42 lines
1.4 KiB
Gnuplot
42 lines
1.4 KiB
Gnuplot
set size ratio 1.3
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set grid
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set xrange [1/2.5:2.5]
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set yrange [0.2:5]
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set samples 2000
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set parametric
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set log x
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set log y
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set terminal pngcairo size 1000, 1200
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set output "barbot-symmetric.png"
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# solves the equation rho(s)q^2 - (s+1)q + 1 = 0
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# (s^2 + cs + 1)q^2 - (s+1)q + 1 = q^2 s^2 + (cq - 1)qs + (q^2 - q + 1)
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c = 2*cos(4*pi/5)
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rho(s) = s**2 + c*s + 1
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# qp(s) = (s+1+sqrt((s+1)**2 - 4*rho(s)))/(2*rho(s))
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# qm(s) = (s+1-sqrt((s+1)**2 - 4*rho(s)))/(2*rho(s))
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# d(q) = q**2*(c*q-1)**2 - 4*(q**2-q+1)*q**2
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# sp(q) = (-(c*q-1)*q + sqrt(d(q)))/(2*q**2)
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# sm(q) = (-(c*q-1)*q - sqrt(d(q)))/(2*q**2)
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qp(s) = (s+1+sqrt((s+1)**2 - 4*rho(s)))/(2*sqrt(rho(s)))
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qm(s) = (s+1-sqrt((s+1)**2 - 4*rho(s)))/(2*sqrt(rho(s)))
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d(q) = q**2*(c*q-1)**2 - 4*(q**2-q+1)*q**2
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sp(q) = (-(c*q-1)*q + sqrt(d(q)))/(2*q**2)
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sm(q) = (-(c*q-1)*q - sqrt(d(q)))/(2*q**2)
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plot "output/barbot_map_5000_frequencies" \
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using ($1/100.0):($2/100.0*sqrt(rho($1/100.0))):(($3==0)?1/0:$4) w p pt 5 ps 0.5 lc palette t '', \
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"output/barbot_map_500000" \
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using ($1/10.0) :($2/10.0*sqrt(rho($1/10.0))) :($3*0.7+0.3) w p pt 7 ps variable lc 3 t '', \
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sm(t), d(t) > 0 ? t*sqrt(rho(sm(t))) : 1/0 w l lw 2 lc 7 t "", \
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sp(t), d(t) > 0 ? t*sqrt(rho(sp(t))) : 1/0 w l lw 2 lc 7 t "", \
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t, qm(t) w l lw 2 lc 7 t "", \
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t, qp(t) w l lw 2 lc 7 t ""
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# 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 ''
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# pause mouse keypress
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# reread
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