A computer program for the Fourier transform of data with crystal symmetry

Summary form only given. Auslander has used algebraic methods to give a mathematical structure to a study of the symmetries of crystals. An approach to implementing Auslander´s methods that has several important features is described. Only nonredundant data need be stored. Thus, for the case of threefold symmetry, only slightly more than 1/3 of the full set of data need be stored. The problem is broken down into small modules that employ efficient Winograd-type fast Fourier transform algorithms. Most of the calculation is done by calling subroutines which compute smaller conventional 3-D Fourier transforms. This permits the use of efficient available Fourier transform subroutines for the time-consuming parts of the calculations. Indexing and permutations are done on small arrays, thereby reducing data transfer time and storage of index vectors. The method can be implemented on a vector processor. A prototype program was written and tested for a case of 120° rotational symmetry in a 60 by 60 by 60 cube. It was 5.2 times as fast as a conventional 3-D program for the same data