antiderivative(self, n=1)
Order of antiderivative to evaluate. Default: 1
Spline of order k2=k+n representing the antiderivative of this spline.
Construct a new spline representing the antiderivative of this spline.
>>> from scipy.interpolate import UnivariateSpline
... x = np.linspace(0, np.pi/2, 70)
... y = 1 / np.sqrt(1 - 0.8*np.sin(x)**2)
... spl = UnivariateSpline(x, y, s=0)
The derivative is the inverse operation of the antiderivative, although some floating point error accumulates:
>>> spl(1.7), spl.antiderivative().derivative()(1.7) (array(2.1565429877197317), array(2.1565429877201865))
Antiderivative can be used to evaluate definite integrals:
>>> ispl = spl.antiderivative()
... ispl(np.pi/2) - ispl(0) 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._fitpack2.UnivariateSpline.derivative
scipy.interpolate._fitpack2.UnivariateSpline.antiderivative
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