Create stacked histograms?

claudemante · November 25, 2016, 2:58pm

I have to compare histogram of rational numbers, associated each time with 3 dataset and, sometimes, one of these datasets is empty.

Example: consider

Data = {{3/194, 1/194, 1/194, 1/194, 2/97, 3/194, 1/194, 2/97, 9/194, 
    1/97, 1/194, 7/194, 1/194, 1/97, 2/97, 3/194, 2/97, 1/194, 2/97, 
    1/194, 1/194, 1/194, 2/97, 1/194, 4/97, 4/97, 1/194, 3/194, 1/194,
     3/194, 2/97, 1/194, 1/97, 1/194, 4/97, 7/194, 1/194, 1/194, 2/97,
     5/194, 1/97, 1/194, 1/194, 5/194, 3/194, 1/97, 5/194, 3/194, 
    1/194, 1/194, 1/97, 3/194, 3/194, 1/97, 3/194, 1/194, 2/97, 1/97, 
    1/97, 3/194, 1/97, 1/97, 3/194, 1/194, 1/194, 2/97, 1/97, 1/97, 
    3/194, 2/97, 1/97, 5/194, 3/194, 3/194, 1/194, 3/194, 1/97, 3/194,
     1/97, 1/194, 2/97, 1/97, 1/97, 2/97, 1/97, 1/97, 1/97, 1/194, 
    1/97, 1/194, 1/194, 5/194, 5/194, 1/97, 1/194, 1/194, 1/97, 3/194,
     5/194, 1/194, 3/194, 1/194, 3/194, 1/194, 2/97, 1/194, 3/194, 
    3/194, 1/194, 1/97, 1/194, 1/194, 1/97, 3/194, 3/194, 3/97, 1/194,
     3/194, 2/97, 1/194, 5/194, 1/194, 1/97, 3/194, 2/97, 1/194, 
    3/194, 5/194, 1/97, 2/97, 1/97, 2/97, 2/97, 5/194, 1/194, 1/194, 
    1/194, 1/97, 5/194, 2/97, 3/194, 1/194, 2/97, 1/194, 3/97, 2/97, 
    1/194, 1/194, 1/97, 2/97, 3/194, 1/194, 1/97, 1/194, 1/194, 1/97, 
    3/194, 1/194, 1/194, 1/194, 2/97, 1/194, 1/194, 2/97, 1/194, 
    1/194, 2/97, 3/194, 2/97, 3/194, 2/97, 1/194, 1/97, 1/194, 1/194, 
    3/194, 1/97, 1/194, 3/194, 1/194, 3/194, 1/97, 1/194, 3/194, 
    1/194, 1/194, 1/194, 1/194, 5/194, 1/97, 2/97, 1/97, 1/194, 2/97, 
    2/97, 1/194, 1/97, 1/194, 2/97, 5/194, 1/194, 1/97, 1/194, 1/194, 
    1/97, 2/97, 1/194, 1/97, 1/194, 2/97, 3/194, 5/194, 1/194, 2/97, 
    1/194, 2/97, 1/194, 1/194, 2/97, 3/194, 1/97, 1/194, 1/97, 1/97, 
    5/194, 3/194, 3/194, 3/194, 1/194, 1/194, 1/97, 1/97, 3/194, 2/97,
     1/97, 1/97, 3/194, 1/97, 1/97, 1/97, 1/194, 2/97, 1/194, 1/97, 
    1/194, 1/97, 1/194}, {1/97, 1/97}, {1/97, 3/194, 3/194, 1/194, 
    1/97, 1/97, 3/194, 3/194, 1/194, 3/194, 1/97, 1/194, 1/194, 1/97, 
    1/194, 1/194, 1/194, 1/194, 3/194, 1/97, 1/194, 1/194, 1/97, 
    1/194, 1/194, 1/194, 1/194, 1/97, 1/97, 1/194, 1/97, 5/194, 1/194,
     1/97, 1/194, 1/97, 1/97, 1/194, 3/194, 3/194, 1/194, 1/194, 1/97,
     1/97, 3/194, 1/97, 1/97, 3/97, 1/97, 2/97, 1/97, 3/194, 1/97, 
    3/97, 3/194, 1/194, 1/194, 1/97, 3/97, 5/194, 1/97, 3/194, 1/194, 
    1/194, 1/97, 1/97, 1/97, 1/97, 1/97, 1/194, 3/194, 1/194, 1/194, 
    5/194, 1/194, 2/97, 3/194, 1/194, 1/97, 1/194, 3/194, 1/194, 
    1/194, 1/97, 3/194, 1/194, 7/194, 1/97, 3/194, 3/194, 2/97, 1/97, 
    1/97, 1/194, 2/97, 1/194, 2/97, 1/97, 3/97, 1/97, 1/97, 1/194, 
    1/97, 3/194, 5/194, 5/194, 1/194, 3/194, 1/97, 1/194, 3/97, 1/97, 
    1/194, 2/97, 5/97, 1/194, 1/194, 2/97, 3/97, 1/194, 1/97, 4/97, 
    1/194, 4/97, 1/97, 1/194, 2/97, 1/194, 1/194, 1/194, 3/194, 1/194,
     1/194, 1/97, 1/194, 1/194, 1/97, 3/194, 1/194, 1/194, 5/194, 
    3/97, 3/194, 2/97, 1/194, 1/97, 1/97, 3/194, 3/194, 3/194, 1/97, 
    1/97, 1/97, 1/194, 1/194, 1/194, 1/97, 3/194, 1/97, 2/97, 3/194, 
    1/194, 5/194, 1/97, 2/97, 1/97, 1/97, 1/97, 3/194, 2/97, 1/97, 
    1/97, 4/97, 1/97, 1/194, 2/97, 1/97, 1/97, 3/194, 3/194, 2/97, 
    1/97, 1/194, 3/194, 2/97, 1/97, 1/97, 3/194, 1/194, 5/194, 1/97, 
    3/194, 1/194, 1/194, 1/194, 2/97, 1/194, 1/97, 1/97, 3/194, 1/97, 
    1/97, 1/97, 3/194, 7/194, 1/97, 3/194, 3/194, 1/194, 1/194, 2/97, 
    1/97, 1/194, 1/97, 1/194, 2/97, 1/97, 3/194, 3/194, 11/194, 5/194,
     1/194, 3/194, 3/97, 1/194, 1/194, 2/97, 1/194, 3/194, 1/97, 
    3/194, 1/97, 1/194, 2/97, 1/194, 3/194, 1/97, 1/97, 1/194, 1/194, 
    1/194, 1/97, 3/194, 3/194, 1/194, 1/97, 1/97, 1/97, 3/194, 3/194, 
    1/97, 1/194, 3/194, 1/194, 3/194, 1/97, 1/194, 1/194, 1/97, 1/194,
     3/194, 1/194, 1/194, 1/97, 1/97, 1/194, 1/97, 3/194, 2/97, 1/97, 
    3/194, 1/194, 1/97, 2/97, 1/194, 3/194, 1/97, 2/97, 5/194, 1/194, 
    1/97, 1/97, 1/97, 1/194, 1/194, 3/194, 2/97, 1/97, 1/194, 1/97, 
    1/194, 1/194, 2/97, 2/97, 1/194, 1/194, 5/194}};
Masques = {"Matrice", "Résine", "Revetement"};
h = 1/194;

Then, build 2 lists, with an empty member:

artificial1 = {First@Data, Last@Data, {}};
artificial2 = {First@Data, {}, Last@Data};

and plot these histograms:

Histogram[Data, {h}, "Probability", 
 ChartLegends -> Placed[Masques, Above] , 
 ChartStyle -> {Red, Green, Blue, Yellow}, ChartLayout -> "Stacked", 
 ImageSize -> Medium]
Histogram[artificial1, {h}, "Probability", 
 ChartLegends -> Placed[Masques, Above] , 
 ChartStyle -> {Red, Green, Blue, Yellow}, ChartLayout -> "Stacked", 
 ImageSize -> Medium]

As it was requested, they are stacked. But the third one, with an intermediate empty list, is not stacked!

Histogram[artificial2, {h}, "Probability", 
 ChartLegends -> Placed[Masques, Above] , 
 ChartStyle -> {Red, Green, Blue, Yellow}, ChartLayout -> "Stacked", 
 ImageSize -> Medium]

Is it a bug, or did I made a mistake somewhere?

Best regards, Claude

jbaldwin · November 27, 2016, 2:17am

I don’t see any mistake or the rationale for how Mathematica is choosing the colors when one of the rows of data is empty. I also think that stacked histograms and stacked barcharts should be a criminal offense especially when the “Probability” option is chosen. However, here’s a way to achieve a consistent color scheme automatically.

Masques = {"Matrice", "Résine", "Revetement"};
h = 1/194;
artificial1 = {Data[[1]], Data[[2]], {}};
artificial2 = {Data[[1]], {}, Data[[3]]};
colors = {Red, Green, Blue};

keep = (Length[#] > 0 &) /@ Data;
Histogram[Pick[Data, keep], {h}, "Probability", 
 ChartLegends -> Placed[Masques, Above], 
 ChartStyle -> Pick[colors, keep], ChartLayout -> "Stacked", 
 ImageSize -> Medium]

keep = (Length[#] > 0 &) /@ artificial1;
Histogram[Pick[artificial1, keep], {h}, "Probability", 
 ChartLegends -> Placed[Pick[Masques, keep], Above], 
 ChartStyle -> Pick[colors, keep], ChartLayout -> "Stacked", 
 ImageSize -> Medium]

keep = (Length[#] > 0 &) /@ artificial2; Histogram[
 Pick[artificial2, keep], {h}, "Probability", 
 ChartLegends -> Placed[Pick[Masques, keep], Above], 
 ChartStyle -> Pick[colors, keep], ChartLayout -> "Stacked", 
 ImageSize -> Medium]

Note that I’ve changed the definition of artificial1 so that the relative bar sizes can be compared across the figures to be more convincing.

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Create stacked histograms?

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