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         ctx = tab->mat->ctx;
  64         dim = tab->n_var;
  65         B = tab->basis;
  66         if (!B)
  67                 return tab;
  68
  69         n_bounded = dim - tab->n_unbounded;
  70         if (n_bounded <= tab->n_zero + 1)
  71                 return tab;
  72
  73         isl_int_init(tmp);
  74         isl_int_init(mu[0]);
  75         isl_int_init(mu[1]);
  76
  77         GBR_init(alpha);
  78         GBR_init(F_old);
  79         GBR_init(F_new);
  80         GBR_init(F_saved);
  81         GBR_init(mu_F[0]);
  82         GBR_init(mu_F[1]);
  83         GBR_init(two);
  84         GBR_init(one);
  85
  86         b_tmp = isl_vec_alloc(ctx, dim);
  87         if (!b_tmp)
  88                 goto error;
  89
  90         F = isl_alloc_array(ctx, GBR_type, n_bounded);
  91         alpha_buffer[0] = isl_alloc_array(ctx, GBR_type, n_bounded);
  92         alpha_buffer[1] = isl_alloc_array(ctx, GBR_type, n_bounded);
  93         alpha_saved = alpha_buffer[0];
  94
  95         if (!F || !alpha_buffer[0] || !alpha_buffer[1])
  96                 goto error;
  97
  98         for (i = 0; i < n_bounded; ++i) {
  99                 GBR_init(F[i]);
 100                 GBR_init(alpha_buffer[0][i]);
 101                 GBR_init(alpha_buffer[1][i]);
 102         }
 103
 104         GBR_set_ui(two, 2);
 105         GBR_set_ui(one, 1);
 106
 107         lp = GBR_lp_init(tab);
 108         if (!lp)
 109                 goto error;
 110
 111         i = tab->n_zero;
 112
 113         GBR_lp_set_obj(lp, B->row[1+i]+1, dim);
 114         ctx->stats->gbr_solved_lps++;
 115         unbounded = GBR_lp_solve(lp);
 116         isl_assert(ctx, !unbounded, goto error);
 117         GBR_lp_get_obj_val(lp, &F[i]);
 118
 119         if (GBR_lt(F[i], one)) {
 120                 if (!GBR_is_zero(F[i])) {
 121                         empty = GBR_lp_cut(lp, B->row[1+i]+1);
 122                         if (empty)
 123                                 goto done;
 124                         GBR_set_ui(F[i], 0);
 125                 }
 126                 tab->n_zero++;
 127         }
 128
 129         do {
 130                 if (i+1 == tab->n_zero) {
 131                         GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim);
 132                         ctx->stats->gbr_solved_lps++;
 133                         unbounded = GBR_lp_solve(lp);
 134                         isl_assert(ctx, !unbounded, goto error);
 135                         GBR_lp_get_obj_val(lp, &F_new);
 136                         fixed = GBR_lp_is_fixed(lp);
 137                         GBR_set_ui(alpha, 0);
 138                 } else
 139                 if (use_saved) {
 140                         row = GBR_lp_next_row(lp);
 141                         GBR_set(F_new, F_saved);
 142                         fixed = fixed_saved;
 143                         GBR_set(alpha, alpha_saved[i]);
 144                 } else {
 145                         row = GBR_lp_add_row(lp, B->row[1+i]+1, dim);
 146                         GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim);
 147                         ctx->stats->gbr_solved_lps++;
 148                         unbounded = GBR_lp_solve(lp);
 149                         isl_assert(ctx, !unbounded, goto error);
 150                         GBR_lp_get_obj_val(lp, &F_new);
 151                         fixed = GBR_lp_is_fixed(lp);
 152
 153                         GBR_lp_get_alpha(lp, row, &alpha);
 154
 155                         if (i > 0)
 156                                 save_alpha(lp, row-i, i, alpha_saved);
 157
 158                         GBR_lp_del_row(lp);
 159                 }
 160                 GBR_set(F[i+1], F_new);
 161
 162                 GBR_floor(mu[0], alpha);
 163                 GBR_ceil(mu[1], alpha);
 164
 165                 if (isl_int_eq(mu[0], mu[1]))
 166                         isl_int_set(tmp, mu[0]);
 167                 else {
 168                         int j;
 169
 170                         for (j = 0; j <= 1; ++j) {
 171                                 isl_int_set(tmp, mu[j]);
 172                                 isl_seq_combine(b_tmp->el,
 173                                                 ctx->one, B->row[1+i+1]+1,
 174                                                 tmp, B->row[1+i]+1, dim);
 175                                 GBR_lp_set_obj(lp, b_tmp->el, dim);
 176                                 ctx->stats->gbr_solved_lps++;
 177                                 unbounded = GBR_lp_solve(lp);
 178                                 isl_assert(ctx, !unbounded, goto error);
 179                                 GBR_lp_get_obj_val(lp, &mu_F[j]);
 180                                 mu_fixed[j] = GBR_lp_is_fixed(lp);
