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NFST

direct and fast computation of the discrete sine transform at nonequispaced knots in time/spatial domain More...

Data Structures

struct  nfst_plan_
 Structure for a transform plan. More...

Typedefs

typedef nfst_plan_ nfst_plan
 Structure for a transform plan.

Functions

void nfst_init_1d (nfst_plan *ths_plan, int N0, int M_total)
 Creates a 1-dimensional transform plan.
void nfst_init_2d (nfst_plan *ths_plan, int N0, int N1, int M_total)
 Creates a 3-dimensional transform plan.
void nfst_init_3d (nfst_plan *ths_plan, int N0, int N1, int N2, int M_total)
 Creates a 3-dimensional transform plan.
void nfst_init (nfst_plan *ths_plan, int d, int *N, int M_total)
 Creates a d-dimensional transform plan.
void nfst_init_m (nfst_plan *ths_plan, int d, int *N, int M_total, int m)
 Creates a d-dimensional transform plan with pcific m.
void nfst_init_guru (nfst_plan *ths_plan, int d, int *N, int M_total, int *n, int m, unsigned nfst_flags, unsigned fftw_flags)
 Creates a d-dimensional transform plan.
void nfst_precompute_psi (nfst_plan *ths_plan)
 precomputes the values psi if the PRE_PSI is set the application program has to call this routine after setting the nodes this_plan->x
void nfst_trafo (nfst_plan *ths_plan)
 executes a NFST (approximate,fast), computes for $j=0,...,M\_total-1$ $f_j^S(x_j) = sum_{k \in I_1^{N,d}} \hat{f}_k^S * sin(2 \pi k x_j)$
void ndst_trafo (nfst_plan *ths_plan)
 executes a NDST (exact,slow), computes for $j=0,...,M\_total-1$ $f_j^S(x_j) = sum_{k \in I_1^{N,d}} \hat{f}_k^S * sin(2 \pi k x_j)$
void nfst_adjoint (nfst_plan *ths_plan)
 executes a transposed NFST (approximate,fast), computes for $k \in I_1^{N,d}$ $h^S(k) = sum_{j \in I_0^{M\_total,1}} f_j^S * cos(2 \pi k x_j)$
void ndst_adjoint (nfst_plan *ths_plan)
 executes a direct transposed NDST (exact,slow), computes for $k \in I_1^{N,d}$ $h^S(k) = sum_{j \in I_0^{M\_total,1}} f_j^S * cos(2 \pi k x_j)$
void nfst_finalize (nfst_plan *ths_plan)
 Destroys a plan.
void nfst_full_psi (nfst_plan *ths_plan, double eps)
 more memory usage, a bit faster
double nfst_phi_hut (nfst_plan *ths_plan, int k, int d)
 do some adjustments (N,n) then compute PHI_HUT
double nfst_phi (nfst_plan *ths_plan, double x, int d)
 do some adjustments (N,n) then compute PHI
int nfst_fftw_2N (int n)
 returns 2(n+1), fftw related issue
int nfst_fftw_2N_rev (int n)
 returns 0.5n-1, fftw related issue

Detailed Description

direct and fast computation of the discrete sine transform at nonequispaced knots in time/spatial domain

Function Documentation

void ndst_adjoint (  nfst_plan *  ths_plan  ) 
 

executes a direct transposed NDST (exact,slow), computes for $k \in I_1^{N,d}$ $h^S(k) = sum_{j \in I_0^{M\_total,1}} f_j^S * cos(2 \pi k x_j)$

  • ths_plan The plan for the transform
Author:
Steffen Klatt

void ndst_trafo (  nfst_plan *  ths_plan  ) 
 

executes a NDST (exact,slow), computes for $j=0,...,M\_total-1$ $f_j^S(x_j) = sum_{k \in I_1^{N,d}} \hat{f}_k^S * sin(2 \pi k x_j)$

