#include <GTransformation.hpp>

Inheritance diagram for GQCP::GTransformation< _Scalar >:

Collaboration diagram for GQCP::GTransformation< _Scalar >:

Public Types
using	Scalar = _Scalar

Public Types inherited from GQCP::SimpleTransformation< _Scalar, GTransformation< _Scalar > >
using	Scalar = _Scalar

using	DerivedTransformation = GTransformation< _Scalar >

using	Self = SimpleTransformation< Scalar, DerivedTransformation >

using	JacobiRotationType = JacobiRotation

using	OrbitalRotationGeneratorType = typename OrbitalRotationGeneratorTraits< DerivedTransformation >::OrbitalRotationGenerators

Public Types inherited from GQCP::BasisTransformable< Type >
using	Transformation = typename BasisTransformableTraits< Type >::Transformation

Public Types inherited from GQCP::JacobiRotatable< T >
using	JacobiRotationType = typename JacobiRotatableTraits< T >::JacobiRotationType

Public Member Functions
	GTransformation (const SquareMatrix< Scalar > &T)

	GTransformation (const SquareMatrix< Scalar > &T, const size_t K_alpha, const size_t K_beta)

MatrixX< Scalar >	alpha () const

MatrixX< Scalar >	beta () const

MatrixX< Scalar >	component (const Spin sigma) const

Public Member Functions inherited from GQCP::SimpleTransformation< _Scalar, GTransformation< _Scalar > >
	SimpleTransformation (const SquareMatrix< Scalar > &T)

	SimpleTransformation (const OrbitalRotationGeneratorType &kappa)

size_t	numberOfOrbitals () const

size_t	dimension () const

const SquareMatrix< Scalar > &	matrix () const

DerivedTransformation	adjoint () const

DerivedTransformation	inverse () const

bool	isUnitary (const double threshold=1.0e-12) const

DerivedTransformation	transformed (const DerivedTransformation &T) const override

DerivedTransformation	rotated (const JacobiRotationType &jacobi_rotation) const override

Public Member Functions inherited from GQCP::BasisTransformable< Type >
virtual Type	transformed (const Transformation &T) const =0

virtual void	transform (const Transformation &T)

virtual Type	rotated (const Transformation &U) const

void	rotate (const Transformation &U)

Public Member Functions inherited from GQCP::JacobiRotatable< T >
virtual T	rotated (const JacobiRotationType &jacobi_rotation) const =0

void	rotate (const JacobiRotationType &jacobi_rotation)

Static Public Member Functions
static GTransformation< Scalar >	FromRestricted (const RTransformation< Scalar > &r_transformation)

static GTransformation< Scalar >	FromUnrestricted (const UTransformation< Scalar > &u_transformation)

static GTransformation< Scalar >	Identity (const size_t K_alpha, const size_t K_beta)

Static Public Member Functions inherited from GQCP::SimpleTransformation< _Scalar, GTransformation< _Scalar > >
static DerivedTransformation	FromJacobi (const JacobiRotation &jacobi_rotation, const size_t dim)

static DerivedTransformation	Identity (const size_t dim)

static DerivedTransformation	Random (const size_t dim)

static DerivedTransformation	RandomUnitary (const size_t dim)

static DerivedTransformation	Zero (const size_t dim)

Additional Inherited Members
Protected Attributes inherited from GQCP::SimpleTransformation< _Scalar, GTransformation< _Scalar > >
SquareMatrix< Scalar >	T

Detailed Description

template<typename _Scalar>
class GQCP::GTransformation< _Scalar >

A 'general' basis transformation, i.e. a general, full-spinor basis transformation where the transformation mixes the alpha- and beta components of the two-component spinors.

In general, we adopt the convention outlined in (https://gqcg-res.github.io/knowdes/spinor-transformations.html), where the new orbitals' coefficients can be found in the respective column of the related transformation matrix.

Template Parameters

_Scalar The scalar type used for a transformation coefficient: real or complex.

Member Typedef Documentation

◆ Scalar

template<typename _Scalar >

using GQCP::GTransformation< _Scalar >::Scalar = _Scalar

Constructor & Destructor Documentation

◆ GTransformation() [1/2]

template<typename _Scalar >

GQCP::GTransformation< _Scalar >::GTransformation ( const SquareMatrix< Scalar > & T )

inline

Construct a GTransformation from the transformation matrix that it encapsulates.

Parameters

T	The transformation matrix that collects the expansion coefficients of the new basis (vectors) in the old basis as columns.

◆ GTransformation() [2/2]

template<typename _Scalar >

GQCP::GTransformation< _Scalar >::GTransformation	(	const SquareMatrix< Scalar > &	T,
		const size_t	K_alpha,
		const size_t	K_beta
	)

inline

Construct a GTransformation from the transformation matrix that it encapsulates, where the number of basis functions used for the expansion of the alpha components may differ from the number of basis functions for the beta components.

Parameters

T	The transformation matrix that collects the expansion coefficients of the new basis (vectors) in the old basis as columns.
K_alpha	The number of basis functions that are used for the expansion of the alpha components.
K_beta	The number of basis functions that are used for the expansion of the beta components.

Member Function Documentation

◆ alpha()

template<typename _Scalar >

MatrixX< Scalar > GQCP::GTransformation< _Scalar >::alpha ( ) const

inline

Returns: The part of the general transformation matrix that describes the expansion coefficients of the alpha components of the spinors.

◆ beta()

template<typename _Scalar >

MatrixX< Scalar > GQCP::GTransformation< _Scalar >::beta ( ) const

inline

Returns: The part of the general transformation matrix that describes the expansion coefficients of the beta components of the spinors.

◆ component()

template<typename _Scalar >

MatrixX< Scalar > GQCP::GTransformation< _Scalar >::component ( const Spin sigma ) const

inline

Parameters

sigma Alpha or beta.

Returns: The part of the general transformation that describes the spinors of the requested component.

◆ FromRestricted()

template<typename _Scalar >

static GTransformation< Scalar > GQCP::GTransformation< _Scalar >::FromRestricted ( const RTransformation< Scalar > & r_transformation )

inlinestatic

Convert an RTransformation into its generalized counterpart.

Parameters

r_transformation The restricted transformation.

Returns: The GTransformation that corresponds to the RTransformation.

◆ FromUnrestricted()

template<typename _Scalar >

static GTransformation< Scalar > GQCP::GTransformation< _Scalar >::FromUnrestricted ( const UTransformation< Scalar > & u_transformation )

inlinestatic

Convert an UTransformation into its generalized counterpart.

Parameters

u_transformation The unrestricted transformation.

Returns: The GTransformation that corresponds to the UTransformation.

◆ Identity()

template<typename _Scalar >

static GTransformation< Scalar > GQCP::GTransformation< _Scalar >::Identity	(	const size_t	K_alpha,
		const size_t	K_beta
	)

inlinestatic

Construct an identity transformation related to different number of alpha and beta atomic spinors.

The documentation for this class was generated from the following file:

/__w/GQCP/GQCP/gqcp/include/Basis/Transformations/GTransformation.hpp

Public Types

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Scalar

Constructor & Destructor Documentation

◆ GTransformation() [1/2]

◆ GTransformation() [2/2]

Member Function Documentation

◆ alpha()

◆ beta()

◆ component()

◆ FromRestricted()

◆ FromUnrestricted()

◆ Identity()