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isl_basic_map_from_constraint: only return copy of bmap on equality constraints
[isl.git] / isl_mat.c
bloba019ce1950ff48c45eff6a8608230f765ba36890
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 old = mat->block.data;
85 mat->block = isl_blk_extend(mat->ctx, mat->block, n_row * mat->max_col);
86 if (isl_blk_is_error(mat->block))
87 goto error;
88 mat->row = isl_realloc_array(mat->ctx, mat->row, isl_int *, n_row);
89 if (!mat->row)
90 goto error;
91
92 for (i = 0; i < mat->n_row; ++i)
93 mat->row[i] = mat->block.data + (mat->row[i] - old);
94 for (i = mat->n_row; i < n_row; ++i)
95 mat->row[i] = mat->block.data + i * mat->max_col;
96 mat->n_row = n_row;
97 if (mat->n_col < n_col)
98 mat->n_col = n_col;
99
100 return mat;
101 error:
102 isl_mat_free(mat);
103 return NULL;
104 }
105
106 struct isl_mat *isl_mat_sub_alloc(struct isl_ctx *ctx, isl_int **row,
107 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
108 {
109 int i;
110 struct isl_mat *mat;
111
112 mat = isl_alloc_type(ctx, struct isl_mat);
113 if (!mat)
114 return NULL;
115 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
116 if (!mat->row)
117 goto error;
118 for (i = 0; i < n_row; ++i)
119 mat->row[i] = row[first_row+i] + first_col;
120 mat->ctx = ctx;
121 isl_ctx_ref(ctx);
122 mat->ref = 1;
123 mat->n_row = n_row;
124 mat->n_col = n_col;
125 mat->block = isl_blk_empty();
126 mat->flags = ISL_MAT_BORROWED;
127 return mat;
128 error:
129 free(mat);
130 return NULL;
131 }
132
133 void isl_mat_sub_copy(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
134 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
135 {
136 int i;
137
138 for (i = 0; i < n_row; ++i)
139 isl_seq_cpy(dst[i]+dst_col, src[i]+src_col, n_col);
140 }
141
142 void isl_mat_sub_neg(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
143 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
144 {
145 int i;
146
147 for (i = 0; i < n_row; ++i)
148 isl_seq_neg(dst[i]+dst_col, src[i]+src_col, n_col);
149 }
150
151 struct isl_mat *isl_mat_copy(struct isl_mat *mat)
152 {
153 if (!mat)
154 return NULL;
155
156 mat->ref++;
157 return mat;
158 }
159
160 struct isl_mat *isl_mat_dup(struct isl_mat *mat)
161 {
162 int i;
163 struct isl_mat *mat2;
164
165 if (!mat)
166 return NULL;
167 mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
168 if (!mat2)
169 return NULL;
170 for (i = 0; i < mat->n_row; ++i)
171 isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);
172 return mat2;
173 }
174
175 struct isl_mat *isl_mat_cow(struct isl_mat *mat)
176 {
177 struct isl_mat *mat2;
178 if (!mat)
179 return NULL;
180
181 if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))
182 return mat;
183
184 mat2 = isl_mat_dup(mat);
185 isl_mat_free(mat);
186 return mat2;
187 }
188
189 void isl_mat_free(struct isl_mat *mat)
190 {
191 if (!mat)
192 return;
193
194 if (--mat->ref > 0)
195 return;
196
197 if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))
198 isl_blk_free(mat->ctx, mat->block);
199 isl_ctx_deref(mat->ctx);
200 free(mat->row);
201 free(mat);
202 }
203
204 struct isl_mat *isl_mat_identity(struct isl_ctx *ctx, unsigned n_row)
205 {
206 int i;
207 struct isl_mat *mat;
208
209 mat = isl_mat_alloc(ctx, n_row, n_row);
210 if (!mat)
211 return NULL;
212 for (i = 0; i < n_row; ++i) {
213 isl_seq_clr(mat->row[i], i);
214 isl_int_set_si(mat->row[i][i], 1);
215 isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
216 }
217
218 return mat;
219 }
220
221 struct isl_vec *isl_mat_vec_product(struct isl_mat *mat, struct isl_vec *vec)
222 {
223 int i;
224 struct isl_vec *prod;
225
226 if (!mat || !vec)
227 goto error;
228
229 isl_assert(mat->ctx, mat->n_col == vec->size, goto error);
230
231 prod = isl_vec_alloc(mat->ctx, mat->n_row);
232 if (!prod)
233 goto error;
234
235 for (i = 0; i < prod->size; ++i)
236 isl_seq_inner_product(mat->row[i], vec->el, vec->size,
237 &prod->block.data[i]);
238 isl_mat_free(mat);
239 isl_vec_free(vec);
240 return prod;
241 error:
242 isl_mat_free(mat);
243 isl_vec_free(vec);
244 return NULL;
245 }
246
247 __isl_give isl_vec *isl_mat_vec_inverse_product(__isl_take isl_mat *mat,
248 __isl_take isl_vec *vec)
249 {
250 struct isl_mat *vec_mat;
251 int i;
252
253 if (!mat || !vec)
254 goto error;
255 vec_mat = isl_mat_alloc(vec->ctx, vec->size, 1);
256 if (!vec_mat)
257 goto error;
