autofit 0.59.6

Classy non-linear optimisation

PyAutoFit

PyAutoFit is a Python-based probablistic programming language that allows complex model fitting techniques to be straightforwardly integrated into scientific modeling software. PyAutoFit specializes in:

• Black box models with complex and expensive log likelihood functions.
• Fitting many different model parametrizations to a data-set.
• Modeling extremely large-datasets with a homogenous fitting procedure.
• Automating complex model-fitting tasks via transdimensional model-fitting pipelines.

API Overview

To illustrate the PyAutoFit API, we'll use an illustrative toy model of fitting a one-dimensional Gaussian to noisy 1D data of a Gaussian's line profile. Here's an example of the data (blue) and the model we'll fit (orange):

.. image:: https://raw.githubusercontent.com/rhayes777/PyAutoFit/master/toy_model_fit.png :width: 400 :alt: Alternative text

We define our model, a 1D Gaussian, by writing a Python class using the format below.

.. code-block:: python

class Gaussian:

    def __init__(
        self,            # <- PyAutoFit recognises these
        centre = 0.0,    # <- constructor arguments are
        intensity = 0.1, # <- the model parameters of .
        sigma = 0.01,    # <- the Gaussian.
    ):
        self.centre = centre
        self.intensity = intensity
        self.sigma = sigma

"""
An instance of the Gaussian class will be available during model fitting.
This method will be used to fit the model to data and compute a likelihood.
"""

def line_from_xvalues(self, xvalues):

    transformed_xvalues = xvalues - self.centre

    return (self.intensity / (self.sigma * (2.0 * np.pi) ** 0.5)) * \
            np.exp(-0.5 * transformed_xvalues / self.sigma)

PyAutoFit recognises that this Gaussian may be treated as a model component whose parameters can be fitted for via a non-linear search like emcee <https://github.com/dfm/emcee>_..

To fit this Gaussian to the data we create an Analysis object, which gives PyAutoFit the data and a likelihood function describing how to fit the data with the model:

.. code-block:: python

class Analysis(af.Analysis):

    def __init__(self, data, noise_map):

        self.data = data
        self.noise_map = noise_map

    def log_likelihood_function(self, instance):

        """
        The 'instance' that comes into this method is an instance of the Gaussian class
        above, with the parameters set to (random) values chosen by the non-linear search.
        """

        print("Gaussian Instance:")
        print("Centre = ", instance.centre)
        print("Intensity = ", instance.intensity)
        print("Sigma = ", instance.sigma)

        """
        We fit the data with the Gaussian instance, using its
        "line_from_xvalues" function to create the model data.
        """

        xvalues = np.arange(self.data.shape[0])

        model_data = instance.line_from_xvalues(xvalues=xvalues)
        residual_map = self.data - model_data
        chi_squared_map = (residual_map / self.noise_map) ** 2.0
        log_likelihood = -0.5 * sum(chi_squared_map)

        return log_likelihood

We can now fit data to the model using a non-linear search of our choice.

.. code-block:: python

model = af.PriorModel(Gaussian)

analysis = a.Analysis(data=data, noise_map=noise_map)

emcee = af.Emcee(nwalkers=50, nsteps=2000)

result = emcee.fit(model=model, analysis=analysis)

The result object contains information on the model-fit, for example the parameter samples, best-fit model and marginalized probability density functions.

Getting Started

To get started checkout our readthedocs <https://pyautofit.readthedocs.io/>_, where you'll find our installation guide, a complete overview of PyAutoFit's features, examples scripts and tutorials and detailed API documentation.

Slack

We're building a PyAutoFit community on Slack, so you should contact us on our Slack channel <https://pyautofit.slack.com/>_ before getting started. Here, I give the latest updates on the software & can discuss how best to use PyAutoFit for your science case.

Unfortunately, Slack is invitation-only, so first send me an email <https://github.com/Jammy2211>_ requesting an invite.