* Implementation of GiNaC's indexed expressions. */
/*
- * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2002 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 <iostream>
#include <stdexcept>
-#include <algorithm>
#include "indexed.h"
#include "idx.h"
#include "mul.h"
#include "ncmul.h"
#include "power.h"
+#include "relational.h"
#include "symmetry.h"
#include "lst.h"
#include "print.h"
#include "archive.h"
#include "utils.h"
-#include "debugmsg.h"
namespace GiNaC {
GINAC_IMPLEMENT_REGISTERED_CLASS(indexed, exprseq)
//////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default ctor, dtor, copy ctor, assignment operator and helpers
//////////
indexed::indexed() : symtree(sy_none())
{
- debugmsg("indexed default constructor", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
}
indexed::indexed(const ex & b) : inherited(b), symtree(sy_none())
{
- debugmsg("indexed constructor from ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
validate();
}
indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symtree(sy_none())
{
- debugmsg("indexed constructor from ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
validate();
}
indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(sy_none())
{
- debugmsg("indexed constructor from ex,ex,ex", LOGLEVEL_CONSTRUCT);
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())
{
- debugmsg("indexed constructor from ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
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())
{
- debugmsg("indexed constructor from ex,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
validate();
}
indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(symm)
{
- debugmsg("indexed constructor from ex,symmetry,ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
validate();
}
indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(symm)
{
- debugmsg("indexed constructor from ex,symmetry,ex,ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
validate();
}
indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symtree(symm)
{
- debugmsg("indexed constructor from ex,symmetry,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
validate();
}
indexed::indexed(const ex & b, const exvector & v) : inherited(b), symtree(sy_none())
{
- debugmsg("indexed constructor from ex,exvector", LOGLEVEL_CONSTRUCT);
seq.insert(seq.end(), v.begin(), v.end());
tinfo_key = TINFO_indexed;
validate();
indexed::indexed(const ex & b, const symmetry & symm, const exvector & v) : inherited(b), symtree(symm)
{
- debugmsg("indexed constructor from ex,symmetry,exvector", LOGLEVEL_CONSTRUCT);
seq.insert(seq.end(), v.begin(), v.end());
tinfo_key = TINFO_indexed;
validate();
indexed::indexed(const symmetry & symm, const exprseq & es) : inherited(es), symtree(symm)
{
- debugmsg("indexed constructor from symmetry,exprseq", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
}
indexed::indexed(const symmetry & symm, const exvector & v, bool discardable) : inherited(v, discardable), symtree(symm)
{
- debugmsg("indexed constructor from symmetry,exvector", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
}
indexed::indexed(const symmetry & symm, exvector * vp) : inherited(vp), symtree(symm)
{
- debugmsg("indexed constructor from symmetry,exvector *", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_indexed;
}
indexed::indexed(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
{
- debugmsg("indexed constructor from archive_node", LOGLEVEL_CONSTRUCT);
if (!n.find_ex("symmetry", symtree, sym_lst)) {
// GiNaC versions <= 0.9.0 had an unsigned "symmetry" property
unsigned symm = 0;
symtree = sy_none();
break;
}
- ex_to_nonconst_symmetry(symtree).validate(seq.size() - 1);
