Re: Suming InterpolatingFunction Objects

*To*: mathgroup at smc.vnet.net*Subject*: [mg120254] Re: Suming InterpolatingFunction Objects*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Thu, 14 Jul 2011 21:21:35 -0400 (EDT)*References*: <201107140922.FAA15682@smc.vnet.net>*Reply-to*: drmajorbob at yahoo.com

How did you discover the InterpolationPoints option, given that Help lists no options (at all) for FunctionInterpolation? Bobby On Thu, 14 Jul 2011 06:14:09 -0500, Oliver Ruebenkoenig <ruebenko at wolfram.com> wrote: > On Thu, 14 Jul 2011, Gabriel Landi wrote: > >> Hello everyone. >> >> I encountered the following problem, which I am not sure is a bug or >> simply >> a annoying detail. >> I will use as an example a piece of code from the mathematica tutorials. >> >> Say I solve a system of ODEs >> >> s = NDSolve[{x'[t] == -y[t] - x[t]^2, y'[t] == 2 x[t] - y[t]^3, >> x[0] == y[0] == 1}, {x, y}, {t, 20}] >> >> My quantity of interest could be x[t] + y[t]. I can plot it: >> >> Plot[x[t] + y[t] /. s, {t, 0, 20}] >> >> But say I wish to store it as a single object. >> So I do (this is the kinky part): >> >> sum = FunctionInterpolation[x[t] + y[t] /. s, {t, 0, 20}] >> >> Now, when I plot the result, it comes out completely different. It looks >> like something changed with the interpolation order or something. >> >> Plot[sum[t], {t, 0, 20}] >> >> What do you guys think? >> >> Best regards, >> >> Gabriel >> > > Gabriel, > > here are two alternatives: > > You could sample at more points via > > sum = FunctionInterpolation[Evaluate[x[t] + y[t] /. s], {t, 0, 20}, > InterpolationPoints -> 100] > > > additionally specifying the derivatives may be a good idea: > > sum = FunctionInterpolation[ > Evaluate[Table[ > D[Evaluate[x[t] + y[t] /. s], {{t}, k}], {k, 0, 2}]], {t, 0, 20}, > InterpolationPoints -> 30] > (* then you get away with less InterpolationPoints *) > > or do it manually as follows: > > The good thing here is that the NDSolve solutions are sampled at the same > points. > > tutorial/NDSolvePackages#120436095 > > s = NDSolve[{x'[t] == -y[t] - x[t]^2, y'[t] == 2 x[t] - y[t]^3, > x[0] == y[0] == 1}, {x, y}, {t, 20}] > > Needs["DifferentialEquations`InterpolatingFunctionAnatomy`"] > > domain = InterpolatingFunctionDomain[if1] > > {coords1} = InterpolatingFunctionCoordinates[if1]; > {coords2} = InterpolatingFunctionCoordinates[if2]; > > Norm[coords1 - coords2, 1] > > vals1 = InterpolatingFunctionValuesOnGrid[if1]; > vals2 = InterpolatingFunctionValuesOnGrid[if2]; > > if3 = Interpolation[Transpose[{coords1, vals1 + vals2}]] > > Plot[if3[x], {x, 0, 20}] > > Hope this helps. > > Oliver > -- DrMajorBob at yahoo.com

**References**:**Suming InterpolatingFunction Objects***From:*Gabriel Landi <gtlandi@gmail.com>