Example 1 works with bug.

Errors are distant

src/afgl/main.py

@@ -2,8 +2,11 @@
 import sys
 
 import matplotlib.pyplot as plt
+import matplotlib.ticker as ticker
 import numpy as np
 import numpy.linalg as LA
+import scienceplots  # noqa: F401
+import scipy
 
 # Requires latex installed
 from pygsp import graphs, plotting
@@ -39,39 +42,80 @@ def g_extended(t):
 
 """
 Evaluates the function sin(0.5*pi*cos(pi*t)^2)chi_[-1/2,1/2] where chi_I is the
-characteristic function of I, as defined in example 1 of the paper.
+characteristic function of I, as defined in example 1 (see [1]).
 """
 
 
 def g(T):
-    Ind = ((T >= -1 / 2) & (T <= 1 / 2)).astype(int)
+    if scipy.sparse.issparse(T):
-    Val = g_extended(T)
+        # Operator & not supporting sparse matrix
-    # Perform element wise multiplication to resemble applying indicating
+        T = T.toarray()
-    # function to all matrix.
+    Chi = ((T >= -1 / 2) & (T <= 1 / 2)).astype(int)
-    return np.multiply(Val, Ind)
+    # Apply g_extended where Chi is True, else output 0
+    return np.where(Chi, g_extended(T), 0)
+
+
+""" 
+Computes the approximation g_M (see [1]) using Lanczos
+"""
+
+
+def compute_g_M(L, s, M):
+    [V, alp, beta] = lanczos(L, s, M)
+    e_1 = np.zeros(M)
+    e_1[0] = 1
+    T = build_T_matrix(alp, beta)
+    y = LA.norm(s) * (g(T) @ e_1)
+    return V @ y
+
+
+def latex_log_formatter(y, pos):
+    """Custom formatter to render tick labels as LaTeX 10^{n}."""
+    if y <= 0:
+        return ""
+    # Extract the exponent using log10
+    n = int(np.round(np.log10(y)))
+    return f"$10^{{{n}}}$"
 
 
 def example_1():
     N = 500
-    M = 300
+    M_MAX = 200
     p = 0.04
 
     G = graphs.ErdosRenyi(N, p)
+    # G = graphs.Sensor(N)
 
     G.compute_laplacian("combinatorial")
     L = G.L
 
     s = np.random.randint(1, 10000, N)
+    # Normalize s as in request
+    s = s / LA.norm(s)
 
-    [V, alp, beta] = lanczos(L, s, M)
+    lanczos_err = np.zeros(M_MAX)
+    true_err = np.zeros(M_MAX)
 
-    T = build_T_matrix(alp, beta)
+    GLs = g(L) @ s
+    for M in range(1, M_MAX + 1):
+        g_M = compute_g_M(L, s, M)
+        j = 3
+        g_Mj = compute_g_M(L, s, M + j)
 
-    e_1 = np.zeros(M)
+        lanczos_err[M - 1] = LA.norm(g_Mj - g_M)
-    e_1[0] = 1
+        true_err[M - 1] = LA.norm(GLs - g_M)
-    y = LA.norm(s) * (g(T) * e_1)
+
-    G_L_s = V @ y
+    fig, ax = plt.subplots(figsize=(3.3, 2.5))
-    return G_L_s
+
+    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))
+
+    ax.legend()
+    plt.savefig("./out/erdos_estimate.pdf", bbox_inches="tight")
 
 
 def run():