Customizing BarLegend for Missing[ ] data

Question

My apologies if something similar has been asked, I could not find a question on the same issue. I have created the following colour map (heat map) using a toy sample with RandomReal.

s = RandomReal[{-1, 1}, {80, 50}];

ListDensityPlot[s, Mesh -> Automatic, Mesh -> All, 
  ColorFunction -> "Rainbow", FrameLabel -> {Number, Year}, 
  FrameTicks -> {{{{0, "Y1"}, {20, "Y2"}, {40, "Y3"}, {60, "Y4"}, {80,
        "Y5"}}, 
     None}, {{{1, "One"}, {10, "Two"}, {20, "Three"}, {30, 
       "Four"}, {40, "Five"}, {50, "Six"}}, None}}, 
  PlotLabel -> "Heat Map", PlotLegends -> Automatic, 
  PlotRange -> {-1, 1}] /. 
 x : (FrameTicks -> _) :> (x /. s_String :> Rotate[s, 45 Degree])

However, I may have missing observations on the map. If I fill the gaps with 0,they will appear green. If they are left balnk, the spaces will look white. Is it possible to set all values equal to 0 being coloured with something that is not in the palette (legend), e.g. black or grey?

The issue is one of presentation, since with my actual data a part of the map is missing and I would like to see if it having white or a different colour would make it look better.

On a side note, if you have a better colour palette or idea on how to visualise more-or-less random looking data, please be my guest.

Answer 1

A data set with missing observations:

SeedRandom[1];
s = Map[If[Abs[#] < 10^-1, Missing[], #] &, RandomReal[{-1, 1}, {80, 50}], {-1}];

Update:

In general, since non-numeric / missing data do not lie in the numeric range of plotted values, a more accurate legend would be a combination of BarLegend showing numerical values depicted in the plot and a seperate legend showing the color used for rendering non-numeric/missing values.

A simple way to achieve this is to combine a BarLegend with a SwatchLegend showing the label and color used to render missing/non-numeric values:

ListDensityPlot[s, Mesh -> Automatic, PlotRange -> {-1, 1}, 
 ColorFunction -> "Rainbow", 
 PlotLegends -> Column[
   {BarLegend["Rainbow", Frame -> False, LegendMargins -> 0], 
    SwatchLegend[{White}, {"Missing[]"}, LegendMarkerSize -> 14]}]]

The custom legend barLegendWithMissingValues below adds a rectangle with desired color/label/size for missing values below a regular BarLegend:

ClearAll[barLegendWithMissingValues]

barLegendWithMissingValues[label_ : Automatic, color_ : Automatic,  
   size_ : 30, gap_ : 3, offset_ : 10] := 
 Module[{coord = First@Cases[ToBoxes@#, RasterBox[_, a_, ___] :> First@a, All]},
   With[{txt = {label /. Automatic -> "Missing[]" /. Style -> StyleBox, 
        Offset[{offset, 0}, coord {-1, 1} - {0, gap + size/2}], Left},
     clr = color /. Automatic -> LightGray,
     rct = {#, # {-1, 1} + {0, size}} &@(coord - {0, size + gap}),
     ef = EdgeForm[Directive[AbsoluteThickness[.5], RGBColor[.5, .5, .5]]]},
    RawBoxes @ Replace[ToBoxes @ #,
      {a___, r_RasterBox, b___} :> RuleCondition @
        {a, r, InsetBox @@ txt, clr, ef, RectangleBox @@ rct, b}, All]]] &

Examples:

Row[{barLegendWithMissingValues[] @ BarLegend["Rainbow"],
  barLegendWithMissingValues[Style["NaN", 12], Brown, 50, 5]@
     BarLegend["Rainbow", LabelStyle -> 14],
  barLegendWithMissingValues[Style["NaN", 12], Black, 40, 15]@
     BarLegend[{"TemperatureMap", {-5, 15}}, LabelStyle -> 14, 
       LegendMarkerSize -> {90, 300}]}, Spacer[30]]

ReplaceAll[b_BarLegend :> barLegendWithMissingValues[Automatic, White]@b]@
 ListDensityPlot[s, Mesh -> Automatic, PlotRange -> {-1, 1}, 
  ColorFunction -> "Rainbow", PlotLegends -> Automatic]

ReplaceAll[b_BarLegend :> barLegendWithMissingValues[] @ b] @
 ListDensityPlot[s, Mesh -> Automatic, PlotRange -> {-1, 1}, 
  ColorFunction -> "Rainbow", BoundaryStyle -> White, 
  Prolog -> {LightGray, Rectangle[Scaled[{0, 0}], Scaled[{1, 1}]]}, 
  PlotLegends -> Automatic]

Original answer:

ListDensityPlot excludes (renders as White) areas where data is non-real. So we need to modify the BarLegend to show the color used for excluded areas. This can be done using the (undocumented) option StyledContours (or "StyledContours") and adding the associated tick label using the (also undocumented) option Ticks ("Ticks" also works) in BarLegend:

ListDensityPlot[s, Mesh -> Automatic, PlotRange -> {-1, 1}, 
 ColorFunction -> "Rainbow", 
 PlotLegends -> BarLegend[Automatic, 
   StyledContours -> {{0, Directive[Thick, White]}}, 
   Ticks -> (Range[-1, 1, .5] /. 0. -> {0, Missing[]})]]

We can set the color of excluded areas using Prolog and use the same color for styled contours in BarLegend:

ListDensityPlot[s, Mesh -> Automatic, PlotRange -> {-1, 1}, 
 ColorFunction -> "Rainbow",
 BoundaryStyle -> White, 
 Prolog -> {LightGray, Rectangle[Scaled[{0, 0}], Scaled[{1, 1}]]}, 
 PlotLegends ->  BarLegend[Automatic, 
    "StyledContours" -> {{0, Directive[AbsoluteThickness[5], LightGray]}}, 
    "Ticks" -> (Range[-1, 1, .5] /. 0. -> {0, Missing[]})]]

Answer 2

SeedRandom[1];
s = RandomReal[{-1, 1}, {80, 50}];
Clear[cf]
cf[x_] := Blend[ReplacePart[
    ColorData["Rainbow"][#] & /@ Range[0, 1, 1/30]
    , {{15}, {16}, {17}} -> White
    ]
   , x
   ];

ListDensityPlot[s
  , Mesh -> Automatic
  , ColorFunction -> cf
  , FrameLabel -> {Number, "Year"}, 
  FrameTicks -> {{{{0, "Y1"}, {20, "Y2"}, {40, "Y3"}, {60, "Y4"}, {80,
        "Y5"}}, 
     None}, {{{1, "One"}, {10, "Two"}, {20, "Three"}, {30, 
       "Four"}, {40, "Five"}, {50, "Six"}}, None}}, 
  PlotLabel -> "Heat Map"
  , PlotLegends -> Placed[BarLegend[Automatic], After]
  , PlotRange -> {-1, 1}] /. 
 x : (FrameTicks -> _) :> (x /. s_String :> Rotate[s, 45 Degree])

---

EDIT

It is difficult to visually verify results with random numbers, so the following example is included.

data = Flatten[#, 1] &@
  Table[{x, y, Sin[x] Sin[y]}, {x, 0, 2 \[Pi], 0.1}, {y, 0, 2 \[Pi], 
    0.1}]

GraphicsRow[
 ListDensityPlot[data, PlotRange -> All, ColorFunction -> #, 
    PlotLegends -> {BarLegend[Automatic, LegendMarkerSize -> 180]}
    , ColorFunctionScaling -> True
    ] & /@ {"Rainbow", cf}
 ]