Re: Suming InterpolatingFunction Objects

*To*: mathgroup at smc.vnet.net*Subject*: [mg120239] Re: Suming InterpolatingFunction Objects*From*: Oliver Ruebenkoenig <ruebenko at wolfram.com>*Date*: Thu, 14 Jul 2011 21:18:52 -0400 (EDT)*References*: <201107140922.FAA15682@smc.vnet.net> <201107141114.HAA17001@smc.vnet.net>

On Thu, 14 Jul 2011, DrMajorBob wrote: > How did you discover the InterpolationPoints option, given that Help lists no > options (at all) for FunctionInterpolation? > > Bobby Options[FunctionInterpolation] ;-) Oliver > > 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 >> > > >

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

**Re: Suming InterpolatingFunction Objects***From:*Oliver Ruebenkoenig <ruebenko@wolfram.com>