June 24 2002 12:55:43.253 PM LAWSON_PRB Tests for the LAWSON package of least squares routines. TEST01 HFT factors a least squares problem; HS1 solves a factored least squares problem; COV computes the associated covariance matrix. No checking will be made for rank deficiency in this test. Such checks are made in later tests. No noise used in matrix generation. m n 1 1 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 0.21111111E+01 residual length = 0.0000E+00 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.49382716E-03 m n 2 1 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.80780644E+00 residual length = 0.6410E+02 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.45651678E-05 m n 2 2 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.10750000E+01 2 0.11583333E+01 residual length = 0.0000E+00 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.28450000E-03 1 2 -0.26283333E-03 2 2 0.24672222E-03 m n 3 1 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.29803816E+00 residual length = 0.3119E+03 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.35832661E-05 m n 3 2 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.16166667E+01 2 0.21166667E+01 residual length = 0.2041E+03 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.14461458E-03 1 2 -0.13867708E-03 2 2 0.13586458E-03 m n 3 3 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.21600000E+01 2 -0.68000000E+00 3 -0.16000000E+00 residual length = 0.0000E+00 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.22140000E-04 1 2 0.51200000E-05 1 3 0.47400000E-05 2 2 0.94600000E-05 2 3 -0.35800000E-05 3 3 0.58400000E-05 m n 6 6 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 0.15128223E+01 2 0.92550667E+16 3 -0.92550667E+16 4 -0.92550667E+16 5 0.92550667E+16 6 0.10295255E+01 residual length = 0.0000E+00 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.17461301E-03 1 2 0.68485095E+12 1 3 -0.68485095E+12 1 4 -0.68485095E+12 1 5 0.68485095E+12 1 6 0.77182222E-04 2 2 0.27410003E+28 2 3 -0.27410003E+28 2 4 -0.27410003E+28 2 5 0.27410003E+28 2 6 0.30490648E+12 3 3 0.27410003E+28 3 4 0.27410003E+28 3 5 -0.27410003E+28 3 6 -0.30490648E+12 4 4 0.27410003E+28 4 5 -0.27410003E+28 4 6 -0.30490648E+12 5 5 0.27410003E+28 5 6 0.30490648E+12 6 6 0.37917531E-04 m n 7 6 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.47750233E+00 2 0.38864135E+15 3 -0.38864135E+15 4 -0.38864135E+15 5 0.38864135E+15 6 -0.28847709E+00 residual length = 0.5579E+03 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.86248660E-05 1 2 0.24933192E+11 1 3 -0.24933192E+11 1 4 -0.24933192E+11 1 5 0.24933192E+11 1 6 -0.19684886E-05 2 2 0.12130348E+27 2 3 -0.12130348E+27 2 4 -0.12130348E+27 2 5 0.12130348E+27 2 6 -0.12009543E+11 3 3 0.12130348E+27 3 4 0.12130348E+27 3 5 -0.12130348E+27 3 6 0.12009543E+11 4 4 0.12130348E+27 4 5 -0.12130348E+27 4 6 0.12009543E+11 5 5 0.12130348E+27 5 6 -0.12009543E+11 6 6 0.41889942E-05 m n 7 7 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 0.92590453E+15 2 -0.92590453E+15 3 0.92590453E+15 4 -0.18518091E+16 5 0.92590453E+15 6 -0.92590453E+15 7 0.92590453E+15 residual length = 0.0000E+00 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.34291968E+25 1 2 -0.34291968E+25 1 3 0.34291968E+25 1 4 -0.68583936E+25 1 5 0.34291968E+25 1 6 -0.34291968E+25 1 7 0.34291968E+25 2 2 0.34291968E+25 2 3 -0.34291968E+25 2 4 0.68583936E+25 2 5 -0.34291968E+25 2 6 0.34291968E+25 2 7 -0.34291968E+25 3 3 0.34291968E+25 3 4 -0.68583936E+25 3 5 0.34291968E+25 3 6 -0.34291968E+25 3 7 0.34291968E+25 4 4 0.13716787E+26 4 5 -0.68583936E+25 4 6 0.68583936E+25 4 7 -0.68583936E+25 5 5 0.34291968E+25 5 6 -0.34291968E+25 5 7 0.34291968E+25 6 6 0.34291968E+25 6 7 -0.34291968E+25 7 7 0.34291968E+25 m n 8 6 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.72655819E+16 2 0.72655819E+16 3 0.11090652E+16 4 -0.11090652E+16 5 0.61565166E+16 6 -0.61565166E+16 residual length = 0.1724E+03 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.25705630E+27 1 2 -0.25705630E+27 1 3 -0.63722566E+26 1 4 0.63722566E+26 1 5 -0.19333373E+27 1 6 0.19333373E+27 2 2 0.25705630E+27 2 3 0.63722566E+26 2 4 -0.63722566E+26 2 5 0.19333373E+27 2 6 -0.19333373E+27 3 3 0.25055820E+26 3 4 -0.25055820E+26 3 5 0.38666746E+26 3 6 -0.38666746E+26 4 4 0.25055820E+26 4 5 -0.38666746E+26 4 6 0.38666746E+26 5 5 0.15466698E+27 5 6 -0.15466698E+27 6 6 0.15466698E+27 m n 8 7 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 0.10000000E+01 2 -0.60000000E+00 3 0.60000000E+00 4 0.40000000E+00 5 0.60000000E+00 6 0.43175676E-16 7 0.10000000E+01 residual length = 0.2842E-13 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.37142857E-05 1 2 0.32857143E-05 1 3 -0.15714286E-05 1 4 0.47142857E-05 1 5 -0.14285714E-05 1 6 -0.42857143E-06 1 7 0.17142857E-05 2 2 0.28214286E-04 2 3 -0.21928571E-04 2 4 0.29285714E-04 2 5 -0.19571429E-04 2 6 0.14285714E-05 2 7 0.42857143E-05 3 3 0.19357143E-04 3 4 -0.23571429E-04 3 5 0.17142857E-04 3 6 -0.18571429E-05 3 7 -0.25714286E-05 4 4 0.33714286E-04 4 5 -0.21428571E-04 4 6 0.25714286E-05 4 7 0.47142857E-05 5 5 0.18857143E-04 5 6 -0.31428571E-05 5 7 -0.42857143E-06 6 6 0.28571429E-05 6 7 -0.14285714E-05 7 7 0.37142857E-05 m n 8 8 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.14707742E+17 2 0.14707742E+17 3 0.77893591E+16 4 -0.77893591E+16 5 0.42329139E+16 6 -0.42329139E+16 7 0.26854688E+16 8 -0.26854688E+16 residual length = 0.0000E+00 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.17227220E+28 1 2 -0.20322070E+28 1 3 -0.12022919E+28 1 4 0.12444809E+28 1 5 -0.47824110E+27 1 6 0.47824110E+27 1 7 -0.30948501E+27 1 8 0.30948501E+27 2 2 0.24190633E+28 2 3 0.14344056E+28 2 4 -0.14765947E+28 2 5 0.55561235E+27 2 6 -0.55561235E+27 2 7 0.38685626E+27 2 8 -0.38685626E+27 3 3 0.88725824E+27 3 4 -0.90384222E+27 3 5 0.29844968E+27 3 6 -0.29844968E+27 3 7 0.23211376E+27 3 8 -0.23211376E+27 4 4 0.92554720E+27 4 5 -0.31893371E+27 4 6 0.31893371E+27 4 7 -0.23211376E+27 4 8 0.23211376E+27 5 5 0.15930739E+27 5 6 -0.15930739E+27 5 7 0.77371252E+26 5 8 -0.77371252E+26 6 6 0.15930739E+27 6 7 -0.77371252E+26 6 8 0.77371252E+26 7 7 0.77371252E+26 7 8 -0.77371252E+26 8 8 0.77371252E+26 Matrix generation noise level = 0.100000E-03 m n 1 1 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 0.11123223E+01 residual length = 0.0000E+00 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.50492093E-05 m n 2 1 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.40695327E+01 residual length = 0.1901E+03 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.90530818E-04 m n 2 2 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.96370364E+01 2 0.95124532E+01 residual length = 0.0000E+00 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.24511343E-03 1 2 -0.22137344E-03 2 2 0.21013310E-03 m n 3 1 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.69428673E+00 residual length = 0.4171E+03 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.72957361E-05 m n 3 2 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 0.23692936E+01 2 -0.24939969E+01 residual length = 0.4675E+03 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.18944584E-03 1 2 -0.17213917E-03 2 2 0.16018680E-03 m n 3 3 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 0.10751053E+01 2 -0.49996100E+00 3 0.14247923E+01 residual length = 0.0000E+00 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.12722618E-04 1 2 -0.13002844E-04 1 3 0.22784034E-04 2 2 0.18501388E-04 2 3 -0.30498328E-04 3 3 0.60207429E-04 m n 6 6 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.45677909E+00 2 0.10475609E+05 3 -0.10476890E+05 4 -0.10473560E+05 5 0.10473113E+05 6 0.16405831E+00 residual length = 0.0000E+00 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.47444240E-05 1 2 -0.17002788E-01 1 3 0.17008075E-01 1 4 0.17014241E-01 1 5 -0.17012324E-01 1 6 0.93882706E-06 2 2 0.39017780E+03 2 3 -0.39023014E+03 2 4 -0.39002692E+03 2 5 0.39002892E+03 2 6 0.14589896E-02 3 3 0.39028249E+03 3 4 0.39007926E+03 3 5 -0.39008126E+03 3 6 -0.14566808E-02 4 4 0.38987632E+03 4 5 -0.38987830E+03 4 6 -0.14448998E-02 5 5 0.38988028E+03 5 6 0.14479109E-02 6 6 0.35074430E-05 m n 7 6 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 0.78632426E+00 2 -0.50120787E+04 3 0.50133380E+04 4 0.50172103E+04 5 -0.50167476E+04 6 0.57601592E+00 residual length = 0.1306E+03 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.26648062E-04 1 2 -0.11435856E+00 1 3 0.11437554E+00 1 4 0.11447776E+00 1 5 -0.11446284E+00 1 6 0.10793976E-04 2 2 0.55313816E+03 2 3 -0.55320814E+03 2 4 -0.55362859E+03 2 5 0.55356373E+03 2 6 -0.49777020E-01 3 3 0.55327814E+03 3 4 0.55369866E+03 3 5 -0.55363379E+03 3 6 0.49784822E-01 4 4 0.55411966E+03 4 5 -0.55405473E+03 4 6 0.49833931E-01 5 5 0.55398981E+03 5 6 -0.49826092E-01 6 6 0.79812218E-05 m n 7 7 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 0.33332214E+00 2 -0.99997122E+00 3 -0.26654090E+00 4 0.59983930E+00 5 -0.26641738E+00 6 -0.66791850E-01 7 0.33338016E+00 residual length = 0.0000E+00 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.24455006E-05 1 2 -0.66696439E-06 1 3 0.61184722E-05 1 4 -0.43393297E-05 1 5 0.51179208E-05 1 6 -0.35601579E-05 1 7 0.44477080E-06 2 2 0.40001259E-05 2 3 0.33310048E-05 2 4 -0.19976616E-05 2 5 0.43305681E-05 2 6 -0.26644104E-05 2 7 0.33250224E-06 3 3 0.53817238E-04 3 4 -0.41364503E-04 3 5 0.49811129E-04 3 6 -0.37909980E-04 3 7 0.51083935E-05 4 4 0.34025098E-04 4 5 -0.39359544E-04 4 6 0.30683641E-04 4 7 -0.43310510E-05 5 5 0.49805216E-04 5 6 -0.36905835E-04 5 7 0.61078545E-05 6 6 0.30454285E-04 6 7 -0.45525108E-05 7 7 0.24430926E-05 m n 8 6 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.37207578E+04 2 0.37206533E+04 3 0.64680206E+04 4 -0.64673582E+04 5 -0.27529358E+04 6 0.27529040E+04 residual length = 0.1706E+03 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.67040534E+02 1 2 -0.67047211E+02 1 3 -0.46002202E+02 1 4 0.45995183E+02 1 5 -0.21030576E+02 1 6 0.21033131E+02 2 2 0.67053892E+02 2 3 0.46013337E+02 2 4 -0.46006315E+02 2 5 0.21026123E+02 2 6 -0.21028677E+02 3 3 0.12485850E+03 3 4 -0.12485075E+03 3 5 -0.78912026E+02 3 6 0.78916474E+02 4 4 0.12484301E+03 4 5 0.78911303E+02 4 6 -0.78915750E+02 5 5 0.99990721E+02 5 6 -0.99997716E+02 6 6 0.10000471E+03 m n 8 7 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 0.25009074E+00 2 0.24979726E+00 3 -0.49978034E+00 4 0.11495343E+01 5 -0.39969275E+00 6 0.64964410E+00 7 -0.89977249E+00 residual length = 0.5000E+03 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.32503599E-05 1 2 -0.17505416E-05 1 3 0.20011361E-05 1 4 0.27502120E-05 1 5 -0.25007109E-05 1 6 0.27511207E-05 1 7 -0.40010562E-05 2 2 0.32494504E-05 2 3 -0.20000998E-05 2 4 0.27440134E-05 2 5 -0.14948534E-05 2 6 0.17439902E-05 2 7 0.52600379E-08 3 3 0.45012083E-05 3 4 0.10060274E-05 3 5 -0.50518441E-06 3 6 0.25063151E-05 3 7 -0.25059961E-05 4 4 0.29226864E-04 4 5 -0.22482761E-04 4 6 0.26231051E-04 4 7 -0.21984098E-04 5 5 0.19487559E-04 5 6 -0.20986132E-04 5 7 0.18488737E-04 6 6 0.26235022E-04 6 7 -0.20988013E-04 7 7 0.20990475E-04 m n 8 8 estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 0.48763252E+04 2 -0.48766523E+04 3 0.27205143E+04 4 -0.27213537E+04 5 0.75123613E+03 6 -0.75188221E+03 7 -0.83532178E+04 8 0.83536376E+04 residual length = 0.0000E+00 covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.84347759E+03 1 2 -0.84360139E+03 1 3 0.13574188E+04 1 4 -0.13576892E+04 1 5 -0.11624339E+04 1 6 0.11621044E+04 1 7 -0.10408951E+04 1 8 0.10407174E+04 2 2 0.84372522E+03 2 3 -0.13576901E+04 2 4 0.13579605E+04 2 5 0.11626529E+04 2 6 -0.11623233E+04 2 7 0.10410716E+04 2 8 -0.10408939E+04 3 3 0.27797253E+04 3 4 -0.27802617E+04 3 5 -0.22523699E+04 3 6 0.22517301E+04 3 7 -0.18896054E+04 3 8 0.18892624E+04 4 4 0.27807983E+04 4 5 0.22528148E+04 4 6 -0.22521749E+04 4 7 0.18899683E+04 4 8 -0.18896252E+04 5 5 0.19112742E+04 5 6 -0.19107430E+04 5 7 0.15075219E+04 5 8 -0.15072353E+04 6 6 0.19102120E+04 6 7 -0.15070826E+04 6 8 0.15067961E+04 7 7 0.14262588E+04 7 8 -0.14260240E+04 8 8 0.14257893E+04 TEST02 Demonstrate the algorithms HFTI and COV. Use a relative noise level of 0.00000 The matrix norm is approximately 500.000 The absolute pseudorank tolerance is 0.500000 M = 1 N = 1 Pseudorank = 1 Parameters X = A**(+)*B, estimated by HFTI: 0.677419 Residual norm = 0.E+0 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.41623309E-04 M = 1 N = 2 Pseudorank = 1 Parameters X = A**(+)*B, estimated by HFTI: 0.451981E-01 0.502765E-01 Residual norm = 0.E+0 M = 1 N = 3 Pseudorank = 1 Parameters X = A**(+)*B, estimated by HFTI: 0.102050 -0.381344 -0.327633 Residual norm = 0.E+0 M = 2 N = 1 Pseudorank = 1 Parameters X = A**(+)*B, estimated by HFTI: -0.900045 Residual norm = 345.09491415388345 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.90049527E-05 M = 2 N = 2 Pseudorank = 2 Parameters X = A**(+)*B, estimated by HFTI: -0.540278 -0.834722 Residual norm = 0.E+0 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.39521605E-05 1 2 0.35339506E-06 2 2 0.78410494E-05 M = 2 N = 3 Pseudorank = 2 Parameters X = A**(+)*B, estimated by HFTI: -0.713597E-01 -0.638187 -0.163163 Residual norm = 0.E+0 M = 3 N = 1 Pseudorank = 1 Parameters X = A**(+)*B, estimated by HFTI: 0.636572 Residual norm = 368.49816645065766 