r"""
Kernel localization.
===================

In classical signal processing, a filter can be translated in the vertex
domain. We cannot do that on graphs. Instead, we can
:meth:`~pygsp2.filters.Filter.localize` a filter kernel. Note how on classic
structures (like the ring), the localized kernel is the same everywhere, while
it changes when localized on irregular graphs.
"""

import numpy as np
from matplotlib import pyplot as plt

import pygsp2 as pg

fig, axes = plt.subplots(2, 4, figsize=(10, 4))

graphs = [
    pg.graphs.Ring(40),
    pg.graphs.Sensor(64, seed=42),
]

locations = [0, 10, 20]

for graph, axs in zip(graphs, axes):
    graph.compute_fourier_basis()
    g = pg.filters.Heat(graph)
    g.plot(ax=axs[0], title='heat kernel')
    axs[0].set_xlabel(r'eigenvalues $\lambda$')
    axs[0].set_ylabel(r'$g(\lambda) = \exp \left( \frac{{-{}\lambda}}{{\lambda_{{max}}}} \right)$'.format(g.scale[0]))
    maximum = 0
    for loc in locations:
        x = g.localize(loc)
        maximum = np.maximum(maximum, x.max())
    for loc, ax in zip(locations, axs[1:]):
        graph.plot(g.localize(loc), limits=[0, maximum], highlight=loc, ax=ax, title=r'$g(L) \delta_{{{}}}$'.format(loc))
        ax.set_axis_off()

fig.tight_layout()
plt.show()