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TWISS drift with EXACT flag has errors in the time variable #1123

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merged 9 commits into from
Aug 15, 2022
Merged

TWISS drift with EXACT flag has errors in the time variable #1123

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b3c0bf0
Fix first order transfer map for a drift computed by TWISS when EXACT…
Jun 15, 2022
4123357
Define some intermediate values for the twiss exact drift case
Jun 17, 2022
6481e68
Fix errors in third order for exact drift in twiss.
Jun 17, 2022
5d38fa2
Simplification of the intermediate variables
Jun 17, 2022
3d10a8e
Rewrite formula for time in exact drift for better numerical precision
Jun 17, 2022
7d7fabd
Add test case for an exact drift to second order
Jun 21, 2022
693518f
Fix reference for test-twiss-16 main output
Jun 22, 2022
e4d7d90
Add code to handle nonzero DELTAP for EXACT flag to TWISS
Jun 22, 2022
ebace2d
Add line to Changes.md for fix to EXACT flag to TWISS
Jun 22, 2022
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3 changes: 2 additions & 1 deletion Changes.md
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Original file line number Diff line number Diff line change
@@ -1,5 +1,6 @@
MAD-X master
* [PR 1081](https://github.com/MethodicalAcceleratorDesign/MAD-X/pull/1108) Fix potential buffer overrun when node_name calls stoupper (S. Berg)
* (https://github.com/MethodicalAcceleratorDesign/MAD-X/pull/1123) Fix errors in the time variable with EXACT flag to TWISS (J. S. Berg)
* [PR 1081](https://github.com/MethodicalAcceleratorDesign/MAD-X/pull/1108) Fix potential buffer overrun when node_name calls stoupper (J. S. Berg)
* [PR 1107](https://github.com/MethodicalAcceleratorDesign/MAD-X/pull/1107) Stabizes few tests due to compiler dependent numerical noise (R. De Maria)
* [PR 1095](https://github.com/MethodicalAcceleratorDesign/MAD-X/pull/1095) Implement more robust, optional, PTC DA map output (L. Deniau)
* [PR 1088](https://github.com/MethodicalAcceleratorDesign/MAD-X/pull/1088) Additional explanation bv flag (J. Dilly)
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4 changes: 3 additions & 1 deletion Makefile_test
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Expand Up @@ -30,6 +30,8 @@
# added test-twiss-12 for sigma matrix calculation
# 2021-Sep-02 20:59:00 ghislain:
# added test-taper
# 2022-Jun-21 jsberg-bnl:
# added test-twiss-16 for exact TWISS drift compared to PTC
#################################################
# testsuite

Expand All @@ -55,7 +57,7 @@ test-track-7 test-track-8 test-track-9 test-track-10 test-track-11 test-track-12
test-track-acd test-track-rotations test-beambeam-npart \
test-twiss test-twiss-2 test-twiss-3 test-twiss-4 test-twiss-5 \
test-twiss-6 test-twiss-8 test-twiss-9 test-twiss-10 test-twiss-11 \
test-twiss-12 test-twiss-13 test-twiss-14 test-twiss-15 test-twiss-exact test-translation test-crabcavity \
test-twiss-12 test-twiss-13 test-twiss-14 test-twiss-15 test-twiss-16 test-twiss-exact test-translation test-crabcavity \
test-xrotation test-yrotation test-rotations test-interpolate test-rf-fringe \
test-cororbit test-cororbit-2 test-cororbit-3 test-cororbit-4 \
test-emit test-emit-2 \
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105 changes: 58 additions & 47 deletions src/twiss.f90
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Expand Up @@ -7159,7 +7159,8 @@ SUBROUTINE tmdrf(fsec,ftrk,orbit,fmap,dl,ek,re,te)
logical :: fsec, ftrk, fmap
double precision :: dl
double precision :: orbit(6), ek(6), re(6,6), te(6,6,6)
double precision :: px, py, pt, csq, l_pz, c3sq, c52sq
double precision :: px, py, pt, csq, l_pz
real(kind(1d0)) :: beti, dl3, dl5, pp2, ptb, ptot2, px2, py2, pz

