In this algebra, it’s possible to compute on a mesh of arbitrary 5 dimensional conformal geometric algebra simplices, which can be represented by a bundle of nested dyadic tensors. julia> using Grassmann, StaticArrays; basis"+-+++" (⟨+-+++⟩, v, v₁, v₂, v₃, v₄, v₅, v₁₂, v₁₃, v₁₄, v₁₅, v₂₃, v₂₄, v₂₅…

It’s definitely an interesting paper, but I don’t see the advantage it shows over LU. It appears to be 2x slower and not more stable. Am I missing something?

Except that it appears to be faster for small matrices.

What you’re missing (if anything) is only that I’m not claiming it’s better or worse in terms of performance for small matrices :slight_smile:, just that it’s interesting that Cramer’s rule is not a total loss numerically. The actual speed of small matrix kernels depends so much on the microarchite…

Base.@pure function Grassmann.Cramer(N::Int) I hate to always be that guy, but the xy return value allocation is definitely not pure and that can introduce issues into your program. Try to avoid ever marking functions as @pure as that can introduce serious issues if you’re wrong—and generally sho…

[image] tkoolen: What version of Grassmann does this require? On 0.5.12 (latest released version), Julia 1.4.2, I get allocations: So, there is a strange thing happening where if you only run using Grassmann the Base.:\ method is slower than if you additionally paste the Base.:\ method into t…

[image] chakravala: I am not aware of any bug reports for Grassmann.jl outside of my repositories (any references?). This would be one of them as an example: Mysterious internal error when using Grassmann.jl · Issue #31185 · JuliaLang/julia · GitHub

[image] chakravala: Can you elaborate what the potential issues are? I am not necessarily inclined to believe your claim. If you don’t understand what the annotation means, then you should probably not be using it at all. I don’t really care what you believe—I implemented @pure, so I’m gener…

Yes, I’m aware you implemented it, but you’ve not yet convinced me to not use it here. This Grassmann program is my playground for experiments with mathematics and programming. It works fine for me, and I am always willing to consider changing its application in any use of Base.@pure if it’s a mista…

willing to consider changing its application in any use of Base.@pure if it’s a mistake You’re clearly not actually willing to, since it’s been pointed out before that the bug report mentioned above ( Mysterious internal error when using Grassmann.jl · Issue #31185 · JuliaLang/julia · GitHub ) de…

That bug was fixed already, and the fix didn’t involve changing anything with @pure as it was a bug with the type system in a conversion method.

Grassmann.jl A\b 3x faster than Julia's StaticArrays.jl

General Usage Performance

kristoffer.carlsson June 16, 2020, 3:11pm 10

This would be one of them as an example: Mysterious internal error when using Grassmann.jl · Issue #31185 · JuliaLang/julia · GitHub

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Grassmann.jl A\b 3x faster than Julia's StaticArrays.jl

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