`scipy.interpolate._fitpack_py:splantider`

source: /scipy/interpolate/_fitpack_py.py :838

Signature

def splantider ( tck , n = 1 )

Summary

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

Parameters

tck : BSpline instance or a tuple of (t, c, k): Spline whose antiderivative to compute
n : int, optional: Order of antiderivative to evaluate. Default: 1

Returns

: BSpline instance or a tuple of (t2, c2, k2): Spline of order k2=k+n representing the antiderivative of the input spline. A tuple is returned iff the input argument tck is a tuple, otherwise a BSpline object is constructed and returned.

Notes

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

Array API Standard Support

splantider is not in-scope for support of Python Array API Standard compatible backends other than NumPy.

See dev-arrayapi for more information.

Examples

from scipy.interpolate import splrep, splder, splantider, splev
import numpy as np
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)

`scipy.interpolate._fitpack_py:splantider`

Signature

Summary

Parameters

Returns

Notes

Examples

See also

Aliases

Referenced by

This package