From 46cbfb4d84e12f74026d16b1fb1db517c98679e7 Mon Sep 17 00:00:00 2001 From: mattsignorelli Date: Tue, 25 Jun 2024 17:14:48 -0400 Subject: [PATCH] Courant Snyder (canonization) done --- fpp-ptc-sandbox/code/Makefile | 41 ++ .../code/z_canonize_matt_fake_maps.f90 | 11 +- src/canonize/ac.map | 124 ++++ src/canonize/test.map | 576 ++++++++++++++++++ src/normal.jl | 76 ++- src/utils/misc.jl | 43 +- 6 files changed, 845 insertions(+), 26 deletions(-) create mode 100644 src/canonize/ac.map create mode 100644 src/canonize/test.map diff --git a/fpp-ptc-sandbox/code/Makefile b/fpp-ptc-sandbox/code/Makefile index 3627e8e..6005f14 100644 --- a/fpp-ptc-sandbox/code/Makefile +++ b/fpp-ptc-sandbox/code/Makefile @@ -389,6 +389,19 @@ z_radiation_matt_fake_maps-exe/fast: $(MAKE) $(MAKESILENT) -f CMakeFiles/z_radiation_matt_fake_maps-exe.dir/build.make CMakeFiles/z_radiation_matt_fake_maps-exe.dir/build .PHONY : z_radiation_matt_fake_maps-exe/fast +#============================================================================= +# Target rules for targets named z_canonize_matt_fake_maps-exe + +# Build rule for target. +z_canonize_matt_fake_maps-exe: cmake_check_build_system + $(MAKE) $(MAKESILENT) -f CMakeFiles/Makefile2 z_canonize_matt_fake_maps-exe +.PHONY : z_canonize_matt_fake_maps-exe + +# fast build rule for target. +z_canonize_matt_fake_maps-exe/fast: + $(MAKE) $(MAKESILENT) -f CMakeFiles/z_canonize_matt_fake_maps-exe.dir/build.make CMakeFiles/z_canonize_matt_fake_maps-exe.dir/build +.PHONY : z_canonize_matt_fake_maps-exe/fast + normal_simple.o: normal_simple.f90.o .PHONY : normal_simple.o @@ -413,6 +426,30 @@ normal_simple.f90.s: $(MAKE) $(MAKESILENT) -f CMakeFiles/normal_simple-exe.dir/build.make CMakeFiles/normal_simple-exe.dir/normal_simple.f90.s .PHONY : normal_simple.f90.s +z_canonize_matt_fake_maps.o: z_canonize_matt_fake_maps.f90.o +.PHONY : z_canonize_matt_fake_maps.o + +# target to build an object file +z_canonize_matt_fake_maps.f90.o: + $(MAKE) $(MAKESILENT) -f CMakeFiles/z_canonize_matt_fake_maps-exe.dir/build.make CMakeFiles/z_canonize_matt_fake_maps-exe.dir/z_canonize_matt_fake_maps.f90.o +.PHONY : z_canonize_matt_fake_maps.f90.o + +z_canonize_matt_fake_maps.i: z_canonize_matt_fake_maps.f90.i +.PHONY : z_canonize_matt_fake_maps.i + +# target to preprocess a source file +z_canonize_matt_fake_maps.f90.i: + $(MAKE) $(MAKESILENT) -f CMakeFiles/z_canonize_matt_fake_maps-exe.dir/build.make CMakeFiles/z_canonize_matt_fake_maps-exe.dir/z_canonize_matt_fake_maps.f90.i +.PHONY : z_canonize_matt_fake_maps.f90.i + +z_canonize_matt_fake_maps.s: z_canonize_matt_fake_maps.f90.s +.PHONY : z_canonize_matt_fake_maps.s + +# target to generate assembly for a file +z_canonize_matt_fake_maps.f90.s: + $(MAKE) $(MAKESILENT) -f CMakeFiles/z_canonize_matt_fake_maps-exe.dir/build.make CMakeFiles/z_canonize_matt_fake_maps-exe.dir/z_canonize_matt_fake_maps.f90.s +.PHONY : z_canonize_matt_fake_maps.f90.s + z_coast_matt_fake_maps.o: z_coast_matt_fake_maps.f90.o .PHONY : z_coast_matt_fake_maps.o @@ -902,6 +939,7 @@ help: @echo "... edit_cache" @echo "... rebuild_cache" @echo "... normal_simple-exe" + @echo "... z_canonize_matt_fake_maps-exe" @echo "... z_coast_matt_fake_maps-exe" @echo "... z_cut-exe" @echo "... z_cut_sub-exe" @@ -925,6 +963,9 @@ help: @echo "... normal_simple.o" @echo "... normal_simple.i" @echo "... normal_simple.s" + @echo "... z_canonize_matt_fake_maps.o" + @echo "... z_canonize_matt_fake_maps.i" + @echo "... z_canonize_matt_fake_maps.s" @echo "... z_coast_matt_fake_maps.o" @echo "... z_coast_matt_fake_maps.i" @echo "... z_coast_matt_fake_maps.s" diff --git a/fpp-ptc-sandbox/code/z_canonize_matt_fake_maps.f90 b/fpp-ptc-sandbox/code/z_canonize_matt_fake_maps.f90 index 2ed958b..de98205 100644 --- a/fpp-ptc-sandbox/code/z_canonize_matt_fake_maps.f90 +++ b/fpp-ptc-sandbox/code/z_canonize_matt_fake_maps.f90 @@ -159,7 +159,8 @@ program example do i=1,c_%nd2 m%v(i)=m%v(i) !*decrement(i) enddo - ! call print(m) + call print(m) + stop lielib_print(4)=0 call c_normal(m,normal,dospin=putspin,phase=phase,nu_spin=nu_spin) @@ -168,7 +169,7 @@ program example call c_fast_canonise_clean_julia(normal%atot,a1,dospin=putspin) call print(a1) - + stop normal%atot=a1 write(6,*) normal%damping(1:3) @@ -1259,6 +1260,8 @@ subroutine c_fast_canonise_clean_julia(u,u_c,phase,damping,q_cs,q_as,q_orb,q_rot type(c_damap) uct integer ndt,ndptb,ndpt,ndct + ! nd = number dimensions + ! ndt = number harmonic oscillators = 4 if coastings ndt=c_%nd2t/2 ndptb=c_%ndptb @@ -1284,8 +1287,8 @@ subroutine c_fast_canonise_clean_julia(u,u_c,phase,damping,q_cs,q_as,q_orb,q_rot b0=0 id=0 do i=1,nd - b0(2*i-1,2*i-1)=1 - b0(2*i,2*i)=1 + b0(2*i-1,2*i-1)=1 ! I + b0(2*i,2*i)=1 ! s(2*i-1,2*i)=1 s(2*i,2*i-1)=-1 enddo diff --git a/src/canonize/ac.map b/src/canonize/ac.map new file mode 100644 index 0000000..87a352a --- /dev/null +++ b/src/canonize/ac.map @@ -0,0 +1,124 @@ + 6 Dimensional TPSA/DA map + + 1, NO = 3, NV = 6, INA = 30 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 1.000312298776967 0.000000000000000 1 0 0 0 0 0 + 1 -0.4830800052522120E-16 0.000000000000000 0 1 0 0 0 0 + 1 0.1078435759919717E-01 0.000000000000000 0 0 1 0 0 0 + 1 -0.1979756005464457E-02 0.000000000000000 0 0 0 1 0 0 + 1 0.5630792227601156E-02 0.000000000000000 0 0 0 0 0 1 + -5 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 