!---- Initialize.
EK = zero
Expand All @@ -7171,56 +7172,66 @@ SUBROUTINE tmdrf(fsec,ftrk,orbit,fmap,dl,ek,re,te)
px = orbit(2)
py = orbit(4)
pt = orbit(6)

csq = 1 + 2*pt/beta + pt**2 - px**2 - py**2
l_pz = dl / sqrt(csq)
c3sq = csq**(3d0/2d0)
c52sq =csq**(5d0/2d0)

re(1,2) = dl/sqrt(csq) + dl*px**2/c3sq
re(1,4) = dl*px*py/c3sq
re(1,6) = dl*px*(-pt - 1d0/beta)/c3sq
re(3,2) = dl*px*py/c3sq
re(3,4) = dl/sqrt(csq) + dl*py**2/c3sq
re(3,6) = dl*py*(-pt - 1d0/beta)/c3sq
re(5,2) = -dl*px*(beta + pt)/c3sq
re(5,4) = -dl*py*(beta + pt)/c3sq
re(5,6) = -dl/sqrt(csq) - dl*(beta + pt)*(-pt - 1d0/beta)/c3sq
px2 = px*px
py2 = py*py

beti = 1/beta
ptb = beti + pt
ptot2 = 1 + pt*(2*beti + pt)
pp2 = (beta*gamma)**(-2)+px2+py2
csq = ptot2 - px2 - py2
pz = sqrt(csq)
l_pz = dl / pz
dl3 = l_pz / csq


re(1,2) = dl3*(ptot2 - py2)
re(1,4) = dl3*px*py
re(1,6) = -dl3*px*ptb
re(3,2) = re(1,4)
re(3,4) = dl3*(ptot2 - px2)
re(3,6) = -dl3*py*ptb
re(5,2) = re(1,6)
re(5,4) = re(3,6)
re(5,6) = dl3*pp2

