index.rst

Models and Fitting (astropy.modeling)

Introduction

astropy.modeling provides a framework for representing models and performing model evaluation and fitting. A number of predefined 1-D and 2-D models are provided and the capability for custom, user defined models is supported. Different fitting algorithms can be used with any model. For those fitters with the capabilities fitting can be done using uncertainties, parameters with bounds, and priors.

Using Modeling

.. toctree::
   :maxdepth: 2

   Models <models.rst>
   Compound Models <compound-models.rst>
   Model Parameters <parameters.rst>
   Fitting <fitting.rst>
   Using Units with Models and Fitting <units.rst>

A Simple Example

This simple example illustrates defining a model, calculating values based on input x values, and using fitting data with a model.

.. plot::
    :include-source:

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

    # define a model for a line
    line_orig = models.Linear1D(slope=1.0, intercept=0.5)

    # generate x, y data non-uniformly spaced in x
    # add noise to y measurements
    npts = 30
    rng = np.random.default_rng(10)
    x = rng.uniform(0.0, 10.0, npts)
    y = line_orig(x)
    y += rng.normal(0.0, 1.5, npts)

    # initialize a linear fitter
    fit = fitting.LinearLSQFitter()

    # initialize a linear model
    line_init = models.Linear1D()

    # fit the data with the fitter
    fitted_line = fit(line_init, x, y)

    # plot the model
    plt.figure()
    plt.plot(x, y, 'ko', label='Data')
    plt.plot(x, fitted_line(x), 'k-', label='Fitted Model')
    plt.xlabel('x')
    plt.ylabel('y')
    plt.legend()

Advanced Topics

.. toctree::
   :maxdepth: 2

   Performance Tips <performance.rst>
   Extending Models <new-model.rst>
   Extending Fitters <new-fitter.rst>
   Adding support for units to models <add-units.rst>
   Joint Fitting <jointfitter.rst>

Pre-Defined Models

Some of the pre-defined models are listed and illustrated.

.. toctree::
   :maxdepth: 2

   1D Models <predef_models1D.rst>
   2D Models <predef_models2D.rst>
   Physical Models <physical_models.rst>
   Polynomial Models <polynomial_models.rst>
   Powerlaw Models <powerlaw_models.rst>
   Spline Models <spline_models.rst>

Examples

.. toctree::
   :maxdepth: 2

   Fitting a line <example-fitting-line>
   example-fitting-constraints
   example-fitting-model-sets

Reference/API

.. toctree::
   :maxdepth: 2

   reference_api