su2.h File Reference

#include "matrix.h"
#include "complex"

Go to the source code of this file.

Namespaces

namespace su2

Typedefs

typedef std::complex< double > cdouble

Functions

void mat_to_cart3 (const Matrix< cdouble > &U, double *c)

Calculate cartesian form of the 3D Bloch vector for U.

void cart3_to_mat (double *c, Matrix< cdouble > &U)

Construct a matrix U from the 3D cartesian Bloch vector.

void mat_to_polar3 (const Matrix< cdouble > &U, double *p)

Calculate polar form of the 3D Bloch vector for U.

void polar3_to_mat (double *p, Matrix< cdouble > &U)

Construct a matrix U from the 3D polar Bloch vector.

void polar_to_cart3 (double *p, double *c)

Convert a polar 3D vector to a cartesian 3D vector.

void cart_to_polar3 (double *c, double *p)

Convert a cartesian 3D vector to a polar 3D vector.

void x_factor (double *z, double *x, double *y)

Given a 3D cartesian vector z, find vectors x,y s.t. $z = x \times y$ .

void mat_to_cart4 (const Matrix< cdouble > &U, double *a)

Calculate cartesian form of the 4D unit vector for U.

void cart4_to_mat (double *a, Matrix< cdouble > &U)

Construct a matrix U from the 4D cartesian unit vector.

void mat_to_polar4 (const Matrix< cdouble > &, double *)

Calculate the polar form of the 4D unit vector for U.

void polar4_to_mat (double *, Matrix< cdouble > &)

Construct a matrix U from the 4D polar unit vector.

void polar_to_cart4 (double *, double *)

Convert a polar form 4D vector to cartesian form.

void cart_to_polar4 (double *, double *)

Convert a cartesian form 4D vector to polar form.

void polar_to_cart4 (polar &p, double *r)

Legacy conversion from a 4D polar struct to cartesian form.

void polar4_to_mat (polar &, Matrix< cdouble > &)

Legacy conversion from a 4D cartesian vector to a polar struct.

void eig_vals (Matrix< cdouble > &U, cdouble *evals)

Quick and dirty calculation of the eigenvalues of an SU(2) matrix.

void eig_vecs (Matrix< cdouble > &U, cdouble *evecs)

Quick and dirty calculation of the eigenvectors of an SU(2) matrix.

double trace_dist (const Matrix< cdouble > &U, const Matrix< cdouble > &V)

Trace distance between SU(2) matrices U,V.

double trace_dist (const Matrix< cdouble > &U, double *coord4)

Trace distance between SU(2) matrices U,V.

double proj_trace_dist (const Matrix< cdouble > &U, const Matrix< cdouble > &V)

'Projective' trace distance between SU(2) matrices U,V

double proj_trace_dist (const Matrix< cdouble > &U, double *coord4)

'Projective' trace distance between SU(2) matrices U,V

void group_factor (const Matrix< cdouble > &U, Matrix< cdouble > &V, Matrix< cdouble > &W)

Find 'balanced' V,W in SU(2) such that U = [V,W].

void x_group_factor (const Matrix< cdouble > &, Matrix< cdouble > &, Matrix< cdouble > &)

'Balanced' group commutator decomposition for U a rotation about the x-axis

void similarity_matrix (const Matrix< cdouble > &V, Matrix< cdouble > &W, Matrix< cdouble > &)

Find an SU(2) matrix S such that $V = S W S^\dagger$ .

double norm (double *v, int n)

Norm of a real vector v of length n.

Typedef Documentation

typedef std::complex<double> cdouble

Examples:
example.cpp.

Function Documentation

void su2::cart3_to_mat ( double * c,

Matrix< cdouble > & U

)

Construct a matrix U from the 3D cartesian Bloch vector.

void su2::cart4_to_mat ( double * a,

Matrix< cdouble > & U

)

Construct a matrix U from the 4D cartesian unit vector.

Examples:
example.cpp.

void su2::cart_to_polar3 ( double * c,

double * p

)

Convert a cartesian 3D vector to a polar 3D vector.

void su2::cart_to_polar4 ( double * ,

double *

)

Convert a cartesian form 4D vector to polar form.

void su2::eig_vals ( Matrix< cdouble > & U,

cdouble * evals

)

Quick and dirty calculation of the eigenvalues of an SU(2) matrix.

void su2::eig_vecs ( Matrix< cdouble > & U,

cdouble * evecs

)

Quick and dirty calculation of the eigenvectors of an SU(2) matrix.

void su2::group_factor ( const Matrix< cdouble > & U,

Matrix< cdouble > & V,

Matrix< cdouble > & W

)

Find 'balanced' V,W in SU(2) such that U = [V,W].

void su2::mat_to_cart3 ( const Matrix< cdouble > & U,

double * c

)

Calculate cartesian form of the 3D Bloch vector for U.

void su2::mat_to_cart4 ( const Matrix< cdouble > & U,

double * a

)

Calculate cartesian form of the 4D unit vector for U.

void su2::mat_to_polar3 ( const Matrix< cdouble > & U,

double * p

)

Calculate polar form of the 3D Bloch vector for U.

void su2::mat_to_polar4 ( const Matrix< cdouble > & ,

double *

)

Calculate the polar form of the 4D unit vector for U.

double su2::norm ( double * v,

int n

)

Norm of a real vector v of length n.

void su2::polar3_to_mat ( double * p,

Matrix< cdouble > & U

)

Construct a matrix U from the 3D polar Bloch vector.

