Re: [Gnuplot-info] Finding thresholds with gnuplot

[theozh <th...@gm...>]

Thank you, Ethan, for your hint.
ah, once again the powerful ternary operator ;-)
Theo.

The first example gets the first x value where y(x) is above the threshold and the last x value where y(x) is still below the threshold.
Actually, this method could also be used to find FWHM of spectral data (see second example). However, if the spectrum is a Gaussian or Lorentzian or whatever peak, fitting with appropriate parameters might probably give better results.

First example:

### find x range when data passes a certain threshold 
# getting the first x value where y(x) is above the threshold
# and the last x value wher y(x) is below the threshold
reset session
# generate some dummy data
set print $Data
do for [i=1:100] {
    print sprintf("%g %.3f",i*2+rand(0), rand(0)*20+i)
}
set print

Threshold = 50
     
set table $Dummy
plot $Data u 1:($2<Threshold ? ($2) : NaN):($2>=Threshold ? ($2) : NaN) with table
unset table
# print $Dummy

stats $Dummy u 1:3 nooutput
Min_x = STATS_min_x
stats $Dummy u 1:2 nooutput
Max_x = STATS_max_x

set label sprintf("min: %.1f, max: %.1f", Min_x, Max_x) at Min_x, Threshold+20 center

set key top left
plot $Data using 1:2 with lp lt 6, \
    Threshold w l,\
    $Dummy u 1:2 w impulse lc rgb "green",\
    $Dummy u 1:3 w impulse lc rgb "red"
### end of code


Second example:
### find Full Width at Half Maximum (FWHM)
reset session 
# generate some dummy data
set print $Data
Intensity = rand(0)*100
Position = rand(0)*200+480
Width = rand(0)*50+50
do for [i=380:780] {
    print sprintf("%g %.3f",i, Intensity*exp(-((i-Position)/Width)**2)+rand(0)*Intensity*0.1)
}
set print

stats $Data nooutput
Int_max = STATS_max_y
set table $Dummy
plot $Data u (Peak=$1,$1) every ::STATS_index_max_y::STATS_index_max_y with table
unset table
Threshold = 0.5*Int_max

set table $FWHM
plot $Data u ($2>=Threshold ? ($1) : NaN):($2>=Threshold ? Threshold : NaN) with table
unset table
stats $FWHM nooutput
FWHM = STATS_max_x - STATS_min_x

reset
set label 1 sprintf("Peak %.1f", Peak) at Peak*1.1, Int_max*0.95 center boxed
set label 2 sprintf("FWHM %.1f", FWHM) at Peak, Threshold*1.1 center boxed
set arrow 1 nohead from Peak,graph 0 to Peak,Int_max
set yrange[*:*]

plot $Data using 1:2 with l lc rgb "red" t "Spectrum", \
    $FWHM using 1:2 w l lc rgb "blue" not
    
### end of code