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isl_tab_basic_map_partial_lexopt: remove samples that are no longer useful
[isl.git] / isl_mat.c
blob2b8f5401645c770cee8c150e754bfc1a33cf6c59
1 #include "isl_dim.h"
2 #include "isl_seq.h"
3 #include "isl_mat.h"
4 #include "isl_map_private.h"
5
6 struct isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
7 unsigned n_row, unsigned n_col)
8 {
9 int i;
10 struct isl_mat *mat;
11
12 mat = isl_alloc_type(ctx, struct isl_mat);
13 if (!mat)
14 return NULL;
15
16 mat->row = NULL;
17 mat->block = isl_blk_alloc(ctx, n_row * n_col);
18 if (isl_blk_is_error(mat->block))
19 goto error;
20 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
21 if (!mat->row)
22 goto error;
23
24 for (i = 0; i < n_row; ++i)
25 mat->row[i] = mat->block.data + i * n_col;
26
27 mat->ctx = ctx;
28 isl_ctx_ref(ctx);
29 mat->ref = 1;
30 mat->n_row = n_row;
31 mat->n_col = n_col;
32 mat->max_col = n_col;
33 mat->flags = 0;
34
35 return mat;
36 error:
37 isl_blk_free(ctx, mat->block);
38 free(mat);
39 return NULL;
40 }
41
42 struct isl_mat *isl_mat_extend(struct isl_mat *mat,
43 unsigned n_row, unsigned n_col)
44 {
45 int i;
46 isl_int *old;
47
48 if (!mat)
49 return NULL;
50
51 if (mat->max_col >= n_col && mat->n_row >= n_row) {
52 if (mat->n_col < n_col)
53 mat->n_col = n_col;
54 return mat;
55 }
56
57 if (mat->max_col < n_col) {
58 struct isl_mat *new_mat;
59
60 if (n_row < mat->n_row)
61 n_row = mat->n_row;
62 new_mat = isl_mat_alloc(mat->ctx, n_row, n_col);
63 if (!new_mat)
64 goto error;
65 for (i = 0; i < mat->n_row; ++i)
66 isl_seq_cpy(new_mat->row[i], mat->row[i], mat->n_col);
67 isl_mat_free(mat);
68 return new_mat;
69 }
70
71 mat = isl_mat_cow(mat);
72 if (!mat)
73 goto error;
74
75 assert(mat->ref == 1);
76 old = mat->block.data;
77 mat->block = isl_blk_extend(mat->ctx, mat->block, n_row * mat->max_col);
78 if (isl_blk_is_error(mat->block))
79 goto error;
80 mat->row = isl_realloc_array(mat->ctx, mat->row, isl_int *, n_row);
81 if (!mat->row)
82 goto error;
83
84 for (i = 0; i < mat->n_row; ++i)
85 mat->row[i] = mat->block.data + (mat->row[i] - old);
86 for (i = mat->n_row; i < n_row; ++i)
87 mat->row[i] = mat->block.data + i * mat->max_col;
88 mat->n_row = n_row;
89 if (mat->n_col < n_col)
90 mat->n_col = n_col;
91
92 return mat;
93 error:
94 isl_mat_free(mat);
95 return NULL;
96 }
97
98 struct isl_mat *isl_mat_sub_alloc(struct isl_ctx *ctx, isl_int **row,
99 unsigned first_row, unsigned n_row, unsigned first_col, unsigned n_col)
100 {
101 int i;
102 struct isl_mat *mat;
103
104 mat = isl_alloc_type(ctx, struct isl_mat);
105 if (!mat)
106 return NULL;
107 mat->row = isl_alloc_array(ctx, isl_int *, n_row);
108 if (!mat->row)
109 goto error;
110 for (i = 0; i < n_row; ++i)
111 mat->row[i] = row[first_row+i] + first_col;
112 mat->ctx = ctx;
113 isl_ctx_ref(ctx);
114 mat->ref = 1;
115 mat->n_row = n_row;
116 mat->n_col = n_col;
117 mat->block = isl_blk_empty();
118 mat->flags = ISL_MAT_BORROWED;
119 return mat;
120 error:
121 free(mat);
122 return NULL;
123 }
124
125 void isl_mat_sub_copy(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
126 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
127 {
128 int i;
129
130 for (i = 0; i < n_row; ++i)
131 isl_seq_cpy(dst[i]+dst_col, src[i]+src_col, n_col);
132 }
133
134 void isl_mat_sub_neg(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_neg(dst[i]+dst_col, src[i]+src_col, n_col);
