# staticMatrix: staticMatrix Iterate until transition probabilities converge... In vocaldia: Create and Manipulate Vocalisation Diagrams

## Description

Compute the stationary distribution for a Markov diagram

## Usage

 `1` ```staticMatrix(matrix, limit = 1000, digits = 4, history = F) ```

## Arguments

 `matrix` an adjecency matrix of trnasition probabilities `limit` maximum number of iterations until we give up on convergence `digits` the number of decimal places to compare `history` if TRUE, keep track of all matrix products

## Details

Return static matrix (i.e. the stationary distribution) for the Markov process represented by the given adjacency matrix. In the particular case of vocaldia's, each column should roughly correspond to the amount of time a speaker held the floor for). Of course, not all Markov chains converge, an example being:

 ``` 1 2 3 4 5 6 7 8 9 10``` ``` 1 /----->-------\ A B \----<--------/ 1 which gives . | 0 1 | | 0x0+1x1 0x1+1x0| | 1 0 | . M = | 1 0 | and M^2 = | 1x0+0x1 1x1+1x0| = | 0 1 | ```

## Value

a matrixseries object; that is, a list where each element is either the initial matrix or the product of the two preceding matrices

## Examples

 ```1 2 3 4 5 6``` ```data(vocdia) x2 <- staticMatrix(vocmatrix\$ttarray, digits=4, history=TRUE) ## original matrix round(x2[[1]],3) ## stationary matrix (M^139) round(x2[[length(x2)]],3) ```

vocaldia documentation built on July 2, 2020, 2 a.m.