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

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

.. _sphx_glr_auto_examples_metrics_plot_itakura.py:


=====================
Itakura parallelogram
=====================

This example explains how to set the `max_slope` parameter of the itakura
parallelogram when computing the Dynamic Time Warping (DTW) with
``method == "itakura"``. The Itakura parallelogram is defined through a
``max_slope`` parameter which determines the slope of the steeper side. It is
implemented in :func:`pyts.metrics.itakura_parallelogram`. The slope of the
other side is set to ``1 / max_slope``. For a feasible region, ``max_slope``
must be larger than or equal to 1. This example visualizes the itakura
parallelogram with different slopes and temporal dimensions.

.. GENERATED FROM PYTHON SOURCE LINES 15-89



.. image-sg:: /auto_examples/metrics/images/sphx_glr_plot_itakura_001.png
   :alt: max_slope = 1.0, max_slope = 1.5, max_slope = 3.0, max_slope = 1.0, max_slope = 1.5, max_slope = 3.0, max_slope = 1.0, max_slope = 1.5, max_slope = 3.0
   :srcset: /auto_examples/metrics/images/sphx_glr_plot_itakura_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 itakura_parallelogram
    from pyts.metrics.dtw import _get_itakura_slopes

    # #####################################################################
    # We write a function to visualize the itakura parallelogram for different
    # time series lengths.


    def plot_itakura(n_timestamps_1, n_timestamps_2, max_slope=1., ax=None):
        """Plot Itakura parallelogram."""
        region = itakura_parallelogram(n_timestamps_1, n_timestamps_2, max_slope)
        max_slope, min_slope = _get_itakura_slopes(
            n_timestamps_1, n_timestamps_2, max_slope)
        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')

        sz = max(n_timestamps_1, n_timestamps_2)
        x = np.arange(-1, sz + 1)

        low_max_line = ((n_timestamps_2 - 1) - max_slope * (n_timestamps_1 - 1)) +\
            max_slope * np.arange(-1, sz + 1)
        up_min_line = ((n_timestamps_2 - 1) - min_slope * (n_timestamps_1 - 1)) +\
            min_slope * np.arange(-1, sz + 1)
        diag = (n_timestamps_2 - 1) / (n_timestamps_1 - 1) * np.arange(-1, sz + 1)
        plt.plot(x, diag, 'black', lw=1)
        plt.plot(x, max_slope * np.arange(-1, sz + 1), 'b', lw=1.5)
        plt.plot(x, min_slope * np.arange(-1, sz + 1), 'r', lw=1.5)
        plt.plot(x, low_max_line, 'g', lw=1.5)
        plt.plot(x, up_min_line, 'y', lw=1.5)

        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))


    slopes = [1., 1.5, 3.]
    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, slope in enumerate(slopes):
            ax = plt.subplot(3, 3, i * 3 + j + 1)
            plot_itakura(n1, n2, max_slope=slope, ax=ax)
            plt.title('max_slope = {}'.format(slope))
            if j == 1:
                plt.figtext(0.5, y, 'itakura_parallelogram({}, {})'.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  1.398 seconds)


.. _sphx_glr_download_auto_examples_metrics_plot_itakura.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_itakura.py <plot_itakura.py>`

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

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


.. only:: html

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

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