stevensonmt
Matrix operation for "shoelace formula"
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:
input = [{x1, y1}, {x2, y2}, {x3, y3}]
matrix = | x1 x2 x3 |
| y1 y2 y3 |
output = x1 * y2 + x2 * y3 + x3 * y1 - x2 * y1 - x3 * y2 - x1 * y3
Is there a name for that matrix operation?
Marked As Solved
shanesveller
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 viaNx.transpose - Extend it along the axis with
Nx.tile, compare withList.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
dbgto 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.
Pretty much what I arrived at!
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gregvaughn
That looks closely related to a determinant, but those are for square matrices, so I’m not sure what the generalized name might be.
shanesveller
If you’re fine with doing the transform inside the vanilla Elixir surroundings, it’s tough to beat Enum.slide:
Enum.slide(1..5, 0, -1)
[2, 3, 4, 5, 1]
Enum.slide(1..5, 0..1, -1)
[3, 4, 5, 1, 2]
Enum.slide(1..5, 2..3, 0)
[3, 4, 1, 2, 5]
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