258 for (i = 0; i < vec->size; ++i)
259 isl_int_set(vec_mat->row[i][0], vec->el[i]);
260 vec_mat = isl_mat_inverse_product(mat, vec_mat);
261 isl_vec_free(vec);
262 if (!vec_mat)
263 return NULL;
264 vec = isl_vec_alloc(vec_mat->ctx, vec_mat->n_row);
265 if (vec)
266 for (i = 0; i < vec->size; ++i)
267 isl_int_set(vec->el[i], vec_mat->row[i][0]);
268 isl_mat_free(vec_mat);
269 return vec;
270 error:
271 isl_mat_free(mat);
272 isl_vec_free(vec);
273 return NULL;
274 }
275
276 struct isl_vec *isl_vec_mat_product(struct isl_vec *vec, struct isl_mat *mat)
277 {
278 int i, j;
279 struct isl_vec *prod;
280
281 if (!mat || !vec)
282 goto error;
283
284 isl_assert(mat->ctx, mat->n_row == vec->size, goto error);
285
286 prod = isl_vec_alloc(mat->ctx, mat->n_col);
287 if (!prod)
288 goto error;
289
290 for (i = 0; i < prod->size; ++i) {
291 isl_int_set_si(prod->el[i], 0);
292 for (j = 0; j < vec->size; ++j)
293 isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);
294 }
295 isl_mat_free(mat);
296 isl_vec_free(vec);
297 return prod;
298 error:
299 isl_mat_free(mat);
300 isl_vec_free(vec);
301 return NULL;
302 }
303
304 struct isl_mat *isl_mat_aff_direct_sum(struct isl_mat *left,
305 struct isl_mat *right)
306 {
307 int i;
308 struct isl_mat *sum;
309
310 if (!left || !right)
311 goto error;
312
313 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
314 isl_assert(left->ctx, left->n_row >= 1, goto error);
315 isl_assert(left->ctx, left->n_col >= 1, goto error);
316 isl_assert(left->ctx, right->n_col >= 1, goto error);
317 isl_assert(left->ctx,
318 isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,
319 goto error);
320 isl_assert(left->ctx,
321 isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
322 goto error);
323
324 sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);
325 if (!sum)
326 goto error;
327 isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);
328 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
329 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
330
331 isl_seq_clr(sum->row[0]+1, sum->n_col-1);
332 for (i = 1; i < sum->n_row; ++i) {
333 isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);
334 isl_int_addmul(sum->row[i][0],
335 right->row[0][0], right->row[i][0]);
336 isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],
337 left->n_col-1);
338 isl_seq_scale(sum->row[i]+left->n_col,
339 right->row[i]+1, right->row[0][0],
340 right->n_col-1);
341 }
342
343 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
344 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
345 isl_mat_free(left);
346 isl_mat_free(right);
347 return sum;
348 error:
349 isl_mat_free(left);
350 isl_mat_free(right);
351 return NULL;
352 }
353
354 static void exchange(struct isl_mat *M, struct isl_mat **U,
355 struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
356 {
357 int r;
358 for (r = row; r < M->n_row; ++r)
359 isl_int_swap(M->row[r][i], M->row[r][j]);
360 if (U) {
361 for (r = 0; r < (*U)->n_row; ++r)
362 isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
363 }
364 if (Q)
365 isl_mat_swap_rows(*Q, i, j);
366 }
367
368 static void subtract(struct isl_mat *M, struct isl_mat **U,
369 struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)
370 {
371 int r;
372 for (r = row; r < M->n_row; ++r)
373 isl_int_submul(M->row[r][j], m, M->row[r][i]);
374 if (U) {
375 for (r = 0; r < (*U)->n_row; ++r)
376 isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);
377 }
378 if (Q) {
379 for (r = 0; r < (*Q)->n_col; ++r)
380 isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);
381 }
382 }
383
384 static void oppose(struct isl_mat *M, struct isl_mat **U,
385 struct isl_mat **Q, unsigned row, unsigned col)
386 {
387 int r;
388 for (r = row; r < M->n_row; ++r)
389 isl_int_neg(M->row[r][col], M->row[r][col]);
390 if (U) {
391 for (r = 0; r < (*U)->n_row; ++r)
392 isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);
393 }
394 if (Q)
395 isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);
396 }
397
398 /* Given matrix M, compute
399 *
400 * M U = H
401 * M = H Q
402 *
403 * with U and Q unimodular matrices and H a matrix in column echelon form
404 * such that on each echelon row the entries in the non-echelon column
405 * are non-negative (if neg == 0) or non-positive (if neg == 1)
406 * and stricly smaller (in absolute value) than the entries in the echelon
407 * column.
