Changing the tick labels in a BarLegend

Question

In the following plot, the colors mean the phase, so I need to label the color bar not in integers, but in increments of $\pi$. I searched, but could not find how to change the ticks. Does anyone have an idea?

ListDensityPlot[
    Table[ArcTan[Cos[x + y], Sin[x + y]], {x, 0, 10, 0.01}, {y, 0, 1.2, 0.01}], 
    DataRange -> {{0, 10}, {0, 1.2}}, PlotLegends -> Automatic, ColorFunction -> Hue]

Answer 1

I consider myself an amateur. I was also interested in this question, and I found the following code solves the problem. However, the command that solves the problem ("Ticks") shows up highlighted in red. You can change many of the features of the legend, like size, add a label, etc.

Legended[
  ListDensityPlot[Table[ArcTan[Cos[x + y], Sin[x + y]], 
    {x, 0, 10, 0.01}, {y, 0, 1.2, 0.01}], 
    DataRange -> {{0, 10}, {0, 1.2}}, 
    ColorFunction -> Hue
   ],
  BarLegend[
    {Hue, {-Pi, Pi}},
    Ticks -> Table[i, {i, -Pi, Pi, Pi/4}],
    LegendMarkerSize -> 300
   ]
 ]

Answer 2

I wonder whether you would be content with a simpler SwatchLegend:

ListDensityPlot[
 Table[{2 Pi Sin[x], 2 Pi Cos[x]}, {x, 0, 2 Pi}],
 ColorFunction -> "BlueGreenYellow",
 ImageSize -> 500,
 PlotLegends -> 
  SwatchLegend[
   Table[
    Blend[{Blue, Green, Yellow}, Rescale[x, {0, 2 Pi}]], 
     {x, 0, 2 Pi, Pi/8}], 
   Range[0, 2 Pi, Pi/8],
   LegendMarkers -> Graphics[Rectangle[]],
   LegendMarkerSize -> 15,
   LegendLayout -> (Grid[Reverse[#]] &)]]

Answer 3

First, I'm not certain if your plot is correct. Notice that ListDensityPlot arranges successive rows of the array up the page, and successive columns across. The first iterator in the table creates the rows and the second iterator creates the columns. So if you want the normal x and y axis you have to reverse the iterators. On the other hand, DataRange coincides with what we normally call the x and y axis. The WRI examples are poor because they seem to all be symmetrical and thus don't illustrate this important issue. Here is a case where all the variation occurs in the x direction.

arrayTest = Table[x/10, {y, 0, 1.2, 0.01}, {x, 1, 10, 0.01}];
ListDensityPlot[arrayTest,
  DataRange -> {{0, 10}, {0, 1.2}},
  FrameLabel -> {"x", "y"},
  ColorFunction -> Hue,
  ImageSize -> 250]

I think that is what is intended. If I'm wrong about this please correct me.

In the sample plot, I would say: why have a legend at all? Why not just draw the constant ArcTan values on the plot and label them. In the following I use Tooltips, and also special labeling along the top x axis. (It would have been easier to reverse the top and bottom.) I also used pastel colors so the constant ArcTan lines would better show. Here is the plot using Show. (I have corrected the following so that it is entirely in regular Mathematica.)

array = Table[
   ArcTan[Cos[x + y], Sin[x + y]], {y, 0, 1.2, 0.01}, {x, 0, 10, 
    0.01}];

xticks = MapThread[{#1, #2} &, {Table[
     1/5 (-6 + 5 k \[Pi]), {k, 1, 3}], {-\[Pi], 0, \[Pi]}}];

Show[
 {ListDensityPlot[array, DataRange -> {{0, 10}, {0, 1.2}},
   ColorFunction -> (ColorData["Pastel"])],
  Table[Plot[
    Tooltip[ \[Pi] k - x , Mod[k \[Pi], 2 \[Pi], -\[Pi]]], {x, 0, 10},
     PlotRange -> {0, 1.2}], {k, 0, 3, 1/2}]},
 FrameLabel -> {"x", "y"},
 FrameTicks -> {{Automatic, Automatic}, {Automatic, xticks}},
 ImageSize -> 250]

Answer 4

http://reference.wolfram.com/mathematica/ref/Files/BarLegend.en/I_70.gif The code in the link as well as documentation of BarLegend may be helpful in customising bar legend. Look at Contours option.

I was overly optimistic, however,

ListDensityPlot[
 Table[ArcTan[Cos[x + y], Sin[x + y]], {x, 0, 10, 0.01}, {y, 0, 1.2, 
   0.01}], DataRange -> {{0, 10}, {0, 1.2}}, 
 PlotLegends -> 
  Placed[BarLegend[Automatic, {-2, -1, -0.5, 0, 0.5, 1, 2}, 
    LegendMarkerSize -> 250, 
    LegendFunction -> (Framed[#, RoundingRadius -> 5] &), 
    LegendLabel -> "z-value"], {After, Top}], ColorFunction -> Hue]

is partially successful. The ticks for -1, 1 are not displayed. The LabelStyle option does not work but perhaps this is a start.

EDIT

Manipulate[
 ListDensityPlot[
  Table[ArcTan[Cos[x + y], Sin[x + y]], {x, 0, 10, 0.01}, {y, 0, 1.2, 
    0.01}], DataRange -> {{0, 10}, {0, 1.2}}, 
  PlotLegends -> 
   Placed[BarLegend[Automatic, p, LegendMarkerSize -> 250], Bottom], 
  ColorFunction -> 
   Hue], {p, {{-2, -1, -0.5, 0, 0.5, 1, 2}, {-Pi/2, Pi/2}, {-1, 0, 
    1}, {-0.3, 0, 0.7}}}]

The above runs slowly on my old machine. However, illustrates the capacity to change tick labels with the caveat that sometimes not all specified contours are given a tick label. Further Dynamic@p does not work as a way to speed up processing. Note {-Pi/2,Pi/2} is presented at 3 decimal places.

An example snapshot follows.