.. 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_example2.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_example2.py>`
        to download the full example code.

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

.. _sphx_glr_intro_scipy_auto_examples_plot_optimize_example2.py:


===============================
Minima and roots of a function
===============================

Demos finding minima and roots of a function.

.. GENERATED FROM PYTHON SOURCE LINES 10-12

Define the function
###########################################################

.. GENERATED FROM PYTHON SOURCE LINES 12-22

.. code-block:: Python


    import numpy as np

    x = np.arange(-10, 10, 0.1)


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









.. GENERATED FROM PYTHON SOURCE LINES 23-25

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

.. GENERATED FROM PYTHON SOURCE LINES 25-37

.. code-block:: Python


    import scipy as sp

    # Global optimization
    grid = (-10, 10, 0.1)
    xmin_global = sp.optimize.brute(f, (grid,))
    print(f"Global minima found {xmin_global}")

    # Constrain optimization
    xmin_local = sp.optimize.fminbound(f, 0, 10)
    print(f"Local minimum found {xmin_local}")





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

 .. code-block:: none

    Global minima found [-1.30641113]
    Local minimum found 3.8374671194983834




.. GENERATED FROM PYTHON SOURCE LINES 38-40

Root finding
###########################################################

.. GENERATED FROM PYTHON SOURCE LINES 40-46

.. code-block:: Python


    root = sp.optimize.root(f, 1)  # our initial guess is 1
    print(f"First root found {root.x}")
    root2 = sp.optimize.root(f, -2.5)
    print(f"Second root found {root2.x}")





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

 .. code-block:: none

    First root found [0.]
    Second root found [-2.47948183]




.. GENERATED FROM PYTHON SOURCE LINES 47-49

Plot function, minima, and roots
###########################################################

.. GENERATED FROM PYTHON SOURCE LINES 49-72

.. code-block:: Python


    import matplotlib.pyplot as plt

    fig = plt.figure(figsize=(6, 4))
    ax = fig.add_subplot(111)

    # Plot the function
    ax.plot(x, f(x), "b-", label="f(x)")

    # Plot the minima
    xmins = np.array([xmin_global[0], xmin_local])
    ax.plot(xmins, f(xmins), "go", label="Minima")

    # Plot the roots
    roots = np.array([root.x, root2.x])
    ax.plot(roots, f(roots), "kv", label="Roots")

    # Decorate the figure
    ax.legend(loc="best")
    ax.set_xlabel("x")
    ax.set_ylabel("f(x)")
    ax.axhline(0, color="gray")
    plt.show()



.. image-sg:: /intro/scipy/auto_examples/images/sphx_glr_plot_optimize_example2_001.png
   :alt: plot optimize example2
   :srcset: /intro/scipy/auto_examples/images/sphx_glr_plot_optimize_example2_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.050 seconds)


.. _sphx_glr_download_intro_scipy_auto_examples_plot_optimize_example2.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_example2.ipynb <plot_optimize_example2.ipynb>`

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

      :download:`Download Python source code: plot_optimize_example2.py <plot_optimize_example2.py>`

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

      :download:`Download zipped: plot_optimize_example2.zip <plot_optimize_example2.zip>`


.. only:: html

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

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