2 * Copyright 2008-2009 Katholieke Universiteit Leuven
4 * Use of this software is governed by the GNU LGPLv2.1 license
6 * Written by Sven Verdoolaege, K.U.Leuven, Departement
7 * Computerwetenschappen, Celestijnenlaan 200A, B-3001 Leuven, Belgium
10 #include <isl_ctx_private.h>
13 #include <isl_mat_private.h>
14 #include "isl_map_private.h"
15 #include <isl_dim_private.h>
17 struct isl_mat
*isl_mat_alloc(struct isl_ctx
*ctx
,
18 unsigned n_row
, unsigned n_col
)
23 mat
= isl_alloc_type(ctx
, struct isl_mat
);
28 mat
->block
= isl_blk_alloc(ctx
, n_row
* n_col
);
29 if (isl_blk_is_error(mat
->block
))
31 mat
->row
= isl_alloc_array(ctx
, isl_int
*, n_row
);
35 for (i
= 0; i
< n_row
; ++i
)
36 mat
->row
[i
] = mat
->block
.data
+ i
* n_col
;
48 isl_blk_free(ctx
, mat
->block
);
53 struct isl_mat
*isl_mat_extend(struct isl_mat
*mat
,
54 unsigned n_row
, unsigned n_col
)
63 if (mat
->max_col
>= n_col
&& mat
->n_row
>= n_row
) {
64 if (mat
->n_col
< n_col
)
69 if (mat
->max_col
< n_col
) {
70 struct isl_mat
*new_mat
;
72 if (n_row
< mat
->n_row
)
74 new_mat
= isl_mat_alloc(mat
->ctx
, n_row
, n_col
);
77 for (i
= 0; i
< mat
->n_row
; ++i
)
78 isl_seq_cpy(new_mat
->row
[i
], mat
->row
[i
], mat
->n_col
);
83 mat
= isl_mat_cow(mat
);
87 old
= mat
->block
.data
;
88 mat
->block
= isl_blk_extend(mat
->ctx
, mat
->block
, n_row
* mat
->max_col
);
89 if (isl_blk_is_error(mat
->block
))
91 row
= isl_realloc_array(mat
->ctx
, mat
->row
, isl_int
*, n_row
);
96 for (i
= 0; i
< mat
->n_row
; ++i
)
97 mat
->row
[i
] = mat
->block
.data
+ (mat
->row
[i
] - old
);
98 for (i
= mat
->n_row
; i
< n_row
; ++i
)
99 mat
->row
[i
] = mat
->block
.data
+ i
* mat
->max_col
;
101 if (mat
->n_col
< n_col
)
110 __isl_give isl_mat
*isl_mat_sub_alloc6(isl_ctx
*ctx
, isl_int
**row
,
111 unsigned first_row
, unsigned n_row
, unsigned first_col
, unsigned n_col
)
116 mat
= isl_alloc_type(ctx
, struct isl_mat
);
119 mat
->row
= isl_alloc_array(ctx
, isl_int
*, n_row
);
122 for (i
= 0; i
< n_row
; ++i
)
123 mat
->row
[i
] = row
[first_row
+i
] + first_col
;
129 mat
->block
= isl_blk_empty();
130 mat
->flags
= ISL_MAT_BORROWED
;
137 __isl_give isl_mat
*isl_mat_sub_alloc(__isl_keep isl_mat
*mat
,
138 unsigned first_row
, unsigned n_row
, unsigned first_col
, unsigned n_col
)
142 return isl_mat_sub_alloc6(mat
->ctx
, mat
->row
, first_row
, n_row
,
146 void isl_mat_sub_copy(struct isl_ctx
*ctx
, isl_int
**dst
, isl_int
**src
,
147 unsigned n_row
, unsigned dst_col
, unsigned src_col
, unsigned n_col
)
151 for (i
= 0; i
< n_row
; ++i
)
152 isl_seq_cpy(dst
[i
]+dst_col
, src
[i
]+src_col
, n_col
);
155 void isl_mat_sub_neg(struct isl_ctx
*ctx
, isl_int
**dst
, isl_int
**src
,
156 unsigned n_row
, unsigned dst_col
, unsigned src_col
, unsigned n_col
)
160 for (i
= 0; i
< n_row
; ++i
)
161 isl_seq_neg(dst
[i
]+dst_col
, src
[i
]+src_col
, n_col
);
164 struct isl_mat
*isl_mat_copy(struct isl_mat
*mat
)
173 struct isl_mat
*isl_mat_dup(struct isl_mat
*mat
)
176 struct isl_mat
*mat2
;
180 mat2
= isl_mat_alloc(mat
->ctx
, mat
->n_row
, mat
->n_col
);
183 for (i
= 0; i
< mat
->n_row
; ++i
)
184 isl_seq_cpy(mat2
->row
[i
], mat
->row
[i
], mat
->n_col
);
188 struct isl_mat
*isl_mat_cow(struct isl_mat
*mat
)
190 struct isl_mat
*mat2
;
194 if (mat
->ref
== 1 && !ISL_F_ISSET(mat
, ISL_MAT_BORROWED
))
197 mat2
= isl_mat_dup(mat
);
202 void isl_mat_free(struct isl_mat
*mat
)
210 if (!ISL_F_ISSET(mat
, ISL_MAT_BORROWED
))
211 isl_blk_free(mat
->ctx
, mat
->block
);
212 isl_ctx_deref(mat
->ctx
);
217 int isl_mat_rows(__isl_keep isl_mat
*mat
)
219 return mat
? mat
->n_row
: -1;
222 int isl_mat_cols(__isl_keep isl_mat
*mat
)
224 return mat
? mat
->n_col
: -1;
227 int isl_mat_get_element(__isl_keep isl_mat
*mat
, int row
, int col
, isl_int
*v
)
231 if (row
< 0 || row
>= mat
->n_row
)
232 isl_die(mat
->ctx
, isl_error_invalid
, "row out of range",
234 if (col
< 0 || col
>= mat
->n_col
)
235 isl_die(mat
->ctx
, isl_error_invalid
, "column out of range",
237 isl_int_set(*v
, mat
->row
[row
][col
]);
241 __isl_give isl_mat
*isl_mat_set_element(__isl_take isl_mat
*mat
,
242 int row
, int col
, isl_int v
)
244 mat
= isl_mat_cow(mat
);
247 if (row
< 0 || row
>= mat
->n_row
)
248 isl_die(mat
->ctx
, isl_error_invalid
, "row out of range",
250 if (col
< 0 || col
>= mat
->n_col
)
251 isl_die(mat
->ctx
, isl_error_invalid
, "column out of range",
253 isl_int_set(mat
->row
[row
][col
], v
);
260 __isl_give isl_mat
*isl_mat_set_element_si(__isl_take isl_mat
*mat
,
261 int row
, int col
, int v
)
263 mat
= isl_mat_cow(mat
);
266 if (row
< 0 || row
>= mat
->n_row
)
267 isl_die(mat
->ctx
, isl_error_invalid
, "row out of range",
269 if (col
< 0 || col
>= mat
->n_col
)
270 isl_die(mat
->ctx
, isl_error_invalid
, "column out of range",
272 isl_int_set_si(mat
->row
[row
][col
], v
);
279 struct isl_mat
*isl_mat_identity(struct isl_ctx
*ctx
, unsigned n_row
)
284 mat
= isl_mat_alloc(ctx
, n_row
, n_row
);
287 for (i
= 0; i
< n_row
; ++i
) {
288 isl_seq_clr(mat
->row
[i
], i
);
289 isl_int_set_si(mat
->row
[i
][i
], 1);
290 isl_seq_clr(mat
->row
[i
]+i
+1, n_row
-(i
+1));
296 struct isl_vec
*isl_mat_vec_product(struct isl_mat
*mat
, struct isl_vec
*vec
)
299 struct isl_vec
*prod
;
304 isl_assert(mat
->ctx
, mat
->n_col
== vec
->size
, goto error
);
306 prod
= isl_vec_alloc(mat
->ctx
, mat
->n_row
);
310 for (i
= 0; i
< prod
->size
; ++i
)
311 isl_seq_inner_product(mat
->row
[i
], vec
->el
, vec
->size
,
312 &prod
->block
.data
[i
]);
322 __isl_give isl_vec
*isl_mat_vec_inverse_product(__isl_take isl_mat
*mat
,
323 __isl_take isl_vec
*vec
)
325 struct isl_mat
*vec_mat
;
330 vec_mat
= isl_mat_alloc(vec
->ctx
, vec
->size
, 1);
333 for (i
= 0; i
< vec
->size
; ++i
)
334 isl_int_set(vec_mat
->row
[i
][0], vec
->el
[i
]);
335 vec_mat
= isl_mat_inverse_product(mat
, vec_mat
);
339 vec
= isl_vec_alloc(vec_mat
->ctx
, vec_mat
->n_row
);
341 for (i
= 0; i
< vec
->size
; ++i
)
342 isl_int_set(vec
->el
[i
], vec_mat
->row
[i
][0]);
343 isl_mat_free(vec_mat
);
351 struct isl_vec
*isl_vec_mat_product(struct isl_vec
*vec
, struct isl_mat
*mat
)
354 struct isl_vec
*prod
;
359 isl_assert(mat
->ctx
, mat
->n_row
== vec
->size
, goto error
);
361 prod
= isl_vec_alloc(mat
->ctx
, mat
->n_col
);
365 for (i
= 0; i
< prod
->size
; ++i
) {
366 isl_int_set_si(prod
->el
[i
], 0);
367 for (j
= 0; j
< vec
->size
; ++j
)
368 isl_int_addmul(prod
->el
[i
], vec
->el
[j
], mat
->row
[j
][i
]);
379 struct isl_mat
*isl_mat_aff_direct_sum(struct isl_mat
*left
,
380 struct isl_mat
*right
)
388 isl_assert(left
->ctx
, left
->n_row
== right
->n_row
, goto error
);
389 isl_assert(left
->ctx
, left
->n_row
>= 1, goto error
);
390 isl_assert(left
->ctx
, left
->n_col
>= 1, goto error
);
391 isl_assert(left
->ctx
, right
->n_col
>= 1, goto error
);
392 isl_assert(left
->ctx
,
393 isl_seq_first_non_zero(left
->row
[0]+1, left
->n_col
-1) == -1,
395 isl_assert(left
->ctx
,
396 isl_seq_first_non_zero(right
->row
[0]+1, right
->n_col
-1) == -1,
399 sum
= isl_mat_alloc(left
->ctx
, left
->n_row
, left
->n_col
+ right
->n_col
- 1);
402 isl_int_lcm(sum
->row
[0][0], left
->row
[0][0], right
->row
[0][0]);
403 isl_int_divexact(left
->row
[0][0], sum
->row
[0][0], left
->row
[0][0]);
404 isl_int_divexact(right
->row
[0][0], sum
->row
[0][0], right
->row
[0][0]);
406 isl_seq_clr(sum
->row
[0]+1, sum
->n_col
-1);
407 for (i
= 1; i
< sum
->n_row
; ++i
) {
408 isl_int_mul(sum
->row
[i
][0], left
->row
[0][0], left
->row
[i
][0]);
409 isl_int_addmul(sum
->row
[i
][0],
410 right
->row
[0][0], right
->row
[i
][0]);
411 isl_seq_scale(sum
->row
[i
]+1, left
->row
[i
]+1, left
->row
[0][0],
413 isl_seq_scale(sum
->row
[i
]+left
->n_col
,
414 right
->row
[i
]+1, right
->row
[0][0],
418 isl_int_divexact(left
->row
[0][0], sum
->row
[0][0], left
->row
[0][0]);
419 isl_int_divexact(right
->row
[0][0], sum
->row
[0][0], right
->row
[0][0]);
429 static void exchange(struct isl_mat
*M
, struct isl_mat
**U
,
430 struct isl_mat
**Q
, unsigned row
, unsigned i
, unsigned j
)
433 for (r
= row
; r
< M
->n_row
; ++r
)
434 isl_int_swap(M
->row
[r
][i
], M
->row
[r
][j
]);
436 for (r
= 0; r
< (*U
)->n_row
; ++r
)
437 isl_int_swap((*U
)->row
[r
][i
], (*U
)->row
[r
][j
]);
440 isl_mat_swap_rows(*Q
, i
, j
);
443 static void subtract(struct isl_mat
*M
, struct isl_mat
**U
,
444 struct isl_mat
**Q
, unsigned row
, unsigned i
, unsigned j
, isl_int m
)
447 for (r
= row
; r
< M
->n_row
; ++r
)
448 isl_int_submul(M
->row
[r
][j
], m
, M
->row
[r
][i
]);
450 for (r
= 0; r
< (*U
)->n_row
; ++r
)
451 isl_int_submul((*U
)->row
[r
][j
], m
, (*U
)->row
[r
][i
]);
454 for (r
= 0; r
< (*Q
)->n_col
; ++r
)
455 isl_int_addmul((*Q
)->row
[i
][r
], m
, (*Q
)->row
[j
][r
]);
459 static void oppose(struct isl_mat
*M
, struct isl_mat
**U
,
460 struct isl_mat
**Q
, unsigned row
, unsigned col
)
463 for (r
= row
; r
< M
->n_row
; ++r
)
464 isl_int_neg(M
->row
[r
][col
], M
->row
[r
][col
]);
466 for (r
= 0; r
< (*U
)->n_row
; ++r
)
467 isl_int_neg((*U
)->row
[r
][col
], (*U
)->row
[r
][col
]);
470 isl_seq_neg((*Q
)->row
[col
], (*Q
)->row
[col
], (*Q
)->n_col
);
473 /* Given matrix M, compute
478 * with U and Q unimodular matrices and H a matrix in column echelon form
479 * such that on each echelon row the entries in the non-echelon column
480 * are non-negative (if neg == 0) or non-positive (if neg == 1)
481 * and stricly smaller (in absolute value) than the entries in the echelon
483 * If U or Q are NULL, then these matrices are not computed.
485 struct isl_mat
*isl_mat_left_hermite(struct isl_mat
*M
, int neg
,
486 struct isl_mat
**U
, struct isl_mat
**Q
)
501 *U
= isl_mat_identity(M
->ctx
, M
->n_col
);
506 *Q
= isl_mat_identity(M
->ctx
, M
->n_col
);
513 for (row
= 0; row
< M
->n_row
; ++row
) {
515 first
= isl_seq_abs_min_non_zero(M
->row
[row
]+col
, M
->n_col
-col
);
520 exchange(M
, U
, Q
, row
, first
, col
);
521 if (isl_int_is_neg(M
->row
[row
][col
]))
522 oppose(M
, U
, Q
, row
, col
);
524 while ((off
= isl_seq_first_non_zero(M
->row
[row
]+first
,
525 M
->n_col
-first
)) != -1) {
527 isl_int_fdiv_q(c
, M
->row
[row
][first
], M
->row
[row
][col
]);
528 subtract(M
, U
, Q
, row
, col
, first
, c
);
529 if (!isl_int_is_zero(M
->row
[row
][first
]))
530 exchange(M
, U
, Q
, row
, first
, col
);
534 for (i
= 0; i
< col
; ++i
) {
535 if (isl_int_is_zero(M
->row
[row
][i
]))
538 isl_int_cdiv_q(c
, M
->row
[row
][i
], M
->row
[row
][col
]);
540 isl_int_fdiv_q(c
, M
->row
[row
][i
], M
->row
[row
][col
]);
541 if (isl_int_is_zero(c
))
543 subtract(M
, U
, Q
, row
, col
, i
, c
);
563 struct isl_mat
*isl_mat_right_kernel(struct isl_mat
*mat
)
566 struct isl_mat
*U
= NULL
;
569 mat
= isl_mat_left_hermite(mat
, 0, &U
, NULL
);
573 for (i
= 0, rank
= 0; rank
< mat
->n_col
; ++rank
) {
574 while (i
< mat
->n_row
&& isl_int_is_zero(mat
->row
[i
][rank
]))
579 K
= isl_mat_alloc(U
->ctx
, U
->n_row
, U
->n_col
- rank
);
582 isl_mat_sub_copy(K
->ctx
, K
->row
, U
->row
, U
->n_row
, 0, rank
, U
->n_col
-rank
);
592 struct isl_mat
*isl_mat_lin_to_aff(struct isl_mat
*mat
)
595 struct isl_mat
*mat2
;
599 mat2
= isl_mat_alloc(mat
->ctx
, 1+mat
->n_row
, 1+mat
->n_col
);
602 isl_int_set_si(mat2
->row
[0][0], 1);
603 isl_seq_clr(mat2
->row
[0]+1, mat
->n_col
);
604 for (i
= 0; i
< mat
->n_row
; ++i
) {
605 isl_int_set_si(mat2
->row
[1+i
][0], 0);
606 isl_seq_cpy(mat2
->row
[1+i
]+1, mat
->row
[i
], mat
->n_col
);
615 /* Given two matrices M1 and M2, return the block matrix
620 __isl_give isl_mat
*isl_mat_diagonal(__isl_take isl_mat
*mat1
,
621 __isl_take isl_mat
*mat2
)
629 mat
= isl_mat_alloc(mat1
->ctx
, mat1
->n_row
+ mat2
->n_row
,
630 mat1
->n_col
+ mat2
->n_col
);
633 for (i
= 0; i
< mat1
->n_row
; ++i
) {
634 isl_seq_cpy(mat
->row
[i
], mat1
->row
[i
], mat1
->n_col
);
635 isl_seq_clr(mat
->row
[i
] + mat1
->n_col
, mat2
->n_col
);
637 for (i
= 0; i
< mat2
->n_row
; ++i
) {
638 isl_seq_clr(mat
->row
[mat1
->n_row
+ i
], mat1
->n_col
);
639 isl_seq_cpy(mat
->row
[mat1
->n_row
+ i
] + mat1
->n_col
,
640 mat2
->row
[i
], mat2
->n_col
);
651 static int row_first_non_zero(isl_int
**row
, unsigned n_row
, unsigned col
)
655 for (i
= 0; i
< n_row
; ++i
)
656 if (!isl_int_is_zero(row
[i
][col
]))
661 static int row_abs_min_non_zero(isl_int
**row
, unsigned n_row
, unsigned col
)
663 int i
, min
= row_first_non_zero(row
, n_row
, col
);
666 for (i
= min
+ 1; i
< n_row
; ++i
) {
667 if (isl_int_is_zero(row
[i
][col
]))
669 if (isl_int_abs_lt(row
[i
][col
], row
[min
][col
]))
675 static void inv_exchange(struct isl_mat
*left
, struct isl_mat
*right
,
676 unsigned i
, unsigned j
)
678 left
= isl_mat_swap_rows(left
, i
, j
);
679 right
= isl_mat_swap_rows(right
, i
, j
);
682 static void inv_oppose(
683 struct isl_mat
*left
, struct isl_mat
*right
, unsigned row
)
685 isl_seq_neg(left
->row
[row
]+row
, left
->row
[row
]+row
, left
->n_col
-row
);
686 isl_seq_neg(right
->row
[row
], right
->row
[row
], right
->n_col
);
689 static void inv_subtract(struct isl_mat
*left
, struct isl_mat
*right
,
690 unsigned row
, unsigned i
, isl_int m
)
693 isl_seq_combine(left
->row
[i
]+row
,
694 left
->ctx
->one
, left
->row
[i
]+row
,
695 m
, left
->row
[row
]+row
,
697 isl_seq_combine(right
->row
[i
], right
->ctx
->one
, right
->row
[i
],
698 m
, right
->row
[row
], right
->n_col
);
701 /* Compute inv(left)*right
703 struct isl_mat
*isl_mat_inverse_product(struct isl_mat
*left
,
704 struct isl_mat
*right
)
712 isl_assert(left
->ctx
, left
->n_row
== left
->n_col
, goto error
);
713 isl_assert(left
->ctx
, left
->n_row
== right
->n_row
, goto error
);
715 if (left
->n_row
== 0) {
720 left
= isl_mat_cow(left
);
721 right
= isl_mat_cow(right
);
727 for (row
= 0; row
< left
->n_row
; ++row
) {
728 int pivot
, first
, i
, off
;
729 pivot
= row_abs_min_non_zero(left
->row
+row
, left
->n_row
-row
, row
);
733 isl_assert(left
->ctx
, pivot
>= 0, goto error
);
737 inv_exchange(left
, right
, pivot
, row
);
738 if (isl_int_is_neg(left
->row
[row
][row
]))
739 inv_oppose(left
, right
, row
);
741 while ((off
= row_first_non_zero(left
->row
+first
,
742 left
->n_row
-first
, row
)) != -1) {
744 isl_int_fdiv_q(a
, left
->row
[first
][row
],
745 left
->row
[row
][row
]);
746 inv_subtract(left
, right
, row
, first
, a
);
747 if (!isl_int_is_zero(left
->row
[first
][row
]))
748 inv_exchange(left
, right
, row
, first
);
752 for (i
= 0; i
< row
; ++i
) {
753 if (isl_int_is_zero(left
->row
[i
][row
]))
755 isl_int_gcd(a
, left
->row
[row
][row
], left
->row
[i
][row
]);
756 isl_int_divexact(b
, left
->row
[i
][row
], a
);
757 isl_int_divexact(a
, left
->row
[row
][row
], a
);
759 isl_seq_combine(left
->row
[i
] + i
,
761 b
, left
->row
[row
] + i
,
763 isl_seq_combine(right
->row
[i
], a
, right
->row
[i
],
764 b
, right
->row
[row
], right
->n_col
);
769 isl_int_set(a
, left
->row
[0][0]);
770 for (row
= 1; row
< left
->n_row
; ++row
)
771 isl_int_lcm(a
, a
, left
->row
[row
][row
]);
772 if (isl_int_is_zero(a
)){
774 isl_assert(left
->ctx
, 0, goto error
);
776 for (row
= 0; row
< left
->n_row
; ++row
) {
777 isl_int_divexact(left
->row
[row
][row
], a
, left
->row
[row
][row
]);
778 if (isl_int_is_one(left
->row
[row
][row
]))
780 isl_seq_scale(right
->row
[row
], right
->row
[row
],
781 left
->row
[row
][row
], right
->n_col
);
793 void isl_mat_col_scale(struct isl_mat
*mat
, unsigned col
, isl_int m
)
797 for (i
= 0; i
< mat
->n_row
; ++i
)
798 isl_int_mul(mat
->row
[i
][col
], mat
->row
[i
][col
], m
);
801 void isl_mat_col_combine(struct isl_mat
*mat
, unsigned dst
,
802 isl_int m1
, unsigned src1
, isl_int m2
, unsigned src2
)
808 for (i
= 0; i
< mat
->n_row
; ++i
) {
809 isl_int_mul(tmp
, m1
, mat
->row
[i
][src1
]);
810 isl_int_addmul(tmp
