how do i fill the entries of this matrix in R?

Question

Given:

h_i=t_(i+1)-t_i for i=1,...,n-1 where n is a positive integer.

The matrix Q is an n by (n-2) matrix with entries q_(i,j) with i=1,...,n and j=2,...n-1 given by:

q_(j-1,j)=1/h_(j-1)
q_(j,j)=-(1/h_(j-1)+1/h_j)
q_(j+1,j)=1/h_j
q_(i,j)=0 for |i-j|>=2

I want to get a matrix Q. How do i write a program for this matrix in R? Many thanx in advance.

Answer 1

If I've figured out the subscripts correctly, I think this will do it:

n <- 100
t <- sort(runif(n))
h <- diff(t)
Q <- matrix(0,n,n-2)
Q[row(Q)==col(Q)-1] <- 1/h[1:(n-3)]
Q[row(Q)==col(Q)+1] <- 1/h[1:(n-2)]
diag(Q) <- c(NA,-1/h[1:(n-3)] - 1/h[2:(n-2)])