17 September 2021 11:54:16.697 PM TEST_NONLIN_TEST FORTRAN90 version Test the TEST_NONLIN library. TEST01 Print the title of each problem. 1 "Generalized Rosenbrock function." 2 "Powell singular function." 3 "Powell badly scaled function." 4 "Wood function." 5 "Helical valley function." 6 "Watson function." 7 "Chebyquad function." 8 "Brown almost linear function." 9 "Discrete boundary value function." 10 "Discrete integral equation function." 11 "Trigonometric function." 12 "Variably dimensioned function." 13 "Broyden tridiagonal function." 14 "Broyden banded function." 15 "Hammarling 2 by 2 matrix square root problem." 16 "Hammarling 3 by 3 matrix square root problem." 17 "Dennis and Schnabel 2 by 2 example." 18 "Sample problem 18." 19 "Sample problem 19." 20 "Scalar problem f(x) = x * ( x - 5 ) * ( x - 5 )." 21 "Freudenstein-Roth function." 22 "Boggs function." 23 "Chandrasekhar function." TEST02 Seek roots of the nonlinear functions in TEST_NONLIN using Newton's method. Problem index 1 Generalized Rosenbrock function. Problem size = 10 Use analytic jacobian Initial X: -1.20000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 Function value at initial X: 2.20000 -4.40000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 3.23110 4.91935 1.05777 1 2.81032 5.37207 0.739331E-03 TEST02 Excessive correction norm = 628.150 Solution norm was 2.81032 The iteration is terminated. The Newton iteration did not converge. Final X: -1.19837 0.996422 0.992843 0.985687 0.971373 0.942746 0.885492 0.770985 0.541970 0.839396E-01 Final F(X): 2.19837 -4.39677 -0.128047E-03 -0.512187E-03 -0.204875E-02 -0.819499E-02 -0.327800E-01 -0.131120 -0.524479 -2.09792 The exact solution X: 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 F(X): 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Problem index 1 Generalized Rosenbrock function. Problem size = 10 Use finite difference jacobian Initial X: -1.20000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 Function value at initial X: 2.20000 -4.40000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 3.23110 4.91935 1.05777 1 2.81036 5.37236 0.738690E-03 TEST02 Excessive correction norm = 628.778 Solution norm was 2.81036 The iteration is terminated. The Newton iteration did not converge. Final X: -1.19837 0.996424 0.992848 0.985695 0.971386 0.942767 0.885523 0.771023 0.542000 0.839090E-01 Final F(X): 2.19837 -4.39678 -0.135002E-03 -0.525808E-03 -0.207504E-02 -0.824457E-02 -0.328704E-01 -0.131279 -0.524762 -2.09855 The exact solution X: 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 F(X): 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Problem index 2 Powell singular function. Problem size = 4 Use analytic jacobian Initial X: 3.00000 -1.00000 0.00000 1.00000 Function value at initial X: -7.00000 -2.23607 1.00000 12.6491 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 3.31662 14.6629 2.17763 1 1.22636 3.17214 0.613182 2 0.613182 0.793036 0.306591 3 0.306591 0.198259 0.153295 4 0.153295 0.495648E-01 0.766477E-01 5 0.766477E-01 0.123912E-01 0.383239E-01 6 0.383239E-01 0.309780E-02 0.191619E-01 7 0.191619E-01 0.774449E-03 0.958097E-02 8 0.958097E-02 0.193612E-03 0.479048E-02 