Get column and row position of nth element in a matrix

Question

Say I have a 10 x 10 two dimensional matrix...

set.seed(1)

mat <- matrix(sample(1:10,size=100,replace = T), ncol = 10)

How would I access the column and row position of the 83rd element in this matrix? It's easy enough to extract the element itself...

mat[83]

But I need the column and row position.

Answer 1

You can use arranyInd with dim(mat):

arrayInd(83, .dim = dim(mat))

#      [,1] [,2]
# [1,]    3    9

# check
all.equal(
  mat[arrayInd(83, .dim = dim(mat))],
  mat[83]
)
# [1] TRUE

Or for ease of reading, add useNames = TRUE:

arrayInd(83, .dim = dim(mat),
         useNames = TRUE)

#       row  col
# [1,]    3    9

For a little more detail, arrayInd is related to which (see ?arrayInd) except its explicitly used to convert linear indices into row/col positions. It will return a matrix.

Note, you can use a vector of indices:

inx <- c(83, 92)
arrayInd(inx, dim(mat))

#      [,1] [,2]
# [1,]    3    9
# [2,]    2   10

And when using a vector of desired positions, if you wanted to clean it up for ease of identifying, could rename rows/cols like this:

indx <- c(83, 92)
`rownames<-`(arrayInd(indx, .dim = dim(mat), useNames = TRUE), paste0("ix", indx))

#      row column
# ix83   3      9
# ix92   2     10