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######################################################################
#' Calculate the probability of being in a particular state for each observation.
#' @param y observed series
#' @param mod list consisting the at least the following items:
#' mod$m = scalar number of states,
#' mod$delta = vector of initial values for prior probabilities,
#' mod$gamma = matrix of initial values for state transition probabilies.
#' mod$mu = list of initial values for means,
#' mod$sigma = list of initial values for covariance matrices.
#' For autoregressive hidden markov models, we also need the additional items:
#' mod$arp = scalar order of autoregressive structure
#' mod$auto = list of initial values for autoregressive coefficient matrices
#' @return a matrix containing the state probabilities
#' @references Rabiner, Lawrence R. "A tutorial on hidden Markov models and
#' selected applications in speech recognition." Proceedings of the
#' IEEE 77.2 (1989): 257-286.
#' @examples
#' set.seed(15562)
#' m <- 2
#' mu <- list(c(3,4,5),c(-2,-3,-4))
#' sigma <- list(diag(1.3,3),
#' matrix(c(1,-0.3,0.2,-0.3,1.5,0.3,0.2,0.3,2),3,3,byrow=TRUE))
#' delta <- c(0.5,0.5)
#' gamma <- matrix(c(0.8,0.2,0.1,0.9),2,2,byrow=TRUE)
#' auto <- list(matrix(c(0.3,0.2,0.1,0.4,0.3,0.2,
#' -0.3,-0.2,-0.1,0.3,0.2,0.1,
#' 0,0,0,0,0,0),3,6,byrow=TRUE),
#' matrix(c(0.2,0,0,0.4,0,0,
#' 0,0.2,0,0,0.4,0,
#' 0,0,0.2,0,0,0.4),3,6,byrow=TRUE))
#' mod <- list(m=m,mu=mu,sigma=sigma,delta=delta,gamma=gamma,auto=auto,arp=2)
#' sim <- hmm.sim(2000,mod)
#' y <- sim$series
#' state <- sim$state
#' fit <- em.hmm(y=y, mod=mod, arp=2)
#' stateprob <- smooth.hmm(y=y,mod=fit)
#' head(cbind(state,stateprob),20)
#' @useDynLib rarhsmm, .registration = TRUE
#' @importFrom Rcpp evalCpp
#' @importFrom graphics points
#' @importFrom stats rnorm
#' @importFrom glmnet glmnet
#' @export
smooth.hmm <- function(y, mod){
if(is.null(mod$auto)) result <- smooth.mvn(y, mod)
if(!is.null(mod$auto)) result <- smooth.mvnarp(y, mod)
return(result)
}
############################################
#em algorithm for multivariate normal
smooth.mvn <- function(y, mod){
ns <- nrow(y)
p <- length(mod$mu[[1]])
Pi <- mod$delta
P <- mod$gamma
K <- mod$m
mu <- mod$mu
sigma <- mod$sigma
#initialization
#state-dependent probs
B <- getnodeprob_nocov_mvn(y, mu, sigma, K, p, 0, 0)
####E-step
#forward-backward
fb <- forwardbackward(Pi,P,B,ns,ns)
gamma <- fb$Gamma
return(gamma)
}
################################################
smooth.mvnarp <- function(y, mod){
ns <- nrow(y)
p <- length(mod$mu[[1]])
Pi <- mod$delta
P <- mod$gamma
K <- mod$m
mu <- mod$mu
sigma <- mod$sigma
auto <- mod$auto
arp <- mod$arp
#initialization
#state-dependent probs
ycov <- rbind(rep(0,p),y[-ns,])
autoarray <- array(as.numeric(unlist(auto)), dim=c(p,p,K))
muarray <- array(as.numeric(unlist(mu)), dim=c(1,p,K))
B <- getnodeprob_part2(y, ycov,autoarray,muarray,sigma,K,p)
fb <- forwardbackward(Pi,P,B,ns,ns)
colsumXi <- fb$colsumxi
gamma <- fb$Gamma
return(gamma)
}
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