basis_reduction_templ.c

   1 #include <stdlib.h>
   2 #include "isl_basis_reduction.h"
   3
   4 static void save_alpha(GBR_LP *lp, int first, int n, GBR_type *alpha)
   5 {
   6         int i;
   7
   8         for (i = 0; i < n; ++i)
   9                 GBR_lp_get_alpha(lp, first + i, &alpha[i]);
  10 }
  11
  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.
  19  * The final tab->n_unbounded rows of the basis are assumed to correspond
  20  * to unbounded directions and are also left untouched.
  21  * In particular this means that the remaining rows are assumed to
  22  * correspond to bounded directions.
  23  *
  24  * This function implements the algorithm described in
  25  * "An Implementation of the Generalized Basis Reduction Algorithm
  26  *  for Integer Programming" of Cook el al. to compute a reduced basis.
  27  * We use \epsilon = 1/4.
  28  *
  29  * If ctx->gbr_only_first is set, the user is only interested
  30  * in the first direction.  In this case we stop the basis reduction when
  31  * the width in the first direction becomes smaller than 2.
  32  */
  33 struct isl_tab *isl_tab_compute_reduced_basis(struct isl_tab *tab)
  34 {
  35         unsigned dim;
  36         struct isl_ctx *ctx;
  37         struct isl_mat *B;
  38         int unbounded;
  39         int i;
  40         GBR_LP *lp = NULL;
  41         GBR_type F_old, alpha, F_new;
  42         int row;
  43         isl_int tmp;
  44         struct isl_vec *b_tmp;
  45         GBR_type *F = NULL;
  46         GBR_type *alpha_buffer[2] = { NULL, NULL };
  47         GBR_type *alpha_saved;
  48         GBR_type F_saved;
  49         int use_saved = 0;
  50         isl_int mu[2];
  51         GBR_type mu_F[2];
  52         GBR_type two;
  53         GBR_type one;
  54         int empty = 0;
  55         int fixed = 0;
  56         int fixed_saved = 0;
  57         int mu_fixed[2];
  58         int n_bounded;
  59
  60         if (!tab)
  61                 return NULL;
  62
  63         if (tab->empty)
  64                 return tab;
  65
  66         ctx = tab->mat->ctx;
  67         dim = tab->n_var;
  68         B = tab->basis;
  69         if (!B)
  70                 return tab;
  71
  72         n_bounded = dim - tab->n_unbounded;
  73         if (n_bounded <= tab->n_zero + 1)
  74                 return tab;
  75
  76         isl_int_init(tmp);
  77         isl_int_init(mu[0]);
  78         isl_int_init(mu[1]);
  79
  80         GBR_init(alpha);
  81         GBR_init(F_old);
  82         GBR_init(F_new);
  83         GBR_init(F_saved);
  84         GBR_init(mu_F[0]);
  85         GBR_init(mu_F[1]);
  86         GBR_init(two);
  87         GBR_init(one);
  88
  89         b_tmp = isl_vec_alloc(ctx, dim);
  90         if (!b_tmp)
  91                 goto error;
  92
  93         F = isl_alloc_array(ctx, GBR_type, n_bounded);
  94         alpha_buffer[0] = isl_alloc_array(ctx, GBR_type, n_bounded);
  95         alpha_buffer[1] = isl_alloc_array(ctx, GBR_type, n_bounded);
  96         alpha_saved = alpha_buffer[0];
  97
  98         if (!F || !alpha_buffer[0] || !alpha_buffer[1])
  99                 goto error;
 100
 101         for (i = 0; i < n_bounded; ++i) {
 102                 GBR_init(F[i]);
 103                 GBR_init(alpha_buffer[0][i]);
 104                 GBR_init(alpha_buffer[1][i]);
 105         }
 106
 107         GBR_set_ui(two, 2);
 108         GBR_set_ui(one, 1);
 109
 110         lp = GBR_lp_init(tab);
 111         if (!lp)
 112                 goto error;
 113
 114         i = tab->n_zero;
 115
 116         GBR_lp_set_obj(lp, B->row[1+i]+1, dim);
 117         ctx->stats->gbr_solved_lps++;
 118         unbounded = GBR_lp_solve(lp);
 119         isl_assert(ctx, !unbounded, goto error);
 120         GBR_lp_get_obj_val(lp, &F[i]);
 121
 122         if (GBR_lt(F[i], one)) {
 123                 if (!GBR_is_zero(F[i])) {