408 * If U or Q are NULL, then these matrices are not computed.
409 */
410 struct isl_mat *isl_mat_left_hermite(struct isl_mat *M, int neg,
411 struct isl_mat **U, struct isl_mat **Q)
412 {
413 isl_int c;
414 int row, col;
415
416 if (U)
417 *U = NULL;
418 if (Q)
419 *Q = NULL;
420 if (!M)
421 goto error;
422 M = isl_mat_cow(M);
423 if (!M)
424 goto error;
425 if (U) {
426 *U = isl_mat_identity(M->ctx, M->n_col);
427 if (!*U)
428 goto error;
429 }
430 if (Q) {
431 *Q = isl_mat_identity(M->ctx, M->n_col);
432 if (!*Q)
433 goto error;
434 }
435
436 col = 0;
437 isl_int_init(c);
438 for (row = 0; row < M->n_row; ++row) {
439 int first, i, off;
440 first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);
441 if (first == -1)
442 continue;
443 first += col;
444 if (first != col)
445 exchange(M, U, Q, row, first, col);
446 if (isl_int_is_neg(M->row[row][col]))
447 oppose(M, U, Q, row, col);
448 first = col+1;
449 while ((off = isl_seq_first_non_zero(M->row[row]+first,
450 M->n_col-first)) != -1) {
451 first += off;
452 isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);
453 subtract(M, U, Q, row, col, first, c);
454 if (!isl_int_is_zero(M->row[row][first]))
455 exchange(M, U, Q, row, first, col);
456 else
457 ++first;
458 }
459 for (i = 0; i < col; ++i) {
460 if (isl_int_is_zero(M->row[row][i]))
461 continue;
462 if (neg)
463 isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);
464 else
465 isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);
466 if (isl_int_is_zero(c))
467 continue;
468 subtract(M, U, Q, row, col, i, c);
469 }
470 ++col;
471 }
472 isl_int_clear(c);
473
474 return M;
475 error:
476 if (Q) {
477 isl_mat_free(*Q);
478 *Q = NULL;
479 }
480 if (U) {
481 isl_mat_free(*U);
482 *U = NULL;
483 }
484 return NULL;
485 }
486
487 struct isl_mat *isl_mat_right_kernel(struct isl_mat *mat)
488 {
489 int i, rank;
490 struct isl_mat *U = NULL;
491 struct isl_mat *K;
492
493 mat = isl_mat_left_hermite(mat, 0, &U, NULL);
494 if (!mat || !U)
495 goto error;
496
497 for (i = 0, rank = 0; rank < mat->n_col; ++rank) {
498 while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))
499 ++i;
500 if (i >= mat->n_row)
501 break;
502 }
503 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
504 if (!K)
505 goto error;
506 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
507 isl_mat_free(mat);
508 isl_mat_free(U);
509 return K;
510 error:
511 isl_mat_free(mat);
512 isl_mat_free(U);
513 return NULL;
514 }
515
516 struct isl_mat *isl_mat_lin_to_aff(struct isl_mat *mat)
517 {
518 int i;
519 struct isl_mat *mat2;
520
521 if (!mat)
522 return NULL;
523 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
524 if (!mat2)
525 goto error;
526 isl_int_set_si(mat2->row[0][0], 1);
527 isl_seq_clr(mat2->row[0]+1, mat->n_col);
528 for (i = 0; i < mat->n_row; ++i) {
529 isl_int_set_si(mat2->row[1+i][0], 0);
530 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
531 }
532 isl_mat_free(mat);
533 return mat2;
534 error:
535 isl_mat_free(mat);
536 return NULL;
537 }
538
539 /* Given two matrices M1 and M2, return the block matrix
540 *
541 * [ M1 0 ]
542 * [ 0 M2 ]
543 */
544 __isl_give isl_mat *isl_mat_diagonal(__isl_take isl_mat *mat1,
545 __isl_take isl_mat *mat2)
546 {
547 int i;
548 isl_mat *mat;
549
550 if (!mat1 || !mat2)
551 goto error;
552
553 mat = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
554 mat1->n_col + mat2->n_col);
555 if (!mat)
556 goto error;
557 for (i = 0; i < mat1->n_row; ++i) {
558 isl_seq_cpy(mat->row[i], mat1->row[i], mat1->n_col);
559 isl_seq_clr(mat->row[i] + mat1->n_col, mat2->n_col);
560 }
561 for (i = 0; i < mat2->n_row; ++i) {
562 isl_seq_clr(mat->row[mat1->n_row + i], mat1->n_col);
563 isl_seq_cpy(mat->row[mat1->n_row + i] + mat1->n_col,
564 mat2->row[i], mat2->n_col);
565 }
566 isl_mat_free(mat1);
567 isl_mat_free(mat2);
568 return mat;
569 error:
570 isl_mat_free(mat1);
571 isl_mat_free(mat2);
572 return NULL;
573 }
574
575 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
576 {
577 int i;
578
579 for (i = 0; i < n_row; ++i)
580 if (!isl_int_is_zero(row[i][col]))
581 return i;
582 return -1;
583 }
584
585 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
586 {
587 int i, min = row_first_non_zero(row, n_row, col);
588 if (min < 0)
589 return -1;
