.. note::
    :class: sphx-glr-download-link-note

    Click :ref:`here <sphx_glr_download_examples_example_expression_model.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_example_expression_model.py:


Using an ExpressionModel
========================

ExpressionModels allow a model to be built from a user-supplied expression.
See: https://lmfit.github.io/lmfit-py/builtin_models.html#user-defined-models


.. code-block:: default

    import matplotlib.pyplot as plt
    import numpy as np

    from lmfit.models import ExpressionModel








Generate synthetic data for the user-supplied model:


.. code-block:: default

    x = np.linspace(-10, 10, 201)
    amp, cen, wid = 3.4, 1.8, 0.5

    y = amp * np.exp(-(x-cen)**2 / (2*wid**2)) / (np.sqrt(2*np.pi)*wid)
    y = y + np.random.normal(size=x.size, scale=0.01)








Define the ExpressionModel and perform the fit:


.. code-block:: default

    gmod = ExpressionModel("amp * exp(-(x-cen)**2 /(2*wid**2))/(sqrt(2*pi)*wid)")
    result = gmod.fit(y, x=x, amp=5, cen=5, wid=1)








this results in the following output:


.. code-block:: default

    print(result.fit_report())

    plt.plot(x, y, 'bo')
    plt.plot(x, result.init_fit, 'k--', label='initial fit')
    plt.plot(x, result.best_fit, 'r-', label='best fit')
    plt.legend(loc='best')
    plt.show()



.. image:: /examples/images/sphx_glr_example_expression_model_001.png
    :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    [[Model]]
        Model(_eval)
    [[Fit Statistics]]
        # fitting method   = leastsq
        # function evals   = 52
        # data points      = 201
        # variables        = 3
        chi-square         = 0.02184805
        reduced chi-square = 1.1034e-04
        Akaike info crit   = -1828.51661
        Bayesian info crit = -1818.60669
    [[Variables]]
        amp:  3.40725701 +/- 0.00541581 (0.16%) (init = 5)
        cen:  1.80147428 +/- 9.1751e-04 (0.05%) (init = 5)
        wid:  0.49989801 +/- 9.1751e-04 (0.18%) (init = 1)
    [[Correlations]] (unreported correlations are < 0.100)
        C(amp, wid) =  0.577

    /Users/Newville/Codes/lmfit-py/examples/example_expression_model.py:35: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
      plt.show()





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  0.089 seconds)


.. _sphx_glr_download_examples_example_expression_model.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download

     :download:`Download Python source code: example_expression_model.py <example_expression_model.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: example_expression_model.ipynb <example_expression_model.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_