/** @file indexed.cpp
*
- * Implementation of GiNaC's index carrying objects. */
+ * Implementation of GiNaC's indexed expressions. */
/*
- * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
-#include <string>
+#include <stdexcept>
#include "indexed.h"
-#include "ex.h"
#include "idx.h"
+#include "add.h"
+#include "mul.h"
+#include "ncmul.h"
+#include "power.h"
+#include "archive.h"
+#include "utils.h"
#include "debugmsg.h"
-#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
-#endif // ndef NO_NAMESPACE_GINAC
GINAC_IMPLEMENT_REGISTERED_CLASS(indexed, exprseq)
// default constructor, destructor, copy constructor assignment operator and helpers
//////////
-// public
+indexed::indexed() : symmetry(unknown)
+{
+ debugmsg("indexed default constructor", LOGLEVEL_CONSTRUCT);
+ tinfo_key = TINFO_indexed;
+}
-indexed::indexed()
+void indexed::copy(const indexed & other)
{
- debugmsg("indexed default constructor",LOGLEVEL_CONSTRUCT);
- tinfo_key=TINFO_indexed;
+ inherited::copy(other);
+ symmetry = other.symmetry;
}
-indexed::~indexed()
+void indexed::destroy(bool call_parent)
{
- debugmsg("indexed destructor",LOGLEVEL_DESTRUCT);
- destroy(0);
+ if (call_parent)
+ inherited::destroy(call_parent);
}
-indexed::indexed(const indexed & other)
+//////////
+// other constructors
+//////////
+
+indexed::indexed(const ex & b) : inherited(b), symmetry(unknown)
{
- debugmsg("indexed copy constructor",LOGLEVEL_CONSTRUCT);
- copy (other);
+ debugmsg("indexed constructor from ex", LOGLEVEL_CONSTRUCT);
+ tinfo_key = TINFO_indexed;
+ assert_all_indices_of_type_idx();
}
-const indexed & indexed::operator=(const indexed & other)
+indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symmetry(unknown)
{
- debugmsg("indexed operator=",LOGLEVEL_ASSIGNMENT);
- if (this != &other) {
- destroy(1);
- copy(other);
- }
- return *this;
+ debugmsg("indexed constructor from ex,ex", LOGLEVEL_CONSTRUCT);
+ tinfo_key = TINFO_indexed;
+ assert_all_indices_of_type_idx();
}
-// protected
+indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symmetry(unknown)
+{
+ debugmsg("indexed constructor from ex,ex,ex", LOGLEVEL_CONSTRUCT);
+ tinfo_key = TINFO_indexed;
+ assert_all_indices_of_type_idx();
+}
-void indexed::copy(const indexed & other)
+indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symmetry(unknown)
{
- inherited::copy(other);
+ debugmsg("indexed constructor from ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
+ tinfo_key = TINFO_indexed;
+ assert_all_indices_of_type_idx();
}
-void indexed::destroy(bool call_parent)
+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)
{
- if (call_parent) {
- inherited::destroy(call_parent);
- }
+ debugmsg("indexed constructor from ex,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
+ tinfo_key = TINFO_indexed;
+ assert_all_indices_of_type_idx();
}
-//////////
-// other constructors
-//////////
+indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symmetry(symm)
+{
+ debugmsg("indexed constructor from ex,symmetry,ex,ex", LOGLEVEL_CONSTRUCT);
+ tinfo_key = TINFO_indexed;
+ assert_all_indices_of_type_idx();
+}
-// public
+indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symmetry(symm)
+{
+ debugmsg("indexed constructor from ex,symmetry,ex,ex,ex", LOGLEVEL_CONSTRUCT);
+ tinfo_key = TINFO_indexed;
+ assert_all_indices_of_type_idx();
+}
-indexed::indexed(const ex & i1) : inherited(i1)
+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)
{
- debugmsg("indexed constructor from ex",LOGLEVEL_CONSTRUCT);
- tinfo_key=TINFO_indexed;
- GINAC_ASSERT(all_of_type_idx());
+ debugmsg("indexed constructor from ex,symmetry,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
+ tinfo_key = TINFO_indexed;
+ assert_all_indices_of_type_idx();
}
-indexed::indexed(const ex & i1, const ex & i2) : inherited(i1,i2)
+indexed::indexed(const ex & b, const exvector & v) : inherited(b), symmetry(unknown)
{
- debugmsg("indexed constructor from ex,ex",LOGLEVEL_CONSTRUCT);
- tinfo_key=TINFO_indexed;
- GINAC_ASSERT(all_of_type_idx());
+ debugmsg("indexed constructor from ex,exvector", LOGLEVEL_CONSTRUCT);
+ seq.insert(seq.end(), v.begin(), v.end());
+ tinfo_key = TINFO_indexed;
+ assert_all_indices_of_type_idx();
}
-indexed::indexed(const ex & i1, const ex & i2, const ex & i3)
- : inherited(i1,i2,i3)
+indexed::indexed(const ex & b, symmetry_type symm, const exvector & v) : inherited(b), symmetry(symm)
{
- debugmsg("indexed constructor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
- tinfo_key=TINFO_indexed;
- GINAC_ASSERT(all_of_type_idx());
+ debugmsg("indexed constructor from ex,symmetry,exvector", LOGLEVEL_CONSTRUCT);
+ seq.insert(seq.end(), v.begin(), v.end());
+ tinfo_key = TINFO_indexed;
+ assert_all_indices_of_type_idx();
}
-indexed::indexed(const ex & i1, const ex & i2, const ex & i3, const ex & i4)
- : inherited(i1,i2,i3,i4)
+indexed::indexed(symmetry_type symm, const exprseq & es) : inherited(es), symmetry(symm)
{
- debugmsg("indexed constructor from ex,ex,ex,ex",LOGLEVEL_CONSTRUCT);
- tinfo_key=TINFO_indexed;
- GINAC_ASSERT(all_of_type_idx());
+ debugmsg("indexed constructor from symmetry,exprseq", LOGLEVEL_CONSTRUCT);
+ tinfo_key = TINFO_indexed;
+ assert_all_indices_of_type_idx();
}
-indexed::indexed(const exvector & iv) : inherited(iv)
+indexed::indexed(symmetry_type symm, const exvector & v, bool discardable) : inherited(v, discardable), symmetry(symm)
{
- debugmsg("indexed constructor from exvector",LOGLEVEL_CONSTRUCT);
- tinfo_key=TINFO_indexed;
- GINAC_ASSERT(all_of_type_idx());
+ debugmsg("indexed constructor from symmetry,exvector", LOGLEVEL_CONSTRUCT);
+ tinfo_key = TINFO_indexed;
+ assert_all_indices_of_type_idx();
}
-indexed::indexed(exvector * ivp) : inherited(ivp)
+indexed::indexed(symmetry_type symm, exvector * vp) : inherited(vp), symmetry(symm)
{
- debugmsg("indexed constructor from exvector *",LOGLEVEL_CONSTRUCT);
- tinfo_key=TINFO_indexed;
- GINAC_ASSERT(all_of_type_idx());
+ debugmsg("indexed constructor from symmetry,exvector *", LOGLEVEL_CONSTRUCT);
+ tinfo_key = TINFO_indexed;
+ assert_all_indices_of_type_idx();
}
//////////
/** Construct object from archive_node. */
indexed::indexed(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
{
- debugmsg("indexed constructor from archive_node", LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_indexed;
+ debugmsg("indexed constructor from archive_node", LOGLEVEL_CONSTRUCT);
+ unsigned int symm;
+ if (!(n.find_unsigned("symmetry", symm)))
+ throw (std::runtime_error("unknown indexed symmetry type in archive"));
}
/** Unarchive the object. */
ex indexed::unarchive(const archive_node &n, const lst &sym_lst)
{
- return (new indexed(n, sym_lst))->setflag(status_flags::dynallocated);
+ return (new indexed(n, sym_lst))->setflag(status_flags::dynallocated);
}
/** Archive the object. */
void indexed::archive(archive_node &n) const
{
- inherited::archive(n);
+ inherited::archive(n);
+ n.add_unsigned("symmetry", symmetry);
}
