NFFT - Plan

The library defines the structure nfft_plan. The members are int d, int* N, int M, double* sigma, int* n, int m, double* b, int nfft_flags, int fftw_flags (already discussed, see Table 2). Furthermore, it contains all data vectors, see Table 4.

Table 4: Members of nfft_plan.

type	name	description	size (in *type)
double*	x	knots ${x}$$_j \in \mathbb{T}^d$	$dM$
fftw_complex*	f_hat	Fourier coefficients	$N_{\text{\tiny $\Pi$}}$
fftw_complex*	f	samples	$M$
double**	c_phi_inv	precomputed $c_{\mbox{\boldmath\scriptsize {${k}$}}}\left(\tilde\varphi\right)^{-1}$	$\sum_{t=0}^{d-1} N_t$
double*	psi	precomputed $\tilde\psi\left({\mbox{\boldmath {${x}$}}}_j - \mbox{\boldmath {${n}$}}^{-1}\odot \mbox{\boldmath {${l}$}}\right)$	$d\left(2m+2\right)M$
		or (flags *_PSI)	$\left(2m+2\right)^d M$
fftw_complex*	g	$g_{\mbox{\boldmath\scriptsize {${l}$}}}$	$n_{\text{\tiny $\Pi$}}$
fftw_complex*	g_hat	$\hat g_{\mbox{\boldmath\scriptsize {${k}$}}}$	$(n_{\text{\tiny $\Pi$}})$