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1 office 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/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->n_col == mat->n_row) {
913 mat = isl_mat_cow(mat);
914 if (!mat)
915 return NULL;
916 for (i = 0; i < mat->n_row; ++i)
917 for (j = i + 1; j < mat->n_col; ++j)
918 isl_int_swap(mat->row[i][j], mat->row[j][i]);
919 return mat;
920 }
921 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
922 if (!transpose)
923 goto error;
924 for (i = 0; i < mat->n_row; ++i)
925 for (j = 0; j < mat->n_col; ++j)
926 isl_int_set(transpose->row[j][i], mat->row[i][j]);
927 isl_mat_free(mat);
928 return transpose;
929 error:
930 isl_mat_free(mat);
931 return NULL;
932 }
933  
934 struct isl_mat *isl_mat_swap_cols(struct isl_mat *mat, unsigned i, unsigned j)
935 {
936 int r;
937  
938 mat = isl_mat_cow(mat);
939 if (!mat)
940 return NULL;
941 isl_assert(mat->ctx, i < mat->n_col, goto error);
942 isl_assert(mat->ctx, j < mat->n_col, goto error);
943  
944 for (r = 0; r < mat->n_row; ++r)
945 isl_int_swap(mat->row[r][i], mat->row[r][j]);
946 return mat;
947 error:
948 isl_mat_free(mat);
949 return NULL;
950 }
951  
952 struct isl_mat *isl_mat_swap_rows(struct isl_mat *mat, unsigned i, unsigned j)
953 {
954 isl_int *t;
955  
956 if (!mat)
957 return NULL;
958 mat = isl_mat_cow(mat);
959 if (!mat)
960 return NULL;
961 t = mat->row[i];
962 mat->row[i] = mat->row[j];
963 mat->row[j] = t;
964 return mat;
965 }
966  
967 struct isl_mat *isl_mat_product(struct isl_mat *left, struct isl_mat *right)
968 {
969 int i, j, k;
970 struct isl_mat *prod;
971  
972 if (!left || !right)
973 goto error;
974 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
975 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
976 if (!prod)
977 goto error;
978 if (left->n_col == 0) {
979 for (i = 0; i < prod->n_row; ++i)
980 isl_seq_clr(prod->row[i], prod->n_col);
981 isl_mat_free(left);
982 isl_mat_free(right);
983 return prod;
984 }
985 for (i = 0; i < prod->n_row; ++i) {
986 for (j = 0; j < prod->n_col; ++j) {
987 isl_int_mul(prod->row[i][j],
988 left->row[i][0], right->row[0][j]);
989 for (k = 1; k < left->n_col; ++k)
990 isl_int_addmul(prod->row[i][j],
991 left->row[i][k], right->row[k][j]);
992 }
993 }
994 isl_mat_free(left);
995 isl_mat_free(right);
996 return prod;
997 error:
998 isl_mat_free(left);
999 isl_mat_free(right);
1000 return NULL;
1001 }
1002  
1003 /* Replace the variables x in the rows q by x' given by x = M x',
1004 * with M the matrix mat.
1005 *
1006 * If the number of new variables is greater than the original
1007 * number of variables, then the rows q have already been
1008 * preextended. If the new number is smaller, then the coefficients
1009 * of the divs, which are not changed, need to be shifted down.
1010 * The row q may be the equalities, the inequalities or the
1011 * div expressions. In the latter case, has_div is true and
1012 * we need to take into account the extra denominator column.
