Question

Consider a matrix with r rows and c columns and containing v integers between 0 and v-1; in the following example, r=4, c=2, and v=6.

L <- c(0,1,1,2,0,1,2,3)
(x <- matrix(L,nrow=4,ncol=2,byrow = TRUE))

 ## 0 1 
 ## 1 2 
 ## 0 1 
 ## 2 3

The goal is to generate a r*c (row) by v column incidence matrix, as follows:

• each row corresponds to one element of the original matrix (in column-major order, i.e. in the example here the 4th row corresponds to x[4,1] and the 5th row corresponds to x[1,2])
• find the “neighbors” above and below each element, wrapping around (cyclically) from the top to the bottom of the matrix; count the number of neighbor elements for each value of v.

For example, the first element in the matrix (x[1,1]) has neighbours 1 (below) and 2 (“above”, i.e. wrapped around to the bottom of the column; thus we enter 1 in columns 2 and 3 of row 1, matching the corresponding elements of 0:(v-1). The rest of the row is set to zero:

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

The next element (x[2,1]) has 0 on both sides (above and below), so the first column (corresponding to 0) is set to 2, with the rest of the elements equal to zero.

  [2]       2  0  0  0  0  0

The full matrix for the example above is:

  rownames  0  1  2  3  4  5            
  [1]       0  1  1  0  0  0
  [2]       2  0  0  0  0  0
  [3]       0  1  1  0  0  0
  [4]       2  0  0  0  0  0
  [5]       0  0  1  1  0  0
  [6]       0  2  0  0  0  0
  [7]       0  0  1  1  0  0  
  [8]       0  2  0  0  0  0 

The row sums are each 2.

Answer 1

L =c(0,1,1,2,0,1,2,3)
x=matrix(L,nrow=4,ncol=2,byrow = TRUE)

There might be a cleaner way to do this:

wrapind <- function(i,n)
    ifelse((r <- i %% n) == 0, n, r)


n <- nrow(x)
v <- 6
incmat <- matrix(0,ncol=v,nrow=prod(dim(x)),
                 dimnames=list(NULL,0:(v-1)))
k <- 1
for (i in seq(ncol(x)))
    for (j in seq(nrow(x))) {
        cat(i,j,k,"\n")  ## unnecessary
        tt <- table(as.character(x[wrapind(c(j-1,j+1),n),i]))
        incmat[k,names(tt)] <- tt
        k <- k+1
    }