/* -*- Mode: C++; c-file-style: "gnu"; indent-tabs-mode:nil; -*- */
/*
* Copyright (c) 2008 Timo Bingmann
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License version 2 as
* published by the Free Software Foundation;
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
* Author: Timo Bingmann <timo.bingmann@student.kit.edu>
*/
#include "ns3/random-variable.h"
#include "ns3/gnuplot.h"
#include <map>
#include <cmath>
using namespace ns3;
/// Round a double number to the given precision. e.g. dround(0.234, 0.1) = 0.2
/// and dround(0.257, 0.1) = 0.3
double dround(double number, double precision)
{
number /= precision;
if (number >= 0)
number = std::floor(number + 0.5);
else
number = std::ceil(number - 0.5);
number *= precision;
return number;
}
static GnuplotDataset
Histogramm (RandomVariable rndvar, unsigned int probes, double precision, const std::string& title, bool notcontinous = false)
{
typedef std::map<double, unsigned int> histogramm_maptype;
histogramm_maptype histogramm;
for(unsigned int i = 0; i < probes; ++i)
{
double val = dround( rndvar.GetValue(), precision );
++histogramm[val];
}
Gnuplot2dDataset data;
data.SetTitle(title);
if (notcontinous)
{
data.SetStyle(Gnuplot2dDataset::IMPULSES);
}
for(histogramm_maptype::const_iterator hi = histogramm.begin();
hi != histogramm.end(); ++hi)
{
data.Add(hi->first, (double)hi->second / (double)probes / precision);
}
return data;
}
int main (int argc, char *argv[])
{
unsigned int probes = 1000000;
double precision = 0.01;
GnuplotCollection gnuplots("main-random-variables.pdf");
gnuplots.SetTerminal("pdf enhanced");
{
Gnuplot plot;
plot.SetTitle("UniformVariable");
plot.AppendExtra("set yrange [0:]");
plot.AddDataset( Histogramm(UniformVariable(0.0, 1.0), probes, precision,
"UniformVariable [0.0 .. 1.0)") );
plot.AddDataset( Gnuplot2dFunction("0.1",
"0 <= x && x <= 1 ? 1.0 : 0") );
gnuplots.AddPlot(plot);
}
{
Gnuplot plot;
plot.SetTitle("ExponentialVariable");
plot.AppendExtra("set xrange [0:8]");
plot.AppendExtra("ExpDist(x,l) = 1/l * exp(-1/l * x)");
plot.AddDataset( Histogramm(ExponentialVariable(0.5), probes, precision,
"ExponentialVariable m=0.5") );
plot.AddDataset( Gnuplot2dFunction("ExponentialDistribution mean 0.5",
"ExpDist(x, 0.5)") );
plot.AddDataset( Histogramm(ExponentialVariable(1.0), probes, precision,
"ExponentialVariable m=1") );
plot.AddDataset( Gnuplot2dFunction("ExponentialDistribution mean 1.0",
"ExpDist(x, 1.0)") );
plot.AddDataset( Histogramm(ExponentialVariable(1.5), probes, precision,
"ExponentialVariable m=1.5") );
plot.AddDataset( Gnuplot2dFunction("ExponentialDistribution mean 1.5",
"ExpDist(x, 1.5)") );
gnuplots.AddPlot(plot);
}
{
Gnuplot plot;
plot.SetTitle("ParetoVariable");
plot.AppendExtra("set xrange [0:2]");
plot.AddDataset( Histogramm(ParetoVariable(1.0, 1.5), probes, precision,
"ParetoVariable m=1.0 s=1.5") );
plot.AddDataset( Histogramm(ParetoVariable(1.0, 2.0), probes, precision,
"ParetoVariable m=1.0 s=2.0") );
plot.AddDataset( Histogramm(ParetoVariable(1.0, 2.5), probes, precision,
"ParetoVariable m=1.0 s=2.5") );
gnuplots.AddPlot(plot);
}
{
Gnuplot plot;
plot.SetTitle("WeibullVariable");
plot.AppendExtra("set xrange [0:3]");
plot.AddDataset( Histogramm(WeibullVariable(1.0, 1.0), probes, precision,
"WeibullVariable m=1.0 s=1.0") );
plot.AddDataset( Histogramm(WeibullVariable(1.0, 2.0), probes, precision,
"WeibullVariable m=1.0 s=2.0") );
plot.AddDataset( Histogramm(WeibullVariable(1.0, 3.0), probes, precision,
