/* -*- Mode:C++; c-file-style:"gnu"; indent-tabs-mode:nil; -*- */
/*
* Copyright (c) 2006 Georgia Tech Research Corporation
* Copyright (c) 2011 Mathieu Lacage
*
* 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
*
* Authors: Rajib Bhattacharjea<raj.b@gatech.edu>
* Hadi Arbabi<marbabi@cs.odu.edu>
* Mathieu Lacage <mathieu.lacage@gmail.com>
*
* Modified by Mitch Watrous <watrous@u.washington.edu>
*
*/
#ifndef RANDOM_VARIABLE_STREAM_H
#define RANDOM_VARIABLE_STREAM_H
#include "type-id.h"
#include "object.h"
#include "attribute-helper.h"
#include <stdint.h>
namespace ns3 {
/**
* \ingroup core
* \defgroup randomvariable Random Variables
*
* \brief ns-3 random numbers are provided via instances of
* ns3::RandomVariableStream.
*
* - By default, ns-3 simulations use a fixed seed; if there is any
* randomness in the simulation, each run of the program will yield
* identical results unless the seed and/or run number is changed.
* - In ns-3.3 and earlier, ns-3 simulations used a random seed by default;
* this marks a change in policy starting with ns-3.4.
* - In ns-3.14 and earlier, ns-3 simulations used a different wrapper
* class called ns3::RandomVariable. This implementation is documented
* above under Legacy Random Variables. As of ns-3.15, this class has
* been replaced by ns3::RandomVariableStream; the underlying
* pseudo-random number generator has not changed.
* - To obtain randomness across multiple simulation runs, you must
* either set the seed differently or set the run number differently.
* To set a seed, call ns3::RngSeedManager::SetSeed() at the beginning
* of the program; to set a run number with the same seed, call
* ns3::RngSeedManager::SetRun() at the beginning of the program.
* - Each RandomVariableStream used in ns-3 has a virtual random number
* generator associated with it; all random variables use either
* a fixed or random seed based on the use of the global seed.
* - If you intend to perform multiple runs of the same scenario,
* with different random numbers, please be sure to read the manual
* section on how to perform independent replications.
*/
class RngStream;
/**
* \ingroup randomvariable
* \brief The Random Number Generator (RNG) that allows stream numbers to be set deterministically.
*
* Note: The underlying random number generation method used
* by NS-3 is the RngStream code by Pierre L'Ecuyer at
* the University of Montreal.
*
* NS-3 has a rich set of random number generators that allow stream
* numbers to be set deterministically if desired. Class
* RandomVariableStream defines the base class functionalty required
* for all such random number generators.
*
* By default, the underlying generator is seeded all the time with
* the same seed value and run number coming from the ns3::GlobalValue
* \ref GlobalValueRngSeed "RngSeed" and \ref GlobalValueRngRun
* "RngRun". Also by default, the stream number value for this RNG
* stream is automatically allocated.
*/
class RandomVariableStream : public Object
{
public:
static TypeId GetTypeId (void);
RandomVariableStream ();
virtual ~RandomVariableStream();
/**
* \brief Specifies the stream number for this RNG stream.
* \param stream The stream number for this RNG stream. -1 means "allocate a stream number automatically".
*/
void SetStream (int64_t stream);
/**
* \brief Returns the stream number for this RNG stream.
* \return The stream number for this RNG stream. -1 means "allocate a stream number automatically".
*/
int64_t GetStream(void) const;
/**
* \brief Specifies whether antithetic values should be generated.
* \param isAntithetic Set equal to true if antithetic values should
* be generated by this RNG stream.
*/
void SetAntithetic(bool isAntithetic);
/**
* \brief Returns true if antithetic values should be generated.
* \return A bool value that indicates if antithetic values should
* be generated by this RNG stream.
*/
bool IsAntithetic(void) const;
/**
* \brief Returns a random double from the underlying distribution
* \return A floating point random value.
*/
virtual double GetValue (void) = 0;
/**
* \brief Returns a random integer integer from the underlying distribution
* \return Integer cast of RandomVariableStream::GetValue
*/
virtual uint32_t GetInteger (void) = 0;
protected:
/**
* \brief Returns a pointer to the underlying RNG stream.
*/
RngStream *Peek(void) const;
private:
// you can't copy these objects.
// Theoretically, it is possible to give them good copy semantics
// but not enough time to iron out the details.
RandomVariableStream (const RandomVariableStream &o);
RandomVariableStream &operator = (const RandomVariableStream &o);
/// Pointer to the underlying RNG stream.
RngStream *m_rng;
/// Indicates if antithetic values should be generated by this RNG stream.
bool m_isAntithetic;
/// The stream number for this RNG stream.
int64_t m_stream;
};
/**
* \ingroup randomvariable
* \brief The uniform distribution Random Number Generator (RNG) that allows stream numbers to be set deterministically.
*
* This class supports the creation of objects that return random numbers
* from a fixed uniform distribution. It also supports the generation of
* single random numbers from various uniform distributions.
*
* The low end of the range is always included and the high end
* of the range is always excluded.
*
* Here is an example of how to use this class:
* \code
* double min = 0.0;
* double max = 10.0;
*
* Ptr<UniformRandomVariable> x = CreateObject<UniformRandomVariable> ();
* x->SetAttribute ("Min", DoubleValue (min));
* x->SetAttribute ("Max", DoubleValue (max));
*
* // The values returned by a uniformly distributed random
* // variable should always be within the range
* //
* // [min, max) .
* //
* double value = x->GetValue ();
* \endcode
*/
class UniformRandomVariable : public RandomVariableStream
{
public:
static TypeId GetTypeId (void);
/**
* \brief Creates a uniform distribution RNG with the default range.
*/
UniformRandomVariable ();
/**
* \brief Returns the lower bound on values that can be returned by this RNG stream.
* \return The lower bound on values that can be returned by this RNG stream.
*/
double GetMin (void) const;
/**
* \brief Returns the upper bound on values that can be returned by this RNG stream.
* \return The upper bound on values that can be returned by this RNG stream.
*/
double GetMax (void) const;
/**
* \brief Returns a random double from the uniform distribution with the specified range.
* \param min Low end of the range.
* \param max High end of the range.
* \return A floating point random value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$x\f$ is a value that
* would be returned normally, then \f$(max - x\f$) is the distance
* that \f$x\f$ would be from \f$max\f$. The value returned in the
* antithetic case, \f$x'\f$, is calculated as
*
* \f[
* x' = min + (max - x) ,
* \f]
*
* which is the lower bound plus the distance \f$x\f$ is from the
* upper bound.
*/
double GetValue (double min, double max);
/**
* \brief Returns a random unsigned integer from a uniform distribution over the interval [min,max] including both ends.
* \param min Low end of the range.
* \param max High end of the range.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$x\f$ is a value that
* would be returned normally, then \f$(max - x\f$) is the distance
* that \f$x\f$ would be from \f$max\f$. The value returned in the
* antithetic case, \f$x'\f$, is calculated as
*
* \f[
* x' = min + (max - x) ,
* \f]
*
* which is the lower bound plus the distance \f$x\f$ is from the
* upper bound.
*/
uint32_t GetInteger (uint32_t min, uint32_t max);
/**
* \brief Returns a random double from the uniform distribution with the range [min,max), where min and max are the current lower and upper bounds.
* \return A floating point random value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$x\f$ is a value that
* would be returned normally, then \f$(max - x\f$) is the distance
* that \f$x\f$ would be from \f$max\f$. The value returned in the
* antithetic case, \f$x'\f$, is calculated as
*
* \f[
* x' = min + (max - x) ,
* \f]
*
* which is the lower bound plus the distance \f$x\f$ is from the
* upper bound.
*
* Note that we have to re-implement this method here because the method is
* overloaded above for the two-argument variant and the c++ name resolution
* rules don't work well with overloads split between parent and child
* classes.
*/
virtual double GetValue (void);
/**
* \brief Returns a random unsigned integer from a uniform distribution over the interval [min,max] including both ends, where min and max are the current lower and upper bounds.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$x\f$ is a value that
* would be returned normally, then \f$(max - x\f$) is the distance
* that \f$x\f$ would be from \f$max\f$. The value returned in the
* antithetic case, \f$x'\f$, is calculated as
*
* \f[
* x' = min + (max - x) ,
* \f]
*
* which is the lower bound plus the distance \f$x\f$ is from the
* upper bound.
*/
virtual uint32_t GetInteger (void);
private:
/// The lower bound on values that can be returned by this RNG stream.
double m_min;
/// The upper bound on values that can be returned by this RNG stream.
double m_max;
};
/**
* \ingroup randomvariable
* \brief The Random Number Generator (RNG) that returns a constant.
*
* Class ConstantRandomVariable returns the same value for every sample.
*/
class ConstantRandomVariable : public RandomVariableStream
{
public:
static TypeId GetTypeId (void);
/**
* \brief Creates a constant RNG with the default constant value.
*/
ConstantRandomVariable ();
/**
* \brief Returns the constant value returned by this RNG stream.
* \return The constant value returned by this RNG stream.
*/
double GetConstant (void) const;
/**
* \brief Returns the value passed in.
* \return The floating point value passed in.
*/
double GetValue (double constant);
/**
* \brief Returns the value passed in.
* \return The integer value passed in.
*/
uint32_t GetInteger (uint32_t constant);
/**
* \brief Returns the constant value returned by this RNG stream.
* \return The constant value returned by this RNG stream.
*/
virtual double GetValue (void);
/**
* \brief Returns an integer cast of the constant value returned by this RNG stream.
* \return Integer cast of the constant value returned by this RNG stream.
*/
virtual uint32_t GetInteger (void);
private:
/// The constant value returned by this RNG stream.
double m_constant;
};
/**
* \ingroup randomvariable
* \brief The Random Number Generator (RNG) that returns a sequential
* list of values
*
* Class SequentialRandomVariable defines a random number generator
* that returns a sequence of values. The sequence monotonically
* increases for a period, then wraps around to the low value and
* begins monotonically increasing again.
*/
class SequentialRandomVariable : public RandomVariableStream
{
public:
static TypeId GetTypeId (void);
/**
* \brief Creates a sequential RNG with the default values for the sequence parameters.
*/
SequentialRandomVariable ();
/**
* \brief Returns the first value of the sequence.
* \return The first value of the sequence.
*/
double GetMin (void) const;
/**
* \brief Returns one more than the last value of the sequence.
* \return One more than the last value of the sequence.
*/
double GetMax (void) const;
/**
* \brief Returns the random variable increment for the sequence.
* \return The random variable increment for the sequence.
*/
Ptr<RandomVariableStream> GetIncrement (void) const;
/**
* \brief Returns the number of times each member of the sequence is repeated.
* \return The number of times each member of the sequence is repeated.
*/
uint32_t GetConsecutive (void) const;
/**
* \brief Returns the next value in the sequence returned by this RNG stream.
* \return The next value in the sequence returned by this RNG stream.
*
* The following four parameters define the sequence. For example,
*
* - m_min = 0 (First value of the sequence)
* - m_max = 5 (One more than the last value of the sequence)
* - m_increment = 1 (Random variable increment between sequence values)
* - m_consecutive = 2 (Number of times each member of the sequence is repeated)
*
* creates a RNG that has the sequence 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 0, 0 ...
*/
virtual double GetValue (void);
/**
* \brief Returns an integer cast of the next value in the sequence returned by this RNG stream.
* \return Integer cast of the next value in the sequence returned by this RNG stream.
*/
virtual uint32_t GetInteger (void);
private:
/// The first value of the sequence.
double m_min;
/// One more than the last value of the sequence.
double m_max;
/// The sequence random variable increment.
Ptr<RandomVariableStream> m_increment;
/// The number of times each member of the sequence is repeated.
uint32_t m_consecutive;
/// The current sequence value.
double m_current;
/// The number of times the sequence has been repeated.
uint32_t m_currentConsecutive;
/// Indicates if the current sequence value has been set.
bool m_isCurrentSet;
};
/**
* \ingroup randomvariable
* \brief The exponential distribution Random Number Generator (RNG) that allows stream numbers to be set deterministically.
*
* This class supports the creation of objects that return random numbers
* from a fixed exponential distribution. It also supports the generation of
* single random numbers from various exponential distributions.
*
* The probability density function of an exponential variable
* is defined over the interval [0, \f$+\infty\f$) as:
* \f$ \alpha e^{-\alpha x} \f$
* where \f$ \alpha = \frac{1}{mean} \f$
*
* Since exponential distributions can theoretically return unbounded
* values, it is sometimes useful to specify a fixed upper limit. The
* bounded version is defined over the interval [0,b] as: \f$ \alpha
* e^{-\alpha x} \quad x \in [0,b] \f$. Note that in this case the
* true mean of the distribution is slightly smaller than the mean
* value specified: \f$ 1/\alpha - b/(e^{\alpha \, b}-1) \f$.
*
* Here is an example of how to use this class:
* \code
* double mean = 3.14;
* double bound = 0.0;
*
* Ptr<ExponentialRandomVariable> x = CreateObject<ExponentialRandomVariable> ();
* x->SetAttribute ("Mean", DoubleValue (mean));
* x->SetAttribute ("Bound", DoubleValue (bound));
*
* // The expected value for the mean of the values returned by an
* // exponentially distributed random variable is equal to mean.
* double value = x->GetValue ();
* \endcode
*/
class ExponentialRandomVariable : public RandomVariableStream
{
public:
static TypeId GetTypeId (void);
/**
* \brief Creates a exponential distribution RNG with the default
* values for the mean and upper bound.
*/
ExponentialRandomVariable ();
/**
* \brief Returns the mean value of the random variables returned by this RNG stream.
* \return The mean value of the random variables returned by this RNG stream.
*/
double GetMean (void) const;
/**
* \brief Returns the upper bound on values that can be returned by this RNG stream.
* \return The upper bound on values that can be returned by this RNG stream.
*/
double GetBound (void) const;
/**
* \brief Returns a random double from an exponential distribution with the specified mean and upper bound.
* \param mean Mean value of the random variables.
* \param bound Upper bound on values returned.
* \return A floating point random value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$u\f$ is a uniform variable
* over [0,1] and
*
* \f[
* x = - mean * \log(u)
* \f]
*
* is a value that would be returned normally, then \f$(1 - u\f$) is
* the distance that \f$u\f$ would be from \f$1\f$. The value
* returned in the antithetic case, \f$x'\f$, is calculated as
*
* \f[
* x' = - mean * \log(1 - u),
* \f]
*
* which now involves the log of the distance \f$u\f$ is from the 1.
*/
double GetValue (double mean, double bound);
/**
* \brief Returns a random unsigned integer from an exponential distribution with the specified mean and upper bound.
* \param mean Mean value of the random variables.
* \param bound Upper bound on values returned.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$u\f$ is a uniform variable
* over [0,1] and
*
* \f[
* x = - mean * \log(u)
* \f]
*
* is a value that would be returned normally, then \f$(1 - u\f$) is
* the distance that \f$u\f$ would be from \f$1\f$. The value
* returned in the antithetic case, \f$x'\f$, is calculated as
*
* \f[
* x' = - mean * \log(1 - u),
* \f]
*
* which now involves the log of the distance \f$u\f$ is from the 1.
*/
uint32_t GetInteger (uint32_t mean, uint32_t bound);
/**
* \brief Returns a random double from an exponential distribution with the current mean and upper bound.
* \return A floating point random value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$u\f$ is a uniform variable
* over [0,1] and
*
* \f[
* x = - mean * \log(u)
* \f]
*
* is a value that would be returned normally, then \f$(1 - u\f$) is
* the distance that \f$u\f$ would be from \f$1\f$. The value
* returned in the antithetic case, \f$x'\f$, is calculated as
*
* \f[
* x' = - mean * \log(1 - u),
* \f]
*
* which now involves the log of the distance \f$u\f$ is from the 1.
*
* Note that we have to re-implement this method here because the method is
* overloaded above for the two-argument variant and the c++ name resolution
* rules don't work well with overloads split between parent and child
* classes.
*/
virtual double GetValue (void);
/**
* \brief Returns a random unsigned integer from an exponential distribution with the current mean and upper bound.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$u\f$ is a uniform variable
* over [0,1] and
*
* \f[
* x = - mean * \log(u)
* \f]
*
* is a value that would be returned normally, then \f$(1 - u\f$) is
* the distance that \f$u\f$ would be from \f$1\f$. The value
* returned in the antithetic case, \f$x'\f$, is calculated as
*
* \f[
* x' = - mean * \log(1 - u),
* \f]
*
* which now involves the log of the distance \f$u\f$ is from the 1.
*/
virtual uint32_t GetInteger (void);
private:
/// The mean value of the random variables returned by this RNG stream.
double m_mean;
/// The upper bound on values that can be returned by this RNG stream.
double m_bound;
};
/**
* \ingroup randomvariable
* \brief The Pareto distribution Random Number Generator (RNG) that allows stream numbers to be set deterministically.
*
* This class supports the creation of objects that return random numbers
* from a fixed Pareto distribution. It also supports the generation of
* single random numbers from various Pareto distributions.
*
* The probability density function of a Pareto variable is defined
* over the range [\f$x_m\f$,\f$+\infty\f$) as: \f$ k \frac{x_m^k}{x^{k+1}}\f$
* where \f$x_m > 0\f$ is called the scale parameter and \f$ k > 0\f$
* is called the pareto index or shape.
*
* The parameter \f$ x_m \f$ can be infered from the mean and the parameter \f$ k \f$
* with the equation \f$ x_m = mean \frac{k-1}{k}, k > 1\f$.
*
* Since Pareto distributions can theoretically return unbounded values,
* it is sometimes useful to specify a fixed upper limit. Note however
* when the upper limit is specified, the true mean of the distribution
* is slightly smaller than the mean value specified.
*
* Here is an example of how to use this class:
* \code
* double mean = 5.0;
* double shape = 2.0;
*
* Ptr<ParetoRandomVariable> x = CreateObject<ParetoRandomVariable> ();
* x->SetAttribute ("Mean", DoubleValue (mean));
* x->SetAttribute ("Shape", DoubleValue (shape));
*
* // The expected value for the mean of the values returned by a
* // Pareto distributed random variable is
* //
* // shape * scale
* // E[value] = --------------- ,
* // shape - 1
* //
* // where
* //
* // scale = mean * (shape - 1.0) / shape .
* //
* double value = x->GetValue ();
* \endcode
*/
class ParetoRandomVariable : public RandomVariableStream
{
public:
static TypeId GetTypeId (void);
/**
* \brief Creates a Pareto distribution RNG with the default
* values for the mean, the shape, and upper bound.
*/
ParetoRandomVariable ();
/**
* \brief Returns the mean parameter for the Pareto distribution returned by this RNG stream.
* \return The mean parameter for the Pareto distribution returned by this RNG stream.
*/
double GetMean (void) const;
/**
* \brief Returns the shape parameter for the Pareto distribution returned by this RNG stream.
* \return The shape parameter for the Pareto distribution returned by this RNG stream.
*/
double GetShape (void) const;
/**
* \brief Returns the upper bound on values that can be returned by this RNG stream.
* \return The upper bound on values that can be returned by this RNG stream.
*/
double GetBound (void) const;
/**
* \brief Returns a random double from a Pareto distribution with the specified mean, shape, and upper bound.
* \param mean Mean parameter for the Pareto distribution.
* \param shape Shape parameter for the Pareto distribution.
* \param bound Upper bound on values returned.
* \return A floating point random value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$u\f$ is a uniform variable
* over [0,1] and
*
* \f[
* x = \frac{scale}{u^{\frac{1}{shape}}}
* \f]
*
* is a value that would be returned normally, where
*
* \f[
* scale = mean * (shape - 1.0) / shape .
* \f]
*
* Then \f$(1 - u\f$) is the distance that \f$u\f$ would be from
* \f$1\f$. The value returned in the antithetic case, \f$x'\f$, is
* calculated as
*
* \f[
* x' = \frac{scale}{{(1 - u)}^{\frac{1}{shape}}} ,
* \f]
*
* which now involves the distance \f$u\f$ is from 1 in the denonator.
*/
double GetValue (double mean, double shape, double bound);
/**
* \brief Returns a random unsigned integer from a Pareto distribution with the specified mean, shape, and upper bound.
* \param mean Mean parameter for the Pareto distribution.
* \param shape Shape parameter for the Pareto distribution.
* \param bound Upper bound on values returned.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$u\f$ is a uniform variable
* over [0,1] and
*
* \f[
* x = \frac{scale}{u^{\frac{1}{shape}}}
* \f]
*
* is a value that would be returned normally, where
*
* \f[
* scale = mean * (shape - 1.0) / shape .
* \f]
*
* Then \f$(1 - u\f$) is the distance that \f$u\f$ would be from
* \f$1\f$. The value returned in the antithetic case, \f$x'\f$, is
* calculated as
*
* \f[
* x' = \frac{scale}{{(1 - u)}^{\frac{1}{shape}}} ,
* \f]
*
* which now involves the distance \f$u\f$ is from 1 in the denonator.
*/
uint32_t GetInteger (uint32_t mean, uint32_t shape, uint32_t bound);
/**
* \brief Returns a random double from a Pareto distribution with the current mean, shape, and upper bound.
* \return A floating point random value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$u\f$ is a uniform variable
* over [0,1] and
*
* \f[
* x = \frac{scale}{u^{\frac{1}{shape}}}
* \f]
*
* is a value that would be returned normally, where
*
* \f[
* scale = mean * (shape - 1.0) / shape .
* \f]
*
* Then \f$(1 - u\f$) is the distance that \f$u\f$ would be from
* \f$1\f$. The value returned in the antithetic case, \f$x'\f$, is
* calculated as
*
* \f[
* x' = \frac{scale}{{(1 - u)}^{\frac{1}{shape}}} ,
* \f]
*
* which now involves the distance \f$u\f$ is from 1 in the denonator.
*
* Note that we have to re-implement this method here because the method is
* overloaded above for the three-argument variant and the c++ name resolution
* rules don't work well with overloads split between parent and child
* classes.
*/
virtual double GetValue (void);
/**
* \brief Returns a random unsigned integer from a Pareto distribution with the current mean, shape, and upper bound.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$u\f$ is a uniform variable
* over [0,1] and
*
* \f[
* x = \frac{scale}{u^{\frac{1}{shape}}}
* \f]
*
* is a value that would be returned normally, where
*
* \f[
* scale = mean * (shape - 1.0) / shape .
* \f]
*
* Then \f$(1 - u\f$) is the distance that \f$u\f$ would be from
* \f$1\f$. The value returned in the antithetic case, \f$x'\f$, is
* calculated as
*
* \f[
* x' = \frac{scale}{{(1 - u)}^{\frac{1}{shape}}} ,
* \f]
*
* which now involves the distance \f$u\f$ is from 1 in the denonator.
*/
virtual uint32_t GetInteger (void);
private:
/// The mean parameter for the Pareto distribution returned by this RNG stream.
double m_mean;
/// The shape parameter for the Pareto distribution returned by this RNG stream.
double m_shape;
/// The upper bound on values that can be returned by this RNG stream.
double m_bound;
};
/**
* \ingroup randomvariable
* \brief The Weibull distribution Random Number Generator (RNG) that allows stream numbers to be set deterministically.
*
* This class supports the creation of objects that return random numbers
* from a fixed Weibull distribution. It also supports the generation of
* single random numbers from various Weibull distributions.
*
* The probability density function is defined over the interval [0, \f$+\infty\f$]
* as: \f$ \frac{k}{\lambda}\left(\frac{x}{\lambda}\right)^{k-1}e^{-\left(\frac{x}{\lambda}\right)^k} \f$
* where \f$ k > 0\f$ is the shape parameter and \f$ \lambda > 0\f$ is the scale parameter. The
* specified mean is related to the scale and shape parameters by the following relation:
* \f$ mean = \lambda\Gamma\left(1+\frac{1}{k}\right) \f$ where \f$ \Gamma \f$ is the Gamma function.
*
* Since Weibull distributions can theoretically return unbounded values,
* it is sometimes useful to specify a fixed upper limit. Note however
* when the upper limit is specified, the true mean of the distribution
* is slightly smaller than the mean value specified.
*
* Here is an example of how to use this class:
* \code
* double scale = 5.0;
* double shape = 1.0;
*
* Ptr<WeibullRandomVariable> x = CreateObject<WeibullRandomVariable> ();
* x->SetAttribute ("Scale", DoubleValue (scale));
* x->SetAttribute ("Shape", DoubleValue (shape));
*
* // The expected value for the mean of the values returned by a
* // Weibull distributed random variable is
* //
* // E[value] = scale * Gamma(1 + 1 / shape) ,
* //
* // where Gamma() is the Gamma function. Note that
* //
* // Gamma(n) = (n - 1)!
* //
* // if n is a positive integer.
* //
* // For this example,
* //
* // Gamma(1 + 1 / shape) = Gamma(1 + 1 / 1)
* // = Gamma(2)
* // = (2 - 1)!
* // = 1
* //
* // which means
* //
* // E[value] = scale .
* //
* double value = x->GetValue ();
* \endcode
*/
class WeibullRandomVariable : public RandomVariableStream
{
public:
static TypeId GetTypeId (void);
/**
* \brief Creates a Weibull distribution RNG with the default
* values for the scale, shape, and upper bound.
*/
WeibullRandomVariable ();
/**
* \brief Returns the scale parameter for the Weibull distribution returned by this RNG stream.
* \return The scale parameter for the Weibull distribution returned by this RNG stream.
*/
double GetScale (void) const;
/**
* \brief Returns the shape parameter for the Weibull distribution returned by this RNG stream.
* \return The shape parameter for the Weibull distribution returned by this RNG stream.
*/
double GetShape (void) const;
/**
* \brief Returns the upper bound on values that can be returned by this RNG stream.
* \return The upper bound on values that can be returned by this RNG stream.
*/
double GetBound (void) const;
/**
* \brief Returns a random double from a Weibull distribution with the specified scale, shape, and upper bound.
* \param scale Scale parameter for the Weibull distribution.
* \param shape Shape parameter for the Weibull distribution.
* \param bound Upper bound on values returned.
* \return A floating point random value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$u\f$ is a uniform variable
* over [0,1] and
*
* \f[
* x = scale * {(-\log(u))}^{\frac{1}{shape}}
* \f]
*
* is a value that would be returned normally, then \f$(1 - u\f$) is
* the distance that \f$u\f$ would be from \f$1\f$. The value
* returned in the antithetic case, \f$x'\f$, is calculated as
*
* \f[
* x' = scale * {(-\log(1 - u))}^{\frac{1}{shape}} ,
* \f]
*
* which now involves the log of the distance \f$u\f$ is from 1.
*/
double GetValue (double scale, double shape, double bound);
/**
* \brief Returns a random unsigned integer from a Weibull distribution with the specified scale, shape, and upper bound.
* \param scale Scale parameter for the Weibull distribution.
* \param shape Shape parameter for the Weibull distribution.
* \param bound Upper bound on values returned.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$u\f$ is a uniform variable
* over [0,1] and
*
* \f[
* x = scale * {(-\log(u))}^{\frac{1}{shape}}
* \f]
*
* is a value that would be returned normally, then \f$(1 - u\f$) is
* the distance that \f$u\f$ would be from \f$1\f$. The value
* returned in the antithetic case, \f$x'\f$, is calculated as
*
* \f[
* x' = scale * {(-\log(1 - u))}^{\frac{1}{shape}} ,
* \f]
*
* which now involves the log of the distance \f$u\f$ is from 1.
*/
uint32_t GetInteger (uint32_t scale, uint32_t shape, uint32_t bound);
/**
* \brief Returns a random double from a Weibull distribution with the current scale, shape, and upper bound.
* \return A floating point random value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$u\f$ is a uniform variable
* over [0,1] and
*
* \f[
* x = scale * {(-\log(u))}^{\frac{1}{shape}}
* \f]
*
* is a value that would be returned normally, then \f$(1 - u\f$) is
* the distance that \f$u\f$ would be from \f$1\f$. The value
* returned in the antithetic case, \f$x'\f$, is calculated as
*
* \f[
* x' = scale * {(-\log(1 - u))}^{\frac{1}{shape}} ,
* \f]
*
* which now involves the log of the distance \f$u\f$ is from 1.
*
* Note that we have to re-implement this method here because the method is
* overloaded above for the three-argument variant and the c++ name resolution
* rules don't work well with overloads split between parent and child
* classes.
*/
virtual double GetValue (void);
/**
* \brief Returns a random unsigned integer from a Weibull distribution with the current scale, shape, and upper bound.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$u\f$ is a uniform variable
* over [0,1] and
*
* \f[
* x = scale * {(-\log(u))}^{\frac{1}{shape}}
* \f]
*
* is a value that would be returned normally, then \f$(1 - u\f$) is
* the distance that \f$u\f$ would be from \f$1\f$. The value
* returned in the antithetic case, \f$x'\f$, is calculated as
*
* \f[
* x' = scale * {(-\log(1 - u))}^{\frac{1}{shape}} ,
* \f]
*
* which now involves the log of the distance \f$u\f$ is from 1.
*/
virtual uint32_t GetInteger (void);
private:
/// The scale parameter for the Weibull distribution returned by this RNG stream.
double m_scale;
/// The shape parameter for the Weibull distribution returned by this RNG stream.
double m_shape;
/// The upper bound on values that can be returned by this RNG stream.
double m_bound;
};
/**
* \ingroup randomvariable
* \brief The normal (Gaussian) distribution Random Number Generator
* (RNG) that allows stream numbers to be set deterministically.
*
* This class supports the creation of objects that return random numbers
* from a fixed normal distribution. It also supports the generation of
* single random numbers from various normal distributions.
*
* The density probability function is defined over the interval (\f$-\infty\f$,\f$+\infty\f$)
* as: \f$ \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{s\sigma^2}}\f$
* where \f$ mean = \mu \f$ and \f$ variance = \sigma^2 \f$
*
* Since normal distributions can theoretically return unbounded
* values, it is sometimes useful to specify a fixed bound. The
* NormalRandomVariable is bounded symmetrically about the mean by
* this bound, i.e. its values are confined to the interval
* [\f$mean-bound\f$,\f$mean+bound\f$].
*
* Here is an example of how to use this class:
* \code
* double mean = 5.0;
* double variance = 2.0;
*
* Ptr<NormalRandomVariable> x = CreateObject<NormalRandomVariable> ();
* x->SetAttribute ("Mean", DoubleValue (mean));
* x->SetAttribute ("Variance", DoubleValue (variance));
*
* // The expected value for the mean of the values returned by a
* // normally distributed random variable is equal to mean.
* double value = x->GetValue ();
* \endcode
*/
class NormalRandomVariable : public RandomVariableStream
{
public:
static const double INFINITE_VALUE;
static TypeId GetTypeId (void);
/**
* \brief Creates a normal distribution RNG with the default
* values for the mean, variance, and bound.
*/
NormalRandomVariable ();
/**
* \brief Returns the mean value for the normal distribution returned by this RNG stream.
* \return The mean value for the normal distribution returned by this RNG stream.
*/
double GetMean (void) const;
/**
* \brief Returns the variance value for the normal distribution returned by this RNG stream.
* \return The variance value for the normal distribution returned by this RNG stream.
*/
double GetVariance (void) const;
/**
* \brief Returns the bound on values that can be returned by this RNG stream.
* \return The bound on values that can be returned by this RNG stream.
*/
double GetBound (void) const;
/**
* \brief Returns a random double from a normal distribution with the specified mean, variance, and bound.
* \param mean Mean value for the normal distribution.
* \param variance Variance value for the normal distribution.
* \param bound Bound on values returned.
* \return A floating point random value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u1\f$ and \f$u2\f$ are uniform variables
* over [0,1], then the values that would be returned normally, \f$x1\f$ and \f$x2\f$, are calculated as follows:
*
* \f{eqnarray*}{
* v1 & = & 2 * u1 - 1 \\
* v2 & = & 2 * u2 - 1 \\
* w & = & v1 * v1 + v2 * v2 \\
* y & = & \sqrt{\frac{-2 * \log(w)}{w}} \\
* x1 & = & mean + v1 * y * \sqrt{variance} \\
* x2 & = & mean + v2 * y * \sqrt{variance} .
* \f}
*
* For the antithetic case, \f$(1 - u1\f$) and \f$(1 - u2\f$) are
* the distances that \f$u1\f$ and \f$u2\f$ would be from \f$1\f$.
* The antithetic values returned, \f$x1'\f$ and \f$x2'\f$, are
* calculated as follows:
*
* \f{eqnarray*}{
* v1' & = & 2 * (1 - u1) - 1 \\
* v2' & = & 2 * (1 - u2) - 1 \\
* w' & = & v1' * v1' + v2' * v2' \\
* y' & = & \sqrt{\frac{-2 * \log(w')}{w'}} \\
* x1' & = & mean + v1' * y' * \sqrt{variance} \\
* x2' & = & mean + v2' * y' * \sqrt{variance} ,
* \f}
*
* which now involves the distances \f$u1\f$ and \f$u2\f$ are from 1.
*/
double GetValue (double mean, double variance, double bound = NormalRandomVariable::INFINITE_VALUE);
/**
* \brief Returns a random unsigned integer from a normal distribution with the specified mean, variance, and bound.
* \param mean Mean value for the normal distribution.
* \param variance Variance value for the normal distribution.
* \param bound Bound on values returned.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u1\f$ and \f$u2\f$ are uniform variables
* over [0,1], then the values that would be returned normally, \f$x1\f$ and \f$x2\f$, are calculated as follows:
*
* \f{eqnarray*}{
* v1 & = & 2 * u1 - 1 \\
* v2 & = & 2 * u2 - 1 \\
* w & = & v1 * v1 + v2 * v2 \\
* y & = & \sqrt{\frac{-2 * \log(w)}{w}} \\
* x1 & = & mean + v1 * y * \sqrt{variance} \\
* x2 & = & mean + v2 * y * \sqrt{variance} .
* \f}
*
* For the antithetic case, \f$(1 - u1\f$) and \f$(1 - u2\f$) are
* the distances that \f$u1\f$ and \f$u2\f$ would be from \f$1\f$.
* The antithetic values returned, \f$x1'\f$ and \f$x2'\f$, are
* calculated as follows:
*
* \f{eqnarray*}{
* v1' & = & 2 * (1 - u1) - 1 \\
* v2' & = & 2 * (1 - u2) - 1 \\
* w' & = & v1' * v1' + v2' * v2' \\
* y' & = & \sqrt{\frac{-2 * \log(w')}{w'}} \\
* x1' & = & mean + v1' * y' * \sqrt{variance} \\
* x2' & = & mean + v2' * y' * \sqrt{variance} ,
* \f}
*
* which now involves the distances \f$u1\f$ and \f$u2\f$ are from 1.
*/
uint32_t GetInteger (uint32_t mean, uint32_t variance, uint32_t bound);
/**
* \brief Returns a random double from a normal distribution with the current mean, variance, and bound.
* \return A floating point random value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u1\f$ and \f$u2\f$ are uniform variables
* over [0,1], then the values that would be returned normally, \f$x1\f$ and \f$x2\f$, are calculated as follows:
*
* \f{eqnarray*}{
* v1 & = & 2 * u1 - 1 \\
* v2 & = & 2 * u2 - 1 \\
* w & = & v1 * v1 + v2 * v2 \\
* y & = & \sqrt{\frac{-2 * \log(w)}{w}} \\
* x1 & = & mean + v1 * y * \sqrt{variance} \\
* x2 & = & mean + v2 * y * \sqrt{variance} .
* \f}
*
* For the antithetic case, \f$(1 - u1\f$) and \f$(1 - u2\f$) are
* the distances that \f$u1\f$ and \f$u2\f$ would be from \f$1\f$.
* The antithetic values returned, \f$x1'\f$ and \f$x2'\f$, are
* calculated as follows:
*
* \f{eqnarray*}{
* v1' & = & 2 * (1 - u1) - 1 \\
* v2' & = & 2 * (1 - u2) - 1 \\
* w' & = & v1' * v1' + v2' * v2' \\
* y' & = & \sqrt{\frac{-2 * \log(w')}{w'}} \\
* x1' & = & mean + v1' * y' * \sqrt{variance} \\
* x2' & = & mean + v2' * y' * \sqrt{variance} ,
* \f}
*
* which now involves the distances \f$u1\f$ and \f$u2\f$ are from 1.
*
* Note that we have to re-implement this method here because the method is
* overloaded above for the three-argument variant and the c++ name resolution
* rules don't work well with overloads split between parent and child
* classes.
*/
virtual double GetValue (void);
/**
* \brief Returns a random unsigned integer from a normal distribution with the current mean, variance, and bound.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u1\f$ and \f$u2\f$ are uniform variables
* over [0,1], then the values that would be returned normally, \f$x1\f$ and \f$x2\f$, are calculated as follows:
*
* \f{eqnarray*}{
* v1 & = & 2 * u1 - 1 \\
* v2 & = & 2 * u2 - 1 \\
* w & = & v1 * v1 + v2 * v2 \\
* y & = & \sqrt{\frac{-2 * \log(w)}{w}} \\
* x1 & = & mean + v1 * y * \sqrt{variance} \\
* x2 & = & mean + v2 * y * \sqrt{variance} .
* \f}
*
* For the antithetic case, \f$(1 - u1\f$) and \f$(1 - u2\f$) are
* the distances that \f$u1\f$ and \f$u2\f$ would be from \f$1\f$.
* The antithetic values returned, \f$x1'\f$ and \f$x2'\f$, are
* calculated as follows:
*
* \f{eqnarray*}{
* v1' & = & 2 * (1 - u1) - 1 \\
* v2' & = & 2 * (1 - u2) - 1 \\
* w' & = & v1' * v1' + v2' * v2' \\
* y' & = & \sqrt{\frac{-2 * \log(w')}{w'}} \\
* x1' & = & mean + v1' * y' * \sqrt{variance} \\
* x2' & = & mean + v2' * y' * \sqrt{variance} ,
* \f}
*
* which now involves the distances \f$u1\f$ and \f$u2\f$ are from 1.
*/
virtual uint32_t GetInteger (void);
private:
/// The mean value for the normal distribution returned by this RNG stream.
double m_mean;
/// The variance value for the normal distribution returned by this RNG stream.
double m_variance;
/// The bound on values that can be returned by this RNG stream.
double m_bound;
/// True if the next value is valid.
bool m_nextValid;
/// The algorithm produces two values at a time.
double m_next;
};
/**
* \ingroup randomvariable
* \brief The log-normal distribution Random Number Generator
* (RNG) that allows stream numbers to be set deterministically.
*
* This class supports the creation of objects that return random numbers
* from a fixed log-normal distribution. It also supports the generation of
* single random numbers from various log-normal distributions.
*
* LogNormalRandomVariable defines a random variable with a log-normal
* distribution. If one takes the natural logarithm of random
* variable following the log-normal distribution, the obtained values
* follow a normal distribution.
