serie 05

2026-03-25 14:01:08 +01:00
parent 1e8d68210c
commit 96befc4cb3
3 changed files with 239 additions and 0 deletions
--- a/Kuengjoe_S05/Kuengjoe_S05_Aufg3.py
+++ b/Kuengjoe_S05/Kuengjoe_S05_Aufg3.py
@@ -0,0 +1,119 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.interpolate import CubicSpline
+
+from Kuengjoe_S05_Aufg2 import Kuengjoe_S05_Aufg2
+
+
+def main():
+    time_values_years = np.array(
+        [1900, 1910, 1920, 1930, 1940, 1950, 1960, 1970, 1980, 1990, 2000, 2010],
+        dtype=float,
+    )
+
+    population_values_millions = np.array(
+        [75.995, 91.972, 105.711, 123.203, 131.669, 150.697, 179.323, 203.212, 226.505, 249.633, 281.422, 308.745],
+        dtype=float,
+    )
+
+    dense_evaluation_time_values = np.linspace(
+        time_values_years[0],
+        time_values_years[-1],
+        1000,
+    )
+
+    # a) Eigene natürliche kubische Spline aus Aufgabe 2
+    spline_values_custom_implementation = Kuengjoe_S05_Aufg2(
+        time_values_years,
+        population_values_millions,
+        dense_evaluation_time_values,
+        plot_result=False,
+    )
+
+    # b) SciPy CubicSpline mit natürlichen Randbedingungen
+    scipy_natural_cubic_spline = CubicSpline(
+        time_values_years,
+        population_values_millions,
+        bc_type="natural",
+    )
+    spline_values_scipy = scipy_natural_cubic_spline(dense_evaluation_time_values)
+
+    # c) Polynom 11. Grades mit verschobener Zeitachse
+    shifted_time_values_years = time_values_years - 1900.0
+    shifted_dense_evaluation_time_values = dense_evaluation_time_values - 1900.0
+
+    polynomial_degree = 11
+    polynomial_coefficients = np.polyfit(
+        shifted_time_values_years,
+        population_values_millions,
+        polynomial_degree,
+    )
+    polynomial_values_degree_eleven = np.polyval(
+        polynomial_coefficients,
+        shifted_dense_evaluation_time_values,
+    )
+
+    # Plot
+    plt.figure(figsize=(10, 6))
+    plt.plot(
+        dense_evaluation_time_values,
+        spline_values_custom_implementation,
+        label="Aufgabe 2: eigene natürliche kubische Spline",
+    )
+    plt.plot(
+        dense_evaluation_time_values,
+        spline_values_scipy,
+        "--",
+        label="SciPy CubicSpline (natural)",
+    )
+    plt.plot(
+        dense_evaluation_time_values,
+        polynomial_values_degree_eleven,
+        ":",
+        label="Polynom 11. Grades",
+    )
+    plt.plot(
+        time_values_years,
+        population_values_millions,
+        "o",
+        label="Messdaten",
+    )
+
+    plt.xlabel("Jahr")
+    plt.ylabel("Bevölkerung (in Mio.)")
+    plt.title("Vergleich der Interpolationen")
+    plt.grid(True)
+    plt.legend()
+    plt.tight_layout()
+    plt.show()
+
+    custom_values_at_nodes = Kuengjoe_S05_Aufg2(
+        time_values_years,
+        population_values_millions,
+        time_values_years,
+        plot_result=False,
+    )
+    scipy_values_at_nodes = scipy_natural_cubic_spline(time_values_years)
+    polynomial_values_at_nodes = np.polyval(
+        polynomial_coefficients,
+        shifted_time_values_years,
+    )
+
+    print("Original data:")
+    print(population_values_millions)
+    print()
+
+    print("Custom spline at nodes:")
+    print(custom_values_at_nodes)
+    print()
+
+    print("SciPy spline at nodes:")
+    print(scipy_values_at_nodes)
+    print()
+
+    print("Degree-11 polynomial at nodes:")
+    print(polynomial_values_at_nodes)
+
+
+if __name__ == "__main__":
+    main()