Several ListDensityPlots with the same limits of ColorFunction

Question

I have to sample and plot three functions: $f(x,y)=cos(\pi x /2)$, $g(x,y)=2-x^2$ and $r(x,y)=3x$ in the range x and y in [-1;1].

I want to make their density plots with a single ColorFunction to be applied to all: $0<=f(x,y)<=1$, $1<=g(x,y)<=2$, $-3<=r(x,y)<=3$.

All three density plots should be displayed with BarLegend scaled to [-1,1] with natural clipping. I have tried to do this in the following way:

F = Table[Cos[k*(Pi/2)], {j, -1.0, 1.0, 0.01}, {k, -1.0, 1.0, 0.01}];
G = Table[2 - k*k, {j, -1.0, 1.0, 0.01}, {k, -1.0, 1.0, 0.01}];
R = Table[3.0*k, {j, -1.0, 1.0, 0.01}, {k, -1.0, 1.0, 0.01}];

ListDensityPlot[F, ColorFunction -> "BlueGreenYellow", 
 PlotLegends -> Placed[BarLegend[{Automatic, {-1, 1}}], After], 
 FrameLabel -> {{"x", None}, {"y", None}}, ClippingStyle -> Automatic]

ListDensityPlot[G, ColorFunction -> "BlueGreenYellow", 
 PlotLegends -> Placed[BarLegend[{Automatic, {-1, 1}}], After], 
 FrameLabel -> {{"x", None}, {"y", None}}, ClippingStyle -> Automatic]

ListDensityPlot[R, ColorFunction -> "BlueGreenYellow", 
 PlotLegends -> Placed[BarLegend[{Automatic, {-1, 1}}], After], 
 FrameLabel -> {{"x", None}, {"y", None}}, ClippingStyle -> Automatic]

But this affects only legend bars and does not affect the color functions of plots. How can I reach the result I need?

Answer 1

Clear["Global`*"]

F = Table[Cos[k*(Pi/2)], {j, -1., 1., 0.01}, {k, -1.0, 1.0, 0.01}];
G = Table[2 - k*k, {j, -1.0, 1.0, 0.01}, {k, -1.0, 1.0, 0.01}];
R = Table[3.0*k, {j, -1.0, 1.0, 0.01}, {k, -1.0, 1.0, 0.01}];

{min, max} = {-3, 3};

If they are all on the same scale, the common scale would be {-3, 3}. In this case, two of the plots would have reduced range.

Legended[Row[
  ListDensityPlot[ToExpression@#, 
     ColorFunction -> (ColorData["BlueGreenYellow"]
         [1 - (max - #)/(max - min)] &),
     ColorFunctionScaling -> False,
     FrameLabel -> {{"x", None}, {"y", None}},
     PlotLabel -> #,
     ImageSize -> Small] & /@
   {"F", "G", "R"}],
 Placed[
  BarLegend[{"BlueGreenYellow", {min, max}},
   LegendLayout -> "Row"],
  Below]]

If the intent is to clip the function values to {-1, 1}, then use the function Clip rather than the ClippingStyle option. However, G is then just 1

EDIT: Corrected ColorFunction and ColorFunctionScaling

Legended[
 Row[
  ListDensityPlot[
     Clip[ToExpression@#],
     ColorFunction -> 
      (ColorData["BlueGreenYellow"][(# + 1)/2] &),
     ColorFunctionScaling -> False,
     FrameLabel -> {{"x", None}, {"y", None}},
     PlotLabel -> #,
     ImageSize -> Small] & /@
   {"F", "G", "R"}],
 Placed[
  BarLegend[{"BlueGreenYellow", {-1, 1}},
   LegendLayout -> "Row"],
  Below]]