ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2015 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) : inherited(v)
  84 {
  85 }
  86
  87 ncmul::ncmul(exvector && v) : inherited(std::move(v))
  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         exvector v = expandchildren(options);
 124         const exvector &expanded_seq = v.empty() ? this->seq : v;
 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         for (auto & it : expanded_seq) {
 136                 if (is_exactly_a<add>(it)) {
 137                         positions_of_adds[number_of_adds] = current_position;
 138                         size_t num_ops = it.nops();
 139                         number_of_add_operands[number_of_adds] = num_ops;
 140                         number_of_expanded_terms *= num_ops;
 141                         number_of_adds++;
 142                 }
 143                 ++current_position;
 144         }
 145
 146         // If there are no sums, we are done
 147         if (number_of_adds == 0) {
 148                 if (!v.empty())
 149                         return (new ncmul(std::move(v)))->
 150                                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 151                 else
 152                         return *this;
 153         }
 154
 155         // Now, form all possible products of the terms of the sums with the
 156         // remaining factors, and add them together
 157         exvector distrseq;
 158         distrseq.reserve(number_of_expanded_terms);
 159
 160         uintvector k(number_of_adds);
 161
 162         /* Rename indices in the static members of the product */
 163         exvector expanded_seq_mod;
 164         size_t j = 0;
 165         exvector va;
 166
 167         for (size_t i=0; i<expanded_seq.size(); i++) {
 168                 if (i == positions_of_adds[j]) {
 169                         expanded_seq_mod.push_back(_ex1);
 170                         j++;
 171                 } else {
 172                         expanded_seq_mod.push_back(rename_dummy_indices_uniquely(va, expanded_seq[i], true));
 173                 }
 174         }
 175
 176         while (true) {
 177                 exvector term = expanded_seq_mod;
 178                 for (size_t i=0; i<number_of_adds; i++) {
 179                         term[positions_of_adds[i]] = rename_dummy_indices_uniquely(va, expanded_seq[positions_of_adds[i]].op(k[i]), true);
 180                 }
 181
 182                 distrseq.push_back((new ncmul(std::move(term)))->
 183                                     setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 184
 185                 // increment k[]
 186                 int l = number_of_adds-1;
 187                 while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
 188                         k[l] = 0;
 189                         l--;
 190                 }
 191                 if (l<0)
 192                         break;
 193         }
 194
 195         return (new add(distrseq))->
 196                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 197 }
 198
 199 int ncmul::degree(const ex & s) const
 200 {
 201         if (is_equal(ex_to<basic>(s)))
 202                 return 1;
 203
 204         // Sum up degrees of factors
 205         int deg_sum = 0;
 206         for (auto & i : seq)
 207                 deg_sum += i.degree(s);
 208         return deg_sum;
 209 }
 210
 211 int ncmul::ldegree(const ex & s) const
 212 {
 213         if (is_equal(ex_to<basic>(s)))
 214                 return 1;
 215
 216         // Sum up degrees of factors
 217         int deg_sum = 0;
 218         for (auto & i : seq)
 219                 deg_sum += i.degree(s);
 220         return deg_sum;
 221 }
 222
 223 ex ncmul::coeff(const ex & s, int n) const
 224 {
 225         if (is_equal(ex_to<basic>(s)))
 226                 return n==1 ? _ex1 : _ex0;
 227
 228         exvector coeffseq;
 229         coeffseq.reserve(seq.size());
 230
 231         if (n == 0) {
 232                 // product of individual coeffs
 233                 // if a non-zero power of s is found, the resulting product will be 0
 234                 for (auto & it : seq)
 235                         coeffseq.push_back(it.coeff(s,n));
 236                 return (new ncmul(std::move(coeffseq)))->setflag(status_flags::dynallocated);
 237         }
 238
 239         bool coeff_found = false;
 240         for (auto & i : seq) {
 241                 ex c = i.coeff(s,n);
 242                 if (c.is_zero()) {
 243                         coeffseq.push_back(i);
 244                 } else {
 245                         coeffseq.push_back(c);
 246                         coeff_found = true;
 247                 }
 248         }
 249
 250         if (coeff_found)
 251                 return (new ncmul(std::move(coeffseq)))->setflag(status_flags::dynallocated);
 252
 253         return _ex0;
 254 }
 255
 256 size_t ncmul::count_factors(const ex & e) const
 257 {
 258         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 259                 (is_exactly_a<ncmul>(e))) {
 260                 size_t factors=0;
 261                 for (size_t i=0; i<e.nops(); i++)
 262                         factors += count_factors(e.op(i));
 263
 264                 return factors;
 265         }
 266         return 1;
 267 }
 268
 269 void ncmul::append_factors(exvector & v, const ex & e) const
 270 {
 271         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 272                 (is_exactly_a<ncmul>(e))) {
 273                 for (size_t i=0; i<e.nops(); i++)
 274                         append_factors(v, e.op(i));
 275         } else
 276                 v.push_back(e);
 277 }
 278
 279 typedef std::vector<unsigned> unsignedvector;
 280 typedef std::vector<exvector> exvectorvector;
 281
 282 /** Perform automatic term rewriting rules in this class.  In the following
 283  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 284  *  stand for such expressions that contain a plain number.
