Transform x-scale of data for e.g. MatrixPlot

Question

I have to transform in a nonlinear way the x-scale of some data for a MatrixPlot (or ReliefImage or ListDensityPlot etc.).

Let me give an example to explain what I try to do.

I have following fake data:

fakeData=Table[BinCounts[RandomVariate[NormalDistribution[71,1.5],1000],{0,85,0.5}],{j,1,100}];

Which I can plot easily with e.g. MatrixPlot[fakeData], which gives

Or I can plot just one line of the fake data with ListPlot[fakeData[[3]]], which gives

But the xscale of the data is not correct and should be transformed. The initial scale is linear:

xScaleInitially=Range[Length[fakeData[[1,All]]]];

and the transformed scale should be something like, e.g.:

xScaleTransformed=1⁄((10+Sqrt[xScaleInitially]));

Then I can try to transform all my data with e.g.:

fakeDataTransformed=Table[Transpose[{xScaleTransformed,fakeData[[j]]}],{j,1,100}];

If I use ListPlot[fakeDataTransformed[[3]]], I get for these data the result I want to have:

But I cannot manage to use MatrixPlot or ReliefImage on these transformed data to get a picture similar to the first one above.

Could somebody of you tell me how I can transform my data correctly, so that I still can have plots as with MatrixPlot or ReliefImage etc.? I would be very happy about every hint and help!

Answer 1

How about interpolating your fakeDataTransformed, to obtain regularly spaced data points?

func[line_, precision_] := Module[{f},
    f = Interpolation[fakeDataTransformed[[line]]];
    Table[f[x], {x, Min[xScaleTransformed], Max[xScaleTransformed], 
    precision}]]

newdata = Table[func[i, .0002], {i, Length[fakeDataTransformed]}];

MatrixPlot[newdata]

Answer 2

Check this and modify ticks according the way you want:

MatrixPlot[Transpose@Reverse@Transpose@fakeData, AspectRatio -> 3/5,
DataReversed -> {True, False}, DataRange -> {{0,2}, All}]

Question!

I tried to manipulate the FrameTicks but could not get the wanted result.

chosen = Take[xScaleTransformed = 1/((10 + Sqrt[xScaleInitially])) // N, {1, -1,20}]; 
xticks = Transpose[{Range@Length@chosen, chosen}];
yticks = Transpose[{Range@10,Take[Range[First@Dimensions@fakeData], {1, -1, 10}]}];
MatrixPlot[Transpose@Reverse@Transpose@fakeData, AspectRatio -> 3/5, 
DataReversed -> {True, False}, FrameTicks -> {yticks, xticks}]

Can anybody shed some light at this issue?

BR