 124                         empty = GBR_lp_cut(lp, B->row[1+i]+1);
 125                         if (empty)
 126                                 goto done;
 127                         GBR_set_ui(F[i], 0);
 128                 }
 129                 tab->n_zero++;
 130         }
 131
 132         do {
 133                 if (i+1 == tab->n_zero) {
 134                         GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim);
 135                         ctx->stats->gbr_solved_lps++;
 136                         unbounded = GBR_lp_solve(lp);
 137                         isl_assert(ctx, !unbounded, goto error);
 138                         GBR_lp_get_obj_val(lp, &F_new);
 139                         fixed = GBR_lp_is_fixed(lp);
 140                         GBR_set_ui(alpha, 0);
 141                 } else
 142                 if (use_saved) {
 143                         row = GBR_lp_next_row(lp);
 144                         GBR_set(F_new, F_saved);
 145                         fixed = fixed_saved;
 146                         GBR_set(alpha, alpha_saved[i]);
 147                 } else {
 148                         row = GBR_lp_add_row(lp, B->row[1+i]+1, dim);
 149                         GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim);
 150                         ctx->stats->gbr_solved_lps++;
 151                         unbounded = GBR_lp_solve(lp);
 152                         isl_assert(ctx, !unbounded, goto error);
 153                         GBR_lp_get_obj_val(lp, &F_new);
 154                         fixed = GBR_lp_is_fixed(lp);
 155
 156                         GBR_lp_get_alpha(lp, row, &alpha);
 157
 158                         if (i > 0)
 159                                 save_alpha(lp, row-i, i, alpha_saved);
 160
 161                         if (GBR_lp_del_row(lp) < 0)
 162                                 goto error;
 163                 }
 164                 GBR_set(F[i+1], F_new);
 165
 166                 GBR_floor(mu[0], alpha);
 167                 GBR_ceil(mu[1], alpha);
 168
 169                 if (isl_int_eq(mu[0], mu[1]))
 170                         isl_int_set(tmp, mu[0]);
 171                 else {
 172                         int j;
 173
 174                         for (j = 0; j <= 1; ++j) {
 175                                 isl_int_set(tmp, mu[j]);
 176                                 isl_seq_combine(b_tmp->el,
 177                                                 ctx->one, B->row[1+i+1]+1,
 178                                                 tmp, B->row[1+i]+1, dim);
 179                                 GBR_lp_set_obj(lp, b_tmp->el, dim);
 180                                 ctx->stats->gbr_solved_lps++;
 181                                 unbounded = GBR_lp_solve(lp);
 182                                 isl_assert(ctx, !unbounded, goto error);
 183                                 GBR_lp_get_obj_val(lp, &mu_F[j]);
 184                                 mu_fixed[j] = GBR_lp_is_fixed(lp);
 185                                 if (i > 0)
 186                                         save_alpha(lp, row-i, i, alpha_buffer[j]);
 187                         }
 188
 189                         if (GBR_lt(mu_F[0], mu_F[1]))
 190                                 j = 0;
 191                         else
 192                                 j = 1;
 193
 194                         isl_int_set(tmp, mu[j]);
 195                         GBR_set(F_new, mu_F[j]);
 196                         fixed = mu_fixed[j];
 197                         alpha_saved = alpha_buffer[j];
 198                 }
 199                 isl_seq_combine(B->row[1+i+1]+1, ctx->one, B->row[1+i+1]+1,
 200                                 tmp, B->row[1+i]+1, dim);
 201
 202                 if (i+1 == tab->n_zero && fixed) {
 203                         if (!GBR_is_zero(F[i+1])) {
 204                                 empty = GBR_lp_cut(lp, B->row[1+i+1]+1);
