serie 01 and 02

Kuengjoe_S02/Kuengjoe_S2_Aufg2.py

@@ -0,0 +1,36 @@
+import sympy as sp
+
+x1, x2, x3 = sp.symbols("x1 x2 x3", real=True)
+
+
+f_a = sp.Matrix([
+    5 * x1 * x2,
+    x1**2 * x2**2 + x1 + 2 * x2
+])
+
+D_f_a = f_a.jacobian(sp.Matrix([x1, x2]))
+D_f_a_at_point = D_f_a.subs({x1: 1, x2: 2})
+
+print("D_f_a(x) =")
+sp.pprint(D_f_a)
+
+
+print("Aufgabe 2a:")
+
+sp.pprint(D_f_a_at_point)
+
+
+f_b = sp.Matrix([
+    sp.log(x1**2 + x2**2) + x3**2,
+    sp.exp(x2**2 + x3**2) + x1**2,
+    1 / (x3**2 + x1**2) + x2**2
+])
+
+D_f_b = f_b.jacobian(sp.Matrix([x1, x2, x3]))
+D_f_b_at_point = D_f_b.subs({x1: 1, x2: 2, x3: 3})
+
+print("\nD_f_b(x) =")
+sp.pprint(D_f_b)
+
+print("\nAufgabe 2b:")
+sp.pprint(sp.simplify(D_f_b_at_point))

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)