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add isl_qpolynomial_fold_foreach_qpolynomial
[isl.git] / isl_mat.c
blob38bee9903573c825e5beca57f84674fd76399fb5
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_dim.h"
11 #include "isl_seq.h"
12 #include "isl_mat.h"
13 #include "isl_map_private.h"
14
15 struct isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
16 unsigned n_row, unsigned n_col)
17 {
18 int i;
19 struct isl_mat *mat;
20
21 mat = isl_alloc_type(ctx, struct isl_mat);
22 if (!mat)
23 return NULL;
24
25 mat->row = NULL;
26 mat->block = isl_blk_alloc(ctx, n_row * n_col);
27 if (isl_blk_is_error(mat->block))
28 goto error;
29 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
30 if (!mat->row)
31 goto error;
32
33 for (i = 0; i < n_row; ++i)
34 mat->row[i] = mat->block.data + i * n_col;
35
36 mat->ctx = ctx;
37 isl_ctx_ref(ctx);
38 mat->ref = 1;
39 mat->n_row = n_row;
40 mat->n_col = n_col;
41 mat->max_col = n_col;
42 mat->flags = 0;
43
44 return mat;
45 error:
46 isl_blk_free(ctx, mat->block);
47 free(mat);
48 return NULL;
49 }
50
51 struct isl_mat *isl_mat_extend(struct isl_mat *mat,
52 unsigned n_row, unsigned n_col)
53 {
54 int i;
55 isl_int *old;
56
57 if (!mat)
58 return NULL;
59
60 if (mat->max_col >= n_col && mat->n_row >= n_row) {
61 if (mat->n_col < n_col)
62 mat->n_col = n_col;
63 return mat;
64 }
65
66 if (mat->max_col < n_col) {
67 struct isl_mat *new_mat;
68
69 if (n_row < mat->n_row)
70 n_row = mat->n_row;
71 new_mat = isl_mat_alloc(mat->ctx, n_row, n_col);
72 if (!new_mat)
73 goto error;
74 for (i = 0; i < mat->n_row; ++i)
75 isl_seq_cpy(new_mat->row[i], mat->row[i], mat->n_col);
76 isl_mat_free(mat);
77 return new_mat;
78 }
79
80 mat = isl_mat_cow(mat);
81 if (!mat)
82 goto error;
83
84 assert(mat->ref == 1);
85 old = mat->block.data;
86 mat->block = isl_blk_extend(mat->ctx, mat->block, n_row * mat->max_col);
87 if (isl_blk_is_error(mat->block))
88 goto error;
89 mat->row = isl_realloc_array(mat->ctx, mat->row, isl_int *, n_row);
90 if (!mat->row)
91 goto error;
92
93 for (i = 0; i < mat->n_row; ++i)
94 mat->row[i] = mat->block.data + (mat->row[i] - old);
95 for (i = mat->n_row; i < n_row; ++i)
96 mat->row[i] = mat->block.data + i * mat->max_col;
97 mat->n_row = n_row;
98 if (mat->n_col < n_col)
99 mat->n_col = n_col;
100
101 return mat;
102 error:
103 isl_mat_free(mat);
104 return NULL;
105 }
106
107 struct isl_mat *isl_mat_sub_alloc(struct isl_ctx *ctx, isl_int **row,
108 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
109 {
110 int i;
111 struct isl_mat *mat;
112
113 mat = isl_alloc_type(ctx, struct isl_mat);
114 if (!mat)
115 return NULL;
116 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
117 if (!mat->row)
118 goto error;
119 for (i = 0; i < n_row; ++i)
120 mat->row[i] = row[first_row+i] + first_col;
121 mat->ctx = ctx;
122 isl_ctx_ref(ctx);
123 mat->ref = 1;
124 mat->n_row = n_row;
125 mat->n_col = n_col;
126 mat->block = isl_blk_empty();
127 mat->flags = ISL_MAT_BORROWED;
128 return mat;
129 error:
130 free(mat);
131 return NULL;
132 }
133
134 void isl_mat_sub_copy(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
135 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
136 {
137 int i;
138
139 for (i = 0; i < n_row; ++i)
140 isl_seq_cpy(dst[i]+dst_col, src[i]+src_col, n_col);
141 }
142
143 void isl_mat_sub_neg(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
144 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
145 {
146 int i;
147
148 for (i = 0; i < n_row; ++i)
149 isl_seq_neg(dst[i]+dst_col, src[i]+src_col, n_col);
150 }
151
152 struct isl_mat *isl_mat_copy(struct isl_mat *mat)
153 {
154 if (!mat)
155 return NULL;
156
157 mat->ref++;
158 return mat;
159 }
160
161 struct isl_mat *isl_mat_dup(struct isl_mat *mat)
162 {
163 int i;
164 struct isl_mat *mat2;
165
166 if (!mat)
167 return NULL;
168 mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
169 if (!mat2)
170 return NULL;
171 for (i = 0; i < mat->n_row; ++i)
172 isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);
173 return mat2;
174 }
175
176 struct isl_mat *isl_mat_cow(struct isl_mat *mat)
177 {
178 struct isl_mat *mat2;