29 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 0.1306080210285989E-02 0.000000000000000 1 0 0 0 0 0 + 1 0.9995715517477228 0.000000000000000 0 1 0 0 0 0 + 1 0.4917593339866650E-02 0.000000000000000 0 0 1 0 0 0 + 1 0.9879832270829701E-02 0.000000000000000 0 0 0 1 0 0 + 1 0.4464348946484611E-02 0.000000000000000 0 0 0 0 0 1 + -5 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 28 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 -0.9852382729493981E-02 0.000000000000000 1 0 0 0 0 0 + 1 -0.1972277583719225E-02 0.000000000000000 0 1 0 0 0 0 + 1 0.9965336729127154 0.000000000000000 0 0 1 0 0 0 + 1 -0.3263630881646084E-16 0.000000000000000 0 0 0 1 0 0 + 1 0.1239780734022430E-01 0.000000000000000 0 0 0 0 0 1 + -5 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 27 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 0.4807753199428283E-02 0.000000000000000 1 0 0 0 0 0 + 1 -0.1084012449016447E-01 0.000000000000000 0 1 0 0 0 0 + 1 0.1156632979614590E-01 0.000000000000000 0 0 1 0 0 0 + 1 1.003361696547912 0.000000000000000 0 0 0 1 0 0 + 1 0.9355219167887742E-02 0.000000000000000 0 0 0 0 0 1 + -5 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 26 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 -0.4306612093237661E-02 0.000000000000000 1 0 0 0 0 0 + 1 0.5512437038594799E-02 0.000000000000000 0 1 0 0 0 0 + 1 -0.9199848978962361E-02 0.000000000000000 0 0 1 0 0 0 + 1 0.1250395461075949E-01 0.000000000000000 0 0 0 1 0 0 + 1 1.000000000000000 0.000000000000000 0 0 0 0 1 0 + -5 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 25 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 1.000000000000000 0.000000000000000 0 0 0 0 0 1 + -1 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + No Spin Matrix + Quaternion + c_quaternion + + 1, NO = 3, NV = 6, INA = 15 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 0 0.9044197722704104 0.000000000000000 0 0 0 0 0 0 + 1 -1.230805330670363 0.000000000000000 1 0 0 0 0 0 + 1 0.7593604560872026 0.000000000000000 0 1 0 0 0 0 + 1 -0.2005031974645732 0.000000000000000 0 0 1 0 0 0 + 1 0.5873101678547868E-01 0.000000000000000 0 0 0 1 0 0 + 1 0.1062946080338559 0.000000000000000 0 0 0 0 0 1 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 232 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 0 0.3632814512983805 0.000000000000000 0 0 0 0 0 0 + 1 1.206286862714071 0.000000000000000 1 0 0 0 0 0 + 1 -2.545393061216957 0.000000000000000 0 1 0 0 0 0 + 1 -0.7194219382032653 0.000000000000000 0 0 1 0 0 0 + 1 0.2321269775156017 0.000000000000000 0 0 0 1 0 0 + 1 -0.3591574559148977 0.000000000000000 0 0 0 0 0 1 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 233 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 -0.1392966253184698 0.000000000000000 1 0 0 0 0 0 + 1 2.688418743115568 0.000000000000000 0 1 0 0 0 0 + 1 -3.100864700305056 0.000000000000000 0 0 1 0 0 0 + 1 2.355391437568686 0.000000000000000 0 0 0 1 0 0 + 1 0.1387778780781446E-16 0.000000000000000 0 0 0 0 0 1 + -5 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 234 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 0 -0.2237218421810473 0.000000000000000 0 0 0 0 0 0 + 1 -3.016884842915607 0.000000000000000 1 0 0 0 0 0 + 1 -1.063434273197377 0.000000000000000 0 1 0 0 0 0 + 1 -1.978759416966205 0.000000000000000 0 0 1 0 0 0 + 1 0.6143562772582531 0.000000000000000 0 0 0 1 0 0 + 1 -0.1534955027326110 0.000000000000000 0 0 0 0 0 1 + -6 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + No Stochastic Radiation \ No newline at end of file diff --git a/src/canonize/test.map b/src/canonize/test.map new file mode 100644 index 0000000..1ae5f58 --- /dev/null +++ b/src/canonize/test.map @@ -0,0 +1,576 @@ + 6 Dimensional TPSA/DA map + + 1, NO = 3, NV = 6, INA = 182 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 0.9654540003010120 0.000000000000000 1 0 0 0 0 0 + 1 -0.2620448052200881 0.000000000000000 0 1 0 0 0 0 + 1 0.1297198999051410E-02 0.000000000000000 0 0 1 0 0 0 + 1 0.1110799173009398E-02 0.000000000000000 0 0 0 1 0 0 + 1 0.1337906603728656E-02 0.000000000000000 0 0 0 0 0 1 + 2 0.9268153232589755E-03 0.000000000000000 2 0 0 0 0 0 + 2 0.2539229039655350E-02 0.000000000000000 1 1 0 0 0 0 + 2 0.1054584966530460E-02 0.000000000000000 0 2 0 0 0 0 + 2 0.2691357034589230E-02 0.000000000000000 1 0 1 0 0 0 + 2 0.3684541333107649E-02 0.000000000000000 0 1 1 0 0 0 + 2 0.5942579352362492E-03 0.000000000000000 0 0 2 0 0 0 + 2 0.1807974753980744E-02 0.000000000000000 1 0 0 1 0 0 + 2 0.1072614057969575E-02 0.000000000000000 0 1 0 1 0 0 + 2 0.1832746227494020E-02 0.000000000000000 0 0 1 1 0 0 + 2 0.2847981403663723E-02 0.000000000000000 1 0 0 0 0 1 + 2 0.3663233802663970E-02 0.000000000000000 0 1 0 0 0 1 + 2 0.2226278127550360E-02 0.000000000000000 0 0 1 0 0 1 + 2 0.8388417602732386E-03 0.000000000000000 0 0 0 2 0 0 + 2 0.1844911667384833E-02 0.000000000000000 0 0 0 1 0 1 + 2 0.2022180308690506E-02 0.000000000000000 0 0 0 0 0 2 + 3 -0.2797826021236977E-05 0.000000000000000 3 0 0 0 0 0 + 3 0.6860396083869944E-06 0.000000000000000 2 1 0 0 0 0 + 3 0.3025447226976630E-05 0.000000000000000 1 2 0 0 0 0 + 3 0.1420369514100230E-06 0.000000000000000 0 3 0 0 0 0 + 3 -0.7540641297436070E-05 0.000000000000000 2 0 1 0 0 0 + 3 0.4113384090001820E-05 0.000000000000000 1 1 1 0 0 0 + 3 0.3247377345765478E-05 0.000000000000000 0 2 1 0 0 0 + 3 -0.7997969242020277E-05 0.000000000000000 1 0 2 0 0 0 + 3 0.1905251022039348E-05 0.000000000000000 0 1 2 0 0 0 + 3 -0.3617314927700004E-05 0.000000000000000 0 0 3 0 0 0 + 3 0.1845538422725816E-05 0.000000000000000 2 0 0 1 0 0 + 3 0.6249057932424991E-05 0.000000000000000 1 1 0 1 0 0 + 3 0.5391333993248977E-06 0.000000000000000 0 2 0 1 0 0 + 3 0.2536661357046621E-05 0.000000000000000 1 0 1 1 0 0 + 3 0.5923404393556109E-05 0.000000000000000 0 1 1 1 0 0 + 3 -0.9675893735133301E-06 0.000000000000000 0 0 2 1 0 0 + 3 -0.6714980943341581E-05 0.000000000000000 2 0 0 0 0 1 + 3 0.4078019260838459E-05 0.000000000000000 1 1 0 0 0 1 + 3 0.3059550755254267E-05 0.000000000000000 0 2 0 0 0 1 + 3 -0.1305746987742808E-04 0.000000000000000 1 0 1 0 0 1 + 3 0.5447229128386534E-05 0.000000000000000 0 1 1 0 0 1 + 3 -0.6036139608561317E-05 0.000000000000000 0 0 2 0 0 1 + 3 0.8045039883754841E-05 0.000000000000000 1 0 0 2 0 0 + 3 0.9130369025146895E-05 0.000000000000000 0 1 0 2 0 0 + 3 0.2714283500534221E-05 0.000000000000000 0 0 1 2 0 0 + 3 0.5667472113052815E-05 0.000000000000000 1 0 0 1 0 1 + 3 0.6005017700564499E-05 0.000000000000000 0 1 0 1 0 1 + 3 0.9733442869975268E-06 0.000000000000000 0 0 1 1 0 1 + 3 -0.6093870516299175E-05 0.000000000000000 1 0 0 0 0 2 + 3 0.2962217964833560E-05 0.000000000000000 0 1 0 0 0 2 + 3 -0.3542468672841932E-05 0.000000000000000 0 0 1 0 0 2 + 3 0.4028481803884943E-05 0.000000000000000 0 0 0 3 0 0 + 3 0.6474984807198066E-05 0.000000000000000 0 0 0 2 0 1 + 3 0.1919573178783127E-05 0.000000000000000 0 0 0 1 0 2 + 3 -0.9832372628986219E-06 0.000000000000000 0 0 0 0 0 3 + -55 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 181 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 0.2616575299672443 0.000000000000000 1 0 0 0 0 0 + 1 0.9647609165243284 0.000000000000000 0 1 0 0 0 0 + 1 -0.1393904824035921E-02 0.000000000000000 0 0 1 0 0 0 + 1 0.1302687983318346E-03 0.000000000000000 0 0 0 1 0 0 + 1 -0.1299956950543302E-02 0.000000000000000 0 0 0 0 0 1 + 2 -0.1409384305533802E-02 0.000000000000000 2 0 0 0 0 0 + 2 -0.4055533465968261E-03 0.000000000000000 1 1 0 0 0 0 + 2 -0.9283510856750111E-03 0.000000000000000 0 2 0 0 0 0 + 2 -0.2831970299199732E-02 0.000000000000000 1 0 1 0 0 0 + 2 -0.9282751778848036E-03 0.000000000000000 0 1 1 0 0 0 + 2 -0.2023637617796295E-02 0.000000000000000 0 0 2 0 0 0 + 2 0.2068107637483087E-03 0.000000000000000 1 0 0 1 0 0 + 2 -0.1573609112731728E-02 0.000000000000000 0 1 0 1 0 0 + 2 -0.1020056380741541E-02 0.000000000000000 0 0 1 1 0 0 + 2 -0.3852936437257226E-02 0.000000000000000 1 0 0 0 0 1 + 2 -0.8107101905575803E-03 0.000000000000000 0 1 0 0 0 1 + 2 -0.1662981565610318E-02 0.000000000000000 0 0 1 0 0 1 + 2 -0.8721359562881458E-03 0.000000000000000 0 0 0 2 0 0 + 2 -0.1134714379696438E-02 0.000000000000000 0 0 0 1 0 1 + 2 -0.1011183420280390E-02 0.000000000000000 0 0 0 0 0 2 + 3 -0.5960964292035861E-06 0.000000000000000 3 0 0 0 0 0 + 3 -0.3457511355899914E-05 0.000000000000000 2 1 0 0 0 0 + 3 -0.8755298052399885E-06 0.000000000000000 1 2 0 0 0 0 + 3 0.2097874316904380E-05 0.000000000000000 0 3 0 0 0 0 + 3 -0.3600236682545304E-05 0.000000000000000 2 0 1 0 0 0 + 3 -0.7518616229732297E-05 0.000000000000000 1 1 1 0 0 0 + 3 -0.4382385446417593E-06 0.000000000000000 0 2 1 0 0 0 + 3 -0.3024299864891310E-05 0.000000000000000 1 0 2 0 0 0 + 3 -0.5311165501898454E-05 0.000000000000000 0 1 2 0 0 0 + 3 -0.7482573476344562E-06 0.000000000000000 0 0 3 0 0 0 + 3 -0.3228215541408692E-05 0.000000000000000 2 0 0 1 0 0 + 3 -0.1419350608949381E-05 0.000000000000000 1 1 0 1 0 0 + 3 0.4458135323297460E-05 0.000000000000000 0 2 0 1 0 0 + 3 -0.7057494705127850E-05 0.000000000000000 1 0 1 1 0 0 + 3 -0.1242710411396464E-06 0.000000000000000 0 1 1 1 0 0 + 3 -0.4901750429376807E-05 0.000000000000000 0 0 2 1 0 0 + 3 -0.3545600247624579E-05 0.000000000000000 2 0 0 0 0 1 + 3 -0.7472013755275197E-05 0.000000000000000 1 1 0 0 0 1 + 3 0.7890119464316548E-06 0.000000000000000 0 2 0 0 0 1 + 3 -0.7850298233400345E-05 0.000000000000000 1 0 1 0 0 1 + 3 -0.1093318676630622E-04 0.000000000000000 0 1 1 0 0 1 + 3 -0.2416261349835316E-05 0.000000000000000 0 0 2 0 0 1 + 3 -0.8653074142290587E-05 0.000000000000000 1 0 0 2 0 0 + 3 0.1472952690524774E-05 0.000000000000000 0 1 0 2 0 0 + 3 -0.9764703884184859E-05 0.000000000000000 0 0 1 2 0 0 + 3 -0.6526231491592375E-05 0.000000000000000 1 0 0 1 0 1 + 3 0.1720525729424220E-05 0.000000000000000 0 1 0 1 0 1 + 3 -0.7611227285033171E-05 0.000000000000000 0 0 1 1 0 1 + 3 -0.4956726653257464E-05 0.000000000000000 1 0 0 0 0 2 + 3 -0.4555490161855751E-05 0.000000000000000 0 1 0 0 0 2 + 3 -0.4039805752735189E-05 0.000000000000000 0 0 1 0 0 2 + 3 -0.7147933583966711E-06 0.000000000000000 0 0 0 3 0 0 + 3 -0.4166895356074112E-05 0.000000000000000 0 0 0 2 0 1 + 3 -0.2058257611319567E-05 0.000000000000000 0 0 0 1 0 2 + 3 -0.2343634059739413E-05 0.000000000000000 0 0 0 0 0 3 + -55 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 180 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 0.3846073674584712E-03 0.000000000000000 1 0 0 0 0 0 + 1 0.1213971894301787E-02 0.000000000000000 0 1 0 0 0 0 + 1 0.9927634036169313 0.000000000000000 0 0 1 0 0 0 + 1 -0.1310960127869334 0.000000000000000 0 0 0 1 0 0 + 1 0.1308564621091474E-02 0.000000000000000 0 0 0 0 0 1 + 2 0.3575894382207536E-03 0.000000000000000 2 0 0 0 0 0 + 2 