R/rtnorm.r

In SICSresearch/LatentREGpp: Item Response Theory Implemented in R and Cpp

 #reference
#Robert, C. P. Simulation of truncated normal variables. Statistics and Computing (1995) 5, 121?125


rtnorm<- function(n, mean = 0, sd = 1, lower = -Inf, upper = Inf){
  
    if (length(n) > 1)
        n <- length(n)
    mean <- rep(mean, length = n)
    sd <- rep(sd, length = n)
    lower <- rep(lower, length = n)
    upper <- rep(upper, length = n)
    lower <- (lower - mean)/sd
    upper <- (upper - mean)/sd
    ind <- seq(length = n)
    ret <- numeric(n)
    alg <- ifelse(lower > upper, -1, ifelse(((lower < 0 & upper ==
        Inf) | (lower == -Inf & upper > 0) | (is.finite(lower) &
        is.finite(upper) & (lower < 0) & (upper > 0) & (upper -
        lower > sqrt(2 * pi)))), 0, ifelse((lower >= 0 & (upper >
        lower + 2 * sqrt(exp(1))/(lower + sqrt(lower^2 + 4)) *
            exp((lower * 2 - lower * sqrt(lower^2 + 4))/4))),
        1, ifelse(upper <= 0 & (-lower > -upper + 2 * sqrt(exp(1))/(-upper +
            sqrt(upper^2 + 4)) * exp((upper * 2 - -upper * sqrt(upper^2 +
            4))/4)), 2, 3))))
    ind.nan <- ind[alg == -1]
    ind.no <- ind[alg == 0]
    ind.expl <- ind[alg == 1]
    ind.expu <- ind[alg == 2]
    ind.u <- ind[alg == 3]
    ret[ind.nan] <- NaN
    while (length(ind.no) > 0) {
        y <- rnorm(length(ind.no))
        done <- which(y >= lower[ind.no] & y <= upper[ind.no])
        ret[ind.no[done]] <- y[done]
        ind.no <- setdiff(ind.no, ind.no[done])
    }
    stopifnot(length(ind.no) == 0)
    while (length(ind.expl) > 0) {
        a <- (lower[ind.expl] + sqrt(lower[ind.expl]^2 + 4))/2
        z <- rexp(length(ind.expl), a) + lower[ind.expl]
        u <- runif(length(ind.expl))
        done <- which((u <= exp(-(z - a)^2/2)) & (z <= upper[ind.expl]))
        ret[ind.expl[done]] <- z[done]
        ind.expl <- setdiff(ind.expl, ind.expl[done])
    }
    stopifnot(length(ind.expl) == 0)
    while (length(ind.expu) > 0) {
        a <- (-upper[ind.expu] + sqrt(upper[ind.expu]^2 + 4))/2
        z <- rexp(length(ind.expu), a) - upper[ind.expu]
        u <- runif(length(ind.expu))
        done <- which((u <= exp(-(z - a)^2/2)) & (z <= -lower[ind.expu]))
        ret[ind.expu[done]] <- -z[done]
        ind.expu <- setdiff(ind.expu, ind.expu[done])
    }
    stopifnot(length(ind.expu) == 0)
    while (length(ind.u) > 0) {
        z <- runif(length(ind.u), lower[ind.u], upper[ind.u])
        rho <- ifelse(lower[ind.u] > 0, exp((lower[ind.u]^2 -
            z^2)/2), ifelse(upper[ind.u] < 0, exp((upper[ind.u]^2 -
            z^2)/2), exp(-z^2/2)))
        u <- runif(length(ind.u))
        done <- which(u <= rho)
        ret[ind.u[done]] <- z[done]
        ind.u <- setdiff(ind.u, ind.u[done])
    }
    stopifnot(length(ind.u) == 0)
    ret * sd + mean
}


normalize<-function(x){
  if(!is.numeric(x))
    stop("'x' must be numeric")
  if(!is.matrix(x))
    return(x/sqrt(sum(x^2)))
  else
    return(x/matrix(sqrt(apply(x*x,1,sum)),dim(x)[1],dim(x)[2]))
}