1013 */
1014 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
1015 unsigned n_div, int has_div, struct isl_mat *mat)
1016 {
1017 int i;
1018 struct isl_mat *t;
1019 int e;
1020  
1021 if (mat->n_col >= mat->n_row)
1022 e = 0;
1023 else
1024 e = mat->n_row - mat->n_col;
1025 if (has_div)
1026 for (i = 0; i < n; ++i)
1027 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
1028 t = isl_mat_sub_alloc6(mat->ctx, q, 0, n, has_div, mat->n_row);
1029 t = isl_mat_product(t, mat);
1030 if (!t)
1031 return -1;
1032 for (i = 0; i < n; ++i) {
1033 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
1034 isl_seq_cpy(q[i] + has_div + t->n_col,
1035 q[i] + has_div + t->n_col + e, n_div);
1036 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
1037 }
1038 isl_mat_free(t);
1039 return 0;
1040 }
1041  
1042 /* Replace the variables x in bset by x' given by x = M x', with
1043 * M the matrix mat.
1044 *
1045 * If there are fewer variables x' then there are x, then we perform
1046 * the transformation in place, which that, in principle,
1047 * this frees up some extra variables as the number
1048 * of columns remains constant, but we would have to extend
1049 * the div array too as the number of rows in this array is assumed
1050 * to be equal to extra.
1051 */
1052 struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
1053 struct isl_mat *mat)
1054 {
1055 struct isl_ctx *ctx;
1056  
1057 if (!bset || !mat)
1058 goto error;
1059  
1060 ctx = bset->ctx;
1061 bset = isl_basic_set_cow(bset);
1062 if (!bset)
1063 goto error;
1064  
1065 isl_assert(ctx, bset->dim->nparam == 0, goto error);
1066 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
1067 isl_assert(ctx, mat->n_col > 0, goto error);
1068  
1069 if (mat->n_col > mat->n_row) {
1070 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0, 0, 0);
1071 if (!bset)
1072 goto error;
1073 } else if (mat->n_col < mat->n_row) {
1074 bset->dim = isl_space_cow(bset->dim);
1075 if (!bset->dim)
1076 goto error;
1077 bset->dim->n_out -= mat->n_row - mat->n_col;
1078 }
1079  
1080 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
1081 isl_mat_copy(mat)) < 0)
1082 goto error;
1083  
1084 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
1085 isl_mat_copy(mat)) < 0)
1086 goto error;
1087  
1088 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
1089 goto error2;
1090  
1091 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
1092 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
1093 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1094 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1095 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
1096  
1097 bset = isl_basic_set_simplify(bset);
1098 bset = isl_basic_set_finalize(bset);
1099  
1100 return bset;
1101 error:
1102 isl_mat_free(mat);
1103 error2:
1104 isl_basic_set_free(bset);
1105 return NULL;
1106 }
1107  
1108 struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
1109 {
1110 struct isl_ctx *ctx;
1111 int i;
1112  
1113 set = isl_set_cow(set);
1114 if (!set)
1115 return NULL;
1116  
1117 ctx = set->ctx;
1118 for (i = 0; i < set->n; ++i) {
1119 set->p[i] = isl_basic_set_preimage(set->p[i],
1120 isl_mat_copy(mat));
1121 if (!set->p[i])
1122 goto error;
1123 }
1124 if (mat->n_col != mat->n_row) {
1125 set->dim = isl_space_cow(set->dim);
1126 if (!set->dim)
1127 goto error;
1128 set->dim->n_out += mat->n_col;
1129 set->dim->n_out -= mat->n_row;
1130 }
1131 isl_mat_free(mat);
1132 ISL_F_CLR(set, ISL_SET_NORMALIZED);
1133 return set;
1134 error:
1135 isl_set_free(set);
1136 isl_mat_free(mat);
1137 return NULL;
1138 }
1139  
1140 /* Replace the variables x starting at pos in the rows q
1141 * by x' with x = M x' with M the matrix mat.
1142 * That is, replace the corresponding coefficients c by c M.
