From 8521f933eb6bcfa7a33861ea3ed7d417fe358358 Mon Sep 17 00:00:00 2001
From: Alessandrini Antoine <a.alsdrini@gmail.com>
Date: Sun, 19 Apr 2026 11:11:28 +0200
Subject: [PATCH 1/4] feat(example): minimal loop benchmark with simulink
 compare

---
 .../bench_01_minimal_loop/compare.py          |     84 +-
 .../matlab/bench_01_simulink.mat              |    Bin 0 -> 1600480 bytes
 .../matlab/simulink_case.mlx                  |    Bin 0 -> 3573 bytes
 .../matlab/simulink_case.slx                  |    Bin 0 -> 69846 bytes
 .../matlab/simulink_results.csv               | 100002 +++++++++++++++
 .../bench_01_minimal_loop/noise_seq.npy       |    Bin 944 -> 800144 bytes
 .../bench_01_minimal_loop/params.py           |      2 +-
 .../bench_01_minimal_loop/pysimblocks_case.py |      1 +
 .../reference_results.npz                     |    Bin 0 -> 4802062 bytes
 9 files changed, 100064 insertions(+), 25 deletions(-)
 create mode 100644 examples/benchmarks/bench_01_minimal_loop/matlab/bench_01_simulink.mat
 create mode 100644 examples/benchmarks/bench_01_minimal_loop/matlab/simulink_case.mlx
 create mode 100644 examples/benchmarks/bench_01_minimal_loop/matlab/simulink_case.slx
 create mode 100644 examples/benchmarks/bench_01_minimal_loop/matlab/simulink_results.csv
 create mode 100644 examples/benchmarks/bench_01_minimal_loop/reference_results.npz

diff --git a/examples/benchmarks/bench_01_minimal_loop/compare.py b/examples/benchmarks/bench_01_minimal_loop/compare.py
index d79045a..a199180 100644
--- a/examples/benchmarks/bench_01_minimal_loop/compare.py
+++ b/examples/benchmarks/bench_01_minimal_loop/compare.py
@@ -1,3 +1,13 @@
+"""
+Comparaison des résultats de simulation entre différentes librairies (bdsim, PathSim, pySimBlocks, Simulink).
+- Charge les résultats de chaque librairie (temps, signal de bruit, signal de sortie).
+- Calcule les erreurs numériques entre les librairies (norme de la différence).
+- Affiche les résultats dans la console (temps, erreurs).
+- Trace les signaux de bruit et de sortie pour chaque librairie sur un même graphique.
+- Affiche un histogramme comparant les temps de simulation des différentes librairies.
+
+Rq: (Bdsim est commenté car trop lent)
+"""
 import logging
 
 import numpy as np
@@ -13,62 +23,88 @@
 
 
 if __name__ == "__main__":
-    N_RUNS = 1
+    N_RUNS = 100
 
     logger.info(f"Running benchmark ({N_RUNS} runs each)...")
 
     results_bd, results_ps, results_pb = [], [], []
     for i in range(N_RUNS):
         print(f"Run {i+1}/{N_RUNS}...", end="\r")
-        results_bd.append(test_bdsim_case())
+        # results_bd.append(test_bdsim_case())
         results_ps.append(test_pathsim_case())
         results_pb.append(test_pysimblocks_case())
 
-    times_bd = np.array([r[3] for r in results_bd])
+    # times_bd = np.array([r[3] for r in results_bd])
     times_ps = np.array([r[3] for r in results_ps])
     times_pb = np.array([r[3] for r in results_pb])
 
-    t_bd, noise_bd, output_bd, _ = results_bd[-1]
+    sl = np.loadtxt("matlab/simulink_results.csv", delimiter=",", skiprows=1)
+    t_sl      = sl[:, 0]
+    noise_sl  = sl[:, 1]
+    output_sl = sl[:, 2]
+    t_mean_sl = 143.3 # ms
+    t_std_sl = 6.7 # ms
+
+    # t_bd, noise_bd, output_bd, _ = results_bd[-1]
     t_ps, noise_ps, output_ps, _ = results_ps[-1]
     t_pb, noise_pb, output_pb, _ = results_pb[-1]
 
-    n = min(len(t_ps), len(t_pb), len(t_bd))
-    t_bd, noise_bd, output_bd = t_bd[:n], noise_bd[:n], output_bd[:n]
+    n = min(len(t_ps), len(t_pb), len(t_sl))
+    # t_bd, noise_bd, output_bd = t_bd[:n], noise_bd[:n], output_bd[:n]
     t_ps, noise_ps, output_ps = t_ps[:n], noise_ps[:n], output_ps[:n]
     t_pb, noise_pb, output_pb = t_pb[:n], noise_pb[:n], output_pb[:n]
+    t_sl, noise_sl, output_sl = t_sl[:n], noise_sl[:n], output_sl[:n]
     
-    t_error_bd_ps = np.linalg.norm(t_bd - t_ps)
-    noise_error_bd_ps = np.linalg.norm(noise_bd - noise_ps)
-    output_error_bd_ps = np.linalg.norm(output_bd - output_ps)
-    t_error_bd_pb = np.linalg.norm(t_bd - t_pb)
-    noise_error_bd_pb = np.linalg.norm(noise_bd - noise_pb)
-    output_error_bd_pb = np.linalg.norm(output_bd - output_pb)
+    # t_error_bd_pb = np.linalg.norm(t_bd - t_pb)
+    # noise_error_bd_pb = np.linalg.norm(noise_bd - noise_pb)
+    # output_error_bd_pb = np.linalg.norm(output_bd - output_pb)
     t_error_ps_pb = np.linalg.norm(t_ps - t_pb)
     noise_error_ps_pb = np.linalg.norm(noise_ps - noise_pb)
     output_error_ps_pb = np.linalg.norm(output_ps - output_pb)
+    t_error_sl_pb = np.linalg.norm(t_sl - t_pb)
+    noise_error_sl_pb = np.linalg.norm(noise_sl - noise_pb)
+    output_error_sl_pb = np.linalg.norm(output_sl - output_pb)
+
+    # --- Sauvegarder les résultats de référence ---
+    np.savez("reference_results.npz",
+        t            = t_pb,
+        noise        = noise_pb,
+        output_psb   = output_pb,
+        output_ps    = output_ps,
+        # output_bd    = output_bd,
+        output_sl    = output_sl,
+        # times_bd_ms  = times_bd * 1e3,
+        times_ps_ms  = times_ps * 1e3,
+        times_pb_ms  = times_pb * 1e3,
+        t_sl         = t_sl,
+    )
 
     logger.info("")
     logger.info("=== Timing ===")
-    logger.info(f"  bdsim:       median={np.median(times_bd)*1e3:.1f} ms,  std={np.std(times_bd)*1e3:.1f} ms")
+    # logger.info(f"  bdsim:       median={np.median(times_bd)*1e3:.1f} ms,  std={np.std(times_bd)*1e3:.1f} ms")
     logger.info(f"  PathSim:     median={np.median(times_ps)*1e3:.1f} ms,  std={np.std(times_ps)*1e3:.1f} ms")
     logger.info(f"  pySimBlocks: median={np.median(times_pb)*1e3:.1f} ms,  std={np.std(times_pb)*1e3:.1f} ms")
+    logger.info(f"  Simulink:    median={t_mean_sl:.1f} ms,  std={t_std_sl:.1f} ms")
     logger.info(f"  Speedup pySimBlocks vs PathSim: {np.median(times_ps) / np.median(times_pb):.2f}x")
-    logger.info(f"  Speedup pySimBlocks vs bdsim:   {np.median(times_bd) / np.median(times_pb):.2f}x")
+    # logger.info(f"  Speedup pySimBlocks vs bdsim:   {np.median(times_bd) / np.median(times_pb):.2f}x")
+    logger.info(f"  Speedup pySimBlocks vs Simulink: {t_mean_sl*1e-3 / np.median(times_pb):.2f}x")
 
     logger.info("")
     logger.info("=== Numerical errors (last run) ===")
     logger.info("Librairies | Time error (a/b%) | Noise error (a/b%) | Output error (a/b%)")
-    logger.info(f"bdsim vs PathSim | {t_error_bd_ps:.2e} ({t_error_bd_ps / np.linalg.norm(t_ps) * 100:.2f}%) | {noise_error_bd_ps:.2e} ({noise_error_bd_ps / np.linalg.norm(noise_ps) * 100:.2f}%) | {output_error_bd_ps:.2e} ({output_error_bd_ps / np.linalg.norm(output_ps) * 100:.2f}%)")
-    logger.info(f"bdsim vs pySimBlocks | {t_error_bd_pb:.2e} ({t_error_bd_pb / np.linalg.norm(t_pb) * 100:.2f}%) | {noise_error_bd_pb:.2e} ({noise_error_bd_pb / np.linalg.norm(noise_pb) * 100:.2f}%) | {output_error_bd_pb:.2e} ({output_error_bd_pb / np.linalg.norm(output_pb) * 100:.2f}%)")
+    # logger.info(f"bdsim vs pySimBlocks | {t_error_bd_pb:.2e} ({t_error_bd_pb / np.linalg.norm(t_pb) * 100:.2f}%) | {noise_error_bd_pb:.2e} ({noise_error_bd_pb / np.linalg.norm(noise_pb) * 100:.2f}%) | {output_error_bd_pb:.2e} ({output_error_bd_pb / np.linalg.norm(output_pb) * 100:.2f}%)")
     logger.info(f"PathSim vs pySimBlocks | {t_error_ps_pb:.2e} ({t_error_ps_pb / np.linalg.norm(t_pb) * 100:.2f}%) | {noise_error_ps_pb:.2e} ({noise_error_ps_pb / np.linalg.norm(noise_pb) * 100:.2f}%) | {output_error_ps_pb:.2e} ({output_error_ps_pb / np.linalg.norm(output_pb) * 100:.2f}%)")
+    logger.info(f"Simulink vs pySimBlocks | {t_error_sl_pb:.2e} ({t_error_sl_pb / np.linalg.norm(t_pb) * 100:.2f}%) | {noise_error_sl_pb:.2e} ({noise_error_sl_pb / np.linalg.norm(noise_pb) * 100:.2f}%) | {output_error_sl_pb:.2e} ({output_error_sl_pb / np.linalg.norm(output_pb) * 100:.2f}%)")
 
     plt.figure(figsize=(10, 6))
-    plt.plot(t_bd, noise_bd,  "-.r", label="Noise (bdsim)",     alpha=0.7)
-    plt.plot(t_bd, output_bd, "-.b", label="Output (bdsim)",    alpha=0.7)
+    # plt.plot(t_bd, noise_bd,  "-.r", label="Noise (bdsim)",     alpha=0.7)
+    # plt.plot(t_bd, output_bd, "-.b", label="Output (bdsim)",    alpha=0.7)
     plt.plot(t_ps, noise_ps,  "--r", label="Noise (PathSim)",    alpha=0.7)
     plt.plot(t_ps, output_ps, "--b", label="Output (PathSim)",   alpha=0.7)
     plt.plot(t_pb, noise_pb,  ":r",  label="Noise (pySimBlocks)", alpha=0.7)
     plt.plot(t_pb, output_pb, ":b",  label="Output (pySimBlocks)", alpha=0.7)
+    plt.plot(t_sl, noise_sl,  "-.m", label="Noise (Simulink)",   alpha=0.7)
+    plt.plot(t_sl, output_sl, "-.c", label="Output (Simulink)",  alpha=0.7)
     plt.title("Simulation Results Comparison")
     plt.xlabel("Time (s)")
     plt.ylabel("Amplitude")
@@ -79,25 +115,25 @@
     # --- Histogramme des temps ---
     benchmarks = {
         'bench_01': {
-            'bdsim':       np.median(times_bd) * 1e3,
+            # 'bdsim':       np.median(times_bd) * 1e3,
             'PathSim':     np.median(times_ps) * 1e3,
             'pySimBlocks': np.median(times_pb) * 1e3,
+            'Simulink':    t_mean_sl,
         },
-        # 'bench_02': { 'bdsim': ..., 'PathSim': ..., 'pySimBlocks': ... },
-        # 'bench_03': { 'bdsim': ..., 'PathSim': ..., 'pySimBlocks': ... },
     }
 
-    libs = ['bdsim', 'PathSim', 'pySimBlocks']
-    colors = {'bdsim': '#7F77DD', 'PathSim': '#1D9E75', 'pySimBlocks': '#D85A30'}
+    libs = ['PathSim', 'pySimBlocks', 'Simulink']
+    colors = {'PathSim': '#1D9E75', 'pySimBlocks': '#D85A30', 'Simulink': '#E1B000'}
 
     n_bench = len(benchmarks)
-    width = 0.25
+    width = 0.2
     group_gap = 1.0  # espace entre groupes
 
     fig, ax = plt.subplots(figsize=(4 + 2 * n_bench, 5))
 
     for g, (bench_name, values) in enumerate(benchmarks.items()):
         group_center = g * group_gap
+        # offsets = [-1.5*width, -0.5*width, 0.5*width, 1.5*width]
         offsets = [-width, 0, width]
         for lib, offset in zip(libs, offsets):
             val = values[lib]
diff --git a/examples/benchmarks/bench_01_minimal_loop/matlab/bench_01_simulink.mat b/examples/benchmarks/bench_01_minimal_loop/matlab/bench_01_simulink.mat
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diff --git a/examples/benchmarks/bench_01_minimal_loop/matlab/simulink_case.mlx b/examples/benchmarks/bench_01_minimal_loop/matlab/simulink_case.mlx
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diff --git a/examples/benchmarks/bench_01_minimal_loop/matlab/simulink_case.slx b/examples/benchmarks/bench_01_minimal_loop/matlab/simulink_case.slx
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new file mode 100644
index 0000000..e725bfc
--- /dev/null
+++ b/examples/benchmarks/bench_01_minimal_loop/matlab/simulink_results.csv
@@ -0,0 +1,100002 @@
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diff --git a/examples/benchmarks/bench_01_minimal_loop/noise_seq.npy b/examples/benchmarks/bench_01_minimal_loop/noise_seq.npy
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diff --git a/examples/benchmarks/bench_01_minimal_loop/params.py b/examples/benchmarks/bench_01_minimal_loop/params.py
index dd1a9e4..ae2ca3d 100644
--- a/examples/benchmarks/bench_01_minimal_loop/params.py
+++ b/examples/benchmarks/bench_01_minimal_loop/params.py
@@ -1,7 +1,7 @@
 import numpy as np
 
 dt = 0.1
-N = 100
+N = 100_000
 T = N * dt
 alpha = 0.1
 
diff --git a/examples/benchmarks/bench_01_minimal_loop/pysimblocks_case.py b/examples/benchmarks/bench_01_minimal_loop/pysimblocks_case.py
index 8ef3285..1dd7233 100644
--- a/examples/benchmarks/bench_01_minimal_loop/pysimblocks_case.py
+++ b/examples/benchmarks/bench_01_minimal_loop/pysimblocks_case.py
@@ -29,6 +29,7 @@ def test_pysimblocks_case():
     t, noise_data, output_data, dt_sim = test_pysimblocks_case()
 
     print(f"pySimBlocks simulation completed in {dt_sim:.2f} seconds")
+    print(noise_data.shape, output_data.shape)
 
