BarChart and ColorFunction

Question

There are really two questions. The first is: how does one get BarChart to generate x coordinates. That is, ListPlot takes a list of pairs, but BarChart takes a list of y-values only. Is there any way to impart x values to it?

Second question (which is related, because I am using BarChart so I can use ColorFunction) is: how do I invert ColorFunction. That is, "DarkRainbow" makes high values red, low values green. I want it exactly the other way around. What's the trick?

Answer 1

Reversing ColorFunction

To reverse "DarkRainbow" color scheme, you can use ColorData[{"DarkRainbow", "Reverse"}] (or ColorData[{"DarkRainbow", "Reversed"}]):

Row[{BarChart[{2, 1, 3, 4}, 
      ColorFunction ->"DarkRainbow", 
       PlotLabel ->Style[ "DarkRainbow",16], 
       ImageSize -> 300],
    BarChart[{2, 1, 3, 4}, 
       ColorFunction -> ColorData[{"DarkRainbow", "Reverse"}],
       PlotLabel ->Style[HoldForm @ ColorData[{"DarkRainbow", "Reverse"}], 16], 
       ImageSize -> 300]} , 
    Spacer[10]]

Adding horizontal coordinates

BarChart + custom ChartElementFunction

To add x-coordinates you can attach the desired coordinates to input data as metadata and use a custom ChartElementFunction to translate the bars according to the metadata associated with each bar:

data = {2, 1, 3, 4};
SeedRandom[7]
xcoords = Sort @ RandomSample[Range[20], 4]

{5, 11, 14, 18}

cEF = ChartElementData["Rectangle"][{#3[[1]] + 
  {-(#[[1, 2]] - #[[1, 1]])/2, (#[[1, 2]] - #[[1, 1]])/ 2}, #[[2]]}, ##2] &;

Show[BarChart[Thread[data -> xcoords], 
    ColorFunction -> "DarkRainbow", 
    ChartElementFunction -> cEF], 
    Axes -> False,
    Frame -> True]

BarChart + post-processing

An alternative way is to post-process the BarChart output to horizontally translate the rectangles by amounts given by xcoords:

bc = BarChart[data, ColorFunction -> "DarkRainbow", BarSpacing -> 0, Axes -> False];

Show[Module[{k = 1}, bc /. r : Rectangle[{a_, _}, {b_, _}, ___] :> 
    Translate[r, {xcoords[[k++]] - (a + b)/2, 0}]], 
 Frame -> True]

BarChart + pre-processing

We can also pre-process input data to inject non-numeric values between specified x coordinates:

heights = Normal @ SparseArray[Thread[xcoords -> data], 19, Null] ;

BarChart[heights,
  ColorFunction -> "DarkRainbow", ChartLabels -> Range[20], Frame->True]

Histogram + custom height function

heightf = Normal @ SparseArray[Thread[xcoords -> data], 19] ;

Histogram[{1}, {.5, 20, 1}, heightf&, 
  ColorFunction -> "DarkRainbow", Frame -> True]

Histogram + WeightedData

Using Histogram as suggested by Lukas in comments is much easier:

Histogram[WeightedData[xcoords, data], {-.5, 20, 1},
  ColorFunction -> "DarkRainbow", Frame -> True]