scipy.interpolate.lagrange

scipy.interpolate.lagrange(x, w)

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 \(f(x) = x^3\) 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

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

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