0.2028366475714926E-02 0.000000000000000 1 1 0 0 0 0 + 2 0.5251477474396486E-03 0.000000000000000 0 2 0 0 0 0 + 2 0.1998082761007841E-02 0.000000000000000 1 0 1 0 0 0 + 2 0.1499787626781654E-02 0.000000000000000 0 1 1 0 0 0 + 2 0.1100570088024591E-02 0.000000000000000 0 0 2 0 0 0 + 2 0.2281630324851883E-02 0.000000000000000 1 0 0 1 0 0 + 2 0.1341650793916872E-02 0.000000000000000 0 1 0 1 0 0 + 2 0.3333950582028847E-02 0.000000000000000 0 0 1 1 0 0 + 2 0.1844013669501269E-02 0.000000000000000 1 0 0 0 0 1 + 2 0.1694397744228142E-02 0.000000000000000 0 1 0 0 0 1 + 2 0.1514629948124427E-02 0.000000000000000 0 0 1 0 0 1 + 2 0.5603642603249026E-02 0.000000000000000 0 0 0 2 0 0 + 2 0.3063274081185244E-02 0.000000000000000 0 0 0 1 0 1 + 2 0.5738653717593473E-03 0.000000000000000 0 0 0 0 0 2 + 3 -0.3087590953631901E-05 0.000000000000000 3 0 0 0 0 0 + 3 -0.1232934832047512E-05 0.000000000000000 2 1 0 0 0 0 + 3 -0.1062705764585984E-06 0.000000000000000 1 2 0 0 0 0 + 3 -0.2506588675333095E-06 0.000000000000000 0 3 0 0 0 0 + 3 -0.9117543244288725E-05 0.000000000000000 2 0 1 0 0 0 + 3 0.6759124207268783E-06 0.000000000000000 1 1 1 0 0 0 + 3 0.1287149873027603E-05 0.000000000000000 0 2 1 0 0 0 + 3 -0.7917162602038725E-05 0.000000000000000 1 0 2 0 0 0 + 3 0.3208371019039412E-05 0.000000000000000 0 1 2 0 0 0 + 3 -0.1458250808643855E-05 0.000000000000000 0 0 3 0 0 0 + 3 -0.8074328002327159E-05 0.000000000000000 2 0 0 1 0 0 + 3 -0.4189933457734104E-05 0.000000000000000 1 1 0 1 0 0 + 3 -0.8270361506532278E-05 0.000000000000000 0 2 0 1 0 0 + 3 -0.1849045839637575E-04 0.000000000000000 1 0 1 1 0 0 + 3 0.4740429759921871E-05 0.000000000000000 0 1 1 1 0 0 + 3 -0.2545474257680778E-05 0.000000000000000 0 0 2 1 0 0 + 3 -0.7485993393063727E-05 0.000000000000000 2 0 0 0 0 1 + 3 -0.6865436906683487E-06 0.000000000000000 1 1 0 0 0 1 + 3 0.5209759459448874E-06 0.000000000000000 0 2 0 0 0 1 + 3 -0.1237703062796017E-04 0.000000000000000 1 0 1 0 0 1 + 3 0.3836202533500956E-05 0.000000000000000 0 1 1 0 0 1 + 3 -0.4930247915984112E-05 0.000000000000000 0 0 2 0 0 1 + 3 0.9087291597514816E-06 0.000000000000000 1 0 0 2 0 0 + 3 -0.2924311690878184E-05 0.000000000000000 0 1 0 2 0 0 + 3 -0.7448535486591339E-06 0.000000000000000 0 0 1 2 0 0 + 3 -0.7360555692150522E-05 0.000000000000000 1 0 0 1 0 1 + 3 -0.3655082236499350E-05 0.000000000000000 0 1 0 1 0 1 + 3 -0.1055461683642368E-04 0.000000000000000 0 0 1 1 0 1 + 3 -0.5797733161885576E-05 0.000000000000000 1 0 0 0 0 2 + 3 0.9073521514775088E-06 0.000000000000000 0 1 0 0 0 2 + 3 -0.4805890045725299E-05 0.000000000000000 0 0 1 0 0 2 + 3 0.1732031038788174E-05 0.000000000000000 0 0 0 3 0 0 + 3 0.1535434674351127E-05 0.000000000000000 0 0 0 2 0 1 + 3 -0.6294643558309317E-05 0.000000000000000 0 0 0 1 0 2 + 3 -0.1619069405086828E-05 0.000000000000000 0 0 0 0 0 3 + -55 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 179 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 -0.1645959574590753E-02 0.000000000000000 1 0 0 0 0 0 + 1 -0.7301362528990690E-03 0.000000000000000 0 1 0 0 0 0 + 1 0.1329263274995863 0.000000000000000 0 0 1 0 0 0 + 1 0.9897344800963772 0.000000000000000 0 0 0 1 0 0 + 1 -0.1539431170821754E-02 0.000000000000000 0 0 0 0 0 1 + 2 -0.1682401603557956E-02 0.000000000000000 2 0 0 0 0 0 + 2 -0.1602772624197637E-02 0.000000000000000 1 1 0 0 0 0 + 2 -0.1597128961836867E-02 0.000000000000000 0 2 0 0 0 0 + 2 -0.3978552214634526E-02 0.000000000000000 1 0 1 0 0 0 + 2 0.1103111939806334E-03 0.000000000000000 0 1 1 0 0 0 + 2 -0.6003125304790878E-03 0.000000000000000 0 0 2 0 0 0 + 2 -0.1167443417228879E-02 0.000000000000000 1 0 0 1 0 0 + 2 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-0.5102690249619526E-06 0.000000000000000 0 0 3 0 0 0 + 3 -0.4393332711727858E-05 0.000000000000000 2 0 0 1 0 0 + 3 -0.2420851659791101E-05 0.000000000000000 1 1 0 1 0 0 + 3 0.4674041503526250E-05 0.000000000000000 0 2 0 1 0 0 + 3 -0.6680737502138750E-05 0.000000000000000 1 0 1 1 0 0 + 3 -0.9280197306657362E-06 0.000000000000000 0 1 1 1 0 0 + 3 -0.2515803482590575E-05 0.000000000000000 0 0 2 1 0 0 + 3 -0.4223855759011444E-06 0.000000000000000 2 0 0 0 0 1 + 3 -0.3552690952281728E-05 0.000000000000000 1 1 0 0 0 1 + 3 0.1260190585814097E-05 0.000000000000000 0 2 0 0 0 1 + 3 -0.5363184478092097E-05 0.000000000000000 1 0 1 0 0 1 + 3 -0.7337423295107729E-05 0.000000000000000 0 1 1 0 0 1 + 3 -0.1921630148063450E-05 0.000000000000000 0 0 2 0 0 1 + 3 -0.1207837066700741E-04 0.000000000000000 1 0 0 2 0 0 + 3 0.3644334606317871E-05 0.000000000000000 0 1 0 2 0 0 + 3 -0.4589578817064871E-05 0.000000000000000 0 0 1 2 0 0 + 3 -0.8544569747796837E-05 0.000000000000000 1 0 0 1 0 1 + 3 0.8674118655301085E-06 0.000000000000000 0 1 0 1 0 1 + 3 -0.6304418072835670E-05 0.000000000000000 0 0 1 1 0 1 + 3 -0.1728607292222593E-05 0.000000000000000 1 0 0 0 0 2 + 3 -0.1823520342268666E-05 0.000000000000000 0 1 0 0 0 2 + 3 -0.3416861900302787E-05 0.000000000000000 0 0 1 0 0 2 + 3 -0.3025059406181179E-05 0.000000000000000 0 0 0 3 0 0 + 3 -0.8058242052844646E-05 0.000000000000000 0 0 0 2 0 1 + 3 -0.2987562954176349E-05 0.000000000000000 0 0 0 1 0 2 + 3 -0.6699585385603952E-06 0.000000000000000 0 0 0 0 0 3 + -55 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 178 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 0.1603560207482578E-02 0.000000000000000 1 0 0 0 0 0 + 1 