pyat: Optics about at HOT 6 CLOSED

From @bnash on October 11, 2016 14:30

Here is a simple function to compute the 6x6 one turn map matrix. From this we can compute generalized Twiss parameters, invariants, etc. May still be a good idea to have uncoupled limits to get simple Twiss params.
I checked and got approximate agreement with Matlab on this. The Matlab version uses
an epsilon of 6.055454452393343e-006
claiming this is somehow optimal (referencing numerical recipes). I don't really know why.
(I'm trying to make the code display with indentation properly, but it doesn't work)

import at
import numpy

def pyATm66(ring):
    eps=1e-10
    epsmat=eps*numpy.identity(6)
    mm=at.atpass(ring, epsmat, 1)/eps
    return numpy.transpose(mm)

from at.

Three backticks before the code and three backticks afterwards.

from at.

(Backtick is top-left on the UK keyboard).

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From @bnash on October 11, 2016 15:3

Thanks, next step is to make a version of the amat function (linear normal form, converts matrix to 3 rotations)
https://github.com/willrogers/at/blob/pyat/atmat/atphysics/amat.m
in python.

From there, we can also make generalized lattice functions with Forests 'betaoids' and 'etaoids'
http://journals.aps.org/pre/abstract/10.1103/PhysRevE.58.2481

https://github.com/willrogers/at/blob/pyat/atmat/pubtools/local_lattice_params/find_betaoids.m

We also need to make utilities for computing things at different places around the ring. Many of the functions in Matlab AT accept a set of indices that compute the quantities at those positions in the lattice.

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From @bnash on October 11, 2016 15:7

amat can also be used to compute eigenemittance following computing second moment matrix (Sigma) from ohmi-envelope
https://github.com/willrogers/at/blob/pyat/atmat/atphysics/ohmienvelope.m
Though, I think the eigenvalues of J*Sigma also give you the emittances.

from at.

We now have substantial progress on this so I will close the ticket.

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