179 if (!mat)
180 return NULL;
181
182 if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))
183 return mat;
184
185 mat2 = isl_mat_dup(mat);
186 isl_mat_free(mat);
187 return mat2;
188 }
189
190 void isl_mat_free(struct isl_mat *mat)
191 {
192 if (!mat)
193 return;
194
195 if (--mat->ref > 0)
196 return;
197
198 if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))
199 isl_blk_free(mat->ctx, mat->block);
200 isl_ctx_deref(mat->ctx);
201 free(mat->row);
202 free(mat);
203 }
204
205 struct isl_mat *isl_mat_identity(struct isl_ctx *ctx, unsigned n_row)
206 {
207 int i;
208 struct isl_mat *mat;
209
210 mat = isl_mat_alloc(ctx, n_row, n_row);
211 if (!mat)
212 return NULL;
213 for (i = 0; i < n_row; ++i) {
214 isl_seq_clr(mat->row[i], i);
215 isl_int_set_si(mat->row[i][i], 1);
216 isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
217 }
218
219 return mat;
220 }
221
222 struct isl_vec *isl_mat_vec_product(struct isl_mat *mat, struct isl_vec *vec)
223 {
224 int i;
225 struct isl_vec *prod;
226
227 if (!mat || !vec)
228 goto error;
229
230 isl_assert(mat->ctx, mat->n_col == vec->size, goto error);
231
232 prod = isl_vec_alloc(mat->ctx, mat->n_row);
233 if (!prod)
234 goto error;
235
236 for (i = 0; i < prod->size; ++i)
237 isl_seq_inner_product(mat->row[i], vec->el, vec->size,
238 &prod->block.data[i]);
239 isl_mat_free(mat);
240 isl_vec_free(vec);
241 return prod;
242 error:
243 isl_mat_free(mat);
244 isl_vec_free(vec);
245 return NULL;
246 }
247
248 __isl_give isl_vec *isl_mat_vec_inverse_product(__isl_take isl_mat *mat,
249 __isl_take isl_vec *vec)
250 {
251 struct isl_mat *vec_mat;
252 int i;
253
254 if (!mat || !vec)
255 goto error;
256 vec_mat = isl_mat_alloc(vec->ctx, vec->size, 1);
257 if (!vec_mat)
258 goto error;
259 for (i = 0; i < vec->size; ++i)
260 isl_int_set(vec_mat->row[i][0], vec->el[i]);
261 vec_mat = isl_mat_inverse_product(mat, vec_mat);
262 isl_vec_free(vec);
263 if (!vec_mat)
264 return NULL;
265 vec = isl_vec_alloc(vec_mat->ctx, vec_mat->n_row);
266 if (vec)
267 for (i = 0; i < vec->size; ++i)
268 isl_int_set(vec->el[i], vec_mat->row[i][0]);
269 isl_mat_free(vec_mat);
270 return vec;
271 error:
272 isl_mat_free(mat);
273 isl_vec_free(vec);
274 return NULL;
275 }
276
277 struct isl_vec *isl_vec_mat_product(struct isl_vec *vec, struct isl_mat *mat)
278 {
279 int i, j;
280 struct isl_vec *prod;
281
282 if (!mat || !vec)
283 goto error;
284
285 isl_assert(mat->ctx, mat->n_row == vec->size, goto error);
286
287 prod = isl_vec_alloc(mat->ctx, mat->n_col);
288 if (!prod)
289 goto error;
290
291 for (i = 0; i < prod->size; ++i) {
292 isl_int_set_si(prod->el[i], 0);
293 for (j = 0; j < vec->size; ++j)
294 isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);
295 }
296 isl_mat_free(mat);
297 isl_vec_free(vec);
298 return prod;
299 error:
300 isl_mat_free(mat);
301 isl_vec_free(vec);
302 return NULL;
303 }
304
305 struct isl_mat *isl_mat_aff_direct_sum(struct isl_mat *left,
306 struct isl_mat *right)
307 {
308 int i;
309 struct isl_mat *sum;
310
311 if (!left || !right)
312 goto error;
313
314 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
315 isl_assert(left->ctx, left->n_row >= 1, goto error);
316 isl_assert(left->ctx, left->n_col >= 1, goto error);
317 isl_assert(left->ctx, right->n_col >= 1, goto error);
318 isl_assert(left->ctx,
319 isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,
320 goto error);
321 isl_assert(left->ctx,
322 isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
323 goto error);
324
325 sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);
326 if (!sum)
327 goto error;
328 isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);
329 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
330 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
331
332 isl_seq_clr(sum->row[0]+1, sum->n_col-1);
333 for (i = 1; i < sum->n_row; ++i) {
334 isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);
335 isl_int_addmul(sum->row[i][0],
336 right->row[0][0], right->row[i][0]);
337 isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],
338 left->n_col-1);
339 isl_seq_scale(sum->row[i]+left->n_col,
