->n_col);
854 return prod;
855 }
856 for (i = 0; i < prod->n_row; ++i) {
857 for (j = 0; j < prod->n_col; ++j) {
858 isl_int_mul(prod->row[i][j],
859 left->row[i][0], right->row[0][j]);
860 for (k = 1; k < left->n_col; ++k)
861 isl_int_addmul(prod->row[i][j],
862 left->row[i][k], right->row[k][j]);
863 }
864 }
865 isl_mat_free(left);
866 isl_mat_free(right);
867 return prod;
868 error:
869 isl_mat_free(left);
870 isl_mat_free(right);
871 return NULL;
872 }
873
874 /* Replace the variables x in the rows q by x' given by x = M x',
875 * with M the matrix mat.
876 *
877 * If the number of new variables is greater than the original
878 * number of variables, then the rows q have already been
879 * preextended. If the new number is smaller, then the coefficients
880 * of the divs, which are not changed, need to be shifted down.
881 * The row q may be the equalities, the inequalities or the
882 * div expressions. In the latter case, has_div is true and
883 * we need to take into account the extra denominator column.
884 */
885 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
886 unsigned n_div, int has_div, struct isl_mat *mat)
887 {
888 int i;
889 struct isl_mat *t;
890 int e;
891
892 if (mat->n_col >= mat->n_row)
893 e = 0;
894 else
895 e = mat->n_row - mat->n_col;
896 if (has_div)
897 for (i = 0; i < n; ++i)
898 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
899 t = isl_mat_sub_alloc(mat->ctx, q, 0, n, has_div, mat->n_row);
900 t = isl_mat_product(t, mat);
901 if (!t)
902 return -1;
903 for (i = 0; i < n; ++i) {
904 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
905 isl_seq_cpy(q[i] + has_div + t->n_col,
906 q[i] + has_div + t->n_col + e, n_div);
907 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
908 }
909 isl_mat_free(t);
910 return 0;
911 }
912
913 /* Replace the variables x in bset by x' given by x = M x', with
914 * M the matrix mat.
915 *
916 * If there are fewer variables x' then there are x, then we perform
917 * the transformation in place, which that, in principle,
918 * this frees up some extra variables as the number
919 * of columns remains constant, but we would have to extend
920 * the div array too as the number of rows in this array is assumed
921 * to be equal to extra.
922 */
923 struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
924 struct isl_mat *mat)
925 {
926 struct isl_ctx *ctx;
927
928 if (!bset || !mat)
929 goto error;
930
931 ctx = bset->ctx;
932 bset = isl_basic_set_cow(bset);
933 if (!bset)
934 goto error;
935
936 isl_assert(ctx, bset->dim->nparam == 0, goto error);
937 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
938
939 if (mat->n_col > mat->n_row)
940 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0,
941 0, 0);
942 else if (mat->n_col < mat->n_row) {
943 bset->dim = isl_dim_cow(bset->dim);
944 if (!bset->dim)
945 goto error;
946 bset->dim->n_out -= mat->n_row - mat->n_col;
947 }
948
949 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
950 isl_mat_copy(mat)) < 0)
951 goto error;
952
953 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
954 isl_mat_copy(mat)) < 0)
955 goto error;
956
957 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
958 goto error2;
959
960 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
961 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
962 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
963 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
964 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
965
966 bset = isl_basic_set_simplify(bset);
967 bset = isl_basic_set_finalize(bset);
968
969 return bset;
970 error:
971 isl_mat_free(mat);
972 error2:
973 isl_basic_set_free(bset);
974 return NULL;
975 }
976
977 struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
978 {
979 struct isl_ctx *ctx;
980 int i;
981
982 set = isl_set_cow(set);
983 if (!set)
984 return NULL;
985
986 ctx = set->ctx;
987 for (i = 0; i < set->n; ++i) {
988 set->p[i] = isl_basic_set_preimage(set->p[i],
989 isl_mat_copy(mat));
990 if (!set->p[i])
991 goto error;
