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         // First, expand the children
 151         exvector expanded_seq = expandchildren(options);
 152
 153         // Now, look for all the factors that are sums and remember their
 154         // position and number of terms. One remark is in order here: we do not
 155         // take into account the overall_coeff of the add objects. This is
 156         // because in GiNaC, all terms of a sum must be of the same type, so
 157         // a non-zero overall_coeff (which can only be numeric) would imply that
 158         // the sum only has commutative terms. But then it would never appear
 159         // as a factor of an ncmul.
 160         intvector positions_of_adds(expanded_seq.size());
 161         intvector number_of_add_operands(expanded_seq.size());
 162
 163         int number_of_adds = 0;
 164         int number_of_expanded_terms = 1;
 165
 166         unsigned current_position = 0;
 167         exvector::const_iterator last = expanded_seq.end();
 168         for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 169                 if (is_ex_exactly_of_type(*cit, add)) {
 170                         positions_of_adds[number_of_adds] = current_position;
 171                         const add & expanded_addref = ex_to<add>(*cit);
 172                         number_of_add_operands[number_of_adds] = expanded_addref.seq.size();
 173                         number_of_expanded_terms *= expanded_addref.seq.size();
 174                         number_of_adds++;
 175                 }
 176                 current_position++;
 177         }
 178
 179         // If there are no sums, we are done
 180         if (number_of_adds == 0)
 181                 return (new ncmul(expanded_seq, true))->
 182                         setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 183
 184         // Now, form all possible products of the terms of the sums with the
 185         // remaining factors, and add them together
 186         exvector distrseq;
 187         distrseq.reserve(number_of_expanded_terms);
 188
 189         intvector k(number_of_adds);
 190
 191         while (true) {
 192                 exvector term = expanded_seq;
 193                 for (int i=0; i<number_of_adds; i++) {
 194                         GINAC_ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[i]], add));
 195                         const add & addref = ex_to<add>(expanded_seq[positions_of_adds[i]]);
 196                         term[positions_of_adds[i]] = addref.recombine_pair_to_ex(addref.seq[k[i]]);
 197                 }
 198                 distrseq.push_back((new ncmul(term, true))->
 199                                     setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 200
 201                 // increment k[]
 202                 int l = number_of_adds-1;
 203                 while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
 204                         k[l] = 0;
 205                         l--;
 206                 }
 207                 if (l<0)
 208                         break;
 209         }
 210
 211         return (new add(distrseq))->
 212                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 213 }
 214
 215 int ncmul::degree(const ex & s) const
 216 {
 217         // Sum up degrees of factors
 218         int deg_sum = 0;
 219         exvector::const_iterator i = seq.begin(), end = seq.end();
 220         while (i != end) {
 221                 deg_sum += i->degree(s);
 222                 ++i;
 223         }
 224         return deg_sum;
 225 }
 226
 227 int ncmul::ldegree(const ex & s) const
 228 {
 229         // Sum up degrees of factors
 230         int deg_sum = 0;
 231         exvector::const_iterator i = seq.begin(), end = seq.end();
 232         while (i != end) {
 233                 deg_sum += i->degree(s);
 234                 ++i;
 235         }
 236         return deg_sum;
 237 }
 238
 239 ex ncmul::coeff(const ex & s, int n) const
 240 {
 241         exvector coeffseq;
 242         coeffseq.reserve(seq.size());
 243
 244         if (n == 0) {
 245                 // product of individual coeffs
 246                 // if a non-zero power of s is found, the resulting product will be 0
 247                 exvector::const_iterator it=seq.begin();
 248                 while (it!=seq.end()) {
 249                         coeffseq.push_back((*it).coeff(s,n));
 250                         ++it;
 251                 }
 252                 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 253         }
 254
 255         exvector::const_iterator i = seq.begin(), end = seq.end();
 256         bool coeff_found = false;
 257         while (i != end) {
 258                 ex c = i->coeff(s,n);
 259                 if (c.is_zero()) {
 260                         coeffseq.push_back(*i);
 261                 } else {
 262                         coeffseq.push_back(c);
 263                         coeff_found = true;
 264                 }
 265                 ++i;
 266         }
 267
 268         if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 269
 270         return _ex0();
 271 }
 272
 273 unsigned ncmul::count_factors(const ex & e) const
 274 {
 275         if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 276                 (is_ex_exactly_of_type(e,ncmul))) {
 277                 unsigned factors=0;
 278                 for (unsigned i=0; i<e.nops(); i++)
 279                         factors += count_factors(e.op(i));
 280
 281                 return factors;
 282         }
 283         return 1;
 284 }
 285
 286 void ncmul::append_factors(exvector & v, const ex & e) const
 287 {
 288         if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 289                 (is_ex_exactly_of_type(e,ncmul))) {
 290                 for (unsigned i=0; i<e.nops(); i++)
 291                         append_factors(v,e.op(i));
 292         } else
 293                 v.push_back(e);
 294 }
 295
 296 typedef std::vector<unsigned> unsignedvector;
 297 typedef std::vector<exvector> exvectorvector;
 298
 299 ex ncmul::eval(int level) const
 300 {
 301         // simplifications: ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 302         //                      ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 303         //                  ncmul(x) -> x
 304         //                  ncmul() -> 1
 305         //                  ncmul(...,c1,...,c2,...)
 306         //                      *(c1,c2,ncmul(...)) (pull out commutative elements)
 307         //                  ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 308         //                      (collect elements of same type)
 309         //                  ncmul(x1,x2,x3,...) -> x::simplify_ncmul(x1,x2,x3,...)
 310         // the following rule would be nice, but produces a recursion,
 311         // which must be trapped by introducing a flag that the sub-ncmuls()
 312         // are already evaluated (maybe later...)
 313         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 314         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 315         //                      (X noncommutative_composite)
 316
 317         if ((level==1) && (flags & status_flags::evaluated)) {
 318                 return *this;
 319         }
 320
 321         exvector evaledseq=evalchildren(level);
 322
 323         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 324         //     ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 325         unsigned factors = 0;
 326         exvector::const_iterator cit = evaledseq.begin(), citend = evaledseq.end();
 327         while (cit != citend)
 328                 factors += count_factors(*cit++);
 329
 330         exvector assocseq;
 331         assocseq.reserve(factors);
 332         cit = evaledseq.begin();
 333         while (cit != citend)
 334                 append_factors(assocseq, *cit++);
 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         unsigned i = 0;
 346         unsigned count_commutative=0;
 347         unsigned count_noncommutative=0;
 348         unsigned 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                 unsigned num = assocseq.size();
 376                 for (unsigned 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                 unsigned assoc_num = assocseq.size();
 395                 exvectorvector evv;
 396                 unsignedvector rttinfos;
 397                 evv.reserve(assoc_num);
 398                 rttinfos.reserve(assoc_num);
 399
 400                 cit = assocseq.begin(), citend = assocseq.end();
 401                 while (cit != citend) {
 402                         unsigned ti = cit->return_type_tinfo();
 403                         unsigned 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                 unsigned evv_num = evv.size();
 422 #ifdef DO_GINAC_ASSERT
 423                 GINAC_ASSERT(evv_num == rttinfos.size());
 424                 GINAC_ASSERT(evv_num > 0);
 425                 unsigned 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].simplify_ncmul(evv[0]);
 434
 435                 exvector splitseq;
 436                 splitseq.reserve(evv_num);
 437                 for (i=0; i<evv_num; ++i)
 438                         splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
 439
 440                 return (new mul(splitseq))->setflag(status_flags::dynallocated);
 441         }
 442
 443         return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 444                                                                                   status_flags::evaluated);
 445 }
 446
 447 ex ncmul::evalm(void) const
 448 {
 449         // Evaluate children first
 450         exvector *s = new exvector;
 451         s->reserve(seq.size());
 452         exvector::const_iterator it = seq.begin(), itend = seq.end();
 453         while (it != itend) {
 454                 s->push_back(it->evalm());
 455                 it++;
 456         }
 457
 458         // If there are only matrices, simply multiply them
 459         it = s->begin(); itend = s->end();
 460         if (is_ex_of_type(*it, matrix)) {
 461                 matrix prod(ex_to<matrix>(*it));
 462                 it++;
 463                 while (it != itend) {
 464                         if (!is_ex_of_type(*it, matrix))
 465                                 goto no_matrix;
 466                         prod = prod.mul(ex_to<matrix>(*it));
 467                         it++;
 468                 }
 469                 delete s;
 470                 return prod;
 471         }
 472
 473 no_matrix:
 474         return (new ncmul(s))->setflag(status_flags::dynallocated);
 475 }
 476
 477 ex ncmul::thisexprseq(const exvector & v) const
 478 {
 479         return (new ncmul(v))->setflag(status_flags::dynallocated);
 480 }
 481
 482 ex ncmul::thisexprseq(exvector * vp) const
 483 {
 484         return (new ncmul(vp))->setflag(status_flags::dynallocated);
 485 }
 486
 487 // protected
 488
 489 /** Implementation of ex::diff() for a non-commutative product. It applies
 490  *  the product rule.
 491  *  @see ex::diff */
 492 ex ncmul::derivative(const symbol & s) const
 493 {
 494         unsigned num = seq.size();
 495         exvector addseq;
 496         addseq.reserve(num);
 497
 498         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 499         exvector ncmulseq = seq;
 500         for (unsigned i=0; i<num; ++i) {
 501                 ex e = seq[i].diff(s);
 502                 e.swap(ncmulseq[i]);
 503                 addseq.push_back((new ncmul(ncmulseq))->setflag(status_flags::dynallocated));
 504                 e.swap(ncmulseq[i]);
 505         }
 506         return (new add(addseq))->setflag(status_flags::dynallocated);
 507 }
 508
 509 int ncmul::compare_same_type(const basic & other) const
 510 {
 511         return inherited::compare_same_type(other);
 512 }
 513
 514 unsigned ncmul::return_type(void) const
 515 {
 516         if (seq.empty())
 517                 return return_types::commutative;
 518
 519         bool all_commutative = true;
 520         exvector::const_iterator noncommutative_element; // point to first found nc element
 521
 522         exvector::const_iterator i = seq.begin(), end = seq.end();
 523         while (i != end) {
 524                 unsigned rt = i->return_type();
 525                 if (rt == return_types::noncommutative_composite)
 526                         return rt; // one ncc -> mul also ncc
 527                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 528                         // first nc element found, remember position
 529                         noncommutative_element = i;
 530                         all_commutative = false;
 531                 }
 532                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 533                         // another nc element found, compare type_infos
 534                         if (noncommutative_element->return_type_tinfo() != i->return_type_tinfo()) {
 535                                 // diffent types -> mul is ncc
 536                                 return return_types::noncommutative_composite;
 537                         }
 538                 }
 539                 ++i;
 540         }
 541         // all factors checked
 542         GINAC_ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
 543         return all_commutative ? return_types::commutative : return_types::noncommutative;
 544 }
 545
 546 unsigned ncmul::return_type_tinfo(void) const
 547 {
 548         if (seq.empty())
 549                 return tinfo_key;
 550
 551         // return type_info of first noncommutative element
 552         exvector::const_iterator i = seq.begin(), end = seq.end();
 553         while (i != end) {
 554                 if (i->return_type() == return_types::noncommutative)
 555                         return i->return_type_tinfo();
 556                 ++i;
 557         }
 558
 559         // no noncommutative element found, should not happen
 560         return tinfo_key;
 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         exvector s;
 576         s.reserve(seq.size());
 577         exvector::const_iterator it = seq.begin(), itend = seq.end();
 578         while (it != itend) {
 579                 s.push_back(it->expand(options));
 580                 it++;
 581         }
 582         return s;
 583 }
 584
 585 const exvector & ncmul::get_factors(void) const
 586 {
 587         return seq;
 588 }
 589
 590 //////////
 591 // friend functions
 592 //////////
 593
 594 ex nonsimplified_ncmul(const exvector & v)
 595 {
 596         return (new ncmul(v))->setflag(status_flags::dynallocated);
 597 }
 598
 599 ex simplified_ncmul(const exvector & v)
 600 {
 601         if (v.empty())
 602                 return _ex1();
 603         else if (v.size() == 1)
 604                 return v[0];
 605         else
 606                 return (new ncmul(v))->setflag(status_flags::dynallocated |
 607                                                status_flags::evaluated);
 608 }
 609
 610 } // namespace GiNaC