# scipy.interpolate.splantider¶

scipy.interpolate.splantider(tck, n=1)[source]

Compute the spline for the antiderivative (integral) of a given spline.

New in version 0.13.0.

Parameters : tck : tuple of (t, c, k) Spline whose antiderivative to compute n : int, optional Order of antiderivative to evaluate. Default: 1 tck_ader : tuple of (t2, c2, k2) Spline of order k2=k+n representing the antiderivative of the input spline.

Notes

The splder function is the inverse operation of this function. Namely, splder(splantider(tck)) is identical to tck, modulo rounding error.

Examples

>>> from scipy.interpolate import splrep, splder, splantider, splev
>>> x = np.linspace(0, np.pi/2, 70)
>>> y = 1 / np.sqrt(1 - 0.8*np.sin(x)**2)
>>> spl = splrep(x, y)


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

>>> splev(1.7, spl), splev(1.7, splder(splantider(spl)))
(array(2.1565429877197317), array(2.1565429877201865))


Antiderivative can be used to evaluate definite integrals:

>>> ispl = splantider(spl)
>>> splev(np.pi/2, ispl) - splev(0, ispl)
2.2572053588768486


This is indeed an approximation to the complete elliptic integral :

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


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