Can not specify PlotRange for DensityHistogram[] with Method DistributionAxes

Question

I have a problem specifying the PlotRange for the DensityHistogram plot if Method ->{DistributionAxes ->"Histogram"} is given.

The behaviour I would like to see is the following:

DensityHistogram[
 Partition[
  Riffle[RandomReal[NormalDistribution[0, 1], 1000], 
   RandomReal[NormalDistribution[0, 1], 1000]], 2], {{1}, {1}}, 
 Method -> {"DistributionAxes" -> "Histogram"}, 
 PlotRange -> {{0, 4}, {0, 4}}]

But if I change the range of the input data the behaviour does change in an unexpected way (at least for me) as there is some white space added at the y-axis.

DensityHistogram[
 Partition[
  Riffle[RandomReal[NormalDistribution[0, 100], 1000], 
   RandomReal[NormalDistribution[0, 1], 1000]], 2], {{1}, {1}}, 
 Method -> {"DistributionAxes" -> "Histogram"}, 
 PlotRange -> Automatic]

Even stranger the plot does not adhere the PlotRange anymore if it is explicitly given.

DensityHistogram[
 Partition[
  Riffle[RandomReal[NormalDistribution[0, 100], 1000], 
   RandomReal[NormalDistribution[0, 1], 1000]], 2], {{1}, {1}}, 
 Method -> {"DistributionAxes" -> "Histogram"}, 
 PlotRange -> {{0, 200}, {0, 5}}]

Does anybody have an idea what is happening and maybe how to workaround? (I am on Mathematica 10.4)

Answer 1

Feyre proposed to use Show[] to fix the output of DensityHistogram[]. PlotRange together with PlotRangePadding will then do the job.

As DensityHistogram[] was planed to be used in an automated script, tuning PlotRange and PlotRangePadding by hand is not possible.

I wrote a small function which does the fixing by extracting the relevant information from a plot as explained by tomd1. This fixes my problem but I am not sure how reliable this is (good enough for me). It will work if the original PlotRange was specified as Automatic. Further I suspect that specifying an Inset[] will break this function. I doubt also that the Automatic definition of the lower bound of PlotRange will work in all cases.

CorrectPlotRange[PlotData_] := Module[{SideHist, Result, SizeX, SizeY, PointData, RangeX, RangeY},

  SideHist = Cases[InputForm[PlotData] , Inset[___], Infinity];
  SizeX = SideHist[[1, 4, 2]]*1.5;
  SizeY = SideHist[[2, 4, 1]]*1.5;
  PointData = Cases[Cases[InputForm[PlotData], RectangleBox[___], Infinity], {_?NumericQ, _?NumericQ}, Infinity];
  RangeX = MinMax@PointData[[All, 1]];
  RangeY = MinMax@PointData[[All, 2]];

  Result = Show[
    PlotData,
    PlotRange -> {{Automatic, RangeX[[2]]}, {Automatic, RangeY[[2]]}},
    PlotRangePadding -> {{SizeY, Scaled[0.01]}, {SizeX, Scaled[0.01]}}

  ];
  (*{Result,SizeX,SizeY,RangeX,RangeY}*)
  Result
];

DensityHistogram[
 Partition[Riffle[RandomReal[NormalDistribution[0, 1000], 1000],RandomReal[NormalDistribution[0, 1], 1000]], 2], 
 {{1}, {2}}, 
 Method -> {"DistributionAxes" -> "Histogram"}, 
 PlotRange -> Automatic]
CorrectPlotRange[%]

This will fix the output of DensityHistogram[] but I am still curious what the actual problem is.