Flags

The flags, set in nfft_flags concern memory allocation and precomputations. For the knot vector ${x}$, the vector of Fourier coefficients ${\hat f}$, and the vector of samples ${f}$ memory is allocated iff MALLOC_X, MALLOC_F_HAT, and MALLOC_F are set, respectively.

The flag FFTW_INIT causes the library to initialise the plans for the fft; iff FFT_OUT_OF_PLACE is set, the vectors ${g}$ and ${\hat g}$ have their own allocated memory, otherwise they share.

Precomputation can be customised by the flags PRE_PHI_HUT, PRE_PSI, and PRE_FULL_PSI; PRE_PHI_HUT causes the initialisation routine to precompute the values $c_{\mbox{\boldmath\scriptsize {${k}$}}}(\tilde \phi)$ in their tensor product form. The flag PRE_PSI causes the allocation of memory for $\tilde\psi\left({\mbox{\boldmath {${x}$}}}_j - \mbox{\boldmath {${n}$}}^{-1}\odot \mbox{\boldmath {${l}$}}\right)$, used in the 3rd step of Algorithm 1. The routine $\tt nfft\_precompute\_psi$ has to be called for the actual precomputation. Again, the library uses the tensor product form, which leads to a memory usage of $d (2m+2)$ doubles per knot, but an arithmetic complexity of $d (2m+2)^d$ per knot; similar to what is called 'fast gridding' in [13], where the storage requirements are further decreased for the Gaussian window function. In contrast, if in addition the flag PRE_FULL_PSI is set, the library uses $(2m+2)^d$ doubles and $2 (2m+2)^d$ integers (for indices) per knot, which leads to an arithmetic complexity of $(2m+2)^d$ per knot. In this case the nfft_full_psi has to be called.