usermodel.rst

Writing your own model

A model class can be created to fit any function, or interface with external code.

There should be some description of what needs to be done, as well as examples. Does the 1D example need to be cleaned up to separate out unnescessary code, perhaps just hiding the setup code (and it would be nice if this could be shared with the setup). Should the 2D example add commentary to point out the following note I added at the time: "Hmmm, this looks similar to the Sherpa results. In particular the 0,0 value is -80 not 1. Aha, is it a normalization at (0,0) vs (1,1) sort of thing?"

A one-dimensional model

An example is the AstroPy trapezoidal model, which has four parameters: the amplitude of the central region, the center and width of this region, and the slope. The following model class, which was not written for efficiancy or robustness, implements this interface:

../code/trap.py

This can be used in the same manner as the :py~sherpa.models.basic.Gauss1D model in the quick guide to Sherpa<quick-gauss1d>.

First, create the data to fit:

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> np.random.seed(0)
>>> x = np.linspace(-5., 5., 200)
>>> ampl_true = 3
>>> pos_true = 1.3
>>> sigma_true = 0.8
>>> err_true = 0.2
>>> y = ampl_true * np.exp(-0.5 * (x - pos_true)**2 / sigma_true**2)
>>> y += np.random.normal(0., err_true, x.shape)

Now create a Sherpa data object:

>>> from sherpa.data import Data1D
>>> d = Data1D('example', x, y)

Set up the user model:

>>> from trap import Trap1D
>>> t = Trap1D()
>>> print(t)
trap1d
   Param        Type          Value          Min          Max      Units
   -----        ----          -----          ---          ---      -----
   trap1d.ampl  thawed            1            0  3.40282e+38           
   trap1d.center thawed            1 -3.40282e+38  3.40282e+38           
   trap1d.width thawed            1            0  3.40282e+38           
   trap1d.slope thawed            1            0  3.40282e+38           

Finally, perform the fit:

>>> from sherpa.fit import Fit
>>> from sherpa.stats import LeastSq
>>> from sherpa.optmethods import LevMar
>>> tfit = Fit(d, t, stat=LeastSq(), method=LevMar())
>>> tres = tfit.fit()
>>> if not tres.succeeded: print(tres.message)

Rather than use a :py~sherpa.plot.ModelPlot object, the overplot argument can be set to allow multiple values in the same plot:

>>> from sherpa import plot
>>> dplot = plot.DataPlot()
>>> dplot.prepare(d)
>>> dplot.plot()
>>> mplot = plot.ModelPlot()
>>> mplot.prepare(d, t)
>>> mplot.plot(overplot=True)

A two-dimensional model

The two-dimensional case is similar to the one-dimensional case, with the major difference being the number of independent axes to deal with. In the following example the model is assumed to only be applied to non-integrated data sets, as it simplifies the implementation of the calc method.

It also shows one way of embedding models from a different system, in this case the two-dimemensional polynomial model from the AstroPy package.

../code/poly.py

Repeating the 2D fit by first setting up the data to fit:

>>> np.random.seed(0)
>>> y2, x2 = np.mgrid[:128, :128]
>>> z = 2. * x2 ** 2 - 0.5 * y2 ** 2 + 1.5 * x2 * y2 - 1.
>>> z += np.random.normal(0., 0.1, z.shape) * 50000.

Put this data into a Sherpa data object:

>>> from sherpa.data import Data2D
>>> x0axis = x2.ravel()
>>> x1axis = y2.ravel()
>>> d2 = Data2D('img', x0axis, x1axis, z.ravel(), shape=(128,128))

Create an instance of the user model:

>>> from poly import WrapPoly2D
>>> wp2 = WrapPoly2D('wp2')
>>> wp2.c1_0.frozen = True
>>> wp2.c0_1.frozen = True

Finally, perform the fit:

>>> f2 = Fit(d2, wp2, stat=LeastSq(), method=LevMar())
>>> res2 = f2.fit()
>>> if not res2.succeeded: print(res2.message)
>>> print(res2)
datasets       = None
itermethodname = none
methodname     = levmar
statname       = leastsq
succeeded      = True
parnames       = ('wp2.c0_0', 'wp2.c2_0', 'wp2.c0_2', 'wp2.c1_1')
parvals        = (-80.289475553599914, 1.9894112623565667, -0.4817452191363118, 1.5022711710873158)
statval        = 400658883390.6685
istatval       = 6571934382318.328
dstatval       = 6.17127549893e+12
numpoints      = 16384
dof            = 16380
qval           = None
rstat          = None
message        = successful termination
nfev           = 80
>>> print(wp2)
wp2
   Param        Type          Value          Min          Max      Units
   -----        ----          -----          ---          ---      -----
   wp2.c0_0     thawed     -80.2895 -3.40282e+38  3.40282e+38           
   wp2.c1_0     frozen            0 -3.40282e+38  3.40282e+38           
   wp2.c2_0     thawed      1.98941 -3.40282e+38  3.40282e+38           
   wp2.c0_1     frozen            0 -3.40282e+38  3.40282e+38           
   wp2.c0_2     thawed    -0.481745 -3.40282e+38  3.40282e+38           
   wp2.c1_1     thawed      1.50227 -3.40282e+38  3.40282e+38