Automatic multiplication between vector and matrix

Question

I have this R code:

> coef
[1] 1.5 2.4 3.9 4.4
> y
     [,1] [,2] [,3] [,4]
[1,]    1    2   12   45
[2,]    5    6    7    8
[3,]    9   10    2   12
         


        

Answer 1

Two more possibilities: sweep and scale (the latter only operates columnwise, and seems to me to be a bit of hack).

coef <- c(1.5,2.4,3.9,4.4)
y <- matrix(c(seq(1,17,by=4),
              seq(2,18,by=4),
              c(12,7,2,15,39,
                45,8,12,45,7)),
              ncol=4)

t(t(y)*coef)
t(apply(y,1,"*",coef))
sweep(y,2,coef,"*")
scale(y,center=FALSE,scale=1/coef)

library(rbenchmark)

benchmark(t(t(y)*coef),
           y %*% diag(coef),
           t(apply(y,1,"*",coef)),
           sweep(y,2,coef,"*"),
           scale(y,center=FALSE,scale=1/coef),
           replications=1e4)

                                      test replications elapsed relative
5 scale(y, center = FALSE, scale = 1/coef)        10000   0.990 4.342105
4                   sweep(y, 2, coef, "*")        10000   0.846 3.710526
3                t(apply(y, 1, "*", coef))        10000   1.537 6.741228
1                           t(t(y) * coef)        10000   0.228 1.000000
2                         y %*% diag(coef)        10000   0.365 1.600877

edit: added y %*% diag(coef) from @baptiste [not fastest, although it might be so for a big problem with a sufficiently optimized BLAS package ...] [and it was fastest in another trial, so I may just not have had a stable estimate]

edit: fixed typo in t(t(y)*coef) [thanks to Timur Shtatland] (but did not update timings, so they might be slightly off ...)

I also tried library(Matrix); y %*% Diagonal(x=coef), which is very slow for this example but might be fast for a large matrix (??). (I also tried constructing the diagonal matrix just once, but even multiplication by a predefined matrix was slow in this example (25x slower than the best, vs. 47x slower when defining the matrix on the fly.)

I have a mild preference for sweep as I think it expresses most clearly the operation being done ("multiply the columns by the elements of coef")

Answer 2

 apply(y, 1, "*", coef)
#  -- result --    
  [,1] [,2] [,3]  [,4]  [,5]
[1,]   1.5  7.5 13.5  19.5  25.5
[2,]   4.8 14.4 24.0  33.6  43.2
[3,]  46.8 27.3  7.8  58.5 152.1
[4,] 198.0 35.2 52.8 198.0  30.8

Answer 3

This will give you what you want:

t( t(y) * coef  )

Answer 4

A late entry:

coef[col(y)]*y

On my system, this is the fastest.

                                      test replications elapsed relative
6                         coef[col(y)] * y        10000   0.068    1.000
5 scale(y, center = FALSE, scale = 1/coef)        10000   0.640    9.412
4                   sweep(y, 2, coef, "*")        10000   0.535    7.868
3                t(apply(y, 1, "*", coef))        10000   0.837   12.309
1                           t(t(y) * coef)        10000   0.176    2.588
2                         y %*% diag(coef)        10000   0.187    2.750