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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 tck, modulo rounding error.

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.

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)))

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

from scipy.special import ellipk
ellipk(0.8)

See :

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them

GitHub : /scipy/interpolate/_fitpack_impl.py#1235
type: <class 'function'>
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Notes

Parameters

Returns

See Also

Examples

Local connectivity graph