gnuplotlinear-interpolation

How to resample or interpolate data with gnuplot?

In some cases you might need to resample your data. How can this be done platform-independently with gnuplot? Below is one attempt.

The dataset $Dummy contains the interpolated values, however, with a lot of unnecessary lines containing NaN. The dataset $DataResampled finally contains the desired data.

My question is: can this be done simpler and faster?

Script:


### resampling data with linear interpolation
reset session

$Data <<EOD
0   1
1   4
2   10
5   15
10  5
20  11
EOD

# get the x-range
stats $Data u 1 nooutput
MinX = STATS_min
MaxX = STATS_max
Resamples=20
# or alternatively fix the step size 
# StepSize=1
# Resamples = int(MaxX-MinX)/StepSize+1

Interpolate(xi) = y0 + (y1-y0)/(x1-x0)*(xi-x0) 
x1=y1=NaN

# resample the data
set print $DataResampled
set table $Dummy
do for [i=1:Resamples] {
    xi = MinX + (i-1)*(MaxX-MinX)/(Resamples-1)
    Flag=0
    plot $Data u (x0=x1, x1=$1, y0=y1, y1=$2,\
        (xi>=x0 && xi<=x1 && Flag==0 ? (Flag=1, yi=Interpolate(xi), xi) : NaN)): \
        (Flag==1 ? yi : NaN) with table
    print sprintf("%g\t%g",xi,yi)
}
unset table
set print

set xrange[-1:21]
plot $Data u 1:2 w lp pt 6 ps 2 lc rgb "black" t "original data",\
     $DataResampled u 1:2 w lp pt 7 lc rgb "web-green" t "resampled with linear interpolation",\
     $Dummy u 1:2 w impulses lc rgb "red" not
### end of script

Result:

enter image description here

Solution

  • Preamble: I'm aware that gnuplot wants to be a plotting program and not a data analysis or data processing tool. However, a few data handling functions would be useful, e.g. like linear interpolation/resampling of data.
    In gnuplot there are a few smooting options implemented check help smooth, but these are for smoothing noisy data with many datapoints. There are: smooth bezier, smooth cplines, smooth acsplines, smooth mcsplines, smooth sbeziers, and since gnuplot 5.5. smooth path for interpolating along a path. Something like smooth linear doesn't exist (yet) and seems to be not interesting enough to be implemented.

    One application example:
    You have spectral raw data from a spectrometer with oddly spaced wavelengths, e.g. 380.71, 383.53, 386.21, ... and you have a filter function at wavelengths 380, 382, 384, 386, 388, ... and you want to multiply this data for each wavelength. So, you need to have the y-values of both datasets at identical x-values. And of course, you could do it with an external program.

    However, if it is not too complicated and not too inefficient why not doing it within gnuplot? So, I think the following script is a fast gnuplot-only way for linear resampling/interpolation of data.

    Comments:

    Data: SO54362441.dat

    0   1
1   4
2   10
5   15
10  5
20  11

    Script: (works for gnuplot>=5.4.0 July 2020)

    ### resampling of data via linear interpolation
reset session

FILE = "SO54362441.dat"

set table $InterpolX
    set samples 20    # set number of samples
    plot [0:20] '+' u 1 w table
unset table

set table $Temp
    plot x1=y1=NaN FILE u (x0=x1,x1=$1,x0):(y0=y1,y1=$2,y0):(atan2(y1-y0,x1-x0)) w table, \
         '+' every ::::0 u (x1):(y1):(0) w table, \
         OoR=999 $InterpolX u 1:(0):(OoR) w table
set table $Temp2
    plot $Temp u 2:3:1:1 smooth zsort lc var
set table $Interpolated
    p = 0    # include original datapoints? 0=no, 1=yes
    plot x1=y2=xb=yb=NaN $Temp2 u (x0=x1, x1=$3, y1=$1, a1=$2, \
         a1==OoR ? ( y2=yb+(x1-xb)*tan(ab) ) : \
         (ab=a1, xb=x1, yb=y1, y2 = x0==x1 ? y1 : p ? yb : ''), x1) : (y2) w table
unset table

plot FILE          u 1:2 w lp pt 7     lc "black"     ti "Original data", \
     $Interpolated u 1:2 w impulses    lc "web-green" notitle, \
     $Interpolated u 1:2 w p pt 6 ps 2 lc "red"       ti "Interpolated"
### end of script

    Result:

    enter image description here