Issue with HS.4.1 typing

Codebook
1

I was recently trying the Hamiltonian Simulation Codebook and ran into an issue, where it says I’m not producing the correct type of output.

My code is as follows:

`bessel_1 = [
    0.7651976865579666,
    0.44005058574493355,
    0.1149034849319005,
    0.019563353982668414,
]

def approximation_error(theta):
    """
    Returns the absolute error in the Jacobi-Anger expansion

    Args:
    - theta (float): The angle argument of the expansion.
    Returns:
    - (float): The absolute error.
    """

    ####################
    ###YOUR CODE HERE###
    ####################
    exact = np.exp(1j * np.cos(theta))
    approx = 0
    for n in range(-3, 0):
        approx +=(-1)**(np.abs(n))*((1j) ** (n)) * (bessel_1[np.abs(n)]) * np.exp(1j * n * theta)
    for n in range(0, 4):
        approx += (1j) ** (n) * (bessel_1[n]) * np.exp(1j * n * theta)
    return np.abs(exact - approx)`

I tried comparing it to the result when using the Scipy Bessel function, and it yields the same result, so I think it is correct in that front. The typing of my result is also type float, so I’m not sure where exactly the error resides.

Also, I believe the description text needs updating with regards to the behaviour of the bessel function. J-n(z)=(-1)^(n)Jn(z)

2

Hi @zachelgood, welcome to the Forum!
You are right about those two things.

  1. Your code outputs the correct result but our evaluation code is not marking it as such. I will fix this tomorrow and you can check back in a few days to test it.
  2. I’ll change the description to have the correct expression.

Thanks for catching these, I hope you are enjoying the Codebook.