       Re: Re: Combining InterpolatingFunctions

```Thanks to those who have responded. In the responses everyone defines a
new function f[x_] using piecewise. However, I want to be able to use
the interpolatingfunctions as a replacement rule, as that is what the
rest of my code requires. In particular I use the f[x_]:=f[x] =... trick
so I don't have to compute the same pieces of code repeatedly.

Here are some example interpolatingfunctions from NDSolve,

f1 = NDSolve[{y''[x] + y[x] == 0, y == 0, y' == 1},
y, {x, 0, Pi}][];
f2 = NDSolve[{y''[x] + y[x] == 0, y[Pi] == -1, y' == =
1},
y, {x, Pi, 2 Pi}][];

And then I want to be able to combine the two replacement functions to
act on an expression involving y, say A. If I just had one function I'd
do A/.f1, which gives me a function that I can then plot, evaluate at
different points etc. But I want the correct function f1 or f2 for the
appropriate ranges of x in A, but I don't want to specify x in the
piecewise.

So I can write Piecewise[{{ff1, 0 <= x <= Pi}, {ff2, Pi < x <= 2 Pi}}],
but that doesn't work as it doesn't have a value of x when used as a
replacement. It does work if I specify x beforehand, but I don't want
to!

Any ideas?

Thanks,
Simon

-----Original Message-----
From: DrMajorBob [mailto:btreat1 at austin.rr.com]
Sent: 03 February 2010 11:12
To: mathgroup at smc.vnet.net
Subject: [mg107171] [mg107129] Re: [mg107092] Combining InterpolatingFunctions

For instance:

Clear[f]
f1 = Interpolation@Table[{x, Sin@x}, {x, 0, Pi, 1/10}];
f2 = Interpolation@Table[{x, Cos@x}, {x, Pi, 2 Pi, 1/10}];
f[x_] = Piecewise[{{f1@x, 0 <= x <= Pi}, {f2@x, Pi < x <= 2 Pi}}];
Plot[f@x, {x, 0, 2 Pi}]

Bobby

On Tue, 02 Feb 2010 02:30:36 -0600, Simon Pearce
<Simon.Pearce at nottingham.ac.uk> wrote:

> Hi MathGroup,
>
>
>
> I have two sets of InterpolatingFunctions coming from two separate
> NDSolve's. One of them is defined over the region [0,rc] and the other
> over the region [rc,2]. I would like Mathematica to automatically
choose
> the correct one when I use a replacement rule. If I could tell it
never
> to extrapolate this would be perfect, though I don't seem to be able
to.
>
>
>
> I've tried using FunctionInterpolation, but in order to keep my error
> terms down I had to increase the InterpolationPoints to 1000, which
> increases the calculation time from approximately .5sec to 1.5sec.
>
>
>
> Can anyone suggest an efficient way of combining
InterpolatingFunctions
> without re-interpolating them? Or turning the extrapolation off!
>
>
>
> Thanks,
>
>
>
> Simon Pearce
>
>

--
DrMajorBob at yahoo.com

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```

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