Add W_v output eigenvalues fix

[bford26]

Potential Bug find and Fix.

Comparisons between W_t and reconstructed matrix from eigen values and vectors was not working.

Matrix reconstruction tests were done with this script. (both before and after changes are included in comments of script)
dcon_W_reconstruction_test.py

The changes to dcon/free.f and dcon/dcon_netcdf.f now reflect that 'ev' is defined as explicitly real eigenvalues.

This can be seen from the call to zheev line305, ev needs to be real zheev doc

[jhalpern30]

Question on this - I believe Wv should be Hermitian, but can accumulate numerical errors (like Wp). In vacuum, it is forced Hermitian with lsymz (line 526 of vacuum_vac.f), which is set to true for most of the gpec example inputs. From my understanding, it seems like this fix assumes lsymz = t, correct? But this is technically still a quantity exposed to the user. So what happens with this fix if lsymz = f?

If this breaks, perhaps another option is to use zgeev for the Wv matrix in free.f as well to avoid making any Hermitian assumptions, since this isn't a numerically costly section of the code so zheev vs. zgeev isn't going to make much of a difference in terms of runtime. But open to thoughts on this

[matt-pharr]

I agree with @jhalpern30

[bford26]

So not sure if this fixes the lsymz = false case. (i tested it with lsymz false and got similar output, so that means it's fine? The simple fix might just be using a new variable ev_real ?

The versions i tested reinstate ev as COMPLEX(r8). From the outputs i test, the ev_real addition seems to work best.

  CALL zheev('V','U',mpert,wv,mpert,ev_real,work,lwork,rwork,info)
  ev = CMPLX(ev_real, 0.0_r8, KIND=r8)

vs

  lwork=2*mpert+1
  CALL zgeev('V','V',mpert,wv,mpert,ev,
 $     vl,mpert,vr,mpert,work2,lwork,rwork2,info)
  eindex(1:mpert)=(/(ipert,ipert=1,mpert)/)
  CALL bubble(REAL(ev),eindex,1,mpert)
  tt=ev
  DO ipert=1,mpert
     wv(:,ipert)=vr(:,eindex(mpert+1-ipert))
     ev(ipert)=tt(eindex(mpert+1-ipert))
  ENDDO

Test Script:
test_Wreconstruct_script.py

Test outputs:
w_reconstruct_outputs.txt