the transition probability matrix
Animate this Markov Chain.
Animate this Markov Chain. Place the nodes around a circle and connect them if there is a such a transition.
Show the flaw by printing the error message.
Show the flaw by printing the error message.
the method where the error occurred
the error message
Check whether the transition matrix is stochastic.
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.
Compute the kth next probabilistic state (p * tr^k).
Compute the kth next probabilistic state (p * tr^k).
the current state probability vector
compute for the kth step/epoch
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.
the initial/start state
the end time for the simulation
Convert this discrete-time Markov Chain to s string.
Convert this discrete-time Markov Chain to s string.
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.