ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2001 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 ctor, dtor, copy ctor, assignment operator and helpers
  42 //////////
  43
  44 ncmul::ncmul()
  45 {
  46         tinfo_key = TINFO_ncmul;
  47 }
  48
  49 DEFAULT_COPY(ncmul)
  50 DEFAULT_DESTROY(ncmul)
  51
  52 //////////
  53 // other constructors
  54 //////////
  55
  56 // public
  57
  58 ncmul::ncmul(const ex & lh, const ex & rh) : inherited(lh,rh)
  59 {
  60         tinfo_key = TINFO_ncmul;
  61 }
  62
  63 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited(f1,f2,f3)
  64 {
  65         tinfo_key = TINFO_ncmul;
  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         tinfo_key = TINFO_ncmul;
  72 }
  73
  74 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  75              const ex & f4, const ex & f5) : inherited(f1,f2,f3,f4,f5)
  76 {
  77         tinfo_key = TINFO_ncmul;
  78 }
  79
  80 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  81              const ex & f4, const ex & f5, const ex & f6) : inherited(f1,f2,f3,f4,f5,f6)
  82 {
  83         tinfo_key = TINFO_ncmul;
  84 }
  85
  86 ncmul::ncmul(const exvector & v, bool discardable) : inherited(v,discardable)
  87 {
  88         tinfo_key = TINFO_ncmul;
  89 }
  90
  91 ncmul::ncmul(exvector * vp) : inherited(vp)
  92 {
  93         tinfo_key = TINFO_ncmul;
  94 }
  95
  96 //////////
  97 // archiving
  98 //////////
  99
 100 DEFAULT_ARCHIVING(ncmul)
 101
 102 //////////
 103 // functions overriding virtual functions from base classes
 104 //////////
 105
 106 // public
 107
 108 void ncmul::print(const print_context & c, unsigned level) const
 109 {
 110         if (is_a<print_tree>(c)) {
 111
 112                 inherited::print(c, level);
 113
 114         } else if (is_a<print_csrc>(c)) {
 115
 116                 c.s << "ncmul(";
 117                 exvector::const_iterator it = seq.begin(), itend = seq.end()-1;
 118                 while (it != itend) {
 119                         it->print(c, precedence());
 120                         c.s << ",";
 121                         it++;
 122                 }
 123                 it->print(c, precedence());
 124                 c.s << ")";
 125
 126         } else
 127                 printseq(c, '(', '*', ')', precedence(), level);
 128 }
 129
 130 bool ncmul::info(unsigned inf) const
 131 {
 132         return inherited::info(inf);
 133 }
 134
 135 typedef std::vector<int> intvector;
 136
 137 ex ncmul::expand(unsigned options) const
 138 {
 139         // First, expand the children
 140         exvector expanded_seq = expandchildren(options);
 141
 142         // Now, look for all the factors that are sums and remember their
 143         // position and number of terms.
 144         intvector positions_of_adds(expanded_seq.size());
 145         intvector number_of_add_operands(expanded_seq.size());
 146
 147         int number_of_adds = 0;
 148         int number_of_expanded_terms = 1;
 149
 150         unsigned current_position = 0;
 151         exvector::const_iterator last = expanded_seq.end();
 152         for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 153                 if (is_exactly_a<add>(*cit)) {
 154                         positions_of_adds[number_of_adds] = current_position;
 155                         unsigned num_ops = cit->nops();
 156                         number_of_add_operands[number_of_adds] = num_ops;
 157                         number_of_expanded_terms *= num_ops;
 158                         number_of_adds++;
 159                 }
 160                 ++current_position;
 161         }
 162
 163         // If there are no sums, we are done
 164         if (number_of_adds == 0)
 165                 return (new ncmul(expanded_seq, true))->
 166                         setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 167
 168         // Now, form all possible products of the terms of the sums with the
 169         // remaining factors, and add them together
 170         exvector distrseq;
 171         distrseq.reserve(number_of_expanded_terms);
 172
 173         intvector k(number_of_adds);
 174
 175         while (true) {
 176                 exvector term = expanded_seq;
 177                 for (int i=0; i<number_of_adds; i++)
 178                         term[positions_of_adds[i]] = expanded_seq[positions_of_adds[i]].op(k[i]);
