This section describes how to add a new nonlinear fitting algorithm to this
package or write a user-defined fitter. In short, one needs to define an error
function and a __call__ method and define the types of constraints which
work with this fitter (if any).
The details are described below using scipy's SLSQP algorithm as an example. The base class for all fitters is ~astropy.modeling.fitting.Fitter:
class SLSQPFitter(Fitter):
supported_constraints = ['bounds', 'eqcons', 'ineqcons', 'fixed',
'tied']
def __init__(self):
# Most currently defined fitters take no arguments in their
# __init__, but the option certainly exists for custom fitters
super().__init__()
All fitters take a model (their __call__ method modifies the model's
parameters) as their first argument.
Next, the error function takes a list of parameters returned by an iteration of the fitting algorithm and input coordinates, evaluates the model with them and returns some type of a measure for the fit. In the example the sum of the squared residuals is used as a measure of fitting.:
def objective_function(self, fps, *args):
model = args[0]
meas = args[-1]
model.fitparams(fps)
res = self.model(*args[1:-1]) - meas
return np.sum(res**2)
The __call__ method performs the fitting. As a minimum it takes all
coordinates as separate arguments. Additional arguments are passed as
necessary:
def __call__(self, model, x, y , maxiter=MAXITER, epsilon=EPS):
if model.linear:
raise ModelLinearityException(
'Model is linear in parameters; '
'non-linear fitting methods should not be used.')
model_copy = model.copy()
init_values, _ = model_to_fit_params(model_copy)
self.fitparams = optimize.fmin_slsqp(self.errorfunc, p0=init_values,
args=(y, x),
bounds=self.bounds,
eqcons=self.eqcons,
ineqcons=self.ineqcons)
return model_copy
astropy.modeling includes a plugin mechanism which allows fitters defined outside of astropy's core to be inserted into the astropy.modeling.fitting namespace through the use of entry points. Entry points are references to importable objects. A tutorial on defining entry points can be found in setuptools' documentation. Plugin fitters must to extend from the ~astropy.modeling.fitting.Fitter base class. For the fitter to be discovered and inserted into astropy.modeling.fitting the entry points must be inserted into the astropy.modeling entry point group
.. doctest-skip::
setup(
# ...
entry_points = {'astropy.modeling': 'PluginFitterName = fitter_module:PlugFitterClass'}
)
This would allow users to import the PlugFitterName through astropy.modeling.fitting by
.. doctest-skip::
from astropy.modeling.fitting import PlugFitterName
One project which uses this functionality is Saba and be can be used as a reference.
This section describes how to write a new fitter with a user-defined statistic function. The example below shows a specialized class which fits a straight line with uncertainties in both variables.
The following import statements are needed:
import numpy as np
from astropy.modeling.fitting import (_validate_model,
fitter_to_model_params,
model_to_fit_params, Fitter,
_convert_input)
from astropy.modeling.optimizers import Simplex
First one needs to define a statistic. This can be a function or a callable class.:
def chi_line(measured_vals, updated_model, x_sigma, y_sigma, x):
"""
Chi^2 statistic for fitting a straight line with uncertainties in x and
y.
Parameters
----------
measured_vals : array
updated_model : `~astropy.modeling.ParametricModel`
model with parameters set by the current iteration of the optimizer
x_sigma : array
uncertainties in x
y_sigma : array
uncertainties in y
"""
model_vals = updated_model(x)
if x_sigma is None and y_sigma is None:
return np.sum((model_vals - measured_vals) ** 2)
elif x_sigma is not None and y_sigma is not None:
weights = 1 / (y_sigma ** 2 + updated_model.parameters[1] ** 2 *
x_sigma ** 2)
return np.sum((weights * (model_vals - measured_vals)) ** 2)
else:
if x_sigma is not None:
weights = 1 / x_sigma ** 2
else:
weights = 1 / y_sigma ** 2
return np.sum((weights * (model_vals - measured_vals)) ** 2)
In general, to define a new fitter, all one needs to do is provide a statistic
function and an optimizer. In this example we will let the optimizer be an
optional argument to the fitter and will set the statistic to chi_line
above:
class LineFitter(Fitter):
"""
Fit a straight line with uncertainties in both variables
Parameters
----------
optimizer : class or callable
one of the classes in optimizers.py (default: Simplex)
"""
def __init__(self, optimizer=Simplex):
self.statistic = chi_line
super().__init__(optimizer, statistic=self.statistic)
The last thing to define is the __call__ method:
def __call__(self, model, x, y, x_sigma=None, y_sigma=None, **kwargs):
"""
Fit data to this model.
Parameters
----------
model : `~astropy.modeling.core.ParametricModel`
model to fit to x, y
x : array
input coordinates
y : array
input coordinates
x_sigma : array
uncertainties in x
y_sigma : array
uncertainties in y
kwargs : dict
optional keyword arguments to be passed to the optimizer
Returns
------
model_copy : `~astropy.modeling.core.ParametricModel`
a copy of the input model with parameters set by the fitter
"""
model_copy = _validate_model(model,
self._opt_method.supported_constraints)
farg = _convert_input(x, y)
farg = (model_copy, x_sigma, y_sigma) + farg
p0, _, _ = model_to_fit_params(model_copy)
fitparams, self.fit_info = self._opt_method(
self.objective_function, p0, farg, **kwargs)
fitter_to_model_params(model_copy, fitparams)
return model_copy