wigner.h File Reference

Header file for functions related to Wigner-d/D functions. More...

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## Functions

double | SO3_alpha (int k, int m, int l)
| Computes three-term recurrence coefficients of Wigner-d functions. More...
double | SO3_beta (int k, int m, int l)
| Computes three-term recurrence coefficients of Wigner-d functions. More...
double | SO3_gamma (int k, int m, int l)
| Computes three-term recurrence coefficients of Wigner-d functions. More...
void | SO3_alpha_row (double *alpha, int N, int m, int n)
| Compute three-term-recurrence coefficients of Wigner-d functions for all degrees . More...
void | SO3_beta_row (double *beta, int N, int m, int n)
| Compute three-term-recurrence coefficients of Wigner-d functions for all degrees . More...
void | SO3_gamma_row (double *gamma, int N, int m, int n)
| Compute three-term-recurrence coefficients of Wigner-d functions for all degrees . More...
void | SO3_alpha_matrix (double *alpha, int N, int n)
| Compute three-term-recurrence coefficients of Wigner-d functions for all order and degrees . More...
void | SO3_beta_matrix (double *beta, int N, int n)
| Compute three-term-recurrence coefficients of Wigner-d functions for all order and degrees . More...
void | SO3_gamma_matrix (double *gamma, int N, int n)
| Compute three-term-recurrence coefficients of Wigner-d functions for all order and degrees . More...
void | SO3_alpha_all (double *alpha, int N)
| Compute three-term-recurrence coefficients of Wigner-d functions for all and . More...
void | SO3_beta_all (double *beta, int N)
| Compute three-term-recurrence coefficients of Wigner-d functions for all and . More...
void | SO3_gamma_all (double *gamma, int N)
| Compute three-term-recurrence coefficients of Wigner-d functions for all and . More...
void | eval_wigner (double *x, double *y, int size, int l, double *alpha, double *beta, double *gamma)
| Evaluates Wigner-d functions using the Clenshaw-algorithm. More...
int | eval_wigner_thresh (double *x, double *y, int size, int l, double *alpha, double *beta, double *gamma, double threshold)
| Evaluates Wigner-d functions using the Clenshaw-algorithm if it not exceeds a given threshold. More...
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 WHERE THE DEGREE l OF THE FUNCTION IS EQUAL TO THE MAXIMUM OF ITS ORDERS. More...

## 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
| ) |  |

Computes three-term recurrence coefficients of Wigner-d functions.

- k The order
- m The order
- l The degree

Definition at line 25 of file wigner.c.

Referenced by SO3_alpha_all(), SO3_alpha_matrix(), and SO3_alpha_row().

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

Computes three-term recurrence coefficients of Wigner-d functions.

- k The order
- m The order
- l The degree

Definition at line 52 of file wigner.c.

Referenced by SO3_beta_all(), SO3_beta_matrix(), and SO3_beta_row().

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

Computes three-term recurrence coefficients of Wigner-d functions.

- k The order
- m The order
- l The degree

Definition at line 73 of file wigner.c.

Referenced by SO3_gamma_all(), SO3_gamma_matrix(), and SO3_gamma_row().

void SO3_alpha_row | ( | double * | alpha,
|  | int | N,
|  | int | m,
|  | int | n
| ) |  |

inline

Compute three-term-recurrence coefficients of Wigner-d functions for all degrees .

- alpha A pointer to an array of doubles of size
- m the first order
- n the second order
- N The upper bound .

Definition at line 88 of file wigner.c.

References SO3_alpha().

Referenced by nfsoft_init_guru_advanced().

void SO3_beta_row | ( | double * | beta,
|  | int | N,
|  | int | m,
|  | int | n
| ) |  |

inline

Compute three-term-recurrence coefficients of Wigner-d functions for all degrees .

- alpha A pointer to an array of doubles of size
- m the first order
- n the second order
- N The upper bound .

Definition at line 96 of file wigner.c.

References SO3_beta().

Referenced by nfsoft_init_guru_advanced().

void SO3_gamma_row | ( | double * | gamma,
|  | int | N,
|  | int | m,
|  | int | n
| ) |  |

inline

Compute three-term-recurrence coefficients of Wigner-d functions for all degrees .

- alpha A pointer to an array of doubles of size
- m the first order
- n the second order
- N The upper bound .

Definition at line 104 of file wigner.c.

References SO3_gamma().

Referenced by nfsoft_init_guru_advanced().

void SO3_alpha_matrix | ( | double * | alpha,
|  | int | N,
|  | int | n
| ) |  |

inline

Compute three-term-recurrence coefficients of Wigner-d functions for all order and degrees .

- alpha A pointer to an array of doubles of size
- n the second order
- N The upper bound .

Definition at line 114 of file wigner.c.

References SO3_alpha().

void SO3_beta_matrix | ( | double * | beta,
|  | int | N,
|  | int | n
| ) |  |

inline

Compute three-term-recurrence coefficients of Wigner-d functions for all order and degrees .

- alpha A pointer to an array of doubles of size
- n the second order
- N The upper bound .

Definition at line 128 of file wigner.c.

References SO3_beta().

void SO3_gamma_matrix | ( | double * | gamma,
|  | int | N,
|  | int | n
| ) |  |

inline

Compute three-term-recurrence coefficients of Wigner-d functions for all order and degrees .

- alpha A pointer to an array of doubles of size
- n the second order
- N The upper bound .

Definition at line 142 of file wigner.c.

References SO3_gamma().

void SO3_alpha_all | ( | double * | alpha,
|  | int | N
| ) |  |

inline

Compute three-term-recurrence coefficients of Wigner-d functions for all and .

- alpha A pointer to an array of doubles of size

- N The upper bound .

Definition at line 158 of file wigner.c.

References SO3_alpha().

void SO3_beta_all | ( | double * | beta,
|  | int | N
| ) |  |

inline

Compute three-term-recurrence coefficients of Wigner-d functions for all and .

- alpha A pointer to an array of doubles of size

- N The upper bound .

Definition at line 181 of file wigner.c.

References SO3_beta().

void SO3_gamma_all | ( | double * | gamma,
|  | int | N
| ) |  |

inline

Compute three-term-recurrence coefficients of Wigner-d functions for all and .

- alpha A pointer to an array of doubles of size

- N The upper bound .

Definition at line 198 of file wigner.c.

References SO3_gamma().

void eval_wigner | ( | double * | x,
|  | double * | y,
|  | int | size,
|  | int | l,
|  | double * | alpha,
|  | double * | beta,
|  | double * | gamma
| ) |  |

inline

Evaluates Wigner-d functions using the Clenshaw-algorithm.

- x A pointer to an array of nodes where the function is to be evaluated
- y A pointer to an array where the function values are returned
- size The length of x and y
- l The degree
- alpha A pointer to an array containing the recurrence coefficients
- beta A pointer to an array containing the recurrence coefficients
- gamma A pointer to an array containing the recurrence coefficients

Definition at line 215 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 using the Clenshaw-algorithm if it not exceeds a given threshold.

- x A pointer to an array of nodes where the function is to be evaluated
- y A pointer to an array where the function values are returned
- size The length of x and y
- l The degree
- alpha A pointer to an array containing the recurrence coefficients
- beta A pointer to an array containing the recurrence coefficients
- gamma A pointer to an array containing the recurrence coefficients
- threshold The threshold

Definition at line 260 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 WHERE THE DEGREE l OF THE FUNCTION IS EQUAL TO THE MAXIMUM OF ITS ORDERS.

- theta the argument of
- n1 the first order
- n2 the second order

Returns
  the function value

Definition at line 317 of file wigner.c.