//////////
// functions overriding virtual functions from bases classes
//////////
-// public
-
-basic * indexed::duplicate() const
+void indexed::printraw(std::ostream & os) const
{
- debugmsg("indexed duplicate",LOGLEVEL_DUPLICATE);
- return new indexed(*this);
-}
+ debugmsg("indexed printraw", LOGLEVEL_PRINT);
+ GINAC_ASSERT(seq.size() > 0);
-void indexed::printraw(ostream & os) const
-{
- debugmsg("indexed printraw",LOGLEVEL_PRINT);
- os << "indexed(indices=";
- printrawindices(os);
- os << ",hash=" << hashvalue << ",flags=" << flags << ")";
+ os << class_name() << "(";
+ seq[0].printraw(os);
+ os << ",indices=";
+ printrawindices(os);
+ os << ",hash=" << hashvalue << ",flags=" << flags << ")";
}
-void indexed::printtree(ostream & os, unsigned indent) const
+void indexed::printtree(std::ostream & os, unsigned indent) const
{
- debugmsg("indexed printtree",LOGLEVEL_PRINT);
- os << string(indent,' ') << "indexed: " << seq.size() << " indices";
- os << ",hash=" << hashvalue << ",flags=" << flags << endl;
- printtreeindices(os,indent);
-}
+ debugmsg("indexed printtree", LOGLEVEL_PRINT);
+ GINAC_ASSERT(seq.size() > 0);
-void indexed::print(ostream & os, unsigned upper_precedence) const
-{
- debugmsg("indexed print",LOGLEVEL_PRINT);
- os << "UNNAMEDINDEX";
- printindices(os);
+ os << std::string(indent, ' ') << class_name() << ", " << seq.size()-1 << " indices";
+ os << ",hash=" << hashvalue << ",flags=" << flags << std::endl;
+ printtreeindices(os, indent);
}
-void indexed::printcsrc(ostream & os, unsigned type,
- unsigned upper_precedence) const
+void indexed::print(std::ostream & os, unsigned upper_precedence) const
{
- debugmsg("indexed print csrc",LOGLEVEL_PRINT);
- print(os,upper_precedence);
+ debugmsg("indexed print", LOGLEVEL_PRINT);
+ GINAC_ASSERT(seq.size() > 0);
+
+ const ex & base = seq[0];
+ bool need_parens = is_ex_exactly_of_type(base, add) || is_ex_exactly_of_type(base, mul)
+ || is_ex_exactly_of_type(base, ncmul) || is_ex_exactly_of_type(base, power);
+ if (need_parens)
+ os << "(";
+ os << base;
+ if (need_parens)
+ os << ")";
+ printindices(os);
}
bool indexed::info(unsigned inf) const
{
- if (inf==info_flags::indexed) return true;
- if (inf==info_flags::has_indices) return seq.size()!=0;
- return inherited::info(inf);
+ if (inf == info_flags::indexed) return true;
+ if (inf == info_flags::has_indices) return seq.size() > 1;
+ return inherited::info(inf);
}
-exvector indexed::get_indices(void) const
+bool indexed::all_index_values_are(unsigned inf) const
{
- return seq;
+ // No indices? Then no property can be fulfilled
+ if (seq.size() < 2)
+ return false;
- /*
- idxvector filtered_indices;
- filtered_indices.reserve(indices.size());
- for (idxvector::const_iterator cit=indices.begin(); cit!=indices.end(); ++cit) {
- if ((*cit).get_type()==t) {
- filtered_indices.push_back(*cit);
- }
- }
- return filtered_indices;
- */
+ // Check all indices
+ exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
+ while (it != itend) {
+ GINAC_ASSERT(is_ex_of_type(*it, idx));
+ if (!ex_to_idx(*it).get_value().info(inf))
+ return false;
+ it++;
+ }
+ return true;
}
-// protected
-
int indexed::compare_same_type(const basic & other) const
{
- GINAC_ASSERT(is_of_type(other,indexed));
- return inherited::compare_same_type(other);
+ GINAC_ASSERT(is_of_type(other, indexed));
+ return inherited::compare_same_type(other);
}
-bool indexed::is_equal_same_type(const basic & other) const
-{
- GINAC_ASSERT(is_of_type(other,indexed));
- return inherited::is_equal_same_type(other);
-}
+// The main difference between sort_index_vector() and canonicalize_indices()
+// is that the latter takes the symmetry of the object into account. Once we
+// implement mixed symmetries, canonicalize_indices() will only be able to
+// reorder index pairs with known symmetry properties, while sort_index_vector()
+// always sorts the whole vector.
-unsigned indexed::return_type(void) const
-{
- return return_types::noncommutative;
-}
-
-unsigned indexed::return_type_tinfo(void) const
-{
- return tinfo_key;
+/** Bring a vector of indices into a canonic order (don't care about the
+ * symmetry of the objects carrying the indices). Dummy indices will lie
+ * next to each other after the sorting.
+ *
+ * @param v Index vector to be sorted */
+static void sort_index_vector(exvector &v)
+{
+ // Nothing to sort if less than 2 elements
+ if (v.size() < 2)
+ return;
+
+ // Simple bubble sort algorithm should be sufficient for the small
+ // number of indices expected
+ exvector::iterator it1 = v.begin(), itend = v.end(), next_to_last_idx = itend - 1;
+ while (it1 != next_to_last_idx) {
+ exvector::iterator it2 = it1 + 1;
+ while (it2 != itend) {
+ if (it1->compare(*it2) > 0)
+ it1->swap(*it2);
+ it2++;
+ }
+ it1++;
+ }
+}
+
+/** Bring a vector of indices into a canonic order. This operation only makes
+ * sense if the object carrying these indices is either symmetric or totally
+ * antisymmetric with respect to the indices.
+ *
+ * @param itbegin Start of index vector
+ * @param itend End of index vector
+ * @param antisymm Whether the object is antisymmetric
+ * @return the sign introduced by the reordering of the indices if the object
+ * is antisymmetric (or 0 if two equal indices are encountered). For
+ * symmetric objects, this is always +1. If the index vector was
+ * already in a canonic order this function returns INT_MAX. */
+static int canonicalize_indices(exvector::iterator itbegin, exvector::iterator itend, bool antisymm)
+{
+ bool something_changed = false;
+ int sig = 1;
+
+ // Simple bubble sort algorithm should be sufficient for the small
+ // number of indices expected
+ exvector::iterator it1 = itbegin, next_to_last_idx = itend - 1;
+ while (it1 != next_to_last_idx) {
+ exvector::iterator it2 = it1 + 1;
+ while (it2 != itend) {
+ int cmpval = it1->compare(*it2);
+ if (cmpval == 1) {
+ it1->swap(*it2);
+ something_changed = true;
+ if (antisymm)
+ sig = -sig;
+ } else if (cmpval == 0 && antisymm) {
+ something_changed = true;
+ sig = 0;
+ }
+ it2++;
+ }
+ it1++;
+ }
+
+ return something_changed ? sig : INT_MAX;
+}
+
+ex indexed::eval(int level) const
+{
+ // First evaluate children, then we will end up here again
+ if (level > 1)
+ return indexed(symmetry, evalchildren(level));
+
+ // Canonicalize indices according to the symmetry properties
+ if (seq.size() > 2 && (symmetry != unknown && symmetry != mixed)) {
+ exvector v = seq;
+ int sig = canonicalize_indices(v.begin() + 1, v.end(), symmetry == antisymmetric);
+ if (sig != INT_MAX) {
+ // Something has changed while sorting indices, more evaluations later
+ if (sig == 0)
+ return _ex0();
+ return ex(sig) * thisexprseq(v);
+ }
+ }
+
+ // Let the class of the base object perform additional evaluations
+ return op(0).bp->eval_indexed(*this);
}
ex indexed::thisexprseq(const exvector & v) const
{
- return indexed(v);
+ return indexed(symmetry, v);
}
ex indexed::thisexprseq(exvector * vp) const
