Fix plots.
This commit is contained in:
alberto
+4
-2
@@ -28,11 +28,13 @@ Nell'analisi consideriamo i grafi di Erdo''s-Reiny (Figura)
|
||||
|
||||
Consideriamo un grafo non diretto e pesato $ G = (V, E, W)$.
|
||||
|
||||
Studiamo i grafi di Erdos-Reiny e di tipo Sensors. (Metti figure)
|
||||
|
||||
\section{Esperimento 1}
|
||||
|
||||
Di seguito consideriamo
|
||||
Studiamo i grafi di Erdos-Reiny e di tipo Sensors. Dal plot possiamo
|
||||
|
||||
Figura (dida: Grafi di ER e sensor colorati in base al segnale (non filtrato, sopra) e filtrato
|
||||
attraverso la valutazione $g(\mathcal{L})s$.
|
||||
|
||||
|
||||
\printbibliography
|
||||
|
||||
+91
-31
@@ -21,19 +21,52 @@ def plot_setup():
|
||||
# TODO match font with document
|
||||
|
||||
|
||||
def test_plot():
|
||||
fig, ax = plt.subplots(figsize=(3.3, 2.5))
|
||||
G = graphs.ErdosRenyi()
|
||||
# G = graphs.Sensor()
|
||||
def latex_sci(val, decimals=2):
|
||||
"""Converts a value to LaTeX scientific notation A x 10^{B}."""
|
||||
if val == 0:
|
||||
return "0"
|
||||
exponent = int(np.floor(np.log10(abs(val))))
|
||||
mantissa = val / 10**exponent
|
||||
return rf"{mantissa:.{decimals}f} \times 10^{{{exponent}}}"
|
||||
|
||||
G.set_coordinates()
|
||||
|
||||
signal = np.sin(G.coords[:, 0] * 10)
|
||||
def plot_graphs(G_ER, G_Sensor, s, N, p):
|
||||
fig, axs = plt.subplots(2, 2, figsize=(6.6, 5))
|
||||
|
||||
G.plot(signal, ax=ax, vertex_size=15, edge_width=0.5, edge_color="gray")
|
||||
ax.set_title(r"Sensor Network $\mathcal{G} = (\mathcal{V}, \mathcal{E})$")
|
||||
ax.set_axis_off()
|
||||
plt.savefig("./out/test.pdf", bbox_inches="tight")
|
||||
# Set coordinates
|
||||
G_ER.set_coordinates()
|
||||
G_Sensor.set_coordinates()
|
||||
|
||||
signal_ER = filter_signal_with_fourier(G_ER, s)
|
||||
signal_S = filter_signal_with_fourier(G_Sensor, s)
|
||||
|
||||
# TOP LEFT
|
||||
G_ER.plot(s, ax=axs[0, 0], vertex_size=15, edge_width=0.5, edge_color="gray")
|
||||
axs[0, 0].set_title(rf"Erdős-Rényi Graph $(N = {N}, p = {p})$", pad=20)
|
||||
axs[0, 0].set_axis_off()
|
||||
|
||||
# BOTTOM LEFT
|
||||
G_ER.plot(
|
||||
signal_ER, ax=axs[1, 0], vertex_size=15, edge_width=0.5, edge_color="gray"
|
||||
)
|
||||
axs[1, 0].set_title("", pad=20)
|
||||
axs[1, 0].set_axis_off()
|
||||
|
||||
# TOP RIGHT
|
||||
G_Sensor.plot(s, ax=axs[0, 1], vertex_size=15, edge_width=0.5, edge_color="gray")
|
||||
axs[0, 1].set_title(rf"Sensor Network $(N = {N})$", pad=20)
|
||||
axs[0, 1].set_axis_off()
|
||||
|
||||
# BOTTOM RIGHT
|
||||
G_Sensor.plot(
|
||||
signal_S, ax=axs[1, 1], vertex_size=15, edge_width=0.5, edge_color="gray"
|
||||
)
|
||||
axs[1, 1].set_title("", pad=20)
|
||||
axs[1, 1].set_axis_off()
|
||||
|
||||
# Prevent label/title overlap
|
||||
|
||||
plt.savefig("./out/printed_graphs.pdf", bbox_inches="tight")
|
||||
|
||||
|
||||
def g_extended(t):
|
||||
@@ -78,30 +111,25 @@ def latex_log_formatter(y, pos):
|
||||
return f"$10^{{{n}}}$"
|
||||
|
||||
|
||||
def example_1():
|
||||
N = 500
|
||||
M_MAX = 200
|
||||
p = 0.04
|
||||
def filter_signal_with_fourier(G, s):
|
||||
G.compute_fourier_basis()
|
||||
U = G.U
|
||||
GLs = (U @ np.diag(g(G.e)) @ U.T) @ s
|
||||
# GLs = g(L) @ s
|
||||
return GLs
|
||||
|
||||
G = graphs.ErdosRenyi(N, p)
|
||||
# G = graphs.Sensor(N)
|
||||
|
||||
def run_comparison_1_for_graph(G, s, M_MAX):
|
||||
G.compute_laplacian("combinatorial")
|
||||
L = G.L
|
||||
|
||||
s = np.random.randint(1, 10000, N)
|
||||
# Normalize s as in request
|
||||
s = s / LA.norm(s)
|
||||
|
||||
j = 3
|
||||
[V, alp, beta] = lanczos(L, s, M_MAX + j)
|
||||
|
||||
lanczos_err = np.zeros(M_MAX + j)
|
||||
true_err = np.zeros(M_MAX + j)
|
||||
|
||||
G.compute_fourier_basis()
|
||||
U = G.U
|
||||
GLs = (U @ np.diag(g(G.e)) @ U.T) @ s
|
||||
GLs = filter_signal_with_fourier(G, s)
|
||||
# GLs = g(L) @ s
|
||||
for M in range(2, M_MAX + j):
|
||||
g_M = compute_g_M(V[:, 0:M], alp[0:M], beta[0 : M - 1], s)
|
||||
@@ -110,17 +138,49 @@ def example_1():
|
||||
lanczos_err[M - 1] = LA.norm(g_Mj - g_M)
|
||||
true_err[M - 1] = LA.norm(GLs - g_M)
|
||||
|
||||
fig, ax = plt.subplots(figsize=(3.3, 2.5))
|
||||
return [lanczos_err, true_err]
|
||||
|
||||
ax.plot(lanczos_err, label="Error estimate")
|
||||
ax.plot(true_err, label="Error")
|
||||
|
||||
ax.xaxis.set_major_locator(ticker.MultipleLocator(50))
|
||||
ax.set_yscale("log")
|
||||
ax.yaxis.set_major_formatter(ticker.FuncFormatter(latex_log_formatter))
|
||||
def example_1():
|
||||
N = 500
|
||||
M_MAX = 200
|
||||
p = 0.04
|
||||
|
||||
ax.legend()
|
||||
plt.savefig("./out/erdos_estimate.pdf", bbox_inches="tight")
|
||||
s = np.random.randint(1, 10000, N)
|
||||
# Normalize s as in request
|
||||
s = s / LA.norm(s)
|
||||
|
||||
G_ER = graphs.ErdosRenyi(N, p)
|
||||
G_S = graphs.Sensor(N)
|
||||
|
||||
[l_err_ER, t_err_ER] = run_comparison_1_for_graph(G_ER, s, M_MAX)
|
||||
[l_err_S, t_err_S] = run_comparison_1_for_graph(G_S, s, M_MAX)
|
||||
|
||||
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(6.6, 2.5))
|
||||
|
||||
# Left plot (Erdos-Renyi)
|
||||
ax1.plot(l_err_ER, label=r"$\left\lVert g_{M+3} - g_M \right\rVert_2$")
|
||||
ax1.plot(t_err_ER, label=r"$\left\lVert e_M \right\rVert_2$")
|
||||
ax1.set_title("Erdős-Rényi graph")
|
||||
|
||||
# Right plot (Sensor)
|
||||
ax2.plot(l_err_S, label=r"$\left\lVert g_{M+3} - g_M \right\rVert_2$")
|
||||
ax2.plot(t_err_S, label=r"$\left\lVert e_M \right\rVert_2$")
|
||||
ax2.set_title("Sensor graph")
|
||||
|
||||
# Apply identical formatting to both subplots
|
||||
for ax in (ax1, ax2):
|
||||
ax.xaxis.set_major_locator(ticker.MultipleLocator(50))
|
||||
ax.set_yscale("log")
|
||||
ax.yaxis.set_major_formatter(ticker.FuncFormatter(latex_log_formatter))
|
||||
ax.legend()
|
||||
|
||||
# Prevents overlapping of labels between the subplots
|
||||
plt.tight_layout()
|
||||
|
||||
plt.savefig("./out/ex1_estimate.pdf", bbox_inches="tight")
|
||||
|
||||
plot_graphs(G_ER, G_S, s, N, p)
|
||||
|
||||
|
||||
def run():
|
||||
|
||||
Reference in New Issue
Block a user