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

.. only:: html

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

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

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

.. _sphx_glr_examples_eigenvalue_concentration.py:


Concentration of the eigenvalues.
================================

The eigenvalues of the graph Laplacian concentrates to the same value as the
graph becomes full.

.. GENERATED FROM PYTHON SOURCE LINES 8-41



.. image-sg:: /examples/images/sphx_glr_eigenvalue_concentration_001.png
   :alt: Ring(n_vertices=17, n_edges=17, k=1), Ring(n_vertices=17, n_edges=34, k=2), Ring(n_vertices=17, n_edges=85, k=5), Ring(n_vertices=17, n_edges=136, k=8), k=1, k=2, k=5, k=8
   :srcset: /examples/images/sphx_glr_eigenvalue_concentration_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_neighbors = [1, 2, 5, 8]
    fig, axes = plt.subplots(3, len(n_neighbors), figsize=(15, 8))

    for k, ax in zip(n_neighbors, axes.T):

        graph = pg.graphs.Ring(17, k=k)
        graph.compute_fourier_basis()
        graph.plot(graph.U[:, 1], ax=ax[0])
        ax[0].axis('equal')
        ax[1].spy(graph.W)
        ax[2].plot(graph.e, '.')
        ax[2].set_title('k={}'.format(k))
        #graph.set_coordinates('line1D')
        #graph.plot(graph.U[:, :4], ax=ax[3], title='')

        # Check that the DFT matrix is an eigenbasis of the Laplacian.
        U = np.fft.fft(np.identity(graph.n_vertices))
        LambdaM = (graph.L.todense().dot(U)) / (U + 1e-15)
        # Eigenvalues should be real.
        assert np.all(np.abs(np.imag(LambdaM)) < 1e-10)
        LambdaM = np.real(LambdaM)
        # Check that the eigenvectors are really eigenvectors of the laplacian.
        Lambda = np.mean(LambdaM, axis=0)
        assert np.all(np.abs(LambdaM - Lambda) < 1e-10)

    fig.tight_layout()
    plt.show()


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

   **Total running time of the script:** (0 minutes 0.698 seconds)

**Estimated memory usage:**  182 MB


.. _sphx_glr_download_examples_eigenvalue_concentration.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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