symmetry.cpp

Go to the documentation of this file.

/*
 *  GiNaC Copyright (C) 1999-2011 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 "symmetry.h"
#include "lst.h"
#include "add.h"
#include "numeric.h" // for factorial()
#include "operators.h"
#include "archive.h"
#include "utils.h"
#include "hash_seed.h"

#include <functional>
#include <iostream>
#include <limits>
#include <stdexcept>

namespace GiNaC {

GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(symmetry, basic,
  print_func<print_context>(&symmetry::do_print).
  print_func<print_tree>(&symmetry::do_print_tree))

/*
   Some notes about the structure of a symmetry tree:
    - The leaf nodes of the tree are of type "none", have one index, and no
      children (of course). They are constructed by the symmetry(unsigned)
      constructor.
    - Leaf nodes are the only nodes that only have one index.
    - Container nodes contain two or more children. The "indices" set member
      is the set union of the index sets of all children, and the "children"
      vector stores the children themselves.
    - The index set of each child of a "symm", "anti" or "cycl" node must
      have the same size. It follows that the children of such a node are
      either all leaf nodes, or all container nodes with two or more indices.
*/


// default constructor

symmetry::symmetry() :  type(none)
{
    setflag(status_flags::evaluated | status_flags::expanded);
}

// other constructors

symmetry::symmetry(unsigned i) :  type(none)
{
    indices.insert(i);
    setflag(status_flags::evaluated | status_flags::expanded);
}

symmetry::symmetry(symmetry_type t, const symmetry &c1, const symmetry &c2) :  type(t)
{
    add(c1); add(c2);
    setflag(status_flags::evaluated | status_flags::expanded);
}

// archiving

void symmetry::read_archive(const archive_node &n, lst &sym_lst)
{
    inherited::read_archive(n, sym_lst);
    unsigned t;
    if (!(n.find_unsigned("type", t)))
        throw (std::runtime_error("unknown symmetry type in archive"));
    type = (symmetry_type)t;

    unsigned i = 0;
    while (true) {
        ex e;
        if (n.find_ex("child", e, sym_lst, i))
            add(ex_to<symmetry>(e));
        else
            break;
        i++;
    }

    if (i == 0) {
        while (true) {
            unsigned u;
            if (n.find_unsigned("index", u, i))
                indices.insert(u);
            else
                break;
            i++;
        }
    }
}
GINAC_BIND_UNARCHIVER(symmetry);

void symmetry::archive(archive_node &n) const
{
    inherited::archive(n);

    n.add_unsigned("type", type);

    if (children.empty()) {
        std::set<unsigned>::const_iterator i = indices.begin(), iend = indices.end();
        while (i != iend) {
            n.add_unsigned("index", *i);
            i++;
        }
    } else {
        exvector::const_iterator i = children.begin(), iend = children.end();
        while (i != iend) {
            n.add_ex("child", *i);
            i++;
        }
    }
}

// functions overriding virtual functions from base classes

int symmetry::compare_same_type(const basic & other) const
{
    GINAC_ASSERT(is_a<symmetry>(other));

    // For archiving purposes we need to have an ordering of symmetries.
    const symmetry &othersymm = ex_to<symmetry>(other);

    // Compare type.
    if (type > othersymm.type)
        return 1;
    if (type < othersymm.type)
        return -1;

    // Compare the index set.
    size_t this_size = indices.size();
    size_t that_size = othersymm.indices.size();
    if (this_size > that_size)
        return 1;
    if (this_size < that_size)
        return -1;
    typedef std::set<unsigned>::const_iterator set_it;
    set_it end = indices.end();
    for (set_it i=indices.begin(),j=othersymm.indices.begin(); i!=end; ++i,++j) {
        if(*i < *j)
            return 1;
        if(*i > *j)
            return -1;
    }

