Custom scaling of x-axis in ListPlot

Question

I'd like to plot a list of the following form with a customized scale

data=ConstantArray[1, 1000]

The scale of x-axis is kind of non-linear. The first 500 observations of the data has a distance 1. The next 300 observations have distance 3 from each other. Lastly, the last 200 observations have distance 10.

How can I scale x-axis of ListPlot to reflect such changing distances?

Answer 1

I will try to do exactly what you asked, which can be seen from the gridlines of x-axis. I will use range $50,80,100$ so you can actually see distances between the points (too many points overlap visually and look like a line). You can easily generalize to your range (500,800,1000). First define a scaling function:

scale[x_]:=Piecewise[{{x,x<50},{x 2-50,50<=x<80},{x 3-50-80,80<=x}}]

Now with your data

data = ConstantArray[1, 100];

the plot scaling functions works as $\{f,f^{-1}\}$ setting:

ListPlot[data,ScalingFunctions->{{scale,InverseFunction[scale]},None},
PlotTheme->"Detailed",AspectRatio->1/7,GridLines->{Range[100],Automatic}]

In the docs on ScalingFunctions this general form of arbitrarily defined scaling is mentioned in the details:

Answer 2

You could generate your own abscissa list according to your specifications:

abscissae = Join[
     Range[500], 
     Range[503, 299*3 + 503, 3], 
     Range[1410, 1410 + 199*10, 10]
    ];

ListPlot[Transpose@{abscissae,data}]