Question

I have a matrix with diagonals equal to zero and off-diagonals all equal to one (the inverse of an identity matrix):

mat1 <- matrix(c(0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0), 5, 5)

I also have a vector that is always the same length as the dims of the matrix and always starts at zero:

vec1 <- c(0,1,2,3,4)

using these two objects I want to create a matrix that looks like this:

mat2 <- matrix(c(0,1,2,3,4,1,0,1,2,3,2,1,0,1,2,3,2,1,0,1,4,3,2,1,0), 5, 5)

     [,1] [,2] [,3] [,4] [,5]
[1,]    0    1    2    3    4
[2,]    1    0    1    2    3
[3,]    2    1    0    1    2
[4,]    3    2    1    0    1
[5,]    4    3    2    1    0

I want an operation that will generalize so that if I have a matrix of dims 9 by 9, for example, and a vector of 0:8 I can achieve the equivalent result. Any ideas for how to approach this?

Answer 1

As vec1 starts with a zero, then you can do :

MakeMatrix <- function(x){
  n <- length(x)
  id <- abs(rep(1:n,n)-rep(1:n,each=n)) + 1
  matrix(x[id],ncol=n)
}

MakeMatrix(vec1)

So there’s no need to take the mat1 in the input, as that one is actually redundant. You can just construct the matrix within the function.

The trick is in providing a sequence of id values to select from the vector, and then transform everything to a matrix.

---

Edit : If you’re only going to use sequences, you could as well do :

MakeMatrix <- function(n){
  id <- abs(rep(1:n,n)-rep(1:n,each=n))
  matrix(id,ncol=n)
}

MakeMatrix(7)