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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 Valeev
* Department of Chemistry, Virginia Tech
*
* symm_repreentation.cpp
* September 12, 2015
*
*/
#include <chrono>
#include <iostream>
#include <random>
#include "TiledArray/symm/permutation_group.h"
#include "TiledArray/symm/representation.h"
#include "unit_test_config.h"
using TiledArray::symmetry::Permutation;
using TiledArray::symmetry::PermutationGroup;
using TiledArray::symmetry::Representation;
using TiledArray::symmetry::SymmetricGroup;
struct GroupRepresentationFixture {
GroupRepresentationFixture()
: generator(std::chrono::system_clock::now().time_since_epoch().count()),
uniform_int_distribution(0, 100) {}
~GroupRepresentationFixture() {}
template <size_t N>
std::array<int, N> random_index() {
std::array<int, N> result;
for (auto& value : result) value = uniform_int_distribution(generator);
return result;
}
// random number generation
std::default_random_engine generator;
std::uniform_int_distribution<int> uniform_int_distribution;
}; // GroupRepresentationFixture
struct U1_Operator {
enum operator_type {
_i = 0,
_n = 1,
_cc = 2,
_n_cc = 3
}; // bitwise encoding; multiplication = XOR
public:
U1_Operator(operator_type t = _i) : type_(t) {}
U1_Operator(const U1_Operator&) = default;
static U1_Operator identity;
static U1_Operator negate;
static U1_Operator complex_conjugate;
static U1_Operator negate_complex_conjugate;
// computes *this * rhs
U1_Operator operator*(const U1_Operator& rhs) const {
return U1_Operator(static_cast<operator_type>(type_ ^ rhs.type_));
}
// compares *this and rhs
bool operator==(const U1_Operator& rhs) const { return type_ == rhs.type_; }
private:
operator_type type_;
};
U1_Operator U1_Operator::identity = U1_Operator{_i};
U1_Operator U1_Operator::negate = U1_Operator{_n};
U1_Operator U1_Operator::complex_conjugate = U1_Operator{_cc};
U1_Operator U1_Operator::negate_complex_conjugate = U1_Operator{_n_cc};
namespace TiledArray {
namespace symmetry {
template <>
U1_Operator identity<U1_Operator>() {
return U1_Operator::identity;
}
} // namespace symmetry
} // namespace TiledArray
BOOST_FIXTURE_TEST_SUITE(symm_representation_suite, GroupRepresentationFixture)
BOOST_AUTO_TEST_CASE(constructor) {
// representation for permutation symmetry
// <01||23> = -<10||23> = -<01||32> = <10||32> = <23||01>* = -<23||10>* =
// -<32||01>* = <32||10>*
{
// generators are permutations (in cycle notation): (0,1), (2,3), and
// (0,2)(1,3) the corresponding operators are negate, negate, and
// compl_conjugate
std::map<Permutation, U1_Operator> genops;
genops[Permutation{1, 0, 2, 3}] = U1_Operator::negate;
genops[Permutation{0, 1, 3, 2}] = U1_Operator::negate;
genops[Permutation{2, 3, 0, 1}] = U1_Operator::complex_conjugate;
Representation<PermutationGroup, U1_Operator> rep(genops);
BOOST_CHECK_EQUAL(rep.order(), 8u);
for (const auto& g_op_pair : rep.representatives()) {
auto g = g_op_pair.first;
auto op = g_op_pair.second;
if (g == Permutation{0, 1, 2, 3})
BOOST_CHECK(op == U1_Operator::identity);
if (g == Permutation{1, 0, 2, 3}) BOOST_CHECK(op == U1_Operator::negate);
if (g == Permutation{0, 1, 3, 2}) BOOST_CHECK(op == U1_Operator::negate);
if (g == Permutation{1, 0, 3, 2})
BOOST_CHECK(op == U1_Operator::identity);
if (g == Permutation{2, 3, 0, 1})
BOOST_CHECK(op == U1_Operator::complex_conjugate);
if (g == Permutation{2, 3, 1, 0})
BOOST_CHECK(op == U1_Operator::negate_complex_conjugate);
if (g == Permutation{3, 2, 0, 1})
BOOST_CHECK(op == U1_Operator::negate_complex_conjugate);
if (g == Permutation{3, 2, 1, 0})
BOOST_CHECK(op == U1_Operator::complex_conjugate);
}
}
}
BOOST_AUTO_TEST_SUITE_END()
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