# zetaweights: Power-Law Weights According to Neighbourhood Order

### Description

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.

### Usage

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

### Arguments

 `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?

### Value

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

### Author(s)

Sebastian Meyer

`W_powerlaw`

### Examples

 ```1 2 3 4 5 6 7``` ```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 ```

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