# The R apply function – a tutorial with examples

July 2, 2011
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(This article was first published on Musings of a forgetful functor, and kindly contributed to R-bloggers)

Today I had one of those special moments that is uniquely associated with R. One of my colleagues was trying to solve what I term an 'Excel problem'. That is, one where the problem magically disappears once a programming language is employed. Put simply, the problem was to take a range, and randomly shift the elements of the list in order. For example, 12345 could become 34512 or 51234.

The list in question had forty-thousand elements, and this process needed to be repeated numerous times as part of a simulation. Try doing this in Excel and you will go insane: the shift function is doable but resource intensive. After ten minutes of waiting for your VBA script to run you will be begging for mercy or access to a supercomputer. However, in R the same can be achieved with the function:
translate<-function(x){  if (length(x)!=1){    r<-sample(1:(length(x)),1)    x<-append(x[r:length(x)],x[1:r-1])  }  return(x)
}
My colleague ran this function against his results several thousand times and had the pleasure of seeing his results spit out in less than thirty seconds: problem solved. Ain't R grand.

More R magic courtesy of the apply function
The translate function above is not rocket science, but it does demonstrate how powerful a few lines of R can be. This is best exemplified by the incredible functionality offered by the apply function. However, I have noticed that this tool is often under-utilised by less experienced R users.

The usage from the R Documenation is as follows:
apply(X, MARGIN, FUN, ...)

where:
• X is an array or matrix;
• MARGIN is a variable that determines whether the function is applied over rows (MARGIN=1), columns (MARGIN=2), or both (MARGIN=c(1,2));
• FUN is the function to be applied.
In essence, the apply function allows us to make entry-by-entry changes to data frames and matrices. If MARGIN=1, the function accepts each row of X as a vector argument, and returns a vector of the results. Similarly, if MARGIN=2 the function acts on the  columns of X. Most impressively,  when MARGIN=c(1,2) the function is applied to every entry of X. As for the FUN argument, this can be anything from a standard R function, such as sum or mean, to a custom function like translate above.

An illustrative example
Consider the code below:
# Create the matrixm<-matrix(c(seq(from=-98,to=100,by=2)),nrow=10,ncol=10)# Return the product of each of the rowsapply(m,1,prod)# Return the sum of each of the columnsapply(m,2,sum)# Return a new matrix whose entries are those of 'm' modulo 10apply(m,c(1,2),function(x) x%%10)

In the last example, we apply a custom function to every entry of the matrix. Without this functionality, we would be at something of a disadvantage using R versus that old stalwart of the analyst: Excel. But with the apply function we can edit every entry of a data frame with a single line command. No autofilling, no wasted CPU cycles.

In the next edition of this blog, I will return to looking at R's plotting capabilities with a focus on the ggplot2 package. In the meantime, enjoy using the apply function and all it has to offer.