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homogeneous1DRandomWalk Class Reference

The 1-dimensional random walk with homogeneous transition probabilities. This model is characterized by: More...

#include <homogeneous1DRandomWalk.h>

Inheritance diagram for homogeneous1DRandomWalk:
markovChain markovChain

Public Member Functions

 homogeneous1DRandomWalk (double l, double m)
 Constructor for a homogeneous1DRandomWalk chain with infinite state space. More...
 
 homogeneous1DRandomWalk (int sz, double l, double m)
 Constructor for a homogeneous1DRandomWalk chain. More...
 
 ~homogeneous1DRandomWalk ()
 Destructor for a homogeneous1DRandomWalk chain. More...
 
void makeMarkovChain ()
 Instantiation of the generator for the markovChain ancestor. More...
 
discreteDistributiontransientDistribution (int t, int nMax)
 Computes the transient distribution for a RW1D Markov Chain. More...
 
geometricDistributionstationaryDistribution ()
 Computes the stationary distribution for a homogeneous1DRandomWalk chain with infinite state space. When the chain is not stable, the (improper) geometric distribution with parameter is returned. More...
 
discreteDistributionstationaryDistribution (int nMax)
 Computes the stationary distribution for a finite homogeneous1DRandomWalk chain. More...
 
simulationResultsimulateChain (long int tMax, bool stat, bool traj, bool trace)
 Simulates the evolution of a homogeneous1DRandomWalk chain. More...
 
void write (string format, string prefix)
 Writes a homogeneous1DRandomWalk chain in files with some specified format. Supported formats: More...
 
 homogeneous1DRandomWalk (double l, double m)
 
 homogeneous1DRandomWalk (int sz, double l, double m)
 
void makeMarkovChain ()
 
discreteDistributiontransientDistribution (int t, int nMax)
 
geometricDistributionstationaryDistribution ()
 
discreteDistributionstationaryDistribution (int nMax)
 
simulationResultsimulateChain (long int tMax, bool stat, bool traj, bool trace)
 
void write (string format, string prefix)
 
- Public Member Functions inherited from markovChain
 markovChain (int sz, timeType t)
 Simple constructor for the Markov chain from the size. More...
 
 markovChain (transitionStructure *tr)
 Constructor for the Markov chain using a transition structure. More...
 
 markovChain (string format, string param[], int nbreParam, string modelName, bool isAbstract)
 Constructor for Markov chains from files in various formats. In the abstract form, the object just stores the name(s) of the files that define the mode. In the non-abstract (concrete) form, the chain is instantiated in the memory with a concrete transition structure. Only the ERS, PSI and Xborne formats are supported at this time for concrete chains. More...
 
virtual ~markovChain ()
 Standard destructor. The generator and the initial distrib are destroyed. More...
 
int stateSpaceSize ()
 Read accessor to get the number of states in the state space of the Markov chain. More...
 
transitionStructuregenerator ()
 Read accessor to get the value of _generator which is a transitionStructure. More...
 
void setInitDistribution (discreteDistribution *d)
 Write accessor to set the value of _initDistribution which is a discreteDistribution. More...
 
void setGenerator (transitionStructure *tr)
 Write accessor to set the value of _generator which is a transitionStructure. More...
 
Distributionread ()
 Method(s) for deserializing Distribution from Xborne file (.pi). More...
 
void setFormat (string format)
 Utility to set the value of _format. More...
 
void setModelName (string modelName)
 Utility to set the value of _modelName. More...
 
void setAbstractNbre (int abstractNbre)
 Utility to set the value of _abstractNbre. More...
 
void setAbstract (string abstract[])
 Utility to set the value of the table containing names related to the model: file names, extensions etc. More...
 
int abstractNbre ()
 Utility to get _abstractNbre. More...
 
string modelName ()
 Utility to get _modelName. More...
 
string format ()
 Utility to get _format. More...
 
void abstract ()
 Utility to display the value of the table _abstract[]. More...
 
virtual simulationResultsimulateChain (double tMax, bool Stats, bool Traj, bool withIncrements, bool Print)
 Simulates the evolution of a Markov Chain using the PSI program. This is a front-end function to both discrete-time and the continuous-time simulators. More...
 
virtual simulationResultsimulateChainDT (int tMax, bool stats, bool traj, bool trace)
 Simulates the evolution of a discrete-time Markov Chain. More...
 
