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

Returns :

tck_ader : tuple of (t2, c2, k2)

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

See also

splder, splev, spalde


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


>>> 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)

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)