340 right->row[i]+1, right->row[0][0],
341 right->n_col-1);
342 }
343
344 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
345 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
346 isl_mat_free(left);
347 isl_mat_free(right);
348 return sum;
349 error:
350 isl_mat_free(left);
351 isl_mat_free(right);
352 return NULL;
353 }
354
355 static void exchange(struct isl_mat *M, struct isl_mat **U,
356 struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
357 {
358 int r;
359 for (r = row; r < M->n_row; ++r)
360 isl_int_swap(M->row[r][i], M->row[r][j]);
361 if (U) {
362 for (r = 0; r < (*U)->n_row; ++r)
363 isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
364 }
365 if (Q)
366 isl_mat_swap_rows(*Q, i, j);
367 }
368
369 static void subtract(struct isl_mat *M, struct isl_mat **U,
370 struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)
371 {
372 int r;
373 for (r = row; r < M->n_row; ++r)
374 isl_int_submul(M->row[r][j], m, M->row[r][i]);
375 if (U) {
376 for (r = 0; r < (*U)->n_row; ++r)
377 isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);
378 }
379 if (Q) {
380 for (r = 0; r < (*Q)->n_col; ++r)
381 isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);
382 }
383 }
384
385 static void oppose(struct isl_mat *M, struct isl_mat **U,
386 struct isl_mat **Q, unsigned row, unsigned col)
387 {
388 int r;
389 for (r = row; r < M->n_row; ++r)
390 isl_int_neg(M->row[r][col], M->row[r][col]);
391 if (U) {
392 for (r = 0; r < (*U)->n_row; ++r)
393 isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);
394 }
395 if (Q)
396 isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);
397 }
398
399 /* Given matrix M, compute
400 *
401 * M U = H
402 * M = H Q
403 *
404 * with U and Q unimodular matrices and H a matrix in column echelon form
405 * such that on each echelon row the entries in the non-echelon column
406 * are non-negative (if neg == 0) or non-positive (if neg == 1)
407 * and stricly smaller (in absolute value) than the entries in the echelon
408 * column.
409 * If U or Q are NULL, then these matrices are not computed.
410 */
411 struct isl_mat *isl_mat_left_hermite(struct isl_mat *M, int neg,
412 struct isl_mat **U, struct isl_mat **Q)
413 {
414 isl_int c;
415 int row, col;
416
417 if (U)
418 *U = NULL;
419 if (Q)
420 *Q = NULL;
421 if (!M)
422 goto error;
423 M = isl_mat_cow(M);
424 if (!M)
425 goto error;
426 if (U) {
427 *U = isl_mat_identity(M->ctx, M->n_col);
428 if (!*U)
429 goto error;
430 }
431 if (Q) {
432 *Q = isl_mat_identity(M->ctx, M->n_col);
433 if (!*Q)
434 goto error;
435 }
436
437 col = 0;
438 isl_int_init(c);
439 for (row = 0; row < M->n_row; ++row) {
440 int first, i, off;
441 first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);
442 if (first == -1)
443 continue;
444 first += col;
445 if (first != col)
446 exchange(M, U, Q, row, first, col);
447 if (isl_int_is_neg(M->row[row][col]))
448 oppose(M, U, Q, row, col);
449 first = col+1;
450 while ((off = isl_seq_first_non_zero(M->row[row]+first,
451 M->n_col-first)) != -1) {
452 first += off;
453 isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);
454 subtract(M, U, Q, row, col, first, c);
455 if (!isl_int_is_zero(M->row[row][first]))
456 exchange(M, U, Q, row, first, col);
457 else
458 ++first;
459 }
460 for (i = 0; i < col; ++i) {
461 if (isl_int_is_zero(M->row[row][i]))
462 continue;
463 if (neg)
464 isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);
465 else
466 isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);
467 if (isl_int_is_zero(c))
468 continue;
469 subtract(M, U, Q, row, col, i, c);
470 }
471 ++col;
472 }
473 isl_int_clear(c);
474
475 return M;
476 error:
477 if (Q) {
478 isl_mat_free(*Q);
479 *Q = NULL;
480 }
481 if (U) {
482 isl_mat_free(*U);
483 *U = NULL;
484 }
485 return NULL;
486 }
487
488 struct isl_mat *isl_mat_right_kernel(struct isl_mat *mat)
489 {
490 int i, rank;
491 struct isl_mat *U = NULL;
492 struct isl_mat *K;
493
494 mat = isl_mat_left_hermite(mat, 0, &U, NULL);
495 if (!mat || !U)
496 goto error;
497
498 for (i = 0, rank = 0; rank < mat->n_col; ++rank) {
499 while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))
