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NNFFT

Direct and fast computation of the discrete Fourier transform at nonequispaced knots in time and Fourier domain. More...

Data Structures

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

Functions

void nnfft_init (nnfft_plan *ths_plan, int d, int N_total, int M_total, int *N)
 Creates a transform plan.
void nnfft_init_guru (nnfft_plan *ths_plan, int d, int N_total, int M_total, int *N, int *N1, int m, unsigned nnfft_flags)
 Creates a transform plan.
void nndft_trafo (nnfft_plan *ths_plan)
 Executes a direct NNDFT, i.e.
void nndft_adjoint (nnfft_plan *ths_plan)
 Executes a direct adjoint NNDFT, i.e.
void nnfft_trafo (nnfft_plan *ths_plan)
 Executes a NNFFT, i.e.
void nnfft_adjoint (nnfft_plan *ths_plan)
 Executes a adjoint NNFFT, i.e.
void nnfft_precompute_lin_psi (nnfft_plan *ths_plan)
 Precomputation for a transform plan.
void nnfft_precompute_psi (nnfft_plan *ths_plan)
 Precomputation for a transform plan.
void nnfft_precompute_full_psi (nnfft_plan *ths_plan)
 Precomputation for a transform plan.
void nnfft_precompute_phi_hut (nnfft_plan *ths_plan)
 Precomputation for a transform plan.
void nnfft_finalize (nnfft_plan *ths_plan)
 Destroys a plan.

Detailed Description

Direct and fast computation of the discrete Fourier transform at nonequispaced knots in time and Fourier domain.


Function Documentation

void nndft_adjoint nnfft_plan ths_plan  ) 
 

Executes a direct adjoint NNDFT, i.e.

computes for $k=0,...,N_{total}-1$

\[ \hat{f}(v_k) = \sum_{j = 0}^{M_{total}-1} f(x_j) {\rm e}^{2 \pi \mbox{\rm\scriptsize i} v_k x_j \odot N} \]

  • ths_plan The plan
Author:
Tobias Knopp

void nndft_trafo nnfft_plan ths_plan  ) 
 

Executes a direct NNDFT, i.e.

computes for $j=0,...,M_{total}-1$

\[ f(x_j) = \sum_{k = 0}^{N_{total}-1} \hat{f}(v_k) {\rm e}^{-2 \pi \mbox{\rm\scriptsize i} v_k x_j \odot N} \]

  • ths_plan The plan
Author:
Tobias Knopp

void nnfft_adjoint nnfft_plan ths_plan  ) 
 

Executes a adjoint NNFFT, i.e.

computes for $k=0,...,N_{total}-1$

\[ \hat{f}(v_k) = \sum_{j = 0}^{M_{tota}l-1} f(x_j) {\rm e}^{2 \pi \mbox{\rm\scriptsize i} v_k x_j \odot N} \]

  • ths_plan The plan
Author:
Tobias Knopp

void nnfft_finalize nnfft_plan ths_plan  ) 
 

Destroys a plan.

  • ths_plan The plan
Author:
Tobias Knopp

void nnfft_init nnfft_plan ths,
int  d,
int  N_total,
int  M_total,
int *  N
 

Creates a transform plan.

< index over all dimensions

void nnfft_init_guru nnfft_plan ths,
int  d,
int  N_total,
int  M_total,
int *  N,
int *  N1,
int  m,
unsigned  nnfft_flags
 

Creates a transform plan.

< index over all dimensions

void nnfft_precompute_full_psi nnfft_plan ths  ) 
 

Precomputation for a transform plan.

< index over all dimensions

< index over all nodes

< plain index 0<=l_L<lprod

< multi index u<=l<=o

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

< postfix plain index

< 'bandwidth' of matrix B

< depends on x_j

void nnfft_precompute_lin_psi nnfft_plan ths  ) 
 

Precomputation for a transform plan.

< index over all dimensions

< index over all nodes

< step size in [0,(m+1)/n]

void nnfft_precompute_phi_hut nnfft_plan ths  ) 
 

Precomputation for a transform plan.

< index over all frequencies

< index over all dimensions

void nnfft_precompute_psi nnfft_plan ths  ) 
 

Precomputation for a transform plan.

< index over all dimensions

< index over all nodes

< index u<=l<=o

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

< depends on v_j

void nnfft_trafo nnfft_plan ths_plan  ) 
 

Executes a NNFFT, i.e.

computes for $j=0,...,M_{total}-1$

\[ f(x_j) = \sum_{k = 0}^{N_{total}-1} \hat{f}(v_k) {\rm e}^{-2 \pi \mbox{\rm\scriptsize i} v_k x_j \odot N} \]

  • ths_plan The plan
Author:
Tobias Knopp


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