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

.. only:: html

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

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

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

.. _sphx_glr_examples_heat_diffusion.py:


Heat diffusion.
==============

Solve the heat equation by filtering the initial conditions with the heat
kernel :class:`pygsp2.filters.Heat`.

.. GENERATED FROM PYTHON SOURCE LINES 8-48



.. image-sg:: /examples/images/sphx_glr_heat_diffusion_001.png
   :alt: $\hat{f}(0) = g_{1,0} \odot \hat{f}(0)$, $\hat{f}(5) = g_{1,5} \odot \hat{f}(0)$, $\hat{f}(10) = g_{1,10} \odot \hat{f}(0)$, $\hat{f}(20) = g_{1,20} \odot \hat{f}(0)$, $f(0)$, $f(5)$, $f(10)$, $f(20)$
   :srcset: /examples/images/sphx_glr_heat_diffusion_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    from os import path

    import numpy as np
    from matplotlib import pyplot as plt

    import pygsp2 as pg

    n_side = 13
    G = pg.graphs.Grid2d(n_side)
    G.compute_fourier_basis()

    sources = [
        (n_side // 4 * n_side) + (n_side // 4),
        (n_side * 3 // 4 * n_side) + (n_side * 3 // 4),
    ]
    x = np.zeros(G.n_vertices)
    x[sources] = 5

    times = [0, 5, 10, 20]

    fig, axes = plt.subplots(2, len(times), figsize=(12, 5))
    for i, t in enumerate(times):
        g = pg.filters.Heat(G, scale=t)
        title = r'$\hat{{f}}({0}) = g_{{1,{0}}} \odot \hat{{f}}(0)$'.format(t)
        g.plot(alpha=1, ax=axes[0, i], title=title)
        axes[0, i].set_xlabel(r'$\lambda$')
        #    axes[0, i].set_ylabel(r'$g(\lambda)$')
        if i > 0:
            axes[0, i].set_ylabel('')
        y = g.filter(x)
        line, = axes[0, i].plot(G.e, G.gft(y))
        labels = [r'$\hat{{f}}({})$'.format(t), r'$g_{{1,{}}}$'.format(t)]
        axes[0, i].legend([line, axes[0, i].lines[-3]], labels, loc='lower right')
        G.plot(y, edges=False, highlight=sources, ax=axes[1, i], title=r'$f({})$'.format(t))
        axes[1, i].set_aspect('equal', 'box')
        axes[1, i].set_axis_off()

    fig.tight_layout()
    plt.show()


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

   **Total running time of the script:** (0 minutes 0.514 seconds)

**Estimated memory usage:**  176 MB


.. _sphx_glr_download_examples_heat_diffusion.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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