barvinok_enumerate.cc

   1 #include <assert.h>
   2 #include <unistd.h>
   3 #include <stdlib.h>
   4 #include <barvinok/evalue.h>
   5 #include <barvinok/util.h>
   6 #include <barvinok/barvinok.h>
   7 #include "argp.h"
   8 #include "progname.h"
   9 #include "verify.h"
  10 #include "verif_ehrhart.h"
  11 #include "remove_equalities.h"
  12 #include "evalue_convert.h"
  13 #include "conversion.h"
  14
  15 #undef CS   /* for Solaris 10 */
  16
  17 using std::cout;
  18 using std::endl;
  19
  20 /* The input of this example program is the same as that of testehrhart
  21  * in the PolyLib distribution, i.e., a polytope in combined
  22  * data and parameter space, a context polytope in parameter space
  23  * and (optionally) the names of the parameters.
  24  * Both polytopes are in PolyLib notation.
  25  */
  26
  27 #define PRINT_STATS         (BV_OPT_LAST+1)
  28
  29 struct argp_option argp_options[] = {
  30     { "size",      'S' },
  31     { "series",    's', 0, 0, "compute rational generating function" },
  32     { "explicit",  'e', 0, 0, "convert rgf to psp" },
  33     { "verbose",    'v' },
  34     { "print-stats",        PRINT_STATS,  0,    0 },
  35     { 0 }
  36 };
  37
  38 struct arguments {
  39     int size;
  40     int series;
  41     int function;
  42     int verbose;
  43     int print_stats;
  44     struct verify_options    verify;
  45     struct convert_options   convert;
  46 };
  47
  48 static error_t parse_opt(int key, char *arg, struct argp_state *state)
  49 {
  50     struct arguments *options = (struct arguments*) state->input;
  51
  52     switch (key) {
  53     case ARGP_KEY_INIT:
  54         state->child_inputs[0] = options->verify.barvinok;
  55         state->child_inputs[1] = &options->verify;
  56         state->child_inputs[2] = &options->convert;
  57         options->size = 0;
  58         options->series = 0;
  59         options->function = 0;
  60         options->verbose = 0;
  61         options->print_stats = 0;
  62         break;
  63     case PRINT_STATS:
  64         options->print_stats = 1;
  65         break;
  66     case 'S':
  67         options->size = 1;
  68         break;
  69     case 'e':
  70         options->function = 1;
  71         /* fall through */
  72     case 's':
  73         options->series = 1;
  74         break;
  75     case 'v':
  76         options->verbose = 1;
  77         break;
  78     default:
  79         return ARGP_ERR_UNKNOWN;
  80     }
  81     return 0;
  82 }
  83
  84 struct skewed_gen_fun {
  85     gen_fun *gf;
  86     /* maps original space to space in which gf is defined */
  87     Matrix  *T;
  88     /* equalities in the original space that need to be satisfied for
  89      * gf to be valid
  90      */
  91     Matrix  *eq;
  92     /* divisibilities in the original space that need to be satisfied for
  93      * gf to be valid
  94      */
  95     Matrix  *div;
  96
  97     skewed_gen_fun(gen_fun *gf, Matrix *T, Matrix *eq, Matrix *div) :
  98                     gf(gf), T(T), eq(eq), div(div) {}
  99     ~skewed_gen_fun() {
 100         if (T)
 101             Matrix_Free(T);
 102         if (eq)
 103             Matrix_Free(eq);
 104         if (div)
 105             Matrix_Free(div);
 106         delete gf;
 107     }
 108
 109     void print(std::ostream& os, unsigned int nparam, char **param_name) const;
 110     operator evalue *() const {
 111         assert(T == NULL && eq == NULL); /* other cases not supported for now */
 112         return *gf;
 113     }
 114     void coefficient(Value* params, Value* c, barvinok_options *options) const;
 115 };
 116
 117 void skewed_gen_fun::print(std::ostream& os, unsigned int nparam,
 118                             char **param_name) const
 119 {
 120     mat_ZZ m;
 121     if (T) {
 122         os << "T:" << endl;
 123         matrix2zz(T, m, T->NbRows, T->NbColumns);
 124         os << m << endl;
 125     }
 126     if (eq) {
 127         os << "eq:" << endl;
 128         matrix2zz(eq, m, eq->NbRows, eq->NbColumns);
 129         os << m << endl;
 130     }
 131     if (div) {
 132         os << "div:" << endl;
 133         matrix2zz(div, m, div->NbRows, div->NbColumns);
 134         os << m << endl;
 135     }
 136     gf->print(os, nparam, param_name);
 137 }
 138
 139 void skewed_gen_fun::coefficient(Value* params, Value* c,
 140                                  barvinok_options *options) const
 141 {
 142     if (eq) {
 143         for (int i = 0; i < eq->NbRows; ++i) {
 144             Inner_Product(eq->p[i]+1, params, eq->NbColumns-2, eq->p[i]);
 145             if (value_notzero_p(eq->p[i][0])) {
 146                 value_set_si(*c, 0);
 147                 return;
 148             }
 149         }
 150     }
 151     if (div) {
 152         Value tmp;
 153         value_init(tmp);
 154         for (int i = 0; i < div->NbRows; ++i) {
 155             Inner_Product(div->p[i], params, div->NbColumns-1, &tmp);
 156             if (!mpz_divisible_p(tmp, div->p[i][div->NbColumns-1])) {
 157                 value_set_si(*c, 0);
 158                 return;
 159             }
 160         }
 161         value_clear(tmp);
 162     }
 163
 164     ZZ coeff;
 165     if (!T)
 166         coeff = gf->coefficient(params, options);
 167     else {
 168         Vector *p2 = Vector_Alloc(T->NbRows);
 169         Matrix_Vector_Product(T, params, p2->p);
 170         if (value_notone_p(p2->p[T->NbRows-1]))
 171             Vector_AntiScale(p2->p, p2->p, p2->p[T->NbRows-1], T->NbRows);
 172         coeff = gf->coefficient(p2->p, options);
 173         Vector_Free(p2);
 174     }
 175
 176     zz2value(coeff, *c);
 177 }
 178
 179 static int check_series(Polyhedron *S, Polyhedron *CS, skewed_gen_fun *gf,
 180                         int nparam, int pos, Value *z, verify_options *options)
 181 {
 182     int k;
 183     Value c, tmp;
 184     Value LB, UB;
 185
 186     value_init(c);
 187     value_init(tmp);
 188     value_init(LB);
 189     value_init(UB);
 190
 191     if (pos == nparam) {
 192         /* Computes the coefficient */
 193         gf->coefficient(&z[S->Dimension-nparam+1], &c, options->barvinok);
 194
 195         /* if c=0 we may be out of context. */
 196         /* scanning is useless in this case*/
 197
 198         if (options->print_all) {
 199             printf("EP( ");
 200             value_print(stdout,VALUE_FMT,z[S->Dimension-nparam+1]);
 201             for(k=S->Dimension-nparam+2;k<=S->Dimension;++k) {
 202                 printf(", ");
 203                 value_print(stdout,VALUE_FMT,z[k]);
 204             }
 205             printf(" ) = ");
 206             value_print(stdout,VALUE_FMT,c);
 207             printf(" ");
 208         }
 209
 210         /* Manually count the number of points */
 211         count_points(1,S,z,&tmp);
 212         if (options->print_all) {
 213             printf(", count = ");
 214             value_print(stdout, P_VALUE_FMT, tmp);
 215             printf(". ");
 216         }
 217
 218         if (value_ne(tmp,c)) {
 219             printf("\n");
 220             fflush(stdout);
 221             fprintf(stderr,"Error !\n");
 222             fprintf(stderr,"EP( ");
 223             value_print(stderr,VALUE_FMT,z[S->Dimension-nparam+1]);
 224             for (k=S->Dimension-nparam+2;k<=S->Dimension;++k) {
 225                 fprintf(stderr,", ");
 226                 value_print(stderr,VALUE_FMT,z[k]);
 227             }
 228             fprintf(stderr," ) should be ");
 229             value_print(stderr,VALUE_FMT,tmp);
 230             fprintf(stderr,", while EP eval gives ");
 231             value_print(stderr,VALUE_FMT,c);
 232             fprintf(stderr,".\n");
 233             if (!options->continue_on_error) {
 234                 value_clear(c); value_clear(tmp);
