.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/optimization/gradient_descent/plot_01_fixed_vs_line_search.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_api_gallery_optimization_gradient_descent_plot_01_fixed_vs_line_search.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_optimization_gradient_descent_plot_01_fixed_vs_line_search.py:


Fixed step vs. backtracking line search on an ill-conditioned bowl
=========================================================================

Gradient descent zig-zags across a narrow, elongated quadratic bowl.
Backtracking line search adapts its step length automatically and
converges in far fewer iterations than any single fixed step size.

.. GENERATED FROM PYTHON SOURCE LINES 11-14

.. code-block:: Python

    from mathematicskit.optimization import GradientDescent, GradientDescentLineSearch, quadratic_bowl, quadratic_bowl_grad
    from mathematicskit.optimization.visualizers.plots import plot_contour_path








.. GENERATED FROM PYTHON SOURCE LINES 15-17

Run both methods from the same starting point
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 17-25

.. code-block:: Python


    x0 = [1.8, 2.5]
    result_fixed = GradientDescent(alpha=0.09, tol=1e-8, max_iter=5000).minimize(quadratic_bowl, quadratic_bowl_grad, x0)
    result_ls = GradientDescentLineSearch(tol=1e-8, max_iter=5000).minimize(quadratic_bowl, quadratic_bowl_grad, x0)

    print(f"fixed step:   {result_fixed.iterations} iterations, x = {result_fixed.x}")
    print(f"line search:  {result_ls.iterations} iterations, x = {result_ls.x}")





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

 .. code-block:: none

    fixed step:   202 iterations, x = [9.58591898e-009 2.50000000e-202]
    line search:  76 iterations, x = [4.24022886e-09 5.38868804e-10]




.. GENERATED FROM PYTHON SOURCE LINES 26-28

Plot both iterate paths over the bowl's contours
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 28-31

.. code-block:: Python


    plot_contour_path(quadratic_bowl, result_fixed, x_range=(-2.0, 2.0), y_range=(-1.0, 3.0))
    plot_contour_path(quadratic_bowl, result_ls, x_range=(-2.0, 2.0), y_range=(-1.0, 3.0))



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


    *

      .. image-sg:: /api/gallery/optimization/gradient_descent/images/sphx_glr_plot_01_fixed_vs_line_search_001.png
         :alt: Optimizer iterate path
         :srcset: /api/gallery/optimization/gradient_descent/images/sphx_glr_plot_01_fixed_vs_line_search_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /api/gallery/optimization/gradient_descent/images/sphx_glr_plot_01_fixed_vs_line_search_002.png
         :alt: Optimizer iterate path
         :srcset: /api/gallery/optimization/gradient_descent/images/sphx_glr_plot_01_fixed_vs_line_search_002.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    <Axes: title={'center': 'Optimizer iterate path'}, xlabel='x', ylabel='y'>




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

   **Total running time of the script:** (0 minutes 0.310 seconds)


.. _sphx_glr_download_api_gallery_optimization_gradient_descent_plot_01_fixed_vs_line_search.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_01_fixed_vs_line_search.ipynb <plot_01_fixed_vs_line_search.ipynb>`

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

      :download:`Download Python source code: plot_01_fixed_vs_line_search.py <plot_01_fixed_vs_line_search.py>`

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

      :download:`Download zipped: plot_01_fixed_vs_line_search.zip <plot_01_fixed_vs_line_search.zip>`


.. only:: html

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

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