Ellipse2D() only fitting amplitude

Description

When I fit a simple ellipse with models.fitting it will fit the amplitude, but none of the other parameters in Ellipse2D()

Expected behavior

It would fit all the parameters!

Actual behavior

It successfully ran, but only fit the ellipse amplitude. It does seem to do an OK job at that.

Steps to Reproduce

import numpy as np
import matplotlib.pyplot as plt
from astropy.modeling import models, fitting
from astropy.modeling.models import Ellipse2D

#make some random ellipse
e = Ellipse2D(amplitude=100., x_0=20, y_0=30, a=12, b=18,
              theta=0.2)
y, x = np.mgrid[0:50, 0:50]
#add some noise 
emap = e(x, y)+np.random.random([50,50])*100

#fit 
fit = fitting.LevMarLSQFitter()

# initialize a linear model
ellip_init = models.Ellipse2D()
e_init = Ellipse2D(amplitude=1200., x_0=20, y_0=30, a=200, b=900,
              theta=2)

# fit the data with the fitter
fitted_ellip = fit(e_init, x, y, emap)

fitted_ellip

System Details

macOS-10.16-x86_64-i386-64bit Python 3.8.3 (default, Jul 2 2020, 11:26:31) [Clang 10.0.0 ] Numpy 1.22.4 pyerfa 2.0.0 astropy 5.1 Scipy 1.7.3 Matplotlib 3.5.2

[jegpeek]

@eteq gave me some comments on this – he believes it has to do with the mathematical architecture of the problem itself, not astropy. Please stand by while I test his method and then we/you can decide whether to just close this or add some documentation or what?

[github-actions[bot]]

I’m going to close this issue as per my previous message, but if you feel that this issue should stay open, then feel free to re-open and remove the Close? label.

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