Re: Re: Combining InterpolatingFunctions

*To*: mathgroup at smc.vnet.net*Subject*: [mg107171] Re: [mg107129] Re: [mg107092] Combining InterpolatingFunctions*From*: Simon Pearce <Simon.Pearce at nottingham.ac.uk>*Date*: Thu, 4 Feb 2010 07:00:05 -0500 (EST)*References*: <201002020830.DAA08963@smc.vnet.net> <201002031112.GAA19632@smc.vnet.net>

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] == 0, y'[0] == 1}, y, {x, 0, Pi}][[1]]; f2 = NDSolve[{y''[x] + y[x] == 0, y[Pi] == -1, y'[0] == = 1}, y, {x, Pi, 2 Pi}][[1]]; 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 This message has been checked for viruses but the contents of an attachment may still contain software viruses which could damage your computer system: you are advised to perform your own checks. Email communications with the University of Nottingham may be monitored as permitted by UK legislation.

**References**:**Combining InterpolatingFunctions***From:*Simon Pearce <Simon.Pearce@nottingham.ac.uk>

**Re: Combining InterpolatingFunctions***From:*DrMajorBob <btreat1@austin.rr.com>

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**Re: Combining InterpolatingFunctions**