[NumCS] Add more sympy tricks

semester3/numcs/parts/06_python/03_sympy-hessian.py

@@ -0,0 +1,14 @@
+import sympy as sp
+
+sym = sp.symbols("x, y")
+x, y = sym
+f = x**2 + y**2
+
+# Compute gradient and hessian
+grad = [sp.diff(f, k) for k in sym]
+hess = [[sp.diff(f, k).diff(j) for j in sym] for k in sym]
+
+# Compute jacobian of vector function
+x_m = sp.MatrixSymbol('x', 2, 1)
+two_d_func = sp.Matrix([[x_m[0]**2], [x_m[1]**2]])
+jacobi = two_d_func.jacobian(x_m)