0.9510264310430606E-03 0.000000000000000 0 1 0 0 0 0 + 1 0.1702055006542588E-02 0.000000000000000 0 0 1 0 0 0 + 1 0.1094936515064990E-02 0.000000000000000 0 0 0 1 0 0 + 1 1.000000000000000 0.000000000000000 0 0 0 0 1 0 + 1 -0.8672151543665493E-01 0.000000000000000 0 0 0 0 0 1 + 2 0.2229040768905493E-02 0.000000000000000 2 0 0 0 0 0 + 2 0.1742789061661052E-02 0.000000000000000 1 1 0 0 0 0 + 2 0.1659992767535323E-02 0.000000000000000 0 2 0 0 0 0 + 2 0.2184138000622157E-02 0.000000000000000 1 0 1 0 0 0 + 2 0.1720092214842905E-02 0.000000000000000 0 1 1 0 0 0 + 2 0.1385818204349835E-02 0.000000000000000 0 0 2 0 0 0 + 2 0.1578111881447581E-02 0.000000000000000 1 0 0 1 0 0 + 2 0.1480852222258609E-02 0.000000000000000 0 1 0 1 0 0 + 2 0.1165472672147152E-02 0.000000000000000 0 0 1 1 0 0 + 2 0.3008885517240091E-02 0.000000000000000 1 0 0 0 0 1 + 2 0.3379178873238560E-02 0.000000000000000 0 1 0 0 0 1 + 2 0.3263726085019827E-02 0.000000000000000 0 0 1 0 0 1 + 2 0.1474287814060032E-02 0.000000000000000 0 0 0 2 0 0 + 2 0.7320385804566534E-03 0.000000000000000 0 0 0 1 0 1 + 2 0.3540433355191132E-02 0.000000000000000 0 0 0 0 0 2 + 3 -0.1345723106420645E-05 0.000000000000000 3 0 0 0 0 0 + 3 0.2226547067598423E-05 0.000000000000000 2 1 0 0 0 0 + 3 0.9481452763770875E-06 0.000000000000000 1 2 0 0 0 0 + 3 -0.1917113002910602E-05 0.000000000000000 0 3 0 0 0 0 + 3 -0.1718468883296858E-05 0.000000000000000 2 0 1 0 0 0 + 3 0.6187138636480626E-05 0.000000000000000 1 1 1 0 0 0 + 3 0.8466628905515724E-06 0.000000000000000 0 2 1 0 0 0 + 3 -0.1942384499118134E-05 0.000000000000000 1 0 2 0 0 0 + 3 0.1659226470140038E-05 0.000000000000000 0 1 2 0 0 0 + 3 -0.6362783003978229E-06 0.000000000000000 0 0 3 0 0 0 + 3 0.2380245346135610E-05 0.000000000000000 2 0 0 1 0 0 + 3 0.2355387906533344E-05 0.000000000000000 1 1 0 1 0 0 + 3 -0.4452370507241018E-05 0.000000000000000 0 2 0 1 0 0 + 3 0.2354323087734165E-05 0.000000000000000 1 0 1 1 0 0 + 3 0.2662789988374512E-05 0.000000000000000 0 1 1 1 0 0 + 3 0.1857557398732373E-05 0.000000000000000 0 0 2 1 0 0 + 3 -0.1459144595584379E-05 0.000000000000000 2 0 0 0 0 1 + 3 0.6009360279443624E-05 0.000000000000000 1 1 0 0 0 1 + 3 -0.1342475125601368E-06 0.000000000000000 0 2 0 0 0 1 + 3 -0.4190185753565231E-06 0.000000000000000 1 0 1 0 0 1 + 3 0.5981946716288856E-05 0.000000000000000 0 1 1 0 0 1 + 3 -0.1476422962701330E-05 0.000000000000000 0 0 2 0 0 1 + 3 0.6295027989975730E-05 0.000000000000000 1 0 0 2 0 0 + 3 0.4348164952554013E-06 0.000000000000000 0 1 0 2 0 0 + 3 0.6030842928739117E-05 0.000000000000000 0 0 1 2 0 0 + 3 0.6827926316023598E-05 0.000000000000000 1 0 0 1 0 1 + 3 0.4771827520713560E-06 0.000000000000000 0 1 0 1 0 1 + 3 0.5104751701099309E-05 0.000000000000000 0 0 1 1 0 1 + 3 -0.2819104796199353E-06 0.000000000000000 1 0 0 0 0 2 + 3 0.3034002168909716E-05 0.000000000000000 0 1 0 0 0 2 + 3 0.8945057804959364E-06 0.000000000000000 0 0 1 0 0 2 + 3 0.9153886185412738E-06 0.000000000000000 0 0 0 3 0 0 + 3 0.8198676541137758E-05 0.000000000000000 0 0 0 2 0 1 + 3 0.2801725340475678E-05 0.000000000000000 0 0 0 1 0 2 + 3 0.5719289236164361E-06 0.000000000000000 0 0 0 0 0 3 + -56 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 177 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 1 1.000000000000000 0.000000000000000 0 0 0 0 0 1 + -1 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + Spin Matrix is identity + Quaternion + c_quaternion + + 1, NO = 3, NV = 6, INA = 162 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 0 0.9880666220707530 0.000000000000000 0 0 0 0 0 0 + 1 -0.6474997162702630E-01 0.000000000000000 1 0 0 0 0 0 + 1 -0.3135924788527270E-01 0.000000000000000 0 1 0 0 0 0 + 1 -0.5236825184173392E-01 0.000000000000000 0 0 1 0 0 0 + 1 -0.7123538638072406E-01 0.000000000000000 0 0 0 1 0 0 + 1 -0.5670541816522255E-01 0.000000000000000 0 0 0 0 0 1 + 2 -0.1542558859685270 0.000000000000000 2 0 0 0 0 0 + 2 -0.1327841699826285 0.000000000000000 1 1 0 0 0 0 + 2 -0.9297224843507255E-01 0.000000000000000 0 2 0 0 0 0 + 2 -0.2321106971461660 0.000000000000000 1 0 1 0 0 0 + 2 -0.1161585855095408 0.000000000000000 0 1 1 0 0 0 + 2 -0.1365064466917515 0.000000000000000 0 0 2 0 0 0 + 2 -0.2396462562100007 0.000000000000000 1 0 0 1 0 0 + 2 -0.1641735044453395 0.000000000000000 0 1 0 1 0 0 + 2 -0.2147811252049298 0.000000000000000 0 0 1 1 0 0 + 2 -0.2062935400283608 0.000000000000000 1 0 0 0 0 1 + 2 -0.1396775481690075 0.000000000000000 0 1 0 0 0 1 + 2 -0.1876930736509832 0.000000000000000 0 0 1 0 0 1 + 2 -0.1507929012511762 0.000000000000000 0 0 0 2 0 0 + 2 -0.2291059366522780 0.000000000000000 0 0 0 1 0 1 + 2 -0.1201785840940721 0.000000000000000 0 0 0 0 0 2 + 3 -0.2408468535777538 0.000000000000000 3 0 0 0 0 0 + 3 -0.2009552501137616 0.000000000000000 2 1 0 0 0 0 + 3 -0.1522595360433371 0.000000000000000 1 2 0 0 0 0 + 3 -0.6220833059242448E-01 0.000000000000000 0 3 0 0 0 0 + 3 -0.4341880095856990 0.000000000000000 2 0 1 0 0 0 + 3 -0.2597697472749825 0.000000000000000 1 1 1 0 0 0 + 3 -0.1188881757490391 0.000000000000000 0 2 1 0 0 0 + 3 -0.4163198143884970 0.000000000000000 1 0 2 0 0 0 + 3 -0.1705862468289219 0.000000000000000 0 1 2 0 0 0 + 3 -0.2083788312543714 0.000000000000000 0 0 3 0 0 0 + 3 -0.3523069551296106 0.000000000000000 2 0 0 1 0 0 + 3 -0.3653481168953884 0.000000000000000 1 1 0 1 0 0 + 3 -0.2410788216121745 0.000000000000000 0 2 