**** GENERATION OF THE TLS MATRICES **** ** input control information ** Libration rms around L-axes dx ,dy ,dz = 0.1000000 0.3000000 0.3000000 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 0.200000 0.200000 0.200000 Vibration rms along V-axes tx ,ty ,tz = 0.4000000 0.4000000 0.4000000 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 0.3000000 0.3000000 unit vectors defining three Libration axes -0.70711 -0.70711 0.00000 0.57735 -0.57735 0.57735 -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 0.200000 0.200000 0.200000 Vibration rms along V-axes tx ,ty ,tz = 0.4000000 0.4000000 0.4000000 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 0.16199999651872 -0.00160000007600 0.00000000005743 -0.00160000007600 0.16199999651872 -0.00000000005743 0.00000000005743 -0.00000000005743 0.16359999659471 matrix L 0.05000000074506 -0.03999999910593 0.00000000067104 -0.03999999910593 0.05000000074506 -0.00000000067104 0.00000000067104 -0.00000000067104 0.08999999612570 matrix S 0.00999999977648 -0.00800000037998 -0.00000000060144 -0.00800000037998 0.00999999977648 0.00000000060144 -0.00000000060144 0.00000000060144 0.01799999922514 ================ 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 0.162000 -0.001600 0.000000 0.050000 -0.040000 0.000000 0.010000 -0.008000 0.000000 -0.001600 0.162000 0.000000 -0.040000 0.050000 0.000000 -0.008000 0.010000 0.000000 0.000000 0.000000 0.163600 0.000000 0.000000 0.090000 0.000000 0.000000 0.018000 ***** STEP B : libration amplitudes and axes three eigenvalues and corresponding eigenvectors: 0.010000 0.707107 0.707107 0.000000 0.090000 -0.707107 0.707107 0.000000 0.090000 0.000000 0.000000 1.000000 rotation matrix P->L and its transposal: 0.707107 -0.707107 0.000000 0.707107 0.707107 0.000000 0.707107 0.707107 0.000000 -0.707107 0.707107 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 0.160400 0.000000 0.000000 0.010000 0.000000 0.000000 0.002000 0.000000 0.000000 0.000000 0.163600 0.000000 0.000000 0.090000 0.000000 0.000000 0.018000 0.000000 0.000000 0.000000 0.163600 0.000000 0.000000 0.090000 0.000000 0.000000 0.018000 libration amplitudes around the L axes: 0.100000 0.300000 0.300000 ***** 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 0.160400 0.000000 0.000000 0.010000 0.000000 0.000000 0.002000 0.000000 0.000000 0.000000 0.163600 0.000000 0.000000 0.090000 0.000000 0.000000 0.018000 0.000000 0.000000 0.000000 0.163600 0.000000 0.000000 0.090000 0.000000 0.000000 0.018000 diagonal shift for the unconstrained min[tr(S)] 0.012667 checking Cauchy enequality general case : three librations ts limits : tminc,tmaxc -0.038050 0.042050 checking positive definition of the residual matrix eigenvalues of T[lambda] 0.00160 0.01472 0.01472 ts limits : tmint,tmaxt -0.079293 0.123342 ts limits : tmina,tmaxa -0.079293 0.123342 final limits : tmin,tmax -0.038050 0.042050 constrained ts to be removed from the S diagonal 0.012661 screw parameters sx,sy,sz -1.06613 0.05932 0.05932 C[L] matrix diagonal elements 0.01137 0.00032 0.00032 ***** STEP E : vibration parameters matrix V[L]: 0.149034 0.000000 0.000000 0.000000 0.163283 0.000000 0.000000 0.000000 0.163283 eigenvalues and eigenvectors in base [L]: 0.149034 1.000000 0.000000 0.000000 0.163283 0.000000 1.000000 0.000000 0.163284 0.000000 0.000000 1.000000 rotation matrix [P] -> [L]: 0.707107 -0.707107 0.000000 0.707107 0.707107 0.000000 0.000000 0.000000 1.000000 vibration tx,ty,tz along V axes & axes in base [M]: 0.386049 0.707107 0.707107 0.000000 0.404083 -0.707107 0.707107 0.000000 0.404084 0.000000 0.000000 1.000000 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 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 ==================================================== *** TLS DECOMPOSED : BASIC ELEMENTS *** Libration rms around L-axes dx ,dy ,dz = 0.1000000 0.3000000 0.3000000 unit vectors defining three Libration axes 0.70711 0.70711 0.00000 -0.70711 0.70711 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 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 -1.066130 0.059319 0.059319 Vibration rms along V-axes tx ,ty ,tz = 0.3860488 0.4040829 0.4040837 vectors defining three Vibration axes 0.70711 0.70711 0.00000 -0.70711 0.70711 0.00000 0.00000 0.00000 1.00000 =================== TLS BUILT FROM THE BASE ELEMENTS ================== matrices T L S in the original M-base 0.162000 -0.001600 0.000000 0.050000 -0.040000 0.000000 -0.002661 -0.008000 0.000000 -0.001600 0.162000 0.000000 -0.040000 0.050000 0.000000 -0.008000 -0.002661 0.000000 0.000000 0.000000 0.163600 0.000000 0.000000 0.090000 0.000000 0.000000 0.005339 =================== REMINDER OF THE INPUT MATRICES =================== matrices T L S in the original M-base 0.162000 -0.001600 0.000000 0.050000 -0.040000 0.000000 0.010000 -0.008000 0.000000 -0.001600 0.162000 0.000000 -0.040000 0.050000 0.000000 -0.008000 0.010000 0.000000 0.000000 0.000000 0.163600 0.000000 0.000000 0.090000 0.000000 0.000000 0.018000 =============== MATRICES DIFFERENCE =============== matrices T L S : new - inital 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.012661 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.012661 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.012661