`focal.Rd`

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 or

`NA`

- 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`

may not be a good idea in this function because it can 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`

`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.

Note that there is a difference between 0 and NA in the weights matrix. A zero weight cell is included in the computation, whereas a NA weight cell is excluded. This does not matter for "sum", nor for "mean" (zeros are removed), but it affects many other functions such as "var" as you could be adding a lot of zeros that should not be there.

RasterLayer

```
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
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 0 1 1
#> [3,] 0 1 1
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))
if (FALSE) {
## 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)
}
}
```