 181                                 if (i > 0)
 182                                         save_alpha(lp, row-i, i, alpha_buffer[j]);
 183                         }
 184
 185                         if (GBR_lt(mu_F[0], mu_F[1]))
 186                                 j = 0;
 187                         else
 188                                 j = 1;
 189
 190                         isl_int_set(tmp, mu[j]);
 191                         GBR_set(F_new, mu_F[j]);
 192                         fixed = mu_fixed[j];
 193                         alpha_saved = alpha_buffer[j];
 194                 }
 195                 isl_seq_combine(B->row[1+i+1]+1, ctx->one, B->row[1+i+1]+1,
 196                                 tmp, B->row[1+i]+1, dim);
 197
 198                 if (i+1 == tab->n_zero && fixed) {
 199                         if (!GBR_is_zero(F[i+1])) {
 200                                 empty = GBR_lp_cut(lp, B->row[1+i+1]+1);
 201                                 if (empty)
 202                                         goto done;
 203                                 GBR_set_ui(F[i+1], 0);
 204                         }
 205                         tab->n_zero++;
 206                 }
 207
 208                 GBR_set(F_old, F[i]);
 209
 210                 use_saved = 0;
 211                 /* mu_F[0] = 4 * F_new; mu_F[1] = 3 * F_old */
 212                 GBR_set_ui(mu_F[0], 4);
 213                 GBR_mul(mu_F[0], mu_F[0], F_new);
 214                 GBR_set_ui(mu_F[1], 3);
 215                 GBR_mul(mu_F[1], mu_F[1], F_old);
 216                 if (GBR_lt(mu_F[0], mu_F[1])) {
 217                         B = isl_mat_swap_rows(B, 1 + i, 1 + i + 1);
 218                         if (i > tab->n_zero) {
 219                                 use_saved = 1;
 220                                 GBR_set(F_saved, F_new);
 221                                 fixed_saved = fixed;
 222                                 GBR_lp_del_row(lp);
 223                                 --i;
 224                         } else {
 225                                 GBR_set(F[tab->n_zero], F_new);
 226                                 if (ctx->gbr_only_first && GBR_lt(F[tab->n_zero], two))
 227                                         break;
 228
 229                                 if (fixed) {
 230                                         if (!GBR_is_zero(F[tab->n_zero])) {
 231                                                 empty = GBR_lp_cut(lp, B->row[1+tab->n_zero]+1);
 232                                                 if (empty)
 233                                                         goto done;
 234                                                 GBR_set_ui(F[tab->n_zero], 0);
 235                                         }
 236                                         tab->n_zero++;
 237                                 }
 238                         }
 239                 } else {
 240                         GBR_lp_add_row(lp, B->row[1+i]+1, dim);
 241                         ++i;
 242                 }
 243         } while (i < n_bounded - 1);
 244
 245         if (0) {
 246 done:
 247                 if (empty < 0) {
 248 error:
 249                         isl_mat_free(B);
 250                         B = NULL;
 251                 }
 252         }
 253
 254         GBR_lp_delete(lp);
 255
 256         if (alpha_buffer[1])
 257                 for (i = 0; i < n_bounded; ++i) {
 258                         GBR_clear(F[i]);
 259                         GBR_clear(alpha_buffer[0][i]);
 260                         GBR_clear(alpha_buffer[1][i]);
 261                 }
 262         free(F);
 263         free(alpha_buffer[0]);
 264         free(alpha_buffer[1]);
 265
 266         isl_vec_free(b_tmp);
 267
 268         GBR_clear(alpha);
 269         GBR_clear(F_old);
 270         GBR_clear(F_new);
 271         GBR_clear(F_saved);
 272         GBR_clear(mu_F[0]);
 273         GBR_clear(mu_F[1]);
 274         GBR_clear(two);
 275         GBR_clear(one);
 276
 277         isl_int_clear(tmp);
 278         isl_int_clear(mu[0]);
 279         isl_int_clear(mu[1]);
 280
 281         tab->basis = B;
 282
 283         return tab;
 284 }
 285
 286 struct isl_mat *isl_basic_set_reduced_basis(struct isl_basic_set *bset)
 287 {
 288         struct isl_mat *basis;
 289         struct isl_tab *tab;
 290
 291         isl_assert(bset->ctx, bset->n_eq == 0, return NULL);
 292
 293         tab = isl_tab_from_basic_set(bset);
 294         tab->basis = isl_mat_identity(bset->ctx, 1 + tab->n_var);
 295         tab = isl_tab_compute_reduced_basis(tab);
 296         if (!tab)
 297                 return NULL;
 298
 299         basis = isl_mat_copy(tab->basis);
 300
 301         isl_tab_free(tab);
 302
 303         return basis;
 304 }