Fast R method for matrix product with final product instead of sum

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In R it's possible to perform a cross-product by using %*% between two matrices M1: n x p and M2: p x d, that is having one dimension length in common.

To do the cross-product one multiplies for each row 1..n in M1 and column 1..d in M2 the relative p_M1 x p_M2 and then sums the resulting vector.

But instead of the sum I would like to have the product prod(p_M1 x p_M2).

I can do this with nested loops in R, but it's very slow and my matrices are very big. Is there an alternative as fast as %*%?

EXAMPLE:

    set.seed(1)
    a <- matrix(sample((1:100) / 100, 15), ncol = 3)
    b <- matrix(sample((1:100) / 100, 15), ncol = 5)

    # This produces the usual cross-product...
    a %*% b

    # ...which can be done also using loops
    do.call('cbind', lapply(1:5, function(i) {
        sapply(1:5, function(j) {
            sum(a[i,] * b[,j])
        })
    }))

    # But I need to do the product of the paired vectors instead of the sum. I could use a nested loop but it takes hours.
    do.call('cbind', lapply(1:5, function(i) {
        sapply(1:5, function(j) {
            prod(a[i,] * b[,j])
        })
    }))
r performance
1 Answers

Following my comment, here is a method with the matrixStats package and outer to perform the calculation.

# nested loop
mat1 <- 
    do.call('cbind', lapply(1:5, function(i) {
        sapply(1:5, function(j) {
            prod(a[i,] * b[,j])
        })
    }))

# vectorized-ish
library(matrixStats)

mat2 <- outer(colProds(b), rowProds(a))

Now, check that they are numerically equivalent.

all.equal(mat1, mat2)
[1] TRUE

If you want the look and feel of %*%, you could change this to

mat2 <- colProds(b) %o% rowProds(a)

You can stick with base R if you want to avoid packages. Here is one method.

mat3 <- outer(
               vapply(seq_len(ncol(b)), function(x) prod(b[, x]), numeric(1L)),
               vapply(seq_len(nrow(a)), function(x) prod(a[x, ]), numeric(1L))
              ))

testing the speed of these two, I get the following

library(microbenchmark)

microbenchmark(nest=
                do.call('cbind', lapply(1:5, function(i) {
                        sapply(1:5, function(j) {
                                prod(a[i,] * b[,j])
                               })
                        })),
               vect=outer(colProds(b), rowProds(a)),
               baseVect=outer(
                  vapply(seq_len(ncol(b)), function(x) prod(b[, x]), numeric(1L)),
                  vapply(seq_len(nrow(a)), function(x) prod(a[x, ]), numeric(1L))
               ))

Unit: microseconds
  expr     min       lq      mean  median       uq      max neval
  nest    129.228 133.2225 172.43874 136.833 142.9640 3531.144   100
  vect     23.831  25.8690  28.38306  27.705  29.1815   94.546   100
 baseVect  27.223  29.8970  57.85946  31.471  32.8400 2647.373   100
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