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isl_mat_drop_cols: special case dropping of zero columns
[isl.git] / isl_mat.c
blob16a79f755a23e51b4dac4e37a69041108d2a994c
1 /*
2 * Copyright 2008-2009 Katholieke Universiteit Leuven
3 *
4 * Use of this software is governed by the MIT 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/space.h>
12 #include <isl/seq.h>
13 #include <isl_mat_private.h>
14 #include "isl_map_private.h"
15 #include <isl_space_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 __isl_give isl_mat *isl_mat_diag(isl_ctx *ctx, unsigned n_row, isl_int d)
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(mat->row[i][i], d);
295 isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
296 }
297
298 return mat;
299 }
300
301 __isl_give isl_mat *isl_mat_identity(isl_ctx *ctx, unsigned n_row)
302 {
303 if (!ctx)
304 return NULL;
305 return isl_mat_diag(ctx, n_row, ctx->one);
306 }
307
308 struct isl_vec *isl_mat_vec_product(struct isl_mat *mat, struct isl_vec *vec)
309 {
310 int i;
311 struct isl_vec *prod;
312
313 if (!mat || !vec)
314 goto error;
315
316 isl_assert(mat->ctx, mat->n_col == vec->size, goto error);
317
318 prod = isl_vec_alloc(mat->ctx, mat->n_row);
319 if (!prod)
320 goto error;
321
322 for (i = 0; i < prod->size; ++i)
323 isl_seq_inner_product(mat->row[i], vec->el, vec->size,
324 &prod->block.data[i]);
325 isl_mat_free(mat);
326 isl_vec_free(vec);
327 return prod;
328 error:
329 isl_mat_free(mat);
330 isl_vec_free(vec);
331 return NULL;
332 }
333
334 __isl_give isl_vec *isl_mat_vec_inverse_product(__isl_take isl_mat *mat,
335 __isl_take isl_vec *vec)
336 {
337 struct isl_mat *vec_mat;
338 int i;
339
340 if (!mat || !vec)
341 goto error;
342 vec_mat = isl_mat_alloc(vec->ctx, vec->size, 1);
343 if (!vec_mat)
344 goto error;
345 for (i = 0; i < vec->size; ++i)
346 isl_int_set(vec_mat->row[i][0], vec->el[i]);
347 vec_mat = isl_mat_inverse_product(mat, vec_mat);
348 isl_vec_free(vec);
349 if (!vec_mat)
350 return NULL;
351 vec = isl_vec_alloc(vec_mat->ctx, vec_mat->n_row);
352 if (vec)
353 for (i = 0; i < vec->size; ++i)
354 isl_int_set(vec->el[i], vec_mat->row[i][0]);
355 isl_mat_free(vec_mat);
356 return vec;
357 error:
358 isl_mat_free(mat);
359 isl_vec_free(vec);
360 return NULL;
361 }
362
363 struct isl_vec *isl_vec_mat_product(struct isl_vec *vec, struct isl_mat *mat)
364 {
365 int i, j;
366 struct isl_vec *prod;
367
368 if (!mat || !vec)
369 goto error;
370
371 isl_assert(mat->ctx, mat->n_row == vec->size, goto error);
372
373 prod = isl_vec_alloc(mat->ctx, mat->n_col);
374 if (!prod)
375 goto error;
376
377 for (i = 0; i < prod->size; ++i) {
378 isl_int_set_si(prod->el[i], 0);
379 for (j = 0; j < vec->size; ++j)
380 isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);
381 }
382 isl_mat_free(mat);
383 isl_vec_free(vec);
384 return prod;
385 error:
386 isl_mat_free(mat);
387 isl_vec_free(vec);
388 return NULL;
389 }
390
391 struct isl_mat *isl_mat_aff_direct_sum(struct isl_mat *left,
392 struct isl_mat *right)
393 {
394 int i;
395 struct isl_mat *sum;
396
397 if (!left || !right)
398 goto error;
399
400 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
401 isl_assert(left->ctx, left->n_row >= 1, goto error);
402 isl_assert(left->ctx, left->n_col >= 1, goto error);
403 isl_assert(left->ctx, right->n_col >= 1, goto error);
404 isl_assert(left->ctx,
405 isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,
406 goto error);
407 isl_assert(left->ctx,
408 isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
409 goto error);
410
411 sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);
412 if (!sum)
413 goto error;
414 isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);
415 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
416 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
417
418 isl_seq_clr(sum->row[0]+1, sum->n_col-1);
419 for (i = 1; i < sum->n_row; ++i) {
420 isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);
421 isl_int_addmul(sum->row[i][0],
422 right->row[0][0], right->row[i][0]);
423 isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],
424 left->n_col-1);
425 isl_seq_scale(sum->row[i]+left->n_col,
426 right->row[i]+1, right->row[0][0],
427 right->n_col-1);
428 }
429
430 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
431 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
432 isl_mat_free(left);
433 isl_mat_free(right);
434 return sum;
435 error:
436 isl_mat_free(left);
437 isl_mat_free(right);
438 return NULL;
439 }
440
441 static void exchange(struct isl_mat *M, struct isl_mat **U,
442 struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
443 {
444 int r;
445 for (r = row; r < M->n_row; ++r)
446 isl_int_swap(M->row[r][i], M->row[r][j]);
447 if (U) {
448 for (r = 0; r < (*U)->n_row; ++r)
449 isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
450 }
451 if (Q)
452 isl_mat_swap_rows(*Q, i, j);
453 }
454
455 static void subtract(struct isl_mat *M, struct isl_mat **U,
456 struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)
457 {
458 int r;
459 for (r = row; r < M->n_row; ++r)
460 isl_int_submul(M->row[r][j], m, M->row[r][i]);
461 if (U) {
462 for (r = 0; r < (*U)->n_row; ++r)
463 isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);
464 }
465 if (Q) {
466 for (r = 0; r < (*Q)->n_col; ++r)
467 isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);
468 }
469 }
470
471 static void oppose(struct isl_mat *M, struct isl_mat **U,
472 struct isl_mat **Q, unsigned row, unsigned col)
473 {
474 int r;
475 for (r = row; r < M->n_row; ++r)
476 isl_int_neg(M->row[r][col], M->row[r][col]);
477 if (U) {
478 for (r = 0; r < (*U)->n_row; ++r)
479 isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);
480 }
481 if (Q)
482 isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);
483 }
484
485 /* Given matrix M, compute
486 *
487 * M U = H
488 * M = H Q
489 *
490 * with U and Q unimodular matrices and H a matrix in column echelon form
491 * such that on each echelon row the entries in the non-echelon column
492 * are non-negative (if neg == 0) or non-positive (if neg == 1)
493 * and stricly smaller (in absolute value) than the entries in the echelon
494 * column.
