6  Comparing Vectors

6.1 Comparing Numerical Vectors

Consider the following two vectors:

a <- 1:5
a

[1] 1 2 3 4 5

b <- 5:1
b

[1] 5 4 3 2 1

To find the indices of elements where a > b, we can use a > b. This returns a logical vector which is TRUE when a is greater than b and is FALSE otherwise:

a > b

[1] FALSE FALSE FALSE  TRUE  TRUE

Thus a>b in the 4th and 5th element only, as 4>2 in the 4th element and 5>1 in the 5th element.

For a\geq b (greater than or equal to) we use a >= b.

a >= b

[1] FALSE FALSE  TRUE  TRUE  TRUE

The condition is satisfied in the 3rd element too, as 3\geq 3.

Similarly, for “less than” we use < and for less than or equal to we use <=:

a < b

[1]  TRUE  TRUE FALSE FALSE FALSE

a <= b

[1]  TRUE  TRUE  TRUE FALSE FALSE

For a = b, we use a == b. We need to use two equal signs, because if we did a = b, it would replace the vector a with the vector b. Thus we use == to ask if the respective elements of the two vectors are equal:

a == b

[1] FALSE FALSE  TRUE FALSE FALSE

Thus a=b only in the 3rd element.

For a \neq b (a not equal to b), we use a != b:

a != b

[1]  TRUE  TRUE FALSE  TRUE  TRUE

It’s also possible to compare a vector to a single number. For example, like:

a > 3

[1] FALSE FALSE FALSE  TRUE  TRUE

But what is not possible is comparing a vector with 5 elements to a vector with only 4 elements. Either the two vectors should have the same length, or at least one of them has only 1 element.

6.2 Comparing Logical Vectors

Consider the following two logical vectors:

a <- c(TRUE, TRUE, FALSE, FALSE)
b <- c(TRUE, FALSE, TRUE, FALSE)

If we want to know where both a and b are TRUE, we use the logical AND operator &:

a & b

[1]  TRUE FALSE FALSE FALSE

a and b are only both TRUE in first element.

To see when either a or b are TRUE, we use the logical OR operator |:

a | b

[1]  TRUE  TRUE  TRUE FALSE

At least one of a or b are TRUE in all but the last element.

Suppose we wanted to return a logical vector which tells us when both a and b are FALSE. We can do that using the logical NOT operator !. First let’s see what happens when we use the NOT operator on just a::

!a

[1] FALSE FALSE  TRUE  TRUE

Essentially it just flips the TRUEs to FALSEs and the FALSEs to TRUEs. To see when both a are b are FALSE we do:

!a & !b

[1] FALSE FALSE FALSE  TRUE

Thus, this only happens in the 4th element.