How to merge a ListLogPlot including a discrete set of data points with a LogPlot including some analytical functions?

Question

I have an analytical 1d-function of a variable called $M$ and I have plotted that function using the following code:

yfunc[M_] := 10^(12 - M);
sigma[M_] := (16.9*(yfunc[M])^0.41)/(1 + 1.102*(yfunc[M])^0.20 + 6.22*(yfunc[M])^0.333);
dsigmadM[M_] := (Log[10]*10^M)^-1*D[sigma[x], x] //. x -> M;
xfunc[M_] := 1.686/sigma[M];
func[M_] := 0.322*Sqrt[(2*0.707)/\[Pi]]*(1 + (0.707*(xfunc[M])^2)^-0.3)* xfunc[M]*Exp[-((0.707*(xfunc[M])^2)/2)];
h[M_] := -0.05152*10^12*func[M]/sigma[M]*dsigmadM[M];
f[M_] := 0.54*(M - 12) + 2.73;
g[M_?NumericQ] := 1301.98*(0.7)^2*10^-6*NIntegrate[(10^f[x])*h[x]*Log[10], {x, M, \[Infinity]}];


LogPlot[g[M], {M, 8, 16}, PlotRange -> {10^-17, 10}, 
             Frame -> True, 
             FrameLabel -> {Style["Log(M)", FontSize -> 24], Style["Y-axis Log scale", FontSize -> 24]}, 
             FrameTicksStyle -> Directive[FontSize -> 24]]

I also have a set of 32 discrete points $(M, u[M])$ corresponding to some other function whose analytical form is unknown but it is fair enough to join the data points in a dot-to-dot manner. I was able to do so using the following code:

    a = 25;
    MyData = {{8.90 + Log10[a], 0.0003256}, {9.0 + Log10[a], 
        0.0002971}, {9.10 + Log10[a], 0.0002980}, {9.20 + Log10[a], 
        0.0002757}, {9.30 + Log10[a], 0.0002546}, {9.40 + Log10[a], 
        0.0002400}, {9.50 + Log10[a], 0.0002253}, {9.60 + Log10[a], 
        0.0002015}, {9.70 + Log10[a], 0.0001900}, {9.80 + Log10[a], 
        0.0001856}, {9.90 + Log10[a], 0.0001750}, {10.0 + Log10[a], 
        0.0001753}, {10.10 + Log10[a], 0.0001732}, {10.20 + Log10[a], 
        0.0001692}, {10.30 + Log10[a], 0.0001630}, {10.40 + Log10[a], 
        0.0001503}, {10.50 + Log10[a], 0.0001309}, {10.60 + Log10[a], 
        0.0001135}, {10.70 + Log10[a], 0.00009117}, {10.80 + Log10[a], 
        0.00007193}, {10.90 + Log10[a], 0.00005419}, {11.00 + Log10[a], 
        0.00003707}, {11.10 + Log10[a], 0.00002439}, {11.20 + Log10[a], 
        0.00001501}, {11.30 + Log10[a], 0.000008719}, {11.40 + Log10[a], 
        0.000004783}, {11.50 + Log10[a], 0.000002529}, {11.60 + Log10[a], 
        0.000001170}, {11.70 + Log10[a], 0.0000004598}, {11.80 + Log10[a],
         0.0000001803}, {11.90 + Log10[a], 
        0.00000006044}, {12.00 + Log10[a], 0.00000001651}};
    error = {0.0000146, 0.0000119, 0.0000112, 0.00000903, 0.00000774, 
       0.00000672, 0.00000578, 0.00000469, 0.00000443, 0.00000389, 
       0.00000325, 0.00000326, 0.00000281, 0.00000235, 0.00000227, 
       0.00000174, 0.00000152, 0.00000131, 0.00000106, 0.000000833, 
       0.000000627, 0.000000429, 0.000000339, 0.000000244, 0.000000162, 
       0.000000100, 0.0000000709, 0.0000000411, 0.0000000239, 
       0.0000000142, 0.00000000769, 0.00000000390};
    withError = Transpose[{MyData[[All, 1]], MyData[[All, 2]], error}];
    errorplot = ErrorListPlot[withError, Joined -> True, Frame -> True];
    lerrorplot = errorplot /. {x_Real, y_Real} -> {x, Log@y};
    Show[ListLogPlot[MyData, PlotRange -> {10^-17, 10}, 
    PlotStyle -> {Red, Thick}, Joined -> True, Frame -> True, 
    FrameLabel -> {Style["Log(M)", FontSize -> 24], Style["Y-axis Log scale", FontSize -> 24]}, 
    FrameTicksStyle -> Directive[FontSize -> 24]], lerrorplot]

Now, I am trying to merge two plots into one by adding my second set of data points into my first plot. My first question is how to do it? and my second question is assuming $a$ is the Interval[50 + 25 {-1, 1}] rather than a fixed value of $a=25,$ how to plot the confidence region of the best fit (or joined data) on the single plot produced by merging the two?