1143 */
1144 static int transform(isl_ctx *ctx, isl_int **q, unsigned n,
1145 unsigned pos, __isl_take isl_mat *mat)
1146 {
1147 int i;
1148 isl_mat *t;
1149  
1150 t = isl_mat_sub_alloc6(ctx, q, 0, n, pos, mat->n_row);
1151 t = isl_mat_product(t, mat);
1152 if (!t)
1153 return -1;
1154 for (i = 0; i < n; ++i)
1155 isl_seq_swp_or_cpy(q[i] + pos, t->row[i], t->n_col);
1156 isl_mat_free(t);
1157 return 0;
1158 }
1159  
1160 /* Replace the variables x of type "type" starting at "first" in "bset"
1161 * by x' with x = M x' with M the matrix trans.
1162 * That is, replace the corresponding coefficients c by c M.
1163 *
1164 * The transformation matrix should be a square matrix.
1165 */
1166 __isl_give isl_basic_set *isl_basic_set_transform_dims(
1167 __isl_take isl_basic_set *bset, enum isl_dim_type type, unsigned first,
1168 __isl_take isl_mat *trans)
1169 {
1170 isl_ctx *ctx;
1171 unsigned pos;
1172  
1173 bset = isl_basic_set_cow(bset);
1174 if (!bset || !trans)
1175 goto error;
1176  
1177 ctx = isl_basic_set_get_ctx(bset);
1178 if (trans->n_row != trans->n_col)
1179 isl_die(trans->ctx, isl_error_invalid,
1180 "expecting square transformation matrix", goto error);
1181 if (first + trans->n_row > isl_basic_set_dim(bset, type))
1182 isl_die(trans->ctx, isl_error_invalid,
1183 "oversized transformation matrix", goto error);
1184  
1185 pos = isl_basic_set_offset(bset, type) + first;
1186  
1187 if (transform(ctx, bset->eq, bset->n_eq, pos, isl_mat_copy(trans)) < 0)
1188 goto error;
1189 if (transform(ctx, bset->ineq, bset->n_ineq, pos,
1190 isl_mat_copy(trans)) < 0)
1191 goto error;
1192 if (transform(ctx, bset->div, bset->n_div, 1 + pos,
1193 isl_mat_copy(trans)) < 0)
1194 goto error;
1195  
1196 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1197 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1198  
1199 isl_mat_free(trans);
1200 return bset;
1201 error:
1202 isl_mat_free(trans);
1203 isl_basic_set_free(bset);
1204 return NULL;
1205 }
1206  
1207 void isl_mat_print_internal(__isl_keep isl_mat *mat, FILE *out, int indent)
1208 {
1209 int i, j;
1210  
1211 if (!mat) {
1212 fprintf(out, "%*snull mat\n", indent, "");
1213 return;
1214 }
1215  
1216 if (mat->n_row == 0)
1217 fprintf(out, "%*s[]\n", indent, "");
1218  
1219 for (i = 0; i < mat->n_row; ++i) {
1220 if (!i)
1221 fprintf(out, "%*s[[", indent, "");
1222 else
1223 fprintf(out, "%*s[", indent+1, "");
1224 for (j = 0; j < mat->n_col; ++j) {
1225 if (j)
1226 fprintf(out, ",");
1227 isl_int_print(out, mat->row[i][j], 0);
1228 }
1229 if (i == mat->n_row-1)
1230 fprintf(out, "]]\n");
1231 else
1232 fprintf(out, "]\n");
1233 }
1234 }
1235  
1236 void isl_mat_dump(__isl_keep isl_mat *mat)
1237 {
1238 isl_mat_print_internal(mat, stderr, 0);
1239 }
1240  
1241 struct isl_mat *isl_mat_drop_cols(struct isl_mat *mat, unsigned col, unsigned n)
1242 {
1243 int r;
1244  
1245 mat = isl_mat_cow(mat);
1246 if (!mat)
1247 return NULL;
1248  
1249 if (col != mat->n_col-n) {
1250 for (r = 0; r < mat->n_row; ++r)
1251 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1252 mat->n_col - col - n);
1253 }
