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 struct isl_mat *isl_mat_sub_alloc(struct 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 void isl_mat_sub_copy(struct isl_ctx *ctx, isl_int **dst, isl_int **src,
138 unsigned n_row, unsigned dst_col, unsigned src_col, unsigned n_col)
142 for (i = 0; i < n_row; ++i)
143 isl_seq_cpy(dst[i]+dst_col, src[i]+src_col, n_col);
146 void isl_mat_sub_neg(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_neg(dst[i]+dst_col, src[i]+src_col, n_col);
155 struct isl_mat *isl_mat_copy(struct isl_mat *mat)
164 struct isl_mat *isl_mat_dup(struct isl_mat *mat)
167 struct isl_mat *mat2;
171 mat2 = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
174 for (i = 0; i < mat->n_row; ++i)
175 isl_seq_cpy(mat2->row[i], mat->row[i], mat->n_col);
179 struct isl_mat *isl_mat_cow(struct isl_mat *mat)
181 struct isl_mat *mat2;
185 if (mat->ref == 1 && !ISL_F_ISSET(mat, ISL_MAT_BORROWED))
188 mat2 = isl_mat_dup(mat);
193 void isl_mat_free(struct isl_mat *mat)
201 if (!ISL_F_ISSET(mat, ISL_MAT_BORROWED))
202 isl_blk_free(mat->ctx, mat->block);
203 isl_ctx_deref(mat->ctx);
208 int isl_mat_rows(__isl_keep isl_mat *mat)
210 return mat ? mat->n_row : -1;
213 int isl_mat_cols(__isl_keep isl_mat *mat)
215 return mat ? mat->n_col : -1;
218 int isl_mat_get_element(__isl_keep isl_mat *mat, int row, int col, isl_int *v)
222 if (row < 0 || row >= mat->n_row)
223 isl_die(mat->ctx, isl_error_invalid, "row out of range",
225 if (col < 0 || col >= mat->n_col)
226 isl_die(mat->ctx, isl_error_invalid, "column out of range",
228 isl_int_set(*v, mat->row[row][col]);
232 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
233 int row, int col, isl_int v)
235 mat = isl_mat_cow(mat);
238 if (row < 0 || row >= mat->n_row)
239 isl_die(mat->ctx, isl_error_invalid, "row out of range",
241 if (col < 0 || col >= mat->n_col)
242 isl_die(mat->ctx, isl_error_invalid, "column out of range",
244 isl_int_set(mat->row[row][col], v);
251 struct isl_mat *isl_mat_identity(struct isl_ctx *ctx, unsigned n_row)
256 mat = isl_mat_alloc(ctx, n_row, n_row);
259 for (i = 0; i < n_row; ++i) {
260 isl_seq_clr(mat->row[i], i);
261 isl_int_set_si(mat->row[i][i], 1);
262 isl_seq_clr(mat->row[i]+i+1, n_row-(i+1));
268 struct isl_vec *isl_mat_vec_product(struct isl_mat *mat, struct isl_vec *vec)
271 struct isl_vec *prod;
276 isl_assert(mat->ctx, mat->n_col == vec->size, goto error);
278 prod = isl_vec_alloc(mat->ctx, mat->n_row);
282 for (i = 0; i < prod->size; ++i)
283 isl_seq_inner_product(mat->row[i], vec->el, vec->size,
284 &prod->block.data[i]);
294 __isl_give isl_vec *isl_mat_vec_inverse_product(__isl_take isl_mat *mat,
295 __isl_take isl_vec *vec)
297 struct isl_mat *vec_mat;
302 vec_mat = isl_mat_alloc(vec->ctx, vec->size, 1);
305 for (i = 0; i < vec->size; ++i)
306 isl_int_set(vec_mat->row[i][0], vec->el[i]);
307 vec_mat = isl_mat_inverse_product(mat, vec_mat);
311 vec = isl_vec_alloc(vec_mat->ctx, vec_mat->n_row);
313 for (i = 0; i < vec->size; ++i)
314 isl_int_set(vec->el[i], vec_mat->row[i][0]);
315 isl_mat_free(vec_mat);
323 struct isl_vec *isl_vec_mat_product(struct isl_vec *vec, struct isl_mat *mat)