590 for (i = min + 1; i < n_row; ++i) {
591 if (isl_int_is_zero(row[i][col]))
592 continue;
593 if (isl_int_abs_lt(row[i][col], row[min][col]))
594 min = i;
595 }
596 return min;
597 }
598
599 static void inv_exchange(struct isl_mat *left, struct isl_mat *right,
600 unsigned i, unsigned j)
601 {
602 left = isl_mat_swap_rows(left, i, j);
603 right = isl_mat_swap_rows(right, i, j);
604 }
605
606 static void inv_oppose(
607 struct isl_mat *left, struct isl_mat *right, unsigned row)
608 {
609 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
610 isl_seq_neg(right->row[row], right->row[row], right->n_col);
611 }
612
613 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
614 unsigned row, unsigned i, isl_int m)
615 {
616 isl_int_neg(m, m);
617 isl_seq_combine(left->row[i]+row,
618 left->ctx->one, left->row[i]+row,
619 m, left->row[row]+row,
620 left->n_col-row);
621 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
622 m, right->row[row], right->n_col);
623 }
624
625 /* Compute inv(left)*right
626 */
627 struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
628 struct isl_mat *right)
629 {
630 int row;
631 isl_int a, b;
632
633 if (!left || !right)
634 goto error;
635
636 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
637 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
638
639 if (left->n_row == 0) {
640 isl_mat_free(left);
641 return right;
642 }
643
644 left = isl_mat_cow(left);
645 right = isl_mat_cow(right);
646 if (!left || !right)
647 goto error;
648
649 isl_int_init(a);
650 isl_int_init(b);
651 for (row = 0; row < left->n_row; ++row) {
652 int pivot, first, i, off;
653 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
654 if (pivot < 0) {
655 isl_int_clear(a);
656 isl_int_clear(b);
657 isl_assert(left->ctx, pivot >= 0, goto error);
658 }
659 pivot += row;
660 if (pivot != row)
661 inv_exchange(left, right, pivot, row);
662 if (isl_int_is_neg(left->row[row][row]))
663 inv_oppose(left, right, row);
664 first = row+1;
665 while ((off = row_first_non_zero(left->row+first,
666 left->n_row-first, row)) != -1) {
667 first += off;
668 isl_int_fdiv_q(a, left->row[first][row],
669 left->row[row][row]);
670 inv_subtract(left, right, row, first, a);
671 if (!isl_int_is_zero(left->row[first][row]))
672 inv_exchange(left, right, row, first);
673 else
674 ++first;
675 }
676 for (i = 0; i < row; ++i) {
677 if (isl_int_is_zero(left->row[i][row]))
678 continue;
679 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
680 isl_int_divexact(b, left->row[i][row], a);
681 isl_int_divexact(a, left->row[row][row], a);
682 isl_int_neg(b, b);
683 isl_seq_combine(left->row[i] + i,
684 a, left->row[i] + i,
685 b, left->row[row] + i,
686 left->n_col - i);
687 isl_seq_combine(right->row[i], a, right->row[i],
688 b, right->row[row], right->n_col);
689 }
690 }
691 isl_int_clear(b);
692
693 isl_int_set(a, left->row[0][0]);
694 for (row = 1; row < left->n_row; ++row)
695 isl_int_lcm(a, a, left->row[row][row]);
696 if (isl_int_is_zero(a)){
697 isl_int_clear(a);
698 isl_assert(left->ctx, 0, goto error);
699 }
700 for (row = 0; row < left->n_row; ++row) {
701 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
702 if (isl_int_is_one(left->row[row][row]))
703 continue;
704 isl_seq_scale(right->row[row], right->row[row],
705 left->row[row][row], right->n_col);
706 }
707 isl_int_clear(a);
708
709 isl_mat_free(left);
710 return right;
711 error:
712 isl_mat_free(left);
713 isl_mat_free(right);
714 return NULL;
715 }
716
717 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
718 {
719 int i;
720
721 for (i = 0; i < mat->n_row; ++i)
722 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
723 }
724
725 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
726 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
727 {
728 int i;
729 isl_int tmp;
730
731 isl_int_init(tmp);
732 for (i = 0; i < mat->n_row; ++i) {
733 isl_int_mul(tmp, m1, mat->row[i][src1]);
734 isl_int_addmul(tmp, m2, mat->row[i][src2]);
735 isl_int_set(mat->row[i][dst], tmp);
736 }
737 isl_int_clear(tmp);
738 }
739
740 struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
741 {
742 struct isl_mat *inv;
743 int row;
744 isl_int a, b;
745
746 mat = isl_mat_cow(mat);
747 if (!mat)
748 return NULL;
749
750 inv = isl_mat_identity(mat->ctx, mat->n_col);
