Doing the transform

Algorithm 1 is implemented as

nfft_trafo(&my_plan);

takes my_plan.f_hat as its input and overwrites my_plan.f. One only needs one plan for several transforms of the same kind, i.e. transforms with equal initialisation parameters. For comparison, the direct calculation of (2.3) is done by ndft_trafo. The adjoint transforms are given by nfft_adjoint and ndft_adjoint, respectively.

All data with multi-indices is stored plain, in particular the Fourier coefficient $\hat f_{\ensuremath{\boldsymbol{k}}}$ is stored in my_plan.f_hat[k] with ${\text{\tt k}}:=\sum_{t=0}^{d-1} (k_t+\frac{N_t}{2}) \prod_{t'=t+1}^{d-1} N_{t'}$ . Data vectors might be exchanged by

NFFT_SWAP_complex(my_plan.f_hat,new_f_hat);.