idx.cpp

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/*
 *  GiNaC Copyright (C) 1999-2020 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
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */
 
#include "idx.h"
#include "symbol.h"
#include "lst.h"
#include "relational.h"
#include "operators.h"
#include "archive.h"
#include "utils.h"
#include "hash_seed.h"
 
#include <iostream>
#include <sstream>
#include <stdexcept>
 
namespace GiNaC {
 
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_csrc>(&idx::do_print_csrc).
  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
 
idx::idx() {}
 
varidx::varidx() : covariant(false)
{
}
 
spinidx::spinidx() : dotted(false)
{
}
 
// other constructors
 
idx::idx(const ex & v, const ex & d) :  value(v), dim(d)
{
    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)
{
}
 
spinidx::spinidx(const ex & v, const ex & d, bool cov, bool dot) : inherited(v, d, cov), dotted(dot)
{
}
 
// archiving
 
void idx::read_archive(const archive_node& n, lst& sym_lst) 
{
    inherited::read_archive(n, sym_lst);
    n.find_ex("value", value, sym_lst);
    n.find_ex("dim", dim, sym_lst);
}
GINAC_BIND_UNARCHIVER(idx);
 
void varidx::read_archive(const archive_node& n, lst& sym_lst)
{
    inherited::read_archive(n, sym_lst);
    n.find_bool("covariant", covariant);
}
GINAC_BIND_UNARCHIVER(varidx);
 
void spinidx::read_archive(const archive_node& n, lst& sym_lst)
{
    inherited::read_archive(n, sym_lst);
    n.find_bool("dotted", dotted);
}
GINAC_BIND_UNARCHIVER(spinidx);
 
void idx::archive(archive_node &n) const
{
    inherited::archive(n);
    n.add_ex("value", value);
    n.add_ex("dim", dim);
}
 
void varidx::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);
}
 
// functions overriding virtual functions from base classes
 
void idx::print_index(const print_context & c, unsigned level) const
{
    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::do_print(const print_context & c, unsigned level) const
{
    c.s << ".";
    print_index(c, level);
}
 
void idx::do_print_latex(const print_latex & c, unsigned level) const
{
    c.s << "{";
    print_index(c, level);
    c.s << "}";
}
 
void idx::do_print_csrc(const print_csrc & c, unsigned level) const
{
    c.s << "[";
    if (value.info(info_flags::integer))
        c.s << ex_to<numeric>(value).to_int();
    else
        value.print(c);
    c.s << "]";
}
 
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 << ".";
    else
        c.s << "~";
    print_index(c, level);
}
 
void varidx::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")
        << 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)
        c.s << ".";
    else
        c.s << "~";
    if (dotted)
        c.s << "*";
    print_index(c, level);
}
 
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
{
    switch(inf) {
        case info_flags::idx:
        case info_flags::has_indices:
            return true;
    }
    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
{
    const ex &mapped_value = f(value);
    if (are_ex_trivially_equal(value, mapped_value))
        return *this;
    else {
        idx *copy = duplicate();
        copy->clearflag(status_flags::hash_calculated);
        copy->value = mapped_value;
        return *copy;
    }
}
 
int idx::compare_same_type(const basic & other) const
{
    GINAC_ASSERT(is_a<idx>(other));
    const idx &o = static_cast<const idx &>(other);
 
    int cmpval = value.compare(o.value);
    if (cmpval)
        return cmpval;
    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_a<varidx>(other));
    const varidx &o = static_cast<const varidx &>(other);
 
    int cmpval = inherited::compare_same_type(other);
    if (cmpval)
        return cmpval;
 
    // Check variance last so dummy indices will end up next to each other
    if (covariant != o.covariant)
        return covariant ? -1 : 1;
 
    return 0;
}
 
bool varidx::match_same_type(const basic & other) const
{
    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 = make_hash_seed(typeid(*this));
    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;
}
 
ex idx::evalf() const
{
    return *this;
}
 
ex idx::subs(const exmap & m, unsigned options) const
{
    // First look for index substitutions
    auto 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;
    }
 
    // None, substitute objects in value (not in dimension)
    const ex &subsed_value = value.subs(m, options);
    if (are_ex_trivially_equal(value, subsed_value))
        return *this;
 
    idx *i_copy = duplicate();
    i_copy->value = subsed_value;
    i_copy->clearflag(status_flags::hash_calculated);
    return *i_copy;
}
 
ex idx::derivative(const symbol & s) const
{
    return _ex0;
}
 
// new virtual functions
 
bool idx::is_dummy_pair_same_type(const basic & other) const
{
    const idx &o = static_cast<const idx &>(other);
 
    // Only pure symbols form dummy pairs, "2n+1" doesn't
    if (!is_a<symbol>(value))
        return false;
 
    // Value must be equal, of course
    if (!value.is_equal(o.value))
        return false;
 
    // 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
{
    const varidx &o = static_cast<const varidx &>(other);
 
    // Variance must be opposite
    if (covariant == o.covariant)
        return false;
 
    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 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;
}
 
ex idx::minimal_dim(const idx & other) const
{
    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;
}
 
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;
}
 
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;
}
 
// global functions
 
bool is_dummy_pair(const idx & i1, const idx & i2)
{
    // The indices must be of exactly the same type
    if (typeid(i1) != typeid(i2))
        return false;
 
    // Same type, let the indices decide whether they are paired
    return i1.is_dummy_pair_same_type(i2);
}
 
bool is_dummy_pair(const ex & e1, const ex & e2)
{
    // The expressions must be indices
    if (!is_a<idx>(e1) || !is_a<idx>(e2))
        return false;
 
    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();
    auto 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<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()));
    }
}
 
} // namespace GiNaC