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isl_union_map_range_product: only consider pairs of maps with matching domains
[isl.git] / isl_mat.c
blob4e6315c399bd636360287561ae32d621d79593f6
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_ctx_private.h>
11 #include <isl/dim.h>
12 #include <isl/seq.h>
13 #include <isl_mat_private.h>
14 #include "isl_map_private.h"
15 #include <isl_dim_private.h>
16
17 struct isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
18 unsigned n_row, unsigned n_col)
19 {
20 int i;
21 struct isl_mat *mat;
22
23 mat = isl_alloc_type(ctx, struct isl_mat);
24 if (!mat)
25 return NULL;
26
27 mat->row = NULL;
28 mat->block = isl_blk_alloc(ctx, n_row * n_col);
29 if (isl_blk_is_error(mat->block))
30 goto error;
31 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
32 if (!mat->row)
33 goto error;
34
35 for (i = 0; i < n_row; ++i)
36 mat->row[i] = mat->block.data + i * n_col;
37
38 mat->ctx = ctx;
39 isl_ctx_ref(ctx);
40 mat->ref = 1;
41 mat->n_row = n_row;
42 mat->n_col = n_col;
43 mat->max_col = n_col;
44 mat->flags = 0;
45
46 return mat;
47 error:
48 isl_blk_free(ctx, mat->block);
49 free(mat);
50 return NULL;
51 }
52
53 struct isl_mat *isl_mat_extend(struct isl_mat *mat,
54 unsigned n_row, unsigned n_col)
55 {
56 int i;
57 isl_int *old;
58 isl_int **row;
59
60 if (!mat)
61 return NULL;
62
63 if (mat->max_col >= n_col && mat->n_row >= n_row) {
64 if (mat->n_col < n_col)
65 mat->n_col = n_col;
66 return mat;
67 }
68
69 if (mat->max_col < n_col) {
70 struct isl_mat *new_mat;
71
72 if (n_row < mat->n_row)
73 n_row = mat->n_row;
74 new_mat = isl_mat_alloc(mat->ctx, n_row, n_col);
75 if (!new_mat)
76 goto error;
77 for (i = 0; i < mat->n_row; ++i)
78 isl_seq_cpy(new_mat->row[i], mat->row[i], mat->n_col);
79 isl_mat_free(mat);
80 return new_mat;
81 }
82
83 mat = isl_mat_cow(mat);
84 if (!mat)
85 goto error;
86
87 old = mat->block.data;
88 mat->block = isl_blk_extend(mat->ctx, mat->block, n_row * mat->max_col);
89 if (isl_blk_is_error(mat->block))
90 goto error;
91 row = isl_realloc_array(mat->ctx, mat->row, isl_int *, n_row);
92 if (!row)
93 goto error;
94 mat->row = row;
95
96 for (i = 0; i < mat->n_row; ++i)
97 mat->row[i] = mat->block.data + (mat->row[i] - old);
98 for (i = mat->n_row; i < n_row; ++i)
99 mat->row[i] = mat->block.data + i * mat->max_col;
100 mat->n_row = n_row;
101 if (mat->n_col < n_col)
102 mat->n_col = n_col;
103
104 return mat;
105 error:
106 isl_mat_free(mat);
107 return NULL;
108 }
109
110 struct isl_mat *isl_mat_sub_alloc(struct isl_ctx *ctx, isl_int **row,
111 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
112 {
113 int i;
114 struct isl_mat *mat;
115
116 mat = isl_alloc_type(ctx, struct isl_mat);
117 if (!mat)
118 return NULL;
119 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
120 if (!mat->row)
121 goto error;
122 for (i = 0; i < n_row; ++i)
123 mat->row[i] = row[first_row+i] + first_col;
124 mat->ctx = ctx;
125 isl_ctx_ref(ctx);
126 mat->ref = 1;
127 mat->n_row = n_row;
128 mat->n_col = n_col;
129 mat->block = isl_blk_empty();
130 mat->flags = ISL_MAT_BORROWED;
131 return mat;
132 error:
133 free(mat);
134 return NULL;
135 }
136
137 void isl_mat_sub_copy(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
138 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
139 {
140 int i;
141
142 for (i = 0; i < n_row; ++i)
143 isl_seq_cpy(dst[i]+dst_col, src[i]+src_col, n_col);
144 }
145
146 void isl_mat_sub_neg(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
147 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
148 {
149 int i;
150
151 for (i = 0; i < n_row; ++i)
152 isl_seq_neg(dst[i]+dst_col, src[i]+src_col, n_col);
153 }
154
155 struct isl_mat *isl_mat_copy(struct isl_mat *mat)
156 {
157 if (!mat)
158 return NULL;
159
160 mat->ref++;
161 return mat;
162 }
163
164 struct isl_mat *isl_mat_dup(struct isl_mat *mat)
165 {
166 int i;
167 struct isl_mat *mat2;
168
169 if (!mat)
170 return NULL;
171 mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
172 if (!mat2)
173 return NULL;
174 for (i = 0; i < mat->n_row; ++i)
175 isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);
176 return mat2;
177 }
178
179 struct isl_mat *isl_mat_cow(struct isl_mat *mat)
180 {
181 struct isl_mat *mat2;
182 if (!mat)
183 return NULL;
184
185 if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))
186 return mat;
187
188 mat2 = isl_mat_dup(mat);
189 isl_mat_free(mat);
190 return mat2;
191 }
192
193 void isl_mat_free(struct isl_mat *mat)
194 {
195 if (!mat)
196 return;
197
198 if (--mat->ref > 0)
199 return;
200
201 if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))
202 isl_blk_free(mat->ctx, mat->block);
203 isl_ctx_deref(mat->ctx);
204 free(mat->row);
205 free(mat);
206 }
207
208 int isl_mat_rows(__isl_keep isl_mat *mat)
209 {
210 return mat ? mat->n_row : -1;
211 }
212
213 int isl_mat_cols(__isl_keep isl_mat *mat)
214 {
215 return mat ? mat->n_col : -1;
216 }
217
218 int isl_mat_get_element(__isl_keep isl_mat *mat, int row, int col, isl_int *v)
219 {
220 if (!mat)
221 return -1;
222 if (row < 0 || row >= mat->n_row)
223 isl_die(mat->ctx, isl_error_invalid, "row out of range",
224 return -1);
225 if (col < 0 || col >= mat->n_col)
226 isl_die(mat->ctx, isl_error_invalid, "column out of range",
227 return -1);
228 isl_int_set(*v, mat->row[row][col]);
229 return 0;
230 }
231
232 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
233 int row, int col, isl_int v)
234 {
235 mat = isl_mat_cow(mat);
236 if (!mat)
237 return NULL;
238 if (row < 0 || row >= mat->n_row)
239 isl_die(mat->ctx, isl_error_invalid, "row out of range",
240 goto error);
241 if (col < 0 || col >= mat->n_col)
242 isl_die(mat->ctx, isl_error_invalid, "column out of range",
243 goto error);
244 isl_int_set(mat->row[row][col], v);
245 return mat;
246 error:
247 isl_mat_free(mat);
248 return NULL;
249 }
250
251 struct isl_mat *isl_mat_identity(struct isl_ctx *ctx, unsigned n_row)
252 {
253 int i;
254 struct isl_mat *mat;
255
256 mat = isl_mat_alloc(ctx, n_row, n_row);
257 if (!mat)
258 return NULL;
259 for (i = 0; i < n_row; ++i) {
260 isl_seq_clr(mat->row[i], i);
261 isl_int_set_si(mat->row[i][i], 1);
262 isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
263 }
264
265 return mat;
266 }
267
268 struct isl_vec *isl_mat_vec_product(struct isl_mat *mat, struct isl_vec *vec)
269 {
270 int i;
271 struct isl_vec *prod;
272
273 if (!mat || !vec)
274 goto error;
275
276 isl_assert(mat->ctx, mat->n_col == vec->size, goto error);
277
278 prod = isl_vec_alloc(mat->ctx, mat->n_row);
279 if (!prod)
280 goto error;
281
282 for (i = 0; i < prod->size; ++i)
283 isl_seq_inner_product(mat->row[i], vec->el, vec->size,
284 &prod->block.data[i]);
285 isl_mat_free(mat);
286 isl_vec_free(vec);
287 return prod;
288 error:
289 isl_mat_free(mat);
290 isl_vec_free(vec);
291 return NULL;
292 }
293
294 __isl_give isl_vec *isl_mat_vec_inverse_product(__isl_take isl_mat *mat,
295 __isl_take isl_vec *vec)
296 {
297 struct isl_mat *vec_mat;
298 int i;
299
300 if (!mat || !vec)
301 goto error;
302 vec_mat = isl_mat_alloc(vec->ctx, vec->size, 1);
303 if (!vec_mat)
304 goto error;
305 for (i = 0; i < vec->size; ++i)
306 isl_int_set(vec_mat->row[i][0], vec->el[i]);
307 vec_mat = isl_mat_inverse_product(mat, vec_mat);
308 isl_vec_free(vec);
309 if (!vec_mat)
310 return NULL;
311 vec = isl_vec_alloc(vec_mat->ctx, vec_mat->n_row);
312 if (vec)
313 for (i = 0; i < vec->size; ++i)
314 isl_int_set(vec->el[i], vec_mat->row[i][0]);
315 isl_mat_free(vec_mat);
316 return vec;
317 error:
318 isl_mat_free(mat);
319 isl_vec_free(vec);
320 return NULL;
321 }
322
323 struct isl_vec *isl_vec_mat_product(struct isl_vec *vec, struct isl_mat *mat)
324 {
325 int i, j;
326 struct isl_vec *prod;
327
328 if (!mat || !vec)
329 goto error;
330
331 isl_assert(mat->ctx, mat->n_row == vec->size, goto error);
332
333 prod = isl_vec_alloc(mat->ctx, mat->n_col);
334 if (!prod)
335 goto error;
336
337 for (i = 0; i < prod->size; ++i) {
338 isl_int_set_si(prod->el[i], 0);
339 for (j = 0; j < vec->size; ++j)
340 isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);
341 }
342 isl_mat_free(mat);
343 isl_vec_free(vec);
344 return prod;
345 error:
346 isl_mat_free(mat);
347 isl_vec_free(vec);
348 return NULL;
349 }
350
351 struct isl_mat *isl_mat_aff_direct_sum(struct isl_mat *left,
352 struct isl_mat *right)
353 {
354 int i;
355 struct isl_mat *sum;
356
357 if (!left || !right)
358 goto error;
359
360 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
361 isl_assert(left->ctx, left->n_row >= 1, goto error);
362 isl_assert(left->ctx, left->n_col >= 1, goto error);
363 isl_assert(left->ctx, right->n_col >= 1, goto error);
364 isl_assert(left->ctx,
365 isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,
366 goto error);
367 isl_assert(left->ctx,
368 isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
369 goto error);
370
371 sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);
372 if (!sum)
373 goto error;
374 isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);
375 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
376 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
377
378 isl_seq_clr(sum->row[0]+1, sum->n_col-1);
379 for (i = 1; i < sum->n_row; ++i) {
380 isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);
381 isl_int_addmul(sum->row[i][0],
382 right->row[0][0], right->row[i][0]);
383 isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],
384 left->n_col-1);
385 isl_seq_scale(sum->row[i]+left->n_col,
386 right->row[i]+1, right->row[0][0],
387 right->n_col-1);
388 }
389
390 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
391 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
392 isl_mat_free(left);
393 isl_mat_free(right);
394 return sum;
395 error:
396 isl_mat_free(left);
397 isl_mat_free(right);
398 return NULL;
399 }
400
401 static void exchange(struct isl_mat *M, struct isl_mat **U,
402 struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
403 {
404 int r;
405 for (r = row; r < M->n_row; ++r)
406 isl_int_swap(M->row[r][i], M->row[r][j]);
407 if (U) {
408 for (r = 0; r < (*U)->n_row; ++r)
409 isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
410 }
411 if (Q)
412 isl_mat_swap_rows(*Q, i, j);
413 }
414
415 static void subtract(struct isl_mat *M, struct isl_mat **U,
416 struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)
417 {
418 int r;
419 for (r = row; r < M->n_row; ++r)
420 isl_int_submul(M->row[r][j], m, M->row[r][i]);
421 if (U) {
422 for (r = 0; r < (*U)->n_row; ++r)
423 isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);
424 }
425 if (Q) {
426 for (r = 0; r < (*Q)->n_col; ++r)
427 isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);
428 }
429 }
430
431 static void oppose(struct isl_mat *M, struct isl_mat **U,
432 struct isl_mat **Q, unsigned row, unsigned col)
433 {
434 int r;
435 for (r = row; r < M->n_row; ++r)
436 isl_int_neg(M->row[r][col], M->row[r][col]);
437 if (U) {
438 for (r = 0; r < (*U)->n_row; ++r)
439 isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);
440 }
441 if (Q)
442 isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);
443 }
444
445 /* Given matrix M, compute
446 *
447 * M U = H
448 * M = H Q
449 *
450 * with U and Q unimodular matrices and H a matrix in column echelon form
451 * such that on each echelon row the entries in the non-echelon column
452 * are non-negative (if neg == 0) or non-positive (if neg == 1)
453 * and stricly smaller (in absolute value) than the entries in the echelon
454 * column.
455 * If U or Q are NULL, then these matrices are not computed.
456 */
457 struct isl_mat *isl_mat_left_hermite(struct isl_mat *M, int neg,
458 struct isl_mat **U, struct isl_mat **Q)
459 {
460 isl_int c;
461 int row, col;
462
463 if (U)
464 *U = NULL;
465 if (Q)
466 *Q = NULL;
467 if (!M)
468 goto error;
469 M = isl_mat_cow(M);
470 if (!M)
471 goto error;
472 if (U) {
473 *U = isl_mat_identity(M->ctx, M->n_col);
474 if (!*U)
475 goto error;
476 }
477 if (Q) {
478 *Q = isl_mat_identity(M->ctx, M->n_col);
479 if (!*Q)
480 goto error;
481 }
482
483 col = 0;
484 isl_int_init(c);
485 for (row = 0; row < M->n_row; ++row) {
486 int first, i, off;
487 first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);
488 if (first == -1)
489 continue;
490 first += col;
491 if (first != col)
492 exchange(M, U, Q, row, first, col);
493 if (isl_int_is_neg(M->row[row][col]))
494 oppose(M, U, Q, row, col);
495 first = col+1;
496 while ((off = isl_seq_first_non_zero(M->row[row]+first,
497 M->n_col-first)) != -1) {
498 first += off;
499 isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);
500 subtract(M, U, Q, row, col, first, c);
501 if (!isl_int_is_zero(M->row[row][first]))
502 exchange(M, U, Q, row, first, col);
503 else
504 ++first;
505 }
506 for (i = 0; i < col; ++i) {
507 if (isl_int_is_zero(M->row[row][i]))
508 continue;
509 if (neg)
510 isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);
511 else
512 isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);
513 if (isl_int_is_zero(c))
514 continue;
515 subtract(M, U, Q, row, col, i, c);
516 }
517 ++col;
518 }
519 isl_int_clear(c);
520
521 return M;
522 error:
523 if (Q) {
524 isl_mat_free(*Q);
525 *Q = NULL;
526 }
527 if (U) {
528 isl_mat_free(*U);
529 *U = NULL;
530 }
531 isl_mat_free(M);
532 return NULL;
533 }
534
535 struct isl_mat *isl_mat_right_kernel(struct isl_mat *mat)
536 {
537 int i, rank;
538 struct isl_mat *U = NULL;
539 struct isl_mat *K;
540
541 mat = isl_mat_left_hermite(mat, 0, &U, NULL);
542 if (!mat || !U)
543 goto error;
544
545 for (i = 0, rank = 0; rank < mat->n_col; ++rank) {
546 while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))
547 ++i;
548 if (i >= mat->n_row)
549 break;
550 }
551 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
552 if (!K)
553 goto error;
554 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
555 isl_mat_free(mat);
556 isl_mat_free(U);
557 return K;
558 error:
559 isl_mat_free(mat);
560 isl_mat_free(U);
561 return NULL;
562 }
563
564 struct isl_mat *isl_mat_lin_to_aff(struct isl_mat *mat)
565 {
566 int i;
567 struct isl_mat *mat2;
568
569 if (!mat)
570 return NULL;
571 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
572 if (!mat2)
573 goto error;
574 isl_int_set_si(mat2->row[0][0], 1);
575 isl_seq_clr(mat2->row[0]+1, mat->n_col);
576 for (i = 0; i < mat->n_row; ++i) {
577 isl_int_set_si(mat2->row[1+i][0], 0);
578 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
579 }
580 isl_mat_free(mat);
581 return mat2;
582 error:
583 isl_mat_free(mat);
584 return NULL;
585 }
586
587 /* Given two matrices M1 and M2, return the block matrix
588 *
589 * [ M1 0 ]
590 * [ 0 M2 ]
591 */