, m2
, mat
->row
[i
][src2
]);
811 isl_int_set(mat
->row
[i
][dst
], tmp
);
816 struct isl_mat
*isl_mat_right_inverse(struct isl_mat
*mat
)
822 mat
= isl_mat_cow(mat
);
826 inv
= isl_mat_identity(mat
->ctx
, mat
->n_col
);
827 inv
= isl_mat_cow(inv
);
833 for (row
= 0; row
< mat
->n_row
; ++row
) {
834 int pivot
, first
, i
, off
;
835 pivot
= isl_seq_abs_min_non_zero(mat
->row
[row
]+row
, mat
->n_col
-row
);
839 isl_assert(mat
->ctx
, pivot
>= 0, goto error
);
843 exchange(mat
, &inv
, NULL
, row
, pivot
, row
);
844 if (isl_int_is_neg(mat
->row
[row
][row
]))
845 oppose(mat
, &inv
, NULL
, row
, row
);
847 while ((off
= isl_seq_first_non_zero(mat
->row
[row
]+first
,
848 mat
->n_col
-first
)) != -1) {
850 isl_int_fdiv_q(a
, mat
->row
[row
][first
],
852 subtract(mat
, &inv
, NULL
, row
, row
, first
, a
);
853 if (!isl_int_is_zero(mat
->row
[row
][first
]))
854 exchange(mat
, &inv
, NULL
, row
, row
, first
);
858 for (i
= 0; i
< row
; ++i
) {
859 if (isl_int_is_zero(mat
->row
[row
][i
]))
861 isl_int_gcd(a
, mat
->row
[row
][row
], mat
->row
[row
][i
]);
862 isl_int_divexact(b
, mat
->row
[row
][i
], a
);
863 isl_int_divexact(a
, mat
->row
[row
][row
], a
);
865 isl_mat_col_combine(mat
, i
, a
, i
, b
, row
);
866 isl_mat_col_combine(inv
, i
, a
, i
, b
, row
);
871 isl_int_set(a
, mat
->row
[0][0]);
872 for (row
= 1; row
< mat
->n_row
; ++row
)
873 isl_int_lcm(a
, a
, mat
->row
[row
][row
]);
874 if (isl_int_is_zero(a
)){
878 for (row
= 0; row
< mat
->n_row
; ++row
) {
879 isl_int_divexact(mat
->row
[row
][row
], a
, mat
->row
[row
][row
]);
880 if (isl_int_is_one(mat
->row
[row
][row
]))
882 isl_mat_col_scale(inv
, row
, mat
->row
[row
][row
]);
895 struct isl_mat
*isl_mat_transpose(struct isl_mat
*mat
)
897 struct isl_mat
*transpose
= NULL
;
900 if (mat
->n_col
== mat
->n_row
) {
901 mat
= isl_mat_cow(mat
);
904 for (i
= 0; i
< mat
->n_row
; ++i
)
905 for (j
= i
+ 1; j
< mat
->n_col
; ++j
)
906 isl_int_swap(mat
->row
[i
][j
], mat
->row
[j
][i
]);
909 transpose
= isl_mat_alloc(mat
->ctx
, mat
->n_col
, mat
->n_row
);
912 for (i
= 0; i
< mat
->n_row
; ++i
)
913 for (j
= 0; j
< mat
->n_col
; ++j
)
914 isl_int_set(transpose
->row
[j
][i
], mat
->row
[i
][j
]);
922 struct isl_mat
*isl_mat_swap_cols(struct isl_mat
*mat
, unsigned i
, unsigned j
)
926 mat
= isl_mat_cow(mat
);
929 isl_assert(mat
->ctx
, i
< mat
->n_col
, goto error
);
930 isl_assert(mat
->ctx
, j
< mat
->n_col
, goto error
);
932 for (r
= 0; r
< mat
->n_row
; ++r
)
933 isl_int_swap(mat
->row
[r
][i
], mat
->row
[r
][j
]);
940 struct isl_mat
*isl_mat_swap_rows(struct isl_mat
*mat
, unsigned i
, unsigned j
)
946 mat
= isl_mat_cow(mat
);
950 mat
->row
[i
] = mat
->row
[j
];
955 struct isl_mat
*isl_mat_product(struct isl_mat
*left
, struct isl_mat
*right
)
958 struct isl_mat
*prod
;
962 isl_assert(left
->ctx
, left
->n_col
== right
->n_row
, goto error
);
963 prod
= isl_mat_alloc(left
->ctx
, left
->n_row
, right
->n_col
);
966 if (left
->n_col
== 0) {
967 for (i
= 0; i
< prod
->n_row
; ++i
)
968 isl_seq_clr(prod
->row
[i
], prod
->n_col
);
973 for (i
= 0; i
< prod
->n_row
; ++i
) {
974 for (j
= 0; j
< prod
->n_col
; ++j
) {
975 isl_int_mul(prod
->row
[i
][j
],
976 left
->row
[i
][0], right
->row
[0][j
]);
977 for (k
= 1; k
< left
->n_col
; ++k
)
978 isl_int_addmul(prod
->row
[i
][j
],
979 left
->row
[i
][k
], right
->row
[k
][j
]);
991 /* Replace the variables x in the rows q by x' given by x = M x',
992 * with M the matrix mat.
994 * If the number of new variables is greater than the original
995 * number of variables, then the rows q have already been
996 * preextended. If the new number is smaller, then the coefficients
997 * of the divs, which are not changed, need to be shifted down.
998 * The row q may be the equalities, the inequalities or the
999 * div expressions. In the latter case, has_div is true and
1000 * we need to take into account the extra denominator column.
1002 static int preimage(struct isl_ctx
*ctx
, isl_int
**q
, unsigned n
,
1003 unsigned n_div
, int has_div
, struct isl_mat
*mat
)
1009 if (mat
->n_col
>= mat
->n_row
)
1012 e
= mat
->n_row
- mat
->n_col
;
1014 for (i
= 0; i
< n
; ++i
)
1015 isl_int_mul(q
[i
][0], q
[i
][0], mat
->row
[0][0]);
1016 t
= isl_mat_sub_alloc6(mat
->ctx
, q
, 0, n
, has_div
, mat
->n_row
);
1017 t
= isl_mat_product(t
, mat
);
1020 for (i
= 0; i
< n
; ++i
) {
1021 isl_seq_swp_or_cpy(q
[i
] + has_div
, t
->row
[i
], t
->n_col
);
1022 isl_seq_cpy(q
[i
] + has_div
+ t
->n_col
,
1023 q
[i
] + has_div
+ t
->n_col
+ e
, n_div
);
1024 isl_seq_clr(q
[i
] + has_div
+ t
->n_col
+ n_div
, e
);
1030 /* Replace the variables x in bset by x' given by x = M x', with
1033 * If there are fewer variables x' then there are x, then we perform
1034 * the transformation in place, which that, in principle,
1035 * this frees up some extra variables as the number
1036 * of columns remains constant, but we would have to extend
1037 * the div array too as the number of rows in this array is assumed
1038 * to be equal to extra.
1040 struct isl_basic_set
*isl_basic_set_preimage(struct isl_basic_set
*bset
,
1041 struct isl_mat
*mat
)
1043 struct isl_ctx
*ctx
;
1049 bset
= isl_basic_set_cow(bset
);
1053 isl_assert(ctx
, bset
->dim
->nparam
== 0, goto error
);
1054 isl_assert(ctx
, 1+bset
->dim
->n_out
== mat
->n_row
, goto error
);
1055 isl_assert(ctx
, mat
->n_col
> 0, goto error
);
1057 if (mat
->n_col
> mat
->n_row
) {
1058 bset
= isl_basic_set_extend(bset
, 0, mat
->n_col
-1, 0, 0, 0);
1061 } else if (mat
->n_col
< mat
->n_row
) {
1062 bset
->dim
= isl_dim_cow(bset
->dim
);
1065 bset
->dim
->n_out
-= mat
->n_row
- mat
->n_col
;
1068 if (preimage(ctx
, bset
->eq
, bset
->n_eq
, bset
->n_div
, 0,
1069 isl_mat_copy(mat
)) < 0)
1072 if (preimage(ctx
, bset
->ineq
, bset
->n_ineq
, bset
->n_div
, 0,
1073 isl_mat_copy(mat
)) < 0)
1076 if (preimage(ctx
, bset
->div
, bset
->n_div
, bset
->n_div
, 1, mat
) < 0)
1079 ISL_F_CLR(bset
, ISL_BASIC_SET_NO_IMPLICIT
);
1080 ISL_F_CLR(bset
, ISL_BASIC_SET_NO_REDUNDANT
);
1081 ISL_F_CLR(bset
, ISL_BASIC_SET_NORMALIZED
);
1082 ISL_F_CLR(bset
, ISL_BASIC_SET_NORMALIZED_DIVS
);
1083 ISL_F_CLR(bset
, ISL_BASIC_SET_ALL_EQUALITIES
);
1085 bset
= isl_basic_set_simplify(bset
);
1086 bset
= isl_basic_set_finalize(bset
);
1092 isl_basic_set_free(bset
);
1096 struct isl_set
*isl_set_preimage(struct isl_set
*set
, struct isl_mat
*mat
)
1098 struct isl_ctx
*ctx
;
1101 set
= isl_set_cow(set
);
1106 for (i
= 0; i
< set
->n
; ++i
) {
1107 set
->p
[i
] = isl_basic_set_preimage(set
->p
[i
],
1112 if (mat
->n_col
!= mat
->n_row
) {
1113 set
->dim
= isl_dim_cow(set
->dim
);
1116 set
->dim
->n_out
+= mat
->n_col
;
1117 set
->dim
->n_out
-= mat
->n_row
;
1120 ISL_F_CLR(set
, ISL_SET_NORMALIZED
);
1128 /* Replace the variables x starting at pos in the rows q
1129 * by x' with x = M x' with M the matrix mat.
1130 * That is, replace the corresponding coefficients c by c M.
1132 static int transform(isl_ctx
*ctx
, isl_int
**q
, unsigned n
,
1133 unsigned pos
, __isl_take isl_mat
*mat
)
1138 t
= isl_mat_sub_alloc6(ctx
, q
, 0, n
, pos
, mat
->n_row
);
1139 t
= isl_mat_product(t
, mat
);
1142 for (i
= 0; i
< n
; ++i
)
1143 isl_seq_swp_or_cpy(q
[i
] + pos
, t
->row
[i
], t
->n_col
);
1148 /* Replace the variables x of type "type" starting at "first" in "bset"
1149 * by x' with x = M x' with M the matrix trans.
1150 * That is, replace the corresponding coefficients c by c M.
1152 * The transformation matrix should be a square matrix.
1154 __isl_give isl_basic_set
*isl_basic_set_transform_dims(
1155 __isl_take isl_basic_set
*bset
, enum isl_dim_type type
, unsigned first
,
1156 __isl_take isl_mat
*trans
)
1161 bset
= isl_basic_set_cow(bset
);
1162 if (!bset
|| !trans
)
1165 ctx
= isl_basic_set_get_ctx(bset
);
1166 if (trans
->n_row
!= trans
->n_col
)
1167 isl_die(trans
->ctx
, isl_error_invalid
,
1168 "expecting square transformation matrix", goto error
);
1169 if (first
+ trans
->n_row
> isl_basic_set_dim(bset
, type
))
1170 isl_die(trans
->ctx
, isl_error_invalid
,
1171 "oversized transformation matrix", goto error
);
1173 pos
= isl_basic_set_offset(bset
, type
) + first
;
1175 if (transform(ctx
, bset
->eq
, bset
->n_eq
, pos
, isl_mat_copy(trans
)) < 0)
1177 if (transform(ctx
, bset
->ineq
, bset
->n_ineq
, pos
,
1178 isl_mat_copy(trans
)) < 0)
1180 if (transform(ctx
, bset
->div
, bset
->n_div
, 1 + pos
,
1181 isl_mat_copy(trans
)) < 0)
1184 ISL_F_CLR(bset
, ISL_BASIC_SET_NORMALIZED
);
1185 ISL_F_CLR(bset
, ISL_BASIC_SET_NORMALIZED_DIVS
);
1187 isl_mat_free(trans
);
1190 isl_mat_free(trans
);
1191 isl_basic_set_free(bset
);
1195 void isl_mat_dump(struct isl_mat
*mat
, FILE *out
, int indent
)
1200 fprintf(out
, "%*snull mat\n", indent
, "");
1204 if (mat
->n_row
== 0)
1205 fprintf(out
, "%*s[]\n", indent
, "");
1207 for (i
= 0; i
< mat
->n_row
; ++i
) {
1209 fprintf(out
, "%*s[[", indent
, "");
1211 fprintf(out
, "%*s[", indent
+1, "");
1212 for (j
= 0; j
< mat
->n_col
; ++j
) {
1215 isl_int_print(out
, mat
->row
[i
][j
], 0);
1217 if (i
== mat
->n_row
-1)
1218 fprintf(out
, "]]\n");
1220 fprintf(out
, "]\n");
1224 struct isl_mat
*isl_mat_drop_cols(struct isl_mat
*mat
, unsigned col
, unsigned n
)
1228 mat
= isl_mat_cow(mat
);
1232 if (col
!= mat
->n_col
-n
) {
1233 for (r
= 0; r
< mat
->n_row
; ++r
)
1234 isl_seq_cpy(mat
->row
[r
]+col
, mat
->row
[r
]+col
+n
,
1235 mat
->n_col
- col
- n
);
1241 struct isl_mat
*isl_mat_drop_rows(struct isl_mat
*mat
, unsigned row
, unsigned n
)
1245 mat
= isl_mat_cow(mat
);
1249 for (r
= row
; r
+n
< mat
->n_row
; ++r
)
1250 mat
->row
[r
] = mat
->row
[r
+n
];
1256 __isl_give isl_mat
*isl_mat_insert_cols(__isl_take isl_mat
*mat
,
1257 unsigned col
, unsigned n
)
1266 ext
= isl_mat_alloc(mat
->ctx
, mat
->n_row
, mat
->n_col
+ n
);
1270 isl_mat_sub_copy(mat
->ctx
, ext
->row
, mat
->row
, mat
->n_row
, 0, 0, col
);
1271 isl_mat_sub_copy(mat
->ctx
, ext
->row
, mat
->row
, mat
->n_row
,
1272 col
+ n
, col
, mat
->n_col
- col
);
1281 __isl_give isl_mat
*isl_mat_insert_zero_cols(__isl_take isl_mat
*mat
,
1282 unsigned first
, unsigned n
)
1288 mat
= isl_mat_insert_cols(mat
, first
, n
);
1292 for (i
= 0; i
< mat
->n_row
; ++i
)
1293 isl_seq_clr(mat
->row
[i
] + first
, n
);
1298 __isl_give isl_mat
*isl_mat_add_zero_cols(__isl_take isl_mat
*mat
, unsigned n
)
1303 return isl_mat_insert_zero_cols(mat
, mat
->n_col
, n
);
1306 __isl_give isl_mat
*isl_mat_insert_rows(__isl_take isl_mat
*mat
,
1307 unsigned row
, unsigned n
)
1316 ext
= isl_mat_alloc(mat
->ctx
, mat
->n_row
+ n
, mat
->n_col
);
1320 isl_mat_sub_copy(mat
->ctx
, ext
->row
, mat
->row
, row
, 0, 0, mat
->n_col
);
1321 isl_mat_sub_copy(mat
->ctx
, ext
->row
+ row
+ n
, mat
->row
+ row
,
1322 mat
->n_row
- row
, 0, 0, mat
->n_col
);
1331 __isl_give isl_mat
*isl_mat_add_rows(__isl_take isl_mat
*mat
, unsigned n
)
1336 return isl_mat_insert_rows(mat
, mat
->n_row
, n
);
1339 __isl_give isl_mat
*isl_mat_insert_zero_rows(__isl_take isl_mat
*mat
,
1340 unsigned row
, unsigned n
)
1344 mat
= isl_mat_insert_rows(mat
, row
, n
);
1348 for (i
= 0; i
< n
; ++i
)
1349 isl_seq_clr(mat
->row
[row
+ i
], mat
->n_col
);
1354 __isl_give isl_mat
*isl_mat_add_zero_rows(__isl_take isl_mat
*mat
, unsigned n
)
1359 return isl_mat_insert_zero_rows(mat
, mat
->n_row
, n
);
1362 void isl_mat_col_submul(struct isl_mat
*mat
,
1363 int dst_col
, isl_int f
, int src_col
)
1367 for (i
= 0; i
< mat
->n_row
; ++i
)
1368 isl_int_submul(mat
->row
[i
][dst_col
], f
, mat
->row