virtual simulationResultsimulateChainCT (double tMax, bool stats, bool traj, bool withIncrements, bool trace)
 Simulates the evolution of a continuous-time Markov Chain. More...
 
simulationResultsimulatePSI (int tMax, bool stats, bool Traj, bool Print)
 Simulates the evolution of a Markov Chain. This is a front-end function to the discrete-time simulator. For continuous time, the PSI simulator does not allow to control the simulation horizon. The effect of "Print" is to be handled in the specific simulation function, not here. More...
 
virtual DistributionstationaryDistribution (bool progress)
 Entry point for methods Computing the stationary distribution of chains using the iterative method. More...
 
virtual DistributionstationaryDistributionCT (bool progress)
 Computing the stationary distribution of a CTMC using uniformization and the iterative method. More...
 
virtual DistributionstationaryDistributionDT (bool progress)
 Computing the stationary distribution of a DTMC using uniformization and the iterative method. More...
 
DistributionstationaryDistributionGthLD ()
 Entry point for methods computing stationary distributions using the GTH method for solving the linear system. More...
 
DistributionstationaryDistributionSOR ()
 Entry point for methods computing stationary distributions using the SOR method for solving the linear system. More...
 
simulationResultstationaryDistributionSample (int nbSamples)
 Methods to sample from the stationary distribution using backwards coupling. The result is returned in a simulationResult object, but the interpretation is different: it does not represent trajectories. Here, "state" entries are the measured states, and "time" entries are the measured coupling time. More...
 
DistributionhittingTimeDistribution (int iState, bool *hitSetIndicator)
 Entry point for methods computing the distribution of the hitting time (first entry times) from some state to some set of states. More...
 
int * simulateHittingTime (int iState, bool *hittingSet, int nbSamples, int tMax)
 Obtain samples of hitting times through Monte Carlo simulation. A trajectory is simulated until it hits the target set, or its length attains a maximum, whichever comes first. Samples with the maximum are returned although they do not represent a proper hitting time. It is the responsibility of the calling party to ignore these values. More...
 
double * averageHittingTime (bool *hitSetIndicator)
 Entry point for methods computing average hitting times (first entry times) from every state to some set of states. More...
 
double * averageHittingTimeDT (bool *hitSetIndicator)
 Computing the average hitting times in a discrete-time Markov chain. Uses a direct Gauss-Seidel matrix inversion. More...
 
double * averageHittingTimeDT_iterative (bool *hitSetIndicator)
 Computing the average hitting times in a discrete-time Markov chain. Uses an iterative approximate computation. More...
 
virtual markovChaincopy ()
 copy utility More...
 
virtual markovChainuniformize ()
 Uniformize Markov Chain, by uniformizing the generator. If the chain is already discrete time, a copy is returned. More...
 
void setSizeType (const string path)
 Function to find out the size and the type of a Markov chain described in the MARCA format. Both quantities are directly set in the method, which returns nothing. Adapted from the method HBF::read_marka of Psi/Unix/v1.0. More...
 
virtual void write (FILE *out, bool withReward)
 Method(s) for writing Markov chains in files with various formats. Only the ERS format is supported at this time. More...
 
 markovChain (int sz, timeType t)
 Simple constructor for the Markov chain from the size. More...
 
 markovChain (transitionStructure *tr)
 Constructor for the Markov chain using a transition structure. More...
 
 markovChain (string format, string param[], int nbreParam, string modelName, bool isAbstract)
 Constructor for Markov chains from files in various formats. In the abstract form, the object just stores the name(s) of the files that define the mode. In the non-abstract (concrete) form, the chain is instantiated in the memory with a concrete transition structure. Only the ERS, PSI and Xborne formats are supported at this time for concrete chains. More...
 
virtual ~markovChain ()
 Standard destructor. The generator and the initial distrib are destroyed. More...
 
int stateSpaceSize ()
 Read accessor to get the number of states in the state space of the Markov chain. More...
 
transitionStructuregenerator ()
 Read accessor to get the value of _generator which is a transitionStructure. More...
 
void setInitDistribution (discreteDistribution *d)
 Write accessor to set the value of _initDistribution which is a discreteDistribution. More...
 
void setGenerator (transitionStructure *tr)
 Write accessor to set the value of _generator which is a transitionStructure. More...
 