500 ++i;
501 if (i >= mat->n_row)
502 break;
503 }
504 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
505 if (!K)
506 goto error;
507 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
508 isl_mat_free(mat);
509 isl_mat_free(U);
510 return K;
511 error:
512 isl_mat_free(mat);
513 isl_mat_free(U);
514 return NULL;
515 }
516
517 struct isl_mat *isl_mat_lin_to_aff(struct isl_mat *mat)
518 {
519 int i;
520 struct isl_mat *mat2;
521
522 if (!mat)
523 return NULL;
524 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
525 if (!mat2)
526 goto error;
527 isl_int_set_si(mat2->row[0][0], 1);
528 isl_seq_clr(mat2->row[0]+1, mat->n_col);
529 for (i = 0; i < mat->n_row; ++i) {
530 isl_int_set_si(mat2->row[1+i][0], 0);
531 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
532 }
533 isl_mat_free(mat);
534 return mat2;
535 error:
536 isl_mat_free(mat);
537 return NULL;
538 }
539
540 /* Given two matrices M1 and M2, return the block matrix
541 *
542 * [ M1 0 ]
543 * [ 0 M2 ]
544 */
545 __isl_give isl_mat *isl_mat_diagonal(__isl_take isl_mat *mat1,
546 __isl_take isl_mat *mat2)
547 {
548 int i;
549 isl_mat *mat;
550
551 if (!mat1 || !mat2)
552 goto error;
553
554 mat = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
555 mat1->n_col + mat2->n_col);
556 if (!mat)
557 goto error;
558 for (i = 0; i < mat1->n_row; ++i) {
559 isl_seq_cpy(mat->row[i], mat1->row[i], mat1->n_col);
560 isl_seq_clr(mat->row[i] + mat1->n_col, mat2->n_col);
561 }
562 for (i = 0; i < mat2->n_row; ++i) {
563 isl_seq_clr(mat->row[mat1->n_row + i], mat1->n_col);
564 isl_seq_cpy(mat->row[mat1->n_row + i] + mat1->n_col,
565 mat2->row[i], mat2->n_col);
566 }
567 isl_mat_free(mat1);
568 isl_mat_free(mat2);
569 return mat;
570 error:
571 isl_mat_free(mat1);
572 isl_mat_free(mat2);
573 return NULL;
574 }
575
576 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
577 {
578 int i;
579
580 for (i = 0; i < n_row; ++i)
581 if (!isl_int_is_zero(row[i][col]))
582 return i;
583 return -1;
584 }
585
586 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
587 {
588 int i, min = row_first_non_zero(row, n_row, col);
589 if (min < 0)
590 return -1;
591 for (i = min + 1; i < n_row; ++i) {
592 if (isl_int_is_zero(row[i][col]))
593 continue;
594 if (isl_int_abs_lt(row[i][col], row[min][col]))
595 min = i;
596 }
597 return min;
598 }
599
600 static void inv_exchange(struct isl_mat *left, struct isl_mat *right,
601 unsigned i, unsigned j)
602 {
603 left = isl_mat_swap_rows(left, i, j);
604 right = isl_mat_swap_rows(right, i, j);
605 }
606
607 static void inv_oppose(
608 struct isl_mat *left, struct isl_mat *right, unsigned row)
609 {
610 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
611 isl_seq_neg(right->row[row], right->row[row], right->n_col);
612 }
613
614 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
615 unsigned row, unsigned i, isl_int m)
616 {
617 isl_int_neg(m, m);
618 isl_seq_combine(left->row[i]+row,
619 left->ctx->one, left->row[i]+row,
620 m, left->row[row]+row,
621 left->n_col-row);
622 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
623 m, right->row[row], right->n_col);
624 }
625
626 /* Compute inv(left)*right
627 */
628 struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
629 struct isl_mat *right)
630 {
631 int row;
632 isl_int a, b;
633
634 if (!left || !right)
635 goto error;
636
637 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
638 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
639
640 if (left->n_row == 0) {
641 isl_mat_free(left);
642 return right;
643 }
644
645 left = isl_mat_cow(left);
646 right = isl_mat_cow(right);
647 if (!left || !right)
648 goto error;
649
650 isl_int_init(a);
651 isl_int_init(b);
652 for (row = 0; row < left->n_row; ++row) {
653 int pivot, first, i, off;
654 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
655 if (pivot < 0) {
656 isl_int_clear(a);
657 isl_int_clear(b);
658 isl_assert(left->ctx, pivot >= 0, goto error);
659 }
660 pivot += row;
661 if (pivot != row)
662 inv_exchange(left, right, pivot, row);
663 if (isl_int_is_neg(left->row[row][row]))
664 inv_oppose(left, right, row);
