scalation.state

MarkovC

class MarkovC extends Error

This class supports the creation and use of Continuous-Time Markov Chains (CTMC). Note: the transition matrix tr gives the state transition rates off-diagonal. The diagonal elements must equal minus the sum of the rest of their row. Transient solution: Solve the Chapman-Kolmogorov differemtial equations. Equilibrium solution (steady-state): solve for p in p * tr = 0. See: www.math.wustl.edu/~feres/Math450Lect05.pdf

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Instance Constructors

  1. new MarkovC(tr: MatrixD)

    tr

    the transition rate matrix

Value Members

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

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  2. final def ##(): Int

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

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  4. def animate(): Unit

    Animate this continuous-time Markov Chain.

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

  5. final def asInstanceOf[T0]: T0

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  6. def clone(): AnyRef

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

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  8. def equals(arg0: Any): Boolean

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  9. def finalize(): Unit

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    protected[java.lang]
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    @throws( classOf[java.lang.Throwable] )
  10. 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
  11. final def getClass(): Class[_]

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  12. def hashCode(): Int

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  13. final def isInstanceOf[T0]: Boolean

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  14. val jump: MatrixD

    The jump matrix derived from the transition rate matrix (tr)

  15. def limit: VectorD

    Compute the limiting probabilistic state as t -> infinity, by finding the left nullspace of the tr matrix: solve for p such that p * tr = 0 and normalize p, i.

    Compute the limiting probabilistic state as t -> infinity, by finding the left nullspace of the tr matrix: solve for p such that p * tr = 0 and normalize p, i.e.0, ||p|| = 1.

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

    Definition Classes
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  17. def next(p: VectorD, t: Double = 1.0): VectorD

    Compute the next probabilistic state at t time units in the future.

    Compute the next probabilistic state at t time units in the future.

    p

    the current state probability vector

    t

    compute for time t

  18. final def notify(): Unit

    Definition Classes
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  19. final def notifyAll(): Unit

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  20. def simulate(i0: Int, endTime: Double): Unit

    Simulate the continuous-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 continuous-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

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

    Definition Classes
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  22. def toString(): String

    Convert this continuous-time Markov Chain to s string.

    Convert this continuous-time Markov Chain to s string.

    Definition Classes
    MarkovC → AnyRef → Any
  23. final def wait(): Unit

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

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

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