feat: working newton schema

src/serie_3.py

@@ -3,11 +3,9 @@ import numpy as np
 import matplotlib.pyplot as plt
 
 # %%
-print("----------------------------------------------------------------")
+print(60 * "-")
 print(__file__)
 print("Aufgabe 2. Interpolationspolynome gemäss NEWTON-Schema berechnen")
-print("----------------------------------------------------------------")
-
 # punkte [[x0, x1, x2, xn], [y0, y1, y2, yn]]
 punkte = [
     [np.array([4, 8]), np.array([1, -1])],
@@ -21,30 +19,43 @@ for punkt in punkte:
     x_data = punkt[0]
     y_data = punkt[1]
     x_0 = x_data[0]
-    x_e = x_data[-1]
+    x_E = x_data[-1]
     N = 201
-    lw = 30
+    lw = 3
     fig = 1
 
     # Berechnung
     n = np.size(y_data)
-    TAB = np.block([[y_data], [np.zeros((n-1, n))]])
+    TAB = np.block([[y_data], [np.zeros((n - 1, n))]])
     c_data = np.zeros(n)
     c_data[0] = y_data[0]
-    print(x_data)
-
-    print(TAB)
 
     for i in range(1, n):
         for j in range(1, n):
-            print(TAB[i][j-1])
+            TAB[i][j] = (TAB[i - 1][j] - TAB[i - 1][j - 1]) / (
-            print(TAB[i-1][j-1])
+                x_data[j] - x_data[j - i]
-            print(x_data[i])
+            )
-            print(x_data[i-1])
+        c_data[i] = TAB[i][i]
-            TAB[i][j] = (TAB[i][j-1]-TAB[i-1][j-1])/(x_data[i]-x_data[i-1])
-            break
 
-    print(TAB)
+    # Funktionen:
-    print()
+    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
 
-print("----------------------------------------------------------------")
+    # 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 * "-")