[acidflask]

Most people don't need more than a handful of linear algebra operations (or think they don't), so Breeze and most wrappers of LAPACK or similar libraries don't implement or wrap them. But most people who work seriously on numerical routines will quickly run into performance problems if all they do is call LAPACK routines for general matrices instead of taking advantage of matrix structure.

I have yet to come across any other linear algebra library for any other high level language that provides the depth of integration available in the Julia base library. Want all eigenvalues of a symmetric tridiagonal 10x10 matrix between 1.0 and 12.0? Simply call T=SymTridiagonal(randn(10), randn(9)); eigvals(T, 1.0, 12.0). Or if you want to work closer to LAPACK, simply call LAPACK.stein!. I don't see a wrapper in Breeze or SciPy for this function. Want an LU factorization on a matrix of high precision floats? lufact(big(randn(5,4))). And so on.

Julia may not have everything users want, but its base library really tries to make matrix computations easy and accessible.

[lmm]

Something like the Scala type system seems like the best way to keep track of that kind of structure information and make use of it (perhaps even transparently). I can easily believe the current wrappers aren't there yet though. (Afraid I switched jobs six months ago and haven't been using Breeze or Spark since, so I can't justify working on it myself at the moment)

[conjectures]

+1 this kind of issue is why I went for Julia - the support for lin alg (including with CUDA) is very good indeed.

The other issue being that Julia gives fine grained control over a cluster in a way something more abstract couldn't. (After cobbling together a scripting-style map reducer based on the default functionality - ClusterUtils.jl.)