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Generic representation and evaluation of properties as a function of position in reciprocal space
Author(s) -
Cowtan Kevin
Publication year - 2002
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889802013420
Subject(s) - classification of discontinuities , position (finance) , reciprocal , usable , function (biology) , basis (linear algebra) , simple (philosophy) , generalization , representation (politics) , computer science , range (aeronautics) , space (punctuation) , algorithm , basis function , scaling , theoretical computer science , resolution (logic) , mathematics , mathematical analysis , geometry , artificial intelligence , epistemology , philosophy , materials science , law , linguistics , world wide web , composite material , biology , operating system , evolutionary biology , political science , finance , politics , economics
A generalized approach is described for evaluating arbitrary functions of position in reciprocal space. This is a generalization which subsumes a whole range of calculations that form a part of almost every crystallographic software application. Examples include scaling of structure factors, the calculation of structure‐factor statistics, and some simple likelihood calculations for a single parameter. The generalized approach has a number of advantages: all these calculations may now be performed by a single software routine which need only be debugged and optimized once; the existing approach of dividing reciprocal space into resolution shells with discontinuities at the boundaries is no longer necessary; the implementation provided makes employing the new functionality extremely simple and concise. The calculation is split into three standard components, for which a number of implementations are provided for different tasks. A `basis function' describes some function of position in reciprocal space, the shape of which is determined by a small number of parameters. A `target function' describes the property for which a functional representation is required, for example . An `evaluator' takes a basis and target function and optimizes the parameters of the basis function to fit the target function. Ideally the components should be usable in any combination.