141 }
142
143 struct isl_mat *isl_mat_copy(struct isl_mat *mat)
144 {
145 if (!mat)
146 return NULL;
147
148 mat->ref++;
149 return mat;
150 }
151
152 struct isl_mat *isl_mat_dup(struct isl_mat *mat)
153 {
154 int i;
155 struct isl_mat *mat2;
156
157 if (!mat)
158 return NULL;
159 mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
160 if (!mat2)
161 return NULL;
162 for (i = 0; i < mat->n_row; ++i)
163 isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);
164 return mat2;
165 }
166
167 struct isl_mat *isl_mat_cow(struct isl_mat *mat)
168 {
169 struct isl_mat *mat2;
170 if (!mat)
171 return NULL;
172
173 if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))
174 return mat;
175
176 mat2 = isl_mat_dup(mat);
177 isl_mat_free(mat);
178 return mat2;
179 }
180
181 void isl_mat_free(struct isl_mat *mat)
182 {
183 if (!mat)
184 return;
185
186 if (--mat->ref > 0)
187 return;
188
189 if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))
190 isl_blk_free(mat->ctx, mat->block);
191 isl_ctx_deref(mat->ctx);
192 free(mat->row);
193 free(mat);
194 }
195
196 struct isl_mat *isl_mat_identity(struct isl_ctx *ctx, unsigned n_row)
197 {
198 int i;
199 struct isl_mat *mat;
200
201 mat = isl_mat_alloc(ctx, n_row, n_row);
202 if (!mat)
203 return NULL;
204 for (i = 0; i < n_row; ++i) {
205 isl_seq_clr(mat->row[i], i);
206 isl_int_set_si(mat->row[i][i], 1);
207 isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
208 }
209
210 return mat;
211 }
212
213 struct isl_vec *isl_mat_vec_product(struct isl_mat *mat, struct isl_vec *vec)
214 {
215 int i;
216 struct isl_vec *prod;
217
218 if (!mat || !vec)
219 goto error;
220
221 isl_assert(mat->ctx, mat->n_col == vec->size, goto error);
222
223 prod = isl_vec_alloc(mat->ctx, mat->n_row);
224 if (!prod)
225 goto error;
226
227 for (i = 0; i < prod->size; ++i)
228 isl_seq_inner_product(mat->row[i], vec->el, vec->size,
229 &prod->block.data[i]);
230 isl_mat_free(mat);
231 isl_vec_free(vec);
232 return prod;
233 error:
234 isl_mat_free(mat);
235 isl_vec_free(vec);
236 return NULL;
237 }
238
239 __isl_give isl_vec *isl_mat_vec_inverse_product(__isl_take isl_mat *mat,
240 __isl_take isl_vec *vec)
241 {
242 struct isl_mat *vec_mat;
243 int i;
244
245 if (!mat || !vec)
246 goto error;
247 vec_mat = isl_mat_alloc(vec->ctx, vec->size, 1);
248 if (!vec_mat)
249 goto error;
250 for (i = 0; i < vec->size; ++i)
251 isl_int_set(vec_mat->row[i][0], vec->el[i]);
252 vec_mat = isl_mat_inverse_product(mat, vec_mat);
253 isl_vec_free(vec);
254 if (!vec_mat)
255 return NULL;
256 vec = isl_vec_alloc(vec_mat->ctx, vec_mat->n_row);
257 if (vec)
258 for (i = 0; i < vec->size; ++i)
259 isl_int_set(vec->el[i], vec_mat->row[i][0]);
260 isl_mat_free(vec_mat);
261 return vec;
262 error:
263 isl_mat_free(mat);
264 isl_vec_free(vec);
265 return NULL;
266 }
267
268 struct isl_vec *isl_vec_mat_product(struct isl_vec *vec, struct isl_mat *mat)
269 {
270 int i, j;
271 struct isl_vec *prod;
272
273 if (!mat || !vec)
274 goto error;
275
276 isl_assert(mat->ctx, mat->n_row == vec->size, goto error);
277
278 prod = isl_vec_alloc(mat->ctx, mat->n_col);
279 if (!prod)
280 goto error;
281
282 for (i = 0; i < prod->size; ++i) {
283 isl_int_set_si(prod->el[i], 0);
284 for (j = 0; j < vec->size; ++j)
285 isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);
286 }
287 isl_mat_free(mat);
288 isl_vec_free(vec);
289 return prod;