if (fsec) then
te(1,2,2) = 3d0*dl*px/(2d0*c3sq) + 3d0*dl*px**3d0/(2d0*c52sq)
te(1,2,4) = dl*py/(2d0*c3sq) + 3d0*dl*px**2d0*py/(2d0*c52sq)
te(1,2,6) = dl*(-pt - 1d0/beta)/(2d0*c3sq) + dl*px**2d0*(-3d0*pt - 3d0/beta)/(2d0*c52sq)
te(1,4,2) = dl*py/(2d0*c3sq) + 3d0*dl*px**2d0*py/(2d0*c52sq)
te(1,4,4) = dl*px/(2d0*c3sq) + 3d0*dl*px*py**2d0/(2d0*c52sq)
te(1,4,6) = dl*px*py*(-3d0*pt - 3d0/beta)/(2d0*c52sq)
te(1,6,2) = dl*(-pt - 1d0/beta)/(2d0*c3sq) + 3d0*dl*px**2d0*(-pt - 1d0/beta)/(2d0*c52sq)
te(1,6,4) = 3d0*dl*px*py*(-pt - 1d0/beta)/(2d0*c52sq)
te(1,6,6) = -dl*px/(2d0*c3sq) + dl*px*(-3d0*pt - 3d0/beta)*(-pt - 1d0/beta)/(2d0*c52sq)
te(3,2,2) = dl*py/(2d0*c3sq) + 3d0*dl*px**2d0*py/(2d0*c52sq)
te(3,2,4) = dl*px/(2d0*c3sq) + 3d0*dl*px*py**2d0/(2d0*c52sq)
te(3,2,6) = dl*px*py*(-3d0*pt - 3d0/beta)/(2d0*c52sq)
te(3,4,2) = dl*px/(2d0*c3sq) + 3d0*dl*px*py**2d0/(2d0*c52sq)
te(3,4,4) = 3d0*dl*py/(2d0*c3sq) + 3d0*dl*py**3d0/(2d0*c52sq)
te(3,4,6) = dl*(-pt - 1d0/beta)/(2d0*c3sq) + dl*py**2d0*(-3d0*pt - 3d0/beta)/(2d0*c52sq)
te(3,6,2) = 3d0*dl*px*py*(-pt - 1d0/beta)/(2d0*c52sq)
te(3,6,4) = dl*(-pt - 1d0/beta)/(2d0*c3sq) + 3d0*dl*py**2d0*(-pt - 1d0/beta)/(2d0*c52sq)
te(3,6,6) = -dl*py/(2d0*c3sq) + dl*py*(-3d0*pt - 3d0/beta)*(-pt - 1d0/beta)/(2d0*c52sq)
te(5,2,2) = -dl*(beta + pt)/(2d0*c3sq) - 3d0*dl*px**2d0*(beta + pt)/(2d0*c52sq)
te(5,2,4) = -3d0*dl*px*py*(beta + pt)/(2d0*c52sq)
te(5,2,6) = -dl*px/(2d0*c3sq) - dl*px*(beta + pt)*(-3d0*pt - 3d0/beta)/(2d0*c52sq)
te(5,4,2) = -3d0*dl*px*py*(beta + pt)/(2d0*c52sq)
te(5,4,4) = -dl*(beta + pt)/(2d0*c3sq) - 3d0*dl*py**2d0*(beta + pt)/(2d0*c52sq)
te(5,4,6) = -dl*py/(2d0*c3sq) - dl*py*(beta + pt)*(-3d0*pt - 3d0/beta)/(2d0*c52sq)
te(5,6,2) = -dl*px/(2d0*c3sq) - 3d0*dl*px*(beta + pt)*(-pt - 1d0/beta)/(2d0*c52sq)
te(5,6,4) = -dl*py/(2d0*c3sq) - 3d0*dl*py*(beta + pt)*(-pt - 1d0/beta)/(2d0*c52sq)
te(5,6,6) = dl*(beta + pt)/(2d0*c3sq) - dl*(-pt - 1d0/beta)/c3sq - &
dl*(beta + pt)*(-3d0*pt - 3d0/beta)*(-pt - 1d0/beta)/(2d0*c52sq)
dl5 = 0.5d0*dl3/csq
te(1,2,2) = 3*dl5*px*(ptot2 - py2)
te(1,2,4) = dl5*py*(ptot2 + 2*px2 - py2)
te(1,2,6) = -dl5*ptb*(ptot2 + 2*px2 - py2)
te(1,4,2) = te(1,2,4)
te(1,4,4) = dl5*px*(ptot2 - px2 + 2*py2)
te(1,4,6) = -3*dl5*px*py*ptb
te(1,6,2) = te(1,2,6)
te(1,6,4) = te(1,4,6)
te(1,6,6) = dl5*px*(2*ptb*ptb + pp2)
te(3,2,2) = te(1,2,4)
te(3,2,4) = te(1,4,4)
te(3,2,6) = te(1,4,6)
te(3,4,2) = te(3,2,4)
te(3,4,4) = 3*dl5*py*(ptot2 - px2)
te(3,4,6) = -dl5*ptb*(ptot2 - px2 + 2*py2)
te(3,6,2) = te(3,2,6)
te(3,6,4) = te(3,4,6)
te(3,6,6) = dl5*py*(2*ptb*ptb + pp2)
te(5,2,2) = te(1,2,6)
te(5,2,4) = te(1,4,6)
te(5,2,6) = te(1,6,6)
te(5,4,2) = te(5,2,4)
te(5,4,4) = te(3,4,6)
te(5,4,6) = te(3,6,6)
te(5,6,2) = te(5,2,6)
te(5,6,4) = te(5,4,6)
te(5,6,6) = -3*dl5*pp2*ptb
endif

