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splantider(tck, n=1)

Notes

The splder function is the inverse operation of this function. Namely, splder(splantider(tck)) is identical to :None:None:`tck`, modulo rounding error.

versionadded

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.

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

See Also

spalde
splder
splev

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
See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.interpolate._fitpack_impl.splder

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GitHub : /scipy/interpolate/_fitpack_impl.py#1237
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