290 error:
291 isl_mat_free(mat);
292 isl_vec_free(vec);
293 return NULL;
294 }
295
296 struct isl_mat *isl_mat_aff_direct_sum(struct isl_mat *left,
297 struct isl_mat *right)
298 {
299 int i;
300 struct isl_mat *sum;
301
302 if (!left || !right)
303 goto error;
304
305 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
306 isl_assert(left->ctx, left->n_row >= 1, goto error);
307 isl_assert(left->ctx, left->n_col >= 1, goto error);
308 isl_assert(left->ctx, right->n_col >= 1, goto error);
309 isl_assert(left->ctx,
310 isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,
311 goto error);
312 isl_assert(left->ctx,
313 isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
314 goto error);
315
316 sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);
317 if (!sum)
318 goto error;
319 isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);
320 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
321 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
322
323 isl_seq_clr(sum->row[0]+1, sum->n_col-1);
324 for (i = 1; i < sum->n_row; ++i) {
325 isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);
326 isl_int_addmul(sum->row[i][0],
327 right->row[0][0], right->row[i][0]);
328 isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],
329 left->n_col-1);
330 isl_seq_scale(sum->row[i]+left->n_col,
331 right->row[i]+1, right->row[0][0],
332 right->n_col-1);
333 }
334
335 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
336 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
337 isl_mat_free(left);
338 isl_mat_free(right);
339 return sum;
340 error:
341 isl_mat_free(left);
342 isl_mat_free(right);
343 return NULL;
344 }
345
346 static void exchange(struct isl_mat *M, struct isl_mat **U,
347 struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
348 {
349 int r;
350 for (r = row; r < M->n_row; ++r)
351 isl_int_swap(M->row[r][i], M->row[r][j]);
352 if (U) {
353 for (r = 0; r < (*U)->n_row; ++r)
354 isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
355 }
356 if (Q)
357 isl_mat_swap_rows(*Q, i, j);
358 }
359
360 static void subtract(struct isl_mat *M, struct isl_mat **U,
361 struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)
362 {
363 int r;
364 for (r = row; r < M->n_row; ++r)
365 isl_int_submul(M->row[r][j], m, M->row[r][i]);
366 if (U) {
367 for (r = 0; r < (*U)->n_row; ++r)
368 isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);
369 }
370 if (Q) {
371 for (r = 0; r < (*Q)->n_col; ++r)
372 isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);
373 }
374 }
375
376 static void oppose(struct isl_mat *M, struct isl_mat **U,
377 struct isl_mat **Q, unsigned row, unsigned col)
378 {
379 int r;
380 for (r = row; r < M->n_row; ++r)
381 isl_int_neg(M->row[r][col], M->row[r][col]);
382 if (U) {
383 for (r = 0; r < (*U)->n_row; ++r)
384 isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);
385 }
386 if (Q)
387 isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);
388 }
389
390 /* Given matrix M, compute
391 *
392 * M U = H
393 * M = H Q
394 *
395 * with U and Q unimodular matrices and H a matrix in column echelon form
396 * such that on each echelon row the entries in the non-echelon column
397 * are non-negative (if neg == 0) or non-positive (if neg == 1)
398 * and stricly smaller (in absolute value) than the entries in the echelon
399 * column.
400 * If U or Q are NULL, then these matrices are not computed.
401 */
402 struct isl_mat *isl_mat_left_hermite(struct isl_mat *M, int neg,
403 struct isl_mat **U, struct isl_mat **Q)
404 {
405 isl_int c;
406 int row, col;
407
408 if (U)
409 *U = NULL;
410 if (Q)
411 *Q = NULL;
412 if (!M)
413 goto error;
414 M = isl_mat_cow(M);
415 if (!M)
416 goto error;
417 if (U) {
418 *U = isl_mat_identity(M->ctx, M->n_col);
419 if (!*U)
420 goto error;
421 }
422 if (Q) {
423 *Q = isl_mat_identity(M->ctx, M->n_col);
424 if (!*Q)
425 goto error;
426 }
427
428 col = 0;
429 isl_int_init(c);
430 for (row = 0; row < M->n_row; ++row) {
431 int first, i, off;
432 first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);
433 if (first == -1)
434 continue;
435 first += col;
436 if (first != col)
437 exchange(M, U, Q, row, first, col);
438 if (isl_int_is_neg(M->row[row][col]))
439 oppose(M, U, Q, row, col);
440 first = col+1;
441 while ((off = isl_seq_first_non_zero(M->row[row]+first,
442 M->n_col-first)) != -1) {
443 first += off;
444 isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);
445 subtract(M, U, Q, row, col, first, c);
446 if (!isl_int_is_zero(M->row[row][first]))
447 exchange(M, U, Q, row, first, col);
448 else
449 ++first;
450 }
451 for (i = 0; i < col; ++i) {
452 if (isl_int_is_zero(M->row[row][i]))
453 continue;
454 if (neg)
455 isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);
456 else
457 isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);
458 if (isl_int_is_zero(c))
459 continue;
460 subtract(M, U, Q, row, col, i, c);
461 }
462 ++col;
463 }
464 isl_int_clear(c);
465
466 return M;
467 error:
468 if (Q) {
469 isl_mat_free(*Q);
470 *Q = NULL;
471 }
472 if (U) {
473 isl_mat_free(*U);
474 *U = NULL;
475 }
476 return NULL;
477 }
478
479 struct isl_mat *isl_mat_right_kernel(struct isl_mat *mat)
480 {
481 int i, rank;
482 struct isl_mat *U = NULL;
483 struct isl_mat *K;
484
485 mat = isl_mat_left_hermite(mat, 0, &U, NULL);
486 if (!mat || !U)
487 goto error;
488
489 for (i = 0, rank = 0; rank < mat->n_col; ++rank) {
490 while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))
491 ++i;
492 if (i >= mat->n_row)
493 break;
494 }
495 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
496 if (!K)
497 goto error;
498 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
499 isl_mat_free(mat);
500 isl_mat_free(U);
501 return K;
502 error:
503 isl_mat_free(mat);
504 isl_mat_free(U);
505 return NULL;
506 }
507
508 struct isl_mat *isl_mat_lin_to_aff(struct isl_mat *mat)
509 {
510 int i;
511 struct isl_mat *mat2;
512
513 if (!mat)
514 return NULL;
515 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
516 if (!mat2)
517 return NULL;
518 isl_int_set_si(mat2->row[0][0], 1);
519 isl_seq_clr(mat2->row[0]+1, mat->n_col);
520 for (i = 0; i < mat->n_row; ++i) {
521 isl_int_set_si(mat2->row[1+i][0], 0);
522 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
523 }
524 isl_mat_free(mat);
525 return mat2;
526 }
527
528 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
529 {
530 int i;
531
532 for (i = 0; i < n_row; ++i)
533 if (!isl_int_is_zero(row[i][col]))
534 return i;
535 return -1;
536 }
537
538 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
539 {
540 int i, min = row_first_non_zero(row, n_row, col);
541 if (min < 0)
542 return -1;
543 for (i = min + 1; i < n_row; ++i) {
544 if (isl_int_is_zero(row[i][col]))
545 continue;
546 if (isl_int_abs_lt(row[i][col], row[min][col]))
547 min = i;
548 }
549 return min;
550 }
551
552 static void inv_exchange(struct isl_mat *left, struct isl_mat *right,
553 unsigned i, unsigned j)
554 {
555 left = isl_mat_swap_rows(left, i, j);
556 right = isl_mat_swap_rows(right, i, j);
557 }
558
559 static void inv_oppose(
560 struct isl_mat *left, struct isl_mat *right, unsigned row)
561 {
562 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
563 isl_seq_neg(right->row[row], right->row[row], right->n_col);
564 }
565
566 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
567 unsigned row, unsigned i, isl_int m)
568 {
569 isl_int_neg(m, m);
570 isl_seq_combine(left->row[i]+row,
571 left->ctx->one, left->row[i]+row,
572 m, left->row[row]+row,
573 left->n_col-row);
574 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
575 m, right->row[row], right->n_col);
576 }
577
578 /* Compute inv(left)*right
579 */
580 struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
581 struct isl_mat *right)
582 {
583 int row;
584 isl_int a, b;
585
586 if (!left || !right)
587 goto error;
588
589 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
590 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
591
592 if (left->n_row == 0) {
593 isl_mat_free(left);
594 return right;
595 }
596
597 left = isl_mat_cow(left);
598 right = isl_mat_cow(right);
599 if (!left || !right)
600 goto error;
601
602 isl_int_init(a);
603 isl_int_init(b);
604 for (row = 0; row < left->n_row; ++row) {
605 int pivot, first, i, off;
606 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
607 if (pivot < 0) {
608 isl_int_clear(a);
609 isl_int_clear(b);
610 isl_assert(left->ctx, pivot >= 0, goto error);
611 }
612 pivot += row;
613 if (pivot != row)
614 inv_exchange(left, right, pivot, row);
615 if (isl_int_is_neg(left->row[row][row]))
616 inv_oppose(left, right, row);
617 first = row+1;
618 while ((off = row_first_non_zero(left->row+first,
619 left->n_row-first, row)) != -1) {
620 first += off;
621 isl_int_fdiv_q(a, left->row[first][row],
622 left->row[row][row]);
623 inv_subtract(left, right, row, first, a);
624 if (!isl_int_is_zero(left->row[first][row]))
625 inv_exchange(left, right, row, first);
626 else
627 ++first;
628 }
629 for (i = 0; i < row; ++i) {
630 if (isl_int_is_zero(left->row[i][row]))
631 continue;
632 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
633 isl_int_divexact(b, left->row[i][row], a);
634 isl_int_divexact(a, left->row[row][row], a);
635 isl_int_neg(b, b);
636 isl_seq_combine(left->row[i] + i,
637 a, left->row[i] + i,
638 b, left->row[row] + i,
639 left->n_col - i);
640 isl_seq_combine(right->row[i], a, right->row[i],
641 b, right->row[row], right->n_col);
642 }
643 }
644 isl_int_clear(b);
645
646 isl_int_set(a, left->row[0][0]);
647 for (row = 1; row < left->n_row; ++row)
648 isl_int_lcm(a, a, left->row[row][row]);
649 if (isl_int_is_zero(a)){
650 isl_int_clear(a);
651 isl_assert(left->ctx, 0, goto error);
652 }
653 for (row = 0; row < left->n_row; ++row) {
654 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
655 if (isl_int_is_one(left->row[row][row]))
656 continue;
657 isl_seq_scale(right->row[row], right->row[row],
658 left->row[row][row], right->n_col);
659 }
660 isl_int_clear(a);
661
662 isl_mat_free(left);
663 return right;
664 error:
665 isl_mat_free(left);
666 isl_mat_free(right);
667 return NULL;
668 }
669
670 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
671 {
672 int i;
673
674 for (i = 0; i < mat->n_row; ++i)
675 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
676 }
677
678 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
679 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
680 {
681 int i;
682 isl_int tmp;
683
684 isl_int_init(tmp);
685 for (i = 0; i < mat->n_row; ++i) {
686 isl_int_mul(tmp, m1, mat->row[i][src1]);
687 isl_int_addmul(tmp, m2, mat->row[i][src2]);
688 isl_int_set(mat->row[i][dst], tmp);
689 }
690 isl_int_clear(tmp);
691 }
692
693 struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
694 {
695 struct isl_mat *inv;
696 int row;
697 isl_int a, b;
698
699 mat = isl_mat_cow(mat);
700 if (!mat)
701 return NULL;
702
703 inv = isl_mat_identity(mat->ctx, mat->n_col);
704 inv = isl_mat_cow(inv);
705 if (!inv)
706 goto error;
707
708 isl_int_init(a);
709 isl_int_init(b);
710 for (row = 0; row < mat->n_row; ++row) {
711 int pivot, first, i, off;
712 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
713 if (pivot < 0) {
714 isl_int_clear(a);
715 isl_int_clear(b);
