Manhatten, taxicab, or l1 distance.

    ..math::
        D(x, y) = \sum_i |x_i - y_i|

def manhattan(x, y):
    """Manhatten, taxicab, or l1 distance.

    ..math::
        D(x, y) = \sum_i |x_i - y_i|
    """
    result = 0.0
    for i in range(x.shape[0]):
        result += np.abs(x[i] - y[i])

    return result