     # Plot results
     plt.figure(figsize=(10, 6))
diff --git a/examples/benchmarks/bench_01_minimal_loop/reference_results.npz b/examples/benchmarks/bench_01_minimal_loop/reference_results.npz
new file mode 100644
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From f020496039c54271877c8f4f2fc7924effbca80b Mon Sep 17 00:00:00 2001
From: Alessandrini Antoine <a.alsdrini@gmail.com>
Date: Sun, 19 Apr 2026 18:44:01 +0200
Subject: [PATCH 2/4] feat(example): dense benchmark with simulink compare

---
 .gitignore                                    |     36 +
 .../reference_results.npz                     |    Bin 4802062 -> 4803646 bytes
 .../bench_02_dense_network/compare.py         |    138 +
 .../matlab/bench_02_simulink.mat              |    Bin 0 -> 1600424 bytes
 .../matlab/simulink_case.mlx                  |    Bin 0 -> 3590 bytes
 .../matlab/simulink_case.slx                  |    Bin 0 -> 80978 bytes
 .../matlab/simulink_results.csv               | 100002 +++++++++++++++
 .../bench_02_dense_network/noise_seq.npy      |    Bin 0 -> 800144 bytes
 .../bench_02_dense_network/params.py          |     25 +
 .../bench_02_dense_network/pathsim_case.py    |    185 +
 .../bench_02_dense_network/project.yaml       |    197 +
 .../pysimblocks_case.py                       |     44 +
 .../reference_results.npz                     |    Bin 0 -> 4802062 bytes
 13 files changed, 100627 insertions(+)
 create mode 100644 examples/benchmarks/bench_02_dense_network/compare.py
 create mode 100644 examples/benchmarks/bench_02_dense_network/matlab/bench_02_simulink.mat
 create mode 100644 examples/benchmarks/bench_02_dense_network/matlab/simulink_case.mlx
 create mode 100644 examples/benchmarks/bench_02_dense_network/matlab/simulink_case.slx
 create mode 100644 examples/benchmarks/bench_02_dense_network/matlab/simulink_results.csv
 create mode 100644 examples/benchmarks/bench_02_dense_network/noise_seq.npy
 create mode 100644 examples/benchmarks/bench_02_dense_network/params.py
 create mode 100644 examples/benchmarks/bench_02_dense_network/pathsim_case.py
 create mode 100644 examples/benchmarks/bench_02_dense_network/project.yaml
 create mode 100644 examples/benchmarks/bench_02_dense_network/pysimblocks_case.py
 create mode 100644 examples/benchmarks/bench_02_dense_network/reference_results.npz

diff --git a/.gitignore b/.gitignore
index 16893d0..456c819 100644
--- a/.gitignore
+++ b/.gitignore
@@ -215,3 +215,39 @@ cython_debug/
 marimo/_static/
 marimo/_lsp/
 __marimo__/
+
+
+# MATLAB specific ignores
+# Autosave files
+*.asv
+*.m~
+*.autosave
+*.slx.r*
+*.mdl.r*
+
+# Derived content-obscured files
+*.p
+
+# Compiled MEX files
+*.mex*
+
+# Packaged app and toolbox files
+*.mlappinstall
+*.mltbx
+
+# Deployable archives
+*.ctf
+
+# Generated helpsearch folders
+helpsearch*/
+
+# Code generation folders
+slprj/
+sccprj/
+codegen/
+
+# Cache files
+*.slxc
+
+# Cloud based storage dotfile
+.MATLABDriveTag
diff --git a/examples/benchmarks/bench_01_minimal_loop/reference_results.npz b/examples/benchmarks/bench_01_minimal_loop/reference_results.npz
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diff --git a/examples/benchmarks/bench_02_dense_network/compare.py b/examples/benchmarks/bench_02_dense_network/compare.py
new file mode 100644
index 0000000..a7d442a
--- /dev/null
+++ b/examples/benchmarks/bench_02_dense_network/compare.py
@@ -0,0 +1,138 @@
+"""
+Comparaison des résultats de simulation entre différentes librairies (bdsim, PathSim, pySimBlocks, Simulink).
+- Charge les résultats de chaque librairie (temps, signal de bruit, signal de sortie).
+- Calcule les erreurs numériques entre les librairies (norme de la différence).
+- Affiche les résultats dans la console (temps, erreurs).
+- Trace les signaux de bruit et de sortie pour chaque librairie sur un même graphique.
+- Affiche un histogramme comparant les temps de simulation des différentes librairies.
+
+Rq: (Bdsim est commenté car trop lent)
+"""
+import logging
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+from pathsim_case import test_pathsim_case
+from pysimblocks_case import test_pysimblocks_case
+
+
+logging.basicConfig(level=logging.INFO, format="%(message)s")
+logger = logging.getLogger(__name__)
+
+
+if __name__ == "__main__":
+    N_RUNS = 1
+
+    logger.info(f"Running benchmark ({N_RUNS} runs each)...")
+
+    results_bd, results_ps, results_pb = [], [], []
+    for i in range(N_RUNS):
+        print(f"Run {i+1}/{N_RUNS}...", end="\r")
+        results_ps.append(test_pathsim_case())
+        results_pb.append(test_pysimblocks_case())
+
+    times_ps = np.array([r[3] for r in results_ps])
+    times_pb = np.array([r[3] for r in results_pb])
+
+    sl = np.loadtxt("matlab/simulink_results.csv", delimiter=",", skiprows=1)
+    t_sl      = sl[:, 0]
+    noise_sl  = sl[:, 1]
+    output_sl = sl[:, 2]
+    t_mean_sl = 253.5 # ms
+    t_std_sl = 12.5 # ms
+
+    t_ps, noise_ps, output_ps, _ = results_ps[-1]
+    t_pb, noise_pb, output_pb, _ = results_pb[-1]
+
+    n = min(len(t_ps), len(t_pb), len(t_sl))
+    t_ps, noise_ps, output_ps = t_ps[:n], noise_ps[:n], output_ps[:n]
+    t_pb, noise_pb, output_pb = t_pb[:n], noise_pb[:n], output_pb[:n]
+    t_sl, noise_sl, output_sl = t_sl[:n], noise_sl[:n], output_sl[:n]
+    
+    t_error_ps_pb = np.linalg.norm(t_ps - t_pb)
+    noise_error_ps_pb = np.linalg.norm(noise_ps - noise_pb)
+    output_error_ps_pb = np.linalg.norm(output_ps - output_pb)
+    t_error_sl_pb = np.linalg.norm(t_sl - t_pb)
+    noise_error_sl_pb = np.linalg.norm(noise_sl - noise_pb)
+    output_error_sl_pb = np.linalg.norm(output_sl - output_pb)
+
+    # --- Sauvegarder les résultats de référence ---
+    np.savez("reference_results.npz",
+        t            = t_pb,
+        noise        = noise_pb,
+        output_psb   = output_pb,
+        output_ps    = output_ps,
+        output_sl    = output_sl,
+        times_ps_ms  = times_ps * 1e3,
+        times_pb_ms  = times_pb * 1e3,
+        t_sl         = t_sl,
+    )
+
+    logger.info("")
+    logger.info("=== Timing ===")
+    logger.info(f"  PathSim:     median={np.median(times_ps)*1e3:.1f} ms,  std={np.std(times_ps)*1e3:.1f} ms")
+    logger.info(f"  pySimBlocks: median={np.median(times_pb)*1e3:.1f} ms,  std={np.std(times_pb)*1e3:.1f} ms")
+    logger.info(f"  Simulink:    median={t_mean_sl:.1f} ms,  std={t_std_sl:.1f} ms")
+    logger.info(f"  Speedup pySimBlocks vs PathSim: {np.median(times_ps) / np.median(times_pb):.2f}x")
+    logger.info(f"  Speedup pySimBlocks vs Simulink: {t_mean_sl*1e-3 / np.median(times_pb):.2f}x")
+
+    logger.info("")
+    logger.info("=== Numerical errors (last run) ===")
+    logger.info("Librairies | Time error (a/b%) | Noise error (a/b%) | Output error (a/b%)")
+    logger.info(f"PathSim vs pySimBlocks | {t_error_ps_pb:.2e} ({t_error_ps_pb / np.linalg.norm(t_pb) * 100:.2f}%) | {noise_error_ps_pb:.2e} ({noise_error_ps_pb / np.linalg.norm(noise_pb) * 100:.2f}%) | {output_error_ps_pb:.2e} ({output_error_ps_pb / np.linalg.norm(output_pb) * 100:.2f}%)")
+    logger.info(f"Simulink vs pySimBlocks | {t_error_sl_pb:.2e} ({t_error_sl_pb / np.linalg.norm(t_pb) * 100:.2f}%) | {noise_error_sl_pb:.2e} ({noise_error_sl_pb / np.linalg.norm(noise_pb) * 100:.2f}%) | {output_error_sl_pb:.2e} ({output_error_sl_pb / np.linalg.norm(output_pb) * 100:.2f}%)")
+
+    plt.figure(figsize=(10, 6))
+    plt.plot(t_ps, noise_ps,  "--r", label="Noise (PathSim)",    alpha=0.7)
+    plt.plot(t_ps, output_ps, "--b", label="Output (PathSim)",   alpha=0.7)
+    plt.plot(t_pb, noise_pb,  ":r",  label="Noise (pySimBlocks)", alpha=0.7)
+    plt.plot(t_pb, output_pb, ":b",  label="Output (pySimBlocks)", alpha=0.7)
+    plt.plot(t_sl, noise_sl,  "-.m", label="Noise (Simulink)",   alpha=0.7)
+    plt.plot(t_sl, output_sl, "-.c", label="Output (Simulink)",  alpha=0.7)
+    plt.title("Simulation Results Comparison")
+    plt.xlabel("Time (s)")
+    plt.ylabel("Amplitude")
+    plt.legend()
+    plt.grid()
+    plt.tight_layout()
+
+    # --- Histogramme des temps ---
+    benchmarks = {
+        'bench_01': {
+            'PathSim':     np.median(times_ps) * 1e3,
+            'pySimBlocks': np.median(times_pb) * 1e3,
+            'Simulink':    t_mean_sl,
+        },
+    }
+
+    libs = ['PathSim', 'pySimBlocks', 'Simulink']
+    colors = {'PathSim': '#1D9E75', 'pySimBlocks': '#D85A30', 'Simulink': '#E1B000'}
+
+    n_bench = len(benchmarks)
+    width = 0.2
+    group_gap = 1.0  # espace entre groupes
+
+    fig, ax = plt.subplots(figsize=(4 + 2 * n_bench, 5))
+
+    for g, (bench_name, values) in enumerate(benchmarks.items()):
+        group_center = g * group_gap
+        offsets = [-width, 0, width]
+        for lib, offset in zip(libs, offsets):
+            val = values[lib]
+            bar = ax.bar(group_center + offset, val, width=width,
+                         color=colors[lib], label=lib if g == 0 else None)
+            ax.bar_label(bar, fmt='%.1f', padding=3, fontsize=8)
+
+    ax.set_xticks([g * group_gap for g in range(n_bench)])
+    ax.set_xticklabels(list(benchmarks.keys()))
+    ax.set_ylabel('Median time (ms)')
+    ax.set_title('Time benchmark comparison')
+    ax.set_yscale('log')
+    ax.legend(loc='upper right')
+    ax.grid(axis='y', linestyle='--', alpha=0.4)
+    ax.spines[['top', 'right']].set_visible(False)
+
+    plt.tight_layout()
+    plt.show()
+
diff --git a/examples/benchmarks/bench_02_dense_network/matlab/bench_02_simulink.mat b/examples/benchmarks/bench_02_dense_network/matlab/bench_02_simulink.mat
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diff --git a/examples/benchmarks/bench_02_dense_network/matlab/simulink_case.slx b/examples/benchmarks/bench_02_dense_network/matlab/simulink_case.slx
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new file mode 100644
index 0000000..b71430c
--- /dev/null
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diff --git a/examples/benchmarks/bench_02_dense_network/noise_seq.npy b/examples/benchmarks/bench_02_dense_network/noise_seq.npy
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diff --git a/examples/benchmarks/bench_02_dense_network/params.py b/examples/benchmarks/bench_02_dense_network/params.py
new file mode 100644
index 0000000..953e0a1
--- /dev/null
+++ b/examples/benchmarks/bench_02_dense_network/params.py
@@ -0,0 +1,25 @@
+import numpy as np
+import scipy.io as sio
+
+dt = 0.001
+N = 100_000
+T = N * dt
+vec_size = 1
+
+seed = 0
+rng = np.random.default_rng(seed)
+noise_sequence = rng.standard_normal((N + 2, vec_size))
+np.save("noise_seq.npy", noise_sequence)
+
+x0 = np.zeros((vec_size, 1))
+
+# Sauvegarde .mat
+t_vec = np.arange(N + 2) * dt
+noise_data_simulink = np.column_stack([t_vec, noise_sequence])
+
+sio.savemat("matlab/bench_02_simulink.mat", {
+    "dt": dt,
+    "T": T,
+    "x0": x0,
+    "noise_data": noise_data_simulink,
+})
diff --git a/examples/benchmarks/bench_02_dense_network/pathsim_case.py b/examples/benchmarks/bench_02_dense_network/pathsim_case.py
new file mode 100644
index 0000000..98246be
--- /dev/null
+++ b/examples/benchmarks/bench_02_dense_network/pathsim_case.py
@@ -0,0 +1,185 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+PathSim Simulation
+==================
+
+Generated by PathView on 2026-04-19 15:57:26
+https://view.pathsim.org
+
+PathSim documentation: https://docs.pathsim.org
+"""
+
+# ────────────────────────────────────────────────────────────────────────────
+# IMPORTS
+# ────────────────────────────────────────────────────────────────────────────
+import time
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+from pathsim import Simulation, Connection
+from pathsim.blocks import (
+    Adder,
+    Amplifier,
+    Integrator,
+    Scope,
+    Source,
+)
+from pathsim.solvers import RK4
+
+import params as prm
+
+def make_noise_source(seq, dt):
+    def f(t):
+        k = int(round(t / dt))
+        return float(seq[min(k, len(seq) - 1)])
+    return Source(f)
+
+def test_pathsim_case():
+    # ────────────────────────────────────────────────────────────────────────────
+    # BLOCKS
+    # ────────────────────────────────────────────────────────────────────────────
+
+    # Sources
+    src = make_noise_source(prm.noise_sequence, prm.dt)
+
+    # Dynamic
+    integrator = Integrator()
+
+    # Algebraic
+    gain_1 = Amplifier(
+        gain=0.5
+    )
+    gain_2 = Amplifier(
+        gain=0.3
+    )
+    gain_3 = Amplifier(
+        gain=-0.1
+    )
+    sum1 = Adder(
+        operations="+++"
+    )
+    sum2 = Adder(
+        operations="++"
+    )
+    sum3 = Adder(
+        operations="++"
+    )
+    gainfb1 = Amplifier(
+        gain=0.2
+    )
+    gainfb2 = Amplifier(
+        gain=0.15
+    )
+
+    # Recording
+    scope = Scope()
+
+    blocks = [
+        src,
+        integrator,
+        gain_1,
+        gain_2,
+        gain_3,
+        sum1,
+        sum2,
+        sum3,
+        gainfb1,
+        gainfb2,
+        scope,
+    ]
+
+    # ────────────────────────────────────────────────────────────────────────────
+    # CONNECTIONS
+    # ────────────────────────────────────────────────────────────────────────────
+
+    conn_0 = Connection(src[0], gain_1[0])
+    conn_1 = Connection(src[0], gain_2[0])
+    conn_2 = Connection(src[0], gain_3[0])
+    conn_3 = Connection(sum3[0], sum1[2])
+    conn_4 = Connection(sum2[0], sum1[1])
+    conn_5 = Connection(gain_1[0], sum1[0])
+    conn_6 = Connection(gain_3[0], sum3[0])
+    conn_7 = Connection(gain_2[0], sum2[0])
+    conn_8 = Connection(sum1[0], integrator[0])
+    conn_9 = Connection(gainfb1[0], sum2[1])
+    conn_10 = Connection(integrator[0], gainfb1[0])
+    conn_11 = Connection(gainfb2[0], sum3[1])
+    conn_12 = Connection(integrator[0], gainfb2[0])
+    conn_13 = Connection(integrator[0], scope[1])
+    conn_14 = Connection(src[0], scope[0])
+
+    connections = [
+        conn_0,
+        conn_1,
+        conn_2,
+        conn_3,
+        conn_4,
+        conn_5,
+        conn_6,
+        conn_7,
+        conn_8,
+        conn_9,
+        conn_10,
+        conn_11,
+        conn_12,
+        conn_13,
+        conn_14,
+    ]
+
+    # ────────────────────────────────────────────────────────────────────────────
+    # SIMULATION
+    # ────────────────────────────────────────────────────────────────────────────
+
+    sim = Simulation(
+        blocks,
+        connections,
+        Solver=RK4,
+        dt=prm.dt,
+        dt_min=prm.dt,
+        dt_max=prm.dt,
+        tolerance_lte_rel=0.0001,
+        tolerance_lte_abs=1e-08,
+        tolerance_fpi=1e-10,
+        log=False,
+    )
+
+    # ────────────────────────────────────────────────────────────────────────────
+    # MAIN
+    # ────────────────────────────────────────────────────────────────────────────
+
+    # Run simulation
+    t0 = time.perf_counter()
+    sim.run(duration=prm.T, reset=True, adaptive=False)
+    t1 = time.perf_counter()
+    dt_sim = t1 - t0
+
+    t = np.array(scope.recording_time)
+    data = np.array(scope.recording_data)
+    noise_data = data[:, 0]
+    output_data = data[:, 1]
+
+    return t, noise_data, output_data, dt_sim
+
+
+if __name__ == "__main__":
+
+    import matplotlib.pyplot as plt
+
+    t, noise_data, output_data, dt_sim = test_pathsim_case()
+
+    print(f"PathSim simulation completed in {dt_sim:.2f} seconds")
+
+    # Plot results
+    plt.figure(figsize=(10, 6))
+    plt.plot(t, noise_data, "--r", label='Noise', alpha=0.7)
+    plt.plot(t, output_data, "--b", label='Output', alpha=0.7)
+    plt.title('PathSim Simulation Results')
+    plt.xlabel('Time (s)')
+    plt.ylabel('Amplitude')
+    plt.legend()
+    plt.grid()
+    plt.tight_layout()
+    plt.show()
+
diff --git a/examples/benchmarks/bench_02_dense_network/project.yaml b/examples/benchmarks/bench_02_dense_network/project.yaml
new file mode 100644
index 0000000..cb90626
--- /dev/null
+++ b/examples/benchmarks/bench_02_dense_network/project.yaml
@@ -0,0 +1,197 @@
+schema_version: 1
+project:
+  name: bench_02_dense_network
+simulation:
+  dt: '#dt'
+  T: '#T'
+  solver: fixed
+  external_module: params.py
+  logging:
+  - WhiteNoise.outputs.out
+  - Integrator.outputs.out
+  plots: []
+diagram:
+  blocks:
+  - name: WhiteNoise
+    category: sources
+    type: file_source
+    parameters:
+      file_path: noise_seq.npy
+      repeat: false
+  - name: Gain1
+    category: operators
+    type: gain
+    parameters:
+      gain: 0.5
+      multiplication: Element wise (K * u)
+  - name: Sum1
+    category: operators
+    type: sum
+    parameters:
+      signs: +++
+  - name: Integrator
+    category: operators
+    type: discrete_integrator
+    parameters:
+      initial_state: x0
+      method: euler forward
+  - name: Gain2
+    category: operators
+    type: gain
+    parameters:
+      gain: 0.3
+      multiplication: Element wise (K * u)
+  - name: Sum2
+    category: operators
+    type: sum
+    parameters:
+      signs: ++
+  - name: Gain3
+    category: operators
+    type: gain
+    parameters:
+      gain: -0.1
+      multiplication: Element wise (K * u)
+  - name: Sum3
+    category: operators
+    type: sum
+    parameters:
+      signs: ++
+  - name: GainFb1
+    category: operators
+    type: gain
+    parameters:
+      gain: 0.2
+      multiplication: Element wise (K * u)
+  - name: GainFb2
+    category: operators
+    type: gain
+    parameters:
+      gain: 0.15
+      multiplication: Element wise (K * u)
+  connections:
+  - name: c1
+    ports:
+    - WhiteNoise.out
+    - Gain1.in
+  - name: c2
+    ports:
+    - WhiteNoise.out
+    - Gain2.in
+  - name: c3
+    ports:
+    - WhiteNoise.out
+    - Gain3.in
+  - name: c4
+    ports:
+    - Gain1.out
+    - Sum1.in1
+  - name: c5
+    ports:
+    - Sum1.out
+    - Integrator.in
+  - name: c6
+    ports:
+    - Gain2.out
+    - Sum2.in1
+  - name: c7
+    ports:
+    - Sum2.out
+    - Sum1.in2
+  - name: c8
+    ports:
+    - Gain3.out
+    - Sum3.in1
+  - name: c9
+    ports:
+    - Sum3.out
+    - Sum1.in3
+  - name: c10
+    ports:
+    - GainFb1.out
+    - Sum2.in2
+  - name: c11
+    ports:
+    - GainFb2.out
+    - Sum3.in2
+  - name: c12
+    ports:
+    - Integrator.out
+    - GainFb1.in
+  - name: c13
+    ports:
+    - Integrator.out
+    - GainFb2.in
+gui:
+  layout:
+    blocks:
+      WhiteNoise:
+        x: -130.0
+        y: -100.0
+        orientation: normal
+        width: 120.0
+        height: 60.0
+      Gain1:
+        x: 180.0
+        y: -170.0
+        orientation: normal
+        width: 120.0
+        height: 60.0
+      Sum1:
+        x: 605.0
+        y: -155.0
+        orientation: normal
+        width: 120.0
+        height: 60.0
+      Integrator:
+        x: 840.0
+        y: -155.0
+        orientation: normal
+        width: 120.0
+        height: 60.0
+      Gain2:
+        x: 175.0
+        y: -100.0
+        orientation: normal
+        width: 120.0
+        height: 60.0
+      Sum2:
+        x: 385.0
+        y: -90.0
+        orientation: normal
+        width: 120.0
+        height: 60.0
+      Gain3:
+        x: 175.0
+        y: 110.0
+        orientation: normal
+        width: 120.0
+        height: 60.0
+      Sum3:
+        x: 375.0
+        y: 120.0
+        orientation: normal
+        width: 120.0
+        height: 60.0
+      GainFb1:
+        x: 395.0
+        y: 5.0
+        orientation: flipped
+        width: 120.0
+        height: 60.0
+      GainFb2:
+        x: 385.0
+        y: 220.0
+        orientation: flipped
+        width: 120.0
+        height: 60.0
+    connections:
+      c9:
+        route: [[510.0, 150.0], [518.0, 150.0], [580.0, 150.0], [580.0, -110.0], [
+            591.0, -110.0], [599.0, -110.0]]
+      c12:
+        route: [[975.0, -125.0], [983.0, -125.0], [983.0, 35.0], [529.0, 35.0], [
+            529.0, 35.0], [521.0, 35.0]]
+      c13:
+        route: [[975.0, -125.0], [983.0, -125.0], [983.0, 62.5], [980.0, 62.5], [
+            980.0, 250.0], [511.0, 250.0]]
diff --git a/examples/benchmarks/bench_02_dense_network/pysimblocks_case.py b/examples/benchmarks/bench_02_dense_network/pysimblocks_case.py
new file mode 100644
index 0000000..7e90bc8
--- /dev/null
+++ b/examples/benchmarks/bench_02_dense_network/pysimblocks_case.py
@@ -0,0 +1,44 @@
+import time
+from pathlib import Path
+from pySimBlocks.project import load_simulator_from_project
+
+
+try:
+    BASE_DIR = Path(__file__).parent.resolve()
+except Exception:
+    BASE_DIR = Path("")
+
+def test_pysimblocks_case():
+    sim, _ = load_simulator_from_project(BASE_DIR / 'project.yaml')
+
+    t0 = time.perf_counter()
+    _ = sim.run()
+    t1 = time.perf_counter()
+    dt_sim = t1 - t0
+
+    t = sim.get_data("time").reshape(-1)
+    noise_data = sim.get_data(block="WhiteNoise", port="out").squeeze()
+    output_data = sim.get_data(block="Integrator", port="out").squeeze()
+
+    return t, noise_data, output_data, dt_sim
+
+# Plot results
+if __name__ == "__main__":
+    import matplotlib.pyplot as plt
+
+    t, noise_data, output_data, dt_sim = test_pysimblocks_case()
+
+    print(f"pySimBlocks simulation completed in {dt_sim:.2f} seconds")
+
+    # Plot results
+    plt.figure(figsize=(10, 6))
+    plt.plot(t, noise_data, "--r", label='Noise', alpha=0.7)
+    plt.plot(t, output_data, "--b", label='Output', alpha=0.7)
+    plt.title('pySimBlocks Simulation Results')
+    plt.xlabel('Time (s)')
+    plt.ylabel('Amplitude')
+    plt.legend()
+    plt.grid()
+    plt.tight_layout()
+    plt.show()
+
diff --git a/examples/benchmarks/bench_02_dense_network/reference_results.npz b/examples/benchmarks/bench_02_dense_network/reference_results.npz
new file mode 100644
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literal 0
HcmV?d00001


