series.cc

   1 #include <assert.h>
   2 #include <barvinok/barvinok.h>
   3 #include <barvinok/util.h>
   4 #include "genfun_constructor.h"
   5 #include "lattice_width.h"
   6 #include "remove_equalities.h"
   7
   8 using std::cerr;
   9 using std::endl;
  10
  11 static gen_fun *enumerate_series(Polyhedron *P, unsigned nparam,
  12                                     barvinok_options *options)
  13 {
  14     Matrix *CP = NULL;
  15     gen_fun *gf;
  16     Polyhedron *P_orig = P;
  17
  18     if (emptyQ2(P))
  19         return new gen_fun(Empty_Polyhedron(nparam));
  20
  21     if (P->NbEq != 0)
  22         remove_all_equalities(&P, NULL, &CP, NULL, nparam, options->MaxRays);
  23     assert(emptyQ2(P) || P->NbEq == 0);
  24     if (CP)
  25         nparam = CP->NbColumns-1;
  26
  27     if (nparam == 0) {
  28         Value c;
  29         value_init(c);
  30         barvinok_count_with_options(P, &c, options);
  31         gf = new gen_fun(c);
  32         value_clear(c);
  33     } else {
  34         POL_ENSURE_VERTICES(P);
  35         if (P->NbEq)
  36             gf = enumerate_series(P, nparam, options);
  37         else {
  38             gf_base *red;
  39             red = gf_base::create(Polyhedron_Project(P, nparam),
  40                                   P->Dimension, nparam, options);
  41             red->start_gf(P, options);
  42             gf = red->gf;
  43             delete red;
  44         }
  45     }
  46     if (CP) {
  47         gf->substitute(CP);
  48         Matrix_Free(CP);
  49     }
  50     if (P != P_orig)
  51         Polyhedron_Free(P);
  52     return gf;
  53 }
  54
  55 gen_fun *barvinok_enumerate_series(Polyhedron *P, unsigned nparam,
  56                                     barvinok_options *options)
  57 {
  58     if (emptyQ2(P))
  59         return new gen_fun(Empty_Polyhedron(nparam));
  60
  61     assert(!Polyhedron_is_unbounded(P, nparam, options->MaxRays));
  62     assert(P->NbBid == 0);
  63     assert(Polyhedron_has_revlex_positive_rays(P, nparam));
  64     return enumerate_series(P, nparam, options);
  65 }
  66
  67 gen_fun * barvinok_series_with_options(Polyhedron *P, Polyhedron* C,
  68                                        barvinok_options *options)
  69 {
  70     Polyhedron *CA;
  71     unsigned nparam = C->Dimension;
  72     gen_fun *gf;
  73
  74     CA = align_context(C, P->Dimension, options->MaxRays);
  75     P = DomainIntersection(P, CA, options->MaxRays);
  76     Polyhedron_Free(CA);
  77
  78     gf = barvinok_enumerate_series(P, nparam, options);
  79     Polyhedron_Free(P);
  80
  81     return gf;
  82 }
  83
  84 gen_fun * barvinok_series(Polyhedron *P, Polyhedron* C, unsigned MaxRays)
  85 {
  86     gen_fun *gf;
  87     barvinok_options *options = barvinok_options_new_with_defaults();
  88     options->MaxRays = MaxRays;
  89     gf = barvinok_series_with_options(P, C, options);
  90     barvinok_options_free(options);
  91     return gf;
  92 }
  93
  94 gen_fun* barvinok_enumerate_union_series_with_options(Polyhedron *D, Polyhedron* C,
  95                                                       barvinok_options *options)
  96 {
  97     Polyhedron *CA;
  98     gen_fun *gf = NULL, *gf2;
  99     unsigned nparam = C->Dimension;
 100
 101     CA = align_context(C, D->Dimension, options->MaxRays);
 102     D = DomainIntersection(D, CA, options->MaxRays);
 103     Polyhedron_Free(CA);
 104
 105     for (Polyhedron *P = D; P; P = P->next) {
 106         assert(P->Dimension == D->Dimension);
 107         gen_fun *P_gf;
 108
 109         P_gf = barvinok_enumerate_series(P, P->Dimension, options);
 110         if (!gf)
 111             gf = P_gf;
 112         else {
 113             gf->add_union(P_gf, options);
 114             delete P_gf;
 115         }
 116     }
 117     /* we actually only need the convex union of the parameter space
 118      * but the reducer classes currently expect a polyhedron in
 119      * the combined space
 120      */
 121     Polyhedron_Free(gf->context);
 122     gf->context = DomainConvex(D, options->MaxRays);
 123
 124     gf2 = gf->summate(D->Dimension - nparam, options);
 125
 126     delete gf;
 127     Domain_Free(D);
 128     return gf2;
 129 }
 130
 131 gen_fun* barvinok_enumerate_union_series(Polyhedron *D, Polyhedron* C,
 132                                          unsigned MaxRays)
 133 {
 134     gen_fun *gf;
 135     barvinok_options *options = barvinok_options_new_with_defaults();
 136     options->MaxRays = MaxRays;
 137     gf = barvinok_enumerate_union_series_with_options(D, C, options);
 138     barvinok_options_free(options);
 139     return gf;
 140 }
 141
 142 /* Unimodularly transform the polyhedron P, such that
 143  * the direction specified by dir corresponds to the last
 144  * variable in the transformed polyhedron.