orbit(1) = orbit(1) + px*l_pz
orbit(3) = orbit(3) + py*l_pz
orbit(5) = orbit(5) + (dl/beta - (1d0/beta + pt) * l_pz)
ek(1) = px*l_pz
ek(3) = py*l_pz
ek(5) = dl*dtbyds + l_pz*(pt*(2*beti+pt)/(gamma*gamma) - px2 - py2)/(beta*beta*(ptb + beti*pz))

if (ftrk) orbit(1:5:2) = orbit(1:5:2) + ek(1:5:2)

else

re(1,2) = dl
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3 changes: 3 additions & 0 deletions tests/test-twiss-16/test-twiss-16-mad3.tfs.cfg
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1-9 * skip
10 * rel=1e-14
11-$ * skip
11 changes: 11 additions & 0 deletions tests/test-twiss-16/test-twiss-16-mad3.tfs.ref
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@ NAME %04s "MAD3"
@ TYPE %09s "SECTORMAP"
@ TITLE %08s "no-title"
@ ORIGIN %16s "5.08.01 Linux 64"
@ DATE %08s "21/06/22"
@ TIME %08s "13.30.36"
* NAME T122 T124 T126 T144 T146 T166 T322 T324 T326 T344 T346 T366 T522 T524 T526 T544 T546 T566
$ %s %le %le %le %le %le %le %le %le %le %le %le %le %le %le %le %le %le %le
"L$START" 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00
"O" 7.95552195596275907e-02 3.44810984420141561e-02 -2.95832272960501763e+00 2.65296302746198774e-02 -1.19954398173697098e-03 7.63998146067667028e-02 3.44810984420141561e-02 2.65296302746198774e-02 -1.19954398173697098e-03 1.03429206342507532e-01 -2.95895941064147783e+00 9.93197589887966914e-02 -2.95832272960501763e+00 -1.19954398173697098e-03 7.63998146067667028e-02 -2.95895941064147783e+00 9.93197589887966914e-02 -2.60638736213083666e+00
"L$END" 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00
4 changes: 4 additions & 0 deletions tests/test-twiss-16/test-twiss-16-ptc.tfs.cfg
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1-91 * skip
92 2-8 rel=1e-14
92 10-18 rel=1e-14
93-$ * skip
93 changes: 93 additions & 0 deletions tests/test-twiss-16/test-twiss-16-ptc.tfs.ref
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@ NAME %09s "PTC_TWISS"
@ TYPE %05s "TWISS"
@ SEQUENCE %01s "L"
@ PARTICLE %06s "PROTON"
@ MASS %le 9.38272088159999962e-01
@ CHARGE %le 1.00000000000000000e+00
@ ENERGY %le 2.00000000000000000e+00
@ PC %le 1.76625181912995433e+00
@ GAMMA %le 2.13157784957890328e+00
@ KBUNCH %le 1.00000000000000000e+00
@ BCURRENT %le 7.49214795614770220e-12
@ SIGE %le 1.00000000000000002e-03
@ SIGT %le 1.00000000000000000e+00
@ NPART %le 1.00000000000000000e+00
@ EX %le 1.00000000000000000e+00
@ EY %le 1.00000000000000000e+00
@ ET %le 1.00000000000000002e-03
@ DELTAP %le 0.00000000000000000e+00
@ LENGTH %le 5.00000000000000000e+00
@ ALPHA_C %le -1.00000000000000000e+06
@ ALPHA_C_P %le -1.00000000000000000e+06
@ ALPHA_C_P2 %le -1.00000000000000000e+06
@ ALPHA_C_P3 %le -1.00000000000000000e+06
@ ETA_C %le -1.00000000000000000e+06
@ GAMMA_TR %le -1.00000000000000000e+06
@ Q1 %le 2.18662318680467038e-01