{
- return indexed(vp);
+ return indexed(symmetry, vp);
+}
+
+ex indexed::expand(unsigned options) const
+{
+ GINAC_ASSERT(seq.size() > 0);
+
+ if ((options & expand_options::expand_indexed) && is_ex_exactly_of_type(seq[0], add)) {
+
+ // expand_indexed expands (a+b).i -> a.i + b.i
+ const ex & base = seq[0];
+ ex sum = _ex0();
+ for (unsigned i=0; i<base.nops(); i++) {
+ exvector s = seq;
+ s[0] = base.op(i);
+ sum += thisexprseq(s).expand();
+ }
+ return sum;
+
+ } else
+ return inherited::expand(options);
}
//////////
// non-virtual functions in this class
//////////
-// protected
-
-void indexed::printrawindices(ostream & os) const
+void indexed::printrawindices(std::ostream & os) const
{
- if (seq.size()!=0) {
- for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- (*cit).printraw(os);
- os << ",";
- }
- }
+ if (seq.size() > 1) {
+ exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
+ while (it != itend) {
+ it->printraw(os);
+ it++;
+ if (it != itend)
+ os << ",";
+ }
+ }
}
-void indexed::printtreeindices(ostream & os, unsigned indent) const
+void indexed::printtreeindices(std::ostream & os, unsigned indent) const
{
- if (seq.size()!=0) {
- for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- os << string(indent+delta_indent,' ');
- (*cit).printraw(os);
- os << endl;
- }
- }
+ if (seq.size() > 1) {
+ exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
+ while (it != itend) {
+ os << std::string(indent + delta_indent, ' ');
+ it->printraw(os);
+ os << std::endl;
+ it++;
+ }
+ }
}
-void indexed::printindices(ostream & os) const
+void indexed::printindices(std::ostream & os) const
{
- if (seq.size()!=0) {
- if (seq.size()>1) {
- os << "{";
- }
- exvector::const_iterator last=seq.end()-1;
- exvector::const_iterator cit=seq.begin();
- for (; cit!=last; ++cit) {
- (*cit).print(os);
- os << ",";
- }
- (*cit).print(os);
- if (seq.size()>1) {
- os << "}";
- }
- }
+ if (seq.size() > 1) {
+ exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
+ while (it != itend) {
+ it->print(os);
+ it++;
+ }
+ }
}
-bool indexed::all_of_type_idx(void) const
+/** Check whether all indices are of class idx. This function is used
+ * internally to make sure that all constructed indexed objects really
+ * carry indices and not some other classes. */
+void indexed::assert_all_indices_of_type_idx(void) const
{
- // used only inside of ASSERTs
- for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- if (!is_ex_of_type(*cit,idx)) return false;
- }
- return true;
+ GINAC_ASSERT(seq.size() > 0);
+ exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
+ while (it != itend) {
+ if (!is_ex_of_type(*it, idx))
+ throw(std::invalid_argument("indices of indexed object must be of type idx"));
+ it++;
+ }
}
//////////
-// static member variables
+// global functions
//////////
-// none
+/** Given a vector of indices, split them into two vectors, one containing
+ * the free indices, the other containing the dummy indices. */
+static void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy)
+{
+ out_free.clear();
+ out_dummy.clear();
+
+ // No indices? Then do nothing
+ if (it == itend)
+ return;
+
+ // Only one index? Then it is a free one if it's not numeric
+ if (itend - it == 1) {
+ if (ex_to_idx(*it).is_symbolic())
+ out_free.push_back(*it);
+ return;
+ }
+
+ // Sort index vector. This will cause dummy indices come to lie next
+ // to each other (because the sort order is defined to guarantee this).
