ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2008 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 <algorithm>
  24 #include <iostream>
  25 #include <stdexcept>
  26
  27 #include "ncmul.h"
  28 #include "ex.h"
  29 #include "add.h"
  30 #include "mul.h"
  31 #include "clifford.h"
  32 #include "matrix.h"
  33 #include "archive.h"
  34 #include "indexed.h"
  35 #include "utils.h"
  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, bool discardable) : inherited(v,discardable)
  84 {
  85 }
  86
  87 ncmul::ncmul(std::auto_ptr<exvector> vp) : inherited(vp)
  88 {
  89 }
  90
  91 //////////
  92 // archiving
  93 //////////
  94
  95 DEFAULT_ARCHIVING(ncmul)
  96
  97 //////////
  98 // functions overriding virtual functions from base classes
  99 //////////
 100
 101 // public
 102
 103 void ncmul::do_print(const print_context & c, unsigned level) const
 104 {
 105         printseq(c, '(', '*', ')', precedence(), level);
 106 }
 107
 108 void ncmul::do_print_csrc(const print_context & c, unsigned level) const
 109 {
 110         c.s << class_name();
 111         printseq(c, '(', ',', ')', precedence(), precedence());
 112 }
 113
 114 bool ncmul::info(unsigned inf) const
 115 {
 116         return inherited::info(inf);
 117 }
 118
 119 typedef std::vector<std::size_t> uintvector;
 120
 121 ex ncmul::expand(unsigned options) const
 122 {
 123         // First, expand the children
 124         std::auto_ptr<exvector> vp = expandchildren(options);
 125         const exvector &expanded_seq = vp.get() ? *vp : this->seq;
 126
 127         // Now, look for all the factors that are sums and remember their
 128         // position and number of terms.
 129         uintvector positions_of_adds(expanded_seq.size());
 130         uintvector number_of_add_operands(expanded_seq.size());
 131
 132         size_t number_of_adds = 0;
 133         size_t number_of_expanded_terms = 1;
 134
 135         size_t current_position = 0;
 136         exvector::const_iterator last = expanded_seq.end();
 137         for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 138                 if (is_exactly_a<add>(*cit)) {
 139                         positions_of_adds[number_of_adds] = current_position;
 140                         size_t num_ops = cit->nops();
 141                         number_of_add_operands[number_of_adds] = num_ops;
 142                         number_of_expanded_terms *= num_ops;
 143                         number_of_adds++;
 144                 }
 145                 ++current_position;
 146         }
 147
 148         // If there are no sums, we are done
 149         if (number_of_adds == 0) {
 150                 if (vp.get())
 151                         return (new ncmul(vp))->
 152                                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 153                 else
 154                         return *this;
 155         }
 156
 157         // Now, form all possible products of the terms of the sums with the
 158         // remaining factors, and add them together
 159         exvector distrseq;
 160         distrseq.reserve(number_of_expanded_terms);
 161
 162         uintvector k(number_of_adds);
 163
 164         /* Rename indices in the static members of the product */
 165         exvector expanded_seq_mod;
 166         size_t j = 0;
 167         exvector va;
 168
 169         for (size_t i=0; i<expanded_seq.size(); i++) {
 170                 if (i == positions_of_adds[j]) {
 171                         expanded_seq_mod.push_back(_ex1);
 172                         j++;
 173                 } else {
 174                         expanded_seq_mod.push_back(rename_dummy_indices_uniquely(va, expanded_seq[i], true));
 175                 }
 176         }
 177
 178         while (true) {
 179                 exvector term = expanded_seq_mod;
 180                 for (size_t i=0; i<number_of_adds; i++) {
 181                         term[positions_of_adds[i]] = rename_dummy_indices_uniquely(va, expanded_seq[positions_of_adds[i]].op(k[i]), true);
 182                 }
 183
 184                 distrseq.push_back((new ncmul(term, true))->
 185                                     setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 186
 187                 // increment k[]
 188                 int l = number_of_adds-1;
 189                 while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
 190                         k[l] = 0;
 191                         l--;
 192                 }
 193                 if (l<0)
 194                         break;
 195         }
 196
 197         return (new add(distrseq))->
 198                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 199 }
 200
 201 int ncmul::degree(const ex & s) const
 202 {
 203         if (is_equal(ex_to<basic>(s)))
 204                 return 1;
 205
 206         // Sum up degrees of factors
 207         int deg_sum = 0;
 208         exvector::const_iterator i = seq.begin(), end = seq.end();
 209         while (i != end) {
 210                 deg_sum += i->degree(s);
 211                 ++i;
 212         }
 213         return deg_sum;
 214 }
 215
 216 int ncmul::ldegree(const ex & s) const
 217 {
 218         if (is_equal(ex_to<basic>(s)))
 219                 return 1;
 220
 221         // Sum up degrees of factors
 222         int deg_sum = 0;
 223         exvector::const_iterator i = seq.begin(), end = seq.end();
 224         while (i != end) {
 225                 deg_sum += i->degree(s);
 226                 ++i;
 227         }
 228         return deg_sum;
 229 }
 230
 231 ex ncmul::coeff(const ex & s, int n) const
 232 {
 233         if (is_equal(ex_to<basic>(s)))
 234                 return n==1 ? _ex1 : _ex0;
 235
 236         exvector coeffseq;
 237         coeffseq.reserve(seq.size());
 238
 239         if (n == 0) {
 240                 // product of individual coeffs
 241                 // if a non-zero power of s is found, the resulting product will be 0
 242                 exvector::const_iterator it=seq.begin();
 243                 while (it!=seq.end()) {
 244                         coeffseq.push_back((*it).coeff(s,n));
 245                         ++it;
 246                 }
 247                 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 248         }
 249
 250         exvector::const_iterator i = seq.begin(), end = seq.end();
 251         bool coeff_found = false;
 252         while (i != end) {
 253                 ex c = i->coeff(s,n);
 254                 if (c.is_zero()) {
 255                         coeffseq.push_back(*i);
 256                 } else {
 257                         coeffseq.push_back(c);
 258                         coeff_found = true;
 259                 }
 260                 ++i;
 261         }
 262
 263         if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 264
 265         return _ex0;
 266 }
 267
 268 size_t ncmul::count_factors(const ex & e) const
 269 {
 270         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 271                 (is_exactly_a<ncmul>(e))) {
 272                 size_t factors=0;
 273                 for (size_t i=0; i<e.nops(); i++)
 274                         factors += count_factors(e.op(i));
 275
 276                 return factors;
 277         }
 278         return 1;
 279 }
 280
 281 void ncmul::append_factors(exvector & v, const ex & e) const
 282 {
 283         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 284                 (is_exactly_a<ncmul>(e))) {
 285                 for (size_t i=0; i<e.nops(); i++)
 286                         append_factors(v, e.op(i));
 287         } else
 288                 v.push_back(e);
 289 }
 290
 291 typedef std::vector<unsigned> unsignedvector;
 292 typedef std::vector<exvector> exvectorvector;
 293
 294 /** Perform automatic term rewriting rules in this class.  In the following
 295  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 296  *  stand for such expressions that contain a plain number.
 297  *  - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 298  *  - ncmul(x) -> x
 299  *  - ncmul() -> 1
 300  *  - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...))  (pull out commutative elements)
 301  *  - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))  (collect elements of same type)
 302  *  - ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 303  *
 304  *  @param level cut-off in recursive evaluation */
 305 ex ncmul::eval(int level) const
 306 {
 307         // The following additional rule would be nice, but produces a recursion,
 308         // which must be trapped by introducing a flag that the sub-ncmuls()
 309         // are already evaluated (maybe later...)
 310         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 311         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 312         //                      (X noncommutative_composite)
 313
 314         if ((level==1) && (flags & status_flags::evaluated)) {
 315                 return *this;
 316         }
 317
 318         exvector evaledseq=evalchildren(level);
 319
 320         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 321         //     ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 322         size_t factors = 0;
 323         exvector::const_iterator cit = evaledseq.begin(), citend = evaledseq.end();
 324         while (cit != citend)
 325                 factors += count_factors(*cit++);
 326
 327         exvector assocseq;
 328         assocseq.reserve(factors);
 329         cit = evaledseq.begin();
 330         make_flat_inserter mf(evaledseq, true);
 331         while (cit != citend)
 332         {       ex factor = mf.handle_factor(*(cit++), 1);
 333                 append_factors(assocseq, factor);
 334         }
 335
 336         // ncmul(x) -> x
 337         if (assocseq.size()==1) return *(seq.begin());
 338
 339         // ncmul() -> 1
 340         if (assocseq.empty()) return _ex1;
 341
 342         // determine return types
 343         unsignedvector rettypes;
 344         rettypes.reserve(assocseq.size());
 345         size_t i = 0;
 346         size_t count_commutative=0;
 347         size_t count_noncommutative=0;
 348         size_t count_noncommutative_composite=0;
 349         cit = assocseq.begin(); citend = assocseq.end();
 350         while (cit != citend) {
 351                 switch (rettypes[i] = cit->return_type()) {
 352                 case return_types::commutative:
 353                         count_commutative++;
 354                         break;
 355                 case return_types::noncommutative:
 356                         count_noncommutative++;
 357                         break;
 358                 case return_types::noncommutative_composite:
 359                         count_noncommutative_composite++;
 360                         break;
 361                 default:
 362                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 363                 }
 364                 ++i; ++cit;
 365         }
 366         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 367
 368         // ncmul(...,c1,...,c2,...) ->
 369         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 370         if (count_commutative!=0) {
 371                 exvector commutativeseq;
 372                 commutativeseq.reserve(count_commutative+1);
 373                 exvector noncommutativeseq;
