10 January 2011 1:22:03.671 PM LAWSON_PRB FORTRAN90 version Tests the LAWSON library. 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 0.21101002E+01 Residual length = 0.0000E+00 Covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.49319129E-03 M N 2 1 Estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.80773327E+00 Residual length = 0.6405E+02 Covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.45650669E-05 M N 2 2 Estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.10750444E+01 2 0.11583237E+01 Residual length = 0.0000E+00 Covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.28457970E-03 1 2 -0.26290467E-03 2 2 0.24678590E-03 M N 3 1 Estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.29811741E+00 Residual length = 0.3119E+03 Covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.35833195E-05 M N 3 2 Estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.16175460E+01 2 0.21173123E+01 Residual length = 0.2042E+03 Covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.14486547E-03 1 2 -0.13890623E-03 2 2 0.13607315E-03 M N 3 3 Estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.21600841E+01 2 -0.68024079E+00 3 -0.15983038E+00 Residual length = 0.0000E+00 Covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.22140491E-04 1 2 0.51234869E-05 1 3 0.47375109E-05 2 2 0.94613964E-05 2 3 -0.35799028E-05 3 3 0.58392283E-05 M N 6 6 Estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 -0.59223702E-01 2 -0.34921113E+04 3 0.34924409E+04 4 0.34855795E+04 5 -0.34861198E+04 6 -0.15173577E+00 Residual length = 0.0000E+00 Covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.66999461E-05 1 2 -0.35311311E-01 1 3 0.35312593E-01 1 4 0.35304463E-01 1 5 -0.35303632E-01 1 6 -0.53805905E-06 2 2 0.39013478E+03 2 3 -0.39011576E+03 2 4 -0.38983794E+03 2 5 0.38985640E+03 2 6 0.16989886E-01 3 3 0.39009674E+03 3 4 0.38981896E+03 3 5 -0.38983741E+03 3 6 -0.16987060E-01 4 4 0.38954154E+03 4 5 -0.38955996E+03 4 6 -0.16961976E-01 5 5 0.38957840E+03 5 6 0.16965779E-01 6 6 0.47378477E-05 M N 7 6 Estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 0.26929812E+00 2 0.11153336E+05 3 -0.11152214E+05 4 -0.11147944E+05 5 0.11149120E+05 6 0.20539553E+01 Residual length = 0.2966E+03 Covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.70704879E-05 1 2 0.44509520E-01 1 3 -0.44503539E-01 1 4 -0.44463012E-01 1 5 0.44469704E-01 1 6 0.96918244E-05 2 2 0.55478823E+03 2 3 -0.55473861E+03 2 4 -0.55435499E+03 2 5 0.55441972E+03 2 6 0.11459104E+00 3 3 0.55468899E+03 3 4 0.55430542E+03 3 5 -0.55437014E+03 3 6 -0.11457929E+00 4 4 0.55392222E+03 4 5 -0.55398688E+03 4 6 -0.11449432E+00 5 5 0.55405156E+03 5 6 0.11451019E+00 6 6 0.26666816E-04 M N 7 7 Estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 0.47644367E+04 2 -0.47655669E+04 3 0.47648132E+04 4 -0.95285494E+04 5 0.47638991E+04 6 -0.47648024E+04 7 0.47639603E+04 Residual length = 0.0000E+00 Covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.90823921E+02 1 2 -0.90835927E+02 1 3 0.90816802E+02 1 4 -0.18159685E+03 1 5 0.90778400E+02 1 6 -0.90809903E+02 1 7 0.90779562E+02 2 2 0.90847938E+02 2 3 -0.90828809E+02 2 4 0.18162086E+03 2 5 -0.90790406E+02 2 6 0.90821913E+02 2 7 -0.90791568E+02 3 3 0.90809687E+02 3 4 -0.18158262E+03 3 5 0.90771288E+02 3 6 -0.90802787E+02 3 7 0.90772450E+02 4 4 0.36309180E+03 4 5 -0.18150587E+03 4 6 0.18156886E+03 4 7 -0.18150820E+03 5 5 0.90732930E+02 5 6 -0.90764419E+02 5 7 0.90734092E+02 6 6 0.90795922E+02 6 7 -0.90765582E+02 7 7 0.90735257E+02 M N 8 6 Estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 0.28686955E+04 2 -0.28691345E+04 3 -0.59045875E+03 4 0.59083910E+03 5 -0.22811876E+04 6 0.22815599E+04 Residual length = 0.3880E+03 Covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.63069425E+02 1 2 -0.63070902E+02 1 3 -0.15212550E+02 1 4 0.15220667E+02 1 5 -0.47835430E+02 1 6 0.47840648E+02 2 2 0.63072382E+02 2 3 0.15216884E+02 2 4 -0.15224999E+02 2 5 0.47832580E+02 2 6 -0.47837798E+02 3 3 0.11863716E+03 3 4 -0.11862622E+03 3 5 -0.10348447E+03 3 6 0.10349421E+03 4 4 0.11861529E+03 4 5 0.10346542E+03 4 6 -0.10347516E+03 5 5 0.15135846E+03 5 6 -0.15137342E+03 6 6 0.15138838E+03 M N 8 7 Estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 0.99995743E+00 2 -0.59988181E+00 3 0.59985406E+00 4 0.40030663E+00 5 0.59977131E+00 6 0.15447409E-03 7 0.10000066E+01 Residual length = 0.2122E-01 Covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.37151089E-05 1 2 0.32893730E-05 1 3 -0.15745695E-05 1 4 0.47189104E-05 1 5 -0.14312325E-05 1 6 -0.42753361E-06 1 7 0.17145646E-05 2 2 0.28220564E-04 2 3 -0.21933044E-04 2 4 0.29292744E-04 2 5 -0.19570714E-04 2 6 0.14295002E-05 2 7 0.42884264E-05 3 3 0.19360250E-04 3 4 -0.23576420E-04 3 5 0.17141613E-04 3 6 -0.18574269E-05 3 7 -0.25737569E-05 4 4 0.33722859E-04 4 5 -0.21427869E-04 4 6 0.25725724E-05 4 7 0.47175514E-05 5 5 0.18851685E-04 5 6 -0.31423520E-05 5 7 -0.43052022E-06 6 6 0.28567407E-05 6 7 -0.14275348E-05 7 7 0.37144039E-05 M N 8 8 Estimated parameters, x = a**(+)*b, computed by 'hft,hs1' 1 0.25506475E+04 2 -0.25506720E+04 3 0.11229331E+05 4 -0.11229634E+05 5 -0.78361115E+04 6 0.78361385E+04 7 -0.59471114E+04 8 0.59482148E+04 Residual length = 0.0000E+00 Covariance matrix (unscaled) of estimated parameters computed by 'cov'. 1 1 0.84379056E+03 1 2 -0.84393711E+03 1 3 0.13584793E+04 1 4 -0.13586850E+04 1 5 -0.11624490E+04 1 6 0.11623952E+04 1 7 -0.10410772E+04 1 8 0.10412012E+04 2 2 0.84408369E+03 2 3 -0.13587446E+04 2 4 0.13589503E+04 2 5 0.11626748E+04 2 6 -0.11626210E+04 2 7 0.10412635E+04 2 8 -0.10413875E+04 3 3 0.27827117E+04 3 4 -0.27830804E+04 3 5 -0.22529639E+04 3 6 0.22528923E+04 3 7 -0.18904819E+04 3 8 0.18907535E+04 4 4 0.27834492E+04 4 5 0.22532760E+04 4 6 -0.22532043E+04 4 7 0.18907447E+04 4 8 -0.18910163E+04 5 5 0.19102841E+04 5 6 -0.19102167E+04 5 7 0.15070396E+04 5 8 -0.15072587E+04 6 6 0.19101493E+04 6 7 -0.15069815E+04 6 8 0.15072006E+04 7 7 0.14261223E+04 7 8 -0.14262989E+04 8 8 0.14264756E+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 Estimated parameters X = A**(+)*B from HFTI: 2.11111 Residual norm = 0.00000 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.49382716E-03 M = 1 N = 2 Pseudorank = 1 Estimated parameters X = A**(+)*B from HFTI: -0.397055 -0.341132 Residual norm = 0.00000 M = 1 N = 3 Pseudorank = 1 Estimated parameters X = A**(+)*B from HFTI: 1.07536 -0.565022 -0.382757 Residual norm = 0.00000 M = 2 N = 1 Pseudorank = 1 Estimated parameters X = A**(+)*B from HFTI: 0.125683 Residual norm = 362.143 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.40477636E-05 M = 2 N = 2 Pseudorank = 2 Estimated parameters X = A**(+)*B from HFTI: 3.71000 4.19000 Residual norm = 0.00000 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.13448000E-03 1 2 0.19272000E-03 2 2 0.28808000E-03 M = 2 N = 3 Pseudorank = 2 Estimated parameters X = A**(+)*B from HFTI: 0.563056 -0.684151E-02 0.174686 Residual norm = 0.00000 M = 3 N = 1 Pseudorank = 1 Estimated parameters X = A**(+)*B from HFTI: -0.304300 Residual norm = 308.267 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.22022794E-05 M = 3 N = 2 Pseudorank = 2 Estimated parameters X = A**(+)*B from HFTI: -0.596532 0.201541 Residual norm = 369.359 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.10869942E-04 1 2 0.64421965E-05 2 2 0.73631985E-05 M = 3 N = 3 Pseudorank = 3 Estimated parameters X = A**(+)*B from HFTI: -1.18182 0.509091 -0.690909 Residual norm = 0.00000 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.83140496E-05 1 2 -0.56611570E-05 1 3 0.83388430E-05 2 2 0.67603306E-05 2 3 -0.42396694E-05 3 3 0.22760331E-04 M = 6 N = 6 Pseudorank = 4 Estimated parameters X = A**(+)*B from HFTI: 0.529762 0.773810E-01 0.119048E-01 -0.440476 0.190476 -0.261905 Residual norm = 188.982 M = 6 N = 7 Pseudorank = 6 Estimated parameters X = A**(+)*B from HFTI: -1.40714 -0.285714 0.285714 -0.285714 -0.307143 0.500000 -0.500000 Residual norm = 0.00000 M = 6 N = 8 Pseudorank = 5 Estimated parameters X = A**(+)*B from HFTI: -0.618750 0.743750 -1.11875 0.243750 -1.18125 0.181250 -0.993750 0.368750 Residual norm = 176.777 M = 7 N = 6 Pseudorank = 4 Estimated parameters X = A**(+)*B from HFTI: 0.145833 -0.208333E-01 0.833333E-01 -0.833333E-01 -0.104167 -0.270833 Residual norm = 530.330 M = 7 N = 7 Pseudorank = 7 Estimated parameters X = A**(+)*B from HFTI: -0.500000 0.500000 -1.50000 -1.10000 1.10000 -2.10000 1.60000 Residual norm = 0.00000 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.55000000E-05 1 2 -0.25000000E-05 1 3 0.50000000E-05 1 4 0.12500000E-04 1 5 -0.10000000E-04 1 6 0.11000000E-04 1 7 -0.11500000E-04 2 2 0.35000000E-05 2 3 -0.30000000E-05 2 4 -0.50000000E-06 2 5 0.10000000E-05 2 6 -0.10000000E-05 2 7 0.25000000E-05 3 3 0.85000000E-05 3 4 0.14000000E-04 3 5 -0.10500000E-04 3 6 0.13500000E-04 3 7 -0.12500000E-04 4 4 0.71500000E-04 4 5 -0.55000000E-04 4 6 0.62000000E-04 4 7 -0.54500000E-04 5 5 0.44500000E-04 5 6 -0.48500000E-04 5 7 0.43500000E-04 6 6 0.56500000E-04 6 7 -0.48500000E-04 7 7 0.46000000E-04 M = 7 N = 8 Pseudorank = 5 Estimated parameters X = A**(+)*B from HFTI: -0.242281 -0.261463 -0.230818 -0.198963 -0.168318 0.363537 0.394182 0.507719 Residual norm = 250.000 M = 8 N = 6 Pseudorank = 4 Estimated parameters X = A**(+)*B from HFTI: -1.43750 1.06250 -1.25000 1.25000 -1.18750 1.31250 Residual norm = 530.330 M = 8 N = 7 Pseudorank = 7 Estimated parameters X = A**(+)*B from HFTI: 1.00000 -0.600000 0.600000 0.400000 0.600000 -0.219288E-15 1.00000 Residual norm = 0.216716E-12 Unscaled covariance matrix 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 = 8 N = 8 Pseudorank = 5 Estimated parameters X = A**(+)*B from HFTI: 1.00625 -0.256250 1.00625 -0.256250 0.631250 -0.631250 0.568750 -0.693750 Residual norm = 306.186 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 Estimated parameters X = A**(+)*B from HFTI: 2.11010 Residual norm = 0.00000 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.49319129E-03 M = 1 N = 2 Pseudorank = 1 Estimated parameters X = A**(+)*B from HFTI: -0.397006 -0.341142 Residual norm = 0.00000 M = 1 N = 3 Pseudorank = 1 Estimated parameters X = A**(+)*B from HFTI: 1.07534 -0.565131 -0.382886 Residual norm = 0.00000 M = 2 N = 1 Pseudorank = 1 Estimated parameters X = A**(+)*B from HFTI: 0.125656 Residual norm = 362.127 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.40477419E-05 M = 2 N = 2 Pseudorank = 2 Estimated parameters X = A**(+)*B from HFTI: 3.70686 4.18574 Residual norm = 0.00000 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.13423435E-03 1 2 0.19237195E-03 2 2 0.28758786E-03 M = 2 N = 3 Pseudorank = 2 Estimated parameters X = A**(+)*B from HFTI: 0.563128 -0.682907E-02 0.174624 Residual norm = 0.00000 M = 3 N = 1 Pseudorank = 1 Estimated parameters X = A**(+)*B from HFTI: -0.304353 Residual norm = 308.268 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.22024792E-05 M = 3 N = 2 Pseudorank = 2 Estimated parameters X = A**(+)*B from HFTI: -0.596771 0.201342 Residual norm = 369.325 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.10872442E-04 1 2 0.64433772E-05 2 2 0.73635751E-05 M = 3 N = 3 Pseudorank = 3 Estimated parameters X = A**(+)*B from HFTI: -1.18177 0.509007 -0.691372 Residual norm = 0.00000 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.83145004E-05 1 2 -0.56614608E-05 1 3 0.83418947E-05 2 2 0.67603833E-05 2 3 -0.42411833E-05 3 3 0.22771642E-04 M = 6 N = 6 Pseudorank = 4 Estimated parameters X = A**(+)*B from HFTI: 0.529948 0.772853E-01 0.118425E-01 -0.440433 0.190245 -0.261721 Residual norm = 188.963 M = 6 N = 7 Pseudorank = 6 Estimated parameters X = A**(+)*B from HFTI: -1.40669 -0.285771 0.285954 -0.285682 -0.307316 0.500173 -0.500022 Residual norm = 0.00000 M = 6 N = 8 Pseudorank = 5 Estimated parameters X = A**(+)*B from HFTI: -0.618420 0.743632 -1.11778 0.243198 -1.18020 0.180591 -0.993105 0.368538 Residual norm = 176.955 M = 7 N = 6 Pseudorank = 4 Estimated parameters X = A**(+)*B from HFTI: 0.147021 -0.216822E-01 0.846493E-01 -0.840829E-01 -0.103045 -0.271659 Residual norm = 530.329 M = 7 N = 7 Pseudorank = 7 Estimated parameters X = A**(+)*B from HFTI: -0.499800 0.500065 -1.50011 -1.09921 1.09947 -2.09944 1.59919 Residual norm = 0.00000 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.54968934E-05 1 2 -0.24991411E-05 1 3 0.49980365E-05 1 4 0.12488463E-04 1 5 -0.99911272E-05 1 6 0.10989641E-04 1 7 -0.11488261E-04 2 2 0.34993976E-05 2 3 -0.29995210E-05 2 4 -0.49954663E-06 2 5 0.99977536E-06 2 6 -0.10000508E-05 2 7 0.24990843E-05 3 3 0.85000540E-05 3 4 0.13994819E-04 3 5 -0.10496246E-04 3 6 0.13495787E-04 3 7 -0.12493116E-04 4 4 0.71448870E-04 4 5 -0.54960721E-04 4 6 0.61953019E-04 4 7 -0.54448037E-04 5 5 0.44469996E-04 5 6 -0.48464108E-04 5 7 0.43460110E-04 6 6 0.56457484E-04 6 7 -0.48453035E-04 7 7 0.45949651E-04 M = 7 N = 8 Pseudorank = 5 Estimated parameters X = A**(+)*B from HFTI: -0.242416 -0.261540 -0.230898 -0.198979 -0.168381 0.363506 0.394150 0.507755 Residual norm = 249.946 M = 8 N = 6 Pseudorank = 4 Estimated parameters X = A**(+)*B from HFTI: -1.43611 1.06146 -1.24989 1.25047 -1.18678 1.31217 Residual norm = 530.392 M = 8 N = 7 Pseudorank = 7 Estimated parameters X = A**(+)*B from HFTI: 0.999946 -0.600159 0.600121 0.399828 0.600158 -0.262090E-05 0.999883 Residual norm = 0.108058 Unscaled covariance matrix of estimated parameters computed by COV 1 1 0.37159078E-05 1 2 0.32930821E-05 1 3 -0.15772315E-05 1 4 0.47228027E-05 1 5 -0.14336211E-05 1 6 -0.42822373E-06 1 7 0.17159930E-05 2 2 0.28241214E-04 2 3 -0.21949311E-04 2 4 0.29318122E-04 2 5 -0.19588066E-04 2 6 0.14291202E-05 2 7 0.42946771E-05 3 3 0.19373168E-04 3 4 -0.23596619E-04 3 5 0.17156026E-04 3 6 -0.18578873E-05 3 7 -0.25782927E-05 4 4 0.33753355E-04 4 5 -0.21449648E-04 4 6 0.25728577E-05 4 7 0.47241140E-05 5 5 0.18868189E-04 5 6 -0.31438487E-05 5 7 -0.43436704E-06 6 6 0.28577294E-05 6 7 -0.14285363E-05 7 7 0.37163341E-05 M = 8 N = 8 Pseudorank = 5 Estimated parameters X = A**(+)*B from HFTI: 1.00619 -0.256249 1.00623 -0.256366 0.631268 -0.631161 0.568455 -0.693398 Residual norm = 306.220 TEST03 Demonstrate the use of SVDRS. The relative noise level in the data will be 0.0000000000000000 The relative pseudorank tolerance will be 1.00000000000000002E-003 M = 1 N = 1 The singular value vector S: 45.000000 Transformed right side, U'*B 1 -0.95000000E+02 Absolute pseudorank tolerance TAU = 4.49999999999999983E-002 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: 2.11111 Residual norm = 0.0000000000000000 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: 468.027777 0.000000 Transformed right side, U'*B 1 -0.24500000E+03 Absolute pseudorank tolerance TAU = 0.46802777695346248 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: -0.397055 -0.341132 Residual norm = 0.0000000000000000 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.8588E-16 sqrt(n) * spectral norm of a M = 1 N = 3 The singular value vector S: 349.392330 0.000000 0.000000 Transformed right side, U'*B 1 -0.44500000E+03 Absolute pseudorank tolerance TAU = 0.34939232962387712 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: 1.07536 -0.565022 -0.382757 Residual norm = 0.0000000000000000 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.6642E-16 sqrt(n) * spectral norm of a M = 2 N = 1 The singular value vector S: 497.041246 Transformed right side, U'*B 1 0.62469665E+02 2 0.36214298E+03 Absolute pseudorank tolerance TAU = 0.49704124577342679 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: 0.125683 Residual norm = 362.14298417007410 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.2287E-15 sqrt(n) * spectral norm of a M = 2 N = 2 The singular value vector S: 511.577831 48.868419 Transformed right side, U'*B 1 -0.36808949E+03 2 -0.27121970E+03 Absolute pseudorank tolerance TAU = 0.51157783140922664 Pseudorank = 2 Estimated X = A**(+) * B, computed by SVDRS: 3.71000 4.19000 Residual norm = 0.0000000000000000 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.2079E-15 sqrt(n) * spectral norm of a M = 2 N = 3 The singular value vector S: 658.898663 317.808986 0.000000 Transformed right side, U'*B 1 0.31458889E+03 2 -0.10992648E+03 Absolute pseudorank tolerance TAU = 0.65889866335969161 Pseudorank = 2 Estimated X = A**(+) * B, computed by SVDRS: 0.563056 -0.684151E-02 0.174686 Residual norm = 0.0000000000000000 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.1783E-15 sqrt(n) * spectral norm of a M = 3 N = 1 The singular value vector S: 673.850874 Transformed right side, U'*B 1 0.20505279E+03 2 -0.23786880E+03 