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

.. only:: html

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

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

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

.. _sphx_glr_examples_fourier_basis.py:


Fourier basis.
=============

The eigenvectors of the graph Laplacian form the Fourier basis.
The eigenvalues are a measure of variation of their corresponding eigenvector.
The lower the eigenvalue, the smoother the eigenvector. They are hence a
measure of "frequency".

In classical signal processing, Fourier modes are completely delocalized, like
on the grid graph. For general graphs however, Fourier modes might be
localized. See :attr:`pygsp2.graphs.Graph.coherence`.

.. GENERATED FROM PYTHON SOURCE LINES 14-47



.. image-sg:: /examples/images/sphx_glr_fourier_basis_001.png
   :alt: $u_1^\top L u_1 = 0.00$, $u_2^\top L u_2 = 0.10$, $u_3^\top L u_3 = 0.10$, $u_4^\top L u_4 = 0.20$, $u_5^\top L u_5 = 0.38$, $u_6^\top L u_6 = 0.38$, $u_7^\top L u_7 = 0.48$, $u_1^\top L u_1 = 0.00$, $u_2^\top L u_2 = 0.05$, $u_3^\top L u_3 = 0.13$, $u_4^\top L u_4 = 0.16$, $u_5^\top L u_5 = 0.28$, $u_6^\top L u_6 = 0.45$, $u_7^\top L u_7 = 0.49$
   :srcset: /examples/images/sphx_glr_fourier_basis_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import numpy as np
    from matplotlib import pyplot as plt

    import pygsp2 as pg

    n_eigenvectors = 7

    fig, axes = plt.subplots(2, 7, figsize=(15, 4))


    def plot_eigenvectors(G, axes):
        G.compute_fourier_basis(n_eigenvectors)
        limits = [f(G.U) for f in (np.min, np.max)]
        for i, ax in enumerate(axes):
            G.plot(G.U[:, i], limits=limits, colorbar=False, vertex_size=50, ax=ax)
            energy = abs(G.dirichlet_energy(G.U[:, i]))
            ax.set_title(r'$u_{0}^\top L u_{0} = {1:.2f}$'.format(i + 1, energy))
            ax.set_axis_off()


    G = pg.graphs.Grid2d(10, 10)
    plot_eigenvectors(G, axes[0])
    fig.subplots_adjust(hspace=0.5, right=0.8)
    cax = fig.add_axes([0.82, 0.60, 0.01, 0.26])
    fig.colorbar(axes[0, -1].collections[1], cax=cax, ticks=[-0.2, 0, 0.2])

    G = pg.graphs.Sensor(seed=42)
    plot_eigenvectors(G, axes[1])
    fig.subplots_adjust(hspace=0.5, right=0.8)
    cax = fig.add_axes([0.82, 0.16, 0.01, 0.26])
    _ = fig.colorbar(axes[1, -1].collections[1], cax=cax, ticks=[-0.4, 0, 0.4])
    plt.show()


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

   **Total running time of the script:** (0 minutes 0.375 seconds)

**Estimated memory usage:**  180 MB


.. _sphx_glr_download_examples_fourier_basis.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: fourier_basis.zip <fourier_basis.zip>`


.. only:: html

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

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