efficiently replacing data frame with cumulative frequency

Question

I'm trying to write a program that takes a large data frame and replaces each column of values by the cumulative frequency of those values (sorted ascending). For instance, if the column of values are: 5, 8, 3, 5, 4, 3, 8, 5, 5, 1. Then the relative and cumulative frequencies are:

• 1: rel_freq=0.1, cum_freq = 0.1
• 3: rel_freq=0.2, cum_freq = 0.3
• 4: rel_freq=0.1, cum_freq = 0.4
• 5: rel_freq=0.4, cum_freq = 0.8
• 8: rel_freq=0.2, cum_freq = 1.0

Then the original column becomes: 0.8, 1.0, 0.3, 0.8, 0.4, 0.3, 1.0, 0.8, 0.8, 0.1

The following code performs this operation correctly, but it scales poorly probably due to the nested loop. Any idea how to perform this task more efficiently?

mydata = read.table(.....)

totalcols = ncol(mydata)
totalrows = nrow(mydata)

for (i in 1:totalcols) {
    freqtable = data.frame(table(mydata[,i])/totalrows)  # create freq table
    freqtable$CumSum = cumsum(freqtable$Freq)   # calc cumulative freq

    hashtable = new.env(hash=TRUE)
    nrows = nrow(freqtable)

    # store cum freq in hash
    for (x in 1:nrows) {
        dummy = toString(freqtable$Var1[x])
        hashtable[[dummy]] = freqtable$CumSum[x]
    }

    # replace original data with cum freq
    for (j in 1:totalrows) {
        dummy = toString(mydata[j,i])
        mydata[j,i] = hashtable[[dummy]]
    }
}

Answer 1

This handles a single column without the for-loop:

R> x <- c(5, 8, 3, 5, 4, 3, 8, 5, 5, 1)
R> y <- cumsum(table(x)/length(x))
R> y[as.character(x)]
  5   8   3   5   4   3   8   5   5   1 
0.8 1.0 0.3 0.8 0.4 0.3 1.0 0.8 0.8 0.1 

Answer 2

Here is one way. Using a data frame with two variables each containing your example data

d <- data.frame(var1 = c(5, 8, 3, 5, 4, 3, 8, 5, 5, 1),
                var2 = c(5, 8, 3, 5, 4, 3, 8, 5, 5, 1))

use a simple function to

1. generate the cumsum() of the relative proportions given by table(x) / length(x), then
2. match() the observations in a variable with the names of the table of cumulative sums, then
3. use the id matches to select from the table of cumulative sums (and un-name it)

Such a functions is:

f <- function(x) {
    tab <- cumsum(table(x) / length(x))
    ind <- match(x, as.numeric(names(tab)))
    unname(tab[ind])
}

In practice we use lapply() and coerce to a data frame:

out <- data.frame(lapply(d, f))
out

which gives:

R> out
   var1 var2
1   0.8  0.8
2   1.0  1.0
3   0.3  0.3
4   0.8  0.8
5   0.4  0.4
6   0.3  0.3
7   1.0  1.0
8   0.8  0.8
9   0.8  0.8
10  0.1  0.1