delta = sp.dot(sp.transpose(Vprime - V), Vprime - V)

    return psi


import solutions as sol

prob11, prob12 = Problem1Real()
prob2 = Problem2Real()
prob3 = Problem3Real()

x, y = sol.Problem1()

if (np.allclose(prob11, x) and np.allclose(prob12, y)):
    print("Problem1 Passed")
else:
    print("Problem1 Falied")

x = sol.Problem2()

if (np.allclose(prob2, x)):
    print("Problem2 Passed")
else:
    print("Problem2 Falied")

x = sol.Problem3()

if (np.allclose(prob3, x)):
    print("Problem3 Passed")
else:
    print("Problem3 Falied")
    print(prob12)

x, y = sol.Problem2()

if (np.allclose(prob21, np.array(x)) and np.allclose(prob22, y)):
    print("Problem2 Passed")
else:
    print("Problem2 Falied")
    print("Your answer:")
    print(x)
    print(y)
    print("Correct answer:")
    print(prob21)
    print(prob22)

x, y = sol.Problem3()

if (np.allclose(prob31, np.array(x)) and np.allclose(prob32, y)):
    print("Problem3 Passed")
else:
    print("Problem3 Falied")
    print("Your answer:")
    print(x)
    print(y)
    print("Correct answer:")
    print(prob31)
    print(prob32)

x, y = sol.Problem4()

if (np.allclose(prob41, np.array(x)) and np.allclose(prob42, y)):