+ const_cast<symmetry &>(ex_to<symmetry>(symtree)).validate(seq.size() - 1);
}
}
DEFAULT_UNARCHIVE(indexed)
//////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
//////////
void indexed::print(const print_context & c, unsigned level) const
{
- debugmsg("indexed print", LOGLEVEL_PRINT);
GINAC_ASSERT(seq.size() > 0);
if (is_of_type(c, print_tree)) {
<< std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
<< ", " << seq.size()-1 << " indices"
<< ", symmetry=" << symtree << std::endl;
- c.s << std::endl;
unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
seq[0].print(c, level + delta_indent);
printindices(c, level + delta_indent);
int indexed::compare_same_type(const basic & other) const
{
- GINAC_ASSERT(is_of_type(other, indexed));
+ GINAC_ASSERT(is_a<indexed>(other));
return inherited::compare_same_type(other);
}
// If the base object is 0, the whole object is 0
if (base.is_zero())
- return _ex0();
+ return _ex0;
// If the base object is a product, pull out the numeric factor
if (is_ex_exactly_of_type(base, mul) && is_ex_exactly_of_type(base.op(base.nops() - 1), numeric)) {
// Canonicalize indices according to the symmetry properties
if (seq.size() > 2) {
exvector v = seq;
- GINAC_ASSERT(is_ex_exactly_of_type(symtree, symmetry));
+ GINAC_ASSERT(is_exactly_a<symmetry>(symtree));
int sig = canonicalize(v.begin() + 1, ex_to<symmetry>(symtree));
if (sig != INT_MAX) {
// Something has changed while sorting indices, more evaluations later
if (sig == 0)
- return _ex0();
+ return _ex0;
return ex(sig) * thisexprseq(v);
}
}
// Let the class of the base object perform additional evaluations
- return base.bp->eval_indexed(*this);
-}
-
-int indexed::degree(const ex & s) const
-{
- return is_equal(*s.bp) ? 1 : 0;
-}
-
-int indexed::ldegree(const ex & s) const
-{
- return is_equal(*s.bp) ? 1 : 0;
-}
-
-ex indexed::coeff(const ex & s, int n) const
-{
- if (is_equal(*s.bp))
- return n==1 ? _ex1() : _ex0();
- else
- return n==0 ? ex(*this) : _ex0();
+ return ex_to<basic>(base).eval_indexed(*this);
}
ex indexed::thisexprseq(const exvector & v) const
// expand_indexed expands (a+b).i -> a.i + b.i
const ex & base = seq[0];
- ex sum = _ex0();
+ ex sum = _ex0;
for (unsigned i=0; i<base.nops(); i++) {
exvector s = seq;
s[0] = base.op(i);
while (it != itend) {
bool cur_covariant = (is_ex_of_type(*it, varidx) ? ex_to<varidx>(*it).is_covariant() : true);
- if (first || cur_covariant != covariant) {
+ if (first || cur_covariant != covariant) { // Variance changed
+ // The empty {} prevents indices from ending up on top of each other
if (!first)
- c.s << "}";
+ c.s << "}{}";
covariant = cur_covariant;
if (covariant)
c.s << "_{";
if (!symtree.is_zero()) {
if (!is_ex_exactly_of_type(symtree, symmetry))
throw(std::invalid_argument("symmetry of indexed object must be of type symmetry"));
- ex_to_nonconst_symmetry(symtree).validate(seq.size() - 1);
+ const_cast<symmetry &>(ex_to<symmetry>(symtree)).validate(seq.size() - 1);
}
}
* @see ex::diff */
ex indexed::derivative(const symbol & s) const
{
- return _ex0();
+ return _ex0;
}
//////////
/** Rename dummy indices in an expression.
*
- * @param e Expression to be worked on
+ * @param e Expression to work on
* @param local_dummy_indices The set of dummy indices that appear in the
* expression "e"
* @param global_dummy_indices The set of dummy indices that have appeared
* by the function */
static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, exvector & local_dummy_indices)
{
- int global_size = global_dummy_indices.size(),
- local_size = local_dummy_indices.size();
+ unsigned global_size = global_dummy_indices.size(),
+ local_size = local_dummy_indices.size();
// Any local dummy indices at all?
if (local_size == 0)
// More local indices than we encountered before, add the new ones
// to the global set
+ int old_global_size = global_size;
int remaining = local_size - global_size;
exvector::const_iterator it = local_dummy_indices.begin(), itend = local_dummy_indices.end();
while (it != itend && remaining > 0) {
}
it++;
}
- }
- // Replace index symbols in expression
+ // If this is the first set of local indices, do nothing
+ if (old_global_size == 0)
+ return e;
+ }
GINAC_ASSERT(local_size <= global_size);
- bool all_equal = true;
- lst local_syms, global_syms;
- for (unsigned i=0; i<local_size; i++) {
- ex loc_sym = local_dummy_indices[i].op(0);
- ex glob_sym = global_dummy_indices[i].op(0);
- if (!loc_sym.is_equal(glob_sym)
- && ex_to<idx>(local_dummy_indices[i]).get_dim().is_equal(ex_to<idx>(global_dummy_indices[i]).get_dim())) {
- all_equal = false;
- local_syms.append(loc_sym);
- global_syms.append(glob_sym);
+
+ // Construct lists of index symbols
+ exlist local_syms, global_syms;
+ for (unsigned i=0; i<local_size; 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 (unsigned i=0; i<global_size; 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
+ exlist local_uniq, global_uniq;
+ set_difference(local_syms.begin(), local_syms.end(), global_syms.begin(), global_syms.end(), std::back_insert_iterator<exlist>(local_uniq), ex_is_less());
+ set_difference(global_syms.begin(), global_syms.end(), local_syms.begin(), local_syms.end(), std::back_insert_iterator<exlist>(global_uniq), ex_is_less());
+
+ // Replace remaining non-common local index symbols by global ones
+ if (local_uniq.empty())
+ return e;
+ else {
+ while (global_uniq.size() > local_uniq.size())
+ global_uniq.pop_back();
+ return e.subs(lst(local_uniq), lst(global_uniq));
+ }
+}
+
+/** Given a set of indices, extract those of class varidx. */
+static void find_variant_indices(const exvector & v, exvector & variant_indices)
+{
+ exvector::const_iterator it1, itend;
+ for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
+ if (is_exactly_a<varidx>(*it1))
+ variant_indices.push_back(*it1);
+ }
+}
+
+/** Raise/lower dummy indices in a single indexed objects to canonicalize their
+ * variance.
+ *
+ * @param e Object to work on
+ * @param variant_dummy_indices The set of indices that might need repositioning (will be changed by this function)
+ * @param moved_indices The set of indices that have been repositioned (will be changed by this function)
+ * @return true if 'e' was changed */
+bool reposition_dummy_indices(ex & e, exvector & variant_dummy_indices, exvector & moved_indices)
+{
+ bool something_changed = false;
+
+ // If a dummy index is encountered for the first time in the
+ // product, pull it up, otherwise, pull it down
+ exvector::const_iterator it2, it2start, it2end;
+ for (it2start = ex_to<indexed>(e).seq.begin(), it2end = ex_to<indexed>(e).seq.end(), it2 = it2start + 1; it2 != it2end; ++it2) {
+ if (!is_exactly_a<varidx>(*it2))
+ continue;
+
+ exvector::iterator vit, vitend;
+ for (vit = variant_dummy_indices.begin(), vitend = variant_dummy_indices.end(); vit != vitend; ++vit) {
+ if (it2->op(0).is_equal(vit->op(0))) {
+ if (ex_to<varidx>(*it2).is_covariant()) {
+ e = e.subs(lst(
+ *it2 == ex_to<varidx>(*it2).toggle_variance(),
+ ex_to<varidx>(*it2).toggle_variance() == *it2
+ ));
+ something_changed = true;
+ it2 = ex_to<indexed>(e).seq.begin() + (it2 - it2start);
+ it2start = ex_to<indexed>(e).seq.begin();
+ it2end = ex_to<indexed>(e).seq.end();
+ }
+ moved_indices.push_back(*vit);
+ variant_dummy_indices.erase(vit);
+ goto next_index;
+ }
+ }
+
+ for (vit = moved_indices.begin(), vitend = moved_indices.end(); vit != vitend; ++vit) {
