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doc: add some implementation details on parametric integer programming
[isl.git] / isl_mat.c
blob271c64948b36cdc45e0dcb841c2595f78c3a3020
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 return NULL;
532 }
533
534 struct isl_mat *isl_mat_right_kernel(struct isl_mat *mat)
535 {
536 int i, rank;
537 struct isl_mat *U = NULL;
538 struct isl_mat *K;
539
540 mat = isl_mat_left_hermite(mat, 0, &U, NULL);
541 if (!mat || !U)
542 goto error;
543
544 for (i = 0, rank = 0; rank < mat->n_col; ++rank) {
545 while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))
546 ++i;
547 if (i >= mat->n_row)
548 break;
549 }
550 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
551 if (!K)
552 goto error;
553 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
554 isl_mat_free(mat);
555 isl_mat_free(U);
556 return K;
557 error:
558 isl_mat_free(mat);
559 isl_mat_free(U);
560 return NULL;
561 }
562
563 struct isl_mat *isl_mat_lin_to_aff(struct isl_mat *mat)
564 {
565 int i;
566 struct isl_mat *mat2;
567
568 if (!mat)
569 return NULL;
570 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
571 if (!mat2)
572 goto error;
573 isl_int_set_si(mat2->row[0][0], 1);
574 isl_seq_clr(mat2->row[0]+1, mat->n_col);
575 for (i = 0; i < mat->n_row; ++i) {
576 isl_int_set_si(mat2->row[1+i][0], 0);
577 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
578 }
579 isl_mat_free(mat);
580 return mat2;
581 error:
582 isl_mat_free(mat);
583 return NULL;
584 }
585
586 /* Given two matrices M1 and M2, return the block matrix
587 *
588 * [ M1 0 ]
589 * [ 0 M2 ]
590 */
591 __isl_give isl_mat *isl_mat_diagonal(__isl_take isl_mat *mat1,
592 __isl_take isl_mat *mat2)
593 {
594 int i;
595 isl_mat *mat;
596
597 if (!mat1 || !mat2)
598 goto error;
599
600 mat = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
601 mat1->n_col + mat2->n_col);
602 if (!mat)
603 goto error;
604 for (i = 0; i < mat1->n_row; ++i) {
605 isl_seq_cpy(mat->row[i], mat1->row[i], mat1->n_col);
606 isl_seq_clr(mat->row[i] + mat1->n_col, mat2->n_col);
607 }
608 for (i = 0; i < mat2->n_row; ++i) {
609 isl_seq_clr(mat->row[mat1->n_row + i], mat1->n_col);
610 isl_seq_cpy(mat->row[mat1->n_row + i] + mat1->n_col,
611 mat2->row[i], mat2->n_col);
612 }
613 isl_mat_free(mat1);
614 isl_mat_free(mat2);
615 return mat;
616 error:
617 isl_mat_free(mat1);
618 isl_mat_free(mat2);
619 return NULL;
620 }
621
622 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
623 {
624 int i;
625
626 for (i = 0; i < n_row; ++i)
627 if (!isl_int_is_zero(row[i][col]))
628 return i;
629 return -1;
630 }
631
632 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
633 {
634 int i, min = row_first_non_zero(row, n_row, col);
635 if (min < 0)
636 return -1;
637 for (i = min + 1; i < n_row; ++i) {
638 if (isl_int_is_zero(row[i][col]))
639 continue;
640 if (isl_int_abs_lt(row[i][col], row[min][col]))
641 min = i;
642 }
643 return min;
644 }
645
646 static void inv_exchange(struct isl_mat *left, struct isl_mat *right,
647 unsigned i, unsigned j)
648 {
649 left = isl_mat_swap_rows(left, i, j);
650 right = isl_mat_swap_rows(right, i, j);
651 }
652
653 static void inv_oppose(
654 struct isl_mat *left, struct isl_mat *right, unsigned row)
655 {
656 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
657 isl_seq_neg(right->row[row], right->row[row], right->n_col);
658 }
659
660 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
661 unsigned row, unsigned i, isl_int m)
662 {
663 isl_int_neg(m, m);
664 isl_seq_combine(left->row[i]+row,
665 left->ctx->one, left->row[i]+row,
666 m, left->row[row]+row,
667 left->n_col-row);
668 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
669 m, right->row[row], right->n_col);
670 }
671
672 /* Compute inv(left)*right
673 */
674 struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
675 struct isl_mat *right)
676 {
677 int row;
678 isl_int a, b;
679
680 if (!left || !right)
681 goto error;
682
683 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
684 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
685
686 if (left->n_row == 0) {
687 isl_mat_free(left);
688 return right;
689 }
690
691 left = isl_mat_cow(left);
692 right = isl_mat_cow(right);
693 if (!left || !right)
694 goto error;
695
696 isl_int_init(a);
697 isl_int_init(b);
698 for (row = 0; row < left->n_row; ++row) {
699 int pivot, first, i, off;
700 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
701 if (pivot < 0) {
702 isl_int_clear(a);
703 isl_int_clear(b);
704 isl_assert(left->ctx, pivot >= 0, goto error);
705 }
706 pivot += row;
707 if (pivot != row)
708 inv_exchange(left, right, pivot, row);
709 if (isl_int_is_neg(left->row[row][row]))
710 inv_oppose(left, right, row);
711 first = row+1;
712 while ((off = row_first_non_zero(left->row+first,
713 left->n_row-first, row)) != -1) {
714 first += off;
715 isl_int_fdiv_q(a, left->row[first][row],
716 left->row[row][row]);
717 inv_subtract(left, right, row, first, a);
718 if (!isl_int_is_zero(left->row[first][row]))
719 inv_exchange(left, right, row, first);
720 else
721 ++first;
722 }
723 for (i = 0; i < row; ++i) {
724 if (isl_int_is_zero(left->row[i][row]))
725 continue;
726 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
727 isl_int_divexact(b, left->row[i][row], a);
728 isl_int_divexact(a, left->row[row][row], a);
729 isl_int_neg(b, b);
730 isl_seq_combine(left->row[i] + i,
731 a, left->row[i] + i,
732 b, left->row[row] + i,
733 left->n_col - i);
734 isl_seq_combine(right->row[i], a, right->row[i],
735 b, right->row[row], right->n_col);
736 }
737 }
738 isl_int_clear(b);
739
740 isl_int_set(a, left->row[0][0]);
741 for (row = 1; row < left->n_row; ++row)
742 isl_int_lcm(a, a, left->row[row][row]);
743 if (isl_int_is_zero(a)){
744 isl_int_clear(a);
745 isl_assert(left->ctx, 0, goto error);
746 }
747 for (row = 0; row < left->n_row; ++row) {
748 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
749 if (isl_int_is_one(left->row[row][row]))
750 continue;
751 isl_seq_scale(right->row[row], right->row[row],
752 left->row[row][row], right->n_col);
753 }
754 isl_int_clear(a);
755
756 isl_mat_free(left);
757 return right;
758 error:
759 isl_mat_free(left);
760 isl_mat_free(right);
761 return NULL;
762 }
763
764 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
765 {
766 int i;
767
768 for (i = 0; i < mat->n_row; ++i)
769 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
770 }
771
772 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
773 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
774 {
775 int i;
776 isl_int tmp;
777
778 isl_int_init(tmp);
779 for (i = 0; i < mat->n_row; ++i) {
780 isl_int_mul(tmp, m1, mat->row[i][src1]);
781 isl_int_addmul(tmp, m2, mat->row[i][src2]);
782 isl_int_set(mat->row[i][dst], tmp);
783 }
784 isl_int_clear(tmp);
785 }
786
787 struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
788 {
789 struct isl_mat *inv;
790 int row;
791 isl_int a, b;
792
793 mat = isl_mat_cow(mat);
794 if (!mat)
795 return NULL;
796
797 inv = isl_mat_identity(mat->ctx, mat->n_col);
798 inv = isl_mat_cow(inv);
799 if (!inv)
800 goto error;
801
802 isl_int_init(a);
803 isl_int_init(b);
804 for (row = 0; row < mat->n_row; ++row) {
805 int pivot, first, i, off;
806 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
807 if (pivot < 0) {
808 isl_int_clear(a);
809 isl_int_clear(b);
810 isl_assert(mat->ctx, pivot >= 0, goto error);
811 }
812 pivot += row;
813 if (pivot != row)
814 exchange(mat, &inv, NULL, row, pivot, row);
815 if (isl_int_is_neg(mat->row[row][row]))
816 oppose(mat, &inv, NULL, row, row);
817 first = row+1;
818 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
819 mat->n_col-first)) != -1) {
820 first += off;
821 isl_int_fdiv_q(a, mat->row[row][first],
822 mat->row[row][row]);
823 subtract(mat, &inv, NULL, row, row, first, a);
824 if (!isl_int_is_zero(mat->row[row][first]))
825 exchange(mat, &inv, NULL, row, row, first);
826 else
827 ++first;
828 }
829 for (i = 0; i < row; ++i) {
830 if (isl_int_is_zero(mat->row[row][i]))
831 continue;
832 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
833 isl_int_divexact(b, mat->row[row][i], a);
834 isl_int_divexact(a, mat->row[row][row], a);
835 isl_int_neg(a, a);
836 isl_mat_col_combine(mat, i, a, i, b, row);
837 isl_mat_col_combine(inv, i, a, i, b, row);
838 }
839 }
840 isl_int_clear(b);
841
842 isl_int_set(a, mat->row[0][0]);
843 for (row = 1; row < mat->n_row; ++row)
844 isl_int_lcm(a, a, mat->row[row][row]);
845 if (isl_int_is_zero(a)){
846 isl_int_clear(a);
847 goto error;
848 }
849 for (row = 0; row < mat->n_row; ++row) {
850 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
851 if (isl_int_is_one(mat->row[row][row]))
852 continue;
853 isl_mat_col_scale(inv, row, mat->row[row][row]);
854 }
855 isl_int_clear(a);
856
857 isl_mat_free(mat);
858
859 return inv;
860 error:
861 isl_mat_free(mat);
862 isl_mat_free(inv);
863 return NULL;
864 }
865
866 struct isl_mat *isl_mat_transpose(struct isl_mat *mat)
867 {
868 struct isl_mat *transpose = NULL;
869 int i, j;
870
871 if (mat->n_col == mat->n_row) {
872 mat = isl_mat_cow(mat);
873 if (!mat)
874 return NULL;
875 for (i = 0; i < mat->n_row; ++i)
876 for (j = i + 1; j < mat->n_col; ++j)
877 isl_int_swap(mat->row[i][j], mat->row[j][i]);
878 return mat;
879 }
880 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
881 if (!transpose)
882 goto error;
883 for (i = 0; i < mat->n_row; ++i)
884 for (j = 0; j < mat->n_col; ++j)
885 isl_int_set(transpose->row[j][i], mat->row[i][j]);
886 isl_mat_free(mat);
887 return transpose;
888 error:
889 isl_mat_free(mat);
890 return NULL;
891 }
892
893 struct isl_mat *isl_mat_swap_cols(struct isl_mat *mat, unsigned i, unsigned j)
894 {
895 int r;
896
897 mat = isl_mat_cow(mat);
898 if (!mat)
899 return NULL;
900 isl_assert(mat->ctx, i < mat->n_col, goto error);
901 isl_assert(mat->ctx, j < mat->n_col, goto error);
902
903 for (r = 0; r < mat->n_row; ++r)
904 isl_int_swap(mat->row[r][i], mat->row[r][j]);
905 return mat;
906 error:
907 isl_mat_free(mat);
908 return NULL;
909 }
910
911 struct isl_mat *isl_mat_swap_rows(struct isl_mat *mat, unsigned i, unsigned j)
912 {
913 isl_int *t;
914
915 if (!mat)
916 return NULL;
917 mat = isl_mat_cow(mat);
918 if (!mat)
919 return NULL;
920 t = mat->row[i];
921 mat->row[i] = mat->row[j];
922 mat->row[j] = t;
923 return mat;
924 }
925
926 struct isl_mat *isl_mat_product(struct isl_mat *left, struct isl_mat *right)
927 {
928 int i, j, k;
929 struct isl_mat *prod;
930
931 if (!left || !right)
932 goto error;
933 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
934 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
935 if (!prod)
936 goto error;
937 if (left->n_col == 0) {
938 for (i = 0; i < prod->n_row; ++i)
939 isl_seq_clr(prod->row[i], prod->n_col);
940 return prod;
941 }
942 for (i = 0; i < prod->n_row; ++i) {
943 for (j = 0; j < prod->n_col; ++j) {
944 isl_int_mul(prod->row[i][j],
945 left->row[i][0], right->row[0][j]);
946 for (k = 1; k < left->n_col; ++k)
947 isl_int_addmul(prod->row[i][j],
948 left->row[i][k], right->row[k][j]);
949 }
950 }
951 isl_mat_free(left);
952 isl_mat_free(right);
953 return prod;
954 error:
955 isl_mat_free(left);
956 isl_mat_free(right);
957 return NULL;
958 }
959
960 /* Replace the variables x in the rows q by x' given by x = M x',
961 * with M the matrix mat.
962 *
963 * If the number of new variables is greater than the original
964 * number of variables, then the rows q have already been
965 * preextended. If the new number is smaller, then the coefficients
966 * of the divs, which are not changed, need to be shifted down.
967 * The row q may be the equalities, the inequalities or the
968 * div expressions. In the latter case, has_div is true and
969 * we need to take into account the extra denominator column.
970 */
971 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
972 unsigned n_div, int has_div, struct isl_mat *mat)
973 {
974 int i;
975 struct isl_mat *t;
976 int e;
977
978 if (mat->n_col >= mat->n_row)
979 e = 0;
980 else
981 e = mat->n_row - mat->n_col;
982 if (has_div)
983 for (i = 0; i < n; ++i)
984 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
985 t = isl_mat_sub_alloc(mat->ctx, q, 0, n, has_div, mat->n_row);
986 t = isl_mat_product(t, mat);
987 if (!t)
988 return -1;
989 for (i = 0; i < n; ++i) {
990 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
991 isl_seq_cpy(q[i] + has_div + t->n_col,
992 q[i] + has_div + t->n_col + e, n_div);
993 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
994 }
995 isl_mat_free(t);
996 return 0;
997 }
998
999 /* Replace the variables x in bset by x' given by x = M x', with
1000 * M the matrix mat.
1001 *
1002 * If there are fewer variables x' then there are x, then we perform
1003 * the transformation in place, which that, in principle,
1004 * this frees up some extra variables as the number
1005 * of columns remains constant, but we would have to extend
1006 * the div array too as the number of rows in this array is assumed
1007 * to be equal to extra.
1008 */
1009 struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
1010 struct isl_mat *mat)
1011 {
1012 struct isl_ctx *ctx;
1013
1014 if (!bset || !mat)
1015 goto error;
1016
1017 ctx = bset->ctx;
1018 bset = isl_basic_set_cow(bset);
1019 if (!bset)
1020 goto error;
1021
1022 isl_assert(ctx, bset->dim->nparam == 0, goto error);
1023 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
1024 isl_assert(ctx, mat->n_col > 0, goto error);
1025
1026 if (mat->n_col > mat->n_row) {
1027 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0, 0, 0);
1028 if (!bset)
1029 goto error;
1030 } else if (mat->n_col < mat->n_row) {
1031 bset->dim = isl_dim_cow(bset->dim);
1032 if (!bset->dim)
1033 goto error;
1034 bset->dim->n_out -= mat->n_row - mat->n_col;
1035 }
1036
1037 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
1038 isl_mat_copy(mat)) < 0)
1039 goto error;
1040
1041 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
1042 isl_mat_copy(mat)) < 0)
1043 goto error;
1044
1045 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
1046 goto error2;
1047
1048 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
1049 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
1050 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1051 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1052 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
1053
1054 bset = isl_basic_set_simplify(bset);
1055 bset = isl_basic_set_finalize(bset);
1056
1057 return bset;
1058 error:
1059 isl_mat_free(mat);
1060 error2:
1061 isl_basic_set_free(bset);
1062 return NULL;
1063 }
1064
1065 struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
1066 {
1067 struct isl_ctx *ctx;
1068 int i;
1069
1070 set = isl_set_cow(set);
1071 if (!set)
1072 return NULL;
1073
1074 ctx = set->ctx;
1075 for (i = 0; i < set->n; ++i) {
1076 set->p[i] = isl_basic_set_preimage(set->p[i],
1077 isl_mat_copy(mat));
1078 if (!set->p[i])
1079 goto error;
1080 }
1081 if (mat->n_col != mat->n_row) {
1082 set->dim = isl_dim_cow(set->dim);
1083 if (!set->dim)
1084 goto error;
1085 set->dim->n_out += mat->n_col;
1086 set->dim->n_out -= mat->n_row;
1087 }
1088 isl_mat_free(mat);
1089 ISL_F_CLR(set, ISL_SET_NORMALIZED);
1090 return set;
1091 error:
1092 isl_set_free(set);
1093 isl_mat_free(mat);
1094 return NULL;
1095 }
1096
1097 void isl_mat_dump(struct isl_mat *mat, FILE *out, int indent)
1098 {
1099 int i, j;
1100
1101 if (!mat) {
1102 fprintf(out, "%*snull mat\n", indent, "");
1103 return;
1104 }
1105
1106 if (mat->n_row == 0)
1107 fprintf(out, "%*s[]\n", indent, "");
1108
1109 for (i = 0; i < mat->n_row; ++i) {
1110 if (!i)
1111 fprintf(out, "%*s[[", indent, "");
1112 else
1113 fprintf(out, "%*s[", indent+1, "");
1114 for (j = 0; j < mat->n_col; ++j) {
1115 if (j)
1116 fprintf(out, ",");
1117 isl_int_print(out, mat->row[i][j], 0);
1118 }
1119 if (i == mat->n_row-1)
1120 fprintf(out, "]]\n");
1121 else
1122 fprintf(out, "]\n");
1123 }
1124 }
1125
1126 struct isl_mat *isl_mat_drop_cols(struct isl_mat *mat, unsigned col, unsigned n)
1127 {
1128 int r;
1129
1130 mat = isl_mat_cow(mat);
1131 if (!mat)
1132 return NULL;
1133
1134 if (col != mat->n_col-n) {
1135 for (r = 0; r < mat->n_row; ++r)
1136 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1137 mat->n_col - col - n);
1138 }
1139 mat->n_col -= n;
1140 return mat;
1141 }
1142
1143 struct isl_mat *isl_mat_drop_rows(struct isl_mat *mat, unsigned row, unsigned n)
1144 {
1145 int r;
1146
1147 mat = isl_mat_cow(mat);
1148 if (!mat)
1149 return NULL;
1150
1151 for (r = row; r+n < mat->n_row; ++r)
1152 mat->row[r] = mat->row[r+n];
1153
1154 mat->n_row -= n;
1155 return mat;
1156 }
1157
1158 __isl_give isl_mat *isl_mat_insert_cols(__isl_take isl_mat *mat,
1159 unsigned col, unsigned n)
1160 {
1161 isl_mat *ext;
1162
1163 if (!mat)
1164 return NULL;
1165 if (n == 0)
1166 return mat;
1167
1168 ext = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col + n);
1169 if (!ext)
1170 goto error;
1171
1172 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row, 0, 0, col);
1173 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row,
1174 col + n, col, mat->n_col - col);
1175
1176 isl_mat_free(mat);
1177 return ext;
1178 error:
1179 isl_mat_free(mat);
1180 return NULL;
1181 }
1182
1183 __isl_give isl_mat *isl_mat_insert_zero_cols(__isl_take isl_mat *mat,
1184 unsigned first, unsigned n)
1185 {
1186 int i;
1187
1188 if (!mat)
1189 return NULL;
1190 mat = isl_mat_insert_cols(mat, first, n);
1191 if (!mat)
1192 return NULL;
1193
1194 for (i = 0; i < mat->n_row; ++i)
1195 isl_seq_clr(mat->row[i] + first, n);
1196
1197 return mat;
1198 }
1199
1200 __isl_give isl_mat *isl_mat_add_zero_cols(__isl_take isl_mat *mat, unsigned n)
1201 {
1202 if (!mat)
1203 return NULL;
1204
1205 return isl_mat_insert_zero_cols(mat, mat->n_col, n);
1206 }
1207
1208 __isl_give isl_mat *isl_mat_insert_rows(__isl_take isl_mat *mat,
1209 unsigned row, unsigned n)
1210 {
1211 isl_mat *ext;
1212
1213 if (!mat)
1214 return NULL;
1215 if (n == 0)
1216 return mat;
1217
1218 ext = isl_mat_alloc(mat->ctx, mat->n_row + n, mat->n_col);
1219 if (!ext)
1220 goto error;
1221
1222 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, row, 0, 0, mat->n_col);
1223 isl_mat_sub_copy(mat->ctx, ext->row + row + n, mat->row + row,
1224 mat->n_row - row, 0, 0, mat->n_col);
1225
1226 isl_mat_free(mat);
1227 return ext;
1228 error:
1229 isl_mat_free(mat);
1230 return NULL;
1231 }
1232
1233 __isl_give isl_mat *isl_mat_add_rows(__isl_take isl_mat *mat, unsigned n)
1234 {
1235 if (!mat)
1236 return NULL;
1237
1238 return isl_mat_insert_rows(mat, mat->n_row, n);
1239 }
1240
1241 void isl_mat_col_submul(struct isl_mat *mat,
1242 int dst_col, isl_int f, int src_col)
1243 {
1244 int i;
1245
1246 for (i = 0; i < mat->n_row; ++i)
1247 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1248 }
1249
1250 void isl_mat_col_add(__isl_keep isl_mat *mat, int dst_col, int src_col)
1251 {
1252 int i;
1253
1254 if (!mat)
1255 return;
1256
1257 for (i = 0; i < mat->n_row; ++i)
1258 isl_int_add(mat->row[i][dst_col],
1259 mat->row[i][dst_col], mat->row[i][src_col]);
1260 }
1261
1262 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1263 {
1264 int i;
1265
1266 for (i = 0; i < mat->n_row; ++i)
1267 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1268 }
1269
1270 struct isl_mat *isl_mat_unimodular_complete(struct isl_mat *M, int row)
1271 {
1272 int r;
1273 struct isl_mat *H = NULL, *Q = NULL;
1274
1275 if (!M)
1276 return NULL;
1277
1278 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1279 M->n_row = row;
1280 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1281 M->n_row = M->n_col;
1282 if (!H)
1283 goto error;
1284 for (r = 0; r < row; ++r)
1285 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1286 for (r = row; r < M->n_row; ++r)
1287 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1288 isl_mat_free(H);
1289 isl_mat_free(Q);
1290 return M;
1291 error:
1292 isl_mat_free(H);
1293 isl_mat_free(Q);
1294 isl_mat_free(M);
1295 return NULL;
1296 }
1297
1298 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1299 __isl_take isl_mat *bot)
1300 {
1301 struct isl_mat *mat;
1302
1303 if (!top || !bot)
1304 goto error;
1305
1306 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1307 if (top->n_row == 0) {
1308 isl_mat_free(top);
1309 return bot;
1310 }
1311 if (bot->n_row == 0) {
1312 isl_mat_free(bot);
1313 return top;
1314 }
1315
1316 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1317 if (!mat)
1318 goto error;
1319 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1320 0, 0, mat->n_col);
1321 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1322 0, 0, mat->n_col);
1323 isl_mat_free(top);
1324 isl_mat_free(bot);
1325 return mat;
1326 error:
1327 isl_mat_free(top);
1328 isl_mat_free(bot);
1329 return NULL;
1330 }
1331
1332 int isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
1333 {
1334 int i;
1335
1336 if (!mat1 || !mat2)
1337 return -1;
1338
1339 if (mat1->n_row != mat2->n_row)
1340 return 0;
1341
1342 if (mat1->n_col != mat2->n_col)
1343 return 0;
1344
1345 for (i = 0; i < mat1->n_row; ++i)
1346 if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
1347 return 0;
1348
1349 return 1;
1350 }
1351
1352 __isl_give isl_mat *isl_mat_from_row_vec(__isl_take isl_vec *vec)
1353 {
1354 struct isl_mat *mat;
1355
1356 if (!vec)
1357 return NULL;
1358 mat = isl_mat_alloc(vec->ctx, 1, vec->size);
1359 if (!mat)
1360 goto error;
1361
1362 isl_seq_cpy(mat->row[0], vec->el, vec->size);
1363
1364 isl_vec_free(vec);
1365 return mat;
1366 error:
1367 isl_vec_free(vec);
1368 return NULL;
1369 }
1370
1371 __isl_give isl_mat *isl_mat_vec_concat(__isl_take isl_mat *top,
1372 __isl_take isl_vec *bot)
1373 {
1374 return isl_mat_concat(top, isl_mat_from_row_vec(bot));
1375 }
1376
1377 __isl_give isl_mat *isl_mat_move_cols(__isl_take isl_mat *mat,
1378 unsigned dst_col, unsigned src_col, unsigned n)
1379 {
1380 isl_mat *res;
1381
1382 if (!mat)
1383 return NULL;
1384 if (n == 0 || dst_col == src_col)
1385 return mat;
1386
1387 res = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
1388 if (!res)
1389 goto error;
1390
1391 if (dst_col < src_col) {
1392 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1393 0, 0, dst_col);
1394 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1395 dst_col, src_col, n);
1396 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1397 dst_col + n, dst_col, src_col - dst_col);
1398 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1399 src_col + n, src_col + n,
1400 res->n_col - src_col - n);
1401 } else {
1402 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1403 0, 0, src_col);
1404 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1405 src_col, src_col + n, dst_col - src_col);
1406 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1407 dst_col, src_col, n);
1408 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1409 dst_col + n, dst_col + n,
1410 res->n_col - dst_col - n);
1411 }
1412 isl_mat_free(mat);
1413
1414 return res;
1415 error:
1416 isl_mat_free(mat);
1417 return NULL;
1418 }
1419
1420 void isl_mat_gcd(__isl_keep isl_mat *mat, isl_int *gcd)
1421 {
1422 int i;
1423 isl_int g;
1424
1425 isl_int_set_si(*gcd, 0);
1426 if (!mat)
1427 return;
1428
1429 isl_int_init(g);
1430 for (i = 0; i < mat->n_row; ++i) {
1431 isl_seq_gcd(mat->row[i], mat->n_col, &g);
1432 isl_int_gcd(*gcd, *gcd, g);
1433 }
1434 isl_int_clear(g);
1435 }
1436
1437 __isl_give isl_mat *isl_mat_scale_down(__isl_take isl_mat *mat, isl_int m)
1438 {
1439 int i;
1440
1441 if (!mat)
1442 return NULL;
1443
1444 for (i = 0; i < mat->n_row; ++i)
1445 isl_seq_scale_down(mat->row[i], mat->row[i], m, mat->n_col);
1446
1447 return mat;
1448 }
1449
1450 __isl_give isl_mat *isl_mat_normalize(__isl_take isl_mat *mat)
1451 {
1452 isl_int gcd;
1453
1454 if (!mat)
1455 return NULL;
1456
1457 isl_int_init(gcd);
1458 isl_mat_gcd(mat, &gcd);
1459 mat = isl_mat_scale_down(mat, gcd);
1460 isl_int_clear(gcd);
1461
1462 return mat;
1463 }
Integer set library