Forum Discussion
A generalisation of the MAP lambda helper function
- Sep 08, 2024
This is a demonstration of the proposed MAP function used to solve a challenge provided by Oz_Sunray and Wyn Hopkins on data cleansing and vote counting. The key element of my solution is to build a table of validated votes for each voter ID and each candidate (i.e. an array of arrays - much the same as any other problem of interest). The formula is modularised using Lambda functions. They are not that pretty, but neither are they impossible to follow.
"Worksheet formula" = AggregateVotesλ( tblVOTES[VoterID], tblVOTES[[Vote1]:[Vote3]], weight, tblAvailable[AVAILABLE] )
which calls
/* "FUNCTION NAME: AggregateVotesλ" "DESCRIPTION: Aggregates all votes to candidate colors" */ /* "REVISIONS: Date Developer Description" " 08 Sep 2024 Peter Bartholomew Original Development" */ AggregateVotesλ = LAMBDA(voterID, votesCast, weight, available, LET( person, TOROW(UNIQUE(voterID)), votes, MAPλ(person, AssignVotesλ(voterID, votesCast, weight, available)), count, HSTACK(available, BYROW(votes, SUM)), return, TAKE(SORT(count, 2, -1), 4), return ) );
to build and aggregate the table of votes. This, in turn, calls another Lambda function to clean and validate the votes corresponding to a single voterID
/* "FUNCTION NAME: AssignVotesλ" "DESCRIPTION: Validates and assigns votes to candidate colors for a single voterID " */ /* "REVISIONS: Date Developer Description" " 08 Sep 2024 Peter Bartholomew Original Development" */ AssignVotesλ = LAMBDA(voterID, ballots, weight, available, LAMBDA(p, LET( // "In the case of duplicate ballots return first" votesCast, XLOOKUP(p, voterID, ballots), // "Remove invalid and repeated votes" valid, COUNTIFS(available, votesCast), distinct, EXPAND(UNIQUE(FILTER(votesCast, valid), TRUE), , 3, ""), // "Assign votes to candidate colours" assigned, BYROW((distinct = available) * weight, SUM), assigned ) ) );
I took the problem from Wyn's recording
https://www.youtube.com/watch?v=FIcxyLqzWcE
I hope the Excel team takes note of your terrific work here in working around the array of arrays limitations (and doing it very efficiently calculation wise). I'm still thinking of all the possibilities of where I might use Mapλ. It certainly broadens the horizons!
Re: Kronecker product
It seems silly we must jump through hoops to obtain a Kronecker product when Python and numpy can do it out of the box:
a = xl("firstArray")
b = xl("secondArray")
result = np.kron(a,b)