gnuplot: how to set custom non linear scales

Question

is there any possibility for using non linear scales with self defined break of slope points? For example: i want the half of the y-scale shows the range [0:1] and the other half [1:5] and i do not want to use logarithmic scale.

The best thing would be the possibility to provide a mapping function. Sure one could directly map the function results but then the labes will not fit to the actual data.

Is there any possiblilty? I searched a bit but iam not sure if i missed something or if it is not possible.

Answer 1

This can be done with set link, which is available only in the 4.7 development version.

The following script does the mapping, but the labels are on the y2-axis:

reset
f(x) = x <= 1 ? x : 1 + (x-1)*4
i(x) = x <= 1 ? x : (x-1)/4.0 + 1
set link y2 via f(y) inverse i(y)

unset ytics
set y2tics mirror

set xrange[0:5]
set yrange[0:2]
plot x axes x1y2

Result with 4.7:

With some offset, you can move the labels from the y2-axis to the y-axis:

reset
set terminal pngcairo size 800,500
set output 'output.png'

f(x) = x <= 1 ? x : 1 + (x-1)*4
i(x) = x <= 1 ? x : (x-1)/4.0 + 1
set link y2 via f(y) inverse i(y)

unset ytics
set lmargin at screen 0.1
set rmargin at screen 0.95
set y2tics mirror offset graph -1.04 right
# set y2tics add (0.5)
set my2tics 2
set y2tics add ('' 0.25 1, '' 0.75 1)
set ylabel 'ylabel' offset -4

set xrange[0:5]
set yrange[0:2]
plot x axes x1y2

That's quite ugly, but it works. It requires just a little fiddling with the left and right margins and the y2tics offset.

EDIT: I added minor tics, with a higher frequency between 0 and 1. I think it might be useful to add one label for 0.5 to show that the scale is linear, but with a different gradient (in which case you also might want to set y2tics format '%.1f' to have one decimal digit for all labels). However, this tic would also appear as a major tics, because using labels for minor tics is not supported, yet.

The result is: