I usually work with full diagonalisation of Hermitian matrices. After some research I realised that there are two options to retrieve the eigenvalues and eigenvectors of such a matrix.
eigen!(). From the source code of
eigen!() it seems that it is calling a general eigensolver routine called
LinearAlgebra.LAPACK.syev!() routine required some digging into the source code to figure out that it is also intended for Hermitian matrices (docs.julialang.org only talks about symmetric matrices). I realised that it is calling specialised Hermitian routines in LAPACK.
Now after building up a 2000x2000 Hermitian matrix I called both routines the following way and timed their peformance:
H = weyl(10, 10, 10) Ht = deepcopy(H) @time eigsys = LAPACK.syev!('V', 'U', H) @time eigsyst = eigen!(Hermitian(Ht))
To my surprise the
eigen! routine is quite a bit faster:
8.998029 seconds (6 allocations: 1.068 MiB) 6.128692 seconds (16 allocations: 123.658 MiB, 1.71% gc time)
To me this is quite counterintuitive behaviour. I would have guessed that the specialised routines should work faster.