ginac/idx.cpp

   1 /** @file idx.cpp
   2  *
   3  *  Implementation of GiNaC's indices. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2000 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 <stdexcept>
  24
  25 #include "idx.h"
  26 #include "ex.h"
  27 #include "lst.h"
  28 #include "relational.h"
  29 #include "archive.h"
  30 #include "utils.h"
  31 #include "debugmsg.h"
  32
  33 #ifndef NO_NAMESPACE_GINAC
  34 namespace GiNaC {
  35 #endif // ndef NO_NAMESPACE_GINAC
  36
  37 GINAC_IMPLEMENT_REGISTERED_CLASS(idx, basic)
  38
  39 //////////
  40 // default constructor, destructor, copy constructor assignment operator and helpers
  41 //////////
  42
  43 // public
  44
  45 idx::idx() : inherited(TINFO_idx), symbolic(true), covariant(false)
  46 {
  47         debugmsg("idx default constructor",LOGLEVEL_CONSTRUCT);
  48         serial=next_serial++;
  49         name="index"+ToString(serial);
  50 }
  51
  52 idx::~idx()
  53 {
  54         debugmsg("idx destructor",LOGLEVEL_DESTRUCT);
  55         destroy(0);
  56 }
  57
  58 idx::idx(const idx & other)
  59 {
  60         debugmsg("idx copy constructor",LOGLEVEL_CONSTRUCT);
  61         copy(other);
  62 }
  63
  64 const idx & idx::operator=(const idx & other)
  65 {
  66         debugmsg("idx operator=",LOGLEVEL_ASSIGNMENT);
  67         if (this != &other) {
  68                 destroy(1);
  69                 copy(other);
  70         }
  71         return *this;
  72 }
  73
  74 // protected
  75
  76 void idx::copy(const idx & other)
  77 {
  78         inherited::copy(other);
  79         serial=other.serial;
  80         symbolic=other.symbolic;
  81         name=other.name;
  82         value=other.value;
  83         covariant=other.covariant;
  84 }
  85
  86 void idx::destroy(bool call_parent)
  87 {
  88         if (call_parent) inherited::destroy(call_parent);
  89 }
  90
  91 //////////
  92 // other constructors
  93 //////////
  94
  95 // public
  96
  97 idx::idx(bool cov) : inherited(TINFO_idx), symbolic(true), covariant(cov)
  98 {
  99         debugmsg("idx constructor from bool",LOGLEVEL_CONSTRUCT);
 100         serial = next_serial++;
 101         name = "index"+ToString(serial);
 102 }
 103
 104 idx::idx(const std::string & n, bool cov) : inherited(TINFO_idx),
 105         symbolic(true), name(n), covariant(cov)
 106 {
 107         debugmsg("idx constructor from string,bool",LOGLEVEL_CONSTRUCT);
 108         serial = next_serial++;
 109 }
 110
 111 idx::idx(const char * n, bool cov) : inherited(TINFO_idx),
 112         symbolic(true), name(n), covariant(cov)
 113 {
 114         debugmsg("idx constructor from char*,bool",LOGLEVEL_CONSTRUCT);
 115         serial = next_serial++;
 116 }
 117
 118 idx::idx(unsigned v, bool cov) : inherited(TINFO_idx),
 119         symbolic(false), value(v), covariant(cov)
 120 {
 121         debugmsg("idx constructor from unsigned,bool",LOGLEVEL_CONSTRUCT);
 122         serial = 0;
 123 }
 124
 125 //////////
 126 // archiving
 127 //////////
 128
 129 /** Construct object from archive_node. */
 130 idx::idx(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 131 {
 132         debugmsg("idx constructor from archive_node", LOGLEVEL_CONSTRUCT);
 133         n.find_bool("symbolic", symbolic);
 134         n.find_bool("covariant", covariant);
 135         if (symbolic) {
 136                 serial = next_serial++;
 137                 if (!(n.find_string("name", name)))
 138                         name = "index" + ToString(serial);
 139         } else {
 140                 serial = 0;
 141                 n.find_unsigned("value", value);
 142         }
 143 }
 144
 145 /** Unarchive the object. */
 146 ex idx::unarchive(const archive_node &n, const lst &sym_lst)
 147 {
 148         ex s = (new idx(n, sym_lst))->setflag(status_flags::dynallocated);
 149
 150         if (ex_to_idx(s).symbolic) {
 151                 // If idx is in sym_lst, return the existing idx
