**** GENERATION OF THE TLS MATRICES **** ** input control information ** Libration rms around L-axes dx ,dy ,dz = 0.2000000 0.3000000 0.1000000 vectors defining two first Libration axes 1.00000 1.00000 0.00000 0.00000 1.00000 1.00000 rotation axes pass through the points in the M(main) base parallel to lx : (wix,wiy,wiz)= 0.11000 0.31000 0.21000 parallel to ly : (wjx,wjy,wjz)= -0.22000 0.32000 0.42000 parallel to lz : (wkx,wky,wkz)= 0.43000 0.33000 0.23000 correlation shifts sx,sy,sz for libration 0.240000 0.130000 0.150000 Vibration rms along V-axes tx ,ty ,tz = 0.0000000 0.0000000 0.0000000 vectors defining two first Vibration axes 1.00000 0.00000 0.00000 0.00000 1.00000 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 0.57735 -0.57735 0.57735 0.70711 0.70711 0.00000 -0.40825 0.40825 0.81650 rotation axes pass through the points in the M base axis 1 : (w1x,w1y,w1z)= 0.43000 0.33000 0.23000 axis 2 : (w2x,w2y,w2z)= 0.11000 0.31000 0.21000 axis 3 : (w3x,w3y,w3z)= -0.22000 0.32000 0.42000 rotation axes pass through the points in the L base parallel to lx : (wix,wiy,wiz)= 0.19053 0.53740 0.14697 parallel to ly : (wjx,wjy,wjz)= 0.00577 0.29698 0.25311 parallel to lz : (wkx,wky,wkz)= -0.06928 0.07071 0.56338 correlation shifts sx,sy,sz for libration 0.150000 0.240000 0.130000 Vibration rms along V-axes tx ,ty ,tz = 0.0000000 0.0000000 0.0000000 vectors defining three Vibration axes 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000 =================== TLS BUILT FROM THE BASE ELEMENTS ================== matrices T L S in the original M-base matrix T 0.00413383357227 -0.00036583305337 -0.00068066676613 -0.00036583311157 0.00250183325261 0.00012866679754 -0.00068066664971 0.00012866685574 0.00396433332935 matrix L 0.03833333402872 0.00166666635778 -0.02666666544974 0.00166666635778 0.03833333402872 0.02666666544974 -0.02666666544974 0.02666666544974 0.06333333253860 matrix S 0.00161666655913 0.00558333238587 -0.01143333222717 -0.00041666621109 0.01241666637361 0.00343333324417 0.00506666814908 0.00333333481103 0.00876666605473 ================ 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 0.004134 -0.000366 -0.000681 0.038333 0.001667 -0.026667 0.001617 0.005583 -0.011433 -0.000366 0.002502 0.000129 0.001667 0.038333 0.026667 -0.000417 0.012417 0.003433 -0.000681 0.000129 0.003964 -0.026667 0.026667 0.063333 0.005067 0.003333 0.008767 ***** STEP B : libration amplitudes and axes three eigenvalues and corresponding eigenvectors: 0.010000 0.577350 -0.577350 0.577350 0.040000 0.707107 0.707107 0.000000 0.090000 -0.408248 0.408248 0.816497 rotation matrix P->L and its transposal: 0.577350 0.707107 -0.408248 0.577350 -0.577350 0.577350 -0.577350 0.707107 0.408248 0.707107 0.707107 0.000000 0.577350 0.000000 0.816497 -0.408248 0.408248 0.816497 resulted matrices T[L] L[L] S[L] in the L-base 0.003238 0.000441 -0.000058 0.010000 0.000000 0.000000 0.001500 0.001470 -0.005374 0.000441 0.002952 -0.000790 0.000000 0.040000 0.000000 -0.010125 0.009600 0.000231 -0.000058 -0.000790 0.004410 0.000000 0.000000 0.090000 0.006364 0.006235 0.011700 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 0.537401 0.146969 axis Ly crosses the point 0.005774 0.000000 0.253114 axis Lz crosses the point -0.069282 0.070711 0.000000 ***** STEP D : optimal screw parameters D[L] matrix to be removed from the T matrix : -0.003013 -0.000441 0.000058 -0.000441 -0.000648 0.000790 0.000058 0.000790 -0.002889 resulted matrices TC[L] L[L] S[L] in the L-base 0.000225 0.000000 0.000000 0.010000 0.000000 0.000000 0.001500 0.001470 -0.005374 0.000000 0.002304 0.000000 0.000000 0.040000 0.000000 -0.010125 0.009600 0.000231 0.000000 0.000000 0.001521 0.000000 0.000000 0.090000 0.006364 0.006235 0.011700 diagonal shift for the unconstrained min[tr(S)] 0.007600 checking Cauchy enequality general case : three librations ts limits : tminc,tmaxc 0.000000 0.003000 checking positive definition of the residual matrix eigenvalues of T[lambda] 0.00000 0.00009 0.00014 ts limits : tmint,tmaxt 0.000000 0.013200 ts limits : tmina,tmaxa 0.000000 0.013200 final limits : tmin,tmax 0.000000 0.003000 constrained ts to be removed from the S diagonal 0.003000 screw parameters sx,sy,sz -0.14997 0.16501 0.09667 C[L] matrix diagonal elements 0.00022 0.00109 0.00084 ***** STEP E : vibration parameters matrix V[L]: 0.000000 0.000000 0.000000 0.000000 0.001215 0.000000 0.000000 0.000000 0.000680 eigenvalues and eigenvectors in base [L]: 0.000000 -1.000000 0.000000 0.000000 0.000680 0.000000 -0.000001 1.000000 0.001215 0.000000 1.000000 0.000001 rotation matrix [P] -> [L]: 0.577350 0.707107 -0.408248 -0.577350 0.707107 0.408248 0.577350 0.000000 0.816497 vibration tx,ty,tz along V axes & axes in base [M]: 0.000300 -0.577350 0.577350 -0.577350 0.026076 -0.408248 0.408248 0.816497 0.034855 0.707106 0.707107 0.000000 W points recalculated in the P and M bases 0.320000 0.440000 0.120000 0.320000 0.440000 0.120000 -0.100000 0.100000 0.210000 -0.100000 0.100000 0.210000 0.010000 0.090000 -0.040000 0.010000 0.090000 -0.040000 ==================================================== *** TLS DECOMPOSED : BASIC ELEMENTS *** Libration rms around L-axes dx ,dy ,dz = 0.1000000 0.2000000 0.3000000 unit vectors defining three Libration axes 0.57735 -0.57735 0.57735 0.70711 0.70711 0.00000 -0.40825 0.40825 0.81650 rotation axes pass through the points in the M base parallel to lx : (wix,wiy,wiz)= 0.32000 0.44000 0.12000 parallel to ly : (wjx,wjy,wjz)= -0.10000 0.10000 0.21000 parallel to lz : (wkx,wky,wkz)= 0.01000 0.09000 -0.04000 rotation axes pass through the points in the L base parallel to lx : (wix,wiy,wiz)= 0.00000 0.53740 0.14697 parallel to ly : (wjx,wjy,wjz)= 0.00577 0.00000 0.25311 parallel to lz : (wkx,wky,wkz)= -0.06928 0.07071 0.00000 correlation shifts sx,sy,sz for libration -0.149970 0.165007 0.096670 Vibration rms along V-axes tx ,ty ,tz = 0.0003000 0.0260757 0.0348554 vectors defining three Vibration axes -0.57735 0.57735 -0.57735 -0.40825 0.40825 0.81650 0.70711 0.70711 0.00000 =================== TLS BUILT FROM THE BASE ELEMENTS ================== matrices T L S in the original M-base 0.004134 -0.000366 -0.000681 0.038333 0.001667 -0.026667 -0.001383 0.005583 -0.011433 -0.000366 0.002502 0.000129 0.001667 0.038333 0.026667 -0.000417 0.009417 0.003433 -0.000681 0.000129 0.003964 -0.026667 0.026667 0.063333 0.005067 0.003333 0.005767 =================== REMINDER OF THE INPUT MATRICES =================== matrices T L S in the original M-base 0.004134 -0.000366 -0.000681 0.038333 0.001667 -0.026667 0.001617 0.005583 -0.011433 -0.000366 0.002502 0.000129 0.001667 0.038333 0.026667 -0.000417 0.012417 0.003433 -0.000681 0.000129 0.003964 -0.026667 0.026667 0.063333 0.005067 0.003333 0.008767 =============== MATRICES DIFFERENCE =============== matrices T L S : new - inital 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.003000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.003000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.003000