[Feature Request] `Frequency` merge operations

Merge operations for Maps

Data can be sorted into bins of predefined width using the Frequency or EmpiricalDistribution module. If two datasets are binned and should be merged afterwards, several merging strategies are possible. A simple merge of freqA and freqB is straightforward with keys that are present in freqA and freqB are replaced with the values of freqB.

let a =
    [("k1",1);("k2",3)]
    |> Map.ofList

let b =
    [("k2",1);("k3",4)]
    |> Map.ofList

merge a b

results in the following combination with ("k2",3) from a being replaced by ("k2",1) from b:

val it: Map<float,int> = map [("k1", 1); ("k2", 1); ("k3", 4)]

Generic formulation of merge operations

I'm in the process of adding a generic function that gets an additional function that handles key duplicates. E.g.:

add a b

resulting in the combination of a and b with ("k2",3) from a being added to ("k2",1) from b:

val it: Map<float,int> = map [("k1", 1); ("k2", 4); ("k3", 4)]

While this is trivial, I'm not sure how to handle a subtraction. Should the result from subtract a b result in:

• a) val it: Map<float,int> = map [("k1", 1); ("k2", 2); ("k3", 4)]
  • counts from a are subtracted by the corresponding values from b if keys are present in both maps
  • here the values of a that are not present in b are untouched
• b) val it: Map<float,int> = map [("k1", 1); ("k2", 2); ("k3", -4)]
  • counts from a are subtracted by the values from b, even for keys that are not present in a

The latter option (b) makes no sense to me since frequency counts should not be negative, but I cannot think of applications in which the result of (a) makes any sense. Maybe the subtract function is not the best to start with because in this post they implemented (a) with addition and multiplication examples. Especially for the addition, a and b would give the correct result and I think it is intuitive to just apply the function to values of keys that are present in both maps.

@HarryMcCarney, do you know use cases that use subtract? Do you have any thoughts about this? I would suggest to add version (a) to Frequency as well as EmpiricalDistribution

Additional remark: When applied to continuous data bandwidths must be equal, to not merge counts from overlapping bins!