Add albedo correction

[samaloney]

PR Description

A a function to read in precomputed greens table and return spectrum with albedo correction, would close #128

• Split function at the moment every time the function is called we would make web request and load a file from disk both very slow not ideal for fitting. The idea would be split up into at least two parts depending on the use case/s. As far as I know often $\theta$ is fix so the loading and interpolation between $\theta$ can be cached. So one function to load the appropriate greens matrix file and interpolate for given angle. A second function would call the previous function and do the energy intepotalation (as this could change in a fit e.g. gain correction) and fold the given spectrum through obtained green matrix.
• Turn in to astropy model e.g. spec | albedo (still waiting on proper units support in astroy for this work Should the model composition operator, |, support units changing astropy/astropy#17302)
• Docs and tests

Recreated Fig 2 upper from the paper

[edkontar]

I have found IDL code used in 2005 to generate Green Matrices for OSPEX and put it on github:

https://github.com/edkontar/albedo

[natsat0919]

I have added the changes we made to the albedo model during the workshop. For now we made the model "unitless" until we resolve the astropy model unit problems with SRM. All the units-related lines are commented so it can be easily updated.

[samaloney]

One of the main reason to separate things is to make them testable with these change it will be harder to test so I wonder are they necessary?

[edkontar]

In OSPEX/drm_correct_albedo.pro, the anisotropy parameter is “a coefficient showing the ratio of the flux in observer direction to the flux downwards." A smaller value means more of an effect from albedo. A value of 1000 means very little effect. if anisotropy=1 (default) the source is isotropic. However, in the paper, the coefficient α that accounts for anisotropy of the source in the Eddington approximation – that is, "distinct but constant specific intensities in the downward and in the upward hemispheres, in the ratio α” i.e. the anisotropy described as the reciprocal of the anisotropy parameter in the OSPEX.

Should the description state the definition of "α" was assumed as in OSPEX?

class Albedo(FittableModel):
r"""
Aldedo model which adds albdeo correction to input spectrum.
Following [Kontar2006]_ using precomputed green matrices distributed as part of [SSW]_.
.. [Kontar2006] https://doi.org/10.1051/0004-6361:20053672
.. [SSW] https://www.lmsal.com/solarsoft/
Parameters
==========
energy_edges :
Energy edges associated with input spectrum
theta :
Angle between Sun-observer line and X-ray source
anisotropy :
Ratio of the flux in observer direction to the flux downwards, 1 for an isotropic source

[jajmitchell]

I have reverted the code back to its state before the previous commit with some small edits, the functions are now defined outside of the class and the class is used a wrapper, therefore the tests should now work, is it ok for me to push these changes? The albedo model is now functional with astropy fitters.

[samaloney]

Go for it, sounds good

[samaloney]

Ok so I think this is good to go, @natsat0919 and @jajmitchell could you review?

[jajmitchell]

I think that this PR is ready to be merged. I am still trying to get the albedo model to work with a matrix model in astropy class format and with the thermal model in astropy format, which may require some fiddling with the unit handling, we could delay the merge here and get the unit handling all working together before merging, or merge and then deal with this in a differently titled pull request as the albedo model does function now as a stand alone and this is a wider problem. My instinct would be to merge, then open a "compound model unit handling" pull request or issue, but am easy either way.

[jajmitchell]

@samaloney, just realised that the anisotropy parameter needs to have the "name" argument added in its definition, apologies that I spotted this after adding my review, are you happy for me to push this minor change then re-review?

[samaloney]

pre-commit.ci autofix