Question

I’m experimenting with spectral simulation for generating unconditional Gaussian realizations of a spatial variable. The variable has a covariance function c(h) = exp(-h/a), where a is the range of the covariance function and h is distance. In the first step, I need to discretize the covariance function into an array/matrix. The entries in the matrix correspond to physical locations in space (i.e. the matrix indices correspond to x and y coordinates):

cov(i,j) = exp(-sqrt((i-64)^2 + (j-64)^2) / 20) for i,j = 1 to 128

I am looking to generate a matrix in R and fill it with the covariance function related to the indices of the array. As a total beginner with R, I’m a bit lost.

Answer 1

stuff that expression into a function:

myfun <- function(i, j) {
  exp(-sqrt((i-64)^2 + (j-64)^2) / 20)
}

Then make your “matrix” of possible i, j combinations:

n <- 128
combos <- expand.grid(i=1:n, j=1:n)

Then call your function with those two vectors:

matrix(myfun(combos$i, combos$j), nrow=n)

Using a smaller number:

> n <- 5
> combos <- expand.grid(i=1:n, j=1:n)
> matrix(myfun(combos$i, combos$j), nrow=n)
           [,1]       [,2]       [,3]       [,4]       [,5]
[1,] 0.01162296 0.01203954 0.01246747 0.01290681 0.01335761
[2,] 0.01203954 0.01247458 0.01292166 0.01338085 0.01385221
[3,] 0.01246747 0.01292166 0.01338860 0.01386840 0.01436113
[4,] 0.01290681 0.01338085 0.01386840 0.01436960 0.01488451
[5,] 0.01335761 0.01385221 0.01436113 0.01488451 0.01542247
>