**** GENERATION OF THE TLS MATRICES **** ** input control information ** Libration rms around L-axes dx ,dy ,dz = 0.2000000 0.0000000 0.0000000 vectors defining two first Libration axes 1.00000 1.00000 0.00000 -1.00000 1.00000 0.00000 rotation axes pass through the points in the M(main) base parallel to lx : (wix,wiy,wiz)= 0.50000 1.50000 2.50000 parallel to ly : (wjx,wjy,wjz)= 0.00000 0.00000 0.00000 parallel to lz : (wkx,wky,wkz)= 0.00000 0.00000 0.00000 correlation shifts sx,sy,sz for libration 0.000000 0.000000 0.000000 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 = 0.0000000 0.0000000 0.2000000 unit vectors defining three Libration axes -0.70711 0.70711 0.00000 0.00000 0.00000 1.00000 0.70711 0.70711 0.00000 rotation axes pass through the points in the M base axis 1 : (w1x,w1y,w1z)= 0.00000 0.00000 0.00000 axis 2 : (w2x,w2y,w2z)= 0.00000 0.00000 0.00000 axis 3 : (w3x,w3y,w3z)= 0.50000 1.50000 2.50000 rotation axes pass through the points in the L base parallel to lx : (wix,wiy,wiz)= 0.00000 0.00000 0.00000 parallel to ly : (wjx,wjy,wjz)= 0.00000 0.00000 0.00000 parallel to lz : (wkx,wky,wkz)= 0.70711 2.50000 1.41421 correlation shifts sx,sy,sz for libration 0.000000 0.000000 0.000000 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 0.12500000000000 -0.12500000000000 0.05000000447035 -0.12500000000000 0.12500000000000 -0.05000000447035 0.05000000074506 -0.05000000074506 0.02000000327826 matrix L 0.01999999955297 0.01999999955297 0.00000000000000 0.01999999955297 0.01999999955297 0.00000000000000 0.00000000000000 0.00000000000000 0.00000000000000 matrix S -0.05000000074506 0.05000000074506 -0.02000000141561 -0.05000000074506 0.05000000074506 -0.02000000141561 0.00000000000000 0.00000000000000 0.00000000000000 ================ 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 0.125000 -0.125000 0.050000 0.020000 0.020000 0.000000 -0.050000 0.050000 -0.020000 -0.125000 0.125000 -0.050000 0.020000 0.020000 0.000000 -0.050000 0.050000 -0.020000 0.050000 -0.050000 0.020000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 ***** STEP B : libration amplitudes and axes three eigenvalues and corresponding eigenvectors: 0.000000 -0.707107 0.707107 0.000000 0.000002 0.000000 0.000000 1.000000 0.040000 0.707107 0.707107 0.000000 rotation matrix P->L and its transposal: -0.707107 0.000000 0.707107 -0.707107 0.707107 0.000000 0.707107 0.000000 0.707107 0.000000 0.000000 1.000000 0.000000 1.000000 0.000000 0.707107 0.707107 0.000000 resulted matrices T[L] L[L] S[L] in the L-base 0.250000 -0.070711 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.070711 0.020000 0.000000 0.000000 0.000002 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.040000 0.100000 -0.028284 0.000000 libration amplitudes around the L axes: 0.000000 0.001494 0.200000 ***** STEP C : W points in the L-base axis Lx crosses the point 0.000000 0.000000 0.000000 axis Ly crosses the point 0.000000 0.000000 0.000000 axis Lz crosses the point 0.707107 2.500000 0.000000 ***** STEP D : optimal screw parameters D[L] matrix to be removed from the T matrix : -0.250000 0.070711 0.000000 0.070711 -0.020000 0.000000 0.000000 0.000000 0.000000 resulted matrices TC[L] L[L] S[L] in the L-base 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 0.000002 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.040000 0.100000 -0.028284 0.000000 diagonal shift for the unconstrained min[tr(S)] - non applicable checking Cauchy enequality special case : one of librations is degenerated ts limits : tminc,tmaxc - non applicable checking positive definition of the residual matrix eigenvalues of T[lambda] - non applicable ts limits : tmint,tmaxt - non applicable ts limits : tmina,tmaxa - non applicable final limits : tmin,tmax - non applicable constrained ts to be removed from the S diagonal 0.000000 screw parameters sx,sy,sz 0.00000 -0.00077 0.00000 C[L] matrix diagonal elements 0.00000 0.00000 0.00000 ***** STEP E : vibration parameters matrix V[L]: 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 eigenvalues and eigenvectors in base [L]: 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 1.000000 rotation matrix [P] -> [L]: -0.707107 0.000000 0.707107 0.707107 0.000000 0.707107 0.000000 1.000000 0.000000 vibration tx,ty,tz along V axes & axes in base [M]: 0.000000 -0.707107 0.707107 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.707107 0.707107 0.000000 W points recalculated in the P and M bases 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.500000 0.500000 2.500000 -0.500000 0.500000 2.500000 ==================================================== *** TLS DECOMPOSED : BASIC ELEMENTS *** Libration rms around L-axes dx ,dy ,dz = 0.0000000 0.0014937 0.2000000 unit vectors defining three Libration axes -0.70711 0.70711 0.00000 0.00000 0.00000 1.00000 0.70711 0.70711 0.00000 rotation axes pass through the points in the M base parallel to lx : (wix,wiy,wiz)= 0.00000 0.00000 0.00000 parallel to ly : (wjx,wjy,wjz)= 0.00000 0.00000 0.00000 parallel to lz : (wkx,wky,wkz)= -0.50000 0.50000 2.50000 rotation axes pass through the points in the L base parallel to lx : (wix,wiy,wiz)= 0.00000 0.00000 0.00000 parallel to ly : (wjx,wjy,wjz)= 0.00000 0.00000 0.00000 parallel to lz : (wkx,wky,wkz)= 0.70711 2.50000 0.00000 correlation shifts sx,sy,sz for libration 0.000000 -0.000769 0.000000 Vibration rms along V-axes tx ,ty ,tz = 0.0000000 0.0000000 0.0000000 vectors defining three Vibration axes -0.70711 0.70711 0.00000 0.00000 0.00000 1.00000 0.70711 0.70711 0.00000 =================== TLS BUILT FROM THE BASE ELEMENTS ================== matrices T L S in the original M-base 0.125000 -0.125000 0.050000 0.020000 0.020000 0.000000 -0.050000 0.050000 -0.020000 -0.125000 0.125000 -0.050000 0.020000 0.020000 0.000000 -0.050000 0.050000 -0.020000 0.050000 -0.050000 0.020000 0.000000 0.000000 0.000002 0.000000 0.000000 0.000000 =================== REMINDER OF THE INPUT MATRICES =================== matrices T L S in the original M-base 0.125000 -0.125000 0.050000 0.020000 0.020000 0.000000 -0.050000 0.050000 -0.020000 -0.125000 0.125000 -0.050000 0.020000 0.020000 0.000000 -0.050000 0.050000 -0.020000 0.050000 -0.050000 0.020000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 =============== MATRICES DIFFERENCE =============== matrices T L S : new - inital 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 0.000000 0.000000 0.000000 0.000000 0.000000 0.000002 0.000000 0.000000 0.000000