SpinResolved1DM.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/SpinResolvedBasisTransformable.hpp"
#include "Basis/Transformations/SpinResolvedJacobiRotatable.hpp"
#include "Basis/Transformations/UTransformation.hpp"
#include "DensityMatrix/Orbital1DM.hpp"
#include "DensityMatrix/SpinDensity1DM.hpp"
#include "DensityMatrix/SpinResolved1DMComponent.hpp"
#include "Mathematical/Functions/VectorSpaceArithmetic.hpp"
#include "QuantumChemical/SpinResolved.hpp"
 
 
namespace GQCP {
 
 
template <typename _Scalar>
class SpinResolved1DM:
    public SpinResolvedBase<SpinResolved1DMComponent<_Scalar>, SpinResolved1DM<_Scalar>>,
    public SpinResolvedBasisTransformable<SpinResolved1DM<_Scalar>>,
    public SpinResolvedJacobiRotatable<SpinResolved1DM<_Scalar>>,
    public VectorSpaceArithmetic<SpinResolved1DM<_Scalar>, _Scalar> {
public:
    // The scalar type of one of the density matrix elements: real or complex.
    using Scalar = _Scalar;
 
    // The type of the transformation that is naturally related to a `SpinResolved1DM`.
    using Transformation = UTransformation<Scalar>;
 
    // The type of 'this'.
    using Self = SpinResolved1DM<Scalar>;
 
    // The type component this spin resolved object is made of.
    using ComponentType = typename SpinResolvedBase<SpinResolved1DMComponent<Scalar>, Self>::Of;
 
 
public:
    /*
     *  MARK: Constructors
     */
 
    // Inherit `SpinResolvedBase`'s constructors.
    using SpinResolvedBase<SpinResolved1DMComponent<_Scalar>, SpinResolved1DM<_Scalar>>::SpinResolvedBase;
 
 
    /*
     *  MARK: Named constructors
     */
 
    static SpinResolved1DM<Scalar> FromOrbital1DM(const Orbital1DM<Scalar>& D) {
 
        const SpinResolved1DMComponent<Scalar> D_half {(D / 2).matrix()};
        return SpinResolved1DM<Scalar>(D_half, D_half);
    }
 
 
    /*
     *  MARK: General information
     */
 
    double norm() const {
 
        // Determine the dimensions of the generalized, spin-blocked 1-DM.
        const auto K_alpha = this->alpha().numberOfOrbitals();
        const auto K_beta = this->beta().numberOfOrbitals();
        const auto M = K_alpha + K_beta;
 
        // The generalized 1-DM contains the alpha part in the top-left corner, and the beta part in the bottom right corner.
        SquareMatrix<Scalar> D_generalized = SquareMatrix<Scalar>::Zero(M);
        D_generalized.topLeftCorner(K_alpha, K_alpha) = this->alpha().matrix();
        D_generalized.bottomRightCorner(K_beta, K_beta) = this->beta().matrix();
 
        return D_generalized.norm();
    }
 
    size_t numberOfOrbitals(const Spin sigma) const { return this->component(sigma).numberOfOrbitals(); }
 
 
    /*
     *  MARK: Spin-related operations
     */
 
    SpinDensity1DM<Scalar> spinDensity() const {
        return SpinDensity1DM<Scalar> {(this->alpha() - this->beta()).matrix()};
    }
 
    Orbital1DM<Scalar> orbitalDensity() const {
        return Orbital1DM<Scalar> {(this->alpha() + this->beta()).matrix()};
    }
 
 
    /*
     *  MARK: Conforming to `VectorSpaceArithmetic`
     */
 
    Self& operator+=(const Self& rhs) override {
 
        // For addition, the alpha- and beta-parts should be added component-wise.
        this->alpha() += rhs.alpha();
        this->beta() += rhs.beta();
 
        return *this;
    }
 
    Self& operator*=(const Scalar& a) override {
 
        // For scalar multiplication, the alpha- and beta-parts should be multiplied with the scalar.
        this->alpha() *= a;
        this->beta() *= a;
 
        return *this;
    }
 
 
    // Since `rotate` and `rotated` are both defined in `SpinResolvedBasisTransformable` and `SpinResolvedJacobiRotatable`, we have to explicitly enable these methods here.
 
    // Allow the `rotate` method from `SpinResolvedBasisTransformable`, since there's also a `rotate` from `SpinResolvedJacobiRotatable`.
    using SpinResolvedBasisTransformable<Self>::rotate;
 
    // Allow the `rotated` method from `SpinResolvedBasisTransformable`, since there's also a `rotated` from `SpinResolvedJacobiRotatable`.
    using SpinResolvedBasisTransformable<Self>::rotated;
 
    // Allow the `rotate` method from `SpinResolvedJacobiRotatable`, since there's also a `rotate` from `SpinResolvedBasisTransformable`.
    using SpinResolvedJacobiRotatable<Self>::rotate;
 
    // Allow the `rotated` method from `SpinResolvedJacobiRotatable`, since there's also a `rotated` from `SpinResolvedBasisTransformable`.
    using SpinResolvedJacobiRotatable<Self>::rotated;
};
 
 
/*
 *  MARK: BasisTransformableTraits
 */
 
template <typename Scalar>
struct BasisTransformableTraits<SpinResolved1DM<Scalar>> {
 
    // The type of the transformation that is naturally related to a `SpinResolved1DM`.
    using Transformation = UTransformation<Scalar>;
};
 
 
/*
 *  MARK: JacobiRotatableTraits
 */
 
template <typename Scalar>
struct JacobiRotatableTraits<SpinResolved1DM<Scalar>> {
 
    // The type of Jacobi rotation for which the Jacobi rotation should be defined.
    using JacobiRotationType = UJacobiRotation;
};
 
 
}  // namespace GQCP