19 October 2008 6:57:58.687 PM LAWSON_PRB4 DEMONSTRATE SINGULAR VALUE ANALYSIS Read data from file: lawson_prb4_input.txt 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 No. 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 0000. -12526. 0000. 0000. 2 Water 10196. -0000. 0000. -11349. 3 Earth 0000. 11510. 0000. 0000. 4 Air 0000. 0000. -0000. 11877. 5 Cosmos 0000. 0000. -12388. -0000. COL 5 1 Fire 0000. 2 Water -10195. 3 Earth 0000. 4 Air -0000. 5 Cosmos 0000. 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 LAWSON_PRB4: Normal end of execution. 19 October 2008 6:57:58.710 PM