* Implementation of GiNaC's indexed expressions. */
/*
- * GiNaC Copyright (C) 1999-2004 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2005 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
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#include <iostream>
#include "operators.h"
#include "lst.h"
#include "archive.h"
+#include "symbol.h"
#include "utils.h"
+#include "integral.h"
+#include "matrix.h"
namespace GiNaC {
// default constructor
//////////
-indexed::indexed() : symtree(sy_none())
+indexed::indexed() : symtree(not_symmetric())
{
tinfo_key = TINFO_indexed;
}
// other constructors
//////////
-indexed::indexed(const ex & b) : inherited(b), symtree(sy_none())
+indexed::indexed(const ex & b) : inherited(b), symtree(not_symmetric())
{
tinfo_key = TINFO_indexed;
validate();
}
-indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symtree(sy_none())
+indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symtree(not_symmetric())
{
tinfo_key = TINFO_indexed;
validate();
}
-indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(sy_none())
+indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(not_symmetric())
{
tinfo_key = TINFO_indexed;
validate();
}
-indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(sy_none())
+indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(not_symmetric())
{
tinfo_key = TINFO_indexed;
validate();
}
-indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symtree(sy_none())
+indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symtree(not_symmetric())
{
tinfo_key = TINFO_indexed;
validate();
validate();
}
-indexed::indexed(const ex & b, const exvector & v) : inherited(b), symtree(sy_none())
+indexed::indexed(const ex & b, const exvector & v) : inherited(b), symtree(not_symmetric())
{
seq.insert(seq.end(), v.begin(), v.end());
tinfo_key = TINFO_indexed;
symtree = sy_anti();
break;
default:
- symtree = sy_none();
+ symtree = not_symmetric();
break;
}
const_cast<symmetry &>(ex_to<symmetry>(symtree)).validate(seq.size() - 1);
return f * thiscontainer(v);
}
+ if(this->tinfo()==TINFO_indexed && seq.size()==1)
+ return base;
+
// Canonicalize indices according to the symmetry properties
if (seq.size() > 2) {
exvector v = seq;
return indexed(ex_to<symmetry>(symtree), vp);
}
+unsigned indexed::return_type() const
+{
+ if(is_a<matrix>(op(0)))
+ return return_types::commutative;
+ else
+ return op(0).return_type();
+}
+
ex indexed::expand(unsigned options) const
{
GINAC_ASSERT(seq.size() > 0);
return free_indices;
}
+struct is_summation_idx : public std::unary_function<ex, bool> {
+ bool operator()(const ex & e)
+ {
+ return is_dummy_pair(e, e);
+ }
+};
+
exvector power::get_free_indices() const
{
- // Return free indices of basis
- return basis.get_free_indices();
+ // Get free indices of basis
+ exvector basis_indices = basis.get_free_indices();
+
+ if (exponent.info(info_flags::even)) {
+ // If the exponent is an even number, then any "free" index that
+ // forms a dummy pair with itself is actually a summation index
+ exvector really_free;
+ std::remove_copy_if(basis_indices.begin(), basis_indices.end(),
+ std::back_inserter(really_free), is_summation_idx());
+ return really_free;
+ } else
+ return basis_indices;
+}
+
+exvector integral::get_free_indices() const
+{
+ if (a.get_free_indices().size() || b.get_free_indices().size())
+ throw (std::runtime_error("integral::get_free_indices: boundary values should not have free indices"));
+ return f.get_free_indices();
+}
+
+template<class T> size_t number_of_type(const exvector&v)
+{
+ size_t number = 0;
+ for(exvector::const_iterator i=v.begin(); i!=v.end(); ++i)
+ if(is_exactly_a<T>(*i))
+ ++number;
+ return number;
}
/** Rename dummy indices in an expression.
* @param global_dummy_indices The set of dummy indices that have appeared
* before and which we would like to use in "e", too. This gets updated
* by the function */
-static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, exvector & local_dummy_indices)
+template<class T> static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, exvector & local_dummy_indices)
{
- size_t global_size = global_dummy_indices.size(),
- local_size = local_dummy_indices.size();
+ size_t global_size = number_of_type<T>(global_dummy_indices),
+ local_size = number_of_type<T>(local_dummy_indices);
// Any local dummy indices at all?
if (local_size == 0)
int remaining = local_size - global_size;
exvector::const_iterator it = local_dummy_indices.begin(), itend = local_dummy_indices.end();
while (it != itend && remaining > 0) {
- if (find_if(global_dummy_indices.begin(), global_dummy_indices.end(), bind2nd(op0_is_equal(), *it)) == global_dummy_indices.end()) {
+ if (is_exactly_a<T>(*it) && find_if(global_dummy_indices.begin(), global_dummy_indices.end(), bind2nd(idx_is_equal_ignore_dim(), *it)) == global_dummy_indices.end()) {
global_dummy_indices.push_back(*it);
global_size++;
remaining--;
exvector local_syms, global_syms;
local_syms.reserve(local_size);
global_syms.reserve(local_size);
- for (size_t i=0; i<local_size; i++)
- local_syms.push_back(local_dummy_indices[i].op(0));
+ for (size_t i=0; local_syms.size()!=local_size; i++)
+ if(is_exactly_a<T>(local_dummy_indices[i]))
+ local_syms.push_back(local_dummy_indices[i].op(0));
shaker_sort(local_syms.begin(), local_syms.end(), ex_is_less(), ex_swap());
- for (size_t i=0; i<local_size; i++) // don't use more global symbols than necessary
- global_syms.push_back(global_dummy_indices[i].op(0));
+ for (size_t i=0; global_syms.size()!=local_size; i++) // don't use more global symbols than necessary
+ if(is_exactly_a<T>(global_dummy_indices[i]))
+ global_syms.push_back(global_dummy_indices[i].op(0));
shaker_sort(global_syms.begin(), global_syms.end(), ex_is_less(), ex_swap());
// Remove common 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, exvector & dummy_indices, const scalar_products & sp)
+/* An auxiliary function used by simplify_indexed() and expand_dummy_sum()
+ * It returns an exvector of factors from the supplied product */
+static void product_to_exvector(const ex & e, exvector & v, bool & non_commutative)
{
// Remember whether the product was commutative or noncommutative
// (because we chop it into factors and need to reassemble later)
- bool non_commutative = is_exactly_a<ncmul>(e);
+ non_commutative = is_exactly_a<ncmul>(e);
// Collect factors in an exvector, store squares twice
- exvector v;
v.reserve(e.nops() * 2);
if (is_exactly_a<power>(e)) {
ex f = e.op(i);
if (is_exactly_a<power>(f) && f.op(1).is_equal(_ex2)) {
v.push_back(f.op(0));
- v.push_back(f.op(0));
+ v.push_back(f.op(0));
} else if (is_exactly_a<ncmul>(f)) {
// Noncommutative factor found, split it as well
non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later
v.push_back(f);
}
}
+}
+
+template<class T> ex idx_symmetrization(const ex& r,const exvector& local_dummy_indices)
+{ exvector dummy_syms;
+ dummy_syms.reserve(r.nops());
+ for (exvector::const_iterator it = local_dummy_indices.begin(); it != local_dummy_indices.end(); ++it)
+ if(is_exactly_a<T>(*it))
+ dummy_syms.push_back(it->op(0));
+ if(dummy_syms.size() < 2)
+ return r;
+ ex q=symmetrize(r, dummy_syms);
+ return q;
+}
+
+// Forward declaration needed in absence of friend injection, C.f. [namespace.memdef]:
+ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp);
+
+/** 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, exvector & dummy_indices, const scalar_products & sp)
+{
+ // Collect factors in an exvector
+ exvector v;
+
+ // Remember whether the product was commutative or noncommutative
+ // (because we chop it into factors and need to reassemble later)
+ bool non_commutative;
+ product_to_exvector(e, v, non_commutative);
// Perform contractions
bool something_changed = false;
bool contracted = false;
if (free.empty()) {
- // Find minimal dimension of all indices of both factors
- exvector::const_iterator dit = ex_to<indexed>(*it1).seq.begin() + 1, ditend = ex_to<indexed>(*it1).seq.end();
- ex dim = ex_to<idx>(*dit).get_dim();
- ++dit;
- for (; dit != ditend; ++dit) {
- dim = minimal_dim(dim, ex_to<idx>(*dit).get_dim());
- }
- dit = ex_to<indexed>(*it2).seq.begin() + 1;
- ditend = ex_to<indexed>(*it2).seq.end();
- for (; dit != ditend; ++dit) {
- dim = minimal_dim(dim, ex_to<idx>(*dit).get_dim());
- }
+ try {
+ // Find minimal dimension of all indices of both factors
+ exvector::const_iterator dit = ex_to<indexed>(*it1).seq.begin() + 1, ditend = ex_to<indexed>(*it1).seq.end();
+ ex dim = ex_to<idx>(*dit).get_dim();
+ ++dit;
+ for (; dit != ditend; ++dit) {
+ dim = minimal_dim(dim, ex_to<idx>(*dit).get_dim());
+ }
+ dit = ex_to<indexed>(*it2).seq.begin() + 1;
+ ditend = ex_to<indexed>(*it2).seq.end();
+ for (; dit != ditend; ++dit) {
+ dim = minimal_dim(dim, ex_to<idx>(*dit).get_dim());
+ }
- // User-defined scalar product?
- if (sp.is_defined(*it1, *it2, dim)) {
+ // User-defined scalar product?
+ if (sp.is_defined(*it1, *it2, dim)) {
- // Yes, substitute it
- *it1 = sp.evaluate(*it1, *it2, dim);
- *it2 = _ex1;
- goto contraction_done;
- }
+ // Yes, substitute it
+ *it1 = sp.evaluate(*it1, *it2, dim);
+ *it2 = _ex1;
+ goto contraction_done;
+ }
+ } catch (const std::runtime_error&) {}
}
// Try to contract the first one with the second one
// The result should be symmetric with respect to exchange of dummy
// indices, so if the symmetrization vanishes, the whole expression is
// zero. This detects things like eps.i.j.k * p.j * p.k = 0.
- if (local_dummy_indices.size() >= 2) {
- exvector dummy_syms;
- dummy_syms.reserve(local_dummy_indices.size());
- for (exvector::const_iterator it = local_dummy_indices.begin(); it != local_dummy_indices.end(); ++it)
- dummy_syms.push_back(it->op(0));
- if (symmetrize(r, dummy_syms).is_zero()) {
- free_indices.clear();
- return _ex0;
- }
+ ex q = idx_symmetrization<idx>(r, local_dummy_indices);
+ if (q.is_zero()) {
+ free_indices.clear();
+ return _ex0;
+ }
+ q = idx_symmetrization<varidx>(q, local_dummy_indices);
+ if (q.is_zero()) {
+ free_indices.clear();
+ return _ex0;
+ }
+ q = idx_symmetrization<spinidx>(q, local_dummy_indices);
+ if (q.is_zero()) {
+ free_indices.clear();
+ return _ex0;
}
// Dummy index renaming
- r = rename_dummy_indices(r, dummy_indices, local_dummy_indices);
+ r = rename_dummy_indices<idx>(r, dummy_indices, local_dummy_indices);
+ r = rename_dummy_indices<varidx>(r, dummy_indices, local_dummy_indices);
+ r = rename_dummy_indices<spinidx>(r, dummy_indices, local_dummy_indices);
// Product of indexed object with a scalar?
if (is_exactly_a<mul>(r) && r.nops() == 2
}
};
+bool hasindex(const ex &x, const ex &sym)
+{
+ if(is_a<idx>(x) && x.op(0)==sym)
+ return true;
+ else
+ for(size_t i=0; i<x.nops(); ++i)
+ if(hasindex(x.op(i), sym))
+ return true;
+ return false;
+}
+
/** Simplify indexed expression, return list of free indices. */
ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp)
{
}
// Rename the dummy indices
- return rename_dummy_indices(e_expanded, dummy_indices, local_dummy_indices);
+ e_expanded = rename_dummy_indices<idx>(e_expanded, dummy_indices, local_dummy_indices);
+ e_expanded = rename_dummy_indices<varidx>(e_expanded, dummy_indices, local_dummy_indices);
+ e_expanded = rename_dummy_indices<spinidx>(e_expanded, dummy_indices, local_dummy_indices);
+ return e_expanded;
}
// Simplification of sum = sum of simplifications, check consistency of
if (num_terms_orig < 2 || dummy_indices.size() < 2)
return sum;
- // Yes, construct vector of all dummy index symbols
- exvector dummy_syms;
- dummy_syms.reserve(dummy_indices.size());
- for (exvector::const_iterator it = dummy_indices.begin(); it != dummy_indices.end(); ++it)
- dummy_syms.push_back(it->op(0));
-
// Chop the sum into terms and symmetrize each one over the dummy
// indices
std::vector<terminfo> terms;
for (size_t i=0; i<sum.nops(); i++) {
const ex & term = sum.op(i);
- ex term_symm = symmetrize(term, dummy_syms);
+ exvector dummy_indices_of_term;
+ dummy_indices_of_term.reserve(dummy_indices.size());
+ for(exvector::iterator i=dummy_indices.begin(); i!=dummy_indices.end(); ++i)
+ if(hasindex(term,i->op(0)))
+ dummy_indices_of_term.push_back(*i);
+ ex term_symm = idx_symmetrization<idx>(term, dummy_indices_of_term);
+ term_symm = idx_symmetrization<varidx>(term_symm, dummy_indices_of_term);
+ term_symm = idx_symmetrization<spinidx>(term_symm, dummy_indices_of_term);
if (term_symm.is_zero())
continue;
terms.push_back(terminfo(term, term_symm));
* performs contraction of dummy indices where possible and checks whether
* the free indices in sums are consistent.
*
+ * @param options Simplification options (currently unused)
* @return simplified expression */
ex ex::simplify_indexed(unsigned options) const
{
* scalar products by known values if desired.
*
* @param sp Scalar products to be replaced automatically
+ * @param options Simplification options (currently unused)
* @return simplified expression */
ex ex::simplify_indexed(const scalar_products & sp, unsigned options) const
{
}
}
+/** Returns all dummy indices from the exvector */
+exvector get_all_dummy_indices(const ex & e)
+{
+ exvector p;
+ bool nc;
+ product_to_exvector(e, p, nc);
+ exvector::const_iterator ip = p.begin(), ipend = p.end();
+ exvector v, v1;
+ while (ip != ipend) {
+ if (is_a<indexed>(*ip)) {
+ v1 = ex_to<indexed>(*ip).get_dummy_indices();
+ v.insert(v.end(), v1.begin(), v1.end());
+ exvector::const_iterator ip1 = ip+1;
+ while (ip1 != ipend) {
+ if (is_a<indexed>(*ip1)) {
+ v1 = ex_to<indexed>(*ip).get_dummy_indices(ex_to<indexed>(*ip1));
+ v.insert(v.end(), v1.begin(), v1.end());
+ }
+ ++ip1;
+ }
+ }
+ ++ip;
+ }
+ return v;
+}
+
+lst rename_dummy_indices_uniquely(const exvector & va, const exvector & vb)
+{
+ exvector common_indices;
+ set_intersection(va.begin(), va.end(), vb.begin(), vb.end(), std::back_insert_iterator<exvector>(common_indices), ex_is_less());
+ if (common_indices.empty()) {
+ return lst(lst(), lst());
+ } else {
+ exvector new_indices, old_indices;
+ old_indices.reserve(2*common_indices.size());
+ new_indices.reserve(2*common_indices.size());
+ exvector::const_iterator ip = common_indices.begin(), ipend = common_indices.end();
+ while (ip != ipend) {
+ ex newsym=(new symbol)->setflag(status_flags::dynallocated);
+ ex newidx;
+ if(is_exactly_a<spinidx>(*ip))
+ newidx = (new spinidx(newsym, ex_to<spinidx>(*ip).get_dim(),
+ ex_to<spinidx>(*ip).is_covariant(),
+ ex_to<spinidx>(*ip).is_dotted()))
+ -> setflag(status_flags::dynallocated);
+ else if (is_exactly_a<varidx>(*ip))
+ newidx = (new varidx(newsym, ex_to<varidx>(*ip).get_dim(),
+ ex_to<varidx>(*ip).is_covariant()))
+ -> setflag(status_flags::dynallocated);
+ else
+ newidx = (new idx(newsym, ex_to<idx>(*ip).get_dim()))
+ -> setflag(status_flags::dynallocated);
+ old_indices.push_back(*ip);
+ new_indices.push_back(newidx);
+ if(is_a<varidx>(*ip)) {
+ old_indices.push_back(ex_to<varidx>(*ip).toggle_variance());
+ new_indices.push_back(ex_to<varidx>(newidx).toggle_variance());
+ }
+ ++ip;
+ }
+ return lst(lst(old_indices.begin(), old_indices.end()), lst(new_indices.begin(), new_indices.end()));
+ }
+}
+
+ex rename_dummy_indices_uniquely(const exvector & va, const exvector & vb, const ex & b)
+{
+ lst indices_subs = rename_dummy_indices_uniquely(va, vb);
+ return (indices_subs.op(0).nops()>0 ? b.subs((lst)indices_subs.op(0), (lst)indices_subs.op(1), subs_options::no_pattern) : b);
+}
+
+ex rename_dummy_indices_uniquely(const ex & a, const ex & b)
+{
+ exvector va = get_all_dummy_indices(a);
+ if (va.size() > 0) {
+ exvector vb = get_all_dummy_indices(b);
+ if (vb.size() > 0) {
