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

.. only:: html

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

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

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

.. _sphx_glr_auto_examples_simulated_plot_riemannian_gaussian.py:


=====================================================================
Sample from the Riemannian Gaussian distribution in the SPD manifold
=====================================================================

Spectral embedding of samples from the Riemannian Gaussian distribution
with different centerings and dispersions.

.. GENERATED FROM PYTHON SOURCE LINES 10-23

.. code-block:: Python

    # Authors: Pedro Rodrigues <pedro.rodrigues@melix.org>
    #
    # License: BSD (3-clause)

    import numpy as np
    import matplotlib.pyplot as plt

    from pyriemann.embedding import SpectralEmbedding
    from pyriemann.datasets import sample_gaussian_spd, generate_random_spd_matrix


    print(__doc__)








.. GENERATED FROM PYTHON SOURCE LINES 24-25

Set parameters for sampling from the Riemannian Gaussian distribution

.. GENERATED FROM PYTHON SOURCE LINES 25-51

.. code-block:: Python

    n_matrices = 100  # how many SPD matrices to generate
    n_dim = 2  # number of dimensions of the SPD matrices
    sigma = 1.0  # dispersion of the Gaussian distribution
    epsilon = 4.0  # parameter for controlling the distance between centers
    random_state = 42  # ensure reproducibility

    # Generate the samples on three different conditions
    mean = generate_random_spd_matrix(n_dim)  # random reference point

    samples_1 = sample_gaussian_spd(n_matrices=n_matrices,
                                    mean=mean,
                                    sigma=sigma,
                                    random_state=random_state)
    samples_2 = sample_gaussian_spd(n_matrices=n_matrices,
                                    mean=mean,
                                    sigma=sigma/2,
                                    random_state=random_state)
    samples_3 = sample_gaussian_spd(n_matrices=n_matrices,
                                    mean=epsilon*mean,
                                    sigma=sigma,
                                    random_state=random_state)

    # Stack all of the samples into one data array for the embedding
    samples = np.concatenate([samples_1, samples_2, samples_3])
    labels = np.array(n_matrices*[1] + n_matrices*[2] + n_matrices*[3])








.. GENERATED FROM PYTHON SOURCE LINES 52-53

Apply the spectral embedding over the SPD matrices

.. GENERATED FROM PYTHON SOURCE LINES 53-56

.. code-block:: Python

    lapl = SpectralEmbedding(metric='riemann', n_components=2)
    embd = lapl.fit_transform(X=samples)








.. GENERATED FROM PYTHON SOURCE LINES 57-58

Plot the results

.. GENERATED FROM PYTHON SOURCE LINES 58-78

.. code-block:: Python


    fig, ax = plt.subplots(figsize=(8, 6))

    colors = {1: 'C0', 2: 'C1', 3: 'C2'}
    for i in range(len(samples)):
        ax.scatter(embd[i, 0], embd[i, 1], c=colors[labels[i]], s=50)
    ax.scatter([], [], c='C0', s=50, label=r'$\varepsilon = 1.00, \sigma = 1.00$')
    ax.scatter([], [], c='C1', s=50, label=r'$\varepsilon = 1.00, \sigma = 0.50$')
    ax.scatter([], [], c='C2', s=50, label=r'$\varepsilon = 4.00, \sigma = 1.00$')
    ax.set_xticks([-1, -0.5, 0, 0.5, 1.0])
    ax.set_xticklabels([-1, -0.5, 0, 0.5, 1.0], fontsize=12)
    ax.set_yticks([-1, -0.5, 0, 0.5, 1.0])
    ax.set_yticklabels([-1, -0.5, 0, 0.5, 1.0], fontsize=12)
    ax.set_title(r'Spectral embedding of data points (fixed $n_{dim} = 4$)',
                 fontsize=14)
    ax.set_xlabel(r'$\phi_1$', fontsize=14)
    ax.set_ylabel(r'$\phi_2$', fontsize=14)
    ax.legend()

    plt.show()



.. image-sg:: /auto_examples/simulated/images/sphx_glr_plot_riemannian_gaussian_001.png
   :alt: Spectral embedding of data points (fixed $n_{dim} = 4$)
   :srcset: /auto_examples/simulated/images/sphx_glr_plot_riemannian_gaussian_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 2.603 seconds)


.. _sphx_glr_download_auto_examples_simulated_plot_riemannian_gaussian.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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