lagrange(x, w)
Given two 1-D arrays x and :None:None:`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.
x represents the x-coordinates of a set of datapoints.
w represents the y-coordinates of a set of datapoints, i.e., f(x).
The Lagrange interpolating polynomial.
Return a Lagrange interpolating polynomial.
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
$$$$>>> 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()
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.interpolate._interpolate.lagrange
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