 179                 distrseq.push_back((new ncmul(term, true))->
 180                                     setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 181
 182                 // increment k[]
 183                 int l = number_of_adds-1;
 184                 while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
 185                         k[l] = 0;
 186                         l--;
 187                 }
 188                 if (l<0)
 189                         break;
 190         }
 191
 192         return (new add(distrseq))->
 193                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 194 }
 195
 196 int ncmul::degree(const ex & s) const
 197 {
 198         // Sum up degrees of factors
 199         int deg_sum = 0;
 200         exvector::const_iterator i = seq.begin(), end = seq.end();
 201         while (i != end) {
 202                 deg_sum += i->degree(s);
 203                 ++i;
 204         }
 205         return deg_sum;
 206 }
 207
 208 int ncmul::ldegree(const ex & s) const
 209 {
 210         // Sum up degrees of factors
 211         int deg_sum = 0;
 212         exvector::const_iterator i = seq.begin(), end = seq.end();
 213         while (i != end) {
 214                 deg_sum += i->degree(s);
 215                 ++i;
 216         }
 217         return deg_sum;
 218 }
 219
 220 ex ncmul::coeff(const ex & s, int n) const
 221 {
 222         exvector coeffseq;
 223         coeffseq.reserve(seq.size());
 224
 225         if (n == 0) {
 226                 // product of individual coeffs
 227                 // if a non-zero power of s is found, the resulting product will be 0
 228                 exvector::const_iterator it=seq.begin();
 229                 while (it!=seq.end()) {
 230                         coeffseq.push_back((*it).coeff(s,n));
 231                         ++it;
 232                 }
 233                 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 234         }
 235
 236         exvector::const_iterator i = seq.begin(), end = seq.end();
 237         bool coeff_found = false;
 238         while (i != end) {
 239                 ex c = i->coeff(s,n);
 240                 if (c.is_zero()) {
 241                         coeffseq.push_back(*i);
 242                 } else {
 243                         coeffseq.push_back(c);
 244                         coeff_found = true;
 245                 }
 246                 ++i;
 247         }
 248
 249         if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 250
 251         return _ex0;
 252 }
 253
 254 unsigned ncmul::count_factors(const ex & e) const
 255 {
 256         if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 257                 (is_ex_exactly_of_type(e,ncmul))) {
 258                 unsigned factors=0;
 259                 for (unsigned i=0; i<e.nops(); i++)
 260                         factors += count_factors(e.op(i));
 261
 262                 return factors;
 263         }
 264         return 1;
 265 }
 266
 267 void ncmul::append_factors(exvector & v, const ex & e) const
 268 {
 269         if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 270                 (is_ex_exactly_of_type(e,ncmul))) {
 271                 for (unsigned i=0; i<e.nops(); i++)
 272                         append_factors(v,e.op(i));
 273         } else
 274                 v.push_back(e);
 275 }
 276
 277 typedef std::vector<unsigned> unsignedvector;
 278 typedef std::vector<exvector> exvectorvector;
 279
 280 /** Perform automatic term rewriting rules in this class.  In the following
 281  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 282  *  stand for such expressions that contain a plain number.
 283  *  - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 284  *  - ncmul(x) -> x
 285  *  - ncmul() -> 1
 286  *  - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...))  (pull out commutative elements)
 287  *  - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))  (collect elements of same type)
 288  *  - ncmul(x1,x2,x3,...) -> x::simplify_ncmul(x1,x2,x3,...)
 289  *
 290  *  @param level cut-off in recursive evaluation */
 291 ex ncmul::eval(int level) const
 292 {
 293         // The following additional rule would be nice, but produces a recursion,
 294         // which must be trapped by introducing a flag that the sub-ncmuls()
 295         // are already evaluated (maybe later...)