1254 mat->n_col -= n;
1255 return mat;
1256 }
1257  
1258 struct isl_mat *isl_mat_drop_rows(struct isl_mat *mat, unsigned row, unsigned n)
1259 {
1260 int r;
1261  
1262 mat = isl_mat_cow(mat);
1263 if (!mat)
1264 return NULL;
1265  
1266 for (r = row; r+n < mat->n_row; ++r)
1267 mat->row[r] = mat->row[r+n];
1268  
1269 mat->n_row -= n;
1270 return mat;
1271 }
1272  
1273 __isl_give isl_mat *isl_mat_insert_cols(__isl_take isl_mat *mat,
1274 unsigned col, unsigned n)
1275 {
1276 isl_mat *ext;
1277  
1278 if (!mat)
1279 return NULL;
1280 if (n == 0)
1281 return mat;
1282  
1283 ext = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col + n);
1284 if (!ext)
1285 goto error;
1286  
1287 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row, 0, 0, col);
1288 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row,
1289 col + n, col, mat->n_col - col);
1290  
1291 isl_mat_free(mat);
1292 return ext;
1293 error:
1294 isl_mat_free(mat);
1295 return NULL;
1296 }
1297  
1298 __isl_give isl_mat *isl_mat_insert_zero_cols(__isl_take isl_mat *mat,
1299 unsigned first, unsigned n)
1300 {
1301 int i;
1302  
1303 if (!mat)
1304 return NULL;
1305 mat = isl_mat_insert_cols(mat, first, n);
1306 if (!mat)
1307 return NULL;
1308  
1309 for (i = 0; i < mat->n_row; ++i)
1310 isl_seq_clr(mat->row[i] + first, n);
1311  
1312 return mat;
1313 }
1314  
1315 __isl_give isl_mat *isl_mat_add_zero_cols(__isl_take isl_mat *mat, unsigned n)
1316 {
1317 if (!mat)
1318 return NULL;
1319  
1320 return isl_mat_insert_zero_cols(mat, mat->n_col, n);
1321 }
1322  
1323 __isl_give isl_mat *isl_mat_insert_rows(__isl_take isl_mat *mat,
1324 unsigned row, unsigned n)
1325 {
1326 isl_mat *ext;
1327  
1328 if (!mat)
1329 return NULL;
1330 if (n == 0)
1331 return mat;
1332  
1333 ext = isl_mat_alloc(mat->ctx, mat->n_row + n, mat->n_col);
1334 if (!ext)
1335 goto error;
1336  
1337 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, row, 0, 0, mat->n_col);
1338 isl_mat_sub_copy(mat->ctx, ext->row + row + n, mat->row + row,
1339 mat->n_row - row, 0, 0, mat->n_col);
1340  
1341 isl_mat_free(mat);
1342 return ext;
1343 error:
1344 isl_mat_free(mat);
1345 return NULL;
1346 }
1347  
1348 __isl_give isl_mat *isl_mat_add_rows(__isl_take isl_mat *mat, unsigned n)
1349 {
1350 if (!mat)
1351 return NULL;
1352  
1353 return isl_mat_insert_rows(mat, mat->n_row, n);
1354 }
1355  
1356 __isl_give isl_mat *isl_mat_insert_zero_rows(__isl_take isl_mat *mat,
1357 unsigned row, unsigned n)
1358 {
1359 int i;
1360  
1361 mat = isl_mat_insert_rows(mat, row, n);
1362 if (!mat)
1363 return NULL;
1364  
1365 for (i = 0; i < n; ++i)
1366 isl_seq_clr(mat->row[row + i], mat->n_col);
1367  
1368 return mat;
1369 }
1370  
1371 __isl_give isl_mat *isl_mat_add_zero_rows(__isl_take isl_mat *mat, unsigned n)
1372 {
1373 if (!mat)
1374 return NULL;
1375  
1376 return isl_mat_insert_zero_rows(mat, mat->n_row, n);
1377 }
1378  
1379 void isl_mat_col_submul(struct isl_mat *mat,
1380 int dst_col, isl_int f, int src_col)
1381 {
1382 int i;
1383  
1384 for (i = 0; i < mat->n_row; ++i)
1385 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1386 }
