scipy.interpolate.lagrange¶
-
scipy.interpolate.
lagrange
(x, w)[source]¶ 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.])