<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><br><div><div>On Jan 15, 2008, at 9:00 AM, Min Seung Kyu wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite">Dear users and developers,<br><br>I have a question about eigenfunctions in PWSCF codes.<br><br>I looked at PWSCF source files and I found that the 'evc' variable is <br>KS eigenvectors in G-space, right?<br><br>Because Hamiltonian matrix H(G,G') is hermitian, 'evc' should be real.</blockquote><div><br class="webkit-block-placeholder"></div>Who said this? </div><div><br class="webkit-block-placeholder"></div><div>The eigenvalues of a Hermitean matrix are real, the eigenvectors not necessarily so. If in addition to being Hermitean the matrix is also real (which implies it is symmetric), the the eigenvectors CAN BE CHOSEN to be real. If you feed a real matrix to a complex eigenvalue solver, then the eigenvectors will most probably come out complex, but can they be easily converted to real (if needed) by an appropriate choice of phases (again, if the original matrix is real symmetric, not merely Hermitean)</div><div><br class="webkit-block-placeholder"></div><div>Hope this helps</div><div>Stefano</div><div><br><blockquote type="cite"><br><br>When I print out 'evc', however, 'evc' contains imaginary parts.<br><br>For example, when I run 'co.rx.in' (example03 folder), I got these values:<br><br> DBLE(evc(1:4,1)) 0.186884 0.154551 0.154551 0.142085<br>AIMAG(evc(1:4,1)) 0.000000 0.000000 0.000000 -0.048560<br> DBLE(evc(1:4,2)) -0.024799 -0.021751 -0.021751 -0.068645<br>AIMAG(evc(1:4,2)) 0.000000 0.000000 0.000000 -0.145963<br> DBLE(evc(1:4,3)) 0.000000 0.000000 0.000000 0.000000<br>AIMAG(evc(1:4,3)) 0.000000 -0.005668 0.152298 0.000000<br> DBLE(evc(1:4,4)) 0.000000 0.000000 0.000000 0.000000<br>AIMAG(evc(1:4,4)) 0.000000 -0.152298 -0.005668 0.000000<br> DBLE(evc(1:4,5)) -0.299154 -0.185970 -0.185970 0.011252<br>AIMAG(evc(1:4,5)) 0.000000 0.000000 0.000000 0.168998<br><br>( I added 'WRITE(*,*) evc(1:4,ibnd)' in 'sum_band.f90'. )<br><br>What is the problem?<br><br>Thank you in advance.<br><br>Sincerely, Min.<br><br>-------------------------------Sig.---------------------------<br>Center for Superfunctional Materials, Department of Chemistry,<br>Pohang University of Science and Technology (POSTECH)<br><br>Mr. Seung Kyu, Min<br><br>Ph.D. Candidate<br><br>E-Mail: <a href="mailto:min0220@postech.ac.kr">min0220@postech.ac.kr</a><br>Tel. : 82-54-279-5858<br>----------------------------------------------<br><br><br><br><br><br>_______________________________________________<br>Pw_forum mailing list<br><a href="mailto:Pw_forum@pwscf.org">Pw_forum@pwscf.org</a><br>http://www.democritos.it/mailman/listinfo/pw_forum<br></blockquote></div><br><div> <span class="Apple-style-span" style="border-collapse: separate; 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