[cctbxbb] Reindexing matrix -> transform orientation matrix

Phil Evans pre at mrc-lmb.cam.ac.uk
Tue May 5 04:14:21 PDT 2009


Not sure that I understand the context, but the basic diffractometer  
equation is

x = [Phi] [U] [B] h

where h =(h k l), [B] is the orthogonalisation matrix (from cell), [U]  
is the orientation matrix (a rotation matrix) & [Phi] is the spindle  

In my definition anyway, a reindexing matrix [H]  post-multiplies the  
row vector hT , ie h'T = hT [H] or h' = [H]T h, ie h = [H]T^-1  
h' (where T indicates transpose)

Then we want   [U] [B] h = [U'] [B'] h' = [U] [B] [H]T^-1 h'

ie [U'] [B']  = [U] [B] [H]T^-1

we can disentangle the orthogonal matrices [U] & [U'] from the cell  
matrices [B] & [B'] via the reciprocal metric tensor

[[U'][B']]T []U'][B']] = [B']T [U']T [U'] [B']  = [B']T [B'] since    
[U']T [U']  = I  from which we can reconstruct [B'] & hence get [U']  
which is what you want


On 5 May 2009, at 10:28, Winter, G (Graeme) wrote:

> Hi Folks,
> I'm just trying to figure out how to do the following, given a  
> triclinic orientation matrix (real or reciprocal space, differ  
> by .inverse() -> triclinic unit cell)
> (like iotbx.lattice_symmetry) stuff -> set of unit cell, Bravais  
> lattice options with reindex operations
> apply reindex operation to orientation matrix -> new basis a, b, c
> The former I have historically done using iotbx.lattice_symmetry but  
> given the move from python to cctbx.python, it seems wasteful. I  
> looked at the source code but got a little confused. The latter  
> seems to be more problematic - even reconstructing the change of  
> basis from a known reindexing operation I don't seem to be able to  
> get the right answer :o(
> Has anyone done anything like this with the CCTBX tools?
> The context is autoindexing with XDS using a full sweep's worth of  
> images, then inspecting the indexes in SPOT.XDS based on the  
> contents of XPARM.XDS.
> Thanks,
> Graeme
> Graeme Winter
> Software and MX Support Scientist
> Diamond Light Source
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