Finds the stationary distribution (proportional utilization distribution) implied by a CTMC movement model with a given rate matrix.
get.UD(R,method="lu",maxiter, start, tol)Vector of the stationary distribution at each raster grid cell
Rate matrix with R[i,j] equal to the CTMC rate of movement from raster cell i to neighboring raster cell j. R[i,j]=0 implies that cells i and j are not first order neighbors.
Either "lu" (default) or "limit". See Details for a description of the two methods.
A value for the starting distribution for the 'limit' method. Defaults to 1/num. cells. Ignored for method='lu'.
Total number of iterations for limit method if tolerance not reached first. Defaults to 100. Ignored for method='lu'.
Value used to assess convergence for limit method. If max(abs(pi1-pi0))<tol, limit method has converged. Defaults to sqrt(.Machine$double.eps)
Ephraim M. Hanks
This calculates the stationary distribution of the CTMC. If method="lu", then the method used is the method on pg. 455 of Harrod and Plemmons (1984). If method="limit", then the stationary distribution is approximated by brute-force simulation. If R is a sparse Matrix object, then sparse matrix methods are used, making this calculation extremely efficient.
Harrod, W. J. & Plemmons, R. J. Comparison of some direct methods for computing stationary distributions of Markov chains. SIAM Journal on Scientific and Statistical Computing, 1984, 5, 453-469
## For example code, do
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## > help(ctmcMove)
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