How can I create a legend for a Heat Map when I don't want to show the full range of colors?

Question

I produce a heat map with legend with the code shown below

Needs["PlotLegends`"]

mydata = Table[2 + Sin[x y/5.], {x, -10, 10}, {y, -10, 10}];

ShowLegend[
   MatrixPlot[mydata, 
       Mesh -> True, ColorFunction -> "TemperatureMap",
       FrameTicks -> None, MeshStyle -> Thin, 
       FrameStyle -> AbsoluteThickness[0], 
       PlotRangePadding -> 0.0
   ], 
  {ColorData["TemperatureMap"][1 - #1] &, 4, 
   ToString[NumberForm[Max[mydata], 4]], "", 
   LegendPosition -> {1.1, -0.8}, LegendSize -> {.25, 0.5}, 
   LegendShadow -> None
  }
]

The data used to generate the meat map does not contain negative values, so the plotted heat map only shows a color range from white to red. But when I plot the legend, the color range shown is from blue to red. How can I adjust the legend's color range to the data. Alternatively, how can I manually adjust the labelling in the legend so as to label the red area with Max[mydata], add something like "<0" to the blue area and also attach a label to other colors? Many thanks for anyone's help!

Answer 1

An alternative to the solution suggested by kguler in comments would be to stretch the color range used in the plot by circumventing MatrixPlot's own ColorFunctionScaling:

ShowLegend[
   MatrixPlot[mydata, 
       Mesh -> True, 
       ColorFunctionScaling -> False,
       ColorFunction -> (ColorData["TemperatureMap"][Rescale[#, {Min[mydata], Max[mydata]}]] &),
       FrameTicks -> None, MeshStyle -> Thin, 
       FrameStyle -> AbsoluteThickness[0], 
       PlotRangePadding -> 0.0
   ], 
  {ColorData["TemperatureMap"][1 - #1] &, 4, 
   ToString[NumberForm[Max[mydata], 4]], ToString[NumberForm[Min[mydata], 4]], 
   LegendPosition -> {1.1, -0.8}, LegendSize -> {.25, 0.5}, 
   LegendShadow -> None
  }
]

Answer 2

To get the color range in the legend to match that in the plot, replace ColorData["TemperatureMap"][1 - #1]& in the original code with

ColorData["TemperatureMap"][.5 + (1 - #1)/2]& 

To add additional labels to the legend can prove painful if you need more than the two extreme labels.

Using

Needs["PlotLegends`"]

mydata = Table[2 + Sin[x y/5.], {x, -10, 10}, {y, -10, 10}];
mplt = MatrixPlot[mydata, Mesh -> True,
  ColorFunction -> "TemperatureMap", FrameTicks -> None, 
  MeshStyle -> Thin,  FrameStyle -> AbsoluteThickness[0], PlotRangePadding -> 0.0, 
  ImageSize -> 400];  

The settings needed to add a second label at the bottom is straightforward:

legendsettings1 = {ColorData["TemperatureMap"][.5 + (1 - #1)/2] &, 4,
  " " <> ToString@NumberForm[Max[Flatten@mydata], {3, 2}],
  " " <> ToString@NumberForm[Min[Flatten@mydata], {3, 2}],
 LegendPosition -> {1.1, -0.8}, LegendSize -> {.25, 0.5},
 LegendBorderSpace -> .2, LegendShadow -> None}; 

The above syntax does not allow more than two labels. To label all colors, after a long trial-and-error series, I could not get anything simpler than the following:

 legendsettings2 = {Graphics[{ColorData["TemperatureMap"][.5 + (1 - #1)/2],
   EdgeForm[{Thickness[.2], ColorData["TemperatureMap"][.5 + (1 - #1)/2]}],
   Rectangle[{0.2, -.2}, {.8, 1.}],
   Black, Text[NumberForm[Quantile[Flatten@mydata, 1 - #1], {3, 2}], {2.2, 1/2}]},
   PlotRange -> {{0, 3}, {-.2, 1.1}}] &, 4,
  LegendPosition -> {1.1, -0.8}, LegendSize -> {.3, .5},
  LegendBorderSpace -> .10, LegendShadow -> None}; 

With these two settings,

 Row[{ShowLegend[mplt, legendsettings1], ShowLegend[mplt, legendsettings2]}, Spacer[5]]

gives