*
* The probability density function is defined over the interval [0,\f$+\infty\f$) as:
* \f$ \frac{1}{x\sigma\sqrt{2\pi}} e^{-\frac{(ln(x) - \mu)^2}{2\sigma^2}}\f$
* where \f$ mean = e^{\mu+\frac{\sigma^2}{2}} \f$ and
* \f$ variance = (e^{\sigma^2}-1)e^{2\mu+\sigma^2}\f$
*
* The \f$ \mu \f$ and \f$ \sigma \f$ parameters can be calculated instead if
* the mean and variance are known with the following equations:
* \f$ \mu = ln(mean) - \frac{1}{2}ln\left(1+\frac{variance}{mean^2}\right)\f$, and,
* \f$ \sigma = \sqrt{ln\left(1+\frac{variance}{mean^2}\right)}\f$
*
* Here is an example of how to use this class:
* \code
* double mu = 5.0;
* double sigma = 2.0;
*
* Ptr<LogNormalRandomVariable> x = CreateObject<LogNormalRandomVariable> ();
* x->SetAttribute ("Mu", DoubleValue (mu));
* x->SetAttribute ("Sigma", DoubleValue (sigma));
*
* // The expected value for the mean of the values returned by a
* // log-normally distributed random variable is equal to
* //
* // 2
* // mu + sigma / 2
* // E[value] = e .
* //
* double value = x->GetValue ();
* \endcode
*/
class LogNormalRandomVariable : public RandomVariableStream
{
public:
static TypeId GetTypeId (void);
/**
* \brief Creates a log-normal distribution RNG with the default
* values for mu and sigma.
*/
LogNormalRandomVariable ();
/**
* \brief Returns the mu value for the log-normal distribution returned by this RNG stream.
* \return The mu value for the log-normal distribution returned by this RNG stream.
*/
double GetMu (void) const;
/**
* \brief Returns the sigma value for the log-normal distribution returned by this RNG stream.
* \return The sigma value for the log-normal distribution returned by this RNG stream.
*/
double GetSigma (void) const;
/**
* \brief Returns a random double from a log-normal distribution with the specified mu and sigma.
* \param mu Mu value for the log-normal distribution.
* \param sigma Sigma value for the log-normal distribution.
* \return A floating point random value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u1\f$ and \f$u2\f$ are uniform variables
* over [0,1], then the value that would be returned normally, \f$x\f$, is calculated as follows:
*
* \f{eqnarray*}{
* v1 & = & -1 + 2 * u1 \\
* v2 & = & -1 + 2 * u2 \\
* r2 & = & v1 * v1 + v2 * v2 \\
* normal & = & v1 * \sqrt{\frac{-2.0 * \log{r2}}{r2}} \\
* x & = & \exp{sigma * normal + mu} .
* \f}
*
* For the antithetic case, \f$(1 - u1\f$) and \f$(1 - u2\f$) are
* the distances that \f$u1\f$ and \f$u2\f$ would be from \f$1\f$.
* The antithetic value returned, \f$x'\f$, is calculated as
* follows:
*
* \f{eqnarray*}{
* v1' & = & -1 + 2 * (1 - u1) \\
* v2' & = & -1 + 2 * (1 - u2) \\
* r2' & = & v1' * v1' + v2' * v2' \\
* normal' & = & v1' * \sqrt{\frac{-2.0 * \log{r2'}}{r2'}} \\
* x' & = & \exp{sigma * normal' + mu} .
* \f}
*
* which now involves the distances \f$u1\f$ and \f$u2\f$ are from 1.
*/
double GetValue (double mu, double sigma);
/**
* \brief Returns a random unsigned integer from a log-normal distribution with the specified mu and sigma.
* \param mu Mu value for the log-normal distribution.
* \param sigma Sigma value for the log-normal distribution.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u1\f$ and \f$u2\f$ are uniform variables
* over [0,1], then the value that would be returned normally, \f$x\f$, is calculated as follows:
*
* \f{eqnarray*}{
* v1 & = & -1 + 2 * u1 \\
* v2 & = & -1 + 2 * u2 \\
* r2 & = & v1 * v1 + v2 * v2 \\
* normal & = & v1 * \sqrt{\frac{-2.0 * \log{r2}}{r2}} \\
* x & = & \exp{sigma * normal + mu} .
* \f}
*
* For the antithetic case, \f$(1 - u1\f$) and \f$(1 - u2\f$) are
* the distances that \f$u1\f$ and \f$u2\f$ would be from \f$1\f$.
* The antithetic value returned, \f$x'\f$, is calculated as
* follows:
*
* \f{eqnarray*}{
* v1' & = & -1 + 2 * (1 - u1) \\
* v2' & = & -1 + 2 * (1 - u2) \\
* r2' & = & v1' * v1' + v2' * v2' \\
* normal' & = & v1' * \sqrt{\frac{-2.0 * \log{r2'}}{r2'}} \\
* x' & = & \exp{sigma * normal' + mu} .
* \f}
*
* which now involves the distances \f$u1\f$ and \f$u2\f$ are from 1.
*/
uint32_t GetInteger (uint32_t mu, uint32_t sigma);
/**
* \brief Returns a random double from a log-normal distribution with the current mu and sigma.
* \return A floating point random value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u1\f$ and \f$u2\f$ are uniform variables
* over [0,1], then the value that would be returned normally, \f$x\f$, is calculated as follows:
*
* \f{eqnarray*}{
* v1 & = & -1 + 2 * u1 \\
* v2 & = & -1 + 2 * u2 \\
* r2 & = & v1 * v1 + v2 * v2 \\
* normal & = & v1 * \sqrt{\frac{-2.0 * \log{r2}}{r2}} \\
* x & = & \exp{sigma * normal + mu} .
* \f}
*
* For the antithetic case, \f$(1 - u1\f$) and \f$(1 - u2\f$) are
* the distances that \f$u1\f$ and \f$u2\f$ would be from \f$1\f$.
* The antithetic value returned, \f$x'\f$, is calculated as
* follows:
*
* \f{eqnarray*}{
* v1' & = & -1 + 2 * (1 - u1) \\
* v2' & = & -1 + 2 * (1 - u2) \\
* r2' & = & v1' * v1' + v2' * v2' \\
* normal' & = & v1' * \sqrt{\frac{-2.0 * \log{r2'}}{r2'}} \\
* x' & = & \exp{sigma * normal' + mu} .
* \f}
*
* which now involves the distances \f$u1\f$ and \f$u2\f$ are from 1.
*
* Note that we have to re-implement this method here because the method is
* overloaded above for the two-argument variant and the c++ name resolution
* rules don't work well with overloads split between parent and child
* classes.
*/
virtual double GetValue (void);
/**
* \brief Returns a random unsigned integer from a log-normal distribution with the current mu and sigma.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u1\f$ and \f$u2\f$ are uniform variables
* over [0,1], then the value that would be returned normally, \f$x\f$, is calculated as follows:
*
* \f{eqnarray*}{
* v1 & = & -1 + 2 * u1 \\
* v2 & = & -1 + 2 * u2 \\
* r2 & = & v1 * v1 + v2 * v2 \\
* normal & = & v1 * \sqrt{\frac{-2.0 * \log{r2}}{r2}} \\
* x & = & \exp{sigma * normal + mu} .
* \f}
*
* For the antithetic case, \f$(1 - u1\f$) and \f$(1 - u2\f$) are
* the distances that \f$u1\f$ and \f$u2\f$ would be from \f$1\f$.
* The antithetic value returned, \f$x'\f$, is calculated as
* follows:
*
* \f{eqnarray*}{
* v1' & = & -1 + 2 * (1 - u1) \\
* v2' & = & -1 + 2 * (1 - u2) \\
* r2' & = & v1' * v1' + v2' * v2' \\
* normal' & = & v1' * \sqrt{\frac{-2.0 * \log{r2'}}{r2'}} \\
* x' & = & \exp{sigma * normal' + mu} .
* \f}
*
* which now involves the distances \f$u1\f$ and \f$u2\f$ are from 1.
*/
virtual uint32_t GetInteger (void);
private:
/// The mu value for the log-normal distribution returned by this RNG stream.
double m_mu;
/// The sigma value for the log-normal distribution returned by this RNG stream.
double m_sigma;
};
/**
* \ingroup randomvariable
* \brief The gamma distribution Random Number Generator (RNG) that
* allows stream numbers to be set deterministically.
*
* 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,\f$+\infty\f$) 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$
*
* Here is an example of how to use this class:
* \code
* double alpha = 5.0;
* double beta = 2.0;
*
* Ptr<GammaRandomVariable> x = CreateObject<GammaRandomVariable> ();
* x->SetAttribute ("Alpha", DoubleValue (alpha));
* x->SetAttribute ("Beta", DoubleValue (beta));
*
* // The expected value for the mean of the values returned by a
* // gammaly distributed random variable is equal to
* //
* // E[value] = alpha * beta .
* //
* double value = x->GetValue ();
* \endcode
*/
class GammaRandomVariable : public RandomVariableStream
{
public:
static TypeId GetTypeId (void);
/**
* \brief Creates a gamma distribution RNG with the default values
* for alpha and beta.
*/
GammaRandomVariable ();
/**
* \brief Returns the alpha value for the gamma distribution returned by this RNG stream.
* \return The alpha value for the gamma distribution returned by this RNG stream.
*/
double GetAlpha (void) const;
/**
* \brief Returns the beta value for the gamma distribution returned by this RNG stream.
* \return The beta value for the gamma distribution returned by this RNG stream.
*/
double GetBeta (void) const;
/**
* \brief Returns a random double from a gamma distribution with the specified alpha and beta.
* \param alpha Alpha value for the gamma distribution.
* \param beta Beta value for the gamma distribution.
* \return A floating point random value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u\f$ is a uniform variable over [0,1]
* and \f$x\f$ is a value that would be returned normally, then
* \f$(1 - u\f$) is the distance that \f$u\f$ would be from \f$1\f$.
* The value returned in the antithetic case, \f$x'\f$, uses (1-u),
* which is the distance \f$u\f$ is from the 1.
*/
double GetValue (double alpha, double beta);
/**
* \brief Returns a random unsigned integer from a gamma distribution with the specified alpha and beta.
* \param alpha Alpha value for the gamma distribution.
* \param beta Beta value for the gamma distribution.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u\f$ is a uniform variable over [0,1]
* and \f$x\f$ is a value that would be returned normally, then
* \f$(1 - u\f$) is the distance that \f$u\f$ would be from \f$1\f$.
* The value returned in the antithetic case, \f$x'\f$, uses (1-u),
* which is the distance \f$u\f$ is from the 1.
*/
uint32_t GetInteger (uint32_t alpha, uint32_t beta);
/**
* \brief Returns a random double from a gamma distribution with the current alpha and beta.
* \return A floating point random value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u\f$ is a uniform variable over [0,1]
* and \f$x\f$ is a value that would be returned normally, then
* \f$(1 - u\f$) is the distance that \f$u\f$ would be from \f$1\f$.
* The value returned in the antithetic case, \f$x'\f$, uses (1-u),
* which is the distance \f$u\f$ is from the 1.
*
* Note that we have to re-implement this method here because the method is
* overloaded above for the two-argument variant and the c++ name resolution
* rules don't work well with overloads split between parent and child
* classes.
*/
virtual double GetValue (void);
/**
* \brief Returns a random unsigned integer from a gamma distribution with the current alpha and beta.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u\f$ is a uniform variable over [0,1]
* and \f$x\f$ is a value that would be returned normally, then
* \f$(1 - u\f$) is the distance that \f$u\f$ would be from \f$1\f$.
* The value returned in the antithetic case, \f$x'\f$, uses (1-u),
* which is the distance \f$u\f$ is from the 1.
*/
virtual uint32_t GetInteger (void);
private:
/**
* \brief Returns a random double from a normal distribution with the specified mean, variance, and bound.
* \param mean Mean value for the normal distribution.
* \param variance Variance value for the normal distribution.
* \param bound Bound on values returned.
* \return A floating point random value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u1\f$ and \f$u2\f$ are uniform variables
* over [0,1], then the values that would be returned normally, \f$x1\f$ and \f$x2\f$, are calculated as follows:
*
* \f{eqnarray*}{
* v1 & = & 2 * u1 - 1 \\
* v2 & = & 2 * u2 - 1 \\
* w & = & v1 * v1 + v2 * v2 \\
* y & = & \sqrt{\frac{-2 * \log(w)}{w}} \\
* x1 & = & mean + v1 * y * \sqrt{variance} \\
* x2 & = & mean + v2 * y * \sqrt{variance} .
* \f}
*
* For the antithetic case, \f$(1 - u1\f$) and \f$(1 - u2\f$) are
* the distances that \f$u1\f$ and \f$u2\f$ would be from \f$1\f$.
* The antithetic values returned, \f$x1'\f$ and \f$x2'\f$, are
* calculated as follows:
*
* \f{eqnarray*}{
* v1' & = & 2 * (1 - u1) - 1 \\
* v2' & = & 2 * (1 - u2) - 1 \\
* w' & = & v1' * v1' + v2' * v2' \\
* y' & = & \sqrt{\frac{-2 * \log(w')}{w'}} \\
* x1' & = & mean + v1' * y' * \sqrt{variance} \\
* x2' & = & mean + v2' * y' * \sqrt{variance} ,
* \f}
*
* which now involves the distances \f$u1\f$ and \f$u2\f$ are from 1.
*/
double GetNormalValue (double mean, double variance, double bound);
/// The alpha value for the gamma distribution returned by this RNG stream.
double m_alpha;
/// The beta value for the gamma distribution returned by this RNG stream.
double m_beta;
/// True if the next normal value is valid.
bool m_nextValid;
/// The algorithm produces two normal values at a time.
double m_next;
};
/**
* \ingroup randomvariable
* \brief The Erlang distribution Random Number Generator (RNG) that
* allows stream numbers to be set deterministically.
*
* 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 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.
*
* The probability density function is defined over the interval [0,\f$+\infty\f$) 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$
*
* Here is an example of how to use this class:
* \code
* uint32_t k = 5;
* double lambda = 2.0;
*
* Ptr<ErlangRandomVariable> x = CreateObject<ErlangRandomVariable> ();
* x->SetAttribute ("K", IntegerValue (k));
* x->SetAttribute ("Lambda", DoubleValue (lambda));
*
* // The expected value for the mean of the values returned by a
* // Erlangly distributed random variable is equal to
* //
* // E[value] = k * lambda .
* //
* double value = x->GetValue ();
* \endcode
*/
class ErlangRandomVariable : public RandomVariableStream
{
public:
static TypeId GetTypeId (void);
/**
* \brief Creates an Erlang distribution RNG with the default values
* for k and lambda.
*/
ErlangRandomVariable ();
/**
* \brief Returns the k value for the Erlang distribution returned by this RNG stream.
* \return The k value for the Erlang distribution returned by this RNG stream.
*/
uint32_t GetK (void) const;
/**
* \brief Returns the lambda value for the Erlang distribution returned by this RNG stream.
* \return The lambda value for the Erlang distribution returned by this RNG stream.
*/
double GetLambda (void) const;
/**
* \brief Returns a random double from an Erlang distribution with the specified k and lambda.
* \param k K value for the Erlang distribution.
* \param lambda Lambda value for the Erlang distribution.
* \return A floating point random value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u\f$ is a uniform variable over [0,1]
* and \f$x\f$ is a value that would be returned normally, then
* \f$(1 - u\f$) is the distance that \f$u\f$ would be from \f$1\f$.
* The value returned in the antithetic case, \f$x'\f$, uses (1-u),
* which is the distance \f$u\f$ is from the 1.
*/
double GetValue (uint32_t k, double lambda);
/**
* \brief Returns a random unsigned integer from an Erlang distribution with the specified k and lambda.
* \param k K value for the Erlang distribution.
* \param lambda Lambda value for the Erlang distribution.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u\f$ is a uniform variable over [0,1]
* and \f$x\f$ is a value that would be returned normally, then
* \f$(1 - u\f$) is the distance that \f$u\f$ would be from \f$1\f$.
* The value returned in the antithetic case, \f$x'\f$, uses (1-u),
* which is the distance \f$u\f$ is from the 1.
*/
uint32_t GetInteger (uint32_t k, uint32_t lambda);
/**
* \brief Returns a random double from an Erlang distribution with the current k and lambda.
* \return A floating point random value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u\f$ is a uniform variable over [0,1]
* and \f$x\f$ is a value that would be returned normally, then
* \f$(1 - u\f$) is the distance that \f$u\f$ would be from \f$1\f$.
* The value returned in the antithetic case, \f$x'\f$, uses (1-u),
* which is the distance \f$u\f$ is from the 1.
*
* Note that we have to re-implement this method here because the method is
* overloaded above for the two-argument variant and the c++ name resolution
* rules don't work well with overloads split between parent and child
* classes.
*/
virtual double GetValue (void);
/**
* \brief Returns a random unsigned integer from an Erlang distribution with the current k and lambda.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u\f$ is a uniform variable over [0,1]
* and \f$x\f$ is a value that would be returned normally, then
* \f$(1 - u\f$) is the distance that \f$u\f$ would be from \f$1\f$.
* The value returned in the antithetic case, \f$x'\f$, uses (1-u),
* which is the distance \f$u\f$ is from the 1.
*/
virtual uint32_t GetInteger (void);
private:
/**
* \brief Returns a random double from an exponential distribution with the specified mean and upper bound.
* \param mean Mean value of the random variables.
* \param bound Upper bound on values returned.
* \return A floating point random value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$u\f$ is a uniform variable
* over [0,1] and
*
* \f[
* x = - mean * \log(u)
* \f]
*
* is a value that would be returned normally, then \f$(1 - u\f$) is
* the distance that \f$u\f$ would be from \f$1\f$. The value
* returned in the antithetic case, \f$x'\f$, is calculated as
*
* \f[
* x' = - mean * \log(1 - u),
* \f]
*
* which now involves the log of the distance \f$u\f$ is from the 1.
*/
double GetExponentialValue (double mean, double bound);
/// The k value for the Erlang distribution returned by this RNG stream.
uint32_t m_k;
/// The lambda value for the Erlang distribution returned by this RNG stream.
double m_lambda;
};
/**
* \ingroup randomvariable
* \brief The triangular distribution Random Number Generator (RNG) that
* allows stream numbers to be set deterministically.
*
* This class supports the creation of objects that return random numbers
* from a fixed triangular distribution. It also supports the generation of
* single random numbers from various triangular distributions.
*
* This distribution is a triangular distribution. The probability density
* is in the shape of a triangle.
*
* Here is an example of how to use this class:
* \code
* double mean = 5.0;
* double min = 2.0;
* double max = 10.0;
*
* Ptr<TriangularRandomVariable> x = CreateObject<TriangularRandomVariable> ();
* x->SetAttribute ("Mean", DoubleValue (mean));
* x->SetAttribute ("Min", DoubleValue (min));
* x->SetAttribute ("Max", DoubleValue (max));
*
* // The expected value for the mean of the values returned by a
* // triangularly distributed random variable is equal to mean.
* double value = x->GetValue ();
* \endcode
*/
class TriangularRandomVariable : public RandomVariableStream
{
public:
static TypeId GetTypeId (void);
/**
* \brief Creates a triangular distribution RNG with the default
* values for the mean, lower bound, and upper bound.
*/
TriangularRandomVariable ();
/**
* \brief Returns the mean value for the triangular distribution returned by this RNG stream.
* \return The mean value for the triangular distribution returned by this RNG stream.
*/
double GetMean (void) const;
/**
* \brief Returns the lower bound for the triangular distribution returned by this RNG stream.
* \return The lower bound for the triangular distribution returned by this RNG stream.
*/
double GetMin (void) const;
/**
* \brief Returns the upper bound on values that can be returned by this RNG stream.
* \return The upper bound on values that can be returned by this RNG stream.
*/
double GetMax (void) const;
/**
* \brief Returns a random double from a triangular distribution with the specified mean, min, and max.
* \param mean Mean value for the triangular distribution.
* \param min Low end of the range.
* \param max High end of the range.
* \return A floating point random value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$u\f$ is a uniform variable
* over [0,1] and
*
* \f[
* x = \left\{ \begin{array}{rl}
* min + \sqrt{u * (max - min) * (mode - min)} &\mbox{ if $u <= (mode - min)/(max - min)$} \\
* max - \sqrt{ (1 - u) * (max - min) * (max - mode) } &\mbox{ otherwise}
* \end{array} \right.
* \f]
*
* is a value that would be returned normally, where the mode or
* peak of the triangle is calculated as
*
* \f[
* mode = 3.0 * mean - min - max .
* \f]
*
* Then, \f$(1 - u\f$) is the distance that \f$u\f$ would be from
* \f$1\f$. The value returned in the antithetic case, \f$x'\f$, is
* calculated as
*
* \f[
* x' = \left\{ \begin{array}{rl}
* min + \sqrt{(1 - u) * (max - min) * (mode - min)} &\mbox{ if $(1 - u) <= (mode - min)/(max - min)$} \\
* max - \sqrt{ u * (max - min) * (max - mode) } &\mbox{ otherwise}
* \end{array} \right.
* \f]
*
* which now involves the distance \f$u\f$ is from the 1.
*/
double GetValue (double mean, double min, double max);
/**
* \brief Returns a random unsigned integer from a triangular distribution with the specified mean, min, and max.
* \param mean Mean value for the triangular distribution.
* \param min Low end of the range.
* \param max High end of the range.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$u\f$ is a uniform variable
* over [0,1] and
*
* \f[
* x = \left\{ \begin{array}{rl}
* min + \sqrt{u * (max - min) * (mode - min)} &\mbox{ if $u <= (mode - min)/(max - min)$} \\
* max - \sqrt{ (1 - u) * (max - min) * (max - mode) } &\mbox{ otherwise}
* \end{array} \right.
* \f]
*
* is a value that would be returned normally, where the mode or
* peak of the triangle is calculated as
*
* \f[
* mode = 3.0 * mean - min - max .
* \f]
*
* Then, \f$(1 - u\f$) is the distance that \f$u\f$ would be from
* \f$1\f$. The value returned in the antithetic case, \f$x'\f$, is
* calculated as
*
* \f[
* x' = \left\{ \begin{array}{rl}
* min + \sqrt{(1 - u) * (max - min) * (mode - min)} &\mbox{ if $(1 - u) <= (mode - min)/(max - min)$} \\
* max - \sqrt{ u * (max - min) * (max - mode) } &\mbox{ otherwise}
* \end{array} \right.
* \f]
*
* which now involves the distance \f$u\f$ is from the 1.
*/
uint32_t GetInteger (uint32_t mean, uint32_t min, uint32_t max);
/**
* \brief Returns a random double from a triangular distribution with the current mean, min, and max.
* \return A floating point random value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$u\f$ is a uniform variable
* over [0,1] and
*
* \f[
* x = \left\{ \begin{array}{rl}
* min + \sqrt{u * (max - min) * (mode - min)} &\mbox{ if $u <= (mode - min)/(max - min)$} \\
* max - \sqrt{ (1 - u) * (max - min) * (max - mode) } &\mbox{ otherwise}
* \end{array} \right.
* \f]
*
* is a value that would be returned normally, where the mode or
* peak of the triangle is calculated as
*
* \f[
* mode = 3.0 * mean - min - max .
* \f]
*
* Then, \f$(1 - u\f$) is the distance that \f$u\f$ would be from
* \f$1\f$. The value returned in the antithetic case, \f$x'\f$, is
* calculated as
*
* \f[
* x' = \left\{ \begin{array}{rl}
* min + \sqrt{(1 - u) * (max - min) * (mode - min)} &\mbox{ if $(1 - u) <= (mode - min)/(max - min)$} \\
* max - \sqrt{ u * (max - min) * (max - mode) } &\mbox{ otherwise}
* \end{array} \right.
* \f]
*
* which now involves the distance \f$u\f$ is from the 1.
*
* Note that we have to re-implement this method here because the method is
* overloaded above for the three-argument variant and the c++ name resolution
* rules don't work well with overloads split between parent and child
* classes.
*/
virtual double GetValue (void);
/**
* \brief Returns a random unsigned integer from a triangular distribution with the current mean, min, and max.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if
* m_isAntithetic is equal to true. If \f$u\f$ is a uniform variable
* over [0,1] and
*
* \f[
* x = \left\{ \begin{array}{rl}
* min + \sqrt{u * (max - min) * (mode - min)} &\mbox{ if $u <= (mode - min)/(max - min)$} \\
* max - \sqrt{ (1 - u) * (max - min) * (max - mode) } &\mbox{ otherwise}
* \end{array} \right.
* \f]
*
* is a value that would be returned normally, where the mode or
* peak of the triangle is calculated as
*
* \f[
* mode = 3.0 * mean - min - max .
* \f]
*
* Then, \f$(1 - u\f$) is the distance that \f$u\f$ would be from
* \f$1\f$. The value returned in the antithetic case, \f$x'\f$, is
* calculated as
*
* \f[
* x' = \left\{ \begin{array}{rl}
* min + \sqrt{(1 - u) * (max - min) * (mode - min)} &\mbox{ if $(1 - u) <= (mode - min)/(max - min)$} \\
* max - \sqrt{ u * (max - min) * (max - mode) } &\mbox{ otherwise}
* \end{array} \right.
* \f]
*
* which now involves the distance \f$u\f$ is from the 1.
*/
virtual uint32_t GetInteger (void);
private:
/// The mean value for the triangular distribution returned by this RNG stream.
double m_mean;
/// The lower bound on values that can be returned by this RNG stream.
double m_min;
/// The upper bound on values that can be returned by this RNG stream.
double m_max;
/// It's easier to work with the mode internally instead of the
/// mean. They are related by the simple: mean = (min+max+mode)/3.
double m_mode;
};
/**
* \ingroup randomvariable
* \brief The Zipf distribution Random Number Generator (RNG) that
* allows stream numbers to be set deterministically.
*
* This class supports the creation of objects that return random numbers
* from a fixed Zipf distribution. It also supports the generation of
* single random numbers from various Zipf distributions.
*
* The Zipf's law states that given some corpus of natural language
* utterances, the frequency of any word is inversely proportional
* to its rank in the frequency table.
*
* Zipf's distribution has two parameters, alpha and N, where:
* \f$ \alpha > 0 \f$ (real) and \f$ N \in \{1,2,3 \dots\}\f$ (integer).
* Probability Mass Function is \f$ f(k; \alpha, N) = k^{-\alpha}/ H_{N,\alpha} \f$
* where \f$ H_{N,\alpha} = \sum_{m=1}^N m^{-\alpha} \f$
*
* Here is an example of how to use this class:
* \code
* uint32_t n = 1;
* double alpha = 2.0;
*
* Ptr<ZipfRandomVariable> x = CreateObject<ZipfRandomVariable> ();
* x->SetAttribute ("N", IntegerValue (n));
* x->SetAttribute ("Alpha", DoubleValue (alpha));
*
* // The expected value for the mean of the values returned by a
* // Zipfly distributed random variable is equal to
* //
* // H
* // N, alpha - 1
* // E[value] = ---------------
* // H
* // N, alpha
* //
* // where
* //
* // N
* // ---
* // \ -alpha
* // H = / m .
* // N, alpha ---
* // m=1
* //
* // For this test,
* //
* // -(alpha - 1)
* // 1
* // E[value] = ---------------
* // -alpha
* // 1
* //
* // = 1 .
* //
* double value = x->GetValue ();
* \endcode
*/
class ZipfRandomVariable : public RandomVariableStream
{
public:
static TypeId GetTypeId (void);
/**
* \brief Creates a Zipf distribution RNG with the default values
* for n and alpha.
*/
ZipfRandomVariable ();
/**
* \brief Returns the n value for the Zipf distribution returned by this RNG stream.
* \return The n value for the Zipf distribution returned by this RNG stream.
*/
uint32_t GetN (void) const;
/**
* \brief Returns the alpha value for the Zipf distribution returned by this RNG stream.
* \return The alpha value for the Zipf distribution returned by this RNG stream.
*/
double GetAlpha (void) const;
/**
* \brief Returns a random double from a Zipf distribution with the specified n and alpha.
* \param n N value for the Zipf distribution.
* \param alpha Alpha value for the Zipf distribution.
* \return A floating point random value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u\f$ is a uniform variable over [0,1]
* and \f$x\f$ is a value that would be returned normally, then
* \f$(1 - u\f$) is the distance that \f$u\f$ would be from \f$1\f$.
* The value returned in the antithetic case, \f$x'\f$, uses (1-u),
* which is the distance \f$u\f$ is from the 1.
*/
double GetValue (uint32_t n, double alpha);
/**
* \brief Returns a random unsigned integer from a Zipf distribution with the specified n and alpha.
* \param n N value for the Zipf distribution.
* \param alpha Alpha value for the Zipf distribution.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u\f$ is a uniform variable over [0,1]
* and \f$x\f$ is a value that would be returned normally, then
* \f$(1 - u\f$) is the distance that \f$u\f$ would be from \f$1\f$.
* The value returned in the antithetic case, \f$x'\f$, uses (1-u),
* which is the distance \f$u\f$ is from the 1.
*/
uint32_t GetInteger (uint32_t n, uint32_t alpha);
/**
* \brief Returns a random double from a Zipf distribution with the current n and alpha.
* \return A floating point random value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u\f$ is a uniform variable over [0,1]
* and \f$x\f$ is a value that would be returned normally, then
* \f$(1 - u\f$) is the distance that \f$u\f$ would be from \f$1\f$.
* The value returned in the antithetic case, \f$x'\f$, uses (1-u),
* which is the distance \f$u\f$ is from the 1.
*
* Note that we have to re-implement this method here because the method is
* overloaded above for the two-argument variant and the c++ name resolution
* rules don't work well with overloads split between parent and child
* classes.
*/
virtual double GetValue (void);
/**
* \brief Returns a random unsigned integer from a Zipf distribution with the current n and alpha.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u\f$ is a uniform variable over [0,1]
* and \f$x\f$ is a value that would be returned normally, then
* \f$(1 - u\f$) is the distance that \f$u\f$ would be from \f$1\f$.
* The value returned in the antithetic case, \f$x'\f$, uses (1-u),
* which is the distance \f$u\f$ is from the 1.
*/
virtual uint32_t GetInteger (void);
private:
/// The n value for the Zipf distribution returned by this RNG stream.
uint32_t m_n;
/// The alpha value for the Zipf distribution returned by this RNG stream.
double m_alpha;
/// The normalization constant.
double m_c;
};
/**
* \ingroup randomvariable
* \brief The zeta distribution Random Number Generator (RNG) that
* allows stream numbers to be set deterministically.
*
* This class supports the creation of objects that return random numbers
* from a fixed zeta distribution. It also supports the generation of
* single random numbers from various zeta distributions.
*
* The Zeta distribution is closely related to Zipf distribution when
* N goes to infinity.
*
* Zeta distribution has one parameter, alpha, \f$ \alpha > 1 \f$ (real).
* Probability Mass Function is \f$ f(k; \alpha) = k^{-\alpha}/\zeta(\alpha) \f$
* where \f$ \zeta(\alpha) \f$ is the Riemann zeta function ( \f$ \sum_{n=1}^\infty n^{-\alpha} ) \f$
*
* Here is an example of how to use this class:
* \code
* double alpha = 2.0;
*
* Ptr<ZetaRandomVariable> x = CreateObject<ZetaRandomVariable> ();
* x->SetAttribute ("Alpha", DoubleValue (alpha));
*
* // The expected value for the mean of the values returned by a
* // zetaly distributed random variable is equal to
* //
* // zeta(alpha - 1)
* // E[value] = --------------- for alpha > 2 ,
* // zeta(alpha)
* //
* // where zeta(alpha) is the Riemann zeta function.
* //
* // There are no simple analytic forms for the Riemann zeta
* // function, which is the reason the known mean of the values
* // cannot be calculated in this example.
* //
* double value = x->GetValue ();
* \endcode
*/
class ZetaRandomVariable : public RandomVariableStream
{
public:
static TypeId GetTypeId (void);
/**
* \brief Creates a zeta distribution RNG with the default value for
* alpha.
*/
ZetaRandomVariable ();
/**
* \brief Returns the alpha value for the zeta distribution returned by this RNG stream.
* \return The alpha value for the zeta distribution returned by this RNG stream.
*/
double GetAlpha (void) const;
/**
* \brief Returns a random double from a zeta distribution with the specified alpha.
* \param alpha Alpha value for the zeta distribution.
* \return A floating point random value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u\f$ is a uniform variable over [0,1]
* and \f$x\f$ is a value that would be returned normally, then
* \f$(1 - u\f$) is the distance that \f$u\f$ would be from \f$1\f$.
* The value returned in the antithetic case, \f$x'\f$, uses (1-u),
* which is the distance \f$u\f$ is from the 1.
*/
double GetValue (double alpha);
/**
* \brief Returns a random unsigned integer from a zeta distribution with the specified alpha.
* \param alpha Alpha value for the zeta distribution.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u\f$ is a uniform variable over [0,1]
* and \f$x\f$ is a value that would be returned normally, then
* \f$(1 - u\f$) is the distance that \f$u\f$ would be from \f$1\f$.
* The value returned in the antithetic case, \f$x'\f$, uses (1-u),
* which is the distance \f$u\f$ is from the 1.
*/
uint32_t GetInteger (uint32_t alpha);
/**
* \brief Returns a random double from a zeta distribution with the current alpha.
* \return A floating point random value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u\f$ is a uniform variable over [0,1]
* and \f$x\f$ is a value that would be returned normally, then
* \f$(1 - u\f$) is the distance that \f$u\f$ would be from \f$1\f$.
* The value returned in the antithetic case, \f$x'\f$, uses (1-u),
* which is the distance \f$u\f$ is from the 1.
*
* Note that we have to re-implement this method here because the method is
* overloaded above for the two-argument variant and the c++ name resolution
* rules don't work well with overloads split between parent and child
* classes.
*/
virtual double GetValue (void);
/**
* \brief Returns a random unsigned integer from a zeta distribution with the current alpha.
* \return A random unsigned integer value.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u\f$ is a uniform variable over [0,1]
* and \f$x\f$ is a value that would be returned normally, then
* \f$(1 - u\f$) is the distance that \f$u\f$ would be from \f$1\f$.
* The value returned in the antithetic case, \f$x'\f$, uses (1-u),
* which is the distance \f$u\f$ is from the 1.
*/
virtual uint32_t GetInteger (void);
private:
/// The alpha value for the zeta distribution returned by this RNG stream.
double m_alpha;
/// Just for calculus simplifications.
double m_b;
};
/**
* \ingroup randomvariable
* \brief The Random Number Generator (RNG) that returns a predetermined sequence.
*
* Defines a random variable that has a specified, predetermined
* sequence. This would be useful when trying to force the RNG to
* return a known sequence, perhaps to compare NS-3 to some other
* simulator
*
* Creates a generator that returns successive elements of the values
* array on successive calls to RandomVariableStream::GetValue. Note
* that the values in the array are copied and stored by the generator
* (deep-copy). Also note that the sequence repeats if more values
* are requested than are present in the array.
*
* Here is an example of how to use this class:
* \code
* Ptr<DeterministicRandomVariable> s = CreateObject<DeterministicRandomVariable> ();
*
* // The following array should give the sequence
* //
* // 4, 4, 7, 7, 10, 10 .
* //
* double array [] = { 4, 4, 7, 7, 10, 10};
* uint64_t count = 6;
* s->SetValueArray (array, count);
*
* double value = x->GetValue ();
* \endcode
*/
class DeterministicRandomVariable : public RandomVariableStream
{
public:
static TypeId GetTypeId (void);
/**
* \brief Creates a deterministic RNG that will have a predetermined
* sequence of values.
*/
DeterministicRandomVariable ();
virtual ~DeterministicRandomVariable ();
/**
* \brief Sets the array of values that holds the predetermined sequence.
* \param values Array of random values to return in sequence.
* \param length Number of values in the array.
*
* Note that the values in the array are copied and stored
* (deep-copy).
*/
void SetValueArray (double* values, uint64_t length);
/**
* \brief Returns the next value in the sequence.
* \return The floating point next value in the sequence.
*/
virtual double GetValue (void);
/**
* \brief Returns the next value in the sequence.
* \return The integer next value in the sequence.
*/
virtual uint32_t GetInteger (void);
private:
/// Position in the array of values.
uint64_t m_count;
/// Position of the next value in the array of values.
uint64_t m_next;
/// Array of values to return in sequence.
double* m_data;
};
/**
* \ingroup randomvariable
* \brief The Random Number Generator (RNG) that has a specified empirical distribution.
*
* Defines a random variable that has a specified, empirical
* distribution. The distribution is specified by a
* series of calls to the CDF member function, specifying a
* value and the probability that the function value is less than
* the specified value. When values are requested,
* a uniform random variable is used to select a probability,
* and the return value is interpreted linearly between the
* two appropriate points in the CDF. The method is known
* as inverse transform sampling:
* (http://en.wikipedia.org/wiki/Inverse_transform_sampling).
*
* Here is an example of how to use this class:
* \code
* // Create the RNG with a uniform distribution between 0 and 10.
* Ptr<EmpiricalRandomVariable> x = CreateObject<EmpiricalRandomVariable> ();
* x->CDF ( 0.0, 0.0);
* x->CDF ( 5.0, 0.5);
* x->CDF (10.0, 1.0);
*
* // The expected value for the mean of the values returned by this
* // empirical distribution is the midpoint of the distribution
* //
* // E[value] = 5 .
* //
* double value = x->GetValue ();
* \endcode
*/
class EmpiricalRandomVariable : public RandomVariableStream
{
public:
static TypeId GetTypeId (void);
/**
* \brief Creates an empirical RNG that has a specified, empirical
* distribution.
*/
EmpiricalRandomVariable ();
/**
* \brief Specifies a point in the empirical distribution
* \param v The function value for this point
* \param c Probability that the function is less than or equal to v
*/
void CDF (double v, double c); // Value, prob <= Value
/**
* \brief Returns the next value in the empirical distribution.
* \return The floating point next value in the empirical distribution.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u\f$ is a uniform variable over [0,1]
* and \f$x\f$ is a value that would be returned normally, then
* \f$(1 - u\f$) is the distance that \f$u\f$ would be from \f$1\f$.
* The value returned in the antithetic case, \f$x'\f$, uses (1-u),
* which is the distance \f$u\f$ is from the 1.
*/
virtual double GetValue (void);
/**
* \brief Returns the next value in the empirical distribution.
* \return The integer next value in the empirical distribution.
*
* Note that antithetic values are being generated if m_isAntithetic
* is equal to true. If \f$u\f$ is a uniform variable over [0,1]
* and \f$x\f$ is a value that would be returned normally, then
* \f$(1 - u\f$) is the distance that \f$u\f$ would be from \f$1\f$.
* The value returned in the antithetic case, \f$x'\f$, uses (1-u),
* which is the distance \f$u\f$ is from the 1.
*/
virtual uint32_t GetInteger (void);
private:
class ValueCDF
{
public:
ValueCDF ();
ValueCDF (double v, double c);
ValueCDF (const ValueCDF& c);
double value;
double cdf;
};
virtual void Validate (); // Insure non-decreasing emiprical values
virtual double Interpolate (double, double, double, double, double);
bool validated; // True if non-decreasing validated
std::vector<ValueCDF> emp; // Empicical CDF
};
} // namespace ns3
#endif /* RANDOM_VARIABLE_STREAM_H */