Try graph plotting and add breakdown.

pyproject.toml

@@ -7,6 +7,7 @@ dependencies = [
     "matplotlib>=3.10.8",
     "numpy>=2.0.0",
     "pygsp>=0.6.1",
+    "scienceplots>=2.2.1",
     "scipy>=1.10.0",
 ]
 requires-python = ">=3.10"

report/main.tex

@@ -3,11 +3,12 @@
 
 % Load bibliography
 \addbibresource{references.bib}
-\usepackage{lipsum} % Just for the demo text
 
 % --- Document Metadata ---
-\title{\normalfont\scshape\Large The Geometry of Complex Systems}
-\author{\normalfont\itshape A. N. Other}
+\title{%
+    Accelerated filtering on graphs using Lanczos method
+    \\ \large Relazione del progetto di Calcolo Scientifico}
+\author{Alberto Defendi}
 \date{\small\today}
 
 \begin{document}
@@ -15,30 +16,15 @@
 \maketitle
 
 \begin{abstract}
-    \noindent \small \textbf{\textit{Abstract.}} \lipsum[1][1-4]
+    \noindent \small \textbf{\textit{Abstract.}}
 \end{abstract}
 
 \section{Introduction}
-This document uses a custom class file (\texttt{mathreport.cls}). This keeps the main file clean. The typography is set to Bringhurst's standards: wide margins, Palatino font, and old-style figures (e.g., 12345).
 
-\section{Mathematical Theory}
-We define our primary operator in the Hilbert space $\mathcal{H}$.
+Introduciamo alcuni concetti di teoria dei grafi e alcuni risultati del corso che verranno usati nel corso della sperimentazione.
+Scopo del progetto è verificare numericamente i risultati 
 
-\begin{definition}[Compact Operator]
-    An operator $T: X \to Y$ is compact if $\overline{T(B_X)}$ is compact in $Y$.
-\end{definition}
-
-\begin{theorem}[Spectral Theorem]
-    There exists an orthonormal basis of eigenvectors.
-\end{theorem}
-
-Consider the harmonic series shown in \cref{eq:harmonic}. The styling is handled entirely by the external class file.
-\begin{equation} \label{eq:harmonic}
-    H_n = \sum_{k=1}^n \frac{1}{k} \approx \ln n + \gamma
-\end{equation}
-
-\section{Results and Discussion}
-\lipsum[2-4]
+Nell'analisi consideriamo i grafi di Erdo''s-Reiny (Figura)
 
 \printbibliography
 

src/afgl/lanczos.py

@@ -35,6 +35,8 @@ def lanczos(L, s, M):
 
         if j < M - 1:
             beta[j] = LA.norm(v_tilde)
+            if beta[j] == 0:
+                break
             V[:, j + 1] = v_tilde / beta[j]
 
     return [V, alp, beta]

src/afgl/main.py

@@ -1,10 +1,30 @@
 # src/afgl/main.py
 import sys
 
+import matplotlib.pyplot as plt
+import numpy as np
+from pygsp import graphs, plotting
+
+
+def test_plot():
+    plotting.BACKEND = "matplotlib"
+    plt.style.use(["science"])
+    fig, ax = plt.subplots(figsize=(3.3, 2.5))
+    # G = graphs.ErdosRenyi()
+    G = graphs.Sensor()
+
+    G.set_coordinates()
+
+    signal = np.sin(G.coords[:, 0] * 10)
+
+    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")
+
 
 def run():
-    """Main execution function."""
-    print("Starting the Accelerated Filtering Graphs Lanczos (AFGL) process...")
+    test_plot()
 
 
 if __name__ == "__main__":

uv.lock

@@ -15,6 +15,7 @@ dependencies = [
     { name = "numpy", version = "2.2.6", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version < '3.11'" },
     { name = "numpy", version = "2.4.3", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
     { name = "pygsp" },
+    { name = "scienceplots" },
     { name = "scipy", version = "1.15.3", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version < '3.11'" },
     { name = "scipy", version = "1.17.1", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
 ]
@@ -24,6 +25,7 @@ requires-dist = [
     { name = "matplotlib", specifier = ">=3.10.8" },
     { name = "numpy", specifier = ">=2.0.0" },
     { name = "pygsp", specifier = ">=0.6.1" },
+    { name = "scienceplots", specifier = ">=2.2.1" },
     { name = "scipy", specifier = ">=1.10.0" },
 ]
 
@@ -737,6 +739,18 @@ wheels = [
     { url = "https://files.pythonhosted.org/packages/ec/57/56b9bcc3c9c6a792fcbaf139543cee77261f3651ca9da0c93f5c1221264b/python_dateutil-2.9.0.post0-py2.py3-none-any.whl", hash = "sha256:a8b2bc7bffae282281c8140a97d3aa9c14da0b136dfe83f850eea9a5f7470427", size = 229892, upload-time = "2024-03-01T18:36:18.57Z" },
 ]
 
+[[package]]
+name = "scienceplots"
+version = "2.2.1"
+source = { registry = "https://pypi.org/simple" }
+dependencies = [
+    { name = "matplotlib" },
+]
+sdist = { url = "https://files.pythonhosted.org/packages/ae/a5/5f858668ca1a513033a7f0d55cd12b0940a12e822f9f61f317ce344e07c6/scienceplots-2.2.1.tar.gz", hash = "sha256:51ad98c420e499d3284d07b6447a4b3aedd8ec122aca39ba91c58205226c408a", size = 17966, upload-time = "2026-02-25T01:26:54.603Z" }
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/cc/22/14e7b20f7d11f3e9ea9b5ae6acf9ea695c423eee785906cd5c5914a841dc/scienceplots-2.2.1-py3-none-any.whl", hash = "sha256:a1a9f670cbf5b59d92cdd3250be85b079ee4cf08bcaf2ace5ef57995be0b6c42", size = 30237, upload-time = "2026-02-25T01:26:53.298Z" },
+]
+
 [[package]]
 name = "scipy"
 version = "1.15.3"