Skip to main content

plotting - Control parameters of different styles of DistributionChart


Using DistributionChart, you can choose among several styles aka ChartElementFunction:


ChartElementData["DistributionChart"]

{"Density", "DensityQuantile", "FadingQuantile",
 "GlassQuantile", "HistogramDensity", "LineDensity", "PointDensity", 
 "Quantile", "SmoothDensity"}

Is there a way to control their parameters? The documentation does not seem to say.




The problem is that the defaults are less than optimal for my data. Consider these:


Using SmoothDensity:


SmoothDensity


Using HistogramDensity:


HistogramDensity


Using LineDensity:


<code>LineDensity</code>


Clearly, SmoothDensity grossly misrepresents the data (just compare with the LineDensity version); the violins should all look like the ones for 2 and 9. HistogramDensity does a better job but its resolution is horrible; there are 100 data points per size, about 70 of which fall into the upper class -- that should be plenty of points to draw more bars.


I would like to tell HistogramDensity to use more/smaller bins, and/or SmoothDensity to smooth less. How is this possible?



Answer




To get the options available for various ChartElementDataFunctions you can use:


 {#, Column[ChartElementData[#, "Options"]]} & /@ 
   ChartElementData["DistributionChart"] // Grid[#, Frame -> All] &

enter image description here



For "HistogramDensity", any bin specification accepted by Histogram > MoreInformation can be used as the setting for the suboption "Bins":



enter image description here




data = Table[RandomVariate[NormalDistribution[RandomInteger[5], 1], 100], {3}];

Partition[Table[DistributionChart[data, ChartStyle -> "SolarColors",
ChartElementFunction -> (ChartElementDataFunction["HistogramDensity", "Bins" -> i]),
PlotLabel -> Row[{"\"Bins\"", "->", ToString@i}], ImageSize -> 200],
{i, {10, 5, {.3}, {0, 8, .5}, {{0, 1, 2, 5, 6, 8}},
 Automatic, "Sturges", "Scott", "FreedmanDiaconis", "Knuth", 
 "Wand", "Log",
 {"Log", "Sturges"}, {"Log", "Scott"}, {"Log", 
  "FreedmanDiaconis"}, {"Log", "Knuth"}}}], 4] //

Grid[#, Frame -> All, Spacings -> 5] &

enter image description here


... including custom bin specifications like


binFunc1 = Union[IntegerPart[#]] &;
binFunc2 = Quantile[#, {0, .05, .1, .25, .5, .75, .9, .95, 1.}] &;
binFunc3 = First[HistogramList[#, "FreedmanDiaconis"]] &;
binFunc4 = Sort@#[[RandomSample[Range@Length@#, 10]]] &;

Partition[Table[DistributionChart[data, ChartStyle -> "Rainbow",

 ChartElementFunction -> (ChartElementDataFunction[
   "HistogramDensity", "Bins" -> i]),
 PlotLabel -> Row[{"\"Bins\"", "->\n", ToString@i}], 
 ImageSize -> 300],
 {i, {binFunc1, binFunc2, binFunc3, binFunc4}}], 2] //
 Grid[#, Frame -> All, Spacings -> 5] &

enter image description here



For "Quantile", "FadingQuantile", "GlassQuantile" and "DensityQuantile", the settings for suboption "Quantile" can be either an integer n (short for the n-1 quantiles 100 i/n (i = 1, ... , n-1) or an explicit list of integers between 0 and 100. Furthermore, each of the explicitly specified quantiles can be styled individually using the suboption "QuantileStyle".



Partition[Table[DistributionChart[data, 
ChartElementFunction -> (ChartElementDataFunction["GlassQuantile",
   "Quantile" -> i,
   "QuantileStyle" -> (Directive[Thick, Hue[#/100]] & /@ i),
   "QuantileShading" -> True]),
PlotLabel -> Row[{"Quantiles:  ", ToString@i}], ImageSize -> 300],
{i, {4, {25, 50, 75}, {10, 90}, {5, 10, 25, 50, 75, 90, 95}}}], 2] //
Grid[#, Frame -> All, Spacings -> 5] &

enter image description here




The option setting for "Threshold" seems to control symmetric trimming at the two tails as the following examples suggest. (Perhaps, further fishing may reveal that it accepts additional values to control the bandwidths)


Row@Table[DistributionChart[data, 
 ChartElementFunction -> (ChartElementDataFunction["SmoothDensity", 
  "ColorScheme" -> "DeepSeaColors", "Threshold" -> i]), 
 ImageSize -> 300], {i, {.05, .1, .5}}]

enter image description here


Row@Table[DistributionChart[data, ChartStyle -> "SolarColors", 
 ChartElementFunction -> (ChartElementDataFunction["Density", "Threshold" -> i]),

 ImageSize -> 300], {i, {.05, .1, .5}}]

enter image description here


Comments

Post a Comment

Popular posts from this blog

mathematical optimization - Minimizing using indices, error: Part::pkspec1: The expression cannot be used as a part specification

I want to use Minimize where the variables to minimize are indices pointing into an array. Here a MWE that hopefully shows what my problem is. vars = u@# & /@ Range[3]; cons = Flatten@ { Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; Minimize[{Total@((vec1[[#]] - vec2[[u[#]]])^2 & /@ Range[1, 3]), cons}, vars, Integers] The error I get: Part::pkspec1: The expression u[1] cannot be used as a part specification. >> Answer Ok, it seems that one can get around Mathematica trying to evaluate vec2[[u[1]]] too early by using the function Indexed[vec2,u[1]] . The working MWE would then look like the following: vars = u@# & /@ Range[3]; cons = Flatten@{ Table[(u[j] != #) & /@ vars[[j + 1 ;; -1]], {j, 1, 3 - 1}], 1 vec1 = {1, 2, 3}; vec2 = {1, 2, 3}; NMinimize[ {Total@((vec1[[#]] - Indexed[vec2, u[#]])^2 & /@ R...
Post a Comment
Read more

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

What is and isn't a valid variable specification for Manipulate?

I have an expression whose terms have arguments (representing subscripts), like this: myExpr = A[0] + V[1,T] I would like to put it inside a Manipulate to see its value as I move around the parameters. (The goal is eventually to plot it wrt one of the variables inside.) However, Mathematica complains when I set V[1,T] as a manipulated variable: Manipulate[Evaluate[myExpr], {A[0], 0, 1}, {V[1, T], 0, 1}] (*Manipulate::vsform: Manipulate argument {V[1,T],0,1} does not have the correct form for a variable specification. >> *) As a workaround, if I get rid of the symbol T inside the argument, it works fine: Manipulate[ Evaluate[myExpr /. T -> 15], {A[0], 0, 1}, {V[1, 15], 0, 1}] Why this behavior? Can anyone point me to the documentation that says what counts as a valid variable? And is there a way to get Manpiulate to accept an expression with a symbolic argument as a variable? Investigations I've done so far: I tried using variableQ from this answer , but it says V[1...
Post a Comment
Read more