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 "print.h"
  33 #include "archive.h"
  34 #include "utils.h"
  35
  36 namespace GiNaC {
  37
  38 GINAC_IMPLEMENT_REGISTERED_CLASS(ncmul, exprseq)
  39
  40 //////////
  41 // default constructor
  42 //////////
  43
  44 ncmul::ncmul()
  45 {
  46         tinfo_key = TINFO_ncmul;
  47 }
  48
  49 //////////
  50 // other constructors
  51 //////////
  52
  53 // public
  54
  55 ncmul::ncmul(const ex & lh, const ex & rh) : inherited(lh,rh)
  56 {
  57         tinfo_key = TINFO_ncmul;
  58 }
  59
  60 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited(f1,f2,f3)
  61 {
  62         tinfo_key = TINFO_ncmul;
  63 }
  64
  65 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  66              const ex & f4) : inherited(f1,f2,f3,f4)
  67 {
  68         tinfo_key = TINFO_ncmul;
  69 }
  70
  71 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  72              const ex & f4, const ex & f5) : inherited(f1,f2,f3,f4,f5)
  73 {
  74         tinfo_key = TINFO_ncmul;
  75 }
  76
  77 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  78              const ex & f4, const ex & f5, const ex & f6) : inherited(f1,f2,f3,f4,f5,f6)
  79 {
  80         tinfo_key = TINFO_ncmul;
  81 }
  82
  83 ncmul::ncmul(const exvector & v, bool discardable) : inherited(v,discardable)
  84 {
  85         tinfo_key = TINFO_ncmul;
  86 }
  87
  88 ncmul::ncmul(exvector * vp) : inherited(vp)
  89 {
  90         tinfo_key = TINFO_ncmul;
  91 }
  92
  93 //////////
  94 // archiving
  95 //////////
  96
  97 DEFAULT_ARCHIVING(ncmul)
  98
  99 //////////
 100 // functions overriding virtual functions from base classes
 101 //////////
 102
 103 // public
 104
 105 void ncmul::print(const print_context & c, unsigned level) const
 106 {
 107         if (is_a<print_tree>(c)) {
 108
 109                 inherited::print(c, level);
 110
 111         } else if (is_a<print_csrc>(c) || is_a<print_python_repr>(c)) {
 112
 113                 c.s << class_name() << "(";
 114                 exvector::const_iterator it = seq.begin(), itend = seq.end()-1;
 115                 while (it != itend) {
 116                         it->print(c, precedence());
 117                         c.s << ",";
 118                         it++;
 119                 }
 120                 it->print(c, precedence());
 121                 c.s << ")";
 122
 123         } else
 124                 printseq(c, '(', '*', ')', precedence(), level);
 125 }
 126
 127 bool ncmul::info(unsigned inf) const
 128 {
 129         return inherited::info(inf);
 130 }
 131
 132 typedef std::vector<int> intvector;
 133
 134 ex ncmul::expand(unsigned options) const
 135 {
 136         // First, expand the children
 137         exvector expanded_seq = expandchildren(options);
 138
 139         // Now, look for all the factors that are sums and remember their
 140         // position and number of terms.
