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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 from_simplex(x):
 r""" Inteprets the last index of x as unit simplices and returns a real array of the sampe shape in logit space. Inverse to :func:`to_simplex` ; see that function for more details. :param np.ndarray: Array of unit simplices along the last index. :rtype: ``np.ndarray`` """

    n = x.shape[-1]
    # z are the stick breaking fractions in [0,1]
    # the last one is always 1, so don't worry about it
    z = np.empty(shape=x.shape)
    z[..., 0] = x[..., 0]
    z[..., 1:-1] = x[..., 1:-1] / (1 - x[..., :-2].cumsum(axis=-1))

    # now z are the logit-transformed breaking fractions
    z[..., :-1] = logit(z[..., :-1]) - logit(1 / (n - np.arange(n-1, dtype=np.float)))
    # set this to 0 manually to avoid subtracting inf-inf
    z[..., -1] = 0
    return z