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Group and subtract all rows in a dataframe

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Consider the following example:

t1 t2 t3 t4 t5 t6 
A  4  6  7  8  5
A  3  6  8  1  4
A  2  3  5  3  1
A  3  4  3  1  3
B  3  6  8  3  4
B  3  9  3  7  3
B  5  2  3  2  1

I hope to get a dataframe which checks for differences between every pair of rows possible within a group (A and B seperately).

I have been trying to subset the dataframe based on a loop and manually calculate the differences between rows. This is leading to a lot of computation and it is hard to manage the referencing after all the differences have been calculated. I am basically ending up with several lists.

The resulting dataframe needs to contain the row differences for all possible row combinations(or permutations?) within a group.

For example, for B, without considering the first column i.e. characters, the following is the expected result:

t2 t3 t4 t5 t6
0  -3  5 -4  1
-2  4  5  1  3
-2  7  0  5  2 

The sign is not very important. Only the magnitude


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