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

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

.. _sphx_glr_advanced_mathematical_optimization_auto_examples_plot_smooth.py:


Smooth vs non-smooth
=====================

Draws a figure to explain smooth versus non smooth optimization.




.. rst-class:: sphx-glr-horizontal


    *

      .. image:: /advanced/mathematical_optimization/auto_examples/images/sphx_glr_plot_smooth_001.png
            :class: sphx-glr-multi-img

    *

      .. image:: /advanced/mathematical_optimization/auto_examples/images/sphx_glr_plot_smooth_002.png
            :class: sphx-glr-multi-img





.. code-block:: python

    import numpy as np
    import matplotlib.pyplot as plt

    x = np.linspace(-1.5, 1.5, 101)

    # A smooth function
    plt.figure(1, figsize=(3, 2.5))
    plt.clf()

    plt.plot(x, np.sqrt(.2 + x**2), linewidth=2)
    plt.text(-1, 0, '$f$', size=20)

    plt.ylim(ymin=-.2)
    plt.axis('off')
    plt.tight_layout()

    # A non-smooth function
    plt.figure(2, figsize=(3, 2.5))
    plt.clf()
    plt.plot(x, np.abs(x), linewidth=2)
    plt.text(-1, 0, '$f$', size=20)

    plt.ylim(ymin=-.2)
    plt.axis('off')
    plt.tight_layout()
    plt.show()

**Total running time of the script:** ( 0 minutes  0.057 seconds)


.. _sphx_glr_download_advanced_mathematical_optimization_auto_examples_plot_smooth.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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