scipy.interpolate.splantider

scipy.interpolate.splantider(tck, n=1)

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

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

Notes

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

New in version 0.13.0.

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

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