How to format x axis to a smaller scale? - gnuplot

Question

So here is what I'm trying to do.
The values on x axis are from 10000, 20000, 30000, ... 100000. I'm trying to write it like this: 10, 20, 30, 40, ... 100 (only x axis)
Is there some way to do this in Gnuplot?
I have this so far:
(data.dat - example of data)
# x y
10000 +1.24241522E-04
11000 +1.28623514E-04
12000 +1.35229020E-04
13000 +1.43767741E-04
14000 +1.53409148E-04
15000 +1.63788695E-04
16000 +1.75429485E-04
17000 +1.88827813E-04
18000 +2.02984785E-04
19000 +2.20830420E-04
...
(my gnuplot script)
set term png
set out 'example.png'
U0 = 0.00732 #parameters for this particular problem
v1 = 68000
b1 = 6550
v2 = 59600
b2 = 6050
I = sqrt(-1)
A(w, w0, b) = ((w0)**2)/(((w0)**2) - ((w)**2) + 2*I*w*b)
f(x) = U0*abs(A(2*pi*x, 2*pi*v1, b1) - A(2*pi*x, 2*pi*v2, b2))
set xlabel "x"
set ylabel "y"
fit f(x) 'data.dat' u 1:2 via U0, v1, b1, v2, b2
plot 'data.dat' u 1:2 t "Title1" w p, U(x) t "Title2"
set out
But how do I do this?
I've tried this example
How to scale the axes in Gnuplot
but it doesn't work.
See below.
# I modified the things a little bit
f(x) = (.... ... ....)/1000
fit f(x) 'data.dat' u ($1/1000.):2 via U0, v1, b1, v2, b2
plot 'data.dat' u ($1/1000.):2 t "Title1" w p, f(x) t "Title2"
But now the fitted function disappears!
How can I modify x-axis without other function disappearing?
Does there exist a line command in gnuplot for this? I'm sure there has to be a more elegant way of writing this insted of dividing each function by a desired factor.

Answer 1

Two possible ways come to my mind:
if you want to avoid too many zeros in the xtic labels, simply set the xtic label format to engineering
set format x "%.0s%c"
This will show, e.g. 10000 and 100000 as 10k and 100k, respectively.
if you scale (in your case: divide) the x values of the data by factor of 1000, gnuplot will take this x range for plotting the function f(x). Since this is will give x values which are a factor of 1000 too small you have to scale your x values by a factor of 1000 accordingly (in your case: multiply).
Code:
### avoid too many zeros in xtic labels
reset session
# create some random test data
set print $Data
A = rand(0)*10+5
B = rand(0)*50000+25000
C = rand(0)*5000+5000
do for [i=10000:100000:500] {
print sprintf("%g %g",i,A*exp(-((real(i)-B)/C)**2))
}
set print
a=1; b=50000; c=5000 # give some reasonable starting values
f(x) = a*exp(-((x-b)/c)**2)
set fit quiet nolog
fit f(x) $Data u 1:2 via a,b,c
set multiplot layout 1,2
set format x "%.0s%c" # set xtics to engineering
plot $Data u 1:2 w p, \
f(x) w l lc "red"
set format x "%g" # set xtics to default
plot $Data u ($1/1000):2 w p, \
f(x*1000) w l lc "red"
unset multiplot
### end of code
Result: