Re: Derivatives of InterpolatingFunctions

*To*: mathgroup at smc.vnet.net*Subject*: [mg5106] Re: Derivatives of InterpolatingFunctions*From*: Robert Knapp <rknapp>*Date*: Wed, 30 Oct 1996 22:04:01 -0500*Organization*: Wolfram Research*Sender*: owner-wri-mathgroup at wolfram.com

Paul Abbott wrote: > > Paul E Howland wrote: > > > > I'm using an InterpolatingFunction to model a set of data that is a > > function of three variables (range,height,frequency). I need to > > generate the partial derivatives of this InterpolatingFunction with > > respect to each of the variables. Unfortunately, version 2.2 of > > Mathematica appears unable to do this, unless the > > InterpolatingFunction is a function of only one variable. > > > > My questions are: > > 1. Has this been fixed in v3.0 of Mathematica? > > 2. If not, has anyone written a package to address this shortfall? > > See "Partial Derivatives" in the Mathematica Journal (Volume 4, Issue > 2): > > Presently, Mathematica cannot handle partial derivatives of > InterpolatingFunctions. The DInterpolatingFunction` package provided by > Hon Wah Tam (tam at wri.com), and supplied with the electronic supplement, > computes partial derivatives of two dimensional InterpolatingFunctions. > Enhancements > <cut> It is correct that Mathemtica 2.2 cannot handle partial derivatives. Howerver, in answer to the original question of Paul Howland, YES, this has been fixed and partial derivatives work correctly in Mathematica 3.0. The partial derivatives are computed as the polynomial is being evaluated, so the process is faster than it was in version 2.2 where the InterpolatingFunction object has to be entirely recomputed to obtain derivatives. Furthermore, Mathematica 3.0 supports integration of one- and multi-dimensional InterpolatingFunction objects. With the use of a new function called FunctionInterpolation, you can do more general operations on InterpolatingFunctions. FunctionInterpolation preserves the original data when it is reasonably possible given the transformation desired. Rob Knapp Wolfram Research, Inc.