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add isl_mat_normalize_row
[isl.git] / isl_mat.c
blobe64beaee9aed0bacc1ac1c9e58b2669ae081710b
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 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat)
18 {
19 return mat ? mat->ctx : NULL;
20 }
21
22 struct isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
23 unsigned n_row, unsigned n_col)
24 {
25 int i;
26 struct isl_mat *mat;
27
28 mat = isl_alloc_type(ctx, struct isl_mat);
29 if (!mat)
30 return NULL;
31
32 mat->row = NULL;
33 mat->block = isl_blk_alloc(ctx, n_row * n_col);
34 if (isl_blk_is_error(mat->block))
35 goto error;
36 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
37 if (!mat->row)
38 goto error;
39
40 for (i = 0; i < n_row; ++i)
41 mat->row[i] = mat->block.data + i * n_col;
42
43 mat->ctx = ctx;
44 isl_ctx_ref(ctx);
45 mat->ref = 1;
46 mat->n_row = n_row;
47 mat->n_col = n_col;
48 mat->max_col = n_col;
49 mat->flags = 0;
50
51 return mat;
52 error:
53 isl_blk_free(ctx, mat->block);
54 free(mat);
55 return NULL;
56 }
57
58 struct isl_mat *isl_mat_extend(struct isl_mat *mat,
59 unsigned n_row, unsigned n_col)
60 {
61 int i;
62 isl_int *old;
63 isl_int **row;
64
65 if (!mat)
66 return NULL;
67
68 if (mat->max_col >= n_col && mat->n_row >= n_row) {
69 if (mat->n_col < n_col)
70 mat->n_col = n_col;
71 return mat;
72 }
73
74 if (mat->max_col < n_col) {
75 struct isl_mat *new_mat;
76
77 if (n_row < mat->n_row)
78 n_row = mat->n_row;
79 new_mat = isl_mat_alloc(mat->ctx, n_row, n_col);
80 if (!new_mat)
81 goto error;
82 for (i = 0; i < mat->n_row; ++i)
83 isl_seq_cpy(new_mat->row[i], mat->row[i], mat->n_col);
84 isl_mat_free(mat);
85 return new_mat;
86 }
87
88 mat = isl_mat_cow(mat);
89 if (!mat)
90 goto error;
91
92 old = mat->block.data;
93 mat->block = isl_blk_extend(mat->ctx, mat->block, n_row * mat->max_col);
94 if (isl_blk_is_error(mat->block))
95 goto error;
96 row = isl_realloc_array(mat->ctx, mat->row, isl_int *, n_row);
97 if (!row)
98 goto error;
99 mat->row = row;
100
101 for (i = 0; i < mat->n_row; ++i)
102 mat->row[i] = mat->block.data + (mat->row[i] - old);
103 for (i = mat->n_row; i < n_row; ++i)
104 mat->row[i] = mat->block.data + i * mat->max_col;
105 mat->n_row = n_row;
106 if (mat->n_col < n_col)
107 mat->n_col = n_col;
108
109 return mat;
110 error:
111 isl_mat_free(mat);
112 return NULL;
113 }
114
115 __isl_give isl_mat *isl_mat_sub_alloc6(isl_ctx *ctx, isl_int **row,
116 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
117 {
118 int i;
119 struct isl_mat *mat;
120
121 mat = isl_alloc_type(ctx, struct isl_mat);
122 if (!mat)
123 return NULL;
124 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
125 if (!mat->row)
126 goto error;
127 for (i = 0; i < n_row; ++i)
128 mat->row[i] = row[first_row+i] + first_col;
129 mat->ctx = ctx;
130 isl_ctx_ref(ctx);
131 mat->ref = 1;
132 mat->n_row = n_row;
133 mat->n_col = n_col;
134 mat->block = isl_blk_empty();
135 mat->flags = ISL_MAT_BORROWED;
136 return mat;
137 error:
138 free(mat);
139 return NULL;
140 }
141
142 __isl_give isl_mat *isl_mat_sub_alloc(__isl_keep isl_mat *mat,
143 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
144 {
145 if (!mat)
146 return NULL;
147 return isl_mat_sub_alloc6(mat->ctx, mat->row, first_row, n_row,
148 first_col, n_col);
149 }
150
151 void isl_mat_sub_copy(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
152 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
153 {
154 int i;
155
156 for (i = 0; i < n_row; ++i)
157 isl_seq_cpy(dst[i]+dst_col, src[i]+src_col, n_col);
158 }
159
160 void isl_mat_sub_neg(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
161 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
162 {
163 int i;
164
165 for (i = 0; i < n_row; ++i)
166 isl_seq_neg(dst[i]+dst_col, src[i]+src_col, n_col);
167 }
168
169 struct isl_mat *isl_mat_copy(struct isl_mat *mat)
170 {
171 if (!mat)
172 return NULL;
173
174 mat->ref++;
175 return mat;
176 }
177
178 struct isl_mat *isl_mat_dup(struct isl_mat *mat)
179 {
180 int i;
181 struct isl_mat *mat2;
182
183 if (!mat)
184 return NULL;
185 mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
186 if (!mat2)
187 return NULL;
188 for (i = 0; i < mat->n_row; ++i)
189 isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);
190 return mat2;
191 }
192
193 struct isl_mat *isl_mat_cow(struct isl_mat *mat)
194 {
195 struct isl_mat *mat2;
196 if (!mat)
197 return NULL;
198
199 if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))
200 return mat;
201
202 mat2 = isl_mat_dup(mat);
203 isl_mat_free(mat);
204 return mat2;
205 }
206
207 void isl_mat_free(struct isl_mat *mat)
208 {
209 if (!mat)
210 return;
211
212 if (--mat->ref > 0)
213 return;
214
215 if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))
216 isl_blk_free(mat->ctx, mat->block);
217 isl_ctx_deref(mat->ctx);
218 free(mat->row);
219 free(mat);
220 }
221
222 int isl_mat_rows(__isl_keep isl_mat *mat)
223 {
224 return mat ? mat->n_row : -1;
225 }
226
227 int isl_mat_cols(__isl_keep isl_mat *mat)
228 {
229 return mat ? mat->n_col : -1;
230 }
231
232 int isl_mat_get_element(__isl_keep isl_mat *mat, int row, int col, isl_int *v)
233 {
234 if (!mat)
235 return -1;
236 if (row < 0 || row >= mat->n_row)
237 isl_die(mat->ctx, isl_error_invalid, "row out of range",
238 return -1);
239 if (col < 0 || col >= mat->n_col)
240 isl_die(mat->ctx, isl_error_invalid, "column out of range",
241 return -1);
242 isl_int_set(*v, mat->row[row][col]);
243 return 0;
244 }
245
246 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
247 int row, int col, isl_int v)
248 {
249 mat = isl_mat_cow(mat);
250 if (!mat)
251 return NULL;
252 if (row < 0 || row >= mat->n_row)
253 isl_die(mat->ctx, isl_error_invalid, "row out of range",
254 goto error);
255 if (col < 0 || col >= mat->n_col)
256 isl_die(mat->ctx, isl_error_invalid, "column out of range",
257 goto error);
258 isl_int_set(mat->row[row][col], v);
259 return mat;
260 error:
261 isl_mat_free(mat);
262 return NULL;
263 }
264
265 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
266 int row, int col, int v)
267 {
268 mat = isl_mat_cow(mat);
269 if (!mat)
270 return NULL;
271 if (row < 0 || row >= mat->n_row)
272 isl_die(mat->ctx, isl_error_invalid, "row out of range",
273 goto error);
274 if (col < 0 || col >= mat->n_col)
275 isl_die(mat->ctx, isl_error_invalid, "column out of range",
276 goto error);
277 isl_int_set_si(mat->row[row][col], v);
278 return mat;
279 error:
280 isl_mat_free(mat);
281 return NULL;
282 }
283
284 struct isl_mat *isl_mat_identity(struct isl_ctx *ctx, unsigned n_row)
285 {
286 int i;
287 struct isl_mat *mat;
288
289 mat = isl_mat_alloc(ctx, n_row, n_row);
290 if (!mat)
291 return NULL;
292 for (i = 0; i < n_row; ++i) {
293 isl_seq_clr(mat->row[i], i);
294 isl_int_set_si(mat->row[i][i], 1);
295 isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
296 }
297
298 return mat;
299 }
300
301 struct isl_vec *isl_mat_vec_product(struct isl_mat *mat, struct isl_vec *vec)
302 {
303 int i;
304 struct isl_vec *prod;
305
306 if (!mat || !vec)
307 goto error;
308
309 isl_assert(mat->ctx, mat->n_col == vec->size, goto error);
310
311 prod = isl_vec_alloc(mat->ctx, mat->n_row);
312 if (!prod)
313 goto error;
314
315 for (i = 0; i < prod->size; ++i)
316 isl_seq_inner_product(mat->row[i], vec->el, vec->size,
317 &prod->block.data[i]);
318 isl_mat_free(mat);
319 isl_vec_free(vec);
320 return prod;
321 error:
322 isl_mat_free(mat);
323 isl_vec_free(vec);
324 return NULL;
325 }
326
327 __isl_give isl_vec *isl_mat_vec_inverse_product(__isl_take isl_mat *mat,
328 __isl_take isl_vec *vec)
329 {
330 struct isl_mat *vec_mat;
331 int i;
332
333 if (!mat || !vec)
334 goto error;
335 vec_mat = isl_mat_alloc(vec->ctx, vec->size, 1);
336 if (!vec_mat)
337 goto error;
338 for (i = 0; i < vec->size; ++i)
339 isl_int_set(vec_mat->row[i][0], vec->el[i]);
340 vec_mat = isl_mat_inverse_product(mat, vec_mat);
341 isl_vec_free(vec);
342 if (!vec_mat)
343 return NULL;
344 vec = isl_vec_alloc(vec_mat->ctx, vec_mat->n_row);
345 if (vec)
346 for (i = 0; i < vec->size; ++i)
347 isl_int_set(vec->el[i], vec_mat->row[i][0]);
348 isl_mat_free(vec_mat);
349 return vec;
350 error:
351 isl_mat_free(mat);
352 isl_vec_free(vec);
353 return NULL;
354 }
355
356 struct isl_vec *isl_vec_mat_product(struct isl_vec *vec, struct isl_mat *mat)
357 {
358 int i, j;
359 struct isl_vec *prod;
360
361 if (!mat || !vec)
362 goto error;
363
364 isl_assert(mat->ctx, mat->n_row == vec->size, goto error);
365
366 prod = isl_vec_alloc(mat->ctx, mat->n_col);
367 if (!prod)
368 goto error;
369
370 for (i = 0; i < prod->size; ++i) {
371 isl_int_set_si(prod->el[i], 0);
372 for (j = 0; j < vec->size; ++j)
373 isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);
374 }
375 isl_mat_free(mat);
376 isl_vec_free(vec);
377 return prod;
378 error:
379 isl_mat_free(mat);
380 isl_vec_free(vec);
381 return NULL;
382 }
383
384 struct isl_mat *isl_mat_aff_direct_sum(struct isl_mat *left,
385 struct isl_mat *right)
386 {
387 int i;
388 struct isl_mat *sum;
389
390 if (!left || !right)
391 goto error;
392
393 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
394 isl_assert(left->ctx, left->n_row >= 1, goto error);
395 isl_assert(left->ctx, left->n_col >= 1, goto error);
396 isl_assert(left->ctx, right->n_col >= 1, goto error);
397 isl_assert(left->ctx,
398 isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,
399 goto error);
400 isl_assert(left->ctx,
401 isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
402 goto error);
403
404 sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);
405 if (!sum)
406 goto error;
407 isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);
408 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
409 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
410
411 isl_seq_clr(sum->row[0]+1, sum->n_col-1);
412 for (i = 1; i < sum->n_row; ++i) {
413 isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);
414 isl_int_addmul(sum->row[i][0],
415 right->row[0][0], right->row[i][0]);
416 isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],
417 left->n_col-1);
418 isl_seq_scale(sum->row[i]+left->n_col,
419 right->row[i]+1, right->row[0][0],
420 right->n_col-1);
421 }
422
423 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
424 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
425 isl_mat_free(left);
426 isl_mat_free(right);
427 return sum;
428 error:
429 isl_mat_free(left);
430 isl_mat_free(right);
431 return NULL;
432 }
433
434 static void exchange(struct isl_mat *M, struct isl_mat **U,
435 struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
436 {
437 int r;
438 for (r = row; r < M->n_row; ++r)
439 isl_int_swap(M->row[r][i], M->row[r][j]);
440 if (U) {
441 for (r = 0; r < (*U)->n_row; ++r)
442 isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
443 }
444 if (Q)
445 isl_mat_swap_rows(*Q, i, j);
446 }
447
448 static void subtract(struct isl_mat *M, struct isl_mat **U,
449 struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)
450 {
451 int r;
452 for (r = row; r < M->n_row; ++r)
453 isl_int_submul(M->row[r][j], m, M->row[r][i]);
454 if (U) {
455 for (r = 0; r < (*U)->n_row; ++r)
456 isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);
457 }
458 if (Q) {
459 for (r = 0; r < (*Q)->n_col; ++r)
460 isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);
461 }
462 }
463
464 static void oppose(struct isl_mat *M, struct isl_mat **U,
465 struct isl_mat **Q, unsigned row, unsigned col)
466 {
467 int r;
468 for (r = row; r < M->n_row; ++r)
469 isl_int_neg(M->row[r][col], M->row[r][col]);
470 if (U) {
471 for (r = 0; r < (*U)->n_row; ++r)
472 isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);
473 }
474 if (Q)
475 isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);
476 }
477
478 /* Given matrix M, compute
479 *
480 * M U = H
481 * M = H Q
482 *
483 * with U and Q unimodular matrices and H a matrix in column echelon form
484 * such that on each echelon row the entries in the non-echelon column
485 * are non-negative (if neg == 0) or non-positive (if neg == 1)
486 * and stricly smaller (in absolute value) than the entries in the echelon
487 * column.
488 * If U or Q are NULL, then these matrices are not computed.
489 */
490 struct isl_mat *isl_mat_left_hermite(struct isl_mat *M, int neg,
491 struct isl_mat **U, struct isl_mat **Q)
492 {
493 isl_int c;
494 int row, col;
495
496 if (U)
497 *U = NULL;
498 if (Q)
499 *Q = NULL;
500 if (!M)
501 goto error;
502 M = isl_mat_cow(M);
503 if (!M)
504 goto error;
505 if (U) {
506 *U = isl_mat_identity(M->ctx, M->n_col);
507 if (!*U)
508 goto error;
509 }
510 if (Q) {
511 *Q = isl_mat_identity(M->ctx, M->n_col);
512 if (!*Q)
513 goto error;
514 }
515
516 col = 0;
517 isl_int_init(c);
518 for (row = 0; row < M->n_row; ++row) {
519 int first, i, off;
520 first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);
521 if (first == -1)
522 continue;
523 first += col;
524 if (first != col)
525 exchange(M, U, Q, row, first, col);
526 if (isl_int_is_neg(M->row[row][col]))
527 oppose(M, U, Q, row, col);
528 first = col+1;
529 while ((off = isl_seq_first_non_zero(M->row[row]+first,
530 M->n_col-first)) != -1) {
531 first += off;
532 isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);
533 subtract(M, U, Q, row, col, first, c);
534 if (!isl_int_is_zero(M->row[row][first]))
535 exchange(M, U, Q, row, first, col);
536 else
537 ++first;
538 }
539 for (i = 0; i < col; ++i) {
540 if (isl_int_is_zero(M->row[row][i]))
541 continue;
542 if (neg)
543 isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);
544 else
545 isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);
546 if (isl_int_is_zero(c))
547 continue;
548 subtract(M, U, Q, row, col, i, c);
549 }
550 ++col;
551 }
552 isl_int_clear(c);
553
554 return M;
555 error:
556 if (Q) {
557 isl_mat_free(*Q);
558 *Q = NULL;
559 }
560 if (U) {
561 isl_mat_free(*U);
562 *U = NULL;
563 }
564 isl_mat_free(M);
565 return NULL;
566 }
567
568 struct isl_mat *isl_mat_right_kernel(struct isl_mat *mat)
569 {
570 int i, rank;
571 struct isl_mat *U = NULL;
572 struct isl_mat *K;
573
574 mat = isl_mat_left_hermite(mat, 0, &U, NULL);
575 if (!mat || !U)
576 goto error;
577
578 for (i = 0, rank = 0; rank < mat->n_col; ++rank) {
579 while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))
580 ++i;
581 if (i >= mat->n_row)
582 break;
583 }
584 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
585 if (!K)
586 goto error;
587 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
588 isl_mat_free(mat);
589 isl_mat_free(U);
590 return K;
591 error:
592 isl_mat_free(mat);
593 isl_mat_free(U);
594 return NULL;
595 }
596
597 struct isl_mat *isl_mat_lin_to_aff(struct isl_mat *mat)
598 {
599 int i;
600 struct isl_mat *mat2;
601
602 if (!mat)
603 return NULL;
604 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
605 if (!mat2)
606 goto error;
607 isl_int_set_si(mat2->row[0][0], 1);
608 isl_seq_clr(mat2->row[0]+1, mat->n_col);
609 for (i = 0; i < mat->n_row; ++i) {
610 isl_int_set_si(mat2->row[1+i][0], 0);
611 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
612 }
613 isl_mat_free(mat);
614 return mat2;
615 error:
616 isl_mat_free(mat);
617 return NULL;
618 }
619
620 /* Given two matrices M1 and M2, return the block matrix
621 *
622 * [ M1 0 ]
623 * [ 0 M2 ]
624 */
625 __isl_give isl_mat *isl_mat_diagonal(__isl_take isl_mat *mat1,
626 __isl_take isl_mat *mat2)
627 {
628 int i;
629 isl_mat *mat;
630
631 if (!mat1 || !mat2)
632 goto error;
633
634 mat = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
635 mat1->n_col + mat2->n_col);
636 if (!mat)
637 goto error;
638 for (i = 0; i < mat1->n_row; ++i) {
639 isl_seq_cpy(mat->row[i], mat1->row[i], mat1->n_col);
640 isl_seq_clr(mat->row[i] + mat1->n_col, mat2->n_col);
641 }
642 for (i = 0; i < mat2->n_row; ++i) {
643 isl_seq_clr(mat->row[mat1->n_row + i], mat1->n_col);
644 isl_seq_cpy(mat->row[mat1->n_row + i] + mat1->n_col,
645 mat2->row[i], mat2->n_col);
646 }
647 isl_mat_free(mat1);
648 isl_mat_free(mat2);
649 return mat;
650 error:
651 isl_mat_free(mat1);
652 isl_mat_free(mat2);
653 return NULL;
654 }
655
656 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
657 {
658 int i;
659
660 for (i = 0; i < n_row; ++i)
661 if (!isl_int_is_zero(row[i][col]))
662 return i;
663 return -1;
664 }
665
666 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
667 {
668 int i, min = row_first_non_zero(row, n_row, col);
669 if (min < 0)
670 return -1;
671 for (i = min + 1; i < n_row; ++i) {
672 if (isl_int_is_zero(row[i][col]))
673 continue;
674 if (isl_int_abs_lt(row[i][col], row[min][col]))
675 min = i;
676 }
677 return min;
678 }
679
680 static void inv_exchange(struct isl_mat *left, struct isl_mat *right,
681 unsigned i, unsigned j)
682 {
683 left = isl_mat_swap_rows(left, i, j);
684 right = isl_mat_swap_rows(right, i, j);
685 }
686
687 static void inv_oppose(
688 struct isl_mat *left, struct isl_mat *right, unsigned row)
689 {
690 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
691 isl_seq_neg(right->row[row], right->row[row], right->n_col);
692 }
693
694 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
695 unsigned row, unsigned i, isl_int m)
696 {
697 isl_int_neg(m, m);
698 isl_seq_combine(left->row[i]+row,
699 left->ctx->one, left->row[i]+row,
700 m, left->row[row]+row,
701 left->n_col-row);
702 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
703 m, right->row[row], right->n_col);
704 }
705
706 /* Compute inv(left)*right
707 */
708 struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
709 struct isl_mat *right)
710 {
711 int row;
712 isl_int a, b;
713
714 if (!left || !right)
715 goto error;
716
717 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
718 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
719
720 if (left->n_row == 0) {
721 isl_mat_free(left);
722 return right;
723 }
724
725 left = isl_mat_cow(left);
726 right = isl_mat_cow(right);
727 if (!left || !right)
728 goto error;
729
730 isl_int_init(a);
731 isl_int_init(b);
732 for (row = 0; row < left->n_row; ++row) {
733 int pivot, first, i, off;
734 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
735 if (pivot < 0) {
736 isl_int_clear(a);
737 isl_int_clear(b);
738 isl_assert(left->ctx, pivot >= 0, goto error);
739 }
740 pivot += row;
741 if (pivot != row)
742 inv_exchange(left, right, pivot, row);
743 if (isl_int_is_neg(left->row[row][row]))
744 inv_oppose(left, right, row);
745 first = row+1;
746 while ((off = row_first_non_zero(left->row+first,
747 left->n_row-first, row)) != -1) {
748 first += off;
749 isl_int_fdiv_q(a, left->row[first][row],
750 left->row[row][row]);
751 inv_subtract(left, right, row, first, a);
752 if (!isl_int_is_zero(left->row[first][row]))
753 inv_exchange(left, right, row, first);
754 else
755 ++first;
756 }
757 for (i = 0; i < row; ++i) {
758 if (isl_int_is_zero(left->row[i][row]))
759 continue;
760 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
761 isl_int_divexact(b, left->row[i][row], a);
762 isl_int_divexact(a, left->row[row][row], a);
763 isl_int_neg(b, b);
764 isl_seq_combine(left->row[i] + i,
765 a, left->row[i] + i,
766 b, left->row[row] + i,
767 left->n_col - i);
768 isl_seq_combine(right->row[i], a, right->row[i],
769 b, right->row[row], right->n_col);
770 }
771 }
772 isl_int_clear(b);
773
774 isl_int_set(a, left->row[0][0]);
775 for (row = 1; row < left->n_row; ++row)
776 isl_int_lcm(a, a, left->row[row][row]);
777 if (isl_int_is_zero(a)){
778 isl_int_clear(a);
779 isl_assert(left->ctx, 0, goto error);
780 }
781 for (row = 0; row < left->n_row; ++row) {
782 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
783 if (isl_int_is_one(left->row[row][row]))
784 continue;
785 isl_seq_scale(right->row[row], right->row[row],
786 left->row[row][row], right->n_col);
787 }
788 isl_int_clear(a);
789
790 isl_mat_free(left);
791 return right;
792 error:
793 isl_mat_free(left);
794 isl_mat_free(right);
795 return NULL;
796 }
797
798 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
799 {
800 int i;
801
802 for (i = 0; i < mat->n_row; ++i)
803 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
804 }
805
806 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
807 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
808 {
809 int i;
810 isl_int tmp;
811
812 isl_int_init(tmp);
813 for (i = 0; i < mat->n_row; ++i) {
814 isl_int_mul(tmp, m1, mat->row[i][src1]);
815 isl_int_addmul(tmp, m2, mat->row[i][src2]);
816 isl_int_set(mat->row[i][dst], tmp);
817 }
818 isl_int_clear(tmp);
819 }
820
821 struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
822 {
823 struct isl_mat *inv;
824 int row;
825 isl_int a, b;
826
827 mat = isl_mat_cow(mat);
828 if (!mat)
829 return NULL;
830
831 inv = isl_mat_identity(mat->ctx, mat->n_col);
832 inv = isl_mat_cow(inv);
833 if (!inv)
834 goto error;
835
836 isl_int_init(a);
837 isl_int_init(b);
838 for (row = 0; row < mat->n_row; ++row) {
839 int pivot, first, i, off;
840 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
841 if (pivot < 0) {
842 isl_int_clear(a);
843 isl_int_clear(b);
844 isl_assert(mat->ctx, pivot >= 0, goto error);
845 }
846 pivot += row;
847 if (pivot != row)
848 exchange(mat, &inv, NULL, row, pivot, row);
849 if (isl_int_is_neg(mat->row[row][row]))
850 oppose(mat, &inv, NULL, row, row);
851 first = row+1;
852 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
853 mat->n_col-first)) != -1) {
854 first += off;
855 isl_int_fdiv_q(a, mat->row[row][first],
856 mat->row[row][row]);
857 subtract(mat, &inv, NULL, row, row, first, a);
858 if (!isl_int_is_zero(mat->row[row][first]))
859 exchange(mat, &inv, NULL, row, row, first);
860 else
861 ++first;
862 }
863 for (i = 0; i < row; ++i) {
864 if (isl_int_is_zero(mat->row[row][i]))
865 continue;
866 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
867 isl_int_divexact(b, mat->row[row][i], a);
868 isl_int_divexact(a, mat->row[row][row], a);
869 isl_int_neg(a, a);
870 isl_mat_col_combine(mat, i, a, i, b, row);
871 isl_mat_col_combine(inv, i, a, i, b, row);
872 }
873 }
874 isl_int_clear(b);
875
876 isl_int_set(a, mat->row[0][0]);
877 for (row = 1; row < mat->n_row; ++row)
878 isl_int_lcm(a, a, mat->row[row][row]);
879 if (isl_int_is_zero(a)){
880 isl_int_clear(a);
881 goto error;
882 }
883 for (row = 0; row < mat->n_row; ++row) {
884 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
885 if (isl_int_is_one(mat->row[row][row]))
886 continue;
887 isl_mat_col_scale(inv, row, mat->row[row][row]);
888 }
889 isl_int_clear(a);
890
891 isl_mat_free(mat);
892
893 return inv;
894 error:
895 isl_mat_free(mat);
896 isl_mat_free(inv);
897 return NULL;
898 }
899
900 struct isl_mat *isl_mat_transpose(struct isl_mat *mat)
901 {
902 struct isl_mat *transpose = NULL;
903 int i, j;
904
905 if (mat->n_col == mat->n_row) {
906 mat = isl_mat_cow(mat);
907 if (!mat)
908 return NULL;
909 for (i = 0; i < mat->n_row; ++i)
910 for (j = i + 1; j < mat->n_col; ++j)
911 isl_int_swap(mat->row[i][j], mat->row[j][i]);
912 return mat;
913 }
914 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
915 if (!transpose)
916 goto error;
917 for (i = 0; i < mat->n_row; ++i)
918 for (j = 0; j < mat->n_col; ++j)
919 isl_int_set(transpose->row[j][i], mat->row[i][j]);
920 isl_mat_free(mat);
921 return transpose;
922 error:
923 isl_mat_free(mat);
924 return NULL;
925 }
926
927 struct isl_mat *isl_mat_swap_cols(struct isl_mat *mat, unsigned i, unsigned j)
928 {
929 int r;
930
931 mat = isl_mat_cow(mat);
932 if (!mat)
933 return NULL;
934 isl_assert(mat->ctx, i < mat->n_col, goto error);
935 isl_assert(mat->ctx, j < mat->n_col, goto error);
936
937 for (r = 0; r < mat->n_row; ++r)
938 isl_int_swap(mat->row[r][i], mat->row[r][j]);
939 return mat;
940 error:
941 isl_mat_free(mat);
942 return NULL;
943 }
944
945 struct isl_mat *isl_mat_swap_rows(struct isl_mat *mat, unsigned i, unsigned j)
946 {
947 isl_int *t;
948
949 if (!mat)
950 return NULL;
951 mat = isl_mat_cow(mat);
952 if (!mat)
953 return NULL;
954 t = mat->row[i];
955 mat->row[i] = mat->row[j];
956 mat->row[j] = t;
957 return mat;
958 }
959
960 struct isl_mat *isl_mat_product(struct isl_mat *left, struct isl_mat *right)
961 {
962 int i, j, k;
963 struct isl_mat *prod;
964
965 if (!left || !right)
966 goto error;
967 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
968 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
969 if (!prod)
970 goto error;
971 if (left->n_col == 0) {
972 for (i = 0; i < prod->n_row; ++i)
973 isl_seq_clr(prod->row[i], prod->n_col);
974 isl_mat_free(left);
975 isl_mat_free(right);
976 return prod;
977 }
978 for (i = 0; i < prod->n_row; ++i) {
979 for (j = 0; j < prod->n_col; ++j) {
980 isl_int_mul(prod->row[i][j],
981 left->row[i][0], right->row[0][j]);
982 for (k = 1; k < left->n_col; ++k)
983 isl_int_addmul(prod->row[i][j],
984 left->row[i][k], right->row[k][j]);
985 }
986 }
987 isl_mat_free(left);
988 isl_mat_free(right);
989 return prod;
990 error:
991 isl_mat_free(left);
992 isl_mat_free(right);
993 return NULL;
994 }
995
996 /* Replace the variables x in the rows q by x' given by x = M x',
997 * with M the matrix mat.
998 *
999 * If the number of new variables is greater than the original
1000 * number of variables, then the rows q have already been
1001 * preextended. If the new number is smaller, then the coefficients
1002 * of the divs, which are not changed, need to be shifted down.
1003 * The row q may be the equalities, the inequalities or the
1004 * div expressions. In the latter case, has_div is true and
1005 * we need to take into account the extra denominator column.
1006 */
1007 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
1008 unsigned n_div, int has_div, struct isl_mat *mat)
1009 {
1010 int i;
1011 struct isl_mat *t;
1012 int e;
1013
1014 if (mat->n_col >= mat->n_row)
1015 e = 0;
1016 else
1017 e = mat->n_row - mat->n_col;
1018 if (has_div)
1019 for (i = 0; i < n; ++i)
1020 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
1021 t = isl_mat_sub_alloc6(mat->ctx, q, 0, n, has_div, mat->n_row);
1022 t = isl_mat_product(t, mat);
1023 if (!t)
1024 return -1;
1025 for (i = 0; i < n; ++i) {
1026 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
1027 isl_seq_cpy(q[i] + has_div + t->n_col,
1028 q[i] + has_div + t->n_col + e, n_div);
1029 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
1030 }
1031 isl_mat_free(t);
1032 return 0;
1033 }
1034
1035 /* Replace the variables x in bset by x' given by x = M x', with
1036 * M the matrix mat.
1037 *
1038 * If there are fewer variables x' then there are x, then we perform
1039 * the transformation in place, which that, in principle,
1040 * this frees up some extra variables as the number
1041 * of columns remains constant, but we would have to extend
1042 * the div array too as the number of rows in this array is assumed
1043 * to be equal to extra.
1044 */
1045 struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
1046 struct isl_mat *mat)
1047 {
1048 struct isl_ctx *ctx;
1049
1050 if (!bset || !mat)
1051 goto error;
1052
1053 ctx = bset->ctx;
1054 bset = isl_basic_set_cow(bset);
1055 if (!bset)
1056 goto error;
1057
1058 isl_assert(ctx, bset->dim->nparam == 0, goto error);
1059 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
1060 isl_assert(ctx, mat->n_col > 0, goto error);
1061
1062 if (mat->n_col > mat->n_row) {
1063 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0, 0, 0);
1064 if (!bset)
1065 goto error;
1066 } else if (mat->n_col < mat->n_row) {
1067 bset->dim = isl_dim_cow(bset->dim);
1068 if (!bset->dim)
1069 goto error;
1070 bset->dim->n_out -= mat->n_row - mat->n_col;
1071 }
1072
1073 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
1074 isl_mat_copy(mat)) < 0)
1075 goto error;
1076
1077 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
1078 isl_mat_copy(mat)) < 0)
1079 goto error;
1080
1081 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
1082 goto error2;
1083
1084 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
1085 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
1086 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1087 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1088 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
1089
1090 bset = isl_basic_set_simplify(bset);
1091 bset = isl_basic_set_finalize(bset);
1092
1093 return bset;
1094 error:
1095 isl_mat_free(mat);
1096 error2:
1097 isl_basic_set_free(bset);
1098 return NULL;
1099 }
1100
1101 struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
1102 {
1103 struct isl_ctx *ctx;
1104 int i;
1105
1106 set = isl_set_cow(set);
1107 if (!set)
1108 return NULL;
1109
1110 ctx = set->ctx;
1111 for (i = 0; i < set->n; ++i) {
1112 set->p[i] = isl_basic_set_preimage(set->p[i],
1113 isl_mat_copy(mat));
1114 if (!set->p[i])
1115 goto error;
1116 }
1117 if (mat->n_col != mat->n_row) {
1118 set->dim = isl_dim_cow(set->dim);
1119 if (!set->dim)
1120 goto error;
1121 set->dim->n_out += mat->n_col;
1122 set->dim->n_out -= mat->n_row;
1123 }
1124 isl_mat_free(mat);
1125 ISL_F_CLR(set, ISL_SET_NORMALIZED);
1126 return set;
1127 error:
1128 isl_set_free(set);
1129 isl_mat_free(mat);
1130 return NULL;
1131 }
1132
1133 /* Replace the variables x starting at pos in the rows q
1134 * by x' with x = M x' with M the matrix mat.
1135 * That is, replace the corresponding coefficients c by c M.
1136 */
1137 static int transform(isl_ctx *ctx, isl_int **q, unsigned n,
1138 unsigned pos, __isl_take isl_mat *mat)
1139 {
1140 int i;
1141 isl_mat *t;
1142
1143 t = isl_mat_sub_alloc6(ctx, q, 0, n, pos, mat->n_row);
1144 t = isl_mat_product(t, mat);
1145 if (!t)
1146 return -1;
1147 for (i = 0; i < n; ++i)
1148 isl_seq_swp_or_cpy(q[i] + pos, t->row[i], t->n_col);
1149 isl_mat_free(t);
1150 return 0;
1151 }
1152
1153 /* Replace the variables x of type "type" starting at "first" in "bset"
1154 * by x' with x = M x' with M the matrix trans.
1155 * That is, replace the corresponding coefficients c by c M.
1156 *
1157 * The transformation matrix should be a square matrix.
1158 */
1159 __isl_give isl_basic_set *isl_basic_set_transform_dims(
1160 __isl_take isl_basic_set *bset, enum isl_dim_type type, unsigned first,
1161 __isl_take isl_mat *trans)
1162 {
1163 isl_ctx *ctx;
1164 unsigned pos;
1165
1166 bset = isl_basic_set_cow(bset);
1167 if (!bset || !trans)
1168 goto error;
1169
1170 ctx = isl_basic_set_get_ctx(bset);
1171 if (trans->n_row != trans->n_col)
1172 isl_die(trans->ctx, isl_error_invalid,
1173 "expecting square transformation matrix", goto error);
1174 if (first + trans->n_row > isl_basic_set_dim(bset, type))
1175 isl_die(trans->ctx, isl_error_invalid,
1176 "oversized transformation matrix", goto error);
1177
1178 pos = isl_basic_set_offset(bset, type) + first;
1179
1180 if (transform(ctx, bset->eq, bset->n_eq, pos, isl_mat_copy(trans)) < 0)
1181 goto error;
1182 if (transform(ctx, bset->ineq, bset->n_ineq, pos,
1183 isl_mat_copy(trans)) < 0)
1184 goto error;
1185 if (transform(ctx, bset->div, bset->n_div, 1 + pos,
1186 isl_mat_copy(trans)) < 0)
1187 goto error;
1188
1189 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1190 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1191
1192 isl_mat_free(trans);
1193 return bset;
1194 error:
1195 isl_mat_free(trans);
1196 isl_basic_set_free(bset);
1197 return NULL;
1198 }
1199
1200 void isl_mat_print_internal(__isl_keep isl_mat *mat, FILE *out, int indent)
1201 {
1202 int i, j;
1203
1204 if (!mat) {
1205 fprintf(out, "%*snull mat\n", indent, "");
1206 return;
1207 }
1208
1209 if (mat->n_row == 0)
1210 fprintf(out, "%*s[]\n", indent, "");
1211
1212 for (i = 0; i < mat->n_row; ++i) {
1213 if (!i)
1214 fprintf(out, "%*s[[", indent, "");
1215 else
1216 fprintf(out, "%*s[", indent+1, "");
1217 for (j = 0; j < mat->n_col; ++j) {
1218 if (j)
1219 fprintf(out, ",");
1220 isl_int_print(out, mat->row[i][j], 0);
1221 }
1222 if (i == mat->n_row-1)
1223 fprintf(out, "]]\n");
1224 else
1225 fprintf(out, "]\n");
1226 }
1227 }
1228
1229 void isl_mat_dump(__isl_keep isl_mat *mat)
1230 {
1231 isl_mat_print_internal(mat, stderr, 0);
1232 }
1233
1234 struct isl_mat *isl_mat_drop_cols(struct isl_mat *mat, unsigned col, unsigned n)
1235 {
1236 int r;
1237
1238 mat = isl_mat_cow(mat);
1239 if (!mat)
1240 return NULL;
1241
1242 if (col != mat->n_col-n) {
1243 for (r = 0; r < mat->n_row; ++r)
1244 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1245 mat->n_col - col - n);
1246 }
1247 mat->n_col -= n;
1248 return mat;
1249 }
1250
1251 struct isl_mat *isl_mat_drop_rows(struct isl_mat *mat, unsigned row, unsigned n)
1252 {
1253 int r;
1254
1255 mat = isl_mat_cow(mat);
1256 if (!mat)
1257 return NULL;
1258
1259 for (r = row; r+n < mat->n_row; ++r)
1260 mat->row[r] = mat->row[r+n];
1261
1262 mat->n_row -= n;
1263 return mat;
1264 }
1265
1266 __isl_give isl_mat *isl_mat_insert_cols(__isl_take isl_mat *mat,
1267 unsigned col, unsigned n)
1268 {
1269 isl_mat *ext;
1270
1271 if (!mat)
1272 return NULL;
1273 if (n == 0)
1274 return mat;
1275
1276 ext = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col + n);
1277 if (!ext)
1278 goto error;
1279
1280 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row, 0, 0, col);
1281 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row,
1282 col + n, col, mat->n_col - col);
1283
1284 isl_mat_free(mat);
1285 return ext;
1286 error:
1287 isl_mat_free(mat);
1288 return NULL;
1289 }
1290
1291 __isl_give isl_mat *isl_mat_insert_zero_cols(__isl_take isl_mat *mat,
1292 unsigned first, unsigned n)
1293 {
1294 int i;
1295
1296 if (!mat)
1297 return NULL;
1298 mat = isl_mat_insert_cols(mat, first, n);
1299 if (!mat)
1300 return NULL;
1301
1302 for (i = 0; i < mat->n_row; ++i)
1303 isl_seq_clr(mat->row[i] + first, n);
1304
1305 return mat;
1306 }
1307
1308 __isl_give isl_mat *isl_mat_add_zero_cols(__isl_take isl_mat *mat, unsigned n)
1309 {
1310 if (!mat)
1311 return NULL;
1312
1313 return isl_mat_insert_zero_cols(mat, mat->n_col, n);
1314 }
1315
1316 __isl_give isl_mat *isl_mat_insert_rows(__isl_take isl_mat *mat,
1317 unsigned row, unsigned n)
1318 {
1319 isl_mat *ext;
1320
1321 if (!mat)
1322 return NULL;
1323 if (n == 0)
1324 return mat;
1325
1326 ext = isl_mat_alloc(mat->ctx, mat->n_row + n, mat->n_col);
1327 if (!ext)
1328 goto error;
1329
1330 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, row, 0, 0, mat->n_col);
1331 isl_mat_sub_copy(mat->ctx, ext->row + row + n, mat->row + row,
1332 mat->n_row - row, 0, 0, mat->n_col);
1333
1334 isl_mat_free(mat);
1335 return ext;
1336 error:
1337 isl_mat_free(mat);
1338 return NULL;
1339 }
1340
1341 __isl_give isl_mat *isl_mat_add_rows(__isl_take isl_mat *mat, unsigned n)
1342 {
1343 if (!mat)
1344 return NULL;
1345
1346 return isl_mat_insert_rows(mat, mat->n_row, n);
1347 }
1348
1349 __isl_give isl_mat *isl_mat_insert_zero_rows(__isl_take isl_mat *mat,
1350 unsigned row, unsigned n)
1351 {
1352 int i;
1353
1354 mat = isl_mat_insert_rows(mat, row, n);
1355 if (!mat)
1356 return NULL;
1357
1358 for (i = 0; i < n; ++i)
1359 isl_seq_clr(mat->row[row + i], mat->n_col);
1360
1361 return mat;
1362 }
1363
1364 __isl_give isl_mat *isl_mat_add_zero_rows(__isl_take isl_mat *mat, unsigned n)
1365 {
1366 if (!mat)
1367 return NULL;
1368
1369 return isl_mat_insert_zero_rows(mat, mat->n_row, n);
1370 }
1371
1372 void isl_mat_col_submul(struct isl_mat *mat,
1373 int dst_col, isl_int f, int src_col)
1374 {
1375 int i;
1376
1377 for (i = 0; i < mat->n_row; ++i)
1378 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1379 }
1380
1381 void isl_mat_col_add(__isl_keep isl_mat *mat, int dst_col, int src_col)
1382 {
1383 int i;
1384
1385 if (!mat)
1386 return;
1387
1388 for (i = 0; i < mat->n_row; ++i)
1389 isl_int_add(mat->row[i][dst_col],
1390 mat->row[i][dst_col], mat->row[i][src_col]);
1391 }
1392
1393 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1394 {
1395 int i;
1396
1397 for (i = 0; i < mat->n_row; ++i)
1398 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1399 }
1400
1401 struct isl_mat *isl_mat_unimodular_complete(struct isl_mat *M, int row)
1402 {
1403 int r;
1404 struct isl_mat *H = NULL, *Q = NULL;
1405
1406 if (!M)
1407 return NULL;
1408
1409 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1410 M->n_row = row;
1411 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1412 M->n_row = M->n_col;
1413 if (!H)
1414 goto error;
1415 for (r = 0; r < row; ++r)
1416 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1417 for (r = row; r < M->n_row; ++r)
1418 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1419 isl_mat_free(H);
1420 isl_mat_free(Q);
1421 return M;
1422 error:
1423 isl_mat_free(H);
1424 isl_mat_free(Q);
1425 isl_mat_free(M);
1426 return NULL;
1427 }
1428
1429 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1430 __isl_take isl_mat *bot)
1431 {
1432 struct isl_mat *mat;
1433
1434 if (!top || !bot)
1435 goto error;
1436
1437 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1438 if (top->n_row == 0) {
1439 isl_mat_free(top);
1440 return bot;
1441 }
1442 if (bot->n_row == 0) {
1443 isl_mat_free(bot);
1444 return top;
1445 }
1446
1447 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1448 if (!mat)
1449 goto error;
1450 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1451 0, 0, mat->n_col);
1452 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1453 0, 0, mat->n_col);
1454 isl_mat_free(top);
1455 isl_mat_free(bot);
1456 return mat;
1457 error:
1458 isl_mat_free(top);
1459 isl_mat_free(bot);
1460 return NULL;
1461 }
1462
1463 int isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
1464 {
1465 int i;
1466
1467 if (!mat1 || !mat2)
1468 return -1;
1469
1470 if (mat1->n_row != mat2->n_row)
1471 return 0;
1472
1473 if (mat1->n_col != mat2->n_col)
1474 return 0;
1475
1476 for (i = 0; i < mat1->n_row; ++i)
1477 if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
1478 return 0;
1479
1480 return 1;
1481 }
1482
1483 __isl_give isl_mat *isl_mat_from_row_vec(__isl_take isl_vec *vec)
1484 {
1485 struct isl_mat *mat;
1486
1487 if (!vec)
1488 return NULL;
1489 mat = isl_mat_alloc(vec->ctx, 1, vec->size);
1490 if (!mat)
1491 goto error;
1492
1493 isl_seq_cpy(mat->row[0], vec->el, vec->size);
1494
1495 isl_vec_free(vec);
1496 return mat;
1497 error:
1498 isl_vec_free(vec);
1499 return NULL;
1500 }
1501
1502 __isl_give isl_mat *isl_mat_vec_concat(__isl_take isl_mat *top,
1503 __isl_take isl_vec *bot)
1504 {
1505 return isl_mat_concat(top, isl_mat_from_row_vec(bot));
1506 }
1507
1508 __isl_give isl_mat *isl_mat_move_cols(__isl_take isl_mat *mat,
1509 unsigned dst_col, unsigned src_col, unsigned n)
1510 {
1511 isl_mat *res;
1512
1513 if (!mat)
1514 return NULL;
1515 if (n == 0 || dst_col == src_col)
1516 return mat;
1517
1518 res = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
1519 if (!res)
1520 goto error;
1521
1522 if (dst_col < src_col) {
1523 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1524 0, 0, dst_col);
1525 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1526 dst_col, src_col, n);
1527 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1528 dst_col + n, dst_col, src_col - dst_col);
1529 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1530 src_col + n, src_col + n,
1531 res->n_col - src_col - n);
1532 } else {
1533 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1534 0, 0, src_col);
1535 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1536 src_col, src_col + n, dst_col - src_col);
1537 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1538 dst_col, src_col, n);
1539 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1540 dst_col + n, dst_col + n,
1541 res->n_col - dst_col - n);
1542 }
1543 isl_mat_free(mat);
1544
1545 return res;
1546 error:
1547 isl_mat_free(mat);
1548 return NULL;
1549 }
1550
1551 void isl_mat_gcd(__isl_keep isl_mat *mat, isl_int *gcd)
1552 {
1553 int i;
1554 isl_int g;
1555
1556 isl_int_set_si(*gcd, 0);
1557 if (!mat)
1558 return;
1559
1560 isl_int_init(g);
1561 for (i = 0; i < mat->n_row; ++i) {
1562 isl_seq_gcd(mat->row[i], mat->n_col, &g);
1563 isl_int_gcd(*gcd, *gcd, g);
1564 }
1565 isl_int_clear(g);
1566 }
1567
1568 __isl_give isl_mat *isl_mat_scale_down(__isl_take isl_mat *mat, isl_int m)
1569 {
1570 int i;
1571
1572 if (isl_int_is_one(m))
1573 return mat;
1574
1575 mat = isl_mat_cow(mat);
1576 if (!mat)
1577 return NULL;
1578
1579 for (i = 0; i < mat->n_row; ++i)
1580 isl_seq_scale_down(mat->row[i], mat->row[i], m, mat->n_col);
1581
1582 return mat;
1583 }
1584
1585 __isl_give isl_mat *isl_mat_normalize(__isl_take isl_mat *mat)
1586 {
1587 isl_int gcd;
1588
1589 if (!mat)
1590 return NULL;
1591
1592 isl_int_init(gcd);
1593 isl_mat_gcd(mat, &gcd);
1594 mat = isl_mat_scale_down(mat, gcd);
1595 isl_int_clear(gcd);
1596
1597 return mat;
1598 }
1599
1600 __isl_give isl_mat *isl_mat_normalize_row(__isl_take isl_mat *mat, int row)
1601 {
1602 mat = isl_mat_cow(mat);
1603 if (!mat)
1604 return NULL;
1605
1606 isl_seq_normalize(mat->ctx, mat->row[row], mat->n_col);
1607
1608 return mat;
1609 }
1610
1611 /* Number of initial non-zero columns.
1612 */
1613 int isl_mat_initial_non_zero_cols(__isl_keep isl_mat *mat)
1614 {
1615 int i;
1616
1617 if (!mat)
1618 return -1;
1619
1620 for (i = 0; i < mat->n_col; ++i)
1621 if (row_first_non_zero(mat->row, mat->n_row, i) < 0)
1622 break;
1623
1624 return i;
1625 }
Integer set library