R/qemiss_gr.R

In shimlab/riboHMM2: Analysis tool for Ribo-seq

#' qemiss_gr
#'
#' \code{qemiss_gr} calculates the gradient of \code{qemiss}.
#'
#' @export
#' @param pars a vector of length 42. c(alpha, beta)
#' @param X    a list of vectors of observed states x
#' @param E    a vector of normalizing constant for each observed chain in X
#' @param L    a list of matrix L from \code{computeL}
#' @return     A vector of length 42, the gradient for qemiss.
#'
#' @examples
#' df <- uORF
#' X <- L <- list()
#' E <- c()
#' for (i in 1:2){
#'   X[[i]] <- df[[i]]$x
#'   RNA <- df[[i]]$RNA
#'   E[i]=df[[i]]$E;   trans=df[[i]]$trans;
#'   a=df[[i]]$v;      b=df[[i]]$v/df[[i]]$m
#'   la <- forwardAlg(X[[i]], RNA, trans, a, b, E[i])
#'   lb <- backwardAlg(X[[i]], RNA, trans, a, b, E[i])
#'   L[[i]] <- computeL(la, lb)
#' }
#' pars <- c(df[[1]]$v, df[[1]]$v/df[[1]]$m)
#'
#' # check by comparing with numeric approximation
#' D1 <- qemiss_gr(pars,X,E,L)
#' require(numDeriv)
#' D2 <- grad(function(u) qemiss(u,X,E,L) , pars)
#' print(round(D1-D2, 10))

qemiss_gr <- function(pars, X, E, L){
  pars <- abs(pars)
  a <- pars[1:21]    # short for alpha
  b <- pars[22:42]   # short for beta
  da <- db <- rep(0, 21)
  for (k in 1:21){
    for (i in 1:length(X)){
      for (t in 1:length(X[[i]])){
        da[k] <- da[k] - (sum(1/seq(a[k],a[k]+X[[i]][t]-1)) - log(1+E[i]/b[k]))*L[[i]][t,k]
        db[k] <- db[k] - (a[k]/b[k] - (a[k]+X[[i]][t])/(E[i]+b[k])) * L[[i]][t,k]
      }
    }
  }
  return(c(da, db))
}