Re: Interpolation

*To*: mathgroup at smc.vnet.net*Subject*: [mg32309] Re: Interpolation*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Sat, 12 Jan 2002 05:18:28 -0500 (EST)*References*: <a1mbl8$2ot$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Yas, Here is an idea that might be refined: dat=Table[{t,Sin[0.75+Exp[Pi*t]]},{t,0.,1.,.001}]; ListPlot[dat] Cases[Partition[dat,3, 1],{a_,b_,c_}/;a[[2]]\[LessEqual]b[[2]]&&b[[2]]\[GreaterEqual]c[[2]]:>b] Of course the value {0., 0.983986} is not found. -- Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 "Yas" <y.tesiram at pgrad.unimelb.edu.au> wrote in message news:a1mbl8$2ot$1 at smc.vnet.net... > G'day mathgroup, > I have some general questions on Interpolation as implemented in > Mathematica. Essentially, I have a series of profiles for which I have > no general function. The profile is generated by repetitive > multiplication of rotation matrices and so it is difficult (and also > impractical) to deduce an analytic function. Instead to answer the > questions I have, I have decided to use Interpolation -- a pitiful > state, nevertheless a shade better than extrapolation. The first step > involves creating the Interpolating function, > > thing1 = Interpolation[data]; > > Then I find the first derivative, > > thing2 = D[thing1[x], {x, 0, lastdatapoint}] > > Next I want to find the points where thing2 = 0, but I have run into > problems with Mathematica complaining about inverse functions etc, > although plots of thing2 versus x look fine. > > My primary question is, > > 1. The profiles that I have, have maxima and minima whose co-ordinates I > want to find, hence the differentiation step. Interpolation does a good > job reproducing the data points and in finding a derivative that can be > plotted but not when asked to Solve for thing2 = 0. How do I go about > finding the accuracy of the Interpolating Function to test whether the > value near thing2 = 0 is well behaved? > > And a secondary question is, > > 2. Is there another efficient method of estimating the co-ordinates of > the minima and maxima by computer of data sets? > > The length of each of these data sets is 1000 points and for that reason > I have not pasted it into the email. As a demonstrative example, the > Table of values generated by, > > Table[Sin[0.75 + Exp[Pi*t]], {t, 0, 1, 1/1000}]; > ListPlot[%] > > is closely related. > > Any help or comments will be appreciated. > > Thanks > Yas > >