import numpy as np

# This function implements S(x) as given in the exercise sheet

# If matrix A or vector b are not specified through "args", the function assumes
# that A and b are those given in Exercise 1

# Note that you CANNOT only specify A or b, both must be specified such that
# args[0] = A and args[1] = b

# Note also that the function is implemented with the factor 1/2 as in Exercise 2
# Hence the scaling of matrix A with 2 in order to reproduce the case in Exercise 1
def quadratic_function(x, *args):

    if len(args) == 0:
        A = np.array([[4.0, 0], [1, 3]]) * 2.0
        b = np.array([0, 1])
    else:
        A = args[0]
        b = args[1]

    # reshape into column vectors
    x.reshape(-1, 1)
    b.reshape(-1, 1)

    # return S(x)
    return 0.5*((x.transpose() @ A) @ x) - (x.transpose() @ b)

# TESTING AND VALIDATING FUNCTION
#print(quadratic_function(np.array([1,2]) ))
#print(quadratic_function(np.array([1,2]), np.array([[4, 0], [1, 3]]), np.array([0, 1]) ))