ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2001 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  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 "matrix.h"
  32 #include "print.h"
  33 #include "archive.h"
  34 #include "debugmsg.h"
  35 #include "utils.h"
  36
  37 namespace GiNaC {
  38
  39 GINAC_IMPLEMENT_REGISTERED_CLASS(ncmul, exprseq)
  40
  41 //////////
  42 // default constructor, destructor, copy constructor assignment operator and helpers
  43 //////////
  44
  45 ncmul::ncmul()
  46 {
  47         debugmsg("ncmul default constructor",LOGLEVEL_CONSTRUCT);
  48         tinfo_key = TINFO_ncmul;
  49 }
  50
  51 DEFAULT_COPY(ncmul)
  52 DEFAULT_DESTROY(ncmul)
  53
  54 //////////
  55 // other constructors
  56 //////////
  57
  58 // public
  59
  60 ncmul::ncmul(const ex & lh, const ex & rh) : inherited(lh,rh)
  61 {
  62         debugmsg("ncmul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  63         tinfo_key = TINFO_ncmul;
  64 }
  65
  66 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited(f1,f2,f3)
  67 {
  68         debugmsg("ncmul constructor from 3 ex",LOGLEVEL_CONSTRUCT);
  69         tinfo_key = TINFO_ncmul;
  70 }
  71
  72 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  73              const ex & f4) : inherited(f1,f2,f3,f4)
  74 {
  75         debugmsg("ncmul constructor from 4 ex",LOGLEVEL_CONSTRUCT);
  76         tinfo_key = TINFO_ncmul;
  77 }
  78
  79 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  80              const ex & f4, const ex & f5) : inherited(f1,f2,f3,f4,f5)
  81 {
  82         debugmsg("ncmul constructor from 5 ex",LOGLEVEL_CONSTRUCT);
  83         tinfo_key = TINFO_ncmul;
  84 }
  85
  86 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  87              const ex & f4, const ex & f5, const ex & f6) : inherited(f1,f2,f3,f4,f5,f6)
  88 {
  89         debugmsg("ncmul constructor from 6 ex",LOGLEVEL_CONSTRUCT);
  90         tinfo_key = TINFO_ncmul;
  91 }
  92
  93 ncmul::ncmul(const exvector & v, bool discardable) : inherited(v,discardable)
  94 {
  95         debugmsg("ncmul constructor from exvector,bool",LOGLEVEL_CONSTRUCT);
  96         tinfo_key = TINFO_ncmul;
  97 }
  98
  99 ncmul::ncmul(exvector * vp) : inherited(vp)
 100 {
 101         debugmsg("ncmul constructor from exvector *",LOGLEVEL_CONSTRUCT);
 102         tinfo_key = TINFO_ncmul;
 103 }
 104
 105 //////////
 106 // archiving
 107 //////////
 108
 109 DEFAULT_ARCHIVING(ncmul)
 110
 111 //////////
 112 // functions overriding virtual functions from bases classes
 113 //////////
 114
 115 // public
 116
 117 void ncmul::print(const print_context & c, unsigned level) const
 118 {
 119         debugmsg("ncmul print", LOGLEVEL_PRINT);
 120
 121         if (is_of_type(c, print_tree)) {
 122
 123                 inherited::print(c, level);
 124
 125         } else if (is_of_type(c, print_csrc)) {
 126
 127                 c.s << "ncmul(";
 128                 exvector::const_iterator it = seq.begin(), itend = seq.end()-1;
 129                 while (it != itend) {
 130                         it->print(c, precedence());
 131                         c.s << ",";
 132                         it++;
 133                 }
 134                 it->print(c, precedence());
 135                 c.s << ")";
 136
 137         } else
 138                 printseq(c, '(', '*', ')', precedence(), level);
 139 }
 140
 141 bool ncmul::info(unsigned inf) const
 142 {
 143         throw(std::logic_error("which flags have to be implemented in ncmul::info()?"));
 144 }
 145
 146 typedef std::vector<int> intvector;
 147
 148 ex ncmul::expand(unsigned options) const
 149 {
 150         exvector sub_expanded_seq;
 151         intvector positions_of_adds;
 152         intvector number_of_add_operands;
 153
 154         exvector expanded_seq=expandchildren(options);
 155
 156         positions_of_adds.resize(expanded_seq.size());
 157         number_of_add_operands.resize(expanded_seq.size());
 158
 159         int number_of_adds=0;
 160         int number_of_expanded_terms=1;
 161
 162         unsigned current_position=0;
 163         exvector::const_iterator last=expanded_seq.end();
 164         for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 165                 if (is_ex_exactly_of_type((*cit),add)) {
 166                         positions_of_adds[number_of_adds]=current_position;
 167                         const add & expanded_addref=ex_to<add>(*cit);
 168                         number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
 169                         number_of_expanded_terms *= expanded_addref.seq.size();
 170                         number_of_adds++;
 171                 }
 172                 current_position++;
 173         }
 174
 175         if (number_of_adds==0) {
 176                 return (new ncmul(expanded_seq,1))->setflag(status_flags::dynallocated ||
 177                                                                                                         status_flags::expanded);
 178         }
 179
 180         exvector distrseq;
 181         distrseq.reserve(number_of_expanded_terms);
 182
 183         intvector k;
 184         k.resize(number_of_adds);
 185
 186         int l;
 187         for (l=0; l<number_of_adds; l++) {
 188                 k[l]=0;
 189         }
 190
 191         while (1) {
 192                 exvector term;
 193                 term=expanded_seq;
 194                 for (l=0; l<number_of_adds; l++) {
 195                         GINAC_ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[l]],add));
 196                         const add & addref=ex_to<add>(expanded_seq[positions_of_adds[l]]);
 197                         term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
 198                 }
 199                 distrseq.push_back((new ncmul(term,1))->setflag(status_flags::dynallocated |
 200                                                                                                                 status_flags::expanded));
 201
 202                 // increment k[]
 203                 l=number_of_adds-1;
 204                 while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 205                         k[l]=0;
 206                         l--;
 207                 }
 208                 if (l<0) break;
 209         }
 210
 211         return (new add(distrseq))->setflag(status_flags::dynallocated |
 212                                                                                 status_flags::expanded);
 213 }
 214
 215 int ncmul::degree(const ex & s) const
 216 {
 217         int deg_sum=0;
 218         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 219                 deg_sum+=(*cit).degree(s);
 220         }
 221         return deg_sum;
 222 }
 223
 224 int ncmul::ldegree(const ex & s) const
 225 {
 226         int deg_sum=0;
 227         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 228                 deg_sum+=(*cit).ldegree(s);
 229         }
 230         return deg_sum;
 231 }
 232
 233 ex ncmul::coeff(const ex & s, int n) const
 234 {
 235         exvector coeffseq;
 236         coeffseq.reserve(seq.size());
 237
 238         if (n==0) {
 239                 // product of individual coeffs
 240                 // if a non-zero power of s is found, the resulting product will be 0
 241                 exvector::const_iterator it=seq.begin();
 242                 while (it!=seq.end()) {
 243                         coeffseq.push_back((*it).coeff(s,n));
 244                         ++it;
 245                 }
 246                 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 247         }
 248
 249         exvector::const_iterator it=seq.begin();
 250         bool coeff_found=0;
 251         while (it!=seq.end()) {
 252                 ex c=(*it).coeff(s,n);
 253                 if (!c.is_zero()) {
 254                         coeffseq.push_back(c);
 255                         coeff_found=1;
 256                 } else {
 257                         coeffseq.push_back(*it);
 258                 }
 259                 ++it;
 260         }
 261
 262         if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 263
 264         return _ex0();
 265 }
 266
 267 unsigned ncmul::count_factors(const ex & e) const
 268 {
 269         if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 270                 (is_ex_exactly_of_type(e,ncmul))) {
 271                 unsigned factors=0;
 272                 for (unsigned i=0; i<e.nops(); i++)
 273                         factors += count_factors(e.op(i));
 274
 275                 return factors;
 276         }
 277         return 1;
 278 }
 279
 280 void ncmul::append_factors(exvector & v, const ex & e) const
 281 {
 282         if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 283                 (is_ex_exactly_of_type(e,ncmul))) {
 284                 for (unsigned i=0; i<e.nops(); i++)
 285                         append_factors(v,e.op(i));
 286
 287                 return;
 288         }
 289         v.push_back(e);
 290 }
 291
 292 typedef std::vector<unsigned> unsignedvector;
 293 typedef std::vector<exvector> exvectorvector;
 294
 295 ex ncmul::eval(int level) const
 296 {
 297         // simplifications: ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 298         //                      ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 299         //                  ncmul(x) -> x
 300         //                  ncmul() -> 1
 301         //                  ncmul(...,c1,...,c2,...)
 302         //                      *(c1,c2,ncmul(...)) (pull out commutative elements)
 303         //                  ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 304         //                      (collect elements of same type)
 305         //                  ncmul(x1,x2,x3,...) -> x::simplify_ncmul(x1,x2,x3,...)
 306         // the following rule would be nice, but produces a recursion,
 307         // which must be trapped by introducing a flag that the sub-ncmuls()
 308         // are already evaluated (maybe later...)
 309         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 310         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 311         //                      (X noncommutative_composite)
 312
 313         if ((level==1) && (flags & status_flags::evaluated)) {
 314                 return *this;
 315         }
 316
 317         exvector evaledseq=evalchildren(level);
 318
 319         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 320         //     ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 321         unsigned factors=0;
 322         for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit)
 323                 factors += count_factors(*cit);
 324
 325         exvector assocseq;
 326         assocseq.reserve(factors);
 327         for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit)
 328                 append_factors(assocseq,*cit);
 329
 330         // ncmul(x) -> x
 331         if (assocseq.size()==1) return *(seq.begin());
 332
 333         // ncmul() -> 1
 334         if (assocseq.size()==0) return _ex1();
 335
 336         // determine return types
 337         unsignedvector rettypes;
 338         rettypes.reserve(assocseq.size());
 339         unsigned i=0;
 340         unsigned count_commutative=0;
 341         unsigned count_noncommutative=0;
 342         unsigned count_noncommutative_composite=0;
 343         for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 344                 switch (rettypes[i]=(*cit).return_type()) {
 345                 case return_types::commutative:
 346                         count_commutative++;
 347                         break;
 348                 case return_types::noncommutative:
 349                         count_noncommutative++;
 350                         break;
 351                 case return_types::noncommutative_composite:
 352                         count_noncommutative_composite++;
 353                         break;
 354                 default:
 355                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 356                 }
 357                 ++i;
 358         }
 359         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 360
 361         // ncmul(...,c1,...,c2,...) ->
 362         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 363         if (count_commutative!=0) {
 364                 exvector commutativeseq;
 365                 commutativeseq.reserve(count_commutative+1);
 366                 exvector noncommutativeseq;
 367                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 368                 for (i=0; i<assocseq.size(); ++i) {
 369                         if (rettypes[i]==return_types::commutative)
 370                                 commutativeseq.push_back(assocseq[i]);
 371                         else
 372                                 noncommutativeseq.push_back(assocseq[i]);
 373                 }
 374                 commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
 375                 return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 376         }
 377
 378         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 379         //     (collect elements of same type)
 380
 381         if (count_noncommutative_composite==0) {
 382                 // there are neither commutative nor noncommutative_composite
 383                 // elements in assocseq
 384                 GINAC_ASSERT(count_commutative==0);
 385
 386                 exvectorvector evv;
 387                 unsignedvector rttinfos;
 388                 evv.reserve(assocseq.size());
 389                 rttinfos.reserve(assocseq.size());
 390
 391                 for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 392                         unsigned ti=(*cit).return_type_tinfo();
 393                         // search type in vector of known types
 394                         for (i=0; i<rttinfos.size(); ++i) {
 395                                 if (ti==rttinfos[i]) {
 396                                         evv[i].push_back(*cit);
 397                                         break;
 398                                 }
 399                         }
 400                         if (i>=rttinfos.size()) {
 401                                 // new type
 402                                 rttinfos.push_back(ti);
 403                                 evv.push_back(exvector());
 404                                 (*(evv.end()-1)).reserve(assocseq.size());
 405                                 (*(evv.end()-1)).push_back(*cit);
 406                         }
 407                 }
 408
 409 #ifdef DO_GINAC_ASSERT
 410                 GINAC_ASSERT(evv.size()==rttinfos.size());
 411                 GINAC_ASSERT(evv.size()>0);
 412                 unsigned s=0;
 413                 for (i=0; i<evv.size(); ++i) {
 414                         s += evv[i].size();
 415                 }
 416                 GINAC_ASSERT(s==assocseq.size());
 417 #endif // def DO_GINAC_ASSERT
 418
 419                 // if all elements are of same type, simplify the string
 420                 if (evv.size()==1)
 421                         return evv[0][0].simplify_ncmul(evv[0]);
 422
 423                 exvector splitseq;
 424                 splitseq.reserve(evv.size());
 425                 for (i=0; i<evv.size(); ++i) {
 426                         splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
 427                 }
 428
 429                 return (new mul(splitseq))->setflag(status_flags::dynallocated);
 430         }
 431
 432         return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 433                                                                                   status_flags::evaluated);
 434 }
 435
 436 ex ncmul::evalm(void) const
 437 {
 438         // Evaluate children first
 439         exvector *s = new exvector;
 440         s->reserve(seq.size());
 441         exvector::const_iterator it = seq.begin(), itend = seq.end();
 442         while (it != itend) {
 443                 s->push_back(it->evalm());
 444                 it++;
 445         }
 446
 447         // If there are only matrices, simply multiply them
 448         it = s->begin(); itend = s->end();
 449         if (is_ex_of_type(*it, matrix)) {
 450                 matrix prod(ex_to<matrix>(*it));
 451                 it++;
 452                 while (it != itend) {
 453                         if (!is_ex_of_type(*it, matrix))
 454                                 goto no_matrix;
 455                         prod = prod.mul(ex_to<matrix>(*it));
 456                         it++;
 457                 }
 458                 delete s;
 459                 return prod;
 460         }
 461
 462 no_matrix:
 463         return (new ncmul(s))->setflag(status_flags::dynallocated);
 464 }
 465
 466 ex ncmul::thisexprseq(const exvector & v) const
 467 {
 468         return (new ncmul(v))->setflag(status_flags::dynallocated);
 469 }
 470
 471 ex ncmul::thisexprseq(exvector * vp) const
 472 {
 473         return (new ncmul(vp))->setflag(status_flags::dynallocated);
 474 }
 475
 476 // protected
 477
 478 /** Implementation of ex::diff() for a non-commutative product. It always returns 0.
 479  *  @see ex::diff */
 480 ex ncmul::derivative(const symbol & s) const
 481 {
 482         return _ex0();
 483 }
 484
 485 int ncmul::compare_same_type(const basic & other) const
 486 {
 487         return inherited::compare_same_type(other);
 488 }
 489
 490 unsigned ncmul::return_type(void) const
 491 {
 492         if (seq.size()==0) {
 493                 // ncmul without factors: should not happen, but commutes
 494                 return return_types::commutative;
 495         }
 496
 497         bool all_commutative=1;
 498         unsigned rt;
 499         exvector::const_iterator cit_noncommutative_element; // point to first found nc element
 500
 501         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 502                 rt=(*cit).return_type();
 503                 if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 504                 if ((rt==return_types::noncommutative)&&(all_commutative)) {
 505                         // first nc element found, remember position
 506                         cit_noncommutative_element=cit;
 507                         all_commutative=0;
 508                 }
 509                 if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 510                         // another nc element found, compare type_infos
 511                         if ((*cit_noncommutative_element).return_type_tinfo()!=(*cit).return_type_tinfo()) {
 512                                 // diffent types -> mul is ncc
 513                                 return return_types::noncommutative_composite;
 514                         }
 515                 }
 516         }
 517         // all factors checked
 518         GINAC_ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
 519         return all_commutative ? return_types::commutative : return_types::noncommutative;
 520 }
 521
 522 unsigned ncmul::return_type_tinfo(void) const
 523 {
 524         if (seq.size()==0) {
 525                 // mul without factors: should not happen
 526                 return tinfo_key;
 527         }
 528         // return type_info of first noncommutative element
 529         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 530                 if ((*cit).return_type()==return_types::noncommutative) {
 531                         return (*cit).return_type_tinfo();
 532                 }
 533         }
 534         // no noncommutative element found, should not happen
 535         return tinfo_key;
 536 }
 537
 538 //////////
 539 // new virtual functions which can be overridden by derived classes
 540 //////////
 541
 542 // none
 543
 544 //////////
 545 // non-virtual functions in this class
 546 //////////
 547
 548 exvector ncmul::expandchildren(unsigned options) const
 549 {
 550         exvector s;
 551         s.reserve(seq.size());
 552         exvector::const_iterator it = seq.begin(), itend = seq.end();
 553         while (it != itend) {
 554                 s.push_back(it->expand(options));
 555                 it++;
 556         }
 557         return s;
 558 }
 559
 560 const exvector & ncmul::get_factors(void) const
 561 {
 562         return seq;
 563 }
 564
 565 //////////
 566 // friend functions
 567 //////////
 568
 569 ex nonsimplified_ncmul(const exvector & v)
 570 {
 571         return (new ncmul(v))->setflag(status_flags::dynallocated);
 572 }
 573
 574 ex simplified_ncmul(const exvector & v)
 575 {
 576         if (v.size()==0) {
 577                 return _ex1();
 578         } else if (v.size()==1) {
 579                 return v[0];
 580         }
 581         return (new ncmul(v))->setflag(status_flags::dynallocated |
 582                                        status_flags::evaluated);
 583 }
 584
 585 } // namespace GiNaC