* Implementation of GiNaC's indices. */
/*
- * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2006 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 <sstream>
#include <stdexcept>
#include "idx.h"
#include "symbol.h"
#include "lst.h"
-#include "print.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_func<print_latex>(&varidx::do_print_latex).
+ 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(&idx::tinfo_static) {}
varidx::varidx() : covariant(false)
{
- debugmsg("varidx default constructor", LOGLEVEL_CONSTRUCT);
- tinfo_key = TINFO_varidx;
+ tinfo_key = &varidx::tinfo_static;
}
-void idx::copy(const idx & other)
+spinidx::spinidx() : dotted(false)
{
- inherited::copy(other);
- value = other.value;
- dim = other.dim;
+ tinfo_key = &spinidx::tinfo_static;
}
-void varidx::copy(const varidx & other)
-{
- inherited::copy(other);
- covariant = other.covariant;
-}
-
-DEFAULT_DESTROY(idx)
-DEFAULT_DESTROY(varidx)
-
//////////
// other constructors
//////////
-idx::idx(const ex & v, const ex & d) : inherited(TINFO_idx), value(v), dim(d)
+idx::idx(const ex & v, const ex & d) : inherited(&idx::tinfo_static), 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;
+ tinfo_key = &varidx::tinfo_static;
+}
+
+spinidx::spinidx(const ex & v, const ex & d, bool cov, bool dot) : inherited(v, d, cov), dotted(dot)
+{
+ tinfo_key = &spinidx::tinfo_static;
}
//////////
// 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);
}
+spinidx::spinidx(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
+{
+ n.find_bool("dotted", dotted);
+}
+
void idx::archive(archive_node &n) const
{
inherited::archive(n);
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::print(const print_context & c, unsigned level) const
+void idx::print_index(const print_context & c, unsigned level) const
{
- debugmsg("idx print", LOGLEVEL_PRINT);
+ 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 << "]";
+ }
+}
- if (is_of_type(c, print_tree)) {
+void idx::do_print(const print_context & c, unsigned level) const
+{
+ c.s << ".";
+ print_index(c, level);
+}
- c.s << std::string(level, ' ') << class_name()
- << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
- << std::endl;
- unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
- value.print(c, level + delta_indent);
- dim.print(c, level + delta_indent);
+void idx::do_print_latex(const print_latex & c, unsigned level) const
+{
+ c.s << "{";
+ print_index(c, level);
+ c.s << "}";
+}
- } else {
+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);
+}
+void varidx::do_print(const print_context & c, unsigned level) const
+{
+ if (covariant)
c.s << ".";
- bool need_parens = !(is_ex_exactly_of_type(value, numeric) || is_ex_of_type(value, symbol));
- if (need_parens)
- c.s << "(";
- c.s << value;
- if (need_parens)
- c.s << ")";
- }
+ else
+ c.s << "~";
+ print_index(c, level);
}
-void varidx::print(const print_context & c, unsigned level) const
+void varidx::do_print_tree(const print_tree & c, unsigned level) const
{
- debugmsg("varidx print", LOGLEVEL_PRINT);
-
- if (is_of_type(c, print_tree)) {
+ 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);
+}
- c.s << std::string(level, ' ') << class_name()
- << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
- << (covariant ? ", covariant" : ", contravariant")
- << std::endl;
- unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
- value.print(c, level + delta_indent);
- dim.print(c, level + delta_indent);
+void spinidx::do_print(const print_context & c, unsigned level) const
+{
+ if (covariant)
+ c.s << ".";
+ else
+ c.s << "~";
+ if (dotted)
+ c.s << "*";
+ print_index(c, level);
+}
- } else {
+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 << "}";
+}
- if (covariant)
- c.s << ".";
- else
- c.s << "~";
- bool need_parens = !(is_ex_exactly_of_type(value, numeric) || is_ex_of_type(value, symbol));
- if (need_parens)
- c.s << "(";
- c.s << value;
- if (need_parens)
- 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);
}
-unsigned idx::nops() const
+size_t idx::nops() const
{
// don't count the dimension as that is not really a sub-expression
return 1;
}
-ex & idx::let_op(int i)
+ex idx::op(size_t i) const
{
GINAC_ASSERT(i == 0);
return value;
}
+ex idx::map(map_function & f) const
+{
+ const ex &mapped_value = f(value);
+ if (are_ex_trivially_equal(value, mapped_value))
+ return *this;
+ else {
+ idx *copy = duplicate();
+ copy->setflag(status_flags::dynallocated);
+ copy->clearflag(status_flags::hash_calculated);
+ copy->value = mapped_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);
+
+ if (covariant != o.covariant)
+ return false;
+
+ return inherited::match_same_type(other);
+}
+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((p_int)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
- for (unsigned i=0; i<ls.nops(); i++) {
- if (is_equal(*(ls.op(i)).bp)) {
-
- // Substitution index->index
- if (is_ex_of_type(lr.op(i), idx))
- return lr.op(i);
-
- // Otherwise substitute value
- idx *i_copy = static_cast<idx *>(duplicate());
- i_copy->value = lr.op(i);
- i_copy->clearflag(status_flags::hash_calculated);
- return i_copy->setflag(status_flags::dynallocated);
- }
+ exmap::const_iterator it = m.find(*this);
+ if (it != m.end()) {
+
+ // Substitution index->index
+ if (is_a<idx>(it->second) || (options & subs_options::really_subs_idx))
+ 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 is_exactly_a<numeric>(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
+{
+ return GiNaC::minimal_dim(dim, other.dim);
+}
+
+ex varidx::toggle_variance() const
{
- varidx *i_copy = static_cast<varidx *>(duplicate());
+ 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));
}
-/** Bring a vector of indices into a canonic order. Dummy indices will lie
- * next to each other after the sorting. */
-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++;
- }
-}
-
-
void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy)
{
out_free.clear();
// 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())
+ 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);
+ shaker_sort(v.begin(), v.end(), ex_is_less(), ex_swap());
// Find dummy pairs and free indices
it = v.begin(); itend = v.end();
if (it == itend)
return;
} else {
- if (!it->is_equal(*last) && ex_to_idx(*last).is_symbolic())
+ 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())
+ if (ex_to<idx>(*last).is_symbolic())
out_free.push_back(*last);
}
-exvector index_set_difference(const exvector & set1, const exvector & set2)
+ex minimal_dim(const ex & dim1, const ex & dim2)
{
- exvector ret;
-
- exvector::const_iterator ait = set1.begin(), aitend = set1.end();
- while (ait != aitend) {
- exvector::const_iterator bit = set2.begin(), bitend = set2.end();
- bool found = false;
- while (bit != bitend) {
- if (ait->is_equal(*bit)) {
- found = true;
- break;
- }
- bit++;
- }
- if (!found)
- ret.push_back(*ait);
- ait++;
+ if (dim1.is_equal(dim2) || dim1 < dim2 || (is_exactly_a<numeric>(dim1) && !is_a<numeric>(dim2)))
+ return dim1;
+ else if (dim1 > dim2 || (!is_a<numeric>(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()));
}
-
- return ret;
}
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff