ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2008 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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  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 "clifford.h"
  32 #include "matrix.h"
  33 #include "archive.h"
  34 #include "indexed.h"
  35 #include "utils.h"
  36
  37 namespace GiNaC {
  38
  39 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(ncmul, exprseq,
  40   print_func<print_context>(&ncmul::do_print).
  41   print_func<print_tree>(&ncmul::do_print_tree).
  42   print_func<print_csrc>(&ncmul::do_print_csrc).
  43   print_func<print_python_repr>(&ncmul::do_print_csrc))
  44
  45
  46 //////////
  47 // default constructor
  48 //////////
  49
  50 ncmul::ncmul()
  51 {
  52         tinfo_key = &ncmul::tinfo_static;
  53 }
  54
  55 //////////
  56 // other constructors
  57 //////////
  58
  59 // public
  60
  61 ncmul::ncmul(const ex & lh, const ex & rh) : inherited(lh,rh)
  62 {
  63         tinfo_key = &ncmul::tinfo_static;
  64 }
  65
  66 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited(f1,f2,f3)
  67 {
  68         tinfo_key = &ncmul::tinfo_static;
  69 }
  70
  71 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  72              const ex & f4) : inherited(f1,f2,f3,f4)
  73 {
  74         tinfo_key = &ncmul::tinfo_static;
  75 }
  76
  77 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  78              const ex & f4, const ex & f5) : inherited(f1,f2,f3,f4,f5)
  79 {
  80         tinfo_key = &ncmul::tinfo_static;
  81 }
  82
  83 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  84              const ex & f4, const ex & f5, const ex & f6) : inherited(f1,f2,f3,f4,f5,f6)
  85 {
  86         tinfo_key = &ncmul::tinfo_static;
  87 }
  88
  89 ncmul::ncmul(const exvector & v, bool discardable) : inherited(v,discardable)
  90 {
  91         tinfo_key = &ncmul::tinfo_static;
  92 }
  93
  94 ncmul::ncmul(std::auto_ptr<exvector> vp) : inherited(vp)
  95 {
  96         tinfo_key = &ncmul::tinfo_static;
  97 }
  98
  99 //////////
 100 // archiving
 101 //////////
 102
 103 DEFAULT_ARCHIVING(ncmul)
 104
 105 //////////
 106 // functions overriding virtual functions from base classes
 107 //////////
 108
 109 // public
 110
 111 void ncmul::do_print(const print_context & c, unsigned level) const
 112 {
 113         printseq(c, '(', '*', ')', precedence(), level);
 114 }
 115
 116 void ncmul::do_print_csrc(const print_context & c, unsigned level) const
 117 {
 118         c.s << class_name();
 119         printseq(c, '(', ',', ')', precedence(), precedence());
 120 }
 121
 122 bool ncmul::info(unsigned inf) const
 123 {
 124         return inherited::info(inf);
 125 }
 126
 127 typedef std::vector<int> intvector;
 128
 129 ex ncmul::expand(unsigned options) const
 130 {
 131         // First, expand the children
 132         std::auto_ptr<exvector> vp = expandchildren(options);
 133         const exvector &expanded_seq = vp.get() ? *vp : this->seq;
 134
 135         // Now, look for all the factors that are sums and remember their
 136         // position and number of terms.
