[cctbxbb] real-space symmetry operators

[Nathaniel Echols]

Hi all--

I'm trying to figure out how to orthogonalize symmetry operators given a
unit cell, which doesn't seem to be something we have code for.  These
appear in PDB files in the REMARK 290 section but I haven't been able to
find any other software that generates them, and the relationship between
the symops and the real-space equivalents is unclear.  I assume this is
conceptually similar to orthogonalizing fractional coordinates, but
unit_cell.orthogonalize() does not quite do what I wanted.  In the PDB, for
P63 it has this (excerpted):

REMARK 290       2555   -Y,X-Y,Z
...
REMARK 290   SMTRY1   2 -0.500000 -0.866025  0.000000        0.00000
REMARK 290   SMTRY2   2  0.866025 -0.500000  0.000000        0.00000
REMARK 290   SMTRY3   2  0.000000  0.000000  1.000000        0.00000

which looks like it should be relatively straightforward, but I'm not very
good with matrices.  Does anyone know the correct math for this?  The
corresponding rt_mx object from sgtbx looks like this:

r=(0.0, -1.0, 0.0, 1.0, -1.0, 0.0, 0.0, 0.0, 1.0) t=(0.0, 0.0, 0.0)

(Yes, I realize that there are much easier ways to apply symmetry operators
to coordinates, but I want to limit the number of matrix multiplications
involved when starting from Cartesian coordinates.)

thanks,
Nat
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