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<p>Hello Stefano</p>
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<p>I believe this was an issue that was discussed in another thread opened by me (this one I think: <a href="https://lists.mcs.anl.gov/pipermail/petsc-users/2021-April/043629.html" class="OWAAutoLink" id="LPlnk77785" previewremoved="true">https://lists.mcs.anl.gov/pipermail/petsc-users/2021-April/043629.html</a>).</p>
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<p>In any case thanks for fixing it, and glad to be of service!</p>
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<p>- Peder</p>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>Fra:</b> Stefano Zampini <stefano.zampini@gmail.com><br>
<b>Sendt:</b> 2. juni 2021 21:43:43<br>
<b>Til:</b> Peder Jørgensgaard Olesen<br>
<b>Cc:</b> Jose E. Roman; petsc-users@mcs.anl.gov<br>
<b>Emne:</b> Re: [petsc-users] SLEPc: non-real singular vectors from SVD of real matrix</font>
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<div>Peder
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<div class="">We have a fix for the hdf5 complex reader here if you want to give it a try
<a href="https://gitlab.com/petsc/petsc/-/merge_requests/4044" class="" id="LPlnk596682" previewremoved="true">
https://gitlab.com/petsc/petsc/-/merge_requests/4044</a>
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<a id="LPUrlAnchor_16226680419130.7919128806170257" href="https://gitlab.com/petsc/petsc/-/merge_requests/4044" target="_blank" style="text-decoration: none;">fix MatLoad_Dense_HDF5 (!4044) · Merge requests · PETSc / petsc · GitLab</a></div>
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follow-up !3903 add src/mat/tests/ex84.c...</div>
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<div>Sorry it took so long and thank you for reporting the bug</div>
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<blockquote type="cite" class="">
<div class="">On Apr 29, 2021, at 2:55 PM, Peder Jørgensgaard Olesen via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov" class="">petsc-users@mcs.anl.gov</a>> wrote:</div>
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<div class="" style="margin-top:0px; margin-bottom:0px">Thank you for your advice, Jose.</div>
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<div class="" style="margin-top:0px; margin-bottom:0px">I tried<span class="Apple-converted-space"> </span><span class="" style="font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; font-size:16px">using
a single column of the data matrix as a </span>basis for left singular vector space, and a row for the right one - and lo and behold, all singular vectors become real.</div>
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<div class="" style="margin-top:0px; margin-bottom:0px">Somehow it did not occur to me that I was I was looking at was simply a complex phase on U and V which would cancel upon computing UΣV*. In other words, rather than an incorrect result it was a slightly inconvenient
representation of a correct result.</div>
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<div class="" style="margin-top:0px; margin-bottom:0px">Best regards</div>
<div class="" style="margin-top:0px; margin-bottom:0px">Peder</div>
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<div id="x_divRplyFwdMsg" dir="ltr" class=""><font face="Calibri, sans-serif" class="" style="font-size:11pt"><b class="">Fra:</b><span class="Apple-converted-space"> </span>Jose E. Roman <<a href="mailto:jroman@dsic.upv.es" class="">jroman@dsic.upv.es</a>><br class="">
<b class="">Sendt:</b><span class="Apple-converted-space"> </span>29. april 2021 13:00:03<br class="">
<b class="">Til:</b><span class="Apple-converted-space"> </span>Peder Jørgensgaard Olesen<br class="">
<b class="">Cc:</b><span class="Apple-converted-space"> </span><a href="mailto:petsc-users@mcs.anl.gov" class="">petsc-users@mcs.anl.gov</a><br class="">
<b class="">Emne:</b><span class="Apple-converted-space"> </span>Re: [petsc-users] SLEPc: non-real singular vectors from SVD of real matrix</font>
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<div class="PlainText">In complex scalars there is no way of knowing if the user-provided matrix is real or not. If there was an option of MatSetOption() we could use it.<br class="">
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If you set a real initial vector with SVDSetInitialSpaces(), then most probably the computed singular vectors will be real. But still rounding errors could introduce a nonzero imaginary part.<br class="">
<br class="">
In any case, you could normalize the computed singular vectors, as is done for instance in FixSign() in this example<a href="https://slepc.upv.es/documentation/current/src/nep/tutorials/ex20.c.html" class="">https://slepc.upv.es/documentation/current/src/nep/tutorials/ex20.c.html</a><br class="">
<br class="">
Jose<br class="">
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> El 29 abr 2021, a las 12:42, Peder Jørgensgaard Olesen via petsc-users <<a href="mailto:petsc-users@mcs.anl.gov" class="">petsc-users@mcs.anl.gov</a>> escribió:<br class="">
><span class="Apple-converted-space"> </span><br class="">
> Hello<br class="">
><span class="Apple-converted-space"> </span><br class="">
> I've noticed that doing a singular value decomposition of a real matrix appears to result in non-real singular vectors. This should not be the case - singular vectors of a real matrix must be real-valued.<br class="">
><span class="Apple-converted-space"> </span><br class="">
> In the example attached I read a matrix from a binary file (also attached), perform the SVD, and write singular vectors to an HDF5 file which I subsequently inspect using h5dump, revealing non-zero imaginary parts of vector elements as highlighted below:<br class="">
> [pjool@svol mwes]$ h5dump -d U0_sample_svd -c "5,2" sample_svecs.h5<span class="Apple-converted-space"> </span><br class="">
> HDF5 "sample_svecs.h5" {<br class="">
> DATASET "U0_sample_svd" {<br class="">
> DATATYPE H5T_IEEE_F64LE<br class="">
> DATASPACE SIMPLE { ( 882, 2 ) / ( 882, 2 ) }<br class="">
> SUBSET {<br class="">
> START ( 0, 0 );<br class="">
> STRIDE ( 1, 1 );<br class="">
> COUNT ( 5, 2 );<br class="">
> BLOCK ( 1, 1 );<br class="">
> DATA {<br class="">
> (0,0): 0.0226108, 0.0299595,<br class="">
> (1,0): 0.035414, 0.0469237,<br class="">
> (2,0): 0.0276317, 0.0366122,<br class="">
> (3,0): 0.0145344, 0.0192581,<br class="">
> (4,0): 0.0110376, 0.0146249<br class="">
> }<br class="">
> }<br class="">
> ATTRIBUTE "complex" {<br class="">
> DATATYPE H5T_STD_I32LE<br class="">
> DATASPACE SCALAR<br class="">
> DATA {<br class="">
> (0): 1<br class="">
> }<br class="">
> }<br class="">
> }<br class="">
> }<br class="">
> I also extract the imaginary part of the input matrix and print its norm to ensure that the matrix is indeed real.<br class="">
><span class="Apple-converted-space"> </span><br class="">
> I'm running v3.14, but I don't believe that alone should cause the issue, since it what I'm trying to do appears like a rather common and basic task.<br class="">
><span class="Apple-converted-space"> </span><br class="">
> What might be the reason behind this behavior, and what can be done to resolve it?<br class="">
><span class="Apple-converted-space"> </span><br class="">
><span class="Apple-converted-space"> </span><br class="">
> Med venlig hilsen / Best Regards<br class="">
><span class="Apple-converted-space"> </span><br class="">
> Peder Jørgensgaard Olesen<br class="">
> PhD Student, Turbulence Research Lab<br class="">
> Dept. of Mechanical Engineering<br class="">
> Technical University of Denmark<br class="">
> Niels Koppels Allé<br class="">
> Bygning 403, Rum 105<br class="">
> DK-2800 Kgs. Lyngby<br class="">
> <read_bin.c><sample_data></div>
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