+ sort(va.begin(), va.end(), ex_is_less());
+ sort(vb.begin(), vb.end(), ex_is_less());
+ lst indices_subs = rename_dummy_indices_uniquely(va, vb);
+ if (indices_subs.op(0).nops() > 0)
+ return b.subs((lst)indices_subs.op(0), (lst)indices_subs.op(1), subs_options::no_pattern);
+ }
+ }
+ return b;
+}
+
+ex rename_dummy_indices_uniquely(exvector & va, const ex & b, bool modify_va)
+{
+ if (va.size() > 0) {
+ exvector vb = get_all_dummy_indices(b);
+ if (vb.size() > 0) {
+ sort(vb.begin(), vb.end(), ex_is_less());
+ lst indices_subs = rename_dummy_indices_uniquely(va, vb);
+ if (indices_subs.op(0).nops() > 0) {
+ if (modify_va) {
+ for (lst::const_iterator i = ex_to<lst>(indices_subs.op(1)).begin(); i != ex_to<lst>(indices_subs.op(1)).end(); ++i)
+ va.push_back(*i);
+ exvector uncommon_indices;
+ set_difference(vb.begin(), vb.end(), indices_subs.op(0).begin(), indices_subs.op(0).end(), std::back_insert_iterator<exvector>(uncommon_indices), ex_is_less());
+ exvector::const_iterator ip = uncommon_indices.begin(), ipend = uncommon_indices.end();
+ while (ip != ipend) {
+ va.push_back(*ip);
+ ++ip;
+ }
+ sort(va.begin(), va.end(), ex_is_less());
+ }
+ return b.subs((lst)indices_subs.op(0), (lst)indices_subs.op(1), subs_options::no_pattern);
+ }
+ }
+ }
+ return b;
+}
+
+ex expand_dummy_sum(const ex & e, bool subs_idx)
+{
+ ex e_expanded = e.expand();
+ pointer_to_map_function_1arg<bool> fcn(expand_dummy_sum, subs_idx);
+ if (is_a<add>(e_expanded) || is_a<lst>(e_expanded) || is_a<matrix>(e_expanded)) {
+ return e_expanded.map(fcn);
+ } else if (is_a<ncmul>(e_expanded) || is_a<mul>(e_expanded) || is_a<power>(e_expanded)) {
+ exvector v = get_all_dummy_indices(e_expanded);
+ exvector::const_iterator it = v.begin(), itend = v.end();
+ while (it != itend) {
+ varidx nu = ex_to<varidx>(*it);
+ if (nu.is_dim_numeric()) {
+ ex en = 0;
+ for (int i=0; i < ex_to<numeric>(nu.get_dim()).to_int(); i++) {
+ if (is_a<varidx>(nu) && !subs_idx) {
+ en += e_expanded.subs(lst(nu == varidx(i, nu.get_dim(), true), nu.toggle_variance() == varidx(i, nu.get_dim())));
+ } else {
+ en += e_expanded.subs(lst(nu == idx(i, nu.get_dim()), nu.toggle_variance() == idx(i, nu.get_dim())));
+ }
+ }
+ return expand_dummy_sum(en, subs_idx);
+ }
+ ++it;
+ }
+ return e;
+ } else if (is_a<indexed>(e_expanded)) {
+ exvector v = ex_to<indexed>(e_expanded).get_dummy_indices();
+ exvector::const_iterator it = v.begin(), itend = v.end();
+ while (it != itend) {
+ varidx nu = ex_to<varidx>(*it);
+ if (nu.is_dim_numeric()) {
+ ex en = 0;
+ for (int i=0; i < ex_to<numeric>(nu.get_dim()).to_int(); i++) {
+ if (is_a<varidx>(nu) && !subs_idx) {
+ en += e_expanded.subs(lst(nu == varidx(i, nu.get_dim(), true), nu.toggle_variance() == varidx(i, nu.get_dim())));
+ } else {
+ en += e_expanded.subs(lst(nu == idx(i, nu.get_dim()), nu.toggle_variance() == idx(i, nu.get_dim())));
+ }
+ }
+ return expand_dummy_sum(en, subs_idx);
+ }
+ ++it;
+ }
+ return e;
+ } else {
+ return e;
+ }
+}
+
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff