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homogeneousMultiDRandomWalk Class Reference

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

#include <homogeneousMultiDRandomWalk.h>

Inheritance diagram for homogeneousMultiDRandomWalk:
markovChain

Public Member Functions

 homogeneousMultiDRandomWalk (int nbDims, int *sz, double *p, double *q)
 Constructor for the class. The initial state is set arbitrarily to (0,...,0). More...
 
 homogeneousMultiDRandomWalk (int nbDims, double *p, double *q)
 Constructor for the class with infinite dimensions. The initial state is set arbitrarily to (0,...,0). More...
 
 ~homogeneousMultiDRandomWalk ()
 Standard destructor. More...
 
void makeMarkovChain ()
 Instantiation of the generator for the markovChain ancestor Works only for dimension 2. More...
 
discreteDistributionstationaryDistribution ()
 Computes the stationary distribution of the chain. These Markov chains have a product-form stationary distribution. 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...
 
void write (string format)
 General output procedure for this class of Markov chains. More...
 
- 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...
 
RInsideRmotor ()
 Read accessor to the embedded R engine, a static variable named _Rmotor. When accessed for the first time, an instance of RInside is created. 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...
 
DistributionstationaryDistribution_iterative (string method, int tmax, double precision, string initDistribType, discreteDistribution *initDistrib, bool progress)
 Multi-purpose entry point for iterative methods for approximating the stationary distribution of discrete-time Markov chains. Offers the maximal flexibility with respect to parameters, as well as the possibility to set defaults. More...
 
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 DistributionstationaryDistributionCT_embedding (int tMax, double epsilon, discreteDistribution *iDis, bool progress)
 Computing the stationary distribution of a CTMC using embedding and the iterative method. More...
 
virtual DistributionstationaryDistribution_power (int tMax, double epsilon, discreteDistribution *iDis, bool progress)
 Computing the stationary distribution of a DTMC using the standard iterative power method. More...
 
void NCDProperty (double epsilon)
 Entry point for NCD command of XBORNE (Near Complete Decomposibility) More...
 
void BandIMSUB (std::string modelName="modelName")
 Entry point for BandIMSUB command of XBORNE. More...
 
void Vincent ()
 Entry point for Vincent command of XBORNE. More...
 
void RowVincent ()
 Entry point for RowVincent command of XBORNE. More...
 
void Absorbing ()
 Entry point for Absorbing command of XBORNE: computes the absorbing states of a DTMC. More...
 
void ProdFundSW (std::string modelName="modelName")
 Entry point for ProdFundSW command of XBORNE. More...
 
void RowSum (std::string modelName="modelName")
 Entry point for RowSum command of XBORNE. 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...
 
DistributiontransientDistributionR (int fromState, double t)
 Method for computing the transient distribution of a Markov chain. It wraps the 'solve.uc' method of the R package of L. Cerda-Alabern. More...
 
DistributiontransientDistributionDT (int fromState, int t)
 Method for computing the transient distribution of a DTMC. Uses the general method evaluateMeasure. More...
 
DistributionstationaryDistributionR ()
 Entry point for methods computing stationary distributions using the R package 'markovchain' for solving the linear system. More...
 
simulationResultsimulateChainR (double tMax, bool stats, bool traj, bool trace)
 Simulates the evolution of a discrete-time Markov Chain. Wraps the 'rmarkovchain' method of the R package 'markovchain'. More...
 
double transitionProbability (int stateFrom, int stateTo)
 Method to get the transition probabilities from some intial to some destination state. It wraps the 'transitionProbability' method of the R package 'markovchain'. More...
 
std::vector< int > absorbingStates ()
 Method that returns the list of absorbing states of the markovchain object. It wraps the 'absorbingStates()' method of the R package 'markovchain'. More...
 
std::vector< std::vector< int > > recurrentClasses ()
 Method that returns the recurrent classes of the markovchain object as a list of lists of states. It wraps the 'recurrentClasses()' method of the R package 'markovchain'. More...
 
std::vector< std::vector< int > > communicatingClasses ()
 Method that returns the communicating classes of the markovchain object as a list of lists of states. It wraps the 'communicatingClasses()' method of the R package 'markovchain'. More...
 
bool isirreducible ()
 Method verifing whether a Markov chain is irreducible. It wraps the "is.irreducible()' method of the R package 'markovchain'. More...
 
bool isaccessible (int stateFrom, int stateTo)
 Method verifying if two states communicate in a Markov chain. Wraps the 'is.accessible()' method from the R package 'markovchain'. 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...
 
virtual markovChainembed ()
 Construct discrete-time Markov Chain obtained at transition times. 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...
 
int charVectorElt2State (SEXP elt, std::string function)
 Utility function to convert the element of a Rcpp::CharacterVector to a state number. More...
 
virtual void write (FILE *out, bool withReward)
 Method for writing Markov chains in a file with the ERS format. More...
 
virtual void write (string format, string modelName)
 Method for writing Markov chains in files with various formats. The ERS and R formats are supported at this time. More...
 
void write (string format)
 Method for writing Markov chains in files with various formats. This version uses the given model name. More...
 
std::string toString (std::string format)
 String serialization method for a Markov chain. More...
 

Protected Attributes

int _nbDims
 number of dimensions of the grid More...
 
double * _stateSpace
 representation of the state space when finite More...
 
int * _dimSize
 size of the state space in each dimension 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 - sum_i( p_i + q_i ) 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...
 

Additional Inherited Members

- Protected Types inherited from markovChain
typedef void * RInside
 recast nonexisting RInside type to void More...
 
typedef void * SEXP
 recast nonexisting SEXP type to void More...
 

Detailed Description

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

Constructor & Destructor Documentation

homogeneousMultiDRandomWalk::homogeneousMultiDRandomWalk ( int  nbDims,
int *  sz,
double *  p,
double *  q 
)

Constructor for the class. The initial state is set arbitrarily to (0,...,0).

Parameters
nbDimsthe number of dimensions
szthe array of sizes in each dimension
pthe array of probabilities to jump to the right
qthe array of probabilities to jump to the left
homogeneousMultiDRandomWalk::homogeneousMultiDRandomWalk ( int  nbDims,
double *  p,
double *  q 
)

Constructor for the class with infinite dimensions. The initial state is set arbitrarily to (0,...,0).

Parameters
nbDimsthe array of sizes in each dimension
pthe array of probabilities to jump to the right
qthe array of probabilities to jump to the left
homogeneousMultiDRandomWalk::~homogeneousMultiDRandomWalk ( )

Standard destructor.

Member Function Documentation

void homogeneousMultiDRandomWalk::makeMarkovChain ( )

Instantiation of the generator for the markovChain ancestor Works only for dimension 2.

Author
Alain Jean-Marie
int * homogeneousMultiDRandomWalk::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.

Parameters
iStatethe initial state from which trajectories start
hittingSetboolean array indicating with true which states are in the target
nbSamplesnumber of samples to collect
tMaxmaximum length of trajectories
Returns
an array with the samples
discreteDistribution * homogeneousMultiDRandomWalk::stationaryDistribution ( )

Computes the stationary distribution of the chain. These Markov chains have a product-form stationary distribution.

Returns
The stationary distribution.
void homogeneousMultiDRandomWalk::write ( string  format)

General output procedure for this class of Markov chains.

Parameters
formatthe format/language to use

Member Data Documentation

int* homogeneousMultiDRandomWalk::_dimSize
protected

size of the state space in each dimension

int homogeneousMultiDRandomWalk::_nbDims
protected

number of dimensions of the grid

double* homogeneousMultiDRandomWalk::_p
protected

the probability to jump to the right

double* homogeneousMultiDRandomWalk::_q
protected

the probability to jump to the left

double homogeneousMultiDRandomWalk::_r
protected

r = 1 - sum_i( p_i + q_i ) is the proba of staying in the same state

double* homogeneousMultiDRandomWalk::_stateSpace
protected

representation of the state space when finite


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