Add Beta1D model

[mirca]

cc @pllim @eteq
First time contributing in modeling.models, let me know if I'm missing something

[astropy-bot]

Hi there @mirca 👋 - thanks for the pull request! I'm just a friendly 🤖 that checks for issues related to the changelog and making sure that this pull request is milestoned and labelled correctly. This is mainly intended for the maintainers, so if you are not a maintainer you can ignore this, and a maintainer will let you know if any action is required on your part 😃.

Everything looks good from my point of view! 👍

[nden]

Add a . at the end of the definition in all docstrings.

[nden]

The same terms are computed many times. For those that makes sense could you compute them once at the beginning and reuse that.

[nden]

@mirca Thanks for adding this model. Please add also a fitting test if possible,

[pllim]

Need a change log.

Also you don't need to write new functions for the testing. Most of the models are tested in https://github.com/astropy/astropy/blob/master/astropy/modeling/tests/example_models.py .

[pllim]

Also, I wonder if this should really belong in powerlaws.py or not... 🤔

[mirca]

import numpy as np
from astropy.modeling import models
from astropy.modeling.fitting import LevMarLSQFitter
from matplotlib import pyplot as plt

x = np.linspace(0, 5, 50)
noise = np.random.normal(loc=0, scale=0.05, size=len(x))
fake_data = models.Beta1D(xpos=1)(x) + noise

plt.plot(x, fake_data, 'x')

# initial guess model
f0_model = models.Beta1D(amplitude=1.5, beta=1.1, r0=0.75, xpos=0.9)
fitter = LevMarLSQFitter()
f_model = fitter(f0_model, x, fake_data)

plt.plot(x, f_model(x), '-')
print(f_model)
print(np.sqrt(np.diag(fitter.fit_info['param_cov'])))
plt.show()

Model: Beta1D
Inputs: ('x',)
Outputs: ('y',)
Model set size: 1
Parameters:
      amplitude        beta           r0           xpos
    ------------- ------------- ------------- --------------
    1.02990367011 1.12561141593 1.05475525089 0.996366721785
[ 0.02092153  0.28918073  0.20110149  0.01010909]

@nden where should I add this fitting test?

[nden]

@mirca If you add the model to tests/example_models.py it will be picked up by the fitting testers.

[mirca]

• add change log entry
• move implementation from functional_models.py to powerlaws.py
• add Beta1D to tests/example_models.py

[mirca]

travis failures look unrelated?

[bsipocz]

this causes the sphinx fail, use the full namespace as Lorentz1D is not defined in this file.

[bsipocz]

@mirca - The sphinx fail is real, and I've restarted the other one that timed out (it was probably unrelated, but we'll see).

[larrybradley]

Thanks, @mirca. The Beta1D model is simply a slight reparameterization of the existing Moffat1D model. Astropy used to have both Beta1Dand Beta2D models (from Sherpa ), but it was decided to change them to Moffat1D and Moffat2D. Previous discussions:

#3029

https://groups.google.com/d/msg/astropy-dev/vizuhH8I3PA/IuhNz6qrlX4J

[nden]

Given all this is anyone opposed to adding a note to the Moffat classes to the effect that they are reparameterization of the Beta models in Sherpa?

@larrybradley Could you look over this list and see if it is up to date.

[mirca]

@larrybradley Oh ok, thanks for pointing that out!

[larrybradley]

@nden shell2d looks to be the same as the already implemented Ring2D model (http://docs.astropy.org/en/stable/api/astropy.modeling.functional_models.Ring2D.html)

And there is now a PR to add Schechter1D (you can remove the closed doc PR reference).

Everything else looks up to date.