 235                 return 0;
 236             }
 237         } else if (options->print_all)
 238             printf("OK.\n");
 239     } else {
 240         int ok =
 241           !(lower_upper_bounds(1+pos, CS, &z[S->Dimension-nparam], &LB, &UB));
 242         assert(ok);
 243         for (value_assign(tmp,LB); value_le(tmp,UB); value_increment(tmp,tmp)) {
 244             if (!options->print_all) {
 245                 k = VALUE_TO_INT(tmp);
 246                 if(!pos && !(k % options->st)) {
 247                     printf("o");
 248                     fflush(stdout);
 249                 }
 250             }
 251             value_assign(z[pos+S->Dimension-nparam+1],tmp);
 252             if (!check_series(S, CS->next, gf, nparam, pos+1, z, options)) {
 253                 value_clear(c); value_clear(tmp);
 254                 value_clear(LB);
 255                 value_clear(UB);
 256                 return(0);
 257             }
 258         }
 259         value_set_si(z[pos+S->Dimension-nparam+1],0);
 260     }
 261
 262     value_clear(c);
 263     value_clear(tmp);
 264     value_clear(LB);
 265     value_clear(UB);
 266     return 1;
 267 }
 268
 269 static int verify(Polyhedron *P, Polyhedron *C, evalue *EP, skewed_gen_fun *gf,
 270                    arguments *options)
 271 {
 272     Polyhedron *CS, *S;
 273     Vector *p;
 274     int result = 0;
 275
 276     CS = check_poly_context_scan(P, &C, C->Dimension, &options->verify);
 277
 278     p = Vector_Alloc(P->Dimension+2);
 279     value_set_si(p->p[P->Dimension+1], 1);
 280
 281     /* S = scanning list of polyhedra */
 282     S = Polyhedron_Scan(P, C, options->verify.barvinok->MaxRays);
 283
 284     check_poly_init(C, &options->verify);
 285
 286     /******* CHECK NOW *********/
 287     if (S) {
 288         if (!options->series || options->function) {
 289             if (!check_poly_EP(S, CS, EP, 0, C->Dimension, 0, p->p,
 290                                 &options->verify))
 291                 result = -1;
 292         } else {
 293             if (!check_series(S, CS, gf, C->Dimension, 0, p->p, &options->verify))
 294                 result = -1;
 295         }
 296         Domain_Free(S);
 297     }
 298
 299     if (result == -1)
 300         fprintf(stderr,"Check failed !\n");
 301
 302     if (!options->verify.print_all)
 303         printf( "\n" );
 304
 305     Vector_Free(p);
 306     if (CS) {
 307         Domain_Free(CS);
 308         Domain_Free(C);
 309     }
 310
 311     return result;
 312 }
 313
 314 /* frees M and Minv */
 315 static void apply_transformation(Polyhedron **P, Polyhedron **C,
 316                                  bool free_P, bool free_C,
 317                                  Matrix *M, Matrix *Minv, Matrix **inv,
 318                                  barvinok_options *options)
 319 {
 320     Polyhedron *T;
 321     Matrix *M2;
 322
 323     M2 = align_matrix(M, (*P)->Dimension + 1);
 324     T = *P;
 325     *P = Polyhedron_Preimage(*P, M2, options->MaxRays);
 326     if (free_P)
 327         Polyhedron_Free(T);
 328     Matrix_Free(M2);
 329
 330     T = *C;
 331     *C = Polyhedron_Preimage(*C, M, options->MaxRays);
 332     if (free_C)
 333         Polyhedron_Free(T);
 334
 335     Matrix_Free(M);
 336
 337     if (*inv) {
 338         Matrix *T = *inv;
 339         *inv = Matrix_Alloc(Minv->NbRows, T->NbColumns);
 340         Matrix_Product(Minv, T, *inv);
 341         Matrix_Free(T);
 342         Matrix_Free(Minv);
 343     } else
 344         *inv = Minv;
 345 }
 346
 347 /* Since we have "compressed" the parameters (in case there were
 348  * any equalities), the result is independent of the coordinates in the
 349  * coordinate subspace spanned by the lines.  We can therefore assume
 350  * these coordinates are zero and compute the inverse image of the map
 351  * from a lower dimensional space that adds zeros in the appropriate
 352  * places.
