reducer.cc

   1 #include <vector>
   2 #include <barvinok/util.h>
   3 #include "reducer.h"
   4 #include "lattice_point.h"
   5
   6 using std::vector;
   7 using std::cerr;
   8 using std::endl;
   9
  10 struct OrthogonalException Orthogonal;
  11
  12 void np_base::handle(const signed_cone& sc, barvinok_options *options)
  13 {
  14     assert(sc.rays.NumRows() == dim);
  15     factor.n *= sc.sign;
  16     handle(sc.rays, current_vertex, factor, sc.det, sc.closed, options);
  17     factor.n *= sc.sign;
  18 }
  19
  20 void np_base::start(Polyhedron *P, barvinok_options *options)
  21 {
  22     QQ factor(1, 1);
  23     for (;;) {
  24         try {
  25             init(P);
  26             for (int i = 0; i < P->NbRays; ++i) {
  27                 if (!value_pos_p(P->Ray[i][dim+1]))
  28                     continue;
  29
  30                 Polyhedron *C = supporting_cone(P, i);
  31                 do_vertex_cone(factor, C, P->Ray[i]+1, options);
  32             }
  33             break;
  34         } catch (OrthogonalException &e) {
  35             reset();
  36         }
  37     }
  38 }
  39
  40 /* input:
  41  *      f: the powers in the denominator for the remaining vars
  42  *            each row refers to a factor
  43  *      den_s: for each factor, the power of  (s+1)
  44  *      sign
  45  *      num_s: powers in the numerator corresponding to the summed vars
  46  *      num_p: powers in the numerator corresponding to the remaining vars
  47  * number of rays in cone: "dim" = "k"
  48  * length of each ray: "dim" = "d"
  49  * for now, it is assumed: k == d
  50  * output:
  51  *      den_p: for each factor
  52  *              0: independent of remaining vars
  53  *              1: power corresponds to corresponding row in f
  54  *
  55  * all inputs are subject to change
  56  */
  57 void normalize(ZZ& sign, vec_ZZ& num_s, mat_ZZ& num_p, vec_ZZ& den_s, vec_ZZ& den_p,
  58                mat_ZZ& f)
  59 {
  60     unsigned dim = f.NumRows();
  61     unsigned nparam = num_p.NumCols();
  62     unsigned nvar = dim - nparam;
  63
  64     int change = 0;
  65
  66     for (int j = 0; j < den_s.length(); ++j) {
  67         if (den_s[j] == 0) {
  68             den_p[j] = 1;
  69             continue;
  70         }
  71         int k;
  72         for (k = 0; k < nparam; ++k)
  73             if (f[j][k] != 0)
  74                 break;
  75         if (k < nparam) {
  76             den_p[j] = 1;
  77             if (den_s[j] > 0) {
  78                 f[j] = -f[j];
  79                 for (int i = 0; i < num_p.NumRows(); ++i)
  80                     num_p[i] += f[j];
  81             }
  82         } else
  83             den_p[j] = 0;
  84         if (den_s[j] > 0)
  85             change ^= 1;
  86         else {
  87             den_s[j] = abs(den_s[j]);
  88             for (int i = 0; i < num_p.NumRows(); ++i)
  89                 num_s[i] += den_s[j];
  90         }
  91     }
  92
  93     if (change)
  94         sign = -sign;
  95 }
  96
  97 void reducer::base(const vec_QQ& c, const mat_ZZ& num, const mat_ZZ& den_f)
  98 {
  99     for (int i = 0; i < num.NumRows(); ++i)
 100         base(c[i], num[i], den_f);
 101 }
 102
 103 struct dpoly_r_scanner {
 104     const dpoly_r *rc;
 105     const dpoly * const *num;
 106     int n;
 107     int dim;
 108     dpoly_r_term_list::iterator *iter;
 109     vector<int> powers;
 110     vec_ZZ coeff;
 111
 112     dpoly_r_scanner(const dpoly * const *num, int n, const dpoly_r *rc, int dim)
 113                     : num(num), rc(rc), n(n), dim(dim), powers(dim, 0) {
 114         coeff.SetLength(n);
 115         iter = new dpoly_r_term_list::iterator[rc->len];
 116         for (int i = 0; i < rc->len; ++i) {
 117             int k;
 118             for (k = 0; k < n; ++k)
 119                 if (num[k]->coeff[rc->len-1-i] != 0)
 120                     break;
 121             if (k < n)
 122                 iter[i] = rc->c[i].begin();
 123             else
 124                 iter[i] = rc->c[i].end();
 125         }
 126     }
 127     bool next() {
 128         int pos[rc->len];
 129         int len = 0;
 130
 131         for (int i = 0; i < rc->len; ++i) {
 132             if (iter[i] == rc->c[i].end())
 133                 continue;
 134             if (!len)
 135                 pos[len++] = i;
 136             else {
 137                 if ((*iter[i])->powers < (*iter[pos[0]])->powers) {
 138                     pos[0] = i;
 139                     len = 1;
 140                 } else if ((*iter[i])->powers == (*iter[pos[0]])->powers)
 141                     pos[len++] = i;
 142             }
 143         }
 144
 145         if (!len)
 146             return false;
 147
 148         powers = (*iter[pos[0]])->powers;
 149         for (int k = 0; k < n; ++k)
 150             mul(coeff[k], (*iter[pos[0]])->coeff, num[k]->coeff[rc->len-1-pos[0]]);
 151         ++iter[pos[0]];
 152         for (int i = 1; i < len; ++i) {
 153             for (int k = 0; k < n; ++k) {
 154                 mul(tmp, (*iter[pos[i]])->coeff, num[k]->coeff[rc->len-1-pos[i]]);
 155                 add(coeff[k], coeff[k], tmp);
 156             }
 157             ++iter[pos[i]];
 158         }
 159
 160         return true;
 161     }
 162     ~dpoly_r_scanner() {
 163         delete [] iter;
 164     }
 165 private:
 166     ZZ tmp;
 167 };
 168
 169 void reducer::reduce(const vec_QQ& c, const mat_ZZ& num, const mat_ZZ& den_f)
 170 {
 171     assert(c.length() == num.NumRows());
 172     unsigned len = den_f.NumRows();  // number of factors in den
 173     vec_QQ c2 = c;
 174
 175     if (num.NumCols() == lower) {
 176         base(c, num, den_f);
 177         return;
 178     }
 179     assert(num.NumCols() > 1);
 180     assert(num.NumRows() > 0);
 181
 182     vec_ZZ den_s;
 183     mat_ZZ den_r;
 184     vec_ZZ num_s;
 185     mat_ZZ num_p;
 186
 187     split(num, num_s, num_p, den_f, den_s, den_r);
 188
 189     vec_ZZ den_p;
 190     den_p.SetLength(len);
 191
 192     ZZ sign(INIT_VAL, 1);
 193     normalize(sign, num_s, num_p, den_s, den_p, den_r);
 194     c2 *= sign;
 195
 196     int only_param = 0;     // k-r-s from text
 197     int no_param = 0;       // r from text
 198     for (int k = 0; k < len; ++k) {
 199         if (den_p[k] == 0)
 200             ++no_param;
 201         else if (den_s[k] == 0)
 202             ++only_param;
 203     }
 204     if (no_param == 0) {
 205         reduce(c2, num_p, den_r);
 206     } else {
 207         int k, l;
 208         mat_ZZ pden;
 209         pden.SetDims(only_param, den_r.NumCols());
 210
 211         for (k = 0, l = 0; k < len; ++k)
 212             if (den_s[k] == 0)
 213                 pden[l++] = den_r[k];
 214
 215         for (k = 0; k < len; ++k)
 216             if (den_p[k] == 0)
 217                 break;
 218
 219         dpoly *n[num_s.length()];
 220         for (int i = 0; i < num_s.length(); ++i) {
 221             n[i] = new dpoly(no_param, num_s[i]);
 222             /* Search for other numerator (j) with same num_p.
 223              * If found, replace a[j]/b[j] * n[j] and a[i]/b[i] * n[i]
 224              * by 1/(b[j]*b[i]/g) * (a[j]*b[i]/g * n[j] + a[i]*b[j]/g * n[i])
 225              * where g = gcd(b[i], b[j].
 226              */
 227             for (int j = 0; j < i; ++j) {
 228                 if (num_p[i] != num_p[j])
 229                     continue;
 230                 ZZ g = GCD(c2[i].d, c2[j].d);
 231                 *n[j] *= c2[j].n * c2[i].d/g;
 232                 *n[i] *= c2[i].n * c2[j].d/g;
 233                 *n[j] += *n[i];
 234                 c2[j].n = 1;
 235                 c2[j].d *= c2[i].d/g;
 236                 delete n[i];
 237                 if (i < num_s.length()-1) {
 238                     num_s[i] = num_s[num_s.length()-1];
 239                     num_p[i] = num_p[num_s.length()-1];
 240                     c2[i] = c2[num_s.length()-1];
 241                 }
 242                 num_s.SetLength(num_s.length()-1);
 243                 c2.SetLength(c2.length()-1);
 244                 num_p.SetDims(num_p.NumRows()-1, num_p.NumCols());
 245                 --i;
 246                 break;
 247             }
 248         }
 249         dpoly D(no_param, den_s[k], 1);
 250         for ( ; ++k < len; )
 251             if (den_p[k] == 0) {
 252                 dpoly fact(no_param, den_s[k], 1);
 253                 D *= fact;
 254             }
 255
 256         if (no_param + only_param == len) {
 257             vec_QQ q;
 258             q.SetLength(num_s.length());
 259             for (int i = 0; i < num_s.length(); ++i) {
 260                 mpq_set_si(tcount, 0, 1);
 261                 n[i]->div(D, tcount, one);
 262
 263                 value2zz(mpq_numref(tcount), q[i].n);
 264                 value2zz(mpq_denref(tcount), q[i].d);
 265                 q[i] *= c2[i];
 266             }
 267             for (int i = q.length()-1; i >= 0; --i) {
 268                 if (q[i].n == 0) {
 269                     q[i] = q[q.length()-1];
 270                     num_p[i] = num_p[q.length()-1];
 271                     q.SetLength(q.length()-1);
 272                     num_p.SetDims(num_p.NumRows()-1, num_p.NumCols());
 273                 }
 274             }
 275
 276             if (q.length() != 0)
 277                 reduce(q, num_p, pden);
 278         } else {
 279             ZZ zz_zero(INIT_VAL, 0);
 280             dpoly one(no_param, zz_zero);
 281             dpoly_r *r = NULL;
 282
 283             for (k = 0; k < len; ++k) {
 284                 if (den_s[k] == 0 || den_p[k] == 0)
 285                     continue;
 286
 287                 dpoly pd(no_param-1, den_s[k], 1);
 288
 289                 int l;
 290                 for (l = 0; l < k; ++l)
 291                     if (den_r[l] == den_r[k])
 292                         break;
 293
 294                 if (!r)
 295                     r = new dpoly_r(one, pd, l, len);
 296                 else {
 297                     dpoly_r *nr = new dpoly_r(r, pd, l, len);
 298                     delete r;
 299                     r = nr;
 300                 }
 301             }
 302
 303             vec_QQ factor;
 304             factor.SetLength(c2.length());
 305             int common = pden.NumRows();
 306             dpoly_r *rc = r->div(D);
 307             for (int i = 0; i < num_s.length(); ++i) {
 308                 factor[i].d = c2[i].d;
 309                 factor[i].d *= rc->denom;
 310             }
 311
 312             dpoly_r_scanner scanner(n, num_s.length(), rc, len);
 313             int rows;
 314             while (scanner.next()) {
 315                 int i;
 316                 for (i = 0; i < num_s.length(); ++i)
 317                     if (scanner.coeff[i] != 0)
 318                         break;
 319                 if (i == num_s.length())
 320                     continue;
 321                 rows = common;
 322                 pden.SetDims(rows, pden.NumCols());
 323                 for (int k = 0; k < rc->dim; ++k) {
 324                     int n = scanner.powers[k];
 325                     if (n == 0)
 326                         continue;
 327                     pden.SetDims(rows+n, pden.NumCols());
 328                     for (int l = 0; l < n; ++l)
 329                         pden[rows+l] = den_r[k];
 330                     rows += n;
 331                 }
 332                 for (int i = 0; i < num_s.length(); ++i) {
 333                     factor[i].n = c2[i].n;
 334                     factor[i].n *= scanner.coeff[i];
 335                 }
 336                 reduce(factor, num_p, pden);
 337             }
 338
 339             delete rc;
 340             delete r;
 341         }
 342         for (int i = 0; i < num_s.length(); ++i)
 343             delete n[i];
 344     }
 345 }
 346
 347 void reducer::handle(const mat_ZZ& den, Value *V, const QQ& c, unsigned long det,
 348                      int *closed, barvinok_options *options)
 349 {
 350     vec_QQ vc;
 351
 352     lattice_point(V, den, vertex, det, closed);
 353
 354     vc.SetLength(vertex.NumRows());
 355     for (int i = 0; i < vc.length(); ++i)
 356         vc[i] = c;
 357
 358     reduce(vc, vertex, den);
 359 }
 360
 361 void split_one(const mat_ZZ& num, vec_ZZ& num_s, mat_ZZ& num_p,
 362                const mat_ZZ& den_f, vec_ZZ& den_s, mat_ZZ& den_r)
 363 {
 364     unsigned len = den_f.NumRows();  // number of factors in den
 365     unsigned d = num.NumCols() - 1;
 366
 367     den_s.SetLength(len);
 368     den_r.SetDims(len, d);
 369
 370     for (int r = 0; r < len; ++r) {
 371         den_s[r] = den_f[r][0];
 372         for (int k = 1; k <= d; ++k)
 373             den_r[r][k-1] = den_f[r][k];
 374     }
 375
 376     num_s.SetLength(num.NumRows());
 377     num_p.SetDims(num.NumRows(), d);
 378     for (int i = 0; i < num.NumRows(); ++i) {
 379         num_s[i] = num[i][0];
 380         for (int k = 1 ; k <= d; ++k)
 381             num_p[i][k-1] = num[i][k];
 382     }
 383 }
 384
 385 void normalize(ZZ& sign, ZZ& num, vec_ZZ& den)
 386 {
 387     unsigned dim = den.length();
 388
 389     int change = 0;
 390
 391     for (int j = 0; j < den.length(); ++j) {
 392         if (den[j] > 0)
 393             change ^= 1;
 394         else {
 395             den[j] = abs(den[j]);
 396             num += den[j];
 397         }
 398     }
 399     if (change)
 400         sign = -sign;
 401 }
 402
 403 void icounter::base(const QQ& c, const vec_ZZ& num, const mat_ZZ& den_f)
 404 {
 405     int r;
 406     unsigned len = den_f.NumRows();  // number of factors in den
 407     vec_ZZ den_s;
 408     den_s.SetLength(len);
 409     assert(num.length() == 1);
 410     ZZ num_s = num[0];
 411     for (r = 0; r < len; ++r)
 412         den_s[r] = den_f[r][0];
 413     ZZ sign = ZZ(INIT_VAL, 1);
 414     normalize(sign, num_s, den_s);
 415
 416     dpoly n(len, num_s);
 417     dpoly D(len, den_s[0], 1);
 418     for (int k = 1; k < len; ++k) {
 419         dpoly fact(len, den_s[k], 1);
 420         D *= fact;
 421     }
 422     mpq_set_si(tcount, 0, 1);
 423     n.div(D, tcount, one);
 424     zz2value(c.n, tn);
 425     if (sign == -1)
 426         value_oppose(tn, tn);
 427     zz2value(c.d, td);
 428     mpz_mul(mpq_numref(tcount), mpq_numref(tcount), tn);
 429     mpz_mul(mpq_denref(tcount), mpq_denref(tcount), td);
 430     mpq_canonicalize(tcount);
 431     mpq_add(count, count, tcount);
 432 }
 433
 434 void infinite_icounter::base(const QQ& c, const vec_ZZ& num, const mat_ZZ& den_f)
 435 {
 436     int r;
 437     unsigned len = den_f.NumRows();  // number of factors in den
 438     vec_ZZ den_s;
 439     den_s.SetLength(len);
 440     assert(num.length() == 1);
 441     ZZ num_s = num[0];
 442
 443     for (r = 0; r < len; ++r)
 444         den_s[r] = den_f[r][0];
 445     ZZ sign = ZZ(INIT_VAL, 1);
 446     normalize(sign, num_s, den_s);
 447
 448     dpoly n(len, num_s);
 449     dpoly D(len, den_s[0], 1);
 450     for (int k = 1; k < len; ++k) {
 451         dpoly fact(len, den_s[k], 1);
 452         D *= fact;
 453     }
 454
 455     Value tmp;
 456     mpq_t factor;
 457     mpq_init(factor);
 458     value_init(tmp);
 459     zz2value(c.n, tmp);
 460     if (sign == -1)
 461         value_oppose(tmp, tmp);
 462     value_assign(mpq_numref(factor), tmp);
 463     zz2value(c.d, tmp);
 464     value_assign(mpq_denref(factor), tmp);
 465
 466     n.div(D, count, factor);
 467
 468     value_clear(tmp);
 469     mpq_clear(factor);
 470 }