3 * Implementation of GiNaC's indexed expressions. */
6 * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
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.
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.
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
37 GINAC_IMPLEMENT_REGISTERED_CLASS(indexed, exprseq)
40 // default constructor, destructor, copy constructor assignment operator and helpers
43 indexed::indexed() : symmetry(unknown)
45 debugmsg("indexed default constructor", LOGLEVEL_CONSTRUCT);
46 tinfo_key = TINFO_indexed;
49 void indexed::copy(const indexed & other)
51 inherited::copy(other);
52 symmetry = other.symmetry;
55 DEFAULT_DESTROY(indexed)
61 indexed::indexed(const ex & b) : inherited(b), symmetry(unknown)
63 debugmsg("indexed constructor from ex", LOGLEVEL_CONSTRUCT);
64 tinfo_key = TINFO_indexed;
65 assert_all_indices_of_type_idx();
68 indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symmetry(unknown)
70 debugmsg("indexed constructor from ex,ex", LOGLEVEL_CONSTRUCT);
71 tinfo_key = TINFO_indexed;
72 assert_all_indices_of_type_idx();
75 indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symmetry(unknown)
77 debugmsg("indexed constructor from ex,ex,ex", LOGLEVEL_CONSTRUCT);
78 tinfo_key = TINFO_indexed;
79 assert_all_indices_of_type_idx();
82 indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symmetry(unknown)
84 debugmsg("indexed constructor from ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
85 tinfo_key = TINFO_indexed;
86 assert_all_indices_of_type_idx();
89 indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symmetry(unknown)
91 debugmsg("indexed constructor from ex,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
92 tinfo_key = TINFO_indexed;
93 assert_all_indices_of_type_idx();
96 indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symmetry(symm)
98 debugmsg("indexed constructor from ex,symmetry,ex,ex", LOGLEVEL_CONSTRUCT);
99 tinfo_key = TINFO_indexed;
100 assert_all_indices_of_type_idx();
103 indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symmetry(symm)
105 debugmsg("indexed constructor from ex,symmetry,ex,ex,ex", LOGLEVEL_CONSTRUCT);
106 tinfo_key = TINFO_indexed;
107 assert_all_indices_of_type_idx();
110 indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symmetry(symm)
112 debugmsg("indexed constructor from ex,symmetry,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
113 tinfo_key = TINFO_indexed;
114 assert_all_indices_of_type_idx();
117 indexed::indexed(const ex & b, const exvector & v) : inherited(b), symmetry(unknown)
119 debugmsg("indexed constructor from ex,exvector", LOGLEVEL_CONSTRUCT);
120 seq.insert(seq.end(), v.begin(), v.end());
121 tinfo_key = TINFO_indexed;
122 assert_all_indices_of_type_idx();
125 indexed::indexed(const ex & b, symmetry_type symm, const exvector & v) : inherited(b), symmetry(symm)
127 debugmsg("indexed constructor from ex,symmetry,exvector", LOGLEVEL_CONSTRUCT);
128 seq.insert(seq.end(), v.begin(), v.end());
129 tinfo_key = TINFO_indexed;
130 assert_all_indices_of_type_idx();
133 indexed::indexed(symmetry_type symm, const exprseq & es) : inherited(es), symmetry(symm)
135 debugmsg("indexed constructor from symmetry,exprseq", LOGLEVEL_CONSTRUCT);
136 tinfo_key = TINFO_indexed;
137 assert_all_indices_of_type_idx();
140 indexed::indexed(symmetry_type symm, const exvector & v, bool discardable) : inherited(v, discardable), symmetry(symm)
142 debugmsg("indexed constructor from symmetry,exvector", LOGLEVEL_CONSTRUCT);
143 tinfo_key = TINFO_indexed;
144 assert_all_indices_of_type_idx();
147 indexed::indexed(symmetry_type symm, exvector * vp) : inherited(vp), symmetry(symm)
149 debugmsg("indexed constructor from symmetry,exvector *", LOGLEVEL_CONSTRUCT);
150 tinfo_key = TINFO_indexed;
151 assert_all_indices_of_type_idx();
158 indexed::indexed(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
160 debugmsg("indexed constructor from archive_node", LOGLEVEL_CONSTRUCT);
162 if (!(n.find_unsigned("symmetry", symm)))
163 throw (std::runtime_error("unknown indexed symmetry type in archive"));
166 void indexed::archive(archive_node &n) const
168 inherited::archive(n);
169 n.add_unsigned("symmetry", symmetry);
172 DEFAULT_UNARCHIVE(indexed)
175 // functions overriding virtual functions from bases classes
178 void indexed::printraw(std::ostream & os) const
180 debugmsg("indexed printraw", LOGLEVEL_PRINT);
181 GINAC_ASSERT(seq.size() > 0);
183 os << class_name() << "(";
187 os << ",hash=" << hashvalue << ",flags=" << flags << ")";
190 void indexed::printtree(std::ostream & os, unsigned indent) const
192 debugmsg("indexed printtree", LOGLEVEL_PRINT);
193 GINAC_ASSERT(seq.size() > 0);
195 os << std::string(indent, ' ') << class_name() << ", " << seq.size()-1 << " indices";
196 os << ",hash=" << hashvalue << ",flags=" << flags << std::endl;
197 printtreeindices(os, indent);
200 void indexed::print(std::ostream & os, unsigned upper_precedence) const
202 debugmsg("indexed print", LOGLEVEL_PRINT);
203 GINAC_ASSERT(seq.size() > 0);
205 const ex & base = seq[0];
206 bool need_parens = is_ex_exactly_of_type(base, add) || is_ex_exactly_of_type(base, mul)
207 || is_ex_exactly_of_type(base, ncmul) || is_ex_exactly_of_type(base, power);
216 bool indexed::info(unsigned inf) const
218 if (inf == info_flags::indexed) return true;
219 if (inf == info_flags::has_indices) return seq.size() > 1;
220 return inherited::info(inf);
223 bool indexed::all_index_values_are(unsigned inf) const
225 // No indices? Then no property can be fulfilled
230 exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
231 while (it != itend) {
232 GINAC_ASSERT(is_ex_of_type(*it, idx));
233 if (!ex_to_idx(*it).get_value().info(inf))
240 int indexed::compare_same_type(const basic & other) const
242 GINAC_ASSERT(is_of_type(other, indexed));
243 return inherited::compare_same_type(other);
246 // The main difference between sort_index_vector() and canonicalize_indices()
247 // is that the latter takes the symmetry of the object into account. Once we
248 // implement mixed symmetries, canonicalize_indices() will only be able to
249 // reorder index pairs with known symmetry properties, while sort_index_vector()
250 // always sorts the whole vector.
252 /** Bring a vector of indices into a canonic order (don't care about the
253 * symmetry of the objects carrying the indices). Dummy indices will lie
254 * next to each other after the sorting.
256 * @param v Index vector to be sorted */
257 static void sort_index_vector(exvector &v)
259 // Nothing to sort if less than 2 elements
263 // Simple bubble sort algorithm should be sufficient for the small
264 // number of indices expected
265 exvector::iterator it1 = v.begin(), itend = v.end(), next_to_last_idx = itend - 1;
266 while (it1 != next_to_last_idx) {
267 exvector::iterator it2 = it1 + 1;
268 while (it2 != itend) {
269 if (it1->compare(*it2) > 0)
277 /** Bring a vector of indices into a canonic order. This operation only makes
278 * sense if the object carrying these indices is either symmetric or totally
279 * antisymmetric with respect to the indices.
