### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 172-182 |

Number of pages | 11 |

Journal | Acta Crystallographica Section A: Foundations of Crystallography |

Volume | 59 |

Issue number | 2 |

DOIs | |

State | Published - Mar 2003 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Structural Biology

### Cite this

*Acta Crystallographica Section A: Foundations of Crystallography*,

*59*(2), 172-182. https://doi.org/10.1107/S0108767303002320

**The crystallographic fast Fourier transform. II. One-step symmetry reduction.** / Rowicka-Kudlicka, Malgorzata; Kudlicki, Andrzej; Otwinowski, Zbyszek.

Research output: Contribution to journal › Article

*Acta Crystallographica Section A: Foundations of Crystallography*, vol. 59, no. 2, pp. 172-182. https://doi.org/10.1107/S0108767303002320

}

TY - JOUR

T1 - The crystallographic fast Fourier transform. II. One-step symmetry reduction

AU - Rowicka-Kudlicka, Malgorzata

AU - Kudlicki, Andrzej

AU - Otwinowski, Zbyszek

PY - 2003/3

Y1 - 2003/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0037361372&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037361372&partnerID=8YFLogxK

U2 - 10.1107/S0108767303002320

DO - 10.1107/S0108767303002320

M3 - Article

VL - 59

SP - 172

EP - 182

JO - Acta Crystallographica Section A: Foundations and Advances

JF - Acta Crystallographica Section A: Foundations and Advances

SN - 0108-7673

IS - 2

ER -