3 0.19607852E+03 Absolute pseudorank tolerance TAU = 0.67385087371020003 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: -0.304300 Residual norm = 308.26669354107798 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.8695E-16 sqrt(n) * spectral norm of a M = 3 N = 2 The singular value vector S: 640.180644 251.632158 Transformed right side, U'*B 1 -0.33439744E+03 2 -0.88473345E+02 3 0.36935866E+03 Absolute pseudorank tolerance TAU = 0.64018064411696829 Pseudorank = 2 Estimated X = A**(+) * B, computed by SVDRS: -0.596532 0.201541 Residual norm = 369.35865887029956 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.1803E-15 sqrt(n) * spectral norm of a M = 3 N = 3 The singular value vector S: 828.108139 353.893388 187.673601 Transformed right side, U'*B 1 0.35173128E+03 2 -0.22248603E+03 3 0.23422227E+03 Absolute pseudorank tolerance TAU = 0.82810813862877242 Pseudorank = 3 Estimated X = A**(+) * B, computed by SVDRS: -1.18182 0.509091 -0.690909 Residual norm = 0.0000000000000000 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.2827E-15 sqrt(n) * spectral norm of a M = 6 N = 6 The singular value vector S: 1370.683112 909.389449 688.277714 106.828951 0.000000 0.000000 Transformed right side, U'*B 1 0.43693249E+03 2 -0.37288436E+03 3 -0.89844011E+02 4 -0.58403984E+02 5 -0.80218078E+02 6 -0.17111209E+03 Absolute pseudorank tolerance TAU = 1.3706831120290186 Pseudorank = 4 Estimated X = A**(+) * B, computed by SVDRS: 0.529762 0.773810E-01 0.119048E-01 -0.440476 0.190476 -0.261905 Residual norm = 188.98223650461361 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.2885E-15 sqrt(n) * spectral norm of a M = 6 N = 7 The singular value vector S: 1133.091987 1015.171454 773.338710 634.193192 308.291326 215.132895 0.000000 Transformed right side, U'*B 1 0.32251485E+03 2 -0.55017435E+03 3 -0.13280965E+03 4 0.27904995E+03 5 0.36438832E+03 6 0.19533619E+03 Absolute pseudorank tolerance TAU = 1.1330919867148335 Pseudorank = 6 Estimated X = A**(+) * B, computed by SVDRS: -1.40714 -0.285714 0.285714 -0.285714 -0.307143 0.500000 -0.500000 Residual norm = 0.0000000000000000 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.5829E-15 sqrt(n) * spectral norm of a M = 6 N = 8 The singular value vector S: 1381.304157 1035.606977 767.514335 690.287156 105.557577 0.000000 0.000000 0.000000 Transformed right side, U'*B 1 0.88823196E+01 2 -0.20255290E+03 3 0.46315700E+03 4 -0.25856731E+03 5 0.21776585E+03 6 -0.17677670E+03 Absolute pseudorank tolerance TAU = 1.3813041571973010 Pseudorank = 5 Estimated X = A**(+) * B, computed by SVDRS: -0.618750 0.743750 -1.11875 0.243750 -1.18125 0.181250 -0.993750 0.368750 Residual norm = 176.77669529663680 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.5852E-15 sqrt(n) * spectral norm of a M = 7 N = 6 The singular value vector S: 1372.559276 1211.132427 707.925490 110.139817 0.000000 0.000000 Transformed right side, U'*B 1 -0.22502484E+03 2 -0.24926150E+03 3 -0.81893694E+02 4 -0.21235637E+02 5 0.50358563E+03 6 -0.87007748E+02 7 -0.14170803E+03 Absolute pseudorank tolerance TAU = 1.3725592759107133 Pseudorank = 4 Estimated X = A**(+) * B, computed by SVDRS: 0.145833 -0.208333E-01 0.833333E-01 -0.833333E-01 -0.104167 -0.270833 Residual norm = 530.33008588991038 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.7371E-15 sqrt(n) * spectral norm of a M = 7 N = 7 The singular value vector S: 1152.347336 1063.984792 889.708900 768.781892 549.905167 320.428166 67.672405 Transformed right side, U'*B 1 0.14077866E+03 2 -0.13632525E+03 3 -0.22910985E+02 4 0.51857788E+03 5 0.33042939E+03 6 -0.39148988E+03 7 -0.21183947E+03 Absolute pseudorank tolerance TAU = 1.1523473357693743 Pseudorank = 7 Estimated X = A**(+) * B, computed by SVDRS: -0.500000 0.500000 -1.50000 -1.10000 1.10000 -2.10000 1.60000 Residual norm = 0.0000000000000000 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.6817E-15 sqrt(n) * spectral norm of a M = 7 N = 8 The singular value vector S: 1540.606324 1002.386946 804.308038 706.062238 475.097110 0.000000 0.000000 0.000000 Transformed right side, U'*B 1 0.30756227E+03 2 0.23204856E+03 3 0.52075186E+03 