# Foal Getis-ord on rasters¶

The rasterized Focal Getis-Ord formula looks as follows:

FocalG^*(R, W, N, M, S) = \frac{ R{\stackrel{\mathtt{sum}}{\circ}}W - M*\sum_{w \in W}{w} }{ S \sqrt{ \frac{ N*\sum_{w \in W}{w^2} - (\sum_{w \in W}{w})^2 }{ N - 1 } } }

where:

• $R$ is the input raster.
• $W$ is a weight matrix of values between 0 and 1. The matrix is square and has odd dimensions, e.g. $5 \times 5$, $31 \times 31$ ...
• $N$ represents the focal count of pixels TODO (there can be NA values)
• $M$ represents the focal mean TODO.
• $S$ represents the focal standard deviation TODO.

It can be seen that the formula can be nicely refactored into:

• TODO