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Module « scipy.interpolate »

Fonction lagrange - module scipy.interpolate

Signature de la fonction lagrange

def lagrange(x, w) 

Description

help(scipy.interpolate.lagrange)

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.

>>> import numpy as np
>>> 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[::-1]).coef
array([ 0., -2.,  3.])

>>> import matplotlib.pyplot as plt
>>> x_new = np.arange(0, 2.1, 0.1)
>>> plt.scatter(x, y, label='data')
>>> plt.plot(x_new, Polynomial(poly.coef[::-1])(x_new), label='Polynomial')
>>> plt.plot(x_new, 3*x_new**2 - 2*x_new + 0*x_new,
...          label=r"$3 x^2 - 2 x$", linestyle='-.')
>>> plt.legend()
>>> plt.show()

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