ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2003 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 "archive.h"
  33 #include "utils.h"
  34
  35 namespace GiNaC {
  36
  37 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(ncmul, exprseq,
  38   print_func<print_context>(&ncmul::do_print).
  39   print_func<print_tree>(&basic::do_print_tree).
  40   print_func<print_csrc>(&ncmul::do_print_csrc).
  41   print_func<print_python_repr>(&ncmul::do_print_csrc))
  42
  43
  44 //////////
  45 // default constructor
  46 //////////
  47
  48 ncmul::ncmul()
  49 {
  50         tinfo_key = TINFO_ncmul;
  51 }
  52
  53 //////////
  54 // other constructors
  55 //////////
  56
  57 // public
  58
  59 ncmul::ncmul(const ex & lh, const ex & rh) : inherited(lh,rh)
  60 {
  61         tinfo_key = TINFO_ncmul;
  62 }
  63
  64 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited(f1,f2,f3)
  65 {
  66         tinfo_key = TINFO_ncmul;
  67 }
  68
  69 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  70              const ex & f4) : inherited(f1,f2,f3,f4)
  71 {
  72         tinfo_key = TINFO_ncmul;
  73 }
  74
  75 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  76              const ex & f4, const ex & f5) : inherited(f1,f2,f3,f4,f5)
  77 {
  78         tinfo_key = TINFO_ncmul;
  79 }
  80
  81 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  82              const ex & f4, const ex & f5, const ex & f6) : inherited(f1,f2,f3,f4,f5,f6)
  83 {
  84         tinfo_key = TINFO_ncmul;
  85 }
  86
  87 ncmul::ncmul(const exvector & v, bool discardable) : inherited(v,discardable)
  88 {
  89         tinfo_key = TINFO_ncmul;
  90 }
  91
  92 ncmul::ncmul(std::auto_ptr<exvector> vp) : inherited(vp)
  93 {
  94         tinfo_key = TINFO_ncmul;
  95 }
  96
  97 //////////
  98 // archiving
  99 //////////
 100
 101 DEFAULT_ARCHIVING(ncmul)
 102
 103 //////////
 104 // functions overriding virtual functions from base classes
 105 //////////
 106
 107 // public
 108
 109 void ncmul::do_print(const print_context & c, unsigned level) const
 110 {
 111         printseq(c, '(', '*', ')', precedence(), level);
 112 }
 113
 114 void ncmul::do_print_csrc(const print_context & c, unsigned level) const
 115 {
 116         c.s << class_name();
 117         printseq(c, '(', ',', ')', precedence(), precedence());
 118 }
 119
 120 bool ncmul::info(unsigned inf) const
 121 {
 122         return inherited::info(inf);
 123 }
 124
 125 typedef std::vector<int> intvector;
 126
 127 ex ncmul::expand(unsigned options) const
 128 {
 129         // First, expand the children
 130         exvector expanded_seq = expandchildren(options);
 131
 132         // Now, look for all the factors that are sums and remember their
 133         // position and number of terms.
 134         intvector positions_of_adds(expanded_seq.size());
 135         intvector number_of_add_operands(expanded_seq.size());
 136
 137         size_t number_of_adds = 0;
 138         size_t number_of_expanded_terms = 1;
 139
 140         size_t current_position = 0;
 141         exvector::const_iterator last = expanded_seq.end();
 142         for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 143                 if (is_exactly_a<add>(*cit)) {
 144                         positions_of_adds[number_of_adds] = current_position;
 145                         size_t num_ops = cit->nops();
 146                         number_of_add_operands[number_of_adds] = num_ops;
 147                         number_of_expanded_terms *= num_ops;
 148                         number_of_adds++;
 149                 }
 150                 ++current_position;
 151         }
 152
 153         // If there are no sums, we are done
 154         if (number_of_adds == 0)
 155                 return (new ncmul(expanded_seq, true))->
 156                         setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 157
 158         // Now, form all possible products of the terms of the sums with the
 159         // remaining factors, and add them together
 160         exvector distrseq;
 161         distrseq.reserve(number_of_expanded_terms);
 162
 163         intvector k(number_of_adds);
 164
 165         while (true) {
 166                 exvector term = expanded_seq;
 167                 for (size_t i=0; i<number_of_adds; i++)
 168                         term[positions_of_adds[i]] = expanded_seq[positions_of_adds[i]].op(k[i]);
 169                 distrseq.push_back((new ncmul(term, true))->
 170                                     setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 171
 172                 // increment k[]
 173                 int l = number_of_adds-1;
 174                 while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
 175                         k[l] = 0;
 176                         l--;
 177                 }
 178                 if (l<0)
 179                         break;
 180         }
 181
 182         return (new add(distrseq))->
 183                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 184 }
 185
 186 int ncmul::degree(const ex & s) const
 187 {
 188         // Sum up degrees of factors
 189         int deg_sum = 0;
 190         exvector::const_iterator i = seq.begin(), end = seq.end();
 191         while (i != end) {
 192                 deg_sum += i->degree(s);
 193                 ++i;
 194         }
 195         return deg_sum;
 196 }
 197
 198 int ncmul::ldegree(const ex & s) const
 199 {
 200         // Sum up degrees of factors
 201         int deg_sum = 0;
 202         exvector::const_iterator i = seq.begin(), end = seq.end();
 203         while (i != end) {
 204                 deg_sum += i->degree(s);
 205                 ++i;
 206         }
 207         return deg_sum;
 208 }
 209
 210 ex ncmul::coeff(const ex & s, int n) const
 211 {
 212         exvector coeffseq;
 213         coeffseq.reserve(seq.size());
 214
 215         if (n == 0) {
 216                 // product of individual coeffs
 217                 // if a non-zero power of s is found, the resulting product will be 0
 218                 exvector::const_iterator it=seq.begin();
 219                 while (it!=seq.end()) {
 220                         coeffseq.push_back((*it).coeff(s,n));
 221                         ++it;
 222                 }
 223                 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 224         }
 225
 226         exvector::const_iterator i = seq.begin(), end = seq.end();
 227         bool coeff_found = false;
 228         while (i != end) {
 229                 ex c = i->coeff(s,n);
 230                 if (c.is_zero()) {
 231                         coeffseq.push_back(*i);
 232                 } else {
 233                         coeffseq.push_back(c);
 234                         coeff_found = true;
 235                 }
 236                 ++i;
 237         }
 238
 239         if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 240
 241         return _ex0;
 242 }
 243
 244 size_t ncmul::count_factors(const ex & e) const
 245 {
 246         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 247                 (is_exactly_a<ncmul>(e))) {
 248                 size_t factors=0;
 249                 for (size_t i=0; i<e.nops(); i++)
 250                         factors += count_factors(e.op(i));
 251
 252                 return factors;
 253         }
 254         return 1;
 255 }
 256
 257 void ncmul::append_factors(exvector & v, const ex & e) const
 258 {
 259         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 260                 (is_exactly_a<ncmul>(e))) {
 261                 for (size_t i=0; i<e.nops(); i++)
 262                         append_factors(v, e.op(i));
 263         } else
 264                 v.push_back(e);
 265 }
 266
 267 typedef std::vector<unsigned> unsignedvector;
 268 typedef std::vector<exvector> exvectorvector;
 269
 270 /** Perform automatic term rewriting rules in this class.  In the following
 271  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 272  *  stand for such expressions that contain a plain number.
 273  *  - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 274  *  - ncmul(x) -> x
 275  *  - ncmul() -> 1
 276  *  - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...))  (pull out commutative elements)
 277  *  - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))  (collect elements of same type)
 278  *  - ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 279  *
 280  *  @param level cut-off in recursive evaluation */
 281 ex ncmul::eval(int level) const
 282 {
 283         // The following additional rule would be nice, but produces a recursion,
 284         // which must be trapped by introducing a flag that the sub-ncmuls()
 285         // are already evaluated (maybe later...)
 286         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 287         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 288         //                      (X noncommutative_composite)
 289
 290         if ((level==1) && (flags & status_flags::evaluated)) {
 291                 return *this;
 292         }
 293
 294         exvector evaledseq=evalchildren(level);
 295
 296         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 297         //     ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 298         size_t factors = 0;
 299         exvector::const_iterator cit = evaledseq.begin(), citend = evaledseq.end();
 300         while (cit != citend)
 301                 factors += count_factors(*cit++);
 302
 303         exvector assocseq;
 304         assocseq.reserve(factors);
 305         cit = evaledseq.begin();
 306         while (cit != citend)
 307                 append_factors(assocseq, *cit++);
 308
 309         // ncmul(x) -> x
 310         if (assocseq.size()==1) return *(seq.begin());
 311
 312         // ncmul() -> 1
 313         if (assocseq.empty()) return _ex1;
 314
 315         // determine return types
 316         unsignedvector rettypes;
 317         rettypes.reserve(assocseq.size());
 318         size_t i = 0;
 319         size_t count_commutative=0;
 320         size_t count_noncommutative=0;
 321         size_t count_noncommutative_composite=0;
 322         cit = assocseq.begin(); citend = assocseq.end();
 323         while (cit != citend) {
 324                 switch (rettypes[i] = cit->return_type()) {
 325                 case return_types::commutative:
 326                         count_commutative++;
 327                         break;
 328                 case return_types::noncommutative:
 329                         count_noncommutative++;
 330                         break;
 331                 case return_types::noncommutative_composite:
 332                         count_noncommutative_composite++;
 333                         break;
 334                 default:
 335                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 336                 }
 337                 ++i; ++cit;
 338         }
 339         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 340
 341         // ncmul(...,c1,...,c2,...) ->
 342         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 343         if (count_commutative!=0) {
 344                 exvector commutativeseq;
 345                 commutativeseq.reserve(count_commutative+1);
 346                 exvector noncommutativeseq;
 347                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 348                 size_t num = assocseq.size();
 349                 for (size_t i=0; i<num; ++i) {
 350                         if (rettypes[i]==return_types::commutative)
 351                                 commutativeseq.push_back(assocseq[i]);
 352                         else
 353                                 noncommutativeseq.push_back(assocseq[i]);
 354                 }
 355                 commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
 356                 return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 357         }
 358
 359         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 360         //     (collect elements of same type)
 361
 362         if (count_noncommutative_composite==0) {
 363                 // there are neither commutative nor noncommutative_composite
 364                 // elements in assocseq
 365                 GINAC_ASSERT(count_commutative==0);
 366
 367                 size_t assoc_num = assocseq.size();
 368                 exvectorvector evv;
 369                 unsignedvector rttinfos;
 370                 evv.reserve(assoc_num);
 371                 rttinfos.reserve(assoc_num);
 372
 373                 cit = assocseq.begin(), citend = assocseq.end();
 374                 while (cit != citend) {
 375                         unsigned ti = cit->return_type_tinfo();
 376                         size_t rtt_num = rttinfos.size();
 377                         // search type in vector of known types
 378                         for (i=0; i<rtt_num; ++i) {
 379                                 if (ti == rttinfos[i]) {
 380                                         evv[i].push_back(*cit);
 381                                         break;
 382                                 }
 383                         }
 384                         if (i >= rtt_num) {
 385                                 // new type
 386                                 rttinfos.push_back(ti);
 387                                 evv.push_back(exvector());
 388                                 (evv.end()-1)->reserve(assoc_num);
 389                                 (evv.end()-1)->push_back(*cit);
 390                         }
 391                         ++cit;
 392                 }
 393
 394                 size_t evv_num = evv.size();
 395 #ifdef DO_GINAC_ASSERT
 396                 GINAC_ASSERT(evv_num == rttinfos.size());
 397                 GINAC_ASSERT(evv_num > 0);
 398                 size_t s=0;
 399                 for (i=0; i<evv_num; ++i)
 400                         s += evv[i].size();
 401                 GINAC_ASSERT(s == assoc_num);
 402 #endif // def DO_GINAC_ASSERT
 403
 404                 // if all elements are of same type, simplify the string
 405                 if (evv_num == 1)
 406                         return evv[0][0].eval_ncmul(evv[0]);
 407
 408                 exvector splitseq;
 409                 splitseq.reserve(evv_num);
 410                 for (i=0; i<evv_num; ++i)
 411                         splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
 412
 413                 return (new mul(splitseq))->setflag(status_flags::dynallocated);
 414         }
 415
 416         return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 417                                                                                   status_flags::evaluated);
 418 }
 419
 420 ex ncmul::evalm() const
 421 {
 422         // Evaluate children first
 423         std::auto_ptr<exvector> s(new exvector);
 424         s->reserve(seq.size());
 425         exvector::const_iterator it = seq.begin(), itend = seq.end();
 426         while (it != itend) {
 427                 s->push_back(it->evalm());
 428                 it++;
 429         }
 430
 431         // If there are only matrices, simply multiply them
 432         it = s->begin(); itend = s->end();
 433         if (is_a<matrix>(*it)) {
 434                 matrix prod(ex_to<matrix>(*it));
 435                 it++;
 436                 while (it != itend) {
 437                         if (!is_a<matrix>(*it))
 438                                 goto no_matrix;
 439                         prod = prod.mul(ex_to<matrix>(*it));
 440                         it++;
 441                 }
 442                 return prod;
 443         }
 444
 445 no_matrix:
 446         return (new ncmul(s))->setflag(status_flags::dynallocated);
 447 }
 448
 449 ex ncmul::thiscontainer(const exvector & v) const
 450 {
 451         return (new ncmul(v))->setflag(status_flags::dynallocated);
 452 }
 453
 454 ex ncmul::thiscontainer(std::auto_ptr<exvector> vp) const
 455 {
 456         return (new ncmul(vp))->setflag(status_flags::dynallocated);
 457 }
 458
 459 // protected
 460
 461 /** Implementation of ex::diff() for a non-commutative product. It applies
 462  *  the product rule.
 463  *  @see ex::diff */
 464 ex ncmul::derivative(const symbol & s) const
 465 {
 466         size_t num = seq.size();
 467         exvector addseq;
 468         addseq.reserve(num);
 469
 470         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 471         exvector ncmulseq = seq;
 472         for (size_t i=0; i<num; ++i) {
 473                 ex e = seq[i].diff(s);
 474                 e.swap(ncmulseq[i]);
 475                 addseq.push_back((new ncmul(ncmulseq))->setflag(status_flags::dynallocated));
 476                 e.swap(ncmulseq[i]);
 477         }
 478         return (new add(addseq))->setflag(status_flags::dynallocated);
 479 }
 480
 481 int ncmul::compare_same_type(const basic & other) const
 482 {
 483         return inherited::compare_same_type(other);
 484 }
 485
 486 unsigned ncmul::return_type() const
 487 {
 488         if (seq.empty())
 489                 return return_types::commutative;
 490
 491         bool all_commutative = true;
 492         exvector::const_iterator noncommutative_element; // point to first found nc element
 493
 494         exvector::const_iterator i = seq.begin(), end = seq.end();
 495         while (i != end) {
 496                 unsigned rt = i->return_type();
 497                 if (rt == return_types::noncommutative_composite)
 498                         return rt; // one ncc -> mul also ncc
 499                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 500                         // first nc element found, remember position
 501                         noncommutative_element = i;
 502                         all_commutative = false;
 503                 }
 504                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 505                         // another nc element found, compare type_infos
 506                         if (noncommutative_element->return_type_tinfo() != i->return_type_tinfo()) {
 507                                 // diffent types -> mul is ncc
 508                                 return return_types::noncommutative_composite;
 509                         }
 510                 }
 511                 ++i;
 512         }
 513         // all factors checked
 514         GINAC_ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
 515         return all_commutative ? return_types::commutative : return_types::noncommutative;
 516 }
 517
 518 unsigned ncmul::return_type_tinfo() const
 519 {
 520         if (seq.empty())
 521                 return tinfo_key;
 522
 523         // return type_info of first noncommutative element
 524         exvector::const_iterator i = seq.begin(), end = seq.end();
 525         while (i != end) {
 526                 if (i->return_type() == return_types::noncommutative)
 527                         return i->return_type_tinfo();
 528                 ++i;
 529         }
 530
 531         // no noncommutative element found, should not happen
 532         return tinfo_key;
 533 }
 534
 535 //////////
 536 // new virtual functions which can be overridden by derived classes
 537 //////////
 538
 539 // none
 540
 541 //////////
 542 // non-virtual functions in this class
 543 //////////
 544
 545 exvector ncmul::expandchildren(unsigned options) const
 546 {
 547         exvector s;
 548         s.reserve(seq.size());
 549         exvector::const_iterator it = seq.begin(), itend = seq.end();
 550         while (it != itend) {
 551                 s.push_back(it->expand(options));
 552                 it++;
 553         }
 554         return s;
 555 }
 556
 557 const exvector & ncmul::get_factors() const
 558 {
 559         return seq;
 560 }
 561
 562 //////////
 563 // friend functions
 564 //////////
 565
 566 ex reeval_ncmul(const exvector & v)
 567 {
 568         return (new ncmul(v))->setflag(status_flags::dynallocated);
 569 }
 570
 571 ex hold_ncmul(const exvector & v)
 572 {
 573         if (v.empty())
 574                 return _ex1;
 575         else if (v.size() == 1)
 576                 return v[0];
 577         else
 578                 return (new ncmul(v))->setflag(status_flags::dynallocated |
 579                                                status_flags::evaluated);
 580 }
 581
 582 } // namespace GiNaC