Use Blend to specify different colors for different ranges of values

Question

I have the following MatrixPlot for which I want to specify a custom color function:

MatrixPlot[RandomReal[1, {10, 10}], ColorFunction -> customColorFunction]

The function should behave as follows: White only for a value smaller than 0.2. Then for the range of >0.2 to 0.7 it should be a continuous blend from red to blue and for the range >0.7 it should be black.

Is it possible to specify something like this with Blend or some other function?

Answer 1

In:

Clear[customColorFunction]
customColorFunction[x_] := Piecewise[{
   {White, x <= 0.2}, {Blend[{Red, Blue},
     (x - 0.2)/0.5], 0.2 < x <= 0.7},
   {Black, True}}]
Table[customColorFunction[x], {x, 0.01, 1, 0.01}]

SeedRandom[1]
m = RandomReal[{0, 1}, {10, 10}];

MatrixPlot[m, ColorFunction -> customColorFunction, 
 ColorFunctionScaling -> False]
ArrayPlot[m, ColorFunction -> customColorFunction]

Out:

Answer 2

I found that ArrayPlot kinda works a little better for me.

ArrayPlot[RandomReal[1, {10, 10}], ColorFunction -> Function[{c},
Which[c < 0.2, White, (c >= 0.2 && c <= 0.7), 
Blend[{Red, Blue}, (c - 0.2)*2], c > 0.7, Black]]]