Re: plotting the derivative of a splined/interpolated function

• To: mathgroup at smc.vnet.net
• Subject: [mg50727] Re: plotting the derivative of a splined/interpolated function
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Sat, 18 Sep 2004 05:48:20 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <cidt8u\$bsq\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

data = Table[{x, Sin[x]}, {x, 0, Pi, Pi/256}];
f = Interpolation[data]
Plot[{f[x], f'[x]}, {x, 0, Pi}]

but a spline ahs usual no smooth derivatives.
I also don't think that ther derivative is
implementet for spine approximations.

Regards
Jens

Todd Jurhs wrote:
>
> I'm attempting to read in a time ordered data file, create eiteher a
> splined or interpolated data function, take the derivative of the
> splined or interpolated function, and plot the resulting velocity
> curve.
>
> Here's what I've done:
>
> dat2=Import["Documents/Rocketry_Files/MAWD_Flight_Data/bttb_i285r-2.txt","Table"]
>
> Using Interpolating Funtions:
> approx=Interpolation[dat2, InterpolationOrder\[Rule]5]
> InterpolatingFunction[{{0.,91.}},<>]
>
> checking that it works:
> approx[t]/.{t->11.2}
> 3993.
>
> and plotting the position curve:
> Plot[approx[t],{t,0,91}]
> I get a nice plot :)
>
> Doing the same thing with the SplineFit function:
>
> <<NumericalMath`SplineFit`
>
> approx2 = SplineFit[dat2, Cubic]
> SplineFunction[Cubic, {0., 1820.}, <>]
>
> checking that it works:
> approx2[11.2]
>
> {0.56,128.802}
>
> ParametricPlot[approx2[t], {t, 0, 1820},
>  PlotRange -> All, Compiled -> False]
> Again I get a nice plot :)
>
> Taking the derrivative of either the splined or interpolated functions
> also seems to work:
>
> dervie[t]=D[approx[t],t]
> InterpolatingFunction[{{0.,91.}},<>][t]
>
> dervie[t]/.{t->10.}
>
> 220.
>
> AND
>
> dervie2=D[approx2[t],t]
> (SplineFunction[Cubic, {0., 1820.}, <>])'[t]
>
> BUT I can't seem to plot either dervie or dervie2 with the standard
> Plot ParametricPlot commands
>
> So the question becomes is, how to I plot the derrivative of an
> interpolated or slpined function?
>