Derivative of SVD V and U matrices

[saulg]

sorry I am new and posted instead of previewing...im currently writing the post

 

[saulg]

I find a rotation matrix which best describes how to get from one set of atomic coordinates (molecular geometry) to another by just a pure rotation.

The rotation matrix R is defined

$$R=V \left( \begin{array}{ccc}<br /> 1 & & \\<br /> & 1 & \\<br /> & & \left|VU^T\right| \end{array} \right)U^T$$

where V and U are from the SVD of matrix K:

$$K=V\Lambda U^T[\tex]<br /> <br /> K is formed by summing over i the outer products of the coordinate vectors of atom i in the first and second geometry. (i follow the method described at http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/MARBLE/high/pose/least.htm" )<br /> <br /> <br /> I.e K depends on atomic coordinates, and so do U and V.<br /> <br /> I require the derivative of each element of R with respect to atomic coordinate. (The rotation matrix is used in an energy approximation and I need analytic forces)<br /> <br /> <br /> Any answers or hints much appreciated.$$

 

[saulg]

I think I've found the answer I needed in the following paper:

http://www.ics.forth.gr/cvrl/publications/conferences/2000_eccv_SVD_jacobian.pdf