**** GENERATION OF THE TLS MATRICES **** ** input control information ** Libration rms around L-axes dx ,dy ,dz = 2.0000000 3.0000000 1.0000000 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)= 0.00000 0.00000 0.00000 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 = 1.0000000 2.0000000 3.0000000 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)= 0.00000 0.00000 0.00000 axis 2 : (w2x,w2y,w2z)= 0.00000 0.00000 0.00000 axis 3 : (w3x,w3y,w3z)= 0.00000 0.00000 0.00000 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)= 0.00000 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 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 0.00000000000000 0.00000000000000 0.00000000000000 0.00000000000000 0.00000000000000 0.00000000000000 0.00000000000000 0.00000000000000 0.00000000000000 matrix L 3.83333325386047 0.16666662693024 -2.66666674613953 0.16666662693024 3.83333325386047 2.66666674613953 -2.66666674613953 2.66666674613953 6.33333349227905 matrix S 0.00000000000000 0.00000000000000 0.00000000000000 0.00000000000000 0.00000000000000 0.00000000000000 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 0.000000 0.000000 0.000000 3.833333 0.166667 -2.666667 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.166667 3.833333 2.666667 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.666667 2.666667 6.333333 0.000000 0.000000 0.000000 ***** STEP B : libration amplitudes and axes three eigenvalues and corresponding eigenvectors: 1.000000 0.577350 -0.577350 0.577350 4.000000 0.707107 0.707107 0.000000 9.000000 -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 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 4.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 9.000000 0.000000 0.000000 0.000000 libration amplitudes around the L axes: 1.000000 2.000000 3.000000 ***** 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 0.000000 0.000000 0.000000 ***** STEP D : optimal screw parameters D[L] matrix to be removed from the T matrix : 0.000000 0.000000 0.000000 0.000000 0.000000 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 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 4.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 9.000000 0.000000 0.000000 0.000000 diagonal shift for the unconstrained min[tr(S)] 0.000000 checking Cauchy enequality general case : three librations ts limits : tminc,tmaxc 0.000000 0.000000 checking positive definition of the residual matrix eigenvalues of T[lambda] 0.00000 0.00000 0.00000 ts limits : tmint,tmaxt 0.000000 0.000000 ts limits : tmina,tmaxa 0.000000 0.000000 final limits : tmin,tmax 0.000000 0.000000 constrained ts to be removed from the S diagonal 0.000000 screw parameters sx,sy,sz 0.00000 0.00000 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]: 0.577350 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]: 0.000000 0.577350 -0.577350 0.577350 0.000000 0.707107 0.707107 0.000000 0.000000 -0.408248 0.408248 0.816497 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 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 ==================================================== *** TLS DECOMPOSED : BASIC ELEMENTS *** Libration rms around L-axes dx ,dy ,dz = 0.9999999 1.9999999 3.0000000 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)= 0.00000 0.00000 0.00000 parallel to ly : (wjx,wjy,wjz)= 0.00000 0.00000 0.00000 parallel to lz : (wkx,wky,wkz)= 0.00000 0.00000 0.00000 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)= 0.00000 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 three Vibration axes 0.57735 -0.57735 0.57735 0.70711 0.70711 0.00000 -0.40825 0.40825 0.81650 =================== TLS BUILT FROM THE BASE ELEMENTS ================== matrices T L S in the original M-base 0.000000 0.000000 0.000000 3.833333 0.166666 -2.666667 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.166667 3.833333 2.666667 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.666667 2.666667 6.333333 0.000000 0.000000 0.000000 =================== REMINDER OF THE INPUT MATRICES =================== matrices T L S in the original M-base 0.000000 0.000000 0.000000 3.833333 0.166667 -2.666667 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.166667 3.833333 2.666667 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -2.666667 2.666667 6.333333 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 0.000000 0.000000 0.000000 0.000000