 141         intvector positions_of_adds(expanded_seq.size());
 142         intvector number_of_add_operands(expanded_seq.size());
 143
 144         size_t number_of_adds = 0;
 145         size_t number_of_expanded_terms = 1;
 146
 147         size_t current_position = 0;
 148         exvector::const_iterator last = expanded_seq.end();
 149         for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 150                 if (is_exactly_a<add>(*cit)) {
 151                         positions_of_adds[number_of_adds] = current_position;
 152                         size_t num_ops = cit->nops();
 153                         number_of_add_operands[number_of_adds] = num_ops;
 154                         number_of_expanded_terms *= num_ops;
 155                         number_of_adds++;
 156                 }
 157                 ++current_position;
 158         }
 159
 160         // If there are no sums, we are done
 161         if (number_of_adds == 0)
 162                 return (new ncmul(expanded_seq, true))->
 163                         setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 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         while (true) {
 173                 exvector term = expanded_seq;
 174                 for (size_t i=0; i<number_of_adds; i++)
 175                         term[positions_of_adds[i]] = expanded_seq[positions_of_adds[i]].op(k[i]);
 176                 distrseq.push_back((new ncmul(term, true))->
 177                                     setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 178
 179                 // increment k[]
 180                 int l = number_of_adds-1;
 181                 while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
 182                         k[l] = 0;
 183                         l--;
 184                 }
 185                 if (l<0)
 186                         break;
 187         }
 188
 189         return (new add(distrseq))->
 190                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 191 }
 192
 193 int ncmul::degree(const ex & s) const
 194 {
 195         // Sum up degrees of factors
 196         int deg_sum = 0;
 197         exvector::const_iterator i = seq.begin(), end = seq.end();
 198         while (i != end) {
 199                 deg_sum += i->degree(s);
 200                 ++i;
 201         }
 202         return deg_sum;
 203 }
 204
 205 int ncmul::ldegree(const ex & s) const
 206 {
 207         // Sum up degrees of factors
 208         int deg_sum = 0;
 209         exvector::const_iterator i = seq.begin(), end = seq.end();
 210         while (i != end) {
 211                 deg_sum += i->degree(s);
 212                 ++i;
 213         }
 214         return deg_sum;
 215 }
 216
 217 ex ncmul::coeff(const ex & s, int n) const
 218 {
 219         exvector coeffseq;
 220         coeffseq.reserve(seq.size());
 221
 222         if (n == 0) {
 223                 // product of individual coeffs
 224                 // if a non-zero power of s is found, the resulting product will be 0
 225                 exvector::const_iterator it=seq.begin();
 226                 while (it!=seq.end()) {
 227                         coeffseq.push_back((*it).coeff(s,n));
 228                         ++it;
 229                 }
 230                 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 231         }
 232
 233         exvector::const_iterator i = seq.begin(), end = seq.end();
 234         bool coeff_found = false;
 235         while (i != end) {
 236                 ex c = i->coeff(s,n);
 237                 if (c.is_zero()) {
 238                         coeffseq.push_back(*i);
 239                 } else {
 240                         coeffseq.push_back(c);
 241                         coeff_found = true;
 242                 }
 243                 ++i;
 244         }
 245
 246         if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 247
 248         return _ex0;
 249 }
 250
 251 size_t ncmul::count_factors(const ex & e) const
 252 {
 253         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 254                 (is_exactly_a<ncmul>(e))) {
 255                 size_t factors=0;
 256                 for (size_t i=0; i<e.nops(); i++)
 257                         factors += count_factors(e.op(i));
 258
 259                 return factors;
 260         }
 261         return 1;
 262 }
 263
 264 void ncmul::append_factors(exvector & v, const ex & e) const
 265 {
 266         if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
 267                 (is_exactly_a<ncmul>(e))) {
 268                 for (size_t i=0; i<e.nops(); i++)
 269                         append_factors(v, e.op(i));
 270         } else
 271                 v.push_back(e);
 272 }
 273
 274 typedef std::vector<unsigned> unsignedvector;
 275 typedef std::vector<exvector> exvectorvector;
 276
 277 /** Perform automatic term rewriting rules in this class.  In the following
 278  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 279  *  stand for such expressions that contain a plain number.
 280  *  - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 281  *  - ncmul(x) -> x
 282  *  - ncmul() -> 1
 283  *  - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...))  (pull out commutative elements)
 284  *  - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))  (collect elements of same type)
 285  *  - ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 286  *
 287  *  @param level cut-off in recursive evaluation */
 288 ex ncmul::eval(int level) const
 289 {
 290         // The following additional rule would be nice, but produces a recursion,
 291         // which must be trapped by introducing a flag that the sub-ncmuls()
 292         // are already evaluated (maybe later...)
