splantider(tck, n=1)
The splder
function is the inverse operation of this function. Namely, splder(splantider(tck))
is identical to :None:None:`tck`, modulo rounding error.
Spline whose antiderivative to compute
Order of antiderivative to evaluate. Default: 1
Spline of order k2=k+n representing the antiderivative of the input spline. A tuple is returned iff the input argument :None:None:`tck` is a tuple, otherwise a BSpline object is constructed and returned.
Compute the spline for the antiderivative (integral) of a given spline.
>>> 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 ellipkSee :
... ellipk(0.8) 2.2572053268208538
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.interpolate._fitpack_py.splder
scipy.interpolate._fitpack_py.splantider
scipy.interpolate._fitpack_impl.splantider
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