[cctbxbb] Reindexing matrix -> transform orientation matrix
Phil Evans
pre at mrc-lmb.cam.ac.uk
Tue May 5 04:14:21 PDT 2009
Graeme
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
rotation
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
Phil
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
>
> +44 1235 778091 (work)
> +44 7786 662784 (work mobile)
>
>
>
> This e-mail and any attachments may contain confidential, copyright
> and or privileged material, and are for the use of the intended
> addressee only. If you are not the intended addressee or an
> authorised recipient of the addressee please notify us of receipt by
> returning the e-mail and do not use, copy, retain, distribute or
> disclose the information in or attached to the e-mail.
> Any opinions expressed within this e-mail are those of the
> individual and not necessarily of Diamond Light Source Ltd.
> Diamond Light Source Ltd. cannot guarantee that this e-mail or any
> attachments are free from viruses and we cannot accept liability for
> any damage which you may sustain as a result of software viruses
> which may be transmitted in or with the message.
> Diamond Light Source Limited (company no. 4375679). Registered in
> England and Wales with its registered office at Diamond House,
> Harwell Science and Innovation Campus, Didcot, Oxfordshire, OX11
> 0DE, United Kingdom
>
>
>
> _______________________________________________
> cctbxbb mailing list
> cctbxbb at phenix-online.org
> http://www.phenix-online.org/mailman/listinfo/cctbxbb
More information about the cctbxbb
mailing list