 293         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 294         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 295         //                      (X noncommutative_composite)
 296
 297         if ((level==1) && (flags & status_flags::evaluated)) {
 298                 return *this;
 299         }
 300
 301         exvector evaledseq=evalchildren(level);
 302
 303         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 304         //     ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 305         size_t factors = 0;
 306         exvector::const_iterator cit = evaledseq.begin(), citend = evaledseq.end();
 307         while (cit != citend)
 308                 factors += count_factors(*cit++);
 309
 310         exvector assocseq;
 311         assocseq.reserve(factors);
 312         cit = evaledseq.begin();
 313         while (cit != citend)
 314                 append_factors(assocseq, *cit++);
 315
 316         // ncmul(x) -> x
 317         if (assocseq.size()==1) return *(seq.begin());
 318
 319         // ncmul() -> 1
 320         if (assocseq.empty()) return _ex1;
 321
 322         // determine return types
 323         unsignedvector rettypes;
 324         rettypes.reserve(assocseq.size());
 325         size_t i = 0;
 326         size_t count_commutative=0;
 327         size_t count_noncommutative=0;
 328         size_t count_noncommutative_composite=0;
 329         cit = assocseq.begin(); citend = assocseq.end();
 330         while (cit != citend) {
 331                 switch (rettypes[i] = cit->return_type()) {
 332                 case return_types::commutative:
 333                         count_commutative++;
 334                         break;
 335                 case return_types::noncommutative:
 336                         count_noncommutative++;
 337                         break;
 338                 case return_types::noncommutative_composite:
 339                         count_noncommutative_composite++;
 340                         break;
 341                 default:
 342                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 343                 }
 344                 ++i; ++cit;
 345         }
 346         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 347
 348         // ncmul(...,c1,...,c2,...) ->
 349         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 350         if (count_commutative!=0) {
 351                 exvector commutativeseq;
 352                 commutativeseq.reserve(count_commutative+1);
 353                 exvector noncommutativeseq;
 354                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 355                 size_t num = assocseq.size();
 356                 for (size_t i=0; i<num; ++i) {
 357                         if (rettypes[i]==return_types::commutative)
 358                                 commutativeseq.push_back(assocseq[i]);
 359                         else
 360                                 noncommutativeseq.push_back(assocseq[i]);
 361                 }
 362                 commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
 363                 return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 364         }
 365
 366         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 367         //     (collect elements of same type)
 368
 369         if (count_noncommutative_composite==0) {
 370                 // there are neither commutative nor noncommutative_composite
 371                 // elements in assocseq
 372                 GINAC_ASSERT(count_commutative==0);
 373
 374                 size_t assoc_num = assocseq.size();
 375                 exvectorvector evv;
 376                 unsignedvector rttinfos;
 377                 evv.reserve(assoc_num);
 378                 rttinfos.reserve(assoc_num);
 379
 380                 cit = assocseq.begin(), citend = assocseq.end();
 381                 while (cit != citend) {
 382                         unsigned ti = cit->return_type_tinfo();
 383                         size_t rtt_num = rttinfos.size();
 384                         // search type in vector of known types
 385                         for (i=0; i<rtt_num; ++i) {
 386                                 if (ti == rttinfos[i]) {
 387                                         evv[i].push_back(*cit);
 388                                         break;
 389                                 }
 390                         }
 391                         if (i >= rtt_num) {
 392                                 // new type
 393                                 rttinfos.push_back(ti);
 394                                 evv.push_back(exvector());
 395                                 (evv.end()-1)->reserve(assoc_num);
 396                                 (evv.end()-1)->push_back(*cit);
 397                         }
 398                         ++cit;
 399                 }
 400
 401                 size_t evv_num = evv.size();
 402 #ifdef DO_GINAC_ASSERT
 403                 GINAC_ASSERT(evv_num == rttinfos.size());
 404                 GINAC_ASSERT(evv_num > 0);
 405                 size_t s=0;
 406                 for (i=0; i<evv_num; ++i)
 407                         s += evv[i].size();
 408                 GINAC_ASSERT(s == assoc_num);
 409 #endif // def DO_GINAC_ASSERT
 410
 411                 // if all elements are of same type, simplify the string
 412                 if (evv_num == 1)
 413                         return evv[0][0].eval_ncmul(evv[0]);
 414
 415                 exvector splitseq;
 416                 splitseq.reserve(evv_num);
 417                 for (i=0; i<evv_num; ++i)
 418                         splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
 419
 420                 return (new mul(splitseq))->setflag(status_flags::dynallocated);
 421         }
 422
 423         return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 424                                                                                   status_flags::evaluated);
 425 }
 426
 427 ex ncmul::evalm() const
 428 {
 429         // Evaluate children first
 430         exvector *s = new exvector;
 431         s->reserve(seq.size());
 432         exvector::const_iterator it = seq.begin(), itend = seq.end();
 433         while (it != itend) {
 434                 s->push_back(it->evalm());
 435                 it++;
 436         }
 437
 438         // If there are only matrices, simply multiply them
 439         it = s->begin(); itend = s->end();
 440         if (is_a<matrix>(*it)) {
 441                 matrix prod(ex_to<matrix>(*it));
 442                 it++;
 443                 while (it != itend) {
 444                         if (!is_a<matrix>(*it))
 445                                 goto no_matrix;
 446                         prod = prod.mul(ex_to<matrix>(*it));
 447                         it++;
 448                 }
 449                 delete s;
 450                 return prod;
 451         }
 452
 453 no_matrix:
 454         return (new ncmul(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 * vp) const
 463 {
 464         return (new ncmul(vp))->setflag(status_flags::dynallocated);
 465 }
 466
 467 // protected
 468
 469 /** Implementation of ex::diff() for a non-commutative product. It applies
 470  *  the product rule.
 471  *  @see ex::diff */
 472 ex ncmul::derivative(const symbol & s) const
 473 {
 474         size_t num = seq.size();
 475         exvector addseq;
 476         addseq.reserve(num);
 477
 478         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 479         exvector ncmulseq = seq;
 480         for (size_t i=0; i<num; ++i) {
 481                 ex e = seq[i].diff(s);
 482                 e.swap(ncmulseq[i]);
 483                 addseq.push_back((new ncmul(ncmulseq))->setflag(status_flags::dynallocated));
 484                 e.swap(ncmulseq[i]);
 485         }
 486         return (new add(addseq))->setflag(status_flags::dynallocated);
 487 }
 488
 489 int ncmul::compare_same_type(const basic & other) const
 490 {
 491         return inherited::compare_same_type(other);
 492 }
 493
 494 unsigned ncmul::return_type() const
 495 {
 496         if (seq.empty())
 497                 return return_types::commutative;
 498
 499         bool all_commutative = true;
 500         exvector::const_iterator noncommutative_element; // point to first found nc element
 501
 502         exvector::const_iterator i = seq.begin(), end = seq.end();
 503         while (i != end) {
 504                 unsigned rt = i->return_type();
 505                 if (rt == return_types::noncommutative_composite)
 506                         return rt; // one ncc -> mul also ncc
 507                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 508                         // first nc element found, remember position
 509                         noncommutative_element = i;
 510                         all_commutative = false;
 511                 }
 512                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 513                         // another nc element found, compare type_infos
 514                         if (noncommutative_element->return_type_tinfo() != i->return_type_tinfo()) {
 515                                 // diffent types -> mul is ncc
 516                                 return return_types::noncommutative_composite;
 517                         }
 518                 }
 519                 ++i;
 520         }
 521         // all factors checked
 522         GINAC_ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
 523         return all_commutative ? return_types::commutative : return_types::noncommutative;
 524 }
 525
 526 unsigned ncmul::return_type_tinfo() const
 527 {
 528         if (seq.empty())
 529                 return tinfo_key;
 530
 531         // return type_info of first noncommutative element
 532         exvector::const_iterator i = seq.begin(), end = seq.end();
 533         while (i != end) {
 534                 if (i->return_type() == return_types::noncommutative)
 535                         return i->return_type_tinfo();
 536                 ++i;
 537         }
 538
 539         // no noncommutative element found, should not happen
 540         return tinfo_key;
 541 }
 542
 543 //////////
 544 // new virtual functions which can be overridden by derived classes
 545 //////////
 546
 547 // none
 548
 549 //////////
 550 // non-virtual functions in this class
 551 //////////
 552
 553 exvector ncmul::expandchildren(unsigned options) const
 554 {
 555         exvector s;
 556         s.reserve(seq.size());
 557         exvector::const_iterator it = seq.begin(), itend = seq.end();
 558         while (it != itend) {
 559                 s.push_back(it->expand(options));
 560                 it++;
 561         }
 562         return s;
 563 }
 564
 565 const exvector & ncmul::get_factors() const
 566 {
 567         return seq;
 568 }
 569
 570 //////////
 571 // friend functions
 572 //////////
 573
 574 ex reeval_ncmul(const exvector & v)
 575 {
 576         return (new ncmul(v))->setflag(status_flags::dynallocated);
 577 }
 578
 579 ex hold_ncmul(const exvector & v)
 580 {
 581         if (v.empty())
 582                 return _ex1;
 583         else if (v.size() == 1)
 584                 return v[0];
 585         else
 586                 return (new ncmul(v))->setflag(status_flags::dynallocated |
 587                                                status_flags::evaluated);
 588 }
 589
 590 } // namespace GiNaC