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Before I ask the exact question, I would like to add that I know similar questions have been asked multiple times but I have tried several of those techniques but have failed to get the desired result in Mathematica 11.3. I have two lists of data which I want to compare with each other by having two contour plots that have the same color axis.

list1={{150, 5, 3.9716}, {300, 5, 4.093}, {450, 5, 4.153}, {600, 5, 
  4.1736}, {750, 5, 4.2122}, {900, 5, 4.2176}, {1000, 5, 
  4.1704}, {150, 10, 1.5728}, {300, 10, 1.6434}, {450, 10, 
  1.6508}, {600, 10, 1.6888}, {750, 10, 1.701}, {900, 10, 
  1.7276}, {1000, 10, 1.7168}, {150, 15, 0.9102}, {300, 15, 
  0.913}, {450, 15, 0.934}, {600, 15, 0.9244}, {750, 15, 0.927}, {900,
   15, 0.9382}, {1000, 15, 0.9612}, {150, 20, 0.615}, {300, 20, 
  0.5922}, {450, 20, 0.5916}, {600, 20, 0.6032}, {750, 20, 
  0.6132}, {900, 20, 0.6264}, {1000, 20, 0.6418}, {150, 25, 
  0.4348}, {300, 25, 0.4268}, {450, 25, 0.4322}, {600, 25, 
  0.4404}, {750, 25, 0.4442}, {900, 25, 0.4566}, {1000, 25, 
  0.4446}, {150, 30, 0.3236}, {300, 30, 0.3232}, {450, 30, 
  0.318}, {600, 30, 0.331}, {750, 30, 0.3322}, {900, 30, 
  0.3384}, {1000, 30, 0.3396}};
list2={{150, 5, 3.1898}, {300, 5, 3.4746}, {450, 5, 3.6446}, {600, 5, 
  3.6668}, {750, 5, 3.6532}, {900, 5, 3.6914}, {1000, 5, 
  3.7056}, {150, 10, 1.2118}, {300, 10, 1.4098}, {450, 10, 
  1.464}, {600, 10, 1.5088}, {750, 10, 1.4864}, {900, 10, 
  1.5074}, {1000, 10, 1.4844}, {150, 15, 0.6198}, {300, 15, 
  0.749}, {450, 15, 0.7956}, {600, 15, 0.8304}, {750, 15, 
  0.8528}, {900, 15, 0.8412}, {1000, 15, 0.831}, {150, 20, 
  0.358}, {300, 20, 0.4734}, {450, 20, 0.5176}, {600, 20, 
  0.5346}, {750, 20, 0.5352}, {900, 20, 0.5604}, {1000, 20, 
  0.5614}, {150, 25, 0.2494}, {300, 25, 0.3254}, {450, 25, 
  0.3538}, {600, 25, 0.3774}, {750, 25, 0.397}, {900, 25, 
  0.3896}, {1000, 25, 0.3982}, {150, 30, 0.169}, {300, 30, 
  0.2262}, {450, 30, 0.2672}, {600, 30, 0.285}, {750, 30, 
  0.3014}, {900, 30, 0.3068}, {1000, 30, 0.2946}};
min=0.01;max=5;
ListContourPlot[list1, 
  ScalingFunctions -> {"Linear", "Linear", "Log10"}, 
  ColorFunction -> MPLColorMap["Viridis"], 
  PlotLegends -> 
   BarLegend[{MPLColorMap["Viridis"], {min, max}}, 
    LabelStyle -> Directive[Black], LegendMarkerSize -> 350]]

(MPLColorMap is from here.)

This gave me an empty picture, albeit with the proper legend also empty

After a survey of posted questions on the forum, I tried the following but to no avail.

ListContourPlot[list1,ScalingFunctions -> "Log10", PlotRange->{min,max},ColorFunctionScaling->False,
 ColorFunction -> (MPLColorMap["Viridis"][Rescale[#, {min, max}]] &), 
 PlotLegends -> 
  BarLegend[{MPLColorMap["Viridis"], {min, max}}, 
   LegendMarkerSize -> 370]]]

This gives me:

also empty

If I use:

min=0.1;
ListDensityPlot[list1, 
  ScalingFunctions -> {"Linear", "Linear", "Log10"}, 
  ColorFunction -> MPLColorMap["Viridis"], 
  PlotLegends -> 
   BarLegend[{MPLColorMap["Viridis"], {min, max}}, 
    LabelStyle -> Directive[Black], LegendMarkerSize -> 350]]

This gives me something I would expect: almost there

Consequently if I change scaling functions in the contour plot to ScalingFunctions -> {"Linear", "Linear", "Log10"}, I get an error until I remove the plot range I provide. Can anyone shed any light as to what is it am I doing wrong and what I can do to have a logarithmic color axis in contour plots to compare the two lists.

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  • $\begingroup$ I would like to add that the solution presented here: link does work for this instance but the issue is that there are some lists I have whose maximum value is <1 in which case the logscalelegend function in the solution does not work anymore as it encounters an infinity. $\endgroup$
    – WaleeK
    Apr 20, 2020 at 15:06
  • $\begingroup$ Your first ListDensityPlot works with MMA11.1.10 and MMA11.2. Could you check your code again? In first case with empty plot the barlegend shows 2.0 to 5.0 not 0.1 to 5.0. $\endgroup$
    – Sumit
    Apr 20, 2020 at 15:45
  • $\begingroup$ Ah sorry, yes that works with ListDensityPlot, I mixed up the figures but it doesn't work with ListContourPlot. let me edit that and fix it $\endgroup$
    – WaleeK
    Apr 20, 2020 at 15:55

1 Answer 1

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How about scaling your data.

ListContourPlot[list1 /. {x_, y_, z_} -> {x, y, Log10[z]}, 
   ColorFunction -> MPLColorMap["Viridis"], 
   PlotLegends ->BarLegend[{MPLColorMap["Viridis"], {min, max}}, 
   LabelStyle -> Directive[Black], LegendMarkerSize -> 350]]

plot

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  • $\begingroup$ If I do that, the legend will be scaled accordingly as well for any list I use? Because from here it is not clear that the color scales are in log scale. So I have to scale the barlegend accordingly to make it clear, no? $\endgroup$
    – WaleeK
    Apr 21, 2020 at 14:41
  • $\begingroup$ I would put LegendLabel -> "Log(z)" to denote that. If you rescale the colour in BarLegend you will see mostly yellow and very little of others - that would not give much information. Or you can put some custom Ticks on the legend but that might need some extra work. $\endgroup$
    – Sumit
    Apr 21, 2020 at 15:21
  • $\begingroup$ Yea I can understand, because to put in the extra ticks on the legend I will be in the same boat as the one I was before in the link I mentioned in the comment to my question. Thanks $\endgroup$
    – WaleeK
    Apr 21, 2020 at 15:34

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