Re: Combining several InterploatingFunction to one

• To: mathgroup at smc.vnet.net
• Subject: [mg30254] Re: Combining several InterploatingFunction to one
• From: Max Ulbrich <ulbrich at biochem.mpg.de>
• Date: Sat, 4 Aug 2001 01:14:22 -0400 (EDT)
• References: <9kb06q\$c4d\$1@smc.vnet.net> <9kdb83\$f1k\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Jens,

This works really well if the number of x- and y-values in the
InterpolatingFunction are equal. However, when I tried to apply it to my
problem, it didn't work!
You can see the problem when you try to combine Sin1 and Sin2 from

Sin1 = n /.
NDSolve[{n''[x] == -n[x], n[0] == 0, n'[0] == 1}, n, {x, 0, 2}][[1]]
Sin2 = n /.
NDSolve[{n''[x] == -n[x], n[2] == Sin1[2], n'[2] == Sin1'[2]},
n, {x, 2, 4}][[1]]

I found the difference using InputForm[Sin1]. In your answer, you get an
interpolation table in your Sin interpolations with the same number of x- and
y-values. In my example, the lists have various lengths. Do you have any idea
how to proceed now?

Max

>Hi,
>
>have the functions continuous derivatives at the interval ends ???
>If yes
>
>GlueInterpolation[ips : {__InterpolatingFunction}] :=
>  Module[{dta},
>    dta =
>      Union[Transpose[
>          Join @@@ Transpose[{#[[3, 1]], Last[Last[#]]} & /@ ips]]];
>    Interpolation[dta]
>    ]
>
>
>and
>
>itab = Table[
>    FunctionInterpolation[Sin[x], {x, i*0.6, (i + 1)*0.6}], {i, 0, 2}];
>
>dd = GlueInterpolation[itab];
>
>Plot[Evaluate[dd[x]], {x, 0, 1.8}];
>
>works fine. You should be carefull look if you have a argument
>in the interpolation function.
>
>Regards
>  Jens
>
>
>Max Ulbrich wrote:
>
> Hi,
>
> does anyone know how to combine several interpolating functions to ONE
> single interploating function?
> I now have
>
> Which[0. <= t <= 0.01, InterpolatingFunction[{{0., 0.01}}, "<>"],
>         0.01 <= t <= 0.02, InterpolatingFunction[{{0.01, 0.02}}, "<>"],
>         0.02 <= t <= 0.03, InterpolatingFunction[{{0.02, 0.03}},
> "<>"]][t]
>
> but I would like to have
>
> InterpolatingFunction[{{0., 0.03}}, "<>"][t]
>
> that is piecewise defined from all of the three.
> Suggestions please to
>
> ulbrich at biochem.mpg.de
>
> Thanks!
>
> Max

```

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