.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "advanced/mathematical_optimization/auto_examples/plot_1d_optim.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_advanced_mathematical_optimization_auto_examples_plot_1d_optim.py>`
        to download the full example code.

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

.. _sphx_glr_advanced_mathematical_optimization_auto_examples_plot_1d_optim.py:


Brent's method
================

Illustration of 1D optimization: Brent's method

.. GENERATED FROM PYTHON SOURCE LINES 7-67



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


    *

      .. image-sg:: /advanced/mathematical_optimization/auto_examples/images/sphx_glr_plot_1d_optim_001.png
         :alt: plot 1d optim
         :srcset: /advanced/mathematical_optimization/auto_examples/images/sphx_glr_plot_1d_optim_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /advanced/mathematical_optimization/auto_examples/images/sphx_glr_plot_1d_optim_002.png
         :alt: plot 1d optim
         :srcset: /advanced/mathematical_optimization/auto_examples/images/sphx_glr_plot_1d_optim_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /advanced/mathematical_optimization/auto_examples/images/sphx_glr_plot_1d_optim_003.png
         :alt: plot 1d optim
         :srcset: /advanced/mathematical_optimization/auto_examples/images/sphx_glr_plot_1d_optim_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /advanced/mathematical_optimization/auto_examples/images/sphx_glr_plot_1d_optim_004.png
         :alt: plot 1d optim
         :srcset: /advanced/mathematical_optimization/auto_examples/images/sphx_glr_plot_1d_optim_004.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none

    Converged at  6
    Converged at  24






|

.. code-block:: Python


    import numpy as np
    import matplotlib.pyplot as plt
    import scipy as sp

    x = np.linspace(-1, 3, 100)
    x_0 = np.exp(-1)


    def f(x):
        return (x - x_0) ** 2 + epsilon * np.exp(-5 * (x - 0.5 - x_0) ** 2)


    for epsilon in (0, 1):
        plt.figure(figsize=(3, 2.5))
        plt.axes((0, 0, 1, 1))

        # A convex function
        plt.plot(x, f(x), linewidth=2)

        # Apply brent method. To have access to the iteration, do this in an
        # artificial way: allow the algorithm to iter only once
        all_x = []
        all_y = []
        for iter in range(30):
            result = sp.optimize.minimize_scalar(
                f,
                bracket=(-5, 2.9, 4.5),
                method="Brent",
                options={"maxiter": iter},
                tol=np.finfo(1.0).eps,
            )
            if result.success:
                print("Converged at ", iter)
                break

            this_x = result.x
            all_x.append(this_x)
            all_y.append(f(this_x))
            if iter < 6:
                plt.text(
                    this_x - 0.05 * np.sign(this_x) - 0.05,
                    f(this_x) + 1.2 * (0.3 - iter % 2),
                    str(iter + 1),
                    size=12,
                )

        plt.plot(all_x[:10], all_y[:10], "k+", markersize=12, markeredgewidth=2)

        plt.plot(all_x[-1], all_y[-1], "rx", markersize=12)
        plt.axis("off")
        plt.ylim(ymin=-1, ymax=8)

        plt.figure(figsize=(4, 3))
        plt.semilogy(np.abs(all_y - all_y[-1]), linewidth=2)
        plt.ylabel("Error on f(x)")
        plt.xlabel("Iteration")
        plt.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.169 seconds)


.. _sphx_glr_download_advanced_mathematical_optimization_auto_examples_plot_1d_optim.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_1d_optim.ipynb <plot_1d_optim.ipynb>`

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

      :download:`Download Python source code: plot_1d_optim.py <plot_1d_optim.py>`

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

      :download:`Download zipped: plot_1d_optim.zip <plot_1d_optim.zip>`


.. only:: html

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

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