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Merge pull request #1123 from jsberg-bnl/twiss-drift-exact
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TWISS drift with EXACT flag has errors in the time variable
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@rdemaria
rdemaria committed Aug 15, 2022
2 parents 17858dd + ebace2d commit 674e770
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3 changes: 2 additions & 1 deletion Changes.md
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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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1-53 * skip
54 2-8 rel=1e-14
54 10-18 rel=1e-14
55-$ * skip

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