Distributionread ()
 Method(s) for deserializing Distribution from Xborne file (.pi). More...
 
void setFormat (string format)
 Utility to set the value of _format. More...
 
void setModelName (string modelName)
 Utility to set the value of _modelName. More...
 
void setAbstractNbre (int abstractNbre)
 Utility to set the value of _abstractNbre. More...
 
void setAbstract (string abstract[])
 Utility to set the value of the table containing names related to the model: file names, extensions etc. More...
 
int abstractNbre ()
 Utility to get _abstractNbre. More...
 
string modelName ()
 Utility to get _modelName. More...
 
string format ()
 Utility to get _format. More...
 
void abstract ()
 Utility to display the value of the table _abstract[]. More...
 
virtual simulationResultsimulateChain (double tMax, bool Stats, bool Traj, bool withIncrements, bool Print)
 Simulates the evolution of a Markov Chain using the PSI program. This is a front-end function to both discrete-time and the continuous-time simulators. More...
 
virtual simulationResultsimulateChainDT (int tMax, bool stats, bool traj, bool trace)
 Simulates the evolution of a discrete-time Markov Chain. More...
 
virtual simulationResultsimulateChainCT (double tMax, bool stats, bool traj, bool withIncrements, bool trace)
 Simulates the evolution of a continuous-time Markov Chain. More...
 
simulationResultsimulatePSI (int tMax, bool stats, bool Traj, bool Print)
 Simulates the evolution of a Markov Chain. This is a front-end function to the discrete-time simulator. For continuous time, the PSI simulator does not allow to control the simulation horizon. The effect of "Print" is to be handled in the specific simulation function, not here. More...
 
virtual DistributionstationaryDistribution (bool progress)
 Entry point for methods Computing the stationary distribution of chains using the iterative method. More...
 
virtual DistributionstationaryDistributionCT (bool progress)
 Computing the stationary distribution of a CTMC using uniformization and the iterative method. More...
 
virtual DistributionstationaryDistributionDT (bool progress)
 Computing the stationary distribution of a DTMC using uniformization and the iterative method. More...
 
DistributionstationaryDistributionGthLD ()
 Entry point for methods computing stationary distributions using the GTH method for solving the linear system. More...
 
DistributionstationaryDistributionSOR ()
 Entry point for methods computing stationary distributions using the SOR method for solving the linear system. More...
 
simulationResultstationaryDistributionSample (int nbSamples)
 Methods to sample from the stationary distribution using backwards coupling. The result is returned in a simulationResult object, but the interpretation is different: it does not represent trajectories. Here, "state" entries are the measured states, and "time" entries are the measured coupling time. More...
 
DistributionhittingTimeDistribution (int iState, bool *hitSetIndicator)
 Entry point for methods computing the distribution of the hitting time (first entry times) from some state to some set of states. More...
 
int * simulateHittingTime (int iState, bool *hittingSet, int nbSamples, int tMax)
 Obtain samples of hitting times through Monte Carlo simulation. A trajectory is simulated until it hits the target set, or its length attains a maximum, whichever comes first. Samples with the maximum are returned although they do not represent a proper hitting time. It is the responsibility of the calling party to ignore these values. More...
 
double * averageHittingTime (bool *hitSetIndicator)
 Entry point for methods computing average hitting times (first entry times) from every state to some set of states. More...
 
double * averageHittingTimeDT (bool *hitSetIndicator)
 Computing the average hitting times in a discrete-time Markov chain. Uses a direct Gauss-Seidel matrix inversion. More...
 
double * averageHittingTimeDT_iterative (bool *hitSetIndicator)
 Computing the average hitting times in a discrete-time Markov chain. Uses an iterative approximate computation. More...
 
virtual markovChaincopy ()
 copy utility More...
 
virtual markovChainuniformize ()
 Uniformize Markov Chain, by uniformizing the generator. If the chain is already discrete time, a copy is returned. More...
 
void setSizeType (const string path)
 Function to find out the size and the type of a Markov chain described in the MARCA format. Both quantities are directly set in the method, which returns nothing. Adapted from the method HBF::read_marka of Psi/Unix/v1.0. More...
 
virtual void write (FILE *out, bool withReward)
 Method(s) for writing Markov chains in files with various formats. Only the ERS format is supported at this time. More...
 

Protected Attributes

int _size
 the number of states; possibly infinite More...
 
double * _stateSpace
 representation of the state space when finite More...
 
double _p
 the probability to jump to the right More...
 
double _q
 the probability to jump to the left More...
 
double _r
 r = 1 - p - q is the proba of staying in the same state More...
 
- Protected Attributes inherited from markovChain
timeType _type
 time type: discrete or continuous More...
 
int _stateSpaceSize
 size of the state space (should be a pointer on the state space itself) More...
 
transitionStructure_generator
 transition structure of the chain More...
 
discreteDistribution_initDistribution
 initial distribution of the process More...
 
bool _debug
 internal debugging indicator More...
 
bool _isAbstract
 true if the object is "abstract", i.e. a pointer to some files More...
 
int _abstractNbre
 number of abstraction parameters More...
 
string * _abstract
 table of abstraction parameters More...
 
string _format
 format/language of the model More...
 
string _modelName
 name of the model More...
 

Detailed Description

The 1-dimensional random walk with homogeneous transition probabilities. This model is characterized by:

Constructor & Destructor Documentation

homogeneous1DRandomWalk::homogeneous1DRandomWalk ( double  p,
double  q 
)

Constructor for a homogeneous1DRandomWalk chain with infinite state space.

Author
Alain Jean-Marie
Parameters
pright-jump probability
qleft-jump probability
Returns
an object of type homogeneous1DRandomWalk, with initial state set arbitrarily to 0.
homogeneous1DRandomWalk::homogeneous1DRandomWalk ( int  n,
double  p,
double  q 
)

Constructor for a homogeneous1DRandomWalk chain.

Author
Alain Jean-Marie
Parameters
nsize of the state space of the chain
pright-jump probability
qleft-jump probability
Returns
an object of type markovChain, with initial state set arbitrarily to 0.
homogeneous1DRandomWalk::~homogeneous1DRandomWalk ( )

Destructor for a homogeneous1DRandomWalk chain.

Author
Alain Jean-Marie

Member Function Documentation

void homogeneous1DRandomWalk::makeMarkovChain ( )

Instantiation of the generator for the markovChain ancestor.

Author
Alain Jean-Marie
simulationResult * homogeneous1DRandomWalk::simulateChain ( long int  tMax,
bool  stats,
bool  traj,
bool  trace 
)

Simulates the evolution of a homogeneous1DRandomWalk chain.

Author
Alain Jean-Marie
Parameters
tMaxtime until which the Markov chain is simulated
statsindicates whether occupancy statistics are collected and returned
trajindicates whether a trajectory is returned
traceindicates whether the trajectory should be printed along the way (on stdout)
Returns
a structure with the results of the simulation
geometricDistribution * homogeneous1DRandomWalk::stationaryDistribution ( )

Computes the stationary distribution for a homogeneous1DRandomWalk chain with infinite state space. When the chain is not stable, the (improper) geometric distribution with parameter is returned.

Author
Alain Jean-Marie
Returns
a geometric distribution
discreteDistribution * homogeneous1DRandomWalk::stationaryDistribution ( int  nMax)

Computes the stationary distribution for a finite homogeneous1DRandomWalk chain.

Author
Alain Jean-Marie
Returns
the stationary distribution
discreteDistribution * homogeneous1DRandomWalk::transientDistribution ( int  t,
int  nMax 
)

Computes the transient distribution for a RW1D Markov Chain.

Author
Alain Jean-Marie
Parameters
ttime at which the distribution is to be computed
nMaxmaximal state for the range on which the distribution is to be computed
Returns
a discrete distribution where the result is stored
void homogeneous1DRandomWalk::write ( string  format,
string  modelName 
)
virtual

Writes a homogeneous1DRandomWalk chain in files with some specified format. Supported formats:

  • Xborne: both Rii and Cuu files are written
  • Psi, Ers
    Author
    Alain Jean-Marie
    Parameters
    formatformat/language to be used
    modelNamethe name of the model, usually used as prefix for the different files

Reimplemented from markovChain.

Member Data Documentation

double homogeneous1DRandomWalk::_p
protected

the probability to jump to the right

double homogeneous1DRandomWalk::_q
protected

the probability to jump to the left

double homogeneous1DRandomWalk::_r
protected

r = 1 - p - q is the proba of staying in the same state

int homogeneous1DRandomWalk::_size
protected

the number of states; possibly infinite

double * homogeneous1DRandomWalk::_stateSpace
protected

representation of the state space when finite


The documentation for this class was generated from the following files: