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I have the following defintion

arr = SymmetrizedArray[{1, 2} -> 1, {4, 4}, Antisymmetric[{1, 2}]]

which gives a StructuredArray with one entry {1,2}->1. I would like to map this array to a new one on a (key,value) basis, i.e. the desired result would look like something like this:

desiredResult = SymmetrizedArray[f[{1, 2}] -> g[1], {4, 4}, Antisymmetric[{1, 2}]]

How do I go about this without converting to a normal matrix?

I found out that for SparseArray one can do

SparseArray[{{1, 2} -> 1, {2, 1} -> -1}, {4, 4}]["NonzeroPositions"]

to get all available keys, but I actually would like to not convert my StructuredArray to a SparseArray to keep the number of entries at a minimum. Unfortunately an analogous syntax doesn't work with SparseArray.

Thanks a lot!

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