I’m not terribly familiar with matrix calculations but I’d like to start using Nx to see if I can speed up some things. This question is not directly about Nx so much as generally about the appropriate term for this type of calculation in matrix lingo. To whit:

I’ve been recently goofing around with Nx a bunch, including for AOC solutions, and I don’t claim to have a good handle on it, but I’ve been nerd sniped. This is what I tried in a Livebook. Sample inputs were based on the Rosetta Code link from upthread.

Shorter summary:

Get to an {2, N} tensor via Nx.transpose

Extend it along the axis with Nx.tile, compare with List.duplicate

Slice along the same axis to get cells that are offset by one step from the original pairs

Stack them a few times so that the tensor contains [[first row, offset second row], [second row, offset first]]

I didn’t quickly find out a good way to do this without intermediate variables and Access syntax, but it’s probably quite possible for someone more deft

Perform pair-wise multiplication along a single axis to get the x1 * y2... bits

Negate the second row of one axis to subtract

Sum, absolute value, divide by 2, wrapped in a dbg to see the shorter steps

Very happy to receive pointers and critique. I’m almost certain some of my steps could be elided, beyond just the places where I left intermediate steps to illuminate how the data was shifting in the Markdown output. Also notably I’ll bet this is very not-optimal for allocations.

Brilliant! The code for the offset is a bit more complex than I expected. I would probably default to using the input lists to generate both the original and the offset as lists of lists and then make tensors of the results.