class Markov extends Error
The Markov class supports the creation and use of Discrete-Time Markov Chains
'DTMC's. Transient solution: compute the next state 'pp = 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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- new Markov(tr: MatriD)
- tr
the transition probability matrix
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- 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.
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- def isStochastic: Boolean
Check whether the transition matrix is stochastic.
- def limit: VectoD
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'.
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- def next(p: VectoD, k: Int = 1): VectoD
Compute the 'k'th next probabilistic state 'p * tr^k'.
Compute the 'k'th next probabilistic state 'p * tr^k'.
- p
the current state probability vector
- k
compute for the 'k'th step/epoch
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- 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
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- def toString(): String
Convert 'this' discrete-time Markov Chain to a string.
Convert 'this' discrete-time Markov Chain to a string.
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