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

.. only:: html

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

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

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

.. _sphx_glr_auto_examples_image_plot_single_mtf.py:


==============================
Single Markov transition field
==============================

A Markov transition field is an image obtained from a time series, representing
a field of transition probabilities for a discretized time series.
Different strategies can be used to bin time series.
It is implemented as :class:`pyts.image.MarkovTransitionField`.

In this example, the considered time series is the sequence of the sine
function values for 1000 equally-spaced points in the interval
:math:`[0, 4\pi]`.
One can see on the Markov transition field that the sine function is periodic
with period :math:`2\pi` and smooth (only neighbor bins have a positive
transition probability).

Since the API is designed for machine learning, the
:meth:`~pyts.image.MarkovTransitionField.transform` method of the
:class:`pyts.image.MarkovTransitionField` class expects a data set of time
series as input, so the time series is transformed into a data set with a
single time series (``X = np.array([x])``) and the first element of the data
set of Gramian angular fields is retrieved (``ax_mtf.imshow(X_mtf[0], ...``).

.. GENERATED FROM PYTHON SOURCE LINES 25-96



.. image-sg:: /auto_examples/image/images/sphx_glr_plot_single_mtf_001.png
   :alt: Markov Transition Field
   :srcset: /auto_examples/image/images/sphx_glr_plot_single_mtf_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.image import MarkovTransitionField


    # Create a toy time series using the sine function
    time_points = np.linspace(0, 4 * np.pi, 1000)
    x = np.sin(time_points)
    X = np.array([x])

    # Compute Gramian angular fields
    mtf = MarkovTransitionField(n_bins=8)
    X_mtf = mtf.fit_transform(X)

    # Plot the time series and its Markov transition field
    width_ratios = (2, 7, 0.4)
    height_ratios = (2, 7)
    width = 6
    height = width * sum(height_ratios) / sum(width_ratios)
    fig = plt.figure(figsize=(width, height))
    gs = fig.add_gridspec(2, 3,  width_ratios=width_ratios,
                          height_ratios=height_ratios,
                          left=0.1, right=0.9, bottom=0.1, top=0.9,
                          wspace=0.05, hspace=0.05)

    # Define the ticks and their labels for both axes
    time_ticks = np.linspace(0, 4 * np.pi, 9)
    time_ticklabels = [r'$0$', r'$\frac{\pi}{2}$', r'$\pi$',
                       r'$\frac{3\pi}{2}$', r'$2\pi$', r'$\frac{5\pi}{2}$',
                       r'$3\pi$', r'$\frac{7\pi}{2}$', r'$4\pi$']
    value_ticks = [-1, 0, 1]
    reversed_value_ticks = value_ticks[::-1]

    # Plot the time series on the left with inverted axes
    ax_left = fig.add_subplot(gs[1, 0])
    ax_left.plot(x, time_points)
    ax_left.set_xticks(reversed_value_ticks)
    ax_left.set_xticklabels(reversed_value_ticks, rotation=90)
    ax_left.set_yticks(time_ticks)
    ax_left.set_yticklabels(time_ticklabels, rotation=90)
    ax_left.set_ylim((0, 4 * np.pi))
    ax_left.invert_xaxis()

    # Plot the time series on the top
    ax_top = fig.add_subplot(gs[0, 1])
    ax_top.plot(time_points, x)
    ax_top.set_xticks(time_ticks)
    ax_top.set_xticklabels(time_ticklabels)
    ax_top.set_yticks(value_ticks)
    ax_top.set_yticklabels(value_ticks)
    ax_top.xaxis.tick_top()
    ax_top.set_xlim((0, 4 * np.pi))
    ax_top.set_yticklabels(value_ticks)

    # Plot the Gramian angular fields on the bottom right
    ax_mtf = fig.add_subplot(gs[1, 1])
    im = ax_mtf.imshow(X_mtf[0], cmap='rainbow', origin='lower', vmin=0., vmax=1.,
                       extent=[0, 4 * np.pi, 0, 4 * np.pi])
    ax_mtf.set_xticks([])
    ax_mtf.set_yticks([])
    ax_mtf.set_title('Markov Transition Field', y=-0.09)

    # Add colorbar
    ax_cbar = fig.add_subplot(gs[1, 2])
    fig.colorbar(im, cax=ax_cbar)

    plt.show()


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

   **Total running time of the script:** ( 0 minutes  0.368 seconds)


.. _sphx_glr_download_auto_examples_image_plot_single_mtf.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_single_mtf.py <plot_single_mtf.py>`

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

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


.. only:: html

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

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