Efficiently computing a linear combination of data.table columns

Question

I have nc columns in a data.table, and nc scalars in a vector. I want to take a linear combination of the columns, but I don't know ahead of time which columns I will be using. What is the most efficient way to do this?

setup

require(data.table)
set.seed(1)

n  <- 1e5
nc <- 5
cf <- setNames(rnorm(nc),LETTERS[1:nc])
DT <- setnames(data.table(replicate(nc,rnorm(n))),LETTERS[1:nc])

ways to do it

Suppose I want to use the first four columns. I can manually write:

DT[,list(cf['A']*A+cf['B']*B+cf['C']*C+cf['D']*D)]

I can think of two automatic ways (that work without knowing that A-E should all be used):

mycols <- LETTERS[1:4] # the first four columns
DT[,list(as.matrix(.SD)%*%cf[mycols]),.SDcols=mycols]
DT[,list(Reduce(`+`,Map(`*`,cf[mycols],.SD))),.SDcols=mycols]

benchmarking

I expect the as.matrix to make the second option slow, and really have no intuition for the speed of Map-Reduce combinations.

require(rbenchmark)
options(datatable.verbose=FALSE) # in case you have it turned on

benchmark(
    manual=DT[,list(cf['A']*A+cf['B']*B+cf['C']*C+cf['D']*D)],
    coerce=DT[,list(as.matrix(.SD)%*%cf[mycols]),.SDcols=mycols],
    maprdc=DT[,list(Reduce(`+`,Map(`*`,cf[mycols],.SD))),.SDcols=mycols]
)[,1:6]

    test replications elapsed relative user.self sys.self
2 coerce          100    2.47    1.342      1.95     0.51
1 manual          100    1.84    1.000      1.53     0.31
3 maprdc          100    2.40    1.304      1.62     0.75

I get anywhere from a 5% to 40% percent slowdown relative to the manual approach when I repeat the benchmark call.

my application

The dimensions here -- n and length(mycols) -- are close to what I am working with, but I will be running these computations many times, altering the coefficient vector, cf.

Answer 1

This is almost 2x faster for me than your manual version:

Reduce("+", lapply(names(DT), function(x) DT[[x]] * cf[x]))

benchmark(manual = DT[, list(cf['A']*A+cf['B']*B+cf['C']*C+cf['D']*D)],
          reduce = Reduce('+', lapply(names(DT), function(x) DT[[x]] * cf[x])))
#    test replications elapsed relative user.self sys.self user.child sys.child
#1 manual          100    1.43    1.744      1.08     0.36         NA        NA
#2 reduce          100    0.82    1.000      0.58     0.24         NA        NA

And to iterate over just mycols, replace names(DT) with mycols in lapply.

Answer 2

Add this option to your benchmark call:

ops = as.matrix(DT) %*% cf

On my device it was 30% faster than the matrix multiplication you tried.