.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "intro/scipy/auto_examples/plot_optimize_example1.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_optimize_example1.py>`
        to download the full example code.

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

.. _sphx_glr_intro_scipy_auto_examples_plot_optimize_example1.py:


=========================================
Finding the minimum of a smooth function
=========================================

Demos various methods to find the minimum of a function.

.. GENERATED FROM PYTHON SOURCE LINES 8-20

.. code-block:: Python


    import numpy as np
    import matplotlib.pyplot as plt


    def f(x):
        return x**2 + 10 * np.sin(x)


    x = np.arange(-5, 5, 0.1)
    plt.plot(x, f(x))




.. image-sg:: /intro/scipy/auto_examples/images/sphx_glr_plot_optimize_example1_001.png
   :alt: plot optimize example1
   :srcset: /intro/scipy/auto_examples/images/sphx_glr_plot_optimize_example1_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    [<matplotlib.lines.Line2D object at 0x7f726ff4b0e0>]



.. GENERATED FROM PYTHON SOURCE LINES 21-22

Now find the minimum with a few methods

.. GENERATED FROM PYTHON SOURCE LINES 22-27

.. code-block:: Python

    import scipy as sp

    # The default (Nelder Mead)
    print(sp.optimize.minimize(f, x0=0))





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

 .. code-block:: none

      message: Optimization terminated successfully.
      success: True
       status: 0
          fun: -7.945823375615215
            x: [-1.306e+00]
          nit: 5
          jac: [-1.192e-06]
     hess_inv: [[ 8.589e-02]]
         nfev: 12
         njev: 6




.. GENERATED FROM PYTHON SOURCE LINES 28-30

.. code-block:: Python


    plt.show()








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

   **Total running time of the script:** (0 minutes 0.045 seconds)


.. _sphx_glr_download_intro_scipy_auto_examples_plot_optimize_example1.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_optimize_example1.ipynb <plot_optimize_example1.ipynb>`

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

      :download:`Download Python source code: plot_optimize_example1.py <plot_optimize_example1.py>`

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

      :download:`Download zipped: plot_optimize_example1.zip <plot_optimize_example1.zip>`


.. only:: html

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

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