751 inv = isl_mat_cow(inv);
752 if (!inv)
753 goto error;
754
755 isl_int_init(a);
756 isl_int_init(b);
757 for (row = 0; row < mat->n_row; ++row) {
758 int pivot, first, i, off;
759 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
760 if (pivot < 0) {
761 isl_int_clear(a);
762 isl_int_clear(b);
763 isl_assert(mat->ctx, pivot >= 0, goto error);
764 }
765 pivot += row;
766 if (pivot != row)
767 exchange(mat, &inv, NULL, row, pivot, row);
768 if (isl_int_is_neg(mat->row[row][row]))
769 oppose(mat, &inv, NULL, row, row);
770 first = row+1;
771 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
772 mat->n_col-first)) != -1) {
773 first += off;
774 isl_int_fdiv_q(a, mat->row[row][first],
775 mat->row[row][row]);
776 subtract(mat, &inv, NULL, row, row, first, a);
777 if (!isl_int_is_zero(mat->row[row][first]))
778 exchange(mat, &inv, NULL, row, row, first);
779 else
780 ++first;
781 }
782 for (i = 0; i < row; ++i) {
783 if (isl_int_is_zero(mat->row[row][i]))
784 continue;
785 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
786 isl_int_divexact(b, mat->row[row][i], a);
787 isl_int_divexact(a, mat->row[row][row], a);
788 isl_int_neg(a, a);
789 isl_mat_col_combine(mat, i, a, i, b, row);
790 isl_mat_col_combine(inv, i, a, i, b, row);
791 }
792 }
793 isl_int_clear(b);
794
795 isl_int_set(a, mat->row[0][0]);
796 for (row = 1; row < mat->n_row; ++row)
797 isl_int_lcm(a, a, mat->row[row][row]);
798 if (isl_int_is_zero(a)){
799 isl_int_clear(a);
800 goto error;
801 }
802 for (row = 0; row < mat->n_row; ++row) {
803 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
804 if (isl_int_is_one(mat->row[row][row]))
805 continue;
806 isl_mat_col_scale(inv, row, mat->row[row][row]);
807 }
808 isl_int_clear(a);
809
810 isl_mat_free(mat);
811
812 return inv;
813 error:
814 isl_mat_free(mat);
815 return NULL;
816 }
817
818 struct isl_mat *isl_mat_transpose(struct isl_mat *mat)
819 {
820 struct isl_mat *transpose = NULL;
821 int i, j;
822
823 if (mat->n_col == mat->n_row) {
824 mat = isl_mat_cow(mat);
825 if (!mat)
826 return NULL;
827 for (i = 0; i < mat->n_row; ++i)
828 for (j = i + 1; j < mat->n_col; ++j)
829 isl_int_swap(mat->row[i][j], mat->row[j][i]);
830 return mat;
831 }
832 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
833 if (!transpose)
834 goto error;
835 for (i = 0; i < mat->n_row; ++i)
836 for (j = 0; j < mat->n_col; ++j)
837 isl_int_set(transpose->row[j][i], mat->row[i][j]);
838 isl_mat_free(mat);
839 return transpose;
840 error:
841 isl_mat_free(mat);
842 return NULL;
843 }
844
845 struct isl_mat *isl_mat_swap_cols(struct isl_mat *mat, unsigned i, unsigned j)
846 {
847 int r;
848
849 mat = isl_mat_cow(mat);
850 if (!mat)
851 return NULL;
852 isl_assert(mat->ctx, i < mat->n_col, goto error);
853 isl_assert(mat->ctx, j < mat->n_col, goto error);
854
855 for (r = 0; r < mat->n_row; ++r)
856 isl_int_swap(mat->row[r][i], mat->row[r][j]);
857 return mat;
858 error:
859 isl_mat_free(mat);
860 return NULL;
861 }
862
863 struct isl_mat *isl_mat_swap_rows(struct isl_mat *mat, unsigned i, unsigned j)
864 {
865 isl_int *t;
866
867 if (!mat)
868 return NULL;
869 mat = isl_mat_cow(mat);
870 if (!mat)
871 return NULL;
872 t = mat->row[i];
873 mat->row[i] = mat->row[j];
874 mat->row[j] = t;
875 return mat;
876 }
877
878 struct isl_mat *isl_mat_product(struct isl_mat *left, struct isl_mat *right)
879 {
880 int i, j, k;
881 struct isl_mat *prod;
882
883 if (!left || !right)
884 goto error;
885 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
886 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
887 if (!prod)
888 goto error;
889 if (left->n_col == 0) {
890 for (i = 0; i < prod->n_row; ++i)
891 isl_seq_clr(prod->row[i], prod->n_col);
892 return prod;
893 }
894 for (i = 0; i < prod->n_row; ++i) {
895 for (j = 0; j < prod->n_col; ++j) {
896 isl_int_mul(prod->row[i][j],
897 left->row[i][0], right->row[0][j]);
898 for (k = 1; k < left->n_col; ++k)
899 isl_int_addmul(prod->row[i][j],
900 left->row[i][k], right->row[k][j]);
901 }
902 }
903 isl_mat_free(left);
904 isl_mat_free(right);
905 return prod;
906 error:
907 isl_mat_free(left);
908 isl_mat_free(right);
909 return NULL;
910 }
911
912 /* Replace the variables x in the rows q by x' given by x = M x',
913 * with M the matrix mat.