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.41653650E-05 M = 3 N = 2 Pseudorank = 2 Parameters X = A**(+)*B, estimated by HFTI: 0.594404 0.498725 Residual norm = 61.325392807047223 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.32510804E-05 1 2 0.14896283E-05 2 2 0.59995678E-05 M = 3 N = 3 Pseudorank = 3 Parameters X = A**(+)*B, estimated by HFTI: -1.05000 1.00000 -2.95000 Residual norm = 0.E+0 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.29593750E-04 1 2 -0.21750000E-04 1 3 0.27156250E-04 2 2 0.18500000E-04 2 3 -0.21750000E-04 3 3 0.34593750E-04 M = 6 N = 6 Pseudorank = 4 Parameters X = A**(+)*B, estimated by HFTI: -1.44643 1.48214 -1.55357 1.37500 -1.87500 1.05357 Residual norm = 377.96447300922733 M = 6 N = 7 Pseudorank = 6 Parameters X = A**(+)*B, estimated by HFTI: 0.909091E-01 -4.05455 3.60000 -4.50909 4.23636 -1.00000 0.909091E-01 Residual norm = 0.E+0 M = 6 N = 8 Pseudorank = 5 Parameters X = A**(+)*B, estimated by HFTI: 0.131250 0.743750 -0.306250 0.306250 -0.493750 0.118750 -0.493750 0.118750 Residual norm = 530.33008588991061 M = 7 N = 6 Pseudorank = 4 Parameters X = A**(+)*B, estimated by HFTI: -0.819444 0.569444 -0.277778 1.11111 -0.694444 0.694444 Residual norm = 288.67513459481296 M = 7 N = 7 Pseudorank = 6 Parameters X = A**(+)*B, estimated by HFTI: 1.90000 -0.900000 1.90000 0.600000 -0.500000 1.50000 -1.50000 Residual norm = 5.68434188608080149E-14 M = 7 N = 8 Pseudorank = 5 Parameters X = A**(+)*B, estimated by HFTI: 0.280184 -0.135311 0.165495 -0.103111E-01 0.290495 0.364689 0.665495 1.15518 Residual norm = 250.00000000000006 M = 8 N = 6 Pseudorank = 4 Parameters X = A**(+)*B, estimated by HFTI: 0.312500 -0.437500 0.687500 -0.625000E-01 0.312500 -0.437500 Residual norm = 306.18621784789735 M = 8 N = 7 Pseudorank = 7 Parameters X = A**(+)*B, estimated by HFTI: -0.434783E-01 0.947826 -0.720497E-01 0.965217 -0.496894E-01 0.947826 -0.434783E-01 Residual norm = 66.873385509042208 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.20217391E-05 1 2 -0.11739130E-05 1 3 0.15217391E-05 1 4 -0.78260870E-06 1 5 0.73913043E-06 1 6 -0.17391304E-06 1 7 0.21739130E-07 2 2 0.33913043E-05 2 3 -0.21739130E-05 2 4 0.22608696E-05 2 5 -0.91304348E-06 2 6 0.13913043E-05 2 7 -0.17391304E-06 3 3 0.39503106E-05 3 4 -0.27826087E-05 3 5 0.23105590E-05 3 6 -0.11739130E-05 3 7 0.52173913E-06 4 4 0.41739130E-05 4 5 -0.26086957E-05 4 6 0.22608696E-05 4 7 -0.78260870E-06 5 5 0.45590062E-05 5 6 -0.19130435E-05 5 7 0.17391304E-05 6 6 0.33913043E-05 6 7 -0.11739130E-05 7 7 0.20217391E-05 M = 8 N = 8 Pseudorank = 5 Parameters X = A**(+)*B, estimated by HFTI: 0.318750 0.562500E-01 0.631250 0.368750 0.256250 -0.625000E-02 0.625000E-02 -0.256250 Residual norm = 586.30196997792871 Use a relative noise level of 0.100000E-03 The matrix norm is approximately 500.000 The absolute pseudorank tolerance is 0.500000 M = 1 N = 1 Pseudorank = 1 Parameters X = A**(+)*B, estimated by HFTI: 1.20400 Residual norm = 0.E+0 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.16655306E-04 M = 1 N = 2 Pseudorank = 1 Parameters X = A**(+)*B, estimated by HFTI: -1.96808 -1.33285 Residual norm = 0.E+0 M = 1 N = 3 Pseudorank = 1 Parameters X = A**(+)*B, estimated by HFTI: -0.686332 -0.624506E-01 -0.131711 Residual norm = 0.E+0 M = 2 N = 1 Pseudorank = 1 Parameters X = A**(+)*B, estimated by HFTI: -0.835889 Residual norm = 63.852379703717077 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.65322521E-05 M = 2 N = 2 Pseudorank = 2 Parameters X = A**(+)*B, estimated by HFTI: -0.721103 0.433384E-01 Residual norm = 0.E+0 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.39516646E-05 1 2 0.48294159E-06 2 2 0.50588092E-05 M = 2 N = 3 Pseudorank = 2 Parameters X = A**(+)*B, estimated by HFTI: -0.706648 1.02397 0.966582E-01 Residual norm = 0.E+0 M = 3 N = 1 Pseudorank = 1 Parameters X = A**(+)*B, estimated by HFTI: -0.149710 Residual norm = 407.37673071171139 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.43852890E-05 M = 3 N = 2 Pseudorank = 2 Parameters X = A**(+)*B, estimated by HFTI: 0.551222 -0.605232 Residual norm = 35.637495127628142 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.39255797E-05 1 2 0.70008376E-06 2 2 0.31915596E-05 M = 3 N = 3 Pseudorank = 3 Parameters X = A**(+)*B, estimated by HFTI: -0.639995 1.78007 0.860138 Residual norm = 0.E+0 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.58417450E-05 1 2 -0.10585837E-04 1 3 -0.22629622E-05 2 2 0.37480681E-04 2 3 0.12129209E-04 3 3 0.81429093E-05 M = 6 N = 6 Pseudorank = 4 Parameters X = A**(+)*B, estimated by HFTI: -1.18565 1.31116 -1.24899 1.24920 -1.43557 1.06079 Residual norm = 530.63320370376971 M = 6 N = 7 Pseudorank = 5 Parameters X = A**(+)*B, estimated by HFTI: -0.416091E-01 -0.341717 0.916963E-01 0.199990 -0.416381E-01 0.291717 0.341629 Residual norm = 499.97314023352089 M = 6 N = 8 Pseudorank = 5 Parameters X = A**(+)*B, estimated by HFTI: -0.212995 0.878228E-01 -0.255286E-01 0.275237 0.287002 0.587723 0.349490 0.650291 Residual norm = 176.81749595345229 M = 7 N = 6 Pseudorank = 4 Parameters X = A**(+)*B, estimated by HFTI: -0.991358 0.794840 -0.607221 1.17852 -1.02699 0.759177 Residual norm = 258.57984447824839 M = 7 N = 7 Pseudorank = 7 Parameters X = A**(+)*B, estimated by HFTI: -0.154112E-04 -0.626162E-04 -2.10227 1.60162 -2.60173 2.10200 -1.00043 Residual norm = 0.E+0 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.40000082E-05 1 2 -0.19994214E-05 1 3 0.16014171E-04 1 4 -0.11009909E-04 1 5 0.13010981E-04 1 6 -0.12012229E-04 1 7 0.20029886E-05 2 2 0.39994642E-05 2 3 -0.80019322E-05 2 4 0.60007936E-05 2 5 -0.50008042E-05 2 6 0.60017372E-05 2 7 -0.10008469E-05 3 3 0.10968681E-03 3 4 -0.78132008E-04 3 5 0.93653653E-04 3 6 -0.88154607E-04 3 7 0.15033242E-04 4 4 0.58092821E-04 4 5 -0.68108542E-04 4 6 0.64109052E-04 4 7 -0.11023544E-04 5 5 0.84126112E-04 5 6 -0.76627198E-04 5 7 0.14027492E-04 6 6 0.74627389E-04 6 7 -0.13027249E-04 7 7 0.40056128E-05 M = 7 N = 8 Pseudorank = 5 Parameters X = A**(+)*B, estimated by HFTI: -0.150108 0.208021 0.266915 0.333078 0.391976 0.208090 0.266964 -0.274993 Residual norm = 558.96642580633602 M = 8 N = 6 Pseudorank = 4 Parameters X = A**(+)*B, estimated by HFTI: -0.875303 0.625286 -0.625049 0.875010 -0.875099 0.625170 Residual norm = 707.08292812749562 M = 8 N = 7 Pseudorank = 7 Parameters X = A**(+)*B, estimated by HFTI: 0.401007 0.349304 -0.989547E-01 -0.150757 0.500237 -0.749935 0.250094 Residual norm = 499.9317095623145 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.42018655E-04 1 2 -0.31513781E-04 1 3 0.39521253E-04 1 4 -0.32518077E-04 1 5 0.45012532E-05 1 6 0.35000572E-05 