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nintegrate vs nintegrateinterpolatingfunction vs integrate


Dear MathGroup,

I'm trying to get distance versus time functions from lists of time
and velocity data. I've done this before, but with the data sets I am
using now, I keep running into complex number errors. The only working
implementation I found is to use nintegrate (& functioninterpolation),
but it is much slower than nintegrateinterpolatingfunction or
integrate (& functioninterpolation), at least for working on
interpolated data:

My data sets (errors "work" with either; I use both below):
http://www.epa.gov/otaq/emisslab/methods/uddscol.txt
&
http://www.epa.gov/otaq/emisslab/methods/hwycol.txt

What do you think is causing the problem? Do you have any solutions or
workarounds?

BTW, I multiplied the mph by 1397/3125 after I imported the data (mph
to meters per second).

Thank you for your valuable time,

some working example code:

nbname=ToFileName["FileName"/.NotebookInformation[EvaluationNotebook[]]];
nbdir=DirectoryName[nbname];
englishtracedata=
    MapThread[
      Partition[
          Drop[Import[ToFileName[nbdir,#1],"List"],#2],{2}]&,{{"uddscol.txt",
          "hwycol.txt"},{11,11}}];
tracedata=Apply[{#1,1397 #2/3125}&,englishtracedata,{2}];
tracedatafuncs=Interpolation/@tracedata;
outerlimits=Map[{Min@#,Max@#}&,Transpose/@tracedata,{2}];
MapThread[
  Plot[#1[x],Evaluate[{x,Sequence@@#2[[1]]}]]&,{tracedatafuncs,
    outerlimits}];(*I wonder why the Evaluate is required and*how*
    it actually solves the problem???*)distancefuncs=
  MapThread[
    Block[{t,arbittime,dist},
        dist[arbittime_?NumericQ]:=NIntegrate[#1[t],{t,0,arbittime}];
        FunctionInterpolation[
          dist[t],{t,Evaluate[Sequence@@#2[[1]]]}]]&,{tracedatafuncs,
      outerlimits}]
MapThread[
    Plot[#1[x],Evaluate[{x,Sequence@@#2[[1]]}]]&,{distancefuncs,outerlimits}];


-- 
Chris Chiasson
Kettering University
Mechanical Engineering
Graduate Student
1 810 265 3161


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