495 * If U or Q are NULL, then these matrices are not computed.
496 */
497 struct isl_mat *isl_mat_left_hermite(struct isl_mat *M, int neg,
498 struct isl_mat **U, struct isl_mat **Q)
499 {
500 isl_int c;
501 int row, col;
502
503 if (U)
504 *U = NULL;
505 if (Q)
506 *Q = NULL;
507 if (!M)
508 goto error;
509 M = isl_mat_cow(M);
510 if (!M)
511 goto error;
512 if (U) {
513 *U = isl_mat_identity(M->ctx, M->n_col);
514 if (!*U)
515 goto error;
516 }
517 if (Q) {
518 *Q = isl_mat_identity(M->ctx, M->n_col);
519 if (!*Q)
520 goto error;
521 }
522
523 col = 0;
524 isl_int_init(c);
525 for (row = 0; row < M->n_row; ++row) {
526 int first, i, off;
527 first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);
528 if (first == -1)
529 continue;
530 first += col;
531 if (first != col)
532 exchange(M, U, Q, row, first, col);
533 if (isl_int_is_neg(M->row[row][col]))
534 oppose(M, U, Q, row, col);
535 first = col+1;
536 while ((off = isl_seq_first_non_zero(M->row[row]+first,
537 M->n_col-first)) != -1) {
538 first += off;
539 isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);
540 subtract(M, U, Q, row, col, first, c);
541 if (!isl_int_is_zero(M->row[row][first]))
542 exchange(M, U, Q, row, first, col);
543 else
544 ++first;
545 }
546 for (i = 0; i < col; ++i) {
547 if (isl_int_is_zero(M->row[row][i]))
548 continue;
549 if (neg)
550 isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);
551 else
552 isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);
553 if (isl_int_is_zero(c))
554 continue;
555 subtract(M, U, Q, row, col, i, c);
556 }
557 ++col;
558 }
559 isl_int_clear(c);
560
561 return M;
562 error:
563 if (Q) {
564 isl_mat_free(*Q);
565 *Q = NULL;
566 }
567 if (U) {
568 isl_mat_free(*U);
569 *U = NULL;
570 }
571 isl_mat_free(M);
572 return NULL;
573 }
574
575 struct isl_mat *isl_mat_right_kernel(struct isl_mat *mat)
576 {
577 int i, rank;
578 struct isl_mat *U = NULL;
579 struct isl_mat *K;
580
581 mat = isl_mat_left_hermite(mat, 0, &U, NULL);
582 if (!mat || !U)
583 goto error;
584
585 for (i = 0, rank = 0; rank < mat->n_col; ++rank) {
586 while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))
587 ++i;
588 if (i >= mat->n_row)
589 break;
590 }
591 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
592 if (!K)
593 goto error;
594 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
595 isl_mat_free(mat);
596 isl_mat_free(U);
597 return K;
598 error:
599 isl_mat_free(mat);
600 isl_mat_free(U);
601 return NULL;
602 }
603
604 struct isl_mat *isl_mat_lin_to_aff(struct isl_mat *mat)
605 {
606 int i;
607 struct isl_mat *mat2;
608
609 if (!mat)
610 return NULL;
611 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
612 if (!mat2)
613 goto error;
614 isl_int_set_si(mat2->row[0][0], 1);
615 isl_seq_clr(mat2->row[0]+1, mat->n_col);
616 for (i = 0; i < mat->n_row; ++i) {
617 isl_int_set_si(mat2->row[1+i][0], 0);
618 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
619 }
620 isl_mat_free(mat);
621 return mat2;
622 error:
623 isl_mat_free(mat);
624 return NULL;
625 }
626
627 /* Given two matrices M1 and M2, return the block matrix
628 *
629 * [ M1 0 ]
630 * [ 0 M2 ]
631 */
632 __isl_give isl_mat *isl_mat_diagonal(__isl_take isl_mat *mat1,
633 __isl_take isl_mat *mat2)
634 {
635 int i;
636 isl_mat *mat;
637
638 if (!mat1 || !mat2)
639 goto error;
640
641 mat = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
642 mat1->n_col + mat2->n_col);
643 if (!mat)
644 goto error;
645 for (i = 0; i < mat1->n_row; ++i) {
646 isl_seq_cpy(mat->row[i], mat1->row[i], mat1->n_col);
647 isl_seq_clr(mat->row[i] + mat1->n_col, mat2->n_col);
648 }
649 for (i = 0; i < mat2->n_row; ++i) {
650 isl_seq_clr(mat->row[mat1->n_row + i], mat1->n_col);
651 isl_seq_cpy(mat->row[mat1->n_row + i] + mat1->n_col,
652 mat2->row[i], mat2->n_col);
653 }
654 isl_mat_free(mat1);
655 isl_mat_free(mat2);
656 return mat;
657 error:
658 isl_mat_free(mat1);
659 isl_mat_free(mat2);
660 return NULL;
661 }
662
663 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
664 {
665 int i;
666
667 for (i = 0; i < n_row; ++i)
668 if (!isl_int_is_zero(row[i][col]))
669 return i;
670 return -1;
671 }
672
673 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
674 {
675 int i, min = row_first_non_zero(row, n_row, col);
676 if (min < 0)
677 return -1;
678 for (i = min + 1; i < n_row; ++i) {