From eb7cddce1981a25297a033f1c4ddb83d9b9829fc Mon Sep 17 00:00:00 2001
From: Alessandrini Antoine <a.alsdrini@gmail.com>
Date: Mon, 20 Apr 2026 23:54:38 +0200
Subject: [PATCH 3/4] fix(docs): add all time benchmarks

---
 examples/benchmarks/README.md                 |  37 +++
 .../bench_01_minimal_loop/compare.py          | 229 +++++++-------
 .../bench_01_minimal_loop/params.py           |   4 +-
 .../bench_01_minimal_loop/pysimblocks_case.py |   1 -
 .../reference_results.npz                     | Bin 4803646 -> 4803646 bytes
 .../bench_01_minimal_loop/results.py          |  64 ++++
 .../bench_02_dense_network/compare.py         | 203 ++++++------
 .../bench_02_dense_network/params.py          |  16 +-
 .../reference_results.npz                     | Bin 4802062 -> 4803646 bytes
 .../bench_02_dense_network/results.py         |  63 ++++
 .../bench_scaling_results.npz                 | Bin 0 -> 1828 bytes
 .../bench_03_scaling/pysimblocks_case.py      | 296 ++++++++++++++++++
 .../benchmarks/bench_03_scaling/results.py    |  68 ++++
 13 files changed, 777 insertions(+), 204 deletions(-)
 create mode 100644 examples/benchmarks/README.md
 create mode 100644 examples/benchmarks/bench_01_minimal_loop/results.py
 create mode 100644 examples/benchmarks/bench_02_dense_network/results.py
 create mode 100644 examples/benchmarks/bench_03_scaling/bench_scaling_results.npz
 create mode 100644 examples/benchmarks/bench_03_scaling/pysimblocks_case.py
 create mode 100644 examples/benchmarks/bench_03_scaling/results.py

diff --git a/examples/benchmarks/README.md b/examples/benchmarks/README.md
new file mode 100644
index 0000000..9e74029
--- /dev/null
+++ b/examples/benchmarks/README.md
@@ -0,0 +1,37 @@
+# pySimBlocks — Benchmarks
+
+Three benchmarks to measure and characterize the performance of the simulation engine.
+Each benchmark is self-contained and can be run independently.
+
+---
+
+## bench_01_minimal_loop — Pure overhead
+
+**Model:** first-order low-pass filter (5 blocks, scalar, 1 feedback loop)  
+**Duration:** 100,000 steps, dt = 0.1 s
+
+Isolates the irreducible cost of the simulation loop (scheduling, propagation, commit_state) without numerical computation dominating. Serves as a baseline: if this benchmark is slow, the bottleneck is in the engine core itself.
+
+**Comparison:** pySimBlocks · PathSim · bdsim · Simulink
+
+---
+
+## bench_02_multi_feedback — Propagation and feedback stress test
+
+**Model:** 10 blocks (gains, sums, discrete integrator), 2 nested feedback loops, 13 connections, vector signals  
+**Duration:** 100,000 steps, dt = 0.001 s
+
+Specifically targets the cost of inter-block data exchanges (`_propagate_from`, input/output dictionary accesses) in a model with multiple simultaneous feedbacks. Execution time was found to be insensitive to vector size (tested from 1 to 100) — the dominant cost is therefore structural (Python overhead per time step), not numerical.
+
+**Comparison:** pySimBlocks · PathSim · Simulink
+
+---
+
+## bench_03_scaling — Engine scaling with number of blocks
+
+**Model:** N cells in cascade, generated programmatically. Each cell contains a feedforward gain, a sum, a dynamic block (discrete integrator and delay alternating), a local feedback gain, and a coupling gain to the next cell — **5N blocks** and **~5N connections** in total.  
+**Duration:** 100,000 steps, dt = 0.001 s · points: N ∈ {5, 10, 20, 50, 100} cells (25 to 500 blocks)
+
+Characterizes how execution time scales with model size. **Linear scaling** (constant cost per step per block) indicates the engine handles each block independently and that execution order is properly cached. **Superlinear scaling** would reveal an architectural issue — typically execution order being recomputed or the dependency graph being rebuilt at each step.
+
+**Comparison:** pySimBlocks only (scaling curve before/after optimization)
diff --git a/examples/benchmarks/bench_01_minimal_loop/compare.py b/examples/benchmarks/bench_01_minimal_loop/compare.py
index a199180..dd0a278 100644
--- a/examples/benchmarks/bench_01_minimal_loop/compare.py
+++ b/examples/benchmarks/bench_01_minimal_loop/compare.py
@@ -1,21 +1,25 @@
 """
-Comparaison des résultats de simulation entre différentes librairies (bdsim, PathSim, pySimBlocks, Simulink).
-- Charge les résultats de chaque librairie (temps, signal de bruit, signal de sortie).
-- Calcule les erreurs numériques entre les librairies (norme de la différence).
-- Affiche les résultats dans la console (temps, erreurs).
-- Trace les signaux de bruit et de sortie pour chaque librairie sur un même graphique.
-- Affiche un histogramme comparant les temps de simulation des différentes librairies.
-
-Rq: (Bdsim est commenté car trop lent)
+bench_01_minimal_loop — Comparison
+====================================
+Runs the benchmark across all simulators and reports:
+  - Execution times (median, std)
+  - Numerical errors between simulators (L2 norm)
+  - Signal plots
+  - Execution time bar chart (log scale)
+
+Simulink results are loaded from a pre-generated CSV file (matlab/simulink_results.csv).
+bdsim is commented out as it is too slow for repeated runs.
 """
+
 import logging
 
+from pathlib import Path
 import numpy as np
 import matplotlib.pyplot as plt
 
-from bdsim_case import test_bdsim_case
 from pathsim_case import test_pathsim_case
 from pysimblocks_case import test_pysimblocks_case
+# from bdsim_case import test_bdsim_case
 
 
 logging.basicConfig(level=logging.INFO, format="%(message)s")
@@ -27,128 +31,143 @@
 
     logger.info(f"Running benchmark ({N_RUNS} runs each)...")
 
-    results_bd, results_ps, results_pb = [], [], []
+    results_ps, results_pb = [], []
+    # results_bd = []
     for i in range(N_RUNS):
-        print(f"Run {i+1}/{N_RUNS}...", end="\r")
-        # results_bd.append(test_bdsim_case())
+        print(f"  Run {i+1}/{N_RUNS}...", end="\r")
         results_ps.append(test_pathsim_case())
         results_pb.append(test_pysimblocks_case())
+        # results_bd.append(test_bdsim_case())
+
+    print()
 
-    # times_bd = np.array([r[3] for r in results_bd])
-    times_ps = np.array([r[3] for r in results_ps])
-    times_pb = np.array([r[3] for r in results_pb])
+    # ── Timing arrays ─────────────────────────────────────────────────────────
+    times_ps = np.array([r[3] for r in results_ps]) * 1e3   # s → ms
+    times_pb = np.array([r[3] for r in results_pb]) * 1e3
+    # times_bd = np.array([r[3] for r in results_bd]) * 1e3
 
-    sl = np.loadtxt("matlab/simulink_results.csv", delimiter=",", skiprows=1)
+    # ── Simulink results (pre-generated) ─────────────────────────────────────
+    sl        = np.loadtxt(Path(__file__).parent / "matlab" / "simulink_results.csv", delimiter=",", skiprows=1)
     t_sl      = sl[:, 0]
     noise_sl  = sl[:, 1]
     output_sl = sl[:, 2]
-    t_mean_sl = 143.3 # ms
-    t_std_sl = 6.7 # ms
+    t_mean_sl = 143.3   # ms  — measured separately over 100 runs
+    t_std_sl  = 6.7     # ms
 
-    # t_bd, noise_bd, output_bd, _ = results_bd[-1]
+    # ── Last-run signals ──────────────────────────────────────────────────────
     t_ps, noise_ps, output_ps, _ = results_ps[-1]
     t_pb, noise_pb, output_pb, _ = results_pb[-1]
+    # t_bd, noise_bd, output_bd, _ = results_bd[-1]
 
     n = min(len(t_ps), len(t_pb), len(t_sl))
-    # t_bd, noise_bd, output_bd = t_bd[:n], noise_bd[:n], output_bd[:n]
     t_ps, noise_ps, output_ps = t_ps[:n], noise_ps[:n], output_ps[:n]
     t_pb, noise_pb, output_pb = t_pb[:n], noise_pb[:n], output_pb[:n]
     t_sl, noise_sl, output_sl = t_sl[:n], noise_sl[:n], output_sl[:n]
-    
-    # t_error_bd_pb = np.linalg.norm(t_bd - t_pb)
-    # noise_error_bd_pb = np.linalg.norm(noise_bd - noise_pb)
-    # output_error_bd_pb = np.linalg.norm(output_bd - output_pb)
-    t_error_ps_pb = np.linalg.norm(t_ps - t_pb)
-    noise_error_ps_pb = np.linalg.norm(noise_ps - noise_pb)
-    output_error_ps_pb = np.linalg.norm(output_ps - output_pb)
-    t_error_sl_pb = np.linalg.norm(t_sl - t_pb)
-    noise_error_sl_pb = np.linalg.norm(noise_sl - noise_pb)
-    output_error_sl_pb = np.linalg.norm(output_sl - output_pb)
-
-    # --- Sauvegarder les résultats de référence ---
-    np.savez("reference_results.npz",
-        t            = t_pb,
-        noise        = noise_pb,
-        output_psb   = output_pb,
-        output_ps    = output_ps,
-        # output_bd    = output_bd,
-        output_sl    = output_sl,
-        # times_bd_ms  = times_bd * 1e3,
-        times_ps_ms  = times_ps * 1e3,
-        times_pb_ms  = times_pb * 1e3,
-        t_sl         = t_sl,
+    # t_bd, noise_bd, output_bd = t_bd[:n], noise_bd[:n], output_bd[:n]
+
+    # ── Numerical errors (L2 norm) ────────────────────────────────────────────
+    def rel(err, ref):
+        return err / np.linalg.norm(ref) * 100 if np.linalg.norm(ref) > 0 else 0.0
+
+    t_err_ps     = np.linalg.norm(t_ps    - t_pb)
+    noise_err_ps = np.linalg.norm(noise_ps - noise_pb)
+    out_err_ps   = np.linalg.norm(output_ps - output_pb)
+
+    t_err_sl     = np.linalg.norm(t_sl    - t_pb)
+    noise_err_sl = np.linalg.norm(noise_sl - noise_pb)
+    out_err_sl   = np.linalg.norm(output_sl - output_pb)
+
+    # ── Save reference results ────────────────────────────────────────────────
+    np.savez(Path(__file__).parent / "reference_results.npz",
+        t           = t_pb,
+        noise       = noise_pb,
+        output_psb  = output_pb,
+        output_ps   = output_ps,
+        # output_bd   = output_bd,
+        output_sl   = output_sl,
+        times_ps_ms = times_ps,
+        times_pb_ms = times_pb,
+        # times_bd_ms = times_bd,
+        t_sl        = t_sl,
     )
 
+    # ── Console report ────────────────────────────────────────────────────────
     logger.info("")
     logger.info("=== Timing ===")
-    # logger.info(f"  bdsim:       median={np.median(times_bd)*1e3:.1f} ms,  std={np.std(times_bd)*1e3:.1f} ms")
-    logger.info(f"  PathSim:     median={np.median(times_ps)*1e3:.1f} ms,  std={np.std(times_ps)*1e3:.1f} ms")
-    logger.info(f"  pySimBlocks: median={np.median(times_pb)*1e3:.1f} ms,  std={np.std(times_pb)*1e3:.1f} ms")
+    logger.info(f"  PathSim:     median={np.median(times_ps):.1f} ms,  std={np.std(times_ps):.1f} ms")
+    logger.info(f"  pySimBlocks: median={np.median(times_pb):.1f} ms,  std={np.std(times_pb):.1f} ms")
     logger.info(f"  Simulink:    median={t_mean_sl:.1f} ms,  std={t_std_sl:.1f} ms")
-    logger.info(f"  Speedup pySimBlocks vs PathSim: {np.median(times_ps) / np.median(times_pb):.2f}x")
-    # logger.info(f"  Speedup pySimBlocks vs bdsim:   {np.median(times_bd) / np.median(times_pb):.2f}x")
-    logger.info(f"  Speedup pySimBlocks vs Simulink: {t_mean_sl*1e-3 / np.median(times_pb):.2f}x")
+    # logger.info(f"  bdsim:       median={np.median(times_bd):.1f} ms,  std={np.std(times_bd):.1f} ms")
+    logger.info(f"  Speedup pySimBlocks vs PathSim:  {np.median(times_ps) / np.median(times_pb):.2f}x")
+    logger.info(f"  Speedup pySimBlocks vs Simulink: {t_mean_sl / np.median(times_pb):.2f}x")
 
     logger.info("")
-    logger.info("=== Numerical errors (last run) ===")
-    logger.info("Librairies | Time error (a/b%) | Noise error (a/b%) | Output error (a/b%)")
-    # logger.info(f"bdsim vs pySimBlocks | {t_error_bd_pb:.2e} ({t_error_bd_pb / np.linalg.norm(t_pb) * 100:.2f}%) | {noise_error_bd_pb:.2e} ({noise_error_bd_pb / np.linalg.norm(noise_pb) * 100:.2f}%) | {output_error_bd_pb:.2e} ({output_error_bd_pb / np.linalg.norm(output_pb) * 100:.2f}%)")
-    logger.info(f"PathSim vs pySimBlocks | {t_error_ps_pb:.2e} ({t_error_ps_pb / np.linalg.norm(t_pb) * 100:.2f}%) | {noise_error_ps_pb:.2e} ({noise_error_ps_pb / np.linalg.norm(noise_pb) * 100:.2f}%) | {output_error_ps_pb:.2e} ({output_error_ps_pb / np.linalg.norm(output_pb) * 100:.2f}%)")
-    logger.info(f"Simulink vs pySimBlocks | {t_error_sl_pb:.2e} ({t_error_sl_pb / np.linalg.norm(t_pb) * 100:.2f}%) | {noise_error_sl_pb:.2e} ({noise_error_sl_pb / np.linalg.norm(noise_pb) * 100:.2f}%) | {output_error_sl_pb:.2e} ({output_error_sl_pb / np.linalg.norm(output_pb) * 100:.2f}%)")
-
-    plt.figure(figsize=(10, 6))
-    # plt.plot(t_bd, noise_bd,  "-.r", label="Noise (bdsim)",     alpha=0.7)
-    # plt.plot(t_bd, output_bd, "-.b", label="Output (bdsim)",    alpha=0.7)
-    plt.plot(t_ps, noise_ps,  "--r", label="Noise (PathSim)",    alpha=0.7)
-    plt.plot(t_ps, output_ps, "--b", label="Output (PathSim)",   alpha=0.7)
-    plt.plot(t_pb, noise_pb,  ":r",  label="Noise (pySimBlocks)", alpha=0.7)
-    plt.plot(t_pb, output_pb, ":b",  label="Output (pySimBlocks)", alpha=0.7)
-    plt.plot(t_sl, noise_sl,  "-.m", label="Noise (Simulink)",   alpha=0.7)
-    plt.plot(t_sl, output_sl, "-.c", label="Output (Simulink)",  alpha=0.7)
-    plt.title("Simulation Results Comparison")
-    plt.xlabel("Time (s)")
-    plt.ylabel("Amplitude")
-    plt.legend()
-    plt.grid()
+    logger.info("=== Numerical errors — L2 norm (last run) ===")
+    logger.info(f"{'Comparison':<30} {'Time':>16} {'Noise':>16} {'Output':>16}")
+    logger.info("-" * 82)
+    logger.info(
+        f"{'PathSim vs pySimBlocks':<30} "
+        f"{t_err_ps:.2e} ({rel(t_err_ps, t_pb):.2f}%)  "
+        f"{noise_err_ps:.2e} ({rel(noise_err_ps, noise_pb):.2f}%)  "
+        f"{out_err_ps:.2e} ({rel(out_err_ps, output_pb):.2f}%)"
+    )
+    logger.info(
+        f"{'Simulink vs pySimBlocks':<30} "
+        f"{t_err_sl:.2e} ({rel(t_err_sl, t_pb):.2f}%)  "
+        f"{noise_err_sl:.2e} ({rel(noise_err_sl, noise_pb):.2f}%)  "
+        f"{out_err_sl:.2e} ({rel(out_err_sl, output_pb):.2f}%)"
+    )
+
+    # ── Signal plot ───────────────────────────────────────────────────────────
+    fig, ax = plt.subplots(figsize=(10, 5))
+    ax.plot(t_ps, noise_ps,  "--r",  label="Noise (PathSim)",     alpha=0.7)
+    ax.plot(t_ps, output_ps, "--b",  label="Output (PathSim)",    alpha=0.7)
+    ax.plot(t_pb, noise_pb,  ":r",   label="Noise (pySimBlocks)", alpha=0.7)
+    ax.plot(t_pb, output_pb, ":b",   label="Output (pySimBlocks)",alpha=0.7)
+    ax.plot(t_sl, noise_sl,  "-.m",  label="Noise (Simulink)",    alpha=0.7)
+    ax.plot(t_sl, output_sl, "-.c",  label="Output (Simulink)",   alpha=0.7)
+    # ax.plot(t_bd, noise_bd,  "-.r", label="Noise (bdsim)",       alpha=0.7)
+    # ax.plot(t_bd, output_bd, "-.b", label="Output (bdsim)",      alpha=0.7)
+    ax.set_title("bench_01 — Signal comparison")
+    ax.set_xlabel("Time (s)")
+    ax.set_ylabel("Amplitude")
+    ax.legend()
+    ax.grid(True, alpha=0.3)
     plt.tight_layout()
 
-    # --- Histogramme des temps ---
-    benchmarks = {
-        'bench_01': {
-            # 'bdsim':       np.median(times_bd) * 1e3,
-            'PathSim':     np.median(times_ps) * 1e3,
-            'pySimBlocks': np.median(times_pb) * 1e3,
-            'Simulink':    t_mean_sl,
-        },
+    # ── Timing bar chart (log scale) ──────────────────────────────────────────
+    timings = {
+        "PathSim":     np.median(times_ps),
+        "pySimBlocks": np.median(times_pb),
+        "Simulink":    t_mean_sl,
+        # "bdsim":       np.median(times_bd),
+    }
+    errors = {
+        "PathSim":     np.std(times_ps),
+        "pySimBlocks": np.std(times_pb),
+        "Simulink":    t_std_sl,
+    }
+    colors = {
+        "PathSim":     "#1D9E75",
+        "pySimBlocks": "#D85A30",
+        "Simulink":    "#E1B000",
+        # "bdsim":       "#5B7FD4",
     }
 