326 struct isl_vec *prod;
331 isl_assert(mat->ctx, mat->n_row == vec->size, goto error);
333 prod = isl_vec_alloc(mat->ctx, mat->n_col);
337 for (i = 0; i < prod->size; ++i) {
338 isl_int_set_si(prod->el[i], 0);
339 for (j = 0; j < vec->size; ++j)
340 isl_int_addmul(prod->el[i], vec->el[j], mat->row[j][i]);
351 struct isl_mat *isl_mat_aff_direct_sum(struct isl_mat *left,
352 struct isl_mat *right)
360 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
361 isl_assert(left->ctx, left->n_row >= 1, goto error);
362 isl_assert(left->ctx, left->n_col >= 1, goto error);
363 isl_assert(left->ctx, right->n_col >= 1, goto error);
364 isl_assert(left->ctx,
365 isl_seq_first_non_zero(left->row[0]+1, left->n_col-1) == -1,
367 isl_assert(left->ctx,
368 isl_seq_first_non_zero(right->row[0]+1, right->n_col-1) == -1,
371 sum = isl_mat_alloc(left->ctx, left->n_row, left->n_col + right->n_col - 1);
374 isl_int_lcm(sum->row[0][0], left->row[0][0], right->row[0][0]);
375 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
376 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
378 isl_seq_clr(sum->row[0]+1, sum->n_col-1);
379 for (i = 1; i < sum->n_row; ++i) {
380 isl_int_mul(sum->row[i][0], left->row[0][0], left->row[i][0]);
381 isl_int_addmul(sum->row[i][0],
382 right->row[0][0], right->row[i][0]);
383 isl_seq_scale(sum->row[i]+1, left->row[i]+1, left->row[0][0],
385 isl_seq_scale(sum->row[i]+left->n_col,
386 right->row[i]+1, right->row[0][0],
390 isl_int_divexact(left->row[0][0], sum->row[0][0], left->row[0][0]);
391 isl_int_divexact(right->row[0][0], sum->row[0][0], right->row[0][0]);
401 static void exchange(struct isl_mat *M, struct isl_mat **U,
402 struct isl_mat **Q, unsigned row, unsigned i, unsigned j)
405 for (r = row; r < M->n_row; ++r)
406 isl_int_swap(M->row[r][i], M->row[r][j]);
408 for (r = 0; r < (*U)->n_row; ++r)
409 isl_int_swap((*U)->row[r][i], (*U)->row[r][j]);
412 isl_mat_swap_rows(*Q, i, j);
415 static void subtract(struct isl_mat *M, struct isl_mat **U,
416 struct isl_mat **Q, unsigned row, unsigned i, unsigned j, isl_int m)
419 for (r = row; r < M->n_row; ++r)
420 isl_int_submul(M->row[r][j], m, M->row[r][i]);
422 for (r = 0; r < (*U)->n_row; ++r)
423 isl_int_submul((*U)->row[r][j], m, (*U)->row[r][i]);
426 for (r = 0; r < (*Q)->n_col; ++r)
427 isl_int_addmul((*Q)->row[i][r], m, (*Q)->row[j][r]);
431 static void oppose(struct isl_mat *M, struct isl_mat **U,
432 struct isl_mat **Q, unsigned row, unsigned col)
435 for (r = row; r < M->n_row; ++r)
436 isl_int_neg(M->row[r][col], M->row[r][col]);
438 for (r = 0; r < (*U)->n_row; ++r)
439 isl_int_neg((*U)->row[r][col], (*U)->row[r][col]);
442 isl_seq_neg((*Q)->row[col], (*Q)->row[col], (*Q)->n_col);
445 /* Given matrix M, compute
450 * with U and Q unimodular matrices and H a matrix in column echelon form
451 * such that on each echelon row the entries in the non-echelon column
452 * are non-negative (if neg == 0) or non-positive (if neg == 1)
453 * and stricly smaller (in absolute value) than the entries in the echelon
455 * If U or Q are NULL, then these matrices are not computed.
457 struct isl_mat *isl_mat_left_hermite(struct isl_mat *M, int neg,
458 struct isl_mat **U, struct isl_mat **Q)
473 *U = isl_mat_identity(M->ctx, M->n_col);
478 *Q = isl_mat_identity(M->ctx, M->n_col);
485 for (row = 0; row < M->n_row; ++row) {
487 first = isl_seq_abs_min_non_zero(M->row[row]+col, M->n_col-col);
492 exchange(M, U, Q, row, first, col);
493 if (isl_int_is_neg(M->row[row][col]))
494 oppose(M, U, Q, row, col);
496 while ((off = isl_seq_first_non_zero(M->row[row]+first,
497 M->n_col-first)) != -1) {
499 isl_int_fdiv_q(c, M->row[row][first], M->row[row][col]);
500 subtract(M, U, Q, row, col, first, c);
501 if (!isl_int_is_zero(M->row[row][first]))
502 exchange(M, U, Q, row, first, col);
506 for (i = 0; i < col; ++i) {
507 if (isl_int_is_zero(M->row[row][i]))
510 isl_int_cdiv_q(c, M->row[row][i], M->row[row][col]);
512 isl_int_fdiv_q(c, M->row[row][i], M->row[row][col]);
513 if (isl_int_is_zero(c))
515 subtract(M, U, Q, row, col, i, c);
534 struct isl_mat *isl_mat_right_kernel(struct isl_mat *mat)
537 struct isl_mat *U = NULL;
540 mat = isl_mat_left_hermite(mat, 0, &U, NULL);
544 for (i = 0, rank = 0; rank < mat->n_col; ++rank) {
545 while (i < mat->n_row && isl_int_is_zero(mat->row[i][rank]))
550 K = isl_mat_alloc(U->ctx, U->n_row, U->n_col - rank);
553 isl_mat_sub_copy(K->ctx, K->row, U->row, U->n_row, 0, rank, U->n_col-rank);
563 struct isl_mat *isl_mat_lin_to_aff(struct isl_mat *mat)
566 struct isl_mat *mat2;
570 mat2 = isl_mat_alloc(mat->ctx, 1+mat->n_row, 1+mat->n_col);
573 isl_int_set_si(mat2->row[0][0], 1);
574 isl_seq_clr(mat2->row[0]+1, mat->n_col);
575 for (i = 0; i < mat->n_row; ++i) {
576 isl_int_set_si(mat2->row[1+i][0], 0);
577 isl_seq_cpy(mat2->row[1+i]+1, mat->row[i], mat->n_col);
586 /* Given two matrices M1 and M2, return the block matrix
591 __isl_give isl_mat *isl_mat_diagonal(__isl_take isl_mat *mat1,
592 __isl_take isl_mat *mat2)
600 mat = isl_mat_alloc(mat1->ctx, mat1->n_row + mat2->n_row,
601 mat1->n_col + mat2->n_col);
604 for (i = 0; i < mat1->n_row; ++i) {
605 isl_seq_cpy(mat->row[i], mat1->row[i], mat1->n_col);
606 isl_seq_clr(mat->row[i] + mat1->n_col, mat2->n_col);
608 for (i = 0; i < mat2->n_row; ++i) {
609 isl_seq_clr(mat->row[mat1->n_row + i], mat1->n_col);
610 isl_seq_cpy(mat->row[mat1->n_row + i] + mat1->n_col,
611 mat2->row[i], mat2->n_col);
622 static int row_first_non_zero(isl_int **row, unsigned n_row, unsigned col)
626 for (i = 0; i < n_row; ++i)
627 if (!isl_int_is_zero(row[i][col]))
632 static int row_abs_min_non_zero(isl_int **row, unsigned n_row, unsigned col)
634 int i, min = row_first_non_zero(row, n_row, col);
637 for (i = min + 1; i < n_row; ++i) {
638 if (isl_int_is_zero(row[i][col]))
640 if (isl_int_abs_lt(row[i][col], row[min][col]))
646 static void inv_exchange(struct isl_mat *left, struct isl_mat *right,
647 unsigned i, unsigned j)
649 left = isl_mat_swap_rows(left, i, j);
650 right = isl_mat_swap_rows(right, i, j);
653 static void inv_oppose(