9 0.479048E-02 0.484031E-04 0.239524E-02 10 0.239524E-02 0.121008E-04 0.119762E-02 11 0.119762E-02 0.302519E-05 0.598810E-03 12 0.598810E-03 0.756298E-06 0.299405E-03 13 0.299405E-03 0.189075E-06 0.149703E-03 14 0.149703E-03 0.472686E-07 0.748513E-04 15 0.748513E-04 0.118172E-07 0.374257E-04 16 0.374257E-04 0.295429E-08 0.187128E-04 17 0.187128E-04 0.738572E-09 0.935641E-05 18 0.935641E-05 0.184643E-09 0.467821E-05 19 0.467821E-05 0.461608E-10 0.233910E-05 20 0.233910E-05 0.115402E-10 0.116955E-05 21 0.116955E-05 0.288505E-11 0.584776E-06 22 0.584776E-06 0.721262E-12 Convergence criteria satisfied. Final X: 0.567663E-06 -0.567663E-07 0.908261E-07 0.908261E-07 Final F(X): 0.00000 0.00000 0.568434E-13 0.719019E-12 The exact solution X: 0.00000 0.00000 0.00000 0.00000 F(X): 0.00000 0.00000 0.00000 0.00000 Problem index 2 Powell singular function. Problem size = 4 Use finite difference jacobian Initial X: 3.00000 -1.00000 0.00000 1.00000 Function value at initial X: -7.00000 -2.23607 1.00000 12.6491 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 3.31662 14.6629 2.17742 1 1.22660 3.17354 0.613202 2 0.613396 0.793612 0.306620 3 0.306776 0.198487 0.153320 4 0.153456 0.496566E-01 0.766646E-01 5 0.767917E-01 0.124298E-01 0.383348E-01 6 0.384569E-01 0.311481E-02 0.191687E-01 7 0.192883E-01 0.782276E-03 0.958516E-02 8 0.970312E-02 0.197330E-03 0.479330E-02 9 0.490986E-02 0.502081E-04 0.239759E-02 10 0.251235E-02 0.129903E-04 0.120030E-02 11 0.131218E-02 0.346852E-05 0.602554E-03 12 0.709808E-03 0.979782E-06 0.304805E-03 13 0.405225E-03 0.303530E-06 0.156961E-03 14 0.248469E-03 0.107355E-06 0.836475E-04 15 0.164966E-03 0.445467E-07 0.470232E-04 16 0.118025E-03 0.216810E-07 0.282540E-04 17 0.898104E-04 0.120928E-07 0.181731E-04 18 0.716555E-04 0.749865E-08 0.124224E-04 19 0.592414E-04 0.503382E-08 0.893207E-05 20 0.503132E-04 0.358589E-08 0.669051E-05 21 0.436245E-04 0.267240E-08 0.517929E-05 22 0.384462E-04 0.206270E-08 0.411803E-05 23 0.343287E-04 0.163708E-08 0.334690E-05 24 0.309820E-04 0.132896E-08 0.277032E-05 25 0.282119E-04 0.109913E-08 0.232867E-05 26 0.258833E-04 0.923363E-09 0.198332E-05 27 0.239000E-04 0.786080E-09 0.170843E-05 28 0.221916E-04 0.676900E-09 0.148623E-05 29 0.207054E-04 0.588701E-09 0.130417E-05 30 0.194012E-04 0.516472E-09 0.115321E-05 31 0.182480E-04 0.456607E-09 0.102671E-05 32 0.172213E-04 0.406457E-09 0.919698E-06 33 0.163016E-04 0.364043E-09 Convergence criteria satisfied. Final X: 0.149512E-04 -0.149512E-05 0.447039E-05 0.447039E-05 Final F(X): 0.00000 0.00000 0.108908E-09 0.347370E-09 The exact solution X: 0.00000 0.00000 0.00000 0.00000 F(X): 0.00000 0.00000 0.00000 0.00000 Problem index 3 Powell badly scaled function. Problem size = 2 Use analytic jacobian Initial X: 0.00000 1.00000 Function value at initial X: -1.00000 0.367779 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 1.00000 1.06549 0.999456 1 1.99946 1.00856 0.999261 2 2.99872 1.00013 0.997325 3 3.99604 0.332594 0.993652 4 4.98969 0.165078 0.982851 5 5.97255 0.243266E-02 0.238807 6 6.21135 0.243349E-02 0.250000 0.117919 7 6.32927 0.237921E-02 0.125000 0.117047 8 6.44632 0.234191E-02 0.125000 0.116074 9 6.56239 0.231232E-02 