"WeibullVariable m=1.0 s=3.0") );
gnuplots.AddPlot(plot);
}
{
Gnuplot plot;
plot.SetTitle("NormalVariable");
plot.AppendExtra("set xrange [-3:3]");
plot.AppendExtra("NormalDist(x,m,s) = 1 / (s * sqrt(2*pi)) * exp(-1.0 / 2.0 * ((x-m) / s)**2)");
plot.AddDataset( Histogramm(NormalVariable(0.0, 1.0), probes, precision,
"NormalVariable m=0.0 v=1.0") );
plot.AddDataset( Gnuplot2dFunction("NormalDist {/Symbol m}=0.0 {/Symbol s}=1.0",
"NormalDist(x,0.0,1.0)") );
plot.AddDataset( Histogramm(NormalVariable(0.0, 2.0), probes, precision,
"NormalVariable m=0.0 v=2.0") );
plot.AddDataset( Gnuplot2dFunction("NormalDist {/Symbol m}=0.0 {/Symbol s}=sqrt(2.0)",
"NormalDist(x,0.0,sqrt(2.0))") );
plot.AddDataset( Histogramm(NormalVariable(0.0, 3.0), probes, precision,
"NormalVariable m=0.0 v=3.0") );
plot.AddDataset( Gnuplot2dFunction("NormalDist {/Symbol m}=0.0 {/Symbol s}=sqrt(3.0)",
"NormalDist(x,0.0,sqrt(3.0))") );
gnuplots.AddPlot(plot);
}
{
Gnuplot plot;
plot.SetTitle("EmpiricalVariable");
plot.AppendExtra("set xrange [*:*]");
EmpiricalVariable emp1;
emp1.CDF(0.0, 0.0 / 15.0);
emp1.CDF(0.2, 1.0 / 15.0);
emp1.CDF(0.4, 3.0 / 15.0);
emp1.CDF(0.6, 6.0 / 15.0);
emp1.CDF(0.8, 10.0 / 15.0);
emp1.CDF(1.0, 15.0 / 15.0);
plot.AddDataset( Histogramm(emp1, probes, precision,
"EmpiricalVariable (Stairs)") );
gnuplots.AddPlot(plot);
}
{
Gnuplot plot;
plot.SetTitle("DeterministicVariable");
plot.AppendExtra("set xrange [*:*]");
double values[] = { 0.0, 0.2, 0.2, 0.4, 0.2, 0.6, 0.8, 0.8, 1.0 };
DeterministicVariable det1 (values, sizeof(values) / sizeof(values[0]));
plot.AddDataset( Histogramm(det1, probes, precision,
"DeterministicVariable", true) );
gnuplots.AddPlot(plot);
}
{
Gnuplot plot;
plot.SetTitle("LogNormalVariable");
plot.AppendExtra("set xrange [0:3]");
plot.AppendExtra("LogNormalDist(x,m,s) = 1.0/x * NormalDist(log(x), m, s)");
plot.AddDataset( Histogramm(LogNormalVariable(0.0, 1.0), probes, precision,
"LogNormalVariable m=0.0 s=1.0") );
plot.AddDataset( Gnuplot2dFunction("LogNormalDist(x, 0.0, 1.0)",
"LogNormalDist(x, 0.0, 1.0)") );
plot.AddDataset( Histogramm(LogNormalVariable(0.0, 0.5), probes, precision,
"LogNormalVariable m=0.0 s=0.5") );
plot.AddDataset( Histogramm(LogNormalVariable(0.0, 0.25), probes, precision,
"LogNormalVariable m=0.0 s=0.25") );
plot.AddDataset( Gnuplot2dFunction("LogNormalDist(x, 0.0, 0.25)",
"LogNormalDist(x, 0.0, 0.25)") );
plot.AddDataset( Histogramm(LogNormalVariable(0.0, 0.125), probes, precision,
"LogNormalVariable m=0.0 s=0.125") );
plot.AddDataset( Histogramm(LogNormalVariable(0.0, 2.0), probes, precision,
"LogNormalVariable m=0.0 s=2.0") );
plot.AddDataset( Gnuplot2dFunction("LogNormalDist(x, 0.0, 2.0)",
"LogNormalDist(x, 0.0, 2.0)") );
plot.AddDataset( Histogramm(LogNormalVariable(0.0, 2.5), probes, precision,
"LogNormalVariable m=0.0 s=2.5") );
gnuplots.AddPlot(plot);
}
{
Gnuplot plot;
plot.SetTitle("TriangularVariable");
plot.AppendExtra("set xrange [*:*]");
plot.AddDataset( Histogramm(TriangularVariable(0.0, 1.0, 0.5), probes, precision,
"TriangularVariable [0.0 .. 1.0) m=0.5") );
plot.AddDataset( Histogramm(TriangularVariable(0.0, 1.0, 0.4), probes, precision,
"TriangularVariable [0.0 .. 1.0) m=0.4") );
plot.AddDataset( Histogramm(TriangularVariable(0.0, 1.0, 0.65), probes, precision,
"TriangularVariable [0.0 .. 1.0) m=0.65") );
gnuplots.AddPlot(plot);
}
{
Gnuplot plot;
plot.SetTitle("GammaVariable");
plot.AppendExtra("set xrange [0:10]");
