`zetaweights.Rd`

Compute power-law weights with decay parameter `d`

based on a matrix of neighbourhood orders `nbmat`

(e.g., as obtained via `nbOrder`

).
Without normalization and truncation,
this is just \(o^{-d}\) (where \(o\) is a neighbourhood order).
This function is mainly used internally for `W_powerlaw`

weights in `hhh4`

models.

`zetaweights(nbmat, d = 1, maxlag = max(nbmat), normalize = FALSE)`

- nbmat
numeric, symmetric matrix of neighbourhood orders.

- d
single numeric decay parameter (default: 1). Should be positive.

- maxlag
single numeric specifying an upper limit for the power law. For neighbourhood orders >

`maxlag`

, the resulting weight is 0. Defaults to no truncation.- normalize
Should the resulting weight matrix be normalized such that rows sum to 1?

a numeric matrix with same dimensions and names as the input matrix.

Sebastian Meyer

```
nbmat <- matrix(c(0,1,2,2,
1,0,1,1,
2,1,0,2,
2,1,2,0), 4, 4, byrow=TRUE)
zetaweights(nbmat, d=1, normalize=FALSE) # harmonic: o^-1
zetaweights(nbmat, d=1, normalize=TRUE) # rowSums=1
zetaweights(nbmat, maxlag=1, normalize=FALSE) # results in adjacency matrix
```