0.125000 0.114991 10 6.67738 0.228430E-02 0.125000 0.113788 11 6.79117 0.225401E-02 0.125000 0.224908 12 7.01608 0.270539E-02 0.250000 0.218663 13 7.23474 0.295390E-02 0.250000 0.211096 14 7.44584 0.303263E-02 0.250000 0.202054 15 7.64789 0.298309E-02 0.250000 0.191426 16 7.83932 0.284066E-02 0.250000 0.179181 17 8.01850 0.263378E-02 0.250000 0.330792 18 8.34929 0.295830E-02 0.500000 0.264928 19 8.61422 0.243580E-02 0.500000 0.387972 20 9.00219 0.191391E-02 0.986920E-01 21 9.10088 0.989796E-04 0.524972E-02 22 9.10613 0.275617E-06 0.139524E-04 23 9.10615 0.192538E-11 0.968977E-10 24 9.10615 0.00000 Convergence criteria satisfied. Final X: 0.109816E-04 9.10615 Final F(X): 0.00000 0.00000 The exact solution X: 0.109816E-04 9.10615 F(X): -0.381479E-06 0.854086E-10 Problem index 3 Powell badly scaled function. Problem size = 2 Use finite difference jacobian Initial X: 0.00000 1.00000 Function value at initial X: -1.00000 0.367779 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 1.00000 1.06549 0.999556 1 1.99956 1.00866 0.999411 2 2.99897 1.00035 0.997524 3 3.99649 0.332732 0.993897 4 4.99039 0.165154 0.983134 5 5.97352 0.243070E-02 0.238880 6 6.21240 0.242602E-02 0.250000 0.117955 7 6.33036 0.237216E-02 0.125000 0.117081 8 6.44744 0.233543E-02 0.125000 0.116107 9 6.56355 0.230649E-02 0.125000 0.115023 10 6.67857 0.227912E-02 0.125000 0.113818 11 6.79239 0.224945E-02 0.125000 0.112483 12 6.90487 0.221525E-02 0.125000 0.222013 13 7.12688 0.262932E-02 0.250000 0.215121 14 7.34200 0.284331E-02 0.250000 0.206825 15 7.54883 0.289586E-02 0.250000 0.196988 16 7.74582 0.282807E-02 0.250000 0.185535 17 7.93135 0.267417E-02 0.250000 0.344971 18 8.27632 0.316343E-02 0.500000 0.281514 19 8.55784 0.268089E-02 0.500000 0.421601 20 8.97944 0.228856E-02 0.119008 21 9.09845 0.144921E-03 0.767483E-02 22 9.10612 0.589206E-06 0.259390E-04 23 9.10615 0.658947E-11 0.129020E-07 24 9.10615 0.666134E-15 Convergence criteria satisfied. Final X: 0.109816E-04 9.10615 Final F(X): 0.00000 0.666134E-15 The exact solution X: 0.109816E-04 9.10615 F(X): -0.381479E-06 0.854086E-10 Problem index 4 Wood function. Problem size = 4 Use analytic jacobian Initial X: -3.00000 -1.00000 -3.00000 -1.00000 Function value at initial X: -6004.00 -2080.00 -5404.00 -1880.00 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 4.47214 8550.56 8.59818 1 8.12774 1366.39 5.09135 2 4.16653 550.808 0.525801 3 3.66205 112.629 1.17314 4 2.89004 74.2670 0.356173 5 2.63434 24.6778 0.363026 6 2.46757 15.2630 0.184343 7 2.39297 6.61920 0.175626 8 2.35276 4.97520 0.156739 9 2.33704 4.47407 0.121282 10 2.33593 5.08431 0.500000 0.748751E-01 11 2.33652 4.92003 0.250000 0.844433E-01 12 2.33803 5.05193 0.250000 0.743410E-01 13 2.33939 4.78660 0.250000 0.130870 14 2.34308 5.35613 0.500000 0.159076 15 2.34195 4.08679 0.843728E-01 16 2.32598 3.16804 0.608586E-01 17 2.30561 3.20564 0.496447E-01 18 2.28376 3.11272 0.481033E-01 19 2.26314 3.03019 0.466215E-01 20 2.24362 2.95258 0.454653E-01 21 2.22519 2.88246 0.443924E-01 22 2.20778 2.81839 0.434091E-01 23 2.19132 2.75953 0.425008E-01 24 2.17576 2.70515 0.416588E-01 25 2.16106 2.65467 0.408754E-01 26 2.14718 2.60759 0.401444E-01 27 2.13407 2.56353 