The crystallographic fast Fourier transform. II. One-step symmetry reduction.

An algorithm for evaluation of the crystallographic FFT for 67 crystallographic space groups is presented. The symmetry is reduced in such a way that it is enough to calculate P1 FFT in the asymmetric unit only and then, in a computationally simpler step, recover the final result. The algorithm yields the maximal symmetry reduction for every space group considered. For the central step in the calculation consisting of general P1 FFTs, any generic fast Fourier subroutine can be used. The approach developed in this paper is an extension of the scheme derived for p3-symmetric data [Rowicka, Kudlicki & Otwinowski (2002). Acta Cryst. A58, 574-579]. Algorithms described here will also be used in our forthcoming papers [Rowicka, Kudlicki & Otwinowski (2003). Acta Cryst A59, 183-192; Rowicka, Kudlicki & Otwinowski (2003), in preparation], where more complicated groups will be considered.