 285  *  - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 286  *  - ncmul(x) -> x
 287  *  - ncmul() -> 1
 288  *  - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...))  (pull out commutative elements)
 289  *  - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))  (collect elements of same type)
 290  *  - ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 291  *
 292  *  @param level cut-off in recursive evaluation */
 293 ex ncmul::eval(int level) const
 294 {
 295         // The following additional rule would be nice, but produces a recursion,
 296         // which must be trapped by introducing a flag that the sub-ncmuls()
 297         // are already evaluated (maybe later...)
 298         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 299         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 300         //                      (X noncommutative_composite)
 301
 302         if ((level==1) && (flags & status_flags::evaluated)) {
 303                 return *this;
 304         }
 305
 306         exvector evaledseq=evalchildren(level);
 307
 308         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 309         //     ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 310         size_t factors = 0;
 311         for (auto & it : evaledseq)
 312                 factors += count_factors(it);
 313
 314         exvector assocseq;
 315         assocseq.reserve(factors);
 316         make_flat_inserter mf(evaledseq, true);
 317         for (auto & it : evaledseq) {
 318                 ex factor = mf.handle_factor(it, 1);
 319                 append_factors(assocseq, factor);
 320         }
 321
 322         // ncmul(x) -> x
 323         if (assocseq.size()==1) return *(seq.begin());
 324
 325         // ncmul() -> 1
 326         if (assocseq.empty()) return _ex1;
 327
 328         // determine return types
 329         unsignedvector rettypes(assocseq.size());
 330         size_t i = 0;
 331         size_t count_commutative=0;
 332         size_t count_noncommutative=0;
 333         size_t count_noncommutative_composite=0;
 334         for (auto & it : assocseq) {
 335                 rettypes[i] = it.return_type();
 336                 switch (rettypes[i]) {
 337                 case return_types::commutative:
 338                         count_commutative++;
 339                         break;
 340                 case return_types::noncommutative:
 341                         count_noncommutative++;
 342                         break;
 343                 case return_types::noncommutative_composite:
 344                         count_noncommutative_composite++;
 345                         break;
 346                 default:
 347                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 348                 }
 349                 ++i;
 350         }
 351         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 352
 353         // ncmul(...,c1,...,c2,...) ->
 354         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 355         if (count_commutative!=0) {
 356                 exvector commutativeseq;
 357                 commutativeseq.reserve(count_commutative+1);
 358                 exvector noncommutativeseq;
 359                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 360                 size_t num = assocseq.size();
 361                 for (size_t i=0; i<num; ++i) {
 362                         if (rettypes[i]==return_types::commutative)
 363                                 commutativeseq.push_back(assocseq[i]);
 364                         else
 365                                 noncommutativeseq.push_back(assocseq[i]);
 366                 }
 367                 commutativeseq.push_back((new ncmul(std::move(noncommutativeseq)))->setflag(status_flags::dynallocated));
 368                 return (new mul(std::move(commutativeseq)))->setflag(status_flags::dynallocated);
 369         }
 370
 371         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 372         //     (collect elements of same type)
 373
 374         if (count_noncommutative_composite==0) {
 375                 // there are neither commutative nor noncommutative_composite
 376                 // elements in assocseq
 377                 GINAC_ASSERT(count_commutative==0);
 378
 379                 size_t assoc_num = assocseq.size();
 380                 exvectorvector evv;
 381                 std::vector<return_type_t> rttinfos;
 382                 evv.reserve(assoc_num);
 383                 rttinfos.reserve(assoc_num);
 384
 385                 for (auto & it : assocseq) {
 386                         return_type_t ti = it.return_type_tinfo();
 387                         size_t rtt_num = rttinfos.size();
 388                         // search type in vector of known types
 389                         for (i=0; i<rtt_num; ++i) {
 390                                 if(ti == rttinfos[i]) {
 391                                         evv[i].push_back(it);
 392                                         break;
 393                                 }
 394                         }
 395                         if (i >= rtt_num) {
 396                                 // new type
 397                                 rttinfos.push_back(ti);
 398                                 evv.push_back(exvector());
 399                                 (evv.end()-1)->reserve(assoc_num);
 400                                 (evv.end()-1)->push_back(it);
 401                         }
 402                 }
 403
 404                 size_t evv_num = evv.size();
 405 #ifdef DO_GINAC_ASSERT
 406                 GINAC_ASSERT(evv_num == rttinfos.size());
 407                 GINAC_ASSERT(evv_num > 0);
 408                 size_t s=0;
 409                 for (i=0; i<evv_num; ++i)
 410                         s += evv[i].size();
 411                 GINAC_ASSERT(s == assoc_num);
 412 #endif // def DO_GINAC_ASSERT
 413
 414                 // if all elements are of same type, simplify the string
 415                 if (evv_num == 1) {
 416                         return evv[0][0].eval_ncmul(evv[0]);
 417                 }
 418
 419                 exvector splitseq;
 420                 splitseq.reserve(evv_num);
 421                 for (i=0; i<evv_num; ++i)
 422                         splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
 423
 424                 return (new mul(splitseq))->setflag(status_flags::dynallocated);
 425         }
 426
 427         return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 428                                                                                   status_flags::evaluated);
 429 }
 430
 431 ex ncmul::evalm() const
 432 {
 433         // Evaluate children first
 434         exvector s;
 435         s.reserve(seq.size());
 436         for (auto & it : seq)
 437                 s.push_back(it.evalm());
 438
 439         // If there are only matrices, simply multiply them
 440         auto it = s.begin(), itend = s.end();
 441         if (is_a<matrix>(*it)) {
 442                 matrix prod(ex_to<matrix>(*it));
 443                 it++;
 444                 while (it != itend) {
 445                         if (!is_a<matrix>(*it))
 446                                 goto no_matrix;
 447                         prod = prod.mul(ex_to<matrix>(*it));
 448                         it++;
 449                 }
 450                 return prod;
 451         }
 452
 453 no_matrix:
 454         return (new ncmul(std::move(s)))->setflag(status_flags::dynallocated);
 455 }
 456
 457 ex ncmul::thiscontainer(const exvector & v) const
 458 {
 459         return (new ncmul(v))->setflag(status_flags::dynallocated);
 460 }
 461
 462 ex ncmul::thiscontainer(exvector && v) const
 463 {
 464         return (new ncmul(std::move(v)))->setflag(status_flags::dynallocated);
 465 }
 466
 467 ex ncmul::conjugate() const
 468 {
 469         if (return_type() != return_types::noncommutative) {
 470                 return exprseq::conjugate();
 471         }
 472
 473         if (!is_clifford_tinfo(return_type_tinfo())) {
 474                 return exprseq::conjugate();
 475         }
 476
 477         exvector ev;
 478         ev.reserve(nops());
 479         for (auto i=end(); i!=begin();) {
 480                 --i;
 481                 ev.push_back(i->conjugate());
 482         }
 483         return (new ncmul(std::move(ev)))->setflag(status_flags::dynallocated).eval();
 484 }
 485
 486 ex ncmul::real_part() const
 487 {
 488         return basic::real_part();
 489 }
 490
 491 ex ncmul::imag_part() const
 492 {
 493         return basic::imag_part();
 494 }
 495
 496 // protected
 497
 498 /** Implementation of ex::diff() for a non-commutative product. It applies
 499  *  the product rule.
 500  *  @see ex::diff */
 501 ex ncmul::derivative(const symbol & s) const
 502 {
 503         size_t num = seq.size();
 504         exvector addseq;
 505         addseq.reserve(num);
 506
 507         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 508         exvector ncmulseq = seq;
 509         for (size_t i=0; i<num; ++i) {
 510                 ex e = seq[i].diff(s);
 511                 e.swap(ncmulseq[i]);
 512                 addseq.push_back((new ncmul(ncmulseq))->setflag(status_flags::dynallocated));
 513                 e.swap(ncmulseq[i]);
 514         }
 515         return (new add(addseq))->setflag(status_flags::dynallocated);
 516 }
 517
 518 int ncmul::compare_same_type(const basic & other) const
 519 {
 520         return inherited::compare_same_type(other);
 521 }
 522
 523 unsigned ncmul::return_type() const
 524 {
 525         if (seq.empty())
 526                 return return_types::commutative;
 527
 528         bool all_commutative = true;
 529         exvector::const_iterator noncommutative_element; // point to first found nc element
 530
 531         exvector::const_iterator i = seq.begin(), end = seq.end();
 532         while (i != end) {
 533                 unsigned rt = i->return_type();
 534                 if (rt == return_types::noncommutative_composite)
 535                         return rt; // one ncc -> mul also ncc
 536                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 537                         // first nc element found, remember position
 538                         noncommutative_element = i;
 539                         all_commutative = false;
 540                 }
 541                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 542                         // another nc element found, compare type_infos
 543                         if(noncommutative_element->return_type_tinfo() != i->return_type_tinfo())
 544                                         return return_types::noncommutative_composite;
 545                 }
 546                 ++i;
 547         }
 548         // all factors checked
 549         GINAC_ASSERT(!all_commutative); // not all factors should commutate, because this is a ncmul();
 550         return all_commutative ? return_types::commutative : return_types::noncommutative;
 551 }
 552
 553 return_type_t ncmul::return_type_tinfo() const
 554 {
 555         if (seq.empty())
 556                 return make_return_type_t<ncmul>();
 557
 558         // return type_info of first noncommutative element
 559         for (auto & i : seq)
 560                 if (i.return_type() == return_types::noncommutative)
 561                         return i.return_type_tinfo();
 562
 563         // no noncommutative element found, should not happen
 564         return make_return_type_t<ncmul>();
 565 }
 566
 567 //////////
 568 // new virtual functions which can be overridden by derived classes
 569 //////////
 570
 571 // none
 572
 573 //////////
 574 // non-virtual functions in this class
 575 //////////
 576
 577 exvector ncmul::expandchildren(unsigned options) const
 578 {
 579         auto cit = this->seq.begin(), end = this->seq.end();
 580         while (cit != end) {
 581                 const ex & expanded_ex = cit->expand(options);
 582                 if (!are_ex_trivially_equal(*cit, expanded_ex)) {
 583
 584                         // copy first part of seq which hasn't changed
 585                         exvector s(this->seq.begin(), cit);
 586                         s.reserve(this->seq.size());
 587
 588                         // insert changed element
 589                         s.push_back(expanded_ex);
 590                         ++cit;
 591
 592                         // copy rest
 593                         while (cit != end) {
 594                                 s.push_back(cit->expand(options));
 595                                 ++cit;
 596                         }
 597
 598                         return s;
 599                 }
 600
 601                 ++cit;
 602         }
 603
 604         return exvector(); // nothing has changed
 605 }
 606
 607 const exvector & ncmul::get_factors() const
 608 {
 609         return seq;
 610 }
 611
 612 //////////
 613 // friend functions
 614 //////////
 615
 616 ex reeval_ncmul(const exvector & v)
 617 {
 618         return (new ncmul(v))->setflag(status_flags::dynallocated);
 619 }
 620
 621 ex hold_ncmul(const exvector & v)
 622 {
 623         if (v.empty())
 624                 return _ex1;
 625         else if (v.size() == 1)
 626                 return v[0];
 627         else
 628                 return (new ncmul(v))->setflag(status_flags::dynallocated |
 629                                                status_flags::evaluated);
 630 }
 631
 632 GINAC_BIND_UNARCHIVER(ncmul);
 633
 634 } // namespace GiNaC