    // Compare the children.
    if (children.size() > othersymm.children.size())
        return 1;
    if (children.size() < othersymm.children.size())
        return -1;
    for (size_t i=0; i<children.size(); ++i) {
        int cmpval = ex_to<symmetry>(children[i])
            .compare_same_type(ex_to<symmetry>(othersymm.children[i]));
        if (cmpval)
            return cmpval;
    }

    return 0;
}

unsigned symmetry::calchash() const
{
    unsigned v = make_hash_seed(typeid(*this));

    if (type == none) {
        v = rotate_left(v);
        if (!indices.empty())
            v ^= *(indices.begin());
    } else {
        for (exvector::const_iterator i=children.begin(); i!=children.end(); ++i)
        {
            v = rotate_left(v);
            v ^= i->gethash();
        }
    }

    if (flags & status_flags::evaluated) {
        setflag(status_flags::hash_calculated);
        hashvalue = v;
    }

    return v;
}

void symmetry::do_print(const print_context & c, unsigned level) const
{
    if (children.empty()) {
        if (indices.size() > 0)
            c.s << *(indices.begin());
        else
            c.s << "none";
    } else {
        switch (type) {
            case none: c.s << '!'; break;
            case symmetric: c.s << '+'; break;
            case antisymmetric: c.s << '-'; break;
            case cyclic: c.s << '@'; break;
            default: c.s << '?'; break;
        }
        c.s << '(';
        size_t num = children.size();
        for (size_t i=0; i<num; i++) {
            children[i].print(c);
            if (i != num - 1)
                c.s << ",";
        }
        c.s << ')';
    }
}

void symmetry::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
        << ", type=";

    switch (type) {
        case none: c.s << "none"; break;
        case symmetric: c.s << "symm"; break;
        case antisymmetric: c.s << "anti"; break;
        case cyclic: c.s << "cycl"; break;
        default: c.s << "<unknown>"; break;
    }

    c.s << ", indices=(";
    if (!indices.empty()) {
        std::set<unsigned>::const_iterator i = indices.begin(), end = indices.end();
        --end;
        while (i != end)
            c.s << *i++ << ",";
        c.s << *i;
    }
    c.s << ")\n";

    exvector::const_iterator i = children.begin(), end = children.end();
    while (i != end) {
        i->print(c, level + c.delta_indent);
        ++i;
    }
}

// non-virtual functions in this class

bool symmetry::has_nonsymmetric() const
{
    if (type == antisymmetric || type == cyclic)
        return true;

    for (exvector::const_iterator i=children.begin(); i!=children.end(); ++i)
        if (ex_to<symmetry>(*i).has_nonsymmetric())
            return true;

    return false;
}

bool symmetry::has_cyclic() const
{
    if (type == cyclic)
        return true;

    for (exvector::const_iterator i=children.begin(); i!=children.end(); ++i)
        if (ex_to<symmetry>(*i).has_cyclic())
            return true;

    return false;
}

symmetry &symmetry::add(const symmetry &c)
{
    // All children must have the same number of indices
    if (type != none && !children.empty()) {
        GINAC_ASSERT(is_exactly_a<symmetry>(children[0]));
        if (ex_to<symmetry>(children[0]).indices.size() != c.indices.size())
            throw (std::logic_error("symmetry:add(): children must have same number of indices"));
    }

    // Compute union of indices and check whether the two sets are disjoint
    std::set<unsigned> un;
    set_union(indices.begin(), indices.end(), c.indices.begin(), c.indices.end(), inserter(un, un.begin()));
    if (un.size() != indices.size() + c.indices.size())
        throw (std::logic_error("symmetry::add(): the same index appears in more than one child"));

    // Set new index set
    indices.swap(un);

    // Add child node
    children.push_back(c);
    return *this;
}

void symmetry::validate(unsigned n)
{
    if (indices.upper_bound(n - 1) != indices.end())
        throw (std::range_error("symmetry::verify(): index values are out of range"));
    if (type != none && indices.empty()) {
        for (unsigned i=0; i<n; i++)
            add(i);
    }
}