592 __isl_give isl_mat *isl_mat_diagonal(__isl_take isl_mat *mat1,
593 __isl_take isl_mat *mat2)
594 {
595 int i;
596 isl_mat *mat;
597
598 if (!mat1 || !mat2)
599 goto error;
600
601 mat = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
602 mat1->n_col + mat2->n_col);
603 if (!mat)
604 goto error;
605 for (i = 0; i < mat1->n_row; ++i) {
606 isl_seq_cpy(mat->row[i], mat1->row[i], mat1->n_col);
607 isl_seq_clr(mat->row[i] + mat1->n_col, mat2->n_col);
608 }
609 for (i = 0; i < mat2->n_row; ++i) {
610 isl_seq_clr(mat->row[mat1->n_row + i], mat1->n_col);
611 isl_seq_cpy(mat->row[mat1->n_row + i] + mat1->n_col,
612 mat2->row[i], mat2->n_col);
613 }
614 isl_mat_free(mat1);
615 isl_mat_free(mat2);
616 return mat;
617 error:
618 isl_mat_free(mat1);
619 isl_mat_free(mat2);
620 return NULL;
621 }
622
623 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
624 {
625 int i;
626
627 for (i = 0; i < n_row; ++i)
628 if (!isl_int_is_zero(row[i][col]))
629 return i;
630 return -1;
631 }
632
633 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
634 {
635 int i, min = row_first_non_zero(row, n_row, col);
636 if (min < 0)
637 return -1;
638 for (i = min + 1; i < n_row; ++i) {
639 if (isl_int_is_zero(row[i][col]))
640 continue;
641 if (isl_int_abs_lt(row[i][col], row[min][col]))
642 min = i;
643 }
644 return min;
645 }
646
647 static void inv_exchange(struct isl_mat *left, struct isl_mat *right,
648 unsigned i, unsigned j)
649 {
650 left = isl_mat_swap_rows(left, i, j);
651 right = isl_mat_swap_rows(right, i, j);
652 }
653
654 static void inv_oppose(
655 struct isl_mat *left, struct isl_mat *right, unsigned row)
656 {
657 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
658 isl_seq_neg(right->row[row], right->row[row], right->n_col);
659 }
660
661 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
662 unsigned row, unsigned i, isl_int m)
663 {
664 isl_int_neg(m, m);
665 isl_seq_combine(left->row[i]+row,
666 left->ctx->one, left->row[i]+row,
667 m, left->row[row]+row,
668 left->n_col-row);
669 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
670 m, right->row[row], right->n_col);
671 }
672
673 /* Compute inv(left)*right
674 */
675 struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
676 struct isl_mat *right)
677 {
678 int row;
679 isl_int a, b;
680
681 if (!left || !right)
682 goto error;
683
684 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
685 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
686
687 if (left->n_row == 0) {
688 isl_mat_free(left);
689 return right;
690 }
691
692 left = isl_mat_cow(left);
693 right = isl_mat_cow(right);
694 if (!left || !right)
695 goto error;
696
697 isl_int_init(a);
698 isl_int_init(b);
699 for (row = 0; row < left->n_row; ++row) {
700 int pivot, first, i, off;
701 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
702 if (pivot < 0) {
703 isl_int_clear(a);
704 isl_int_clear(b);
705 isl_assert(left->ctx, pivot >= 0, goto error);
706 }
707 pivot += row;
708 if (pivot != row)
709 inv_exchange(left, right, pivot, row);
710 if (isl_int_is_neg(left->row[row][row]))
711 inv_oppose(left, right, row);
712 first = row+1;
713 while ((off = row_first_non_zero(left->row+first,
714 left->n_row-first, row)) != -1) {
715 first += off;
716 isl_int_fdiv_q(a, left->row[first][row],
717 left->row[row][row]);
718 inv_subtract(left, right, row, first, a);
719 if (!isl_int_is_zero(left->row[first][row]))
720 inv_exchange(left, right, row, first);
721 else
722 ++first;
723 }
724 for (i = 0; i < row; ++i) {
725 if (isl_int_is_zero(left->row[i][row]))
726 continue;
727 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
728 isl_int_divexact(b, left->row[i][row], a);
729 isl_int_divexact(a, left->row[row][row], a);
730 isl_int_neg(b, b);
731 isl_seq_combine(left->row[i] + i,
732 a, left->row[i] + i,
733 b, left->row[row] + i,
734 left->n_col - i);
735 isl_seq_combine(right->row[i], a, right->row[i],
736 b, right->row[row], right->n_col);
737 }
738 }
739 isl_int_clear(b);
740
741 isl_int_set(a, left->row[0][0]);
742 for (row = 1; row < left->n_row; ++row)
743 isl_int_lcm(a, a, left->row[row][row]);
744 if (isl_int_is_zero(a)){
745 isl_int_clear(a);
746 isl_assert(left->ctx, 0, goto error);
747 }
748 for (row = 0; row < left->n_row; ++row) {
749 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
750 if (isl_int_is_one(left->row[row][row]))
751 continue;
752 isl_seq_scale(right->row[row], right->row[row],
753 left->row[row][row], right->n_col);
754 }
755 isl_int_clear(a);
756
757 isl_mat_free(left);
758 return right;
759 error:
760 isl_mat_free(left);
761 isl_mat_free(right);
762 return NULL;
763 }
764
765 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
766 {
767 int i;
768
769 for (i = 0; i < mat->n_row; ++i)
770 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
771 }
772
773 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
774 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
775 {
776 int i;
777 isl_int tmp;
778
779 isl_int_init(tmp);
780 for (i = 0; i < mat->n_row; ++i) {
781 isl_int_mul(tmp, m1, mat->row[i][src1]);
782 isl_int_addmul(tmp, m2, mat->row[i][src2]);
783 isl_int_set(mat->row[i][dst], tmp);
784 }
785 isl_int_clear(tmp);
786 }
787
788 struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
789 {
790 struct isl_mat *inv;
791 int row;
792 isl_int a, b;
793
794 mat = isl_mat_cow(mat);
795 if (!mat)
796 return NULL;
797
798 inv = isl_mat_identity(mat->ctx, mat->n_col);
799 inv = isl_mat_cow(inv);
800 if (!inv)
801 goto error;
802
803 isl_int_init(a);
804 isl_int_init(b);
805 for (row = 0; row < mat->n_row; ++row) {
806 int pivot, first, i, off;
807 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
808 if (pivot < 0) {
809 isl_int_clear(a);
810 isl_int_clear(b);
811 isl_assert(mat->ctx, pivot >= 0, goto error);
812 }
813 pivot += row;
814 if (pivot != row)
815 exchange(mat, &inv, NULL, row, pivot, row);
816 if (isl_int_is_neg(mat->row[row][row]))
817 oppose(mat, &inv, NULL, row, row);
818 first = row+1;
819 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
820 mat->n_col-first)) != -1) {
821 first += off;
822 isl_int_fdiv_q(a, mat->row[row][first],
823 mat->row[row][row]);
824 subtract(mat, &inv, NULL, row, row, first, a);
825 if (!isl_int_is_zero(mat->row[row][first]))
826 exchange(mat, &inv, NULL, row, row, first);
827 else
828 ++first;
829 }
830 for (i = 0; i < row; ++i) {
831 if (isl_int_is_zero(mat->row[row][i]))
832 continue;
833 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
834 isl_int_divexact(b, mat->row[row][i], a);
835 isl_int_divexact(a, mat->row[row][row], a);
836 isl_int_neg(a, a);
837 isl_mat_col_combine(mat, i, a, i, b, row);
838 isl_mat_col_combine(inv, i, a, i, b, row);
839 }
840 }
841 isl_int_clear(b);
842
843 isl_int_set(a, mat->row[0][0]);
844 for (row = 1; row < mat->n_row; ++row)
845 isl_int_lcm(a, a, mat->row[row][row]);
846 if (isl_int_is_zero(a)){
847 isl_int_clear(a);
848 goto error;
849 }
850 for (row = 0; row < mat->n_row; ++row) {
851 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
852 if (isl_int_is_one(mat->row[row][row]))
853 continue;
854 isl_mat_col_scale(inv, row, mat->row[row][row]);
855 }
856 isl_int_clear(a);
857
858 isl_mat_free(mat);
859
860 return inv;
861 error:
862 isl_mat_free(mat);
863 isl_mat_free(inv);
864 return NULL;
865 }
866
867 struct isl_mat *isl_mat_transpose(struct isl_mat *mat)
868 {
869 struct isl_mat *transpose = NULL;
870 int i, j;
871
872 if (mat->n_col == mat->n_row) {
873 mat = isl_mat_cow(mat);
874 if (!mat)
875 return NULL;
876 for (i = 0; i < mat->n_row; ++i)
877 for (j = i + 1; j < mat->n_col; ++j)
878 isl_int_swap(mat->row[i][j], mat->row[j][i]);
879 return mat;
880 }
881 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
882 if (!transpose)
883 goto error;
884 for (i = 0; i < mat->n_row; ++i)
885 for (j = 0; j < mat->n_col; ++j)
886 isl_int_set(transpose->row[j][i], mat->row[i][j]);
887 isl_mat_free(mat);
888 return transpose;
889 error:
890 isl_mat_free(mat);
891 return NULL;
892 }
893
894 struct isl_mat *isl_mat_swap_cols(struct isl_mat *mat, unsigned i, unsigned j)
895 {
896 int r;
897
898 mat = isl_mat_cow(mat);
899 if (!mat)
900 return NULL;
901 isl_assert(mat->ctx, i < mat->n_col, goto error);
902 isl_assert(mat->ctx, j < mat->n_col, goto error);
903
904 for (r = 0; r < mat->n_row; ++r)
905 isl_int_swap(mat->row[r][i], mat->row[r][j]);
906 return mat;
907 error:
908 isl_mat_free(mat);
909 return NULL;
910 }
911
912 struct isl_mat *isl_mat_swap_rows(struct isl_mat *mat, unsigned i, unsigned j)
913 {
914 isl_int *t;
915
916 if (!mat)
917 return NULL;
918 mat = isl_mat_cow(mat);
919 if (!mat)
920 return NULL;
921 t = mat->row[i];
922 mat->row[i] = mat->row[j];
923 mat->row[j] = t;
924 return mat;
925 }
926
927 struct isl_mat *isl_mat_product(struct isl_mat *left, struct isl_mat *right)
928 {
929 int i, j, k;
930 struct isl_mat *prod;
931
932 if (!left || !right)
933 goto error;
934 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
935 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
936 if (!prod)
937 goto error;
938 if (left->n_col == 0) {
939 for (i = 0; i < prod->n_row; ++i)
940 isl_seq_clr(prod->row[i], prod->n_col);
941 isl_mat_free(left);
942 isl_mat_free(right);
943 return prod;
944 }
945 for (i = 0; i < prod->n_row; ++i) {
946 for (j = 0; j < prod->n_col; ++j) {
947 isl_int_mul(prod->row[i][j],
948 left->row[i][0], right->row[0][j]);
949 for (k = 1; k < left->n_col; ++k)
950 isl_int_addmul(prod->row[i][j],
951 left->row[i][k], right->row[k][j]);
952 }
953 }
954 isl_mat_free(left);
955 isl_mat_free(right);
956 return prod;
957 error:
958 isl_mat_free(left);
959 isl_mat_free(right);
960 return NULL;
961 }
962
963 /* Replace the variables x in the rows q by x' given by x = M x',
964 * with M the matrix mat.
965 *
966 * If the number of new variables is greater than the original
967 * number of variables, then the rows q have already been
968 * preextended. If the new number is smaller, then the coefficients
969 * of the divs, which are not changed, need to be shifted down.
970 * The row q may be the equalities, the inequalities or the
971 * div expressions. In the latter case, has_div is true and
972 * we need to take into account the extra denominator column.
973 */
974 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
975 unsigned n_div, int has_div, struct isl_mat *mat)
976 {
977 int i;
978 struct isl_mat *t;
979 int e;
980
981 if (mat->n_col >= mat->n_row)
982 e = 0;
983 else
984 e = mat->n_row - mat->n_col;
985 if (has_div)
986 for (i = 0; i < n; ++i)
987 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
988 t = isl_mat_sub_alloc(mat->ctx, q, 0, n, has_div, mat->n_row);
989 t = isl_mat_product(t, mat);
990 if (!t)
991 return -1;
992 for (i = 0; i < n; ++i) {
993 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
994 isl_seq_cpy(q[i] + has_div + t->n_col,
995 q[i] + has_div + t->n_col + e, n_div);
996 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
997 }
998 isl_mat_free(t);
999 return 0;
1000 }
1001
1002 /* Replace the variables x in bset by x' given by x = M x', with
1003 * M the matrix mat.
1004 *
1005 * If there are fewer variables x' then there are x, then we perform
1006 * the transformation in place, which that, in principle,
1007 * this frees up some extra variables as the number
1008 * of columns remains constant, but we would have to extend
1009 * the div array too as the number of rows in this array is assumed
1010 * to be equal to extra.
1011 */
1012 struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
1013 struct isl_mat *mat)
1014 {
1015 struct isl_ctx *ctx;
1016
1017 if (!bset || !mat)
1018 goto error;
1019
1020 ctx = bset->ctx;
1021 bset = isl_basic_set_cow(bset);
1022 if (!bset)
1023 goto error;
1024
1025 isl_assert(ctx, bset->dim->nparam == 0, goto error);
1026 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
1027 isl_assert(ctx, mat->n_col > 0, goto error);
1028
1029 if (mat->n_col > mat->n_row) {
1030 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0, 0, 0);
1031 if (!bset)
1032 goto error;
1033 } else if (mat->n_col < mat->n_row) {
1034 bset->dim = isl_dim_cow(bset->dim);
1035 if (!bset->dim)
1036 goto error;
1037 bset->dim->n_out -= mat->n_row - mat->n_col;
1038 }
1039
1040 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
1041 isl_mat_copy(mat)) < 0)
1042 goto error;
1043
1044 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
1045 isl_mat_copy(mat)) < 0)
1046 goto error;
1047
1048 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
1049 goto error2;
1050
1051 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
1052 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
1053 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1054 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1055 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
1056
1057 bset = isl_basic_set_simplify(bset);
1058 bset = isl_basic_set_finalize(bset);
1059
1060 return bset;
1061 error:
1062 isl_mat_free(mat);
1063 error2:
1064 isl_basic_set_free(bset);
1065 return NULL;
1066 }
1067
1068 struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
1069 {
1070 struct isl_ctx *ctx;
1071 int i;
1072
1073 set = isl_set_cow(set);
1074 if (!set)
1075 return NULL;
1076
1077 ctx = set->ctx;
1078 for (i = 0; i < set->n; ++i) {
1079 set->p[i] = isl_basic_set_preimage(set->p[i],
1080 isl_mat_copy(mat));
1081 if (!set->p[i])
1082 goto error;
1083 }
1084 if (mat->n_col != mat->n_row) {
1085 set->dim = isl_dim_cow(set->dim);
1086 if (!set->dim)
1087 goto error;
1088 set->dim->n_out += mat->n_col;
1089 set->dim->n_out -= mat->n_row;
1090 }
1091 isl_mat_free(mat);
1092 ISL_F_CLR(set, ISL_SET_NORMALIZED);
1093 return set;
1094 error:
1095 isl_set_free(set);
1096 isl_mat_free(mat);
1097 return NULL;
1098 }
1099
1100 void isl_mat_dump(struct isl_mat *mat, FILE *out, int indent)
1101 {
1102 int i, j;
1103
1104 if (!mat) {
1105 fprintf(out, "%*snull mat\n", indent, "");
1106 return;
1107 }
1108
1109 if (mat->n_row == 0)
1110 fprintf(out, "%*s[]\n", indent, "");
1111
1112 for (i = 0; i < mat->n_row; ++i) {
1113 if (!i)
1114 fprintf(out, "%*s[[", indent, "");
1115 else
1116 fprintf(out, "%*s[", indent+1, "");
1117 for (j = 0; j < mat->n_col; ++j) {
1118 if (j)
1119 fprintf(out, ",");
1120 isl_int_print(out, mat->row[i][j], 0);
1121 }
1122 if (i == mat->n_row-1)
1123 fprintf(out, "]]\n");
1124 else
1125 fprintf(out, "]\n");
1126 }
1127 }
1128
1129 struct isl_mat *isl_mat_drop_cols(struct isl_mat *mat, unsigned col, unsigned n)
1130 {
1131 int r;
1132
1133 mat = isl_mat_cow(mat);
1134 if (!mat)
1135 return NULL;
1136
1137 if (col != mat->n_col-n) {
1138 for (r = 0; r < mat->n_row; ++r)
1139 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1140 mat->n_col - col - n);
1141 }
1142 mat->n_col -= n;
1143 return mat;
1144 }
1145
1146 struct isl_mat *isl_mat_drop_rows(struct isl_mat *mat, unsigned row, unsigned n)
1147 {
1148 int r;
1149
1150 mat = isl_mat_cow(mat);
1151 if (!mat)
1152 return NULL;
1153
1154 for (r = row; r+n < mat->n_row; ++r)
1155 mat->row[r] = mat->row[r+n];
1156
1157 mat->n_row -= n;
1158 return mat;
1159 }
1160
1161 __isl_give isl_mat *isl_mat_insert_cols(__isl_take isl_mat *mat,
1162 unsigned col, unsigned n)
1163 {
1164 isl_mat *ext;
1165
1166 if (!mat)
1167 return NULL;
1168 if (n == 0)
1169 return mat;
1170
1171 ext = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col + n);
1172 if (!ext)
1173 goto error;
1174
1175 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row, 0, 0, col);
1176 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row,
1177 col + n, col, mat->n_col - col);
1178
1179 isl_mat_free(mat);
1180 return ext;
1181 error:
1182 isl_mat_free(mat);
1183 return NULL;
1184 }
1185
1186 __isl_give isl_mat *isl_mat_insert_zero_cols(__isl_take isl_mat *mat,
1187 unsigned first, unsigned n)
1188 {
1189 int i;
1190
1191 if (!mat)
1192 return NULL;
1193 mat = isl_mat_insert_cols(mat, first, n);
1194 if (!mat)
1195 return NULL;
1196
1197 for (i = 0; i < mat->n_row; ++i)
1198 isl_seq_clr(mat->row[i] + first, n);
1199
1200 return mat;
1201 }
1202
1203 __isl_give isl_mat *isl_mat_add_zero_cols(__isl_take isl_mat *mat, unsigned n)
1204 {
1205 if (!mat)
1206 return NULL;
1207
1208 return isl_mat_insert_zero_cols(mat, mat->n_col, n);
1209 }
1210
1211 __isl_give isl_mat *isl_mat_insert_rows(__isl_take isl_mat *mat,
1212 unsigned row, unsigned n)
1213 {
1214 isl_mat *ext;
1215
1216 if (!mat)
1217 return NULL;
1218 if (n == 0)
1219 return mat;
1220
1221 ext = isl_mat_alloc(mat->ctx, mat->n_row + n, mat->n_col);
1222 if (!ext)
1223 goto error;
1224
1225 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, row, 0, 0, mat->n_col);
1226 isl_mat_sub_copy(mat->ctx, ext->row + row + n, mat->row + row,
1227 mat->n_row - row, 0, 0, mat->n_col);
1228
1229 isl_mat_free(mat);
1230 return ext;
1231 error:
1232 isl_mat_free(mat);
1233 return NULL;
1234 }
1235
1236 __isl_give isl_mat *isl_mat_add_rows(__isl_take isl_mat *mat, unsigned n)
1237 {
1238 if (!mat)
1239 return NULL;
1240
1241 return isl_mat_insert_rows(mat, mat->n_row, n);
1242 }
1243
1244 void isl_mat_col_submul(struct isl_mat *mat,
1245 int dst_col, isl_int f, int src_col)
1246 {
1247 int i;
1248
1249 for (i = 0; i < mat->n_row; ++i)
1250 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1251 }
1252
1253 void isl_mat_col_add(__isl_keep isl_mat *mat, int dst_col, int src_col)
1254 {
1255 int i;
1256
1257 if (!mat)
1258 return;
1259
1260 for (i = 0; i < mat->n_row; ++i)
1261 isl_int_add(mat->row[i][dst_col],
1262 mat->row[i][dst_col], mat->row[i][src_col]);
1263 }
1264
1265 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1266 {
1267 int i;
1268
1269 for (i = 0; i < mat->n_row; ++i)
1270 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1271 }
1272
1273 struct isl_mat *isl_mat_unimodular_complete(struct isl_mat *M, int row)
1274 {
1275 int r;
1276 struct isl_mat *H = NULL, *Q = NULL;
1277
1278 if (!M)
1279 return NULL;
1280
1281 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1282 M->n_row = row;
1283 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1284 M->n_row = M->n_col;
1285 if (!H)
1286 goto error;
1287 for (r = 0; r < row; ++r)
1288 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1289 for (r = row; r < M->n_row; ++r)
