ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative products of expressions. */
   4
   5 #include <algorithm>
   6 #include <iostream>
   7 #include <stdexcept>
   8
   9 #include "ginac.h"
  10
  11 //////////
  12 // default constructor, destructor, copy constructor assignment operator and helpers
  13 //////////
  14
  15 // public
  16
  17 ncmul::ncmul()
  18 {
  19     debugmsg("ncmul default constructor",LOGLEVEL_CONSTRUCT);
  20     tinfo_key = TINFO_NCMUL;
  21 }
  22
  23 ncmul::~ncmul()
  24 {
  25     debugmsg("ncmul destructor",LOGLEVEL_DESTRUCT);
  26     destroy(0);
  27 }
  28
  29 ncmul::ncmul(ncmul const & other)
  30 {
  31     debugmsg("ncmul copy constructor",LOGLEVEL_CONSTRUCT);
  32     copy(other);
  33 }
  34
  35 ncmul const & ncmul::operator=(ncmul const & other)
  36 {
  37     debugmsg("ncmul operator=",LOGLEVEL_ASSIGNMENT);
  38     if (this != &other) {
  39         destroy(1);
  40         copy(other);
  41     }
  42     return *this;
  43 }
  44
  45 // protected
  46
  47 void ncmul::copy(ncmul const & other)
  48 {
  49     exprseq::copy(other);
  50 }
  51
  52 void ncmul::destroy(bool call_parent)
  53 {
  54     if (call_parent) exprseq::destroy(call_parent);
  55 }
  56
  57 //////////
  58 // other constructors
  59 //////////
  60
  61 // public
  62
  63 ncmul::ncmul(ex const & lh, ex const & rh) :
  64     exprseq(lh,rh)
  65 {
  66     debugmsg("ncmul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  67     tinfo_key = TINFO_NCMUL;
  68 }
  69
  70 ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3) :
  71     exprseq(f1,f2,f3)
  72 {
  73     debugmsg("ncmul constructor from 3 ex",LOGLEVEL_CONSTRUCT);
  74     tinfo_key = TINFO_NCMUL;
  75 }
  76
  77 ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
  78       ex const & f4) : exprseq(f1,f2,f3,f4)
  79 {
  80     debugmsg("ncmul constructor from 4 ex",LOGLEVEL_CONSTRUCT);
  81     tinfo_key = TINFO_NCMUL;
  82 }
  83
  84 ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
  85       ex const & f4, ex const & f5) : exprseq(f1,f2,f3,f4,f5)
  86 {
  87     debugmsg("ncmul constructor from 5 ex",LOGLEVEL_CONSTRUCT);
  88     tinfo_key = TINFO_NCMUL;
  89 }
  90
  91 ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
  92       ex const & f4, ex const & f5, ex const & f6) :
  93     exprseq(f1,f2,f3,f4,f5,f6)
  94 {
  95     debugmsg("ncmul constructor from 6 ex",LOGLEVEL_CONSTRUCT);
  96     tinfo_key = TINFO_NCMUL;
  97 }
  98
  99 ncmul::ncmul(exvector const & v, bool discardable) : exprseq(v,discardable)
 100 {
 101     debugmsg("ncmul constructor from exvector,bool",LOGLEVEL_CONSTRUCT);
 102     tinfo_key = TINFO_NCMUL;
 103 }
 104
 105 ncmul::ncmul(exvector * vp) : exprseq(vp)
 106 {
 107     debugmsg("ncmul constructor from exvector *",LOGLEVEL_CONSTRUCT);
 108     tinfo_key = TINFO_NCMUL;
 109 }
 110
 111 //////////
 112 // functions overriding virtual functions from bases classes
 113 //////////
 114
 115 // public
 116
 117 basic * ncmul::duplicate() const
 118 {
 119     debugmsg("ncmul duplicate",LOGLEVEL_ASSIGNMENT);
 120     return new ncmul(*this);
 121 }
 122
 123 bool ncmul::info(unsigned inf) const
 124 {
 125     throw(std::logic_error("which flags have to be implemented in ncmul::info()?"));
 126 }
 127
 128 typedef vector<int> intvector;
 129
 130 ex ncmul::expand(unsigned options) const
 131 {
 132     exvector sub_expanded_seq;
 133     intvector positions_of_adds;
 134     intvector number_of_add_operands;
 135
 136     exvector expanded_seq=expandchildren(options);
 137
 138     positions_of_adds.resize(expanded_seq.size());
 139     number_of_add_operands.resize(expanded_seq.size());
 140
 141     int number_of_adds=0;
 142     int number_of_expanded_terms=1;
 143
 144     unsigned current_position=0;
 145     exvector::const_iterator last=expanded_seq.end();
 146     for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 147         if (is_ex_exactly_of_type((*cit),add)) {
 148             positions_of_adds[number_of_adds]=current_position;
 149             add const & expanded_addref=ex_to_add(*cit);
 150             number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
 151             number_of_expanded_terms *= expanded_addref.seq.size();
 152             number_of_adds++;
 153         }
 154         current_position++;
 155     }
 156
 157     if (number_of_adds==0) {
 158         return (new ncmul(expanded_seq,1))->setflag(status_flags::dynallocated ||
 159                                                     status_flags::expanded);
 160     }
 161
 162     exvector distrseq;
 163     distrseq.reserve(number_of_expanded_terms);
 164
 165     intvector k;
 166     k.resize(number_of_adds);
 167
 168     int l;
 169     for (l=0; l<number_of_adds; l++) {
 170         k[l]=0;
 171     }
 172
 173     while (1) {
 174         exvector term;
 175         term=expanded_seq;
 176         for (l=0; l<number_of_adds; l++) {
 177             ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[l]],add));
 178             add const & addref=ex_to_add(expanded_seq[positions_of_adds[l]]);
 179             term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
 180         }
 181         distrseq.push_back((new ncmul(term,1))->setflag(status_flags::dynallocated |
 182                                                         status_flags::expanded));
 183
 184         // increment k[]
 185         l=number_of_adds-1;
 186         while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 187             k[l]=0;
 188             l--;
 189         }
 190         if (l<0) break;
 191     }
 192
 193     return (new add(distrseq))->setflag(status_flags::dynallocated |
 194                                         status_flags::expanded);
 195 }
 196
 197 int ncmul::degree(symbol const & s) const
 198 {
 199     int deg_sum=0;
 200     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 201         deg_sum+=(*cit).degree(s);
 202     }
 203     return deg_sum;
 204 }
 205
 206 int ncmul::ldegree(symbol const & s) const
 207 {
 208     int deg_sum=0;
 209     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 210         deg_sum+=(*cit).ldegree(s);
 211     }
 212     return deg_sum;
 213 }
 214
 215 ex ncmul::coeff(symbol const & s, int const n) const
 216 {
 217     exvector coeffseq;
 218     coeffseq.reserve(seq.size());
 219
 220     if (n==0) {
 221         // product of individual coeffs
 222         // if a non-zero power of s is found, the resulting product will be 0
 223         exvector::const_iterator it=seq.begin();
 224         while (it!=seq.end()) {
 225             coeffseq.push_back((*it).coeff(s,n));
 226             ++it;
 227         }
 228         return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 229     }
 230
 231     exvector::const_iterator it=seq.begin();
 232     bool coeff_found=0;
 233     while (it!=seq.end()) {
 234         ex c=(*it).coeff(s,n);
 235         if (!c.is_zero()) {
 236             coeffseq.push_back(c);
 237             coeff_found=1;
 238         } else {
 239             coeffseq.push_back(*it);
 240         }
 241         ++it;
 242     }
 243
 244     if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 245
 246     return exZERO();
 247 }
 248
 249 unsigned ncmul::count_factors(ex const & e) const
 250 {
 251     if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 252         (is_ex_exactly_of_type(e,ncmul))) {
 253         unsigned factors=0;
 254         for (int i=0; i<e.nops(); i++) {
 255             factors += count_factors(e.op(i));
 256         }
 257         return factors;
 258     }
 259     return 1;
 260 }
 261
 262 void ncmul::append_factors(exvector & v, ex const & e) const
 263 {
 264     if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 265         (is_ex_exactly_of_type(e,ncmul))) {
 266         for (int i=0; i<e.nops(); i++) {
 267             append_factors(v,e.op(i));
 268         }
 269         return;
 270     }
 271     v.push_back(e);
 272 }
 273
 274 typedef vector<unsigned> unsignedvector;
 275 typedef vector<exvector> exvectorvector;
 276
 277 ex ncmul::eval(int level) const
 278 {
 279     // simplifications: ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 280     //                      ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 281     //                  ncmul(x) -> x
 282     //                  ncmul() -> 1
 283     //                  ncmul(...,c1,...,c2,...) ->
 284     //                      *(c1,c2,ncmul(...)) (pull out commutative elements)
 285     //                  ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 286     //                      (collect elements of same type)
 287     //                  ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 288     // the following rule would be nice, but produces a recursion,
 289     // which must be trapped by introducing a flag that the sub-ncmuls()
 290     // are already evaluated (maybe later...)
 291     //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 292     //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 293     //                      (X noncommutative_composite)
 294
 295     if ((level==1)&&(flags & status_flags::evaluated)) {
 296         return *this;
 297     }
 298
 299     exvector evaledseq=evalchildren(level);
 300
 301     // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 302     //     ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 303     unsigned factors=0;
 304     for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 305         factors += count_factors(*cit);
 306     }
 307
 308     exvector assocseq;
 309     assocseq.reserve(factors);
 310     for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 311         append_factors(assocseq,*cit);
 312     }
 313
 314     // ncmul(x) -> x
 315     if (assocseq.size()==1) return *(seq.begin());
 316
 317     // ncmul() -> 1
 318     if (assocseq.size()==0) return exONE();
 319
 320     // determine return types
 321     unsignedvector rettypes;
 322     rettypes.reserve(assocseq.size());
 323     unsigned i=0;
 324     unsigned count_commutative=0;
 325     unsigned count_noncommutative=0;
 326     unsigned count_noncommutative_composite=0;
 327     for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 328         switch (rettypes[i]=(*cit).return_type()) {
 329         case return_types::commutative:
 330             count_commutative++;
 331             break;
 332         case return_types::noncommutative:
 333             count_noncommutative++;
 334             break;
 335         case return_types::noncommutative_composite:
 336             count_noncommutative_composite++;
 337             break;
 338         default:
 339             throw(std::logic_error("ncmul::eval(): invalid return type"));
 340         }
 341         ++i;
 342     }
 343     ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 344
 345     // ncmul(...,c1,...,c2,...) ->
 346     //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 347     if (count_commutative!=0) {
 348         exvector commutativeseq;
 349         commutativeseq.reserve(count_commutative+1);
 350         exvector noncommutativeseq;
 351         noncommutativeseq.reserve(assocseq.size()-count_commutative);
 352         for (i=0; i<assocseq.size(); ++i) {
 353             if (rettypes[i]==return_types::commutative) {
 354                 commutativeseq.push_back(assocseq[i]);
 355             } else {
 356                 noncommutativeseq.push_back(assocseq[i]);
 357             }
 358         }
 359         commutativeseq.push_back((new ncmul(noncommutativeseq,1))->
 360                                   setflag(status_flags::dynallocated));
 361         return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 362     }
 363
 364     // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 365     //     (collect elements of same type)
 366
 367     if (count_noncommutative_composite==0) {
 368         // there are neither commutative nor noncommutative_composite
 369         // elements in assocseq
 370         ASSERT(count_commutative==0);
 371
 372         exvectorvector evv;
 373         unsignedvector rttinfos;
 374         evv.reserve(assocseq.size());
 375         rttinfos.reserve(assocseq.size());
 376
 377         for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 378             unsigned ti=(*cit).return_type_tinfo();
 379             // search type in vector of known types
 380             for (i=0; i<rttinfos.size(); ++i) {
 381                 if (ti==rttinfos[i]) {
 382                     evv[i].push_back(*cit);
 383                     break;
 384                 }
 385             }
 386             if (i>=rttinfos.size()) {
 387                 // new type
 388                 rttinfos.push_back(ti);
 389                 evv.push_back(exvector());
 390                 (*(evv.end()-1)).reserve(assocseq.size());
 391                 (*(evv.end()-1)).push_back(*cit);
 392             }
 393         }
 394
 395 #ifdef DOASSERT
 396         ASSERT(evv.size()==rttinfos.size());
 397         ASSERT(evv.size()>0);
 398         unsigned s=0;
 399         for (i=0; i<evv.size(); ++i) {
 400             s += evv[i].size();
 401         }
 402         ASSERT(s==assocseq.size());
 403 #endif // def DOASSERT
 404
 405         // if all elements are of same type, simplify the string
 406         if (evv.size()==1) {
 407             return evv[0][0].simplify_ncmul(evv[0]);
 408         }
 409
 410         exvector splitseq;
 411         splitseq.reserve(evv.size());
 412         for (i=0; i<evv.size(); ++i) {
 413             splitseq.push_back((new ncmul(evv[i]))->
 414                                setflag(status_flags::dynallocated));
 415         }
 416
 417         return (new mul(splitseq))->setflag(status_flags::dynallocated);
 418     }
 419
 420     return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 421                                           status_flags::evaluated);
 422 }
 423
 424 exvector ncmul::get_indices(void) const
 425 {
 426     // return union of indices of factors
 427     exvector iv;
 428     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 429         exvector subiv=(*cit).get_indices();
 430         iv.reserve(iv.size()+subiv.size());
 431         for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 432             iv.push_back(*cit2);
 433         }
 434     }
 435     return iv;
 436 }
 437
 438 ex ncmul::subs(lst const & ls, lst const & lr) const
 439 {
 440     return ncmul(subschildren(ls, lr));
 441 }
 442
 443 ex ncmul::thisexprseq(exvector const & v) const
 444 {
 445     return (new ncmul(v))->setflag(status_flags::dynallocated);
 446 }
 447
 448 ex ncmul::thisexprseq(exvector * vp) const
 449 {
 450     return (new ncmul(vp))->setflag(status_flags::dynallocated);
 451 }
 452
 453 // protected
 454
 455 int ncmul::compare_same_type(basic const & other) const
 456 {
 457     return exprseq::compare_same_type(other);
 458 }
 459
 460 unsigned ncmul::return_type(void) const
 461 {
 462     if (seq.size()==0) {
 463         // ncmul without factors: should not happen, but commutes
 464         return return_types::commutative;
 465     }
 466
 467     bool all_commutative=1;
 468     unsigned rt;
 469     exvector::const_iterator cit_noncommutative_element; // point to first found nc element
 470
 471     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 472         rt=(*cit).return_type();
 473         if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 474         if ((rt==return_types::noncommutative)&&(all_commutative)) {
 475             // first nc element found, remember position
 476             cit_noncommutative_element=cit;
 477             all_commutative=0;
 478         }
 479         if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 480             // another nc element found, compare type_infos
 481             if ((*cit_noncommutative_element).return_type_tinfo()!=(*cit).return_type_tinfo()) {
 482                 // diffent types -> mul is ncc
 483                 return return_types::noncommutative_composite;
 484             }
 485         }
 486     }
 487     // all factors checked
 488     ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
 489     return all_commutative ? return_types::commutative : return_types::noncommutative;
 490 }
 491
 492 unsigned ncmul::return_type_tinfo(void) const
 493 {
 494     if (seq.size()==0) {
 495         // mul without factors: should not happen
 496         return tinfo_key;
 497     }
 498     // return type_info of first noncommutative element
 499     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 500         if ((*cit).return_type()==return_types::noncommutative) {
 501             return (*cit).return_type_tinfo();
 502         }
 503     }
 504     // no noncommutative element found, should not happen
 505     return tinfo_key;
 506 }
 507
 508 //////////
 509 // new virtual functions which can be overridden by derived classes
 510 //////////
 511
 512 // none
 513
 514 //////////
 515 // non-virtual functions in this class
 516 //////////
 517
 518 exvector ncmul::expandchildren(unsigned options) const
 519 {
 520     exvector s;
 521     s.reserve(seq.size());
 522
 523     for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 524         s.push_back((*it).expand(options));
 525     }
 526     return s;
 527 }
 528
 529 exvector const & ncmul::get_factors(void) const
 530 {
 531     return seq;
 532 }
 533
 534 //////////
 535 // static member variables
 536 //////////
 537
 538 // protected
 539
 540 unsigned ncmul::precedence=50;
 541
 542
 543 //////////
 544 // global constants
 545 //////////
 546
 547 const ncmul some_ncmul;
 548 type_info const & typeid_ncmul=typeid(some_ncmul);
 549
 550 //////////
 551 // friend functions
 552 //////////
 553
 554 ex nonsimplified_ncmul(exvector const & v)
 555 {
 556     return (new ncmul(v))->setflag(status_flags::dynallocated);
 557 }
 558
 559 ex simplified_ncmul(exvector const & v)
 560 {
 561     if (v.size()==0) {
 562         return exONE();
 563     } else if (v.size()==1) {
 564         return v[0];
 565     }
 566     return (new ncmul(v))->setflag(status_flags::dynallocated |
 567                                    status_flags::evaluated);
 568 }
 569
 570