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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


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