Functions for stochastic matrix modifications.
teleport(teleport_prob = 0.15) vote_equal(stoch) vote_self(stoch)
Probability of 'teleportation'.
Input stochastic matrix.
teleport() returns a modifier function.
vote_self() are modifier functions and return modified
version of input stochastic matrix.
Modification logic behind
teleport() assumes that at each step
of Markov chain (described by column-stochastic matrix) the decision is made
whether to change state according to stochastic matrix or to 'teleport' to
any state with equal probability. Probability of 'teleport' is
teleport_prob. This modification is useful because it ensures
irreducibility of stochastic matrix (with
teleport_prob in (0; 1)).
Note that in order to obtain modifier one should call function
teleport() with some parameter.
vote_self() modify columns with elements only equal to
0. The former fills them with
1/nrow(stoch) and the latter changes only the
respective diagonal element to 1. This is equivalent to jump to any state
with equal probability and to stay in the current state respectively.
#> [,1] [,2] #> [1,] 0.5 0.33 #> [2,] 0.5 0.67vote_equal(input_stoch)#> [,1] [,2] #> [1,] 0.5 0.3 #> [2,] 0.5 0.7vote_self(input_stoch)#> [,1] [,2] #> [1,] 1 0.3 #> [2,] 0 0.7