GTransformation.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 "Basis/Transformations/GOrbitalRotationGenerators.hpp"
#include "Basis/Transformations/SimpleTransformation.hpp"
#include "Basis/Transformations/UTransformation.hpp"
#include "QuantumChemical/SpinResolved.hpp"
 
 
namespace GQCP {
 
 
/*
 *  MARK: GTransformation implementation
 */
 
template <typename _Scalar>
class GTransformation:
    public SimpleTransformation<_Scalar, GTransformation<_Scalar>> {
public:
    // The scalar type used for a transformation coefficient: real or complex.
    using Scalar = _Scalar;
 
 
private:
    // The number of alpha and beta orbitals.
    SpinResolved<size_t> K;
 
 
public:
    /*
     *  MARK: Constructors
     */
 
    GTransformation(const SquareMatrix<Scalar>& T) :
        SimpleTransformation<_Scalar, GTransformation<_Scalar>>(T),
        K {SpinResolved<size_t>::FromEqual(T.dimension() / 2)} {}
 
 
    GTransformation(const SquareMatrix<Scalar>& T, const size_t K_alpha, const size_t K_beta) :
        SimpleTransformation<_Scalar, GTransformation<_Scalar>>(T),
        K {K_alpha, K_beta} {
 
        if (T.dimension() != K_alpha + K_beta) {
            throw std::invalid_argument("GTransformation(const SquareMatrix<Scalar>&, const size_t, const size_t): The given transformation matrix is not compatible with the number of given overbitals.");
        }
    }
 
 
    /*
     *  MARK: Named constructors
     */
 
    static GTransformation<Scalar> FromRestricted(const RTransformation<Scalar>& r_transformation) {
 
        const auto u_transformation = GQCP::UTransformation<Scalar>::FromRestricted(r_transformation);
        return GTransformation<Scalar>::FromUnrestricted(u_transformation);
    }
 
 
    static GTransformation<Scalar> FromUnrestricted(const UTransformation<Scalar>& u_transformation) {
 
        // The goal in this named constructor is to build up the general coefficient matrix (2K x 2K) from the unrestricted (K_sigma x K_sigma) ones.
        const auto K_alpha = u_transformation.alpha().numberOfOrbitals();
        const auto K_beta = u_transformation.beta().numberOfOrbitals();
        const auto M = K_alpha + K_beta;
 
        SquareMatrix<Scalar> T_general = SquareMatrix<Scalar>::Zero(M);
 
        //      alpha |  0
        //        0   | beta
        T_general.topLeftCorner(K_alpha, K_alpha) = u_transformation.alpha().matrix();
        T_general.bottomRightCorner(K_beta, K_beta) = u_transformation.beta().matrix();
 
        return GTransformation<Scalar> {T_general, K_alpha, K_beta};
    }
 
 
    static GTransformation<Scalar> Identity(const size_t K_alpha, const size_t K_beta) {
 
        return GTransformation<Scalar> {SquareMatrix<Scalar>::Identity(K_alpha + K_beta), K_alpha, K_beta};
    }
 
 
    /*
     *  MARK: Components
     */
 
    MatrixX<Scalar> alpha() const { return this->matrix().topRows(this->K.alpha()); }
 
    MatrixX<Scalar> beta() const { return this->matrix().bottomRows(this->K.beta()); }
 
    MatrixX<Scalar> component(const Spin sigma) const {
 
        switch (sigma) {
        case Spin::alpha: {
            return this->alpha();
            break;
        }
 
        case Spin::beta: {
            return this->beta();
            break;
        }
        }
    }
};
 
 
/*
 *  MARK: BasisTransformableTraits
 */
 
template <typename Scalar>
struct BasisTransformableTraits<GTransformation<Scalar>> {
 
    // The type of the transformation for which the basis transformation should be defined. A transformation matrix should naturally be transformable with itself.
    using Transformation = GTransformation<Scalar>;
};
 
 
/*
 *  MARK: JacobiRotatableTraits
 */
 
template <typename Scalar>
struct JacobiRotatableTraits<GTransformation<Scalar>> {
 
    // The type of Jacobi rotation for which the Jacobi rotation should be defined.
    using JacobiRotationType = JacobiRotation;
};
 
 
/*
 *  MARK: OrbitalRotationGeneratorTraits
 */
 
template <typename Scalar>
struct OrbitalRotationGeneratorTraits<GTransformation<Scalar>> {
 
    // The type of orbital rotation generators associated with an `GTransformation`.
    using OrbitalRotationGenerators = GOrbitalRotationGenerators<Scalar>;
};
 
 
}  // namespace GQCP