679 if (isl_int_is_zero(row[i][col]))
680 continue;
681 if (isl_int_abs_lt(row[i][col], row[min][col]))
682 min = i;
683 }
684 return min;
685 }
686
687 static void inv_exchange(struct isl_mat *left, struct isl_mat *right,
688 unsigned i, unsigned j)
689 {
690 left = isl_mat_swap_rows(left, i, j);
691 right = isl_mat_swap_rows(right, i, j);
692 }
693
694 static void inv_oppose(
695 struct isl_mat *left, struct isl_mat *right, unsigned row)
696 {
697 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
698 isl_seq_neg(right->row[row], right->row[row], right->n_col);
699 }
700
701 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
702 unsigned row, unsigned i, isl_int m)
703 {
704 isl_int_neg(m, m);
705 isl_seq_combine(left->row[i]+row,
706 left->ctx->one, left->row[i]+row,
707 m, left->row[row]+row,
708 left->n_col-row);
709 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
710 m, right->row[row], right->n_col);
711 }
712
713 /* Compute inv(left)*right
714 */
715 struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
716 struct isl_mat *right)
717 {
718 int row;
719 isl_int a, b;
720
721 if (!left || !right)
722 goto error;
723
724 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
725 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
726
727 if (left->n_row == 0) {
728 isl_mat_free(left);
729 return right;
730 }
731
732 left = isl_mat_cow(left);
733 right = isl_mat_cow(right);
734 if (!left || !right)
735 goto error;
736
737 isl_int_init(a);
738 isl_int_init(b);
739 for (row = 0; row < left->n_row; ++row) {
740 int pivot, first, i, off;
741 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
742 if (pivot < 0) {
743 isl_int_clear(a);
744 isl_int_clear(b);
745 isl_assert(left->ctx, pivot >= 0, goto error);
746 }
747 pivot += row;
748 if (pivot != row)
749 inv_exchange(left, right, pivot, row);
750 if (isl_int_is_neg(left->row[row][row]))
751 inv_oppose(left, right, row);
752 first = row+1;
753 while ((off = row_first_non_zero(left->row+first,
754 left->n_row-first, row)) != -1) {
755 first += off;
756 isl_int_fdiv_q(a, left->row[first][row],
757 left->row[row][row]);
758 inv_subtract(left, right, row, first, a);
759 if (!isl_int_is_zero(left->row[first][row]))
760 inv_exchange(left, right, row, first);
761 else
762 ++first;
763 }
764 for (i = 0; i < row; ++i) {
765 if (isl_int_is_zero(left->row[i][row]))
766 continue;
767 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
768 isl_int_divexact(b, left->row[i][row], a);
769 isl_int_divexact(a, left->row[row][row], a);
770 isl_int_neg(b, b);
771 isl_seq_combine(left->row[i] + i,
772 a, left->row[i] + i,
773 b, left->row[row] + i,
774 left->n_col - i);
775 isl_seq_combine(right->row[i], a, right->row[i],
776 b, right->row[row], right->n_col);
777 }
778 }
779 isl_int_clear(b);
780
781 isl_int_set(a, left->row[0][0]);
782 for (row = 1; row < left->n_row; ++row)
783 isl_int_lcm(a, a, left->row[row][row]);
784 if (isl_int_is_zero(a)){
785 isl_int_clear(a);
786 isl_assert(left->ctx, 0, goto error);
787 }
788 for (row = 0; row < left->n_row; ++row) {
789 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
790 if (isl_int_is_one(left->row[row][row]))
791 continue;
792 isl_seq_scale(right->row[row], right->row[row],
793 left->row[row][row], right->n_col);
794 }
795 isl_int_clear(a);
796
797 isl_mat_free(left);
798 return right;
799 error:
800 isl_mat_free(left);
801 isl_mat_free(right);
802 return NULL;
803 }
804
805 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
806 {
807 int i;
808
809 for (i = 0; i < mat->n_row; ++i)
810 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
811 }
812
813 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
814 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
815 {
816 int i;
817 isl_int tmp;
818
819 isl_int_init(tmp);
820 for (i = 0; i < mat->n_row; ++i) {
821 isl_int_mul(tmp, m1, mat->row[i][src1]);
822 isl_int_addmul(tmp, m2, mat->row[i][src2]);
823 isl_int_set(mat->row[i][dst], tmp);
824 }
825 isl_int_clear(tmp);
826 }
827
828 struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
829 {
830 struct isl_mat *inv;
831 int row;
832 isl_int a, b;
833
834 mat = isl_mat_cow(mat);
835 if (!mat)
836 return NULL;
837
838 inv = isl_mat_identity(mat->ctx, mat->n_col);
839 inv = isl_mat_cow(inv);
840 if (!inv)
841 goto error;