plot.AppendExtra("set yrange [0:1]");
plot.AppendExtra("GammaDist(x,a,b) = x**(a-1) * 1/b**a * exp(-x/b) / gamma(a)");
plot.AppendExtra("set label 1 '{/Symbol g}(x,{/Symbol a},{/Symbol b}) = x^{/Symbol a-1} e^{-x {/Symbol b}^{-1}} ( {/Symbol b}^{/Symbol a} {/Symbol G}({/Symbol a}) )^{-1}' at 0.7, 0.9");
plot.AddDataset( Histogramm(GammaVariable(1.0, 1.0), probes, precision,
"GammaVariable a=1.0 b=1.0") );
plot.AddDataset( Gnuplot2dFunction("{/Symbol g}(x, 1.0, 1.0)",
"GammaDist(x, 1.0, 1.0)") );
plot.AddDataset( Histogramm(GammaVariable(1.5, 1.0), probes, precision,
"GammaVariable a=1.5 b=1.0") );
plot.AddDataset( Gnuplot2dFunction("{/Symbol g}(x, 1.5, 1.0)",
"GammaDist(x, 1.5, 1.0)") );
plot.AddDataset( Histogramm(GammaVariable(2.0, 1.0), probes, precision,
"GammaVariable a=2.0 b=1.0") );
plot.AddDataset( Gnuplot2dFunction("{/Symbol g}(x, 2.0, 1.0)",
"GammaDist(x, 2.0, 1.0)") );
plot.AddDataset( Histogramm(GammaVariable(4.0, 1.0), probes, precision,
"GammaVariable a=4.0 b=1.0") );
plot.AddDataset( Gnuplot2dFunction("{/Symbol g}(x, 4.0, 1.0)",
"GammaDist(x, 4.0, 1.0)") );
plot.AddDataset( Histogramm(GammaVariable(2.0, 2.0), probes, precision,
"GammaVariable a=2.0 b=2.0") );
plot.AddDataset( Gnuplot2dFunction("{/Symbol g}(x, 2.0, 2.0)",
"GammaDist(x, 2.0, 2.0)") );
plot.AddDataset( Histogramm(GammaVariable(2.5, 3.0), probes, precision,
"GammaVariable a=2.5 b=3.0") );
plot.AddDataset( Gnuplot2dFunction("{/Symbol g}(x, 2.5, 3.0)",
"GammaDist(x, 2.5, 3.0)") );
plot.AddDataset( Histogramm(GammaVariable(2.5, 4.5), probes, precision,
"GammaVariable a=2.5 b=4.5") );
plot.AddDataset( Gnuplot2dFunction("{/Symbol g}(x, 2.5, 4.5)",
"GammaDist(x, 2.5, 4.5)") );
gnuplots.AddPlot(plot);
}
{
Gnuplot plot;
plot.SetTitle("ErlangVariable");
plot.AppendExtra("set xrange [0:10]");
plot.AppendExtra("ErlangDist(x,k,l) = x**(k-1) * 1/l**k * exp(-x/l) / (k-1)!");
plot.AppendExtra("set label 1 'Erlang(x,k,{/Symbol l}) = x^{k-1} e^{-x {/Symbol l}^{-1}} ( {/Symbol l}^k (k-1)! )^{-1}' at 0.7, 0.9");
plot.AddDataset( Histogramm(ErlangVariable(1, 1.0), probes, precision,
"ErlangVariable k=1 {/Symbol l}=1.0") );
plot.AddDataset( Gnuplot2dFunction("Erlang(x, 1, 1.0)",
"ErlangDist(x, 1, 1.0)") );
plot.AddDataset( Histogramm(ErlangVariable(2, 1.0), probes, precision,
"ErlangVariable k=2 {/Symbol l}=1.0") );
plot.AddDataset( Gnuplot2dFunction("Erlang(x, 2, 1.0)",
"ErlangDist(x, 2, 1.0)") );
plot.AddDataset( Histogramm(ErlangVariable(3, 1.0), probes, precision,
"ErlangVariable k=3 {/Symbol l}=1.0") );
plot.AddDataset( Gnuplot2dFunction("Erlang(x, 3, 1.0)",
"ErlangDist(x, 3, 1.0)") );
plot.AddDataset( Histogramm(ErlangVariable(5, 1.0), probes, precision,
"ErlangVariable k=5 {/Symbol l}=1.0") );
plot.AddDataset( Gnuplot2dFunction("Erlang(x, 5, 1.0)",
"ErlangDist(x, 5, 1.0)") );
plot.AddDataset( Histogramm(ErlangVariable(2, 2.0), probes, precision,
"ErlangVariable k=2 {/Symbol l}=2.0") );
plot.AddDataset( Gnuplot2dFunction("Erlang(x, 2, 2.0)",
"ErlangDist(x, 2, 2.0)") );
plot.AddDataset( Histogramm(ErlangVariable(2, 3.0), probes, precision,
"ErlangVariable k=2 {/Symbol l}=3.0") );
plot.AddDataset( Gnuplot2dFunction("Erlang(x, 2, 3.0)",
"ErlangDist(x, 2, 3.0)") );
plot.AddDataset( Histogramm(ErlangVariable(2, 5.0), probes, precision,
"ErlangVariable k=2 {/Symbol l}=5.0") );
plot.AddDataset( Gnuplot2dFunction("Erlang(x, 2, 5.0)",
"ErlangDist(x, 2, 5.0)") );
gnuplots.AddPlot(plot);
}
gnuplots.GenerateOutput(std::cout);
return 0;
}