barvinok_enumerate.cc

   1 #include <unistd.h>
   2 #include <stdlib.h>
   3 #include <barvinok/evalue.h>
   4 #include <barvinok/util.h>
   5 #include <barvinok/barvinok.h>
   6 #include "fdstream.h"
   7 #include "argp.h"
   8 #include "verify.h"
   9 #include "verif_ehrhart.h"
  10 #include "remove_equalities.h"
  11 #include "evalue_convert.h"
  12
  13 #undef CS   /* for Solaris 10 */
  14
  15 /* The input of this example program is the same as that of testehrhart
  16  * in the PolyLib distribution, i.e., a polytope in combined
  17  * data and parameter space, a context polytope in parameter space
  18  * and (optionally) the names of the parameters.
  19  * Both polytopes are in PolyLib notation.
  20  */
  21
  22 #define PRINT_STATS         (BV_OPT_LAST+1)
  23
  24 struct argp_option argp_options[] = {
  25     { "size",      'S' },
  26     { "series",    's', 0, 0, "compute rational generating function" },
  27     { "explicit",  'e', 0, 0, "convert rgf to psp" },
  28     { "verbose",    'v' },
  29     { "print-stats",        PRINT_STATS,  0,    0 },
  30     { 0 }
  31 };
  32
  33 struct arguments {
  34     int size;
  35     int series;
  36     int function;
  37     int verbose;
  38     int print_stats;
  39     struct verify_options    verify;
  40     struct convert_options   convert;
  41 };
  42
  43 static error_t parse_opt(int key, char *arg, struct argp_state *state)
  44 {
  45     struct arguments *options = (struct arguments*) state->input;
  46
  47     switch (key) {
  48     case ARGP_KEY_INIT:
  49         state->child_inputs[0] = options->verify.barvinok;
  50         state->child_inputs[1] = &options->verify;
  51         state->child_inputs[2] = &options->convert;
  52         options->size = 0;
  53         options->series = 0;
  54         options->function = 0;
  55         options->verbose = 0;
  56         options->print_stats = 0;
  57         break;
  58     case PRINT_STATS:
  59         options->print_stats = 1;
  60         break;
  61     case 'S':
  62         options->size = 1;
  63         break;
  64     case 'e':
  65         options->function = 1;
  66         /* fall through */
  67     case 's':
  68         options->series = 1;
  69         break;
  70     case 'v':
  71         options->verbose = 1;
  72         break;
  73     default:
  74         return ARGP_ERR_UNKNOWN;
  75     }
  76     return 0;
  77 }
  78
  79 struct skewed_gen_fun {
  80     gen_fun *gf;
  81     /* maps original space to space in which gf is defined */
  82     Matrix  *T;
  83     /* equalities in the original space that need to be satisfied for
  84      * gf to be valid
  85      */
  86     Matrix  *eq;
  87     /* divisibilities in the original space that need to be satisfied for
  88      * gf to be valid
  89      */
  90     Matrix  *div;
  91
  92     skewed_gen_fun(gen_fun *gf, Matrix *T, Matrix *eq, Matrix *div) :
  93                     gf(gf), T(T), eq(eq), div(div) {}
  94     ~skewed_gen_fun() {
  95         if (T)
  96             Matrix_Free(T);
  97         if (eq)
  98             Matrix_Free(eq);
  99         if (div)
 100             Matrix_Free(div);
 101         delete gf;
 102     }
 103
 104     void print(FILE *out, unsigned int nparam, char **param_name) const;
 105     operator evalue *() const {
 106         assert(T == NULL && eq == NULL); /* other cases not supported for now */
 107         return *gf;
 108     }
 109     void coefficient(Value* params, Value* c, barvinok_options *options) const;
 110 };
 111
 112 void skewed_gen_fun::print(FILE *out, unsigned int nparam,
 113                             char **param_name) const
 114 {
 115     fdostream os(dup(fileno(out)));
 116     if (T) {
 117         fprintf(out, "T:\n");
 118         Matrix_Print(out, P_VALUE_FMT, T);
