taylor_nfft.c File Reference

Testing the nfft againt a Taylor expansion based version. More...

#include "config.h"
#include <stdio.h>
#include <math.h>
#include <string.h>
#include <stdlib.h>
#include "nfft3.h"
#include "infft.h"

Go to the source code of this file.

Data Structures
struct	taylor_plan

Functions
static void	taylor_init (taylor_plan *ths, int N, int M, int n, int m)
	Initialisation of a transform plan. More...
static void	taylor_precompute (taylor_plan *ths)
	Precomputation of weights and indices in Taylor expansion. More...
static void	taylor_finalize (taylor_plan *ths)
	Destroys a transform plan. More...
static void	taylor_trafo (taylor_plan *ths)
	Executes a Taylor-NFFT, see equation (1.1) in [Guide], computes fast and approximate by means of a Taylor expansion for j=0,...,M-1 f[j] = sum_{k in I_N^d} f_hat[k] * exp(-2 (pi) k x[j]) More...
static void	taylor_time_accuracy (int N, int M, int n, int m, int n_taylor, int m_taylor, unsigned test_accuracy)
	Compares NDFT, NFFT, and Taylor-NFFT. More...
int	main (int argc, char **argv)

Detailed Description

Testing the nfft againt a Taylor expansion based version.

Author

Stefan Kunis

References: Time and memory requirements of the Nonequispaced FFT

Definition in file taylor_nfft.c.

Function Documentation

static void taylor_init ( taylor_plan *  ths, int  N, int  M, int  n, int  m  )

static

Initialisation of a transform plan.

• ths The pointer to a taylor plan
• N The multi bandwidth
• M The number of nodes
• n The fft length
• m The order of the Taylor expansion

Author

Stefan Kunis

Definition at line 59 of file taylor_nfft.c.

References FFT_OUT_OF_PLACE, FFTW_INIT, MALLOC_F, MALLOC_F_HAT, and MALLOC_X.

Referenced by taylor_time_accuracy().

static void taylor_precompute ( taylor_plan *  ths )

static

Precomputation of weights and indices in Taylor expansion.

• ths The pointer to a taylor plan

Author

Stefan Kunis

Definition at line 77 of file taylor_nfft.c.

Referenced by taylor_time_accuracy().

static void taylor_finalize ( taylor_plan *  ths )

static

Destroys a transform plan.

• ths The pointer to a taylor plan

Author

Stefan Kunis, Daniel Potts

Definition at line 99 of file taylor_nfft.c.

Referenced by taylor_time_accuracy().

static void taylor_trafo ( taylor_plan *  ths )

static

Executes a Taylor-NFFT, see equation (1.1) in [Guide], computes fast and approximate by means of a Taylor expansion for j=0,...,M-1 f[j] = sum_{k in I_N^d} f_hat[k] * exp(-2 (pi) k x[j])

• ths The pointer to a taylor plan

Author

Stefan Kunis

Definition at line 117 of file taylor_nfft.c.

Referenced by taylor_time_accuracy().

static void taylor_time_accuracy ( int  N, int  M, int  n, int  m, int  n_taylor, int  m_taylor, unsigned  test_accuracy  )

static

Compares NDFT, NFFT, and Taylor-NFFT.

• N The bandwidth
• N The number of nodes
• n The FFT-size for the NFFT
• m The cut-off for window function
• n_taylor The FFT-size for the Taylor-NFFT
• m_taylor The order of the Taylor approximation
• test_accuracy Flag for NDFT computation

Author

Stefan Kunis

Definition at line 174 of file taylor_nfft.c.

References CSWAP, FFT_OUT_OF_PLACE, FFTW_INIT, PRE_FG_PSI, PRE_ONE_PSI, PRE_PHI_HUT, taylor_finalize(), taylor_init(), taylor_precompute(), and taylor_trafo().