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<p class="MsoNormal">Yes, though there’s no reason to use SVD. The right way is to use a transposed QR decomposition, which I’ll refer to as a PLQ decomposition. The P is a permutation matrix which we’ll ignore for these purposes, it’s just to help with numerics.
The idea is that you have<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">[L 0][Q1 Q2]^T x = b<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">The columns of Q2 define the space that locally leaves the match in place. QR is direct whereas SVD is iterative, and thus is generally preferable, and SVD intrinsically assumes that orthogonality (i.e., symmetry under rotations) somehow
makes sense in both spaces, which it really doesn’t in the beta function match space.<o:p></o:p></p>
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<p class="MsoNormal">-Scott<o:p></o:p></p>
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<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif">From:</span></b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif"> FFA_CEBAF_Collab <ffa_cebaf_collab-bounces@jlab.org>
<b>On Behalf Of </b>Nick Sereno via FFA_CEBAF_Collab<br>
<b>Sent:</b> Friday, April 4, 2025 12:24 PM<br>
<b>To:</b> Alex Bogacz via FFA_CEBAF_Collab <ffa_cebaf_collab@jlab.org>; Ryan Bodenstein <ryanmb@jlab.org>; Brooks, Stephen <sbrooks@bnl.gov><br>
<b>Subject:</b> Re: [FFA_CEBAF_Collab] [EXTERNAL] Re: FFA@CEBAF WG mtg. this Friday, April 4<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><span style="color:black">Hi Scott,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="color:black">You said something interesting during the meeting I did not quite hear as the audio was going in and out at my end.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="color:black">I think you said to Donish that to understand how to keep the twiss/dispersion parameters constant while trying to<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black">set the R56 to what one wants. You described to consider the matrix equation:<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="color:black">D<b>x</b> = <b>b</b><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="color:black">where <b>x</b> is the vector of quad strengths,
<b>b</b> is the vector of beta functions/dispersion and you want to find the linear combinations<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black">of quad strengths that don't change the vector
<b>b. </b>I think you are searching for the null space of D (the matrix of derivatives) which<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black">can be found using SVD of the matrix D assumed to not be of full rank. Anyway, that was my interpretation of what I partially heard<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black">you say but I think you used a different algorithm to obtain the null space.<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="color:black">Is this the correct interpretation of what you said?<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="color:black">Thanks,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black">Nick<o:p></o:p></span></p>
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<p class="MsoNormal"><b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:black">From:</span></b><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:black"> FFA_CEBAF_Collab <<a href="mailto:ffa_cebaf_collab-bounces@jlab.org">ffa_cebaf_collab-bounces@jlab.org</a>>
on behalf of Brooks, Stephen via FFA_CEBAF_Collab <<a href="mailto:ffa_cebaf_collab@jlab.org">ffa_cebaf_collab@jlab.org</a>><br>
<b>Sent:</b> Friday, April 4, 2025 12:09 PM<br>
