[R] Algorithm needed

[(Ted Harding)]

On 09-Nov-06 hbeltra at sas.upenn.edu wrote:
> I have a matrix of size "n" and I want to create a new one
> in which the columns are sums of the original matrix, with
> some order in the sums. For example, if matrix A has 4 columns,
> then the new matrix should have 6 columns with the following
> info from the columns of A: 1+2, 1+3, 1+4, 2+3, 2+4, 3+4.
> If matrix A has 5 columns, then the new matrix has 10 columns:
> 1+2, 1+3, 1+4, 1+5, 2+3, 2+4, 2+5, 3+4, 3+5, 4+5
> 
> I thought of using a for loop:
> for (i in 1:n-1) {
>   for (j in (i+1):n) {
>       A[,i] + A[,j]
>   }
> }
> 
> but I don't know how to store the results so the new matrix has
> all the columns. I know the number of columns in the new matrix
> is given by n(n-1)/2.
> 
> Any ideas?  Thanks.
> 
> Hiram

What an intriguing little question! The natural place to look for
all the combinations of 2 out of n (in the order you require) is
the function combn() in the package "combinat". Then I noticed
the argument "fun" in "?combn", which led to the following
(using a simple example):

  library(combinat)

  A<-cbind(c(1,2,3,4),c(1,3,5,7),c(1,4,7,10),c(1,5,9,13))
  A
#      [,1] [,2] [,3] [,4]
# [1,]    1    1    1    1
# [2,]    2    3    4    5
# [3,]    3    5    7    9
# [4,]    4    7   10   13

  summit<-function(y)(rowSums(A[,y]))

  S<-combn((1:4),2,fun=summit)
  S
#      [,1] [,2] [,3] [,4] [,5] [,6]
# [1,]    2    2    2    2    2    2
# [2,]    5    6    7    7    8    9
# [3,]    8   10   12   12   14   16
# [4,]   11   14   17   17   20   23

so it looks as though this will do exactly what you want!

Thanks for asking the question: I hadn't spotted this
very useful feature of combn() before.

Best wishes,
Ted.

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Date: 09-Nov-06                                       Time: 22:36:38
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