914 *
915 * If the number of new variables is greater than the original
916 * number of variables, then the rows q have already been
917 * preextended. If the new number is smaller, then the coefficients
918 * of the divs, which are not changed, need to be shifted down.
919 * The row q may be the equalities, the inequalities or the
920 * div expressions. In the latter case, has_div is true and
921 * we need to take into account the extra denominator column.
922 */
923 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
924 unsigned n_div, int has_div, struct isl_mat *mat)
925 {
926 int i;
927 struct isl_mat *t;
928 int e;
929
930 if (mat->n_col >= mat->n_row)
931 e = 0;
932 else
933 e = mat->n_row - mat->n_col;
934 if (has_div)
935 for (i = 0; i < n; ++i)
936 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
937 t = isl_mat_sub_alloc(mat->ctx, q, 0, n, has_div, mat->n_row);
938 t = isl_mat_product(t, mat);
939 if (!t)
940 return -1;
941 for (i = 0; i < n; ++i) {
942 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
943 isl_seq_cpy(q[i] + has_div + t->n_col,
944 q[i] + has_div + t->n_col + e, n_div);
945 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
946 }
947 isl_mat_free(t);
948 return 0;
949 }
950
951 /* Replace the variables x in bset by x' given by x = M x', with
952 * M the matrix mat.
953 *
954 * If there are fewer variables x' then there are x, then we perform
955 * the transformation in place, which that, in principle,
956 * this frees up some extra variables as the number
957 * of columns remains constant, but we would have to extend
958 * the div array too as the number of rows in this array is assumed
959 * to be equal to extra.
960 */
961 struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
962 struct isl_mat *mat)
963 {
964 struct isl_ctx *ctx;
965
966 if (!bset || !mat)
967 goto error;
968
969 ctx = bset->ctx;
970 bset = isl_basic_set_cow(bset);
971 if (!bset)
972 goto error;
973
974 isl_assert(ctx, bset->dim->nparam == 0, goto error);
975 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
976 isl_assert(ctx, mat->n_col > 0, goto error);
977
978 if (mat->n_col > mat->n_row) {
979 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0, 0, 0);
980 if (!bset)
981 goto error;
982 } else if (mat->n_col < mat->n_row) {
983 bset->dim = isl_dim_cow(bset->dim);
984 if (!bset->dim)
985 goto error;
986 bset->dim->n_out -= mat->n_row - mat->n_col;
987 }
988
989 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
990 isl_mat_copy(mat)) < 0)
991 goto error;
992
993 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
994 isl_mat_copy(mat)) < 0)
995 goto error;
996
997 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
998 goto error2;
999
1000 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
1001 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
1002 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1003 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1004 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
1005
1006 bset = isl_basic_set_simplify(bset);
1007 bset = isl_basic_set_finalize(bset);
1008
1009 return bset;
1010 error:
1011 isl_mat_free(mat);
1012 error2:
1013 isl_basic_set_free(bset);
1014 return NULL;
1015 }
1016
1017 struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
1018 {
1019 struct isl_ctx *ctx;
1020 int i;
1021
1022 set = isl_set_cow(set);
1023 if (!set)
1024 return NULL;
1025
1026 ctx = set->ctx;
1027 for (i = 0; i < set->n; ++i) {
1028 set->p[i] = isl_basic_set_preimage(set->p[i],
1029 isl_mat_copy(mat));
1030 if (!set->p[i])
1031 goto error;
1032 }
1033 if (mat->n_col != mat->n_row) {
1034 set->dim = isl_dim_cow(set->dim);
1035 if (!set->dim)
1036 goto error;
1037 set->dim->n_out += mat->n_col;
1038 set->dim->n_out -= mat->n_row;
1039 }
1040 isl_mat_free(mat);
1041 ISL_F_CLR(set, ISL_SET_NORMALIZED);
1042 return set;
1043 error:
1044 isl_set_free(set);
1045 isl_mat_free(mat);
1046 return NULL;
1047 }
1048
1049 void isl_mat_dump(struct isl_mat *mat, FILE *out, int indent)
1050 {
1051 int i, j;
1052
1053 if (!mat) {
1054 fprintf(out, "%*snull mat\n", indent, "");
1055 return;
1056 }
1057
1058 if (mat->n_row == 0)
1059 fprintf(out, "%*s[]\n", indent, "");
1060
1061 for (i = 0; i < mat->n_row; ++i) {
1062 if (!i)
1063 fprintf(out, "%*s[[", indent, "");
1064 else
1065 fprintf(out, "%*s[", indent+1, "");
1066 for (j = 0; j < mat->n_col; ++j) {
1067 if (j)
1068 fprintf(out, ",");
1069 isl_int_print(out, mat->row[i][j], 0);
1070 }
1071 if (i == mat->n_row-1)
1072 fprintf(out, "]]\n");
1073 else
1074 fprintf(out, "]\n");
1075 }
1076 }
1077
1078 struct isl_mat *isl_mat_drop_cols(struct isl_mat *mat, unsigned col, unsigned n)
1079 {
1080 int r;
1081
1082 mat = isl_mat_cow(mat);
1083 if (!mat)
1084 return NULL;
1085
1086 if (col != mat->n_col-n) {
1087 for (r = 0; r < mat->n_row; ++r)
1088 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1089 mat->n_col - col - n);
1090 }
1091 mat->n_col -= n;
1092 return mat;
1093 }
1094
1095 struct isl_mat *isl_mat_drop_rows(struct isl_mat *mat, unsigned row, unsigned n)
1096 {
1097 int r;
1098
1099 mat = isl_mat_cow(mat);
1100 if (!mat)
1101 return NULL;
1102
1103 for (r = row; r+n < mat->n_row; ++r)
1104 mat->row[r] = mat->row[r+n];
1105
1106 mat->n_row -= n;
1107 return mat;
1108 }
1109
1110 __isl_give isl_mat *isl_mat_insert_cols(__isl_take isl_mat *mat,
1111 unsigned col, unsigned n)
1112 {
1113 isl_mat *ext;
1114
1115 if (!mat)
1116 return NULL;
1117 if (n == 0)
1118 return mat;
1119
1120 ext = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col + n);
1121 if (!ext)
1122 goto error;
1123
1124 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row, 0, 0, col);
1125 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row,
1126 col + n, col, mat->n_col - col);
1127
1128 isl_mat_free(mat);
1129 return ext;
1130 error:
1131 isl_mat_free(mat);
1132 return NULL;
1133 }
1134
1135 __isl_give isl_mat *isl_mat_insert_rows(__isl_take isl_mat *mat,
1136 unsigned row, unsigned n)
1137 {
1138 isl_mat *ext;
1139
1140 if (!mat)
1141 return NULL;
1142 if (n == 0)
1143 return mat;
1144
1145 ext = isl_mat_alloc(mat->ctx, mat->n_row + n, mat->n_col);
1146 if (!ext)
1147 goto error;
1148
1149 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, row, 0, 0, mat->n_col);
1150 isl_mat_sub_copy(mat->ctx, ext->row + row + n, mat->row + row,
1151 mat->n_row - row, 0, 0, mat->n_col);
1152
1153 isl_mat_free(mat);
1154 return ext;
1155 error:
1156 isl_mat_free(mat);
1157 return NULL;
1158 }
1159
1160 void isl_mat_col_submul(struct isl_mat *mat,
1161 int dst_col, isl_int f, int src_col)
1162 {
1163 int i;
1164
1165 for (i = 0; i < mat->n_row; ++i)
1166 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1167 }
1168
1169 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1170 {
1171 int i;
1172
1173 for (i = 0; i < mat->n_row; ++i)
1174 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1175 }
1176
1177 struct isl_mat *isl_mat_unimodular_complete(struct isl_mat *M, int row)
1178 {
1179 int r;
1180 struct isl_mat *H = NULL, *Q = NULL;
1181
1182 if (!M)
1183 return NULL;
1184
1185 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1186 M->n_row = row;
1187 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1188 M->n_row = M->n_col;
1189 if (!H)
1190 goto error;
1191 for (r = 0; r < row; ++r)
1192 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1193 for (r = row; r < M->n_row; ++r)
1194 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1195 isl_mat_free(H);
1196 isl_mat_free(Q);
1197 return M;
1198 error:
1199 isl_mat_free(H);
1200 isl_mat_free(Q);
1201 isl_mat_free(M);
1202 return NULL;
1203 }
1204
1205 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1206 __isl_take isl_mat *bot)
1207 {
1208 struct isl_mat *mat;
1209
1210 if (!top || !bot)
1211 goto error;
1212
1213 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1214 if (top->n_row == 0) {
1215 isl_mat_free(top);
1216 return bot;
1217 }
1218 if (bot->n_row == 0) {
1219 isl_mat_free(bot);
1220 return top;
1221 }
1222
1223 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1224 if (!mat)
1225 goto error;
1226 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1227 0, 0, mat->n_col);
1228 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1229 0, 0, mat->n_col);
1230 isl_mat_free(top);
1231 isl_mat_free(bot);
1232 return mat;
1233 error:
1234 isl_mat_free(top);
1235 isl_mat_free(bot);
1236 return NULL;
1237 }
1238
1239 int isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
1240 {
1241 int i;
1242
1243 if (!mat1 || !mat2)
1244 return -1;
1245
1246 if (mat1->n_row != mat2->n_row)
1247 return 0;
1248
1249 if (mat1->n_col != mat2->n_col)
1250 return 0;
1251
1252 for (i = 0; i < mat1->n_row; ++i)
1253 if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
1254 return 0;
1255
1256 return 1;
1257 }
1258
1259 __isl_give isl_mat *isl_mat_from_row_vec(__isl_take isl_vec *vec)
1260 {
1261 struct isl_mat *mat;
1262
1263 if (!vec)
1264 return NULL;
1265 mat = isl_mat_alloc(vec->ctx, 1, vec->size);
1266 if (!mat)
1267 goto error;
1268
1269 isl_seq_cpy(mat->row[0], vec->el, vec->size);
1270
1271 isl_vec_free(vec);
1272 return mat;
1273 error:
1274 isl_vec_free(vec);
1275 return NULL;
1276 }
1277
1278 __isl_give isl_mat *isl_mat_vec_concat(__isl_take isl_mat *top,
1279 __isl_take isl_vec *bot)
1280 {
1281 return isl_mat_concat(top, isl_mat_from_row_vec(bot));
1282 }
1283
1284 __isl_give isl_mat *isl_mat_move_cols(__isl_take isl_mat *mat,
1285 unsigned dst_col, unsigned src_col, unsigned n)
1286 {
1287 isl_mat *res;
1288
1289 if (!mat)
1290 return NULL;
1291 if (n == 0 || dst_col == src_col)
1292 return mat;
1293
1294 res = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
1295 if (!res)
1296 goto error;
1297
1298 if (dst_col < src_col) {
1299 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1300 0, 0, dst_col);
1301 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1302 dst_col, src_col, n);
1303 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1304 dst_col + n, dst_col, src_col - dst_col);
1305 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1306 src_col + n, src_col + n,
1307 res->n_col - src_col - n);
1308 } else {
1309 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1310 0, 0, src_col);
1311 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1312 src_col, src_col + n, dst_col - src_col);
1313 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1314 dst_col, src_col, n);
1315 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1316 dst_col + n, dst_col + n,
1317 res->n_col - dst_col - n);
1318 }
1319 isl_mat_free(mat);
1320
1321 return res;
1322 error:
1323 isl_mat_free(mat);
1324 return NULL;
1325 }
1326
1327 void isl_mat_gcd(__isl_keep isl_mat *mat, isl_int *gcd)
1328 {
1329 int i;
1330 isl_int g;
1331
1332 isl_int_set_si(*gcd, 0);
1333 if (!mat)
1334 return;
1335
1336 isl_int_init(g);
1337 for (i = 0; i < mat->n_row; ++i) {
1338 isl_seq_gcd(mat->row[i], mat->n_col, &g);
1339 isl_int_gcd(*gcd, *gcd, g);
1340 }
1341 isl_int_clear(g);
1342 }
1343
1344 __isl_give isl_mat *isl_mat_scale_down(__isl_take isl_mat *mat, isl_int m)
1345 {
1346 int i;
1347
1348 if (!mat)
1349 return NULL;
1350
1351 for (i = 0; i < mat->n_row; ++i)
1352 isl_seq_scale_down(mat->row[i], mat->row[i], m, mat->n_col);
1353
1354 return mat;
1355 }
1356
1357 __isl_give isl_mat *isl_mat_normalize(__isl_take isl_mat *mat)
1358 {
1359 isl_int gcd;
1360
1361 if (!mat)
1362 return NULL;
1363
1364 isl_int_init(gcd);
1365 isl_mat_gcd(mat, &gcd);
1366 mat = isl_mat_scale_down(mat, gcd);
1367 isl_int_clear(gcd);
1368
1369 return mat;
1370 }
Integer set library