 353  */
 354 static void remove_lines(Polyhedron *C, Matrix **M, Matrix **Minv)
 355 {
 356     Matrix *L = Matrix_Alloc(C->Dimension+1, C->Dimension+1);
 357     for (int r = 0; r < C->NbBid; ++r)
 358         Vector_Copy(C->Ray[r]+1, L->p[r], C->Dimension);
 359     unimodular_complete(L, C->NbBid);
 360     assert(value_one_p(L->p[C->Dimension][C->Dimension]));
 361     assert(First_Non_Zero(L->p[C->Dimension], C->Dimension) == -1);
 362     Matrix_Transposition(L);
 363     assert(First_Non_Zero(L->p[C->Dimension], C->Dimension) == -1);
 364
 365     *M = Matrix_Alloc(C->Dimension+1, C->Dimension-C->NbBid+1);
 366     for (int i = 0; i < C->Dimension+1; ++i)
 367         Vector_Copy(L->p[i]+C->NbBid, (*M)->p[i], C->Dimension-C->NbBid+1);
 368
 369     Matrix *Linv = Matrix_Alloc(C->Dimension+1, C->Dimension+1);
 370     int ok = Matrix_Inverse(L, Linv);
 371     assert(ok);
 372     Matrix_Free(L);
 373
 374     *Minv = Matrix_Alloc(C->Dimension-C->NbBid+1, C->Dimension+1);
 375     for (int i = C->NbBid; i < C->Dimension+1; ++i)
 376         Vector_AntiScale(Linv->p[i], (*Minv)->p[i-C->NbBid],
 377                          Linv->p[C->Dimension][C->Dimension], C->Dimension+1);
 378     Matrix_Free(Linv);
 379 }
 380
 381 static skewed_gen_fun *series(Polyhedron *P, Polyhedron* C,
 382                                 barvinok_options *options)
 383 {
 384     Polyhedron *C1, *C2;
 385     gen_fun *gf;
 386     Matrix *inv = NULL;
 387     Matrix *eq = NULL;
 388     Matrix *div = NULL;
 389     Polyhedron *PT = P;
 390
 391     /* Compute true context */
 392     C1 = Polyhedron_Project(P, C->Dimension);
 393     C2 = DomainIntersection(C, C1, options->MaxRays);
 394     Polyhedron_Free(C1);
 395
 396     POL_ENSURE_VERTICES(C2);
 397     if (C2->NbBid != 0) {
 398         Polyhedron *T;
 399         Matrix *M, *Minv, *M2;
 400         Matrix *CP;
 401         if (C2->NbEq || P->NbEq) {
 402             /* We remove all equalities to be sure all lines are unit vectors */
 403             Polyhedron *CT = C2;
 404             remove_all_equalities(&PT, &CT, &CP, NULL, C2->Dimension,
 405                                   options->MaxRays);
 406             if (CT != C2) {
 407                 Polyhedron_Free(C2);
 408                 C2 = CT;
 409             }
 410             if (CP) {
 411                 inv = left_inverse(CP, &eq);
 412                 Matrix_Free(CP);
 413
 414                 int d = 0;
 415                 Value tmp;
 416                 value_init(tmp);
 417                 div = Matrix_Alloc(inv->NbRows-1, inv->NbColumns+1);
 418                 for (int i = 0; i < inv->NbRows-1; ++i) {
 419                     Vector_Gcd(inv->p[i], inv->NbColumns, &tmp);
 420                     if (mpz_divisible_p(tmp,
 421                                         inv->p[inv->NbRows-1][inv->NbColumns-1]))
 422                         continue;
 423                     Vector_Copy(inv->p[i], div->p[d], inv->NbColumns);
 424                     value_assign(div->p[d][inv->NbColumns],
 425                                  inv->p[inv->NbRows-1][inv->NbColumns-1]);
 426                     ++d;
 427                 }
 428                 value_clear(tmp);
 429
 430                 if (!d) {
 431                     Matrix_Free(div);
 432                     div = NULL;
 433                 } else
 434                     div->NbRows = d;
 435             }
 436         }
 437         POL_ENSURE_VERTICES(C2);
 438
 439         if (C2->NbBid) {
 440             Matrix *M, *Minv;
 441             remove_lines(C2, &M, &Minv);
 442             apply_transformation(&PT, &C2, PT != P, C2 != C, M, Minv, &inv,
 443                                  options);
 444         }
 445     }
 446     POL_ENSURE_VERTICES(C2);
 447     if (!Polyhedron_has_revlex_positive_rays(C2, C2->Dimension)) {
 448         Polyhedron *T;
 449         Matrix *Constraints;
 450         Matrix *H, *Q, *U;
 451         Constraints = Matrix_Alloc(C2->NbConstraints, C2->Dimension+1);
 452         for (int i = 0; i < C2->NbConstraints; ++i)
 453             Vector_Copy(C2->Constraint[i]+1, Constraints->p[i], C2->Dimension);
 454         left_hermite(Constraints, &H, &Q, &U);
 455         Matrix_Free(Constraints);
 456         /* flip rows of Q */
 457         for (int i = 0; i < C2->Dimension/2; ++i)
 458             Vector_Exchange(Q->p[i], Q->p[C2->Dimension-1-i], C2->Dimension);
 459         Matrix_Free(H);
 460         Matrix_Free(U);
 461         Matrix *M = Matrix_Alloc(C2->Dimension+1, C2->Dimension+1);
 462         U = Matrix_Copy(Q);
 463         int ok = Matrix_Inverse(U, M);
 464         assert(ok);
 465         Matrix_Free(U);
 466
 467         apply_transformation(&PT, &C2, PT != P, C2 != C, M, Q, &inv, options);
 468     }
 469     gf = barvinok_series_with_options(PT, C2, options);
 470     Polyhedron_Free(C2);
 471     if (PT != P)
 472         Polyhedron_Free(PT);
 473     return new skewed_gen_fun(gf, inv, eq, div);
 474 }
 475
 476 int main(int argc, char **argv)
 477 {
 478     Polyhedron *A, *C;
 479     Matrix *M;
 480     evalue *EP = NULL;
 481     skewed_gen_fun *gf = NULL;
 482     char **param_name;
 483     int print_solution = 1;
 484     int result = 0;
 485     struct arguments options;
 486     static struct argp_child argp_children[] = {
 487         { &barvinok_argp,       0,      0,              0 },
 488         { &verify_argp,         0,      "verification",         BV_GRP_LAST+1 },
 489         { &convert_argp,        0,      "output conversion",    BV_GRP_LAST+2 },
 490         { 0 }
 491     };
 492     static struct argp argp = { argp_options, parse_opt, 0, 0, argp_children };
 493     struct barvinok_options *bv_options = barvinok_options_new_with_defaults();
 494
 495     options.verify.barvinok = bv_options;
 496     set_program_name(argv[0]);
 497     argp_parse(&argp, argc, argv, 0, 0, &options);
 498
 499     M = Matrix_Read();
 500     assert(M);
 501     A = Constraints2Polyhedron(M, bv_options->MaxRays);
 502     Matrix_Free(M);
 503     M = Matrix_Read();
 504     assert(M);
 505     C = Constraints2Polyhedron(M, bv_options->MaxRays);
 506     Matrix_Free(M);
 507     param_name = Read_ParamNames(stdin, C->Dimension);
 508
 509     if (options.verify.verify) {
 510         verify_options_set_range(&options.verify, A->Dimension);
 511         if (!options.verbose)
 512             print_solution = 0;
 513     }
 514
 515     if (print_solution && options.verbose) {
 516         Polyhedron_Print(stdout, P_VALUE_FMT, A);
 517         Polyhedron_Print(stdout, P_VALUE_FMT, C);
 518     }
 519
 520     if (options.series) {
 521         gf = series(A, C, bv_options);
 522         if (print_solution) {
 523             gf->print(cout, C->Dimension, param_name);
 524             puts("");
 525         }
 526         if (options.function) {
 527             EP = *gf;
 528             if (print_solution)
 529                 print_evalue(stdout, EP, param_name);
 530         }
 531     } else {
 532         EP = barvinok_enumerate_with_options(A, C, bv_options);
 533         if (evalue_convert(EP, &options.convert, options.verbose, C->Dimension,
 534                            param_name))
 535             print_solution = 0;
 536         if (options.size)
 537             printf("\nSize: %d\n", evalue_size(EP));
 538         if (print_solution)
 539             print_evalue(stdout, EP, param_name);
 540     }
 541
 542     if (options.verify.verify) {
 543         options.verify.params = param_name;
 544         result = verify(A, C, EP, gf, &options);
 545     }
 546
 547     if (gf)
 548         delete gf;
 549     if (EP)
 550         evalue_free(EP);
 551
 552     if (options.print_stats)
 553         barvinok_stats_print(options.verify.barvinok->stats, stdout);
 554
 555     Free_ParamNames(param_name, C->Dimension);
 556     Polyhedron_Free(A);
 557     Polyhedron_Free(C);
 558     barvinok_options_free(bv_options);
 559     return result;
 560 }