ArrayPlot with logarithmic legend

Question

I have a matrix that contains numbers in different orders of magnitude and I would like to plot it using ArrayPlot. For example purposes I create the matrix here, but actually it is not a function, so I cannot use DensityPlot.

someTable = 
  Table[Table[
  PDF[ChiDistribution[s], 
   xx], {s, {.5, .75, 1.0, 1.5, 2.5}}], {xx, {10*^-3, 10*^-2, 
   0.1, 2.0, 5.0}}]

I compute the max and min values:

 {minran, maxran} = {Min[someTable], Max[someTable]}

(*Out: {7.73082*10^-7, 4.63842} *)

ArrayPlot[(randomTable), FrameStyle -> Opacity[0], 
 RotateLabel -> False, FrameTicksStyle -> Opacity[1], 
 ImageSize -> 800, 
 PlotLabel -> Style[#, 21, FontColor -> Black] &@("Some Matrix"), 
 ImageMargins -> 10, ColorFunction -> ColorData["Rainbow"], 
 ColorFunctionScaling -> True, 
 PlotLegends -> 
  Placed[BarLegend[{"Rainbow", {minran, maxran}}, 
    LegendMarkerSize -> 500, 
   LabelStyle -> Directive[Black, 25, FontFamily -> "Times"]], {1.0, 
    0.5}]]

I get the following:

Changing to MatrixPlot and ColorFunctionScaling to False, I get:

I just want the different orders of magnitude to be visible with a nice color gradient. I have searched the documentation and S.E. and have found nothing similar. Just some answers for Density or ContourPlot.

I also would like to know why in the second case I see the FrameTicks Labels and in the first case they disappear.

Answer 1

as noted you could just plot Log[array].. but this is how to do it with ColorFunction

someTable = 
 Table[Table[
   PDF[ChiDistribution[s], 
    xx], {s, {.5, .75, 1.0, 1.5, 2.5}}], {xx, {10*^-3, 10*^-2, 0.1, 
    2.0, 5.0}}]


ArrayPlot[(someTable), FrameStyle -> Opacity[0], RotateLabel -> False,
  FrameTicksStyle -> Opacity[1], ImageSize -> 800, 
 PlotLabel -> Style[#, 21, FontColor -> Black] &@("Some Matrix"), 
 ImageMargins -> 10, 
 ColorFunction -> (ColorData["Rainbow"][
     Rescale[Log[#], Log[MinMax[someTable]]]] &), 
 ColorFunctionScaling -> False,
 PlotLegends -> 
  Placed[BarLegend[{(ColorData["Rainbow"][
        Rescale[#, Log[MinMax[someTable]]]] &), 
     Log[MinMax[someTable]]}, LegendMarkerSize -> 500, 
    LabelStyle -> Directive[Black, 25, FontFamily -> "Times"]], {1.0, 
    0.5}]]

note the legend is showing Log value.