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## code from Ben Goodrich posted here
## https://groups.google.com/forum/#!msg/stan-users/3gDvAs_qwN8/Xpgi2rPlx68J
##
rgbeta <- function(num, shape) {
if(shape == Inf) rep(0, num)
else if(shape > 0) -1 + 2 * rbeta(num, shape, shape)
else if(shape == 0) -1 + 2 * rbinom(num, 1, 0.5)
else stop("shape must be non-negative")
}
## LKJ
rcorvine <- function(n, eta = 1, cholesky = FALSE, permute = !cholesky) {
alpha <- eta + (n - 2) / 2
L <- matrix(0, n, n)
L[1,1] <- 1
L[-1,1] <- partials <- rgbeta(n - 1, alpha)
if(n == 2) {
L[2,2] <- sqrt(1 - L[2,1]^2)
if(cholesky) return(L)
Sigma <- tcrossprod(L)
if(permute) {
ord <- sample(n)
Sigma <- Sigma[ord,ord]
}
return(Sigma)
}
W <- log(1 - partials^2)
for(i in 2:(n - 1)) {
gap <- (i+1):n
gap1 <- i:(n-1)
alpha <- alpha - 0.5
partials <- rgbeta(n - i, alpha)
L[i,i] <- exp(0.5 * W[i-1])
L[gap,i] <- partials * exp(0.5 * W[gap1])
W[gap1] <- W[gap1] + log(1 - partials^2)
}
L[n,n] <- exp(0.5 * W[n-1])
if(cholesky) return(L)
Sigma <- tcrossprod(L)
if(permute) {
ord <- sample(n)
Sigma <- Sigma[ord,ord]
}
return(Sigma)
}
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