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 base 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         return inherited::info(inf);
 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.
 155         intvector positions_of_adds(expanded_seq.size());
 156         intvector number_of_add_operands(expanded_seq.size());
 157
 158         int number_of_adds = 0;
 159         int number_of_expanded_terms = 1;
 160
 161         unsigned current_position = 0;
 162         exvector::const_iterator last = expanded_seq.end();
 163         for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 164                 if (is_exactly_a<add>(*cit)) {
 165                         positions_of_adds[number_of_adds] = current_position;
 166                         unsigned num_ops = cit->nops();
 167                         number_of_add_operands[number_of_adds] = num_ops;
 168                         number_of_expanded_terms *= num_ops;
 169                         number_of_adds++;
 170                 }
 171                 ++current_position;
 172         }
 173
 174         // If there are no sums, we are done
 175         if (number_of_adds == 0)
 176                 return (new ncmul(expanded_seq, true))->
 177                         setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 178
 179         // Now, form all possible products of the terms of the sums with the
 180         // remaining factors, and add them together
 181         exvector distrseq;
 182         distrseq.reserve(number_of_expanded_terms);
 183
 184         intvector k(number_of_adds);
 185
 186         while (true) {
 187                 exvector term = expanded_seq;
 188                 for (int i=0; i<number_of_adds; i++)
 189                         term[positions_of_adds[i]] = expanded_seq[positions_of_adds[i]].op(k[i]);
 190                 distrseq.push_back((new ncmul(term, true))->
 191                                     setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 192
 193                 // increment k[]
 194                 int l = number_of_adds-1;
 195                 while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
 196                         k[l] = 0;
 197                         l--;
 198                 }
 199                 if (l<0)
 200                         break;
 201         }
 202
 203         return (new add(distrseq))->
 204                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 205 }
 206
 207 int ncmul::degree(const ex & s) const
 208 {
 209         // Sum up degrees of factors
 210         int deg_sum = 0;
 211         exvector::const_iterator i = seq.begin(), end = seq.end();
 212         while (i != end) {
 213                 deg_sum += i->degree(s);
 214                 ++i;
 215         }
 216         return deg_sum;
 217 }
 218
 219 int ncmul::ldegree(const ex & s) const
 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         exvector coeffseq;
 234         coeffseq.reserve(seq.size());
 235
 236         if (n == 0) {
 237                 // product of individual coeffs
 238                 // if a non-zero power of s is found, the resulting product will be 0
 239                 exvector::const_iterator it=seq.begin();
 240                 while (it!=seq.end()) {
 241                         coeffseq.push_back((*it).coeff(s,n));
 242                         ++it;
 243                 }
 244                 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 245         }
 246
 247         exvector::const_iterator i = seq.begin(), end = seq.end();
 248         bool coeff_found = false;
 249         while (i != end) {
 250                 ex c = i->coeff(s,n);
 251                 if (c.is_zero()) {
 252                         coeffseq.push_back(*i);
 253                 } else {
 254                         coeffseq.push_back(c);
 255                         coeff_found = true;
 256                 }
 257                 ++i;
 258         }
 259
 260         if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 261
 262         return _ex0();
 263 }
 264
 265 unsigned ncmul::count_factors(const ex & e) const
 266 {
 267         if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 268                 (is_ex_exactly_of_type(e,ncmul))) {
 269                 unsigned factors=0;
 270                 for (unsigned i=0; i<e.nops(); i++)
 271                         factors += count_factors(e.op(i));
 272
 273                 return factors;
 274         }
 275         return 1;
 276 }
 277
 278 void ncmul::append_factors(exvector & v, const ex & e) const
 279 {
 280         if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 281                 (is_ex_exactly_of_type(e,ncmul))) {
 282                 for (unsigned i=0; i<e.nops(); i++)
 283                         append_factors(v,e.op(i));
 284         } else
 285                 v.push_back(e);
 286 }
 287
 288 typedef std::vector<unsigned> unsignedvector;
 289 typedef std::vector<exvector> exvectorvector;
 290
 291 /** Perform automatic term rewriting rules in this class.  In the following
 292  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 293  *  stand for such expressions that contain a plain number.
 294  *  - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 295  *  - ncmul(x) -> x
 296  *  - ncmul() -> 1
 297  *  - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...))  (pull out commutative elements)
 298  *  - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))  (collect elements of same type)
 299  *  - ncmul(x1,x2,x3,...) -> x::simplify_ncmul(x1,x2,x3,...)
 300  *
 301  *  @param level cut-off in recursive evaluation */
 302 ex ncmul::eval(int level) const
 303 {
 304         // The following additional rule would be nice, but produces a recursion,
 305         // which must be trapped by introducing a flag that the sub-ncmuls()
 306         // are already evaluated (maybe later...)
