Diagonalization hermitian matrices julia vs fortran

Question

I have a program written in Fortran and in Julia, one of the cases I have symmetric matrices and I get results more or less similar with both programs. When I switch to a case where I have hermitian matrices, the program in Julia and the program in Fortran give me different stuff. I would guess that maybe the difference comes from the diagonalization procedure, in Fortran I use:

ZHEEVD(..)

while in Julia I simply use:

eig(matrix)

The first thing that I notice is that ZHEEVD fixes the first row of the eigenvector matrices to real numbers (no imaginary part), while eig fixes the last row to real numbers.

Any idea how to overcome this tiny differences? Any more info that can be useful when dealing with julia's linear algebra built-ins?

Answer 1

Digging in to the Julia methods (the @less macro is very handy for this), you'll find that it eventually calls the LAPACK.syevr! method, which in the Complex128 case is a wrapper for the ZHEEVR LAPACK method (scroll down a bit to see the actual definition).

If you'd prefer to keep using ZHEEVD, you can access it via the ccall interface: see the manual section on Calling C and Fortran code. The LAPACK wrappers linked above should provide plenty of examples (LAPACK comes as part of OpenBLAS, which is included in Julia, so you shouldn't need to install anything else).