Comparing Numeric Values

There are multiple ways to compare numeric values and vectors. This includes logical operators along with testing for exact equality and also near equality.

Comparison Operators

The normal binary operators allow you to compare numeric values and provides the answer in logical form:

x < y     # is x less than y
x > y     # is x greater than y
x <= y    # is x less than or equal to y
x >= y    # is x greater than or equal to y
x == y    # is x equal to y
x != y    # is x not equal to y


These operations can be used for single number comparison:

x <- 9
y <- 10

x == y
## [1] FALSE


and also for comparison of numbers within vectors:

x <- c(1, 4, 9, 12)
y <- c(4, 4, 9, 13)

x == y
## [1] FALSE  TRUE  TRUE FALSE


Note that logical values TRUE and FALSE equate to 1 and 0 respectively. So if you want to identify the number of equal values in two vectors you can wrap the operation in the sum() function:

# How many pairwise equal values are in vectors x and y
sum(x == y)
## [1] 2


If you need to identify the location of pairwise equalities in two vectors you can wrap the operation in the which() function:

# Where are the pairwise equal values located in vectors x and y
which(x == y)
## [1] 2 3


Exact Equality

To test if two objects are exactly equal:

x <- c(4, 4, 9, 12)
y <- c(4, 4, 9, 13)

identical(x, y)
## [1] FALSE

x <- c(4, 4, 9, 12)
y <- c(4, 4, 9, 12)

identical(x, y)
## [1] TRUE


Floating Point Comparison

Sometimes you wish to test for ‘near equality’. The all.equal() function allows you to test for equality with a difference tolerance of 1.5e-8.

x <- c(4.00000005, 4.00000008)
y <- c(4.00000002, 4.00000006)

all.equal(x, y)
## [1] TRUE


If the difference is greater than the tolerance level the function will return the mean relative difference:

x <- c(4.005, 4.0008)
y <- c(4.002, 4.0006)

all.equal(x, y)
## [1] "Mean relative difference: 0.0003997102"