 296         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 297         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 298         //                      (X noncommutative_composite)
 299
 300         if ((level==1) && (flags & status_flags::evaluated)) {
 301                 return *this;
 302         }
 303
 304         exvector evaledseq=evalchildren(level);
 305
 306         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 307         //     ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
 308         unsigned factors = 0;
 309         exvector::const_iterator cit = evaledseq.begin(), citend = evaledseq.end();
 310         while (cit != citend)
 311                 factors += count_factors(*cit++);
 312
 313         exvector assocseq;
 314         assocseq.reserve(factors);
 315         cit = evaledseq.begin();
 316         while (cit != citend)
 317                 append_factors(assocseq, *cit++);
 318
 319         // ncmul(x) -> x
 320         if (assocseq.size()==1) return *(seq.begin());
 321
 322         // ncmul() -> 1
 323         if (assocseq.empty()) return _ex1;
 324
 325         // determine return types
 326         unsignedvector rettypes;
 327         rettypes.reserve(assocseq.size());
 328         unsigned i = 0;
 329         unsigned count_commutative=0;
 330         unsigned count_noncommutative=0;
 331         unsigned count_noncommutative_composite=0;
 332         cit = assocseq.begin(); citend = assocseq.end();
 333         while (cit != citend) {
 334                 switch (rettypes[i] = cit->return_type()) {
 335                 case return_types::commutative:
 336                         count_commutative++;
 337                         break;
 338                 case return_types::noncommutative:
 339                         count_noncommutative++;
 340                         break;
 341                 case return_types::noncommutative_composite:
 342                         count_noncommutative_composite++;
 343                         break;
 344                 default:
 345                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 346                 }
 347                 ++i; ++cit;
 348         }
 349         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 350
 351         // ncmul(...,c1,...,c2,...) ->
 352         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 353         if (count_commutative!=0) {
 354                 exvector commutativeseq;
 355                 commutativeseq.reserve(count_commutative+1);
 356                 exvector noncommutativeseq;
 357                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 358                 unsigned num = assocseq.size();
 359                 for (unsigned i=0; i<num; ++i) {
 360                         if (rettypes[i]==return_types::commutative)
 361                                 commutativeseq.push_back(assocseq[i]);
 362                         else
 363                                 noncommutativeseq.push_back(assocseq[i]);
 364                 }
 365                 commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
 366                 return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 367         }
 368
 369         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 370         //     (collect elements of same type)
 371
 372         if (count_noncommutative_composite==0) {
 373                 // there are neither commutative nor noncommutative_composite
 374                 // elements in assocseq
 375                 GINAC_ASSERT(count_commutative==0);
 376
 377                 unsigned assoc_num = assocseq.size();
 378                 exvectorvector evv;
 379                 unsignedvector rttinfos;
 380                 evv.reserve(assoc_num);
 381                 rttinfos.reserve(assoc_num);
 382
 383                 cit = assocseq.begin(), citend = assocseq.end();
 384                 while (cit != citend) {
 385                         unsigned ti = cit->return_type_tinfo();
 386                         unsigned rtt_num = rttinfos.size();
 387                         // search type in vector of known types
 388                         for (i=0; i<rtt_num; ++i) {
 389                                 if (ti == rttinfos[i]) {
 390                                         evv[i].push_back(*cit);
 391                                         break;
 392                                 }
 393                         }
 394                         if (i >= rtt_num) {
 395                                 // new type
 396                                 rttinfos.push_back(ti);
 397                                 evv.push_back(exvector());
 398                                 (evv.end()-1)->reserve(assoc_num);
 399                                 (evv.end()-1)->push_back(*cit);
 400                         }
 401                         ++cit;
 402                 }
 403
 404                 unsigned evv_num = evv.size();
 405 #ifdef DO_GINAC_ASSERT
 406                 GINAC_ASSERT(evv_num == rttinfos.size());
 407                 GINAC_ASSERT(evv_num > 0);
 408                 unsigned 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].simplify_ncmul(evv[0]);
 417
 418                 exvector splitseq;
 419                 splitseq.reserve(evv_num);
 420                 for (i=0; i<evv_num; ++i)
 421                         splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
 422
 423                 return (new mul(splitseq))->setflag(status_flags::dynallocated);
 424         }
 425
 426         return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 427                                                                                   status_flags::evaluated);
 428 }
 429
 430 ex ncmul::evalm(void) const
 431 {
 432         // Evaluate children first
 433         exvector *s = new exvector;
 434         s->reserve(seq.size());
 435         exvector::const_iterator it = seq.begin(), itend = seq.end();
 436         while (it != itend) {
 437                 s->push_back(it->evalm());
 438                 it++;
 439         }
 440
 441         // If there are only matrices, simply multiply them
 442         it = s->begin(); itend = s->end();
 443         if (is_ex_of_type(*it, matrix)) {
 444                 matrix prod(ex_to<matrix>(*it));
 445                 it++;
 446                 while (it != itend) {
 447                         if (!is_ex_of_type(*it, matrix))
 448                                 goto no_matrix;
 449                         prod = prod.mul(ex_to<matrix>(*it));
 450                         it++;
 451                 }
 452                 delete s;
 453                 return prod;
 454         }
 455
 456 no_matrix:
 457         return (new ncmul(s))->setflag(status_flags::dynallocated);
 458 }
 459
 460 ex ncmul::thisexprseq(const exvector & v) const
 461 {
 462         return (new ncmul(v))->setflag(status_flags::dynallocated);
 463 }
 464
 465 ex ncmul::thisexprseq(exvector * vp) const
 466 {
 467         return (new ncmul(vp))->setflag(status_flags::dynallocated);
 468 }
 469
 470 // protected
 471
 472 /** Implementation of ex::diff() for a non-commutative product. It applies
 473  *  the product rule.
