HierarchicalO(N) computation of small-angle scattering profiles and their associated derivatives.
The need for fast approximate algorithms for Debye summation arises in computations performed in crystallography, small/wide-angle X-ray scattering and small-angle neutron scattering. When integrated into structure refinement protocols these algorithms can provide significant speed up over direct all-atom-to-all-atom computation. However, these protocols often employ an iterative gradient-based optimization procedure, which then requires derivatives of the profile with respect to atomic coordinates. This article presents an accurate,O(N) cost algorithm for the computation of scattering profile derivatives. The results reported here show orders of magnitude improvement in computational efficiency, while maintaining the prescribed accuracy. This opens the possibility to efficiently integrate small-angle scattering data into the structure determination and refinement of macromolecular systems.
Department of Chemistry and Biochemistry, Center for Biomolecular Structure and Organization, University of Maryland, College Park, MD, USA ; Institute for Advanced Computer Studies, University of Maryland, College Park, MD, USA.
Konstantin
K
Berlin
Institute for Advanced Computer Studies, University of Maryland, College Park, MD, USA ; Fantalgo LLC, Elkridge, MD, USA.
Nail A
NA
Gumerov
Department of Chemistry and Biochemistry, Center for Biomolecular Structure and Organization, University of Maryland, College Park, MD, USA ; Institute for Advanced Computer Studies, University of Maryland, College Park, MD, USA.
David
D
Fushman
Institute for Advanced Computer Studies, University of Maryland, College Park, MD, USA ; Fantalgo LLC, Elkridge, MD, USA.
Ramani
R
Duraiswami
Jacobian; gradients; small-angle scattering; wide-angle scattering