Your help is appreciated,

Minimalistic examples are nice. I would strip away all of the formatting code, such that your goal would be more clear. — Johu, Jun 09 '16 at 07:13
We can not even test your code, as we don't have {f[M], g[M], h[M], p[M], q[M]} definitions. Instead of ugly old PlotLegends\``, check out option for mostPlots calledPlotLegends`. — Johu, Jun 09 '16 at 07:16
@Johu, I am working with version 8.0 and the only way I could get it working was that since PlotLegends is not known in this version. I will see how to modify my question by putting some actual functions. — Benjamin, Jun 09 '16 at 07:20
Show does work for overlaying two different graphics. Your problem might be, that ErrorListPlot and LogPlot have different coordinates - Log[y] vs y. So you need to implement logarithmic ErrorListPlot yourself. Check out Plotting Error Bars on a Log Scale. — Johu, Jun 09 '16 at 07:27
@Johu, do you mean that if I get rid of the error bars by removing lerrorplot option from the Show command, then I can combine two plots? I tried it but it didn't work out. — Benjamin, Jun 09 '16 at 18:38
@Benjamin I have to be more specific than "it does not work out". Show is exactly ment for that. — Johu, Jun 12 '16 at 19:58
@Benjamin In the code above your Show will work, if the first parameter is a list of plots, which you want to have overlaid. You have provided two parameters. You should also add Needs["ErrorBarPlots"]` into the beginning of your code. — Johu, Jun 12 '16 at 21:26

score 1 · Answer 1 · answered Jun 10 '16 at 17:20

I was able to make an interpolating function for my set of discrete points using the following code:

gfunc2 = Boole[
   10 < M < 13] ListInterpolation[{0.0003256, 0.0002971, 0.0002980, 
    0.0002757, 0.0002546, 0.0002400, 0.0002253, 0.0002015, 0.0001900, 
    0.0001856, 0.0001750, 0.0001753, 0.0001732, 0.0001692, 0.0001630, 
    0.0001503, 0.0001309, 0.0001135, 0.00009117, 0.00007193, 
    0.00005419, 0.00003707, 0.00002439, 0.00001501, 0.000008719, 
    0.000004783, 0.000002529, 0.000001170, 0.0000004598, 0.0000001803,
     0.00000006044, 
    0.00000001651}, {{8.90, 9.00, 9.10, 9.20, 9.30, 9.40, 9.50, 9.60, 
     9.70, 9.80, 9.90, 10.00, 10.10, 10.20, 10.30, 10.40, 10.50, 
     10.60, 10.70, 10.80, 10.90, 11.00, 11.10, 11.20, 11.30, 11.40, 
     11.50, 11.60, 11.70, 11.80, 11.90, 12.00}}]

And then running the following code in which the analytical function and the interpolating function are put together and treated on the same footing:

With[{a=25},
LogPlot[{g[M], gfunc2[M - Log10[a]]}, {M, 8, 16}, PlotRange -> {10^-17., 10.}, 
     PlotStyle -> {Black, Blue, Thick}, 
     Frame -> True, 
     FrameLabel -> {Style["Log(M)", FontSize -> 30], Style["Y-axis Log Scale", FontSize -> 30]}, 
     FrameTicksStyle -> Directive[FontSize -> 30], 
     PlotLegend -> {Style["first function", 20], Style["second function", 20]}]]

This actually produced the plot I was looking for. However, I still don't know how to do the job for an interval rather than a fixed value for $a$.

However, I need to show the data points (central values and error bars) rather than an interpolating function along side a continuous function on the same plot. I still don't know how to combine these two formats. — Benjamin, Jul 14 '16 at 17:09

How to merge a ListLogPlot including a discrete set of data points with a LogPlot including some analytical functions?

1 Answers1