Double for loop in R creating a matrix

Question

I would like to create a 5x5 matrix in R using two for loops. I have 5 numbers p_j and q_i with i and j in {1,2,3,4,5}. I would like to create a matrix with where the element in (j,i) is given by p_j * q_j. j-th row and i-th column. So, first of all I would like to create an empty matrix m and then filling the matrix using the for loops.

for (i in 1:5){ for (j in 1:5){ } }

Must you use the double loop? Either p %*% t(q) or outer(p,q, `*`) seem like better solutions. — G5W
– G5W, Commented Jun 5, 2017 at 19:14
I am afraid, my R skills are not sufficient in order to understand your comment. Could you work out your comment as a second answer? — Xarrus
– Xarrus, Commented Jun 5, 2017 at 19:19
As an aside-- R indexes by [row, column], so you would want to assemble your matrix that way. — Matt
– Matt, Commented Jun 5, 2017 at 19:30

G5W · Accepted Answer · 2017-06-05 23:48:34Z

4

I will walk through two solutions that I proposed. Both of these solutions avoid any explicit looping. Mostly in R, if it is easy to avoid a loop, you probably should. First, let's get some example data.

set.seed(2017)
p = sample(5)
q = sample(5)
p
[1] 5 3 2 1 4
q
[1] 4 1 2 5 3

Here p and q are randomly generated. The set.seed part is so that we both get the same "random" numbers.

Solution 1 - matrix multiplication

p %*% t(q)
     [,1] [,2] [,3] [,4] [,5]
[1,]   20    5   10   25   15
[2,]   12    3    6   15    9
[3,]    8    2    4   10    6
[4,]    4    1    2    5    3
[5,]   16    4    8   20   12

%*% is the way to specify matrix multiplication in R.
p %*% t(q) multiplies the 5x1 matrix p by the 1x5 matrix t(q), the transpose of q, resulting in the 5x5 matrix with the desired answer.

Solution 2 - outer

outer(p,q, `*`)
     [,1] [,2] [,3] [,4] [,5]
[1,]   20    5   10   25   15
[2,]   12    3    6   15    9
[3,]    8    2    4   10    6
[4,]    4    1    2    5    3
[5,]   16    4    8   20   12

The function outer in r, creates the "outer product" of two vectors - that is, it takes all combinations of an element of p and an element of q and combines them using the function that you supplied, in this case *, exactly the calculation that you are asking for. Actually, this could have been written more succinctly as outer(p,q) because the default function to use to combine p & q is *.

edited Jun 5, 2017 at 23:48

answered Jun 5, 2017 at 19:35

G5W

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3 Comments

Julian Zucker Over a year ago

P and q are not elements in the global environment: there are 10 variables, named p_1, p_2, ... p_5, and q_1 ... q_5. Also, the question explicitly asks for a solution using two for loops. Even though it's not best practice in R, answering with a non-for-looping answer doesn't answer the question.

G5W Over a year ago

@ConCave I originally wrote this as a comment that noted it did not use loops. The OP asked me to include it as an answer.

Julian Zucker Over a year ago

Nevermind them, sorry about that. Thanks for providing a more detailed explanation of your comment.

Julian Zucker · Accepted Answer · 2017-06-05 19:21:13Z

2

Assuming you have variables named "p_1", "p_2" in the working environment:

mymatrix <- matrix(nrow = 5, ncol = 5)
for (i in 1:5) { 
  for (j in 1:5) { 
    mymatrix[i, j] <- get(paste("p_", j, sep="")) * 
                      get(paste("q_", i, sep=""))
  }
}

edited Jun 5, 2017 at 19:21

answered Jun 5, 2017 at 19:17

Julian Zucker

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2 Comments

Xarrus Over a year ago

mymatrix[i, j] is the element in the i-th row and j-th column, right?

Julian Zucker Over a year ago

mymatrix[i, j] is the ith row and the jth column. I'm not sure exactly what arrangement of your numbers you want, or how your data is represented. If you have variables named "p_1", "p_2", etc, this answer will work, but that's absolutely not the best way to store your data in R. They should be 2 seperate vectors named p and q, and then you can access your numbers with p[1], p[2], etc.

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