 152                 for (unsigned i=0; i<sym_lst.nops(); i++) {
 153                         if (is_ex_of_type(sym_lst.op(i), idx) && (ex_to_idx(sym_lst.op(i)).name == ex_to_idx(s).name))
 154                                 return sym_lst.op(i);
 155                 }
 156         }
 157         return s;
 158 }
 159
 160 /** Archive the object. */
 161 void idx::archive(archive_node &n) const
 162 {
 163         inherited::archive(n);
 164         n.add_bool("symbolic", symbolic);
 165         n.add_bool("covariant", covariant);
 166         if (symbolic)
 167                 n.add_string("name", name);
 168         else
 169                 n.add_unsigned("value", value);
 170 }
 171
 172 //////////
 173 // functions overriding virtual functions from bases classes
 174 //////////
 175
 176 // public
 177
 178 basic * idx::duplicate() const
 179 {
 180         debugmsg("idx duplicate",LOGLEVEL_DUPLICATE);
 181         return new idx(*this);
 182 }
 183
 184 void idx::printraw(std::ostream & os) const
 185 {
 186         debugmsg("idx printraw",LOGLEVEL_PRINT);
 187
 188         os << "idx(";
 189
 190         if (symbolic) {
 191                 os << "symbolic,name=" << name;
 192         } else {
 193                 os << "non symbolic,value=" << value;
 194         }
 195
 196         if (covariant) {
 197                 os << ",covariant";
 198         } else {
 199                 os << ",contravariant";
 200         }
 201
 202         os << ",serial=" << serial;
 203         os << ",hash=" << hashvalue << ",flags=" << flags;
 204         os << ")";
 205 }
 206
 207 void idx::printtree(std::ostream & os, unsigned indent) const
 208 {
 209         debugmsg("idx printtree",LOGLEVEL_PRINT);
 210
 211         os << std::string(indent,' ') << "idx: ";
 212
 213         if (symbolic) {
 214                 os << "symbolic,name=" << name;
 215         } else {
 216                 os << "non symbolic,value=" << value;
 217         }
 218
 219         if (covariant) {
 220                 os << ",covariant";
 221         } else {
 222                 os << ",contravariant";
 223         }
 224
 225         os << ", serial=" << serial
 226            << ", hash=" << hashvalue
 227            << " (0x" << std::hex << hashvalue << std::dec << ")"
 228            << ", flags=" << flags << std::endl;
 229 }
 230
 231 void idx::print(std::ostream & os, unsigned upper_precedence) const
 232 {
 233         debugmsg("idx print",LOGLEVEL_PRINT);
 234
 235         if (covariant) {
 236                 os << "_";
 237         } else {
 238                 os << "~";
 239         }
 240         if (symbolic) {
 241                 os << name;
 242         } else {
 243                 os << value;
 244         }
 245 }
 246
 247 bool idx::info(unsigned inf) const
 248 {
 249         if (inf==info_flags::idx) return true;
 250         return inherited::info(inf);
 251 }
 252
 253 ex idx::subs(const lst & ls, const lst & lr) const
 254 {
 255         GINAC_ASSERT(ls.nops()==lr.nops());
 256 #ifdef DO_GINAC_ASSERT
 257         for (unsigned i=0; i<ls.nops(); i++) {
 258                 GINAC_ASSERT(is_ex_exactly_of_type(ls.op(i),symbol)||
 259                            is_ex_of_type(ls.op(i),idx));
 260         }
 261 #endif // def DO_GINAC_ASSERT
 262
 263         for (unsigned i=0; i<ls.nops(); i++) {
 264                 if (is_equal(*(ls.op(i)).bp)) {
 265                         return lr.op(i);
 266                 }
 267         }
 268         return *this;
 269 }
 270
 271 // protected
 272
 273 int idx::compare_same_type(const basic & other) const
 274 {
 275         GINAC_ASSERT(is_of_type(other,idx));
 276         const idx & o=static_cast<const idx &>
 277                                                          (const_cast<basic &>(other));
 278
 279         if (covariant!=o.covariant) {
 280                 // different co/contravariant
 281                 return covariant ? -1 : 1;