0 1 0 0 + 3 -0.4979770960587672 0.000000000000000 1 0 1 1 0 0 + 3 -0.3528020716176813 0.000000000000000 0 1 1 1 0 0 + 3 -0.3606491690756823 0.000000000000000 0 0 2 1 0 0 + 3 -0.3466258949814798 0.000000000000000 2 0 0 0 0 1 + 3 -0.3301035541420947 0.000000000000000 1 1 0 0 0 1 + 3 -0.2475706873114821 0.000000000000000 0 2 0 0 0 1 + 3 -0.5483274295429599 0.000000000000000 1 0 1 0 0 1 + 3 -0.3405305343035596 0.000000000000000 0 1 1 0 0 1 + 3 -0.3700403700128825 0.000000000000000 0 0 2 0 0 1 + 3 -0.2834750268847265 0.000000000000000 1 0 0 2 0 0 + 3 -0.3369532208107101 0.000000000000000 0 1 0 2 0 0 + 3 -0.2902434498852029 0.000000000000000 0 0 1 2 0 0 + 3 -0.4371273547024849 0.000000000000000 1 0 0 1 0 1 + 3 -0.4091236662406916 0.000000000000000 0 1 0 1 0 1 + 3 -0.5050812007951284 0.000000000000000 0 0 1 1 0 1 + 3 -0.2956667076862365 0.000000000000000 1 0 0 0 0 2 + 3 -0.2577261258461218 0.000000000000000 0 1 0 0 0 2 + 3 -0.3123430010806806 0.000000000000000 0 0 1 0 0 2 + 3 -0.1767983596513641 0.000000000000000 0 0 0 3 0 0 + 3 -0.3645294552881315 0.000000000000000 0 0 0 2 0 1 + 3 -0.3415192899037818 0.000000000000000 0 0 0 1 0 2 + 3 -0.1674703674101819 0.000000000000000 0 0 0 0 0 3 + -56 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 161 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 0 0.6233121537035650E-01 0.000000000000000 0 0 0 0 0 0 + 1 0.2502631865701198 0.000000000000000 1 0 0 0 0 0 + 1 0.2227648148468288 0.000000000000000 0 1 0 0 0 0 + 1 0.2947483940946410 0.000000000000000 0 0 1 0 0 0 + 1 0.2406045244013383 0.000000000000000 0 0 0 1 0 0 + 1 0.1937124314112272 0.000000000000000 0 0 0 0 0 1 + 2 0.2889062530816370 0.000000000000000 2 0 0 0 0 0 + 2 -0.4920798480372769E-01 0.000000000000000 1 1 0 0 0 0 + 2 0.2872326632091725E-01 0.000000000000000 0 2 0 0 0 0 + 2 0.2179213396388605 0.000000000000000 1 0 1 0 0 0 + 2 -0.7990351909049863E-02 0.000000000000000 0 1 1 0 0 0 + 2 0.1848886043369695 0.000000000000000 0 0 2 0 0 0 + 2 0.2120264762444804E-01 0.000000000000000 1 0 0 1 0 0 + 2 0.1956361085569041 0.000000000000000 0 1 0 1 0 0 + 2 0.2053093634944320 0.000000000000000 0 0 1 1 0 0 + 2 0.3137248821079440 0.000000000000000 1 0 0 0 0 1 + 2 0.1975911776824791 0.000000000000000 0 1 0 0 0 1 + 2 0.3025819647370480 0.000000000000000 0 0 1 0 0 1 + 2 0.2016636504233222 0.000000000000000 0 0 0 2 0 0 + 2 0.2390019164694492 0.000000000000000 0 0 0 1 0 1 + 2 0.1699989751396604 0.000000000000000 0 0 0 0 0 2 + 3 0.2023027144023450 0.000000000000000 3 0 0 0 0 0 + 3 -0.3965178840549763E-01 0.000000000000000 2 1 0 0 0 0 + 3 0.2866955788084219 0.000000000000000 1 2 0 0 0 0 + 3 0.5363699725333135E-01 0.000000000000000 0 3 0 0 0 0 + 3 0.1977708685693750 0.000000000000000 2 0 1 0 0 0 + 3 0.1656140835005988 0.000000000000000 1 1 1 0 0 0 + 3 0.8480425108313558E-01 0.000000000000000 0 2 1 0 0 0 + 3 0.1310334418711629 0.000000000000000 1 0 2 0 0 0 + 3 0.3856121204263770E-01 0.000000000000000 0 1 2 0 0 0 + 3 0.1985653745826029 0.000000000000000 0 0 3 0 0 0 + 3 0.1577027481977079 0.000000000000000 2 0 0 1 0 0 + 3 -0.1231999180217261E-01 0.000000000000000 1 1 0 1 0 0 + 3 0.6426191472799021E-01 0.000000000000000 0 2 0 1 0 0 + 3 0.2205983468971064 0.000000000000000 1 0 1 1 0 0 + 3 0.1363398266349981 0.000000000000000 0 1 1 1 0 0 + 3 0.1267364176533123 0.000000000000000 0 0 2 1 0 0 + 3 0.1240634260956249 0.000000000000000 2 0 0 0 0 1 + 3 0.1854166831900833 0.000000000000000 1 1 0 0 0 1 + 3 0.2493602197226676 0.000000000000000 0 2 0 0 0 1 + 3 0.5851754151764284E-01 0.000000000000000 1 0 1 0 0 1 + 3 0.2306710190855494 0.000000000000000 0 1 1 0 0 1 + 3 0.1504330867516487 0.000000000000000 0 0 2 0 0 1 + 3 0.2269935772258534 0.000000000000000 1 0 0 2 0 0 + 3 0.8381980719228382E-01 0.000000000000000 0 1 0 2 0 0 + 3 0.2788636245073257 0.000000000000000 0 0 1 2 0 0 + 3 0.1532835971570136E-02 0.000000000000000 1 0 0 1 0 1 + 3 0.1584152298320525 0.000000000000000 0 1 0 1 0 1 + 3 0.1599906956672875 0.000000000000000 0 0 1 1 0 1 + 3 0.5284490665222227E-01 0.000000000000000 1 0 0 0 0 2 + 3 0.1810952279571412 0.000000000000000 0 1 0 0 0 2 + 3 0.2282915820207495 0.000000000000000 0 0 1 0 0 2 + 3 0.2376613724893651 0.000000000000000 0 0 0 3 0 0 + 3 0.1669674742119246 0.000000000000000 0 0 0 2 0 1 + 3 0.1679337614104826 0.000000000000000 0 0 0 1 0 2 + 3 0.2589382963621846 0.000000000000000 0 0 0 0 0 3 + -56 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 160 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 0 0.9795357840153043E-01 0.000000000000000 0 0 0 0 0 0 + 1 0.2335689674719467 0.000000000000000 1 0 0 0 0 0 + 1 0.2109322935734221 0.000000000000000 0 1 0 0 0 0 + 1 0.1432760338586690 0.000000000000000 0 0 1 0 0 0 + 1 0.2723779088166636 0.000000000000000 0 0 0 1 0 0 + 1 0.2914066599643534 0.000000000000000 0 0 0 0 0 1 + 2 0.1487669526596072 0.000000000000000 2 0 0 0 0 0 + 2 0.7531969261448826E-01 0.000000000000000 1 1 0 0 0 0 + 2 0.1865825361818982 0.000000000000000 0 2 0 0 0 0 + 2 0.2648655520687653 0.000000000000000 1 0 1 0 0 0 + 2 -0.6713860215606193E-02 0.000000000000000 0 1 1 0 0 0 + 2 0.2183778696078235 0.000000000000000 0 0 2 0 0 0 + 2 0.2687608255594044 0.000000000000000 1 0 0 1 0 0 + 2 0.2274571686208059 0.000000000000000 0 1 0 1 0 0 + 2 0.1890759875755463 0.000000000000000 0 0 1 1 0 0 + 2 0.2000929637495528 0.000000000000000 1 0 0 0 0 1 + 2 0.1949899338714610 