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Classe « UnivariateSpline »

Méthode scipy.interpolate.UnivariateSpline.antiderivative

Signature de la méthode antiderivative

def antiderivative(self, n=1) 

Description

help(UnivariateSpline.antiderivative)

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
-----

.. versionadded:: 0.13.0

See Also
--------
splantider, derivative

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
:math:`K(m) = \int_0^{\pi/2} [1 - m\sin^2 x]^{-1/2} dx`:

>>> from scipy.special import ellipk
>>> ellipk(0.8)
2.2572053268208538

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