antiderivative — SciPy v1.15.3 Manual (original) (raw)

scipy.interpolate.LSQUnivariateSpline.

LSQUnivariateSpline.antiderivative(n=1)[source]#

Construct a new spline representing the antiderivative of this spline.

Parameters:

nint, optional

Order of antiderivative to evaluate. Default: 1

Returns:

splineUnivariateSpline

Spline of order k2=k+n representing the antiderivative of this spline.

Notes

Added in version 0.13.0.

Examples

import numpy as np from scipy.interpolate import UnivariateSpline x = np.linspace(0, np.pi/2, 70) y = 1 / np.sqrt(1 - 0.8*np.sin(x)**2) spl = UnivariateSpline(x, y, s=0)

The derivative is the inverse operation of the antiderivative, although some floating point error accumulates:

spl(1.7), spl.antiderivative().derivative()(1.7) (array(2.1565429877197317), array(2.1565429877201865))

Antiderivative can be used to evaluate definite integrals:

ispl = spl.antiderivative() ispl(np.pi/2) - ispl(0) 2.2572053588768486

This is indeed an approximation to the complete elliptic integral\(K(m) = \int_0^{\pi/2} [1 - m\sin^2 x]^{-1/2} dx\):

from scipy.special import ellipk ellipk(0.8) 2.2572053268208538