992 }
993 if (mat->n_col != mat->n_row) {
994 set->dim = isl_dim_cow(set->dim);
995 if (!set->dim)
996 goto error;
997 set->dim->n_out += mat->n_col;
998 set->dim->n_out -= mat->n_row;
999 }
1000 isl_mat_free(mat);
1001 ISL_F_CLR(set, ISL_SET_NORMALIZED);
1002 return set;
1003 error:
1004 isl_set_free(set);
1005 isl_mat_free(mat);
1006 return NULL;
1007 }
1008
1009 void isl_mat_dump(struct isl_mat *mat, FILE *out, int indent)
1010 {
1011 int i, j;
1012
1013 if (!mat) {
1014 fprintf(out, "%*snull mat\n", indent, "");
1015 return;
1016 }
1017
1018 if (mat->n_row == 0)
1019 fprintf(out, "%*s[]\n", indent, "");
1020
1021 for (i = 0; i < mat->n_row; ++i) {
1022 if (!i)
1023 fprintf(out, "%*s[[", indent, "");
1024 else
1025 fprintf(out, "%*s[", indent+1, "");
1026 for (j = 0; j < mat->n_col; ++j) {
1027 if (j)
1028 fprintf(out, ",");
1029 isl_int_print(out, mat->row[i][j], 0);
1030 }
1031 if (i == mat->n_row-1)
1032 fprintf(out, "]]\n");
1033 else
1034 fprintf(out, "]\n");
1035 }
1036 }
1037
1038 struct isl_mat *isl_mat_drop_cols(struct isl_mat *mat, unsigned col, unsigned n)
1039 {
1040 int r;
1041
1042 mat = isl_mat_cow(mat);
1043 if (!mat)
1044 return NULL;
1045
1046 if (col != mat->n_col-n) {
1047 for (r = 0; r < mat->n_row; ++r)
1048 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1049 mat->n_col - col - n);
1050 }
1051 mat->n_col -= n;
1052 return mat;
1053 }
1054
1055 struct isl_mat *isl_mat_drop_rows(struct isl_mat *mat, unsigned row, unsigned n)
1056 {
1057 int r;
1058
1059 mat = isl_mat_cow(mat);
1060 if (!mat)
1061 return NULL;
1062
1063 for (r = row; r+n < mat->n_row; ++r)
1064 mat->row[r] = mat->row[r+n];
1065
1066 mat->n_row -= n;
1067 return mat;
1068 }
1069
1070 void isl_mat_col_submul(struct isl_mat *mat,
1071 int dst_col, isl_int f, int src_col)
1072 {
1073 int i;
1074
1075 for (i = 0; i < mat->n_row; ++i)
1076 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1077 }
1078
1079 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1080 {
1081 int i;
1082
1083 for (i = 0; i < mat->n_row; ++i)
1084 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1085 }
1086
1087 struct isl_mat *isl_mat_unimodular_complete(struct isl_mat *M, int row)
1088 {
1089 int r;
1090 struct isl_mat *H = NULL, *Q = NULL;
1091
1092 if (!M)
1093 return NULL;
1094
1095 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1096 M->n_row = row;
1097 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1098 M->n_row = M->n_col;
1099 if (!H)
1100 goto error;
1101 for (r = 0; r < row; ++r)
1102 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1103 for (r = row; r < M->n_row; ++r)
1104 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1105 isl_mat_free(H);
1106 isl_mat_free(Q);
1107 return M;
1108 error:
1109 isl_mat_free(H);
1110 isl_mat_free(Q);
1111 isl_mat_free(M);
1112 return NULL;
1113 }
1114
1115 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1116 __isl_take isl_mat *bot)
1117 {
1118 struct isl_mat *mat;
1119
1120 if (!top || !bot)
1121 goto error;
1122
1123 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1124 if (top->n_row == 0) {
1125 isl_mat_free(top);
1126 return bot;
1127 }
1128 if (bot->n_row == 0) {
1129 isl_mat_free(bot);
1130 return top;
1131 }
1132
1133 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1134 if (!mat)
1135 goto error;
1136 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1137 0, 0, mat->n_col);
1138 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1139 0, 0, mat->n_col);
1140 isl_mat_free(top);
1141 isl_mat_free(bot);
1142 return mat;
1143 error:
1144 isl_mat_free(top);
1145 isl_mat_free(bot);
1146 return NULL;
1147 }
1148
1149 int isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
1150 {
1151 int i;
1152
1153 if (!mat1 || !mat2)
1154 return -1;
1155
1156 if (mat1->n_row != mat2->n_row)
1157 return 0;
1158
1159 if (mat1->n_col != mat2->n_col)
1160 return 0;
1161
1162 for (i = 0; i < mat1->n_row; ++i)
1163 if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
1164 return 0;
1165
1166 return 1;
1167 }
Integer set library