@ Q2 %le 2.18664509460172629e-01
@ DQ1 %le -1.00000000000000000e+06
@ DQ2 %le -1.00000000000000000e+06
@ QS %le -1.00000000000000000e+06
@ BETA_X_MIN %le 9.97668990890940632e-01
@ BETA_X_MAX %le 2.60683049153817414e+01
@ BETA_Y_MIN %le 9.97668990890940632e-01
@ BETA_Y_MAX %le 2.60719028755598323e+01
@ BETA11MIN %le 9.97668990890940632e-01
@ BETA11MAX %le 2.60683048258232652e+01
@ BETA12MIN %le 0.00000000000000000e+00
@ BETA12MAX %le 4.58189068032043954e-07
@ BETA13MIN %le 0.00000000000000000e+00
@ BETA13MAX %le 3.49033090966918268e-03
@ BETA21MIN %le 0.00000000000000000e+00
@ BETA21MAX %le 4.58189068032043954e-07
@ BETA22MIN %le 9.97668990890940632e-01
@ BETA22MAX %le 2.60719027859889927e+01
@ BETA23MIN %le 0.00000000000000000e+00
@ BETA23MAX %le 5.89865923734092003e-03
@ BETA31MIN %le 0.00000000000000000e+00
@ BETA31MAX %le 3.37266836437332459e-03
@ BETA32MIN %le 0.00000000000000000e+00
@ BETA32MAX %le 5.69980953579091783e-03
@ BETA33MIN %le 9.64036571539015785e-01
@ BETA33MAX %le 3.20267140640042713e+00
@ DISP1MIN %le -5.96572604168680853e-02
@ DISP1MAX %le 0.00000000000000000e+00
@ DISP2MIN %le 0.00000000000000000e+00
@ DISP2MAX %le 0.00000000000000000e+00
@ DISP3MIN %le -7.75544385419285193e-02
@ DISP3MAX %le 0.00000000000000000e+00
@ DISP4MIN %le 0.00000000000000000e+00
@ DISP4MAX %le 0.00000000000000000e+00
@ ORBIT_X %le 0.00000000000000000e+00
@ ORBIT_PX %le 1.00000000000000002e-02
@ ORBIT_Y %le 0.00000000000000000e+00
@ ORBIT_PY %le 1.29999999999999994e-02
@ ORBIT_PT %le -1.70000000000000012e-02
@ ORBIT_T %le 0.00000000000000000e+00
@ XCORMS %le 4.16337111554961822e-02
@ PXCORMS %le 1.00000000000000002e-02
@ YCORMS %le 5.41238245021450348e-02
@ PYCORMS %le 1.29999999999999994e-02
@ TCORMS %le 2.08157583830212087e-02
@ PTCORMS %le 1.70000000000000012e-02
@ XCOMIN %le 0.00000000000000000e+00
@ XCOMAX %le 5.09906742146927355e-02
@ PXCOMIN %le 1.00000000000000002e-02
@ PXCOMAX %le 1.00000000000000002e-02
@ YCOMIN %le 0.00000000000000000e+00
@ YCOMAX %le 6.62878764791005604e-02
@ PYCOMIN %le 1.29999999999999994e-02
@ PYCOMAX %le 1.29999999999999994e-02
@ TCOMIN %le -2.54939933237317007e-02
@ TCOMAX %le -0.00000000000000000e+00
@ PTCOMIN %le -1.70000000000000012e-02
@ PTCOMAX %le -1.70000000000000012e-02
@ TITLE %08s "no-title"
@ ORIGIN %16s "5.08.01 Linux 64"
@ DATE %08s "21/06/22"
@ TIME %08s "13.30.36"
* NAME KEYWORD S X PX Y PY T PT DISP1 DISP2 RE12 RE14 RE16 RE32 RE34 RE36 RE52 RE54 RE56
$ %s %s %le %le %le %le %le %le %le %le %le %le %le %le %le %le %le %le %le %le
"L$START" "MARKER" 0.00000000000000000e+00 0.00000000000000000e+00 1.00000000000000002e-02 0.00000000000000000e+00 1.29999999999999994e-02 -0.00000000000000000e+00 -1.70000000000000012e-02 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00
