The crystallographic fast Fourier transform. Recursive symmetry reduction
نویسندگان
چکیده
منابع مشابه
The crystallographic fast Fourier transform. Recursive symmetry reduction.
Algorithms are presented for maximally efficient computation of the crystallographic fast Fourier transform (FFT). The approach is applicable to all 230 space groups and allows reduction of both the computation time and the memory usage by a factor equal to the number of symmetry operators. The central idea is a recursive reduction of the problem to a series of transforms on grids with no speci...
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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 c...
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An algorithm for computing the discrete Fourier transform of data with threefold symmetry axes is presented. This algorithm is straightforward and easily implemented. It reduces the computational complexity of such a Fourier transform by a factor of 3. There are no restrictive requirements imposed on the initial data. Explicit formulae and a scheme of computing the Fourier transform are given. ...
متن کاملThe crystallographic fast Fourier transform. III. Centred lattices.
Algorithms for evaluation of the crystallographic FFT for centred lattices are presented. These algorithms can be applied to 80 space groups containing centring operators. For 44 of them, combining these algorithms with those described by Rowicka, Kudlicki & Otwinowski [Acta Cryst A59, 172-182] yields the maximal symmetry reduction. For other groups, new algorithms, to be presented in our forth...
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ژورنال
عنوان ژورنال: Acta Crystallographica Section A Foundations of Crystallography
سال: 2007
ISSN: 0108-7673
DOI: 10.1107/s0108767307047411