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isl_tab: optionally save dual solution
[isl.git] / isl_mat.c
blobd72d929f058aa962e9e068d54315c0cff756e31e
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->ref = 1;
28 mat->n_row = n_row;
29 mat->n_col = n_col;
30 mat->flags = 0;
31
32 return mat;
33 error:
34 isl_blk_free(ctx, mat->block);
35 free(mat);
36 return NULL;
37 }
38
39 struct isl_mat *isl_mat_extend(struct isl_ctx *ctx, struct isl_mat *mat,
40 unsigned n_row, unsigned n_col)
41 {
42 int i;
43 isl_int *old;
44
45 if (!mat)
46 return NULL;
47
48 if (mat->n_col >= n_col && mat->n_row >= n_row)
49 return mat;
50
51 if (mat->n_col < n_col) {
52 struct isl_mat *new_mat;
53
54 new_mat = isl_mat_alloc(ctx, n_row, n_col);
55 if (!new_mat)
56 goto error;
57 for (i = 0; i < mat->n_row; ++i)
58 isl_seq_cpy(new_mat->row[i], mat->row[i], mat->n_col);
59 isl_mat_free(ctx, mat);
60 return new_mat;
61 }
62
63 mat = isl_mat_cow(ctx, mat);
64 if (!mat)
65 goto error;
66
67 assert(mat->ref == 1);
68 old = mat->block.data;
69 mat->block = isl_blk_extend(ctx, mat->block, n_row * mat->n_col);
70 if (isl_blk_is_error(mat->block))
71 goto error;
72 mat->row = isl_realloc_array(ctx, mat->row, isl_int *, n_row);
73 if (!mat->row)
74 goto error;
75
76 for (i = 0; i < mat->n_row; ++i)
77 mat->row[i] = mat->block.data + (mat->row[i] - old);
78 for (i = mat->n_row; i < n_row; ++i)
79 mat->row[i] = mat->block.data + i * mat->n_col;
80 mat->n_row = n_row;
81
82 return mat;
83 error:
84 isl_mat_free(ctx, mat);
85 return NULL;
86 }
87
88 struct isl_mat *isl_mat_sub_alloc(struct isl_ctx *ctx, isl_int **row,
89 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
90 {
91 int i;
92 struct isl_mat *mat;
93
94 mat = isl_alloc_type(ctx, struct isl_mat);
95 if (!mat)
96 return NULL;
97 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
98 if (!mat->row)
99 goto error;
100 for (i = 0; i < n_row; ++i)
101 mat->row[i] = row[first_row+i] + first_col;
102 mat->ref = 1;
103 mat->n_row = n_row;
104 mat->n_col = n_col;
105 mat->block = isl_blk_empty();
106 mat->flags = ISL_MAT_BORROWED;
107 return mat;
108 error:
109 free(mat);
110 return NULL;
111 }
112
113 void isl_mat_sub_copy(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
114 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
115 {
116 int i;
117
118 for (i = 0; i < n_row; ++i)
119 isl_seq_cpy(dst[i]+dst_col, src[i]+src_col, n_col);
120 }
121
122 void isl_mat_sub_neg(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
123 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
124 {
125 int i;
126
127 for (i = 0; i < n_row; ++i)
128 isl_seq_neg(dst[i]+dst_col, src[i]+src_col, n_col);
129 }
130
131 struct isl_mat *isl_mat_copy(struct isl_ctx *ctx, struct isl_mat *mat)
132 {
133 if (!mat)
134 return NULL;
135
136 mat->ref++;
137 return mat;
138 }
139
140 struct isl_mat *isl_mat_dup(struct isl_ctx *ctx, struct isl_mat *mat)
141 {
142 int i;
143 struct isl_mat *mat2;
144
145 if (!mat)
146 return NULL;
147 mat2 = isl_mat_alloc(ctx, mat->n_row, mat->n_col);
148 if (!mat2)
149 return NULL;
150 for (i = 0; i < mat->n_row; ++i)
151 isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);
152 return mat2;
153 }
154
155 struct isl_mat *isl_mat_cow(struct isl_ctx *ctx, struct isl_mat *mat)
156 {
157 struct isl_mat *mat2;
158 if (!mat)
159 return NULL;
160
161 if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))
162 return mat;
163
164 mat2 = isl_mat_dup(ctx, mat);
165 isl_mat_free(ctx, mat);
166 return mat2;
167 }
168
169 void isl_mat_free(struct isl_ctx *ctx, struct isl_mat *mat)
170 {
171 if (!mat)
172 return;
173
174 if (--mat->ref > 0)
175 return;
176
177 if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))
178 isl_blk_free(ctx, mat->block);
179 free(mat->row);
180 free(mat);
181 }
182
183 struct isl_mat *isl_mat_identity(struct isl_ctx *ctx, unsigned n_row)
184 {
185 int i;
186 struct isl_mat *mat;
187
188 mat = isl_mat_alloc(ctx, n_row, n_row);
189 if (!mat)
190 return NULL;
191 for (i = 0; i < n_row; ++i) {
192 isl_seq_clr(mat->row[i], i);
193 isl_int_set_si(mat->row[i][i], 1);
194 isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
195 }
196
197 return mat;
198 }
199
200 struct isl_vec *isl_mat_vec_product(struct isl_ctx *ctx,
201 struct isl_mat *mat, struct isl_vec *vec)
202 {
203 int i;
204 struct isl_vec *prod;
205
206 if (!mat || !vec)
207 goto error;
208
209 isl_assert(ctx, mat->n_col == vec->size, goto error);
210
211 prod = isl_vec_alloc(ctx, mat->n_row);
212 if (!prod)
213 goto error;
214
215 for (i = 0; i < prod->size; ++i)
216 isl_seq_inner_product(mat->row[i], vec->el, vec->size,
217 &prod->block.data[i]);
218 isl_mat_free(ctx, mat);
219 isl_vec_free(vec);
220 return prod;
221 error:
222 isl_mat_free(ctx, mat);
223 isl_vec_free(vec);
224 return NULL;
225 }
226
227 struct isl_mat *isl_mat_aff_direct_sum(struct isl_ctx *ctx,
228 struct isl_mat *left, struct isl_mat *right)
229 {
230 int i;
231 struct isl_mat *sum;
232
233 if (!left || !right)
234 goto error;
235
236 isl_assert(ctx, left->n_row == right->n_row, goto error);
237 isl_assert(ctx, left->n_row >= 1, goto error);
238 isl_assert(ctx, left->n_col >= 1, goto error);
239 isl_assert(ctx, right->n_col >= 1, goto error);
240 isl_assert(ctx,
241 isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,
242 goto error);
243 isl_assert(ctx,
244 isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
245 goto error);
246
247 sum = isl_mat_alloc(ctx, left->n_row, left->n_col + right->n_col - 1);
248 if (!sum)
249 goto error;
250 isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);
251 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
252 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
253
254 isl_seq_clr(sum->row[0]+1, sum->n_col-1);
255 for (i = 1; i < sum->n_row; ++i) {
256 isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);
257 isl_int_addmul(sum->row[i][0],
258 right->row[0][0], right->row[i][0]);
259 isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],
260 left->n_col-1);
261 isl_seq_scale(sum->row[i]+left->n_col,
262 right->row[i]+1, right->row[0][0],
263 right->n_col-1);
264 }
265
266 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
267 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
268 isl_mat_free(ctx, left);
269 isl_mat_free(ctx, right);
270 return sum;
271 error:
272 isl_mat_free(ctx, left);
273 isl_mat_free(ctx, right);
274 return NULL;
275 }
276
277 static void exchange(struct isl_ctx *ctx, struct isl_mat *M, struct isl_mat **U,
278 struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
279 {
280 int r;
281 for (r = row; r < M->n_row; ++r)
282 isl_int_swap(M->row[r][i], M->row[r][j]);
283 if (U) {
284 for (r = 0; r < (*U)->n_row; ++r)
285 isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
286 }
287 if (Q)
288 isl_mat_swap_rows(ctx, *Q, i, j);
289 }
290
291 static void subtract(struct isl_mat *M, struct isl_mat **U,
292 struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)
293 {
294 int r;
295 for (r = row; r < M->n_row; ++r)
296 isl_int_submul(M->row[r][j], m, M->row[r][i]);
297 if (U) {
298 for (r = 0; r < (*U)->n_row; ++r)
299 isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);
300 }
301 if (Q) {
302 for (r = 0; r < (*Q)->n_col; ++r)
303 isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);
304 }
305 }
306
307 static void oppose(struct isl_ctx *ctx, struct isl_mat *M, struct isl_mat **U,
308 struct isl_mat **Q, unsigned row, unsigned col)
309 {
310 int r;
311 for (r = row; r < M->n_row; ++r)
312 isl_int_neg(M->row[r][col], M->row[r][col]);
313 if (U) {
314 for (r = 0; r < (*U)->n_row; ++r)
315 isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);
316 }
317 if (Q)
318 isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);
319 }
320
321 /* Given matrix M, compute
322 *
323 * M U = H
324 * M = H Q
325 *
326 * with U and Q unimodular matrices and H a matrix in column echelon form
327 * such that on each echelon row the entries in the non-echelon column
328 * are non-negative (if neg == 0) or non-positive (if neg == 1)
329 * and stricly smaller (in absolute value) than the entries in the echelon
330 * column.
331 * If U or Q are NULL, then these matrices are not computed.
332 */
333 struct isl_mat *isl_mat_left_hermite(struct isl_ctx *ctx,
334 struct isl_mat *M, int neg, struct isl_mat **U, struct isl_mat **Q)
335 {
336 isl_int c;
337 int row, col;
338
339 if (U)
340 *U = NULL;
341 if (Q)
342 *Q = NULL;
343 if (!M)
344 goto error;
345 M = isl_mat_cow(ctx, M);
346 if (!M)
347 goto error;
348 if (U) {
349 *U = isl_mat_identity(ctx, M->n_col);
350 if (!*U)
351 goto error;
352 }
353 if (Q) {
354 *Q = isl_mat_identity(ctx, M->n_col);
355 if (!*Q)
356 goto error;
357 }
358
359 col = 0;
360 isl_int_init(c);
361 for (row = 0; row < M->n_row; ++row) {
362 int first, i, off;
363 first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);
364 if (first == -1)
365 continue;
366 first += col;
367 if (first != col)
368 exchange(ctx, M, U, Q, row, first, col);
369 if (isl_int_is_neg(M->row[row][col]))
370 oppose(ctx, M, U, Q, row, col);
371 first = col+1;
372 while ((off = isl_seq_first_non_zero(M->row[row]+first,
373 M->n_col-first)) != -1) {
374 first += off;
375 isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);
376 subtract(M, U, Q, row, col, first, c);
377 if (!isl_int_is_zero(M->row[row][first]))
378 exchange(ctx, M, U, Q, row, first, col);
379 else
380 ++first;
381 }
382 for (i = 0; i < col; ++i) {
383 if (isl_int_is_zero(M->row[row][i]))
384 continue;
385 if (neg)
386 isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);
387 else
388 isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);
389 if (isl_int_is_zero(c))
390 continue;
391 subtract(M, U, Q, row, col, i, c);
392 }
393 ++col;
394 }
395 isl_int_clear(c);
396
397 return M;
398 error:
399 if (Q) {
400 isl_mat_free(ctx, *Q);
401 *Q = NULL;
402 }
403 if (U) {
404 isl_mat_free(ctx, *U);
405 *U = NULL;
406 }
407 return NULL;
408 }
409
410 struct isl_mat *isl_mat_right_kernel(struct isl_ctx *ctx, struct isl_mat *mat)
411 {
412 int i, rank;
413 struct isl_mat *U = NULL;
414 struct isl_mat *K;
415
416 mat = isl_mat_left_hermite(ctx, mat, 0, &U, NULL);
417 if (!mat || !U)
418 goto error;
419
420 for (i = 0, rank = 0; rank < mat->n_col; ++rank) {
421 while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))
422 ++i;
423 if (i >= mat->n_row)
424 break;
425 }
426 K = isl_mat_alloc(ctx, U->n_row, U->n_col - rank);
427 if (!K)
428 goto error;
429 isl_mat_sub_copy(ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
430 isl_mat_free(ctx, mat);
431 isl_mat_free(ctx, U);
432 return K;
433 error:
434 isl_mat_free(ctx, mat);
435 isl_mat_free(ctx, U);
436 return NULL;
437 }
438
439 struct isl_mat *isl_mat_lin_to_aff(struct isl_ctx *ctx, struct isl_mat *mat)
440 {
441 int i;
442 struct isl_mat *mat2;
443
444 if (!mat)
445 return NULL;
446 mat2 = isl_mat_alloc(ctx, 1+mat->n_row, 1+mat->n_col);
447 if (!mat2)
448 return NULL;
449 isl_int_set_si(mat2->row[0][0], 1);
450 isl_seq_clr(mat2->row[0]+1, mat->n_col);
451 for (i = 0; i < mat->n_row; ++i) {
452 isl_int_set_si(mat2->row[1+i][0], 0);
453 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
454 }
455 isl_mat_free(ctx, mat);
456 return mat2;
457 }
458
459 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
460 {
461 int i;
462
463 for (i = 0; i < n_row; ++i)
464 if (!isl_int_is_zero(row[i][col]))
465 return i;
466 return -1;
467 }
468
469 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
470 {
471 int i, min = row_first_non_zero(row, n_row, col);
472 if (min < 0)
473 return -1;
474 for (i = min + 1; i < n_row; ++i) {
475 if (isl_int_is_zero(row[i][col]))
476 continue;
477 if (isl_int_abs_lt(row[i][col], row[min][col]))
478 min = i;
479 }
480 return min;
481 }
482
483 static void inv_exchange(struct isl_ctx *ctx,
484 struct isl_mat *left, struct isl_mat *right,
485 unsigned i, unsigned j)
486 {
487 left = isl_mat_swap_rows(ctx, left, i, j);
488 right = isl_mat_swap_rows(ctx, right, i, j);
489 }
490
491 static void inv_oppose(struct isl_ctx *ctx,
492 struct isl_mat *left, struct isl_mat *right, unsigned row)
493 {
494 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
495 isl_seq_neg(right->row[row], right->row[row], right->n_col);
496 }
497
498 static void inv_subtract(struct isl_ctx *ctx,
499 struct isl_mat *left, struct isl_mat *right,
500 unsigned row, unsigned i, isl_int m)
501 {
502 isl_int_neg(m, m);
503 isl_seq_combine(left->row[i]+row,
504 ctx->one, left->row[i]+row,
505 m, left->row[row]+row,
506 left->n_col-row);
507 isl_seq_combine(right->row[i], ctx->one, right->row[i],
508 m, right->row[row], right->n_col);
509 }
510
511 /* Compute inv(left)*right
512 */
513 struct isl_mat *isl_mat_inverse_product(struct isl_ctx *ctx,
514 struct isl_mat *left, struct isl_mat *right)
515 {
516 int row;
517 isl_int a, b;
518
519 if (!left || !right)
520 goto error;
521
522 isl_assert(ctx, left->n_row == left->n_col, goto error);
523 isl_assert(ctx, left->n_row == right->n_row, goto error);
524
525 if (left->n_row == 0) {
526 isl_mat_free(ctx, left);
527 return right;
528 }
529
530 left = isl_mat_cow(ctx, left);
531 right = isl_mat_cow(ctx, right);
532 if (!left || !right)
533 goto error;
534
535 isl_int_init(a);
536 isl_int_init(b);
537 for (row = 0; row < left->n_row; ++row) {
538 int pivot, first, i, off;
539 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
540 if (pivot < 0) {
541 isl_int_clear(a);
542 isl_int_clear(b);
543 isl_assert(ctx, pivot >= 0, goto error);
544 }
545 pivot += row;
546 if (pivot != row)
547 inv_exchange(ctx, left, right, pivot, row);
548 if (isl_int_is_neg(left->row[row][row]))
