1
$\begingroup$

Question:

I'm trying to pull together a graph with labelled axes, a title, and an inset box with information relating to the plot such as the y-intercept (A in this code) and it's uncertainty. However, none of the conditions beyond the initial plot implements, and outputs 3 or 4 pages of errors, but can't see what the error is, even with the description

Code:

fit = NonlinearModelFit[dataHist5, A*Exp[-k*t], {A, k}, t, 
   Weights -> 1/uncertainties^2];
hLife = Log[2]/Around[k, \[Sigma]k]
seA = Around[A, \[Sigma]A]

halfLife = hLife[[1]] /. fit["BestFitParameters"]
sehalfLife = 
 hLife[[2]] /. fit["BestFitParameters"] /. \[Sigma]k -> 
   fit["ParameterErrors"][[2]]

uncertainties = dataHist5[[All, 2, 2]];

Show[ListPlot[dataHist5], 
 Plot[fit[x], {x, 0, 800}, PlotRange -> All, 
  PlotLabel -> "Decay Curve of Phosphorus-31 by \[Beta]^{+} Emission",
  PlotTheme -> "Detailed", PlotStyle -> Red, 
  LabelStyle -> {Black, Bold}, {0.85, 0.75}], 
 Frame -> {{True, False}, {True, False}, 
   FrameLabel -> {"Time /s", 
     "Counts Recorded in the Previous 15 seconds"}, 
   ImageSize -> {700, 500}}, 
 Inset[Framed[
   Grid[{{"Run 0"}, {"N=" Length[
        dataHist5] "/50"}, {"A=" seA}, {"t_{frac{1}{2}}=" PlusMinus[
        halfLife, 
        sehalfLife]}, {"\[Chi]^{2}=" fit[
         "ANOVATableSumsOfSquares"][[2]]}, {"Reduced \[Chi]^{2}=" fit[
         "ANOVATableMeanSquares"][[2]]}}], Background -> White, 
   RoundingRadius -> 5, Scaled[{.85, .9}]]]]

Data:

dataHist5 = {{Around[16.5, 1.5], 
   Around[77.8, 8.8]}, {Around[34.5, 1.5], 
   Around[60.5, 8.0]}, {Around[52.5, 1.5], 
   Around[63.8, 8.0]}, {Around[106.5, 1.5], 
   Around[42.4, 6.5]}, {Around[124.5, 1.5], 
   Around[41.7, 6.5]}, {Around[142.5, 1.5], 
   Around[14.6, 3.8]}, {Around[160.5, 1.5], 
   Around[33.9, 5.8]}, {Around[178.5, 1.5], 
   Around[29.4, 5.4]}, {Around[196.5, 1.5], 
   Around[33.5, 5.8]}, {Around[214.5, 1.5], 
   Around[30.9, 5.6]}, {Around[232.5, 1.5], 
   Around[31.1, 5.8]}, {Around[250.5, 1.5], 
   Around[21.5, 4.6]}, {Around[268.5, 1.5], 
   Around[4.3, 2.1]}, {Around[286.5, 1.5], 
   Around[6.4, 2.5]}, {Around[322.5, 1.5], 
   Around[7.5, 2.7]}, {Around[340.5, 1.5], 
   Around[4.5, 2.1]}, {Around[358.5, 1.5], 
   Around[11., 3.3]}, {Around[376.5, 1.5], 
   Around[14.0, 3.7]}, {Around[394.5, 1.5], 
   Around[14.0, 3.7]}, {Around[466.5, 1.5], 
   Around[0.6, 0.7]}, {Around[502.5, 1.5], 
   Around[2.2, 1.5]}, {Around[520.5, 1.5], 
   Around[9.4, 3.1]}, {Around[538.5, 1.5], 
   Around[4.1, 2.0]}, {Around[646.5, 1.5], 
   Around[2.2, 1.5]}, {Around[682.5, 1.5], Around[0.6, 0.7]}}

Background:

This is the results of a radioactive decay experiment. These are points obtained from gaussian models (which is why they aren't integer), then points are then plotted and a model applied (the model is y=Ae^-(kt)), and then weighted for the uncertainties (weighting is 1/uncertainty^2). The target is then to find A (this is the y-intercept), k (this is the decay constant and will give the half-life, t = ln(2) / k). Half-life being the main desired figured (the time is takes for the decay curve to have reduced by half). Then produces the reduced chi^2 as a measure of a goodness of fit. And express this on a singular graphic, much as m_goldberg has done below.

Re-creating m_goldberg's answer:

Having copied the code across - it errors. I have tried to implement what I thought were fixes but unsuccessfully. I changed NonLinearModelfitData to NonLinearModel[fitData,...], And on the very last line the Show is not closed due to a missing speech mark after 'emission', so I added that in. But it outputs this:

enter image description here

$\endgroup$
2
  • $\begingroup$ What is the definition of uncertainties? Without it being defined, your fit doesn't work and no one can see what is wrong with the rest of your code. $\endgroup$
    – m_goldberg
    Commented Mar 5, 2021 at 12:50
  • $\begingroup$ uncertainties = dataHist5[[All, 2, 2]]; But in practical terms, it's the error bars around each of the data points in dataHist5 $\endgroup$
    – Epideme
    Commented Mar 5, 2021 at 13:00

1 Answer 1

2
$\begingroup$

Edit 2

Well, I have thought more about your code and managed to get what looks like a reasonable fit.

Here is my 2nd revision of your code. I don't have any knowledge of the problem domain, so I can't be sure this is a satisfactory answer, but it looks more like what I think you want.

dataHist5 =
  {{Around[16.5, 1.5], Around[77.8, 8.8]}, 
   {Around[34.5, 1.5], Around[60.5, 8.0]},
   {Around[52.5, 1.5], Around[63.8, 8.0]}, 
   {Around[106.5, 1.5], Around[42.4, 6.5]},
   {Around[124.5, 1.5], Around[41.7, 6.5]}, 
   {Around[142.5, 1.5], Around[14.6, 3.8]},
   {Around[160.5, 1.5], Around[33.9, 5.8]}, 
   {Around[178.5, 1.5], Around[29.4, 5.4]},
   {Around[196.5, 1.5], Around[33.5, 5.8]}, 
   {Around[214.5, 1.5], Around[30.9, 5.6]},
   {Around[232.5, 1.5], Around[31.1, 5.8]}, 
   {Around[250.5, 1.5], Around[21.5, 4.6]},
   {Around[268.5, 1.5], Around[4.3, 2.1]}, 
   {Around[286.5, 1.5], Around[6.4, 2.5]},
   {Around[322.5, 1.5], Around[7.5, 2.7]}, 
   {Around[340.5, 1.5], Around[4.5, 2.1]},
   {Around[358.5, 1.5], Around[11., 3.3]}, 
   {Around[376.5, 1.5], Around[14.0, 3.7]},
   {Around[394.5, 1.5], Around[14.0, 3.7]}, 
   {Around[466.5, 1.5], Around[0.6, 0.7]},
   {Around[502.5, 1.5], Around[2.2, 1.5]}, 
   {Around[520.5, 1.5], Around[9.4, 3.1]},
   {Around[538.5, 1.5], Around[4.1, 2.0]}, 
   {Around[646.5, 1.5], Around[2.2, 1.5]},
   {Around[682.5, 1.5], Around[0.6, 0.7]}};
fitData = {#[[1, 1]], #[[2, 1]]} & /@ dataHist5;

Clear[A, k]
uncertainties = dataHist5[[All, 2, 2]];
fit =
  NonlinearModelFit[fitData, A Exp[-k t], {A, k}, t, Weights -> 1/uncertainties^2]

fit

{A, k} = {A, k} /. fit["BestFitParameters"];
{σA, σk} = fit["ParameterErrors"];
hLife = Log[2]/Around[k, σk];
seA = Around[A, σA];
halfLife = hLife[[1]];
sehalfLife = hLife[[2]];

Here is the combined plot:

Show[
  Plot[fit[x], {x, 0, 800},
    PlotRange -> All,
    PlotTheme -> "Detailed",
    PlotStyle -> Red,
    Axes -> False,
    Frame -> {{True, False}, {True, False}}, 
    FrameLabel -> {"Time /s", "Counts Recorded in the Previous 15 seconds"},
    ImageSize -> Large],
  ListPlot[dataHist5, ImageSize -> Large],
  Graphics[
    Inset[
      Framed[
        Column[
          {"Run 0",
           Row[{"N=" , Length[dataHist5], "/50"}],
           Row[{"A=" , seA}],
           Row[{Subscript[t, 1/2], "=" , PlusMinus[halfLife, sehalfLife]}],
           Row[{"χ^{2}=" , fit["ANOVATableSumsOfSquares"][[2]]}], 
           Row[{"Reduced χ^{2}=", fit["ANOVATableMeanSquares"][[2]]}]}],
        Background -> White,
        RoundingRadius -> 5],
      {Right, Top},
      Scaled[{1.1, 1.2}]]],
  PlotLabel ->
    Row[{"Decay Curve of Phosphorus-31 by ", Superscript[β, "+"], " Emission"}]]

combined_plot

The above code is a very careful cut and paste from the latest version of my Mathematica notebook in which I worked on your problem. I ran the code in Mathematica V12.1.1 running on MacOS 10.13.4.

Please copy and paste the code into a new, empty notebook, run it in a new Mathematica session and see if it still gives you errors.

$\endgroup$
9
  • $\begingroup$ Thank you, this has been a big help. I must've had so many errors in there by comparison. I wonder why my fitting for this set of data returns a different half life (Ln(2)/k) than when JimB did it in this question: mathematica.stackexchange.com/questions/239832/… - it's the same data and should be the same model. Thank you for helping fix the styling. $\endgroup$
    – Epideme
    Commented Mar 9, 2021 at 14:35
  • $\begingroup$ Hi. I tried to recreate this answer by copying the posted code, but it doesn't produce the attached graph, and I haven't managed to chase the error out. I believe there's 2, one I think is a square bracket missing in 'NonLinearModelfitData' to be 'NonLinearModel[fitData,...]. I'm not sure about the other, I think it's another bracket somewhere in the plot code $\endgroup$
    – Epideme
    Commented Mar 9, 2021 at 15:25
  • $\begingroup$ Added the background as mentioned and my attempt to recreate the graph $\endgroup$
    – Epideme
    Commented Mar 9, 2021 at 17:01
  • $\begingroup$ @Epideme There was an error in the Show code, a missing end quote in the PlotLabel option. I have fixed it. $\endgroup$
    – m_goldberg
    Commented Mar 9, 2021 at 18:08
  • $\begingroup$ Yeh I thought it was that, but it doesn't seem to be working. I think the NonLinearModelfitData needs a square bracket, but I've tried adding that in too. I've put the graph I get out in the question but i will have another go in the morning. thank you. $\endgroup$
    – Epideme
    Commented Mar 10, 2021 at 0:01

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.