Iteration and functions allow repeating processes over sets of values in R. Functions define reusable recipes that automate actions, taking inputs as arguments and returning outputs. apply() applies a function over the rows or columns of a matrix or dataframe, allowing aggregation like summing or averaging. lapply() and sapply() similarly apply a function over the elements of a list. Custom functions can be defined and then used with apply() to iterate complex processes like counting values exceeding a number of standard deviations from the mean.

1. Iteration and functions
Day 4 - Introduction to R for Life Sciences

2. What is iteration
Repeating a process to a set of values
Often automatic:
c <- a + b # Works for vectors and matrices
Reminder: value-recycling
matrix(1:4, nrow=2, byrow=TRUE) + c(70,90) →
[,1] [,2]
[1,] 71 72
[2,] 93 94 # (the recycling is column-wise!)

3. Aggregation
You often need to "summarize" a vector as one number:
length(), min(), max(), mean(), median(), sd(), var(), mad(), IQR(),
sum(), prod(), all(), any(), ... # (see also: summary() )
How to do this for all rows or columns of a matrix? apply() !
result <- apply(mat, dir, FUNC, ...)
mat a matrix
dir direction: 1=rows, 2=columns
FUNC a function taking a vector, producing a single value
... additional argument(s) to FUNC

4. apply() cont’d
> m <- matrix(1:6, nrow=2)
> m
[,1] [,2] [,3]
[1,] 1 3 5 # filled column-wise by default
[2,] 2 4 6
> apply(m, 1, sum) # row-wise sum
[1] 9 12
> apply(m, 2, prod, na.rm=TRUE) # column-wise product, ignoring NA’s
[1] 2 12 30
And also:
lapply(lst, FUNC) # iterate over list-contents
tapply(), sapply(), mapply(), …

5. lapply() and sapply()
Works on lists, rather than matrices
> lst <- list(a=runif(7), b=runif(2), <etc>)
$a
[1] 0.971 0.380 0.287 0.787 0.721 0.938 0.364
$b
[1] 0.609 0.658
<etc>
> lapply(lst, mean)
$a
[1] 0.635
$b
[1] 0.633
<etc>

6. Custom built functions
apply() can use existing functions, but they may not suffice
e.g.: number of values exceeding 2*stddev from mean
Define a function n.exceeding2sd(), then call apply() as before
v <- apply(m, 1, n.exceeding2sd)

7. Functions
Functions are "recipes" that automate actions
Needed for reuse and clarity
Easy and cheap
Have to be defined
Can be called
Inputs are called arguments (which can have defaults)
special argument: the triple-dot plot(x, y, …)
Functions can have local variables (try to avoid global variables)
Outputs are called return values

8. Full function example
Definition:
sum.of.squares <- function(x) { # argument(s)
s <- x^2 # variables x, s and tot are local
tot <- sum(s) # note: indentation!
tot # last value is returned
} # end of definition
Call:
ss <- sum.of.squares(some.vector)
ss.percolumn <- apply(data, 2, sum.of.squares)

9. More complex example
Definition:
n.exceeding.SDs <- function(x, n=2, na.rm=FALSE) {
m <- mean(x, na.rm=na.rm)
s <- sd(x, na.rm=na.rm)
abs.z <- abs((x - m)/s) # Z-scores, all made positive
sum( abs.z > n, na.rm=na.rm) # last value is returned
}
Call:
n <- n.exceeding.SDs(some.vector)
outliers.per.column <- apply(data, 2, n.exceeding.sds)