ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2015 Johannes Gutenberg University Mainz, Germany
   7  *
   8  *  This program is free software; you can redistribute it and/or modify
   9  *  it under the terms of the GNU General Public License as published by
  10  *  the Free Software Foundation; either version 2 of the License, or
  11  *  (at your option) any later version.
  12  *
  13  *  This program is distributed in the hope that it will be useful,
  14  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  15  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  16  *  GNU General Public License for more details.
  17  *
  18  *  You should have received a copy of the GNU General Public License
  19  *  along with this program; if not, write to the Free Software
  20  *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  21  */
  22
  23 #include "ncmul.h"
  24 #include "ex.h"
  25 #include "add.h"
  26 #include "mul.h"
  27 #include "clifford.h"
  28 #include "matrix.h"
  29 #include "archive.h"
  30 #include "indexed.h"
  31 #include "utils.h"
  32
  33 #include <algorithm>
  34 #include <iostream>
  35 #include <stdexcept>
  36
  37 namespace GiNaC {
  38
  39 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(ncmul, exprseq,
  40   print_func<print_context>(&ncmul::do_print).
  41   print_func<print_tree>(&ncmul::do_print_tree).
  42   print_func<print_csrc>(&ncmul::do_print_csrc).
  43   print_func<print_python_repr>(&ncmul::do_print_csrc))
  44
  45
  46 //////////
  47 // default constructor
  48 //////////
  49
  50 ncmul::ncmul()
  51 {
  52 }
  53
  54 //////////
  55 // other constructors
  56 //////////
  57
  58 // public
  59
  60 ncmul::ncmul(const ex & lh, const ex & rh) : inherited{lh,rh}
  61 {
  62 }
  63
  64 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited{f1,f2,f3}
  65 {
  66 }
  67
  68 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  69              const ex & f4) : inherited{f1,f2,f3,f4}
  70 {
  71 }
  72
  73 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  74              const ex & f4, const ex & f5) : inherited{f1,f2,f3,f4,f5}
  75 {
  76 }
  77
  78 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  79              const ex & f4, const ex & f5, const ex & f6) : inherited{f1,f2,f3,f4,f5,f6}
  80 {
  81 }
  82
  83 ncmul::ncmul(const exvector & v) : inherited(v)
  84 {
  85 }
  86
  87 ncmul::ncmul(exvector && v) : inherited(std::move(v))
  88 {
  89 }
  90
  91 //////////
  92 // archiving
  93 //////////
  94
  95
  96 //////////
  97 // functions overriding virtual functions from base classes
  98 //////////
  99
 100 // public
 101
 102 void ncmul::do_print(const print_context & c, unsigned level) const
 103 {
 104         printseq(c, '(', '*', ')', precedence(), level);
 105 }
 106
 107 void ncmul::do_print_csrc(const print_context & c, unsigned level) const
 108 {
 109         c.s << class_name();
 110         printseq(c, '(', ',', ')', precedence(), precedence());
 111 }
 112
 113 bool ncmul::info(unsigned inf) const
 114 {
 115         return inherited::info(inf);
 116 }
 117
 118 typedef std::vector<std::size_t> uintvector;
 119
 120 ex ncmul::expand(unsigned options) const
 121 {
 122         // First, expand the children
 123         exvector v = expandchildren(options);
 124         const exvector &expanded_seq = v.empty() ? this->seq : v;
 125
 126         // Now, look for all the factors that are sums and remember their
 127         // position and number of terms.
 128         uintvector positions_of_adds(expanded_seq.size());
 129         uintvector number_of_add_operands(expanded_seq.size());
 130
 131         size_t number_of_adds = 0;
 132         size_t number_of_expanded_terms = 1;
 133
 134         size_t current_position = 0;
 135         for (auto & it : expanded_seq) {
 136                 if (is_exactly_a<add>(it)) {
 137                         positions_of_adds[number_of_adds] = current_position;
 138                         size_t num_ops = it.nops();
 139                         number_of_add_operands[number_of_adds] = num_ops;
 140                         number_of_expanded_terms *= num_ops;
 141                         number_of_adds++;
 142                 }
 143                 ++current_position;
 144         }
 145
 146         // If there are no sums, we are done
 147         if (number_of_adds == 0) {
 148                 if (!v.empty())
 149                         return dynallocate<ncmul>(std::move(v)).setflag(options == 0 ? status_flags::expanded : 0);
 150                 else
 151                         return *this;
 152         }
 153
 154         // Now, form all possible products of the terms of the sums with the
 155         // remaining factors, and add them together
 156         exvector distrseq;
 157         distrseq.reserve(number_of_expanded_terms);
 158
 159         uintvector k(number_of_adds);
 160
 161         /* Rename indices in the static members of the product */
 162         exvector expanded_seq_mod;
 163         size_t j = 0;
 164         exvector va;
 165
 166         for (size_t i=0; i<expanded_seq.size(); i++) {
 167                 if (i == positions_of_adds[j]) {
 168                         expanded_seq_mod.push_back(_ex1);
 169                         j++;
 170                 } else {
 171                         expanded_seq_mod.push_back(rename_dummy_indices_uniquely(va, expanded_seq[i], true));
 172                 }
 173         }
 174
 175         while (true) {
 176                 exvector term = expanded_seq_mod;
 177                 for (size_t i=0; i<number_of_adds; i++) {
 178                         term[positions_of_adds[i]] = rename_dummy_indices_uniquely(va, expanded_seq[positions_of_adds[i]].op(k[i]), true);
 179                 }
 180
 181                 distrseq.push_back(dynallocate<ncmul>(std::move(term)).setflag(options == 0 ? status_flags::expanded : 0));
 182
 183                 // increment k[]
 184                 int l = number_of_adds-1;
 185                 while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
 186                         k[l] = 0;
 187                         l--;
 188                 }
 189                 if (l<0)
 190                         break;
 191         }
 192
 193         return dynallocate<add>(distrseq).setflag(options == 0 ? status_flags::expanded : 0);
 194 }
 195
 196 int ncmul::degree(const ex & s) const
 197 {
 198         if (is_equal(ex_to<basic>(s)))
 199                 return 1;
 200
 201         // Sum up degrees of factors
 202         int deg_sum = 0;
 203         for (auto & i : seq)
 204                 deg_sum += i.degree(s);
 205         return deg_sum;
 206 }
 207
 208 int ncmul::ldegree(const ex & s) const
 209 {
 210         if (is_equal(ex_to<basic>(s)))
 211                 return 1;
 212
 213         // Sum up degrees of factors
 214         int deg_sum = 0;
 215         for (auto & i : seq)
 216                 deg_sum += i.degree(s);
 217         return deg_sum;
 218 }
 219
 220 ex ncmul::coeff(const ex & s, int n) const
 221 {
 222         if (is_equal(ex_to<basic>(s)))
 223                 return n==1 ? _ex1 : _ex0;
 224
 225         exvector coeffseq;
 226         coeffseq.reserve(seq.size());
 227
 228         if (n == 0) {
 229                 // product of individual coeffs
 230                 // if a non-zero power of s is found, the resulting product will be 0
 231                 for (auto & it : seq)
 232                         coeffseq.push_back(it.coeff(s,n));
 233                 return dynallocate<ncmul>(std::move(coeffseq));
 234         }
 235
 236         bool coeff_found = false;
 237         for (auto & i : seq) {
 238                 ex c = i.coeff(s,n);
 239                 if (c.is_zero()) {
 240                         coeffseq.push_back(i);
 241                 } else {
 242                         coeffseq.push_back(c);
 243                         coeff_found = true;
 244                 }
 245         }
 246
 247         if (coeff_found)
 248                 return dynallocate<ncmul>(std::move(coeffseq));
 249
 250         return _ex0;
 251 }
 252
 253 size_t ncmul::count_factors(const ex & e) const
 254 {
 255         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 256                 (is_exactly_a<ncmul>(e))) {
 257                 size_t factors=0;
 258                 for (size_t i=0; i<e.nops(); i++)
 259                         factors += count_factors(e.op(i));
 260
 261                 return factors;
 262         }
 263         return 1;
 264 }
 265
 266 void ncmul::append_factors(exvector & v, const ex & e) const
 267 {
 268         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 269                 (is_exactly_a<ncmul>(e))) {
 270                 for (size_t i=0; i<e.nops(); i++)
 271                         append_factors(v, e.op(i));
 272         } else
 273                 v.push_back(e);
 274 }
 275
 276 typedef std::vector<unsigned> unsignedvector;
 277 typedef std::vector<exvector> exvectorvector;
 278
 279 /** Perform automatic term rewriting rules in this class.  In the following
 280  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 281  *  stand for such expressions that contain a plain number.
 282  *  - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 283  *  - ncmul(x) -> x
 284  *  - ncmul() -> 1
 285  *  - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...))  (pull out commutative elements)
 286  *  - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))  (collect elements of same type)
 287  *  - ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 288  *
 289  *  @param level cut-off in recursive evaluation */
 290 ex ncmul::eval(int level) const
 291 {
 292         // The following additional rule would be nice, but produces a recursion,
 293         // which must be trapped by introducing a flag that the sub-ncmuls()
 294         // are already evaluated (maybe later...)
 295         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 296         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 297         //                      (X noncommutative_composite)
 298
 299         if ((level==1) && (flags & status_flags::evaluated)) {
 300                 return *this;
 301         }
 302
 303         exvector evaledseq=evalchildren(level);
 304
 305         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 306         //     ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 307         size_t factors = 0;
 308         for (auto & it : evaledseq)
 309                 factors += count_factors(it);
 310
 311         exvector assocseq;
 312         assocseq.reserve(factors);
 313         make_flat_inserter mf(evaledseq, true);
 314         for (auto & it : evaledseq) {
 315                 ex factor = mf.handle_factor(it, 1);
 316                 append_factors(assocseq, factor);
 317         }
 318
 319         // ncmul(x) -> x
 320         if (assocseq.size()==1) return *(seq.begin());
 321
 322         // ncmul() -> 1
 323         if (assocseq.empty()) return _ex1;
 324
 325         // determine return types
 326         unsignedvector rettypes(assocseq.size());
 327         size_t i = 0;
 328         size_t count_commutative=0;
 329         size_t count_noncommutative=0;
 330         size_t count_noncommutative_composite=0;
 331         for (auto & it : assocseq) {
 332                 rettypes[i] = it.return_type();
 333                 switch (rettypes[i]) {
 334                 case return_types::commutative:
 335                         count_commutative++;
 336                         break;
 337                 case return_types::noncommutative:
 338                         count_noncommutative++;
 339                         break;
 340                 case return_types::noncommutative_composite:
 341                         count_noncommutative_composite++;
 342                         break;
 343                 default:
 344                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 345                 }
 346                 ++i;
 347         }
 348         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 349
 350         // ncmul(...,c1,...,c2,...) ->
 351         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 352         if (count_commutative!=0) {
 353                 exvector commutativeseq;
 354                 commutativeseq.reserve(count_commutative+1);
 355                 exvector noncommutativeseq;
 356                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 357                 size_t num = assocseq.size();
 358                 for (size_t i=0; i<num; ++i) {
 359                         if (rettypes[i]==return_types::commutative)
 360                                 commutativeseq.push_back(assocseq[i]);
 361                         else
 362                                 noncommutativeseq.push_back(assocseq[i]);
 363                 }
 364                 commutativeseq.push_back(dynallocate<ncmul>(std::move(noncommutativeseq)));
 365                 return dynallocate<mul>(std::move(commutativeseq));
 366         }
 367
 368         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 369         //     (collect elements of same type)
 370
 371         if (count_noncommutative_composite==0) {
 372                 // there are neither commutative nor noncommutative_composite
 373                 // elements in assocseq
 374                 GINAC_ASSERT(count_commutative==0);
 375
 376                 size_t assoc_num = assocseq.size();
 377                 exvectorvector evv;
 378                 std::vector<return_type_t> rttinfos;
 379                 evv.reserve(assoc_num);
 380                 rttinfos.reserve(assoc_num);
 381
 382                 for (auto & it : assocseq) {
 383                         return_type_t ti = it.return_type_tinfo();
 384                         size_t rtt_num = rttinfos.size();
 385                         // search type in vector of known types
 386                         for (i=0; i<rtt_num; ++i) {
 387                                 if(ti == rttinfos[i]) {
 388                                         evv[i].push_back(it);
 389                                         break;
 390                                 }
 391                         }
 392                         if (i >= rtt_num) {
 393                                 // new type
 394                                 rttinfos.push_back(ti);
 395                                 evv.push_back(exvector());
 396                                 (evv.end()-1)->reserve(assoc_num);
 397                                 (evv.end()-1)->push_back(it);
 398                         }
 399                 }
 400
 401                 size_t evv_num = evv.size();
 402 #ifdef DO_GINAC_ASSERT
 403                 GINAC_ASSERT(evv_num == rttinfos.size());
 404                 GINAC_ASSERT(evv_num > 0);
 405                 size_t s=0;
 406                 for (i=0; i<evv_num; ++i)
 407                         s += evv[i].size();
 408                 GINAC_ASSERT(s == assoc_num);
 409 #endif // def DO_GINAC_ASSERT
 410
 411                 // if all elements are of same type, simplify the string
 412                 if (evv_num == 1) {
 413                         return evv[0][0].eval_ncmul(evv[0]);
 414                 }
 415
 416                 exvector splitseq;
 417                 splitseq.reserve(evv_num);
 418                 for (i=0; i<evv_num; ++i)
 419                         splitseq.push_back(dynallocate<ncmul>(evv[i]));
 420
 421                 return dynallocate<mul>(splitseq);
 422         }
 423
 424         return dynallocate<ncmul>(assocseq).setflag(status_flags::evaluated);
 425 }
 426
 427 ex ncmul::evalm() const
 428 {
 429         // Evaluate children first
 430         exvector s;
 431         s.reserve(seq.size());
 432         for (auto & it : seq)
 433                 s.push_back(it.evalm());
 434
 435         // If there are only matrices, simply multiply them
 436         auto it = s.begin(), itend = s.end();
 437         if (is_a<matrix>(*it)) {
 438                 matrix prod(ex_to<matrix>(*it));
 439                 it++;
 440                 while (it != itend) {
 441                         if (!is_a<matrix>(*it))
 442                                 goto no_matrix;
 443                         prod = prod.mul(ex_to<matrix>(*it));
 444                         it++;
 445                 }
 446                 return prod;
 447         }
 448
 449 no_matrix:
 450         return dynallocate<ncmul>(std::move(s));
 451 }
 452
 453 ex ncmul::thiscontainer(const exvector & v) const
 454 {
 455         return dynallocate<ncmul>(v);
 456 }
 457
 458 ex ncmul::thiscontainer(exvector && v) const
 459 {
 460         return dynallocate<ncmul>(std::move(v));
 461 }
 462
 463 ex ncmul::conjugate() const
 464 {
 465         if (return_type() != return_types::noncommutative) {
 466                 return exprseq::conjugate();
 467         }
 468
 469         if (!is_clifford_tinfo(return_type_tinfo())) {
 470                 return exprseq::conjugate();
 471         }
 472
 473         exvector ev;
 474         ev.reserve(nops());
 475         for (auto i=end(); i!=begin();) {
 476                 --i;
 477                 ev.push_back(i->conjugate());
 478         }
 479         return dynallocate<ncmul>(std::move(ev)).eval();
 480 }
 481
 482 ex ncmul::real_part() const
 483 {
 484         return basic::real_part();
 485 }
 486
 487 ex ncmul::imag_part() const
 488 {
 489         return basic::imag_part();
 490 }
 491
 492 // protected
 493
 494 /** Implementation of ex::diff() for a non-commutative product. It applies
 495  *  the product rule.
 496  *  @see ex::diff */
 497 ex ncmul::derivative(const symbol & s) const
 498 {
 499         size_t num = seq.size();
 500         exvector addseq;
 501         addseq.reserve(num);
 502
 503         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 504         exvector ncmulseq = seq;
 505         for (size_t i=0; i<num; ++i) {
 506                 ex e = seq[i].diff(s);
 507                 e.swap(ncmulseq[i]);
 508                 addseq.push_back(dynallocate<ncmul>(ncmulseq));
 509                 e.swap(ncmulseq[i]);
 510         }
 511         return dynallocate<add>(addseq);
 512 }
 513
 514 int ncmul::compare_same_type(const basic & other) const
 515 {
 516         return inherited::compare_same_type(other);
 517 }
 518
 519 unsigned ncmul::return_type() const
 520 {
 521         if (seq.empty())
 522                 return return_types::commutative;
 523
 524         bool all_commutative = true;
 525         exvector::const_iterator noncommutative_element; // point to first found nc element
 526
 527         exvector::const_iterator i = seq.begin(), end = seq.end();
 528         while (i != end) {
 529                 unsigned rt = i->return_type();
 530                 if (rt == return_types::noncommutative_composite)
 531                         return rt; // one ncc -> mul also ncc
 532                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 533                         // first nc element found, remember position
 534                         noncommutative_element = i;
 535                         all_commutative = false;
 536                 }
 537                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 538                         // another nc element found, compare type_infos
 539                         if(noncommutative_element->return_type_tinfo() != i->return_type_tinfo())
 540                                         return return_types::noncommutative_composite;
 541                 }
 542                 ++i;
 543         }
 544         // all factors checked
 545         GINAC_ASSERT(!all_commutative); // not all factors should commutate, because this is a ncmul();
 546         return all_commutative ? return_types::commutative : return_types::noncommutative;
 547 }
 548
 549 return_type_t ncmul::return_type_tinfo() const
 550 {
 551         if (seq.empty())
 552                 return make_return_type_t<ncmul>();
 553
 554         // return type_info of first noncommutative element
 555         for (auto & i : seq)
 556                 if (i.return_type() == return_types::noncommutative)
 557                         return i.return_type_tinfo();
 558
 559         // no noncommutative element found, should not happen
 560         return make_return_type_t<ncmul>();
 561 }
 562
 563 //////////
 564 // new virtual functions which can be overridden by derived classes
 565 //////////
 566
 567 // none
 568
 569 //////////
 570 // non-virtual functions in this class
 571 //////////
 572
 573 exvector ncmul::expandchildren(unsigned options) const
 574 {
 575         auto cit = this->seq.begin(), end = this->seq.end();
 576         while (cit != end) {
 577                 const ex & expanded_ex = cit->expand(options);
 578                 if (!are_ex_trivially_equal(*cit, expanded_ex)) {
 579
 580                         // copy first part of seq which hasn't changed
 581                         exvector s(this->seq.begin(), cit);
 582                         s.reserve(this->seq.size());
 583
 584                         // insert changed element
 585                         s.push_back(expanded_ex);
 586                         ++cit;
 587
 588                         // copy rest
 589                         while (cit != end) {
 590                                 s.push_back(cit->expand(options));
 591                                 ++cit;
 592                         }
 593
 594                         return s;
 595                 }
 596
 597                 ++cit;
 598         }
 599
 600         return exvector(); // nothing has changed
 601 }
 602
 603 const exvector & ncmul::get_factors() const
 604 {
 605         return seq;
 606 }
 607
 608 //////////
 609 // friend functions
 610 //////////
 611
 612 ex reeval_ncmul(const exvector & v)
 613 {
 614         return dynallocate<ncmul>(v);
 615 }
 616
 617 ex hold_ncmul(const exvector & v)
 618 {
 619         if (v.empty())
 620                 return _ex1;
 621         else if (v.size() == 1)
 622                 return v[0];
 623         else
 624                 return dynallocate<ncmul>(v).setflag(status_flags::evaluated);
 625 }
 626
 627 GINAC_BIND_UNARCHIVER(ncmul);
 628
 629 } // namespace GiNaC