void su2::polar4_to_mat ( polar & ,

Matrix< cdouble > &

)

Legacy conversion from a 4D cartesian vector to a polar struct.

void su2::polar4_to_mat ( double * ,

Matrix< cdouble > &

)

Construct a matrix U from the 4D polar unit vector.

void su2::polar_to_cart3 ( double * p,

double * c

)

Convert a polar 3D vector to a cartesian 3D vector.

void su2::polar_to_cart4 ( polar & p,

double * r

)

Legacy conversion from a 4D polar struct to cartesian form.

void su2::polar_to_cart4 ( double * ,

double *

)

Convert a polar form 4D vector to cartesian form.

double su2::proj_trace_dist ( const Matrix< cdouble > & U,

double * coord4

)

'Projective' trace distance between SU(2) matrices U,V
V in this case is given by its 4D cartesian coordinates

double su2::proj_trace_dist ( const Matrix< cdouble > & U,

const Matrix< cdouble > & V

)

'Projective' trace distance between SU(2) matrices U,V

Examples:
example.cpp.

void su2::similarity_matrix ( const Matrix< cdouble > & V,

Matrix< cdouble > & W,

Matrix< cdouble > &

)

Find an SU(2) matrix S such that $V = S W S^\dagger$ .
(or it might be the other way around)

double su2::trace_dist ( const Matrix< cdouble > & U,

double * coord4

)

Trace distance between SU(2) matrices U,V.
Except V in this case is given by its 4D cartesian coordinates

double su2::trace_dist ( const Matrix< cdouble > & U,

const Matrix< cdouble > & V

)

Trace distance between SU(2) matrices U,V.

void su2::x_factor ( double * z,

double * x,

double * y

)

Given a 3D cartesian vector z, find vectors x,y s.t. $z = x \times y$ .

void su2::x_group_factor ( const Matrix< cdouble > & ,

Matrix< cdouble > & ,

Matrix< cdouble > &

)

'Balanced' group commutator decomposition for U a rotation about the x-axis

Generated on Sun Jul 10 21:57:13 2005 by

1.4.1


Namespaces
namespace	su2
Typedefs
typedef std::complex< double >	cdouble
Functions
void	mat_to_cart3 (const Matrix< cdouble > &U, double *c)
	Calculate cartesian form of the 3D Bloch vector for U.
void	cart3_to_mat (double *c, Matrix< cdouble > &U)
	Construct a matrix U from the 3D cartesian Bloch vector.
void	mat_to_polar3 (const Matrix< cdouble > &U, double *p)
	Calculate polar form of the 3D Bloch vector for U.
void	polar3_to_mat (double *p, Matrix< cdouble > &U)
	Construct a matrix U from the 3D polar Bloch vector.
void	polar_to_cart3 (double p, double c)
	Convert a polar 3D vector to a cartesian 3D vector.
void	cart_to_polar3 (double c, double p)
	Convert a cartesian 3D vector to a polar 3D vector.
void	x_factor (double z, double x, double *y)
	Given a 3D cartesian vector z, find vectors x,y s.t. $z = x \times y$ .
void	mat_to_cart4 (const Matrix< cdouble > &U, double *a)
	Calculate cartesian form of the 4D unit vector for U.
void	cart4_to_mat (double *a, Matrix< cdouble > &U)
	Construct a matrix U from the 4D cartesian unit vector.
void	mat_to_polar4 (const Matrix< cdouble > &, double *)
	Calculate the polar form of the 4D unit vector for U.
void	polar4_to_mat (double *, Matrix< cdouble > &)
	Construct a matrix U from the 4D polar unit vector.
void	polar_to_cart4 (double , double )
	Convert a polar form 4D vector to cartesian form.
void	cart_to_polar4 (double , double )
	Convert a cartesian form 4D vector to polar form.
void	polar_to_cart4 (polar &p, double *r)
	Legacy conversion from a 4D polar struct to cartesian form.
void	polar4_to_mat (polar &, Matrix< cdouble > &)
	Legacy conversion from a 4D cartesian vector to a polar struct.
void	eig_vals (Matrix< cdouble > &U, cdouble *evals)
	Quick and dirty calculation of the eigenvalues of an SU(2) matrix.
void	eig_vecs (Matrix< cdouble > &U, cdouble *evecs)
	Quick and dirty calculation of the eigenvectors of an SU(2) matrix.
double	trace_dist (const Matrix< cdouble > &U, const Matrix< cdouble > &V)
	Trace distance between SU(2) matrices U,V.
double	trace_dist (const Matrix< cdouble > &U, double *coord4)
	Trace distance between SU(2) matrices U,V.
double	proj_trace_dist (const Matrix< cdouble > &U, const Matrix< cdouble > &V)
	'Projective' trace distance between SU(2) matrices U,V
double	proj_trace_dist (const Matrix< cdouble > &U, double *coord4)
	'Projective' trace distance between SU(2) matrices U,V
void	group_factor (const Matrix< cdouble > &U, Matrix< cdouble > &V, Matrix< cdouble > &W)
	Find 'balanced' V,W in SU(2) such that U = [V,W].
void	x_group_factor (const Matrix< cdouble > &, Matrix< cdouble > &, Matrix< cdouble > &)
	'Balanced' group commutator decomposition for U a rotation about the x-axis
void	similarity_matrix (const Matrix< cdouble > &V, Matrix< cdouble > &W, Matrix< cdouble > &)
	Find an SU(2) matrix S such that $V = S W S^\dagger$ .
double	norm (double *v, int n)
	Norm of a real vector v of length n.