on
        axis must be equal to the length of ``x``. Use the ``axis``
        parameter to select the interpolation axis.
    axis : int, optional
        Axis in the ``y`` array corresponding to the x-coordinate values. Defaults
        to ``axis=0``.
    extrapolate : bool, optional
        Whether to extrapolate to out-of-bounds points based on first
        and last intervals, or to return NaNs.

    Methods
    -------
    __call__
    derivative
    antiderivative
    roots

    See Also
    --------
    CubicHermiteSpline : Piecewise-cubic interpolator.
    Akima1DInterpolator : Akima 1D interpolator.
    CubicSpline : Cubic spline data interpolator.
    PPoly : Piecewise polynomial in terms of coefficients and breakpoints.

    Notes
    -----
    The interpolator preserves monotonicity in the interpolation data and does
    not overshoot if the data is not smooth.

    The first derivatives are guaranteed to be continuous, but the second
    derivatives may jump at :math:`x_k`.

    Determines the derivatives at the points :math:`x_k`, :math:`f'_k`,
    by using PCHIP algorithm [1]_.

    Let :math:`h_k = x_{k+1} - x_k`, and  :math:`d_k = (y_{k+1} - y_k) / h_k`
    are the slopes at internal points :math:`x_k`.
    If the signs of :math:`d_k` and :math:`d_{k-1}` are different or either of
    them equals zero, then :math:`f'_k = 0`. Otherwise, it is given by the
    weighted harmonic mean

    .. math::

        \frac{w_1 + w_2}{f'_k} = \frac{w_1}{d_{k-1}} + \frac{w_2}{d_k}

    where :math:`w_1 = 2 h_k + h_{k-1}` and :math:`w_2 = h_k + 2 h_{k-1}`.

    The end slopes are set using a one-sided scheme [2]_.


    References
    ----------
    .. [1] F. N. Fritsch and J. Butland,
           A method for constructing local
           monotone piecewise cubic interpolants,
           SIAM J. Sci. Comput., 5(2), 300-304 (1984).
           :doi:`10.1137/0905021`.
    .. [2] see, e.g., C. Moler, Numerical Computing with Matlab, 2004.
           :doi:`10.1137/1.9780898717952`

    r