Rescaling the counts for a DensityHistogram

Question

I have the following problem: I need to rescale the counts given to DensityHistogram, meaning that I want to multiply the total counts per bin by a certain number (4/3).

Consider the following example:

datatest = 
  {{0.15853231238493146`, 0.15958921935208797`}, 
   {0.16003302074891018`, 0.1666286356975967`}, 
   {0.15809478105039676`, 0.1682255807995838`}, 
   {0.15548049076146467`, 0.16773090763023435`}, 
   {0.15373202818516943`, 0.16951942019717853`}, 
   {0.15183606682822046`, 0.17098377258873423`}, 
   {0.14965773201820615`, 0.17326285096337588`}, 
   {0.14869661374136575`, 0.17472879297110966`}, 
   {0.17699943466842`, 0.14614660535485596`}}  

DensityHistogram[datatest, {0.01}, ChartLegends -> Automatic]

Because the total counts per bin for all bins would be multiplied with 4/3 and rounded afterwards, the bin in the upper left of this example would become 2.6666 and rounded to 3).

Does anyone have a solution for this? Manually changing the legend is not an option for me, since the legend would the look awkward.

My approach would be to manipulate the HistogramList:

rescalingfactor = 4/3;  
histogramlist1 = HistogramList[datatest, {0.01}];  
histogramlist1rescaled = 
  Join[histogramlist1[[1]], Round[histogramlist1[[2]]*rescalingfactor]]

{{0.14, 0.15, 0.16, 0.17, 0.18}, {0.14, 0.15, 0.16, 0.17, 0.18}, 
 {0, 0, 0, 3}, {0, 1, 4, 1}, {0, 0, 1, 0}, {1, 0, 0, 0}}

But how can I apply DensityHistogram to the results returned from HistogramList?

Answer 1

You can use the third argument (height spec) of DensityHistogram

DensityHistogram[datatest, {0.01}, Round[#3*rescalingfactor] &, 
 ChartLegends -> Automatic]

Note: how can I apply DensityHistogram to the results returned from HistogramList?

You can use Round[histogramlist1[[2]]*rescalingfactor] & instead of Round[#3*rescalingfactor] & to get the same result.