 282         }
 283         if ((!symbolic) && (!o.symbolic)) {
 284                 // non-symbolic, of equal type: compare values
 285                 if (value==o.value) {
 286                         return 0;
 287                 }
 288                 return value<o.value ? -1 : 1;
 289         }
 290         if (symbolic && o.symbolic) {
 291                 // both symbolic: compare serials
 292                 if (serial==o.serial) {
 293                         return 0;
 294                 }
 295                 return serial<o.serial ? -1 : 1;
 296         }
 297         // one symbolic, one value: value is sorted first
 298         return o.symbolic ? -1 : 1;
 299 }
 300
 301 bool idx::is_equal_same_type(const basic & other) const
 302 {
 303         GINAC_ASSERT(is_of_type(other,idx));
 304         const idx & o=static_cast<const idx &>
 305                                                          (const_cast<basic &>(other));
 306
 307         if (covariant!=o.covariant) return false;
 308         if (symbolic!=o.symbolic) return false;
 309         if (symbolic && o.symbolic) return serial==o.serial;
 310         return value==o.value;
 311 }
 312
 313 unsigned idx::calchash(void) const
 314 {
 315         hashvalue=golden_ratio_hash(golden_ratio_hash(tinfo_key ^ serial));
 316         setflag(status_flags::hash_calculated);
 317         return hashvalue;
 318 }
 319
 320 //////////
 321 // new virtual functions which can be overridden by derived classes
 322 //////////
 323
 324 // public
 325
 326 bool idx::is_co_contra_pair(const basic & other) const
 327 {
 328         // like is_equal_same_type(), but tests for different covariant status
 329         GINAC_ASSERT(is_of_type(other,idx));
 330         const idx & o=static_cast<const idx &>
 331                                                          (const_cast<basic &>(other));
 332
 333         if (covariant==o.covariant) return false;
 334         if (symbolic!=o.symbolic) return false;
 335         if (symbolic && o.symbolic) return serial==o.serial;
 336         return value==o.value;
 337 }
 338
 339 bool idx::is_symbolic(void) const
 340 {
 341         return symbolic;
 342 }
 343
 344 unsigned idx::get_value(void) const
 345 {
 346         return value;
 347 }
 348
 349 bool idx::is_covariant(void) const
 350 {
 351         return covariant;
 352 }
 353
 354 ex idx::toggle_covariant(void) const
 355 {
 356         idx * i_copy=static_cast<idx *>(duplicate());
 357         i_copy->covariant = !i_copy->covariant;
 358         i_copy->clearflag(status_flags::hash_calculated);
 359         return i_copy->setflag(status_flags::dynallocated);
 360 }
 361
 362 //////////
 363 // non-virtual functions in this class
 364 //////////
 365
 366 // none
 367
 368 //////////
 369 // static member variables
 370 //////////
 371
 372 // protected
 373
 374 unsigned idx::next_serial=0;
 375
 376 //////////
 377 // global constants
 378 //////////
 379
 380 const idx some_idx;
 381 const type_info & typeid_idx=typeid(some_idx);
 382
 383 //////////
 384 // other functions
 385 //////////
 386
 387 int canonicalize_indices(exvector & iv, bool antisymmetric)
 388 {
 389         if (iv.size()<2) {
 390                 // nothing do to for 0 or 1 indices
 391                 return INT_MAX;
 392         }
 393
 394         bool something_changed=false;
 395         int sig=1;
 396         // simple bubble sort algorithm should be sufficient for the small number of indices needed
 397         exvector::const_iterator last_idx=iv.end();
 398         exvector::const_iterator next_to_last_idx=iv.end()-1;
 399         for (exvector::iterator it1=iv.begin(); it1!=next_to_last_idx; ++it1) {
 400                 for (exvector::iterator it2=it1+1; it2!=last_idx; ++it2) {
 401                         int cmpval=(*it1).compare(*it2);
 402                         if (cmpval==1) {
 403                                 iter_swap(it1,it2);
