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