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MathGroup Archive 2004

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RE: interpolation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46999] RE: [mg46979] interpolation
  • From: David.Annetts at csiro.au
  • Date: Fri, 19 Mar 2004 01:35:52 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Amanda,

> Is there a way to get Mathematica to display the function it
> uses to interpolate a data set (call it inp)
> of the form {Number, Number}?
> A command like f=Interpolation[inp], for example, just gives assigns
> this rule to a function I am calling f.
> Is there any way to display this function f that interpolates my data 
> set, as a function of an independent variable, rather than just
> have Mathematica generate values of f given a picked 
> numerical domain value?

The obvious way is to create a table from the InterpolatingFunction ...

ord = Range[10];
abs = ord[[#]]^2 & /@ Range[10];
int = Interpolation[Transpose[{ord, abs}]]
val = {#, int[#]} & /@ Range[10]

Another way is via NumericalMaths`Spline ...

Needs["NumericalMath`"]
spl = SplineFit[Transpose[{ord, abs}], Cubic]
val = spl[#] & /@ Range[0, 9]

You can even try 
val = spl[#] & /@ Range[0, 9, .5]
But this will be in error between the sampled points -- continuing the
above example
dif = {#[[1]], Sqrt[#[[2]]]} & /@ val

Regards,

Dave.
==========================================
  Dr. David Annetts
  EM Modelling Analyst
  CSIRO DEM            Tel: +612 9490 5416
  North Ryde           Fax: +612 9490 5467
  Australia         David.Annetts at csiro.au
===========================================


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