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Re: Derivative of InterpolatingFunction

  • To: mathgroup at smc.vnet.net
  • Subject: [mg59753] Re: Derivative of InterpolatingFunction
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Sat, 20 Aug 2005 03:13:41 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <de46fi$r4f$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

whats wrong with
data = Table[x^2 Sin[ y], {x, -2., 2.}, {y, -2., 
2.}];
approx = ListInterpolation[data, {{-2, 2}, {-2, 
2}}];
approxGradient = D[approx[x, y], {{x, y}, 1}];

In[]:=approxGradient /. {x -> 0.4, y -> 0.8}

Out[]={0.568249, 0.115655}

In[]:=D[x^2 Sin[ y], {{x, y}, 1}] /. {x -> 0.4, 
y -> 0.8}

Out[]={0.573885, 0.111473}

Regards

  Jens

<pdickof at scf.sk.ca> schrieb im Newsbeitrag 
news:de46fi$r4f$1 at smc.vnet.net...

|I wish to compute gradients of three-dimensional 
interpolating
| functions. The browser entry for 
InterpolatingFunction claims taking
| derivatives is possible and does not mention 
limitations in the
| dimensionality. My naive attempts based on the 
example for gradients in
| the browser entry for D have failed even for two 
dimensions:
|
| data = Table[x^2 Sin[ y], {x, -2., 2.}, {y, -2., 
2.}];
| approx = ListInterpolation[data, {{-2, 2}, {-2, 
2}}];
| approxGradient = D[approx[x, y], {{x, y}, 1}]
| approxGradient[1, 1]
|
| Searching this newsgroup, the closest thing I 
have found is the 1996
| post by Paul Abbot (extract below). Have 
"enhancements for higher
| dimensions" been incorporated?
|
| Peter Dickof
| +--------------------------
| In The Mathematica Journal 4(2):31 the following 
appears:
|
| Partial Derivatives
|
|
| Presently, Mathematica cannot handle partial 
derivatives of
| InterpolatingFunctions. The package 
DInterpolatingFunction.m, provided
| by Hon  Wah Tam (t... at wri.com) and included in 
the electronic
| supplement, computes partial derivatives of 
two-dimensional
| InterpolatingFunctions. Enhancements for higher 
dimensions will
| eventually be incorporated into Mathematica.
| +----------------------------------
| 



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