1387  
1388 void isl_mat_col_add(__isl_keep isl_mat *mat, int dst_col, int src_col)
1389 {
1390 int i;
1391  
1392 if (!mat)
1393 return;
1394  
1395 for (i = 0; i < mat->n_row; ++i)
1396 isl_int_add(mat->row[i][dst_col],
1397 mat->row[i][dst_col], mat->row[i][src_col]);
1398 }
1399  
1400 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1401 {
1402 int i;
1403  
1404 for (i = 0; i < mat->n_row; ++i)
1405 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1406 }
1407  
1408 struct isl_mat *isl_mat_unimodular_complete(struct isl_mat *M, int row)
1409 {
1410 int r;
1411 struct isl_mat *H = NULL, *Q = NULL;
1412  
1413 if (!M)
1414 return NULL;
1415  
1416 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1417 M->n_row = row;
1418 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1419 M->n_row = M->n_col;
1420 if (!H)
1421 goto error;
1422 for (r = 0; r < row; ++r)
1423 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1424 for (r = row; r < M->n_row; ++r)
1425 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1426 isl_mat_free(H);
1427 isl_mat_free(Q);
1428 return M;
1429 error:
1430 isl_mat_free(H);
1431 isl_mat_free(Q);
1432 isl_mat_free(M);
1433 return NULL;
1434 }
1435  
1436 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1437 __isl_take isl_mat *bot)
1438 {
1439 struct isl_mat *mat;
1440  
1441 if (!top || !bot)
1442 goto error;
1443  
1444 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1445 if (top->n_row == 0) {
1446 isl_mat_free(top);
1447 return bot;
1448 }
1449 if (bot->n_row == 0) {
1450 isl_mat_free(bot);
1451 return top;
1452 }
1453  
1454 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1455 if (!mat)
1456 goto error;
1457 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1458 0, 0, mat->n_col);
1459 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1460 0, 0, mat->n_col);
1461 isl_mat_free(top);
1462 isl_mat_free(bot);
1463 return mat;
1464 error:
1465 isl_mat_free(top);
1466 isl_mat_free(bot);
1467 return NULL;
1468 }
1469  
1470 int isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
1471 {
1472 int i;
1473  
1474 if (!mat1 || !mat2)
1475 return -1;
1476  
1477 if (mat1->n_row != mat2->n_row)
1478 return 0;
1479  
1480 if (mat1->n_col != mat2->n_col)
1481 return 0;
1482  
1483 for (i = 0; i < mat1->n_row; ++i)
1484 if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
1485 return 0;
1486  
1487 return 1;
1488 }
1489  
1490 __isl_give isl_mat *isl_mat_from_row_vec(__isl_take isl_vec *vec)
1491 {
1492 struct isl_mat *mat;
1493  
1494 if (!vec)
1495 return NULL;
1496 mat = isl_mat_alloc(vec->ctx, 1, vec->size);
1497 if (!mat)
1498 goto error;
1499  
1500 isl_seq_cpy(mat->row[0], vec->el, vec->size);
1501  
1502 isl_vec_free(vec);
1503 return mat;
1504 error:
1505 isl_vec_free(vec);
1506 return NULL;
1507 }
1508  
1509 __isl_give isl_mat *isl_mat_vec_concat(__isl_take isl_mat *top,
1510 __isl_take isl_vec *bot)
1511 {
1512 return isl_mat_concat(top, isl_mat_from_row_vec(bot));
1513 }
1514  
1515 __isl_give isl_mat *isl_mat_move_cols(__isl_take isl_mat *mat,
1516 unsigned dst_col, unsigned src_col, unsigned n)
