LMDIF failing due to numerical instability

[rdemaria]

We have an example that returns this error message

call: 4 Penalty function = 0.24802178E-03
call: 9 Penalty function = 0.24262925E-03
call: 13 Penalty function = 0.24118050E-03
Maximum Iteration exceeded in HQR2, increase MAXITER: 150
Unable to find eigenvalues for matrix:
1.955019 118.250905 -0.002977 -0.405826 0.000000 -1.248031
-0.050003 -2.512961 0.000109 0.004085 0.000000 0.047542
-0.021011 -0.370349 -2.808226 208.566941 0.000000 -0.476444
-0.000286 -0.006570 -0.035093 2.250267 0.000000 -0.006737
-0.030547 -2.485026 -0.002193 0.347135 1.000000 -9.042964
0.000000 0.000000 0.000000 0.000000 0.000000 1.000000

+-+-+- fatal: LASEIG Unable to find eigenvalues for matrix

STOP 1

This is strange since the matrix looks innocent.

[rdemaria]

Same file with version 5.02.00 gives

Initial Penalty Function = 0.34334641E-01

call: 4 Penalty function = 0.24802178E-03
call: 9 Penalty function = 0.24262925E-03
call: 13 Penalty function = 0.24118050E-03
call: 35 Penalty function = 0.24118050E-03
++++++++++ LMDIF ended: converged without success
call: 35 Penalty function = 0.24118050E-03

Please note that up to calls 13 results are identical.

[rdemaria]

Sample file is /afs/cern.ch/user/r/rdemaria/public/forfrederik/hl10_injection_chrom_20_oct_-5_B4.44

Please contact Frederik or Pascal for follow-ups and additional sample files.

It cannot be simplified for obvious reasons, since it is impossible to reproduce the same numerical conditions.

[tpersson]

Hi Riccardo, I don't have any immediate idea what the problem could be. Laurent and I are away this week but I will try to have a look next week. cheers Tobias

…

________________________________ From: Riccardo De Maria [notifications@github.com] Sent: 28 July 2017 19:48 To: MethodicalAcceleratorDesign/MAD-X Cc: Subscribed Subject: Re: [MethodicalAcceleratorDesign/MAD-X] LMDIF failing due to numerical instability (#455) Sample file is /afs/cern.ch/user/r/rdemaria/public/forfrederik/hl10_injection_chrom_20_oct_-5_B4.44 Please contact Frederik or Pascal for follow-ups and additional sample files. It cannot be simplified for obvious reasons, since it is impossible to reproduce the same numerical conditions. — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub<#455 (comment)>, or mute the thread<https://github.com/notifications/unsubscribe-auth/AFBJZq5V-_Qd5lfVdJBLpcTi3jrpFhvJks5sSh7RgaJpZM4Om3Jk>.

[tpersson]

Hi,
The calculation of the eigenvalues are done using an iterative algorithm. I don't know why it failed on this matrix. Before it had 150 as maximum iteration, this is now increased to 250 (but even 200 works fine). The eigenvalue I receive for the matrix are consistent with what I get from Octave (see below).
The mask seem to run fine now and I talked to Pascal that the new version is committed to the master and in case there is any other problems they would let us know. I will close this issue for now but in case there is some other issues please let us know.

cheers
Tobias

---

From Madx

-0.28560087625336017 0.95834865236163191i
-0.28560087625336017 -0.95834865236163191i
-0.27234930479082209 0.96219844947897903i
-0.27234930479082209 -0.96219844947897903i
From Octave
-0.285601 + 0.958391i
-0.285601 - 0.958391i
-0.272349 + 0.962187i
-0.272349 - 0.962187i