842
843 isl_int_init(a);
844 isl_int_init(b);
845 for (row = 0; row < mat->n_row; ++row) {
846 int pivot, first, i, off;
847 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
848 if (pivot < 0) {
849 isl_int_clear(a);
850 isl_int_clear(b);
851 isl_assert(mat->ctx, pivot >= 0, goto error);
852 }
853 pivot += row;
854 if (pivot != row)
855 exchange(mat, &inv, NULL, row, pivot, row);
856 if (isl_int_is_neg(mat->row[row][row]))
857 oppose(mat, &inv, NULL, row, row);
858 first = row+1;
859 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
860 mat->n_col-first)) != -1) {
861 first += off;
862 isl_int_fdiv_q(a, mat->row[row][first],
863 mat->row[row][row]);
864 subtract(mat, &inv, NULL, row, row, first, a);
865 if (!isl_int_is_zero(mat->row[row][first]))
866 exchange(mat, &inv, NULL, row, row, first);
867 else
868 ++first;
869 }
870 for (i = 0; i < row; ++i) {
871 if (isl_int_is_zero(mat->row[row][i]))
872 continue;
873 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
874 isl_int_divexact(b, mat->row[row][i], a);
875 isl_int_divexact(a, mat->row[row][row], a);
876 isl_int_neg(a, a);
877 isl_mat_col_combine(mat, i, a, i, b, row);
878 isl_mat_col_combine(inv, i, a, i, b, row);
879 }
880 }
881 isl_int_clear(b);
882
883 isl_int_set(a, mat->row[0][0]);
884 for (row = 1; row < mat->n_row; ++row)
885 isl_int_lcm(a, a, mat->row[row][row]);
886 if (isl_int_is_zero(a)){
887 isl_int_clear(a);
888 goto error;
889 }
890 for (row = 0; row < mat->n_row; ++row) {
891 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
892 if (isl_int_is_one(mat->row[row][row]))
893 continue;
894 isl_mat_col_scale(inv, row, mat->row[row][row]);
895 }
896 isl_int_clear(a);
897
898 isl_mat_free(mat);
899
900 return inv;
901 error:
902 isl_mat_free(mat);
903 isl_mat_free(inv);
904 return NULL;
905 }
906
907 struct isl_mat *isl_mat_transpose(struct isl_mat *mat)
908 {
909 struct isl_mat *transpose = NULL;
910 int i, j;
911
912 if (!mat)
913 return NULL;
914
915 if (mat->n_col == mat->n_row) {
916 mat = isl_mat_cow(mat);
917 if (!mat)
918 return NULL;
919 for (i = 0; i < mat->n_row; ++i)
920 for (j = i + 1; j < mat->n_col; ++j)
921 isl_int_swap(mat->row[i][j], mat->row[j][i]);
922 return mat;
923 }
924 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
925 if (!transpose)
926 goto error;
927 for (i = 0; i < mat->n_row; ++i)
928 for (j = 0; j < mat->n_col; ++j)
929 isl_int_set(transpose->row[j][i], mat->row[i][j]);
930 isl_mat_free(mat);
931 return transpose;
932 error:
933 isl_mat_free(mat);
934 return NULL;
935 }
936
937 struct isl_mat *isl_mat_swap_cols(struct isl_mat *mat, unsigned i, unsigned j)
938 {
939 int r;
940
941 mat = isl_mat_cow(mat);
942 if (!mat)
943 return NULL;
944 isl_assert(mat->ctx, i < mat->n_col, goto error);
945 isl_assert(mat->ctx, j < mat->n_col, goto error);
946
947 for (r = 0; r < mat->n_row; ++r)
948 isl_int_swap(mat->row[r][i], mat->row[r][j]);
949 return mat;
950 error:
951 isl_mat_free(mat);
952 return NULL;
953 }
954
955 struct isl_mat *isl_mat_swap_rows(struct isl_mat *mat, unsigned i, unsigned j)
956 {
957 isl_int *t;
958
959 if (!mat)
960 return NULL;
961 mat = isl_mat_cow(mat);
962 if (!mat)
963 return NULL;
964 t = mat->row[i];
965 mat->row[i] = mat->row[j];
966 mat->row[j] = t;
967 return mat;
968 }
969
970 struct isl_mat *isl_mat_product(struct isl_mat *left, struct isl_mat *right)
971 {
972 int i, j, k;
973 struct isl_mat *prod;
974
975 if (!left || !right)
976 goto error;
977 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
978 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
979 if (!prod)
980 goto error;
981 if (left->n_col == 0) {
982 for (i = 0; i < prod->n_row; ++i)
983 isl_seq_clr(prod->row[i], prod->n_col);
984 isl_mat_free(left);
985 isl_mat_free(right);
986 return prod;
987 }
988 for (i = 0; i < prod->n_row; ++i) {
989 for (j = 0; j < prod->n_col; ++j) {
990 isl_int_mul(prod->row[i][j],
991 left->row[i][0], right->row[0][j]);
992 for (k = 1; k < left->n_col; ++k)
993 isl_int_addmul(prod->row[i][j],
994 left->row[i][k], right->row[k][j]);
995 }
996 }
997 isl_mat_free(left);
998 isl_mat_free(right);
999 return prod;
1000 error:
1001 isl_mat_free(left);
1002 isl_mat_free(right);
1003 return NULL;
1004 }
1005
1006 /* Replace the variables x in the rows q by x' given by x = M x',
1007 * with M the matrix mat.
1008 *
1009 * If the number of new variables is greater than the original
1010 * number of variables, then the rows q have already been
1011 * preextended. If the new number is smaller, then the coefficients
1012 * of the divs, which are not changed, need to be shifted down.
1013 * The row q may be the equalities, the inequalities or the
1014 * div expressions. In the latter case, has_div is true and
1015 * we need to take into account the extra denominator column.
1016 */
1017 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
1018 unsigned n_div, int has_div, struct isl_mat *mat)
1019 {
1020 int i;
1021 struct isl_mat *t;
1022 int e;
1023
1024 if (mat->n_col >= mat->n_row)
1025 e = 0;
1026 else
1027 e = mat->n_row - mat->n_col;
1028 if (has_div)
1029 for (i = 0; i < n; ++i)
1030 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
1031 t = isl_mat_sub_alloc6(mat->ctx, q, 0, n, has_div, mat->n_row);
1032 t = isl_mat_product(t, mat);
1033 if (!t)
1034 return -1;
1035 for (i = 0; i < n; ++i) {
1036 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
1037 isl_seq_cpy(q[i] + has_div + t->n_col,
1038 q[i] + has_div + t->n_col + e, n_div);
1039 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
1040 }
1041 isl_mat_free(t);
1042 return 0;
1043 }
1044
1045 /* Replace the variables x in bset by x' given by x = M x', with
1046 * M the matrix mat.
1047 *
1048 * If there are fewer variables x' then there are x, then we perform
1049 * the transformation in place, which that, in principle,
1050 * this frees up some extra variables as the number
1051 * of columns remains constant, but we would have to extend
1052 * the div array too as the number of rows in this array is assumed
1053 * to be equal to extra.
1054 */
1055 struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
1056 struct isl_mat *mat)
1057 {
1058 struct isl_ctx *ctx;
1059
1060 if (!bset || !mat)
1061 goto error;
1062
1063 ctx = bset->ctx;
1064 bset = isl_basic_set_cow(bset);
1065 if (!bset)
1066 goto error;
1067
1068 isl_assert(ctx, bset->dim->nparam == 0, goto error);
1069 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
1070 isl_assert(ctx, mat->n_col > 0, goto error);
1071
1072 if (mat->n_col > mat->n_row) {
1073 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0, 0, 0);
1074 if (!bset)
1075 goto error;
1076 } else if (mat->n_col < mat->n_row) {
1077 bset->dim = isl_space_cow(bset->dim);
1078 if (!bset->dim)
1079 goto error;
1080 bset->dim->n_out -= mat->n_row - mat->n_col;
1081 }
1082
1083 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
1084 isl_mat_copy(mat)) < 0)
1085 goto error;
1086
1087 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
1088 isl_mat_copy(mat)) < 0)
1089 goto error;
1090
1091 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
1092 goto error2;
1093
1094 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
1095 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
1096 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1097 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1098 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
1099
1100 bset = isl_basic_set_simplify(bset);
1101 bset = isl_basic_set_finalize(bset);
1102
1103 return bset;
1104 error:
1105 isl_mat_free(mat);
1106 error2:
1107 isl_basic_set_free(bset);
1108 return NULL;
1109 }
1110
1111 struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
1112 {
1113 struct isl_ctx *ctx;
1114 int i;
1115
1116 set = isl_set_cow(set);
1117 if (!set)
1118 return NULL;
1119
1120 ctx = set->ctx;
1121 for (i = 0; i < set->n; ++i) {
1122 set->p[i] = isl_basic_set_preimage(set->p[i],
1123 isl_mat_copy(mat));
1124 if (!set->p[i])
1125 goto error;
1126 }
1127 if (mat->n_col != mat->n_row) {
1128 set->dim = isl_space_cow(set->dim);
1129 if (!set->dim)
1130 goto error;
1131 set->dim->n_out += mat->n_col;
1132 set->dim->n_out -= mat->n_row;
1133 }
1134 isl_mat_free(mat);
1135 ISL_F_CLR(set, ISL_SET_NORMALIZED);
1136 return set;
1137 error:
1138 isl_set_free(set);
1139 isl_mat_free(mat);
1140 return NULL;
1141 }
1142
1143 /* Replace the variables x starting at pos in the rows q
1144 * by x' with x = M x' with M the matrix mat.
