* Implementation of GiNaC's indices. */
/*
- * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2003 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 <sstream>
#include <stdexcept>
#include "idx.h"
#include "symbol.h"
#include "lst.h"
+#include "relational.h"
+#include "operators.h"
#include "archive.h"
#include "utils.h"
-#include "debugmsg.h"
namespace GiNaC {
-GINAC_IMPLEMENT_REGISTERED_CLASS(idx, basic)
-GINAC_IMPLEMENT_REGISTERED_CLASS(varidx, idx)
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(idx, basic,
+ print_func<print_context>(&idx::do_print).
+ print_func<print_latex>(&idx::do_print_latex).
+ print_func<print_tree>(&idx::do_print_tree))
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(varidx, idx,
+ print_func<print_context>(&varidx::do_print).
+ // print_latex inherited from idx
+ print_func<print_tree>(&varidx::do_print_tree))
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(spinidx, varidx,
+ print_func<print_context>(&spinidx::do_print).
+ print_func<print_latex>(&spinidx::do_print_latex).
+ print_func<print_tree>(&spinidx::do_print_tree))
//////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default constructor
//////////
-idx::idx() : inherited(TINFO_idx)
-{
- debugmsg("idx default constructor", LOGLEVEL_CONSTRUCT);
-}
+idx::idx() : inherited(TINFO_idx) {}
varidx::varidx() : covariant(false)
{
- debugmsg("varidx default constructor", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_varidx;
}
-void idx::copy(const idx & other)
-{
- inherited::copy(other);
- value = other.value;
- dim = other.dim;
-}
-
-void varidx::copy(const varidx & other)
-{
- inherited::copy(other);
- covariant = other.covariant;
-}
-
-void idx::destroy(bool call_parent)
+spinidx::spinidx() : dotted(false)
{
- if (call_parent)
- inherited::destroy(call_parent);
-}
-
-void varidx::destroy(bool call_parent)
-{
- if (call_parent)
- inherited::destroy(call_parent);
+ tinfo_key = TINFO_spinidx;
}
//////////
idx::idx(const ex & v, const ex & d) : inherited(TINFO_idx), value(v), dim(d)
{
- debugmsg("idx constructor from ex,ex", LOGLEVEL_CONSTRUCT);
if (is_dim_numeric())
if (!dim.info(info_flags::posint))
throw(std::invalid_argument("dimension of space must be a positive integer"));
varidx::varidx(const ex & v, const ex & d, bool cov) : inherited(v, d), covariant(cov)
{
- debugmsg("varidx constructor from ex,ex,bool", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_varidx;
}
+spinidx::spinidx(const ex & v, const ex & d, bool cov, bool dot) : inherited(v, d, cov), dotted(dot)
+{
+ tinfo_key = TINFO_spinidx;
+}
+
//////////
// archiving
//////////
-idx::idx(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+idx::idx(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
{
- debugmsg("idx constructor from archive_node", LOGLEVEL_CONSTRUCT);
n.find_ex("value", value, sym_lst);
n.find_ex("dim", dim, sym_lst);
}
-varidx::varidx(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+varidx::varidx(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
{
- debugmsg("varidx constructor from archive_node", LOGLEVEL_CONSTRUCT);
n.find_bool("covariant", covariant);
}
-ex idx::unarchive(const archive_node &n, const lst &sym_lst)
+spinidx::spinidx(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
{
- return (new idx(n, sym_lst))->setflag(status_flags::dynallocated);
-}
-
-ex varidx::unarchive(const archive_node &n, const lst &sym_lst)
-{
- return (new varidx(n, sym_lst))->setflag(status_flags::dynallocated);
+ n.find_bool("dotted", dotted);
}
void idx::archive(archive_node &n) const
n.add_bool("covariant", covariant);
}
+void spinidx::archive(archive_node &n) const
+{
+ inherited::archive(n);
+ n.add_bool("dotted", dotted);
+}
+
+DEFAULT_UNARCHIVE(idx)
+DEFAULT_UNARCHIVE(varidx)
+DEFAULT_UNARCHIVE(spinidx)
+
//////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
//////////
-void idx::printraw(std::ostream & os) const
+void idx::print_index(const print_context & c, unsigned level) const
{
- debugmsg("idx printraw", LOGLEVEL_PRINT);
-
- os << class_name() << "(";
- value.printraw(os);
- os << ",dim=";
- dim.printraw(os);
- os << ",hash=" << hashvalue << ",flags=" << flags;
- os << ")";
+ bool need_parens = !(is_exactly_a<numeric>(value) || is_a<symbol>(value));
+ if (need_parens)
+ c.s << "(";
+ value.print(c);
+ if (need_parens)
+ c.s << ")";
+ if (c.options & print_options::print_index_dimensions) {
+ c.s << "[";
+ dim.print(c);
+ c.s << "]";
+ }
}
-void idx::printtree(std::ostream & os, unsigned indent) const
+void idx::do_print(const print_context & c, unsigned level) const
{
- debugmsg("idx printtree",LOGLEVEL_PRINT);
-
- os << std::string(indent, ' ') << "type=" << class_name();
- value.printtree(os, indent + delta_indent);
- os << std::string(indent, ' ');
- os << ", hash=" << hashvalue
- << " (0x" << std::hex << hashvalue << std::dec << ")"
- << ", flags=" << flags << std::endl;
+ c.s << ".";
+ print_index(c, level);
}
-void idx::print(std::ostream & os, unsigned upper_precedence) const
+void idx::do_print_latex(const print_latex & c, unsigned level) const
{
- debugmsg("idx print", LOGLEVEL_PRINT);
+ c.s << "{";
+ print_index(c, level);
+ c.s << "}";
+}
- os << ".";
+void idx::do_print_tree(const print_tree & c, unsigned level) const
+{
+ c.s << std::string(level, ' ') << class_name() << " @" << this
+ << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+ << std::endl;
+ value.print(c, level + c.delta_indent);
+ dim.print(c, level + c.delta_indent);
+}
- bool need_parens = !(is_ex_exactly_of_type(value, numeric) || is_ex_of_type(value, symbol));
- if (need_parens)
- os << "(";
- os << value;
- if (need_parens)
- os << ")";
+void varidx::do_print(const print_context & c, unsigned level) const
+{
+ if (covariant)
+ c.s << ".";
+ else
+ c.s << "~";
+ print_index(c, level);
}
-void varidx::print(std::ostream & os, unsigned upper_precedence) const
+void varidx::do_print_tree(const print_tree & c, unsigned level) const
{
- debugmsg("varidx print", LOGLEVEL_PRINT);
+ c.s << std::string(level, ' ') << class_name() << " @" << this
+ << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+ << (covariant ? ", covariant" : ", contravariant")
+ << std::endl;
+ value.print(c, level + c.delta_indent);
+ dim.print(c, level + c.delta_indent);
+}
+void spinidx::do_print(const print_context & c, unsigned level) const
+{
if (covariant)
- os << ".";
+ c.s << ".";
else
- os << "~";
+ c.s << "~";
+ if (dotted)
+ c.s << "*";
+ print_index(c, level);
+}
- bool need_parens = !(is_ex_exactly_of_type(value, numeric) || is_ex_of_type(value, symbol));
- if (need_parens)
- os << "(";
- os << value;
- if (need_parens)
- os << ")";
+void spinidx::do_print_latex(const print_latex & c, unsigned level) const
+{
+ if (dotted)
+ c.s << "\\dot{";
+ else
+ c.s << "{";
+ print_index(c, level);
+ c.s << "}";
+}
+
+void spinidx::do_print_tree(const print_tree & c, unsigned level) const
+{
+ c.s << std::string(level, ' ') << class_name() << " @" << this
+ << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+ << (covariant ? ", covariant" : ", contravariant")
+ << (dotted ? ", dotted" : ", undotted")
+ << std::endl;
+ value.print(c, level + c.delta_indent);
+ dim.print(c, level + c.delta_indent);
}
bool idx::info(unsigned inf) const
return inherited::info(inf);
}
+size_t idx::nops() const
+{
+ // don't count the dimension as that is not really a sub-expression
+ return 1;
+}
+
+ex idx::op(size_t i) const
+{
+ GINAC_ASSERT(i == 0);
+ return value;
+}
+
+ex idx::map(map_function & f) const
+{
+ idx *copy = duplicate();
+ copy->setflag(status_flags::dynallocated);
+ copy->clearflag(status_flags::hash_calculated);
+ copy->value = f(value);
+ return *copy;
+}
+
/** Returns order relation between two indices of the same type. The order
* must be such that dummy indices lie next to each other. */
int idx::compare_same_type(const basic & other) const
{
- GINAC_ASSERT(is_of_type(other, idx));
+ GINAC_ASSERT(is_a<idx>(other));
