added lagrange polynom calculation

lagrange/__init__.py

@@ -0,0 +1,24 @@
+
+def lagrange_polynom(points, j):
+    nom = ""
+    dem = 1
+    xj = points[j][0]
+    for u in range(len(points)):
+        if u == j:
+            continue
+        nom += f"(x - {points[u][0]})"
+        dem *= xj - points[u][0]
+    return (nom, dem)
+
+def interpolate_lagrange(points):
+    n = len(points)
+    poly = ""
+    for i in range(n):
+        (lagrange, dem) = lagrange_polynom(points, i)
+        poly += f" + {points[i][1]*dem}*{lagrange}"
+    return poly
+
+def test():
+    points = [[1,2], [3,5], [4,-1]]
+    print(f"polynom via lagrange: {interpolate_lagrange(points)}")
+

main.py

@@ -15,6 +15,7 @@
 # Copyright (c) Sven Vogel
 
 import fixpoint_approximation
+import lagrange
 import linear_approximation
 import matrix
 import newton_polynom
@@ -30,3 +31,4 @@ if __name__ == '__main__':
     matrix.test()
     taylor_sine_approx.test()
     integral_approximation.test()
+    lagrange.test()