Classe « PchipInterpolator »

Informations générales

Héritage

builtins.object
    _PPolyBase
        PPoly
            CubicHermiteSpline
                PchipInterpolator

Définition

class PchipInterpolator(CubicHermiteSpline):

help(PchipInterpolator)

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, shape (npoints, )
    A 1-D array of monotonically increasing real values. ``x`` cannot
    include duplicate values (otherwise f is overspecified)
y : ndarray, shape (..., npoints, ...)
    A N-D array of real values. ``y``'s length along the interpolation
    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`