0.000000000000000 0 1 0 0 0 1 + 2 0.3014666751907200 0.000000000000000 0 0 1 0 0 1 + 2 0.2750168270029123 0.000000000000000 0 0 0 2 0 0 + 2 0.2584404069909544 0.000000000000000 0 0 0 1 0 1 + 2 0.2641326502322695 0.000000000000000 0 0 0 0 0 2 + 3 0.2149209992416608 0.000000000000000 3 0 0 0 0 0 + 3 0.1158020848622917 0.000000000000000 2 1 0 0 0 0 + 3 0.4438871085066996E-01 0.000000000000000 1 2 0 0 0 0 + 3 0.8026313160075317E-01 0.000000000000000 0 3 0 0 0 0 + 3 0.2248898055441855 0.000000000000000 2 0 1 0 0 0 + 3 -0.5516306595492768E-01 0.000000000000000 1 1 1 0 0 0 + 3 0.1562551395950266 0.000000000000000 0 2 1 0 0 0 + 3 0.2501746801560284 0.000000000000000 1 0 2 0 0 0 + 3 0.2551488260436168 0.000000000000000 0 1 2 0 0 0 + 3 0.2735174857909867 0.000000000000000 0 0 3 0 0 0 + 3 0.1531031215514495 0.000000000000000 2 0 0 1 0 0 + 3 0.7281460315567226E-01 0.000000000000000 1 1 0 1 0 0 + 3 0.5134863923602683E-01 0.000000000000000 0 2 0 1 0 0 + 3 0.1427848490707415 0.000000000000000 1 0 1 1 0 0 + 3 0.1983281247680496 0.000000000000000 0 1 1 1 0 0 + 3 0.1643892059710546 0.000000000000000 0 0 2 1 0 0 + 3 0.1790757734245721 0.000000000000000 2 0 0 0 0 1 + 3 0.1447186452449361 0.000000000000000 1 1 0 0 0 1 + 3 0.2158521944396247 0.000000000000000 0 2 0 0 0 1 + 3 0.1954797120381663 0.000000000000000 1 0 1 0 0 1 + 3 0.2021884812139329 0.000000000000000 0 1 1 0 0 1 + 3 0.2459884039912345 0.000000000000000 0 0 2 0 0 1 + 3 0.2000433338508924 0.000000000000000 1 0 0 2 0 0 + 3 0.1296987926382863 0.000000000000000 0 1 0 2 0 0 + 3 0.9998716495530968E-01 0.000000000000000 0 0 1 2 0 0 + 3 -0.8113529442839516E-01 0.000000000000000 1 0 0 1 0 1 + 3 -0.6455668475553558E-01 0.000000000000000 0 1 0 1 0 1 + 3 0.1406365444651633 0.000000000000000 0 0 1 1 0 1 + 3 0.7123926155463661E-01 0.000000000000000 1 0 0 0 0 2 + 3 0.1551383223826626 0.000000000000000 0 1 0 0 0 2 + 3 0.2105542691628067 0.000000000000000 0 0 1 0 0 2 + 3 0.8974723332698743E-01 0.000000000000000 0 0 0 3 0 0 + 3 0.1881678695360149 0.000000000000000 0 0 0 2 0 1 + 3 0.1431499542577435 0.000000000000000 0 0 0 1 0 2 + 3 0.6164900491442409E-01 0.000000000000000 0 0 0 0 0 3 + -56 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + + 1, NO = 3, NV = 6, INA = 144 + ********************************************* + + I COEFFICIENT ORDER EXPONENTS + NO = 3 NV = 6 + 0 0.1012139635548437 0.000000000000000 0 0 0 0 0 0 + 1 0.2519332323358159 0.000000000000000 1 0 0 0 0 0 + 1 -0.3519028751900755E-01 0.000000000000000 0 1 0 0 0 0 + 1 0.1910496849826397 0.000000000000000 0 0 1 0 0 0 + 1 0.2836342270292717 0.000000000000000 0 0 0 1 0 0 + 1 0.1522524565053303 0.000000000000000 0 0 0 0 0 1 + 2 0.2708167848354243 0.000000000000000 2 0 0 0 0 0 + 2 0.2836267586899650 0.000000000000000 1 1 0 0 0 0 + 2 0.2334343450010245 0.000000000000000 0 2 0 0 0 0 + 2 0.3068834148945262 0.000000000000000 1 0 1 0 0 0 + 2 0.2482648222285416 0.000000000000000 0 1 1 0 0 0 + 2 0.2829521803437524 0.000000000000000 0 0 2 0 0 0 + 2 0.9125160580465032E-01 0.000000000000000 1 0 0 1 0 0 + 2 0.2414256057276833 0.000000000000000 0 1 0 1 0 0 + 2 0.1288209910773847 0.000000000000000 0 0 1 1 0 0 + 2 0.6032088132079269E-01 0.000000000000000 1 0 0 0 0 1 + 2 0.5488217600117865E-01 0.000000000000000 0 1 0 0 0 1 + 2 0.6083996526179314E-01 0.000000000000000 0 0 1 0 0 1 + 2 0.6748585872064456E-02 0.000000000000000 0 0 0 2 0 0 + 2 0.1279983670031224 0.000000000000000 0 0 0 1 0 1 + 2 0.7761908635959314E-01 0.000000000000000 0 0 0 0 0 2 + 3 0.1881650131486588 0.000000000000000 3 0 0 0 0 0 + 3 0.1315054428081735 0.000000000000000 2 1 0 0 0 0 + 3 0.1335557825591945 0.000000000000000 1 2 0 0 0 0 + 3 0.9687320877502106E-01 0.000000000000000 0 3 0 0 0 0 + 3 0.1938299792671747 0.000000000000000 2 0 1 0 0 0 + 3 0.2660631774559422 0.000000000000000 1 1 1 0 0 0 + 3 0.2025653832430804 0.000000000000000 0 2 1 0 0 0 + 3 0.2797214953578896 0.000000000000000 1 0 2 0 0 0 + 3 0.9271663298567401E-01 0.000000000000000 0 1 2 0 0 0 + 3 0.1949619049175016 0.000000000000000 0 0 3 0 0 0 + 3 0.1862859501496422 0.000000000000000 2 0 0 1 0 0 + 3 0.1658317815122189 0.000000000000000 1 1 0 1 0 0 + 3 0.1026578995348418 0.000000000000000 0 2 0 1 0 0 + 3 0.1926579987448984 0.000000000000000 1 0 1 1 0 0 + 3 0.1277746408397872 0.000000000000000 0 1 1 1 0 0 + 3 0.1475519838955697 0.000000000000000 0 0 2 1 0 0 + 3 0.1394632699558256 0.000000000000000 2 0 0 0 0 1 + 3 0.2962874073791368E-01 0.000000000000000 1 1 0 0 0 1 + 3 0.1935166070697097 0.000000000000000 0 2 0 0 0 1 + 3 0.2234890450086370 0.000000000000000 1 0 1 0 0 1 + 3 0.2241463442634456 0.000000000000000 0 1 1 0 0 1 + 3 0.2771208383569415 0.000000000000000 0 0 2 0 0 1 + 3 -0.1066338854976658E-01 0.000000000000000 1 0 0 2 0 0 + 3 0.1816117729212960 0.000000000000000 0 1 0 2 0 0 + 3 -0.1148181323816449E-01 0.000000000000000 0 0 1 2 0 0 + 3 0.7971067193139992E-02 0.000000000000000 1 0 0 1 0 1 + 3 0.1367426850646465 0.000000000000000 0 1 0 1 0 1 + 3 0.1894625407865668 0.000000000000000 0 0 1 1 0 1 + 3 0.1020562607353473 0.000000000000000 1 0 0 0 0 2 + 3 0.2190559645815997 0.000000000000000 0 1 0 0 0 2 + 3 -0.1661354835598449E-01 0.000000000000000 0 0 1 0 0 2 + 3 0.1481826932044978 0.000000000000000 0 0 0 3 0 0 + 3 0.2176781029301927 0.000000000000000 0 0 0 2 0 1 + 3 0.1525769179472764 0.000000000000000 0 0 0 1 0 2 + 3 0.1458276972083779 0.000000000000000 0 0 0 0 0 3 + -56 0.000000000000000 0.000000000000000 0 0 0 0 0 0 + No Stochastic Radiation \ No newline at end of file diff --git a/src/normal.jl b/src/normal.jl index 25e74d0..bc83eb5 100644 --- a/src/normal.jl +++ b/src/normal.jl @@ -9,11 +9,12 @@ function normal(m::DAMap) eye = zero(m) setmatrix!