[Wien] Possible bugs in Mixer

[Guoping Zhang]

Thank you so  much for your speedy help, Laurie!

I really hope there is no issue here, but when I examined the eigenvalues,
I noticed the agreement deteriorates as iteration goes on. In addition,
the momentum matrix elements between bands differ a lot.
Since the first three iterations have no difference, I suspect the mixer
could lead to the difference.
In case.scfm UYTF(J) differs by a minus sign,
:INFO Fp Singular value   3.497E+00 Weight  1.0000E+00 Projections
 -1.728E+02  4.561E+00
:INFO Fp Singular value   3.497E+00 Weight  1.0000E+00 Projections
 -1.728E+02 -4.561E+00
but this may not be the main course.

Do you have any suggestions where I should check to pin down this
disagreement?

(I have the same compiler version, and the codes are the same. the outputs
from both machines are exactly the same for the first three iterations).

Thanks a lot!

Guoping






On Fri, Dec 19, 2025 at 12:10 PM Laurence Marks <laurence.marks at gmail.com>
wrote:

> 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 <gpzhang.physics at gmail.com>
> 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
>>
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