Module « scipy.interpolate »

Classe « KroghInterpolator »

Informations générales

Héritage

builtins.object
    _Interpolator1D
        _Interpolator1DWithDerivatives
            KroghInterpolator

Définition

class KroghInterpolator(_Interpolator1DWithDerivatives):

Description _{[extrait de KroghInterpolator.__doc__]}

    Interpolating polynomial for a set of points.

    The polynomial passes through all the pairs (xi,yi). One may
    additionally specify a number of derivatives at each point xi;
    this is done by repeating the value xi and specifying the
    derivatives as successive yi values.

    Allows evaluation of the polynomial and all its derivatives.
    For reasons of numerical stability, this function does not compute
    the coefficients of the polynomial, although they can be obtained
    by evaluating all the derivatives.

    Parameters
    ----------
    xi : array_like, length N
        Known x-coordinates. Must be sorted in increasing order.
    yi : array_like
        Known y-coordinates. When an xi occurs two or more times in
        a row, the corresponding yi's represent derivative values.
    axis : int, optional
        Axis in the yi array corresponding to the x-coordinate values.

    Notes
    -----
    Be aware that the algorithms implemented here are not necessarily
    the most numerically stable known. Moreover, even in a world of
    exact computation, unless the x coordinates are chosen very
    carefully - Chebyshev zeros (e.g., cos(i*pi/n)) are a good choice -
    polynomial interpolation itself is a very ill-conditioned process
    due to the Runge phenomenon. In general, even with well-chosen
    x values, degrees higher than about thirty cause problems with
    numerical instability in this code.

    Based on [1]_.

    References
    ----------
    .. [1] Krogh, "Efficient Algorithms for Polynomial Interpolation
        and Numerical Differentiation", 1970.

    Examples
    --------
    To produce a polynomial that is zero at 0 and 1 and has
    derivative 2 at 0, call

    >>> from scipy.interpolate import KroghInterpolator
    >>> KroghInterpolator([0,0,1],[0,2,0])

    This constructs the quadratic 2*X**2-2*X. The derivative condition
    is indicated by the repeated zero in the xi array; the corresponding
    yi values are 0, the function value, and 2, the derivative value.

    For another example, given xi, yi, and a derivative ypi for each
    point, appropriate arrays can be constructed as:

    >>> rng = np.random.default_rng()
    >>> xi = np.linspace(0, 1, 5)
    >>> yi, ypi = rng.random((2, 5))
    >>> xi_k, yi_k = np.repeat(xi, 2), np.ravel(np.dstack((yi,ypi)))
    >>> KroghInterpolator(xi_k, yi_k)

    To produce a vector-valued polynomial, supply a higher-dimensional
    array for yi:

    >>> KroghInterpolator([0,1],[[2,3],[4,5]])

    This constructs a linear polynomial giving (2,3) at 0 and (4,5) at 1.

    

Constructeur(s)

Signature du constructeur	Description
__init__(self, xi, yi, axis=0)

Liste des attributs statiques

Attributs statiques hérités de la classe _Interpolator1D

dtype

Liste des opérateurs

Opérateurs hérités de la classe object

__eq__, __ge__, __gt__, __le__, __lt__, __ne__

Méthodes héritées de la classe _Interpolator1DWithDerivatives

__init_subclass__, __subclasshook__, derivative, derivatives

Méthodes héritées de la classe _Interpolator1D

__call__

Méthodes héritées de la classe object

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