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### function that calculates the average unadjusted squared correlations of the each row
###of the correlation matrix including the diagonal
cor2mean <- function(mat){
n <- dim(mat)[2]
p <- dim(mat)[1]
cor2.vec <- rep(0,p)
mat.r <- rowScale(mat)
p <- dim(mat.r)[1]
A <- mat.r%*%(t(mat.r) %*%(mat.r))
for (i in 1:p) cor2.vec[i] <- 1/(p*(n-1)^2)* A[i,]%*%mat.r[i,]
return(cor2.vec)
}
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