scalation.state

Markov

class Markov extends Error

This class supports the creation and use of Discrete-Time Markov Chains (DTMC). Transient solution: compute the next state p' = p * tr where 'p' is the current state probability vector and 'tr' is the transition probability matrix. Equilibrium solution (steady-state): solve for p in p = p * tr.

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Instance Constructors

  1. new Markov(tr: MatrixD)

    tr

    the transition probability matrix

Value Members

  1. final def !=(arg0: AnyRef): Boolean

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  2. final def !=(arg0: Any): Boolean

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  3. final def ##(): Int

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  4. final def ==(arg0: AnyRef): Boolean

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  5. final def ==(arg0: Any): Boolean

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  6. def animate(): Unit

    Animate this Markov Chain.

    Animate this Markov Chain. Place the nodes around a circle and connect them if there is a such a transition.

  7. final def asInstanceOf[T0]: T0

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  8. def clone(): AnyRef

    Attributes
    protected[java.lang]
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    @throws( ... )
  9. final def eq(arg0: AnyRef): Boolean

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  10. def equals(arg0: Any): Boolean

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  11. def finalize(): Unit

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    protected[java.lang]
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    @throws( classOf[java.lang.Throwable] )
  12. def flaw(method: String, message: String): Unit

    Show the flaw by printing the error message.

    Show the flaw by printing the error message.

    method

    the method where the error occurred

    message

    the error message

    Definition Classes
    Error
  13. final def getClass(): Class[_]

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  14. def hashCode(): Int

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  15. final def isInstanceOf[T0]: Boolean

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  16. def isStochastic: Boolean

    Check whether the transition matrix is stochastic.

  17. def limit: VectorD

    Compute the limiting probabilistic state (p * tr^k) as k -> infinity, by solving a left eigenvalue problem: p = p * tr => p * (tr - I) = 0, where the eigenvalue is 1. Solve for p by computing the left nullspace of the tr - I matrix (appropriately sliced) and then normalize p so ||p|| = 1.

  18. final def ne(arg0: AnyRef): Boolean

    Definition Classes
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  19. def next(p: VectorD, k: Int = 1): VectorD

    Compute the kth next probabilistic state (p * tr^k).

    Compute the kth next probabilistic state (p * tr^k).

    p

    the current state probability vector

    k

    compute for the kth step/epoch

  20. final def notify(): Unit

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  21. final def notifyAll(): Unit

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  22. def simulate(i0: Int, endTime: Int): Unit

    Simulate the discrete-time Markov chain, by starting in state i0 and after the state's holding, making a transition to the next state according to the jump matrix.

    Simulate the discrete-time Markov chain, by starting in state i0 and after the state's holding, making a transition to the next state according to the jump matrix.

    i0

    the initial/start state

    endTime

    the end time for the simulation

  23. final def synchronized[T0](arg0: ⇒ T0): T0

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  24. def toString(): String

    Convert this discrete-time Markov Chain to s string.

    Convert this discrete-time Markov Chain to s string.

    Definition Classes
    Markov → AnyRef → Any
  25. final def wait(): Unit

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    @throws( ... )
  26. final def wait(arg0: Long, arg1: Int): Unit

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  27. final def wait(arg0: Long): Unit

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