ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2009 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 "ncmul.h"
  24 #include "ex.h"
  25 #include "add.h"
  26 #include "mul.h"
  27 #include "clifford.h"
  28 #include "matrix.h"
  29 #include "archive.h"
  30 #include "indexed.h"
  31 #include "utils.h"
  32
  33 #include <algorithm>
  34 #include <iostream>
  35 #include <stdexcept>
  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 }
  53
  54 //////////
  55 // other constructors
  56 //////////
  57
  58 // public
  59
  60 ncmul::ncmul(const ex & lh, const ex & rh) : inherited(lh,rh)
  61 {
  62 }
  63
  64 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited(f1,f2,f3)
  65 {
  66 }
  67
  68 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  69              const ex & f4) : inherited(f1,f2,f3,f4)
  70 {
  71 }
  72
  73 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  74              const ex & f4, const ex & f5) : inherited(f1,f2,f3,f4,f5)
  75 {
  76 }
  77
  78 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  79              const ex & f4, const ex & f5, const ex & f6) : inherited(f1,f2,f3,f4,f5,f6)
  80 {
  81 }
  82
  83 ncmul::ncmul(const exvector & v, bool discardable) : inherited(v,discardable)
  84 {
  85 }
  86
  87 ncmul::ncmul(std::auto_ptr<exvector> vp) : inherited(vp)
  88 {
  89 }
  90
  91 //////////
  92 // archiving
  93 //////////
  94
  95
  96 //////////
  97 // functions overriding virtual functions from base classes
  98 //////////
  99
 100 // public
 101
 102 void ncmul::do_print(const print_context & c, unsigned level) const
 103 {
 104         printseq(c, '(', '*', ')', precedence(), level);
 105 }
 106
 107 void ncmul::do_print_csrc(const print_context & c, unsigned level) const
 108 {
 109         c.s << class_name();
 110         printseq(c, '(', ',', ')', precedence(), precedence());
 111 }
 112
 113 bool ncmul::info(unsigned inf) const
 114 {
 115         return inherited::info(inf);
 116 }
 117
 118 typedef std::vector<std::size_t> uintvector;
 119
 120 ex ncmul::expand(unsigned options) const
 121 {
 122         // First, expand the children
 123         std::auto_ptr<exvector> vp = expandchildren(options);
 124         const exvector &expanded_seq = vp.get() ? *vp : this->seq;
 125
 126         // Now, look for all the factors that are sums and remember their
 127         // position and number of terms.
 128         uintvector positions_of_adds(expanded_seq.size());
 129         uintvector number_of_add_operands(expanded_seq.size());
 130
 131         size_t number_of_adds = 0;
 132         size_t number_of_expanded_terms = 1;
 133
 134         size_t current_position = 0;
 135         exvector::const_iterator last = expanded_seq.end();
 136         for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 137                 if (is_exactly_a<add>(*cit)) {
 138                         positions_of_adds[number_of_adds] = current_position;
 139                         size_t num_ops = cit->nops();
 140                         number_of_add_operands[number_of_adds] = num_ops;
 141                         number_of_expanded_terms *= num_ops;
 142                         number_of_adds++;
 143                 }
 144                 ++current_position;
 145         }
 146
 147         // If there are no sums, we are done
 148         if (number_of_adds == 0) {
 149                 if (vp.get())
 150                         return (new ncmul(vp))->
 151                                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 152                 else
 153                         return *this;
 154         }
 155
 156         // Now, form all possible products of the terms of the sums with the
 157         // remaining factors, and add them together
 158         exvector distrseq;
 159         distrseq.reserve(number_of_expanded_terms);
 160
 161         uintvector k(number_of_adds);
 162
 163         /* Rename indices in the static members of the product */
 164         exvector expanded_seq_mod;
 165         size_t j = 0;
 166         exvector va;
 167
 168         for (size_t i=0; i<expanded_seq.size(); i++) {
 169                 if (i == positions_of_adds[j]) {
 170                         expanded_seq_mod.push_back(_ex1);
 171                         j++;
 172                 } else {
 173                         expanded_seq_mod.push_back(rename_dummy_indices_uniquely(va, expanded_seq[i], true));
 174                 }
 175         }
 176
 177         while (true) {
 178                 exvector term = expanded_seq_mod;
 179                 for (size_t i=0; i<number_of_adds; i++) {
 180                         term[positions_of_adds[i]] = rename_dummy_indices_uniquely(va, expanded_seq[positions_of_adds[i]].op(k[i]), true);
 181                 }
 182
 183                 distrseq.push_back((new ncmul(term, true))->
 184                                     setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 185
 186                 // increment k[]
 187                 int l = number_of_adds-1;
 188                 while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
 189                         k[l] = 0;
 190                         l--;
 191                 }
 192                 if (l<0)
 193                         break;
 194         }
 195
 196         return (new add(distrseq))->
 197                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 198 }
 199
 200 int ncmul::degree(const ex & s) const
 201 {
 202         if (is_equal(ex_to<basic>(s)))
 203                 return 1;
 204
 205         // Sum up degrees of factors
 206         int deg_sum = 0;
 207         exvector::const_iterator i = seq.begin(), end = seq.end();
 208         while (i != end) {
 209                 deg_sum += i->degree(s);
 210                 ++i;
 211         }
 212         return deg_sum;
 213 }
 214
 215 int ncmul::ldegree(const ex & s) const
 216 {
 217         if (is_equal(ex_to<basic>(s)))
 218                 return 1;
 219
 220         // Sum up degrees of factors
 221         int deg_sum = 0;
 222         exvector::const_iterator i = seq.begin(), end = seq.end();
 223         while (i != end) {
 224                 deg_sum += i->degree(s);
 225                 ++i;
 226         }
 227         return deg_sum;
 228 }
 229
 230 ex ncmul::coeff(const ex & s, int n) const
 231 {
 232         if (is_equal(ex_to<basic>(s)))
 233                 return n==1 ? _ex1 : _ex0;
 234
 235         exvector coeffseq;
 236         coeffseq.reserve(seq.size());
 237
 238         if (n == 0) {
 239                 // product of individual coeffs
 240                 // if a non-zero power of s is found, the resulting product will be 0
 241                 exvector::const_iterator it=seq.begin();
 242                 while (it!=seq.end()) {
 243                         coeffseq.push_back((*it).coeff(s,n));
 244                         ++it;
 245                 }
 246                 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 247         }
 248
 249         exvector::const_iterator i = seq.begin(), end = seq.end();
 250         bool coeff_found = false;
 251         while (i != end) {
 252                 ex c = i->coeff(s,n);
 253                 if (c.is_zero()) {
 254                         coeffseq.push_back(*i);
 255                 } else {
 256                         coeffseq.push_back(c);
 257                         coeff_found = true;
 258                 }
 259                 ++i;
 260         }
 261
 262         if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 263
 264         return _ex0;
 265 }
 266
 267 size_t ncmul::count_factors(const ex & e) const
 268 {
 269         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 270                 (is_exactly_a<ncmul>(e))) {
 271                 size_t factors=0;
 272                 for (size_t i=0; i<e.nops(); i++)
 273                         factors += count_factors(e.op(i));
 274
 275                 return factors;
 276         }
 277         return 1;
 278 }
 279
 280 void ncmul::append_factors(exvector & v, const ex & e) const
 281 {
 282         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 283                 (is_exactly_a<ncmul>(e))) {
 284                 for (size_t i=0; i<e.nops(); i++)
 285                         append_factors(v, e.op(i));
 286         } else
 287                 v.push_back(e);
 288 }
 289
 290 typedef std::vector<unsigned> unsignedvector;
 291 typedef std::vector<exvector> exvectorvector;
 292
 293 /** Perform automatic term rewriting rules in this class.  In the following
 294  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 295  *  stand for such expressions that contain a plain number.
 296  *  - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 297  *  - ncmul(x) -> x
 298  *  - ncmul() -> 1
 299  *  - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...))  (pull out commutative elements)
 300  *  - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))  (collect elements of same type)
 301  *  - ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 302  *
 303  *  @param level cut-off in recursive evaluation */
 304 ex ncmul::eval(int level) const
 305 {
 306         // The following additional rule would be nice, but produces a recursion,
 307         // which must be trapped by introducing a flag that the sub-ncmuls()
 308         // are already evaluated (maybe later...)
 309         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 310         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 311         //                      (X noncommutative_composite)
 312
 313         if ((level==1) && (flags & status_flags::evaluated)) {
 314                 return *this;
 315         }
 316
 317         exvector evaledseq=evalchildren(level);
 318
 319         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 320         //     ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 321         size_t factors = 0;
 322         exvector::const_iterator cit = evaledseq.begin(), citend = evaledseq.end();
 323         while (cit != citend)
 324                 factors += count_factors(*cit++);
 325
 326         exvector assocseq;
 327         assocseq.reserve(factors);
 328         cit = evaledseq.begin();
 329         make_flat_inserter mf(evaledseq, true);
 330         while (cit != citend)
 331         {       ex factor = mf.handle_factor(*(cit++), 1);
 332                 append_factors(assocseq, factor);
 333         }
 334
 335         // ncmul(x) -> x
 336         if (assocseq.size()==1) return *(seq.begin());
 337
 338         // ncmul() -> 1
 339         if (assocseq.empty()) return _ex1;
 340
 341         // determine return types
 342         unsignedvector rettypes(assocseq.size());
 343         size_t i = 0;
 344         size_t count_commutative=0;
 345         size_t count_noncommutative=0;
 346         size_t count_noncommutative_composite=0;
 347         cit = assocseq.begin(); citend = assocseq.end();
 348         while (cit != citend) {
 349                 rettypes[i] = cit->return_type();
 350                 switch (rettypes[i]) {
 351                 case return_types::commutative:
 352                         count_commutative++;
 353                         break;
 354                 case return_types::noncommutative:
 355                         count_noncommutative++;
 356                         break;
 357                 case return_types::noncommutative_composite:
 358                         count_noncommutative_composite++;
 359                         break;
 360                 default:
 361                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 362                 }
 363                 ++i; ++cit;
 364         }
 365         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 366
 367         // ncmul(...,c1,...,c2,...) ->
 368         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 369         if (count_commutative!=0) {
 370                 exvector commutativeseq;
 371                 commutativeseq.reserve(count_commutative+1);
 372                 exvector noncommutativeseq;
 373                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 374                 size_t num = assocseq.size();
 375                 for (size_t i=0; i<num; ++i) {
 376                         if (rettypes[i]==return_types::commutative)
 377                                 commutativeseq.push_back(assocseq[i]);
 378                         else
 379                                 noncommutativeseq.push_back(assocseq[i]);
 380                 }
 381                 commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
 382                 return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 383         }
 384
 385         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 386         //     (collect elements of same type)
 387
 388         if (count_noncommutative_composite==0) {
 389                 // there are neither commutative nor noncommutative_composite
 390                 // elements in assocseq
 391                 GINAC_ASSERT(count_commutative==0);
 392
 393                 size_t assoc_num = assocseq.size();
 394                 exvectorvector evv;
 395                 std::vector<return_type_t> rttinfos;
 396                 evv.reserve(assoc_num);
 397                 rttinfos.reserve(assoc_num);
 398
 399                 cit = assocseq.begin(), citend = assocseq.end();
 400                 while (cit != citend) {
 401                         return_type_t ti = cit->return_type_tinfo();
 402                         size_t rtt_num = rttinfos.size();
 403                         // search type in vector of known types
 404                         for (i=0; i<rtt_num; ++i) {
 405                                 if(ti == rttinfos[i]) {
 406                                         evv[i].push_back(*cit);
 407                                         break;
 408                                 }
 409                         }
 410                         if (i >= rtt_num) {
 411                                 // new type
 412                                 rttinfos.push_back(ti);
 413                                 evv.push_back(exvector());
 414                                 (evv.end()-1)->reserve(assoc_num);
 415                                 (evv.end()-1)->push_back(*cit);
 416                         }
 417                         ++cit;
 418                 }
 419
 420                 size_t evv_num = evv.size();
 421 #ifdef DO_GINAC_ASSERT
 422                 GINAC_ASSERT(evv_num == rttinfos.size());
 423                 GINAC_ASSERT(evv_num > 0);
 424                 size_t s=0;
 425                 for (i=0; i<evv_num; ++i)
 426                         s += evv[i].size();
 427                 GINAC_ASSERT(s == assoc_num);
 428 #endif // def DO_GINAC_ASSERT
 429
 430                 // if all elements are of same type, simplify the string
 431                 if (evv_num == 1) {
 432                         return evv[0][0].eval_ncmul(evv[0]);
 433                 }
 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() const
 448 {
 449         // Evaluate children first
 450         std::auto_ptr<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_a<matrix>(*it)) {
 461                 matrix prod(ex_to<matrix>(*it));
 462                 it++;
 463                 while (it != itend) {
 464                         if (!is_a<matrix>(*it))
 465                                 goto no_matrix;
 466                         prod = prod.mul(ex_to<matrix>(*it));
 467                         it++;
 468                 }
 469                 return prod;
 470         }
 471
 472 no_matrix:
 473         return (new ncmul(s))->setflag(status_flags::dynallocated);
 474 }
 475
 476 ex ncmul::thiscontainer(const exvector & v) const
 477 {
 478         return (new ncmul(v))->setflag(status_flags::dynallocated);
 479 }
 480
 481 ex ncmul::thiscontainer(std::auto_ptr<exvector> vp) const
 482 {
 483         return (new ncmul(vp))->setflag(status_flags::dynallocated);
 484 }
 485
 486 ex ncmul::conjugate() const
 487 {
 488         if (return_type() != return_types::noncommutative) {
 489                 return exprseq::conjugate();
 490         }
 491
 492         if (!is_clifford_tinfo(return_type_tinfo())) {
 493                 return exprseq::conjugate();
 494         }
 495
 496         exvector ev;
 497         ev.reserve(nops());
 498         for (const_iterator i=end(); i!=begin();) {
 499                 --i;
 500                 ev.push_back(i->conjugate());
 501         }
 502         return (new ncmul(ev, true))->setflag(status_flags::dynallocated).eval();
 503 }
 504
 505 ex ncmul::real_part() const
 506 {
 507         return basic::real_part();
 508 }
 509
 510 ex ncmul::imag_part() const
 511 {
 512         return basic::imag_part();
 513 }
 514
 515 // protected
 516
 517 /** Implementation of ex::diff() for a non-commutative product. It applies
 518  *  the product rule.
 519  *  @see ex::diff */
 520 ex ncmul::derivative(const symbol & s) const
 521 {
 522         size_t num = seq.size();
 523         exvector addseq;
 524         addseq.reserve(num);
 525
 526         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 527         exvector ncmulseq = seq;
 528         for (size_t i=0; i<num; ++i) {
 529                 ex e = seq[i].diff(s);
 530                 e.swap(ncmulseq[i]);
 531                 addseq.push_back((new ncmul(ncmulseq))->setflag(status_flags::dynallocated));
 532                 e.swap(ncmulseq[i]);
 533         }
 534         return (new add(addseq))->setflag(status_flags::dynallocated);
 535 }
 536
 537 int ncmul::compare_same_type(const basic & other) const
 538 {
 539         return inherited::compare_same_type(other);
 540 }
 541
 542 unsigned ncmul::return_type() const
 543 {
 544         if (seq.empty())
 545                 return return_types::commutative;
 546
 547         bool all_commutative = true;
 548         exvector::const_iterator noncommutative_element; // point to first found nc element
 549
 550         exvector::const_iterator i = seq.begin(), end = seq.end();
 551         while (i != end) {
 552                 unsigned rt = i->return_type();
 553                 if (rt == return_types::noncommutative_composite)
 554                         return rt; // one ncc -> mul also ncc
 555                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 556                         // first nc element found, remember position
 557                         noncommutative_element = i;
 558                         all_commutative = false;
 559                 }
 560                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 561                         // another nc element found, compare type_infos
 562                         if(noncommutative_element->return_type_tinfo() != i->return_type_tinfo())
 563                                         return return_types::noncommutative_composite;
 564                 }
 565                 ++i;
 566         }
 567         // all factors checked
 568         GINAC_ASSERT(!all_commutative); // not all factors should commutate, because this is a ncmul();
 569         return all_commutative ? return_types::commutative : return_types::noncommutative;
 570 }
 571
 572 return_type_t ncmul::return_type_tinfo() const
 573 {
 574         if (seq.empty())
 575                 return make_return_type_t<ncmul>();
 576
 577         // return type_info of first noncommutative element
 578         exvector::const_iterator i = seq.begin(), end = seq.end();
 579         while (i != end) {
 580                 if (i->return_type() == return_types::noncommutative)
 581                         return i->return_type_tinfo();
 582                 ++i;
 583         }
 584
 585         // no noncommutative element found, should not happen
 586         return make_return_type_t<ncmul>();
 587 }
 588
 589 //////////
 590 // new virtual functions which can be overridden by derived classes
 591 //////////
 592
 593 // none
 594
 595 //////////
 596 // non-virtual functions in this class
 597 //////////
 598
 599 std::auto_ptr<exvector> ncmul::expandchildren(unsigned options) const
 600 {
 601         const_iterator cit = this->seq.begin(), end = this->seq.end();
 602         while (cit != end) {
 603                 const ex & expanded_ex = cit->expand(options);
 604                 if (!are_ex_trivially_equal(*cit, expanded_ex)) {
 605
 606                         // copy first part of seq which hasn't changed
 607                         std::auto_ptr<exvector> s(new exvector(this->seq.begin(), cit));
 608                         reserve(*s, this->seq.size());
 609
 610                         // insert changed element
 611                         s->push_back(expanded_ex);
 612                         ++cit;
 613
 614                         // copy rest
 615                         while (cit != end) {
 616                                 s->push_back(cit->expand(options));
 617                                 ++cit;
 618                         }
 619
 620                         return s;
 621                 }
 622
 623                 ++cit;
 624         }
 625
 626         return std::auto_ptr<exvector>(0); // nothing has changed
 627 }
 628
 629 const exvector & ncmul::get_factors() const
 630 {
 631         return seq;
 632 }
 633
 634 //////////
 635 // friend functions
 636 //////////
 637
 638 ex reeval_ncmul(const exvector & v)
 639 {
 640         return (new ncmul(v))->setflag(status_flags::dynallocated);
 641 }
 642
 643 ex hold_ncmul(const exvector & v)
 644 {
 645         if (v.empty())
 646                 return _ex1;
 647         else if (v.size() == 1)
 648                 return v[0];
 649         else
 650                 return (new ncmul(v))->setflag(status_flags::dynallocated |
 651                                                status_flags::evaluated);
 652 }
 653
 654 GINAC_BIND_UNARCHIVER(ncmul);
 655
 656 } // namespace GiNaC