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Figure 4
Comparison of four different refinement engines: LBFGS, LBFGS with curvatures, LevMar and sparse LevMar. 50–5000 crystal models and each of the 32 sensors were refined simultaneously. (a) Total run time for refinement, averaged over ten trials. (b) Number of steps taken by each engine during refinement (LevMar and sparse LevMar exactly overlap). (c) Data-set r.m.s.d.s (obs − calc) from each refinement engine. Except for LBFGS, the traces from the engines overlap. (d) Array sizes for Levenberg–Marquardt. A normal matrix used for refining n parameters contains n(n + 1)/2 elements in the upper triangle, of which only a subset are nonzero. Therefore, the number of elements in the normal matrix grows faster than n and faster than the number of nonzero elements in the normal matrix. (e) Extended refinement of 500 images using LBFGS and LBFGS with curvatures. 10 000 steps are shown after removing the r.m.s.d. convergence check during refinement. R.m.s.d. versus step number is shown on the left. Two enlargements are provided on the right. Top enlargement: early refinement steps. Bottom enlargement: all refinement steps but enlarged tightly in r.m.s.d. to show small changes over time.

Journal logoSTRUCTURAL
ISSN: 2059-7983
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