[R] looking for a faster way to compare two columns of a matrix

[Gustavo Carvalho]

Please consider this matrix:

x <- structure(c(5, 4, 3, 2, 1, 6, 3, 2, 1, 0, 3, 2, 1, 0, 0, 2, 1,
1, 0, 0, 2, 0, 0, 0, 0), .Dim = c(5L, 5L))

For each pair of columns, I want to calculate the proportion of entries
different than 0 in column j (i > j) that have lower values than the entries
in the same row in column i:

x[, 1:2]
sum((x[,1] > x[,2]) & (x[,2] > 0))/sum(x[,2] > 0)

Thus, for this pair, 3 of the 4 entries in the second column are
lower than the entries in the same row in the first column.

When both columns of a given pair have the same number of cells different than
0, the value of the metric is 0.

x[, 3:4]
colSums(x[, 3:4] > 0)

The same if column j has more valid (> 0) entries.

I've been doing this using this idea:

combinations <- combn(1:ncol(x), 2)
values <- numeric(ncol(combinations))

for (i in 1:ncol(combinations)) {
  pair <- combinations[,i]
  first <- x[, pair[1]]
  second <- x[, pair[2]]
  if (sum(first > 0) <= sum(second > 0)) next
  values[i] <- sum(first - second > 0 & second > 0) / sum(second > 0)
}
values

Anyway, I was wondering if there is a faster/better way. I've tried
putting the code from
the for loop into a function and passing it to combn but, as expected, it didn't
help much. Any pointers to functions that I should be looking into will be
greatly appreciated.

Thank you very much,

Gustavo.