Generic representation and evaluation of properties as a function of position in reciprocal space

Abstract

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 \langle |F|^2\rangle. 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.