I’m trying to divide every row of a matrix by its norm using the approach suggested by this comment . However, I’m finding that two functionally equivalent implementations are resulting in more than 100x difference in runtime (the first implementation runs in ~1.3s, while the second runs in ~0.002s).…

I think the big thing here is that the broadcast in the first function is fused, and thus calls norm N^2 times, while the second one instead calls it N times, and makes a temporary array to store the results. A simpler example of this might be: julia> using BenchmarkTools julia> let N = 100 …

Preventing broadcast fusing contains more detailed discussion about the broadcasting fusing slowdown (a failure of LICM for a theoretically pure norm function? EDIT: maybe not, because LICM can’t create temporary arrays I suppose?)

There is an issue ( 29285 ) about LICM for broadcasted pure functions, but that’s for scalar inputs. The loop in broadcast.jl is an unnested @simd loop where _broadcast_getindex_evalf (well, it really starts with a getindex(bc::Broadcasted...) evaluates the fused operations on each index of the output…

That particular comment is actually even more damning than just LICM possibly being undoable. It’s that even if you could save pure function calls along some axes by lifting them to higher levels in a nested loop (maybe the Broadcasted struct could hold those intermediate values), there is a functio…

Orders of magnitude runtime difference in row-wise norm

General Usage Performance

tictaccat March 21, 2023, 12:25am 5

Right, I think Preventing broadcast fusing - #18 by Chris_Foster expresses a similar sentiment

Topic		Replies	Views
Improving function performance - Broadcasting vs Loops Performance	14	2152	August 17, 2021
Performance of norm function Performance linearalgebra	21	12685	March 28, 2021
Unexpected broadcasting behavior involving eachrow() General Usage	86	1859	April 4, 2023
Understanding major order performance when broadcasting in column vs row operations Performance question , array , benchmark	9	1075	June 21, 2021
Understanding why one function is faster than the other New to Julia	16	1287	November 1, 2020

Orders of magnitude runtime difference in row-wise norm

Related topics