1 7 -0.49819785E-06 2 2 0.26260342E-04 2 3 -0.31515965E-04 2 4 0.26263590E-04 2 5 -0.45007903E-05 2 6 -0.17499524E-05 2 7 -0.75148872E-06 3 3 0.40524172E-04 3 4 -0.33020220E-04 3 5 0.65018100E-05 3 6 0.20001737E-05 3 7 0.10023144E-05 4 4 0.29267006E-04 4 5 -0.60010811E-05 4 6 -0.75049775E-06 4 7 -0.75161394E-06 5 5 0.44996723E-05 5 6 -0.19998204E-05 5 7 0.20005932E-05 6 6 0.32496972E-05 6 7 -0.17501508E-05 7 7 0.32505516E-05 M = 8 N = 8 Pseudorank = 5 Parameters X = A**(+)*B, estimated by HFTI: -2.05519 1.30577 -2.11728 1.24262 -2.05431 1.30483 -1.67930 1.67956 Residual norm = 306.41512581452224 TEST03 Demonstrate the use of SVDRS. The relative noise level in the data will be 0.E+0 The relative pseudorank tolerance will be 1.00000000000000002E-3 M = 1 N = 1 The singular value vector S: 355.000000 Transformed right side, U'*B 1 0.30500000E+03 Absolute pseudorank tolerance TAU = 0.35499999999999998 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: 0.859155 Residual norm = 0.E+0 S(1) = 355. frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.000 sqrt(n) * spectral norm of a M = 1 N = 2 The singular value vector S: 383.470990 0.000000 Transformed right side, U'*B 1 0.15500000E+03 Absolute pseudorank tolerance TAU = 0.38347098977628019 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: -0.258245 -0.310949 Residual norm = 0.E+0 S(1) = 383.47098977628019 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.5241E-16 sqrt(n) * spectral norm of a M = 1 N = 3 The singular value vector S: 673.850874 0.000000 0.000000 Transformed right side, U'*B 1 -0.45000000E+02 Absolute pseudorank tolerance TAU = 0.67385087371020014 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: -0.104058E-01 0.441006E-01 0.490558E-01 Residual norm = 0.E+0 S(1) = 673.85087371020018 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.000 sqrt(n) * spectral norm of a M = 2 N = 1 The singular value vector S: 367.491497 Transformed right side, U'*B 1 -0.31551750E+03 2 0.23129787E+03 Absolute pseudorank tolerance TAU = 0.36749149650025914 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: -0.858571 Residual norm = 231.29786895610545 S(1) = 367.49149650025913 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.3867E-16 sqrt(n) * spectral norm of a M = 2 N = 2 The singular value vector S: 520.926943 220.760323 Transformed right side, U'*B 1 0.22369798E+03 2 0.44385720E+03 Absolute pseudorank tolerance TAU = 0.52092694301380926 Pseudorank = 2 Estimated X = A**(+) * B, computed by SVDRS: 1.97609 0.567391 Residual norm = 0.E+0 S(1) = 520.92694301380925 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.5854E-15 sqrt(n) * spectral norm of a M = 2 N = 3 The singular value vector S: 494.038683 393.796622 0.000000 Transformed right side, U'*B 1 0.28377158E+03 2 -0.35850201E+03 Absolute pseudorank tolerance TAU = 0.49403868320081051 Pseudorank = 2 Estimated X = A**(+) * B, computed by SVDRS: 0.626816 0.788904 -0.378732 Residual norm = 0.E+0 S(1) = 494.03868320081051 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.1531E-15 sqrt(n) * spectral norm of a M = 3 N = 1 The singular value vector S: 506.038536 Transformed right side, U'*B 1 -0.32838408E+03 2 0.27427962E+03 3 -0.30985413E+03 Absolute pseudorank tolerance TAU = 0.50603853608198657 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: -0.648931 Residual norm = 413.81021598677688 S(1) = 506.03853608198654 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.1132E-15 sqrt(n) * spectral norm of a M = 3 N = 2 The singular value vector S: 612.845203 437.687968 Transformed right side, U'*B 1 0.99925063E+00 2 -0.46875516E+03 3 0.91337829E+02 Absolute pseudorank tolerance TAU = 0.61284520266487985 Pseudorank = 2 Estimated X = A**(+) * B, computed by SVDRS: -0.448645 -0.972481 Residual norm = 91.337829113145403 S(1) = 612.84520266487982 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.2970E-15 sqrt(n) * spectral norm of a M = 3 N = 3 The singular value vector S: 711.311204 485.034715 144.923072 Transformed right side, U'*B 1 0.13014320E+03 2 -0.54356167E+02 3 -0.46923678E+03 Absolute pseudorank tolerance TAU = 0.71131120368543155 Pseudorank = 3 Estimated X = A**(+) * B, computed by SVDRS: -2.96000 0.920000 -0.960000 Residual norm = 0.E+0 S(1) = 711.31120368543156 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.4463E-15 sqrt(n) * spectral norm of a M = 6 N = 6 The singular value vector S: 1297.501135 915.746324 722.071820 106.825840 0.000000 0.000000 Transformed right side, U'*B 1 -0.43221538E+03 2 0.24276687E+03 3 -0.18929294E+03 4 0.21941679E+03 5 0.26526044E+03 6 0.32641571E+02 Absolute pseudorank tolerance TAU = 1.2975011354610542 Pseudorank = 4 Estimated X = A**(+) * B, computed by SVDRS: 1.26786 -0.375000 0.875000 -0.767857 0.910714 -0.732143 Residual norm = 267.2612419124244 S(1) = 1297.5011354610542 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.3869E-15 sqrt(n) * spectral norm of a M = 6 N = 7 The singular value vector S: 1169.639694 989.732100 759.359949 654.071308 568.920906 433.953396 0.000000 Transformed right side, U'*B 1 -0.15961644E+03 2 0.13809759E+02 3 -0.22554847E+02 4 -0.65817970E+02 5 -0.35486878E+03 6 0.46979709E+03 Absolute pseudorank tolerance TAU = 1.1696396942123426 Pseudorank = 6 Estimated X = A**(+) * B, computed by SVDRS: -0.271464 1.00000 0.925558E-01 0.228784 0.499752 0.364516 -0.271464 Residual norm = 0.E+0 S(1) = 1169.6396942123426 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.4968E-15 sqrt(n) * spectral norm of a M = 6 N = 8 The singular value vector S: 1319.698653 1168.478166 795.166990 615.405665 106.016821 0.000000 0.000000 0.000000 Transformed right side, U'*B 1 0.21391408E+03 2 0.10298018E+03 3 0.62618849E+03 4 -0.38037602E+03 5 0.27164554E+02 6 -0.17677670E+03 Absolute pseudorank tolerance TAU = 1.3196986527349253 Pseudorank = 5 Estimated X = A**(+) * B, computed by SVDRS: 0.350000 0.650000 0.287500 0.587500 -0.250000E-01 0.275000 -0.212500 0.875000E-01 Residual norm = 176.77669529663694 S(1) = 1319.6986527349252 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.3925E-15 sqrt(n) * spectral norm of a M = 7 N = 6 The singular value vector S: 1414.213562 945.762279 722.612063 124.159242 0.000000 0.000000 Transformed right side, U'*B 1 -0.40824829E+03 2 -0.29654522E+03 3 0.48070368E+02 4 0.94473115E+02 5 -0.57688812E+03 6 0.16862137E+02 7 -0.15782708E+02 Absolute pseudorank tolerance TAU = 1.4142135623730949 Pseudorank = 4 Estimated X = A**(+) * B, computed by SVDRS: -0.263889 0.347222 -0.180556 0.430556 -0.597222 0.138889E-01 Residual norm = 577.35026918962581 S(1) = 1414.2135623730949 