gnuplot - intersection of two plots

Question

I am using gnuplot to plot data from two separate csv files (found in this link: https://drive.google.com/open?id=0B2Iv8dfU4fTUZGV6X1Bvb3c4TWs) with a different number of rows which generates the following graph.

These data seem to have no common timestamp (the first column) in both csv files and yet gnuplot seems to fit the plotting as shown above.

Here is the gnuplot script that I use to generate my plot.

# ###### GNU Plot

set style data lines
set terminal postscript eps enhanced color "Times" 20

set output "output.eps"

set title "Actual vs. Estimated Comparison"

set style line 99 linetype 1 linecolor rgb "#999999" lw 2
#set border 1 back ls 11
set key right top
set key box linestyle 50
set key width -2
set xrange [0:10]
set key spacing 1.2
#set nokey

set grid xtics ytics mytics
#set size 2
#set size ratio 0.4

#show timestamp
set xlabel "Time [Seconds]"
set ylabel "Segments"

set style line 1 lc rgb "#ff0000" lt 1 pi 0 pt 4 lw 4 ps 0

plot  "estimated.csv" using ($1):2 with lines title "Estimated", "actual.csv" using ($1):2 with lines title "Actual";

Is there any way where we can print out (write to a file) the values of the intersection of these plots by ignoring the peaks above green plot? I also have tried to do an sql-join query but it doesn't seem to print out anything for the same reason I explained above.

PS: If the blue line doesn't touch the green line (i.e. if it is way below the green line), I want to take the values of the closest green line so that it will be a one-to-one correspondence (or very close) with the actual dataset.

Answer 1

Perhaps one could somehow force Gnuplot to reinterpolate both data sets on a fine grid, save this auxiliary data and then compare it row by row. However, I think that it's indeed much more practical to delegate this task to an external tool.

It's certainly not the most efficient way to do it, nevertheless a "lazy approach" could be to read the data points, interpret each dataset as a LineString (collection of line segments, essentially equivalent to assuming a linear interpolation between data points) and then calculate the intersection points. In Python, the script to do this might look like this:

#!/usr/bin/env python
import sys

import numpy as np
from shapely.geometry import LineString
#-------------------------------------------------------------------------------
def load_data(fname):
    return LineString(np.genfromtxt(fname, delimiter = ','))
#-------------------------------------------------------------------------------
lines = list(map(load_data, sys.argv[1:]))

for g in lines[0].intersection(lines[1]):
    if g.geom_type != 'Point':
        continue
    print('%f,%f' % (g.x, g.y))

Then in Gnuplot, one can invoke it directly:

set terminal pngcairo
set output 'fig.png'

set datafile separator comma
set yr [0:700]
set xr [0:10]

set xtics 0,2,10
set ytics 0,100,700

set grid

set xlabel "Time [seconds]"
set ylabel "Segments"

plot \
    'estimated.csv' w l lc rgb 'dark-blue' t 'Estimated', \
    'actual.csv' w l lc rgb 'green' t 'Actual', \
    '<python filter.py estimated.csv actual.csv' w p lc rgb 'red' ps 0.5 pt 7 t ''

which gives: