Re: DiffMaps package
- To: mathgroup at smc.vnet.net
- Subject: [mg89646] Re: DiffMaps package
- From: dh <dh at metrohm.ch>
- Date: Mon, 16 Jun 2008 06:40:05 -0400 (EDT)
- References: <g3036s$mdc$1@smc.vnet.net>
Hi,
Interpolation does a piewise polynomial interpolation. From the manual:
points = {{0,0},{1,1},{2,3},{3,4},{4,3},{5,0}};
ifun = Interpolation[points]
pf[x_] = Piecewise[{
{InterpolatingPolynomial[{{0,0},{1,1},{2,3},{3,4}}, x], x < 2},
{InterpolatingPolynomial[{{1,1},{2,3},{3,4},{4,3}}, x], 2 <= x < 3},
{InterpolatingPolynomial[{{2,3},{3,4},{4,3},{5,0}}, x], x >= 3}
}]
Plot[pf[x] - ifun[x], {x,0,5}, PlotRange->All]
Therefore, the derivative need not be continuous. E.g.:
d=Table[{x,RandomReal[]},{x,0,1,.1}];
f=Interpolation[d];
Plot[f'[x],{x,0,1}]
hope this helps, Daniel
Modeler wrote:
> Thanks, actually I need to automate the procedure below to compute the minima and saddle points for an array of functions f[x,y]. I guess at some point I'll need to doublecheck manually that the procedure you describe below yields the correct critical points.
>
> The above functions are actually outputs of the mathematica interpolation procedure, I am slightly worried they might be nondifferentiable at certain points even if I take a high interpolation order. Do you know where to get further documentation on InterpolatingFunction? It is for me quite a black box. Do you know of any other smoother interpolation procedures like, say, 2d splines in mathematica?
>
--
Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh at metrohm.com>
Internet:<http://www.metrohm.com>