wignerd – WignerD

Module for computing the Wigner D-matrix and d-matrix (big D and little d; Fortran is case insensitive). The d-matrix can be calculated via the analytic expression, but this can overflow for large j due to the ratios of large factoials. The d-matrix can instead be calculated via sparse banded matrix diagonalization. See DOI: 10.1103PhysRevE.92.043307 for more details.

Interfaces

public interface wigner_d

Interface to access the routines to calculate the matrix D(α,β,γ) or d(β) based on the number of arguments

private module function wigner_big_D_jint(j, euler_alpha, euler_beta, euler_gamma, use_analytic) result(D)

Return the wigner D-matrix $D^j_{m',m}(\alpha, \beta, \gamma)$ for integer j

Arguments

Type	Intent	Optional		Name
integer,	intent(in)		::	j	The angular momentum $j$
real(kind=rp),	intent(in)		::	euler_alpha	The Euler angle α
real(kind=rp),	intent(in)		::	euler_beta	The Euler angle β
real(kind=rp),	intent(in)		::	euler_gamma	The Euler angle γ
logical,	intent(in),	optional	::	use_analytic	Force the use of the analytic expression to obtain $d^j(\beta)$ ?

Return Value complex(kind=rp), allocatable, (:,:)

The Wigner D-matrix $D^j(\alpha,\beta,\gamma)$

private module function wigner_big_D_jreal(j, euler_alpha, euler_beta, euler_gamma, use_analytic) result(D)

Return the wigner D-matrix $D^j_{m',m}(\alpha, \beta, \gamma)$ for real j

Arguments

Type	Intent	Optional		Name
real(kind=rp),	intent(in)		::	j	The angular momentum $j$
real(kind=rp),	intent(in)		::	euler_alpha	The Euler angle α
real(kind=rp),	intent(in)		::	euler_beta	The Euler angle β
real(kind=rp),	intent(in)		::	euler_gamma	The Euler angle γ
logical,	intent(in),	optional	::	use_analytic	Force the use of the analytic expression to obtain $d^j(\beta)$ ?

Return Value complex(kind=rp), allocatable, (:,:)

The Wigner D-matrix $D^j(\alpha,\beta,\gamma)$

private module function wigner_little_d_jint(j, euler_beta, use_analytic) result(d)

Return the Wigner d-matrix $d^j_{m'm}(\beta)$ for integer j

Arguments

Type	Intent	Optional		Name
integer,	intent(in)		::	j	The angular momentum $j$
real(kind=rp),	intent(in)		::	euler_beta	The euler angle β
logical,	intent(in),	optional	::	use_analytic	Force the use of the analytic expression to obtain $d^j(\beta)$ ?

Return Value real(kind=rp), allocatable, (:,:)

The matrix $d^j(\beta)$

private module function wigner_little_d_jreal(j, euler_beta, use_analytic) result(d)

Return the Wigner d-matrix $d^j_{m'm}(\beta)$ for real j

Arguments

Type	Intent	Optional		Name
real(kind=rp),	intent(in)		::	j	The angular momentum $j$
real(kind=rp),	intent(in)		::	euler_beta	The euler angle β
logical,	intent(in),	optional	::	use_analytic	Force the use of the analytic expression to obtain $d^j(\beta)$ ?

Return Value real(kind=rp), allocatable, (:,:)

The matrix $d^j(\beta)$

public interface wigner_big_D

Interface to access the routines to calculate D(α,β,γ) via matrix diagonalization or the analytic expression

private module function wigner_big_D_jint(j, euler_alpha, euler_beta, euler_gamma, use_analytic) result(D)

Return the wigner D-matrix $D^j_{m',m}(\alpha, \beta, \gamma)$ for integer j

Arguments

Type	Intent	Optional		Name
integer,	intent(in)		::	j	The angular momentum $j$
real(kind=rp),	intent(in)		::	euler_alpha	The Euler angle α
real(kind=rp),	intent(in)		::	euler_beta	The Euler angle β
real(kind=rp),	intent(in)		::	euler_gamma	The Euler angle γ
logical,	intent(in),	optional	::	use_analytic	Force the use of the analytic expression to obtain $d^j(\beta)$ ?

