Calculate focal ("moving window") values for the neighborhood of focal cells using a matrix of weights, perhaps in combination with a function.

```
# S4 method for RasterLayer
focal(x, w, fun, filename='', na.rm=FALSE, pad=FALSE, padValue=NA, NAonly=FALSE, ...)
```

x

RasterLayer

w

matrix of weights (the moving window), e.g. a 3 by 3 matrix with values 1; see Details. The matrix does not need to be square, but the sides must be odd numbers. If you need even sides, you can add a column or row with weights of zero

fun

function (optional). The function fun should take multiple numbers, and return a single number. For example mean, modal, min or max. It should also accept a `na.rm`

argument (or ignore it, e.g. as one of the 'dots' arguments. For example, `length`

will fail, but `function(x, ...){na.omit(length(x))}`

works.

filename

character. Filename for a new raster (optional)

na.rm

logical. If `TRUE`

, `NA`

will be removed from focal computations. The result will only be `NA`

if all focal cells are `NA`

. Except for some special cases (weights of 1, functions like min, max, mean), using `na.rm=TRUE`

is generally not a good idea in this function because it will unbalance the effect of the weights

pad

logical. If `TRUE`

, additional 'virtual' rows and columns are padded to `x`

such that there are no edge effects. This can be useful when a function needs to have access to the central cell of the filter

padValue

numeric. The value of the cells of the padded rows and columns

NAonly

logical. If `TRUE`

, only cell values that are `NA`

are replaced with the computed focal values

...

Additional arguments as for `writeRaster`

RasterLayer

`focal`

uses a matrix of weights for the neighborhood of the focal cells. The default function is `sum`

. It is computationally much more efficient to adjust the weights-matrix than to use another function through the `fun`

argument. Thus while the following two statements are equivalent (if there are no `NA`

values), the first one is faster than the second one:

`a <- focal(x, w=matrix(1/9, nc=3, nr=3))`

`b <- focal(x, w=matrix(1,3,3), fun=mean)`

There is, however, a difference if `NA`

values are considered. One can use the `na.rm=TRUE`

option which may make sense when using a function like `mean`

. However, the results would be wrong when using a weights matrix.

Laplacian filter: `filter=matrix(c(0,1,0,1,-4,1,0,1,0), nrow=3)`

Sobel filters: `fx=matrix(c(-1,-2,-1,0,0,0,1,2,1) / 4, nrow=3)`

and `fy=matrix(c(1,0,-1,2,0,-2,1,0,-1)/4, nrow=3)`

see the `focalWeight`

function to create distance based circular, rectangular, or Gaussian filters.

# NOT RUN { r <- raster(ncols=36, nrows=18, xmn=0) values(r) <- runif(ncell(r)) # 3x3 mean filter r3 <- focal(r, w=matrix(1/9,nrow=3,ncol=3)) # 5x5 mean filter r5 <- focal(r, w=matrix(1/25,nrow=5,ncol=5)) # Gaussian filter gf <- focalWeight(r, 2, "Gauss") rg <- focal(r, w=gf) # The max value for the lower-rigth corner of a 3x3 matrix around a focal cell f = matrix(c(0,0,0,0,1,1,0,1,1), nrow=3) f rm <- focal(r, w=f, fun=max) # global lon/lat data: no 'edge effect' for the columns xmin(r) <- -180 r3g <- focal(r, w=matrix(1/9,nrow=3,ncol=3)) # } # NOT RUN { ## focal can be used to create a cellular automaton # Conway's Game of Life w <- matrix(c(1,1,1,1,0,1,1,1,1), nr=3,nc=3) gameOfLife <- function(x) { f <- focal(x, w=w, pad=TRUE, padValue=0) # cells with less than two or more than three live neighbours die x[f<2 | f>3] <- 0 # cells with three live neighbours become alive x[f==3] <- 1 x } # simulation function sim <- function(x, fun, n=100, pause=0.25) { for (i in 1:n) { x <- fun(x) plot(x, legend=FALSE, asp=NA, main=i) dev.flush() Sys.sleep(pause) } invisible(x) } # Gosper glider gun m <- matrix(0, nc=48, nr=34) m[c(40, 41, 74, 75, 380, 381, 382, 413, 417, 446, 452, 480, 486, 517, 549, 553, 584, 585, 586, 619, 718, 719, 720, 752, 753, 754, 785, 789, 852, 853, 857, 858, 1194, 1195, 1228, 1229)] <- 1 init <- raster(m) # run the model sim(init, gameOfLife, n=150, pause=0.05) ## Implementation of Sobel edge-detection filter ## for RasterLayer r sobel <- function(r) { fy <- matrix(c(1,0,-1,2,0,-2,1,0,-1), nrow=3) fx <- matrix(c(-1,-2,-1,0,0,0,1,2,1) , nrow=3) rx <- focal(r, fx) ry <- focal(r, fy) sqrt(rx^2 + ry^2) } # }