  • ths_plan The plan for the transform
Author:
Steffen Klatt

void nfst_adjoint (  nfst_plan *  ths  ) 
 

executes a transposed NFST (approximate,fast), computes for $k \in I_1^{N,d}$ $h^S(k) = sum_{j \in I_0^{M\_total,1}} f_j^S * cos(2 \pi k x_j)$

use ths->my_fftw_plan

set $ g_l = \sum_{j=0}^{M-1} f_j \psi\left(x_j-\frac{l}{n}\right) \text{ for } l \in I_n,m(x_j) $

compute by d-variate discrete cosine transform $ \hat g_k = \sum_{l \in I_n} g_l {\rm e}^{-2\pi {\rm i} \frac{kl}{n}} \text{ for } k \in I_N$

form $ \hat f_k = \frac{\hat g_k}{c_k\left(\phi\right)} \text{ for } k \in I_N $

int nfst_fftw_2N (  int  n  ) 
 

returns 2(n+1), fftw related issue

  • n i.e. length of dst-1
Author:
Steffen Klatt

int nfst_fftw_2N_rev (  int  n  ) 
 

returns 0.5n-1, fftw related issue

  • n i.e. length of dct-1
Author:
Steffen Klatt

void nfst_finalize (  nfst_plan *  ths_plan  ) 
 

Destroys a plan.

  • ths_plan The plan for the transform
Author:
Steffen Klatt

void nfst_full_psi (  nfst_plan *  ths,
double  eps
) 
 

more memory usage, a bit faster

< index over all dimensions

< index over all nodes

< plain index 0<=l_L<lprod

< multi index 0<=lj<u+o+1

< postfix plain index

< 'bandwidth' of matrix B

< depends on x_j

void nfst_init (  nfst_plan *  ths,
int  d,
int *  N,
int  M_total
) 
 

Creates a d-dimensional transform plan.

< index over all dimensions

void nfst_init_1d (  nfst_plan *  ths_plan,
int  N0,
int  M_total
) 
 

Creates a 1-dimensional transform plan.

  • ths_plan The plan for the transform
  • N0 The bandwidth $N$
  • M_total The number of nodes $x$
Author:
Steffen Klatt

void nfst_init_2d (  nfst_plan *  ths_plan,
int  N0,
int  N1,
int  M_total
) 
 

Creates a 3-dimensional transform plan.

  • ths_plan The plan for the transform
  • N0 The bandwidth of dimension 1
  • N1 The bandwidth of dimension 2
  • M_total The number of nodes $x$
Author:
Steffen Klatt

void nfst_init_3d (  nfst_plan *  ths_plan,
int  N0,
int  N1,
int  N2,
int  M_total
) 
 

Creates a 3-dimensional transform plan.

  • ths_plan The plan for the transform
  • N0 The bandwidth of dimension 1
  • N1 The bandwidth of dimension 2
  • N2 The bandwidth of dimension 3
  • M_total The number of nodes $x$
Author:
Steffen Klatt

void nfst_init_guru (  nfst_plan *  ths,
int  d,
int *  N,
int  M_total,
int *  n,
int  m,
unsigned  nfst_flags,
unsigned  fftw_flags
) 
 

Creates a d-dimensional transform plan.

< index over all dimensions

void nfst_init_m (  nfst_plan *  ths_plan,
int  d,
int *  N,
int  M_total,
int  m
) 
 

Creates a d-dimensional transform plan with pcific m.

(just for convenience)

  • ths_plan The plan for the transform
  • d the dimension
  • N The bandwidths
  • M_total The number of nodes $x$
  • m cut-off parameter
Author:
Steffen Klatt

double nfst_phi (  nfst_plan *  ths_plan,
double  x,
int  d
) 
 

do some adjustments (N,n) then compute PHI

  • ths_plan the plan for the transform
  • x node $x$
  • d dimension
Author:
Steffen Klatt

double nfst_phi_hut (  nfst_plan *  ths_plan,
int  k,
int  d
) 
 

do some adjustments (N,n) then compute PHI_HUT

  • ths_plan the plan for the transform
  • k index of c_phi
  • d dimension
Author:
Steffen Klatt

void nfst_precompute_psi (  nfst_plan *  ths  ) 
 

precomputes the values psi if the PRE_PSI is set the application program has to call this routine after setting the nodes this_plan->x

< index over all dimensions

< index over all nodes

< index 0<=lj<u+o+1

< depends on x_j

void nfst_trafo (  nfst_plan *  ths_plan  ) 
 

executes a NFST (approximate,fast), computes for $j=0,...,M\_total-1$ $f_j^S(x_j) = sum_{k \in I_1^{N,d}} \hat{f}_k^S * sin(2 \pi k x_j)$

  • ths_plan The plan for the transform
Author:
Steffen Klatt

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