<b>To:</b> Alex Bogacz via FFA_CEBAF_Collab <<a href="mailto:ffa_cebaf_collab@jlab.org">ffa_cebaf_collab@jlab.org</a>>; Ryan Bodenstein <<a href="mailto:ryanmb@jlab.org">ryanmb@jlab.org</a>><br>
<b>Subject:</b> [FFA_CEBAF_Collab] [EXTERNAL] Re: FFA@CEBAF WG mtg. this Friday, April 4</span>
<o:p></o:p></p>
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<p class="MsoNormal"> <o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:11.0pt">Sorry I was in a project review for a different FFA(!)<br>
<br>
-Stephen<br>
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________________________________________<br>
From: FFA_CEBAF_Collab <<a href="mailto:ffa_cebaf_collab-bounces@jlab.org">ffa_cebaf_collab-bounces@jlab.org</a>> on behalf of Ryan Bodenstein via FFA_CEBAF_Collab <<a href="mailto:ffa_cebaf_collab@jlab.org">ffa_cebaf_collab@jlab.org</a>><br>
Sent: 04 April 2025 12:08<br>
To: Alex Bogacz via FFA_CEBAF_Collab<br>
Subject: Re: [FFA_CEBAF_Collab] FFA@CEBAF WG mtg. this Friday, April 4<br>
<br>
Dear Colleagues,<br>
<br>
Thanks for the good discussion!<br>
<br>
Attached are the minutes.<br>
<br>
Cheers!<br>
Ryan<br>
<br>
From: FFA_CEBAF_Collab <<a href="mailto:ffa_cebaf_collab-bounces@jlab.org">ffa_cebaf_collab-bounces@jlab.org</a>> on behalf of Alex Bogacz via FFA_CEBAF_Collab <<a href="mailto:ffa_cebaf_collab@jlab.org">ffa_cebaf_collab@jlab.org</a>><br>
Date: Monday, March 31, 2025 at 5:54</span><span style="font-size:11.0pt;font-family:"Arial",sans-serif"> </span><span style="font-size:11.0pt">PM<br>
To: Alex Bogacz via FFA_CEBAF_Collab <<a href="mailto:ffa_cebaf_collab@jlab.org">ffa_cebaf_collab@jlab.org</a>><br>
Subject: [FFA_CEBAF_Collab] FFA@CEBAF WG mtg. this Friday, April 4<br>
<br>
Dear Colleagues,<br>
We will continue our design efforts this Friday, April 4, at 11:00 am.<br>
<br>
* Splitter design, update - Donish<br>
* AOB - ALL<br>
Please, follow a ZOOM invitation below.<br>
Cheers,<br>
Alex<br>
___________________________________<br>
S. Alex Bogacz,<br>
Accelerator Physics Group Leader<br>
Center for Advanced Studies of Accelerators<br>
Jefferson Lab<br>
<br>
ZOOM connection:<br>
<br>
The link is here: <a href="https://urldefense.proofpoint.com/v2/url?u=https-3A__jlab-2Dorg.zoomgov.com_j_1614898082-3Fpwd-3DTnUzMS81M2sxbDZIbERJU01tYkJCQT09&d=DwIGaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=Ogg4WFNBwvADBq3fkmCLiJ7SaRDPYtawHzJElJMB0jE&m=te-lLg-vSoDwMBjseLUaw3xcu5jYz_Ny2M_wPF-XRVjsU8ew333N0xZUJYc3Tyxf&s=YoiFqr2WlLAR-C_sjdSO0tKTuWhfq-X7S3CyO19BDuc&e=">
https://urldefense.proofpoint.com/v2/url?u=https-3A__jlab-2Dorg.zoomgov.com_j_1614898082-3Fpwd-3DTnUzMS81M2sxbDZIbERJU01tYkJCQT09&d=DwIGaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=Ogg4WFNBwvADBq3fkmCLiJ7SaRDPYtawHzJElJMB0jE&m=te-lLg-vSoDwMBjseLUaw3xcu5jYz_Ny2M_wPF-XRVjsU8ew333N0xZUJYc3Tyxf&s=YoiFqr2WlLAR-C_sjdSO0tKTuWhfq-X7S3CyO19BDuc&e=</a>
<<a href="https://urldefense.com/v3/__https:/jlab-org.zoomgov.com/j/1614898082?pwd=TnUzMS81M2sxbDZIbERJU01tYkJCQT09__;!!P4SdNyxKAPE!Gg4oWbBxGQSSg8iwfieUq9U3j7MLZUDVF3-z6-GshsiVO1GzyT-yu_oHm98C03qrmvDK_S9hywyxdaOgEjjrXV0hnro$%20">https://urldefense.com/v3/__https://jlab-org.zoomgov.com/j/1614898082?pwd=TnUzMS81M2sxbDZIbERJU01tYkJCQT09__;!!P4SdNyxKAPE!Gg4oWbBxGQSSg8iwfieUq9U3j7MLZUDVF3-z6-GshsiVO1GzyT-yu_oHm98C03qrmvDK_S9hywyxdaOgEjjrXV0hnro$
</a>><br>
<br>
In case of problems, the zoom room is below:<br>
Meeting ID: 161 489 8082<br>
Passcode: 123456<br>
________________________<br>
<br>
<br>
<br>
_______________________________________________<br>
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<a href="https://mailman.jlab.org/mailman/listinfo/ffa_cebaf_collab">https://mailman.jlab.org/mailman/listinfo/ffa_cebaf_collab</a><o:p></o:p></span></p>
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