Re: Re: Re: Combining

*To*: mathgroup at smc.vnet.net*Subject*: [mg107198] Re: [mg107171] Re: [mg107129] Re: [mg107092] Combining*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Fri, 5 Feb 2010 03:23:03 -0500 (EST)*References*: <201002020830.DAA08963@smc.vnet.net>*Reply-to*: drmajorbob at yahoo.com

You'd compute things just once with the code I already sent you. Bobby On Thu, 04 Feb 2010 06:00:05 -0600, Simon Pearce <Simon.Pearce at nottingham.ac.uk> wrote: > 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. > -- DrMajorBob at yahoo.com

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

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