Real Dirac Matrix class. More...

#include <rdm.h>

Public Types
typedef Value_type	value_type
	Type of variables. More...

typedef Size_type	size_type
	Type for specifying sizes. More...

typedef boost::numeric::ublas::compressed_matrix < value_type, boost::numeric::ublas::row_major >	sparse_matrix_type
	Sparse matrix type definition. More...

typedef boost::numeric::ublas::matrix < value_type >	matrix_type
	Dense matrix type definition. More...

typedef boost::numeric::ublas::vector < value_type >	vector_type
	Dense vector type definition. More...

Public Member Functions
	RDM ()
	Default constructor (sets only NumOfRDMs and DimOfRDMs) More...

sparse_matrix_type	getRDM (short)
	Returns the i-th Real Dirac matrix. More...

vector_type	decompose (const matrix_type &)
	Decomposes a real-valued 4x4 matrix into a linear combination and returns a vector containing the coefficients. More...

matrix_type	combine (const vector_type &)
	Takes a vector of coefficients, evaluates the linear combination of RDMs with these coefficients and returns a 4x4 matrix. More...

void	diagonalize (matrix_type &, sparse_matrix_type &, sparse_matrix_type &)
	Brings a 4x4 symplex matrix into Hamilton form and computes the transformation matrix and its inverse. More...

matrix_type	symplex (const matrix_type &)
	Returns the symplex part of a 4x4 real-valued matrix. More...

matrix_type	cosymplex (const matrix_type &)
	Returns the cosymplex part of a 4x4 real-valued matrix. More...

Public Attributes
short	NumOfRDMs
	The number of real Dirac matrices. More...

short	DimOfRDMs
	The matrix dimension (4x4) More...

Private Member Functions
void	transform (matrix_type &, short, value_type, sparse_matrix_type &, sparse_matrix_type &)
	Applies a rotation to the matrix M by a given angle. More...

Detailed Description

template<typename Value_type, typename Size_type>
class RDM< Value_type, Size_type >

Real Dirac Matrix class.

Definition at line 27 of file rdm.h.

Member Typedef Documentation

template<typename Value_type , typename Size_type >

typedef boost::numeric::ublas::matrix<value_type> RDM< Value_type, Size_type >::matrix_type

Dense matrix type definition.

Definition at line 37 of file rdm.h.

template<typename Value_type , typename Size_type >

typedef Size_type RDM< Value_type, Size_type >::size_type

Type for specifying sizes.

Definition at line 33 of file rdm.h.

template<typename Value_type , typename Size_type >

typedef boost::numeric::ublas::compressed_matrix<value_type,boost::numeric::ublas::row_major> RDM< Value_type, Size_type >::sparse_matrix_type

Sparse matrix type definition.

Definition at line 35 of file rdm.h.

template<typename Value_type , typename Size_type >

typedef Value_type RDM< Value_type, Size_type >::value_type

Type of variables.

Definition at line 31 of file rdm.h.

template<typename Value_type , typename Size_type >

typedef boost::numeric::ublas::vector<value_type> RDM< Value_type, Size_type >::vector_type

Dense vector type definition.

Definition at line 39 of file rdm.h.

Constructor & Destructor Documentation

template<typename Value_type , typename Size_type >

RDM< Value_type, Size_type >::RDM ( )

Default constructor (sets only NumOfRDMs and DimOfRDMs)

Definition at line 104 of file rdm.h.

Member Function Documentation

template<typename Value_type , typename Size_type >

RDM< Value_type, Size_type >::matrix_type RDM< Value_type, Size_type >::combine ( const vector_type & coeffs )

Takes a vector of coefficients, evaluates the linear combination of RDMs with these coefficients and returns a 4x4 matrix.

Parameters

coeffs is a vector of coefficients (at most length NumOfRDMs)

Definition at line 161 of file rdm.h.

template<typename Value_type , typename Size_type >

RDM< Value_type, Size_type >::matrix_type RDM< Value_type, Size_type >::cosymplex ( const matrix_type & M )

Returns the cosymplex part of a 4x4 real-valued matrix.

Parameters

M	4x4 real-valued matrix

Definition at line 271 of file rdm.h.

template<typename Value_type , typename Size_type >

RDM< Value_type, Size_type >::vector_type RDM< Value_type, Size_type >::decompose ( const matrix_type & M )

Decomposes a real-valued 4x4 matrix into a linear combination and returns a vector containing the coefficients.

Parameters

M	an arbitrary real-valued 4x4 matrix

Definition at line 132 of file rdm.h.

References prod(), and matt_boost::trace().

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template<typename Value_type , typename Size_type >

void RDM< Value_type, Size_type >::diagonalize	(	matrix_type &	Ms,
		sparse_matrix_type &	R,
		sparse_matrix_type &	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 176 of file rdm.h.

References atan2(), matt_boost::cross_prod(), fabs(), prod(), Attrib::Distribution::R, and matt_boost::trace().

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template<typename Value_type , typename Size_type >

RDM< Value_type, Size_type >::sparse_matrix_type RDM< Value_type, Size_type >::getRDM ( short i )

Returns the i-th Real Dirac matrix.

Parameters

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

Definition at line 107 of file rdm.h.

template<typename Value_type , typename Size_type >

RDM< Value_type, Size_type >::matrix_type RDM< Value_type, Size_type >::symplex ( const matrix_type & M )

Returns the symplex part of a 4x4 real-valued matrix.

Parameters

M	4x4 real-valued matrix

Definition at line 261 of file rdm.h.

template<typename Value_type , typename Size_type >

void RDM< Value_type, Size_type >::transform	(	matrix_type &	M,
		short	i,
		value_type	phi,
		sparse_matrix_type &	Rtot,
		sparse_matrix_type &	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 284 of file rdm.h.

References cos(), cosh(), prod(), Attrib::Distribution::R, sin(), and sinh().

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Member Data Documentation

template<typename Value_type , typename Size_type >

short RDM< Value_type, Size_type >::DimOfRDMs

The matrix dimension (4x4)

Definition at line 85 of file rdm.h.

template<typename Value_type , typename Size_type >

short RDM< Value_type, Size_type >::NumOfRDMs

The number of real Dirac matrices.

Definition at line 83 of file rdm.h.

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

src/Distribution/rdm.h

Public Types

Public Member Functions

Public Attributes

Private Member Functions

Detailed Description

template<typename Value_type, typename Size_type> class RDM< Value_type, Size_type >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<typename Value_type, typename Size_type>
class RDM< Value_type, Size_type >