.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "intro/scipy/auto_examples/plot_2d_minimization.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_2d_minimization.py>`
        to download the full example code

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

.. _sphx_glr_intro_scipy_auto_examples_plot_2d_minimization.py:


=========================================
Optimization of a two-parameter function
=========================================

.. GENERATED FROM PYTHON SOURCE LINES 7-23

.. code-block:: default


    import numpy as np


    # Define the function that we are interested in
    def sixhump(x):
        return ((4 - 2.1*x[0]**2 + x[0]**4 / 3) * x[0]**2
                + x[0] * x[1] + (-4 + 4*x[1]**2) * x[1]**2)

    # Make a grid to evaluate the function (for plotting)
    xlim = [-2, 2]
    ylim = [-1, 1]
    x = np.linspace(*xlim)
    y = np.linspace(*ylim)
    xg, yg = np.meshgrid(x, y)








.. GENERATED FROM PYTHON SOURCE LINES 24-27

A 2D image plot of the function
###########################################################
 Simple visualization in 2D

.. GENERATED FROM PYTHON SOURCE LINES 27-34

.. code-block:: default

    import matplotlib.pyplot as plt
    plt.figure()
    plt.imshow(sixhump([xg, yg]),
               extent=xlim+ylim,
               origin="lower")
    plt.colorbar()




.. image-sg:: /intro/scipy/auto_examples/images/sphx_glr_plot_2d_minimization_001.png
   :alt: plot 2d minimization
   :srcset: /intro/scipy/auto_examples/images/sphx_glr_plot_2d_minimization_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <matplotlib.colorbar.Colorbar object at 0x7fe7b05db310>



.. GENERATED FROM PYTHON SOURCE LINES 35-37

A 3D surface plot of the function
###########################################################

.. GENERATED FROM PYTHON SOURCE LINES 37-48

.. code-block:: default

    from mpl_toolkits.mplot3d import Axes3D
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    surf = ax.plot_surface(xg, yg, sixhump([xg, yg]), rstride=1, cstride=1,
                           cmap=plt.cm.viridis, linewidth=0, antialiased=False)

    ax.set_xlabel('x')
    ax.set_ylabel('y')
    ax.set_zlabel('f(x, y)')
    ax.set_title('Six-hump Camelback function')




.. image-sg:: /intro/scipy/auto_examples/images/sphx_glr_plot_2d_minimization_002.png
   :alt: Six-hump Camelback function
   :srcset: /intro/scipy/auto_examples/images/sphx_glr_plot_2d_minimization_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Text(0.5, 1.0, 'Six-hump Camelback function')



.. GENERATED FROM PYTHON SOURCE LINES 49-51

Find minima
###########################################################

.. GENERATED FROM PYTHON SOURCE LINES 51-71

.. code-block:: default

    import scipy as sp

    # local minimization
    res_local = sp.optimize.minimize(sixhump, x0=[0, 0])

    # global minimization
    res_global = sp.optimize.differential_evolution(
        sixhump, bounds=[xlim, ylim])

    plt.figure()
    # Show the function in 2D
    plt.imshow(sixhump([xg, yg]),
               extent=xlim+ylim,
               origin="lower")
    plt.colorbar()
    # Mark the minima
    plt.scatter(res_local.x[0], res_local.x[1], label='local minimizer')
    plt.scatter(res_global.x[0], res_global.x[1], label='global minimizer')
    plt.legend()
    plt.show()



.. image-sg:: /intro/scipy/auto_examples/images/sphx_glr_plot_2d_minimization_003.png
   :alt: plot 2d minimization
   :srcset: /intro/scipy/auto_examples/images/sphx_glr_plot_2d_minimization_003.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.288 seconds)


.. _sphx_glr_download_intro_scipy_auto_examples_plot_2d_minimization.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_2d_minimization.py <plot_2d_minimization.py>`

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

      :download:`Download Jupyter notebook: plot_2d_minimization.ipynb <plot_2d_minimization.ipynb>`


.. only:: html

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

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