716 goto error;
717 }
718 pivot += row;
719 if (pivot != row)
720 exchange(mat, &inv, NULL, row, pivot, row);
721 if (isl_int_is_neg(mat->row[row][row]))
722 oppose(mat, &inv, NULL, row, row);
723 first = row+1;
724 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
725 mat->n_col-first)) != -1) {
726 first += off;
727 isl_int_fdiv_q(a, mat->row[row][first],
728 mat->row[row][row]);
729 subtract(mat, &inv, NULL, row, row, first, a);
730 if (!isl_int_is_zero(mat->row[row][first]))
731 exchange(mat, &inv, NULL, row, row, first);
732 else
733 ++first;
734 }
735 for (i = 0; i < row; ++i) {
736 if (isl_int_is_zero(mat->row[row][i]))
737 continue;
738 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
739 isl_int_divexact(b, mat->row[row][i], a);
740 isl_int_divexact(a, mat->row[row][row], a);
741 isl_int_neg(a, a);
742 isl_mat_col_combine(mat, i, a, i, b, row);
743 isl_mat_col_combine(inv, i, a, i, b, row);
744 }
745 }
746 isl_int_clear(b);
747
748 isl_int_set(a, mat->row[0][0]);
749 for (row = 1; row < mat->n_row; ++row)
750 isl_int_lcm(a, a, mat->row[row][row]);
751 if (isl_int_is_zero(a)){
752 isl_int_clear(a);
753 goto error;
754 }
755 for (row = 0; row < mat->n_row; ++row) {
756 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
757 if (isl_int_is_one(mat->row[row][row]))
758 continue;
759 isl_mat_col_scale(inv, row, mat->row[row][row]);
760 }
761 isl_int_clear(a);
762
763 isl_mat_free(mat);
764
765 return inv;
766 error:
767 isl_mat_free(mat);
768 return NULL;
769 }
770
771 struct isl_mat *isl_mat_transpose(struct isl_mat *mat)
772 {
773 struct isl_mat *transpose = NULL;
774 int i, j;
775
776 if (mat->n_col == mat->n_row) {
777 mat = isl_mat_cow(mat);
778 if (!mat)
779 return NULL;
780 for (i = 0; i < mat->n_row; ++i)
781 for (j = i + 1; j < mat->n_col; ++j)
782 isl_int_swap(mat->row[i][j], mat->row[j][i]);
783 return mat;
784 }
785 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
786 if (!transpose)
787 goto error;
788 for (i = 0; i < mat->n_row; ++i)
789 for (j = 0; j < mat->n_col; ++j)
790 isl_int_set(transpose->row[j][i], mat->row[i][j]);
791 isl_mat_free(mat);
792 return transpose;
793 error:
794 isl_mat_free(mat);
795 return NULL;
796 }
797
798 struct isl_mat *isl_mat_swap_cols(struct isl_mat *mat, unsigned i, unsigned j)
799 {
800 int r;
801
802 mat = isl_mat_cow(mat);
803 if (!mat)
804 return NULL;
805 isl_assert(mat->ctx, i < mat->n_col, goto error);
806 isl_assert(mat->ctx, j < mat->n_col, goto error);
807
808 for (r = 0; r < mat->n_row; ++r)
809 isl_int_swap(mat->row[r][i], mat->row[r][j]);
810 return mat;
811 error:
812 isl_mat_free(mat);
813 return NULL;
814 }
815
816 struct isl_mat *isl_mat_swap_rows(struct isl_mat *mat, unsigned i, unsigned j)
817 {
818 isl_int *t;
819
820 if (!mat)
821 return NULL;
822 mat = isl_mat_cow(mat);
823 if (!mat)
824 return NULL;
825 t = mat->row[i];
826 mat->row[i] = mat->row[j];
827 mat->row[j] = t;
828 return mat;
829 }
830
831 struct isl_mat *isl_mat_product(struct isl_mat *left, struct isl_mat *right)
832 {
833 int i, j, k;
834 struct isl_mat *prod;
835
836 if (!left || !right)
837 goto error;
838 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
839 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
840 if (!prod)
841 goto error;
842 if (left->n_col == 0) {
843 for (i = 0; i < prod->n_row; ++i)
844 isl_seq_clr(prod->row[i], prod->n_col);
845 return prod;
846 }
847 for (i = 0; i < prod->n_row; ++i) {
848 for (j = 0; j < prod->n_col; ++j) {
849 isl_int_mul(prod->row[i][j],
850 left->row[i][0], right->row[0][j]);
851 for (k = 1; k < left->n_col; ++k)
852 isl_int_addmul(prod->row[i][j],
853 left->row[i][k], right->row[k][j]);
854 }
855 }
856 isl_mat_free(left);
857 isl_mat_free(right);
858 return prod;
859 error:
860 isl_mat_free(left);
861 isl_mat_free(right);
862 return NULL;
863 }
864
865 /* Replace the variables x in the rows q by x' given by x = M x',
866 * with M the matrix mat.
