weighting MC gamma to MAGIC log-parabola spectrum

[SeiyaNozaki]

Here I'd like to implement the code for weighting MC gamma to LogParabola spectrum.
Main difference is:

• can select spectral shape for weighting, "PowerLaw" or "LogParabola" in mc/mc.py("rate", "weight")
• apply LogParabola in mc/sensitivity.py("find_best_cuts_sensitivity", "sensitivity")
  Any comments are welcome.

[moralejo]

Same as above, explain w_param, especially signs.

[moralejo]

General comment: for differential sensitivity calculations, using the HEGRA power-law spectrum, or a more accurate log-parabola parametrization, will make no difference. The effect would just go through the difference in hardness within each energy bin , and hence is very small for the usually narrow (5 bins/dex) bins we use.

The log-parabola weighting is instead crucial for comparisons of Crab data with MC gammas, for example to obtain parameter distributions, because in that case the energy range spanned by events entering one such comparison may be arbitrarily wide.

[SeiyaNozaki]

Thanks for the comments @moralejo !

I see, then here I'd like to implement the change for only 'rate', 'weight' function, not sensitivity codes. (If needed in the future, I'll pull request again).
I'll modify the codes following your comments (add explanation of parameters).

[rlopezcoto]

Hi @SeiyaNozaki, I agree with @moralejo that the log-parabola will not make a big difference for the differential sensitivity calculations, but this will be useful for other calculations, thanks for implementing it!
Could you maybe think on adding some test unit along with this PR?

[SeiyaNozaki]

Hi @rlopezcoto Sorry I forgot to answer your message.

Could you maybe think on adding some test unit along with this PR?

For now, no. Just I wanted to implement this function for anyone to use log-parabola weighting.

[rlopezcoto]

Hi @SeiyaNozaki, I'm happy with the changes and would propose this to be accepted if @moralejo approves, just one additional question: if the shape given is LogParabola and no beta parameter is given, will the call throw an error or is there any default value?
Also, what if shape == PowerLaw and I introduce a beta parameter in the call?

[SeiyaNozaki]

Hi @rlopezcoto ,
For the first case(LogParabola without beta), we will get error.
But the second case(PowerLaw with beta), no error and just other parameters are used for the calcurlation.
Would it be better to add the function to check if the param match the shape?

[rlopezcoto]

what kind of error in the first case? (a generic python one I guess).
It would be great if you could check that we are giving the correct parameters depending on the function introduced.

[SeiyaNozaki]

what kind of error in the first case? (a generic python one I guess).

Yes, just a KeyError.

>>> crab_par_hegra
{'f0': <Quantity 2.83e-11 1 / (cm2 s TeV)>, 'alpha': -2.62, 'e0': <Quantity 1. TeV>}
>>> rate_ = rate("LogParabola", 0.1 * u.TeV, 100 * u.TeV, crab_par_hegra, 0, 0)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/home/cta/Work/Install/anaconda3/envs/cta-dev/lib/python3.7/site-packages/lstchain-0.4.5.post9+git66dd663-py3.7.egg/lstchain/mc/mc.py", line 107, in rate
    log_parabola =  LogParabolaSpectralModel.from_log10(amplitude=param['f0'], reference=param['e0'], alpha=-1*param['alpha'], beta=-1*param['beta'])
KeyError: 'beta'

It would be great if you could check that we are giving the correct parameters depending on the function introduced.

I'll introduce such a function in a few days.

[SeiyaNozaki]

I added the function to check if the input parameters correspond to the expected function.

[rlopezcoto]

Thanks a lot @SeiyaNozaki!
If @moralejo approves, I'll merge

[SeiyaNozaki]

Sorry, I got an unit error with Log Parabola function, let me check a little...

[SeiyaNozaki]

I fixed the unit error, sorry.
Now I'm completely sure that this function works fine!