const idx &o = static_cast<const idx &>(other);
int cmpval = value.compare(o.value);
return dim.compare(o.dim);
}
+bool idx::match_same_type(const basic & other) const
+{
+ GINAC_ASSERT(is_a<idx>(other));
+ const idx &o = static_cast<const idx &>(other);
+
+ return dim.is_equal(o.dim);
+}
+
int varidx::compare_same_type(const basic & other) const
{
- GINAC_ASSERT(is_of_type(other, varidx));
+ GINAC_ASSERT(is_a<varidx>(other));
const varidx &o = static_cast<const varidx &>(other);
int cmpval = inherited::compare_same_type(other);
// Check variance last so dummy indices will end up next to each other
if (covariant != o.covariant)
return covariant ? -1 : 1;
+
return 0;
}
-ex idx::subs(const lst & ls, const lst & lr) const
+bool varidx::match_same_type(const basic & other) const
{
- GINAC_ASSERT(ls.nops() == lr.nops());
+ GINAC_ASSERT(is_a<varidx>(other));
+ const varidx &o = static_cast<const varidx &>(other);
- // First look for index substitutions
- for (unsigned i=0; i<ls.nops(); i++) {
- if (is_equal(*(ls.op(i)).bp)) {
+ if (covariant != o.covariant)
+ return false;
- // Substitution index->index
- if (is_ex_of_type(lr.op(i), idx))
- return lr.op(i);
+ return inherited::match_same_type(other);
+}
- // Otherwise substitute value
- idx *i_copy = static_cast<idx *>(duplicate());
- i_copy->value = lr.op(i);
- return i_copy->setflag(status_flags::dynallocated);
- }
+int spinidx::compare_same_type(const basic & other) const
+{
+ GINAC_ASSERT(is_a<spinidx>(other));
+ const spinidx &o = static_cast<const spinidx &>(other);
+
+ // Check dottedness first so dummy indices will end up next to each other
+ if (dotted != o.dotted)
+ return dotted ? -1 : 1;
+
+ int cmpval = inherited::compare_same_type(other);
+ if (cmpval)
+ return cmpval;
+
+ return 0;
+}
+
+bool spinidx::match_same_type(const basic & other) const
+{
+ GINAC_ASSERT(is_a<spinidx>(other));
+ const spinidx &o = static_cast<const spinidx &>(other);
+
+ if (dotted != o.dotted)
+ return false;
+ return inherited::match_same_type(other);
+}
+
+unsigned idx::calchash() const
+{
+ // NOTE: The code in simplify_indexed() assumes that canonically
+ // ordered sequences of indices have the two members of dummy index
+ // pairs lying next to each other. The hash values for indices must
+ // be devised accordingly. The easiest (only?) way to guarantee the
+ // desired ordering is to make indices with the same value have equal
+ // hash keys. That is, the hash values must not depend on the index
+ // dimensions or other attributes (variance etc.).
+ // The compare_same_type() methods will take care of the rest.
+ unsigned v = golden_ratio_hash(tinfo());
+ v = rotate_left(v);
+ v ^= value.gethash();
+
+ // Store calculated hash value only if object is already evaluated
+ if (flags & status_flags::evaluated) {
+ setflag(status_flags::hash_calculated);
+ hashvalue = v;
+ }
+
+ return v;
+}
+
+/** By default, basic::evalf would evaluate the index value but we don't want
+ * a.1 to become a.(1.0). */
+ex idx::evalf(int level) const
+{
+ return *this;
+}
+
+ex idx::subs(const exmap & m, unsigned options) const
+{
+ // First look for index substitutions
+ exmap::const_iterator it = m.find(*this);
+ if (it != m.end()) {
+
+ // Substitution index->index
+ if (is_a<idx>(it->second))
+ return it->second;
+
+ // Otherwise substitute value
+ idx *i_copy = duplicate();
+ i_copy->value = it->second;
+ i_copy->clearflag(status_flags::hash_calculated);
+ return i_copy->setflag(status_flags::dynallocated);
}
// None, substitute objects in value (not in dimension)
- const ex &subsed_value = value.subs(ls, lr);
+ const ex &subsed_value = value.subs(m, options);
if (are_ex_trivially_equal(value, subsed_value))
return *this;
- idx *i_copy = static_cast<idx *>(duplicate());
+ idx *i_copy = duplicate();
i_copy->value = subsed_value;
+ i_copy->clearflag(status_flags::hash_calculated);
return i_copy->setflag(status_flags::dynallocated);
}
+/** Implementation of ex::diff() for an index always returns 0.
+ *
+ * @see ex::diff */
+ex idx::derivative(const symbol & s) const
+{
+ return _ex0;
+}
+
//////////
// new virtual functions
//////////
const idx &o = static_cast<const idx &>(other);
// Only pure symbols form dummy pairs, "2n+1" doesn't
- if (!is_ex_of_type(value, symbol))
+ if (!is_a<symbol>(value))
return false;
// Value must be equal, of course
if (!value.is_equal(o.value))
return false;
- // Also the dimension
- return dim.is_equal(o.dim);
+ // Dimensions need not be equal but must be comparable (so we can
+ // determine the minimum dimension of contractions)
+ if (dim.is_equal(o.dim))
+ return true;
+
+ return (dim < o.dim || dim > o.dim || (is_exactly_a<numeric>(dim) && is_a<symbol>(o.dim)) || (is_a<symbol>(dim) && is_exactly_a<numeric>(o.dim)));
}
bool varidx::is_dummy_pair_same_type(const basic & other) const
return inherited::is_dummy_pair_same_type(other);
}
+bool spinidx::is_dummy_pair_same_type(const basic & other) const
+{
+ const spinidx &o = static_cast<const spinidx &>(other);
+
+ // Dottedness must be the same
+ if (dotted != o.dotted)
+ return false;
+
+ return inherited::is_dummy_pair_same_type(other);
+}
+
+
//////////
// non-virtual functions
//////////
-ex varidx::toggle_variance(void) const
+ex idx::replace_dim(const ex & new_dim) const
+{
+ idx *i_copy = duplicate();
+ i_copy->dim = new_dim;
+ i_copy->clearflag(status_flags::hash_calculated);
+ return i_copy->setflag(status_flags::dynallocated);
+}
+
+ex idx::minimal_dim(const idx & other) const
{
- varidx *i_copy = static_cast<varidx *>(duplicate());
+ return GiNaC::minimal_dim(dim, other.dim);
+}
+
+ex varidx::toggle_variance() const
+{
+ varidx *i_copy = duplicate();
i_copy->covariant = !i_copy->covariant;
i_copy->clearflag(status_flags::hash_calculated);
return i_copy->setflag(status_flags::dynallocated);
}
+ex spinidx::toggle_dot() const
+{
+ spinidx *i_copy = duplicate();
+ i_copy->dotted = !i_copy->dotted;
+ i_copy->clearflag(status_flags::hash_calculated);
+ return i_copy->setflag(status_flags::dynallocated);
+}
+
+ex spinidx::toggle_variance_dot() const
+{
+ spinidx *i_copy = duplicate();
+ i_copy->covariant = !i_copy->covariant;
+ i_copy->dotted = !i_copy->dotted;
+ i_copy->clearflag(status_flags::hash_calculated);
+ return i_copy->setflag(status_flags::dynallocated);
+}
+
//////////
// global functions
//////////
bool is_dummy_pair(const ex & e1, const ex & e2)
{
// The expressions must be indices
- if (!is_ex_of_type(e1, idx) || !is_ex_of_type(e2, idx))
+ if (!is_a<idx>(e1) || !is_a<idx>(e2))
return false;
- return is_dummy_pair(ex_to_idx(e1), ex_to_idx(e2));
+ return is_dummy_pair(ex_to<idx>(e1), ex_to<idx>(e2));
+}
+
+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);
+ shaker_sort(v.begin(), v.end(), ex_is_less(), ex_swap());
+
+ // 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);
+}
+
+ex minimal_dim(const ex & dim1, const ex & dim2)
+{
+ if (dim1.is_equal(dim2) || dim1 < dim2 || (is_exactly_a<numeric>(dim1) && is_a<symbol>(dim2)))
+ return dim1;
+ else if (dim1 > dim2 || (is_a<symbol>(dim1) && is_exactly_a<numeric>(dim2)))
+ return dim2;
+ else {
+ std::ostringstream s;
+ s << "minimal_dim(): index dimensions " << dim1 << " and " << dim2 << " cannot be ordered";
+ throw (std::runtime_error(s.str()));
+ }
}
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff