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#' Compute 1 to k-step transition proportions
#'
#' Computes 1 to k-step forward transition proportions in each state with a single transition matrix or a 3-d array of transition matrices.
#'
#' @param x either a transition matrix, list of transition matrices or 3-d array ( a set of transition matrices)
#' @param k if x is a transition matrix, this is number of steps 1 to k
#' @param labels labels for states except for last which is always dead and is added at end
#' @author Jeff Laake
#' @export
#' @importFrom expm %^%
#' @keywords utility
omega=function(x,k=NULL,labels=NULL)
{
if(is.list(x))
{
y=x
x=array(NA,dim=c(length(y),nrow(y[[1]]),ncol(y[[1]])))
for(i in 1:length(y))
x[i,,]=y[[i]]
}
array_dim=dim(x)
if(length(array_dim)==2)
{
if(is.null(k))stop("k - number of transitions must be specified")
mat=t(sapply(1:k,function(k,x) (x%^%k)[1,] ,x=x))
} else
{
xmat=x[1,,]
k=array_dim[1]
mat=matrix(NA,nrow=k,ncol=nrow(xmat))
mat[1,]=xmat[1,]
for(j in 2:k)
{
xmat=xmat%*%x[j,,]
mat[j,]=xmat[1,]
}
}
if(!is.null(labels))colnames(mat)=c(labels,"Dead")
rownames(mat)=1:k
return(mat)
}
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