 137         intvector positions_of_adds(expanded_seq.size());
 138         intvector number_of_add_operands(expanded_seq.size());
 139
 140         size_t number_of_adds = 0;
 141         size_t number_of_expanded_terms = 1;
 142
 143         size_t current_position = 0;
 144         exvector::const_iterator last = expanded_seq.end();
 145         for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 146                 if (is_exactly_a<add>(*cit)) {
 147                         positions_of_adds[number_of_adds] = current_position;
 148                         size_t num_ops = cit->nops();
 149                         number_of_add_operands[number_of_adds] = num_ops;
 150                         number_of_expanded_terms *= num_ops;
 151                         number_of_adds++;
 152                 }
 153                 ++current_position;
 154         }
 155
 156         // If there are no sums, we are done
 157         if (number_of_adds == 0) {
 158                 if (vp.get())
 159                         return (new ncmul(vp))->
 160                                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 161                 else
 162                         return *this;
 163         }
 164
 165         // Now, form all possible products of the terms of the sums with the
 166         // remaining factors, and add them together
 167         exvector distrseq;
 168         distrseq.reserve(number_of_expanded_terms);
 169
 170         intvector k(number_of_adds);
 171
 172         /* Rename indices in the static members of the product */
 173         exvector expanded_seq_mod;
 174         size_t j = 0;
 175         exvector va;
 176
 177         for (size_t i=0; i<expanded_seq.size(); i++) {
 178                 if (i == positions_of_adds[j]) {
 179                         expanded_seq_mod.push_back(_ex1);
 180                         j++;
 181                 } else {
 182                         expanded_seq_mod.push_back(rename_dummy_indices_uniquely(va, expanded_seq[i], true));
 183                 }
 184         }
 185
 186         while (true) {
 187                 exvector term = expanded_seq_mod;
 188                 for (size_t i=0; i<number_of_adds; i++) {
 189                         term[positions_of_adds[i]] = rename_dummy_indices_uniquely(va, expanded_seq[positions_of_adds[i]].op(k[i]), true);
 190                 }
 191
 192                 distrseq.push_back((new ncmul(term, true))->
 193                                     setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 194
 195                 // increment k[]
 196                 int l = number_of_adds-1;
 197                 while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
 198                         k[l] = 0;
 199                         l--;
 200                 }
 201                 if (l<0)
 202                         break;
 203         }
 204
 205         return (new add(distrseq))->
 206                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 207 }
 208
 209 int ncmul::degree(const ex & s) const
 210 {
 211         if (is_equal(ex_to<basic>(s)))
 212                 return 1;
 213
 214         // Sum up degrees of factors
 215         int deg_sum = 0;
 216         exvector::const_iterator i = seq.begin(), end = seq.end();
 217         while (i != end) {
 218                 deg_sum += i->degree(s);
 219                 ++i;
 220         }
 221         return deg_sum;
 222 }
 223
 224 int ncmul::ldegree(const ex & s) const
 225 {
 226         if (is_equal(ex_to<basic>(s)))
 227                 return 1;
 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         if (is_equal(ex_to<basic>(s)))
 242                 return n==1 ? _ex1 : _ex0;
 243
 244         exvector coeffseq;
 245         coeffseq.reserve(seq.size());
 246
 247         if (n == 0) {
 248                 // product of individual coeffs
 249                 // if a non-zero power of s is found, the resulting product will be 0
 250                 exvector::const_iterator it=seq.begin();
 251                 while (it!=seq.end()) {
 252                         coeffseq.push_back((*it).coeff(s,n));
 253                         ++it;
 254                 }
 255                 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 256         }
 257
 258         exvector::const_iterator i = seq.begin(), end = seq.end();
 259         bool coeff_found = false;
 260         while (i != end) {
 261                 ex c = i->coeff(s,n);
 262                 if (c.is_zero()) {
 263                         coeffseq.push_back(*i);
 264                 } else {
 265                         coeffseq.push_back(c);
 266                         coeff_found = true;
 267                 }
 268                 ++i;
 269         }
 270
 271         if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 272
 273         return _ex0;
 274 }
 275
 276 size_t ncmul::count_factors(const ex & e) const
 277 {
 278         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 279                 (is_exactly_a<ncmul>(e))) {
 280                 size_t factors=0;
 281                 for (size_t i=0; i<e.nops(); i++)
 282                         factors += count_factors(e.op(i));
 283
 284                 return factors;
 285         }
 286         return 1;
 287 }
 288
 289 void ncmul::append_factors(exvector & v, const ex & e) const
 290 {
 291         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 292                 (is_exactly_a<ncmul>(e))) {
 293                 for (size_t i=0; i<e.nops(); i++)
 294                         append_factors(v, e.op(i));
 295         } else
 296                 v.push_back(e);
 297 }
 298
 299 typedef std::vector<unsigned> unsignedvector;
 300 typedef std::vector<exvector> exvectorvector;
 301
 302 /** Perform automatic term rewriting rules in this class.  In the following
 303  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 304  *  stand for such expressions that contain a plain number.
