title: Numerically stable algorithms for the computation of reduced unit cells.
abstract: The computation of reduced unit cells is an important building block for a number of crystallographic applications, but unfortunately it is very easy to demonstrate that the conventional implementation of cell reduction algorithms is not numerically stable. A numerically stable implementation of the Niggli-reduction algorithm of Krivý & Gruber [Acta Cryst. (1976), A32, 297-298] is presented. The stability is achieved by consistently using a tolerance in all floating-point comparisons. The tolerance must be greater than the accumulated rounding errors. A second stable algorithm is also presented, the minimum reduction, that does not require using a tolerance. It produces a cell with minimum lengths and all angles acute or obtuse. The algorithm is a simplified and modified version of the Buerger-reduction algorithm of Gruber [Acta Cryst. (1973), A29, 433-440]. Both algorithms have been enhanced to generate a change-of-basis matrix along with the parameters of the reduced cell.
authors.affiliation: Lawrence Berkeley National Laboratory, One Cyclotron Road, Bldg 4R0230, Berkeley, CA 94720-8235, USA. rwgrosse-kunstleve@lbl.gov
authors.forename: R W
authors.initials: RW
authors.lastname: Grosse-Kunstleve
authors.forename: N K
authors.initials: NK
authors.lastname: Sauter
authors.forename: P D
authors.initials: PD
authors.lastname: Adams
mesh_terms: D000465:Algorithms; D003461:Crystallography