ginac/symmetry.cpp

   1 /** @file symmetry.cpp
   2  *
   3  *  Implementation of GiNaC's symmetry definitions. */
   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 <stdexcept>
  24 #include <functional>
  25 #include <algorithm>
  26
  27 #include "symmetry.h"
  28 #include "lst.h"
  29 #include "numeric.h" // for factorial()
  30 #include "print.h"
  31 #include "archive.h"
  32 #include "utils.h"
  33 #include "debugmsg.h"
  34
  35 namespace GiNaC {
  36
  37 GINAC_IMPLEMENT_REGISTERED_CLASS(symmetry, basic)
  38
  39 //////////
  40 // default constructor, destructor, copy constructor assignment operator and helpers
  41 //////////
  42
  43 symmetry::symmetry() : type(none)
  44 {
  45         debugmsg("symmetry default constructor", LOGLEVEL_CONSTRUCT);
  46         tinfo_key = TINFO_symmetry;
  47 }
  48
  49 void symmetry::copy(const symmetry & other)
  50 {
  51         inherited::copy(other);
  52         type = other.type;
  53         indices = other.indices;
  54         children = other.children;
  55 }
  56
  57 DEFAULT_DESTROY(symmetry)
  58
  59 //////////
  60 // other constructors
  61 //////////
  62
  63 symmetry::symmetry(unsigned i) : type(none)
  64 {
  65         debugmsg("symmetry constructor from unsigned", LOGLEVEL_CONSTRUCT);
  66         indices.insert(i);
  67         tinfo_key = TINFO_symmetry;
  68 }
  69
  70 symmetry::symmetry(symmetry_type t, const symmetry &c1, const symmetry &c2) : type(t)
  71 {
  72         debugmsg("symmetry constructor from symmetry_type,symmetry &,symmetry &", LOGLEVEL_CONSTRUCT);
  73         add(c1); add(c2);
  74         tinfo_key = TINFO_symmetry;
  75 }
  76
  77 //////////
  78 // archiving
  79 //////////
  80
  81 /** Construct object from archive_node. */
  82 symmetry::symmetry(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
  83 {
  84         debugmsg("symmetry ctor from archive_node", LOGLEVEL_CONSTRUCT);
  85
  86         unsigned t;
  87         if (!(n.find_unsigned("type", t)))
  88                 throw (std::runtime_error("unknown symmetry type in archive"));
  89         type = (symmetry_type)t;
  90
  91         unsigned i = 0;
  92         while (true) {
  93                 ex e;
  94                 if (n.find_ex("child", e, sym_lst, i))
  95                         add(ex_to<symmetry>(e));
  96                 else
  97                         break;
  98                 i++;
  99         }
 100
 101         if (i == 0) {
 102                 while (true) {
 103                         unsigned u;
 104                         if (n.find_unsigned("index", u, i))
 105                                 indices.insert(u);
 106                         else
 107                                 break;
 108                         i++;
 109                 }
 110         }
 111 }
 112
 113 /** Archive the object. */
 114 void symmetry::archive(archive_node &n) const
 115 {
 116         inherited::archive(n);
 117
 118         n.add_unsigned("type", type);
 119
 120         if (children.empty()) {
 121                 std::set<unsigned>::const_iterator i = indices.begin(), iend = indices.end();
 122                 while (i != iend) {
 123                         n.add_unsigned("index", *i);
 124                         i++;
 125                 }
 126         } else {
 127                 exvector::const_iterator i = children.begin(), iend = children.end();
 128                 while (i != iend) {
 129                         n.add_ex("child", *i);
 130                         i++;
 131                 }
 132         }
 133 }
 134
 135 DEFAULT_UNARCHIVE(symmetry)
 136
 137 //////////
 138 // functions overriding virtual functions from base classes
 139 //////////
 140
 141 int symmetry::compare_same_type(const basic & other) const
 142 {
 143         GINAC_ASSERT(is_of_type(other, symmetry));
 144
 145         // All symmetry trees are equal. They are not supposed to appear in
 146         // ordinary expressions anyway...
 147         return 0;
 148 }
 149
 150 void symmetry::print(const print_context & c, unsigned level = 0) const
 151 {
 152         debugmsg("symmetry print", LOGLEVEL_PRINT);
 153
 154         if (children.empty()) {
 155                 if (indices.size() > 0)
 156                         c.s << *(indices.begin());
 157                 else
 158                         c.s << "none";
 159         } else {
 160                 switch (type) {
 161                         case none: c.s << '!'; break;
 162                         case symmetric: c.s << '+'; break;
 163                         case antisymmetric: c.s << '-'; break;
 164                         case cyclic: c.s << '@'; break;
 165                         default: c.s << '?'; break;
 166                 }
 167                 c.s << '(';
 168                 unsigned num = children.size();
 169                 for (unsigned i=0; i<num; i++) {
 170                         children[i].print(c);
 171                         if (i != num - 1)
 172                                 c.s << ",";
 173                 }
 174                 c.s << ')';
 175         }
 176 }
 177
 178 //////////
 179 // non-virtual functions in this class
 180 //////////
 181
 182 symmetry &symmetry::add(const symmetry &c)
 183 {
 184         // All children must have the same number of indices
 185         if (type != none && !children.empty()) {
 186                 GINAC_ASSERT(is_ex_exactly_of_type(children[0], symmetry));
 187                 if (ex_to<symmetry>(children[0]).indices.size() != c.indices.size())
 188                         throw (std::logic_error("symmetry:add(): children must have same number of indices"));
 189         }
 190
 191         // Compute union of indices and check whether the two sets are disjoint
 192         std::set<unsigned> un;
 193         set_union(indices.begin(), indices.end(), c.indices.begin(), c.indices.end(), inserter(un, un.begin()));
 194         if (un.size() != indices.size() + c.indices.size())
 195                 throw (std::logic_error("symmetry::add(): the same index appears in more than one child"));
 196
 197         // Set new index set
 198         indices.swap(un);
 199
 200         // Add child node
 201         children.push_back(c);
 202         return *this;
 203 }
 204
 205 void symmetry::validate(unsigned n)
 206 {
 207         if (indices.upper_bound(n - 1) != indices.end())
 208                 throw (std::range_error("symmetry::verify(): index values are out of range"));
 209         if (type != none && indices.empty()) {
 210                 for (unsigned i=0; i<n; i++)
 211                         add(i);
 212         }
 213 }
 214
 215 //////////
 216 // global functions
 217 //////////
 218
 219 class sy_is_less : public std::binary_function<ex, ex, bool> {
 220         exvector::iterator v;
 221
 222 public:
 223         sy_is_less(exvector::iterator v_) : v(v_) {}
 224
 225         bool operator() (const ex &lh, const ex &rh) const
 226         {
 227                 GINAC_ASSERT(is_ex_exactly_of_type(lh, symmetry));
 228                 GINAC_ASSERT(is_ex_exactly_of_type(rh, symmetry));
 229                 GINAC_ASSERT(ex_to<symmetry>(lh).indices.size() == ex_to<symmetry>(rh).indices.size());
 230                 std::set<unsigned>::const_iterator ait = ex_to<symmetry>(lh).indices.begin(), aitend = ex_to<symmetry>(lh).indices.end(), bit = ex_to<symmetry>(rh).indices.begin();
 231                 while (ait != aitend) {
 232                         int cmpval = v[*ait].compare(v[*bit]);
 233                         if (cmpval < 0)
 234                                 return true;
 235                         else if (cmpval > 0)
 236                                 return false;
 237                         ++ait; ++bit;
 238                 }
 239                 return false;
 240         }
 241 };
 242
 243 class sy_swap : public std::binary_function<ex, ex, void> {
 244         exvector::iterator v;
 245
 246 public:
 247         bool &swapped;
 248
 249         sy_swap(exvector::iterator v_, bool &s) : v(v_), swapped(s) {}
 250
 251         void operator() (const ex &lh, const ex &rh)
 252         {
 253                 GINAC_ASSERT(is_ex_exactly_of_type(lh, symmetry));
 254                 GINAC_ASSERT(is_ex_exactly_of_type(rh, symmetry));
 255                 GINAC_ASSERT(ex_to<symmetry>(lh).indices.size() == ex_to<symmetry>(rh).indices.size());
 256                 std::set<unsigned>::const_iterator ait = ex_to<symmetry>(lh).indices.begin(), aitend = ex_to<symmetry>(lh).indices.end(), bit = ex_to<symmetry>(rh).indices.begin();
 257                 while (ait != aitend) {
 258                         v[*ait].swap(v[*bit]);
 259                         ++ait; ++bit;
 260                 }
 261                 swapped = true;
 262         }
 263 };
 264
 265 int canonicalize(exvector::iterator v, const symmetry &symm)
 266 {
 267         // No children? Then do nothing
 268         if (symm.children.empty())
 269                 return INT_MAX;
 270
 271         // Canonicalize children first
 272         bool something_changed = false;
 273         int sign = 1;
 274         exvector::const_iterator first = symm.children.begin(), last = symm.children.end();
 275         while (first != last) {
 276                 GINAC_ASSERT(is_ex_exactly_of_type(*first, symmetry));
