/usr/include/TiledArray/symm/representation.h is in libtiledarray-dev 0.6.0-5.
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* This file is a part of TiledArray.
* Copyright (C) 2015 Virginia Tech
*
* 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 3 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, see <http://www.gnu.org/licenses/>.
*
* Edward F Valeev
* Department of Chemistry, Virginia Tech
*
* representation.h
* May 13, 2015
*
*/
#ifndef TILEDARRAY_SYMM_REPRESENTATION_H__INCLUDED
#define TILEDARRAY_SYMM_REPRESENTATION_H__INCLUDED
#include <map>
#include <vector>
#include <memory>
#include <TiledArray/error.h>
namespace TiledArray {
namespace symmetry {
/// identity for group of objects of type T
template <typename T> T identity();
/// class Representation is a representation of Group in terms of Representatives (typically, (linear) operators)
/// \tparam Group class describing the group of symmetry transformations
/// \tparam Representative class describing the group representatives; in TiledArray these will
/// encode mathematical transformation of tiles under permutations, or symmetry transformations.
template <typename Group, typename Representative>
class Representation {
public:
using group_type = Group;
using element_type = typename Group::element_type;
using representative_type = Representative;
// Compiler generated functions
Representation() = delete;
Representation(const Representation&) = default;
Representation(Representation&&) = default;
Representation& operator=(const Representation&) = default;
Representation& operator=(Representation&&) = default;
/// Construct Representation from a set of {generator,operator} pairs construct operator representation of the permutation group
Representation(std::map<element_type,representative_type> generator_reps) :
generator_representatives_(std::move(generator_reps))
{
// N.B. this may mutate generator_reps, e.g. if it has an identity
init(generator_representatives_, element_representatives_);
}
/// the order of the representation = the order of the group
size_t order() const {
return element_representatives_.size();
}
/// constructs Group object from this
/// \note this redoes all the work that the constructor did
std::shared_ptr<group_type> group() const {
// extract generators and elements
std::vector<element_type> generators;
generators.reserve(generator_representatives_.size());
for(const auto& g_op_pair: generator_representatives_) {
generators.emplace_back(g_op_pair.first);
}
return std::make_shared<group_type>(std::move(generators));
}
const std::map<element_type,representative_type>& representatives() const {
return element_representatives_;
}
private:
std::shared_ptr<group_type> g_;
std::map<element_type,representative_type> generator_representatives_;
std::map<element_type,representative_type> element_representatives_;
/// uses generators to compute representatives for every element
static void init(std::map<element_type,representative_type>& generator_reps,
std::map<element_type,representative_type>& element_reps) {
// make sure identity is not among the generators
TA_ASSERT(generator_reps.end() ==
generator_reps.find(group_type::identity()));
// make element->operator map
// start with generator->operator map
element_reps = generator_reps;
// then add the identity element
element_reps[group_type::identity()] = identity<representative_type>();
// Generate the remaining elements in the group by multiplying by generators
// to keep track of elements already added make an extra vector
std::vector<element_type> elements;
for(const auto& eop: element_reps)
elements.push_back(eop.first);
for(size_t i = 0; i < elements.size(); ++i) {
const auto& e = elements[i];
const auto& e_op = element_reps[e];
for(const auto& g_op_pair: generator_reps) {
const auto& g = g_op_pair.first;
const auto& g_op = g_op_pair.second;
auto h = e * g;
if(element_reps.find(h) == element_reps.end()) {
auto h_op = e_op * g_op;
element_reps[h] = h_op;
elements.emplace_back(std::move(h));
}
}
}
} // init()
}; // class Representation
} // namespace symmetry
} // namespace TiledArray
#endif /* TILEDARRAY_SYMM_REPRESENTATION_H__INCLUDED */
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