4 0.37423390E+03 5 0.63876251E+00 6 0.24616288E+03 7 0.43632990E+02 Absolute pseudorank tolerance TAU = 1.5406063235961929 Pseudorank = 5 Estimated X = A**(+) * B, computed by SVDRS: -0.242281 -0.261463 -0.230818 -0.198963 -0.168318 0.363537 0.394182 0.507719 Residual norm = 250.00000000000003 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.4642E-15 sqrt(n) * spectral norm of a M = 8 N = 6 The singular value vector S: 1450.255998 1197.298480 758.845155 128.794102 0.000000 0.000000 Transformed right side, U'*B 1 0.35254588E+03 2 -0.10789493E+03 3 -0.25535402E+03 4 0.39219181E+03 5 -0.40254153E+03 6 0.30943500E+03 7 0.95038961E+02 8 -0.12011619E+03 Absolute pseudorank tolerance TAU = 1.4502559980006831 Pseudorank = 4 Estimated X = A**(+) * B, computed by SVDRS: -1.43750 1.06250 -1.25000 1.25000 -1.18750 1.31250 Residual norm = 530.33008588991083 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.4530E-15 sqrt(n) * spectral norm of a M = 8 N = 7 The singular value vector S: 1272.386403 1105.091619 930.450481 743.316071 535.253100 349.072341 102.961604 Transformed right side, U'*B 1 -0.86605383E+02 2 -0.32267496E+03 3 -0.47571678E+03 4 -0.12052994E+03 5 0.49779875E+03 6 -0.46659207E+03 7 0.47272605E+02 8 -0.56843419E-13 Absolute pseudorank tolerance TAU = 1.2723864034165784 Pseudorank = 7 Estimated X = A**(+) * B, computed by SVDRS: 1.00000 -0.600000 0.600000 0.400000 0.600000 0.116226E-14 1.00000 Residual norm = 5.68434188608080149E-014 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.4842E-15 sqrt(n) * spectral norm of a M = 8 N = 8 The singular value vector S: 1584.670721 1279.385123 917.031642 780.047274 110.325120 0.000000 0.000000 0.000000 Transformed right side, U'*B 1 -0.10890799E+02 2 -0.20163306E+03 3 -0.39331004E+03 4 0.28532538E+03 5 -0.20389247E+03 6 -0.21785832E+03 7 0.21481332E+03 8 -0.11957851E+02 Absolute pseudorank tolerance TAU = 1.5846707205669455 Pseudorank = 5 Estimated X = A**(+) * B, computed by SVDRS: 1.00625 -0.256250 1.00625 -0.256250 0.631250 -0.631250 0.568750 -0.693750 Residual norm = 306.18621784789735 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.3933E-15 sqrt(n) * spectral norm of a The relative noise level in the data will be 1.00000000000000005E-004 The relative pseudorank tolerance will be 1.00000000000000002E-003 M = 1 N = 1 The singular value vector S: 45.029000 Transformed right side, U'*B 1 -0.95015700E+02 Absolute pseudorank tolerance TAU = 4.50290000000000065E-002 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: 2.11010 Residual norm = 0.0000000000000000 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: 468.032950 0.000000 Transformed right side, U'*B 1 -0.24498830E+03 Absolute pseudorank tolerance TAU = 0.46803295001169520 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: -0.397006 -0.341142 Residual norm = 0.0000000000000000 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: 349.370959 0.000000 0.000000 Transformed right side, U'*B 1 -0.44499690E+03 Absolute pseudorank tolerance TAU = 0.34937095943133284 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: 1.07534 -0.565131 -0.382886 Residual norm = 0.0000000000000000 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.4697E-16 sqrt(n) * spectral norm of a M = 2 N = 1 The singular value vector S: 497.042577 Transformed right side, U'*B 1 0.62456607E+02 2 0.36212682E+03 Absolute pseudorank tolerance TAU = 0.49704257668941193 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: 0.125656 Residual norm = 362.12682279780284 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.000 sqrt(n) * spectral norm of a M = 2 N = 2 The singular value vector S: 511.574471 48.911531 Transformed right side, U'*B 1 -0.36808095E+03 2 -0.27119911E+03 Absolute pseudorank tolerance TAU = 0.51157447115414056 Pseudorank = 2 Estimated X = A**(+) * B, computed by SVDRS: 3.70686 4.18574 Residual norm = 0.0000000000000000 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.1179E-15 sqrt(n) * spectral norm of a M = 2 N = 3 The singular value vector S: 658.897668 317.790330 0.000000 Transformed right side, U'*B 1 0.31463276E+03 2 -0.10991746E+03 Absolute pseudorank tolerance TAU = 0.65889766765444113 Pseudorank = 2 Estimated X = A**(+) * B, computed by SVDRS: 0.563128 -0.682907E-02 0.174624 Residual norm = 0.0000000000000000 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.3014E-15 sqrt(n) * spectral norm of a M = 3 N = 1 The singular value vector S: 673.820304 Transformed right side, U'*B 1 0.20507927E+03 2 -0.23784018E+03 3 0.19611469E+03 Absolute pseudorank tolerance TAU = 0.67382030436380447 Pseudorank = 1 Estimated X = A**(+) * B, computed by SVDRS: -0.304353 Residual norm = 308.26761244457305 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.2271E-15 sqrt(n) * spectral norm of a M = 3 N = 2 The singular value vector S: 640.178000 251.609406 Transformed right side, U'*B 1 0.33437564E+03 2 0.88550792E+02 3 0.36932499E+03 Absolute pseudorank tolerance TAU = 0.64017799991430491 Pseudorank = 2 Estimated X = A**(+) * B, computed by SVDRS: -0.596771 0.201342 Residual norm = 369.32499447408492 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.2106E-15 sqrt(n) * spectral norm of a M = 3 N = 3 The singular value vector S: 828.148074 353.881988 187.635799 Transformed right side, U'*B 1 0.35172659E+03 2 -0.22243783E+03 3 0.23422147E+03 Absolute pseudorank tolerance TAU = 0.82814807445475702 Pseudorank = 3 Estimated X = A**(+) * B, computed by SVDRS: -1.18177 0.509007 -0.691372 Residual norm = 0.0000000000000000 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.4178E-15 sqrt(n) * spectral norm of a M = 6 N = 6 The singular value vector S: 1370.656567 909.356719 688.270306 106.804136 0.075095 0.008643 Transformed right side, U'*B 1 0.43695854E+03 2 -0.37290660E+03 3 -0.89822405E+02 4 -0.58381036E+02 5 0.16791084E+03 6 0.86650203E+02 Absolute pseudorank tolerance TAU = 1.3706565670629556 Pseudorank = 4 Estimated X = A**(+) * B, computed by SVDRS: 0.529938 0.772862E-01 0.118285E-01 -0.440435 0.190242 -0.261713 Residual norm = 188.95053965463424 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.2785E-15 sqrt(n) * spectral norm of a M = 6 N = 7 The singular value vector S: 1133.118932 1015.172432 773.310624 634.228296 308.301409 215.132085 0.000000 Transformed right side, U'*B 1 0.32262746E+03 2 -0.55010544E+03 3 -0.13301769E+03 4 0.27906441E+03 5 0.36440383E+03 6 0.19522781E+03 Absolute pseudorank tolerance TAU = 1.1331189322122583 Pseudorank = 6 Estimated X = A**(+) * B, computed by SVDRS: -1.40669 -0.285771 0.285954 -0.285682 -0.307316 0.500173 -0.500022 Residual norm = 0.0000000000000000 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.4602E-15 sqrt(n) * spectral norm of a M = 6 N = 8 The singular value vector S: 1381.272012 1035.595759 767.495614 690.319541 105.586065 0.069059 0.000000 0.000000 Transformed right side, U'*B 1 0.89108836E+01 2 -0.20252171E+03 3 0.46316961E+03 4 0.25856100E+03 5 -0.21778844E+03 6 -0.17671630E+03 Absolute pseudorank tolerance TAU = 1.3812720115545667 Pseudorank = 5 Estimated X = A**(+) * B, computed by SVDRS: -0.618974 0.744043 -1.11839 0.243554 -1.18079 0.180959 -0.993662 0.368946 Residual norm = 176.71630299144363 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.3655E-15 sqrt(n) * spectral norm of a M = 7 N = 6 The singular value vector S: 1372.562335 1211.133829 707.989339 110.121232 0.059125 0.038142 Transformed right side, U'*B 1 -0.22509957E+03 2 -0.24920425E+03 3 -0.81826823E+02 4 -0.21178502E+02 5 -0.49468614E+03 6 0.18331588E+03 7 0.54252409E+02 Absolute pseudorank tolerance TAU = 1.3725623351269927 Pseudorank = 4 Estimated X = A**(+) * B, computed by SVDRS: 0.145597 -0.206891E-01 0.832108E-01 -0.831033E-01 -0.104399 -0.270597 Residual norm = 530.34178886643974 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.4484E-15 sqrt(n) * spectral norm of a M = 7 N = 7 The singular value vector S: 1152.300873 1063.990445 889.715972 768.723691 549.882244 320.456837 67.699768 Transformed right side, U'*B 1 0.14076309E+03 2 -0.13635612E+03 3 -0.22688757E+02 4 0.51854436E+03 5 0.33038909E+03 6 -0.39160207E+03 7 -0.21183678E+03 Absolute pseudorank tolerance TAU = 1.1523008726349082 Pseudorank = 7 Estimated X = A**(+) * B, computed by SVDRS: -0.499800 0.500065 -1.50011 -1.09921 1.09947 -2.09944 1.59919 Residual norm = 0.0000000000000000 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.9535E-15 sqrt(n) * spectral norm of a M = 7 N = 8 The singular value vector S: 1540.614371 1002.403515 804.289497 706.058614 475.132715 0.074327 0.035046 0.000000 Transformed right side, U'*B 1 0.30754669E+03 2 0.23211049E+03 3 0.52062089E+03 4 -0.37443345E+03 5 0.71221299E+00 6 0.18919369E+03 7 -0.16338768E+03 Absolute pseudorank tolerance TAU = 1.5406143712042877 Pseudorank = 5 Estimated X = A**(+) * B, computed by SVDRS: -0.242418 -0.261534 -0.230891 -0.198967 -0.168369 0.363502 0.394148 0.507748 Residual norm = 249.97957113870976 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.4994E-15 sqrt(n) * spectral norm of a M = 8 N = 6 The singular value vector S: 1450.285348 1197.311559 758.805988 128.808658 0.050263 0.037848 Transformed right side, U'*B 1 0.35257667E+03 2 -0.10792230E+03 3 -0.25536710E+03 4 -0.39231286E+03 5 -0.41524748E+03 6 -0.58441839E+02 7 -0.18157871E+02 8 -0.32396363E+03 Absolute pseudorank tolerance TAU = 1.4502853484467468 Pseudorank = 4 Estimated X = A**(+) * B, computed by SVDRS: -1.43699 1.06211 -1.25081 1.25108 -1.18763 1.31285 Residual norm = 530.21511090081378 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.5358E-15 sqrt(n) * spectral norm of a M = 8 N = 7 The singular value vector S: 1272.399894 1105.118349 930.462535 743.300274 535.209444 349.042031 102.909613 Transformed right side, U'*B 1 -0.86688973E+02 2 -0.32254891E+03 3 -0.47575533E+03 4 -0.12049023E+03 5 0.49786680E+03 6 -0.46651057E+03 7 0.47251653E+02 8 -0.10805757E+00 Absolute pseudorank tolerance TAU = 1.2723998938816852 Pseudorank = 7 Estimated X = A**(+) * B, computed by SVDRS: 0.999946 -0.600159 0.600121 0.399828 0.600158 -0.262090E-05 0.999883 Residual norm = 0.10805756945200073 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.8178E-15 sqrt(n) * spectral norm of a M = 8 N = 8 The singular value vector S: 1584.659050 1279.424779 917.050234 780.070270 110.334806 0.057708 0.038431 0.004426 Transformed right side, U'*B 1 -0.10882689E+02 2 -0.20165650E+03 3 -0.39322860E+03 4 0.28529866E+03 5 -0.20382336E+03 6 0.57000768E+02 7 0.19498182E+03 8 0.22918241E+03 Absolute pseudorank tolerance TAU = 1.5846590500261843 Pseudorank = 5 Estimated X = A**(+) * B, computed by SVDRS: 1.00597 -0.256088 1.00599 -0.256231 0.631034 -0.631018 0.568231 -0.693245 Residual norm = 306.25409728089431 frobenius norm(a-u*(s,0)**t*v**t) --------------------------------- = 0.4870E-15 sqrt(n) * spectral norm of a TEST04 Demonstrate singular value analysis. Read data from file lawson_prb_input.txt 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 SVD 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 0.1000 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 0.1000 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 0.902613 5.30355 3.25993 -10.9492 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: -0.641660 1.22698 4.53821 0.875854 2.81286 5.69157 0.513510 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 0.311187 4.71552 1.61614 1.88721 3.55742 5.46325 0.899027E-01 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: 0.946250 1.01288 3.80426 3.06930 0.959154 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 0.258978 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 = 1 ZNORM = 0.285009 Z = -0.126806 0.255246 The coefficients of the fitted line F(T) = X(1) * T + X(2) are: 0.621315 0.378685 The residual vector: -0.340136E-01 -0.893424E-01 0.106576E-01 0.324263 The residual norm: 0.338229 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: 0.9976 0.7479 0.0000 0.0000 0.5668 0.3674 0.0000 0.0000 0.9659 Error flag IPASS = 1 The singular values of BD: 1 1.31063 2 1.03082 3 0.404261 The factor U: -0.9211 -0.3547 -0.1604 -0.2835 0.3290 0.9008 -0.2667 0.8752 -0.4036 The factor V: -0.7011 -0.2744 -0.6582 -0.6790 -0.0248 0.7337 -0.2176 0.9613 -0.1689 The product U' * S * V' = BD: 0.9976 0.7479 0.0000 -0.0000 0.5668 0.3674 0.0000 0.0000 0.9659 LAWSON_PRB Normal end of execution. 10 January 2011 1:22:03.689 PM