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

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

.. _sphx_glr_examples_documentation_model_composite.py:


doc_model_composite.py
======================



.. image:: /examples/documentation/images/sphx_glr_model_composite_001.png
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    [[Model]]
        (Model(jump) <function convolve at 0x1a1e92b7a0> Model(gaussian))
    [[Fit Statistics]]
        # fitting method   = leastsq
        # function evals   = 25
        # data points      = 201
        # variables        = 3
        chi-square         = 24.7562335
        reduced chi-square = 0.12503148
        Akaike info crit   = -414.939746
        Bayesian info crit = -405.029832
    [[Variables]]
        mid:        5 (fixed)
        amplitude:  0.62508459 +/- 0.00189732 (0.30%) (init = 1)
        center:     4.50853671 +/- 0.00973231 (0.22%) (init = 3.5)
        sigma:      0.59576118 +/- 0.01348582 (2.26%) (init = 1.5)
    [[Correlations]] (unreported correlations are < 0.100)
        C(amplitude, center) =  0.329
        C(amplitude, sigma)  =  0.268






|


.. code-block:: default

    ##
    import warnings
    warnings.filterwarnings("ignore")
    ##
    # <examples/doc_model_composite.py>
    import matplotlib.pyplot as plt
    import numpy as np

    from lmfit import CompositeModel, Model
    from lmfit.lineshapes import gaussian, step

    # create data from broadened step
    x = np.linspace(0, 10, 201)
    y = step(x, amplitude=12.5, center=4.5, sigma=0.88, form='erf')
    np.random.seed(0)
    y = y + np.random.normal(scale=0.35, size=x.size)


    def jump(x, mid):
        """Heaviside step function."""
        o = np.zeros(x.size)
        imid = max(np.where(x <= mid)[0])
        o[imid:] = 1.0
        return o


    def convolve(arr, kernel):
        """Simple convolution of two arrays."""
        npts = min(arr.size, kernel.size)
        pad = np.ones(npts)
        tmp = np.concatenate((pad*arr[0], arr, pad*arr[-1]))
        out = np.convolve(tmp, kernel, mode='valid')
        noff = int((len(out) - npts) / 2)
        return out[noff:noff+npts]


    # create Composite Model using the custom convolution operator
    mod = CompositeModel(Model(jump), Model(gaussian), convolve)
    pars = mod.make_params(amplitude=1, center=3.5, sigma=1.5, mid=5.0)

    # 'mid' and 'center' should be completely correlated, and 'mid' is
    # used as an integer index, so a very poor fit variable:
    pars['mid'].vary = False

    # fit this model to data array y
    result = mod.fit(y, params=pars, x=x)

    print(result.fit_report())

    # generate components
    comps = result.eval_components(x=x)

    # plot results
    fig, axes = plt.subplots(1, 2, figsize=(12.8, 4.8))

    axes[0].plot(x, y, 'bo')
    axes[0].plot(x, result.init_fit, 'k--', label='initial fit')
    axes[0].plot(x, result.best_fit, 'r-', label='best fit')
    axes[0].legend(loc='best')

    axes[1].plot(x, y, 'bo')
    axes[1].plot(x, 10*comps['jump'], 'k--', label='Jump component')
    axes[1].plot(x, 10*comps['gaussian'], 'r-', label='Gaussian component')
    axes[1].legend(loc='best')

    plt.show()
    # <end examples/doc_model_composite.py>


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

   **Total running time of the script:** ( 0 minutes  0.161 seconds)


.. _sphx_glr_download_examples_documentation_model_composite.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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