How can I plot a matrix with a two-dimensional color scheme?

Question

Plotting a matrix with colors depending on the value of each entry is straightforward,

TestMatrix = {{0, 1, 2}, {3, 4, 5}, {6, 7, 8}};
MatrixPlot[TestMatrix, ColorFunction -> "Rainbow"]

But what if the matrix has two-dimensional entries? Something like

TestMatrix = {{{0, 0}, {1, 0}, {2, 0}}, {{3, 1}, {4, 1}, {5, 1}}, {{6,1}, {7, 1}, {8, 1}}};

Defining a two-dimensional color function is simple enough, for instance

Palette = Function[{x, y}, Blend[{Hue[x], GrayLevel[x]}, y]];

But now MatrixPlot won't work! How can it be done?

Bonus points if the method works with ListContourPlot :)

Answer 1

You can use a matrix of colors as input to MatrixPlot:

colorarray = TestMatrix /. {a_?NumericQ, b_} :> Palette[a, b] 

mp = MatrixPlot[colorarray, Frame -> False, ImageSize -> 300, PlotRangePadding -> 0];

img = Image[RGBMap, ImageSize -> 300];

Row[{Labeled[mp, Style["MatrixPlot[colorarray]", 16], Top], 
     Labeled[img, Style["Image[RGBMap]", 16], Top]}, 
    Spacer[5]]

Alternatively, you can construct colorarray Applying Palette to each entry:

colorarray = Apply[Palette, TestMatrix, {-2}];

Note: You can get RGBMap using colorarray /. RGBColor -> List:

RGBMap == colorarray /. RGBColor -> List

True

Answer 2

Okay, I figured out how to do it.

First, we normalize the matrix to be between 0 and 1 for convenience, and define the two-dimensional color palette

TestMatrix = {{{0, 0}, {1, 0}, {2, 0}}, {{3, 1}, {4, 1}, {5, 1}}, {{6,1}, {7, 1}, {8, 1}}};
TestMatrix = TestMatrix/Max[TestMatrix];
Palette = Function[{x, y}, Blend[{Hue[x], GrayLevel[x]}, y]];

Then, we define a function that extracts the RGB values from any color that Palette outputs,

RGBExtractor = Function[x, {x[[1]], x[[2]], x[[3]]}];

Finally, we convert from matrix entries to RGB values and output the result as an image

RGBMap = Table[RGBExtractor[Palette[TestMatrix[[i, j, 1]], TestMatrix[[i, j, 2]]]],
 {i, 1, Length[TestMatrix[[1]]]}, {j, 1, Length[TestMatrix[[1]]]}];
Image[RGBMap, ImageSize -> 300]