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NFSFT: Internal API and functions


Data Structures

struct  nfsft_wisdom
 Wisdom structure. More...
struct  U_type_old
 Datatype for a set of real 2x2 matrices used in FLT. More...
struct  nfsft_plan_s_old
 Structure for a transform plan. More...
struct  infsft_plan_s_old
 Structure for an inverse transform plan. More...
struct  nfsft_wisdom_old
 Toplevel wisdom structure. More...

Functions

void cheb2exp_old (complex *f_hat, complex **cheb, int M, int N)
 Converts Chebyshev coefficients to Fourier coefficients.
void cheb2exp_adjoint_old (complex *f_hat, complex **cheb, int M, int N)
 Adjoint algorithm for cheb2exp_old.
void flft_old (const int M, const int t, const int n, complex *const f_hat, struct nfsft_wisdom_old *const wisdom, int *nstab, int *ntotal)
 Fast Legendre function transform.
void flft_adjoint_old (const int M, const int t, const int n, complex *const f_hat, struct nfsft_wisdom_old *const wisdom)
 Adjoint fast Legendre function transform.
U_type_old **** precomputeU_old (int t, double threshold, double *walpha, double *wbeta, double *wgamma, int window)
 Precomputation of the matrices $U_{n,\tau,l}$.
void forgetU_old (struct U_type_old ****U, int M, int t, int window)
 Forget U.
void multiplyU_old (complex *a, complex *b, struct U_type_old u, int tau, int n, int l, struct nfsft_wisdom_old *tw, double gamma)
 Fast matrix Multiplication with matrices $U_{n,\tau,l}$ .
void multiplyU_adjoint_old (complex *a, complex *b, struct U_type_old u, int tau, int n, int l, struct nfsft_wisdom_old *tw, double gamma)
 Fast adjoint matrix Multiplication with matrices $U_{n,\tau,l}$ .

Function Documentation

void cheb2exp_adjoint_old complex *  f_hat,
complex **  cheb,
int  M,
int  N
[inline]
 

Adjoint algorithm for cheb2exp_old.

Degree $k$

Order $k$

Chebyshev coefficients for fixed $n$

Stores temporary values

Stores temporary values

Auxilliary pointer

Auxilliary pointer

void cheb2exp_old complex *  f_hat,
complex **  cheb,
int  M,
int  N
[inline]
 

Converts Chebyshev coefficients to Fourier coefficients.

Degree $k$

Order $k$

Chebyshev coefficients for fixed $n$

Stores temporary values

Stores temporary values

Auxilliary pointer

Auxilliary pointer

void flft_adjoint_old const int  M,
const int  t,
const int  n,
complex *const   f_hat,
struct nfsft_wisdom_old *const   wisdom
 

Adjoint fast Legendre function transform.

Level index tau

Index of first block at current level

Index of last block at current level

Block index $l$

Length of polynomial coefficient arrays at next level

Polynomial array length for stabilization

Multidimensional array of matrices $U_{n,,l}$

Current matrix U_{n,tau,l}

Loop counter

Save copy of inpute data for stabilization steps.

void flft_old const int  M,
const int  t,
const int  n,
complex *const   f_hat,
struct nfsft_wisdom_old *const   wisdom,
int *  nstab,
int *  ntotal
 

Fast Legendre function transform.

Next greater power of two with respect to M since $t := \left\lceil \log_2 M \right\rceil$

Level index $tau$

Index of first block at current level

Index of last block at current level

Block index $l$

Length of polynomial coefficient arrays at next level

Polynomial array length for stabilization

Multidimensional array of matrices $U_{n,,l}$

Current matrix $U_{n,tau,l}$

Loop counter

void forgetU_old struct U_type_old ****  U,
int  M,
int  t,
int  window
 

Forget U.

Legendre index n

Cascade level

Length of polynomials for the current level in the cascade

First index l for current cascade level and current n

Last index l for current cascade level and current n

Number of matrices U for current cascade level and current n .

Increase polynomial degree to next power of two.

void multiplyU_adjoint_old complex *  a,
complex *  b,
struct U_type_old  u,
int  tau,
int  n,
int  l,
struct nfsft_wisdom_old tw,
double  gamma
[inline]
 

Fast adjoint matrix Multiplication with matrices $U_{n,\tau,l}$ .

The length of the coefficient arrays.

void multiplyU_old complex *  a,
complex *  b,
struct U_type_old  u,
int  tau,
int  n,
int  l,
struct nfsft_wisdom_old tw,
double  gamma
[inline]
 

Fast matrix Multiplication with matrices $U_{n,\tau,l}$ .

The length of the coefficient arrays.

Twice the length of the coefficient arrays.

struct U_type_old**** precomputeU_old int  t,
double  threshold,
double *  walpha,
double *  wbeta,
double *  wgamma,
int  window
 

Precomputation of the matrices $U_{n,\tau,l}$.

Maximum bandwidth

Legendre index n

Cascade level

Level index

Length of polynomials for the next level in the cascade

Degree of polynomials for the current level in the cascade

First index l for current cascade level and current n

Last index l for current cascade level and current n

Number of matrices U for current cascade level and current n .

Cascade level for stabilization

Length of polynomials for the next level in the cascade for stabilization

Degree of polynomials for the current level in the cascade for stabilization

Four-dimensional array of matrices U_{n,tau,l}

Array containing function values of the (1,1)-component of U_k^n.

Array containing function values of the (1,2)-component of U_k^n.

Array containing function values of the (2,1)-component of U_k^n.

Array containing function values of the (2,2)-component of U_k^n.

Array for three-term recurrence coefficients of associated Legendre functions.

Array for three-term recurrence coefficients of associated Legendre functions.

Array for three-term recurrence coefficients of associated Legendre functions.

Array of pointers to arrays containing the Chebyshev nodes

Array for Chebychev-nodes.

loop counter

Used to indicate that stabilization is neccessary.

Increase polynomial degree to next power of two.


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