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rmatrixsymmetric

Create a symmetric matrix from circular shifts of a vector

I'm struggling with the creation of a symmetric matrix.

Let's say a vector v <- c(1,2,3)

I want to create a matrix like this:

matrix(ncol = 3, nrow = 3, c(1,2,3,2,3,1,3,1,2), byrow = FALSE)
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    2    3    1
[3,]    3    1    2

(This is just an reprex, I have many vectors with different lengths.)

Notice this is a symmetric matrix with diagonal c(1,3,2) (different from vector v) and the manual process to create the matrix would be like this:

![![enter image description here

Using the first row as base (vector v) the process is to fill the empty spaces with the remaining values on the left side.

Any help is appreciated. Thanks!

Solution

  • Let me answer my own question in order to close it properly, using the incredible simple and easy solution from Henrik's comment:

    matrix(v, nrow = 3, ncol = 4, byrow = TRUE)[ , 1:3]

    Maybe the byrow = TRUE matches the three steps of the illustration best conceptually, but the output is the same with:

    matrix(v, nrow = 4, ncol = 3)[1:3, ]
#      [,1] [,2] [,3]
# [1,]    1    2    3
# [2,]    2    3    1
# [3,]    3    1    2

    Because there may be "many vectors with different lengths", it could be convenient to make a simple function and apply it to the vectors stored in a list: 

    cycle = function(x){
  len = length(x)
  matrix(x, nrow = len + 1, ncol = len)[1:len , ]
}

l = list(v1 = 1:3, v2 = letters[1:4])    

lapply(l, cycle)    
# $v1
#      [,1] [,2] [,3]
# [1,]    1    2    3
# [2,]    2    3    1
# [3,]    3    1    2
# 
# $v2
#     [,1] [,2] [,3] [,4]
# [1,] "a"  "b"  "c"  "d" 
# [2,] "b"  "c"  "d"  "a" 
# [3,] "c"  "d"  "a"  "b" 
# [4,] "d"  "a"  "b"  "c"