Description Usage Arguments Details Value Author(s) References Examples

Finds the stationary distribution (proportional utilization distribution) implied by a CTMC movement model with a given rate matrix.

1 |

`R` |
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. |

`method` |
Either "lu" (default) or "limit". See Details for a description of the two methods. |

`start` |
A value for the starting distribution for the 'limit' method. Defaults to 1/num. cells. Ignored for method='lu'. |

`maxiter` |
Total number of iterations for limit method if tolerance not reached first. Defaults to 100. Ignored for method='lu'. |

`tol` |
Value used to assess convergence for limit method. If max(abs(pi1-pi0))<tol, limit method has converged. Defaults to sqrt(.Machine$double.eps) |

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.

Vector of the stationary distribution at each raster grid cell

Ephraim M. Hanks

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

1 2 3 | ```
## For example code, do
##
## > help(ctmcMove)
``` |

```
Loading required package: raster
Loading required package: sp
Loading required package: Matrix
Loading required package: fda
Loading required package: splines
Attaching package: 'fda'
The following object is masked from 'package:graphics':
matplot
Loading required package: gdistance
Loading required package: igraph
Attaching package: 'igraph'
The following object is masked from 'package:raster':
union
The following objects are masked from 'package:stats':
decompose, spectrum
The following object is masked from 'package:base':
union
Attaching package: 'gdistance'
The following object is masked from 'package:igraph':
normalize
```

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