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.3901E-15 sqrt(n) * spectral norm of a M = 7 N = 7 The singular value vector S: 1231.292676 1040.003082 815.576956 657.109965 529.781304 308.125544 89.264083 Transformed right side, U'*B 1 -0.12713542E+01 2 -0.68695833E+02 3 0.30327196E+03 4 0.36504287E+03 5 0.52366419E+03 6 0.29533698E+03 7 -0.37653150E+03 Absolute pseudorank tolerance TAU = 1.2312926757621705 Pseudorank = 7 Estimated X = A**(+) * B, computed by SVDRS: 0.127676E-14 -3.10000 2.10000 -2.10000 1.10000 0.500000 -0.500000 Residual norm = 0.E+0 S(1) = 1231.2926757621706 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.6108E-15 sqrt(n) * spectral norm of a M = 7 N = 8 The singular value vector S: 1491.125237 1122.315303 826.033717 702.995761 428.741353 0.000000 0.000000 0.000000 Transformed right side, U'*B 1 0.16698645E+00 2 0.17684859E+03 3 0.11032769E+03 4 -0.55139928E+03 5 0.13644844E+02 6 -0.63675172E+02 7 -0.24175498E+03 Absolute pseudorank tolerance TAU = 1.4911252369081363 Pseudorank = 5 Estimated X = A**(+) * B, computed by SVDRS: 0.410945 0.276843 0.259101 -0.160657 -0.178399 -0.285657 -0.303399 -0.339055 Residual norm = 250.00000000000003 S(1) = 1491.1252369081362 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.4958E-15 sqrt(n) * spectral norm of a M = 8 N = 6 The singular value vector S: 1491.116913 1213.014067 727.839051 128.909035 0.000000 0.000000 Transformed right side, U'*B 1 -0.30199878E+03 2 0.18057908E+03 3 -0.13798581E+03 4 -0.18465602E+03 5 -0.39163287E+03 6 -0.63736693E+02 7 -0.51324114E+03 8 0.33225722E+03 Absolute pseudorank tolerance TAU = 1.4911169133640769 Pseudorank = 4 Estimated X = A**(+) * B, computed by SVDRS: -0.770833 0.395833 -0.458333 0.708333 -0.645833 0.520833 Residual norm = 728.86898685566257 S(1) = 1491.1169133640769 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.4154E-15 sqrt(n) * spectral norm of a M = 8 N = 7 The singular value vector S: 1272.832635 1087.096891 925.040973 753.411945 669.100238 474.079691 61.158730 Transformed right side, U'*B 1 0.71965766E+02 2 0.10472160E+03 3 -0.77627564E+02 4 0.25893161E+03 5 0.35429264E+03 6 -0.32728164E+03 7 0.13754120E+03 8 0.26726124E+03 Absolute pseudorank tolerance TAU = 1.2728326348391354 Pseudorank = 7 Estimated X = A**(+) * B, computed by SVDRS: -0.142857 -0.714286 -1.31429 0.457143 -1.38571 1.24286 -0.142857 Residual norm = 267.26124191242411 S(1) = 1272.8326348391354 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.6002E-15 sqrt(n) * spectral norm of a M = 8 N = 8 The singular value vector S: 1462.797067 1414.213562 931.274430 752.578558 110.354840 0.000000 0.000000 0.000000 Transformed right side, U'*B 1 -0.12367879E+03 2 0.30618622E+03 3 0.89079856E+02 4 -0.58787506E+03 5 0.19460537E+03 6 -0.43910429E+03 7 -0.10469127E+03 8 0.37413521E+03 Absolute pseudorank tolerance TAU = 1.4627970670538821 Pseudorank = 5 Estimated X = A**(+) * B, computed by SVDRS: 0.568750 -0.568750 0.943750 -0.193750 1.13125 -0.625000E-02 0.943750 -0.193750 Residual norm = 586.30196997792882 S(1) = 1462.7970670538821 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.5124E-15 sqrt(n) * spectral norm of a The relative noise level in the data will be 1.00000000000000005E-4 The relative pseudorank tolerance will be 1.00000000000000002E-3 M = 1 N = 1 The singular value vector S: 45.017000 Transformed right side, U'*B 1 -0.95015200E+02 Absolute pseudorank tolerance TAU = 4.50170000000000015E-2 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: 2.11065 Residual norm = 0.E+0 S(1) = 45.017000000000003 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.000 sqrt(n) * spectral norm of a M = 1 N = 2 The singular value vector S: 468.015205 0.000000 Transformed right side, U'*B 1 -0.24499500E+03 Absolute pseudorank tolerance TAU = 0.46801520492237214 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: -0.397080 -0.341109 Residual norm = 0.E+0 S(1) = 468.01520492237211 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.000 sqrt(n) * spectral norm of a M = 1 N = 3 The singular value vector S: 349.416387 0.000000 0.000000 Transformed right side, U'*B 1 -0.44502390E+03 Absolute pseudorank tolerance TAU = 0.34941638746438319 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: 1.07539 -0.565023 -0.382628 Residual norm = 0.E+0 S(1) = 349.41638746438321 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.5251E-16 sqrt(n) * spectral norm of a M = 2 N = 1 The singular value vector S: 497.018033 Transformed right side, U'*B 1 0.62495013E+02 2 0.36216911E+03 Absolute pseudorank tolerance TAU = 0.49701803259022698 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: 0.125740 Residual norm = 362.16911428128623 S(1) = 497.01803259022699 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.2292E-15 sqrt(n) * spectral norm of a M = 2 N = 2 The singular value vector S: 511.568282 48.866818 Transformed right side, U'*B 1 -0.36804573E+03 2 -0.27123891E+03 Absolute pseudorank tolerance TAU = 0.51156828160073597 Pseudorank = 2 Estimated X = A**(+) * B, computed by SVDRS: 3.71029 4.19050 Residual norm = 0.E+0 S(1) = 511.56828160073599 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.2750E-15 sqrt(n) * spectral norm of a M = 2 N = 3 The singular value vector S: 658.863251 317.772156 0.000000 Transformed right side, U'*B 1 0.31463867E+03 2 -0.10993239E+03 Absolute pseudorank tolerance TAU = 0.65886325052452144 Pseudorank = 2 Estimated X = A**(+) * B, computed by SVDRS: 0.563158 -0.685176E-02 0.174750 Residual norm = 0.E+0 S(1) = 658.86325052452139 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.2190E-15 sqrt(n) * spectral norm of a M = 3 N = 1 The singular value vector S: 673.872201 Transformed right side, U'*B 1 0.20509192E+03 2 -0.23787450E+03 3 0.19607323E+03 Absolute pseudorank tolerance TAU = 0.6738722009657987 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: -0.304348 Residual norm = 308.26772179088448 S(1) = 673.8722009657987 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.6327E-16 sqrt(n) * spectral norm of a M = 3 N = 2 The singular value vector S: 640.201685 251.666373 Transformed right side, U'*B 1 0.33445827E+03 2 0.88387974E+02 3 0.36938527E+03 Absolute pseudorank tolerance TAU = 0.64020168465580929 Pseudorank = 2 Estimated X = A**(+) * B, computed by SVDRS: -0.596260 0.201873 Residual norm = 369.3852676068837 S(1) = 640.20168465580923 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.1601E-15 sqrt(n) * spectral norm of a M = 3 N = 3 The singular value vector S: 828.084417 353.946116 187.615295 Transformed right side, U'*B 1 0.35170148E+03 2 -0.22252958E+03 3 0.23420031E+03 Absolute pseudorank tolerance TAU = 0.82808441661281917 Pseudorank = 3 Estimated X = A**(+) * B, computed by SVDRS: -1.18191 0.509155 -0.691211 Residual norm = 0.E+0 S(1) = 828.08441661281915 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.4339E-15 sqrt(n) * spectral norm of a M = 6 N = 6 The singular value vector S: 1370.691032 909.394002 688.271611 106.771247 0.056265 0.017356 Transformed right side, U'*B 1 0.43689425E+03 2 -0.37292252E+03 3 -0.89838057E+02 4 -0.58368711E+02 5 -0.18898441E+03 6 0.13976254E+01 Absolute pseudorank tolerance TAU = 1.3706910320927783 Pseudorank = 4 Estimated X = A**(+) * B, computed by SVDRS: 0.529829 0.772755E-01 0.118794E-01 -0.440490 0.190326 -0.261836 Residual norm = 188.98958201326539 S(1) = 1370.6910320927782 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.3597E-15 sqrt(n) * spectral norm of a M = 6 N = 7 The singular value vector S: 1133.067764 1015.168233 773.273600 634.183792 308.297369 215.172205 0.000000 Transformed right side, U'*B 1 0.32246183E+03 2 -0.55022408E+03 3 -0.13276363E+03 4 0.27899058E+03 5 0.36440569E+03 6 0.19529737E+03 Absolute pseudorank tolerance TAU = 1.1330677641991336 Pseudorank = 6 Estimated X = A**(+) * B, computed by SVDRS: -1.40680 -0.285653 0.285739 -0.285753 -0.307352 0.500137 -0.500074 Residual norm = 0.E+0 S(1) = 1133.0677641991335 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.5006E-15 sqrt(n) * spectral norm of a M = 6 N = 8 The singular value vector S: 1381.317604 1035.640016 767.527945 690.301497 105.567771 0.042141 0.000000 0.000000 Transformed right side, U'*B 1 0.89285537E+01 2 -0.20244576E+03 3 0.46322144E+03 4 0.25848057E+03 5 -0.21779134E+03 6 0.17674547E+03 Absolute pseudorank tolerance TAU = 1.3813176038957176 Pseudorank = 5 Estimated X = A**(+) * B, computed by SVDRS: -0.618596 0.743578 -1.11842 0.243460 -1.18148 0.181658 -0.993978 0.369149 Residual norm = 176.74547099320711 S(1) = 1381.3176038957176 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.4284E-15 sqrt(n) * spectral norm of a M = 7 N = 6 The singular value vector S: 1372.544579 1211.149191 707.860811 110.111420 0.044298 0.005449 Transformed right side, U'*B 1 -0.22505677E+03 2 -0.24922845E+03 3 -0.81913784E+02 4 -0.21108534E+02 5 -0.33691929E+03 6 -0.38093836E+03 7 -0.15050898E+03 Absolute pseudorank tolerance TAU = 1.3725445785363226 Pseudorank = 4 Estimated X = A**(+) * B, computed by SVDRS: 0.145273 -0.204930E-01 0.828055E-01 -0.829813E-01 -0.104686 -0.270455 Residual norm = 530.35987452570555 S(1) = 1372.5445785363227 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.5849E-15 sqrt(n) * spectral norm of a M = 7 N = 7 The singular value vector S: 1152.381427 1063.992044 889.679994 768.771229 549.960039 320.447855 67.659358 Transformed right side, U'*B 1 0.14073030E+03 2 -0.13626330E+03 3 -0.22934690E+02 4 0.51853968E+03 5 0.33052783E+03 6 -0.39147825E+03 7 -0.21187216E+03 Absolute pseudorank tolerance TAU = 1.1523814265449581 Pseudorank = 7 Estimated X = A**(+) * B, computed by SVDRS: -0.500259 0.500215 -1.50001 -1.10055 1.10058 -2.10053 1.60043 Residual norm = 0.E+0 S(1) = 1152.381426544958 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.5256E-15 sqrt(n) * spectral norm of a M = 7 N = 8 The singular value vector S: 1540.602813 1002.339945 804.268713 706.063056 475.066125 0.055979 0.039834 0.000000 Transformed right side, U'*B 1 0.30757507E+03 2 0.23203532E+03 3 -0.52075920E+03 4 -0.37423857E+03 5 0.58796096E+00 6 -0.19868321E+03 7 -0.15183701E+03 Absolute pseudorank tolerance TAU = 1.5406028132252381 Pseudorank = 5 Estimated X = A**(+) * B, computed by SVDRS: -0.242214 -0.261470 -0.230832 -0.199000 -0.168290 0.363523 0.394267 0.507741 Residual norm = 250.05898691691488 S(1) = 1540.6028132252379 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.4289E-15 sqrt(n) * spectral norm of a M = 8 N = 6 The singular value vector S: 1450.261177 1197.292897 758.902408 128.803235 0.027612 0.007199 Transformed right side, U'*B 1 0.35254541E+03 2 -0.10793138E+03 3 -0.25537027E+03 4 -0.39199664E+03 5 -0.47941036E+03 6 0.68112943E+02 7 0.20764747E+03 8 0.61249754E+02 Absolute pseudorank tolerance TAU = 1.4502611768368425 Pseudorank = 4 Estimated X = A**(+) * B, computed by SVDRS: -1.43690 1.06210 -1.24934 1.24959 -1.18633 1.31154 Residual norm = 530.41744752314673 S(1) = 1450.2611768368424 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.4027E-15 sqrt(n) * spectral norm of a M = 8 N = 7 The singular value vector S: 1272.383766 1105.060966 930.494864 743.366946 535.255699 349.078424 102.929402 Transformed right side, U'*B 1 -0.86543007E+02 2 -0.32262093E+03 3 -0.47566756E+03 4 -0.12054668E+03 5 0.49790959E+03 6 -0.46655337E+03 7 0.47413310E+02 8 -0.15543997E-02 Absolute pseudorank tolerance TAU = 1.2723837661046309 Pseudorank = 7 Estimated X = A**(+) * B, computed by SVDRS: 0.999941 -0.600648 0.600743 0.399225 0.600539 0.329422E-04 0.999861 Residual norm = 1.55439973750048921E-3 S(1) = 1272.3837661046309 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.9925E-15 sqrt(n) * spectral norm of a M = 8 N = 8 The singular value vector S: 1584.664692 1279.430400 917.000687 780.006322 110.320368 0.064300 0.030931 0.007530 Transformed right side, U'*B 1 -0.10925247E+02 2 -0.20167355E+03 3 -0.39338384E+03 4 0.28523986E+03 5 -0.20394201E+03 6 -0.23251807E+03 7 0.16838796E+03 8 0.10622710E+03 Absolute pseudorank tolerance TAU = 1.5846646916657876 Pseudorank = 5 Estimated X = A**(+) * B, computed by SVDRS: 1.00621 -0.256312 1.00654 -0.256709 0.631550 -0.631583 0.568824 -0.693980 Residual norm = 306.11003846583759 S(1) = 1584.6646916657876 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.5663E-15 sqrt(n) * spectral norm of a TEST04 Demonstrate singular value analysis. Read data from file lawson_prb.dat Then call SVA. Listing of input matrix, a, and vector, b, follows.. -0.1340555 -0.2016283 -0.1693078 -0.1897199 -0.1738723 -0.4361 -0.1037948 -0.1576634 -0.1334626 -0.1484855 -0.1359769 -0.3437 -0.0877960 -0.1288387 -0.1068301 -0.1201180 -0.1093297 -0.2657 0.0205855 0.0033533 -0.0164127 0.0007861 0.0027166 -0.0392 -0.0324809 -0.0187680 0.0041064 -0.0140589 -0.0138439 0.0193 0.0596766 0.0666771 0.0435215 0.0574044 0.0502496 0.0747 0.0671246 0.0735244 0.0448977 0.0647186 0.0587645 0.0935 0.0868719 0.0936830 0.0567233 0.0814104 0.0730232 0.1079 0.0214966 0.0622266 0.0721349 0.0620007 0.0557093 0.1930 0.0668741 0.1034451 0.0915385 0.0950822 0.0839367 0.2058 0.1587907 0.1808834 0.1154069 0.1616073 0.1479648 0.2606 0.1764289 0.2036183 0.1305786 0.1838573 0.1700555 0.3142 0.1141408 0.1725961 0.1481647 0.1600747 0.1437410 0.3529 0.0784604 0.1466956 0.1436580 0.1400384 0.1257118 0.3615 0.1080317 0.1699462 0.1497152 0.1588531 0.1430155 0.3647 singular value analysis of the least squares problem, a*x = b, scaled as (a*d)*y = b. m = 15, n = 5, mdata = 15 scaling option number 1. d is the identity matrix. v-matrix of the singular value decomposition of a*d. (elements of v scaled up by a factor of 10**4) col 1 col 2 col 3 col 4 1 fire 3742. -7526. 3382. 1981. 2 water 5196. -636. 2301. -6349. 3 earth 4123. 6510. 4741. 1067. 4 air 4796. 689. -2493. 6877. 5 cosmos 4359. 302. -7388. -2707. col 5 1 fire 3741. 2 water -5195. 3 earth 4123. 4 air -4797. 5 cosmos 4359. index sing. val. p coef reciprocal g coef scaled sqrt sing. val. of cum.s.s. 0 0.2635 1 1.000 0.9998 1.000 0.9998 0.5452E-01 2 0.1000E+00 2.000 10.00 0.2000 0.1111E-01 3 0.1000E-01 -4.005 100.0 -0.4005E-01 0.4055E-04 4 0.9997E-05 -1.776 0.1000E+06 -0.1776E-04 0.4201E-04 5 0.9717E-07 -192.7 0.1029E+08 -0.1872E-04 0.4366E-04 index sing. val. g coef g**2 cumulative scaled sqrt sum of sqrs of cum.s.s. 0 1.041 0.2635 1 1.000 0.9998 0.9996 0.4162E-01 0.5452E-01 2 0.1000E+00 0.2000 0.4001E-01 0.1604E-02 0.1111E-01 3 0.1000E-01 -0.4005E-01 0.1604E-02 0.1973E-07 0.4055E-04 4 0.9997E-05 -0.1776E-04 0.3153E-09 0.1941E-07 0.4201E-04 5 0.9717E-07 -0.1872E-04 0.3505E-09 0.1906E-07 0.4366E-04 index ynorm rnorm log10 log10 ynorm rnorm 0 0.000E+00 0.102E+01 -1000.000 0.009 1 0.100E+01 0.204E+00 0.000 -0.690 2 0.224E+01 0.400E-01 0.350 -1.397 3 0.459E+01 0.140E-03 0.662 -3.852 4 0.492E+01 0.139E-03 0.692 -3.856 5 0.193E+03 0.138E-03 2.285 -3.860 norms of solution and residual vectors for a range of values of the levenberg-marquardt parameter, lambda. lambda ynorm rnorm log10 log10 log10 lambda ynorm rnorm 0.100E+02 0.990E-02 0.101E+01 1.000 -2.004 0.005 0.354E+01 0.738E-01 0.948E+00 0.549 -1.132 -0.023 0.126E+01 0.388E+00 0.644E+00 0.099 -0.411 -0.191 0.445E+00 0.840E+00 0.255E+00 -0.352 -0.076 -0.593 0.158E+00 0.113E+01 0.150E+00 -0.802 0.054 -0.824 0.558E-01 0.183E+01 0.614E-01 -1.253 0.262 -1.212 0.198E-01 0.232E+01 0.328E-01 -1.704 0.365 -1.484 0.701E-02 0.349E+01 0.132E-01 -2.154 0.543 -1.878 0.248E-02 0.438E+01 0.233E-02 -2.605 0.642 -2.632 0.880E-03 0.456E+01 0.339E-03 -3.056 0.659 -3.470 0.312E-03 0.458E+01 0.146E-03 -3.506 0.661 -3.836 0.110E-03 0.459E+01 0.141E-03 -3.957 0.661 -3.852 0.391E-04 0.459E+01 0.140E-03 -4.407 0.662 -3.853 0.139E-04 0.463E+01 0.140E-03 -4.858 0.665 -3.854 0.491E-05 0.481E+01 0.139E-03 -5.309 0.682 -3.856 0.174E-05 0.494E+01 0.139E-03 -5.759 0.693 -3.856 0.617E-06 0.678E+01 0.139E-03 -6.210 0.831 -3.856 0.218E-06 0.322E+02 0.139E-03 -6.661 1.508 -3.857 0.774E-07 0.118E+03 0.138E-03 -7.111 2.072 -3.859 0.274E-07 0.179E+03 0.138E-03 -7.562 2.252 -3.860 0.972E-08 0.191E+03 0.138E-03 -8.012 2.281 -3.860 sequence of candidate solutions, x soln 1 soln 2 soln 3 soln 4 1 fire 0.374096 -1.13139 -2.48573 -2.83753 2 water 0.519519 0.392268 -0.529133 0.598666 3 earth 0.412234 1.71454 -0.184141 -0.373618 4 air 0.479494 0.617368 1.61568 0.394121 5 cosmos 0.435809 0.496254 3.45479 3.93558 soln 5 1 fire -74.9158 2 water 100.682 3 earth -79.8044 4 air 92.8170 5 cosmos -80.0529 TEST05 BNDACC accumulates a banded matrix. BNDSOL solves an associated banded least squares problem. Execute a sequence of cubic spline fits to a discrete set of data. The number of breakpoints is 5 Breakpoints: 2.00000 7.50000 13.0000 18.5000 24.0000 c = -8.79159 3.50509 3.28036 0.90261 5.30355 3.25993 -10.94924 RNORM = 0.00000 i x y yfit r = y-yfit/1x 1 2. 2.20 2.13 0.0727 2 4. 4.00 4.30 -0.3025 3 6. 5.00 4.74 0.2581 4 8. 4.60 4.19 0.4068 5 10. 2.80 3.37 -0.5712 6 12. 2.70 2.93 -0.2273 7 14. 3.80 3.47 0.3273 8 16. 5.10 4.85 0.2476 9 18. 6.10 6.15 -0.0460 10 20. 6.30 6.44 -0.1378 11 22. 5.00 5.14 -0.1434 12 24. 2.00 1.85 0.1515 SIGFAC = 0.00000 covariance matrix of the spline coefficients. 1 1 0.000000 2 1 0.000000 3 1 0.000000 4 1 0.000000 5 1 0.000000 6 1 0.000000 7 1 0.000000 1 2 0.000000 2 2 0.000000 3 2 0.000000 4 2 0.000000 5 2 0.000000 6 2 0.000000 7 2 0.000000 1 3 0.000000 2 3 0.000000 3 3 0.000000 4 3 0.000000 5 3 0.000000 6 3 0.000000 7 3 0.000000 1 4 0.000000 2 4 0.000000 3 4 0.000000 4 4 0.000000 5 4 0.000000 6 4 0.000000 7 4 0.000000 1 5 0.000000 2 5 0.000000 3 5 0.000000 4 5 0.000000 5 5 0.000000 6 5 0.000000 7 5 0.000000 1 6 0.000000 2 6 0.000000 3 6 0.000000 4 6 0.000000 5 6 0.000000 6 6 0.000000 7 6 0.000000 1 7 0.000000 2 7 0.000000 3 7 0.000000 4 7 0.000000 5 7 0.000000 6 7 0.000000 7 7 0.000000 The number of breakpoints is 6 Breakpoints: 2.00000 6.40000 10.8000 15.2000 19.6000 24.0000 c = -0.64166 1.22698 4.53821 0.87585 2.81286 5.69157 0.51351 2.02165 RNORM = 0.00000 i x y yfit r = y-yfit/1x 1 2. 2.20 2.20 -0.0011 2 4. 4.00 3.99 0.0071 3 6. 5.00 5.05 -0.0462 4 8. 4.60 4.43 0.1723 5 10. 2.80 3.07 -0.2688 6 12. 2.70 2.65 0.0505 7 14. 3.80 3.55 0.2542 8 16. 5.10 5.12 -0.0212 9 18. 6.10 6.46 -0.3594 10 20. 6.30 6.32 -0.0192 11 22. 5.00 4.38 0.6171 12 24. 2.00 2.44 -0.4418 SIGFAC = 0.00000 covariance matrix of the spline coefficients. 1 1 0.000000 2 1 0.000000 3 1 0.000000 4 1 0.000000 5 1 0.000000 6 1 0.000000 7 1 0.000000 8 1 0.000000 1 2 0.000000 2 2 0.000000 3 2 0.000000 4 2 0.000000 5 2 0.000000 6 2 0.000000 7 2 0.000000 8 2 0.000000 1 3 0.000000 2 3 0.000000 3 3 0.000000 4 3 0.000000 5 3 0.000000 6 3 0.000000 7 3 0.000000 8 3 0.000000 1 4 0.000000 2 4 0.000000 3 4 0.000000 4 4 0.000000 5 4 0.000000 6 4 0.000000 7 4 0.000000 8 4 0.000000 1 5 0.000000 2 5 0.000000 3 5 0.000000 4 5 0.000000 5 5 0.000000 6 5 0.000000 7 5 0.000000 8 5 0.000000 1 6 0.000000 2 6 0.000000 3 6 0.000000 4 6 0.000000 5 6 0.000000 6 6 0.000000 7 6 0.000000 8 6 0.000000 1 7 0.000000 2 7 0.000000 3 7 0.000000 4 7 0.000000 5 7 0.000000 6 7 0.000000 7 7 0.000000 8 7 0.000000 1 8 0.000000 2 8 0.000000 3 8 0.000000 4 8 0.000000 5 8 0.000000 6 8 0.000000 7 8 0.000000 8 8 0.000000 The number of breakpoints is 7 Breakpoints: 2.00000 5.66667 9.33333 13.0000 16.6667 20.3333 24.0000 c = 2.86630 0.31119 4.71552 1.61614 1.88721 3.55742 5.46325 0.08990 3.33603 RNORM = 0.00000 i x y yfit r = y-yfit/1x 1 2. 2.20 2.21 -0.0066 2 4. 4.00 3.93 0.0707 3 6. 5.00 5.24 -0.2419 4 8. 4.60 4.24 0.3583 5 10. 2.80 2.96 -0.1618 6 12. 2.70 2.87 -0.1716 7 14. 3.80 3.65 0.1502 8 16. 5.10 4.91 0.1850 9 18. 6.10 6.30 -0.2034 10 20. 6.30 6.57 -0.2678 11 22. 5.00 4.44 0.5617 12 24. 2.00 2.29 -0.2897 SIGFAC = 0.00000 covariance matrix of the spline coefficients. 1 1 0.000000 2 1 0.000000 3 1 0.000000 4 1 0.000000 5 1 0.000000 6 1 0.000000 7 1 0.000000 8 1 0.000000 9 1 0.000000 1 2 0.000000 2 2 0.000000 3 2 0.000000 4 2 0.000000 5 2 0.000000 6 2 0.000000 7 2 0.000000 8 2 0.000000 9 2 0.000000 1 3 0.000000 2 3 0.000000 3 3 0.000000 4 3 0.000000 5 3 0.000000 6 3 0.000000 7 3 0.000000 8 3 0.000000 9 3 0.000000 1 4 0.000000 2 4 0.000000 3 4 0.000000 4 4 0.000000 5 4 0.000000 6 4 0.000000 7 4 0.000000 8 4 0.000000 9 4 0.000000 1 5 0.000000 2 5 0.000000 3 5 0.000000 4 5 0.000000 5 5 0.000000 6 5 0.000000 7 5 0.000000 8 5 0.000000 9 5 0.000000 1 6 0.000000 2 6 0.000000 3 6 0.000000 4 6 0.000000 5 6 0.000000 6 6 0.000000 7 6 0.000000 8 6 0.000000 9 6 0.000000 1 7 0.000000 2 7 0.000000 3 7 0.000000 4 7 0.000000 5 7 0.000000 6 7 0.000000 7 7 0.000000 8 7 0.000000 9 7 0.000000 1 8 0.000000 2 8 0.000000 3 8 0.000000 4 8 0.000000 5 8 0.000000 6 8 0.000000 7 8 0.000000 8 8 0.000000 9 8 0.000000 1 9 0.000000 2 9 0.000000 3 9 0.000000 4 9 0.000000 5 9 0.000000 6 9 0.000000 7 9 0.000000 8 9 0.000000 9 9 0.000000 The number of breakpoints is 8 Breakpoints: 2.00000 5.14286 8.28571 11.4286 14.5714 17.7143 20.8571 24.0000 c = 0.94625 1.01288 3.80426 3.06930 0.95915 2.98443 4.08269 4.51127 1.77459 -3.67858 RNORM = 0.00000 i x y yfit r = y-yfit/1x 1 2. 2.20 2.20 -0.0005 2 4. 4.00 3.99 0.0106 3 6. 5.00 5.06 -0.0596 4 8. 4.60 4.45 0.1548 5 10. 2.80 3.01 -0.2130 6 12. 2.70 2.56 0.1441 7 14. 3.80 3.80 -0.0036 8 16. 5.10 5.17 -0.0721 9 18. 6.10 6.06 0.0439 10 20. 6.30 6.28 0.0162 11 22. 5.00 5.04 -0.0376 12 24. 2.00 1.98 0.0172 SIGFAC = 0.00000 covariance matrix of the spline coefficients. 1 1 0.000000 2 1 0.000000 3 1 0.000000 4 1 0.000000 5 1 0.000000 6 1 0.000000 7 1 0.000000 8 1 0.000000 9 1 0.000000 10 1 0.000000 1 2 0.000000 2 2 0.000000 3 2 0.000000 4 2 0.000000 5 2 0.000000 6 2 0.000000 7 2 0.000000 8 2 0.000000 9 2 0.000000 10 2 0.000000 1 3 0.000000 2 3 0.000000 3 3 0.000000 4 3 0.000000 5 3 0.000000 6 3 0.000000 7 3 0.000000 8 3 0.000000 9 3 0.000000 10 3 0.000000 1 4 0.000000 2 4 0.000000 3 4 0.000000 4 4 0.000000 5 4 0.000000 6 4 0.000000 7 4 0.000000 8 4 0.000000 9 4 0.000000 10 4 0.000000 1 5 0.000000 2 5 0.000000 3 5 0.000000 4 5 0.000000 5 5 0.000000 6 5 0.000000 7 5 0.000000 8 5 0.000000 9 5 0.000000 10 5 0.000000 1 6 0.000000 2 6 0.000000 3 6 0.000000 4 6 0.000000 5 6 0.000000 6 6 0.000000 7 6 0.000000 8 6 0.000000 9 6 0.000000 10 6 0.000000 1 7 0.000000 2 7 0.000000 3 7 0.000000 4 7 0.000000 5 7 0.000000 6 7 0.000000 7 7 0.000000 8 7 0.000000 9 7 0.000000 10 7 0.000000 1 8 0.000000 2 8 0.000000 3 8 0.000000 4 8 0.000000 5 8 0.000000 6 8 0.000000 7 8 0.000000 8 8 0.000000 9 8 0.000000 10 8 0.000000 1 9 0.000000 2 9 0.000000 3 9 0.000000 4 9 0.000000 5 9 0.000000 6 9 0.000000 7 9 0.000000 8 9 0.000000 9 9 0.000000 10 9 0.000000 1 10 0.000000 2 10 0.000000 3 10 0.000000 4 10 0.000000 5 10 0.000000 6 10 0.000000 7 10 0.000000 8 10 0.000000 9 10 0.000000 10 10 0.000000 The number of breakpoints is 9 Breakpoints: 2.00000 4.75000 7.50000 10.2500 13.0000 15.7500 18.5000 21.2500 24.0000 c = -1.53469 1.82769 3.02393 3.84870 1.22224 1.99252 3.47273 4.09069 4.77102 0.25898 2.46937 RNORM = 0.00000 i x y yfit r = y-yfit/1x 1 2. 2.20 2.20 0.0000 2 4. 4.00 4.00 0.0002 3 6. 5.00 5.00 -0.0021 4 8. 4.60 4.59 0.0107 5 10. 2.80 2.83 -0.0289 6 12. 2.70 2.66 0.0448 7 14. 3.80 3.83 -0.0315 8 16. 5.10 5.13 -0.0314 9 18. 6.10 5.97 0.1253 10 20. 6.30 6.48 -0.1835 11 22. 5.00 4.85 0.1546 12 24. 2.00 2.07 -0.0691 SIGFAC = 0.00000 covariance matrix of the spline coefficients. 1 1 0.000000 2 1 0.000000 3 1 0.000000 4 1 0.000000 5 1 0.000000 6 1 0.000000 7 1 0.000000 8 1 0.000000 9 1 0.000000 10 1 0.000000 11 1 0.000000 1 2 0.000000 2 2 0.000000 3 2 0.000000 4 2 0.000000 5 2 0.000000 6 2 0.000000 7 2 0.000000 8 2 0.000000 9 2 0.000000 10 2 0.000000 11 2 0.000000 1 3 0.000000 2 3 0.000000 3 3 0.000000 4 3 0.000000 5 3 0.000000 6 3 0.000000 7 3 0.000000 8 3 0.000000 9 3 0.000000 10 3 0.000000 11 3 0.000000 1 4 0.000000 2 4 0.000000 3 4 0.000000 4 4 0.000000 5 4 0.000000 6 4 0.000000 7 4 0.000000 8 4 0.000000 9 4 0.000000 10 4 0.000000 11 4 0.000000 1 5 0.000000 2 5 0.000000 3 5 0.000000 4 5 0.000000 5 5 0.000000 6 5 0.000000 7 5 0.000000 8 5 0.000000 9 5 0.000000 10 5 0.000000 11 5 0.000000 1 6 0.000000 2 6 0.000000 3 6 0.000000 4 6 0.000000 5 6 0.000000 6 6 0.000000 7 6 0.000000 8 6 0.000000 9 6 0.000000 10 6 0.000000 11 6 0.000000 1 7 0.000000 2 7 0.000000 3 7 0.000000 4 7 0.000000 5 7 0.000000 6 7 0.000000 7 7 0.000000 8 7 0.000000 9 7 0.000000 10 7 0.000000 11 7 0.000000 1 8 0.000000 2 8 0.000000 3 8 0.000000 4 8 0.000000 5 8 0.000000 6 8 0.000000 7 8 0.000000 8 8 0.000000 9 8 0.000000 10 8 0.000000 11 8 0.000000 1 9 0.000000 2 9 0.000000 3 9 0.000000 4 9 0.000000 5 9 0.000000 6 9 0.000000 7 9 0.000000 8 9 0.000000 9 9 0.000000 10 9 0.000000 11 9 0.000000 1 10 0.000000 2 10 0.000000 3 10 0.000000 4 10 0.000000 5 10 0.000000 6 10 0.000000 7 10 0.000000 8 10 0.000000 9 10 0.000000 10 10 0.000000 11 10 0.000000 1 11 0.000000 2 11 0.000000 3 11 0.000000 4 11 0.000000 5 11 0.000000 6 11 0.000000 7 11 0.000000 8 11 0.000000 9 11 0.000000 10 11 0.000000 11 11 0.000000 The number of breakpoints is 10 Breakpoints: 2.00000 4.44444 6.88889 9.33333 11.7778 14.2222 16.6667 19.1111 21.5556 24.0000 c = -7.06462 3.43609 2.12028 4.29891 1.78956 1.52707 2.63781 3.71920 4.42346 3.98990 1.44331 -1.76312 RNORM = 0.00000 i x y yfit r = y-yfit/1x 1 2. 2.20 2.20 0.0000 2 4. 4.00 4.00 0.0000 3 6. 5.00 5.00 0.0000 4 8. 4.60 4.60 0.0000 5 10. 2.80 2.80 0.0000 6 12. 2.70 2.70 0.0000 7 14. 3.80 3.80 0.0000 8 16. 5.10 5.10 0.0000 9 18. 6.10 6.10 0.0000 10 20. 6.30 6.30 0.0000 11 22. 5.00 5.00 0.0000 12 24. 2.00 2.00 0.0000 TEST06 LDP carries out least distance programming. V: 0.46711 -0.88420 0.88420 0.46711 1.53602 -0.38402 -0.05353 0.17408 Singular value vector S: 2.25455 0.34571 G tilde = 0.20719 -2.55762 0.39219 1.35115 -0.59937 1.20647 H tilde = -1.30041 -0.08354 0.38395 LDP MODE = ****** ZNORM = 0.412138-313 Z = 0.00000 0.871288 The coefficients of the fitted line F(T) = X(1) * T + X(2) are: -0.928016 1.26078 The residual vector: -0.528779 -0.196775 -0.967752E-01 0.681629 The residual norm: 0.182123 TEST07 QRBD computes the singular values S of a bidiagonal matrix BD, and can also compute the decomposition factors U and V, so that S = U * BD * V. The bidiagonal matrix BD: 0.7177 0.4485 0.0000 0.0000 0.6554 0.4345 0.0000 0.0000 0.1152 Error flag IPASS = 1 The singular values of BD: 1 0.983048 2 0.610998 3 0.902531E-01 The factor U: 0.7611 0.6477 0.0340 -0.6472 0.7550 0.1050 0.0423 -0.1019 0.9939 The factor V: 0.5557 -0.7603 0.3365 0.7791 0.3348 -0.5300 0.2903 0.5567 0.7784 The product U' * S * V' = BD: 0.7177 0.4485 0.0000 0.0000 0.6554 0.4345 0.0000 0.0000 0.1152 LAWSON_PRB Normal end of execution.