MarkovChain Class Reference

This class defines a generic Markov chain and provides basic tools to simulate it for a given number of steps or until it stops, and to recover the performance measure. More...

Inheritance diagram for MarkovChain:

Collaboration diagram for MarkovChain:

Public Member Functions
Abstract methods
abstract void	initialState ()
	Sets the Markov chain to its (deterministic) initial state and initializes the collectors for the performance measure, ready to start a simulation. More...
abstract void	nextStep (RandomStream stream)
	Simulates one more step of the chain, from its current state, using stream for the randomness. More...
abstract double	getPerformance ()
	Returns the performance measure (total or average cost or gain) so far, for the current simulation run.
Other methods
Object	clone () throws CloneNotSupportedException
	Returns a clone of the chain.
boolean	hasStopped ()
	Tells if the chain has stopped.
void	simulSteps (int numSteps, RandomStream stream)
	Starts a new simulation run and simulates numSteps steps of the Markov chain or until the chain stops, using the given stream.
void	simulSteps (RandomStream stream)
	Starts a new simulation run and simulates until the stopping time is reached, using the given stream. More...
void	simulRuns (int n, int numSteps, RandomStream stream, Tally statRuns)
	Performs n simulation runs of the chain, for numSteps steps per run, using the given stream. More...
void	simulRunsWithSubstreams (int n, int numSteps, RandomStream stream, Tally statRuns)
	Same as simulRuns, except that the stream is first reset to its initial seed and then reset to the first substream at the beginning and to the next substream after each run.
double	simulMC (int n, int numSteps)
	Perform n simulation runs of the chain, each for numSteps steps, and returns average.
double	simulMC (int n)
	Perform n runs, each one until the chain stops.
void	simulRepMC (int n, int numSteps, int m, Tally t)
	Perform n runs and compute the average, reapeat m times and return the stats in t.
void	simulRepMC (int n, int m, Tally t)
	Same as previous one, but run the chains until they stop.
void	simulRQMC (PointSet p, int m, int numSteps, PointSetRandomization rand, Tally statReps)
	Performs m independent replicates of \(n\) simulation runs of the chain using a RQMC point set, each time storing the average of the performance over the \(n\) chains. More...
String	simulRunsFormat (int n, int numSteps, RandomStream stream, Tally statRuns)
	Same as simulRuns but also returns the results as a formatted string.
String	simulRunsWithSubstreamsFormat (int n, int numSteps, RandomStream stream, Tally statRuns)
	Same as simulRunsWithSubstreams but also returns the results as a formatted string.
String	simulRQMCFormat (PointSet p, int m, int numSteps, PointSetRandomization rand, Tally statReps)
	Same as simulRQMC but also returns the results as a formatted string.
String	testImprovementRQMCFormat (PointSet p, int m, int numSteps, PointSetRandomization rand, double varMC, Tally statReps)
	Similar to simulRQMCFormat, but also gives the variance improvement factor with respect to MC. More...
String	formatResults (Tally stat)
	Returns a string containing the mean, the variance, and a 90% confidence interval for stat.
String	formatResultsRQMC (Tally stat, int numPoints)
	Returns a string containing the mean, the variance multiplied by numPoints, and a 90% confidence interval for stat.

Protected Attributes
boolean	stopped = false

Package Attributes
Chrono	timer = Chrono.createForSingleThread()
int	numSteps

Detailed Description

This class defines a generic Markov chain and provides basic tools to simulate it for a given number of steps or until it stops, and to recover the performance measure.

Chains can be cloned, so one can simulate many replicates in parallel. In a concrete subclass, it suffices to implement the three abstract methods initialState(), nextStep(stream) and getPerformance() to get things going. One would usually implement subclasses of MarkovChainComparable or MarkovChainDouble rather than direct subclasses of MarkovChain. Some other methods are then needed. It is also essential to override the method clone, if the class contains non primitive objects, in order to clone these objects.

The methods in this class permit one to simulate the chain over a certain number of steps via Monte Carlo or randomized quasi-Monte Carlo. Statistics on the performance measure of the chain are computed during these simulations.

Member Function Documentation

initialState()

abstract void initialState ( )

abstract

Sets the Markov chain to its (deterministic) initial state and initializes the collectors for the performance measure, ready to start a simulation.

Must also set variable stopped to false.

nextStep()

abstract void nextStep ( RandomStream  stream )

abstract

Simulates one more step of the chain, from its current state, using stream for the randomness.

If the chain stops, this method must set variable stopped to true.

simulRQMC()

void simulRQMC	(	PointSet	p,
		int	m,
		int	numSteps,
		PointSetRandomization	rand,
		Tally	statReps
	)

Performs m independent replicates of \(n\) simulation runs of the chain using a RQMC point set, each time storing the average of the performance over the \(n\) chains.

\(n\) is the number of points in RQMC point set p. Each run goes for numSteps steps. For each replicate, the point set p is randomized using rand, an iterator is created, and each run uses a different substream of this iterator (i.e., a different point). The statistics on the performance for the m independent replications are placed in statReps.

simulRuns()

void simulRuns	(	int	n,
		int	numSteps,
		RandomStream	stream,
		Tally	statRuns
	)

Performs n simulation runs of the chain, for numSteps steps per run, using the given stream.

The statistics on the performance for the n runs are placed in statRuns.

simulSteps()

void simulSteps

(

RandomStream

stream

)

Starts a new simulation run and simulates until the stopping time is reached, using the given stream.

Same as simulSteps(Integer.MAX_VALUE, stream).

testImprovementRQMCFormat()

String testImprovementRQMCFormat	(	PointSet	p,
		int	m,
		int	numSteps,
		PointSetRandomization	rand,
		double	varMC,
		Tally	statReps
	)

Similar to simulRQMCFormat, but also gives the variance improvement factor with respect to MC.

Assuming that varMC gives the variance per run for MC.

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

• MarkovChain.java