1290 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1291 isl_mat_free(H);
1292 isl_mat_free(Q);
1293 return M;
1294 error:
1295 isl_mat_free(H);
1296 isl_mat_free(Q);
1297 isl_mat_free(M);
1298 return NULL;
1299 }
1300
1301 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1302 __isl_take isl_mat *bot)
1303 {
1304 struct isl_mat *mat;
1305
1306 if (!top || !bot)
1307 goto error;
1308
1309 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1310 if (top->n_row == 0) {
1311 isl_mat_free(top);
1312 return bot;
1313 }
1314 if (bot->n_row == 0) {
1315 isl_mat_free(bot);
1316 return top;
1317 }
1318
1319 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1320 if (!mat)
1321 goto error;
1322 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1323 0, 0, mat->n_col);
1324 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1325 0, 0, mat->n_col);
1326 isl_mat_free(top);
1327 isl_mat_free(bot);
1328 return mat;
1329 error:
1330 isl_mat_free(top);
1331 isl_mat_free(bot);
1332 return NULL;
1333 }
1334
1335 int isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
1336 {
1337 int i;
1338
1339 if (!mat1 || !mat2)
1340 return -1;
1341
1342 if (mat1->n_row != mat2->n_row)
1343 return 0;
1344
1345 if (mat1->n_col != mat2->n_col)
1346 return 0;
1347
1348 for (i = 0; i < mat1->n_row; ++i)
1349 if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
1350 return 0;
1351
1352 return 1;
1353 }
1354
1355 __isl_give isl_mat *isl_mat_from_row_vec(__isl_take isl_vec *vec)
1356 {
1357 struct isl_mat *mat;
1358
1359 if (!vec)
1360 return NULL;
1361 mat = isl_mat_alloc(vec->ctx, 1, vec->size);
1362 if (!mat)
1363 goto error;
1364
1365 isl_seq_cpy(mat->row[0], vec->el, vec->size);
1366
1367 isl_vec_free(vec);
1368 return mat;
1369 error:
1370 isl_vec_free(vec);
1371 return NULL;
1372 }
1373
1374 __isl_give isl_mat *isl_mat_vec_concat(__isl_take isl_mat *top,
1375 __isl_take isl_vec *bot)
1376 {
1377 return isl_mat_concat(top, isl_mat_from_row_vec(bot));
1378 }
1379
1380 __isl_give isl_mat *isl_mat_move_cols(__isl_take isl_mat *mat,
1381 unsigned dst_col, unsigned src_col, unsigned n)
1382 {
1383 isl_mat *res;
1384
1385 if (!mat)
1386 return NULL;
1387 if (n == 0 || dst_col == src_col)
1388 return mat;
1389
1390 res = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
1391 if (!res)
1392 goto error;
1393
1394 if (dst_col < src_col) {
1395 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1396 0, 0, dst_col);
1397 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1398 dst_col, src_col, n);
1399 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1400 dst_col + n, dst_col, src_col - dst_col);
1401 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1402 src_col + n, src_col + n,
1403 res->n_col - src_col - n);
1404 } else {
1405 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1406 0, 0, src_col);
1407 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1408 src_col, src_col + n, dst_col - src_col);
1409 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1410 dst_col, src_col, n);
1411 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1412 dst_col + n, dst_col + n,
1413 res->n_col - dst_col - n);
1414 }
1415 isl_mat_free(mat);
1416
1417 return res;
1418 error:
1419 isl_mat_free(mat);
1420 return NULL;
1421 }
1422
1423 void isl_mat_gcd(__isl_keep isl_mat *mat, isl_int *gcd)
1424 {
1425 int i;
1426 isl_int g;
1427
1428 isl_int_set_si(*gcd, 0);
1429 if (!mat)
1430 return;
1431
1432 isl_int_init(g);
1433 for (i = 0; i < mat->n_row; ++i) {
1434 isl_seq_gcd(mat->row[i], mat->n_col, &g);
1435 isl_int_gcd(*gcd, *gcd, g);
1436 }
1437 isl_int_clear(g);
1438 }
1439
1440 __isl_give isl_mat *isl_mat_scale_down(__isl_take isl_mat *mat, isl_int m)
1441 {
1442 int i;
1443
1444 if (isl_int_is_one(m))
1445 return mat;
1446
1447 mat = isl_mat_cow(mat);
1448 if (!mat)
1449 return NULL;
1450
1451 for (i = 0; i < mat->n_row; ++i)
1452 isl_seq_scale_down(mat->row[i], mat->row[i], m, mat->n_col);
1453
1454 return mat;
1455 }
1456
1457 __isl_give isl_mat *isl_mat_normalize(__isl_take isl_mat *mat)
1458 {
1459 isl_int gcd;
1460
1461 if (!mat)
1462 return NULL;
1463
1464 isl_int_init(gcd);
1465 isl_mat_gcd(mat, &gcd);
1466 mat = isl_mat_scale_down(mat, gcd);
1467 isl_int_clear(gcd);
1468
1469 return mat;
1470 }
Integer set library