
.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/example_fit_with_algebraic_constraint.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        Click :ref:`here <sphx_glr_download_examples_example_fit_with_algebraic_constraint.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_example_fit_with_algebraic_constraint.py:


Fit with Algebraic Constraint
=============================

.. GENERATED FROM PYTHON SOURCE LINES 7-8

Example on how to use algebraic constraints using the ``expr`` attribute.

.. GENERATED FROM PYTHON SOURCE LINES 8-45

.. code-block:: default

    import matplotlib.pyplot as plt
    from numpy import linspace, random

    from lmfit.lineshapes import gaussian, lorentzian
    from lmfit.models import GaussianModel, LinearModel, LorentzianModel

    random.seed(0)
    x = linspace(0.0, 20.0, 601)

    data = (gaussian(x, amplitude=21, center=8.1, sigma=1.2) +
            lorentzian(x, amplitude=10, center=9.6, sigma=2.4) +
            0.01 + x*0.05 + random.normal(scale=0.23, size=x.size))


    model = GaussianModel(prefix='g_') + LorentzianModel(prefix='l_') + LinearModel(prefix='line_')

    params = model.make_params(g_amplitude=10, g_center=9, g_sigma=1,
                               line_slope=0, line_intercept=0)

    params.add(name='total_amplitude', value=20)
    params.set(l_amplitude=dict(expr='total_amplitude - g_amplitude'))
    params.set(l_center=dict(expr='1.5+g_center'))
    params.set(l_sigma=dict(expr='2*g_sigma'))


    data_uncertainty = 0.021  # estimate of data error (for all data points)

    init = model.eval(params, x=x)
    result = model.fit(data, params, x=x, weights=1.0/data_uncertainty)

    print(result.fit_report())

    plt.plot(x, data, '+')
    plt.plot(x, init, '--', label='initial fit')
    plt.plot(x, result.best_fit, '-', label='best fit')
    plt.legend()
    plt.show()



.. image-sg:: /examples/images/sphx_glr_example_fit_with_algebraic_constraint_001.png
   :alt: example fit with algebraic constraint
   :srcset: /examples/images/sphx_glr_example_fit_with_algebraic_constraint_001.png, /examples/images/sphx_glr_example_fit_with_algebraic_constraint_001_3_0x.png 3.0x
   :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    [[Model]]
        ((Model(gaussian, prefix='g_') + Model(lorentzian, prefix='l_')) + Model(linear, prefix='line_'))
    [[Fit Statistics]]
        # fitting method   = leastsq
        # function evals   = 65
        # data points      = 601
        # variables        = 6
        chi-square         = 71878.3055
        reduced chi-square = 120.803875
        Akaike info crit   = 2887.26503
        Bayesian info crit = 2913.65660
        R-squared          = -22.1967107
    [[Variables]]
        g_amplitude:      21.1877635 +/- 0.32192128 (1.52%) (init = 10)
        g_center:         8.11125903 +/- 0.01162987 (0.14%) (init = 9)
        g_sigma:          1.20925819 +/- 0.01170853 (0.97%) (init = 1)
        l_amplitude:      9.41261395 +/- 0.61672968 (6.55%) == 'total_amplitude - g_amplitude'
        l_center:         9.61125903 +/- 0.01162987 (0.12%) == '1.5+g_center'
        l_sigma:          2.41851637 +/- 0.02341707 (0.97%) == '2*g_sigma'
        line_slope:       0.04615727 +/- 0.00170178 (3.69%) (init = 0)
        line_intercept:   0.05128584 +/- 0.02448063 (47.73%) (init = 0)
        g_fwhm:           2.84758536 +/- 0.02757149 (0.97%) == '2.3548200*g_sigma'
        g_height:         6.98998378 +/- 0.05837066 (0.84%) == '0.3989423*g_amplitude/max(1e-15, g_sigma)'
        l_fwhm:           4.83703275 +/- 0.04683414 (0.97%) == '2.0000000*l_sigma'
        l_height:         1.23882899 +/- 0.08992735 (7.26%) == '0.3183099*l_amplitude/max(1e-15, l_sigma)'
        total_amplitude:  30.6003779 +/- 0.36481425 (1.19%) (init = 20)
    [[Correlations]] (unreported correlations are < 0.100)
        C(g_amplitude, g_sigma)            = +0.8662
        C(g_amplitude, g_center)           = +0.7496
        C(line_slope, line_intercept)      = -0.7144
        C(g_center, total_amplitude)       = -0.6952
        C(g_center, g_sigma)               = +0.6227
        C(g_amplitude, total_amplitude)    = -0.6115
        C(line_intercept, total_amplitude) = -0.5883
        C(g_sigma, total_amplitude)        = -0.4115
        C(g_center, line_intercept)        = +0.3868
        C(g_amplitude, line_intercept)     = +0.1834
        C(g_amplitude, line_slope)         = +0.1825
        C(g_sigma, line_slope)             = +0.1739





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

   **Total running time of the script:** ( 0 minutes  0.252 seconds)


.. _sphx_glr_download_examples_example_fit_with_algebraic_constraint.py:


.. only :: html

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



  .. container:: sphx-glr-download sphx-glr-download-python

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



  .. container:: sphx-glr-download sphx-glr-download-jupyter

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


.. only:: html

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

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