1145 * That is, replace the corresponding coefficients c by c M.
1146 */
1147 static int transform(isl_ctx *ctx, isl_int **q, unsigned n,
1148 unsigned pos, __isl_take isl_mat *mat)
1149 {
1150 int i;
1151 isl_mat *t;
1152
1153 t = isl_mat_sub_alloc6(ctx, q, 0, n, pos, mat->n_row);
1154 t = isl_mat_product(t, mat);
1155 if (!t)
1156 return -1;
1157 for (i = 0; i < n; ++i)
1158 isl_seq_swp_or_cpy(q[i] + pos, t->row[i], t->n_col);
1159 isl_mat_free(t);
1160 return 0;
1161 }
1162
1163 /* Replace the variables x of type "type" starting at "first" in "bset"
1164 * by x' with x = M x' with M the matrix trans.
1165 * That is, replace the corresponding coefficients c by c M.
1166 *
1167 * The transformation matrix should be a square matrix.
1168 */
1169 __isl_give isl_basic_set *isl_basic_set_transform_dims(
1170 __isl_take isl_basic_set *bset, enum isl_dim_type type, unsigned first,
1171 __isl_take isl_mat *trans)
1172 {
1173 isl_ctx *ctx;
1174 unsigned pos;
1175
1176 bset = isl_basic_set_cow(bset);
1177 if (!bset || !trans)
1178 goto error;
1179
1180 ctx = isl_basic_set_get_ctx(bset);
1181 if (trans->n_row != trans->n_col)
1182 isl_die(trans->ctx, isl_error_invalid,
1183 "expecting square transformation matrix", goto error);
1184 if (first + trans->n_row > isl_basic_set_dim(bset, type))
1185 isl_die(trans->ctx, isl_error_invalid,
1186 "oversized transformation matrix", goto error);
1187
1188 pos = isl_basic_set_offset(bset, type) + first;
1189
1190 if (transform(ctx, bset->eq, bset->n_eq, pos, isl_mat_copy(trans)) < 0)
1191 goto error;
1192 if (transform(ctx, bset->ineq, bset->n_ineq, pos,
1193 isl_mat_copy(trans)) < 0)
1194 goto error;
1195 if (transform(ctx, bset->div, bset->n_div, 1 + pos,
1196 isl_mat_copy(trans)) < 0)
1197 goto error;
1198
1199 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1200 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1201
1202 isl_mat_free(trans);
1203 return bset;
1204 error:
1205 isl_mat_free(trans);
1206 isl_basic_set_free(bset);
1207 return NULL;
1208 }
1209
1210 void isl_mat_print_internal(__isl_keep isl_mat *mat, FILE *out, int indent)
1211 {
1212 int i, j;
1213
1214 if (!mat) {
1215 fprintf(out, "%*snull mat\n", indent, "");
1216 return;
1217 }
1218
1219 if (mat->n_row == 0)
1220 fprintf(out, "%*s[]\n", indent, "");
1221
1222 for (i = 0; i < mat->n_row; ++i) {
1223 if (!i)
1224 fprintf(out, "%*s[[", indent, "");
1225 else
1226 fprintf(out, "%*s[", indent+1, "");
1227 for (j = 0; j < mat->n_col; ++j) {
1228 if (j)
1229 fprintf(out, ",");
1230 isl_int_print(out, mat->row[i][j], 0);
1231 }
1232 if (i == mat->n_row-1)
1233 fprintf(out, "]]\n");
1234 else
1235 fprintf(out, "]\n");
1236 }
1237 }
1238
1239 void isl_mat_dump(__isl_keep isl_mat *mat)
1240 {
1241 isl_mat_print_internal(mat, stderr, 0);
1242 }
1243
1244 struct isl_mat *isl_mat_drop_cols(struct isl_mat *mat, unsigned col, unsigned n)
1245 {
1246 int r;
1247
1248 if (n == 0)
1249 return mat;
1250
1251 mat = isl_mat_cow(mat);
1252 if (!mat)
1253 return NULL;
1254
1255 if (col != mat->n_col-n) {
1256 for (r = 0; r < mat->n_row; ++r)
1257 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1258 mat->n_col - col - n);
1259 }
1260 mat->n_col -= n;
1261 return mat;
1262 }
1263
1264 struct isl_mat *isl_mat_drop_rows(struct isl_mat *mat, unsigned row, unsigned n)
1265 {
1266 int r;
1267
1268 mat = isl_mat_cow(mat);
1269 if (!mat)
1270 return NULL;
1271
1272 for (r = row; r+n < mat->n_row; ++r)
1273 mat->row[r] = mat->row[r+n];
1274
1275 mat->n_row -= n;
1276 return mat;
1277 }
1278
1279 __isl_give isl_mat *isl_mat_insert_cols(__isl_take isl_mat *mat,
1280 unsigned col, unsigned n)
1281 {
1282 isl_mat *ext;
1283
1284 if (!mat)
1285 return NULL;
1286 if (n == 0)
1287 return mat;
1288
1289 ext = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col + n);
1290 if (!ext)
1291 goto error;
1292
1293 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row, 0, 0, col);
1294 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row,
1295 col + n, col, mat->n_col - col);
1296
1297 isl_mat_free(mat);
1298 return ext;
1299 error:
1300 isl_mat_free(mat);
1301 return NULL;
1302 }
