Warning: matrix by vector division

Dear list,

I just made a very simple mistake, but it was hard to spot. And I
think that I should warn other people, because it is probably so
simple to make...

=== R code  ===

# Let us create a matrix:
(a <- cbind(c(0,1,1), rep(1,3)))

#      [,1] [,2]
# [1,]    0    1
# [2,]    1    1
# [3,]    1    1

# That is a MISTAKE:
a/colSums(a)

#           [,1]      [,2]
# [1,] 0.0000000 0.3333333
# [2,] 0.3333333 0.5000000
# [3,] 0.5000000 0.3333333
# I just wonder if some R warning should be issued here?

# That is what I actually needed (column-wise frequencies):
t(t(a)/colSums(a))

#      [,1]      [,2]
# [1,]  0.0 0.3333333
# [2,]  0.5 0.3333333
# [3,]  0.5 0.3333333

=== end of R code ===

With best wishes and regards,
Alexey Shipunov

or more simply:

 > prop.table(a, 2)
      [,1]      [,2]
[1,]  0.0 0.3333333
[2,]  0.5 0.3333333
[3,]  0.5 0.3333333

See ?prop.table

You need to recognize how matrices are stored in R. They are vectors 
with a 'dim' attribute. Thus 'a' is essentially:

 > as.vector(a)
[1] 0 1 1 1 1 1

If I take that vector, as say 'x':

x <- as.vector(a)

 > x
[1] 0 1 1 1 1 1

dim(x) <- c(3, 2)

 > x
      [,1] [,2]
[1,]    0    1
[2,]    1    1
[3,]    1    1


When you do the division, since colSums(a) contains two values, they are 
recycled as required to get the result. Thus colSums(a) effectively becomes:

 > rep(colSums(a), 3)
[1] 2 3 2 3 2 3

so that it is equal in length to 'a'.

The result is then:

 > as.vector(a) / rep(colSums(a), 3)
[1] 0.0000000 0.3333333 0.5000000 0.3333333 0.5000000 0.3333333

which is then returned as a matrix with the original dimensions:

 > matrix(as.vector(a) / rep(colSums(a), 3), 3, 2)
           [,1]      [,2]
[1,] 0.0000000 0.3333333
[2,] 0.3333333 0.5000000
[3,] 0.5000000 0.3333333


Another option simply for the sake of example, is:

 > t(apply(a, 1, function(x) x / colSums(a)))
      [,1]      [,2]
[1,]  0.0 0.3333333
[2,]  0.5 0.3333333
[3,]  0.5 0.3333333

prop.table() actually uses sweep(), so you might also want to look at that.

So the key to understanding the behavior is to understand how R objects 
are stored and how recycling rules work.

HTH,

Marc Schwartz