feat: Trapez und Simpson Integration. build: scipy zu requirements hinzugefügt

requirements.txt

@@ -1,2 +1,4 @@
-numpy
+numpy==2.4.3
-matplotlib
+matplotlib==3.10.8
+ipykernel==7.2.0
+scipy==1.17.1

src/scipy_integrate.py

@@ -0,0 +1,41 @@
+# %%
+# Python initialisieren
+import matplotlib.pyplot as plt
+import numpy as np
+import scipy.integrate as ig
+
+# Parameter
+x_0 = 0.0
+x_E = np.pi
+N = 11
+n = 5
+pr = 6
+lw = 3
+fig = 1
+
+# Funktion
+f = lambda x: np.sin(x)
+
+# Berechnungen
+for k in range(0, n):
+    x_data = np.linspace(x_0, x_E, N)
+    y_data = f(x_data)
+    I = ig.trapezoid(y=y_data, x=x_data)
+    J = ig.simpson(y=y_data, x=x_data)
+    print(f"I = {I:#.16g}")
+    print(f"J = {J:#.16g}")
+    N *= 2
+
+# Ausgabe
+print(f"I = {I:#.{pr}g}")
+print(f"J = {J:#.{pr}g}")
+
+# Plot
+fh = plt.figure(fig)
+plt.plot(x_data, y_data, linewidth=lw)
+plt.xlabel("x")
+plt.ylabel("y")
+plt.grid(visible=True)
+plt.axis("image")
+plt.show()
+# %%

src/serie_3.py

@@ -0,0 +1,61 @@
+# %%
+import numpy as np
+import matplotlib.pyplot as plt
+
+# %%
+print(60 * "-")
+print(__file__)
+print("Aufgabe 2. Interpolationspolynome gemäss NEWTON-Schema berechnen")
+# punkte [[x0, x1, x2, xn], [y0, y1, y2, yn]]
+punkte = [
+    [np.array([4, 8]), np.array([1, -1])],
+    [np.array([-1, 1, 2]), np.array([15, 5, 9])],
+    [np.array([-1, 0, 1, 2]), np.array([-5, -1, -1, 1])],
+]
+
+for punkt in punkte:
+
+    # Parameter
+    x_data = punkt[0]
+    y_data = punkt[1]
+    x_0 = x_data[0]
+    x_E = x_data[-1]
+    N = 201
+    lw = 3
+    fig = 1
+
+    # Berechnung
+    n = np.size(y_data)
+    TAB = np.block([[y_data], [np.zeros((n - 1, n))]])
+    c_data = np.zeros(n)
+    c_data[0] = y_data[0]
+
+    for i in range(1, n):
+        for j in range(1, n):
+            TAB[i][j] = (TAB[i - 1][j] - TAB[i - 1][j - 1]) / (
+                x_data[j] - x_data[j - i]
+            )
+        c_data[i] = TAB[i][i]
+
+    # Funktionen:
+    def p(x):
+        d = 1
+        y = c_data[0]
+        for k in range(1, n):
+            d = d * (x - x_data[k - 1])
+            y = y + c_data[k] * d
+        return y
+
+    # Daten
+    u_data = np.linspace(x_0, x_E, N)
+    v_data = p(u_data)
+
+    fh = plt.figure(fig)
+    plt.plot(u_data, v_data, linewidth=lw)
+    plt.plot(x_data, y_data, "o", linewidth=lw)
+    plt.xlabel(r"$x$")
+    plt.ylabel(r"$y$")
+    plt.grid(visible=True)
+    plt.axis("image")
+
+print(60 * "-")