Plotting array of vectors with conditions

Question

Given data in the form

list={{{1,2},{3,4},{5,6}},{{7,8},{9,10},{11,12}},...}

a matrix where elements are 2-element vectors, what is a efficient way to plot this as a spatial grid? As I understand

ArrayPlot[array,ColorFunction->(If[#>3,Red,White]&), ColorFunctionScaling->False]

can only be "fed" with normal array (no 2-vector like above), if you want to use Colorfunction If condition.

I want that a cell of the ArrayPlot mesh gets Red, when in {x,y} vector 1<x<2 AND y>3, otherwise White.

I know I could recreate the list into a {{1,0,1},{0,1,0},...} like normal array so ArrayPlot could read it, by using Table and Take, 1 and 0 representing the Red and White Case:

If[1<First[Flatten[Take[list,i]]]<2,1,0]

Then rebuild that list with Table and Join. But as far as I know MM, there has to be easier way, simply reading list and replacing a 2-vector with 1 or 0 1-vector under above conditions. Or do I really have to build the list completely new, problem is it has some million elements.

Thanks for any tips to improve this

Answer 1

It appears you have lied to us about ColorFunction, see:

ArrayPlot[RandomReal[{0, 1}, {10, 10, 3}]] (*this works, therefore...*)
ArrayPlot[RandomReal[{0, 1}, {10, 10, 3}], ColorFunction -> Hue]

These work, therefore:

ArrayPlot[RandomReal[{0, 3}, {10, 10, 2}],
 ColorFunction -> (If[1 < #[[1]] < 2 && #[[2]] < 3, Red, White] &)]

Beautiful. But if we go the extra mile, we can get:

ArrayPlot[RandomReal[{0, 3}, {10, 10, 2}],
 ColorFunctionScaling -> False,
 ColorFunction -> (If[1 < #[[1]] < 2 && #[[2]] < 3, Red, White] &)]

The default for ColorFunctionScaling /. Options[ArrayPlot] is True, which screws up your values. Compare the following to see the difference:

ArrayPlot[RandomReal[{0, 3}, {2, 2, 2}], ColorFunctionScaling -> True, ColorFunction -> Print]
ArrayPlot[RandomReal[{0, 3}, {2, 2, 2}], ColorFunctionScaling -> False, ColorFunction -> Print]

It makes sense in general since typical color functions such as Hue and ColorData[...] go from 0 to 1, but I've found you can often get more useful coloring by disabling the scaling.

$$-$$

Note: Apparently, ColorRules isn't affected by ColorFunctionScaling. This makes sense since ColorRules is typically used for integer data.

ArrayPlot[RandomReal[{0, 3}, {10, 10, 2}],
 ColorRules -> {{x_, y_} /; 1 < x < 3 && y < 3 -> Red, _ -> White}]

Answer 2

There are several ways to do this. Here are two that came to mind although I am sure there are many more

newArray1=Map[If[1 < #[[1]] < 2 && #[[2]] > 3, 1, 0] &, list, {2}]

newArray2=Replace[list, {{a_, b_} /; 1 < a < 3 && b > 3 :> 1, {a_, b_} :> 0}, {2}]

GraphicsRow[
    ArrayPlot[#, ColorFunction -> (If[# == 1, Red, White] &)] & /@ {newArray1,newArray2}
]