867 *
868 * If the number of new variables is greater than the original
869 * number of variables, then the rows q have already been
870 * preextended. If the new number is smaller, then the coefficients
871 * of the divs, which are not changed, need to be shifted down.
872 * The row q may be the equalities, the inequalities or the
873 * div expressions. In the latter case, has_div is true and
874 * we need to take into account the extra denominator column.
875 */
876 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
877 unsigned n_div, int has_div, struct isl_mat *mat)
878 {
879 int i;
880 struct isl_mat *t;
881 int e;
882
883 if (mat->n_col >= mat->n_row)
884 e = 0;
885 else
886 e = mat->n_row - mat->n_col;
887 if (has_div)
888 for (i = 0; i < n; ++i)
889 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
890 t = isl_mat_sub_alloc(mat->ctx, q, 0, n, has_div, mat->n_row);
891 t = isl_mat_product(t, mat);
892 if (!t)
893 return -1;
894 for (i = 0; i < n; ++i) {
895 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
896 isl_seq_cpy(q[i] + has_div + t->n_col,
897 q[i] + has_div + t->n_col + e, n_div);
898 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
899 }
900 isl_mat_free(t);
901 return 0;
902 }
903
904 /* Replace the variables x in bset by x' given by x = M x', with
905 * M the matrix mat.
906 *
907 * If there are fewer variables x' then there are x, then we perform
908 * the transformation in place, which that, in principle,
909 * this frees up some extra variables as the number
910 * of columns remains constant, but we would have to extend
911 * the div array too as the number of rows in this array is assumed
912 * to be equal to extra.
913 */
914 struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
915 struct isl_mat *mat)
916 {
917 struct isl_ctx *ctx;
918
919 if (!bset || !mat)
920 goto error;
921
922 ctx = bset->ctx;
923 bset = isl_basic_set_cow(bset);
924 if (!bset)
925 goto error;
926
927 isl_assert(ctx, bset->dim->nparam == 0, goto error);
928 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
929
930 if (mat->n_col > mat->n_row)
931 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0,
932 0, 0);
933 else if (mat->n_col < mat->n_row) {
934 bset->dim = isl_dim_cow(bset->dim);
935 if (!bset->dim)
936 goto error;
937 bset->dim->n_out -= mat->n_row - mat->n_col;
938 }
939
940 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
941 isl_mat_copy(mat)) < 0)
942 goto error;
943
944 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
945 isl_mat_copy(mat)) < 0)
946 goto error;
947
948 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
949 goto error2;
950
951 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
952 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
953 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
954 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
955 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
956
957 bset = isl_basic_set_simplify(bset);
958 bset = isl_basic_set_finalize(bset);
959
960 return bset;
961 error:
962 isl_mat_free(mat);
963 error2:
964 isl_basic_set_free(bset);
965 return NULL;
966 }
967
968 struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
969 {
970 struct isl_ctx *ctx;
971 int i;
972
973 set = isl_set_cow(set);
974 if (!set)
975 return NULL;
976
977 ctx = set->ctx;
978 for (i = 0; i < set->n; ++i) {
979 set->p[i] = isl_basic_set_preimage(set->p[i],
980 isl_mat_copy(mat));
981 if (!set->p[i])
982 goto error;
983 }
984 if (mat->n_col != mat->n_row) {
985 set->dim = isl_dim_cow(set->dim);
