[Numpy-discussion] Matrix: potential usage case?

[Jon Wright]

Hi everyone,

Despite being a bit lost in the matrix debate, today I was working on 
something which might want to use what is being described. You can see 
an array only version at:

http://fable.svn.sourceforge.net/viewvc/fable/ImageD11/trunk/test/demo/latred.py?revision=2741&view=markup

The problem is in diffraction from crystals. We measure "scattering 
vectors" which are in "reciprocal space" and use these to find crystal 
structures in "real space". These spaces are a covariant/contravariat 
pair*. The purpose of the code in the script is to construct a lattice 
class which can work with vectors that are directly measured, or come 
from an FFT of those vectors, which averages lots of peaks into fewer 
peaks. [nb, for a single lattice this is a solved problem in many 
software packages].

I used a keyword argument space="real" or space="reciprocal" to indicate 
which space a vector is in. It might be a good case to think about 
putting in RowVector and ColumnVector and trying to deal with the 
consequences. It is not in this code yet, but the lattice symmetry 
should show up soon. I have not understood how to distinguish a metric 
tensor (flips RowVector to ColumnVector) from a reciprocal metric tensor 
(flips back) from a simple rotation matrix (applies a symmetry operator, 
like 2-fold rotation, so doesn't flip at all). I fear the limitation is 
in my maths?

Best,

Jon


* Some heretics have been known to scale reciprocal space by 2pi. See 
"Vectors and Tensors in Crystallography" by Donald Sands for an overview.