+ if (it2->op(0).is_equal(vit->op(0))) {
+ if (ex_to<varidx>(*it2).is_contravariant()) {
+ e = e.subs(*it2 == ex_to<varidx>(*it2).toggle_variance());
+ something_changed = true;
+ it2 = ex_to<indexed>(e).seq.begin() + (it2 - it2start);
+ it2start = ex_to<indexed>(e).seq.begin();
+ it2end = ex_to<indexed>(e).seq.end();
+ }
+ goto next_index;
+ }
}
+
+next_index: ;
}
- if (all_equal)
- return e;
- else
- return e.subs(local_syms, global_syms);
+
+ return something_changed;
}
+/* Ordering that only compares the base expressions of indexed objects. */
+struct ex_base_is_less : public std::binary_function<ex, ex, bool> {
+ bool operator() (const ex &lh, const ex &rh) const
+ {
+ return (is_a<indexed>(lh) ? lh.op(0) : lh).compare(is_a<indexed>(rh) ? rh.op(0) : rh) < 0;
+ }
+};
+
/** 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)
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()));
+ 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++) {
+ for (unsigned 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())) {
+ 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(); j++)
+ for (unsigned j=0; j<f.nops(); j++)
v.push_back(f.op(j));
} else
v.push_back(f);
// Check whether the two factors share dummy indices
exvector free, dummy;
find_free_and_dummy(un, free, dummy);
- if (dummy.size() == 0)
+ unsigned num_dummies = dummy.size();
+ if (num_dummies == 0)
continue;
// At least one dummy index, is it a defined scalar product?
bool contracted = false;
- if (free.size() == 0) {
+ if (free.empty()) {
if (sp.is_defined(*it1, *it2)) {
*it1 = sp.evaluate(*it1, *it2);
- *it2 = _ex1();
+ *it2 = _ex1;
goto contraction_done;
}
}
- // Contraction of symmetric with antisymmetric object is zero
- if (dummy.size() > 1
- && ex_to<symmetry>(ex_to<indexed>(*it1).symtree).has_symmetry()
- && ex_to<symmetry>(ex_to<indexed>(*it2).symtree).has_symmetry()) {
-
- // Check all pairs of dummy indices
- for (unsigned idx1=0; idx1<dummy.size()-1; idx1++) {
- for (unsigned idx2=idx1+1; idx2<dummy.size(); idx2++) {
-
- // Try and swap the index pair and check whether the
- // relative sign changed
- lst subs_lst(dummy[idx1].op(0), dummy[idx2].op(0)), repl_lst(dummy[idx2].op(0), dummy[idx1].op(0));
- ex swapped1 = it1->subs(subs_lst, repl_lst);
- ex swapped2 = it2->subs(subs_lst, repl_lst);
- if (it1->is_equal(swapped1) && it2->is_equal(-swapped2)
- || it1->is_equal(-swapped1) && it2->is_equal(swapped2)) {
- free_indices.clear();
- return _ex0();
- }
- }
- }
- }
-
// Try to contract the first one with the second one
- contracted = it1->op(0).bp->contract_with(it1, it2, v);
+ contracted = ex_to<basic>(it1->op(0)).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);
+ contracted = ex_to<basic>(it2->op(0)).contract_with(it2, it1, v);
}
if (contracted) {
contraction_done:
// Find free indices (concatenate them all and call find_free_and_dummy())
// and all dummy indices that appear
exvector un, individual_dummy_indices;
- it1 = v.begin(); itend = v.end();
- while (it1 != itend) {
+ for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
exvector free_indices_of_factor;
if (is_ex_of_type(*it1, indexed)) {
exvector dummy_indices_of_factor;
} else
free_indices_of_factor = it1->get_free_indices();
un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
- it1++;
}
exvector local_dummy_indices;
find_free_and_dummy(un, free_indices, local_dummy_indices);
local_dummy_indices.insert(local_dummy_indices.end(), individual_dummy_indices.begin(), individual_dummy_indices.end());
+ // Filter out the dummy indices with variance
+ exvector variant_dummy_indices;
+ find_variant_indices(local_dummy_indices, variant_dummy_indices);
+
+ // Any indices with variance present at all?
+ if (!variant_dummy_indices.empty()) {
+
+ // Yes, bring the product into a canonical order that only depends on
+ // the base expressions of indexed objects
+ if (!non_commutative)
+ std::sort(v.begin(), v.end(), ex_base_is_less());
+
+ exvector moved_indices;
+
+ // Iterate over all indexed objects in the product
+ for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
+ if (!is_ex_of_type(*it1, indexed))
+ continue;
+
+ if (reposition_dummy_indices(*it1, variant_dummy_indices, moved_indices))
+ something_changed = true;
+ }
+ }
+
ex r;
if (something_changed)
r = non_commutative ? ex(ncmul(v, true)) : ex(mul(v));
else
r = e;
+ // 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) {
+ lst dummy_syms;
+ for (int i=0; i<local_dummy_indices.size(); i++)
+ dummy_syms.append(local_dummy_indices[i].op(0));
+ if (r.symmetrize(dummy_syms).is_zero()) {
+ free_indices.clear();
+ return _ex0;
+ }
+ }
+
// Dummy index renaming
r = rename_dummy_indices(r, dummy_indices, local_dummy_indices);
// Product of indexed object with a scalar?
if (is_ex_exactly_of_type(r, mul) && r.nops() == 2
&& is_ex_exactly_of_type(r.op(1), numeric) && is_ex_of_type(r.op(0), indexed))
- return r.op(0).op(0).bp->scalar_mul_indexed(r.op(0), ex_to<numeric>(r.op(1)));
+ return ex_to<basic>(r.op(0).op(0)).scalar_mul_indexed(r.op(0), ex_to<numeric>(r.op(1)));
else
return r;
}
ex e_expanded = e.expand();
// Simplification of single indexed object: just find the free indices
- // and perform dummy index renaming
+ // and perform dummy index renaming/repositioning
if (is_ex_of_type(e_expanded, indexed)) {
+
+ // Find the dummy indices
const indexed &i = ex_to<indexed>(e_expanded);
exvector local_dummy_indices;
find_free_and_dummy(i.seq.begin() + 1, i.seq.end(), free_indices, local_dummy_indices);
+
+ // Filter out the dummy indices with variance
+ exvector variant_dummy_indices;
+ find_variant_indices(local_dummy_indices, variant_dummy_indices);
+
+ // Any indices with variance present at all?
+ if (!variant_dummy_indices.empty()) {
+
+ // Yes, reposition them
+ exvector moved_indices;
+ reposition_dummy_indices(e_expanded, variant_dummy_indices, moved_indices);
+ }
+
+ // Rename the dummy indices
return rename_dummy_indices(e_expanded, dummy_indices, local_dummy_indices);
}
// free indices in each term
if (is_ex_exactly_of_type(e_expanded, add)) {
bool first = true;
- ex sum = _ex0();
+ ex sum = _ex0;
free_indices.clear();
for (unsigned i=0; i<e_expanded.nops(); i++) {
if (!indices_consistent(free_indices, free_indices_of_term))
throw (std::runtime_error("simplify_indexed: inconsistent indices in sum"));
if (is_ex_of_type(sum, indexed) && is_ex_of_type(term, indexed))
- sum = sum.op(0).bp->add_indexed(sum, term);
+ sum = ex_to<basic>(sum.op(0)).add_indexed(sum, term);
else
sum += term;
}
// 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())))
+ || (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, dummy_indices, sp);
// Cannot do anything
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;
+ spmap::const_iterator i = spm.begin(), end = spm.end();
+ while (i != end) {
+ const spmapkey & k = i->first;
std::cerr << "item key=(" << k.first << "," << k.second;
- std::cerr << "), value=" << cit->second << std::endl;
+ std::cerr << "), value=" << i->second << std::endl;
+ ++i;
}
}
git://www.ginac.de / ginac.git / blobdiff