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, 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 (value_notzero_p(num[k]->coeff->p[rc->len-1-i]))
 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;
 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 = new int[rc->len];
 136                 pos[len++] = i;
 137             } else {
 138                 if ((*iter[i])->powers < (*iter[pos[0]])->powers) {
 139                     pos[0] = i;
 140                     len = 1;
 141                 } else if ((*iter[i])->powers == (*iter[pos[0]])->powers)
 142                     pos[len++] = i;
 143             }
 144         }
 145
 146         if (!len)
 147             return false;
 148
 149         powers = (*iter[pos[0]])->powers;
 150         for (int k = 0; k < n; ++k) {
 151             value2zz(num[k]->coeff->p[rc->len-1-pos[0]], tmp);
 152             mul(coeff[k], (*iter[pos[0]])->coeff, tmp);
 153         }
 154         ++iter[pos[0]];
 155         for (int i = 1; i < len; ++i) {
 156             for (int k = 0; k < n; ++k) {
 157                 value2zz(num[k]->coeff->p[rc->len-1-pos[i]], tmp);
 158                 mul(tmp, (*iter[pos[i]])->coeff, tmp);
 159                 add(coeff[k], coeff[k], tmp);
 160             }
 161             ++iter[pos[i]];
 162         }
 163
 164         delete [] pos;
 165         return true;
 166     }
 167     ~dpoly_r_scanner() {
 168         delete [] iter;
 169     }
 170 private:
 171     ZZ tmp;
 172 };
 173
 174 void reducer::reduce_canonical(const vec_QQ& c, const mat_ZZ& num,
 175                                 const mat_ZZ& den_f)
 176 {
 177     vec_QQ c2 = c;
 178     mat_ZZ num2 = num;
 179
 180     for (int i = 0; i < c2.length(); ++i) {
 181         c2[i].canonicalize();
 182         if (c2[i].n != 0)
 183             continue;
 184
 185         if (i < c2.length()-1) {
 186             num2[i] = num2[c2.length()-1];
 187             c2[i] = c2[c2.length()-1];
 188         }
 189         num2.SetDims(num2.NumRows()-1, num2.NumCols());
 190         c2.SetLength(c2.length()-1);
 191         --i;
 192     }
 193     reduce(c2, num2, den_f);
 194 }
 195
 196 void reducer::reduce(const vec_QQ& c, const mat_ZZ& num, const mat_ZZ& den_f)
 197 {
 198     assert(c.length() == num.NumRows());
 199     unsigned len = den_f.NumRows();  // number of factors in den
 200     vec_QQ c2 = c;
 201
 202     if (num.NumCols() == lower) {
 203         base(c, num, den_f);
 204         return;
 205     }
 206     assert(num.NumCols() > 1);
 207     assert(num.NumRows() > 0);
 208
 209     vec_ZZ den_s;
 210     mat_ZZ den_r;
 211     vec_ZZ num_s;
 212     mat_ZZ num_p;
 213
 214     split(num, num_s, num_p, den_f, den_s, den_r);
 215
 216     vec_ZZ den_p;
 217     den_p.SetLength(len);
 218
 219     ZZ sign(INIT_VAL, 1);
 220     normalize(sign, num_s, num_p, den_s, den_p, den_r);
 221     c2 *= sign;
 222
 223     int only_param = 0;     // k-r-s from text
 224     int no_param = 0;       // r from text
 225     for (int k = 0; k < len; ++k) {
 226         if (den_p[k] == 0)
 227             ++no_param;
 228         else if (den_s[k] == 0)
 229             ++only_param;
 230     }
 231     if (no_param == 0) {
 232         reduce(c2, num_p, den_r);
 233     } else {
 234         int k, l;
 235         mat_ZZ pden;
 236         pden.SetDims(only_param, den_r.NumCols());
 237
 238         for (k = 0, l = 0; k < len; ++k)
 239             if (den_s[k] == 0)
 240                 pden[l++] = den_r[k];
 241
 242         for (k = 0; k < len; ++k)
 243             if (den_p[k] == 0)
 244                 break;
 245
 246         dpoly **n = new dpoly *[num_s.length()];
 247         for (int i = 0; i < num_s.length(); ++i) {
 248             zz2value(num_s[i], tz);
 249             n[i] = new dpoly(no_param, tz);
 250             /* Search for other numerator (j) with same num_p.
