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

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_metrics_plot_sakoe_chiba.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_metrics_plot_sakoe_chiba.py:


================
Sakoe-Chiba band
================

This example explains how to set the `window_size` parameter of the Sakoe-Chiba
band when computing the Dynamic Time Warping (DTW) with
``method == "sakoechiba"``. The Sakoe-Chiba region is defined through a
`window_size` parameter which determines the largest temporal shift allowed
from the diagonal in the direction of the longest time series. It is
implemented in :func:`pyts.metrics.sakoe_chiba_band`. The window size can
be either set relatively to the length of the longest time series as a ratio
between 0 and 1, or manually if an integer is given.

This example visualizes the Sakoe-Chiba band in different scenarios:
  * the degenerate case: ``window_size = 0``,
  * a relative size: ``window_size = 0.4``, and
  * an absolute size: ``window_size = 4``.

The last two cases are equivalent since ``0.4 * 10 = 4``.

.. GENERATED FROM PYTHON SOURCE LINES 22-95



.. image-sg:: /auto_examples/metrics/images/sphx_glr_plot_sakoe_chiba_001.png
   :alt: window_size = 0, window_size = 0.4, window_size = 4, window_size = 0, window_size = 0.4, window_size = 4, window_size = 0, window_size = 0.4, window_size = 4
   :srcset: /auto_examples/metrics/images/sphx_glr_plot_sakoe_chiba_001.png
   :class: sphx-glr-single-img





.. code-block:: default



    # Author: Hicham Janati <hicham.janati@inria.fr>
    #         Johann Faouzi <johann.faouzi@gmail.com>
    # License: BSD-3-Clause

    import numpy as np
    import matplotlib.pyplot as plt

    from pyts.metrics import sakoe_chiba_band
    from pyts.metrics.dtw import _check_sakoe_chiba_params


    # #####################################################################
    # We write a function to visualize the sakoe-chiba band for different
    # time series lengths.


    def plot_sakoe_chiba(n_timestamps_1, n_timestamps_2, window_size=0.5, ax=None):
        """Plot the Sakoe-Chiba band."""
        region = sakoe_chiba_band(n_timestamps_1, n_timestamps_2, window_size)
        scale, horizontal_shift, vertical_shift = \
            _check_sakoe_chiba_params(n_timestamps_1, n_timestamps_2, window_size)
        mask = np.zeros((n_timestamps_2, n_timestamps_1))
        for i, (j, k) in enumerate(region.T):
            mask[j:k, i] = 1.

        plt.imshow(mask, origin='lower', cmap='Wistia', vmin=0, vmax=1)

        sz = max(n_timestamps_1, n_timestamps_2)
        x = np.arange(-1, sz + 1)
        lower_bound = scale * (x - horizontal_shift) - vertical_shift
        upper_bound = scale * (x + horizontal_shift) + vertical_shift
        plt.plot(x, lower_bound, 'b', lw=2)
        plt.plot(x, upper_bound, 'g', lw=2)
        diag = (n_timestamps_2 - 1) / (n_timestamps_1 - 1) * np.arange(-1, sz + 1)
        plt.plot(x, diag, 'black', lw=1)

        for i in range(n_timestamps_1):
            for j in range(n_timestamps_2):
                plt.plot(i, j, 'o', color='green', ms=1)

        ax.set_xticks(np.arange(-.5, n_timestamps_1, 1), minor=True)
        ax.set_yticks(np.arange(-.5, n_timestamps_2, 1), minor=True)
        plt.grid(which='minor', color='b', linestyle='--', linewidth=1)
        plt.xticks(np.arange(0, n_timestamps_1, 2))
        plt.yticks(np.arange(0, n_timestamps_2, 2))
        plt.xlim((-0.5, n_timestamps_1 - 0.5))
        plt.ylim((-0.5, n_timestamps_2 - 0.5))


    window_sizes = [0, 0.4, 4]

    rc = {"font.size": 14, "axes.titlesize": 10,
          "xtick.labelsize": 8, "ytick.labelsize": 8}
    plt.rcParams.update(rc)


    lengths = [(10, 10), (10, 5), (5, 10)]
    y_coordinates = [0.915, 0.60, 0.35]

    plt.figure(figsize=(10, 8))

    for i, ((n1, n2), y) in enumerate(zip(lengths, y_coordinates)):
        for j, window_size in enumerate(window_sizes):
            ax = plt.subplot(3, 3, i * 3 + j + 1)
            plot_sakoe_chiba(n1, n2, window_size, ax)
            plt.title('window_size = {}'.format(window_size))
            if j == 1:
                plt.figtext(0.5, y, 'sakoe_chiba_band({}, {})'.format(n1, n2),
                            ha='center')
    plt.subplots_adjust(hspace=0.4)
    plt.show()


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

   **Total running time of the script:** ( 0 minutes  1.381 seconds)


.. _sphx_glr_download_auto_examples_metrics_plot_sakoe_chiba.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_sakoe_chiba.py <plot_sakoe_chiba.py>`

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

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


.. only:: html

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

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