Classe « BPoly »

Informations générales

Héritage

builtins.object
    _PPolyBase
        BPoly

Définition

class BPoly(_PPolyBase):

help(BPoly)

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

Constructeur(s)

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

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__

Liste des méthodes

Toutes les méthodes Méthodes d'instance Méthodes statiques

Signature de la méthode	Description
antiderivative(self, nu=1)
derivative(self, nu=1)
extend(self, c, x)
from_derivatives(xi, yi, orders=None, extrapolate=None)	Construct a piecewise polynomial in the Bernstein basis, _{[extrait de from_derivatives.__doc__]}
from_power_basis(pp, extrapolate=None)
integrate(self, a, b, extrapolate=None)