665 first = row+1;
666 while ((off = row_first_non_zero(left->row+first,
667 left->n_row-first, row)) != -1) {
668 first += off;
669 isl_int_fdiv_q(a, left->row[first][row],
670 left->row[row][row]);
671 inv_subtract(left, right, row, first, a);
672 if (!isl_int_is_zero(left->row[first][row]))
673 inv_exchange(left, right, row, first);
674 else
675 ++first;
676 }
677 for (i = 0; i < row; ++i) {
678 if (isl_int_is_zero(left->row[i][row]))
679 continue;
680 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
681 isl_int_divexact(b, left->row[i][row], a);
682 isl_int_divexact(a, left->row[row][row], a);
683 isl_int_neg(b, b);
684 isl_seq_combine(left->row[i] + i,
685 a, left->row[i] + i,
686 b, left->row[row] + i,
687 left->n_col - i);
688 isl_seq_combine(right->row[i], a, right->row[i],
689 b, right->row[row], right->n_col);
690 }
691 }
692 isl_int_clear(b);
693
694 isl_int_set(a, left->row[0][0]);
695 for (row = 1; row < left->n_row; ++row)
696 isl_int_lcm(a, a, left->row[row][row]);
697 if (isl_int_is_zero(a)){
698 isl_int_clear(a);
699 isl_assert(left->ctx, 0, goto error);
700 }
701 for (row = 0; row < left->n_row; ++row) {
702 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
703 if (isl_int_is_one(left->row[row][row]))
704 continue;
705 isl_seq_scale(right->row[row], right->row[row],
706 left->row[row][row], right->n_col);
707 }
708 isl_int_clear(a);
709
710 isl_mat_free(left);
711 return right;
712 error:
713 isl_mat_free(left);
714 isl_mat_free(right);
715 return NULL;
716 }
717
718 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
719 {
720 int i;
721
722 for (i = 0; i < mat->n_row; ++i)
723 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
724 }
725
726 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
727 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
728 {
729 int i;
730 isl_int tmp;
731
732 isl_int_init(tmp);
733 for (i = 0; i < mat->n_row; ++i) {
734 isl_int_mul(tmp, m1, mat->row[i][src1]);
735 isl_int_addmul(tmp, m2, mat->row[i][src2]);
736 isl_int_set(mat->row[i][dst], tmp);
737 }
738 isl_int_clear(tmp);
739 }
740
741 struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
742 {
743 struct isl_mat *inv;
744 int row;
745 isl_int a, b;
746
747 mat = isl_mat_cow(mat);
748 if (!mat)
749 return NULL;
750
751 inv = isl_mat_identity(mat->ctx, mat->n_col);
752 inv = isl_mat_cow(inv);
753 if (!inv)
754 goto error;
755
756 isl_int_init(a);
757 isl_int_init(b);
758 for (row = 0; row < mat->n_row; ++row) {
759 int pivot, first, i, off;
760 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
761 if (pivot < 0) {
762 isl_int_clear(a);
763 isl_int_clear(b);
764 isl_assert(mat->ctx, pivot >= 0, goto error);
765 }
766 pivot += row;
767 if (pivot != row)
768 exchange(mat, &inv, NULL, row, pivot, row);
769 if (isl_int_is_neg(mat->row[row][row]))
770 oppose(mat, &inv, NULL, row, row);
771 first = row+1;
772 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
773 mat->n_col-first)) != -1) {
774 first += off;
775 isl_int_fdiv_q(a, mat->row[row][first],
776 mat->row[row][row]);
777 subtract(mat, &inv, NULL, row, row, first, a);
778 if (!isl_int_is_zero(mat->row[row][first]))
779 exchange(mat, &inv, NULL, row, row, first);
780 else
781 ++first;
782 }
783 for (i = 0; i < row; ++i) {
784 if (isl_int_is_zero(mat->row[row][i]))
785 continue;
786 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
787 isl_int_divexact(b, mat->row[row][i], a);
788 isl_int_divexact(a, mat->row[row][row], a);
789 isl_int_neg(a, a);
790 isl_mat_col_combine(mat, i, a, i, b, row);
791 isl_mat_col_combine(inv, i, a, i, b, row);
792 }
793 }
794 isl_int_clear(b);
795
796 isl_int_set(a, mat->row[0][0]);
797 for (row = 1; row < mat->n_row; ++row)
798 isl_int_lcm(a, a, mat->row[row][row]);
799 if (isl_int_is_zero(a)){
800 isl_int_clear(a);
801 goto error;
802 }
803 for (row = 0; row < mat->n_row; ++row) {
804 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
805 if (isl_int_is_one(mat->row[row][row]))
806 continue;
807 isl_mat_col_scale(inv, row, mat->row[row][row]);
808 }
809 isl_int_clear(a);
810
811 isl_mat_free(mat);
812
813 return inv;
814 error:
815 isl_mat_free(mat);
816 return NULL;
817 }
818
819 struct isl_mat *isl_mat_transpose(struct isl_mat *mat)
820 {
821 struct isl_mat *transpose = NULL;
822 int i, j;
823
824 if (mat->n_col == mat->n_row) {
825 mat = isl_mat_cow(mat);
826 if (!mat)
827 return NULL;
828 for (i = 0; i < mat->n_row; ++i)
829 for (j = i + 1; j < mat->n_col; ++j)
830 isl_int_swap(mat->row[i][j], mat->row[j][i]);
831 return mat;
832 }
833 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
834 if (!transpose)
835 goto error;
836 for (i = 0; i < mat->n_row; ++i)
837 for (j = 0; j < mat->n_col; ++j)
838 isl_int_set(transpose->row[j][i], mat->row[i][j]);
839 isl_mat_free(mat);
840 return transpose;
841 error:
842 isl_mat_free(mat);
843 return NULL;
844 }
845
846 struct isl_mat *isl_mat_swap_cols(struct isl_mat *mat, unsigned i, unsigned j)
847 {
848 int r;
849
850 mat = isl_mat_cow(mat);
851 if (!mat)
852 return NULL;
853 isl_assert(mat->ctx, i < mat->n_col, goto error);
854 isl_assert(mat->ctx, j < mat->n_col, goto error);
855
856 for (r = 0; r < mat->n_row; ++r)
857 isl_int_swap(mat->row[r][i], mat->row[r][j]);
858 return mat;
859 error:
860 isl_mat_free(mat);
861 return NULL;
862 }
863
864 struct isl_mat *isl_mat_swap_rows(struct isl_mat *mat, unsigned i, unsigned j)
865 {
866 isl_int *t;
867
868 if (!mat)
869 return NULL;
870 mat = isl_mat_cow(mat);
871 if (!mat)
872 return NULL;
873 t = mat->row[i];
874 mat->row[i] = mat->row[j];
875 mat->row[j] = t;
876 return mat;
877 }
878
879 struct isl_mat *isl_mat_product(struct isl_mat *left, struct isl_mat *right)
880 {
881 int i, j, k;
882 struct isl_mat *prod;
883
884 if (!left || !right)
885 goto error;
886 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
887 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
888 if (!prod)
889 goto error;
890 if (left->n_col == 0) {
891 for (i = 0; i < prod->n_row; ++i)
892 isl_seq_clr(prod->row[i], prod->n_col);
893 return prod;
894 }
895 for (i = 0; i < prod->n_row; ++i) {
896 for (j = 0; j < prod->n_col; ++j) {
897 isl_int_mul(prod->row[i][j],
898 left->row[i][0], right->row[0][j]);
899 for (k = 1; k < left->n_col; ++k)
900 isl_int_addmul(prod->row[i][j],
901 left->row[i][k], right->row[k][j]);
902 }
903 }
904 isl_mat_free(left);
905 isl_mat_free(right);
906 return prod;
907 error:
908 isl_mat_free(left);
909 isl_mat_free(right);
910 return NULL;
911 }
912
913 /* Replace the variables x in the rows q by x' given by x = M x',
914 * with M the matrix mat.
915 *
916 * If the number of new variables is greater than the original
917 * number of variables, then the rows q have already been
918 * preextended. If the new number is smaller, then the coefficients
919 * of the divs, which are not changed, need to be shifted down.
920 * The row q may be the equalities, the inequalities or the
921 * div expressions. In the latter case, has_div is true and
922 * we need to take into account the extra denominator column.
923 */
924 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
925 unsigned n_div, int has_div, struct isl_mat *mat)
926 {
927 int i;
928 struct isl_mat *t;
929 int e;
930
931 if (mat->n_col >= mat->n_row)
932 e = 0;
933 else
934 e = mat->n_row - mat->n_col;
935 if (has_div)
936 for (i = 0; i < n; ++i)
937 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
938 t = isl_mat_sub_alloc(mat->ctx, q, 0, n, has_div, mat->n_row);
939 t = isl_mat_product(t, mat);
940 if (!t)
941 return -1;
942 for (i = 0; i < n; ++i) {
943 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
944 isl_seq_cpy(q[i] + has_div + t->n_col,
945 q[i] + has_div + t->n_col + e, n_div);
946 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
947 }
948 isl_mat_free(t);
949 return 0;
950 }
951
952 /* Replace the variables x in bset by x' given by x = M x', with
953 * M the matrix mat.
954 *
955 * If there are fewer variables x' then there are x, then we perform
956 * the transformation in place, which that, in principle,
957 * this frees up some extra variables as the number
958 * of columns remains constant, but we would have to extend
959 * the div array too as the number of rows in this array is assumed
960 * to be equal to extra.
961 */
962 struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
963 struct isl_mat *mat)
964 {
965 struct isl_ctx *ctx;
966
967 if (!bset || !mat)
968 goto error;
969
970 ctx = bset->ctx;
971 bset = isl_basic_set_cow(bset);
972 if (!bset)
973 goto error;
974
975 isl_assert(ctx, bset->dim->nparam == 0, goto error);
976 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
977 isl_assert(ctx, mat->n_col > 0, goto error);
978
979 if (mat->n_col > mat->n_row)
980 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0,
981 0, 0);
982 else if (mat->n_col < mat->n_row) {
983 bset->dim = isl_dim_cow(bset->dim);
984 if (!bset->dim)
985 goto error;
986 bset->dim->n_out -= mat->n_row - mat->n_col;
987 }
988
989 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
990 isl_mat_copy(mat)) < 0)
991 goto error;
992
993 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
994 isl_mat_copy(mat)) < 0)
995 goto error;
996
997 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
998 goto error2;
999
1000 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
1001 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
1002 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1003 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1004 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
1005
1006 bset = isl_basic_set_simplify(bset);
1007 bset = isl_basic_set_finalize(bset);
1008
1009 return bset;
1010 error:
1011 isl_mat_free(mat);
1012 error2:
1013 isl_basic_set_free(bset);
1014 return NULL;
1015 }
1016
1017 struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
1018 {
1019 struct isl_ctx *ctx;
1020 int i;
1021
1022 set = isl_set_cow(set);
1023 if (!set)
1024 return NULL;
1025
1026 ctx = set->ctx;
1027 for (i = 0; i < set->n; ++i) {
1028 set->p[i] = isl_basic_set_preimage(set->p[i],
1029 isl_mat_copy(mat));
1030 if (!set->p[i])
1031 goto error;
1032 }
1033 if (mat->n_col != mat->n_row) {
1034 set->dim = isl_dim_cow(set->dim);
1035 if (!set->dim)
1036 goto error;
1037 set->dim->n_out += mat->n_col;
1038 set->dim->n_out -= mat->n_row;
1039 }
1040 isl_mat_free(mat);
1041 ISL_F_CLR(set, ISL_SET_NORMALIZED);
1042 return set;
1043 error:
1044 isl_set_free(set);
1045 isl_mat_free(mat);
1046 return NULL;
1047 }
1048
1049 void isl_mat_dump(struct isl_mat *mat, FILE *out, int indent)
1050 {
1051 int i, j;
1052
1053 if (!mat) {
1054 fprintf(out, "%*snull mat\n", indent, "");
1055 return;
1056 }
1057
1058 if (mat->n_row == 0)
1059 fprintf(out, "%*s[]\n", indent, "");
1060
1061 for (i = 0; i < mat->n_row; ++i) {
1062 if (!i)
1063 fprintf(out, "%*s[[", indent, "");
1064 else
1065 fprintf(out, "%*s[", indent+1, "");
1066 for (j = 0; j < mat->n_col; ++j) {
1067 if (j)
1068 fprintf(out, ",");
1069 isl_int_print(out, mat->row[i][j], 0);
1070 }
1071 if (i == mat->n_row-1)
1072 fprintf(out, "]]\n");
1073 else
1074 fprintf(out, "]\n");
1075 }
1076 }
1077
1078 struct isl_mat *isl_mat_drop_cols(struct isl_mat *mat, unsigned col, unsigned n)
1079 {
1080 int r;
1081
1082 mat = isl_mat_cow(mat);
1083 if (!mat)
1084 return NULL;
1085
1086 if (col != mat->n_col-n) {
1087 for (r = 0; r < mat->n_row; ++r)
1088 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1089 mat->n_col - col - n);
1090 }
1091 mat->n_col -= n;
1092 return mat;
1093 }
1094
1095 struct isl_mat *isl_mat_drop_rows(struct isl_mat *mat, unsigned row, unsigned n)
1096 {
1097 int r;
1098
1099 mat = isl_mat_cow(mat);
1100 if (!mat)
1101 return NULL;
1102
1103 for (r = row; r+n < mat->n_row; ++r)
1104 mat->row[r] = mat->row[r+n];
1105
1106 mat->n_row -= n;
1107 return mat;
1108 }
1109
1110 __isl_give isl_mat *isl_mat_insert_cols(__isl_take isl_mat *mat,
1111 unsigned col, unsigned n)
1112 {
1113 isl_mat *ext;
1114
1115 if (!mat)
1116 return NULL;
1117 if (n == 0)
1118 return mat;
1119
1120 ext = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col + n);
1121 if (!ext)
1122 goto error;
1123
1124 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row, 0, 0, col);
1125 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row,
1126 col + n, col, mat->n_col - col);
1127
1128 isl_mat_free(mat);
1129 return ext;
1130 error:
1131 isl_mat_free(mat);
1132 return NULL;
1133 }
1134
1135 __isl_give isl_mat *isl_mat_insert_rows(__isl_take isl_mat *mat,
1136 unsigned row, unsigned n)
1137 {
1138 isl_mat *ext;
1139
1140 if (!mat)
1141 return NULL;
1142 if (n == 0)
1143 return mat;
1144
1145 ext = isl_mat_alloc(mat->ctx, mat->n_row + n, mat->n_col);
1146 if (!ext)
1147 goto error;
1148
1149 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, row, 0, 0, mat->n_col);
1150 isl_mat_sub_copy(mat->ctx, ext->row + row + n, mat->row + row,
1151 mat->n_row - row, 0, 0, mat->n_col);
1152
1153 isl_mat_free(mat);
1154 return ext;
1155 error:
1156 isl_mat_free(mat);
1157 return NULL;
1158 }
1159
1160 void isl_mat_col_submul(struct isl_mat *mat,
1161 int dst_col, isl_int f, int src_col)
1162 {
1163 int i;
1164
1165 for (i = 0; i < mat->n_row; ++i)