 205                                 if (empty)
 206                                         goto done;
 207                                 GBR_set_ui(F[i+1], 0);
 208                         }
 209                         tab->n_zero++;
 210                 }
 211
 212                 GBR_set(F_old, F[i]);
 213
 214                 use_saved = 0;
 215                 /* mu_F[0] = 4 * F_new; mu_F[1] = 3 * F_old */
 216                 GBR_set_ui(mu_F[0], 4);
 217                 GBR_mul(mu_F[0], mu_F[0], F_new);
 218                 GBR_set_ui(mu_F[1], 3);
 219                 GBR_mul(mu_F[1], mu_F[1], F_old);
 220                 if (GBR_lt(mu_F[0], mu_F[1])) {
 221                         B = isl_mat_swap_rows(B, 1 + i, 1 + i + 1);
 222                         if (i > tab->n_zero) {
 223                                 use_saved = 1;
 224                                 GBR_set(F_saved, F_new);
 225                                 fixed_saved = fixed;
 226                                 if (GBR_lp_del_row(lp) < 0)
 227                                         goto error;
 228                                 --i;
 229                         } else {
 230                                 GBR_set(F[tab->n_zero], F_new);
 231                                 if (ctx->gbr_only_first && GBR_lt(F[tab->n_zero], two))
 232                                         break;
 233
 234                                 if (fixed) {
 235                                         if (!GBR_is_zero(F[tab->n_zero])) {
 236                                                 empty = GBR_lp_cut(lp, B->row[1+tab->n_zero]+1);
 237                                                 if (empty)
 238                                                         goto done;
 239                                                 GBR_set_ui(F[tab->n_zero], 0);
 240                                         }
 241                                         tab->n_zero++;
 242                                 }
 243                         }
 244                 } else {
 245                         GBR_lp_add_row(lp, B->row[1+i]+1, dim);
 246                         ++i;
 247                 }
 248         } while (i < n_bounded - 1);
 249
 250         if (0) {
 251 done:
 252                 if (empty < 0) {
 253 error:
 254                         isl_mat_free(B);
 255                         B = NULL;
 256                 }
 257         }
 258
 259         GBR_lp_delete(lp);
 260
 261         if (alpha_buffer[1])
 262                 for (i = 0; i < n_bounded; ++i) {
 263                         GBR_clear(F[i]);
 264                         GBR_clear(alpha_buffer[0][i]);
 265                         GBR_clear(alpha_buffer[1][i]);
 266                 }
 267         free(F);
 268         free(alpha_buffer[0]);
 269         free(alpha_buffer[1]);
 270
 271         isl_vec_free(b_tmp);
 272
 273         GBR_clear(alpha);
 274         GBR_clear(F_old);
 275         GBR_clear(F_new);
 276         GBR_clear(F_saved);
 277         GBR_clear(mu_F[0]);
 278         GBR_clear(mu_F[1]);
 279         GBR_clear(two);
 280         GBR_clear(one);
 281
 282         isl_int_clear(tmp);
 283         isl_int_clear(mu[0]);
 284         isl_int_clear(mu[1]);
 285
 286         tab->basis = B;
 287
 288         return tab;
 289 }
 290
 291 struct isl_mat *isl_basic_set_reduced_basis(struct isl_basic_set *bset)
 292 {
 293         struct isl_mat *basis;
 294         struct isl_tab *tab;
 295
 296         isl_assert(bset->ctx, bset->n_eq == 0, return NULL);
 297
 298         tab = isl_tab_from_basic_set(bset);
 299         tab->basis = isl_mat_identity(bset->ctx, 1 + tab->n_var);
 300         tab = isl_tab_compute_reduced_basis(tab);
 301         if (!tab)
 302                 return NULL;
 303
 304         basis = isl_mat_copy(tab->basis);
 305
 306         isl_tab_free(tab);
 307
 308         return basis;
 309 }