vector moving mean of a matrix in R

Question

I’m doing the following operation with a matrix in the R:

> m <- matrix(1:9, ncol = 3, nrow = 3)
> m
     [,1] [,2] [,3]
[1,]    1    4    7
[2,]    2    5    8
[3,]    3    6    9
> m2 <- m
> for(i in 1:nrow(m)){
+   for(j in 1:ncol(m)){
+     c <- expand.grid((i-1):(i+1), (j-1):(j+1))
+     c <- c[c[,1] > 0 & c[,2]>0 & c[,1] <= nrow(m) & c[,2] <= ncol(m),]
+     m2[i,j] <- mean(m[c[,1], c[,2]])
+   }
+ }
> m2
     [,1] [,2] [,3]
[1,]  3.0  4.5  6.0
[2,]  3.5  5.0  6.5
[3,]  4.0  5.5  7.0

That is, I am calculating for each element of the matrix the average of its adjacent elements.

However, my matrices are images and this method becomes very inefficient for large matrices...

Does anyone know if there is any way to vector this loop?

Answer 1

There are packages with this type of function. Adapting to reply posted on Soen:

library(raster)
r <- raster(m)
as.matrix(focal(r, matrix(1,3,3), mean, pad = TRUE, padValue = NA, na.rm = TRUE))

Resulting in:

     [,1] [,2] [,3]
[1,]  3.0  4.5  6.0
[2,]  3.5  5.0  6.5
[3,]  4.0  5.5  7.0

We can compare the performance using a slightly larger matrix:

mbig <- matrix(1:441, ncol = 21, nrow = 21)

library(microbenchmark)
microbenchmark(Daniel = {
  m2 <- mbig
  for(i in 1:nrow(mbig)){
     for(j in 1:ncol(mbig)){
       c <- expand.grid((i-1):(i+1), (j-1):(j+1))
       c <- c[c[,1] > 0 & c[,2]>0 & c[,1] <= nrow(mbig) & c[,2] <= ncol(mbig),]
       m2[i,j] <- mean(mbig[c[,1], c[,2]])
     }
   }
  },
  Raster = {
    r <- raster(mbig)
    as.matrix(focal(r, matrix(1,nrow(mbig),ncol(mbig)), mean, pad = TRUE, padValue = NA, na.rm = TRUE))
})

The difference seems to be significant:

 Unit: milliseconds
   expr       min        lq     mean    median        uq      max neval cld
 Daniel 116.16301 118.47165 121.1388 119.32912 120.54214 204.8606   100   b
 Raster  13.16006  13.41737  14.0498  13.61459  13.87249  31.2184   100  a