LeviCivitaTensor.hpp

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// This file is part of GQCG-GQCP.
//
// Copyright (C) 2017-2020  the GQCG developers
//
// GQCG-GQCP is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// GQCG-GQCP 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 Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with GQCG-GQCP.  If not, see <http://www.gnu.org/licenses/>.
 
#pragma once
 
 
#include "Mathematical/Representation/Tensor.hpp"
 
#include <unsupported/Eigen/CXX11/TensorSymmetry>
 
 
namespace GQCP {
 
 
template <typename _Scalar>
class LeviCivitaTensor {
public:
    // The scalar type of one of the elements of the tensor.
    using Scalar = _Scalar;
 
private:
    // The values of the Levi-Civita tensor.
    Tensor<Scalar, 3> epsilon;
 
public:
    /*
     *  MARK: Constructors
     */
 
    LeviCivitaTensor() {
 
        // Initialize a zero tensor.
        this->epsilon = Tensor<Scalar, 3>(3, 3, 3);
        this->epsilon.setZero();
 
 
        // Construct the antisymmetries of the Levi-Civita tensor and set its elements.
        Eigen::SGroup<Eigen::AntiSymmetry<0, 1>, Eigen::AntiSymmetry<1, 2>> symmetry;
        symmetry(this->epsilon, 0, 1, 2) = 1.0;
    }
 
 
    /*
     *  MARK: Element access
     */
 
    Scalar operator()(const size_t i, const size_t j, const size_t k) const { return this->epsilon(i, j, k); }
 
    size_t nonZeroIndex(const size_t i, const size_t j) const {
 
        if (i == j) {
            throw std::invalid_argument("LeviCivitaTensor::nonZeroIndex(const size_t, const size_t): The given indices cannot be equal.");
        }
 
        return 3 - (i + j);
        
    }
};
 
 
}  // namespace GQCP