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You're probably confusing ARPACK with BLAS / LAPACK.

Pure julia ARPACK already exists, e.g. https://github.com/haampie/ArnoldiMethod.jl/.

A competive BLAS-gemm is implemented here https://github.com/YingboMa/MaBLAS.jl/blob/master/src/gemm.j... (single-threaded).

A LAPACK-like library could be https://github.com/JuliaLinearAlgebra/GenericLinearAlgebra.j...

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I was mostly referring to the parent comment's suggestion that low level numerical libraries wouldn't benefit from a pure Julia implementation, specifically to the statement that it was still better to write optimized C/FORTRAN and call from Julia. Indeed, MaBLAS, which you linked, is built on top of LoopVectorization.jl.

I don't know how well ArnoldiMethod.jl compares with ARPACK, but if there is a gap my suggestion is simply that these recent developments might help bridge it :)

FWIW, MaBLAS currently does not depend on LoopVectorization.jl, the code to generate kernels is all handwritten.

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