Heat diffusion

Solve the heat equation by filtering the initial conditions with the heat kernel pygsp.filters.Heat.

import numpy as np
from matplotlib import pyplot as plt

import pygsp 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 = [rf"$\hat{{f}}({t})$", rf"$g_{{1,{t}}}$"]
    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=rf"$f({t})$")
    axes[1, i].set_aspect("equal", "box")
    axes[1, i].set_axis_off()

fig.tight_layout()

Estimated memory usage: 160 MB