+ exvector v(it, itend);
+ sort_index_vector(v);
+
+ // Find dummy pairs and free indices
+ it = v.begin(); itend = v.end();
+ exvector::const_iterator last = it++;
+ while (it != itend) {
+ if (is_dummy_pair(*it, *last)) {
+ out_dummy.push_back(*last);
+ it++;
+ if (it == itend)
+ return;
+ } else {
+ if (!it->is_equal(*last) && ex_to_idx(*last).is_symbolic())
+ out_free.push_back(*last);
+ }
+ last = it++;
+ }
+ if (ex_to_idx(*last).is_symbolic())
+ out_free.push_back(*last);
+}
+
+/** Check whether two sorted index vectors are consistent (i.e. equal). */
+static bool indices_consistent(const exvector & v1, const exvector & v2)
+{
+ // Number of indices must be the same
+ if (v1.size() != v2.size())
+ return false;
+
+ // And also the indices themselves
+ exvector::const_iterator ait = v1.begin(), aitend = v1.end(),
+ bit = v2.begin(), bitend = v2.end();
+ while (ait != aitend) {
+ if (!ait->is_equal(*bit))
+ return false;
+ ait++; bit++;
+ }
+ return true;
+}
+
+exvector indexed::get_dummy_indices(void) const
+{
+ exvector free_indices, dummy_indices;
+ find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
+ return dummy_indices;
+}
+
+exvector indexed::get_free_indices(void) const
+{
+ exvector free_indices, dummy_indices;
+ find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
+ return free_indices;
+}
+
+exvector add::get_free_indices(void) const
+{
+ exvector free_indices;
+ for (unsigned i=0; i<nops(); i++) {
+ if (i == 0)
+ free_indices = op(i).get_free_indices();
+ else {
+ exvector free_indices_of_term = op(i).get_free_indices();
+ if (!indices_consistent(free_indices, free_indices_of_term))
+ throw (std::runtime_error("add::get_free_indices: inconsistent indices in sum"));
+ }
+ }
+ return free_indices;
+}
+
+exvector mul::get_free_indices(void) const
+{
+ // Concatenate free indices of all factors
+ exvector un;
+ for (unsigned i=0; i<nops(); i++) {
+ exvector free_indices_of_factor = op(i).get_free_indices();
+ un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
+ }
+
+ // And remove the dummy indices
+ exvector free_indices, dummy_indices;
+ find_free_and_dummy(un.begin(), un.end(), free_indices, dummy_indices);
+ return free_indices;
+}
+
+exvector ncmul::get_free_indices(void) const
+{
+ // Concatenate free indices of all factors
+ exvector un;
+ for (unsigned i=0; i<nops(); i++) {
+ exvector free_indices_of_factor = op(i).get_free_indices();
+ un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
+ }
+
+ // And remove the dummy indices
+ exvector free_indices, dummy_indices;
+ find_free_and_dummy(un.begin(), un.end(), free_indices, dummy_indices);
+ return free_indices;
+}
+
+exvector power::get_free_indices(void) const
+{
+ // Return free indices of basis
+ return basis.get_free_indices();
+}
+
+/** Simplify product of indexed expressions (commutative, noncommutative and
+ * simple squares), return list of free indices. */
+ex simplify_indexed_product(const ex & e, exvector & free_indices, const scalar_products & sp)
+{
+ // Remember whether the product was commutative or noncommutative
