/* -*-  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;

}

    obj = bld.create_ns3_program('main-random-variable')

    obj.source = 'main-random-variable.cc'

// GammaVariableImpl

class GammaVariableImpl : public RandomVariableBase

{

public:

  /**

   * \param alpha alpha parameter of the gamma distribution

   * \param beta beta parameter of the gamma distribution

   */

  GammaVariableImpl (double alpha, double beta);

  /**

   * \return A random value from this distribution

   */

  virtual double GetValue ();

  /**

   * \return A random value from the gamma distribution with parameters alpha

   * and beta

   */

  double GetValue(double alpha, double beta);

  virtual RandomVariableBase* Copy(void) const;

private:

  double m_alpha;

  double m_beta;

  NormalVariable m_normal;

};

RandomVariableBase* GammaVariableImpl::Copy () const

{

  return new GammaVariableImpl (m_alpha, m_beta);

}

GammaVariableImpl::GammaVariableImpl (double alpha, double beta)

  : m_alpha(alpha), m_beta(beta) 

{

}

double

GammaVariableImpl::GetValue ()

{

  return GetValue(m_alpha, m_beta);

}

/*

  The code for the following generator functions was adapted from ns-2

  tools/ranvar.cc

  Originally the algorithm was devised by Marsaglia in 2000:

  G. Marsaglia, W. W. Tsang: A simple method for gereating Gamma variables

  ACM Transactions on mathematical software, Vol. 26, No. 3, Sept. 2000

  The Gamma distribution density function has the form 

	                     x^(alpha-1) * exp(-x/beta)

	p(x; alpha, beta) = ----------------------------

                             beta^alpha * Gamma(alpha)

  for x > 0.

*/

double

GammaVariableImpl::GetValue (double alpha, double beta)

{

  if(!m_generator)

    {

      m_generator = new RngStream();

    }

  if (alpha < 1)

    {

      double u = m_generator->RandU01 ();

      return GetValue(1.0 + alpha, beta) * pow (u, 1.0 / alpha);

    }

  double x, v, u;

  double d = alpha - 1.0 / 3.0;

  double c = (1.0 / 3.0) / sqrt (d);

  while (1)

    {

      do

        {

          x = m_normal.GetValue ();

          v = 1.0 + c * x;

        } while (v <= 0);

      v = v * v * v;

      u = m_generator->RandU01 ();

      if (u < 1 - 0.0331 * x * x * x * x)

        break;

      if (log (u) < 0.5 * x * x + d * (1 - v + log (v)))

        break;

    }

  return beta * d * v;

}

GammaVariable::GammaVariable ()

  : RandomVariable (GammaVariableImpl (1.0, 1.0))

{

}

GammaVariable::GammaVariable (double alpha, double beta)

  : RandomVariable (GammaVariableImpl (alpha, beta))

{

}

double GammaVariable::GetValue(void) const

{

  return this->RandomVariable::GetValue ();

}

double GammaVariable::GetValue(double alpha, double beta) const

{

  return ((GammaVariableImpl*)Peek())->GetValue(alpha, beta);

}

//-----------------------------------------------------------------------------

//-----------------------------------------------------------------------------

// ErlangVariableImpl

class ErlangVariableImpl : public RandomVariableBase

{

public:

  /**

   * \param k k parameter of the Erlang distribution

   * \param lambda lambda parameter of the Erlang distribution

   */

  ErlangVariableImpl (unsigned int k, double lambda);

  /**

   * \return A random value from this distribution

   */

  virtual double GetValue ();

  /**

   * \return A random value from the Erlang distribution with parameters k and

   * lambda.

   */

  double GetValue(unsigned int k, double lambda);

  virtual RandomVariableBase* Copy(void) const;

private:

  unsigned int m_k;

  double m_lambda;

};

RandomVariableBase* ErlangVariableImpl::Copy () const

{

  return new ErlangVariableImpl (m_k, m_lambda);

}

ErlangVariableImpl::ErlangVariableImpl (unsigned int k, double lambda)

  : m_k(k), m_lambda(lambda)

{

}

double

ErlangVariableImpl::GetValue ()

{

  return GetValue(m_k, m_lambda);

}

/*

  The code for the following generator functions was adapted from ns-2

  tools/ranvar.cc

  The Erlang distribution density function has the form 

	                   x^(k-1) * exp(-x/lambda)

	p(x; k, lambda) = ---------------------------

                             lambda^k * (k-1)!

  for x > 0.

*/

double

ErlangVariableImpl::GetValue (unsigned int k, double lambda)

{

  if(!m_generator)

    {

      m_generator = new RngStream();

    }

  ExponentialVariable exponential(lambda);

  double result = 0;

  for (unsigned int i = 0; i < k; ++i)

    {

      result += exponential.GetValue();

    }

  return result;

}

ErlangVariable::ErlangVariable ()

  : RandomVariable (ErlangVariableImpl (1, 1.0))

{

}

ErlangVariable::ErlangVariable (unsigned int k, double lambda)

  : RandomVariable (ErlangVariableImpl (k, lambda))

{

}

double ErlangVariable::GetValue(void) const

{

  return this->RandomVariable::GetValue ();

}

double ErlangVariable::GetValue(unsigned int k, double lambda) const

{

  return ((ErlangVariableImpl*)Peek())->GetValue(k, lambda);

}

//-----------------------------------------------------------------------------

//-----------------------------------------------------------------------------

 * \brief Gamma Distributed Random Variable

 * \ingroup randomvariable

 *

 * GammaVariable defines a random variable with gamma distribution. 

 *

 * This class supports the creation of objects that return random numbers

 * from a fixed gamma distribution. It also supports the generation of 

 * single random numbers from various gamma distributions.

 *

 * The probability density function is defined over the interval [0,+inf) as:

 * \f$ x^{\alpha-1} \frac{e^{-\frac{x}{\beta}}}{\beta^\alpha \Gamma(\alpha)}\f$

 * where \f$ mean = \alpha\beta \f$ and 

 * \f$ variance = \alpha \beta^2\f$

 */

class GammaVariable : public RandomVariable 

{

public:

  /**

   * Constructs a gamma random variable with alpha = 1.0 and beta = 1.0

   */

  GammaVariable ();

  /**

   * \param alpha alpha parameter of the gamma distribution

   * \param beta beta parameter of the gamma distribution

   */

  GammaVariable (double alpha, double beta);

  /**

   * \brief call RandomVariable::GetValue

   * \return A floating point random value 

   *

   * Note: we have to re-implement this method here because the method is

   * overloaded below for the two-argument variant and the c++ name resolution

   * rules don't work well with overloads split between parent and child

   * classes.

   */

  double GetValue (void) const;

  /**

   * \brief Returns a gamma random distributed double with parameters alpha and beta.

   * \param alpha alpha parameter of the gamma distribution

   * \param beta beta parameter of the gamma distribution

   * \return A floating point random value

   */

  double GetValue(double alpha, double beta) const;

};

/**

 * \brief Erlang Distributed Random Variable

 * \ingroup randomvariable

 *

 * ErlangVariable defines a random variable with Erlang distribution.

 *

 * The Erlang distribution is a special case of the Gamma distribution where k

 * (= alpha) is a non-negative integer. Erlang distributed variables can be

 * generated using a much faster algorithm than gamma variables.

 *

 * This class supports the creation of objects that return random numbers from

 * a fixed Erlang distribution. It also supports the generation of single

 * random numbers from various Erlang distributions.

 *

 * The probability density function is defined over the interval [0,+inf) as:

 * \f$ \frac{x^{k-1} e^{-\frac{x}{\lambda}}}{\lambda^k (k-1)!}\f$

 * where \f$ mean = k \lambda \f$ and 

 * \f$ variance = k \lambda^2\f$

 */

class ErlangVariable : public RandomVariable 

{

public:

  /**

   * Constructs an Erlang random variable with k = 1 and lambda = 1.0

   */

  ErlangVariable ();

  /**

   * \param k k parameter of the Erlang distribution. Must be a non-negative integer.

   * \param lambda lambda parameter of the Erlang distribution

   */

  ErlangVariable (unsigned int k, double lambda);

  /**

   * \brief call RandomVariable::GetValue

   * \return A floating point random value 

   *

   * Note: we have to re-implement this method here because the method is

   * overloaded below for the two-argument variant and the c++ name resolution

   * rules don't work well with overloads split between parent and child

   * classes.

   */

  double GetValue (void) const;

  /**

   * \brief Returns an Erlang random distributed double with parameters k and lambda.

   * \param k k parameter of the Erlang distribution. Must be a non-negative integer.

   * \param lambda lambda parameter of the Erlang distribution

   * \return A floating point random value

   */

  double GetValue(unsigned int k, double lambda) const;

};

/**