Main Page | Modules | Data Structures | Directories | File List | Data Fields | Globals | Related Pages

NFSFT: Functions related to associated Legendre
[NFSFT]

functions/polynomials More...

Functions

double alpha_al (int k, int n)
 Computes three-term recurrence coefficients $\alpha_k^n$ of associated Legendre functions.
double beta_al (int k, int n)
 Computes three-term recurrence coefficients $\beta_k^n$ of associated Legendre functions.
double gamma_al (int k, int n)
 Computes three-term recurrence coefficients $\gamma_k^n$ of associated Legendre functions.
void alpha_al_all (double *alpha, int N)
 Compute three-term-recurrence coefficients $\alpha_{k-1}^n$ of associated Legendre functions for $k,n = 0,1,\ldots,N$ .
void beta_al_all (double *beta, int N)
 Compute three-term-recurrence coefficients $\beta_{k-1}^n$ of associated Legendre functions for $k,n = 0,1,\ldots,N$ .
void gamma_al_all (double *gamma, int N)
 Compute three-term-recurrence coefficients $\gamma_{k-1}^n$ of associated Legendre functions for $k,n = 0,1,\ldots,N$ .
void eval_al (double *x, double *y, int size, int k, double *alpha, double *beta, double *gamma)
 Evaluates an associated Legendre polynomials $P_k^n(x,c)$ using the Clenshaw-algorithm.
int eval_al_thresh (double *x, double *y, int size, int k, double *alpha, double *beta, double *gamma, double threshold)
 Evaluates an associated Legendre polynomials $P_k^n(x,c)$ using the Clenshaw-algorithm if it no exceeds a given threshold.
double alpha_al_old (int k, int n)
 Computes three-term recurrence coefficients $\alpha_k^n$ of associated Legendre functions.
double beta_al_old (int k, int n)
 Computes three-term recurrence coefficients $\beta_k^n$ of associated Legendre functions.
double gamma_al_old (int k, int n)
 Computes three-term recurrence coefficients $\gamma_k^n$ of associated Legendre functions.
void alpha_al_all_old (double *alpha, int N)
 Compute three-term-recurrence coefficients $\alpha_{k-1}^n$ of associated Legendre functions for $k,n = 0,1,\ldots,N$ .
void beta_al_all_old (double *beta, int N)
 Compute three-term-recurrence coefficients $\beta_{k-1}^n$ of associated Legendre functions for $k,n = 0,1,\ldots,N$ .
void gamma_al_all_old (double *gamma, int N)
 Compute three-term-recurrence coefficients $\gamma_{k-1}^n$ of associated Legendre functions for $k,n = 0,1,\ldots,N$ .
void eval_al_old (double *x, double *y, int size, int k, double *alpha, double *beta, double *gamma)
 Evaluates an associated Legendre polynomials $P_k^n(x,c)$ using the Clenshaw-algorithm.
int eval_al_thresh_old (double *x, double *y, int size, int k, double *alpha, double *beta, double *gamma, double threshold)
 Evaluates an associated Legendre polynomials $P_k^n(x,c)$ using the Clenshaw-algorithm if it no exceeds a given threshold.

Detailed Description

functions/polynomials

Function Documentation

double alpha_al (  int  k,
int  n
)  [inline]
 

Computes three-term recurrence coefficients $\alpha_k^n$ of associated Legendre functions.

  • k The index $k$
  • n The index $n$

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

Compute three-term-recurrence coefficients $\alpha_{k-1}^n$ of associated Legendre functions for $k,n = 0,1,\ldots,N$ .

  • alpha A pointer to an array of doubles of size $(N+1)^2$ where the coefficients will be stored such that alpha[n+(N+1)+k] = $\alpha_{k-1}^n$ .
  • N The upper bound $N$ .

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

Compute three-term-recurrence coefficients $\alpha_{k-1}^n$ of associated Legendre functions for $k,n = 0,1,\ldots,N$ .

  • alpha A pointer to an array of doubles of size $(N+1)^2$ where the coefficients will be stored such that alpha[n+(N+1)+k] = $\alpha_{k-1}^n$ .
  • N The upper bound $N$ .

double alpha_al_old (  int  k,
int  n
)  [inline]
 

Computes three-term recurrence coefficients $\alpha_k^n$ of associated Legendre functions.

  • k The index $k$
  • n The index $n$

double beta_al (  int  k,
int  n
)  [inline]
 

Computes three-term recurrence coefficients $\beta_k^n$ of associated Legendre functions.

