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

.. only:: html

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

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

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

.. _sphx_glr_intro_scipy_auto_examples_plot_curve_fit.py:


===============
Curve fitting
===============

Demos a simple curve fitting

.. GENERATED FROM PYTHON SOURCE LINES 10-11

First generate some data

.. GENERATED FROM PYTHON SOURCE LINES 11-26

.. code-block:: default

    import numpy as np

    # Seed the random number generator for reproducibility
    np.random.seed(0)

    x_data = np.linspace(-5, 5, num=50)
    noise = 0.01 * np.cos(100 * x_data)
    a, b = 2.9, 1.5
    y_data = a * np.cos(b * x_data) + noise

    # And plot it
    import matplotlib.pyplot as plt
    plt.figure(figsize=(6, 4))
    plt.scatter(x_data, y_data)




.. image-sg:: /intro/scipy/auto_examples/images/sphx_glr_plot_curve_fit_001.png
   :alt: plot curve fit
   :srcset: /intro/scipy/auto_examples/images/sphx_glr_plot_curve_fit_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <matplotlib.collections.PathCollection object at 0x7fe7b042c3d0>



.. GENERATED FROM PYTHON SOURCE LINES 27-28

Now fit a simple sine function to the data

.. GENERATED FROM PYTHON SOURCE LINES 28-38

.. code-block:: default

    import scipy as sp

    def test_func(x, a, b, c):
        return a * np.sin(b * x + c)

    params, params_covariance = sp.optimize.curve_fit(test_func, x_data, y_data,
                                                      p0=[2, 1, 3])

    print(params)





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

 .. code-block:: none

    [2.900026   1.50012043 1.57079633]




.. GENERATED FROM PYTHON SOURCE LINES 39-40

And plot the resulting curve on the data

.. GENERATED FROM PYTHON SOURCE LINES 40-49

.. code-block:: default


    plt.figure(figsize=(6, 4))
    plt.scatter(x_data, y_data, label='Data')
    plt.plot(x_data, test_func(x_data, *params),
             label='Fitted function')

    plt.legend(loc='best')

    plt.show()



.. image-sg:: /intro/scipy/auto_examples/images/sphx_glr_plot_curve_fit_002.png
   :alt: plot curve fit
   :srcset: /intro/scipy/auto_examples/images/sphx_glr_plot_curve_fit_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.100 seconds)


.. _sphx_glr_download_intro_scipy_auto_examples_plot_curve_fit.py:

.. only:: html

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




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

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

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

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


.. only:: html

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

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