@GaelVaroquaux you glimpsed over the ``dtype``:

    In [1]: a = np.zeros(10)

    In [2]: b = np.asfortranarray(a, dtype=np.float64)

    In [3]: c = np.asfortranarray(b, dtype=np.float32)

    In [4]: np.may_share_memory(b, c)
    Out[4]: False