Treatment of equations of constraint in least-squares refinement

With a least-squares program organization, as described by Busing [Acta Cryst. (1971), A27, 683- 684], the constraints have to be put into a form where the dependent parameters are expressed by the independent ones and, possibly, by further constants. Difficulties may arise if (1) several linear or non-linear constraints refer simultaneously to several parameters, and (2) if the constraints are not linear and cannot be solved analytically for the dependent parameters. For both cases a solution is offered which is based on the application of the well known solution of linear equations. Non-linear constraints are linearized. If all constraints are linear, Busing's organization is retained; if they are (partly) non-linear, Busing's organization has to be changed in the main program, and the user's subroutine SETP has to be written according to a different concept. Hints concerning programming are given and some examples are discussed.