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>