PyXPlot

Script

set multiplot
set nodisplay
width = 10
set width width
set size square
set fontsize 2
set nokey

# Plot 0 (left)
set xlabel 'x'
set ylabel 'y'
plot [-10.9:10.9][-10.9:10.9] \
 'example11.dat' i 0 u 1:2:($1+$3):($2+$4) w arrows, \
 4*sin(x/10.9*pi):4*cos(x/10.9*pi) u 2:3 w lt 2 col black

# Plot 1 (right)
set origin width, 0
set ylabel 'linkaxis 0'
set key bottom right
plot [-10.9:10.9] \
 'example11.dat' i 1 t '' with arrows, \
 'example11.dat' i 1 t 'Before correction' u 1:2 w p, \
 'example11.dat' i 1 t 'After  correction' u 3:4 w p

set display
refresh