-    libs = ['PathSim', 'pySimBlocks', 'Simulink']
-    colors = {'PathSim': '#1D9E75', 'pySimBlocks': '#D85A30', 'Simulink': '#E1B000'}
-
-    n_bench = len(benchmarks)
-    width = 0.2
-    group_gap = 1.0  # espace entre groupes
-
-    fig, ax = plt.subplots(figsize=(4 + 2 * n_bench, 5))
-
-    for g, (bench_name, values) in enumerate(benchmarks.items()):
-        group_center = g * group_gap
-        # offsets = [-1.5*width, -0.5*width, 0.5*width, 1.5*width]
-        offsets = [-width, 0, width]
-        for lib, offset in zip(libs, offsets):
-            val = values[lib]
-            bar = ax.bar(group_center + offset, val, width=width,
-                         color=colors[lib], label=lib if g == 0 else None)
-            ax.bar_label(bar, fmt='%.1f', padding=3, fontsize=8)
-
-    ax.set_xticks([g * group_gap for g in range(n_bench)])
-    ax.set_xticklabels(list(benchmarks.keys()))
-    ax.set_ylabel('Median time (ms)')
-    ax.set_title('Time benchmark comparison')
-    ax.set_yscale('log')
-    ax.legend(loc='upper right')
-    ax.grid(axis='y', linestyle='--', alpha=0.4)
-    ax.spines[['top', 'right']].set_visible(False)
-
+    fig2, ax2 = plt.subplots(figsize=(6, 5))
+    for i, (lib, val) in enumerate(timings.items()):
+        bar = ax2.bar(i, val, color=colors[lib], label=lib,
+                      yerr=errors[lib], capsize=4, width=0.5)
+        ax2.bar_label(bar, fmt="%.1f", padding=4, fontsize=9)
+
+    ax2.set_xticks(range(len(timings)))
+    ax2.set_xticklabels(list(timings.keys()))
+    ax2.set_ylabel("Median execution time (ms)")
+    ax2.set_title("bench_01 — Execution time comparison")
+    ax2.set_yscale("log")
+    ax2.legend(loc="upper right")
+    ax2.grid(axis="y", linestyle="--", alpha=0.4)
+    ax2.spines[["top", "right"]].set_visible(False)
     plt.tight_layout()
+
     plt.show()
diff --git a/examples/benchmarks/bench_01_minimal_loop/params.py b/examples/benchmarks/bench_01_minimal_loop/params.py
index ae2ca3d..8a20451 100644
--- a/examples/benchmarks/bench_01_minimal_loop/params.py
+++ b/examples/benchmarks/bench_01_minimal_loop/params.py
@@ -1,3 +1,4 @@
+from pathlib import Path
 import numpy as np
 
 dt = 0.1
@@ -10,5 +11,6 @@
 seed = 0
 rng = np.random.default_rng(seed)
 noise_sequence = rng.standard_normal(N + 2)
-np.save("noise_seq.npy", noise_sequence)
+dir_path = Path(__file__).parent
+np.save(dir_path / "noise_seq.npy", noise_sequence)
 x0 = 0.
diff --git a/examples/benchmarks/bench_01_minimal_loop/pysimblocks_case.py b/examples/benchmarks/bench_01_minimal_loop/pysimblocks_case.py
index 1dd7233..8ef3285 100644
--- a/examples/benchmarks/bench_01_minimal_loop/pysimblocks_case.py
+++ b/examples/benchmarks/bench_01_minimal_loop/pysimblocks_case.py
@@ -29,7 +29,6 @@ def test_pysimblocks_case():
     t, noise_data, output_data, dt_sim = test_pysimblocks_case()
 
     print(f"pySimBlocks simulation completed in {dt_sim:.2f} seconds")
-    print(noise_data.shape, output_data.shape)
 
     # Plot results
     plt.figure(figsize=(10, 6))
diff --git a/examples/benchmarks/bench_01_minimal_loop/reference_results.npz b/examples/benchmarks/bench_01_minimal_loop/reference_results.npz
index 1b6444377978988fd3ea2b4801afb8ea1b6d22f3..6456101011e0e2925edf68e9ce75ff6181efdb2d 100644
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diff --git a/examples/benchmarks/bench_01_minimal_loop/results.py b/examples/benchmarks/bench_01_minimal_loop/results.py
new file mode 100644
index 0000000..5b96712
--- /dev/null
+++ b/examples/benchmarks/bench_01_minimal_loop/results.py
@@ -0,0 +1,64 @@
+from pathlib import Path
+import logging
+import numpy as np
+import matplotlib.pyplot as plt
+
+logging.basicConfig(level=logging.INFO, format="%(message)s")
+logger = logging.getLogger(__name__)
+
+data = np.load(Path(__file__).parent / "reference_results.npz")
+t = data["t"]
+noise = data["noise"]
+output_pb = data["output_psb"]
+output_ps = data["output_ps"]
+output_sl = data["output_sl"]
+times_ps = data["times_ps_ms"]
+times_pb = data["times_pb_ms"]
+t_sl = data["t_sl"]
+t_mean_sl = 143.3 # ms
+t_std_sl = 6.7 # ms
+
+# ── Console report ────────────────────────────────────────────────────────
+logger.info("")
+logger.info("=== Timing ===")
+logger.info(f"  PathSim:     median={np.median(times_ps):.1f} ms,  std={np.std(times_ps):.1f} ms")
+logger.info(f"  pySimBlocks: median={np.median(times_pb):.1f} ms,  std={np.std(times_pb):.1f} ms")
+logger.info(f"  Simulink:    median={t_mean_sl:.1f} ms,  std={t_std_sl:.1f} ms")
+# logger.info(f"  bdsim:       median={np.median(times_bd):.1f} ms,  std={np.std(times_bd):.1f} ms")
+logger.info(f"  Speedup pySimBlocks vs PathSim:  {np.median(times_ps) / np.median(times_pb):.2f}x")
+logger.info(f"  Speedup pySimBlocks vs Simulink: {t_mean_sl / np.median(times_pb):.2f}x")
+
+# ── Timing bar chart (log scale) ──────────────────────────────────────────
+timings = {
+    "PathSim":     np.median(times_ps),
+    "pySimBlocks": np.median(times_pb),
+    "Simulink":    t_mean_sl,
+}
+errors = {
+    "PathSim":     np.std(times_ps),
+    "pySimBlocks": np.std(times_pb),
+    "Simulink":    t_std_sl,
+}
+colors = {
+    "PathSim":     "#1D9E75",
+    "pySimBlocks": "#D85A30",
+    "Simulink":    "#E1B000",
+}
+
+fig2, ax2 = plt.subplots(figsize=(6, 5))
+for i, (lib, val) in enumerate(timings.items()):
+    bar = ax2.bar(i, val, color=colors[lib], label=lib,
+                  yerr=errors[lib], capsize=4, width=0.5)
+    ax2.bar_label(bar, fmt="%.1f", padding=4, fontsize=9)
+
+ax2.set_xticks(range(len(timings)))
+ax2.set_xticklabels(list(timings.keys()))
+ax2.set_ylabel("Median execution time (ms)")
+ax2.set_title("bench_01 — Execution time comparison")
+ax2.set_yscale("log")
+ax2.legend(loc="upper right")
+ax2.grid(axis="y", linestyle="--", alpha=0.4)
+ax2.spines[["top", "right"]].set_visible(False)
+plt.tight_layout()
+
+plt.show()
diff --git a/examples/benchmarks/bench_02_dense_network/compare.py b/examples/benchmarks/bench_02_dense_network/compare.py
index a7d442a..22534e6 100644
--- a/examples/benchmarks/bench_02_dense_network/compare.py
+++ b/examples/benchmarks/bench_02_dense_network/compare.py
@@ -1,15 +1,20 @@
 """
-Comparaison des résultats de simulation entre différentes librairies (bdsim, PathSim, pySimBlocks, Simulink).
-- Charge les résultats de chaque librairie (temps, signal de bruit, signal de sortie).
-- Calcule les erreurs numériques entre les librairies (norme de la différence).
-- Affiche les résultats dans la console (temps, erreurs).
-- Trace les signaux de bruit et de sortie pour chaque librairie sur un même graphique.
-- Affiche un histogramme comparant les temps de simulation des différentes librairies.
-
-Rq: (Bdsim est commenté car trop lent)
+bench_02_multi_feedback — Comparison
+======================================
+Runs the benchmark across all simulators and reports:
+  - Execution times (median, std)
+  - Numerical errors between simulators (L2 norm)
+  - Signal plots
+  - Execution time bar chart (log scale)
+
+Simulink results are loaded from a pre-generated CSV file (matlab/simulink_results.csv).
+Simulink timing (t_mean_sl, t_std_sl) must be updated manually after running the
+Simulink model on the target machine.
 """
+
 import logging
 
+from pathlib import Path
 import numpy as np
 import matplotlib.pyplot as plt
 
@@ -22,26 +27,31 @@
 
 
 if __name__ == "__main__":
-    N_RUNS = 1
+    N_RUNS = 100
 
     logger.info(f"Running benchmark ({N_RUNS} runs each)...")
 
-    results_bd, results_ps, results_pb = [], [], []
+    results_ps, results_pb = [], []
     for i in range(N_RUNS):
-        print(f"Run {i+1}/{N_RUNS}...", end="\r")
+        print(f"  Run {i+1}/{N_RUNS}...", end="\r")
         results_ps.append(test_pathsim_case())
         results_pb.append(test_pysimblocks_case())
 
-    times_ps = np.array([r[3] for r in results_ps])
-    times_pb = np.array([r[3] for r in results_pb])
+    print()
+
+    # ── Timing arrays (ms) ────────────────────────────────────────────────────
+    times_ps = np.array([r[3] for r in results_ps]) * 1e3
+    times_pb = np.array([r[3] for r in results_pb]) * 1e3
 
-    sl = np.loadtxt("matlab/simulink_results.csv", delimiter=",", skiprows=1)
+    # ── Simulink results (pre-generated) ─────────────────────────────────────
+    sl        = np.loadtxt(Path(__file__).parent / "matlab" / "simulink_results.csv", delimiter=",", skiprows=1)
     t_sl      = sl[:, 0]
     noise_sl  = sl[:, 1]
     output_sl = sl[:, 2]
-    t_mean_sl = 253.5 # ms
-    t_std_sl = 12.5 # ms
+    t_mean_sl = 253.5   # ms — measured separately, update if re-running on a different machine
+    t_std_sl  = 12.5    # ms
 
+    # ── Last-run signals ──────────────────────────────────────────────────────
     t_ps, noise_ps, output_ps, _ = results_ps[-1]
     t_pb, noise_pb, output_pb, _ = results_pb[-1]
 
@@ -49,90 +59,103 @@
     t_ps, noise_ps, output_ps = t_ps[:n], noise_ps[:n], output_ps[:n]
     t_pb, noise_pb, output_pb = t_pb[:n], noise_pb[:n], output_pb[:n]
     t_sl, noise_sl, output_sl = t_sl[:n], noise_sl[:n], output_sl[:n]
-    
-    t_error_ps_pb = np.linalg.norm(t_ps - t_pb)
-    noise_error_ps_pb = np.linalg.norm(noise_ps - noise_pb)
-    output_error_ps_pb = np.linalg.norm(output_ps - output_pb)
-    t_error_sl_pb = np.linalg.norm(t_sl - t_pb)
-    noise_error_sl_pb = np.linalg.norm(noise_sl - noise_pb)
-    output_error_sl_pb = np.linalg.norm(output_sl - output_pb)
-
-    # --- Sauvegarder les résultats de référence ---
-    np.savez("reference_results.npz",
-        t            = t_pb,
-        noise        = noise_pb,
-        output_psb   = output_pb,
-        output_ps    = output_ps,
-        output_sl    = output_sl,
-        times_ps_ms  = times_ps * 1e3,
-        times_pb_ms  = times_pb * 1e3,
-        t_sl         = t_sl,
+
+    # ── Numerical errors (L2 norm) ────────────────────────────────────────────
+    def rel(err, ref):
+        return err / np.linalg.norm(ref) * 100 if np.linalg.norm(ref) > 0 else 0.0
+
+    t_err_ps     = np.linalg.norm(t_ps     - t_pb)
+    noise_err_ps = np.linalg.norm(noise_ps  - noise_pb)
+    out_err_ps   = np.linalg.norm(output_ps - output_pb)
+
+    t_err_sl     = np.linalg.norm(t_sl     - t_pb)
+    noise_err_sl = np.linalg.norm(noise_sl  - noise_pb)
+    out_err_sl   = np.linalg.norm(output_sl - output_pb)
+
+    # ── Save reference results ────────────────────────────────────────────────
+    np.savez(Path(__file__).parent / "reference_results.npz",
+        t           = t_pb,
+        noise       = noise_pb,
+        output_psb  = output_pb,
+        output_ps   = output_ps,
+        output_sl   = output_sl,
+        times_ps_ms = times_ps,
+        times_pb_ms = times_pb,
+        t_sl        = t_sl,
     )
 
+    # ── Console report ────────────────────────────────────────────────────────
     logger.info("")
     logger.info("=== Timing ===")
-    logger.info(f"  PathSim:     median={np.median(times_ps)*1e3:.1f} ms,  std={np.std(times_ps)*1e3:.1f} ms")
-    logger.info(f"  pySimBlocks: median={np.median(times_pb)*1e3:.1f} ms,  std={np.std(times_pb)*1e3:.1f} ms")
+    logger.info(f"  PathSim:     median={np.median(times_ps):.1f} ms,  std={np.std(times_ps):.1f} ms")
+    logger.info(f"  pySimBlocks: median={np.median(times_pb):.1f} ms,  std={np.std(times_pb):.1f} ms")
     logger.info(f"  Simulink:    median={t_mean_sl:.1f} ms,  std={t_std_sl:.1f} ms")
-    logger.info(f"  Speedup pySimBlocks vs PathSim: {np.median(times_ps) / np.median(times_pb):.2f}x")
-    logger.info(f"  Speedup pySimBlocks vs Simulink: {t_mean_sl*1e-3 / np.median(times_pb):.2f}x")
+    logger.info(f"  Speedup pySimBlocks vs PathSim:  {np.median(times_ps) / np.median(times_pb):.2f}x")
+    logger.info(f"  Speedup pySimBlocks vs Simulink: {t_mean_sl / np.median(times_pb):.2f}x")
 
     logger.info("")
-    logger.info("=== Numerical errors (last run) ===")
-    logger.info("Librairies | Time error (a/b%) | Noise error (a/b%) | Output error (a/b%)")
-    logger.info(f"PathSim vs pySimBlocks | {t_error_ps_pb:.2e} ({t_error_ps_pb / np.linalg.norm(t_pb) * 100:.2f}%) | {noise_error_ps_pb:.2e} ({noise_error_ps_pb / np.linalg.norm(noise_pb) * 100:.2f}%) | {output_error_ps_pb:.2e} ({output_error_ps_pb / np.linalg.norm(output_pb) * 100:.2f}%)")
-    logger.info(f"Simulink vs pySimBlocks | {t_error_sl_pb:.2e} ({t_error_sl_pb / np.linalg.norm(t_pb) * 100:.2f}%) | {noise_error_sl_pb:.2e} ({noise_error_sl_pb / np.linalg.norm(noise_pb) * 100:.2f}%) | {output_error_sl_pb:.2e} ({output_error_sl_pb / np.linalg.norm(output_pb) * 100:.2f}%)")
-
-    plt.figure(figsize=(10, 6))
-    plt.plot(t_ps, noise_ps,  "--r", label="Noise (PathSim)",    alpha=0.7)
-    plt.plot(t_ps, output_ps, "--b", label="Output (PathSim)",   alpha=0.7)
-    plt.plot(t_pb, noise_pb,  ":r",  label="Noise (pySimBlocks)", alpha=0.7)
-    plt.plot(t_pb, output_pb, ":b",  label="Output (pySimBlocks)", alpha=0.7)
-    plt.plot(t_sl, noise_sl,  "-.m", label="Noise (Simulink)",   alpha=0.7)
-    plt.plot(t_sl, output_sl, "-.c", label="Output (Simulink)",  alpha=0.7)
-    plt.title("Simulation Results Comparison")
-    plt.xlabel("Time (s)")
-    plt.ylabel("Amplitude")
-    plt.legend()
-    plt.grid()
+    logger.info("=== Numerical errors — L2 norm (last run) ===")
+    logger.info(f"{'Comparison':<30} {'Time':>18} {'Noise':>18} {'Output':>18}")
+    logger.info("-" * 88)
+    logger.info(
+        f"{'PathSim vs pySimBlocks':<30} "
+        f"{t_err_ps:.2e} ({rel(t_err_ps, t_pb):.2f}%)  "
+        f"{noise_err_ps:.2e} ({rel(noise_err_ps, noise_pb):.2f}%)  "
+        f"{out_err_ps:.2e} ({rel(out_err_ps, output_pb):.2f}%)"
+    )
+    logger.info(
+        f"{'Simulink vs pySimBlocks':<30} "
+        f"{t_err_sl:.2e} ({rel(t_err_sl, t_pb):.2f}%)  "
+        f"{noise_err_sl:.2e} ({rel(noise_err_sl, noise_pb):.2f}%)  "
+        f"{out_err_sl:.2e} ({rel(out_err_sl, output_pb):.2f}%)"
+    )
+
+    # ── Signal plot ───────────────────────────────────────────────────────────
+    fig, ax = plt.subplots(figsize=(10, 5))
+    ax.plot(t_ps, noise_ps,  "--r",  label="Noise (PathSim)",     alpha=0.7)
+    ax.plot(t_ps, output_ps, "--b",  label="Output (PathSim)",    alpha=0.7)
+    ax.plot(t_pb, noise_pb,  ":r",   label="Noise (pySimBlocks)", alpha=0.7)
+    ax.plot(t_pb, output_pb, ":b",   label="Output (pySimBlocks)",alpha=0.7)
+    ax.plot(t_sl, noise_sl,  "-.m",  label="Noise (Simulink)",    alpha=0.7)
+    ax.plot(t_sl, output_sl, "-.c",  label="Output (Simulink)",   alpha=0.7)
+    ax.set_title("bench_02 — Signal comparison")
+    ax.set_xlabel("Time (s)")
+    ax.set_ylabel("Amplitude")
+    ax.legend()
+    ax.grid(True, alpha=0.3)
     plt.tight_layout()
 
-    # --- Histogramme des temps ---
-    benchmarks = {
-        'bench_01': {
-            'PathSim':     np.median(times_ps) * 1e3,
-            'pySimBlocks': np.median(times_pb) * 1e3,
-            'Simulink':    t_mean_sl,
-        },
+    # ── Timing bar chart (log scale) ──────────────────────────────────────────
+    timings = {
+        "PathSim":     np.median(times_ps),
+        "pySimBlocks": np.median(times_pb),
+        "Simulink":    t_mean_sl,
+    }
+    errors = {
+        "PathSim":     np.std(times_ps),
+        "pySimBlocks": np.std(times_pb),
+        "Simulink":    t_std_sl,
+    }
+    colors = {
+        "PathSim":     "#1D9E75",
+        "pySimBlocks": "#D85A30",
+        "Simulink":    "#E1B000",
     }
 
-    libs = ['PathSim', 'pySimBlocks', 'Simulink']
-    colors = {'PathSim': '#1D9E75', 'pySimBlocks': '#D85A30', 'Simulink': '#E1B000'}
-
-    n_bench = len(benchmarks)
-    width = 0.2
-    group_gap = 1.0  # espace entre groupes
-
-    fig, ax = plt.subplots(figsize=(4 + 2 * n_bench, 5))
-
-    for g, (bench_name, values) in enumerate(benchmarks.items()):
-        group_center = g * group_gap
-        offsets = [-width, 0, width]
-        for lib, offset in zip(libs, offsets):
-            val = values[lib]
-            bar = ax.bar(group_center + offset, val, width=width,
-                         color=colors[lib], label=lib if g == 0 else None)
-            ax.bar_label(bar, fmt='%.1f', padding=3, fontsize=8)
-
-    ax.set_xticks([g * group_gap for g in range(n_bench)])
-    ax.set_xticklabels(list(benchmarks.keys()))
-    ax.set_ylabel('Median time (ms)')
-    ax.set_title('Time benchmark comparison')
-    ax.set_yscale('log')
-    ax.legend(loc='upper right')
-    ax.grid(axis='y', linestyle='--', alpha=0.4)
-    ax.spines[['top', 'right']].set_visible(False)
-
+    fig2, ax2 = plt.subplots(figsize=(6, 5))
+    for i, (lib, val) in enumerate(timings.items()):
+        bar = ax2.bar(i, val, color=colors[lib], label=lib,
+                      yerr=errors[lib], capsize=4, width=0.5)
+        ax2.bar_label(bar, fmt="%.1f", padding=4, fontsize=9)
+
+    ax2.set_xticks(range(len(timings)))
+    ax2.set_xticklabels(list(timings.keys()))
+    ax2.set_ylabel("Median execution time (ms)")
+    ax2.set_title("bench_02 — Execution time comparison")
+    ax2.set_yscale("log")
+    ax2.legend(loc="upper right")
+    ax2.grid(axis="y", linestyle="--", alpha=0.4)
+    ax2.spines[["top", "right"]].set_visible(False)
     plt.tight_layout()
-    plt.show()
 
+    plt.show()
diff --git a/examples/benchmarks/bench_02_dense_network/params.py b/examples/benchmarks/bench_02_dense_network/params.py
index 953e0a1..0553ae7 100644
--- a/examples/benchmarks/bench_02_dense_network/params.py
+++ b/examples/benchmarks/bench_02_dense_network/params.py
@@ -1,3 +1,4 @@
+from pathlib import Path
 import numpy as np
 import scipy.io as sio
 
@@ -9,7 +10,8 @@
 seed = 0
 rng = np.random.default_rng(seed)
 noise_sequence = rng.standard_normal((N + 2, vec_size))
-np.save("noise_seq.npy", noise_sequence)
+dir_path = Path(__file__).parent
+np.save(dir_path / "noise_seq.npy", noise_sequence)
 
 x0 = np.zeros((vec_size, 1))
 
@@ -17,9 +19,9 @@
 t_vec = np.arange(N + 2) * dt
 noise_data_simulink = np.column_stack([t_vec, noise_sequence])
 
-sio.savemat("matlab/bench_02_simulink.mat", {
-    "dt": dt,
-    "T": T,
-    "x0": x0,
-    "noise_data": noise_data_simulink,
-})
+# sio.savemat("matlab/bench_02_simulink.mat", {
+#     "dt": dt,
+#     "T": T,
+#     "x0": x0,
+#     "noise_data": noise_data_simulink,
+# })
diff --git a/examples/benchmarks/bench_02_dense_network/reference_results.npz b/examples/benchmarks/bench_02_dense_network/reference_results.npz
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diff --git a/examples/benchmarks/bench_02_dense_network/results.py b/examples/benchmarks/bench_02_dense_network/results.py
new file mode 100644
index 0000000..47e71c8
--- /dev/null
+++ b/examples/benchmarks/bench_02_dense_network/results.py
@@ -0,0 +1,63 @@
+from pathlib import Path
+import logging
+import numpy as np
+import matplotlib.pyplot as plt
+
+logging.basicConfig(level=logging.INFO, format="%(message)s")
+logger = logging.getLogger(__name__)
+
+data = np.load(Path(__file__).parent / "reference_results.npz")
+t = data["t"]
+noise = data["noise"]
+output_pb = data["output_psb"]
+output_ps = data["output_ps"]
+output_sl = data["output_sl"]
+times_ps = data["times_ps_ms"]
+times_pb = data["times_pb_ms"]
+t_sl = data["t_sl"]
+t_mean_sl = 253.5 # ms
+t_std_sl = 12.5 # ms
+
+logger.info("")
+logger.info("=== Timing ===")
+logger.info(f"  PathSim:     median={np.median(times_ps):.1f} ms,  std={np.std(times_ps):.1f} ms")
+logger.info(f"  pySimBlocks: median={np.median(times_pb):.1f} ms,  std={np.std(times_pb):.1f} ms")
+logger.info(f"  Simulink:    median={t_mean_sl:.1f} ms,  std={t_std_sl:.1f} ms")
+logger.info(f"  Speedup pySimBlocks vs PathSim:  {np.median(times_ps) / np.median(times_pb):.2f}x")
+logger.info(f"  Speedup pySimBlocks vs Simulink: {t_mean_sl / np.median(times_pb):.2f}x")
+
+# ── Timing bar chart (log scale) ──────────────────────────────────────────
+timings = {
+    "PathSim":     np.median(times_ps),
+    "pySimBlocks": np.median(times_pb),
+    "Simulink":    t_mean_sl,
+}
+errors = {
+    "PathSim":     np.std(times_ps),
+    "pySimBlocks": np.std(times_pb),
+    "Simulink":    t_std_sl,
+}
+colors = {
+    "PathSim":     "#1D9E75",
+    "pySimBlocks": "#D85A30",
+    "Simulink":    "#E1B000",
+}
+
+fig2, ax2 = plt.subplots(figsize=(6, 5))
+for i, (lib, val) in enumerate(timings.items()):
+    bar = ax2.bar(i, val, color=colors[lib], label=lib,
+                  yerr=errors[lib], capsize=4, width=0.5)
+    ax2.bar_label(bar, fmt="%.1f", padding=4, fontsize=9)
+
+ax2.set_xticks(range(len(timings)))
+ax2.set_xticklabels(list(timings.keys()))
+ax2.set_ylabel("Median execution time (ms)")
+ax2.set_title("bench_02 — Execution time comparison")
+ax2.set_yscale("log")
+ax2.legend(loc="upper right")
+ax2.grid(axis="y", linestyle="--", alpha=0.4)
+ax2.spines[["top", "right"]].set_visible(False)
+plt.tight_layout()
+
+plt.show()
+
diff --git a/examples/benchmarks/bench_03_scaling/bench_scaling_results.npz b/examples/benchmarks/bench_03_scaling/bench_scaling_results.npz
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diff --git a/examples/benchmarks/bench_03_scaling/pysimblocks_case.py b/examples/benchmarks/bench_03_scaling/pysimblocks_case.py
new file mode 100644
index 0000000..27942f6
--- /dev/null
+++ b/examples/benchmarks/bench_03_scaling/pysimblocks_case.py
@@ -0,0 +1,296 @@
+"""
+bench_03_scaling — pySimBlocks
+================================
+Measures simulation time as a function of the number of blocks.
+
+Topology per cell (N=3 example):
+
+    noise → G0 → S0(++) → Dyn0(Integ) → Gcouple0 → S1(+++) → Dyn1(Delay) → Gcouple1 → S2(+++) → Dyn2(Integ)
+                    ↑           |                       ↑  ↑          |                     ↑  ↑
+                 GainFb0 ←──────┘                Gcouple0 Gain1    GainFb1←──┘          Gcouple1 Gain2
+                                                                                          GainFb2←──┘
+
+Per cell i:
+  - Gain_i      : feedforward from noise
+  - Sum_i       : sum (2 inputs for cell 0, 3 inputs for cells i>0)
+  - Dyn_i       : discrete_integrator if i even, delay if i odd
+  - GainFb_i    : local feedback (Dyn_i.out → GainFb_i → Sum_i.in2)
+  - Gcouple_i   : inter-cell coupling (Dyn_i.out → Gcouple_i → Sum_{i+1}.in1)  [except last]
+
+Total blocks = 5*N (source included)
+Total connections ≈ 5*N
+"""
+
+from __future__ import annotations
+
+import time
+import statistics
+import tempfile
+from pathlib import Path
+
+import numpy as np
+import yaml
+import matplotlib.pyplot as plt
+
+from pySimBlocks.project import load_simulator_from_project
+
+
+# ─────────────────────────────────────────────────────────────────────────────
+# Parameters
+# ─────────────────────────────────────────────────────────────────────────────
+
+DT = 0.001
+N_STEPS = 100_000
+T = N_STEPS * DT
+
+N_RUNS = 3
+N_CELLS_LIST = [5, 10, 20, 50, 100]
+
+
+# ─────────────────────────────────────────────────────────────────────────────
+# YAML generation
+# ─────────────────────────────────────────────────────────────────────────────
+
+def generate_project_dict(n_cells: int, dt: float = DT, T: float = T) -> dict:
+    """Generate a project.yaml dict for n_cells cascaded cells.
+
+    Topology:
+        Sum0 receives: Gain0.out (in1) + GainFb0.out (in2)
+        Sum_i (i>0) receives: Gcouple_{i-1}.out (in1) + GainFb_i.out (in2) + Gain_i.out (in3)
+        Dyn_i.out → GainFb_i → Sum_i.in2  (local feedback)
+        Dyn_i.out → Gcouple_i → Sum_{i+1}.in1  (inter-cell coupling)
+        noise → all Gain_i  (fan-out)
+
+    Args:
+        n_cells: Number of cells (>= 2).
+        dt: Simulation time step.
+        T: Total simulation duration.
+
+    Returns:
+        Dict ready to serialize as YAML.
+    """
+    if n_cells < 2:
+        raise ValueError("n_cells must be >= 2")
+
+    blocks = []
+    connections = []
+    conn_idx = 1
+
+    def add(src: str, dst: str) -> None:
+        nonlocal conn_idx
+        connections.append({"name": f"c{conn_idx}", "ports": [src, dst]})
+        conn_idx += 1
+
+    # ── Source ────────────────────────────────────────────────────────────────
+    blocks.append({
+        "name": "WhiteNoise",
+        "category": "sources",
+        "type": "white_noise",
+        "parameters": {"std": 1.0},
+    })
+
+    # ── Cells ─────────────────────────────────────────────────────────────────
+    for i in range(n_cells):
+        gain_val    = round(0.5 / (i + 1), 6)
+        dyn_type    = "discrete_integrator" if i % 2 == 0 else "delay"
+        couple_gain = round(0.8 / (i + 1), 6)
+        fb_gain     = round(0.2 / (i + 1), 6)
+
+        blocks.append({
+            "name": f"Gain{i}",
+            "category": "operators",
+            "type": "gain",
+            "parameters": {"gain": gain_val, "multiplication": "Element wise (K * u)"},
+        })
+        # Sum0: 2 inputs (++)  |  Sum_i>0: 3 inputs (+++) — corrected below
+        blocks.append({
+            "name": f"Sum{i}",
+            "category": "operators",
+            "type": "sum",
+            "parameters": {"signs": "++"},
+        })
+        blocks.append({
+            "name": f"Dyn{i}",
+            "category": "operators",
+            "type": dyn_type,
+            "parameters": {},
+        })
+        blocks.append({
+            "name": f"GainFb{i}",
+            "category": "operators",
+            "type": "gain",
+            "parameters": {"gain": fb_gain, "multiplication": "Element wise (K * u)"},
+        })
+        if i < n_cells - 1:
+            blocks.append({
+                "name": f"Gcouple{i}",
+                "category": "operators",
+                "type": "gain",
+                "parameters": {"gain": couple_gain, "multiplication": "Element wise (K * u)"},
+            })
+
+    # Cells i>0 have 3 inputs: Gcouple_{i-1} + GainFb_i + Gain_i
+    for b in blocks:
+        if b["name"].startswith("Sum") and b["name"] != "Sum0":
+            b["parameters"]["signs"] = "+++"
+
+    # ── Connections ───────────────────────────────────────────────────────────
+
+    # noise → all Gain_i (fan-out)
+    for i in range(n_cells):
+        add("WhiteNoise.out", f"Gain{i}.in")
+
+    for i in range(n_cells):
+        # Sum_i.in1: Gain0.out for cell 0, Gcouple_{i-1}.out for cells i>0
+        if i == 0:
+            add("Gain0.out", "Sum0.in1")
+        else:
+            add(f"Gcouple{i-1}.out", f"Sum{i}.in1")
+
+        # Sum_i.in2: local feedback
+        add(f"GainFb{i}.out", f"Sum{i}.in2")
+
+        # Sum_i → Dyn_i
+        add(f"Sum{i}.out", f"Dyn{i}.in")
+
+        # Dyn_i → GainFb_i (local feedback loop)
+        add(f"Dyn{i}.out", f"GainFb{i}.in")
+
+        # Dyn_i → Gcouple_i (coupling to next cell)
+        if i < n_cells - 1:
+            add(f"Dyn{i}.out", f"Gcouple{i}.in")
+
+    # Gain_i (i>0) → Sum_i.in3 (feedforward for cells i>0)
+    for i in range(1, n_cells):
+        add(f"Gain{i}.out", f"Sum{i}.in3")
+
+    n_total_blocks = 5 * n_cells  # source + 4 blocks/cell + (n-1) coupling gains ≈ 5N
+    n_connections  = conn_idx - 1
+
+    return {
+        "schema_version": 1,
+        "project": {"name": f"bench_scaling_{n_cells}_cells"},
+        "simulation": {
+            "dt": dt,
+            "T": T,
+            "solver": "fixed",
+            "logging": [f"Dyn{n_cells - 1}.outputs.out"],
+            "plots": [],
+        },
+        "diagram": {
+            "blocks": blocks,
+            "connections": connections,
+        },
+        "_meta": {
+            "n_cells": n_cells,
+            "n_blocks": n_total_blocks,
+            "n_connections": n_connections,
+        },
+    }
+
+
+# ─────────────────────────────────────────────────────────────────────────────
+# Benchmark
+# ─────────────────────────────────────────────────────────────────────────────
+
+def run_benchmark(n_cells: int, n_runs: int) -> dict:
+    """Run n_runs simulations for n_cells cells and return timing stats."""
+    meta = generate_project_dict(n_cells)["_meta"]
+    n_total_blocks = meta["n_blocks"]
+    times = []
+
+    project_dict = generate_project_dict(n_cells)
+
+    with tempfile.TemporaryDirectory() as tmpdir:
+        yaml_path = Path(tmpdir) / "project.yaml"
+        with open(yaml_path, "w") as f:
+            d = {k: v for k, v in project_dict.items() if k != "_meta"}
+            yaml.dump(d, f, default_flow_style=False, sort_keys=False)
+
+        for _ in range(n_runs):
+            sim, _ = load_simulator_from_project(yaml_path)
+            t0 = time.perf_counter()
+            sim.run()
+            t1 = time.perf_counter()
+            times.append((t1 - t0) * 1000)  # ms
+
+    return {
+        "n_cells": n_cells,
+        "n_blocks": n_total_blocks,
+        "n_connections": meta["n_connections"],
+        "median_ms": statistics.median(times),
+        "std_ms": statistics.stdev(times) if len(times) > 1 else 0.0,
+        "min_ms": min(times),
+        "max_ms": max(times),
+    }
+
+
+# ─────────────────────────────────────────────────────────────────────────────
+# Main
+# ─────────────────────────────────────────────────────────────────────────────
+
+if __name__ == "__main__":
+    print(f"Bench Scaling — {N_STEPS} steps, dt={DT}, {N_RUNS} runs each\n")
+    print(f"{'n_cells':>8} {'n_blocks':>10} {'n_conn':>8} {'median (ms)':>14} {'std (ms)':>10}")
+    print("-" * 54)
+
+    results = []
+    for n in N_CELLS_LIST:
+        r = run_benchmark(n, N_RUNS)
+        results.append(r)
+        print(f"{r['n_cells']:>8} {r['n_blocks']:>10} {r['n_connections']:>8} "
+              f"{r['median_ms']:>14.1f} {r['std_ms']:>10.1f}")
+    
+    np.savez(Path(__file__).parent / "bench_scaling_results.npz", 
+             results=results,
+             N_STEPS=N_STEPS,
+             N_RUNS=N_RUNS,
+             DT=DT,
+             N_CELLS_LIST=N_CELLS_LIST
+             )
+
+    # ── Plot ──────────────────────────────────────────────────────────────────
+    n_blocks = [r["n_blocks"] for r in results]
+    medians  = [r["median_ms"] for r in results]
+    stds     = [r["std_ms"] for r in results]
+
+    coeffs   = np.polyfit(n_blocks, medians, 1)
+    fit_line = np.poly1d(coeffs)
+    n_fit    = np.linspace(min(n_blocks), max(n_blocks), 200)
+
+    # Cost per step per block in µs
+    us_per_step_per_block = [
+        (m / N_STEPS * 1000) / nb
+        for m, nb in zip(medians, n_blocks)
+    ]
+
+    fig, axes = plt.subplots(1, 2, figsize=(12, 5))
+    fig.suptitle(
+        f"pySimBlocks — Simulation time scaling\n"
+        f"({N_STEPS} steps, dt={DT}, {N_RUNS} runs/point)",
+        fontsize=12,
+    )
+
+    ax = axes[0]
+    ax.errorbar(n_blocks, medians, yerr=stds, fmt="o-", color="steelblue",
+                capsize=4, label="Measured median")
+    ax.plot(n_fit, fit_line(n_fit), "--", color="tomato", alpha=0.7,
+            label=f"Linear fit ({coeffs[0]:.2f} ms/block)")
+    ax.set_xlabel("Number of blocks")
+    ax.set_ylabel("Simulation time (ms)")
+    ax.set_title("Absolute time")
+    ax.legend()
+    ax.grid(True, alpha=0.3)
+
+    ax2 = axes[1]
+    ax2.plot(n_blocks, us_per_step_per_block, "s-", color="seagreen")
+    ax2.set_xlabel("Number of blocks")
+    ax2.set_ylabel("Cost per step per block (µs)")
+    ax2.set_title("Unit cost per block per step")
+    ax2.grid(True, alpha=0.3)
+    ax2.axhline(y=np.mean(us_per_step_per_block), color="tomato",
+                linestyle="--", alpha=0.7, label=f"Mean: {np.mean(us_per_step_per_block):.2f} µs")
+    ax2.legend()
+
+    plt.tight_layout()
+    plt.show()
diff --git a/examples/benchmarks/bench_03_scaling/results.py b/examples/benchmarks/bench_03_scaling/results.py
new file mode 100644
index 0000000..90dbc0c
--- /dev/null
+++ b/examples/benchmarks/bench_03_scaling/results.py
@@ -0,0 +1,68 @@
+from pathlib import Path
+import numpy as np
+import matplotlib.pyplot as plt
+
+if __name__ == "__main__":
+
+    data = np.load(Path(__file__).parent / "bench_scaling_results.npz", allow_pickle=True)
+    results = data["results"]
+    N_STEPS = data["N_STEPS"].item()
+    N_RUNS = data["N_RUNS"].item()
+    DT = data["DT"].item()
+    N_CELLS_LIST = data["N_CELLS_LIST"]
+
+
+    print(f"Bench Scaling — {N_STEPS} steps, dt={DT}, {N_RUNS} runs each\n")
+    print(f"{'n_cells':>8} {'n_blocks':>10} {'n_conn':>8} {'median (ms)':>14} {'std (ms)':>10}")
+    print("-" * 54)
+
+    for n, r in zip(N_CELLS_LIST, results):
+        print(f"{r['n_cells']:>8} {r['n_blocks']:>10} {r['n_connections']:>8} "
+              f"{r['median_ms']:>14.1f} {r['std_ms']:>10.1f}")
+
+    # ── Plot ──────────────────────────────────────────────────────────────────
+    n_blocks = [r["n_blocks"] for r in results]
+    medians  = [r["median_ms"] for r in results]
+    stds     = [r["std_ms"] for r in results]
+
+    coeffs   = np.polyfit(n_blocks, medians, 1)
+    fit_line = np.poly1d(coeffs)
+    n_fit    = np.linspace(min(n_blocks), max(n_blocks), 200)
+
+    # Cost per step per block in µs
+    us_per_step_per_block = [
+        (m / N_STEPS * 1000) / nb
+        for m, nb in zip(medians, n_blocks)
+    ]
+
+    fig, axes = plt.subplots(1, 2, figsize=(12, 5))
+    fig.suptitle(
+        f"pySimBlocks — Simulation time scaling\n"
+        f"({N_STEPS} steps, dt={DT}, {N_RUNS} runs/point)",
+        fontsize=12,
+    )
+
+    ax = axes[0]
+    ax.errorbar(n_blocks, medians, yerr=stds, fmt="o-", color="steelblue",
+                capsize=4, label="Measured median")
+    ax.plot(n_fit, fit_line(n_fit), "--", color="tomato", alpha=0.7,
+            label=f"Linear fit ({coeffs[0]:.2f} ms/block)")
+    ax.set_xlabel("Number of blocks")
+    ax.set_ylabel("Simulation time (ms)")
+    ax.set_title("Absolute time")
+    ax.legend()
+    ax.grid(True, alpha=0.3)
+
+    ax2 = axes[1]
+    ax2.plot(n_blocks, us_per_step_per_block, "s-", color="seagreen")
+    ax2.set_xlabel("Number of blocks")
+    ax2.set_ylabel("Cost per step per block (µs)")
+    ax2.set_title("Unit cost per block per step")
+    ax2.grid(True, alpha=0.3)
+    ax2.axhline(y=np.mean(us_per_step_per_block), color="tomato",
+                linestyle="--", alpha=0.7, label=f"Mean: {np.mean(us_per_step_per_block):.2f} µs")
+    ax2.legend()
+
+    plt.tight_layout()
+    plt.show()
+

From 92b223153819b33aa6b8b0d688026e27f58ef6b1 Mon Sep 17 00:00:00 2001
From: Alessandrini Antoine <a.alsdrini@gmail.com>
Date: Tue, 21 Apr 2026 09:32:35 +0200
Subject: [PATCH 4/4] fix(docs): pathsim euler forward

---
 .../bench_01_minimal_loop/pathsim_case.py     |   4 +-
 .../reference_results.npz                     | Bin 4803646 -> 4803646 bytes
 .../bench_02_dense_network/pathsim_case.py    |   4 +-
 .../reference_results.npz                     | Bin 4803646 -> 4803646 bytes
 .../bench_scaling_pathsim_results.npz         | Bin 0 -> 1792 bytes
 .../benchmarks/bench_03_scaling/compare.py    | 107 ++++++++
 .../bench_03_scaling/pathsim_case.py          | 253 ++++++++++++++++++
 7 files changed, 364 insertions(+), 4 deletions(-)
 create mode 100644 examples/benchmarks/bench_03_scaling/bench_scaling_pathsim_results.npz
 create mode 100644 examples/benchmarks/bench_03_scaling/compare.py
 create mode 100644 examples/benchmarks/bench_03_scaling/pathsim_case.py

diff --git a/examples/benchmarks/bench_01_minimal_loop/pathsim_case.py b/examples/benchmarks/bench_01_minimal_loop/pathsim_case.py
index 7167988..8c902cb 100644
--- a/examples/benchmarks/bench_01_minimal_loop/pathsim_case.py
+++ b/examples/benchmarks/bench_01_minimal_loop/pathsim_case.py
@@ -25,7 +25,7 @@
     Scope,
     Source,
 )
-from pathsim.solvers import RK4
+from pathsim.solvers import EUF
 
 import params as prm 
 
@@ -102,7 +102,7 @@ def test_pathsim_case():
     sim = Simulation(
         blocks,
         connections,
-        Solver=RK4,
+        Solver=EUF,
         dt=prm.dt,
         dt_min=prm.dt,
         dt_max=prm.dt,
diff --git a/examples/benchmarks/bench_01_minimal_loop/reference_results.npz b/examples/benchmarks/bench_01_minimal_loop/reference_results.npz
index 6456101011e0e2925edf68e9ce75ff6181efdb2d..22b3155c9d4be2dc1f933b86426a2f4d5e2aaf27 100644
GIT binary patch
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diff --git a/examples/benchmarks/bench_02_dense_network/pathsim_case.py b/examples/benchmarks/bench_02_dense_network/pathsim_case.py
index 98246be..0ac425b 100644
--- a/examples/benchmarks/bench_02_dense_network/pathsim_case.py
+++ b/examples/benchmarks/bench_02_dense_network/pathsim_case.py
@@ -26,7 +26,7 @@
     Scope,
     Source,
 )
-from pathsim.solvers import RK4
+from pathsim.solvers import EUF
 
 import params as prm
 
@@ -135,7 +135,7 @@ def test_pathsim_case():
     sim = Simulation(
         blocks,
         connections,
-        Solver=RK4,
+        Solver=EUF,
         dt=prm.dt,
         dt_min=prm.dt,
         dt_max=prm.dt,
diff --git a/examples/benchmarks/bench_02_dense_network/reference_results.npz b/examples/benchmarks/bench_02_dense_network/reference_results.npz
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diff --git a/examples/benchmarks/bench_03_scaling/compare.py b/examples/benchmarks/bench_03_scaling/compare.py
new file mode 100644
index 0000000..392abc7
--- /dev/null
+++ b/examples/benchmarks/bench_03_scaling/compare.py
@@ -0,0 +1,107 @@
+"""
+bench_03_scaling — Comparison
+===============================
+Loads pre-computed results from pySimBlocks and PathSim scaling benchmarks
+and produces a side-by-side comparison:
+  - Absolute time vs number of blocks (both simulators on same plot)
+  - Unit cost per block per step (µs) vs number of blocks
+  - Console report with slopes and mean unit costs
+"""
+
+from pathlib import Path
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+if __name__ == "__main__":
+
+    # ── Load results ──────────────────────────────────────────────────────────
+    data_pb = np.load(Path(__file__).parent / "bench_scaling_results.npz", allow_pickle=True)
+    results_pb = data_pb["results"]
+    N_STEPS    = data_pb["N_STEPS"].item()
+    N_RUNS     = data_pb["N_RUNS"].item()
+    DT         = data_pb["DT"].item()
+
+    data_ps = np.load(Path(__file__).parent / "bench_scaling_pathsim_results.npz", allow_pickle=True)
+    results_ps = data_ps["results"]
+
+    # ── Extract arrays ────────────────────────────────────────────────────────
+    n_blocks_pb = [r["n_blocks"]  for r in results_pb]
+    medians_pb  = [r["median_ms"] for r in results_pb]
+    stds_pb     = [r["std_ms"]    for r in results_pb]
+
+    n_blocks_ps = [r["n_blocks"]  for r in results_ps]
+    medians_ps  = [r["median_ms"] for r in results_ps]
+    stds_ps     = [r["std_ms"]    for r in results_ps]
+
+    # ── Unit costs (µs/block/step) ────────────────────────────────────────────
+    us_pb = [(m / N_STEPS * 1000) / nb for m, nb in zip(medians_pb, n_blocks_pb)]
+    us_ps = [(m / N_STEPS * 1000) / nb for m, nb in zip(medians_ps, n_blocks_ps)]
+
+    # ── Linear fits ───────────────────────────────────────────────────────────
+    coeffs_pb = np.polyfit(n_blocks_pb, medians_pb, 1)
+    coeffs_ps = np.polyfit(n_blocks_ps, medians_ps, 1)
+
+    n_fit = np.linspace(min(min(n_blocks_pb), min(n_blocks_ps)),
+                        max(max(n_blocks_pb), max(n_blocks_ps)), 200)
+
+    # ── Console report ────────────────────────────────────────────────────────
+    print(f"Bench Scaling Comparison — {N_STEPS} steps, dt={DT}, {N_RUNS} runs each\n")
+    print(f"{'n_blocks':>10} {'psb median (ms)':>18} {'psb std':>10} {'ps median (ms)':>16} {'ps std':>10}")
+    print("-" * 68)
+    for nb_pb, m_pb, s_pb, nb_ps, m_ps, s_ps in zip(
+        n_blocks_pb, medians_pb, stds_pb,
+        n_blocks_ps, medians_ps, stds_ps,
+    ):
+        print(f"{nb_pb:>10} {m_pb:>18.1f} {s_pb:>10.1f} {m_ps:>16.1f} {s_ps:>10.1f}")
+
+    print()
+    print(f"Linear fit slope — pySimBlocks : {coeffs_pb[0]:.2f} ms/block")
+    print(f"Linear fit slope — PathSim     : {coeffs_ps[0]:.2f} ms/block")
+    print(f"Mean unit cost   — pySimBlocks : {np.mean(us_pb):.2f} µs/block/step")
+    print(f"Mean unit cost   — PathSim     : {np.mean(us_ps):.2f} µs/block/step")
+    print(f"Slope ratio PathSim / pySimBlocks : {coeffs_ps[0] / coeffs_pb[0]:.2f}x")
+
+    # ── Plot ──────────────────────────────────────────────────────────────────
+    colors = {"pb": "#D85A30", "ps": "#1D9E75"}
+
+    fig, axes = plt.subplots(1, 2, figsize=(13, 5))
+    fig.suptitle(
+        f"bench_03 — Simulation time scaling: pySimBlocks vs PathSim\n"
+        f"({N_STEPS} steps, dt={DT}, {N_RUNS} runs/point)",
+        fontsize=12,
+    )
+
+    # Left: absolute time
+    ax = axes[0]
+    ax.errorbar(n_blocks_pb, medians_pb, yerr=stds_pb, fmt="o-",
+                color=colors["pb"], capsize=4, label="pySimBlocks")
+    ax.errorbar(n_blocks_ps, medians_ps, yerr=stds_ps, fmt="s-",
+                color=colors["ps"], capsize=4, label="PathSim (RK4, fixed step)")
+    ax.plot(n_fit, np.poly1d(coeffs_pb)(n_fit), "--", color=colors["pb"], alpha=0.5,
+            label=f"psb fit ({coeffs_pb[0]:.1f} ms/block)")
+    ax.plot(n_fit, np.poly1d(coeffs_ps)(n_fit), "--", color=colors["ps"], alpha=0.5,
+            label=f"ps fit  ({coeffs_ps[0]:.1f} ms/block)")
+    ax.set_xlabel("Number of blocks")
+    ax.set_ylabel("Simulation time (ms)")
+    ax.set_title("Absolute time")
+    ax.legend()
+    ax.grid(True, alpha=0.3)
+
+    # Right: unit cost per block per step
+    ax2 = axes[1]
+    ax2.plot(n_blocks_pb, us_pb, "o-", color=colors["pb"], label="pySimBlocks")
+    ax2.plot(n_blocks_ps, us_ps, "s-", color=colors["ps"], label="PathSim")
+    ax2.axhline(y=np.mean(us_pb), color=colors["pb"], linestyle="--", alpha=0.6,
+                label=f"psb mean: {np.mean(us_pb):.2f} µs")
+    ax2.axhline(y=np.mean(us_ps), color=colors["ps"], linestyle="--", alpha=0.6,
+                label=f"ps  mean: {np.mean(us_ps):.2f} µs")
+    ax2.set_xlabel("Number of blocks")
+    ax2.set_ylabel("Cost per step per block (µs)")
+    ax2.set_title("Unit cost per block per step")
+    ax2.legend()
+    ax2.grid(True, alpha=0.3)
+
+    plt.tight_layout()
+    plt.show()
diff --git a/examples/benchmarks/bench_03_scaling/pathsim_case.py b/examples/benchmarks/bench_03_scaling/pathsim_case.py
new file mode 100644
index 0000000..2e56bb9
--- /dev/null
+++ b/examples/benchmarks/bench_03_scaling/pathsim_case.py
@@ -0,0 +1,253 @@
+"""
+bench_03_scaling — PathSim
+===========================
+Measures simulation time as a function of the number of blocks.
+
+Same topology as the pySimBlocks version:
+
+    noise → G0 → S0(++) → Dyn0(Integ) → Gcouple0 → S1(+++) → Dyn1(Delay) → Gcouple1 → ...
+                    ↑           |                       ↑  ↑          |
+                 GainFb0 ←──────┘                Gcouple0 Gain1    GainFb1←──┘
+
+Per cell i:
+  - Gain_i      : feedforward Amplifier from noise
+  - Sum_i       : Adder (++ for cell 0, +++ for cells i>0)
+  - Dyn_i       : Integrator if i even, Delay if i odd
+  - GainFb_i    : local feedback Amplifier
+  - Gcouple_i   : inter-cell coupling Amplifier (except last cell)
+
+Total blocks ≈ 5*N  |  RK4 solver, fixed step (adaptive=False)
+"""
+
+from __future__ import annotations
+
+from pathlib import Path
+import time
+import statistics
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+from pathsim import Simulation, Connection
+from pathsim.blocks import Adder, Amplifier, Integrator, Delay, Source
+from pathsim.solvers import EUF
+
+
+# ─────────────────────────────────────────────────────────────────────────────
+# Parameters
+# ─────────────────────────────────────────────────────────────────────────────
+
+DT      = 0.001
+N_STEPS = 100_000
+T       = N_STEPS * DT
+
+N_RUNS       = 3
+N_CELLS_LIST = [5, 10, 20, 50, 100]
+
+
+# ─────────────────────────────────────────────────────────────────────────────
+# Model builder
+# ─────────────────────────────────────────────────────────────────────────────
+
+def build_pathsim_scaling(n_cells: int):
+    """Build PathSim blocks and connections for n_cells cascaded cells.
+
+    Args:
+        n_cells: Number of cells (>= 2).
+
+    Returns:
+        Tuple (blocks, connections).
+    """
+    if n_cells < 2:
+        raise ValueError("n_cells must be >= 2")
+
+    # ── Source ────────────────────────────────────────────────────────────────
+    rng = np.random.default_rng(0)
+    noise_seq = rng.standard_normal(N_STEPS + 2)
+
+    def make_source(seq, dt):
+        def f(t):
+            k = int(round(t / dt))
+            return float(seq[min(k, len(seq) - 1)])
+        return Source(f)
+
+    src = make_source(noise_seq, DT)
+
+    # ── Per-cell blocks ───────────────────────────────────────────────────────
+    gains     = []   # feedforward
+    sums      = []
+    dyns      = []   # Integrator or Delay
+    gainfbs   = []   # local feedback
+    gcouples  = []   # inter-cell coupling
+
+    for i in range(n_cells):
+        gain_val    = 0.5 / (i + 1)
+        fb_gain     = 0.2 / (i + 1)
+        couple_gain = 0.8 / (i + 1)
+
+        gains.append(Amplifier(gain=gain_val))
+
+        # Sum0: 2 inputs; Sum_i>0: 3 inputs — PathSim Adder infers nin from operations string
+        ops = "++" if i == 0 else "+++"
+        sums.append(Adder(operations=ops))
+
+        if i % 2 == 0:
+            dyns.append(Integrator())
+        else:
+            dyns.append(Delay(tau=DT))
+
+        gainfbs.append(Amplifier(gain=fb_gain))
+
+        if i < n_cells - 1:
+            gcouples.append(Amplifier(gain=couple_gain))
+
+    # ── Assemble block list ───────────────────────────────────────────────────
+    blocks = [src]
+    for i in range(n_cells):
+        blocks += [gains[i], sums[i], dyns[i], gainfbs[i]]
+        if i < n_cells - 1:
+            blocks.append(gcouples[i])
+
+    # ── Connections ───────────────────────────────────────────────────────────
+    connections = []
+
+    # noise → all Gain_i (fan-out)
+    for i in range(n_cells):
+        connections.append(Connection(src[0], gains[i][0]))
+
+    for i in range(n_cells):
+        # Sum_i.in1
+        if i == 0:
+            connections.append(Connection(gains[0][0], sums[0][0]))
+        else:
+            connections.append(Connection(gcouples[i - 1][0], sums[i][0]))
+
+        # Sum_i.in2: local feedback
+        connections.append(Connection(gainfbs[i][0], sums[i][1]))
+
+        # Sum_i → Dyn_i
+        connections.append(Connection(sums[i][0], dyns[i][0]))
+
+        # Dyn_i → GainFb_i (local feedback loop)
+        connections.append(Connection(dyns[i][0], gainfbs[i][0]))
+
+        # Dyn_i → Gcouple_i (coupling to next cell)
+        if i < n_cells - 1:
+            connections.append(Connection(dyns[i][0], gcouples[i][0]))
+
+    # Gain_i (i>0) → Sum_i.in3 (feedforward for cells i>0)
+    for i in range(1, n_cells):
+        connections.append(Connection(gains[i][0], sums[i][2]))
+
+    return blocks, connections
+
+
+# ─────────────────────────────────────────────────────────────────────────────
+# Benchmark
+# ─────────────────────────────────────────────────────────────────────────────
+
+def run_benchmark(n_cells: int, n_runs: int) -> dict:
+    """Run n_runs simulations for n_cells cells and return timing stats."""
+    n_total_blocks = 5 * n_cells
+    times = []
+
+    for _ in range(n_runs):
+        blocks, connections = build_pathsim_scaling(n_cells)
+
+        sim = Simulation(
+            blocks,
+            connections,
+            Solver=EUF,
+            dt=DT,
+            dt_min=DT,
+            dt_max=DT,
+            tolerance_lte_rel=1e-4,
+            tolerance_lte_abs=1e-8,
+            tolerance_fpi=1e-10,
+            log=False,
+        )
+
+        t0 = time.perf_counter()
+        sim.run(duration=T, reset=True, adaptive=False)
+        t1 = time.perf_counter()
+        times.append((t1 - t0) * 1000)  # ms
+
+    return {
+        "n_cells": n_cells,
+        "n_blocks": n_total_blocks,
+        "median_ms": statistics.median(times),
+        "std_ms": statistics.stdev(times) if len(times) > 1 else 0.0,
+        "min_ms": min(times),
+        "max_ms": max(times),
+    }
+
+
+# ─────────────────────────────────────────────────────────────────────────────
+# Main
+# ─────────────────────────────────────────────────────────────────────────────
+
+if __name__ == "__main__":
+    print(f"Bench Scaling (PathSim) — {N_STEPS} steps, dt={DT}, {N_RUNS} runs each\n")
+    print(f"{'n_cells':>8} {'n_blocks':>10} {'median (ms)':>14} {'std (ms)':>10}")
+    print("-" * 46)
+
+    results = []
+    for n in N_CELLS_LIST:
+        r = run_benchmark(n, N_RUNS)
+        results.append(r)
+        print(f"{r['n_cells']:>8} {r['n_blocks']:>10} {r['median_ms']:>14.1f} {r['std_ms']:>10.1f}")
+
+    np.savez(
+        Path(__file__).parent / "bench_scaling_pathsim_results.npz",
+        results=results,
+        N_STEPS=N_STEPS,
+        N_RUNS=N_RUNS,
+        DT=DT,
+        N_CELLS_LIST=N_CELLS_LIST,
+    )
+
+    # ── Plot ──────────────────────────────────────────────────────────────────
+    n_blocks = [r["n_blocks"] for r in results]
+    medians  = [r["median_ms"] for r in results]
+    stds     = [r["std_ms"] for r in results]
+
+    coeffs   = np.polyfit(n_blocks, medians, 1)
+    fit_line = np.poly1d(coeffs)
+    n_fit    = np.linspace(min(n_blocks), max(n_blocks), 200)
+
+    us_per_step_per_block = [
+        (m / N_STEPS * 1000) / nb
+        for m, nb in zip(medians, n_blocks)
+    ]
+
+    fig, axes = plt.subplots(1, 2, figsize=(12, 5))
+    fig.suptitle(
+        f"PathSim — Simulation time scaling\n"
+        f"({N_STEPS} steps, dt={DT}, {N_RUNS} runs/point)",
+        fontsize=12,
+    )
+
+    ax = axes[0]
+    ax.errorbar(n_blocks, medians, yerr=stds, fmt="o-", color="#1D9E75",
+                capsize=4, label="Measured median")
+    ax.plot(n_fit, fit_line(n_fit), "--", color="tomato", alpha=0.7,
+            label=f"Linear fit ({coeffs[0]:.2f} ms/block)")
+    ax.set_xlabel("Number of blocks")
+    ax.set_ylabel("Simulation time (ms)")
+    ax.set_title("Absolute time")
+    ax.legend()
+    ax.grid(True, alpha=0.3)
+
+    ax2 = axes[1]
+    ax2.plot(n_blocks, us_per_step_per_block, "s-", color="#1D9E75")
+    ax2.set_xlabel("Number of blocks")
+    ax2.set_ylabel("Cost per step per block (µs)")
+    ax2.set_title("Unit cost per block per step")
+    ax2.grid(True, alpha=0.3)
+    ax2.axhline(y=np.mean(us_per_step_per_block), color="tomato",
+                linestyle="--", alpha=0.7,
+                label=f"Mean: {np.mean(us_per_step_per_block):.2f} µs")
+    ax2.legend()
+
+    plt.tight_layout()
+    plt.show()