Original Demo
# # random.dem
# #
# # Lattice test for random numbers;
# # If you can see any patterns in this plot, the random number generator
# # is not very good.
# #
# # Copyright (c) 1991, Jos van der Woude, jvdwoude@hut.nl
#
# # History:
# # - 6. 6. 2006 ds: added univariate and multivariate normal example
# # - 10. 5. 2006 ds: added univariate and multivariate normal example
# # - ?. ? 1991 jvdw: 1st version
#
# unset key
# set xrange [0: 1]
# set yrange [0: 1]
# set zrange [0: 1]
# set title "Lattice test for random numbers"
# set xlabel "rand(n) ->"
# set ylabel "rand(n + 1) ->"
# set zlabel "rand(n + 2) ->"
# set format x "%3.2f"
# set format y "%3.2f"
# set format z "%3.2f"
# set tics
# set sample 1000
# set style function dots
# set parametric
# plot rand(0), rand(0)
Numo.gnuplot do
unset :key
set xrange:0..1
set yrange:0..1
set zrange:0..1
set title:"Lattice test for random numbers"
set xlabel:"rand(n) ->"
set ylabel:"rand(n + 1) ->"
set zlabel:"rand(n + 2) ->"
set format_x:"%3.2f"
set format_y:"%3.2f"
set format_z:"%3.2f"
set :tics
set sample:1000
set :style, :function, :dots
set :parametric
plot "rand(0)",
"rand(0)"
end
# print "3D plot ahead, one moment please ..."
# set sample 50
# splot rand(0), rand(0), rand(0)
Numo.gnuplot do
set sample:50
splot "rand(0)",
"rand(0)",
"rand(0)"
end
# print ""
# print "Multivariate normal distribution"
# print ""
# print "The surface plot shows a two variable multivariate probability"
# print "density function. On the x-y plane are some samples of the random"
# print "vector and a contour plot illustrating the correlation, which in"
# print "this case is zero, i.e. a circle. (Easier to view in map mode.)"
# print ""
# nsamp = 50
# # Generate N random data points.
# set print "random.tmp"
# do for [i=1:nsamp] {
# print sprintf("%8.5g %8.5g", invnorm(rand(0)), invnorm(rand(0)))
# }
# unset print
# #
# unset xlabel
# unset ylabel
# unset zlabel
# set parametric
# tstring(n) = sprintf("%d random samples from a 2D Gaussian PDF with\nunit variance, zero mean and no dependence", n)
# set title tstring(nsamp)
# unset key
# set hidden3d
# #set dgrid3d
# set contour
# set view 68, 28, 1, 1
# set cntrparam levels discrete 0.1
# unset clabel
# set xrange [-3:3]
# set yrange [-3:3]
# set zrange [-0.2:0.2]
# set ztics 0,0.05
# set urange [-3:3]
# set vrange [-3:3]
# set ticslevel 0
# set isosamples 30
# splot u,v,( 1/(2*pi) * exp(-0.5 * (u**2 + v**2)) ) with line lc rgb "black", \
# "random.tmp" using 1:2:(-0.2) with points pointtype 7 lc rgb "black"
Numo.gnuplot do
run "nsamp = 50"
run <<EOL
set print "random.tmp"
do for [i=1:nsamp] {
print sprintf("%8.5g %8.5g", invnorm(rand(0)), invnorm(rand(0)))
}
unset print
EOL
unset :xlabel
unset :ylabel
unset :zlabel
set :parametric
run "tstring(n) = sprintf(\"%d random samples from a 2D Gaussian PDF with\\nunit variance, zero mean and no dependence\", n)"
set title_nq:'tstring(nsamp)'
unset :key
set :hidden3d
set :contour
set view:[68,28,1,1]
set :cntrparam, :levels, discrete:0.1
unset :clabel
set xrange:-3..3
set yrange:-3..3
set zrange:-0.2..0.2
set ztics:[0,0.05]
set urange:-3..3
set vrange:-3..3
set ticslevel:0
set isosamples:30
splot "u",
"v",
["( 1/(2*pi) * exp(-0.5 * (u**2 + v**2)) )", with:"line", lc_rgb:"black"],
["\"random.tmp\"", using:'1:2:(-0.2)', with:"points", pointtype:7, lc_rgb:"black"]
end
# unset contour
# unset parametric
#
# load "stat.inc"
#
# print ""
# print "Simple Monte Carlo simulation"
# print ""
# print "The first curve is a histogram where the binned frequency of occurence"
# print "of a pseudo random variable distributed according to the normal"
# print "(Gaussian) law is scaled such that the histogram converges to the"
# print "normal probability density function with increasing number of samples"
# print "used in the Monte Carlo simulation. The second curve is the normal"
# print "probability density function with unit variance and zero mean."
# print ""
# nsamp = 5000
# binwidth = 20
# xlow = -3.0
# xhigh = 3.0
# scale = (binwidth/(xhigh-xlow))
# # Generate N random data points.
# set print "random.tmp"
# do for [i=1:nsamp] {
# print sprintf("%8.5g %8.5g", invnorm(rand(0)), (1.0*scale/nsamp))
# }
# unset print
# #
# set samples 200
# tstring(n) = sprintf("Histogram of %d random samples from a univariate\nGaussian PDF with unit variance and zero mean", n)
# set title tstring(nsamp)
# set key
# set grid
# set xrange [-3:3]
# set yrange [0:0.45]
# bin(x) = (1.0/scale)*floor(x*scale)
# plot "random.tmp" using (bin($1)):2 smooth frequency with steps \
# title "scaled bin frequency", \
# normal(x,0,1) with lines title "Gaussian p.d.f."
Numo.gnuplot do
unset :contour
unset :parametric
load "stat.inc"
run "nsamp = 5000"
run "binwidth = 20"
run "xlow = -3.0"
run "xhigh = 3.0"
run "scale = (binwidth/(xhigh-xlow))"
run <<EOL
set print "random.tmp"
do for [i=1:nsamp] {
print sprintf("%8.5g %8.5g", invnorm(rand(0)), (1.0*scale/nsamp))
}
unset print
EOL
set samples:200
run "tstring(n) = sprintf(\"Histogram of %d random samples from a univariate\\nGaussian PDF with unit variance and zero mean\", n)"
set title_nq:'tstring(nsamp)'
set :key
set :grid
set xrange:-3..3
set yrange:0..0.45
run "bin(x) = (1.0/scale)*floor(x*scale)"
plot ["\"random.tmp\"", using:'(bin($1)):2', smooth:"frequency", with:"steps", title:"scaled bin frequency"],
["normal(x,0,1)", with:"lines", title:"Gaussian p.d.f."]
end
# print ""
# print "Another Monte Carlo simulation"
# print ""
# print "This is similar to the previous simulation but uses multivariate"
# print "zero mean, unit variance normal data by computing the distance "
# print "each point is from the origin. That distribution is known to fit"
# print "the Maxwell probability law, as shown."
# print ""
# reset
# nsamp = 3000
# # Generate N random data points.
# set print "random.tmp"
# do for [i=1:nsamp] {
# print sprintf("%8.5g %8.5g %8.5g", invnorm(rand(0)), invnorm(rand(0)), invnorm(rand(0)))
# }
# unset print
# #
# oneplot = 1
# #
# if (oneplot) set multiplot layout 1,2
# #
# unset key
# rlow = -4.0
# rhigh = 4.0
# set parametric
# set xrange [rlow:rhigh]; set yrange [rlow:rhigh]; set zrange [rlow:rhigh]
# set xtics axis nomirror; set ytics axis nomirror; set ztics axis nomirror;
# set border 0
# set xyplane at 0
# set xzeroaxis lt -1
# set yzeroaxis lt -1
# set zzeroaxis lt -1
# set view 68, 28, 1.4, 0.9
# tstring(n) = sprintf("Gaussian 3D cloud of %d random samples\n", n)
# set title tstring(nsamp) offset graph 0.15, graph -0.33
# splot "random.tmp" every :::::0 with dots
Numo.gnuplot do
reset
run "nsamp = 3000"
run <<EOL
set print "random.tmp"
do for [i=1:nsamp] {
print sprintf("%8.5g %8.5g %8.5g", invnorm(rand(0)), invnorm(rand(0)), invnorm(rand(0)))
}
unset print
EOL
run "oneplot = 1"
unset :key
run "rlow = -4.0"
run "rhigh = 4.0"
set :parametric
set xrange:"[rlow:rhigh]"; set yrange:"[rlow:rhigh]"; set zrange:"[rlow:rhigh]"
set :xtics, :axis, :nomirror; set :ytics, :axis, :nomirror; set :ztics, :axis, :nomirror
set border:0
set :xyplane, at:0
set :xzeroaxis, lt:-1
set :yzeroaxis, lt:-1
set :zzeroaxis, lt:-1
set view:[68,28,1.4,0.9]
run "tstring(n) = sprintf(\"Gaussian 3D cloud of %d random samples\\n\", n)"
set title_nq:'tstring(nsamp)', offset:"graph 0.15, graph -0.33"
splot "\"random.tmp\"", every:":::::0", with:"dots"
end
# if (!oneplot) pause -1 "Hit return to continue"
#
# unset parametric
# unset xzeroaxis; unset yzeroaxis;
# set border
# set grid
# set samples 200
# set size 0.47,0.72
# set origin 0.44,0.18
# tstring(n) = sprintf("Histogram of distance from origin of\n%d multivariate unit variance samples", n)
# set title tstring(nsamp) offset graph 0, graph 0.15
# set key bmargin right vertical
# xlow = 0.0
# xhigh = 4.5
# binwidth = 20
# scale = (binwidth/(xhigh-xlow))
# set xrange [0:xhigh]
# set yrange [0:0.65]
# bin(x) = (1.0/scale)*floor(x*scale)
# plot "random.tmp" using (bin(sqrt($1**2+$2**2+$3**2))):(1.0*scale/nsamp) every :::::0 smooth frequency with steps \
# title "scaled bin frequency", \
# maxwell(x, 1/sqrt(2)) with lines title "Maxwell p.d.f."
Numo.gnuplot do
unset :parametric
unset :xzeroaxis; unset :yzeroaxis
set :border
set :grid
set samples:200
set size:[0.47,0.72]
set origin:[0.44,0.18]
run "tstring(n) = sprintf(\"Histogram of distance from origin of\\n%d multivariate unit variance samples\", n)"
set title_nq:'tstring(nsamp)', offset:"graph 0, graph 0.15"
set :key, :bmargin, :right, :vertical
run "xlow = 0.0"
run "xhigh = 4.5"
run "binwidth = 20"
run "scale = (binwidth/(xhigh-xlow))"
set xrange:"[0:xhigh]"
set yrange:0..0.65
run "bin(x) = (1.0/scale)*floor(x*scale)"
plot ["\"random.tmp\"", using:'(bin(sqrt($1**2+$2**2+$3**2))):(1.0*scale/nsamp)', every:":::::0", smooth:"frequency", with:"steps", title:"scaled bin frequency"],
["maxwell(x, 1/sqrt(2))", with:"lines", title:"Maxwell p.d.f."]
end