1303
1304 __isl_give isl_mat *isl_mat_insert_zero_cols(__isl_take isl_mat *mat,
1305 unsigned first, unsigned n)
1306 {
1307 int i;
1308
1309 if (!mat)
1310 return NULL;
1311 mat = isl_mat_insert_cols(mat, first, n);
1312 if (!mat)
1313 return NULL;
1314
1315 for (i = 0; i < mat->n_row; ++i)
1316 isl_seq_clr(mat->row[i] + first, n);
1317
1318 return mat;
1319 }
1320
1321 __isl_give isl_mat *isl_mat_add_zero_cols(__isl_take isl_mat *mat, unsigned n)
1322 {
1323 if (!mat)
1324 return NULL;
1325
1326 return isl_mat_insert_zero_cols(mat, mat->n_col, n);
1327 }
1328
1329 __isl_give isl_mat *isl_mat_insert_rows(__isl_take isl_mat *mat,
1330 unsigned row, unsigned n)
1331 {
1332 isl_mat *ext;
1333
1334 if (!mat)
1335 return NULL;
1336 if (n == 0)
1337 return mat;
1338
1339 ext = isl_mat_alloc(mat->ctx, mat->n_row + n, mat->n_col);
1340 if (!ext)
1341 goto error;
1342
1343 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, row, 0, 0, mat->n_col);
1344 isl_mat_sub_copy(mat->ctx, ext->row + row + n, mat->row + row,
1345 mat->n_row - row, 0, 0, mat->n_col);
1346
1347 isl_mat_free(mat);
1348 return ext;
1349 error:
1350 isl_mat_free(mat);
1351 return NULL;
1352 }
1353
1354 __isl_give isl_mat *isl_mat_add_rows(__isl_take isl_mat *mat, unsigned n)
1355 {
1356 if (!mat)
1357 return NULL;
1358
1359 return isl_mat_insert_rows(mat, mat->n_row, n);
1360 }
1361
1362 __isl_give isl_mat *isl_mat_insert_zero_rows(__isl_take isl_mat *mat,
1363 unsigned row, unsigned n)
1364 {
1365 int i;
1366
1367 mat = isl_mat_insert_rows(mat, row, n);
1368 if (!mat)
1369 return NULL;
1370
1371 for (i = 0; i < n; ++i)
1372 isl_seq_clr(mat->row[row + i], mat->n_col);
1373
1374 return mat;
1375 }
1376
1377 __isl_give isl_mat *isl_mat_add_zero_rows(__isl_take isl_mat *mat, unsigned n)
1378 {
1379 if (!mat)
1380 return NULL;
1381
1382 return isl_mat_insert_zero_rows(mat, mat->n_row, n);
1383 }
1384
1385 void isl_mat_col_submul(struct isl_mat *mat,
1386 int dst_col, isl_int f, int src_col)
1387 {
1388 int i;
1389
1390 for (i = 0; i < mat->n_row; ++i)
1391 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1392 }
1393
1394 void isl_mat_col_add(__isl_keep isl_mat *mat, int dst_col, int src_col)
1395 {
1396 int i;
1397
1398 if (!mat)
1399 return;
1400
1401 for (i = 0; i < mat->n_row; ++i)
1402 isl_int_add(mat->row[i][dst_col],
1403 mat->row[i][dst_col], mat->row[i][src_col]);
1404 }
1405
1406 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1407 {
1408 int i;
1409
1410 for (i = 0; i < mat->n_row; ++i)
1411 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1412 }
1413
1414 struct isl_mat *isl_mat_unimodular_complete(struct isl_mat *M, int row)
1415 {
1416 int r;
1417 struct isl_mat *H = NULL, *Q = NULL;
1418
1419 if (!M)
1420 return NULL;
1421
1422 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1423 M->n_row = row;
1424 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1425 M->n_row = M->n_col;
1426 if (!H)
1427 goto error;
1428 for (r = 0; r < row; ++r)
1429 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1430 for (r = row; r < M->n_row; ++r)
1431 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1432 isl_mat_free(H);
1433 isl_mat_free(Q);
1434 return M;
1435 error:
1436 isl_mat_free(H);
1437 isl_mat_free(Q);
1438 isl_mat_free(M);
1439 return NULL;
1440 }
1441
1442 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1443 __isl_take isl_mat *bot)
1444 {
1445 struct isl_mat *mat;
1446
1447 if (!top || !bot)
1448 goto error;
1449
1450 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1451 if (top->n_row == 0) {
1452 isl_mat_free(top);
1453 return bot;
1454 }
1455 if (bot->n_row == 0) {
1456 isl_mat_free(bot);
1457 return top;
1458 }
1459
1460 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1461 if (!mat)
1462 goto error;
1463 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1464 0, 0, mat->n_col);
1465 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1466 0, 0, mat->n_col);
1467 isl_mat_free(top);
1468 isl_mat_free(bot);
1469 return mat;
1470 error:
1471 isl_mat_free(top);
1472 isl_mat_free(bot);
1473 return NULL;
1474 }
1475