0.394601E-01 28 2.12171 2.52214 0.388178E-01 29 2.11007 2.48315 0.382137E-01 30 2.09911 2.44632 0.376441E-01 31 2.08883 2.41144 0.371061E-01 32 2.07918 2.37834 0.365970E-01 33 2.07016 2.34688 0.361145E-01 34 2.06174 2.31691 0.356568E-01 35 2.05391 2.28833 0.352219E-01 36 2.04665 2.26104 0.348084E-01 37 2.03993 2.23495 0.344148E-01 38 2.03376 2.20999 0.340401E-01 39 2.02811 2.18608 0.336831E-01 40 2.02297 2.16316 The Newton iteration did not converge. Final X: 0.901411 0.811865 -1.08944 1.19743 Final F(X): 0.233391E-01 -0.264260E-01 -0.198104E-01 2.16278 The exact solution X: 1.00000 1.00000 1.00000 1.00000 F(X): -0.00000 0.00000 -0.00000 0.00000 Problem index 4 Wood function. Problem size = 4 Use finite difference jacobian Initial X: -3.00000 -1.00000 -3.00000 -1.00000 Function value at initial X: -6004.00 -2080.00 -5404.00 -1880.00 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 4.47214 8550.56 9.94175 1 9.32292 840.418 4.96596 2 4.54708 522.592 1.12755 3 3.43597 146.964 0.977636 4 2.49103 57.6019 0.403256 5 2.09597 14.4830 0.155230 6 1.94326 2.13117 0.306785E-01 7 1.92013 0.869276E-01 0.181074E-01 8 1.91952 0.858250E-01 0.125000 0.291249E-01 9 1.91881 0.932558E-01 0.250000 0.353356E-01 10 1.91836 0.936443E-01 0.500000 0.873370E-02 11 1.91805 0.326841E-02 0.508543E-02 12 1.91804 0.103468E-02 0.179447E-02 13 1.91804 0.166578E-03 0.623153E-03 14 1.91804 0.350740E-04 0.214978E-03 15 1.91804 0.116826E-04 0.741038E-04 16 1.91804 0.390385E-05 0.255413E-04 17 1.91804 0.135311E-05 0.880317E-05 18 1.91804 0.465174E-06 0.303414E-05 19 1.91804 0.160459E-06 0.104576E-05 20 1.91804 0.552884E-07 Convergence criteria satisfied. Final X: -0.967974 0.947139 -0.969516 0.951247 Final F(X): 0.388151E-07 0.133502E-07 -0.350236E-07 -0.120546E-07 The exact solution X: 1.00000 1.00000 1.00000 1.00000 F(X): -0.00000 0.00000 -0.00000 0.00000 Problem index 5 Helical valley function. Problem size = 3 Use analytic jacobian Initial X: -1.00000 0.00000 0.00000 Function value at initial X: -50.0000 0.00000 0.00000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 1.00000 50.0000 3.14159 1 3.29691 37.7077 3.30345 2 3.76957 31.2881 0.500000 4.42234 3 3.58978 26.5727 2.91691 4 1.67374 11.1292 1.14966 5 1.36668 4.78751 0.452017 6 1.03434 1.09014 0.755030E-01 7 1.00226 0.407522E-01 0.310850E-02 8 1.00000 0.798804E-04 0.532376E-05 9 1.00000 0.209514E-09 0.159460E-10 10 1.00000 0.202067E-20 Convergence criteria satisfied. Final X: 1.00000 0.126963E-21 0.00000 Final F(X): -0.202067E-20 0.00000 0.00000 The exact solution X: 1.00000 0.00000 0.00000 F(X): 0.00000 0.00000 0.00000 Problem index 5 Helical valley function. Problem size = 3 Use finite difference jacobian Initial X: -1.00000 0.00000 0.00000 Function value at initial X: -50.0000 0.00000 0.00000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 1.00000 50.0000 3.14159 1 3.29686 37.7068 3.30334 2 3.76955 31.2878 0.500000 4.42243 3 3.58996 26.5745 2.91705 4 1.67387 11.1298 1.14979 5 1.36678 4.78872 0.452129 6 1.03438 1.09059 0.755399E-01 7 1.00226 0.408179E-01 0.311416E-02 8 1.00000 0.804650E-04 0.538808E-05 9 1.00000 0.253650E-08 0.253245E-09 10 1.00000 0.666134E-14 Convergence criteria satisfied. Final X: 1.00000 0.415107E-19 0.00000 Final F(X): -0.660664E-18 0.666134E-14 0.00000 The exact solution X: 1.00000 0.00000 0.00000 F(X): 0.00000 0.00000 0.00000 Problem index 6 Watson function. Problem size = 10 Use analytic jacobian Initial X: 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Function value at initial X: 0.00000 -30.0000 -30.0000 -30.5172 -31.0345 -31.5575 -32.0862 -32.6206 -33.1608 -33.7067 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 0.00000 94.9722 2.00000 1 2.00000 93.1627 0.191258E-01 6.00000 2 8.00000 87.6964 0.593667E-01 18.0000 3 26.0000 70.9353 0.198627 54.0000 4 79.9984 16.6845 0.900360 24.6455 5 55.4720 1.93648 13.4612 6 42.0130 2.00441 0.500000 8.11948 7 33.8960 1.61848 0.500000 6.36799 8 27.5317 1.31695 0.500000 5.03327 9 22.5041 1.07312 0.500000 3.96047 10 18.5529 0.870005 0.500000 6.15408 11 12.4364 1.04173 1.78666 12 10.7310 0.318963 1.06346 13 9.73328 0.258592 0.500000 1.29613 14 8.60544 0.236242 0.263853 15 8.59349 0.410535E-01 0.149656 16 8.54953 0.110045E-01 0.175560E-01 17 8.55832 0.140346E-03 0.447701E-03 18 8.55833 0.111487E-06 0.192124E-06 19 8.55833 0.490746E-13 Convergence criteria satisfied. Final X: -0.122249E-05 1.00004 -0.508490E-02 0.417429 -0.588443 2.30197 -4.56245 5.59197 -3.64041 1.04237 Final F(X): 0.128755E-13 0.910383E-14 0.604216E-14 0.211480E-14 -0.231236E-14 -0.718794E-14 -0.125109E-13 -0.182847E-13 -0.245032E-13 -0.311514E-13 The exact solution is not known. Problem index 6 Watson function. Problem size = 10 Use finite difference jacobian Initial X: 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Function value at initial X: 0.00000 -30.0000 -30.0000 -30.5172 -31.0345 -31.5575 -32.0862 -32.6206 -33.1608 -33.7067 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 0.00000 94.9722 2.00000 1 2.00000 93.1537 0.192201E-01 6.00000 2 7.99980 86.4401 0.700872E-01 17.9996 3 25.9971 61.1001 0.289800 23.7169 4 49.6779 7.44218 1.90006 5 48.2885 1.23545 2.11245 6 46.1806 1.06888 2.06506 7 44.1159 0.968099 2.01832 8 42.0981 0.897489 1.97001 9 40.1285 0.831585 1.92215 10 38.2069 0.769600 1.87468 11 36.3329 0.711291 1.82750 12 34.5061 0.656465 1.78047 13 32.7264 0.604939 1.73344 14 30.9938 0.556542 1.68624 15 29.3086 0.511109 1.63867 16 27.6711 0.468482 1.59049 17 26.0821 0.428513 1.54143 18 24.5424 0.391062 1.49118 19 23.0533 0.355994 1.43940 20 21.6164 0.323185 1.38568 21 20.2338 0.292512 1.32958 22 18.9081 0.263867 1.27061 23 17.6425 0.237138 1.20824 24 16.4405 0.212222 1.14193 25 15.3066 0.189019 1.07119 26 14.2457 0.167432 0.995571 27 13.2634 0.147359 0.914831 28 12.3656 0.128701 0.829010 29 11.5585 0.111353 0.738578 30 10.8478 0.952100E-01 0.644595 31 10.2381 0.801633E-01 0.548807 32 9.73217 0.661103E-01 0.453659 33 9.32998 0.529659E-01 0.362100 34 9.02757 0.406798E-01 0.277100 35 8.81642 0.292854E-01 0.200872 36 8.68313 0.189933E-01 0.134274 37 8.60987 0.103497E-01 0.779756E-01 38 8.57633 0.425164E-02 0.357483E-01 39 8.56388 0.119949E-02 0.122206E-01 40 8.55999 0.266252E-03 The Newton iteration did not converge. Final X: -0.168351E-03 1.00004 -0.531258E-02 0.417886 -0.590250 2.30519 -4.56525 5.59191 -3.63877 1.04154 Final F(X): 0.120557E-04 -0.214058E-04 -0.420072E-04 -0.590510E-04 -0.737000E-04 -0.866458E-04 -0.983149E-04 -0.108993E-03 -0.118882E-03 -0.128131E-03 The exact solution is not known. Problem index 7 Chebyquad function. Problem size = 9 Use analytic jacobian Initial X: -0.800000 -0.600000 -0.400000 -0.200000 0.00000 0.200000 0.400000 0.600000 0.800000 Function value at initial X: 0.123358E-16 -0.133333 -0.246716E-16 -0.597333E-01 0.00000 0.124648E-01 0.00000 0.859172E-01 0.00000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 1.54919 0.169950 0.178105 1 1.58326 0.172821 0.125000 0.134082 2 1.60822 0.173895 0.125000 0.163882 3 1.64822 0.177815 0.250000 0.205816 4 1.74424 0.957416E-01 0.648044E-01 5 1.73326 0.712490E-02 0.128105E-01 6 1.73210 0.430429E-03 0.980038E-03 7 1.73205 0.271145E-05 0.666209E-05 8 1.73205 0.125313E-09 0.305601E-09 9 1.73205 0.167394E-15 Convergence criteria satisfied. Final X: -0.911589 -0.528762 -0.601019 -0.167906 0.134985E-15 0.167906 0.601019 0.528762 0.911589 Final F(X): -0.616791E-16 0.555112E-16 0.00000 0.00000 0.246716E-16 -0.346945E-16 0.246716E-16 0.173472E-16 -0.135694E-15 The exact solution X: -0.911589 -0.601019 -0.528762 -0.167906 0.00000 0.167906 0.528762 0.601019 0.911589 F(X): -0.246716E-16 0.510436E-11 -0.863507E-16 -0.992995E-10 -0.986865E-16 -0.104162E-09 -0.740149E-16 0.181219E-09 0.616791E-16 Problem index 7 Chebyquad function. Problem size = 9 Use finite difference jacobian Initial X: -0.800000 -0.600000 -0.400000 -0.200000 0.00000 0.200000 0.400000 0.600000 0.800000 Function value at initial X: 0.123358E-16 -0.133333 -0.246716E-16 -0.597333E-01 0.00000 0.124648E-01 0.00000 0.859172E-01 0.00000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 1.54919 0.169950 0.177735 1 1.58322 0.172662 0.125000 0.133407 2 1.60812 0.173409 0.125000 0.165640 3 1.64832 0.178586 0.250000 0.203978 4 1.74401 0.957676E-01 0.642838E-01 5 1.73324 0.745669E-02 0.143331E-01 6 1.73211 0.547082E-03 0.123269E-02 7 1.73205 0.440706E-05 0.114301E-04 8 1.73205 0.633032E-08 0.902081E-08 9 1.73205 0.483080E-11 Convergence criteria satisfied. Final X: -0.911589 -0.528762 -0.601019 -0.167906 0.216180E-15 0.167906 0.601019 0.528762 0.911589 Final F(X): -0.370074E-16 0.452971E-13 0.740149E-16 0.848766E-13 -0.246716E-16 0.208110E-11 -0.246716E-16 -0.435848E-11 0.740149E-16 The exact solution X: -0.911589 -0.601019 -0.528762 -0.167906 0.00000 0.167906 0.528762 0.601019 0.911589 F(X): -0.246716E-16 0.510436E-11 -0.863507E-16 -0.992995E-10 -0.986865E-16 -0.104162E-09 -0.740149E-16 0.181219E-09 0.616791E-16 Problem index 8 Brown almost linear function. Problem size = 10 Use analytic jacobian Initial X: 0.500000 0.500000 0.500000 0.500000 0.500000 0.500000 0.500000 0.500000 0.500000 0.500000 Function value at initial X: -5.50000 -5.50000 -5.50000 -5.50000 -5.50000 -5.50000 -5.50000 -5.50000 -5.50000 -0.999023 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 1.58114 16.5302 5.16228 1 5.44504 16.5142 0.976213E-03 TEST02 Excessive correction norm = 0.121050E+18 Solution norm was 5.44504 The iteration is terminated. The Newton iteration did not converge. Final X: 0.603608E-02 0.603608E-02 0.603608E-02 0.603608E-02 0.603608E-02 0.603608E-02 0.603608E-02 