RealDiracMatrix Class Reference

#include <RealDiracMatrix.h>

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Public Types
typedef boost::numeric::ublas::compressed_matrix< double, boost::numeric::ublas::row_major >	sparse_matrix_t
	Sparse matrix type definition.
typedef boost::numeric::ublas::matrix< double >	matrix_t
	Dense matrix type definition.
typedef boost::numeric::ublas::vector< double, std::vector< double > >	vector_t
	Dense vector type definition.

Public Member Functions
	RealDiracMatrix ()
	Default constructor (sets only NumOfRDMs and DimOfRDMs).
sparse_matrix_t	getRDM (short)
void	diagonalize (matrix_t &, sparse_matrix_t &, sparse_matrix_t &)
sparse_matrix_t	diagonalize (matrix_t &)
matrix_t	symplex (const matrix_t &)

Private Member Functions
void	transform (matrix_t &, short, double, sparse_matrix_t &, sparse_matrix_t &)
void	transform (short, double, sparse_matrix_t &, sparse_matrix_t &)
void	update (matrix_t &sigma, short i, sparse_matrix_t &R, sparse_matrix_t &invR)

Detailed Description

Definition at line 31 of file RealDiracMatrix.h.

Member Typedef Documentation

matrix_t

typedef boost::numeric::ublas::matrix<double> RealDiracMatrix::matrix_t

Dense matrix type definition.

Definition at line 41 of file RealDiracMatrix.h.

sparse_matrix_t

typedef boost::numeric::ublas::compressed_matrix< double, boost::numeric::ublas::row_major > RealDiracMatrix::sparse_matrix_t

Sparse matrix type definition.

Definition at line 38 of file RealDiracMatrix.h.

vector_t

typedef boost::numeric::ublas::vector< double, std::vector<double> > RealDiracMatrix::vector_t

Dense vector type definition.

Definition at line 46 of file RealDiracMatrix.h.

Constructor & Destructor Documentation

RealDiracMatrix()

RealDiracMatrix::RealDiracMatrix

(

)

Default constructor (sets only NumOfRDMs and DimOfRDMs).

Definition at line 32 of file RealDiracMatrix.cpp.

Member Function Documentation

diagonalize() [1/2]

RealDiracMatrix::sparse_matrix_t RealDiracMatrix::diagonalize

(

matrix_t &

sigma

)

Diagonalizes (in-place) the 4x4 sigma matrix. This algorithm is Implemented according to https://arxiv.org/abs/1205.3601

Parameters

sigma

is the 4x4 sigma matrix

Returns

the inverse of the total transformation

Definition at line 149 of file RealDiracMatrix.cpp.

References matt_boost::gemmm(), getRDM(), and update().

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diagonalize() [2/2]

void RealDiracMatrix::diagonalize	(	matrix_t &	Ms,
		sparse_matrix_t &	R,
		sparse_matrix_t &	invR )

Brings a 4x4 symplex matrix into Hamilton form and computes the transformation matrix and its inverse

Parameters

Ms	is a 4x4 symplex matrix
R	is the 4x4 transformation matrix (gets computed)
invR	is the 4x4 inverse transformation matrix (gets computed)

Definition at line 62 of file RealDiracMatrix.cpp.

References matt_boost::cross_prod(), getRDM(), matt_boost::trace(), and transform().

Referenced by Distribution::generateMatchedGauss().

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getRDM()

RealDiracMatrix::sparse_matrix_t RealDiracMatrix::getRDM

(

short

i

)

Parameters

i	specifying the matrix (has to be in the range from 0 to 15)

Returns

the i-th Real Dirac matrix

Definition at line 35 of file RealDiracMatrix.cpp.

Referenced by diagonalize(), diagonalize(), symplex(), and transform().

symplex()

RealDiracMatrix::matrix_t RealDiracMatrix::symplex

(

const matrix_t &

M

)

Parameters

M	4x4 real-valued matrix

Returns

the symplex part of a 4x4 real-valued matrix

Definition at line 169 of file RealDiracMatrix.cpp.

References matt_boost::gemmm(), and getRDM().

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transform() [1/2]

void RealDiracMatrix::transform ( matrix_t & M, short i, double phi, sparse_matrix_t & Rtot, sparse_matrix_t & invRtot )

private

Applies a rotation to the matrix M by a given angle

Parameters

M	is the matrix to be transformed
i	is the i-th RDM used for transformation
phi	is the angle of rotation
Rtot	is a reference to the current transformation matrix
invRtot	is a reference to the inverse of the current transformation matrix

Definition at line 178 of file RealDiracMatrix.cpp.

References matt_boost::gemmm(), and transform().

Referenced by diagonalize(), transform(), and update().

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transform() [2/2]

void RealDiracMatrix::transform ( short i, double phi, sparse_matrix_t & R, sparse_matrix_t & invR )

private

Obtain transformation matrices.

Parameters

i	is the i-th RDM used for transformation
phi	is the angle of rotation
R	is a reference to the transformation matrix
invR	is a reference to the inverse of the transformation matrix

Definition at line 194 of file RealDiracMatrix.cpp.

References getRDM().

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update()

void RealDiracMatrix::update ( matrix_t & sigma, short i, sparse_matrix_t & R, sparse_matrix_t & invR )

private

Update quantites to decouple the sigma-matrix

Parameters

sigma	current state of sigma-matrix
i	is the i-th step
R	is a reference to the transformation matrix
invR	is a reference to the inverse of the transformation matrix

Definition at line 211 of file RealDiracMatrix.cpp.

References matt_boost::cross_prod(), and transform().

Referenced by diagonalize().

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

• RealDiracMatrix.h
• RealDiracMatrix.cpp