1476 int isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
1477 {
1478 int i;
1479
1480 if (!mat1 || !mat2)
1481 return -1;
1482
1483 if (mat1->n_row != mat2->n_row)
1484 return 0;
1485
1486 if (mat1->n_col != mat2->n_col)
1487 return 0;
1488
1489 for (i = 0; i < mat1->n_row; ++i)
1490 if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
1491 return 0;
1492
1493 return 1;
1494 }
1495
1496 __isl_give isl_mat *isl_mat_from_row_vec(__isl_take isl_vec *vec)
1497 {
1498 struct isl_mat *mat;
1499
1500 if (!vec)
1501 return NULL;
1502 mat = isl_mat_alloc(vec->ctx, 1, vec->size);
1503 if (!mat)
1504 goto error;
1505
1506 isl_seq_cpy(mat->row[0], vec->el, vec->size);
1507
1508 isl_vec_free(vec);
1509 return mat;
1510 error:
1511 isl_vec_free(vec);
1512 return NULL;
1513 }
1514
1515 __isl_give isl_mat *isl_mat_vec_concat(__isl_take isl_mat *top,
1516 __isl_take isl_vec *bot)
1517 {
1518 return isl_mat_concat(top, isl_mat_from_row_vec(bot));
1519 }
1520
1521 __isl_give isl_mat *isl_mat_move_cols(__isl_take isl_mat *mat,
1522 unsigned dst_col, unsigned src_col, unsigned n)
1523 {
1524 isl_mat *res;
1525
1526 if (!mat)
1527 return NULL;
1528 if (n == 0 || dst_col == src_col)
1529 return mat;
1530
1531 res = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
1532 if (!res)
1533 goto error;
1534
1535 if (dst_col < src_col) {
1536 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1537 0, 0, dst_col);
1538 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1539 dst_col, src_col, n);
1540 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1541 dst_col + n, dst_col, src_col - dst_col);
1542 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1543 src_col + n, src_col + n,
1544 res->n_col - src_col - n);
1545 } else {
1546 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1547 0, 0, src_col);
1548 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1549 src_col, src_col + n, dst_col - src_col);
1550 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1551 dst_col, src_col, n);
1552 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1553 dst_col + n, dst_col + n,
1554 res->n_col - dst_col - n);
1555 }
1556 isl_mat_free(mat);
1557
1558 return res;
1559 error:
1560 isl_mat_free(mat);
1561 return NULL;
1562 }
1563
1564 void isl_mat_gcd(__isl_keep isl_mat *mat, isl_int *gcd)
1565 {
1566 int i;
1567 isl_int g;
1568
1569 isl_int_set_si(*gcd, 0);
1570 if (!mat)
1571 return;
1572
1573 isl_int_init(g);
1574 for (i = 0; i < mat->n_row; ++i) {
1575 isl_seq_gcd(mat->row[i], mat->n_col, &g);
1576 isl_int_gcd(*gcd, *gcd, g);
1577 }
1578 isl_int_clear(g);
1579 }
1580
1581 __isl_give isl_mat *isl_mat_scale_down(__isl_take isl_mat *mat, isl_int m)
1582 {
1583 int i;
1584
1585 if (isl_int_is_one(m))
1586 return mat;
1587
1588 mat = isl_mat_cow(mat);
1589 if (!mat)
1590 return NULL;
1591
1592 for (i = 0; i < mat->n_row; ++i)
1593 isl_seq_scale_down(mat->row[i], mat->row[i], m, mat->n_col);
1594
1595 return mat;
1596 }
1597
1598 __isl_give isl_mat *isl_mat_scale_down_row(__isl_take isl_mat *mat, int row,
1599 isl_int m)
1600 {
1601 if (isl_int_is_one(m))
1602 return mat;
1603
1604 mat = isl_mat_cow(mat);
1605 if (!mat)
1606 return NULL;
1607
1608 isl_seq_scale_down(mat->row[row], mat->row[row], m, mat->n_col);
1609
1610 return mat;
1611 }
1612
1613 __isl_give isl_mat *isl_mat_normalize(__isl_take isl_mat *mat)
1614 {
1615 isl_int gcd;
1616
1617 if (!mat)
1618 return NULL;
1619
1620 isl_int_init(gcd);
1621 isl_mat_gcd(mat, &gcd);
1622 mat = isl_mat_scale_down(mat, gcd);
1623 isl_int_clear(gcd);
1624
1625 return mat;
1626 }
1627
1628 __isl_give isl_mat *isl_mat_normalize_row(__isl_take isl_mat *mat, int row)
1629 {
1630 mat = isl_mat_cow(mat);
1631 if (!mat)
1632 return NULL;
1633
1634 isl_seq_normalize(mat->ctx, mat->row[row], mat->n_col);
1635
1636 return mat;
1637 }
1638
1639 /* Number of initial non-zero columns.
1640 */
1641 int isl_mat_initial_non_zero_cols(__isl_keep isl_mat *mat)
1642 {
1643 int i;
1644
1645 if (!mat)
1646 return -1;
1647
1648 for (i = 0; i < mat->n_col; ++i)
1649 if (row_first_non_zero(mat->row, mat->n_row, i) < 0)
1650 break;
1651
1652 return i;
1653 }
Integer set library