 374                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 375                 size_t num = assocseq.size();
 376                 for (size_t i=0; i<num; ++i) {
 377                         if (rettypes[i]==return_types::commutative)
 378                                 commutativeseq.push_back(assocseq[i]);
 379                         else
 380                                 noncommutativeseq.push_back(assocseq[i]);
 381                 }
 382                 commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
 383                 return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 384         }
 385
 386         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 387         //     (collect elements of same type)
 388
 389         if (count_noncommutative_composite==0) {
 390                 // there are neither commutative nor noncommutative_composite
 391                 // elements in assocseq
 392                 GINAC_ASSERT(count_commutative==0);
 393
 394                 size_t assoc_num = assocseq.size();
 395                 exvectorvector evv;
 396                 std::vector<return_type_t> rttinfos;
 397                 evv.reserve(assoc_num);
 398                 rttinfos.reserve(assoc_num);
 399
 400                 cit = assocseq.begin(), citend = assocseq.end();
 401                 while (cit != citend) {
 402                         return_type_t ti = cit->return_type_tinfo();
 403                         size_t rtt_num = rttinfos.size();
 404                         // search type in vector of known types
 405                         for (i=0; i<rtt_num; ++i) {
 406                                 if(ti == rttinfos[i]) {
 407                                         evv[i].push_back(*cit);
 408                                         break;
 409                                 }
 410                         }
 411                         if (i >= rtt_num) {
 412                                 // new type
 413                                 rttinfos.push_back(ti);
 414                                 evv.push_back(exvector());
 415                                 (evv.end()-1)->reserve(assoc_num);
 416                                 (evv.end()-1)->push_back(*cit);
 417                         }
 418                         ++cit;
 419                 }
 420
 421                 size_t evv_num = evv.size();
 422 #ifdef DO_GINAC_ASSERT
 423                 GINAC_ASSERT(evv_num == rttinfos.size());
 424                 GINAC_ASSERT(evv_num > 0);
 425                 size_t s=0;
 426                 for (i=0; i<evv_num; ++i)
 427                         s += evv[i].size();
 428                 GINAC_ASSERT(s == assoc_num);
 429 #endif // def DO_GINAC_ASSERT
 430
 431                 // if all elements are of same type, simplify the string
 432                 if (evv_num == 1) {
 433                         return evv[0][0].eval_ncmul(evv[0]);
 434                 }
 435
 436                 exvector splitseq;
 437                 splitseq.reserve(evv_num);
 438                 for (i=0; i<evv_num; ++i)
 439                         splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
 440
 441                 return (new mul(splitseq))->setflag(status_flags::dynallocated);
 442         }
 443
 444         return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 445                                                                                   status_flags::evaluated);
 446 }
 447
 448 ex ncmul::evalm() const
 449 {
 450         // Evaluate children first
 451         std::auto_ptr<exvector> s(new exvector);
 452         s->reserve(seq.size());
 453         exvector::const_iterator it = seq.begin(), itend = seq.end();
 454         while (it != itend) {
 455                 s->push_back(it->evalm());
 456                 it++;
 457         }
 458
 459         // If there are only matrices, simply multiply them
 460         it = s->begin(); itend = s->end();
 461         if (is_a<matrix>(*it)) {
 462                 matrix prod(ex_to<matrix>(*it));
 463                 it++;
 464                 while (it != itend) {
 465                         if (!is_a<matrix>(*it))
 466                                 goto no_matrix;
 467                         prod = prod.mul(ex_to<matrix>(*it));
 468                         it++;
 469                 }
 470                 return prod;
 471         }
 472
 473 no_matrix:
 474         return (new ncmul(s))->setflag(status_flags::dynallocated);
 475 }
 476
 477 ex ncmul::thiscontainer(const exvector & v) const
 478 {
 479         return (new ncmul(v))->setflag(status_flags::dynallocated);
 480 }
 481
 482 ex ncmul::thiscontainer(std::auto_ptr<exvector> vp) const
 483 {
 484         return (new ncmul(vp))->setflag(status_flags::dynallocated);
 485 }
 486
 487 ex ncmul::conjugate() const
 488 {
 489         if (return_type() != return_types::noncommutative) {
 490                 return exprseq::conjugate();
 491         }
 492
 493         if (!is_clifford_tinfo(return_type_tinfo())) {
 494                 return exprseq::conjugate();
 495         }
 496
 497         exvector ev;
 498         ev.reserve(nops());
 499         for (const_iterator i=end(); i!=begin();) {
 500                 --i;
 501                 ev.push_back(i->conjugate());
 502         }
 503         return (new ncmul(ev, true))->setflag(status_flags::dynallocated).eval();
 504 }
 505
 506 ex ncmul::real_part() const
 507 {
 508         return basic::real_part();
 509 }
 510
 511 ex ncmul::imag_part() const
 512 {
 513         return basic::imag_part();
 514 }
 515
 516 // protected
 517
 518 /** Implementation of ex::diff() for a non-commutative product. It applies
 519  *  the product rule.
