Calculate the outer product of two vectors using R
Last Updated :
25 Mar, 2024
In this article, we will explore different ways to Calculate the outer product of two vectors using R Programming Language.
What is the outer product of two vectors
the outer product of two vectors is a matrix where each element is the product of a corresponding element from the first vector with a corresponding element from the second vector. The result of the outer product of two vectors is a matrix where each element is the product of a pair of elements from the two input vectors. If the two vectors have dimensions n and m, then their outer product is an n×m matrix.
for example, Given two vectors a=[a1, a2, a3] and b=[b1, b2, b3] their outer product will be a matrix:
a×b=|a1b1 a1b2 a1b3|
|a2b1 a2b2 a2b3|
|a3b1 a3b2 a3b3|
below are different ways by which we can Calculate the outer product of two vectors:
- Using outer function
- Using for loop
- Using sapply
Calculate the outer product Using outer function
In this approach we will make use The outer function in R which is used to computes the outer product of two arrays or vectors.
in below example we have used outer function to calculate the outer product of two vectors.
R
# Define two vectors
x <- c(1, 2, 3)
y <- c(4, 5, 6)
# Calculate the outer product
outer_product <- outer(x, y)
print("outer product is: ")
print(outer_product)
Output:
[1] "outer product is: "
[,1] [,2] [,3]
[1,] 4 5 6
[2,] 8 10 12
[3,] 12 15 18
Calculate the outer product Using for loop
In this approach, we first create an empty matrix with dimensions corresponding to the lengths of vectors. Then, we use nested loops to iterate over each element of the vectors and calculate the product.
below example show how we can calulate outer product using for loop.
R
# Define two vectors
x <- c(2, 3, 5)
y <- c(4, 1, 6)
# Initialize an empty matrix to store the outer product
outer_product <- matrix(0, nrow = length(x), ncol = length(y))
# Calculate the outer product using loops
for (i in 1:length(x)) {
for (j in 1:length(y)) {
outer_product[i, j] <- x[i] * y[j]
}
}
print("outer product is: ")
print(outer_product)