Hello I have this matrix that is (5 x 7)

and as you can see the matrix has three-diagonals from repeating numbers

I was wondering how to compute this matrix but for (t-2) x t dimension

I have this code, but only get the vector (of repeating numbers) in the diagonal (not 3 diagonal)

> diag(c(1,-2,1), nrow = 5, ncol=7)

     [,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,]    1    0    0    0    0    0    0
[2,]    0   -2    0    0    0    0    0
[3,]    0    0    1    0    0    0    0
[4,]    0    0    0    1    0    0    0
[5,]    0    0    0    0   -2    0    0

How can I accomplish this?

Thanks in advance

>Solution :

You can use toeplitz:

mat <- toeplitz(c(1, -2, 1, 0, 0, 0, 0)) 
mat[lower.tri(mat)] <- 0
mat[1:5, ]

     [,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,]    1   -2    1    0    0    0    0
[2,]    0    1   -2    1    0    0    0
[3,]    0    0    1   -2    1    0    0
[4,]    0    0    0    1   -2    1    0
[5,]    0    0    0    0    1   -2    1

And, as a function (limited to dim > 3):

m <- function(dim){
  vec = c(1, -2, 1, rep(0, dim - 3))
  mat <- toeplitz(vec)
  mat[lower.tri(mat)] <- 0
  mat[seq(dim - 2) , ]
}

> m(10)
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,]    1   -2    1    0    0    0    0    0    0     0
[2,]    0    1   -2    1    0    0    0    0    0     0
[3,]    0    0    1   -2    1    0    0    0    0     0
[4,]    0    0    0    1   -2    1    0    0    0     0
[5,]    0    0    0    0    1   -2    1    0    0     0
[6,]    0    0    0    0    0    1   -2    1    0     0
[7,]    0    0    0    0    0    0    1   -2    1     0
[8,]    0    0    0    0    0    0    0    1   -2     1