"O" "DRIFT" 5.00000000000000000e+00 5.09906742146927355e-02 1.00000000000000002e-02 6.62878764791005604e-02 1.29999999999999994e-02 -2.54939933237317007e-02 -1.70000000000000012e-02 -5.96572604168680853e-02 0.00000000000000000e+00 5.09959773444608544e+00 6.89406869855017164e-04 -5.91480000693044086e-02 6.89406869855017164e-04 5.09996365040008470e+00 -7.68924000900957361e-02 -5.91480000693044086e-02 -7.68924000900957222e-02 1.49795370600283739e+00
"L$END" "MARKER" 5.00000000000000000e+00 5.09906742146927355e-02 1.00000000000000002e-02 6.62878764791005604e-02 1.29999999999999994e-02 -2.54939933237317007e-02 -1.70000000000000012e-02 -5.96572604168680853e-02 0.00000000000000000e+00 5.09959773444608544e+00 6.89406869855017164e-04 -5.91480000693044086e-02 6.89406869855017164e-04 5.09996365040008470e+00 -7.68924000900957361e-02 -5.91480000693044086e-02 -7.68924000900957222e-02 1.49795370600283739e+00
3 changes: 3 additions & 0 deletions tests/test-twiss-16/test-twiss-16-ptc3.tfs.cfg
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1-9 * skip
10 * rel=1e-14
11-$ * skip
11 changes: 11 additions & 0 deletions tests/test-twiss-16/test-twiss-16-ptc3.tfs.ref
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@ NAME %04s "PTC3"
@ TYPE %04s "USER"
@ TITLE %08s "no-title"
@ ORIGIN %16s "5.08.01 Linux 64"
@ DATE %08s "21/06/22"
@ TIME %08s "13.30.36"
* NAME TXPP TXPQ TXPD TXQQ TXQD TXDD TYPP TYPQ TYPD TYQQ TYQD TYDD TTPP TTPQ TTPD TTQQ TTQD TTDD
$ %s %le %le %le %le %le %le %le %le %le %le %le %le %le %le %le %le %le %le
"L$START" 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 0.00000000000000000e+00 -0.00000000000000000e+00 -0.00000000000000000e+00 -0.00000000000000000e+00 -0.00000000000000000e+00 -0.00000000000000000e+00 -0.00000000000000000e+00
"O" 7.95552195596276046e-02 6.89621968840283123e-02 -5.91664545921003615e+00 2.65296302746198809e-02 -2.39908796347394282e-03 7.63998146067667305e-02 3.44810984420141631e-02 5.30592605492397548e-02 -2.39908796347394282e-03 1.03429206342507546e-01 -5.91791882128295654e+00 9.93197589887967469e-02 -2.95832272960501808e+00 -2.39908796347394282e-03 1.52799629213533406e-01 -2.95895941064147827e+00 1.98639517977593438e-01 -2.60638736213083977e+00
"L$END" 7.95552195596276046e-02 6.89621968840283123e-02 -5.91664545921003615e+00 2.65296302746198809e-02 -2.39908796347394282e-03 7.63998146067667305e-02 3.44810984420141631e-02 5.30592605492397548e-02 -2.39908796347394282e-03 1.03429206342507546e-01 -5.91791882128295654e+00 9.93197589887967469e-02 -2.95832272960501808e+00 -2.39908796347394282e-03 1.52799629213533406e-01 -2.95895941064147827e+00 1.98639517977593438e-01 -2.60638736213083977e+00
4 changes: 4 additions & 0 deletions tests/test-twiss-16/test-twiss-16-twiss.tfs.cfg
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