[i
][src_col
]);
1371 void isl_mat_col_add(__isl_keep isl_mat
*mat
, int dst_col
, int src_col
)
1378 for (i
= 0; i
< mat
->n_row
; ++i
)
1379 isl_int_add(mat
->row
[i
][dst_col
],
1380 mat
->row
[i
][dst_col
], mat
->row
[i
][src_col
]);
1383 void isl_mat_col_mul(struct isl_mat
*mat
, int dst_col
, isl_int f
, int src_col
)
1387 for (i
= 0; i
< mat
->n_row
; ++i
)
1388 isl_int_mul(mat
->row
[i
][dst_col
], f
, mat
->row
[i
][src_col
]);
1391 struct isl_mat
*isl_mat_unimodular_complete(struct isl_mat
*M
, int row
)
1394 struct isl_mat
*H
= NULL
, *Q
= NULL
;
1399 isl_assert(M
->ctx
, M
->n_row
== M
->n_col
, goto error
);
1401 H
= isl_mat_left_hermite(isl_mat_copy(M
), 0, NULL
, &Q
);
1402 M
->n_row
= M
->n_col
;
1405 for (r
= 0; r
< row
; ++r
)
1406 isl_assert(M
->ctx
, isl_int_is_one(H
->row
[r
][r
]), goto error
);
1407 for (r
= row
; r
< M
->n_row
; ++r
)
1408 isl_seq_cpy(M
->row
[r
], Q
->row
[r
], M
->n_col
);
1419 __isl_give isl_mat
*isl_mat_concat(__isl_take isl_mat
*top
,
1420 __isl_take isl_mat
*bot
)
1422 struct isl_mat
*mat
;
1427 isl_assert(top
->ctx
, top
->n_col
== bot
->n_col
, goto error
);
1428 if (top
->n_row
== 0) {
1432 if (bot
->n_row
== 0) {
1437 mat
= isl_mat_alloc(top
->ctx
, top
->n_row
+ bot
->n_row
, top
->n_col
);
1440 isl_mat_sub_copy(mat
->ctx
, mat
->row
, top
->row
, top
->n_row
,
1442 isl_mat_sub_copy(mat
->ctx
, mat
->row
+ top
->n_row
, bot
->row
, bot
->n_row
,
1453 int isl_mat_is_equal(__isl_keep isl_mat
*mat1
, __isl_keep isl_mat
*mat2
)
1460 if (mat1
->n_row
!= mat2
->n_row
)
1463 if (mat1
->n_col
!= mat2
->n_col
)
1466 for (i
= 0; i
< mat1
->n_row
; ++i
)
1467 if (!isl_seq_eq(mat1
->row
[i
], mat2
->row
[i
], mat1
->n_col
))
1473 __isl_give isl_mat
*isl_mat_from_row_vec(__isl_take isl_vec
*vec
)
1475 struct isl_mat
*mat
;
1479 mat
= isl_mat_alloc(vec
->ctx
, 1, vec
->size
);
1483 isl_seq_cpy(mat
->row
[0], vec
->el
, vec
->size
);
1492 __isl_give isl_mat
*isl_mat_vec_concat(__isl_take isl_mat
*top
,
1493 __isl_take isl_vec
*bot
)
1495 return isl_mat_concat(top
, isl_mat_from_row_vec(bot
));
1498 __isl_give isl_mat
*isl_mat_move_cols(__isl_take isl_mat
*mat
,
1499 unsigned dst_col
, unsigned src_col
, unsigned n
)
1505 if (n
== 0 || dst_col
== src_col
)
1508 res
= isl_mat_alloc(mat
->ctx
, mat
->n_row
, mat
->n_col
);
1512 if (dst_col
< src_col
) {
1513 isl_mat_sub_copy(res
->ctx
, res
->row
, mat
->row
, mat
->n_row
,
1515 isl_mat_sub_copy(res
->ctx
, res
->row
, mat
->row
, mat
->n_row
,
1516 dst_col
, src_col
, n
);
1517 isl_mat_sub_copy(res
->ctx
, res
->row
, mat
->row
, mat
->n_row
,
1518 dst_col
+ n
, dst_col
, src_col
- dst_col
);
1519 isl_mat_sub_copy(res
->ctx
, res
->row
, mat
->row
, mat
->n_row
,
1520 src_col
+ n
, src_col
+ n
,
1521 res
->n_col
- src_col
- n
);
1523 isl_mat_sub_copy(res
->ctx
, res
->row
, mat
->row
, mat
->n_row
,
1525 isl_mat_sub_copy(res
->ctx
, res
->row
, mat
->row
, mat
->n_row
,
1526 src_col
, src_col
+ n
, dst_col
- src_col
);
1527 isl_mat_sub_copy(res
->ctx
, res
->row
, mat
->row
, mat
->n_row
,
1528 dst_col
, src_col
, n
);
1529 isl_mat_sub_copy(res
->ctx
, res
->row
, mat
->row
, mat
->n_row
,
1530 dst_col
+ n
, dst_col
+ n
,
1531 res
->n_col
- dst_col
- n
);
1541 void isl_mat_gcd(__isl_keep isl_mat
*mat
, isl_int
*gcd
)
1546 isl_int_set_si(*gcd
, 0);
1551 for (i
= 0; i
< mat
->n_row
; ++i
) {
1552 isl_seq_gcd(mat
->row
[i
], mat
->n_col
, &g
);
1553 isl_int_gcd(*gcd
, *gcd
, g
);
1558 __isl_give isl_mat
*isl_mat_scale_down(__isl_take isl_mat
*mat
, isl_int m
)
1565 for (i
= 0; i
< mat
->n_row
; ++i
)
1566 isl_seq_scale_down(mat
->row
[i
], mat
->row
[i
], m
, mat
->n_col
);
1571 __isl_give isl_mat
*isl_mat_normalize(__isl_take isl_mat
*mat
)
1579 isl_mat_gcd(mat
, &gcd
);
1580 mat
= isl_mat_scale_down(mat
, gcd
);
1586 /* Number of initial non-zero columns.
1588 int isl_mat_initial_non_zero_cols(__isl_keep isl_mat
*mat
)
1595 for (i
= 0; i
< mat
->n_col
; ++i
)
1596 if (row_first_non_zero(mat
->row
, mat
->n_row
, i
) < 0)