There is no issue. You can multiply U & VT by -1 and the decomposition and the inverse is identical -- see for instance https://en.wikipedia.org/wiki/Singular_value_decomposition about the non-uniqueness and a stack of more informational. The mixer uses the decomposition for a regularized inverse where this does not matter.
___ Emeritus Professor Laurence Marks (Laurie) Department of Materials Science and Engineering, Northwestern University www.numis.northwestern.edu "Research is to see what everybody else has seen, and to think what nobody else has thought" Albert Szent-Györgyi On Fri, Dec 19, 2025, 10:35 Guoping Zhang <[email protected]> wrote: > Dear Profs. Blaha and Marks and wien users, > > I have a question on how the new Mixer is implemented as it gives me > different results on different computers. Different results mean that > the eigenvalues differ by 10^-6 ry, so the wavefunctions are even > worse. I am using wien2k_13 version, but there is no difference for > newer versions. > > > In FprojmemR1m.F, call DGESVD gets SVD of Vect, but SVD normally > produces an arbitrary sign for U and VT for the same Vect like > vect 1 1 1.7542057564 > vect 1 2 1.7522638412 > vect 2 1 1.7441856025 > vect 2 2 1.7425017533 > > In one case, my U is > > > debug3c.outputm:MMT91 U VT 1 1 -0.7091042206 -0.7074733729 > debug3c.outputm:MMT91 U VT 1 2 -0.7051036834 -0.7067399994 > debug3c.outputm:MMT91 U VT 2 1 -0.7051036834 -0.7067399994 > debug3c.outputm:MMT91 U VT 2 2 0.7091042206 0.7074733729 > > Another case has > > debug11.outputm:MMT91 U VT 1 1 0.7091042206 0.7074733728 > debug11.outputm:MMT91 U VT 1 2 -0.7051036834 0.7067399994 > debug11.outputm:MMT91 U VT 2 1 0.7051036834 -0.7067399994 > debug11.outputm:MMT91 U VT 2 2 0.7091042206 0.7074733728 > > I run 4 iterations to activate the mixer. When I diff case.scf, these two > cases have no difference to the last digit, > > But after the mixing, it differs a lot though the total energy is the > same (which is not my interest). > > My questions are (1) whether the new mixer finally uses some products > like (U x VT) to generate the new charge density, and (2) whether you > have examples that I use to verify this arbitrary sign does not matter. > > Thank you so much in advance! > > Best wishes, > > Guoping > > _______________________________________________ > Wien mailing list > [email protected] > http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien > SEARCH the MAILING-LIST at: > http://www.mail-archive.com/[email protected]/index.html >
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