+ // (because we chop it into factors and need to reassemble later)
+ bool non_commutative = is_ex_exactly_of_type(e, ncmul);
+
+ // Collect factors in an exvector, store squares twice
+ exvector v;
+ v.reserve(e.nops() * 2);
+
+ if (is_ex_exactly_of_type(e, power)) {
+ // We only get called for simple squares, split a^2 -> a*a
+ GINAC_ASSERT(e.op(1).is_equal(_ex2()));
+ v.push_back(e.op(0));
+ v.push_back(e.op(0));
+ } else {
+ for (int i=0; i<e.nops(); i++) {
+ ex f = e.op(i);
+ if (is_ex_exactly_of_type(f, power) && f.op(1).is_equal(_ex2())) {
+ v.push_back(f.op(0));
+ v.push_back(f.op(0));
+ } else if (is_ex_exactly_of_type(f, ncmul)) {
+ // Noncommutative factor found, split it as well
+ non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later
+ for (int j=0; j<f.nops(); i++)
+ v.push_back(f.op(j));
+ } else
+ v.push_back(f);
+ }
+ }
+
+ // Perform contractions
+ bool something_changed = false;
+ GINAC_ASSERT(v.size() > 1);
+ exvector::iterator it1, itend = v.end(), next_to_last = itend - 1;
+ for (it1 = v.begin(); it1 != next_to_last; it1++) {
+
+try_again:
+ if (!is_ex_of_type(*it1, indexed))
+ continue;
+
+ // Indexed factor found, look for contraction candidates
+ exvector::iterator it2;
+ for (it2 = it1 + 1; it2 != itend; it2++) {
+
+ if (!is_ex_of_type(*it2, indexed))
+ continue;
+
+ // Check whether the two factors share dummy indices
+ exvector un(ex_to_indexed(*it1).seq.begin() + 1, ex_to_indexed(*it1).seq.end());
+ un.insert(un.end(), ex_to_indexed(*it2).seq.begin() + 1, ex_to_indexed(*it2).seq.end());
+ exvector free, dummy;
+ find_free_and_dummy(un.begin(), un.end(), free, dummy);
+ if (dummy.size() == 0)
+ continue;
+
+ // At least one dummy index, is it a defined scalar product?
+ if (free.size() == 0) {
+ if (sp.is_defined(*it1, *it2)) {
+ *it1 = sp.evaluate(*it1, *it2);
+ *it2 = _ex1();
+ something_changed = true;
+ goto try_again;
+ }
+ }
+
+ // Try to contract the first one with the second one
+ bool contracted = it1->op(0).bp->contract_with(it1, it2, v);
+ if (!contracted) {
+
+ // That didn't work; maybe the second object knows how to
+ // contract itself with the first one
+ contracted = it2->op(0).bp->contract_with(it2, it1, v);
+ }
+ if (contracted) {
+ something_changed = true;
+
+ // Both objects may have new indices now or they might
+ // even not be indexed objects any more, so we have to
+ // start over
+ goto try_again;
+ }
+ }
+ }
+
+ // Find free indices (concatenate them all and call find_free_and_dummy())
+ exvector un, dummy_indices;
+ it1 = v.begin(); itend = v.end();
+ while (it1 != itend) {
+ if (is_ex_of_type(*it1, indexed)) {
+ const indexed & o = ex_to_indexed(*it1);
+ un.insert(un.end(), o.seq.begin() + 1, o.seq.end());
+ }
+ it1++;
+ }
+ find_free_and_dummy(un.begin(), un.end(), free_indices, dummy_indices);
+
+ if (something_changed) {
+ if (non_commutative)
+ return ncmul(v);
+ else
+ return mul(v);
+ } else
+ return e;
+}
+
+/** Simplify indexed expression, return list of free indices. */
+ex simplify_indexed(const ex & e, exvector & free_indices, const scalar_products & sp)
+{
