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This is probably a very silly question but I am trying to use Interpolation for the following data:

  data={{0.965251, 0.}, {3.0888, 0.}, {5.98456, 0.}, {9.26641, 0.}, {12.5483,
   0.}, {15.8301, 0.}, {18.1467, 0.}, {21.8147, 0.}, {26.2548, 
  0.}, {30.695, 1.12676}, {33.3977, 1.69014}, {36.8726, 
  2.53521}, {39.3822, 3.38028}, {42.8571, 3.94366}, {45.7529, 
  5.35211}, {48.8417, 6.76056}, {51.5444, 8.73239}, {54.0541, 
  10.9859}, {55.7915, 13.2394}, {58.1081, 16.9014}, {59.0734, 
  19.1549}, {61.0039, 22.8169}, {62.1622, 26.4789}, {63.3205, 
  30.4225}, {64.2857, 34.3662}, {65.0579, 38.3099}, {65.8301, 
  42.8169}, {66.7954, 47.8873}, {67.3745, 53.8028}, {68.3398, 
  60.5634}, {68.9189, 65.6338}, {69.112, 71.5493}, {69.6911, 
  78.0282}, {70.2703, 84.507}, {70.6564, 88.4507}, {70.6564, 
  92.3944}, {71.4286, 97.1831}, {72.5869, 100.563}, {73.7452, 
  98.3099}, {74.5174, 92.6761}, {74.7104, 87.3239}, {75.0965, 
  82.2535}, {75.2896, 77.4648}, {75.6757, 72.1127}, {76.0618, 
  63.3803}, {76.6409, 54.6479}, {77.027, 47.3239}, {77.4131, 
  40.}, {78.3784, 35.2113}, {78.5714, 29.8592}, {80.1158, 
  24.2254}, {81.4672, 22.2535}, {82.8185, 19.7183}, {84.3629, 
  18.8732}, {87.2587, 18.5915}, {91.6988, 18.8732}, {94.5946, 
  18.5915}, {98.2626, 18.3099}, {100., 18.3099}, {120., 18.3099}};

Interpolation[data]

but for some reason it does not Interpolated correctly. If I plot the data it looks fine. Can someone tell me why Interpolation doesn't correctly fit this data?

I get the following errro message:

InterpolatingFunction::dmval: Input value {0.00245143} lies outside the range of data in the interpolating function. Extrapolation will be used.

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    $\begingroup$ Probably has something to do with the error message, no? Or you don't get one? $\endgroup$
    – Michael E2
    Commented Nov 22, 2020 at 1:15
  • $\begingroup$ @MichaelE2 yes! I just updated the question for you to see the error that I get $\endgroup$
    – John
    Commented Nov 22, 2020 at 1:16
  • $\begingroup$ Hmm, I get "Interpolation::inddp: The point 70.6564` in dimension 1 is duplicated." $\endgroup$
    – Michael E2
    Commented Nov 22, 2020 at 1:17
  • $\begingroup$ I was getting that too before. But the problem is that I don't really see any problem with the data that will make interpolation not to work $\endgroup$
    – John
    Commented Nov 22, 2020 at 1:19
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    $\begingroup$ Sometimes Mathematica error messages are inscrutable, but here both are clear. Interpolation::inddp: The point 70.6564 in dimension 1 is duplicated. means you have two values for 70.6564 in data. Either nudge one by a small amount or drop one. InterpolatingFunction::dmval: Input value {0.00245143} lies outside the range of data in the interpolating function. Extrapolation will be used. is more a warning than an error: your data start at 0.965251 so when you ask for 0.00245143, Mathematica needs to extrapolate. It might work out fine, it might be catastrophically wrong. $\endgroup$
    – Chris K
    Commented Nov 22, 2020 at 1:23

1 Answer 1

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This is what happens when I drop the second value for 70.6564.

Show[
 ListPlot[data, PlotStyle -> Black],
 Plot[Evaluate@Interpolation[data][x], {x, 0, 120}, PlotRange -> All]
]

enter image description here

If those wiggles bother you, use linear interpolation instead:

Show[
 ListPlot[data, PlotStyle -> Black],
 Plot[Evaluate@Interpolation[data, InterpolationOrder -> 1][x], {x, 0, 120}, PlotRange -> All]
 ]

enter image description here

Or if you don't need the InterpolatingFunction to go exactly through the data, try this approach to regularised Interpolation.

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    $\begingroup$ Awesome! Christ thank you very much for your suggestion and also about the wiggles! This is what I wanted! I really appreciate it $\endgroup$
    – John
    Commented Nov 22, 2020 at 1:35

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