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.
| +----------------------------------
|