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

    Click :ref:`here <sphx_glr_download_auto_examples_metrics_plot_dtw.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_metrics_plot_dtw.py:


====================
Dynamic Time Warping
====================

This example shows how to compute and visualize the optimal path
when computing Dynamic Time Warping (DTW) between two time series and
compare the results with different variants of DTW. It is implemented
as :func:`pyts.metrics.dtw`.



.. image:: /auto_examples/metrics/images/sphx_glr_plot_dtw_001.png
    :class: sphx-glr-single-img






.. code-block:: default


    # Author: Johann Faouzi <johann.faouzi@gmail.com>
    # License: BSD-3-Clause

    import numpy as np
    import matplotlib.pyplot as plt
    from pyts.datasets import load_gunpoint
    from pyts.metrics import dtw, itakura_parallelogram, sakoe_chiba_band
    from pyts.metrics.dtw import (cost_matrix, accumulated_cost_matrix,
                                  _return_path, _blurred_path_region)

    # Parameters
    X, _, _, _ = load_gunpoint(return_X_y=True)
    x, y = X[0], X[1]

    # To compare time series of different lengths, we remove some observations
    mask = np.ones(x.size)
    mask[::5] = 0
    y = y[mask.astype(bool)]
    n_timestamps_1, n_timestamps_2 = x.size, y.size

    plt.figure(figsize=(10, 8))
    timestamps_1 = np.arange(n_timestamps_1 + 1)
    timestamps_2 = np.arange(n_timestamps_2 + 1)

    # Dynamic Time Warping: classic
    dtw_classic, path_classic = dtw(x, y, dist='square',
                                    method='classic', return_path=True)
    matrix_classic = np.zeros((n_timestamps_2 + 1, n_timestamps_1 + 1))
    matrix_classic[tuple(path_classic)[::-1]] = 1.

    plt.subplot(2, 2, 1)
    plt.pcolor(timestamps_1, timestamps_2, matrix_classic,
               edgecolors='k', cmap='Greys')
    plt.xlabel('x', fontsize=12)
    plt.ylabel('y', fontsize=12)
    plt.title("{0}\nDTW(x, y) = {1:.2f}".format('classic', dtw_classic),
              fontsize=14)

    # Dynamic Time Warping: sakoechiba
    window_size = 0.1
    dtw_sakoechiba, path_sakoechiba = dtw(
        x, y, dist='square', method='sakoechiba',
        options={'window_size': window_size}, return_path=True
    )
    band = sakoe_chiba_band(n_timestamps_1, n_timestamps_2,
                            window_size=window_size)
    matrix_sakoechiba = np.zeros((n_timestamps_1 + 1, n_timestamps_2 + 1))
    for i in range(n_timestamps_1):
        matrix_sakoechiba[i, np.arange(*band[:, i])] = 0.5
    matrix_sakoechiba[tuple(path_sakoechiba)] = 1.

    plt.subplot(2, 2, 2)
    plt.pcolor(timestamps_1, timestamps_2, matrix_sakoechiba.T,
               edgecolors='k', cmap='Greys')
    plt.xlabel('x', fontsize=12)
    plt.ylabel('y', fontsize=12)
    plt.title("{0}\nDTW(x, y) = {1:.2f}".format('sakoechiba', dtw_sakoechiba),
              fontsize=14)

    # Dynamic Time Warping: itakura
    slope = 1.2
    dtw_itakura, path_itakura = dtw(
        x, y, dist='square', method='itakura',
        options={'max_slope': slope}, return_path=True
    )
    parallelogram = itakura_parallelogram(n_timestamps_1, n_timestamps_2,
                                          max_slope=slope)
    matrix_itakura = np.zeros((n_timestamps_1 + 1, n_timestamps_2 + 1))
    for i in range(n_timestamps_1):
        matrix_itakura[i, np.arange(*parallelogram[:, i])] = 0.5
    matrix_itakura[tuple(path_itakura)] = 1.
    plt.subplot(2, 2, 3)
    plt.pcolor(timestamps_1, timestamps_2, matrix_itakura.T,
               edgecolors='k', cmap='Greys')
    plt.xlabel('x', fontsize=12)
    plt.ylabel('y', fontsize=12)
    plt.title("{0}\nDTW(x, y) = {1:.2f}".format('itakura', dtw_itakura),
              fontsize=14)

    # Dynamic Time Warping: multiscale
    resolution, radius = 5, 2
    dtw_multiscale, path_multiscale = dtw(
        x, y, dist='square', method='multiscale',
        options={'resolution': resolution, 'radius': radius}, return_path=True
    )

    x_padded = x.reshape(-1, resolution).mean(axis=1)
    y_padded = y.reshape(-1, resolution).mean(axis=1)

    cost_mat_res = cost_matrix(x_padded, y_padded, dist='square', region=None)
    acc_cost_mat_res = accumulated_cost_matrix(cost_mat_res)
    path_res = _return_path(acc_cost_mat_res)

    multiscale_region = _blurred_path_region(
        n_timestamps_1, n_timestamps_2, resolution, x_padded.size, y_padded.size,
        path_res,
        radius=radius
    )
    matrix_multiscale = np.zeros((n_timestamps_1 + 1, n_timestamps_2 + 1))
    for i in range(n_timestamps_1):
        matrix_multiscale[i, np.arange(*multiscale_region[:, i])] = 0.5
    matrix_multiscale[tuple(path_multiscale)] = 1.

    plt.subplot(2, 2, 4)
    plt.pcolor(timestamps_1, timestamps_2, matrix_multiscale.T,
               edgecolors='k', cmap='Greys')
    plt.xlabel('x', fontsize=12)
    plt.ylabel('y', fontsize=12)
    plt.title("{0}\nDTW(x, y) = {1:.2f}".format('multiscale', dtw_multiscale),
              fontsize=14)

    plt.suptitle("Dynamic Time Warping", y=0.995, fontsize=17)
    plt.subplots_adjust(top=0.91, hspace=0.4)
    plt.show()


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

   **Total running time of the script:** ( 0 minutes  4.395 seconds)


.. _sphx_glr_download_auto_examples_metrics_plot_dtw.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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