281 * @param itbegin Start of index vector
282 * @param itend End of index vector
283 * @param antisymm Whether the object is antisymmetric
284 * @return the sign introduced by the reordering of the indices if the object
285 * is antisymmetric (or 0 if two equal indices are encountered). For
286 * symmetric objects, this is always +1. If the index vector was
287 * already in a canonic order this function returns INT_MAX. */
288 static int canonicalize_indices(exvector::iterator itbegin, exvector::iterator itend, bool antisymm)
290 bool something_changed = false;
293 // Simple bubble sort algorithm should be sufficient for the small
294 // number of indices expected
295 exvector::iterator it1 = itbegin, next_to_last_idx = itend - 1;
296 while (it1 != next_to_last_idx) {
297 exvector::iterator it2 = it1 + 1;
298 while (it2 != itend) {
299 int cmpval = it1->compare(*it2);
302 something_changed = true;
305 } else if (cmpval == 0 && antisymm) {
306 something_changed = true;
314 return something_changed ? sig : INT_MAX;
317 ex indexed::eval(int level) const
319 // First evaluate children, then we will end up here again
321 return indexed(symmetry, evalchildren(level));
323 const ex &base = seq[0];
325 // If the base object is 0, the whole object is 0
329 // If the base object is a product, pull out the numeric factor
330 if (is_ex_exactly_of_type(base, mul) && is_ex_exactly_of_type(base.op(base.nops() - 1), numeric)) {
332 ex f = ex_to_numeric(base.op(base.nops() - 1));
334 return f * thisexprseq(v);
337 // Canonicalize indices according to the symmetry properties
338 if (seq.size() > 2 && (symmetry != unknown && symmetry != mixed)) {
340 int sig = canonicalize_indices(v.begin() + 1, v.end(), symmetry == antisymmetric);
341 if (sig != INT_MAX) {
342 // Something has changed while sorting indices, more evaluations later
345 return ex(sig) * thisexprseq(v);
349 // Let the class of the base object perform additional evaluations
350 return base.bp->eval_indexed(*this);
353 ex indexed::thisexprseq(const exvector & v) const
355 return indexed(symmetry, v);
358 ex indexed::thisexprseq(exvector * vp) const
360 return indexed(symmetry, vp);
363 ex indexed::expand(unsigned options) const
365 GINAC_ASSERT(seq.size() > 0);
367 if ((options & expand_options::expand_indexed) && is_ex_exactly_of_type(seq[0], add)) {
369 // expand_indexed expands (a+b).i -> a.i + b.i
370 const ex & base = seq[0];
372 for (unsigned i=0; i<base.nops(); i++) {
375 sum += thisexprseq(s).expand();
380 return inherited::expand(options);
384 // virtual functions which can be overridden by derived classes
390 // non-virtual functions in this class
393 void indexed::printrawindices(std::ostream & os) const
395 if (seq.size() > 1) {
396 exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
397 while (it != itend) {
406 void indexed::printtreeindices(std::ostream & os, unsigned indent) const
408 if (seq.size() > 1) {
409 exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
410 while (it != itend) {
411 os << std::string(indent + delta_indent, ' ');
419 void indexed::printindices(std::ostream & os) const
421 if (seq.size() > 1) {
422 exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
423 while (it != itend) {
430 /** Check whether all indices are of class idx. This function is used
431 * internally to make sure that all constructed indexed objects really
432 * carry indices and not some other classes. */
433 void indexed::assert_all_indices_of_type_idx(void) const
435 GINAC_ASSERT(seq.size() > 0);
436 exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
437 while (it != itend) {
438 if (!is_ex_of_type(*it, idx))
439 throw(std::invalid_argument("indices of indexed object must be of type idx"));
448 /** Given a vector of indices, split them into two vectors, one containing
449 * the free indices, the other containing the dummy indices. */
450 static void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy)
455 // No indices? Then do nothing
459 // Only one index? Then it is a free one if it's not numeric
460 if (itend - it == 1) {
461 if (ex_to_idx(*it).is_symbolic())
462 out_free.push_back(*it);
466 // Sort index vector. This will cause dummy indices come to lie next
467 // to each other (because the sort order is defined to guarantee this).
468 exvector v(it, itend);
469 sort_index_vector(v);
471 // Find dummy pairs and free indices
472 it = v.begin(); itend = v.end();
473 exvector::const_iterator last = it++;
474 while (it != itend) {
475 if (is_dummy_pair(*it, *last)) {
476 out_dummy.push_back(*last);
481 if (!it->is_equal(*last) && ex_to_idx(*last).is_symbolic())
482 out_free.push_back(*last);
486 if (ex_to_idx(*last).is_symbolic())
487 out_free.push_back(*last);
490 /** Check whether two sorted index vectors are consistent (i.e. equal). */
491 static bool indices_consistent(const exvector & v1, const exvector & v2)
493 // Number of indices must be the same
494 if (v1.size() != v2.size())
497 // And also the indices themselves
498 exvector::const_iterator ait = v1.begin(), aitend = v1.end(),
499 bit = v2.begin(), bitend = v2.end();
