class MarkovC extends Error
The MarkovC class supports the creation and use of Continuous-Time Markov Chains
'CTMC's. 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 differential
equations. Equilibrium solution (steady-state): solve for 'p' in 'p * tr = 0'.
- See also
www.math.wustl.edu/~feres/Math450Lect05.pdf
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- new MarkovC(tr: MatrixD)
- tr
the transition rate matrix
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- 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.
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- val jump: MatrixD
The jump matrix derived from the transition rate matrix 'tr'
- 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.e., '||p|| = 1'.
- final def ne(arg0: AnyRef): Boolean
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- 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
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- 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
- final def synchronized[T0](arg0: => T0): T0
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- def toString(): String
Convert 'this' continuous-time Markov Chain to s string.
Convert 'this' continuous-time Markov Chain to s string.
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