549 inv_oppose(ctx, left, right, row);
550 first = row+1;
551 while ((off = row_first_non_zero(left->row+first,
552 left->n_row-first, row)) != -1) {
553 first += off;
554 isl_int_fdiv_q(a, left->row[first][row],
555 left->row[row][row]);
556 inv_subtract(ctx, left, right, row, first, a);
557 if (!isl_int_is_zero(left->row[first][row]))
558 inv_exchange(ctx, left, right, row, first);
559 else
560 ++first;
561 }
562 for (i = 0; i < row; ++i) {
563 if (isl_int_is_zero(left->row[i][row]))
564 continue;
565 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
566 isl_int_divexact(b, left->row[i][row], a);
567 isl_int_divexact(a, left->row[row][row], a);
568 isl_int_neg(a, a);
569 isl_seq_combine(left->row[i]+row,
570 a, left->row[i]+row,
571 b, left->row[row]+row,
572 left->n_col-row);
573 isl_seq_combine(right->row[i], a, right->row[i],
574 b, right->row[row], right->n_col);
575 }
576 }
577 isl_int_clear(b);
578
579 isl_int_set(a, left->row[0][0]);
580 for (row = 1; row < left->n_row; ++row)
581 isl_int_lcm(a, a, left->row[row][row]);
582 if (isl_int_is_zero(a)){
583 isl_int_clear(a);
584 isl_assert(ctx, 0, goto error);
585 }
586 for (row = 0; row < left->n_row; ++row) {
587 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
588 if (isl_int_is_one(left->row[row][row]))
589 continue;
590 isl_seq_scale(right->row[row], right->row[row],
591 left->row[row][row], right->n_col);
592 }
593 isl_int_clear(a);
594
595 isl_mat_free(ctx, left);
596 return right;
597 error:
598 isl_mat_free(ctx, left);
599 isl_mat_free(ctx, right);
600 return NULL;
601 }
602
603 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
604 {
605 int i;
606
607 for (i = 0; i < mat->n_row; ++i)
608 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
609 }
610
611 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
612 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
613 {
614 int i;
615 isl_int tmp;
616
617 isl_int_init(tmp);
618 for (i = 0; i < mat->n_row; ++i) {
619 isl_int_mul(tmp, m1, mat->row[i][src1]);
620 isl_int_addmul(tmp, m2, mat->row[i][src2]);
621 isl_int_set(mat->row[i][dst], tmp);
622 }
623 isl_int_clear(tmp);
624 }
625
626 struct isl_mat *isl_mat_right_inverse(struct isl_ctx *ctx,
627 struct isl_mat *mat)
628 {
629 struct isl_mat *inv;
630 int row;
631 isl_int a, b;
632
633 mat = isl_mat_cow(ctx, mat);
634 if (!mat)
635 return NULL;
636
637 inv = isl_mat_identity(ctx, mat->n_col);
638 inv = isl_mat_cow(ctx, inv);
639 if (!inv)
640 goto error;
641
642 isl_int_init(a);
643 isl_int_init(b);
644 for (row = 0; row < mat->n_row; ++row) {
645 int pivot, first, i, off;
646 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
647 if (pivot < 0) {
648 isl_int_clear(a);
649 isl_int_clear(b);
650 goto error;
651 }
652 pivot += row;
653 if (pivot != row)
654 exchange(ctx, mat, &inv, NULL, row, pivot, row);
655 if (isl_int_is_neg(mat->row[row][row]))
656 oppose(ctx, mat, &inv, NULL, row, row);
657 first = row+1;
658 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
659 mat->n_col-first)) != -1) {
660 first += off;
661 isl_int_fdiv_q(a, mat->row[row][first],
662 mat->row[row][row]);
663 subtract(mat, &inv, NULL, row, row, first, a);
664 if (!isl_int_is_zero(mat->row[row][first]))
665 exchange(ctx, mat, &inv, NULL, row, row, first);
666 else
667 ++first;
668 }
669 for (i = 0; i < row; ++i) {
670 if (isl_int_is_zero(mat->row[row][i]))
671 continue;
672 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
673 isl_int_divexact(b, mat->row[row][i], a);
674 isl_int_divexact(a, mat->row[row][row], a);
675 isl_int_neg(a, a);
676 isl_mat_col_combine(mat, i, a, i, b, row);
677 isl_mat_col_combine(inv, i, a, i, b, row);
678 }
679 }
680 isl_int_clear(b);
681
682 isl_int_set(a, mat->row[0][0]);
683 for (row = 1; row < mat->n_row; ++row)
684 isl_int_lcm(a, a, mat->row[row][row]);
685 if (isl_int_is_zero(a)){
686 isl_int_clear(a);
687 goto error;
688 }
689 for (row = 0; row < mat->n_row; ++row) {
690 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
691 if (isl_int_is_one(mat->row[row][row]))
692 continue;
693 isl_mat_col_scale(inv, row, mat->row[row][row]);
694 }
695 isl_int_clear(a);
696
697 isl_mat_free(ctx, mat);
698
699 return inv;
700 error:
701 isl_mat_free(ctx, mat);
702 return NULL;
703 }
704
705 struct isl_mat *isl_mat_transpose(struct isl_ctx *ctx, struct isl_mat *mat)
706 {
707 struct isl_mat *transpose = NULL;
708 int i, j;
709
710 if (mat->n_col == mat->n_row) {
711 mat = isl_mat_cow(ctx, mat);
712 if (!mat)
713 return NULL;
714 for (i = 0; i < mat->n_row; ++i)
715 for (j = i + 1; j < mat->n_col; ++j)
716 isl_int_swap(mat->row[i][j], mat->row[j][i]);
717 return mat;
718 }
719 transpose = isl_mat_alloc(ctx, mat->n_col, mat->n_row);
720 if (!transpose)
721 goto error;
722 for (i = 0; i < mat->n_row; ++i)
723 for (j = 0; j < mat->n_col; ++j)
724 isl_int_set(transpose->row[j][i], mat->row[i][j]);
725 isl_mat_free(ctx, mat);
726 return transpose;
727 error:
728 isl_mat_free(ctx, mat);
729 return NULL;
730 }
731
732 struct isl_mat *isl_mat_swap_cols(struct isl_ctx *ctx,
733 struct isl_mat *mat, unsigned i, unsigned j)
734 {
735 int r;
736
737 mat = isl_mat_cow(ctx, mat);
738 if (!mat)
739 return NULL;
740 isl_assert(ctx, i < mat->n_col, goto error);
741 isl_assert(ctx, j < mat->n_col, goto error);
742
743 for (r = 0; r < mat->n_row; ++r)
744 isl_int_swap(mat->row[r][i], mat->row[r][j]);
745 return mat;
746 error:
747 isl_mat_free(ctx, mat);
748 return NULL;
749 }
750
751 struct isl_mat *isl_mat_swap_rows(struct isl_ctx *ctx,
752 struct isl_mat *mat, unsigned i, unsigned j)
753 {
754 isl_int *t;
755
756 if (!mat)
757 return NULL;
758 mat = isl_mat_cow(ctx, mat);
759 if (!mat)
760 return NULL;
761 t = mat->row[i];
762 mat->row[i] = mat->row[j];
763 mat->row[j] = t;
764 return mat;
765 }
766
767 struct isl_mat *isl_mat_product(struct isl_ctx *ctx,
768 struct isl_mat *left, struct isl_mat *right)
769 {
770 int i, j, k;
771 struct isl_mat *prod;
772
773 if (!left || !right)
774 goto error;
775 isl_assert(ctx, left->n_col == right->n_row, goto error);
776 prod = isl_mat_alloc(ctx, left->n_row, right->n_col);
777 if (!prod)
778 goto error;
779 if (left->n_col == 0) {
780 for (i = 0; i < prod->n_row; ++i)
781 isl_seq_clr(prod->row[i], prod->n_col);
782 return prod;
783 }
784 for (i = 0; i < prod->n_row; ++i) {
785 for (j = 0; j < prod->n_col; ++j) {
786 isl_int_mul(prod->row[i][j],
787 left->row[i][0], right->row[0][j]);
788 for (k = 1; k < left->n_col; ++k)
789 isl_int_addmul(prod->row[i][j],
790 left->row[i][k], right->row[k][j]);
791 }
792 }
793 isl_mat_free(ctx, left);
794 isl_mat_free(ctx, right);
795 return prod;
796 error:
797 isl_mat_free(ctx, left);
798 isl_mat_free(ctx, right);
799 return NULL;
800 }
801
802 /* Replace the variables x in the rows q by x' given by x = M x',
803 * with M the matrix mat.
804 *
805 * If the number of new variables is greater than the original
806 * number of variables, then the rows q have already been
807 * preextended. If the new number is smaller, then the coefficients
808 * of the divs, which are not changed, need to be shifted down.
809 * The row q may be the equalities, the inequalities or the
810 * div expressions. In the latter case, has_div is true and
811 * we need to take into account the extra denominator column.
812 */
813 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
814 unsigned n_div, int has_div, struct isl_mat *mat)
815 {
816 int i;
817 struct isl_mat *t;
818 int e;
819
820 if (mat->n_col >= mat->n_row)
821 e = 0;
822 else
823 e = mat->n_row - mat->n_col;
824 if (has_div)
825 for (i = 0; i < n; ++i)
826 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
827 t = isl_mat_sub_alloc(ctx, q, 0, n, has_div, mat->n_row);
828 t = isl_mat_product(ctx, t, mat);
829 if (!t)
830 return -1;
831 for (i = 0; i < n; ++i) {
832 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
833 isl_seq_cpy(q[i] + has_div + t->n_col,
834 q[i] + has_div + t->n_col + e, n_div);
835 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
836 }
837 isl_mat_free(ctx, t);
838 return 0;
839 }
840
841 /* Replace the variables x in bset by x' given by x = M x', with
842 * M the matrix mat.
843 *
844 * If there are fewer variables x' then there are x, then we perform
845 * the transformation in place, which that, in principle,
846 * this frees up some extra variables as the number
847 * of columns remains constant, but we would have to extend
848 * the div array too as the number of rows in this array is assumed
849 * to be equal to extra.
850 */
851 struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
852 struct isl_mat *mat)
853 {
854 struct isl_ctx *ctx;
855
856 if (!bset || !mat)
857 goto error;
858
859 ctx = bset->ctx;
860 bset = isl_basic_set_cow(bset);
861 if (!bset)
862 goto error;
863
864 isl_assert(ctx, bset->dim->nparam == 0, goto error);
865 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
866
867 if (mat->n_col > mat->n_row)
868 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0,
869 0, 0);
870 else if (mat->n_col < mat->n_row) {
871 bset->dim = isl_dim_cow(bset->dim);
872 if (!bset->dim)
873 goto error;
874 bset->dim->n_out -= mat->n_row - mat->n_col;
875 }
876
877 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
878 isl_mat_copy(ctx, mat)) < 0)
879 goto error;
880
881 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
882 isl_mat_copy(ctx, mat)) < 0)
883 goto error;
884
885 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
886 goto error2;
887
888 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
889 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
890 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
891 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
892 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
893
894 bset = isl_basic_set_simplify(bset);
895 bset = isl_basic_set_finalize(bset);
896
897 return bset;
898 error:
899 isl_mat_free(ctx, mat);
900 error2:
901 isl_basic_set_free(bset);
902 return NULL;
903 }
904
905 struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
906 {
907 struct isl_ctx *ctx;
908 int i;
909
910 set = isl_set_cow(set);
911 if (!set)
912 return NULL;
913
914 ctx = set->ctx;
915 for (i = 0; i < set->n; ++i) {
916 set->p[i] = isl_basic_set_preimage(set->p[i],
917 isl_mat_copy(ctx, mat));
918 if (!set->p[i])
919 goto error;
920 }
921 if (mat->n_col != mat->n_row) {
922 set->dim = isl_dim_cow(set->dim);
923 if (!set->dim)
924 goto error;
925 set->dim->n_out += mat->n_col;
926 set->dim->n_out -= mat->n_row;
927 }
928 isl_mat_free(ctx, mat);
929 ISL_F_CLR(set, ISL_SET_NORMALIZED);
930 return set;
931 error:
932 isl_set_free(set);
933 isl_mat_free(ctx, mat);
934 return NULL;
935 }
936
937 void isl_mat_dump(struct isl_ctx *ctx, struct isl_mat *mat,
938 FILE *out, int indent)
939 {
940 int i, j;
941
942 if (!mat) {
943 fprintf(out, "%*snull mat\n", indent, "");
944 return;
945 }
946
947 if (mat->n_row == 0)
948 fprintf(out, "%*s[]\n", indent, "");
949
950 for (i = 0; i < mat->n_row; ++i) {
951 if (!i)
952 fprintf(out, "%*s[[", indent, "");
953 else
954 fprintf(out, "%*s[", indent+1, "");
955 for (j = 0; j < mat->n_col; ++j) {
956 if (j)
957 fprintf(out, ",");
958 isl_int_print(out, mat->row[i][j], 0);
959 }
960 if (i == mat->n_row-1)
961 fprintf(out, "]]\n");
962 else
963 fprintf(out, "]\n");
964 }
965 }
966
967 struct isl_mat *isl_mat_drop_cols(struct isl_ctx *ctx, struct isl_mat *mat,
968 unsigned col, unsigned n)
969 {
970 int r;
971
972 mat = isl_mat_cow(ctx, mat);
973 if (!mat)
974 return NULL;
975
976 if (col != mat->n_col-n) {
977 for (r = 0; r < mat->n_row; ++r)
978 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
979 mat->n_col - col - n);
980 }
981 mat->n_col -= n;
982 return mat;
983 }
984
985 struct isl_mat *isl_mat_drop_rows(struct isl_ctx *ctx, struct isl_mat *mat,
986 unsigned row, unsigned n)
987 {
988 int r;
989
990 mat = isl_mat_cow(ctx, mat);
991 if (!mat)
992 return NULL;
993
994 for (r = row; r+n < mat->n_row; ++r)
995 mat->row[r] = mat->row[r+n];
996
997 mat->n_row -= n;
998 return mat;
999 }
1000
1001 void isl_mat_col_submul(struct isl_mat *mat,
1002 int dst_col, isl_int f, int src_col)
1003 {
1004 int i;
1005
1006 for (i = 0; i < mat->n_row; ++i)
1007 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1008 }
1009
1010 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1011 {
1012 int i;
1013
1014 for (i = 0; i < mat->n_row; ++i)
1015 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1016 }
1017
1018 struct isl_mat *isl_mat_unimodular_complete(struct isl_ctx *ctx,
1019 struct isl_mat *M, int row)
1020 {
1021 int r;
1022 struct isl_mat *H = NULL, *Q = NULL;
1023
1024 isl_assert(ctx, M->n_row == M->n_col, goto error);
1025 M->n_row = row;
1026 H = isl_mat_left_hermite(ctx, isl_mat_copy(ctx, M), 0, NULL, &Q);
1027 M->n_row = M->n_col;
1028 if (!H)
1029 goto error;
1030 for (r = 0; r < row; ++r)
1031 isl_assert(ctx, isl_int_is_one(H->row[r][r]), goto error);
1032 for (r = row; r < M->n_row; ++r)
1033 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1034 isl_mat_free(ctx, H);
1035 isl_mat_free(ctx, Q);
1036 return M;
1037 error:
1038 isl_mat_free(ctx, H);
1039 isl_mat_free(ctx, Q);
1040 isl_mat_free(ctx, M);
1041 return NULL;
1042 }
Integer set library