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#' Forward log-probabilities
#'
#' Used in \code{\link{stateProbs}} and \code{\link{pseudoRes}}.
#'
#' @param m A \code{\link{momentuHMM}}, \code{\link{miHMM}}, or \code{\link{miSum}} object.
#'
#' @return A list of length \code{model$conditions$mixtures} where each element is a matrix of forward log-probabilities for each mixture.
#'
#' @examples
#' \dontrun{
#' # m is a momentuHMM object (as returned by fitHMM), automatically loaded with the package
#' m <- example$m
#'
#' la <- momentuHMM:::logAlpha(m)
#' }
logAlpha <- function(m)
{
if(!is.momentuHMM(m) & !is.miHMM(m) & !is.miSum(m))
stop("'m' must be a momentuHMM, miHMM, or miSum object (as output by fitHMM, MIfitHMM, or MIpool)")
if(is.miHMM(m)) m <- m$miSum
m <- delta_bc(m)
if(is.miSum(m)){
beta<-m$Par$beta$beta$est
delta<-m$Par$real$delta$est
g0<-m$Par$beta$g0$est
theta<-m$Par$beta$theta$est
} else {
beta <- m$mle$beta
delta <- m$mle$delta
g0 <- m$mle$g0
theta <- m$mle$theta
}
nbStates <- length(m$stateNames)
nbAnimals <- length(unique(m$data$ID))
nbObs <- nrow(m$data)
# identify covariates
reForm <- formatRecharge(nbStates,m$conditions$formula,m$conditions$betaRef,m$data,par=m$mle)
covs <- reForm$covs
aInd <- reForm$aInd
probs <- allProbs(m)
mixtures <- m$conditions$mixtures
trMat <- lalpha <- list()
lalpha[1:mixtures] <- list(matrix(NA,nbObs,nbStates))
for(mix in 1:mixtures){
if(nbStates>1)
trMat[[mix]] <- trMatrix_rcpp(nbStates,beta[(mix-1)*ncol(covs)+1:ncol(covs),,drop=FALSE],as.matrix(covs),m$conditions$betaRef)
else
trMat[[mix]] <- array(1,dim=c(1,1,nbObs))
}
for(mix in 1:mixtures){
k <- 1
for(i in 1:nbObs) {
gamma <- trMat[[mix]][,,i]
if(any(i==aInd)){
foo <- (delta[(mix-1)*nbAnimals+k,] %*% gamma)*probs[i,]
lscale <- 0
k <- k + 1
} else {
foo <- (foo %*% gamma)*probs[i,]
}
lscale <- lscale+log(sum(foo))
foo <- foo/sum(foo)
lalpha[[mix]][i,] <- log(foo)+lscale
}
}
return(lalpha)
}
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