Return Value complex(kind=rp), allocatable, (:,:)

The Wigner D-matrix $D^j(\alpha,\beta,\gamma)$

private module function wigner_big_D_jreal(j, euler_alpha, euler_beta, euler_gamma, use_analytic) result(D)

Return the wigner D-matrix $D^j_{m',m}(\alpha, \beta, \gamma)$ for real j

Arguments

Type	Intent	Optional		Name
real(kind=rp),	intent(in)		::	j	The angular momentum $j$
real(kind=rp),	intent(in)		::	euler_alpha	The Euler angle α
real(kind=rp),	intent(in)		::	euler_beta	The Euler angle β
real(kind=rp),	intent(in)		::	euler_gamma	The Euler angle γ
logical,	intent(in),	optional	::	use_analytic	Force the use of the analytic expression to obtain $d^j(\beta)$ ?

Return Value complex(kind=rp), allocatable, (:,:)

The Wigner D-matrix $D^j(\alpha,\beta,\gamma)$

public interface wigner_little_d

Interface to access the routines to calculate d(β) via matrix diagonalization or the analytic expression

private module function wigner_little_d_jint(j, euler_beta, use_analytic) result(d)

Return the Wigner d-matrix $d^j_{m'm}(\beta)$ for integer j

Arguments

Type	Intent	Optional		Name
integer,	intent(in)		::	j	The angular momentum $j$
real(kind=rp),	intent(in)		::	euler_beta	The euler angle β
logical,	intent(in),	optional	::	use_analytic	Force the use of the analytic expression to obtain $d^j(\beta)$ ?

Return Value real(kind=rp), allocatable, (:,:)

The matrix $d^j(\beta)$

private module function wigner_little_d_jreal(j, euler_beta, use_analytic) result(d)

Return the Wigner d-matrix $d^j_{m'm}(\beta)$ for real j

Arguments

Type	Intent	Optional		Name
real(kind=rp),	intent(in)		::	j	The angular momentum $j$
real(kind=rp),	intent(in)		::	euler_beta	The euler angle β
logical,	intent(in),	optional	::	use_analytic	Force the use of the analytic expression to obtain $d^j(\beta)$ ?

Return Value real(kind=rp), allocatable, (:,:)

The matrix $d^j(\beta)$

wignerd Module

Contents

Interfaces

Interfaces

public interface wigner_d

private module function wigner_big_D_jint(j, euler_alpha, euler_beta, euler_gamma, use_analytic) result(D)

Arguments

Return Value complex(kind=rp), allocatable, (:,:)

private module function wigner_big_D_jreal(j, euler_alpha, euler_beta, euler_gamma, use_analytic) result(D)

Arguments

Return Value complex(kind=rp), allocatable, (:,:)

private module function wigner_little_d_jint(j, euler_beta, use_analytic) result(d)

Arguments

Return Value real(kind=rp), allocatable, (:,:)

private module function wigner_little_d_jreal(j, euler_beta, use_analytic) result(d)

Arguments

Return Value real(kind=rp), allocatable, (:,:)

public interface wigner_big_D

private module function wigner_big_D_jint(j, euler_alpha, euler_beta, euler_gamma, use_analytic) result(D)

Arguments

Return Value complex(kind=rp), allocatable, (:,:)

private module function wigner_big_D_jreal(j, euler_alpha, euler_beta, euler_gamma, use_analytic) result(D)

Arguments

Return Value complex(kind=rp), allocatable, (:,:)

public interface wigner_little_d

private module function wigner_little_d_jint(j, euler_beta, use_analytic) result(d)

Arguments

Return Value real(kind=rp), allocatable, (:,:)

private module function wigner_little_d_jreal(j, euler_beta, use_analytic) result(d)

Arguments

Return Value real(kind=rp), allocatable, (:,:)