Module « scipy.interpolate »

Classe « PchipInterpolator »

Informations générales

Héritage

builtins.object
    _PPolyBase
        PPoly
            CubicHermiteSpline
                PchipInterpolator

Définition

class PchipInterpolator(CubicHermiteSpline):

Description _{[extrait de PchipInterpolator.__doc__]}

PCHIP 1-D monotonic cubic interpolation.

    ``x`` and ``y`` are arrays of values used to approximate some function f,
    with ``y = f(x)``. The interpolant uses monotonic cubic splines
    to find the value of new points. (PCHIP stands for Piecewise Cubic
    Hermite Interpolating Polynomial).

    Parameters
    ----------
    x : ndarray
        A 1-D array of monotonically increasing real values. ``x`` cannot
        include duplicate values (otherwise f is overspecified)
    y : ndarray
        A 1-D array of real values. ``y``'s length along the interpolation
        axis must be equal to the length of ``x``. If N-D array, use ``axis``
        parameter to select correct axis.
    axis : int, optional
        Axis in the y array corresponding to the x-coordinate values.
    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`


    

Constructeur(s)

Signature du constructeur	Description
__init__(self, x, y, axis=0, extrapolate=None)

Liste des attributs statiques

Attributs statiques hérités de la classe _PPolyBase

axis, c, extrapolate, x

Liste des opérateurs

Opérateurs hérités de la classe object

__eq__, __ge__, __gt__, __le__, __lt__, __ne__

Méthodes héritées de la classe CubicHermiteSpline

__init_subclass__, __subclasshook__

Méthodes héritées de la classe PPoly

antiderivative, derivative, from_bernstein_basis, from_spline, integrate, roots, solve

Méthodes héritées de la classe _PPolyBase

__call__, construct_fast, extend

Méthodes héritées de la classe object

__delattr__, __dir__, __format__, __getattribute__, __hash__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__