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>*Reply-to*: kuska at informatik.uni-leipzig.de*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: > > Reading the Data: > 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? > > Thanks for your help!