set size ratio 1.3
set grid
set xrange [0:2.5]
set yrange [0:5]
set samples 1000
set parametric

# set terminal pngcairo size 1000, 1200
# set output "barbot.png"

# solves the equation rho(s)q^2 - (s+1)q + 1 = 0
# (s^2 + cs + 1)q^2 - (s+1)q + 1 = q^2 s^2 + (cq - 1)qs + (q^2 - q + 1)
c = 2*cos(4*pi/5)
rho(s) = s**2 + c*s + 1
qp(s) = (s+1+sqrt((s+1)**2 - 4*rho(s)))/(2*rho(s))
qm(s) = (s+1-sqrt((s+1)**2 - 4*rho(s)))/(2*rho(s))
d(q) = q**2*(c*q-1)**2 - 4*(q**2-q+1)*q**2
sp(q) = (-(c*q-1)*q + sqrt(d(q)))/(2*q**2)
sm(q) = (-(c*q-1)*q - sqrt(d(q)))/(2*q**2)

#  = sqrt(s**2 + 2*cos(4*pi/5) + 1)
# solplus(x) = x/2 + sqrt((x/2)**2 - 1)
# solminus(x) = x/2 + sqrt((x/2)**2 - 1)
# Tplus(s) = solplus((s+1)/rho(s))
# Tminus(s) = solminus((s+1)/rho(s))
# qinvp(s) = 0.5*(s+1+sqrt(2*s - 8*s*cos(2*pi/5) - 3*s**2 - 3))
# qinvm(s) = 0.5*(s+1-sqrt(2*s - 8*s*cos(2*pi/5) - 3*s**2 - 3))
# set trange [0:5]

# sp(q) = (1-2*q*cos(2*pi/5)+sqrt((1-2*q*cos(2*pi/5))**2 - 4))/(2*q)
# sm(q) = (1-2*q*cos(2*pi/5)-sqrt((1-2*q*cos(2*pi/5))**2 - 4))/(2*q)

plot "output/barbot_map_5000_frequencies" \
	 using ($1/100.0):($2/100.0):(($3==0)?1/0:$4) w p pt 5 ps 0.5 lc palette t '', \
	 "output/barbot_map_500000"	\
	 using ($1/10.0) :($2/10.0) :($3*0.7+0.3) w p pt 7 ps variable lc 3 t '', \
	 sm(t), d(t) > 0 ? t : 1/0 w l lw 2 lc 7 t "", \
	 sp(t), d(t) > 0 ? t : 1/0 w l lw 2 lc 7 t "", \
	 t, qm(t) w l lw 2 lc 7 t "", \
	 t, qp(t) w l lw 2 lc 7 t ""

# plot "output/barbot_map_50000_zoom_b" using ($1/1000.0):($2/5000):(($3==0)?1/0:$4) w p pt 5 ps 0.5 lc palette t ''

pause mouse keypress
reread