# 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
xarray_like

x represents the x-coordinates of a set of datapoints.

warray_like

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

Returns
lagrangenumpy.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.])


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