986 if (!set->dim)
987 goto error;
988 set->dim->n_out += mat->n_col;
989 set->dim->n_out -= mat->n_row;
990 }
991 isl_mat_free(mat);
992 ISL_F_CLR(set, ISL_SET_NORMALIZED);
993 return set;
994 error:
995 isl_set_free(set);
996 isl_mat_free(mat);
997 return NULL;
998 }
999
1000 void isl_mat_dump(struct isl_mat *mat, FILE *out, int indent)
1001 {
1002 int i, j;
1003
1004 if (!mat) {
1005 fprintf(out, "%*snull mat\n", indent, "");
1006 return;
1007 }
1008
1009 if (mat->n_row == 0)
1010 fprintf(out, "%*s[]\n", indent, "");
1011
1012 for (i = 0; i < mat->n_row; ++i) {
1013 if (!i)
1014 fprintf(out, "%*s[[", indent, "");
1015 else
1016 fprintf(out, "%*s[", indent+1, "");
1017 for (j = 0; j < mat->n_col; ++j) {
1018 if (j)
1019 fprintf(out, ",");
1020 isl_int_print(out, mat->row[i][j], 0);
1021 }
1022 if (i == mat->n_row-1)
1023 fprintf(out, "]]\n");
1024 else
1025 fprintf(out, "]\n");
1026 }
1027 }
1028
1029 struct isl_mat *isl_mat_drop_cols(struct isl_mat *mat, unsigned col, unsigned n)
1030 {
1031 int r;
1032
1033 mat = isl_mat_cow(mat);
1034 if (!mat)
1035 return NULL;
1036
1037 if (col != mat->n_col-n) {
1038 for (r = 0; r < mat->n_row; ++r)
1039 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1040 mat->n_col - col - n);
1041 }
1042 mat->n_col -= n;
1043 return mat;
1044 }
1045
1046 struct isl_mat *isl_mat_drop_rows(struct isl_mat *mat, unsigned row, unsigned n)
1047 {
1048 int r;
1049
1050 mat = isl_mat_cow(mat);
1051 if (!mat)
1052 return NULL;
1053
1054 for (r = row; r+n < mat->n_row; ++r)
1055 mat->row[r] = mat->row[r+n];
1056
1057 mat->n_row -= n;
1058 return mat;
1059 }
1060
1061 void isl_mat_col_submul(struct isl_mat *mat,
1062 int dst_col, isl_int f, int src_col)
1063 {
1064 int i;
1065
1066 for (i = 0; i < mat->n_row; ++i)
1067 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1068 }
1069
1070 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1071 {
1072 int i;
1073
1074 for (i = 0; i < mat->n_row; ++i)
1075 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1076 }
1077
1078 struct isl_mat *isl_mat_unimodular_complete(struct isl_mat *M, int row)
1079 {
1080 int r;
1081 struct isl_mat *H = NULL, *Q = NULL;
1082
1083 if (!M)
1084 return NULL;
1085
1086 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1087 M->n_row = row;
1088 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1089 M->n_row = M->n_col;
1090 if (!H)
1091 goto error;
1092 for (r = 0; r < row; ++r)
1093 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1094 for (r = row; r < M->n_row; ++r)
1095 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1096 isl_mat_free(H);
1097 isl_mat_free(Q);
1098 return M;
1099 error:
1100 isl_mat_free(H);
1101 isl_mat_free(Q);
1102 isl_mat_free(M);
1103 return NULL;
1104 }
1105
1106 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1107 __isl_take isl_mat *bot)
1108 {
1109 struct isl_mat *mat;
1110
1111 if (!top || !bot)
1112 goto error;
1113
1114 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1115 if (top->n_row == 0) {
1116 isl_mat_free(top);
1117 return bot;
1118 }
1119 if (bot->n_row == 0) {
1120 isl_mat_free(bot);
1121 return top;
1122 }
1123
1124 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1125 if (!mat)
1126 goto error;
1127 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1128 0, 0, mat->n_col);
1129 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1130 0, 0, mat->n_col);
1131 isl_mat_free(top);
1132 isl_mat_free(bot);
1133 return mat;
1134 error:
1135 isl_mat_free(top);
1136 isl_mat_free(bot);
1137 return NULL;
1138 }
Integer set library