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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def find_n_pc(u, factor=0.5):
 """Find number of principal components This method finds the minimum number of principal components required Parameters u : np.ndarray Left singular vector of the original data factor : float, optional Factor for testing the auto correlation (default is '0.5') Returns ------- int number of principal components Examples -------- array([3]) """


    if np.sqrt(u.shape[0]) % 1:
        raise ValueError('Invalid left singular value. The size of the first '
                         'dimenion of u must be perfect square.')

    # Get the shape of the array
    array_shape = np.repeat(np.int(np.sqrt(u.shape[0])), 2)

    # Find the auto correlation of the left singular vector.
    u_auto = [convolve(a.reshape(array_shape),
              np.rot90(a.reshape(array_shape), 2)) for a in u.T]

    # Return the required number of principal components.
    return np.sum([(a[tuple(zip(array_shape // 2))] ** 2 <= factor *
                   np.sum(a ** 2)) for a in u_auto])