 277                 int child_sign = canonicalize(v, ex_to<symmetry>(*first));
 278                 if (child_sign == 0)
 279                         return 0;
 280                 if (child_sign != INT_MAX) {
 281                         something_changed = true;
 282                         sign *= child_sign;
 283                 }
 284                 first++;
 285         }
 286
 287         // Now reorder the children
 288         first = symm.children.begin();
 289         switch (symm.type) {
 290                 case symmetry::symmetric:
 291                         // Sort the children in ascending order
 292                         shaker_sort(first, last, sy_is_less(v), sy_swap(v, something_changed));
 293                         break;
 294                 case symmetry::antisymmetric:
 295                         // Sort the children in ascending order, keeping track of the signum
 296                         sign *= permutation_sign(first, last, sy_is_less(v), sy_swap(v, something_changed));
 297                         break;
 298                 case symmetry::cyclic:
 299                         // Permute the smallest child to the front
 300                         cyclic_permutation(first, last, min_element(first, last, sy_is_less(v)), sy_swap(v, something_changed));
 301                         break;
 302                 default:
 303                         break;
 304         }
 305         return something_changed ? sign : INT_MAX;
 306 }
 307
 308
 309 // Symmetrize/antisymmetrize over a vector of objects
 310 static ex symm(const ex & e, exvector::const_iterator first, exvector::const_iterator last, bool asymmetric)
 311 {
 312         // Need at least 2 objects for this operation
 313         unsigned num = last - first;
 314         if (num < 2)
 315                 return e;
 316
 317         // Transform object vector to a list
 318         exlist iv_lst;
 319         iv_lst.insert(iv_lst.begin(), first, last);
 320         lst orig_lst(iv_lst, true);
 321
 322         // Create index vectors for permutation
 323         unsigned *iv = new unsigned[num], *iv2;
 324         for (unsigned i=0; i<num; i++)
 325                 iv[i] = i;
 326         iv2 = (asymmetric ? new unsigned[num] : NULL);
 327
 328         // Loop over all permutations (the first permutation, which is the
 329         // identity, is unrolled)
 330         ex sum = e;
 331         while (std::next_permutation(iv, iv + num)) {
 332                 lst new_lst;
 333                 for (unsigned i=0; i<num; i++)
 334                         new_lst.append(orig_lst.op(iv[i]));
 335                 ex term = e.subs(orig_lst, new_lst);
 336                 if (asymmetric) {
 337                         memcpy(iv2, iv, num * sizeof(unsigned));
 338                         term *= permutation_sign(iv2, iv2 + num);
 339                 }
 340                 sum += term;
 341         }
 342
 343         delete[] iv;
 344         delete[] iv2;
 345
 346         return sum / factorial(numeric(num));
 347 }
 348
 349 ex symmetrize(const ex & e, exvector::const_iterator first, exvector::const_iterator last)
 350 {
 351         return symm(e, first, last, false);
 352 }
 353
 354 ex antisymmetrize(const ex & e, exvector::const_iterator first, exvector::const_iterator last)
 355 {
 356         return symm(e, first, last, true);
 357 }
 358
 359 ex symmetrize_cyclic(const ex & e, exvector::const_iterator first, exvector::const_iterator last)
 360 {
 361         // Need at least 2 objects for this operation
 362         unsigned num = last - first;
 363         if (num < 2)
 364                 return e;
 365
 366         // Transform object vector to a list
 367         exlist iv_lst;
 368         iv_lst.insert(iv_lst.begin(), first, last);
 369         lst orig_lst(iv_lst, true);
 370         lst new_lst = orig_lst;
 371
 372         // Loop over all cyclic permutations (the first permutation, which is
 373         // the identity, is unrolled)
 374         ex sum = e;
 375         for (unsigned i=0; i<num-1; i++) {
 376                 ex perm = new_lst.op(0);
 377                 new_lst.remove_first().append(perm);
 378                 sum += e.subs(orig_lst, new_lst);
 379         }
 380         return sum / num;
 381 }
 382
 383 /** Symmetrize expression over a list of objects (symbols, indices). */
 384 ex ex::symmetrize(const lst & l) const
 385 {
 386         exvector v;
 387         v.reserve(l.nops());
 388         for (unsigned i=0; i<l.nops(); i++)
 389                 v.push_back(l.op(i));
 390         return symm(*this, v.begin(), v.end(), false);
 391 }
 392
 393 /** Antisymmetrize expression over a list of objects (symbols, indices). */
 394 ex ex::antisymmetrize(const lst & l) const
 395 {
 396         exvector v;
 397         v.reserve(l.nops());
 398         for (unsigned i=0; i<l.nops(); i++)
 399                 v.push_back(l.op(i));
 400         return symm(*this, v.begin(), v.end(), true);
 401 }
 402
 403 /** Symmetrize expression by cyclic permutation over a list of objects
 404  *  (symbols, indices). */
 405 ex ex::symmetrize_cyclic(const lst & l) const
 406 {
 407         exvector v;
 408         v.reserve(l.nops());
 409         for (unsigned i=0; i<l.nops(); i++)
 410                 v.push_back(l.op(i));
 411         return GiNaC::symmetrize_cyclic(*this, v.begin(), v.end());
 412 }
 413
 414 } // namespace GiNaC