How to sum over diagonals of data frame

Question

Say that I have this data frame:

     1   2   3   4      
100  8   12  5   14 
99   1   6   4   3   
98   2   5   4   11  
97   5   3   7   2   

In this above data frame, the values indicate counts of how many observations take on (100, 1), (99, 1), etc.

In my context, the diagonals have the same meanings:

     1   2   3   4
100  A   B   C   D 
99   B   C   D   E  
98   C   D   E   F 
97   D   E   F   G

How would I sum across the diagonals (i.e., sum the counts of the like letters) in the first data frame?

This would produce:

group  sum
A      8
B      13
C      13
D      28
E      10
F      18
G      2

For example, D is 5+5+4+14

Answer 1

You can use row() and col() to identify row/column relationships.

m <- read.table(text="
    1   2   3   4      
100  8   12  5   14 
99   1   6   4   3   
98   2   5   4   11  
97   5   3   7   2")

vals <- sapply(2:8,
       function(j) sum(m[row(m)+col(m)==j]))

or (as suggested in comments by ?@thelatemail)

vals <- sapply(split(as.matrix(m), row(m) + col(m)), sum)
data.frame(group=LETTERS[seq_along(vals)],sum=vals)

or (@Frank)

data.frame(vals = tapply(as.matrix(m), 
       (LETTERS[row(m) + col(m)-1]), sum))

as.matrix() is required to make split() work correctly ...

Answer 2

Another solution using bgoldst's definition of df1 and df2

sapply(unique(c(as.matrix(df2))),function(x) sum(df1[df2==x]))

Gives

#A  B  C  D  E  F  G 
#8 13 13 28 10 18  2 

(Not quite the format that you wanted, but maybe it's ok...)

Answer 3

Here's a solution using stack(), and aggregate(), although it requires the second data.frame contain character vectors, as opposed to factors (could be forced with lapply(df2,as.character)):

df1 <- data.frame(a=c(8,1,2,5), b=c(12,6,5,3), c=c(5,4,4,7), d=c(14,3,11,2) );
df2 <- data.frame(a=c('A','B','C','D'), b=c('B','C','D','E'), c=c('C','D','E','F'), d=c('D','E','F','G'), stringsAsFactors=F );
aggregate(sum~group,data.frame(sum=stack(df1)[,1],group=stack(df2)[,1]),sum);
##   group sum
## 1     A   8
## 2     B  13
## 3     C  13
## 4     D  28
## 5     E  10
## 6     F  18
## 7     G   2

Answer 4

Another aggregate variation, avoiding the formula interface, which actually complicates matters in this instance:

aggregate(list(Sum=unlist(dat)), list(Group=LETTERS[c(row(dat) + col(dat))-1]), FUN=sum)

#  Group Sum
#1     A   8
#2     B  13
#3     C  13
#4     D  28
#5     E  10
#6     F  18
#7     G   2