I have a matrix mat that looks like:
A B C D E F
1 0.74 1.19 0.01 1.21 16000 0.02
2 0.76 1.17 0.01 1.21 15500 0.02
3 0.79 1.16 0.01 1.17 15625 0.02
4 0.75 1.17 0.01 1.17 15600 0.02
5 0.80 1.19 0.01 1.19 15225 0.02
6 0.79 1.18 0.01 1.18 15625 0.02
And I want to build a Symmetric matrix from this by applying the function Sum(Col1-Col2). The end result will look something like this:
A B C D E F
A 0
B 0
C 0
D 0
E 0
F 0
Such that the blank spaces represent the sum of difference. i.e. [1,2] = Sum(A-B).
I have investigated methods such as:
combs<-combn(names(mat),2)
val<-apply(combs,2,function(x) mat[[x[1]]]-mat[[x[2]]])
But it doesn't give me a nice symmetric matrix.
Anyone have any ideas?
Thanks.
EDIT - Thanks to Troy the above works. But how about if I want to compute Sum((Col1-Col2)^2) in that Sum(((A_1,A_2,..,A_n)-(B_1,B_2,..,B_n))^2) (so can't sum A and B initially and then subtract otherwise the answer will be off).
This seems valid, too:
outer(colSums(mat), colSums(mat), `-`) #I used Troy's `mat`
# A B C D E F
#A 0.00 -2.43 4.57 -2.50 -93570.37 4.51
#B 2.43 0.00 7.00 -0.07 -93567.94 6.94
#C -4.57 -7.00 0.00 -7.07 -93574.94 -0.06
#D 2.50 0.07 7.07 0.00 -93567.87 7.01
#E 93570.37 93567.94 93574.94 93567.87 0.00 93574.88
#F -4.51 -6.94 0.06 -7.01 -93574.88 0.00
EDIT to match edited question:
n = seq_len(ncol(mat))
ff = function(a, b) sum((mat[,a] - mat[,b]) ^ 2)
outer(n, n, Vectorize(ff))
# [,1] [,2] [,3] [,4] [,5] [,6]
#[1,] 0.000000e+00 9.881000e-01 3.48390e+00 1.048400e+00 1459547504 3.393100e+00
#[2,] 9.881000e-01 0.000000e+00 8.16740e+00 2.100000e-03 1459471669 8.028000e+00
#[3,] 3.483900e+00 8.167400e+00 0.00000e+00 8.332500e+00 1459690004 6.000000e-04
#[4,] 1.048400e+00 2.100000e-03 8.33250e+00 0.000000e+00 1459469476 8.191700e+00
#[5,] 1.459548e+09 1.459472e+09 1.45969e+09 1.459469e+09 0 1.459688e+09
#[6,] 3.393100e+00 8.028000e+00 6.00000e-04 8.191700e+00 1459688132 0.000000e+00