 145  * The number of variables is given by the length of dir.
 146  */
 147 static Polyhedron *put_direction_last(Polyhedron *P, Vector *dir,
 148                                       unsigned MaxRays)
 149 {
 150     Polyhedron *R;
 151     Matrix *T;
 152     int n = dir->Size;
 153
 154     T = Matrix_Alloc(P->Dimension+1, P->Dimension+1);
 155     T->NbColumns = T->NbRows = n;
 156     Vector_Copy(dir->p, T->p[0], n);
 157     unimodular_complete(T, 1);
 158     Vector_Exchange(T->p[0], T->p[n-1], n);
 159     T->NbColumns = T->NbRows = P->Dimension+1;
 160     for (int j = n; j < P->Dimension+1; ++j)
 161         value_set_si(T->p[j][j], 1);
 162
 163     R = Polyhedron_Image(P, T, MaxRays);
 164     Matrix_Free(T);
 165
 166     return R;
 167 }
 168
 169 /* Do we need to continue shifting and subtracting?
 170  * i is the number of times we shifted so far
 171  * n is the number of coordinates projected out
 172  */
 173 static bool more_shifts_needed(int j, int n,
 174                                 gen_fun *S, gen_fun *S_divide, const vec_ZZ& up,
 175                                 barvinok_options *options)
 176 {
 177     bool empty;
 178     gen_fun *hp;
 179
 180     /* For the 2-dimensional case, we need to subtract at most once */
 181     if (n == 2 && j > 0)
 182         return false;
 183
 184     S_divide->shift(up);
 185
 186     /* Assume that we have to subtract at least once */
 187     if (j == 0)
 188         return true;
 189
 190     hp = S->Hadamard_product(S_divide, options);
 191
 192     empty = hp->is_zero();
 193     delete hp;
 194
 195     return !empty;
 196 }
 197
 198 static gen_fun *project(Polyhedron *P, unsigned n, barvinok_options *options,
 199                         int free_P);
 200
 201 /* Return gf of P projected on last dim(P)-n coordinates, i.e.,
 202  * project out the first n coordinates.
 203  *
 204  * Assumes P has no equalities.
 205  */
 206 static gen_fun *project_full_dim(Polyhedron *P, unsigned n,
 207         barvinok_options *options)
 208 {
 209     QQ one(1, 1);
 210     QQ mone(-1, 1);
 211     vec_ZZ up;
 212     gen_fun *gf = NULL;
 213     struct width_direction_array *dirs;
 214     Polyhedron *U;
 215
 216     if (n == 0)
 217         return barvinok_enumerate_series(P, P->Dimension, options);
 218
 219     up.SetLength(P->Dimension - (n-1));
 220     up[0] = 1;
 221     for (int i = 1; i < P->Dimension - (n-1); ++i)
 222         up[i] = 0;
 223
 224     if (n == 1) {
 225         gen_fun *S, *S_shift, *hp;
 226
 227         S = barvinok_enumerate_series(P, P->Dimension, options);
 228         S_shift = new gen_fun(S);
 229         S_shift->shift(up);
 230         hp = S->Hadamard_product(S_shift, options);
 231         S->add(mone, hp, options);
 232         delete S_shift;
 233         delete hp;
 234
 235         gf = S->summate(1, options);
 236         delete S;
 237
 238         return gf;
 239     }
 240
 241     U = Universe_Polyhedron(P->Dimension - n);
 242     dirs = Polyhedron_Lattice_Width_Directions(P, U, options);
 243     Polyhedron_Free(U);
 244
 245     for (int i = 0; i < dirs->n; ++i) {
 246         Polyhedron *Pi, *R;
 247         Polyhedron *CA;
 248         gen_fun *S, *S_shift, *S_divide, *sum;
 249
 250         CA = align_context(dirs->wd[i].domain, P->Dimension, options->MaxRays);
 251         R = DomainIntersection(P, CA, options->MaxRays);
 252         Polyhedron_Free(CA);
 253         assert(dirs->wd[i].dir->Size == n);
 254         Pi = put_direction_last(R, dirs->wd[i].dir, options->MaxRays);
 255         Polyhedron_Free(R);
 256
 257         S = project(Pi, n-1, options, 1);
 258
 259         S_shift = new gen_fun(S);
 260         S_divide = new gen_fun(S);
 261         S_divide->divide(up);
 262
 263         for (int j = 0; more_shifts_needed(j, n, S, S_divide, up, options); ++j) {
 264             gen_fun *hp;
 265
 266             S_shift->shift(up);
 267             hp = S->Hadamard_product(S_shift, options);
 268             S->add(mone, hp, options);
 269
 270             delete hp;
 271         }
 272
 273         sum = S->summate(1, options);
 274
 275         delete S_shift;
 276         delete S_divide;
 277         delete S;
 278
 279         if (!gf)
 280             gf = sum;
 281         else {
 282             gf->add(one, sum, options);
 283             delete sum;
 284         }
 285     }
 286     free_width_direction_array(dirs);
 287
 288     return gf;
 289 }
 290
 291 /* Return gf of P projected on last dim(P)-n coordinates, i.e.,
 292  * project out the first n coordinates.
 293  */
 294 static gen_fun *project(Polyhedron *P, unsigned n, barvinok_options *options,
 295                         int free_P)
 296 {
 297     Matrix *CP = NULL;
 298     gen_fun *proj;
 299     unsigned nparam = P->Dimension - n;
 300
 301     if (P->NbEq != 0) {
 302         Polyhedron *Q = P;
 303         remove_all_equalities(&P, NULL, &CP, NULL, nparam, options->MaxRays);
 304         if (CP)
 305             nparam = CP->NbColumns - 1;
 306         n = P->Dimension - nparam;
 307         if (free_P)
 308             Polyhedron_Free(Q);
 309         free_P = 1;
 310     }
 311
 312     if (emptyQ(P))
 313         proj = new gen_fun(Empty_Polyhedron(nparam));
 314     else
 315         proj = project_full_dim(P, n, options);
 316     if (CP) {
 317         proj->substitute(CP);
 318         Matrix_Free(CP);
 319     }
 320
 321     if (free_P)
 322         Polyhedron_Free(P);
 323
 324     return proj;
 325 }
 326
 327 gen_fun *barvinok_enumerate_e_series(Polyhedron *P,
 328                   unsigned exist, unsigned nparam, barvinok_options *options)
 329 {
 330     Polyhedron *P_orig = P;
 331     gen_fun *gf, *proj;
 332     unsigned nvar = P->Dimension - exist - nparam;
 333
 334     if (exist == 0)
 335         return barvinok_enumerate_series(P, nparam, options);
 336
 337     if (emptyQ(P))
 338         return new gen_fun(Empty_Polyhedron(nparam));
 339
 340     assert(!Polyhedron_is_unbounded(P, nparam, options->MaxRays));
 341     assert(P->NbBid == 0);
 342     assert(Polyhedron_has_revlex_positive_rays(P, nparam));
 343
 344     /* Move existentially quantified variables to the front.*/
 345     if (nvar) {
 346         Matrix *T;
 347         T = Matrix_Alloc(exist+nvar+nparam+1, nvar+exist+nparam+1);
 348         for (int i = 0; i < exist; ++i)
 349             value_set_si(T->p[i][nvar+i], 1);
 350         for (int i = 0; i < nvar; ++i)
 351             value_set_si(T->p[exist+i][i], 1);
 352         for (int i = 0; i < nparam+1; ++i)
 353             value_set_si(T->p[exist+nvar+i][nvar+exist+i], 1);
 354         P = Polyhedron_Image(P, T, options->MaxRays);
 355         Matrix_Free(T);
 356     }
 357     proj = project(P, exist, options, P != P_orig);
 358
 359     if (!nvar)
 360         gf = proj;
 361     else {
 362         gf = proj->summate(nvar, options);
 363         delete proj;
 364     }
 365     return gf;
 366 }