Outer() Function in R

A flexible tool for working with matrices and vectors in R is the outer() function. It enables you to create a new matrix or array by applying a function to every conceivable combination of the items from two input vectors. outer() function in R Programming Language is used to apply a function to two arrays.

Syntax: outer(X, Y, FUN = “*”)

Parameters:

• x, y: arrays 
• FUN: function to use on the outer products, default value is multiply

A matrix or array with the same dimensions as the outer product of X and Y is what the outer() function in R produces. The function FUN is applied to the relevant pair of elements from X and Y to produce each element of the result.

Outer() Function in R Programming Example

Example 1: Outer Product of Two Vector

R

# R program to illustrate
# outer function

# Initializing two arrays of elements
x <- c(1, 2, 3, 4, 5)
y<- c(2, 4, 6)

# Multiplying array x elements with array y elements
# Here multiply (*) parameter is not used still this
# function take it as default
outer(x, y)

Output:

     [, 1] [, 2] [, 3]
[1, ]    2    4    6
[2, ]    4    8   12
[3, ]    6   12   18
[4, ]    8   16   24
[5, ]   10   20   30

Example 2: outer Function for Vector and Single Value

R

# R program to illustrate
# outer function

# Initializing two arrays of elements
x <- 1:8
y<- 4

# Multiplying array x elements with array y elements
# Here multiply (*) parameter is not used still this
# function take it as default
outer(x, y, "+")

Output:

      [,1]
[1,]    5
[2,]    6
[3,]    7
[4,]    8
[5,]    9
[6,]   10
[7,]   11
[8,]   12

Types of outer() Functions:

 Since the outer() method is general, you can create your own unique functions and utilize them in conjunction with outer(). The following are a    few of the more typical outer() function types:

1. Arithmetic Functions: The most typical application of outer() involves adding and subtracting two vectors. The arithmetic operations +, -, *,        /,, %%, and %/% can all be used using outer().

      As an illustration, suppose we want to determine the sum of each pair of elements in the two vectors x and y:

R

x <- 1:3
y <- 4:6
outer(x, y, FUN = "+")

Output:

     [,1] [,2] [,3]
[1,]    5    6    7
[2,]    6    7    8
[3,]    7    8    9

2. Statistical Functions: Statistical operations can also be applied to two vectors using the outer() method. For illustration, suppose we want to      determine the correlation between the two vectors x and y:

R

# Creating two matrices
X <- matrix(1:6, nrow = 2, ncol = 3)
Y <- matrix(1:4, nrow = 2, ncol = 2)

# Trying to multiply the two matrices using the outer function
outer(X, Y, "*")

Output:

     [,1] [,2] [,3]
[1,]    1    3    5
[2,]    2    4    6

, , 2, 1

     [,1] [,2] [,3]
[1,]    2    6   10
[2,]    4    8   12

, , 1, 2

     [,1] [,2] [,3]
[1,]    3    9   15
[2,]    6   12   18

, , 2, 2

     [,1] [,2] [,3]
[1,]    4   12   20
[2,]    8   16   24