 305  *  - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 306  *  - ncmul(x) -> x
 307  *  - ncmul() -> 1
 308  *  - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...))  (pull out commutative elements)
 309  *  - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))  (collect elements of same type)
 310  *  - ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 311  *
 312  *  @param level cut-off in recursive evaluation */
 313 ex ncmul::eval(int level) const
 314 {
 315         // The following additional rule would be nice, but produces a recursion,
 316         // which must be trapped by introducing a flag that the sub-ncmuls()
 317         // are already evaluated (maybe later...)
 318         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 319         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 320         //                      (X noncommutative_composite)
 321
 322         if ((level==1) && (flags & status_flags::evaluated)) {
 323                 return *this;
 324         }
 325
 326         exvector evaledseq=evalchildren(level);
 327
 328         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 329         //     ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 330         size_t factors = 0;
 331         exvector::const_iterator cit = evaledseq.begin(), citend = evaledseq.end();
 332         while (cit != citend)
 333                 factors += count_factors(*cit++);
 334
 335         exvector assocseq;
 336         assocseq.reserve(factors);
 337         cit = evaledseq.begin();
 338         make_flat_inserter mf(evaledseq, true);
 339         while (cit != citend)
 340         {       ex factor = mf.handle_factor(*(cit++), 1);
 341                 append_factors(assocseq, factor);
 342         }
 343
 344         // ncmul(x) -> x
 345         if (assocseq.size()==1) return *(seq.begin());
 346
 347         // ncmul() -> 1
 348         if (assocseq.empty()) return _ex1;
 349
 350         // determine return types
 351         unsignedvector rettypes;
 352         rettypes.reserve(assocseq.size());
 353         size_t i = 0;
 354         size_t count_commutative=0;
 355         size_t count_noncommutative=0;
 356         size_t count_noncommutative_composite=0;
 357         cit = assocseq.begin(); citend = assocseq.end();
 358         while (cit != citend) {
 359                 switch (rettypes[i] = cit->return_type()) {
 360                 case return_types::commutative:
 361                         count_commutative++;
 362                         break;
 363                 case return_types::noncommutative:
 364                         count_noncommutative++;
 365                         break;
 366                 case return_types::noncommutative_composite:
 367                         count_noncommutative_composite++;
 368                         break;
 369                 default:
 370                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 371                 }
 372                 ++i; ++cit;
 373         }
 374         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 375
 376         // ncmul(...,c1,...,c2,...) ->
 377         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 378         if (count_commutative!=0) {
 379                 exvector commutativeseq;
 380                 commutativeseq.reserve(count_commutative+1);
 381                 exvector noncommutativeseq;
 382                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 383                 size_t num = assocseq.size();
 384                 for (size_t i=0; i<num; ++i) {
 385                         if (rettypes[i]==return_types::commutative)
 386                                 commutativeseq.push_back(assocseq[i]);
 387                         else
 388                                 noncommutativeseq.push_back(assocseq[i]);
 389                 }
 390                 commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
 391                 return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 392         }
 393
 394         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 395         //     (collect elements of same type)
 396
 397         if (count_noncommutative_composite==0) {
 398                 // there are neither commutative nor noncommutative_composite
 399                 // elements in assocseq
 400                 GINAC_ASSERT(count_commutative==0);
 401
 402                 size_t assoc_num = assocseq.size();
 403                 exvectorvector evv;
 404                 std::vector<tinfo_t> rttinfos;
 405                 evv.reserve(assoc_num);
 406                 rttinfos.reserve(assoc_num);
 407
 408                 cit = assocseq.begin(), citend = assocseq.end();
 409                 while (cit != citend) {
 410                         tinfo_t ti = cit->return_type_tinfo();
 411                         size_t rtt_num = rttinfos.size();
 412                         // search type in vector of known types
 413                         for (i=0; i<rtt_num; ++i) {
 414                                 if(ti == rttinfos[i]) {
 415                                         evv[i].push_back(*cit);
 416                                         break;
 417                                 }
 418                         }
 419                         if (i >= rtt_num) {
 420                                 // new type
 421                                 rttinfos.push_back(ti);
 422                                 evv.push_back(exvector());
 423                                 (evv.end()-1)->reserve(assoc_num);
 424                                 (evv.end()-1)->push_back(*cit);
 425                         }
 426                         ++cit;
 427                 }
 428
 429                 size_t evv_num = evv.size();
 430 #ifdef DO_GINAC_ASSERT
 431                 GINAC_ASSERT(evv_num == rttinfos.size());
 432                 GINAC_ASSERT(evv_num > 0);
 433                 size_t s=0;
 434                 for (i=0; i<evv_num; ++i)
 435                         s += evv[i].size();
 436                 GINAC_ASSERT(s == assoc_num);
 437 #endif // def DO_GINAC_ASSERT
 438
 439                 // if all elements are of same type, simplify the string
 440                 if (evv_num == 1) {
 441                         return evv[0][0].eval_ncmul(evv[0]);
 442                 }
 443
 444                 exvector splitseq;
 445                 splitseq.reserve(evv_num);
 446                 for (i=0; i<evv_num; ++i)
 447                         splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
 448
 449                 return (new mul(splitseq))->setflag(status_flags::dynallocated);
 450         }
 451
 452         return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 453                                                                                   status_flags::evaluated);
 454 }
 455
 456 ex ncmul::evalm() const
 457 {
 458         // Evaluate children first
 459         std::auto_ptr<exvector> s(new exvector);
 460         s->reserve(seq.size());
 461         exvector::const_iterator it = seq.begin(), itend = seq.end();
 462         while (it != itend) {
 463                 s->push_back(it->evalm());
 464                 it++;
 465         }
 466
 467         // If there are only matrices, simply multiply them
 468         it = s->begin(); itend = s->end();
 469         if (is_a<matrix>(*it)) {
 470                 matrix prod(ex_to<matrix>(*it));
 471                 it++;
 472                 while (it != itend) {
 473                         if (!is_a<matrix>(*it))
 474                                 goto no_matrix;
 475                         prod = prod.mul(ex_to<matrix>(*it));
 476                         it++;
 477                 }
 478                 return prod;
 479         }
 480
 481 no_matrix:
 482         return (new ncmul(s))->setflag(status_flags::dynallocated);
 483 }
 484
 485 ex ncmul::thiscontainer(const exvector & v) const
 486 {
 487         return (new ncmul(v))->setflag(status_flags::dynallocated);
 488 }
 489
 490 ex ncmul::thiscontainer(std::auto_ptr<exvector> vp) const
 491 {
 492         return (new ncmul(vp))->setflag(status_flags::dynallocated);
 493 }
 494
 495 ex ncmul::conjugate() const
 496 {
 497         if (return_type() != return_types::noncommutative) {
 498                 return exprseq::conjugate();
 499         }
 500
 501         if (!is_clifford_tinfo(return_type_tinfo())) {
 502                 return exprseq::conjugate();
 503         }
 504
 505         exvector ev;
 506         ev.reserve(nops());
 507         for (const_iterator i=end(); i!=begin();) {
 508                 --i;
 509                 ev.push_back(i->conjugate());
 510         }
 511         return (new ncmul(ev, true))->setflag(status_flags::dynallocated).eval();
 512 }
 513
 514 ex ncmul::real_part() const
 515 {
 516         return basic::real_part();
 517 }
 518
 519 ex ncmul::imag_part() const
 520 {
 521         return basic::imag_part();
 522 }
 523
 524 // protected
 525
 526 /** Implementation of ex::diff() for a non-commutative product. It applies
 527  *  the product rule.
 528  *  @see ex::diff */
 529 ex ncmul::derivative(const symbol & s) const
 530 {
 531         size_t num = seq.size();
 532         exvector addseq;
 533         addseq.reserve(num);
 534
 535         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 536         exvector ncmulseq = seq;
 537         for (size_t i=0; i<num; ++i) {
 538                 ex e = seq[i].diff(s);
 539                 e.swap(ncmulseq[i]);
 540                 addseq.push_back((new ncmul(ncmulseq))->setflag(status_flags::dynallocated));
 541                 e.swap(ncmulseq[i]);
 542         }
 543         return (new add(addseq))->setflag(status_flags::dynallocated);
 544 }
 545
 546 int ncmul::compare_same_type(const basic & other) const
 547 {
 548         return inherited::compare_same_type(other);
 549 }
 550
 551 unsigned ncmul::return_type() const
 552 {
 553         if (seq.empty())
 554                 return return_types::commutative;
 555
 556         bool all_commutative = true;
 557         exvector::const_iterator noncommutative_element; // point to first found nc element
 558
 559         exvector::const_iterator i = seq.begin(), end = seq.end();
 560         while (i != end) {
 561                 unsigned rt = i->return_type();
 562                 if (rt == return_types::noncommutative_composite)
 563                         return rt; // one ncc -> mul also ncc
 564                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 565                         // first nc element found, remember position
 566                         noncommutative_element = i;
 567                         all_commutative = false;
 568                 }
 569                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 570                         // another nc element found, compare type_infos
 571                         if(noncommutative_element->return_type_tinfo() != i->return_type_tinfo())
 572                                         return return_types::noncommutative_composite;
 573                 }
 574                 ++i;
 575         }
 576         // all factors checked
 577         GINAC_ASSERT(!all_commutative); // not all factors should commutate, because this is a ncmul();
 578         return all_commutative ? return_types::commutative : return_types::noncommutative;
 579 }
 580
 581 tinfo_t ncmul::return_type_tinfo() const
 582 {
 583         if (seq.empty())
 584                 return this;
 585
 586         // return type_info of first noncommutative element
 587         exvector::const_iterator i = seq.begin(), end = seq.end();
 588         while (i != end) {
 589                 if (i->return_type() == return_types::noncommutative)
 590                         return i->return_type_tinfo();
 591                 ++i;
 592         }
 593
 594         // no noncommutative element found, should not happen
 595         return this;
 596 }
 597
 598 //////////
 599 // new virtual functions which can be overridden by derived classes
 600 //////////
 601
 602 // none
 603
 604 //////////
 605 // non-virtual functions in this class
 606 //////////
 607
 608 std::auto_ptr<exvector> ncmul::expandchildren(unsigned options) const
 609 {
 610         const_iterator cit = this->seq.begin(), end = this->seq.end();
 611         while (cit != end) {
 612                 const ex & expanded_ex = cit->expand(options);
 613                 if (!are_ex_trivially_equal(*cit, expanded_ex)) {
 614
 615                         // copy first part of seq which hasn't changed
 616                         std::auto_ptr<exvector> s(new exvector(this->seq.begin(), cit));
 617                         reserve(*s, this->seq.size());
 618
 619                         // insert changed element
 620                         s->push_back(expanded_ex);
 621                         ++cit;
 622
 623                         // copy rest
 624                         while (cit != end) {
 625                                 s->push_back(cit->expand(options));
 626                                 ++cit;
 627                         }
 628
 629                         return s;
 630                 }
 631
 632                 ++cit;
 633         }
 634
 635         return std::auto_ptr<exvector>(0); // nothing has changed
 636 }
 637
 638 const exvector & ncmul::get_factors() const
 639 {
 640         return seq;
 641 }
 642
 643 //////////
 644 // friend functions
 645 //////////
 646
 647 ex reeval_ncmul(const exvector & v)
 648 {
 649         return (new ncmul(v))->setflag(status_flags::dynallocated);
 650 }
 651
 652 ex hold_ncmul(const exvector & v)
 653 {
 654         if (v.empty())
 655                 return _ex1;
 656         else if (v.size() == 1)
 657                 return v[0];
 658         else
 659                 return (new ncmul(v))->setflag(status_flags::dynallocated |
 660                                                status_flags::evaluated);
 661 }
 662
 663 } // namespace GiNaC