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I would like to draw a ListContourPlot in Log Log scale as well as bar legend. But I have no idea about how to do it. Could anyone help me to draw the plot in Log Log scale?

ListContourPlot[ConfVar, InterpolationOrder -> 2, PlotLegends -> 
BarLegend[Automatic, LegendLabel -> "sin \!\(\*SubscriptBox[\(\[Theta]\), \(12\)]\)"], 
ContourStyle -> None, Frame -> True]

And the result is a below plot.

enter image description here

Functions and coefficients for this plot are

\[Alpha]em = 1/137

mmu = 102.8/1000

F[x_] := (5*x^4 - 14*x^3 + 39*x^2 - 38*x - 18*x^2*Log[x] + 8)/(12*(1 - x)^4)

\[CapitalGamma]totalmu = 3*10^-19

Brmutoe\[Gamma]expmax = 4.2*10^-13

Brmutoe\[Gamma][MZprime_, s24squad_, s12_] := \[Alpha]em/(1024*Pi^4)*
mmu^5/(MZprime^4*\[CapitalGamma]totalmu)*s24squad^4*s12^2*
F[(mmu/MZprime)^2]^2*(1 + (1 - s24squad)/s24squad*F[(1001/MZprime)^2]/F[(mmu/MZprime)^2])

imax = 10^5

ConfVar = {};
For[i = 1, i <= imax, i++,
MZprimer = RandomReal[{100, 1000}];
s24squadr = RandomReal[{0, 1}];
s12r = RandomReal[{10^-5, 10^-1}];
Brmutoe\[Gamma]r = Brmutoe\[Gamma][MZprimer, s24squadr, s12r];
valf1 = MZprimer;
valf2 = s24squadr;
valf3 = s12r;
valf4 = Brmutoe\[Gamma][MZprimer, s24squadr, s12r]; 
If[valf4 < Brmutoe\[Gamma]expmax, {ConfVar = 
Join[ConfVar, {{valf1, valf2, valf3}}]}]]

Many thanks for someone's help in advance.

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  • $\begingroup$ Look at the ScalingFunctions option. For example ScalingFunctions -> "Log10" $\endgroup$ – David Keith Feb 8 at 18:36
  • $\begingroup$ @DavidKeith Thanks for your suggestion, but when I tried that method, the y-axis of this plot is from 10^-5 to 1. But I need the y-axis to be from 10^-3 to 1. How can I fix that problem? $\endgroup$ – lhcQFT Feb 8 at 18:46
  • $\begingroup$ @lhcQFT by using the PlotRange->{{xmin,xmax},{ymin,ymax},{zmin,zmax}} option... $\endgroup$ – bjorn Feb 8 at 19:02
  • $\begingroup$ @lhcQFT Parameter is not defined ` [CapitalGamma]totalmu` $\endgroup$ – Alex Trounev Feb 8 at 19:03
  • $\begingroup$ @bjorn Thanks, I will try it. $\endgroup$ – lhcQFT Feb 8 at 19:10
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I have not been able to generate data from your code, but here is an example with fake data:

lst = Flatten[
   Table[{x, y, 1 + (Sin[x] + 10) Exp[-(x - 2)^2 - (y - 3)^2]},
    {x, 2, 4, .1}, {y, 2, 4, .1}],
   1];

ListContourPlot[lst, PlotLegends -> Automatic]

enter image description here

ListContourPlot[lst, PlotLegends -> Automatic, 
 ScalingFunctions -> {"Log10", "Log10", "Log10"}]

enter image description here

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  • $\begingroup$ @DaividKeith Thank you for your example. I forgot to write down one important information in my text and edited it. But is there a better way to express bar legend like 10^-n rather than arbitrary number? $\endgroup$ – lhcQFT Feb 8 at 19:30
  • $\begingroup$ @ihcQFT Sorry, I do not know a way to do this. There might well be a way, but I find the behavior of ListContourPlot quite strange when trying to specify contours with a Log scale. Perhaps someone else will point the way. $\endgroup$ – David Keith Feb 8 at 20:36
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If you have the right dynamic range in the data, it will scale appropriately. Otherwise, you can put your own numbers into the PlotLegends field.

PlotLegends -> BarLegend[10^-Range[5]

You can specify the frame ticks (numbers along the axes) with FrameTicks[]. For example, if the default output was not to our liking, we could have achieved the same result with

FrameTicks -> {{10^Range[2], None}, {10.0^Range[2], None}}]

As mentioned in the comments, use PlotRange[] to specify the range of values.

Putting it all together ...

ListContourPlot[ConfVar, InterpolationOrder -> 2, 
  PlotLegends -> BarLegend[10^-Range[5], 
    LegendLabel -> "sin \!\(\*SubscriptBox[\(\[Theta]\), \(12\)]\)"], 
    ContourStyle -> None, Frame -> True, 
    ScalingFunctions -> {"Log10", "Log10", "Log10"}, 
    FrameTicks -> {{10^Range[-3, 0], None}, {10.0^Range[3], None}},
    PlotRange -> {Automatic, {10^-3, 1}, Automatic}]

Resulting image

Best, Mike

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