Multiplying Combinations of a list of lists in R

Question

Given a list of two lists, I am trying to obtain, without using for loops, a list of all element-wise products of the first list with the second. For example:

Answer 1

Pulling ideas from the other answers together, I'll throw another one-liner in for fun:

do.call(mapply, c(FUN=`*`, as.list(expand.grid(b, a))))

which gives

     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
[1,]    1    3    6    2    6   12    4   12   24
[2,]    6    8    4    9   12    6   15   20   10

If you really need it in the format you gave, then you can use the plyr library to transform it into that:

library("plyr")
as.list(unname(alply(do.call(mapply, c(FUN=`*`, as.list(expand.grid(b, a)))), 2)))

which gives

[[1]]
[1] 1 6

[[2]]
[1] 3 8

[[3]]
[1] 6 4

[[4]]
[1] 2 9

[[5]]
[1]  6 12

[[6]]
[1] 12  6

[[7]]
[1]  4 15

[[8]]
[1] 12 20

[[9]]
[1] 24 10

---

Just for fun, benchmarking:

Joris <- function(a, b) {
    mapply(`*`,a,rep(b,each=length(a)))
}

TylerM <- function(a, b) {
    x <- expand.grid(1:length(a), 1:length(b))
    x <- x[order(x$Var1), ]    #gives the order you asked for
    FUN <- function(i)  diag(outer(a[[x[i, 1]]], b[[x[i, 2]]], "*"))
    sapply(1:nrow(x), FUN)
}

TylerL <- function(a, b) {
    x <- expand.grid(1:length(a), 1:length(b))
    x <- x[order(x$Var1), ]    #gives the order you asked for
    FUN <- function(i)  diag(outer(a[[x[i, 1]]], b[[x[i, 2]]], "*"))
    lapply(1:nrow(x), FUN)
}

Wojciech <- function(a, b) {
    # Matrix with indicies for elements to multiply
    G <- expand.grid(1:3,1:3)

    # Coversion of G to list
    L <- lapply(1:nrow(G),function(x,d=G) d[x,])

    lapply(L,function(i,x=a,y=b) x[[i[[2]]]]*y[[i[[1]]]])
}

DiggsM <- function(a, b) {
    do.call(mapply, c(FUN=`*`, as.list(expand.grid(b, a))))
}

DiggsL <- function(a, b) {
    as.list(unname(alply(t(do.call(mapply, c(FUN=`*`, as.list(expand.grid(b, a))))), 1)))
}

and the benchmarks

> library("rbenchmark")
> benchmark(Joris(b,a),
+           TylerM(a,b),
+           TylerL(a,b),
+           Wojciech(a,b),
+           DiggsM(a,b),
+           DiggsL(a,b),
+           order = "relative", 
+           replications = 1000,
+           columns = c("test", "elapsed", "relative"))
            test elapsed relative
1    Joris(b, a)    0.08    1.000
5   DiggsM(a, b)    0.26    3.250
4 Wojciech(a, b)    1.34   16.750
3   TylerL(a, b)    1.36   17.000
2   TylerM(a, b)    1.40   17.500
6   DiggsL(a, b)    3.49   43.625

and to show they are equivalent:

> identical(Joris(b,a), TylerM(a,b))
[1] TRUE
> identical(Joris(b,a), DiggsM(a,b))
[1] TRUE
> identical(TylerL(a,b), Wojciech(a,b))
[1] TRUE
> identical(TylerL(a,b), DiggsL(a,b))
[1] TRUE