Distance Matrix Computation

Question

We have two matrices, for example:

A=
     [,1] [,2] [,3]
[1,]   -2    1    0
[2,]    1    0   -1
[3,]    0   -1    4

and

B=
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    1    2    3
[3,]    3    1    2
[4,]    2    3    1
[5,]    3    1    2

I would to compute the distance matrix between the rows of A and B. In other words and using our example:

      [,1]                   [,2]                    [,3]
[1,]    dist(B[1,]-A[1,])      dist(B[1,]-A[2,])       dist(B[1,]-A[3,])
[2,]    dist(B[2,]-A[1,])      dist(B[2,]-A[2,])       dist(B[2,]-A[3,])
[3,]    dist(B[3,]-A[1,])      dist(B[3,]-A[2,])       dist(B[3,]-A[3,])
[4,]    dist(B[4,]-A[1,])      dist(B[4,]-A[2,])       dist(B[4,]-A[3,])
[5,]    dist(B[5,]-A[1,])      dist(B[5,]-A[2,])       dist(B[5,]-A[3,])

I was thinking of using the function "dist", that computes and returns the distance matrix of the distances between the rows of a data matrix. But it applies only to a single matrix. I have tried to use the command "rbind(A,B)" and to apply "dist" to the resulting matrix, but in this case I have obtained also the distances between the rows of same matrix.

Answer 1

Perhaps this way?

A = matrix(c(-2, 1, 0, 1, 0, -1, 0, -1, 4), ncol = 3, byrow = TRUE)
B = matrix(c(1, 2, 3, 1, 2, 3, 3, 1, 2, 2, 3, 1, 3, 1, 2), ncol = 3, byrow = TRUE)

t(sapply(1:nrow(B), function(x) {
  sqrt(rowSums(t(t(A)-B[x,])^2))
}))

         [,1]     [,2]     [,3]
[1,] 4.358899 4.472136 3.316625
[2,] 4.358899 4.472136 3.316625
[3,] 5.385165 3.741657 4.123106
[4,] 4.582576 3.741657 5.385165
[5,] 5.385165 3.741657 4.123106

Answer 2

# First build a matrix
  Dist.M <- matrix(0, nrow = nrow(A), ncol = ncol(B))

# Complete the matrix
  for (i in 1:nrow(A)){
    for (j in 1:nrow(B)){
         Dist.M[i,j] <- dist(rbind(A[i,],B[j,])
    }
  }