**** GENERATION OF THE TLS MATRICES **** ** input control information ** Libration rms around L-axes dx ,dy ,dz = 0.1000000 0.2000000 0.3000000 vectors defining two first Libration axes 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 rotation axes pass through the points in the M(main) base parallel to lx : (wix,wiy,wiz)= 0.00000 2.00000 3.00000 parallel to ly : (wjx,wjy,wjz)= -1.00000 0.00000 2.00000 parallel to lz : (wkx,wky,wkz)= 4.00000 1.00000 0.00000 correlation shifts sx,sy,sz for libration 0.500000 -0.300000 0.700000 Vibration rms along V-axes tx ,ty ,tz = 0.1000000 0.4000000 0.8000000 vectors defining two first Vibration axes 1.00000 1.00000 1.00000 1.00000 0.00000 0.00000 center of reaction will not be used for decomposition ==================================================== *** ORIGINAL ELEMENTS OF THE TLS MATRICES *** ** after correction of the axes order ** Libration rms around L-axes dx ,dy ,dz = 0.1000000 0.2000000 0.3000000 unit vectors defining three Libration axes 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000 rotation axes pass through the points in the M base axis 1 : (w1x,w1y,w1z)= 0.00000 2.00000 3.00000 axis 2 : (w2x,w2y,w2z)= -1.00000 0.00000 2.00000 axis 3 : (w3x,w3y,w3z)= 4.00000 1.00000 0.00000 rotation axes pass through the points in the L base parallel to lx : (wix,wiy,wiz)= 0.00000 2.00000 3.00000 parallel to ly : (wjx,wjy,wjz)= -1.00000 0.00000 2.00000 parallel to lz : (wkx,wky,wkz)= 4.00000 1.00000 0.00000 correlation shifts sx,sy,sz for libration 0.500000 -0.300000 0.700000 Vibration rms along V-axes tx ,ty ,tz = 0.1000000 0.4000000 0.8000000 vectors defining three Vibration axes 0.57735 0.57735 0.57735 0.81650 -0.40825 -0.40825 0.00000 0.70711 -0.70711 =================== TLS BUILT FROM THE BASE ELEMENTS ================== matrices T L S in the original M-base matrix T 0.36249999701977 -0.41000001132488 0.03000000119209 -0.41000001132488 1.88359996676445 -0.34999999031425 0.03000000119209 -0.34999999031425 0.47409999370575 matrix L 0.00999999977648 0.00000000000000 0.00000000000000 0.00000000000000 0.03999999910593 0.00000000000000 0.00000000000000 0.00000000000000 0.09000000357628 matrix S 0.00499999988824 0.02999999932945 -0.01999999955297 -0.07999999821186 -0.01200000010431 -0.03999999910593 0.09000000357628 -0.36000001430511 0.06300000101328 ================ TLS DECOMPOSITION ================ ***** STEP A : from M-base to P-base P-shift : 0.000000 0.000000 0.000000 transition P-matrix and its transposal 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 resulted matrices T[P] L[P] S[P] in the P-base 0.362500 -0.410000 0.030000 0.010000 0.000000 0.000000 0.005000 0.030000 -0.020000 -0.410000 1.883600 -0.350000 0.000000 0.040000 0.000000 -0.080000 -0.012000 -0.040000 0.030000 -0.350000 0.474100 0.000000 0.000000 0.090000 0.090000 -0.360000 0.063000 ***** STEP B : libration amplitudes and axes three eigenvalues and corresponding eigenvectors: 0.010000 1.000000 0.000000 0.000000 0.040000 0.000000 1.000000 0.000000 0.090000 0.000000 0.000000 1.000000 rotation matrix P->L and its transposal: 1.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 1.000000 resulted matrices T[L] L[L] S[L] in the L-base 0.362500 -0.410000 0.030000 0.010000 0.000000 0.000000 0.005000 0.030000 -0.020000 -0.410000 1.883600 -0.350000 0.000000 0.040000 0.000000 -0.080000 -0.012000 -0.040000 0.030000 -0.350000 0.474100 0.000000 0.000000 0.090000 0.090000 -0.360000 0.063000 libration amplitudes around the L axes: 0.100000 0.200000 0.300000 ***** STEP C : W points in the L-base axis Lx crosses the point 0.000000 2.000000 3.000000 axis Ly crosses the point -1.000000 0.000000 2.000000 axis Lz crosses the point 4.000000 1.000000 0.000000 ***** STEP D : optimal screw parameters D[L] matrix to be removed from the T matrix : -0.250000 0.360000 -0.080000 0.360000 -1.530000 0.060000 -0.080000 0.060000 -0.080000 resulted matrices TC[L] L[L] S[L] in the L-base 0.112500 -0.050000 -0.050000 0.010000 0.000000 0.000000 0.005000 0.030000 -0.020000 -0.050000 0.353600 -0.290000 0.000000 0.040000 0.000000 -0.080000 -0.012000 -0.040000 -0.050000 -0.290000 0.394100 0.000000 0.000000 0.090000 0.090000 -0.360000 0.063000 diagonal shift for the unconstrained min[tr(S)] 0.018667 checking Cauchy enequality general case : three librations ts limits : tminc,tmaxc -0.028541 0.038541 checking positive definition of the residual matrix eigenvalues of T[lambda] 0.00046 0.00505 0.04523 ts limits : tmint,tmaxt -0.149671 0.200671 ts limits : tmina,tmaxa -0.149671 0.200671 final limits : tmin,tmax -0.028541 0.038541 constrained ts to be removed from the S diagonal 0.018665 screw parameters sx,sy,sz -1.36646 -0.76662 0.49262 C[L] matrix diagonal elements 0.01867 0.02351 0.02184 ***** STEP E : vibration parameters matrix V[L]: 0.093828 -0.050000 -0.050000 -0.050000 0.330092 -0.290000 -0.050000 -0.290000 0.372260 eigenvalues and eigenvectors in base [L]: 0.004502 -0.620466 -0.572587 -0.535879 0.149724 0.784219 -0.457151 -0.419540 0.641953 -0.004755 -0.680557 0.732680 rotation matrix [P] -> [L]: 1.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 1.000000 vibration tx,ty,tz along V axes & axes in base [M]: 0.067100 -0.620466 -0.572587 -0.535879 0.386941 0.784219 -0.457151 -0.419540 0.801220 -0.004755 -0.680557 0.732680 W points recalculated in the P and M bases 0.000000 2.000000 3.000000 0.000000 2.000000 3.000000 -1.000000 0.000000 2.000000 -1.000000 0.000000 2.000000 4.000000 1.000000 0.000000 4.000000 1.000000 0.000000 ==================================================== *** TLS DECOMPOSED : BASIC ELEMENTS *** Libration rms around L-axes dx ,dy ,dz = 0.1000000 0.2000000 0.3000000 unit vectors defining three Libration axes 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000 rotation axes pass through the points in the M base parallel to lx : (wix,wiy,wiz)= 0.00000 2.00000 3.00000 parallel to ly : (wjx,wjy,wjz)= -1.00000 0.00000 2.00000 parallel to lz : (wkx,wky,wkz)= 4.00000 1.00000 0.00000 rotation axes pass through the points in the L base parallel to lx : (wix,wiy,wiz)= 0.00000 2.00000 3.00000 parallel to ly : (wjx,wjy,wjz)= -1.00000 0.00000 2.00000 parallel to lz : (wkx,wky,wkz)= 4.00000 1.00000 0.00000 correlation shifts sx,sy,sz for libration -1.366461 -0.766615 0.492615 Vibration rms along V-axes tx ,ty ,tz = 0.0671004 0.3869413 0.8012200 vectors defining three Vibration axes -0.62047 -0.57259 -0.53588 0.78422 -0.45715 -0.41954 -0.00475 -0.68056 0.73268 =================== TLS BUILT FROM THE BASE ELEMENTS ================== matrices T L S in the original M-base 0.362500 -0.410000 0.030000 0.010000 0.000000 0.000000 -0.013665 0.030000 -0.020000 -0.410000 1.883600 -0.350000 0.000000 0.040000 0.000000 -0.080000 -0.030665 -0.040000 0.030000 -0.350000 0.474100 0.000000 0.000000 0.090000 0.090000 -0.360000 0.044335 =================== REMINDER OF THE INPUT MATRICES =================== matrices T L S in the original M-base 0.362500 -0.410000 0.030000 0.010000 0.000000 0.000000 0.005000 0.030000 -0.020000 -0.410000 1.883600 -0.350000 0.000000 0.040000 0.000000 -0.080000 -0.012000 -0.040000 0.030000 -0.350000 0.474100 0.000000 0.000000 0.090000 0.090000 -0.360000 0.063000 =============== MATRICES DIFFERENCE =============== matrices T L S : new - inital 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.018665 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.018665 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.018665