 119     }
 120     if (eq) {
 121         fprintf(out, "eq:\n");
 122         Matrix_Print(out, P_VALUE_FMT, eq);
 123     }
 124     if (div) {
 125         fprintf(out, "div:\n");
 126         Matrix_Print(out, P_VALUE_FMT, div);
 127     }
 128     gf->print(os, nparam, param_name);
 129 }
 130
 131 void skewed_gen_fun::coefficient(Value* params, Value* c,
 132                                  barvinok_options *options) const
 133 {
 134     if (eq) {
 135         for (int i = 0; i < eq->NbRows; ++i) {
 136             Inner_Product(eq->p[i]+1, params, eq->NbColumns-2, eq->p[i]);
 137             if (value_notzero_p(eq->p[i][0])) {
 138                 value_set_si(*c, 0);
 139                 return;
 140             }
 141         }
 142     }
 143     if (div) {
 144         Value tmp;
 145         value_init(tmp);
 146         for (int i = 0; i < div->NbRows; ++i) {
 147             Inner_Product(div->p[i], params, div->NbColumns-1, &tmp);
 148             if (!mpz_divisible_p(tmp, div->p[i][div->NbColumns-1])) {
 149                 value_set_si(*c, 0);
 150                 return;
 151             }
 152         }
 153         value_clear(tmp);
 154     }
 155
 156     ZZ coeff;
 157     if (!T)
 158         coeff = gf->coefficient(params, options);
 159     else {
 160         Vector *p2 = Vector_Alloc(T->NbRows);
 161         Matrix_Vector_Product(T, params, p2->p);
 162         if (value_notone_p(p2->p[T->NbRows-1]))
 163             Vector_AntiScale(p2->p, p2->p, p2->p[T->NbRows-1], T->NbRows);
 164         coeff = gf->coefficient(p2->p, options);
 165         Vector_Free(p2);
 166     }
 167
 168     zz2value(coeff, *c);
 169 }
 170
 171 static int check_series(Polyhedron *S, Polyhedron *CS, skewed_gen_fun *gf,
 172                         int nparam, int pos, Value *z, verify_options *options)
 173 {
 174     int k;
 175     Value c, tmp;
 176     Value LB, UB;
 177
 178     value_init(c);
 179     value_init(tmp);
 180     value_init(LB);
 181     value_init(UB);
 182
 183     if (pos == nparam) {
 184         /* Computes the coefficient */
 185         gf->coefficient(&z[S->Dimension-nparam+1], &c, options->barvinok);
 186
 187         /* if c=0 we may be out of context. */
 188         /* scanning is useless in this case*/
 189
 190         if (options->print_all) {
 191             printf("EP( ");
 192             value_print(stdout,VALUE_FMT,z[S->Dimension-nparam+1]);
 193             for(k=S->Dimension-nparam+2;k<=S->Dimension;++k) {
 194                 printf(", ");
 195                 value_print(stdout,VALUE_FMT,z[k]);
 196             }
 197             printf(" ) = ");
 198             value_print(stdout,VALUE_FMT,c);
 199             printf(" ");
 200         }
 201
 202         /* Manually count the number of points */
 203         count_points(1,S,z,&tmp);
 204         if (options->print_all) {
 205             printf(", count = ");
 206             value_print(stdout, P_VALUE_FMT, tmp);
 207             printf(". ");
 208         }
 209
 210         if (value_ne(tmp,c)) {
 211             printf("\n");
 212             fflush(stdout);
 213             fprintf(stderr,"Error !\n");
 214             fprintf(stderr,"EP( ");
 215             value_print(stderr,VALUE_FMT,z[S->Dimension-nparam+1]);
 216             for (k=S->Dimension-nparam+2;k<=S->Dimension;++k) {
 217                 fprintf(stderr,", ");
 218                 value_print(stderr,VALUE_FMT,z[k]);
 219             }
 220             fprintf(stderr," ) should be ");
 221             value_print(stderr,VALUE_FMT,tmp);
 222             fprintf(stderr,", while EP eval gives ");
 223             value_print(stderr,VALUE_FMT,c);
 224             fprintf(stderr,".\n");
 225             if (!options->continue_on_error) {
 226                 value_clear(c); value_clear(tmp);
 227                 return 0;
 228             }
 229         } else if (options->print_all)
 230             printf("OK.\n");
 231     } else {
 232         int ok =
 233           !(lower_upper_bounds(1+pos, CS, &z[S->Dimension-nparam], &LB, &UB));
 234         assert(ok);
 235         for (value_assign(tmp,LB); value_le(tmp,UB); value_increment(tmp,tmp)) {
 236             if (!options->print_all) {
 237                 k = VALUE_TO_INT(tmp);
 238                 if(!pos && !(k % options->st)) {
 239                     printf("o");
 240                     fflush(stdout);
 241                 }
 242             }
 243             value_assign(z[pos+S->Dimension-nparam+1],tmp);
 244             if (!check_series(S, CS->next, gf, nparam, pos+1, z, options)) {
 245                 value_clear(c); value_clear(tmp);
 246                 value_clear(LB);
 247                 value_clear(UB);
 248                 return(0);
 249             }
 250         }
 251         value_set_si(z[pos+S->Dimension-nparam+1],0);
 252     }
 253
 254     value_clear(c);
 255     value_clear(tmp);
 256     value_clear(LB);
 257     value_clear(UB);
 258     return 1;
 259 }
 260
 261 static int verify(Polyhedron *P, Polyhedron *C, evalue *EP, skewed_gen_fun *gf,
 262                    arguments *options)
 263 {
 264     Polyhedron *CS, *S;
 265     Vector *p;
 266     int result = 0;
 267
 268     CS = check_poly_context_scan(P, &C, C->Dimension, &options->verify);
 269
 270     p = Vector_Alloc(P->Dimension+2);
 271     value_set_si(p->p[P->Dimension+1], 1);
 272
 273     /* S = scanning list of polyhedra */
 274     S = Polyhedron_Scan(P, C, options->verify.barvinok->MaxRays);
 275
 276     check_poly_init(C, &options->verify);
 277
 278     /******* CHECK NOW *********/
 279     if (S) {
 280         if (!options->series || options->function) {
 281             if (!check_poly_EP(S, CS, EP, 0, C->Dimension, 0, p->p,
 282                                 &options->verify))
 283                 result = -1;
 284         } else {
 285             if (!check_series(S, CS, gf, C->Dimension, 0, p->p, &options->verify))
 286                 result = -1;
 287         }
 288         Domain_Free(S);
 289     }
 290
 291     if (result == -1)
 292         fprintf(stderr,"Check failed !\n");
 293
 294     if (!options->verify.print_all)
 295         printf( "\n" );
 296
 297     Vector_Free(p);
 298     if (CS) {
 299         Domain_Free(CS);
 300         Domain_Free(C);
 301     }
 302
 303     return result;
 304 }
 305
 306 static void unimodular_complete(Matrix *M, int row)
 307 {
 308     Matrix *H, *Q, *U;
 309     left_hermite(M, &H, &Q, &U);
 310     Matrix_Free(H);
 311     Matrix_Free(U);
 312     for (int r = row; r < M->NbRows; ++r)
 313         Vector_Copy(Q->p[r], M->p[r], M->NbColumns);
 314     Matrix_Free(Q);
 315 }
 316
 317 /* frees M and Minv */
 318 static void apply_transformation(Polyhedron **P, Polyhedron **C,
 319                                  bool free_P, bool free_C,
 320                                  Matrix *M, Matrix *Minv, Matrix **inv,
 321                                  barvinok_options *options)
 322 {
 323     Polyhedron *T;
 324     Matrix *M2;
 325
 326     M2 = align_matrix(M, (*P)->Dimension + 1);
 327     T = *P;
 328     *P = Polyhedron_Preimage(*P, M2, options->MaxRays);
 329     if (free_P)
 330         Polyhedron_Free(T);
 331     Matrix_Free(M2);
 332
 333     T = *C;
 334     *C = Polyhedron_Preimage(*C, M, options->MaxRays);
 335     if (free_C)
 336         Polyhedron_Free(T);
 337
 338     Matrix_Free(M);
 339
 340     if (*inv) {
 341         Matrix *T = *inv;
 342         *inv = Matrix_Alloc(Minv->NbRows, T->NbColumns);
 343         Matrix_Product(Minv, T, *inv);
 344         Matrix_Free(T);
 345         Matrix_Free(Minv);
 346     } else
 347         *inv = Minv;
 348 }
 349
 350 static skewed_gen_fun *series(Polyhedron *P, Polyhedron* C,
 351                                 barvinok_options *options)
 352 {
 353     Polyhedron *C1, *C2;
 354     gen_fun *gf;
 355     Matrix *inv = NULL;
 356     Matrix *eq = NULL;
 357     Matrix *div = NULL;
 358     Polyhedron *PT = P;
 359
 360     /* Compute true context */
 361     C1 = Polyhedron_Project(P, C->Dimension);
 362     C2 = DomainIntersection(C, C1, options->MaxRays);
 363     Polyhedron_Free(C1);
 364
 365     POL_ENSURE_VERTICES(C2);
 366     if (C2->NbBid != 0) {
 367         Polyhedron *T;
 368         Matrix *M, *Minv, *M2;
 369         Matrix *CP;
 370         if (C2->NbEq || P->NbEq) {
 371             /* We remove all equalities to be sure all lines are unit vectors */
 372             Polyhedron *CT = C2;
 373             remove_all_equalities(&PT, &CT, &CP, NULL, C2->Dimension,
 374                                   options->MaxRays);
 375             if (CT != C2) {
 376                 Polyhedron_Free(C2);
 377                 C2 = CT;
 378             }
 379             if (CP) {
 380                 inv = left_inverse(CP, &eq);
 381                 Matrix_Free(CP);
 382
 383                 int d = 0;
 384                 Value tmp;
 385                 value_init(tmp);
 386                 div = Matrix_Alloc(inv->NbRows-1, inv->NbColumns+1);
 387                 for (int i = 0; i < inv->NbRows-1; ++i) {
 388                     Vector_Gcd(inv->p[i], inv->NbColumns, &tmp);
 389                     if (mpz_divisible_p(tmp,
 390                                         inv->p[inv->NbRows-1][inv->NbColumns-1]))
 391                         continue;
 392                     Vector_Copy(inv->p[i], div->p[d], inv->NbColumns);
 393                     value_assign(div->p[d][inv->NbColumns],
 394                                  inv->p[inv->NbRows-1][inv->NbColumns-1]);
 395                     ++d;
 396                 }
 397                 value_clear(tmp);
 398
 399                 if (!d) {
 400                     Matrix_Free(div);
 401                     div = NULL;
 402                 } else
 403                     div->NbRows = d;
 404             }
 405         }
 406         POL_ENSURE_VERTICES(C2);
 407
 408         /* Since we have "compressed" the parameters (in case there were
 409          * any equalities), the result is independent of the coordinates in the
 410          * coordinate subspace spanned by the lines.  We can therefore assume
 411          * these coordinates are zero and compute the inverse image of the map
 412          * from a lower dimensional space that adds zeros in the appropriate
 413          * places.
 414          */
 415         M = Matrix_Alloc(C2->Dimension+1, C2->Dimension-C2->NbBid+1);
 416         int k = 0;
 417         for (int i = 0; i < C2->NbBid; ++i) {
 418             int j = First_Non_Zero(C2->Ray[i]+1, C2->Dimension);
 419             assert(First_Non_Zero(C2->Ray[i]+1+j+1, C2->Dimension-j-1) == -1);
 420             for ( ; k < j; k++)
 421                 value_set_si(M->p[k+i][k], 1);
 422         }
 423         for ( ; k < C2->Dimension-C2->NbBid+1; k++)
 424             value_set_si(M->p[k+C2->NbBid][k], 1);
 425         Minv = Transpose(M);
 426
 427         apply_transformation(&PT, &C2, PT != P, C2 != C, M, Minv, &inv, options);
 428     }
 429     POL_ENSURE_VERTICES(C2);
 430     if (!Polyhedron_has_revlex_positive_rays(C2, C2->Dimension)) {
 431         Polyhedron *T;
 432         Matrix *Constraints;
 433         Matrix *H, *Q, *U;
 434         Constraints = Matrix_Alloc(C2->NbConstraints, C2->Dimension+1);
 435         for (int i = 0; i < C2->NbConstraints; ++i)
 436             Vector_Copy(C2->Constraint[i]+1, Constraints->p[i], C2->Dimension);
 437         left_hermite(Constraints, &H, &Q, &U);
 438         /* flip rows of Q */
 439         for (int i = 0; i < C2->Dimension/2; ++i)
 440             Vector_Exchange(Q->p[i], Q->p[C2->Dimension-1-i], C2->Dimension);
 441         Matrix_Free(H);
 442         Matrix_Free(U);
 443         Matrix *M = Matrix_Alloc(C2->Dimension+1, C2->Dimension+1);
 444         U = Matrix_Copy(Q);
 445         int ok = Matrix_Inverse(U, M);
 446         assert(ok);
 447         Matrix_Free(U);
 448
 449         apply_transformation(&PT, &C2, PT != P, C2 != C, M, Q, &inv, options);
 450     }
 451     gf = barvinok_series_with_options(PT, C2, options);
 452     Polyhedron_Free(C2);
 453     if (PT != P)
 454         Polyhedron_Free(PT);
 455     return new skewed_gen_fun(gf, inv, eq, div);
 456 }
 457
 458 int main(int argc, char **argv)
 459 {
 460     Polyhedron *A, *C;
 461     Matrix *M;
 462     evalue *EP = NULL;
 463     skewed_gen_fun *gf = NULL;
 464     char **param_name;
 465     int print_solution = 1;
 466     int result = 0;
 467     struct arguments options;
 468     static struct argp_child argp_children[] = {
 469         { &barvinok_argp,       0,      0,              0 },
 470         { &verify_argp,         0,      "verification",         BV_GRP_LAST+1 },
 471         { &convert_argp,        0,      "output conversion",    BV_GRP_LAST+2 },
 472         { 0 }
 473     };
 474     static struct argp argp = { argp_options, parse_opt, 0, 0, argp_children };
 475     struct barvinok_options *bv_options = barvinok_options_new_with_defaults();
 476
 477     options.verify.barvinok = bv_options;
 478     argp_parse(&argp, argc, argv, 0, 0, &options);
 479
 480     M = Matrix_Read();
 481     A = Constraints2Polyhedron(M, bv_options->MaxRays);
 482     Matrix_Free(M);
 483     M = Matrix_Read();
 484     C = Constraints2Polyhedron(M, bv_options->MaxRays);
 485     Matrix_Free(M);
 486     param_name = Read_ParamNames(stdin, C->Dimension);
 487
 488     if (options.verify.verify) {
 489         verify_options_set_range(&options.verify, A->Dimension);
 490         if (!options.verbose)
 491             print_solution = 0;
 492     }
 493
 494     if (print_solution && options.verbose) {
 495         Polyhedron_Print(stdout, P_VALUE_FMT, A);
 496         Polyhedron_Print(stdout, P_VALUE_FMT, C);
 497     }
 498
 499     if (options.series) {
 500         gf = series(A, C, bv_options);
 501         if (print_solution) {
 502             gf->print(stdout, C->Dimension, param_name);
 503             puts("");
 504         }
 505         if (options.function) {
 506             EP = *gf;
 507             if (print_solution)
 508                 print_evalue(stdout, EP, param_name);
 509         }
 510     } else {
 511         EP = barvinok_enumerate_with_options(A, C, bv_options);
 512         if (evalue_convert(EP, &options.convert, options.verbose, C->Dimension,
 513                            param_name))
 514             print_solution = 0;
 515         if (options.size)
 516             printf("\nSize: %d\n", evalue_size(EP));
 517     }
 518     if (print_solution)
 519         print_evalue(stdout, EP, param_name);
 520
 521     if (options.verify.verify) {
 522         options.verify.params = param_name;
 523         result = verify(A, C, EP, gf, &options);
 524     }
 525
 526     if (gf)
 527         delete gf;
 528     if (EP) {
 529         free_evalue_refs(EP);
 530         free(EP);
 531     }
 532
 533     if (options.print_stats)
 534         barvinok_stats_print(options.verify.barvinok->stats, stdout);
 535
 536     Free_ParamNames(param_name, C->Dimension);
 537     Polyhedron_Free(A);
 538     Polyhedron_Free(C);
 539     barvinok_options_free(bv_options);
 540     return result;
 541 }