Module « scipy.interpolate »

Fonction lagrange - module scipy.interpolate

Signature de la fonction lagrange

def lagrange(x, w) 

Description

lagrange.__doc__

    Return a Lagrange interpolating polynomial.

    Given two 1-D arrays `x` and `w,` returns the Lagrange interpolating
    polynomial through the points ``(x, w)``.

    Warning: This implementation is numerically unstable. Do not expect to
    be able to use more than about 20 points even if they are chosen optimally.

    Parameters
    ----------
    x : array_like
        `x` represents the x-coordinates of a set of datapoints.
    w : array_like
        `w` represents the y-coordinates of a set of datapoints, i.e., f(`x`).

    Returns
    -------
    lagrange : `numpy.poly1d` instance
        The Lagrange interpolating polynomial.

    Examples
    --------
    Interpolate :math:`f(x) = x^3` by 3 points.

    >>> from scipy.interpolate import lagrange
    >>> x = np.array([0, 1, 2])
    >>> y = x**3
    >>> poly = lagrange(x, y)

    Since there are only 3 points, Lagrange polynomial has degree 2. Explicitly,
    it is given by

    .. math::

        \begin{aligned}
            L(x) &= 1\times \frac{x (x - 2)}{-1} + 8\times \frac{x (x-1)}{2} \\
                 &= x (-2 + 3x)
        \end{aligned}

    >>> from numpy.polynomial.polynomial import Polynomial
    >>> Polynomial(poly).coef
    array([ 3., -2.,  0.])