Accelerating repeated eigenvalue searches

[juthohaegeman]

@bremez

Perhaps related to the previous item: Using this example to multithread over the set M_iMiM_i, nthreads=4, (i) LinearAlgebra.eigvals! speeds up roughly 3x, whereas (ii) KrylovKit.eigsolve is 2x slower than single-threaded, coincidentally wiping out the advantage and giving comparable runtimes (but with the extra memory usage). Perhaps memory bandwidth issue? So from best to worse, single-thread Krylov → (multithreaded Krylov, multithreaded eigvals) → single-thread eigvals. Thoughts?

Not sure why this happens, but you can disable the multithreading that is within KrylovKit using KrylovKit.disable_threads(). I assume there is some conflict between the threading of BLAS in the matrix vector multiplication, and the threading in KrylovKit, although the latter is purely restricted to the “native KrylovKit” parts of the code where there are no BLAS calls or function calls to the linear operator going on.