# Math Insight

### For-loops in R

In many programming languages, a for-loop is a way to iterate across a sequence of values, repeatedly running some code for each value in the list. In R, the general syntax of a for-loop is

for(var in sequence) {
code
}


where the variable var successively takes on each value in sequence. For each such value, the code represented by code is run with var having that value from the sequence.

Here, we show some simple examples of using a for-loop in R.

#### Printing a list of numbers

Let's say we wanted to print a list of numbers from 0 to 3, inclusive. In R, the command 0:3 will create a vector with the numbers from 0 to 3, as you can see by entering that command at the R > command prompt:

> 0:3 [1] 0 1 2 3 

(At the beginning of the output, R prints a [1] to let you know that lines starts with the first entry of the vector.)

We could create a simple for-loop that iterates through the four numbers of 0:3 and prints each number.

> for(var in 0:3)
{
print(var)
}
[1] 0
[1] 1
[1] 2
[1] 3


R outputs four lines, one for each number. (When typing the for-loop at the R > command prompt, R adds a + at the beginning of the line to indicate the command is continuing. We omit those + signs for clarity.)

If you don't want R to print the [1] at the beginning of the line, you could use the cat (concatenate) command instead, but you need to explicitly add a newline character \n to print each number on its own line.

> for(var in 0:3)
{
cat(var, "\n")
}
0
1
2
3


We could assign the vector of numbers to a variable and then reference the variable in the for-loop. It would work exactly the same way.

my_sequence = 0:3
> for(var in my_sequence)
{
cat(var, "\n")
}
0
1
2
3


#### Using for-loops with vectors

For-loops are especially convenient when working with vectors. Often we want to iterate over each element in a vector and do some computation with each element of the vector. We can also use for-loops to create or extend vectors, as R will automatically make a vector larger to accommodate values we assign to it.

First, lets create a vector using the c (combine) command is illustrated in the page on vector creation.

> x = c(1,3,4,7)
> x
[1] 1 3 4 7


For any integer $i$ between 1 and 4, x[i] denotes the $i$th element of the vector.

> x[1]
[1] 1
> x[2]
[1] 3
> x[3]
[1] 4


We can use a for-loop to add one to the first element of x, add two to the second element of x, etc. We let use the variable n to store the number of elements in x (i.e., 4). In the loop, we will use the variable i to loop through the numbers 1, 2, 3, 4.

> n = length(x)
> for(i in 1:n)
{
x[i] = x[i] + i
}
> x
[1]  2  5  7 11


The for-loop is equivalent to running the four commands:

> x[1] = x[1] + 1
> x[2] = x[2] + 2
> x[3] = x[3] + 3
> x[4] = x[4] + 4


This for-loop creates a vector with five components where each component is double the previous.

> n = 4
a=1
> for(i in 1:n)
{
a[i+1] = 2*a[i]
}
> a
[1]  1 2 4 8 16