Module « scipy.interpolate »

Classe « BPoly »

Informations générales

Héritage

builtins.object
    _PPolyBase
        BPoly

Définition

class BPoly(_PPolyBase):

Description _{[extrait de BPoly.__doc__]}

Piecewise polynomial in terms of coefficients and breakpoints.

    The polynomial between ``x[i]`` and ``x[i + 1]`` is written in the
    Bernstein polynomial basis::

        S = sum(c[a, i] * b(a, k; x) for a in range(k+1)),

    where ``k`` is the degree of the polynomial, and::

        b(a, k; x) = binom(k, a) * t**a * (1 - t)**(k - a),

    with ``t = (x - x[i]) / (x[i+1] - x[i])`` and ``binom`` is the binomial
    coefficient.

    Parameters
    ----------
    c : ndarray, shape (k, m, ...)
        Polynomial coefficients, order `k` and `m` intervals
    x : ndarray, shape (m+1,)
        Polynomial breakpoints. Must be sorted in either increasing or
        decreasing order.
    extrapolate : bool, optional
        If bool, determines whether to extrapolate to out-of-bounds points
        based on first and last intervals, or to return NaNs. If 'periodic',
        periodic extrapolation is used. Default is True.
    axis : int, optional
        Interpolation axis. Default is zero.

    Attributes
    ----------
    x : ndarray
        Breakpoints.
    c : ndarray
        Coefficients of the polynomials. They are reshaped
        to a 3-D array with the last dimension representing
        the trailing dimensions of the original coefficient array.
    axis : int
        Interpolation axis.

    Methods
    -------
    __call__
    extend
    derivative
    antiderivative
    integrate
    construct_fast
    from_power_basis
    from_derivatives

    See also
    --------
    PPoly : piecewise polynomials in the power basis

    Notes
    -----
    Properties of Bernstein polynomials are well documented in the literature,
    see for example [1]_ [2]_ [3]_.

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/Bernstein_polynomial

    .. [2] Kenneth I. Joy, Bernstein polynomials,
       http://www.idav.ucdavis.edu/education/CAGDNotes/Bernstein-Polynomials.pdf

    .. [3] E. H. Doha, A. H. Bhrawy, and M. A. Saker, Boundary Value Problems,
           vol 2011, article ID 829546, :doi:`10.1155/2011/829543`.

    Examples
    --------
    >>> from scipy.interpolate import BPoly
    >>> x = [0, 1]
    >>> c = [[1], [2], [3]]
    >>> bp = BPoly(c, x)

    This creates a 2nd order polynomial

    .. math::

        B(x) = 1 \times b_{0, 2}(x) + 2 \times b_{1, 2}(x) + 3 \times b_{2, 2}(x) \\
             = 1 \times (1-x)^2 + 2 \times 2 x (1 - x) + 3 \times x^2

    

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 _PPolyBase

__call__, __init_subclass__, __subclasshook__, construct_fast

Méthodes héritées de la classe object

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