Fitting 2D data
===============
We will start by doing some necessary imports:

.. code-block:: ipython

        from astropy.modeling.astro_sherpa import SherpaFitter
        from astropy.modeling.models import Gaussian2D
        import numpy as np

We need to define some data so we use the `~astropy.modeling.functional_models.Gaussian2D` model and add some poisson noise:

.. code-block:: ipython

        np.random.seed(123456789)
        x0low, x0high = 3000, 4000
        x1low, x1high = 4000, 4800
        dx = 15
        x1, x0 = np.mgrid[x1low:x1high:dx, x0low:x0high:dx]
        shape = x0.shape

        truth = Gaussian2D(x_mean=3512, y_mean=4418, x_stddev=150, y_stddev=150,
                           theta=20, amplitude=100)

        mexp = truth(x0, x1).reshape(shape)
        merr = abs(np.random.poisson(mexp) - mexp)

.. image:: _generated/example_plot_2d_data.png

Now we have some data so let's fit a model after the parameters have been offset.
Here we flatten the arrays and then adjust the error bars for the fit:

.. code-block:: ipython
	
	sfit = SherpaFitter(statistic=Chi2)
	fitmo = truth.copy()
	fitmo.x_mean = 3650
	fitmo.y_mean = 4250
	fitmo.x_stddev = 100
	fitmo.y_stddev = 100
	fitmo.theta = 10
	fitmo.amplitude = 50

        fitmo = sfit(fitmo, x=x0.flatten(), y=x1.flatten(), z=mexp.flatten()+merr.flatten(),
                     xbinsize=np.ones(x0.size)*dx, ybinsize=np.ones(x1.size)*dx,
                     err=merr.flatten()+np.random.uniform(-0.5,0.5,x0.size))

.. image:: _generated/example_plot_2d_fit.png