 307         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 308         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 309         //                      (X noncommutative_composite)
 310
 311         if ((level==1) && (flags & status_flags::evaluated)) {
 312                 return *this;
 313         }
 314
 315         exvector evaledseq=evalchildren(level);
 316
 317         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 318         //     ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 319         unsigned factors = 0;
 320         exvector::const_iterator cit = evaledseq.begin(), citend = evaledseq.end();
 321         while (cit != citend)
 322                 factors += count_factors(*cit++);
 323
 324         exvector assocseq;
 325         assocseq.reserve(factors);
 326         cit = evaledseq.begin();
 327         while (cit != citend)
 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.empty()) 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         cit = assocseq.begin(); citend = assocseq.end();
 344         while (cit != citend) {
 345                 switch (rettypes[i] = cit->return_type()) {
 346                 case return_types::commutative:
 347                         count_commutative++;
 348                         break;
 349                 case return_types::noncommutative:
 350                         count_noncommutative++;
 351                         break;
 352                 case return_types::noncommutative_composite:
 353                         count_noncommutative_composite++;
 354                         break;
 355                 default:
 356                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 357                 }
 358                 ++i; ++cit;
 359         }
 360         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 361
 362         // ncmul(...,c1,...,c2,...) ->
 363         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 364         if (count_commutative!=0) {
 365                 exvector commutativeseq;
 366                 commutativeseq.reserve(count_commutative+1);
 367                 exvector noncommutativeseq;
 368                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 369                 unsigned num = assocseq.size();
 370                 for (unsigned i=0; i<num; ++i) {
 371                         if (rettypes[i]==return_types::commutative)
 372                                 commutativeseq.push_back(assocseq[i]);
 373                         else
 374                                 noncommutativeseq.push_back(assocseq[i]);
 375                 }
 376                 commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
 377                 return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 378         }
 379
 380         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 381         //     (collect elements of same type)
 382
 383         if (count_noncommutative_composite==0) {
 384                 // there are neither commutative nor noncommutative_composite
 385                 // elements in assocseq
 386                 GINAC_ASSERT(count_commutative==0);
 387
 388                 unsigned assoc_num = assocseq.size();
 389                 exvectorvector evv;
 390                 unsignedvector rttinfos;
 391                 evv.reserve(assoc_num);
 392                 rttinfos.reserve(assoc_num);
 393
 394                 cit = assocseq.begin(), citend = assocseq.end();
 395                 while (cit != citend) {
 396                         unsigned ti = cit->return_type_tinfo();
 397                         unsigned rtt_num = rttinfos.size();
 398                         // search type in vector of known types
 399                         for (i=0; i<rtt_num; ++i) {
 400                                 if (ti == rttinfos[i]) {
 401                                         evv[i].push_back(*cit);
 402                                         break;
 403                                 }
 404                         }
 405                         if (i >= rtt_num) {
 406                                 // new type
 407                                 rttinfos.push_back(ti);
 408                                 evv.push_back(exvector());
 409                                 (evv.end()-1)->reserve(assoc_num);
 410                                 (evv.end()-1)->push_back(*cit);
 411                         }
 412                         ++cit;
 413                 }
 414
 415                 unsigned evv_num = evv.size();
 416 #ifdef DO_GINAC_ASSERT
 417                 GINAC_ASSERT(evv_num == rttinfos.size());
 418                 GINAC_ASSERT(evv_num > 0);
 419                 unsigned s=0;
 420                 for (i=0; i<evv_num; ++i)
 421                         s += evv[i].size();
 422                 GINAC_ASSERT(s == assoc_num);
 423 #endif // def DO_GINAC_ASSERT
 424
 425                 // if all elements are of same type, simplify the string
 426                 if (evv_num == 1)
 427                         return evv[0][0].simplify_ncmul(evv[0]);
 428
 429                 exvector splitseq;
 430                 splitseq.reserve(evv_num);
 431                 for (i=0; i<evv_num; ++i)
 432                         splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
 433
 434                 return (new mul(splitseq))->setflag(status_flags::dynallocated);
 435         }
 436
 437         return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 438                                                                                   status_flags::evaluated);
 439 }
 440
 441 ex ncmul::evalm(void) const
 442 {
 443         // Evaluate children first
 444         exvector *s = new exvector;
 445         s->reserve(seq.size());
 446         exvector::const_iterator it = seq.begin(), itend = seq.end();
 447         while (it != itend) {
 448                 s->push_back(it->evalm());
 449                 it++;
 450         }
 451
 452         // If there are only matrices, simply multiply them
 453         it = s->begin(); itend = s->end();
 454         if (is_ex_of_type(*it, matrix)) {
 455                 matrix prod(ex_to<matrix>(*it));
 456                 it++;
 457                 while (it != itend) {
 458                         if (!is_ex_of_type(*it, matrix))
 459                                 goto no_matrix;
 460                         prod = prod.mul(ex_to<matrix>(*it));
 461                         it++;
 462                 }
 463                 delete s;
 464                 return prod;
 465         }
 466
 467 no_matrix:
 468         return (new ncmul(s))->setflag(status_flags::dynallocated);
 469 }
 470
 471 ex ncmul::thisexprseq(const exvector & v) const
 472 {
 473         return (new ncmul(v))->setflag(status_flags::dynallocated);
 474 }
 475
 476 ex ncmul::thisexprseq(exvector * vp) const
 477 {
 478         return (new ncmul(vp))->setflag(status_flags::dynallocated);
 479 }
 480
 481 // protected
 482
 483 /** Implementation of ex::diff() for a non-commutative product. It applies
 484  *  the product rule.
 485  *  @see ex::diff */
 486 ex ncmul::derivative(const symbol & s) const
 487 {
 488         unsigned num = seq.size();
 489         exvector addseq;
 490         addseq.reserve(num);
 491
 492         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 493         exvector ncmulseq = seq;
 494         for (unsigned i=0; i<num; ++i) {
 495                 ex e = seq[i].diff(s);
 496                 e.swap(ncmulseq[i]);
 497                 addseq.push_back((new ncmul(ncmulseq))->setflag(status_flags::dynallocated));
 498                 e.swap(ncmulseq[i]);
 499         }
 500         return (new add(addseq))->setflag(status_flags::dynallocated);
 501 }
 502
 503 int ncmul::compare_same_type(const basic & other) const
 504 {
 505         return inherited::compare_same_type(other);
 506 }
 507
 508 unsigned ncmul::return_type(void) const
 509 {
 510         if (seq.empty())
 511                 return return_types::commutative;
 512
 513         bool all_commutative = true;
 514         exvector::const_iterator noncommutative_element; // point to first found nc element
 515
 516         exvector::const_iterator i = seq.begin(), end = seq.end();
 517         while (i != end) {
 518                 unsigned rt = i->return_type();
 519                 if (rt == return_types::noncommutative_composite)
 520                         return rt; // one ncc -> mul also ncc
 521                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 522                         // first nc element found, remember position
 523                         noncommutative_element = i;
 524                         all_commutative = false;
 525                 }
 526                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 527                         // another nc element found, compare type_infos
 528                         if (noncommutative_element->return_type_tinfo() != i->return_type_tinfo()) {
 529                                 // diffent types -> mul is ncc
 530                                 return return_types::noncommutative_composite;
 531                         }
 532                 }
 533                 ++i;
 534         }
 535         // all factors checked
 536         GINAC_ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
 537         return all_commutative ? return_types::commutative : return_types::noncommutative;
 538 }
 539
 540 unsigned ncmul::return_type_tinfo(void) const
 541 {
 542         if (seq.empty())
 543                 return tinfo_key;
 544
 545         // return type_info of first noncommutative element
 546         exvector::const_iterator i = seq.begin(), end = seq.end();
 547         while (i != end) {
 548                 if (i->return_type() == return_types::noncommutative)
 549                         return i->return_type_tinfo();
 550                 ++i;
 551         }
 552
 553         // no noncommutative element found, should not happen
 554         return tinfo_key;
 555 }
 556
 557 //////////
 558 // new virtual functions which can be overridden by derived classes
 559 //////////
 560
 561 // none
 562
 563 //////////
 564 // non-virtual functions in this class
 565 //////////
 566
 567 exvector ncmul::expandchildren(unsigned options) const
 568 {
 569         exvector s;
 570         s.reserve(seq.size());
 571         exvector::const_iterator it = seq.begin(), itend = seq.end();
 572         while (it != itend) {
 573                 s.push_back(it->expand(options));
 574                 it++;
 575         }
 576         return s;
 577 }
 578
 579 const exvector & ncmul::get_factors(void) const
 580 {
 581         return seq;
 582 }
 583
 584 //////////
 585 // friend functions
 586 //////////
 587
 588 ex nonsimplified_ncmul(const exvector & v)
 589 {
 590         return (new ncmul(v))->setflag(status_flags::dynallocated);
 591 }
 592
 593 ex simplified_ncmul(const exvector & v)
 594 {
 595         if (v.empty())
 596                 return _ex1();
 597         else if (v.size() == 1)
 598                 return v[0];
 599         else
 600                 return (new ncmul(v))->setflag(status_flags::dynallocated |
 601                                                status_flags::evaluated);
 602 }
 603
 604 } // namespace GiNaC