1166 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1167 }
1168
1169 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1170 {
1171 int i;
1172
1173 for (i = 0; i < mat->n_row; ++i)
1174 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1175 }
1176
1177 struct isl_mat *isl_mat_unimodular_complete(struct isl_mat *M, int row)
1178 {
1179 int r;
1180 struct isl_mat *H = NULL, *Q = NULL;
1181
1182 if (!M)
1183 return NULL;
1184
1185 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1186 M->n_row = row;
1187 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1188 M->n_row = M->n_col;
1189 if (!H)
1190 goto error;
1191 for (r = 0; r < row; ++r)
1192 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1193 for (r = row; r < M->n_row; ++r)
1194 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1195 isl_mat_free(H);
1196 isl_mat_free(Q);
1197 return M;
1198 error:
1199 isl_mat_free(H);
1200 isl_mat_free(Q);
1201 isl_mat_free(M);
1202 return NULL;
1203 }
1204
1205 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1206 __isl_take isl_mat *bot)
1207 {
1208 struct isl_mat *mat;
1209
1210 if (!top || !bot)
1211 goto error;
1212
1213 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1214 if (top->n_row == 0) {
1215 isl_mat_free(top);
1216 return bot;
1217 }
1218 if (bot->n_row == 0) {
1219 isl_mat_free(bot);
1220 return top;
1221 }
1222
1223 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1224 if (!mat)
1225 goto error;
1226 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1227 0, 0, mat->n_col);
1228 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1229 0, 0, mat->n_col);
1230 isl_mat_free(top);
1231 isl_mat_free(bot);
1232 return mat;
1233 error:
1234 isl_mat_free(top);
1235 isl_mat_free(bot);
1236 return NULL;
1237 }
1238
1239 int isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
1240 {
1241 int i;
1242
1243 if (!mat1 || !mat2)
1244 return -1;
1245
1246 if (mat1->n_row != mat2->n_row)
1247 return 0;
1248
1249 if (mat1->n_col != mat2->n_col)
1250 return 0;
1251
1252 for (i = 0; i < mat1->n_row; ++i)
1253 if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
1254 return 0;
1255
1256 return 1;
1257 }
1258
1259 __isl_give isl_mat *isl_mat_from_row_vec(__isl_take isl_vec *vec)
1260 {
1261 struct isl_mat *mat;
1262
1263 if (!vec)
1264 return NULL;
1265 mat = isl_mat_alloc(vec->ctx, 1, vec->size);
1266 if (!mat)
1267 goto error;
1268
1269 isl_seq_cpy(mat->row[0], vec->el, vec->size);
1270
1271 isl_vec_free(vec);
1272 return mat;
1273 error:
1274 isl_vec_free(vec);
1275 return NULL;
1276 }
1277
1278 __isl_give isl_mat *isl_mat_vec_concat(__isl_take isl_mat *top,
1279 __isl_take isl_vec *bot)
1280 {
1281 return isl_mat_concat(top, isl_mat_from_row_vec(bot));
1282 }
1283
1284 __isl_give isl_mat *isl_mat_move_cols(__isl_take isl_mat *mat,
1285 unsigned dst_col, unsigned src_col, unsigned n)
1286 {
1287 isl_mat *res;
1288
1289 if (!mat)
1290 return NULL;
1291 if (n == 0 || dst_col == src_col)
1292 return mat;
1293
1294 res = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
1295 if (!res)
1296 goto error;
1297
1298 if (dst_col < src_col) {
1299 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1300 0, 0, dst_col);
1301 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1302 dst_col, src_col, n);
1303 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1304 dst_col + n, dst_col, src_col - dst_col);
1305 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1306 src_col + n, src_col + n,
1307 res->n_col - src_col - n);
1308 } else {
1309 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1310 0, 0, src_col);
1311 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1312 src_col, src_col + n, dst_col - src_col);
1313 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1314 dst_col, src_col, n);
1315 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1316 dst_col + n, dst_col + n,
1317 res->n_col - dst_col - n);
1318 }
1319 isl_mat_free(mat);
1320
1321 return res;
1322 error:
1323 isl_mat_free(mat);
1324 return NULL;
1325 }
1326
1327 void isl_mat_gcd(__isl_keep isl_mat *mat, isl_int *gcd)
1328 {
1329 int i;
1330 isl_int g;
1331
1332 isl_int_set_si(*gcd, 0);
1333 if (!mat)
1334 return;
1335
1336 isl_int_init(g);
1337 for (i = 0; i < mat->n_row; ++i) {
1338 isl_seq_gcd(mat->row[i], mat->n_col, &g);
1339 isl_int_gcd(*gcd, *gcd, g);
1340 }
1341 isl_int_clear(g);
1342 }
1343
1344 __isl_give isl_mat *isl_mat_scale_down(__isl_take isl_mat *mat, isl_int m)
1345 {
1346 int i;
1347
1348 if (!mat)
1349 return NULL;
1350
1351 for (i = 0; i < mat->n_row; ++i)
1352 isl_seq_scale_down(mat->row[i], mat->row[i], m, mat->n_col);
1353
1354 return mat;
1355 }
1356
1357 __isl_give isl_mat *isl_mat_normalize(__isl_take isl_mat *mat)
1358 {
1359 isl_int gcd;
1360
1361 if (!mat)
1362 return NULL;
1363
1364 isl_int_init(gcd);
1365 isl_mat_gcd(mat, &gcd);
1366 mat = isl_mat_scale_down(mat, gcd);
1367 isl_int_clear(gcd);
1368
1369 return mat;
1370 }
Integer set library