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Calculate a function for all combinations of rows of two matrices in R

I would like to calculate a measure of the distance for all row combinations between two matrices / data frames.

The result will be a matrix with cell i, j corresponding to the result given by the function applied to row i of the first matrix and row j of the second matrix. Here is an example illustrating what I want to do for loops, with an example function.

x<-matrix(rnorm(30),10,3)  ## Example data
y<-matrix(rnorm(12),4,3)

results<-matrix(NA,nrow(x),nrow(y))

for (i in 1:nrow(x)){
  for (j in 1:nrow(y)){
    r1<-x[i,]
    r2<-y[j,]
    results[i,j]<-sum(r1*r2)  ## Example function
  }
}

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+3
2
outer(1:nrow(x), 1:nrow(y), Vectorize(function(i, j) sum(x[i, ] * y[j, ])))
+4

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## For reproducibility
set.seed( 35471 )

## Example data - bigger than the original to get and idea of difference in speed
x<-matrix(rnorm(60),20,3)
y<-matrix(rnorm(300),100,3)

# My function which uses grid.expand to get all combinations of row indices, then rowSums to operate on them
rs <- function( x , y ){
rows <- expand.grid( 1:nrow(x) , 1:nrow(y) )
results <- matrix( rowSums( x[ rows[,1] , ] * y[ rows[,2] , ] ) , nrow(x) , nrow(y) )
return(results)
}

# Your orignal function
flp <- function(x ,y){
results<-matrix(NA,nrow(x),nrow(y))
for (i in 1:nrow(x)){
  for (j in 1:nrow(y)){
    r1<-x[i,]
    r2<-y[j,]
    results[i,j]<-sum(r1*r2)  ## Example function
  }
}
return(results)
}


## Benchmark timings:
library(microbenchmark)
microbenchmark( rs( x, y ) , flp( x ,y ) , times = 100L )
#Unit: microseconds
#     expr      min       lq     median        uq      max neval
#  rs(x, y)  487.500  527.396   558.5425   620.486   679.98   100
# flp(x, y) 9253.385 9656.193 10008.0820 10430.663 11511.70   100

## And a subset of the results returned from each function to confirm they return the same thing!
flp(x,y)[1:3,1:3]
#          [,1]       [,2]       [,3]
#[1,] -0.5528311  0.1095852  0.4461507
#[2,] -1.9495687  1.7814502 -0.3769874
#[3,]  1.8753978 -3.0908057  2.2341414

rs(x,y)[1:3,1:3]
#          [,1]       [,2]       [,3]
#[1,] -0.5528311  0.1095852  0.4461507
#[2,] -1.9495687  1.7814502 -0.3769874
#[3,]  1.8753978 -3.0908057  2.2341414

, , rowSums 20 , for, 2000. , .

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