// global functions

static const symmetry & index0()
{
    static ex s = (new symmetry(0))->setflag(status_flags::dynallocated);
    return ex_to<symmetry>(s);
}

static const symmetry & index1()
{
    static ex s = (new symmetry(1))->setflag(status_flags::dynallocated);
    return ex_to<symmetry>(s);
}

static const symmetry & index2()
{
    static ex s = (new symmetry(2))->setflag(status_flags::dynallocated);
    return ex_to<symmetry>(s);
}

static const symmetry & index3()
{
    static ex s = (new symmetry(3))->setflag(status_flags::dynallocated);
    return ex_to<symmetry>(s);
}

const symmetry & not_symmetric()
{
    static ex s = (new symmetry)->setflag(status_flags::dynallocated);
    return ex_to<symmetry>(s);
}

const symmetry & symmetric2()
{
    static ex s = (new symmetry(symmetry::symmetric, index0(), index1()))->setflag(status_flags::dynallocated);
    return ex_to<symmetry>(s);
}

const symmetry & symmetric3()
{
    static ex s = (new symmetry(symmetry::symmetric, index0(), index1()))->add(index2()).setflag(status_flags::dynallocated);
    return ex_to<symmetry>(s);
}

const symmetry & symmetric4()
{
    static ex s = (new symmetry(symmetry::symmetric, index0(), index1()))->add(index2()).add(index3()).setflag(status_flags::dynallocated);
    return ex_to<symmetry>(s);
}

const symmetry & antisymmetric2()
{
    static ex s = (new symmetry(symmetry::antisymmetric, index0(), index1()))->setflag(status_flags::dynallocated);
    return ex_to<symmetry>(s);
}

const symmetry & antisymmetric3()
{
    static ex s = (new symmetry(symmetry::antisymmetric, index0(), index1()))->add(index2()).setflag(status_flags::dynallocated);
    return ex_to<symmetry>(s);
}

const symmetry & antisymmetric4()
{
    static ex s = (new symmetry(symmetry::antisymmetric, index0(), index1()))->add(index2()).add(index3()).setflag(status_flags::dynallocated);
    return ex_to<symmetry>(s);
}

class sy_is_less : public std::binary_function<ex, ex, bool> {
    exvector::iterator v;

public:
    sy_is_less(exvector::iterator v_) : v(v_) {}

    bool operator() (const ex &lh, const ex &rh) const
    {
        GINAC_ASSERT(is_exactly_a<symmetry>(lh));
        GINAC_ASSERT(is_exactly_a<symmetry>(rh));
        GINAC_ASSERT(ex_to<symmetry>(lh).indices.size() == ex_to<symmetry>(rh).indices.size());
        std::set<unsigned>::const_iterator ait = ex_to<symmetry>(lh).indices.begin(), aitend = ex_to<symmetry>(lh).indices.end(), bit = ex_to<symmetry>(rh).indices.begin();
        while (ait != aitend) {
            int cmpval = v[*ait].compare(v[*bit]);
            if (cmpval < 0)
                return true;
            else if (cmpval > 0)
                return false;
            ++ait; ++bit;
        }
        return false;
    }
};

class sy_swap : public std::binary_function<ex, ex, void> {
    exvector::iterator v;

public:
    bool &swapped;

    sy_swap(exvector::iterator v_, bool &s) : v(v_), swapped(s) {}

    void operator() (const ex &lh, const ex &rh)
    {
        GINAC_ASSERT(is_exactly_a<symmetry>(lh));
        GINAC_ASSERT(is_exactly_a<symmetry>(rh));
        GINAC_ASSERT(ex_to<symmetry>(lh).indices.size() == ex_to<symmetry>(rh).indices.size());
        std::set<unsigned>::const_iterator ait = ex_to<symmetry>(lh).indices.begin(), aitend = ex_to<symmetry>(lh).indices.end(), bit = ex_to<symmetry>(rh).indices.begin();
        while (ait != aitend) {
            v[*ait].swap(v[*bit]);
            ++ait; ++bit;
        }
        swapped = true;
    }
};

int canonicalize(exvector::iterator v, const symmetry &symm)
{
    // Less than two elements? Then do nothing
    if (symm.indices.size() < 2)
        return std::numeric_limits<int>::max();

    // Canonicalize children first
    bool something_changed = false;
    int sign = 1;
    exvector::const_iterator first = symm.children.begin(), last = symm.children.end();
    while (first != last) {
        GINAC_ASSERT(is_exactly_a<symmetry>(*first));
        int child_sign = canonicalize(v, ex_to<symmetry>(*first));
        if (child_sign == 0)
            return 0;
        if (child_sign != std::numeric_limits<int>::max()) {
            something_changed = true;
            sign *= child_sign;
        }
        first++;
    }

    // Now reorder the children
    first = symm.children.begin();
    switch (symm.type) {
        case symmetry::symmetric:
            // Sort the children in ascending order
            shaker_sort(first, last, sy_is_less(v), sy_swap(v, something_changed));
            break;
        case symmetry::antisymmetric:
            // Sort the children in ascending order, keeping track of the signum
            sign *= permutation_sign(first, last, sy_is_less(v), sy_swap(v, something_changed));
            if (sign == 0)
                return 0;
            break;
        case symmetry::cyclic:
            // Permute the smallest child to the front
            cyclic_permutation(first, last, min_element(first, last, sy_is_less(v)), sy_swap(v, something_changed));
            break;
        default:
            break;
    }
    return something_changed ? sign : std::numeric_limits<int>::max();
}


// Symmetrize/antisymmetrize over a vector of objects
static ex symm(const ex & e, exvector::const_iterator first, exvector::const_iterator last, bool asymmetric)
{
    // Need at least 2 objects for this operation
    unsigned num = last - first;
    if (num < 2)
        return e;

    // Transform object vector to a lst (for subs())
    lst orig_lst(first, last);

    // Create index vectors for permutation
    unsigned *iv = new unsigned[num], *iv2;
    for (unsigned i=0; i<num; i++)
        iv[i] = i;
    iv2 = (asymmetric ? new unsigned[num] : NULL);

    // Loop over all permutations (the first permutation, which is the
    // identity, is unrolled)
    exvector sum_v;
    sum_v.push_back(e);
    while (std::next_permutation(iv, iv + num)) {
        lst new_lst;
        for (unsigned i=0; i<num; i++)
            new_lst.append(orig_lst.op(iv[i]));
        ex term = e.subs(orig_lst, new_lst, subs_options::no_pattern|subs_options::no_index_renaming);
        if (asymmetric) {
            memcpy(iv2, iv, num * sizeof(unsigned));
            term *= permutation_sign(iv2, iv2 + num);
        }
        sum_v.push_back(term);
    }
    ex sum = (new add(sum_v))->setflag(status_flags::dynallocated);

    delete[] iv;
    delete[] iv2;

    return sum / factorial(numeric(num));
}

ex symmetrize(const ex & e, exvector::const_iterator first, exvector::const_iterator last)
{
    return symm(e, first, last, false);
}

ex antisymmetrize(const ex & e, exvector::const_iterator first, exvector::const_iterator last)
{
    return symm(e, first, last, true);
}

ex symmetrize_cyclic(const ex & e, exvector::const_iterator first, exvector::const_iterator last)
{
    // Need at least 2 objects for this operation
    unsigned num = last - first;
    if (num < 2)
        return e;

    // Transform object vector to a lst (for subs())
    lst orig_lst(first, last);
    lst new_lst = orig_lst;

    // Loop over all cyclic permutations (the first permutation, which is
    // the identity, is unrolled)
    ex sum = e;
    for (unsigned i=0; i<num-1; i++) {
        ex perm = new_lst.op(0);
        new_lst.remove_first().append(perm);
        sum += e.subs(orig_lst, new_lst, subs_options::no_pattern|subs_options::no_index_renaming);
    }
    return sum / num;
}

ex ex::symmetrize(const lst & l) const
{
    exvector v(l.begin(), l.end());
    return symm(*this, v.begin(), v.end(), false);
}

ex ex::antisymmetrize(const lst & l) const
{
    exvector v(l.begin(), l.end());
    return symm(*this, v.begin(), v.end(), true);
}

ex ex::symmetrize_cyclic(const lst & l) const
{
    exvector v(l.begin(), l.end());
    return GiNaC::symmetrize_cyclic(*this, v.begin(), v.end());
}

} // namespace GiNaC