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plotting - How to plot paired smooth histogram/distribution plots?



I've been trying to get paired distribution (aka "violin") plots like those shown below for a few hours, but all my attempts have failed.


enter image description here


The key features here are



  1. paired smooth histograms/distribution plots with a common vertical abscissa and divergent horizontal ordinates;

  2. different fill colors for the two subplots;


The closest Mathematica has are DistributionCharts, but these plots are not paired (i.e. they are always symmetrical).



I first tried SmoothHistogram, but it appears that there's no simple way to get a SmoothHistogram with a vertical abscissa.



Next I tried PairedSmoothHistogram, but I can't manage to assign different fill colors to the two sides.


BlockRandom[SeedRandom[0];
 Quiet[
  PairedSmoothHistogram[
   RandomVariate[NormalDistribution[], 100]
   , RandomVariate[NormalDistribution[], 100]
   , AspectRatio -> Automatic
   , Axes -> {False, True}
   , Ticks -> None
   , Spacings -> 0

   , ImageSize -> 30
   , Filling -> Axis
   ]
  , OptionValue::nodef
  ]
 ]


Mathematica graphics




Then I tried a combination of SmoothKernelDistribution and either ListPlot, ParametricPlot or ContourPlot, but this won't work because neither ParametricPlot nor ContourPlot accepts a Fill option, and I can't figure out how to get ListPlot to fill the spaces between the curves and the vertical axis.


For example,


violin[data1_, data2_, rest___] := Module[
  {  d1 = SmoothKernelDistribution[data1]
   , d2 = SmoothKernelDistribution[data2]
   , x
   , xrange
  }, xrange = {x, Sequence @@ (#[data1, data2] & /@ {Min, Max})}
   ; ParametricPlot[ {{-PDF[d1, x], x}, {PDF[d2, x], x}}
                   , Evaluate@xrange

                   , rest
                   , PlotRange -> All
                   , Axes -> {None, True}
                   , Ticks -> None
                   , PlotRangePadding -> {Automatic, None}
                   ]
];

BlockRandom[SeedRandom[0];
 violin[RandomVariate[NormalDistribution[], 100],

        RandomVariate[NormalDistribution[], 100],
        ImageSize -> 30
       ]
]


Mathematica graphics




I didn't expect this would be so hard. My brain is now fried.



Does anyone know how one does this?



Answer



Here is something using a custom ChartElementFunction


Module[{c = 0},
 half[{{xmin_, xmax_}, {ymin_, ymax_}}, data_, metadata_] := (c++;   
   Map[Reverse[({0, Mean[{xmin, xmax}]} + # {1, (-1)^c})] &, 
    First@Cases[
      First@Cases[InputForm[SmoothHistogram[data, Filling -> Axis]], 
        gc_GraphicsComplex :> Normal[gc], ∞], 
      p_Polygon, ∞], {2}])]


(thanks to @halirutan for reminding me about how to do closures in WL).


data = RandomVariate[NormalDistribution[0, 1], {4, 2, 100}];

DistributionChart[data, BarSpacing -> -1, ChartElementFunction -> half]

Mathematica graphics


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