654 struct isl_mat *left, struct isl_mat *right, unsigned row)
656 isl_seq_neg(left->row[row]+row, left->row[row]+row, left->n_col-row);
657 isl_seq_neg(right->row[row], right->row[row], right->n_col);
660 static void inv_subtract(struct isl_mat *left, struct isl_mat *right,
661 unsigned row, unsigned i, isl_int m)
664 isl_seq_combine(left->row[i]+row,
665 left->ctx->one, left->row[i]+row,
666 m, left->row[row]+row,
668 isl_seq_combine(right->row[i], right->ctx->one, right->row[i],
669 m, right->row[row], right->n_col);
672 /* Compute inv(left)*right
674 struct isl_mat *isl_mat_inverse_product(struct isl_mat *left,
675 struct isl_mat *right)
683 isl_assert(left->ctx, left->n_row == left->n_col, goto error);
684 isl_assert(left->ctx, left->n_row == right->n_row, goto error);
686 if (left->n_row == 0) {
691 left = isl_mat_cow(left);
692 right = isl_mat_cow(right);
698 for (row = 0; row < left->n_row; ++row) {
699 int pivot, first, i, off;
700 pivot = row_abs_min_non_zero(left->row+row, left->n_row-row, row);
704 isl_assert(left->ctx, pivot >= 0, goto error);
708 inv_exchange(left, right, pivot, row);
709 if (isl_int_is_neg(left->row[row][row]))
710 inv_oppose(left, right, row);
712 while ((off = row_first_non_zero(left->row+first,
713 left->n_row-first, row)) != -1) {
715 isl_int_fdiv_q(a, left->row[first][row],
716 left->row[row][row]);
717 inv_subtract(left, right, row, first, a);
718 if (!isl_int_is_zero(left->row[first][row]))
719 inv_exchange(left, right, row, first);
723 for (i = 0; i < row; ++i) {
724 if (isl_int_is_zero(left->row[i][row]))
726 isl_int_gcd(a, left->row[row][row], left->row[i][row]);
727 isl_int_divexact(b, left->row[i][row], a);
728 isl_int_divexact(a, left->row[row][row], a);
730 isl_seq_combine(left->row[i] + i,
732 b, left->row[row] + i,
734 isl_seq_combine(right->row[i], a, right->row[i],
735 b, right->row[row], right->n_col);
740 isl_int_set(a, left->row[0][0]);
741 for (row = 1; row < left->n_row; ++row)
742 isl_int_lcm(a, a, left->row[row][row]);
743 if (isl_int_is_zero(a)){
745 isl_assert(left->ctx, 0, goto error);
747 for (row = 0; row < left->n_row; ++row) {
748 isl_int_divexact(left->row[row][row], a, left->row[row][row]);
749 if (isl_int_is_one(left->row[row][row]))
751 isl_seq_scale(right->row[row], right->row[row],
752 left->row[row][row], right->n_col);
764 void isl_mat_col_scale(struct isl_mat *mat, unsigned col, isl_int m)
768 for (i = 0; i < mat->n_row; ++i)
769 isl_int_mul(mat->row[i][col], mat->row[i][col], m);
772 void isl_mat_col_combine(struct isl_mat *mat, unsigned dst,
773 isl_int m1, unsigned src1, isl_int m2, unsigned src2)
779 for (i = 0; i < mat->n_row; ++i) {
780 isl_int_mul(tmp, m1, mat->row[i][src1]);
781 isl_int_addmul(tmp, m2, mat->row[i][src2]);
782 isl_int_set(mat->row[i][dst], tmp);
787 struct isl_mat *isl_mat_right_inverse(struct isl_mat *mat)
793 mat = isl_mat_cow(mat);
797 inv = isl_mat_identity(mat->ctx, mat->n_col);
798 inv = isl_mat_cow(inv);
804 for (row = 0; row < mat->n_row; ++row) {
805 int pivot, first, i, off;
806 pivot = isl_seq_abs_min_non_zero(mat->row[row]+row, mat->n_col-row);
810 isl_assert(mat->ctx, pivot >= 0, goto error);
814 exchange(mat, &inv, NULL, row, pivot, row);
815 if (isl_int_is_neg(mat->row[row][row]))
816 oppose(mat, &inv, NULL, row, row);
818 while ((off = isl_seq_first_non_zero(mat->row[row]+first,
819 mat->n_col-first)) != -1) {
821 isl_int_fdiv_q(a, mat->row[row][first],
823 subtract(mat, &inv, NULL, row, row, first, a);
824 if (!isl_int_is_zero(mat->row[row][first]))
825 exchange(mat, &inv, NULL, row, row, first);
829 for (i = 0; i < row; ++i) {
830 if (isl_int_is_zero(mat->row[row][i]))
832 isl_int_gcd(a, mat->row[row][row], mat->row[row][i]);
833 isl_int_divexact(b, mat->row[row][i], a);
834 isl_int_divexact(a, mat->row[row][row], a);
836 isl_mat_col_combine(mat, i, a, i, b, row);
837 isl_mat_col_combine(inv, i, a, i, b, row);
842 isl_int_set(a, mat->row[0][0]);
843 for (row = 1; row < mat->n_row; ++row)
844 isl_int_lcm(a, a, mat->row[row][row]);
845 if (isl_int_is_zero(a)){
849 for (row = 0; row < mat->n_row; ++row) {
850 isl_int_divexact(mat->row[row][row], a, mat->row[row][row]);
851 if (isl_int_is_one(mat->row[row][row]))
853 isl_mat_col_scale(inv, row, mat->row[row][row]);
866 struct isl_mat *isl_mat_transpose(struct isl_mat *mat)
868 struct isl_mat *transpose = NULL;
871 if (mat->n_col == mat->n_row) {
872 mat = isl_mat_cow(mat);
875 for (i = 0; i < mat->n_row; ++i)
876 for (j = i + 1; j < mat->n_col; ++j)
877 isl_int_swap(mat->row[i][j], mat->row[j][i]);
880 transpose = isl_mat_alloc(mat->ctx, mat->n_col, mat->n_row);
883 for (i = 0; i < mat->n_row; ++i)
884 for (j = 0; j < mat->n_col; ++j)
885 isl_int_set(transpose->row[j][i], mat->row[i][j]);
893 struct isl_mat *isl_mat_swap_cols(struct isl_mat *mat, unsigned i, unsigned j)
897 mat = isl_mat_cow(mat);
900 isl_assert(mat->ctx, i < mat->n_col, goto error);
901 isl_assert(mat->ctx, j < mat->n_col, goto error);
903 for (r = 0; r < mat->n_row; ++r)
904 isl_int_swap(mat->row[r][i], mat->row[r][j]);
911 struct isl_mat *isl_mat_swap_rows(struct isl_mat *mat, unsigned i, unsigned j)
917 mat = isl_mat_cow(mat);
921 mat->row[i] = mat->row[j];
926 struct isl_mat *isl_mat_product(struct isl_mat *left, struct isl_mat *right)
929 struct isl_mat *prod;
933 isl_assert(left->ctx, left->n_col == right->n_row, goto error);
934 prod = isl_mat_alloc(left->ctx, left->n_row, right->n_col);
937 if (left->n_col == 0) {
938 for (i = 0; i < prod->n_row; ++i)
939 isl_seq_clr(prod->row[i], prod->n_col);
942 for (i = 0; i < prod->n_row; ++i) {
943 for (j = 0; j < prod->n_col; ++j) {
944 isl_int_mul(prod->row[i][j],
945 left->row[i][0], right->row[0][j]);
946 for (k = 1; k < left->n_col; ++k)
947 isl_int_addmul(prod->row[i][j],
948 left->row[i][k], right->row[k][j]);
960 /* Replace the variables x in the rows q by x' given by x = M x',
961 * with M the matrix mat.
963 * If the number of new variables is greater than the original
964 * number of variables, then the rows q have already been
965 * preextended. If the new number is smaller, then the coefficients
966 * of the divs, which are not changed, need to be shifted down.
967 * The row q may be the equalities, the inequalities or the
968 * div expressions. In the latter case, has_div is true and
969 * we need to take into account the extra denominator column.
971 static int preimage(struct isl_ctx *ctx, isl_int **q, unsigned n,
972 unsigned n_div, int has_div, struct isl_mat *mat)
978 if (mat->n_col >= mat->n_row)
981 e = mat->n_row - mat->n_col;
983 for (i = 0; i < n; ++i)
984 isl_int_mul(q[i][0], q[i][0], mat->row[0][0]);
985 t = isl_mat_sub_alloc(mat->ctx, q, 0, n, has_div, mat->n_row);
986 t = isl_mat_product(t, mat);
989 for (i = 0; i < n; ++i) {
990 isl_seq_swp_or_cpy(q[i] + has_div, t->row[i], t->n_col);
991 isl_seq_cpy(q[i] + has_div + t->n_col,
992 q[i] + has_div + t->n_col + e, n_div);
993 isl_seq_clr(q[i] + has_div + t->n_col + n_div, e);
999 /* Replace the variables x in bset by x' given by x = M x', with
1002 * If there are fewer variables x' then there are x, then we perform
1003 * the transformation in place, which that, in principle,
1004 * this frees up some extra variables as the number
1005 * of columns remains constant, but we would have to extend
1006 * the div array too as the number of rows in this array is assumed
1007 * to be equal to extra.
1009 struct isl_basic_set *isl_basic_set_preimage(struct isl_basic_set *bset,
1010 struct isl_mat *mat)
1012 struct isl_ctx *ctx;
1018 bset = isl_basic_set_cow(bset);
1022 isl_assert(ctx, bset->dim->nparam == 0, goto error);
1023 isl_assert(ctx, 1+bset->dim->n_out == mat->n_row, goto error);
1024 isl_assert(ctx, mat->n_col > 0, goto error);
1026 if (mat->n_col > mat->n_row) {
1027 bset = isl_basic_set_extend(bset, 0, mat->n_col-1, 0, 0, 0);
1030 } else if (mat->n_col < mat->n_row) {
1031 bset->dim = isl_dim_cow(bset->dim);
1034 bset->dim->n_out -= mat->n_row - mat->n_col;
1037 if (preimage(ctx, bset->eq, bset->n_eq, bset->n_div, 0,
1038 isl_mat_copy(mat)) < 0)
1041 if (preimage(ctx, bset->ineq, bset->n_ineq, bset->n_div, 0,
1042 isl_mat_copy(mat)) < 0)
1045 if (preimage(ctx, bset->div, bset->n_div, bset->n_div, 1, mat) < 0)
1048 ISL_F_CLR(bset, ISL_BASIC_SET_NO_IMPLICIT);
1049 ISL_F_CLR(bset, ISL_BASIC_SET_NO_REDUNDANT);
1050 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED);
1051 ISL_F_CLR(bset, ISL_BASIC_SET_NORMALIZED_DIVS);
1052 ISL_F_CLR(bset, ISL_BASIC_SET_ALL_EQUALITIES);
1054 bset = isl_basic_set_simplify(bset);
1055 bset = isl_basic_set_finalize(bset);
1061 isl_basic_set_free(bset);
1065 struct isl_set *isl_set_preimage(struct isl_set *set, struct isl_mat *mat)
1067 struct isl_ctx *ctx;
1070 set = isl_set_cow(set);
1075 for (i = 0; i < set->n; ++i) {
1076 set->p[i] = isl_basic_set_preimage(set->p[i],
1081 if (mat->n_col != mat->n_row) {
1082 set->dim = isl_dim_cow(set->dim);
1085 set->dim->n_out += mat->n_col;
1086 set->dim->n_out -= mat->n_row;
1089 ISL_F_CLR(set, ISL_SET_NORMALIZED);
1097 void isl_mat_dump(struct isl_mat *mat, FILE *out, int indent)
1102 fprintf(out, "%*snull mat\n", indent, "");
1106 if (mat->n_row == 0)
1107 fprintf(out, "%*s[]\n", indent, "");
1109 for (i = 0; i < mat->n_row; ++i) {
1111 fprintf(out, "%*s[[", indent, "");
1113 fprintf(out, "%*s[", indent+1, "");
1114 for (j = 0; j < mat->n_col; ++j) {
1117 isl_int_print(out, mat->row[i][j], 0);
1119 if (i == mat->n_row-1)
1120 fprintf(out, "]]\n");
1122 fprintf(out, "]\n");
1126 struct isl_mat *isl_mat_drop_cols(struct isl_mat *mat, unsigned col, unsigned n)
1130 mat = isl_mat_cow(mat);
1134 if (col != mat->n_col-n) {
1135 for (r = 0; r < mat->n_row; ++r)
1136 isl_seq_cpy(mat->row[r]+col, mat->row[r]+col+n,
1137 mat->n_col - col - n);
1143 struct isl_mat *isl_mat_drop_rows(struct isl_mat *mat, unsigned row, unsigned n)
1147 mat = isl_mat_cow(mat);
1151 for (r = row; r+n < mat->n_row; ++r)
1152 mat->row[r] = mat->row[r+n];
1158 __isl_give isl_mat *isl_mat_insert_cols(__isl_take isl_mat *mat,
1159 unsigned col, unsigned n)
1168 ext = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col + n);
1172 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row, 0, 0, col);
1173 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, mat->n_row,
1174 col + n, col, mat->n_col - col);
1183 __isl_give isl_mat *isl_mat_insert_zero_cols(__isl_take isl_mat *mat,
1184 unsigned first, unsigned n)
1190 mat = isl_mat_insert_cols(mat, first, n);
1194 for (i = 0; i < mat->n_row; ++i)
1195 isl_seq_clr(mat->row[i] + first, n);
1200 __isl_give isl_mat *isl_mat_add_zero_cols(__isl_take isl_mat *mat, unsigned n)
1205 return isl_mat_insert_zero_cols(mat, mat->n_col, n);
1208 __isl_give isl_mat *isl_mat_insert_rows(__isl_take isl_mat *mat,
1209 unsigned row, unsigned n)
1218 ext = isl_mat_alloc(mat->ctx, mat->n_row + n, mat->n_col);
1222 isl_mat_sub_copy(mat->ctx, ext->row, mat->row, row, 0, 0, mat->n_col);
1223 isl_mat_sub_copy(mat->ctx, ext->row + row + n, mat->row + row,
1224 mat->n_row - row, 0, 0, mat->n_col);
1233 __isl_give isl_mat *isl_mat_add_rows(__isl_take isl_mat *mat, unsigned n)
1238 return isl_mat_insert_rows(mat, mat->n_row, n);
1241 void isl_mat_col_submul(struct isl_mat *mat,
1242 int dst_col, isl_int f, int src_col)
1246 for (i = 0; i < mat->n_row; ++i)
1247 isl_int_submul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1250 void isl_mat_col_add(__isl_keep isl_mat *mat, int dst_col, int src_col)
1257 for (i = 0; i < mat->n_row; ++i)
1258 isl_int_add(mat->row[i][dst_col],
1259 mat->row[i][dst_col], mat->row[i][src_col]);
1262 void isl_mat_col_mul(struct isl_mat *mat, int dst_col, isl_int f, int src_col)
1266 for (i = 0; i < mat->n_row; ++i)
1267 isl_int_mul(mat->row[i][dst_col], f, mat->row[i][src_col]);
1270 struct isl_mat *isl_mat_unimodular_complete(struct isl_mat *M, int row)
1273 struct isl_mat *H = NULL, *Q = NULL;
1278 isl_assert(M->ctx, M->n_row == M->n_col, goto error);
1280 H = isl_mat_left_hermite(isl_mat_copy(M), 0, NULL, &Q);
1281 M->n_row = M->n_col;
1284 for (r = 0; r < row; ++r)
1285 isl_assert(M->ctx, isl_int_is_one(H->row[r][r]), goto error);
1286 for (r = row; r < M->n_row; ++r)
1287 isl_seq_cpy(M->row[r], Q->row[r], M->n_col);
1298 __isl_give isl_mat *isl_mat_concat(__isl_take isl_mat *top,
1299 __isl_take isl_mat *bot)
1301 struct isl_mat *mat;
1306 isl_assert(top->ctx, top->n_col == bot->n_col, goto error);
1307 if (top->n_row == 0) {
1311 if (bot->n_row == 0) {
1316 mat = isl_mat_alloc(top->ctx, top->n_row + bot->n_row, top->n_col);
1319 isl_mat_sub_copy(mat->ctx, mat->row, top->row, top->n_row,
1321 isl_mat_sub_copy(mat->ctx, mat->row + top->n_row, bot->row, bot->n_row,
1332 int isl_mat_is_equal(__isl_keep isl_mat *mat1, __isl_keep isl_mat *mat2)
1339 if (mat1->n_row != mat2->n_row)
1342 if (mat1->n_col != mat2->n_col)
1345 for (i = 0; i < mat1->n_row; ++i)
1346 if (!isl_seq_eq(mat1->row[i], mat2->row[i], mat1->n_col))
1352 __isl_give isl_mat *isl_mat_from_row_vec(__isl_take isl_vec *vec)
1354 struct isl_mat *mat;
1358 mat = isl_mat_alloc(vec->ctx, 1, vec->size);
1362 isl_seq_cpy(mat->row[0], vec->el, vec->size);
1371 __isl_give isl_mat *isl_mat_vec_concat(__isl_take isl_mat *top,
1372 __isl_take isl_vec *bot)
1374 return isl_mat_concat(top, isl_mat_from_row_vec(bot));
1377 __isl_give isl_mat *isl_mat_move_cols(__isl_take isl_mat *mat,
1378 unsigned dst_col, unsigned src_col, unsigned n)
1384 if (n == 0 || dst_col == src_col)
1387 res = isl_mat_alloc(mat->ctx, mat->n_row, mat->n_col);
1391 if (dst_col < src_col) {
1392 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1394 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1395 dst_col, src_col, n);
1396 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1397 dst_col + n, dst_col, src_col - dst_col);
1398 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1399 src_col + n, src_col + n,
1400 res->n_col - src_col - n);
1402 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1404 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1405 src_col, src_col + n, dst_col - src_col);
1406 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1407 dst_col, src_col, n);
1408 isl_mat_sub_copy(res->ctx, res->row, mat->row, mat->n_row,
1409 dst_col + n, dst_col + n,
1410 res->n_col - dst_col - n);
1420 void isl_mat_gcd(__isl_keep isl_mat *mat, isl_int *gcd)
1425 isl_int_set_si(*gcd, 0);
1430 for (i = 0; i < mat->n_row; ++i) {
1431 isl_seq_gcd(mat->row[i], mat->n_col, &g);
1432 isl_int_gcd(*gcd, *gcd, g);
1437 __isl_give isl_mat *isl_mat_scale_down(__isl_take isl_mat *mat, isl_int m)
1444 for (i = 0; i < mat->n_row; ++i)
1445 isl_seq_scale_down(mat->row[i], mat->row[i], m, mat->n_col);
1450 __isl_give isl_mat *isl_mat_normalize(__isl_take isl_mat *mat)
1458 isl_mat_gcd(mat, &gcd);
1459 mat = isl_mat_scale_down(mat, gcd);