`scipy.interpolate._fitpack2:UnivariateSpline.antiderivative`

source: build-install/usr/lib/python3.14/site-packages/scipy/interpolate/_fitpack2.py:949

Signature

def antiderivative(self, n = 1)

Summary

Construct a new spline representing the antiderivative of this spline.

Parameters

n : int, optional: Order of antiderivative to evaluate. Default: 1

Returns

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

Notes

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(2.15654), array(2.15654))

Antiderivative can be used to evaluate definite integrals:

ispl = spl.antiderivative()

✓

ispl(np.pi/2) - ispl(0)

✗

np.float64(2.2572053588768486)

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

from scipy.special import ellipk

✓

ellipk(0.8)

✗

np.float64(2.257205326820854)

Aliases

scipy.interpolate.UnivariateSpline.antiderivative