Serie 09

Kuengjoe_S09/Kuengjoe_S09_Aufg3.py

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+
+
+import numpy as np
+import matplotlib.pyplot as plt
+
+try:
+    from Kuengjoe_S09_Aufg2 import Kuengjoe_S09_Aufg2
+except ImportError as exc:
+    raise RuntimeError(
+        "Fehler: Die Datei Kuengjoe_S09_Aufg2.py konnte nicht importiert werden.\n"
+        "Stellen Sie sicher, dass sie im selben Verzeichnis liegt."
+    ) from exc
+
+
+def main():
+    n_iter = 1000
+    size   = 100
+
+    dx_max_vec = np.empty(n_iter)
+    dx_obs_vec = np.empty(n_iter)
+    ratio_vec  = np.empty(n_iter)
+
+    for i in range(n_iter):
+        A = np.random.rand(size, size)
+        b = np.random.rand(size)
+
+        A_tilde = A + np.random.rand(size, size) / 10**5
+        b_tilde = b + np.random.rand(size)       / 10**5
+
+        x, x_tilde, dx_max, dx_obs = Kuengjoe_S09_Aufg2(A, A_tilde, b, b_tilde)
+
+        dx_max_vec[i] = dx_max
+        dx_obs_vec[i] = dx_obs
+
+        if np.isfinite(dx_max) and dx_obs > 0:
+            ratio_vec[i] = dx_max / dx_obs
+        else:
+            ratio_vec[i] = np.nan
+
+
+    plt.figure(figsize=(10, 6))
+    idx = np.arange(n_iter)
+    mask_dxmax = np.isfinite(dx_max_vec)
+    mask_dxobs = np.isfinite(dx_obs_vec)
+
+    plt.semilogy(idx[mask_dxmax], dx_max_vec[mask_dxmax],
+                 label='dx_max', linewidth=1.2, alpha=0.8)
+    plt.semilogy(idx[mask_dxobs], dx_obs_vec[mask_dxobs],
+                 label='dx_obs', linewidth=1.2, alpha=0.8)
+    plt.semilogy(idx[~np.isnan(ratio_vec)], ratio_vec[~np.isnan(ratio_vec)],
+                 label='dx_max / dx_obs', linewidth=1.2, alpha=0.8)
+
+    plt.xlabel('Iteration')
+    plt.ylabel(r'Relative Fehler (∞‑Norm)')
+    plt.title('dx_max, dx_obs und ihr Verhältnis über 1000 zufällige Tests')
+    plt.legend()
+    plt.grid(True, which='both', ls='--', lw=0.5)
+    plt.tight_layout()
+    plt.show()
+
+
+    finite_mask = np.isfinite(ratio_vec)
+    mean_ratio  = np.nanmean(ratio_vec[finite_mask])
+    print(f"\nDurchschnittliches Verhältnis dx_max/dx_obs (nur finite Werte): {mean_ratio:.2f}")
+
+    print("\nKommentar:")
+    print("dx_max usually exceeds dx_obs by 10–1000×; occasional NaNs occur when "
+          "cond(A)*||A−A_tilde||/||A||≥1, shown as gaps.")
+
+
+if __name__ == "__main__":
+    main()