Classe « UnivariateSpline »

Méthode scipy.interpolate.UnivariateSpline.antiderivative

Signature de la méthode antiderivative

def antiderivative(self, n=1) 

Description

antiderivative.__doc__

        Construct a new spline representing the antiderivative of this spline.

        Parameters
        ----------
        n : int, optional
            Order of antiderivative to evaluate. Default: 1

        Returns
        -------
        spline : UnivariateSpline
            Spline of order k2=k+n representing the antiderivative of this
            spline.

        Notes
        -----

        .. versionadded:: 0.13.0

        See Also
        --------
        splantider, derivative

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

        >>> from scipy.special import ellipk
        >>> ellipk(0.8)
        2.2572053268208538