+ // Expand the expression
+ ex e_expanded = e.expand();
+
+ // Simplification of single indexed object: just find the free indices
+ if (is_ex_of_type(e_expanded, indexed)) {
+ const indexed &i = ex_to_indexed(e_expanded);
+ exvector dummy_indices;
+ find_free_and_dummy(i.seq.begin() + 1, i.seq.end(), free_indices, dummy_indices);
+ return e_expanded;
+ }
+
+ // Simplification of sum = sum of simplifications, check consistency of
+ // free indices in each term
+ if (is_ex_exactly_of_type(e_expanded, add)) {
+ ex sum = _ex0();
+
+ for (unsigned i=0; i<e_expanded.nops(); i++) {
+ exvector free_indices_of_term;
+ sum += simplify_indexed(e_expanded.op(i), free_indices_of_term, sp);
+ if (i == 0)
+ free_indices = free_indices_of_term;
+ else if (!indices_consistent(free_indices, free_indices_of_term))
+ throw (std::runtime_error("simplify_indexed: inconsistent indices in sum"));
+ }
+
+ return sum;
+ }
+
+ // Simplification of products
+ if (is_ex_exactly_of_type(e_expanded, mul)
+ || is_ex_exactly_of_type(e_expanded, ncmul)
+ || (is_ex_exactly_of_type(e_expanded, power) && is_ex_of_type(e_expanded.op(0), indexed) && e_expanded.op(1).is_equal(_ex2())))
+ return simplify_indexed_product(e_expanded, free_indices, sp);
+
+ // Cannot do anything
+ free_indices.clear();
+ return e_expanded;
+}
+
+ex simplify_indexed(const ex & e)
+{
+ exvector free_indices;
+ scalar_products sp;
+ return simplify_indexed(e, free_indices, sp);
+}
+
+ex simplify_indexed(const ex & e, const scalar_products & sp)
+{
+ exvector free_indices;
+ return simplify_indexed(e, free_indices, sp);
+}
//////////
-// global constants
+// helper classes
//////////
-const indexed some_indexed;
-const type_info & typeid_indexed=typeid(some_indexed);
+void scalar_products::add(const ex & v1, const ex & v2, const ex & sp)
+{
+ spm[make_key(v1, v2)] = sp;
+}
+
+void scalar_products::clear(void)
+{
+ spm.clear();
+}
+
+/** Check whether scalar product pair is defined. */
+bool scalar_products::is_defined(const ex & v1, const ex & v2) const
+{
+ return spm.find(make_key(v1, v2)) != spm.end();
+}
+
+/** Return value of defined scalar product pair. */
+ex scalar_products::evaluate(const ex & v1, const ex & v2) const
+{
+ return spm.find(make_key(v1, v2))->second;
+}
+
+void scalar_products::debugprint(void) const
+{
+ std::cerr << "map size=" << spm.size() << std::endl;
+ for (spmap::const_iterator cit=spm.begin(); cit!=spm.end(); ++cit) {
+ const spmapkey & k = cit->first;
+ std::cerr << "item key=(" << k.first << "," << k.second;
+ std::cerr << "), value=" << cit->second << std::endl;
+ }
+}
+
+/** Make key from object pair. */
+spmapkey scalar_products::make_key(const ex & v1, const ex & v2)
+{
+ // If indexed, extract base objects
+ ex s1 = is_ex_of_type(v1, indexed) ? v1.op(0) : v1;
+ ex s2 = is_ex_of_type(v2, indexed) ? v2.op(0) : v2;
+
+ // Enforce canonical order in pair
+ if (s1.compare(s2) > 0)
+ return spmapkey(s2, s1);
+ else
+ return spmapkey(s1, s2);
+}
-#ifndef NO_NAMESPACE_GINAC
} // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC
git://www.ginac.de / ginac.git / blobdiff