#

# Various ways of displaying distribution of y values in a data file

# 1) Violin plots (bee swarm with large number of points)

# 2) Gaussian jitter

# 3) Random jitter

# 4) kernel density

#

# Generate a reusable set of data points from a mixture of Gaussians

nsamp = 3000 

set print $viol1

do for [i=1:nsamp] {

    y = (i%4 == 0) ? 300. +  70.*invnorm(rand(0)) \

      : (i%4 == 1) ? 400. +  10.*invnorm(rand(0)) \

      :              120. +  40.*invnorm(rand(0))

    print sprintf(" 35.0 %8.5g", y)

}

unset print

set print $viol2

do for [i=1:nsamp] {

    y = (i%4 == 0) ? 300. +  70.*invnorm(rand(0)) \

      : (i%4 == 1) ? 250. +  10.*invnorm(rand(0)) \

      :               70. +  20.*invnorm(rand(0))

    print sprintf(" 34.0 %8.5g", y)

}

unset print

#

set border 2

set xrange [33:36]

set xtics ("A" 34, "B" 35)

set xtics nomirror scale 0

set ytics nomirror rangelimited

unset key

set jitter overlap first 2

set title font ",15"

set title "swarm jitter with a large number of points\n approximates a violin plot"

set style data points

set linetype  9 lc "#80bbaa44" ps 0.5 pt 5

set linetype 10 lc "#8033bbbb" ps 0.5 pt 5

plot $viol1 lt 9, $viol2 lt 10

pause -1 'Hit <cr> to continue'

set title "Gaussian random jitter"

unset jitter

J = 0.1

plot $viol1 using ($1 + J*invnorm(rand(0))):2 lt 9, \

     $viol2 using ($1 + J*invnorm(rand(0))):2 lt 10 

pause -1 "Hit <cr> to continue"

set title "Same data - kernel density"

set style data filledcurves below

set auto x

set xtics 0,50,500

unset ytics

set border 3

set margins screen .15, screen .85, screen .15, screen .85

set key

plot $viol1 using 2:(1) smooth kdensity bandwidth 10. with filledcurves above y lt 9 title 'B', \

     $viol2 using 2:(1) smooth kdensity bandwidth 10. with filledcurves above y lt 10 title 'A'

pause -1 "Hit <cr> to continue"

#

# Save each kernel density plot to a data block 

# Then replot, mirrored, along the vertical axis

#

set title "kdensity mirrored sideways to give a violin plot"

set table $kdensity1

plot $viol1 using 2:(1) smooth kdensity bandwidth 10. with filledcurves above y lt 9 title 'B'

set table $kdensity2

plot $viol2 using 2:(1) smooth kdensity bandwidth 10. with filledcurves above y lt 10 title 'A'

unset table

unset key

set border 2

unset margins

unset xtics

set ytics nomirror rangelimited

set xrange [-1:5]

plot $kdensity2 using (1 + $2/20.):1 with filledcurve x=1 lt 10, \

     '' using (1 - $2/20.):1 with filledcurve x=1 lt 10, \

     $kdensity1 using (3 + $2/20.):1 with filledcurve x=3 lt 9, \

     '' using (3 - $2/20.):1 with filledcurve x=3 lt 9

pause -1 "Hit <cr> to continue"

set title 'Superimposed violin plot and box plot'

set style fill solid bo -1

set boxwidth 0.075

set errorbars lt black lw 1

replot $viol2 using (1):2 with boxplot fc "white" lw 2, \

       $viol1 using (3):2 with boxplot fc "white" lw 2

pause -1 "Hit <cr> to continue"

reset