How do I get the unique pairs from a Covariance Matrix?

Question

I am trying to get the unique pairs from a covariance matrix obtained through R code. This is what I have tried so far:

data <- tibble(x = 1:3, y = 2:4, z = 3:5, w = 10:12)
cov_m <- reshape2::melt(cov(data))  %>%
    filter(Var1 != Var2) # I do this expecting to remove Cov(Var1, Var1) or similar cases
cov_m <- cov_m[duplicated(m_cov$Var1,]

I'm pretty sure I'm close to the right answer: about 6 unique pairs if my math isn't wrong. Could somebody help me out?

Answer 1

Set the diagonal and upper triangle to be some special value ( Inf in example below) and then remove them after doing melt

m = cov(data)
m[upper.tri(m)] = Inf
diag(m) = Inf
d = reshape2::melt(m)
d[d$value != Inf,]
#   Var1 Var2 value
#2     y    x     1
#3     z    x     1
#4     w    x     1
#7     z    y     1
#8     w    y     1
#12    w    z     1

Or if you want to do it without reshape2

data.frame(m) %>%
    mutate(rows = rownames(.)) %>%
    gather(cols, val, -rows) %>%
    filter(val != Inf)