serie 01 and 02

Kuengjoe_S02/Kuengjoe_S2_Aufg3.py

@@ -0,0 +1,43 @@
+import sympy as sp
+
+x1, x2, x3 = sp.symbols("x1 x2 x3", real=True)
+
+x = sp.Matrix([x1, x2, x3])
+
+f = sp.Matrix([
+    x1 + x2**2 - x3**2 - 13,
+    sp.log(x2 / 4) + sp.exp(sp.Rational(1, 2) * x3 - 1) - 1,
+    (x2 - 3)**2 - x3**3 + 7
+])
+
+x0 = sp.Matrix([
+    sp.Rational(3, 2),
+    3,
+    sp.Rational(5, 2)
+])
+
+substitution_dictionary = {
+    x1: x0[0],
+    x2: x0[1],
+    x3: x0[2]
+}
+
+function_value_at_x0 = f.subs(substitution_dictionary)
+jacobian_matrix = f.jacobian(x)
+jacobian_matrix_at_x0 = jacobian_matrix.subs(substitution_dictionary)
+
+linearized_function = sp.simplify(
+    function_value_at_x0 + jacobian_matrix_at_x0 * (x - x0)
+)
+
+print("f(x0) =")
+sp.pprint(function_value_at_x0)
+
+print("\nDf(x) =")
+sp.pprint(jacobian_matrix)
+
+print("\nDf(x0) =")
+sp.pprint(jacobian_matrix_at_x0)
+
+print("\nL(x) =")
+sp.pprint(linearized_function)