500 while (ait != aitend) {
501 if (!ait->is_equal(*bit))
508 exvector indexed::get_dummy_indices(void) const
510 exvector free_indices, dummy_indices;
511 find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
512 return dummy_indices;
515 exvector indexed::get_free_indices(void) const
517 exvector free_indices, dummy_indices;
518 find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
522 exvector add::get_free_indices(void) const
524 exvector free_indices;
525 for (unsigned i=0; i<nops(); i++) {
527 free_indices = op(i).get_free_indices();
529 exvector free_indices_of_term = op(i).get_free_indices();
530 if (!indices_consistent(free_indices, free_indices_of_term))
531 throw (std::runtime_error("add::get_free_indices: inconsistent indices in sum"));
537 exvector mul::get_free_indices(void) const
539 // Concatenate free indices of all factors
541 for (unsigned i=0; i<nops(); i++) {
542 exvector free_indices_of_factor = op(i).get_free_indices();
543 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
546 // And remove the dummy indices
547 exvector free_indices, dummy_indices;
548 find_free_and_dummy(un.begin(), un.end(), free_indices, dummy_indices);
552 exvector ncmul::get_free_indices(void) const
554 // Concatenate free indices of all factors
556 for (unsigned i=0; i<nops(); i++) {
557 exvector free_indices_of_factor = op(i).get_free_indices();
558 un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
561 // And remove the dummy indices
562 exvector free_indices, dummy_indices;
563 find_free_and_dummy(un.begin(), un.end(), free_indices, dummy_indices);
567 exvector power::get_free_indices(void) const
569 // Return free indices of basis
570 return basis.get_free_indices();
573 /** Simplify product of indexed expressions (commutative, noncommutative and
574 * simple squares), return list of free indices. */
575 ex simplify_indexed_product(const ex & e, exvector & free_indices, const scalar_products & sp)
577 // Remember whether the product was commutative or noncommutative
578 // (because we chop it into factors and need to reassemble later)
579 bool non_commutative = is_ex_exactly_of_type(e, ncmul);
581 // Collect factors in an exvector, store squares twice
583 v.reserve(e.nops() * 2);
585 if (is_ex_exactly_of_type(e, power)) {
586 // We only get called for simple squares, split a^2 -> a*a
587 GINAC_ASSERT(e.op(1).is_equal(_ex2()));
588 v.push_back(e.op(0));
589 v.push_back(e.op(0));
591 for (int i=0; i<e.nops(); i++) {
593 if (is_ex_exactly_of_type(f, power) && f.op(1).is_equal(_ex2())) {
594 v.push_back(f.op(0));
595 v.push_back(f.op(0));
596 } else if (is_ex_exactly_of_type(f, ncmul)) {
597 // Noncommutative factor found, split it as well
598 non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later
599 for (int j=0; j<f.nops(); i++)
600 v.push_back(f.op(j));
606 // Perform contractions
607 bool something_changed = false;
608 GINAC_ASSERT(v.size() > 1);
609 exvector::iterator it1, itend = v.end(), next_to_last = itend - 1;
610 for (it1 = v.begin(); it1 != next_to_last; it1++) {
613 if (!is_ex_of_type(*it1, indexed))
616 // Indexed factor found, look for contraction candidates
617 exvector::iterator it2;
618 for (it2 = it1 + 1; it2 != itend; it2++) {
620 if (!is_ex_of_type(*it2, indexed))
623 // Check whether the two factors share dummy indices
624 exvector un(ex_to_indexed(*it1).seq.begin() + 1, ex_to_indexed(*it1).seq.end());
625 un.insert(un.end(), ex_to_indexed(*it2).seq.begin() + 1, ex_to_indexed(*it2).seq.end());
626 exvector free, dummy;
627 find_free_and_dummy(un.begin(), un.end(), free, dummy);
628 if (dummy.size() == 0)
631 // At least one dummy index, is it a defined scalar product?
632 if (free.size() == 0) {
633 if (sp.is_defined(*it1, *it2)) {
634 *it1 = sp.evaluate(*it1, *it2);
636 something_changed = true;
641 // Contraction of symmetric with antisymmetric object is zero
642 if ((ex_to_indexed(*it1).symmetry == indexed::symmetric &&
643 ex_to_indexed(*it2).symmetry == indexed::antisymmetric
644 || ex_to_indexed(*it1).symmetry == indexed::antisymmetric &&
645 ex_to_indexed(*it2).symmetry == indexed::symmetric)
646 && dummy.size() > 1) {
647 free_indices.clear();
651 // Try to contract the first one with the second one
652 bool contracted = it1->op(0).bp->contract_with(it1, it2, v);
655 // That didn't work; maybe the second object knows how to
656 // contract itself with the first one
657 contracted = it2->op(0).bp->contract_with(it2, it1, v);
660 something_changed = true;
662 // Both objects may have new indices now or they might
663 // even not be indexed objects any more, so we have to
670 // Find free indices (concatenate them all and call find_free_and_dummy())
671 exvector un, dummy_indices;
672 it1 = v.begin(); itend = v.end();
673 while (it1 != itend) {
674 if (is_ex_of_type(*it1, indexed)) {
675 const indexed & o = ex_to_indexed(*it1);
676 un.insert(un.end(), o.seq.begin() + 1, o.seq.end());
680 find_free_and_dummy(un.begin(), un.end(), free_indices, dummy_indices);
683 if (something_changed) {
691 // Product of indexed object with a scalar?