 251              * If found, replace a[j]/b[j] * n[j] and a[i]/b[i] * n[i]
 252              * by 1/(b[j]*b[i]/g) * (a[j]*b[i]/g * n[j] + a[i]*b[j]/g * n[i])
 253              * where g = gcd(b[i], b[j].
 254              */
 255             for (int j = 0; j < i; ++j) {
 256                 if (num_p[i] != num_p[j])
 257                     continue;
 258                 ZZ g = GCD(c2[i].d, c2[j].d);
 259                 zz2value(c2[j].n * c2[i].d/g, tz);
 260                 *n[j] *= tz;
 261                 zz2value(c2[i].n * c2[j].d/g, tz);
 262                 *n[i] *= tz;
 263                 *n[j] += *n[i];
 264                 c2[j].n = 1;
 265                 c2[j].d *= c2[i].d/g;
 266                 delete n[i];
 267                 if (i < num_s.length()-1) {
 268                     num_s[i] = num_s[num_s.length()-1];
 269                     num_p[i] = num_p[num_s.length()-1];
 270                     c2[i] = c2[num_s.length()-1];
 271                 }
 272                 num_s.SetLength(num_s.length()-1);
 273                 c2.SetLength(c2.length()-1);
 274                 num_p.SetDims(num_p.NumRows()-1, num_p.NumCols());
 275                 --i;
 276                 break;
 277             }
 278         }
 279         zz2value(den_s[k], tz);
 280         dpoly D(no_param, tz, 1);
 281         for ( ; ++k < len; )
 282             if (den_p[k] == 0) {
 283                 zz2value(den_s[k], tz);
 284                 dpoly fact(no_param, tz, 1);
 285                 D *= fact;
 286             }
 287
 288         if (no_param + only_param == len) {
 289             vec_QQ q;
 290             q.SetLength(num_s.length());
 291             for (int i = 0; i < num_s.length(); ++i) {
 292                 mpq_set_si(tcount, 0, 1);
 293                 n[i]->div(D, tcount, 1);
 294
 295                 value2zz(mpq_numref(tcount), q[i].n);
 296                 value2zz(mpq_denref(tcount), q[i].d);
 297                 q[i] *= c2[i];
 298             }
 299             for (int i = q.length()-1; i >= 0; --i) {
 300                 if (q[i].n == 0) {
 301                     q[i] = q[q.length()-1];
 302                     num_p[i] = num_p[q.length()-1];
 303                     q.SetLength(q.length()-1);
 304                     num_p.SetDims(num_p.NumRows()-1, num_p.NumCols());
 305                 }
 306             }
 307
 308             if (q.length() != 0)
 309                 reduce(q, num_p, pden);
 310         } else {
 311             value_set_si(tz, 0);
 312             dpoly one(no_param, tz);
 313             dpoly_r *r = NULL;
 314
 315             for (k = 0; k < len; ++k) {
 316                 if (den_s[k] == 0 || den_p[k] == 0)
 317                     continue;
 318
 319                 zz2value(den_s[k], tz);
 320                 dpoly pd(no_param-1, tz, 1);
 321
 322                 int l;
 323                 for (l = 0; l < k; ++l)
 324                     if (den_r[l] == den_r[k])
 325                         break;
 326
 327                 if (!r)
 328                     r = new dpoly_r(one, pd, l, len);
 329                 else {
 330                     dpoly_r *nr = new dpoly_r(r, pd, l, len);
 331                     delete r;
 332                     r = nr;
 333                 }
 334             }
 335
 336             vec_QQ factor;
 337             factor.SetLength(c2.length());
 338             int common = pden.NumRows();
 339             dpoly_r *rc = r->div(D);
 340             for (int i = 0; i < num_s.length(); ++i) {
 341                 factor[i].d = c2[i].d;
 342                 factor[i].d *= rc->denom;
 343             }
 344
 345             dpoly_r_scanner scanner(n, num_s.length(), rc, len);
 346             int rows;
 347             while (scanner.next()) {
 348                 int i;
 349                 for (i = 0; i < num_s.length(); ++i)
 350                     if (scanner.coeff[i] != 0)
 351                         break;
 352                 if (i == num_s.length())
 353                     continue;
 354                 rows = common;
 355                 pden.SetDims(rows, pden.NumCols());
 356                 for (int k = 0; k < rc->dim; ++k) {
 357                     int n = scanner.powers[k];
 358                     if (n == 0)
 359                         continue;
 360                     pden.SetDims(rows+n, pden.NumCols());
 361                     for (int l = 0; l < n; ++l)
 362                         pden[rows+l] = den_r[k];
 363                     rows += n;
 364                 }
 365                 /* The denominators in factor are kept constant
 366                  * over all iterations of the enclosing while loop.
 367                  * The rational numbers in factor may therefore not be
 368                  * canonicalized.  Some may even be zero.
 369                  */
 370                 for (int i = 0; i < num_s.length(); ++i) {
 371                     factor[i].n = c2[i].n;
 372                     factor[i].n *= scanner.coeff[i];
 373                 }
 374                 reduce_canonical(factor, num_p, pden);
 375             }
 376
 377             delete rc;
 378             delete r;
 379         }
 380         for (int i = 0; i < num_s.length(); ++i)
 381             delete n[i];
 382         delete [] n;
 383     }
 384 }
 385
 386 void reducer::handle(const mat_ZZ& den, Value *V, const QQ& c,
 387                      unsigned long det, barvinok_options *options)
 388 {
 389     vec_QQ vc;
 390
 391     Matrix *points = Matrix_Alloc(det, dim);
 392     Matrix* Rays = zz2matrix(den);
 393     lattice_points_fixed(V, V, Rays, Rays, points, det);
 394     Matrix_Free(Rays);
 395     matrix2zz(points, vertex, points->NbRows, points->NbColumns);
 396     Matrix_Free(points);
 397
 398     vc.SetLength(vertex.NumRows());
 399     for (int i = 0; i < vc.length(); ++i)
 400         vc[i] = c;
 401
 402     reduce(vc, vertex, den);
 403 }
 404
 405 void split_one(const mat_ZZ& num, vec_ZZ& num_s, mat_ZZ& num_p,
 406                const mat_ZZ& den_f, vec_ZZ& den_s, mat_ZZ& den_r)
 407 {
 408     unsigned len = den_f.NumRows();  // number of factors in den
 409     unsigned d = num.NumCols() - 1;
 410
 411     den_s.SetLength(len);
 412     den_r.SetDims(len, d);
 413
 414     for (int r = 0; r < len; ++r) {
 415         den_s[r] = den_f[r][0];
 416         for (int k = 1; k <= d; ++k)
 417             den_r[r][k-1] = den_f[r][k];
 418     }
 419
 420     num_s.SetLength(num.NumRows());
 421     num_p.SetDims(num.NumRows(), d);
 422     for (int i = 0; i < num.NumRows(); ++i) {
 423         num_s[i] = num[i][0];
 424         for (int k = 1 ; k <= d; ++k)
 425             num_p[i][k-1] = num[i][k];
 426     }
 427 }
 428
 429 void icounter::base(const QQ& c, const vec_ZZ& num, const mat_ZZ& den_f)
 430 {
 431     zz2value(c.n, tn);
 432     zz2value(c.d, td);
 433
 434     unsigned len = den_f.NumRows();  // number of factors in den
 435
 436     if (len > 0) {
 437         int r;
 438         vec_ZZ den_s;
 439         den_s.SetLength(len);
 440         assert(num.length() == 1);
 441         ZZ num_s = num[0];
 442         for (r = 0; r < len; ++r)
 443             den_s[r] = den_f[r][0];
 444         int sign = (len % 2) ? -1 : 1;
 445
 446         zz2value(num_s, tz);
 447         dpoly n(len, tz);
 448         zz2value(den_s[0], tz);
 449         dpoly D(len, tz, 1);
 450         for (int k = 1; k < len; ++k) {
 451             zz2value(den_s[k], tz);
 452             dpoly fact(len, tz, 1);
 453             D *= fact;
 454         }
 455         mpq_set_si(tcount, 0, 1);
 456         n.div(D, tcount, 1);
 457         if (sign == -1)
 458             value_oppose(tn, tn);
 459
 460         mpz_mul(mpq_numref(tcount), mpq_numref(tcount), tn);
 461         mpz_mul(mpq_denref(tcount), mpq_denref(tcount), td);
 462         mpq_canonicalize(tcount);
 463     } else {
 464         value_assign(mpq_numref(tcount), tn);
 465         value_assign(mpq_denref(tcount), td);
 466     }
 467     mpq_add(count, count, tcount);
 468 }