markov_random_walk

  ↳ simulation

markov_random_walk(probs, initial=None, index=None, regulator=None, halt=None, max_time=100)

Given a set of transition probabilities, generates a random walk through the available nodes. Further, the user may pass regulator and halt functions with complex rules for altering transition probabilities during the walk and determining when to halt the walk, as well as delivering specific reports about notable events during the walk.

The initial node, if not specified, is randomly selected. The method returns two items. The first is the report array R, dimensions M x 2, where the reports are indexed by the axis M. R[i,0] is the content of the report and R[i,1] is the time of the report. The second is the path P, an N-dimensional vector, where N is the number of steps in the random walk and P[j] is the node at time j.

The walk may be regulated. This involves passing a regulator, which is a function that takes the simulation time, the transition probabilities, the current node, and an array of node data. At each time, the regulator returns a bool indicating whether a report is to be made, the content of the report, and a new set of transition probabilities determined by the available information. The regulator also updates node_data in-place.

Lastly, one can either specify a maximum length of time for the walk (using the keyword max_time) or a more general halting condition (using the keyword halt). A halting condition takes the time, current node, and node data. If neither are specified, the maximum length will be set to 100 steps.

For more details on regulators and halting conditions, see the documentation on the submodule regulators.

Arguments

Arguments		Type	Description
probs		np.ndarray	A square Markov matrix indicating the transition probabilities for the walk.
initial	Keyword	flexible	The initial node. If index is not None, then the type of initial should be the type of the elements of index. Otherwise, initial should be the index of the initial node. If not specified, a random node will be chosen.
index	Keyword	Index	An Index whose elements label the indices of probs. If specified, inputs like initial and outputs like the path refer to nodes by their labels. If not specified, nodes will be referred to in inputs and outputs by their index.
regulator	Keyword	function	The regulator determines how the probability matrix will be modified over the course of the walk, and what events will be noted in reports. See the submodule regulators for more details. If not specified, a trivial regulator will be used which never modifies the transition matrix and returns no reports.
halt	Keyword	function	The halt condition determines under what conditions the walk should stop. See the submodule regulators for more details. If not specified, a trivial halt condition to stop after a specified number of steps will be used; the number of steps can be changed using the max_time argument.
max_time	Keyword	int	If a halt condition is not specified, then the walk is halted automatically after max_time steps. The default is set to 100.