692 if (is_ex_exactly_of_type(r, mul) && r.nops() == 2
693 && is_ex_exactly_of_type(r.op(1), numeric) && is_ex_of_type(r.op(0), indexed))
694 return r.op(0).op(0).bp->scalar_mul_indexed(r.op(0), ex_to_numeric(r.op(1)));
699 /** Simplify indexed expression, return list of free indices. */
700 ex simplify_indexed(const ex & e, exvector & free_indices, const scalar_products & sp)
702 // Expand the expression
703 ex e_expanded = e.expand();
705 // Simplification of single indexed object: just find the free indices
706 if (is_ex_of_type(e_expanded, indexed)) {
707 const indexed &i = ex_to_indexed(e_expanded);
708 exvector dummy_indices;
709 find_free_and_dummy(i.seq.begin() + 1, i.seq.end(), free_indices, dummy_indices);
713 // Simplification of sum = sum of simplifications, check consistency of
714 // free indices in each term
715 if (is_ex_exactly_of_type(e_expanded, add)) {
718 free_indices.clear();
720 for (unsigned i=0; i<e_expanded.nops(); i++) {
721 exvector free_indices_of_term;
722 ex term = simplify_indexed(e_expanded.op(i), free_indices_of_term, sp);
723 if (!term.is_zero()) {
725 free_indices = free_indices_of_term;
729 if (!indices_consistent(free_indices, free_indices_of_term))
730 throw (std::runtime_error("simplify_indexed: inconsistent indices in sum"));
731 if (is_ex_of_type(sum, indexed) && is_ex_of_type(term, indexed))
732 sum = sum.op(0).bp->add_indexed(sum, term);
742 // Simplification of products
743 if (is_ex_exactly_of_type(e_expanded, mul)
744 || is_ex_exactly_of_type(e_expanded, ncmul)
745 || (is_ex_exactly_of_type(e_expanded, power) && is_ex_of_type(e_expanded.op(0), indexed) && e_expanded.op(1).is_equal(_ex2())))
746 return simplify_indexed_product(e_expanded, free_indices, sp);
748 // Cannot do anything
749 free_indices.clear();
753 ex simplify_indexed(const ex & e)
755 exvector free_indices;
757 return simplify_indexed(e, free_indices, sp);
760 ex simplify_indexed(const ex & e, const scalar_products & sp)
762 exvector free_indices;
763 return simplify_indexed(e, free_indices, sp);
770 void scalar_products::add(const ex & v1, const ex & v2, const ex & sp)
772 spm[make_key(v1, v2)] = sp;
775 void scalar_products::clear(void)
780 /** Check whether scalar product pair is defined. */
781 bool scalar_products::is_defined(const ex & v1, const ex & v2) const
783 return spm.find(make_key(v1, v2)) != spm.end();
786 /** Return value of defined scalar product pair. */
787 ex scalar_products::evaluate(const ex & v1, const ex & v2) const
789 return spm.find(make_key(v1, v2))->second;
792 void scalar_products::debugprint(void) const
794 std::cerr << "map size=" << spm.size() << std::endl;
795 for (spmap::const_iterator cit=spm.begin(); cit!=spm.end(); ++cit) {
796 const spmapkey & k = cit->first;
797 std::cerr << "item key=(" << k.first << "," << k.second;
798 std::cerr << "), value=" << cit->second << std::endl;
802 /** Make key from object pair. */
803 spmapkey scalar_products::make_key(const ex & v1, const ex & v2)
805 // If indexed, extract base objects
806 ex s1 = is_ex_of_type(v1, indexed) ? v1.op(0) : v1;
807 ex s2 = is_ex_of_type(v2, indexed) ? v2.op(0) : v2;
809 // Enforce canonical order in pair
810 if (s1.compare(s2) > 0)
811 return spmapkey(s2, s1);
813 return spmapkey(s1, s2);