 474  *  @see ex::diff */
 475 ex ncmul::derivative(const symbol & s) const
 476 {
 477         unsigned num = seq.size();
 478         exvector addseq;
 479         addseq.reserve(num);
 480
 481         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 482         exvector ncmulseq = seq;
 483         for (unsigned i=0; i<num; ++i) {
 484                 ex e = seq[i].diff(s);
 485                 e.swap(ncmulseq[i]);
 486                 addseq.push_back((new ncmul(ncmulseq))->setflag(status_flags::dynallocated));
 487                 e.swap(ncmulseq[i]);
 488         }
 489         return (new add(addseq))->setflag(status_flags::dynallocated);
 490 }
 491
 492 int ncmul::compare_same_type(const basic & other) const
 493 {
 494         return inherited::compare_same_type(other);
 495 }
 496
 497 unsigned ncmul::return_type(void) const
 498 {
 499         if (seq.empty())
 500                 return return_types::commutative;
 501
 502         bool all_commutative = true;
 503         exvector::const_iterator noncommutative_element; // point to first found nc element
 504
 505         exvector::const_iterator i = seq.begin(), end = seq.end();
 506         while (i != end) {
 507                 unsigned rt = i->return_type();
 508                 if (rt == return_types::noncommutative_composite)
 509                         return rt; // one ncc -> mul also ncc
 510                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 511                         // first nc element found, remember position
 512                         noncommutative_element = i;
 513                         all_commutative = false;
 514                 }
 515                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 516                         // another nc element found, compare type_infos
 517                         if (noncommutative_element->return_type_tinfo() != i->return_type_tinfo()) {
 518                                 // diffent types -> mul is ncc
 519                                 return return_types::noncommutative_composite;
 520                         }
 521                 }
 522                 ++i;
 523         }
 524         // all factors checked
 525         GINAC_ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
 526         return all_commutative ? return_types::commutative : return_types::noncommutative;
 527 }
 528
 529 unsigned ncmul::return_type_tinfo(void) const
 530 {
 531         if (seq.empty())
 532                 return tinfo_key;
 533
 534         // return type_info of first noncommutative element
 535         exvector::const_iterator i = seq.begin(), end = seq.end();
 536         while (i != end) {
 537                 if (i->return_type() == return_types::noncommutative)
 538                         return i->return_type_tinfo();
 539                 ++i;
 540         }
 541
 542         // no noncommutative element found, should not happen
 543         return tinfo_key;
 544 }
 545
 546 //////////
 547 // new virtual functions which can be overridden by derived classes
 548 //////////
 549
 550 // none
 551
 552 //////////
 553 // non-virtual functions in this class
 554 //////////
 555
 556 exvector ncmul::expandchildren(unsigned options) const
 557 {
 558         exvector s;
 559         s.reserve(seq.size());
 560         exvector::const_iterator it = seq.begin(), itend = seq.end();
 561         while (it != itend) {
 562                 s.push_back(it->expand(options));
 563                 it++;
 564         }
 565         return s;
 566 }
 567
 568 const exvector & ncmul::get_factors(void) const
 569 {
 570         return seq;
 571 }
 572
 573 //////////
 574 // friend functions
 575 //////////
 576
 577 ex nonsimplified_ncmul(const exvector & v)
 578 {
 579         return (new ncmul(v))->setflag(status_flags::dynallocated);
 580 }
 581
 582 ex simplified_ncmul(const exvector & v)
 583 {
 584         if (v.empty())
 585                 return _ex1;
 586         else if (v.size() == 1)
 587                 return v[0];
 588         else
 589                 return (new ncmul(v))->setflag(status_flags::dynallocated |
 590                                                status_flags::evaluated);
 591 }
 592
 593 } // namespace GiNaC