2 #include "isl_basis_reduction.h"
4 static void save_alpha(GBR_LP *lp, int first, int n, GBR_type *alpha)
8 for (i = 0; i < n; ++i)
9 GBR_lp_get_alpha(lp, first + i, &alpha[i]);
12 /* Compute a reduced basis for the set represented by the tableau "tab".
13 * tab->basis, must be initialized by the calling function to an affine
14 * unimodular basis, is updated to reflect the reduced basis.
15 * The first tab->n_zero rows of the basis (ignoring the constant row)
16 * are assumed to correspond to equalities and are left untouched.
17 * tab->n_zero is updated to reflect any additional equalities that
18 * have been detected in the first rows of the new basis.
20 * This function implements the algorithm described in
21 * "An Implementation of the Generalized Basis Reduction Algorithm
22 * for Integer Programming" of Cook el al. to compute a reduced basis.
23 * We use \epsilon = 1/4.
25 * If ctx->gbr_only_first is set, the user is only interested
26 * in the first direction. In this case we stop the basis reduction when
27 * the width in the first direction becomes smaller than 2.
29 struct isl_tab *isl_tab_compute_reduced_basis(struct isl_tab *tab)
37 GBR_type F_old, alpha, F_new;
40 struct isl_vec *b_tmp;
42 GBR_type *alpha_buffer[2] = { NULL, NULL };
43 GBR_type *alpha_saved;
64 if (dim <= tab->n_zero + 1)
80 b_tmp = isl_vec_alloc(ctx, dim);
84 F = isl_alloc_array(ctx, GBR_type, dim);
85 alpha_buffer[0] = isl_alloc_array(ctx, GBR_type, dim);
86 alpha_buffer[1] = isl_alloc_array(ctx, GBR_type, dim);
87 alpha_saved = alpha_buffer[0];
89 if (!F || !alpha_buffer[0] || !alpha_buffer[1])
92 for (i = 0; i < dim; ++i) {
94 GBR_init(alpha_buffer[0][i]);
95 GBR_init(alpha_buffer[1][i]);
101 lp = GBR_lp_init(tab);
107 GBR_lp_set_obj(lp, B->row[1+i]+1, dim);
108 ctx->stats->gbr_solved_lps++;
109 unbounded = GBR_lp_solve(lp);
110 isl_assert(ctx, !unbounded, goto error);
111 GBR_lp_get_obj_val(lp, &F[i]);
113 if (GBR_lt(F[i], one)) {
114 if (!GBR_is_zero(F[i])) {
115 empty = GBR_lp_cut(lp, B->row[1+i]+1);
124 if (i+1 == tab->n_zero) {
125 GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim);
126 ctx->stats->gbr_solved_lps++;
127 unbounded = GBR_lp_solve(lp);
128 isl_assert(ctx, !unbounded, goto error);
129 GBR_lp_get_obj_val(lp, &F_new);
130 fixed = GBR_lp_is_fixed(lp);
131 GBR_set_ui(alpha, 0);
134 row = GBR_lp_next_row(lp);
135 GBR_set(F_new, F_saved);
137 GBR_set(alpha, alpha_saved[i]);
139 row = GBR_lp_add_row(lp, B->row[1+i]+1, dim);
140 GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim);
141 ctx->stats->gbr_solved_lps++;
142 unbounded = GBR_lp_solve(lp);
143 isl_assert(ctx, !unbounded, goto error);
144 GBR_lp_get_obj_val(lp, &F_new);
145 fixed = GBR_lp_is_fixed(lp);
147 GBR_lp_get_alpha(lp, row, &alpha);
150 save_alpha(lp, row-i, i, alpha_saved);
154 GBR_set(F[i+1], F_new);
156 GBR_floor(mu[0], alpha);
157 GBR_ceil(mu[1], alpha);
159 if (isl_int_eq(mu[0], mu[1]))
160 isl_int_set(tmp, mu[0]);
164 for (j = 0; j <= 1; ++j) {
165 isl_int_set(tmp, mu[j]);
166 isl_seq_combine(b_tmp->el,
167 ctx->one, B->row[1+i+1]+1,
168 tmp, B->row[1+i]+1, dim);
169 GBR_lp_set_obj(lp, b_tmp->el, dim);
170 ctx->stats->gbr_solved_lps++;
171 unbounded = GBR_lp_solve(lp);
172 isl_assert(ctx, !unbounded, goto error);
173 GBR_lp_get_obj_val(lp, &mu_F[j]);
174 mu_fixed[j] = GBR_lp_is_fixed(lp);
176 save_alpha(lp, row-i, i, alpha_buffer[j]);
179 if (GBR_lt(mu_F[0], mu_F[1]))
184 isl_int_set(tmp, mu[j]);
185 GBR_set(F_new, mu_F[j]);
187 alpha_saved = alpha_buffer[j];
189 isl_seq_combine(B->row[1+i+1]+1, ctx->one, B->row[1+i+1]+1,
190 tmp, B->row[1+i]+1, dim);
192 if (i+1 == tab->n_zero && fixed) {
193 if (!GBR_is_zero(F[i+1])) {
194 empty = GBR_lp_cut(lp, B->row[1+i+1]+1);
197 GBR_set_ui(F[i+1], 0);
202 GBR_set(F_old, F[i]);
205 /* mu_F[0] = 4 * F_new; mu_F[1] = 3 * F_old */
206 GBR_set_ui(mu_F[0], 4);
207 GBR_mul(mu_F[0], mu_F[0], F_new);
208 GBR_set_ui(mu_F[1], 3);
209 GBR_mul(mu_F[1], mu_F[1], F_old);
210 if (GBR_lt(mu_F[0], mu_F[1])) {
211 B = isl_mat_swap_rows(B, 1 + i, 1 + i + 1);
212 if (i > tab->n_zero) {
214 GBR_set(F_saved, F_new);
219 GBR_set(F[tab->n_zero], F_new);
220 if (ctx->gbr_only_first && GBR_lt(F[tab->n_zero], two))
224 if (!GBR_is_zero(F[tab->n_zero])) {
225 empty = GBR_lp_cut(lp, B->row[1+tab->n_zero]+1);
228 GBR_set_ui(F[tab->n_zero], 0);
234 GBR_lp_add_row(lp, B->row[1+i]+1, dim);
251 for (i = 0; i < dim; ++i) {
253 GBR_clear(alpha_buffer[0][i]);
254 GBR_clear(alpha_buffer[1][i]);
257 free(alpha_buffer[0]);
258 free(alpha_buffer[1]);
272 isl_int_clear(mu[0]);
273 isl_int_clear(mu[1]);
280 struct isl_mat *isl_basic_set_reduced_basis(struct isl_basic_set *bset)
282 struct isl_mat *basis;
285 isl_assert(bset->ctx, bset->n_eq == 0, return NULL);
287 tab = isl_tab_from_basic_set(bset);
288 tab->basis = isl_mat_identity(bset->ctx, 1 + tab->n_var);
289 tab = isl_tab_compute_reduced_basis(tab);
293 basis = isl_mat_copy(tab->basis);