  • k The index $k$
  • n The index $n$

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

Compute three-term-recurrence coefficients $\beta_{k-1}^n$ of associated Legendre functions for $k,n = 0,1,\ldots,N$ .

  • beta A pointer to an array of doubles of size $(N+1)^2$ where the coefficients will be stored such that beta[n+(N+1)+k] = $\beta_{k-1}^n$ .
  • N The upper bound $N$ .

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

Compute three-term-recurrence coefficients $\beta_{k-1}^n$ of associated Legendre functions for $k,n = 0,1,\ldots,N$ .

  • beta A pointer to an array of doubles of size $(N+1)^2$ where the coefficients will be stored such that beta[n+(N+1)+k] = $\beta_{k-1}^n$ .
  • N The upper bound $N$ .

double beta_al_old (  int  k,
int  n
)  [inline]
 

Computes three-term recurrence coefficients $\beta_k^n$ of associated Legendre functions.

  • k The index $k$
  • n The index $n$

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

Evaluates an associated Legendre polynomials $P_k^n(x,c)$ 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
  • k The index $k$
  • alpha A pointer to an array containing the recurrence coefficients $\alpha_c^n,\ldots,\alpha_{c+k}^n$
  • beta A pointer to an array containing the recurrence coefficients $\beta_c^n,\ldots,\beta_{c+k}^n$
  • gamma A pointer to an array containing the recurrence coefficients $\gamma_c^n,\ldots,\gamma_{c+k}^n$

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

Evaluates an associated Legendre polynomials $P_k^n(x,c)$ 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
  • k The index $k$
  • alpha A pointer to an array containing the recurrence coefficients $\alpha_c^n,\ldots,\alpha_{c+k}^n$
  • beta A pointer to an array containing the recurrence coefficients $\beta_c^n,\ldots,\beta_{c+k}^n$
  • gamma A pointer to an array containing the recurrence coefficients $\gamma_c^n,\ldots,\gamma_{c+k}^n$

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

Evaluates an associated Legendre polynomials $P_k^n(x,c)$ using the Clenshaw-algorithm if it no 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
  • k The index $k$
  • alpha A pointer to an array containing the recurrence coefficients $\alpha_c^n,\ldots,\alpha_{c+k}^n$
  • beta A pointer to an array containing the recurrence coefficients $\beta_c^n,\ldots,\beta_{c+k}^n$
  • gamma A pointer to an array containing the recurrence coefficients $\gamma_c^n,\ldots,\gamma_{c+k}^n$
  • threshold The threshold

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

Evaluates an associated Legendre polynomials $P_k^n(x,c)$ using the Clenshaw-algorithm if it no 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
  • k The index $k$
  • alpha A pointer to an array containing the recurrence coefficients $\alpha_c^n,\ldots,\alpha_{c+k}^n$
  • beta A pointer to an array containing the recurrence coefficients $\beta_c^n,\ldots,\beta_{c+k}^n$
  • gamma A pointer to an array containing the recurrence coefficients $\gamma_c^n,\ldots,\gamma_{c+k}^n$
  • threshold The threshold

double gamma_al (  int  k,
int  n
)  [inline]
 

Computes three-term recurrence coefficients $\gamma_k^n$ of associated Legendre functions.

  • k The index $k$
  • n The index $n$

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

Compute three-term-recurrence coefficients $\gamma_{k-1}^n$ of associated Legendre functions for $k,n = 0,1,\ldots,N$ .

  • beta A pointer to an array of doubles of size $(N+1)^2$ where the coefficients will be stored such that gamma[n+(N+1)+k] = $\gamma_{k-1}^n$ .
  • N The upper bound $N$ .

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

Compute three-term-recurrence coefficients $\gamma_{k-1}^n$ of associated Legendre functions for $k,n = 0,1,\ldots,N$ .

  • beta A pointer to an array of doubles of size $(N+1)^2$ where the coefficients will be stored such that gamma[n+(N+1)+k] = $\gamma_{k-1}^n$ .
  • N The upper bound $N$ .

double gamma_al_old (  int  k,
int  n
)  [inline]
 

Computes three-term recurrence coefficients $\gamma_k^n$ of associated Legendre functions.

  • k The index $k$
  • n The index $n$

Generated on Wed May 10 20:39:40 2006 for NFFT by  doxygen 1.4.4