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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_example_fit_with_bounds.py>`
        to download the full example code.

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

.. _sphx_glr_examples_example_fit_with_bounds.py:


Fit Using Bounds
================

A major advantage of using lmfit is that one can specify boundaries on fitting
parameters, even if the underlying algorithm in SciPy does not support this.
For more information on how this is implemented, please refer to:
https://lmfit.github.io/lmfit-py/bounds.html

The example below shows how to set boundaries using the ``min`` and ``max``
attributes to fitting parameters.

.. GENERATED FROM PYTHON SOURCE LINES 14-20

.. code-block:: Python

    import matplotlib.pyplot as plt
    from numpy import exp, linspace, pi, random, sign, sin

    from lmfit import create_params, minimize
    from lmfit.printfuncs import report_fit








.. GENERATED FROM PYTHON SOURCE LINES 21-22

create the 'true' Parameter values and residual function:

.. GENERATED FROM PYTHON SOURCE LINES 22-36

.. code-block:: Python

    p_true = create_params(amp=14.0, period=5.4321, shift=0.12345, decay=0.010)


    def residual(pars, x, data=None):
        argu = (x * pars['decay'])**2
        shift = pars['shift']
        if abs(shift) > pi/2:
            shift = shift - sign(shift)*pi
        model = pars['amp'] * sin(shift + x/pars['period']) * exp(-argu)
        if data is None:
            return model
        return model - data









.. GENERATED FROM PYTHON SOURCE LINES 37-38

Generate synthetic data and initialize fitting Parameters:

.. GENERATED FROM PYTHON SOURCE LINES 38-48

.. code-block:: Python

    random.seed(0)
    x = linspace(0, 250, 1500)
    noise = random.normal(scale=2.8, size=x.size)
    data = residual(p_true, x) + noise

    fit_params = create_params(amp=dict(value=13, max=20, min=0),
                               period=dict(value=2, max=10),
                               shift=dict(value=0, max=pi/2., min=-pi/2.),
                               decay=dict(value=0.02, max=0.1, min=0))








.. GENERATED FROM PYTHON SOURCE LINES 49-50

Perform the fit and show the results:

.. GENERATED FROM PYTHON SOURCE LINES 50-53

.. code-block:: Python

    out = minimize(residual, fit_params, args=(x,), kws={'data': data})
    fit = residual(out.params, x)








.. GENERATED FROM PYTHON SOURCE LINES 54-56

.. code-block:: Python

    report_fit(out, modelpars=p_true, correl_mode='table')





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

 .. code-block:: none

    [[Fit Statistics]]
        # fitting method   = leastsq
        # function evals   = 79
        # data points      = 1500
        # variables        = 4
        chi-square         = 11301.3646
        reduced chi-square = 7.55438813
        Akaike info crit   = 3037.18756
        Bayesian info crit = 3058.44044
    [[Variables]]
        amp:     13.8904759 +/- 0.24410753 (1.76%) (init = 13), model_value = 14
        period:  5.44026387 +/- 0.01416106 (0.26%) (init = 2), model_value = 5.4321
        shift:   0.12464389 +/- 0.02414210 (19.37%) (init = 0), model_value = 0.12345
        decay:   0.00996363 +/- 2.0275e-04 (2.03%) (init = 0.02), model_value = 0.01
    [[Correlations]] 
      +----------+----------+----------+----------+----------+
      | Variable | amp      | period   | shift    | decay    |
      +----------+----------+----------+----------+----------+
      | amp      | +1.0000  | -0.0700  | -0.0870  | +0.5757  |
      | period   | -0.0700  | +1.0000  | +0.7999  | -0.0404  |
      | shift    | -0.0870  | +0.7999  | +1.0000  | -0.0502  |
      | decay    | +0.5757  | -0.0404  | -0.0502  | +1.0000  |
      +----------+----------+----------+----------+----------+




.. GENERATED FROM PYTHON SOURCE LINES 57-61

.. code-block:: Python

    plt.plot(x, data, 'o', label='data')
    plt.plot(x, fit, label='best fit')
    plt.legend()
    plt.show()



.. image-sg:: /examples/images/sphx_glr_example_fit_with_bounds_001.png
   :alt: example fit with bounds
   :srcset: /examples/images/sphx_glr_example_fit_with_bounds_001.png, /examples/images/sphx_glr_example_fit_with_bounds_001_3_00x.png 3.00x
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.279 seconds)


.. _sphx_glr_download_examples_example_fit_with_bounds.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: example_fit_with_bounds.zip <example_fit_with_bounds.zip>`


.. only:: html

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

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