Internal Functions
These functions are not intended to be used by you, the user.
Contents
Index
DiscreteMarkovChains.breadth_first_searchDiscreteMarkovChains.characteristic_matrixDiscreteMarkovChains.digraphDiscreteMarkovChains.is_row_stochasticDiscreteMarkovChains.required_row_sumDiscreteMarkovChains.state_indexDiscreteMarkovChains.strongly_connected_components
Documentation
The main type is DiscreteMarkovChain:
DiscreteMarkovChains.strongly_connected_components — Functionstrongly_connected_components(V::Array, E::Array{Tuple})Strongly connected components of a directed graph in reverse topological order. Translated from sympy/utilities/iteratbles.py/stronglyconnectedcomponents.
DiscreteMarkovChains.breadth_first_search — FunctionComputes the period of an irreducible transition matrix T must be a 2D array
DiscreteMarkovChains.digraph — Functiondigraph(x)Creates a digraph (directed graph) representation of a Markov chain.
Arguments
x: some kind of Markov chain.
Returns
A 1D array of 2-tuples. An element $(i, j)$ is in the array iff the transition matrix at $(i,j)$ is nonzero.
DiscreteMarkovChains.state_index — Functionstate_index(x)Arguments
x: some kind of Markov chain.
Returns
A dictionary mapping each state in a Markov chain to its position in the state space. It is essentially the inverse of state_space(x).
DiscreteMarkovChains.is_row_stochastic — Functionis_row_stochastic(mat, row_sum=1)Tests whether a matrix, x, is row stochasitc. The desired sum of each row can be specified as well.
Definitions
A matrix is said to be row stochasic if all its rows sum to 1. This definition is extened so that all its rows sum to row_sum.
Arguments
mat: a matrix that we want to check.row_sum: the desired value that each row should total to.
Returns
true if the given matrix, mat, is row-stochasitc.
DiscreteMarkovChains.required_row_sum — Functionrequired_row_sum(type)Arguments
type: The type of Markov chain. It can be
DiscreteMarkovChain or ContinuousMarkovChain.
Returns
The number that each row in the transition matrix should sum up to.
DiscreteMarkovChains.characteristic_matrix — Functioncharacteristic_matrix(::AbstractDiscreteMarkovChain)
characteristic_matrix(::AbstractContinuousMarkovChain)Definitions
Many derivations and interesting ideas about Markov chains involve the identity matrix or zero matrix somewhere along the line. Most of the time, the identity matrix appears more often in discrete Markov chains. Instead of the identity matrix, the zero matrix appears in its place for continuous Markov chains.
Returns
The identity matrix if its argument is an instance of AbstractDiscreteMarkovChain. The zero matrix if its argument is an instance of AbstractContinuousMarkovChain