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wigner.h File Reference

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Functions

double SO3_alpha (int k, int m, int l)
 Computes three-term recurrence coefficients $\alpha_l^{km}$ of Wigner-d functions.
double SO3_beta (int k, int m, int l)
 Computes three-term recurrence coefficients $\beta_l^{km}$ of Wigner-d functions.
double SO3_gamma (int k, int m, int l)
 Computes three-term recurrence coefficients $\gamma_l^{km}$ of Wigner-d functions.
void SO3_alpha_row (double *alpha, int N, int m, int n)
 Compute three-term-recurrence coefficients $ \alpha_{l}^{km}$ of Wigner-d functions for all degrees $ l= 0,\ldots,N $.
void SO3_beta_row (double *beta, int N, int m, int n)
 Compute three-term-recurrence coefficients $ \beta_{l}^{km}$ of Wigner-d functions for all degrees $ l= 0,\ldots,N $.
void SO3_gamma_row (double *gamma, int N, int m, int n)
 Compute three-term-recurrence coefficients $ \gamma_{l}^{km}$ of Wigner-d functions for all degrees $ l= 0,\ldots,N $.
void SO3_alpha_matrix (double *alpha, int N, int n)
 Compute three-term-recurrence coefficients $ \alpha_{l}^{km}$ of Wigner-d functions for all order $ m = -N,\ldots,N $ and degrees $ l= 0,\ldots,N $.
void SO3_beta_matrix (double *beta, int N, int n)
 Compute three-term-recurrence coefficients $ \beta_{l}^{km}$ of Wigner-d functions for all order $ m = -N,\ldots,N $ and degrees $ l= 0,\ldots,N $.
void SO3_gamma_matrix (double *gamma, int N, int n)
 Compute three-term-recurrence coefficients $ \gamma_{l}^{km}$ of Wigner-d functions for all order $ m = -N,\ldots,N $ and degrees $ l= 0,\ldots,N $.
void SO3_alpha_all (double *alpha, int N)
 Compute three-term-recurrence coefficients $\alpha_{l}^{km}$ of Wigner-d functions for all $ k,m = -N,\ldots,N $ and $ l= 0,\ldots,N $.
void SO3_beta_all (double *beta, int N)
 Compute three-term-recurrence coefficients $\beta_{l}^{km}$ of Wigner-d functions for all $ k,m = -N,\ldots,N $ and $ l= 0,\ldots,N $.
void SO3_gamma_all (double *gamma, int N)
 Compute three-term-recurrence coefficients $\gamma_{l}^{km}$ of Wigner-d functions for all $ k,m = -N,\ldots,N $ and $ l= 0,\ldots,N $.
void eval_wigner (double *x, double *y, int size, int l, double *alpha, double *beta, double *gamma)
 Evaluates Wigner-d functions $d_l^{km}(x,c)$ using the Clenshaw-algorithm.
int eval_wigner_thresh (double *x, double *y, int size, int l, double *alpha, double *beta, double *gamma, double threshold)
 Evaluates Wigner-d functions $d_l^{km}(x,c)$ using the Clenshaw-algorithm if it not exceeds a given threshold.
double wigner_start (int n1, int n2, double theta)
 A method used for debugging, gives the values to start the "old" three-term recurrence generates $ d^{km}_l(cos(theta)) $ WHERE THE DEGREE l OF THE FUNCTION IS EQUAL TO THE MAXIMUM OF ITS ORDERS.


Detailed Description

Header file for functions related to Wigner-d/D functions
Author:
Antje Vollrath

Definition in file wigner.h.


Function Documentation

double SO3_alpha ( int  k,
int  m,
int  l 
) [inline]

Computes three-term recurrence coefficients $\alpha_l^{km}$ of Wigner-d functions.

Definition at line 70 of file wigner.c.

double SO3_beta ( int  k,
int  m,
int  l 
)

Computes three-term recurrence coefficients $\beta_l^{km}$ of Wigner-d functions.

Definition at line 123 of file wigner.c.

double SO3_gamma ( int  k,
int  m,
int  l 
)

Computes three-term recurrence coefficients $\gamma_l^{km}$ of Wigner-d functions.

Definition at line 26 of file wigner.c.

void SO3_alpha_row ( double *  alpha,
int  N,
int  m,
int  n 
) [inline]

Compute three-term-recurrence coefficients $ \alpha_{l}^{km}$ of Wigner-d functions for all degrees $ l= 0,\ldots,N $.

Definition at line 151 of file wigner.c.

void SO3_beta_row ( double *  beta,
int  N,
int  m,
int  n 
) [inline]

Compute three-term-recurrence coefficients $ \beta_{l}^{km}$ of Wigner-d functions for all degrees $ l= 0,\ldots,N $.

Definition at line 162 of file wigner.c.

void SO3_gamma_row ( double *  gamma,
int  N,
int  m,
int  n 
) [inline]

Compute three-term-recurrence coefficients $ \gamma_{l}^{km}$ of Wigner-d functions for all degrees $ l= 0,\ldots,N $.

Definition at line 173 of file wigner.c.

void SO3_alpha_matrix ( double *  alpha,
int  N,
int  n 
) [inline]

Compute three-term-recurrence coefficients $ \alpha_{l}^{km}$ of Wigner-d functions for all order $ m = -N,\ldots,N $ and degrees $ l= 0,\ldots,N $.

Definition at line 186 of file wigner.c.

void SO3_beta_matrix ( double *  beta,
int  N,
int  n 
) [inline]

Compute three-term-recurrence coefficients $ \beta_{l}^{km}$ of Wigner-d functions for all order $ m = -N,\ldots,N $ and degrees $ l= 0,\ldots,N $.

Definition at line 200 of file wigner.c.

void SO3_gamma_matrix ( double *  gamma,
int  N,
int  n 
) [inline]

Compute three-term-recurrence coefficients $ \gamma_{l}^{km}$ of Wigner-d functions for all order $ m = -N,\ldots,N $ and degrees $ l= 0,\ldots,N $.

Definition at line 214 of file wigner.c.

void SO3_alpha_all ( double *  alpha,
int  N 
) [inline]

Compute three-term-recurrence coefficients $\alpha_{l}^{km}$ of Wigner-d functions for all $ k,m = -N,\ldots,N $ and $ l= 0,\ldots,N $.

Definition at line 230 of file wigner.c.

void SO3_beta_all ( double *  beta,
int  N 
) [inline]

Compute three-term-recurrence coefficients $\beta_{l}^{km}$ of Wigner-d functions for all $ k,m = -N,\ldots,N $ and $ l= 0,\ldots,N $.

Definition at line 253 of file wigner.c.

void SO3_gamma_all ( double *  gamma,
int  N 
) [inline]

Compute three-term-recurrence coefficients $\gamma_{l}^{km}$ of Wigner-d functions for all $ k,m = -N,\ldots,N $ and $ l= 0,\ldots,N $.

Definition at line 270 of file wigner.c.

void eval_wigner ( double *  x,
double *  y,
int  size,
int  l,
double *  alpha,
double *  beta,
double *  gamma 
) [inline]

Evaluates Wigner-d functions $d_l^{km}(x,c)$ using the Clenshaw-algorithm.

Definition at line 287 of file wigner.c.

int eval_wigner_thresh ( double *  x,
double *  y,
int  size,
int  l,
double *  alpha,
double *  beta,
double *  gamma,
double  threshold 
) [inline]

Evaluates Wigner-d functions $d_l^{km}(x,c)$ using the Clenshaw-algorithm if it not exceeds a given threshold.

Definition at line 332 of file wigner.c.

double wigner_start ( int  n1,
int  n2,
double  theta 
)

A method used for debugging, gives the values to start the "old" three-term recurrence generates $ d^{km}_l(cos(theta)) $ WHERE THE DEGREE l OF THE FUNCTION IS EQUAL TO THE MAXIMUM OF ITS ORDERS.

Returns:
the function value $ d^{km}_l(cos(theta)) $

Definition at line 389 of file wigner.c.


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