Upper axis values through linking with lower axis gnu plot

[CAF123]

I am trying to link the upper axis with the lower axis in gnu plot, that is print out values on the upper axis given a relationship between the upper axis, x2, quantities and the lower axis, x, ones. The relationship between them is

x2 = 2*c**2/(2*x**2-c**2)

with

c=3.1

The following should be sufficient

    set xlabel "Quantity lower"
    set xtics nomirror
    set x2label "Quantity Upper"
    set x2tics nomirror
    set link x2 via 2*(3.1)**2/(2*x**2-(3.1)**2) inverse sqrt((3.1)**2*(2+x)/2/x)

    #set link x via 1239.8/x inverse 1239.8/x

    set ylabel "Quantity y"
    set ytics 0.2
    set samples 400
    Spectrum(x) = exp(-(x-500)**2/(400))

    set xrange[30:2000]

    set format x2 "%.2f"
    plot Spectrum(x) w l title "Spectrum"

I've also log formatted the x-axis via

set logscale x
set format x "10^{%L}"

but regardless of whether I include the log formatting I am unable to get any meanginful values printed out on the upper axis. (The function for y is for illustrative purposes only, the value for y in my actual script relies on reading in data from a file)

I'd like to print out values on the upper axis for two values of x=100, 1000 say. Not sure if this is the right place for this but thanks for any comments!

 

[Mark44]

Something like this?
http://gnuplot.sourceforge.net/demo/multiaxis.html

 

[CAF123]

@Mark44 Hi, looks similar but not quite the same - there they are plotting two different relationships (x2 v.s y2) and (x1 v.s y1). All I want to do, and I hoped it would have been trivial to do, is to link the x2 axis (upper axis) with the x-axis (lower axis). That is, for a given tick mark on the x-axis with value $X$, I want to print out the corresponding tick mark on the x2 axis with value $x2(X)$, where

x2 = 2*c**2/(2*x**2-c**2)

as given in my OP. Does my question make sense?

 

[DrClaude]

That is, for a given tick mark on the x-axis with value $X$, I want to print out the corresponding tick mark on the x2 axis with value $x2(X)$

This is not what set link x2 will do. The second x-axis gets its own set of tics, so it will not mirror the position of the tics on the first x axis. To see this, try

set tics nomirror
set xrange[1:10]
set link x2 via 1/x inverse 1/x
set x2tics
plot x

 

[Mark44]

@CAF123, what's happening with your other thread, the one about evaluating a function at numerous points? Your last (and only) post in that thread was almost five days ago.

 

[CAF123]

This is not what set link x2 will do. The second x-axis gets its own set of tics, so it will not mirror the position of the tics on the first x axis. To see this, try

set tics nomirror
set xrange[1:10]
set link x2 via 1/x inverse 1/x
set x2tics
plot x

I see. Can you suggest a way for me to proceed with what I want to do?

 

[CAF123]

@CAF123, what's happening with your other thread, the one about evaluating a function at numerous points? Your last (and only) post in that thread was almost five days ago.

I managed to come up with a solution outside of C++, i may come back to the thread later to discuss more.