 520  *  @see ex::diff */
 521 ex ncmul::derivative(const symbol & s) const
 522 {
 523         size_t num = seq.size();
 524         exvector addseq;
 525         addseq.reserve(num);
 526
 527         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 528         exvector ncmulseq = seq;
 529         for (size_t i=0; i<num; ++i) {
 530                 ex e = seq[i].diff(s);
 531                 e.swap(ncmulseq[i]);
 532                 addseq.push_back((new ncmul(ncmulseq))->setflag(status_flags::dynallocated));
 533                 e.swap(ncmulseq[i]);
 534         }
 535         return (new add(addseq))->setflag(status_flags::dynallocated);
 536 }
 537
 538 int ncmul::compare_same_type(const basic & other) const
 539 {
 540         return inherited::compare_same_type(other);
 541 }
 542
 543 unsigned ncmul::return_type() const
 544 {
 545         if (seq.empty())
 546                 return return_types::commutative;
 547
 548         bool all_commutative = true;
 549         exvector::const_iterator noncommutative_element; // point to first found nc element
 550
 551         exvector::const_iterator i = seq.begin(), end = seq.end();
 552         while (i != end) {
 553                 unsigned rt = i->return_type();
 554                 if (rt == return_types::noncommutative_composite)
 555                         return rt; // one ncc -> mul also ncc
 556                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 557                         // first nc element found, remember position
 558                         noncommutative_element = i;
 559                         all_commutative = false;
 560                 }
 561                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 562                         // another nc element found, compare type_infos
 563                         if(noncommutative_element->return_type_tinfo() != i->return_type_tinfo())
 564                                         return return_types::noncommutative_composite;
 565                 }
 566                 ++i;
 567         }
 568         // all factors checked
 569         GINAC_ASSERT(!all_commutative); // not all factors should commutate, because this is a ncmul();
 570         return all_commutative ? return_types::commutative : return_types::noncommutative;
 571 }
 572
 573 return_type_t ncmul::return_type_tinfo() const
 574 {
 575         if (seq.empty())
 576                 return make_return_type_t<ncmul>();
 577
 578         // return type_info of first noncommutative element
 579         exvector::const_iterator i = seq.begin(), end = seq.end();
 580         while (i != end) {
 581                 if (i->return_type() == return_types::noncommutative)
 582                         return i->return_type_tinfo();
 583                 ++i;
 584         }
 585
 586         // no noncommutative element found, should not happen
 587         return make_return_type_t<ncmul>();
 588 }
 589
 590 //////////
 591 // new virtual functions which can be overridden by derived classes
 592 //////////
 593
 594 // none
 595
 596 //////////
 597 // non-virtual functions in this class
 598 //////////
 599
 600 std::auto_ptr<exvector> ncmul::expandchildren(unsigned options) const
 601 {
 602         const_iterator cit = this->seq.begin(), end = this->seq.end();
 603         while (cit != end) {
 604                 const ex & expanded_ex = cit->expand(options);
 605                 if (!are_ex_trivially_equal(*cit, expanded_ex)) {
 606
 607                         // copy first part of seq which hasn't changed
 608                         std::auto_ptr<exvector> s(new exvector(this->seq.begin(), cit));
 609                         reserve(*s, this->seq.size());
 610
 611                         // insert changed element
 612                         s->push_back(expanded_ex);
 613                         ++cit;
 614
 615                         // copy rest
 616                         while (cit != end) {
 617                                 s->push_back(cit->expand(options));
 618                                 ++cit;
 619                         }
 620
 621                         return s;
 622                 }
 623
 624                 ++cit;
 625         }
 626
 627         return std::auto_ptr<exvector>(0); // nothing has changed
 628 }
 629
 630 const exvector & ncmul::get_factors() const
 631 {
 632         return seq;
 633 }
 634
 635 //////////
 636 // friend functions
 637 //////////
 638
 639 ex reeval_ncmul(const exvector & v)
 640 {
 641         return (new ncmul(v))->setflag(status_flags::dynallocated);
 642 }
 643
 644 ex hold_ncmul(const exvector & v)
 645 {
 646         if (v.empty())
 647                 return _ex1;
 648         else if (v.size() == 1)
 649                 return v[0];
 650         else
 651                 return (new ncmul(v))->setflag(status_flags::dynallocated |
 652                                                status_flags::evaluated);
 653 }
 654
 655 } // namespace GiNaC