UTransformation.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/RTransformation.hpp"
#include "Basis/Transformations/SpinResolvedBasisTransformable.hpp"
#include "Basis/Transformations/SpinResolvedJacobiRotatable.hpp"
#include "Basis/Transformations/UOrbitalRotationGenerators.hpp"
#include "Basis/Transformations/UTransformationComponent.hpp"
#include "QuantumChemical/SpinResolvedBase.hpp"
#include "Utilities/complex.hpp"
 
 
namespace GQCP {
 
 
/*
 *  MARK: UTransformation implementation
 */
 
template <typename _Scalar>
class UTransformation:
    public SpinResolvedBase<UTransformationComponent<_Scalar>, UTransformation<_Scalar>>,
    public SpinResolvedBasisTransformable<UTransformation<_Scalar>>,
    public SpinResolvedJacobiRotatable<UTransformation<_Scalar>> {
public:
    // The scalar type used for a transformation coefficient: real or complex.
    using Scalar = _Scalar;
 
    // The type of the transformation for which the basis transformation should be defined. A transformation should naturally be transformable with itself.
    using Transformation = UTransformation<Scalar>;
 
    // The type of 'this'.
    using Self = UTransformation<Scalar>;
 
    // The type component this spin resolved object is made of.
    using ComponentType = typename SpinResolvedBase<UTransformationComponent<Scalar>, Self>::Of;
 
 
public:
    /*
     *  MARK: Constructors
     */
 
    // Inherit `SpinResolvedBase`'s constructors.
    using SpinResolvedBase<UTransformationComponent<Scalar>, UTransformation<Scalar>>::SpinResolvedBase;
 
 
    /*
     *  MARK: Named constructors
     */
 
    static UTransformation<Scalar> FromRestricted(const RTransformation<Scalar>& T) {
 
        // Wrap the restricted transformation in the correct class and return the result.
        const UTransformationComponent<Scalar> T_component {T.matrix()};
        return UTransformation<Scalar>::FromEqual(T_component);
    }
 
 
    static UTransformation<Scalar> Identity(const size_t dim_alpha, const size_t dim_beta) {
 
        const auto T_alpha = UTransformationComponent<Scalar>::Identity(dim_alpha);
        const auto T_beta = UTransformationComponent<Scalar>::Identity(dim_beta);
 
        return UTransformation<Scalar> {T_alpha, T_beta};
    }
 
 
    static UTransformation<Scalar> Identity(const size_t dim) { return UTransformation<Scalar>::Identity(dim, dim); }
 
 
    static UTransformation<Scalar> Random(const size_t dim) {
 
        const auto T_alpha = UTransformationComponent<Scalar>::Random(dim);
        const auto T_beta = UTransformationComponent<Scalar>::Random(dim);
 
        return UTransformation<Scalar> {T_alpha, T_beta};
    }
 
 
    static UTransformation<Scalar> RandomUnitary(const size_t dim) {
 
        const auto T_alpha = UTransformationComponent<Scalar>::RandomUnitary(dim);
        const auto T_beta = UTransformationComponent<Scalar>::RandomUnitary(dim);
 
        return UTransformation<Scalar> {T_alpha, T_beta};
    }
 
 
    /*
     *  MARK: Linear algebraic operations
     */
 
    bool isUnitary(const double threshold) const { return this->alpha().isUnitary(threshold) && this->beta().isUnitary(threshold); }
 
 
    UTransformation<Scalar> inverse() const {
 
        auto result = *this;
 
        // The inverse of this compound transformation is the transformation where the alpha- and beta-transformations are inverted.
        result.alpha() = this->alpha().inverse();
        result.beta() = this->beta().inverse();
 
        return result;
    }
 
 
    // 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<UTransformation<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 = UTransformation<Scalar>;
};
 
 
/*
 *  MARK: JacobiRotatableTraits
 */
 
template <typename Scalar>
struct JacobiRotatableTraits<UTransformation<Scalar>> {
 
    // The type of Jacobi rotation for which the Jacobi rotation should be defined.
    using JacobiRotationType = UJacobiRotation;
};
 
 
/*
 *  MARK: OrbitalRotationGeneratorTraits
 */
 
template <typename Scalar>
struct OrbitalRotationGeneratorTraits<UTransformation<Scalar>> {
 
    // The type of orbital rotation generators associated with a `UTransformation`.
    using OrbitalRotationGenerators = UOrbitalRotationGenerators<Scalar>;
};
 
 
}  // namespace GQCP