 404                                 something_changed=true;
 405                                 if (antisymmetric) sig=-sig;
 406                         } else if ((cmpval==0) && antisymmetric) {
 407                                 something_changed=true;
 408                                 sig=0;
 409                         }
 410                 }
 411         }
 412         return something_changed ? sig : INT_MAX;
 413 }
 414
 415 exvector idx_intersect(const exvector & iv1, const exvector & iv2)
 416 {
 417         // build a vector of symbolic indices contained in iv1 and iv2 simultaneously
 418         // assumes (but does not test) that each index occurs at most twice
 419         exvector iv_intersect;
 420         for (exvector::const_iterator cit1=iv1.begin(); cit1!=iv1.end(); ++cit1) {
 421                 GINAC_ASSERT(is_ex_of_type(*cit1,idx));
 422                 if (ex_to_idx(*cit1).is_symbolic()) {
 423                         for (exvector::const_iterator cit2=iv2.begin(); cit2!=iv2.end(); ++cit2) {
 424                                 GINAC_ASSERT(is_ex_of_type(*cit2,idx));
 425                                 if ((*cit1).is_equal(*cit2)) {
 426                                         iv_intersect.push_back(*cit1);
 427                                         break;
 428                                 }
 429                         }
 430                 }
 431         }
 432         return iv_intersect;
 433 }
 434
 435 #define TEST_PERMUTATION(A,B,C,P) \
 436         if ((iv3[B].is_equal(iv2[0]))&&(iv3[C].is_equal(iv2[1]))) { \
 437                 if (antisymmetric) *sig=P; \
 438                 return iv3[A]; \
 439         }
 440
 441 ex permute_free_index_to_front(const exvector & iv3, const exvector & iv2,
 442                                                            bool antisymmetric, int * sig)
 443 {
 444         // match (return value,iv2) to iv3 by permuting indices
 445         // iv3 is always cyclic
 446
 447         GINAC_ASSERT(iv3.size()==3);
 448         GINAC_ASSERT(iv2.size()==2);
 449
 450         *sig=1;
 451
 452         TEST_PERMUTATION(0,1,2,  1);
 453         TEST_PERMUTATION(0,2,1, -1);
 454         TEST_PERMUTATION(1,0,2, -1);
 455         TEST_PERMUTATION(1,2,0,  1);
 456         TEST_PERMUTATION(2,0,1,  1);
 457         TEST_PERMUTATION(2,1,0, -1);
 458         throw(std::logic_error("permute_free_index_to_front(): no valid permutation found"));
 459 }
 460
 461 unsigned subs_index_in_exvector(exvector & v, const ex & is, const ex & ir)
 462 {
 463         exvector::iterator it;
 464         unsigned replacements=0;
 465         unsigned current_replacements;
 466
 467         GINAC_ASSERT(is_ex_of_type(is,idx));
 468         GINAC_ASSERT(is_ex_of_type(ir,idx));
 469
 470         for (it=v.begin(); it!=v.end(); ++it) {
 471                 current_replacements=count_index(*it,is);
 472                 if (current_replacements>0) {
 473                         (*it)=(*it).subs(is==ir);
 474                 }
 475                 replacements += current_replacements;
 476         }
 477         return replacements;
 478 }
 479
 480 unsigned count_index(const ex & e, const ex & i)
 481 {
 482         exvector idxv=e.get_indices();
 483         unsigned count=0;
 484         for (exvector::const_iterator cit=idxv.begin(); cit!=idxv.end(); ++cit) {
 485                 if ((*cit).is_equal(i)) count++;
 486         }
 487         return count;
 488 }
 489
 490 ex subs_indices(const ex & e, const exvector & idxv_subs,
 491                                 const exvector & idxv_repl)
 492 {
 493         GINAC_ASSERT(idxv_subs.size()==idxv_repl.size());
 494         ex res=e;
 495         for (unsigned i=0; i<idxv_subs.size(); ++i) {
 496                 res=res.subs(idxv_subs[i]==idxv_repl[i]);
 497         }
 498         return res;
 499 }
 500
 501 #ifndef NO_NAMESPACE_GINAC
 502 } // namespace GiNaC
 503 #endif // ndef NO_NAMESPACE_GINAC