(eye, I(nhv)) #eye = DAMap(I(nhv),use=m,idpt=m.idpt) - ndpt = numvars(m)-1+m.idpt + ndpt = numvars(m)-1+m.idpt # energy like variable index sgn = 1-2*m.idpt - nt = ndpt+sgn + nt = ndpt+sgn # timelike variable index zer = zero(m); zer.x[nt][nt]=1; zer.x[ndpt][ndpt] = 1 a0 = (cutord(m,2)-eye)^-1 * zer + eye + # ensure poisson bracket does not change for i=1:Int(nhv/2) a0.x[nt] += sgn*a0.x[2*i][ndpt]*mono(2*i-1,use=getdesc(m)) - sgn*a0.x[2*i-1][ndpt]*mono(2*i,use=getdesc(m)) end @@ -174,8 +175,79 @@ function equilibrium_moments(m::DAMap, a::DAMap) end +# making the 12, 34, 56 elements 0 in the normalizing map +# and returns the phase added to do so +function fast_canonize(a::DAMap, damping::Bool=!isnothing(a.idpt)) + # Basically rotates a so that we are in Courant-Snyder form of a + + a_matrix = real.(GTPSA.jacobian(a)) + ri = zero(a_matrix) + #ri .= 0 + + if !isnothing(a.idpt) # if coasting, set number of variables executing pseudo-harmonic oscillations + nhv = numvars(a)-2 + else + nhv = numvars(a) + end + + phase = zeros(numvars(a)) + + for i=1:Int(nhv/2) # for each harmonic oscillator + t = sqrt(a_matrix[2*i-1,2*i-1]^2 + a_matrix[2*i-1,2*i]^2) + cphi = a_matrix[2*i-1,2*i-1]/t + sphi = a_matrix[2*i-1,2*i]/t + if sphi*a_matrix[2*i-1,2*i] + cphi*a_matrix[2*i-1,2*i-1] < 0 + cphi = -cphi + sphi = -sphi + end + ri[2*i-1,2*i-1] = cphi + ri[2*i,2*i] = cphi + ri[2*i-1,2*i] = -sphi + ri[2*i,2*i-1] = sphi + + phase[i] += atan(sphi,cphi)/(2*pi) + end + if !isnothing(a.idpt) + ndpt = numvars(a)-1+a.idpt + sgn = 1-2*a.idpt + nt = ndpt+sgn + ri[nt,nt] = 1 + ri[ndpt,ndpt] = 1 + ri[nt,ndpt] = -a_matrix[nt,ndpt] + phase[end] += a_matrix[nt,ndpt] + end + #return ri + a_rot = a_matrix*ri + return a_rot + + # Now we have rotated a so that a_12, a_34, a_56, etc are 0 (Courant Snyder) + # But if we have damping, we also have + # A*S*transpose(A) != S + # We can multiply the normalizing map A by some dilation to make it so that, + # even though we don't have exactly A*S*transpose(A) == S, that + # we atleast have (A*S*transpose(A))[1,2] == 1, (A*S*transpose(A))[2,1] == -1, etc + + # note that with damping we have M as + # A*Λ*R*A^-1 where R is the amplitude dependent rotation (diagonal matrix with + # complex values on unit circle) and Λ is a diagonal matrix with real values + # which correspond to the damping (same in each plane, Diagonal(lambda1, lambda1, lambda2, lambda2, etc) + + if damping + damp = zeros(numvars(a)) + a = zeros(Int(numvars(a)/2), Int(numvars(a)/2)) + for i=1:Int(numvars(a)/2) + a[i,i] = a_rot[2*i-1,2*i-1]*a_rot[2*i,2*i]-a_rot[2*i-1,2*i]*a_rot[2*i,2*i-1] + for j=1:Int(numvars(a)/2) + if i != j + + end + end + end + end + +end diff --git a/src/utils/misc.jl b/src/utils/misc.jl index 0df8ac7..025347e 100644 --- a/src/utils/misc.jl +++ b/src/utils/misc.jl @@ -77,7 +77,7 @@ end isnothing(m.Q) || eltype(m.Q) == eltype(m.x) || error("Quaternion type $(eltype(m.Q)) must be $(eltype(m.x)) (equal to orbital)") isnothing(m.E)|| eltype(m.E) == numtype(eltype(m.x)) || error("Stochastic matrix type $(eltype(m.E)) must be $(numtype(eltype(m.x))) (equal to scalar of orbital)") end - +#= # --- random symplectic map --- function rand(t::Union{Type{DAMap},Type{TPSAMap}}; spin::Union{Bool,Nothing}=nothing, FD::Union{Bool,Nothing}=nothing, use::Union{Descriptor,TPS,ComplexTPS}=GTPSA.desc_current, ndpt::Union{Nothing,Integer}=nothing) if isnothing(spin) @@ -107,12 +107,7 @@ end """ Generate map symplectic up to order in Descriptor """ -function rand(t::Union{Type{DAMap{S,T,U,V}},Type{TPSAMap{S,T,U,V}}}; require_stable::Bool=false, use::Union{Descriptor,TPS,ComplexTPS}=GTPSA.desc_current) where {S,T,U,V} - if require_stable # make hamiltonian in phasors basis then reverse - - - end - +function rand(t::Union{Type{DAMap},Type{TPSAMap}}; require_stable::Bool=true, use::Union{Descriptor,TPS,ComplexTPS}=GTPSA.desc_current, spin::Bool=false, FD::Bool=false) where {S,T,U,V} desc = getdesc(use) desc.desc != C_NULL || error("No Descriptor defined!") @@ -130,19 +125,27 @@ function rand(t::Union{Type{DAMap{S,T,U,V}},Type{TPSAMap{S,T,U,V}}}; require_sta @views dtmp = Descriptor(no[1:nv].+1, mo+1) end - # If require_stable, we need to go into phasors basis - - - - h = T(use=dtmp) - len = length(h) - - # random coefficients for hamiltonian except 0th and 1st order terms - for i=nv+1:len-1 - h[i] = rand(numtype(T)) + if require_stable # make hamiltonian in phasors basis then reverse + h = ComplexTPS(use=dtmp) + len = length(h) + # random coefficients for hamiltonian except 0th and 1st order terms + for i=nv+1:len-1 + h[i] = rand(numtype(T)) + end + c = from_phasor(DAMap(spin=spin,FD=FD)) + hc = h * c + else + h = TPS(use=dtmp) + len = length(h) + + # random coefficients for hamiltonian except 0th and 1st order terms + for i=nv+1:len-1 + h[i] = rand(numtype(T)) + end + hc = h end - - F = VectorField{T,U}(h) + + F = VectorField(h) mtmp = exp(F) # Make a copy and change the descriptor @@ -167,7 +170,7 @@ function rand(t::Union{Type{DAMap{S,T,U,V}},Type{TPSAMap{S,T,U,V}}}; require_sta return m end - +=#