1517 {
1518 isl_mat *res;
1519  
1520 if (!mat)
1521 return NULL;
1522 if (n == 0 || dst_col == src_col)
1523 return mat;
1524  
1525 res = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
1526 if (!res)
1527 goto error;
1528  
1529 if (dst_col < src_col) {
1530 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1531 0, 0, dst_col);
1532 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1533 dst_col, src_col, n);
1534 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1535 dst_col + n, dst_col, src_col - dst_col);
1536 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1537 src_col + n, src_col + n,
1538 res->n_col - src_col - n);
1539 } else {
1540 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1541 0, 0, src_col);
1542 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1543 src_col, src_col + n, dst_col - src_col);
1544 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1545 dst_col, src_col, n);
1546 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1547 dst_col + n, dst_col + n,
1548 res->n_col - dst_col - n);
1549 }
1550 isl_mat_free(mat);
1551  
1552 return res;
1553 error:
1554 isl_mat_free(mat);
1555 return NULL;
1556 }
1557  
1558 void isl_mat_gcd(__isl_keep isl_mat *mat, isl_int *gcd)
1559 {
1560 int i;
1561 isl_int g;
1562  
1563 isl_int_set_si(*gcd, 0);
1564 if (!mat)
1565 return;
1566  
1567 isl_int_init(g);
1568 for (i = 0; i < mat->n_row; ++i) {
1569 isl_seq_gcd(mat->row[i], mat->n_col, &g);
1570 isl_int_gcd(*gcd, *gcd, g);
1571 }
1572 isl_int_clear(g);
1573 }
1574  
1575 __isl_give isl_mat *isl_mat_scale_down(__isl_take isl_mat *mat, isl_int m)
1576 {
1577 int i;
1578  
1579 if (isl_int_is_one(m))
1580 return mat;
1581  
1582 mat = isl_mat_cow(mat);
1583 if (!mat)
1584 return NULL;
1585  
1586 for (i = 0; i < mat->n_row; ++i)
1587 isl_seq_scale_down(mat->row[i], mat->row[i], m, mat->n_col);
1588  
1589 return mat;
1590 }
1591  
1592 __isl_give isl_mat *isl_mat_scale_down_row(__isl_take isl_mat *mat, int row,
1593 isl_int m)
1594 {
1595 if (isl_int_is_one(m))
1596 return mat;
1597  
1598 mat = isl_mat_cow(mat);
1599 if (!mat)
1600 return NULL;
1601  
1602 isl_seq_scale_down(mat->row[row], mat->row[row], m, mat->n_col);
1603  
1604 return mat;
1605 }
1606  
1607 __isl_give isl_mat *isl_mat_normalize(__isl_take isl_mat *mat)
1608 {
1609 isl_int gcd;
1610  
1611 if (!mat)
1612 return NULL;
1613  
1614 isl_int_init(gcd);
1615 isl_mat_gcd(mat, &gcd);
1616 mat = isl_mat_scale_down(mat, gcd);
1617 isl_int_clear(gcd);
1618  
1619 return mat;
1620 }
1621  
1622 __isl_give isl_mat *isl_mat_normalize_row(__isl_take isl_mat *mat, int row)
1623 {
1624 mat = isl_mat_cow(mat);
1625 if (!mat)
1626 return NULL;
1627  
1628 isl_seq_normalize(mat->ctx, mat->row[row], mat->n_col);
1629  
1630 return mat;
1631 }
1632  
1633 /* Number of initial non-zero columns.
1634 */
1635 int isl_mat_initial_non_zero_cols(__isl_keep isl_mat *mat)
1636 {
1637 int i;
1638  
1639 if (!mat)
1640 return -1;
1641  
1642 for (i = 0; i < mat->n_col; ++i)
1643 if (row_first_non_zero(mat->row, mat->n_row, i) < 0)
1644 break;
1645  
1646 return i;
1647 }