0.603608E-02 0.603608E-02 5.44501 Final F(X): -5.49463 -5.49463 -5.49463 -5.49463 -5.49463 -5.49463 -5.49463 -5.49463 -5.49463 -1.00000 The exact solution X: 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 F(X): 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Problem index 8 Brown almost linear function. Problem size = 10 Use finite difference jacobian Initial X: 0.500000 0.500000 0.500000 0.500000 0.500000 0.500000 0.500000 0.500000 0.500000 0.500000 Function value at initial X: -5.50000 -5.50000 -5.50000 -5.50000 -5.50000 -5.50000 -5.50000 -5.50000 -5.50000 -0.999023 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 1.58114 16.5302 5.16228 1 5.44504 16.5142 0.976213E-03 R8GE_FA - Fatal error! Zero pivot on step 10 TEST02 - Warning: The iteration must be halted. The jacobian matrix is singular! The Newton iteration did not converge. Final X: 0.603608E-02 0.603608E-02 0.603608E-02 0.603608E-02 0.603608E-02 0.603608E-02 0.603608E-02 0.603608E-02 0.603608E-02 5.44501 Final F(X): -5.49463 -5.49463 -5.49463 -5.49463 -5.49463 -5.49463 -5.49463 -5.49463 -5.49463 -1.00000 The exact solution X: 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 F(X): 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Problem index 9 Discrete boundary value function. Problem size = 10 Use analytic jacobian Initial X: -0.826446E-01 -0.148760 -0.198347 -0.231405 -0.247934 -0.247934 -0.231405 -0.198347 -0.148760 -0.826446E-01 Function value at initial X: -0.122934E-01 -0.119732E-01 -0.114043E-01 -0.105311E-01 -0.926975E-02 -0.750226E-02 -0.506917E-02 -0.176018E-02 0.269680E-02 0.864815E-02 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 0.605509 0.280806E-01 0.205845 1 0.410161 0.244479E-03 0.224454E-02 2 0.412338 0.310992E-07 0.290904E-06 3 0.412339 0.545487E-15 Convergence criteria satisfied. Final X: -0.431650E-01 -0.815772E-01 -0.114486 -0.140974 -0.159909 -0.169877 -0.169090 -0.155250 -0.125356 -0.754165E-01 Final F(X): 0.00000 0.693889E-16 0.138778E-15 0.249800E-15 0.277556E-15 0.222045E-15 0.222045E-15 0.166533E-15 0.832667E-16 0.277556E-16 The exact solution is not known. Problem index 9 Discrete boundary value function. Problem size = 10 Use finite difference jacobian Initial X: -0.826446E-01 -0.148760 -0.198347 -0.231405 -0.247934 -0.247934 -0.231405 -0.198347 -0.148760 -0.826446E-01 Function value at initial X: -0.122934E-01 -0.119732E-01 -0.114043E-01 -0.105311E-01 -0.926975E-02 -0.750226E-02 -0.506917E-02 -0.176018E-02 0.269680E-02 0.864815E-02 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 0.605509 0.280806E-01 0.205848 1 0.410158 0.244854E-03 0.224823E-02 2 0.412338 0.270629E-07 0.251098E-06 3 0.412339 0.481853E-12 Convergence criteria satisfied. Final X: -0.431650E-01 -0.815772E-01 -0.114486 -0.140974 -0.159909 -0.169877 -0.169090 -0.155250 -0.125356 -0.754165E-01 Final F(X): -0.391770E-13 -0.848072E-13 -0.133116E-12 -0.176748E-12 -0.206668E-12 -0.215522E-12 -0.201228E-12 -0.166200E-12 -0.116823E-12 -0.597578E-13 The exact solution is not known. Problem index 10 Discrete integral equation function. Problem size = 10 Use analytic jacobian Initial X: -0.826446E-01 -0.148760 -0.198347 -0.231405 -0.247934 -0.247934 -0.231405 -0.198347 -0.148760 -0.826446E-01 Function value at initial X: -0.454810E-01 -0.786686E-01 -0.998829E-01 -0.109693 -0.108972 -0.989810E-01 -0.814879E-01 -0.589256E-01 -0.346032E-01 -0.129775E-01 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 0.605509 0.251827 0.205845 1 0.410161 0.285931E-02 0.224454E-02 2 0.412338 0.372516E-06 0.290904E-06 3 0.412339 0.635045E-14 Convergence criteria satisfied. Final X: -0.431650E-01 -0.815772E-01 -0.114486 -0.140974 -0.159909 -0.169877 -0.169090 -0.155250 -0.125356 -0.754165E-01 Final F(X): 0.686950E-15 0.138778E-14 0.198452E-14 0.244249E-14 0.274780E-14 0.277556E-14 0.249800E-14 0.202616E-14 0.138778E-14 0.707767E-15 The exact solution is not known. Problem index 10 Discrete integral equation function. Problem size = 10 Use finite difference jacobian Initial X: -0.826446E-01 -0.148760 -0.198347 -0.231405 -0.247934 -0.247934 -0.231405 -0.198347 -0.148760 -0.826446E-01 Function value at initial X: -0.454810E-01 -0.786686E-01 -0.998829E-01 -0.109693 -0.108972 -0.989810E-01 -0.814879E-01 -0.589256E-01 -0.346032E-01 -0.129775E-01 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 0.605509 0.251827 0.205848 1 0.410158 0.286399E-02 0.224823E-02 2 0.412338 0.321380E-06 0.251098E-06 3 0.412339 0.592132E-11 Convergence criteria satisfied. Final X: -0.431650E-01 -0.815772E-01 -0.114486 -0.140974 -0.159909 -0.169877 -0.169090 -0.155250 -0.125356 -0.754165E-01 Final F(X): -0.670110E-12 -0.130104E-11 -0.184719E-11 -0.226022E-11 -0.249653E-11 -0.252620E-11 -0.234032E-11 -0.195330E-11 -0.139999E-11 -0.729888E-12 The exact solution is not known. Problem index 11 Trigonometric function. Problem size = 10 Use analytic jacobian Initial X: 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 Function value at initial X: -0.448792E-01 -0.398834E-01 -0.348876E-01 -0.298917E-01 -0.248959E-01 -0.199001E-01 -0.149042E-01 -0.990839E-02 -0.491256E-02 0.832778E-04 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 0.316228 0.841175E-01 0.128260 1 0.340001 0.922724E-01 0.250000 0.999404E-01 2 0.392756 0.800430E-01 0.250000 0.864658E-01 3 0.382361 0.722156E-01 0.250000 0.124127 4 0.316986 0.364424E-01 0.381262E-01 5 0.308887 0.419575E-02 0.587729E-02 6 0.306216 0.180941E-03 0.494658E-03 7 0.306048 0.129335E-05 0.361767E-05 8 0.306047 0.689503E-10 0.192476E-09 9 0.306047 0.311779E-14 Convergence criteria satisfied. Final X: 0.479119E-01 0.491845E-01 0.506087E-01 0.522230E-01 0.540831E-01 0.562733E-01 0.589321E-01 0.186397 0.154342 0.124625 Final F(X): 0.104083E-14 0.957567E-15 0.804912E-15 0.120737E-14 0.548173E-15 0.985323E-15 0.138778E-14 0.555112E-15 0.102696E-14 0.102696E-14 The exact solution is not known. Problem index 11 Trigonometric function. Problem size = 10 Use finite difference jacobian Initial X: 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 Function value at initial X: -0.448792E-01 -0.398834E-01 -0.348876E-01 -0.298917E-01 -0.248959E-01 -0.199001E-01 -0.149042E-01 -0.990839E-02 -0.491256E-02 0.832778E-04 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 0.316228 0.841175E-01 0.130000 1 0.340447 0.938952E-01 0.250000 0.102780 2 0.395258 0.821929E-01 0.250000 0.988306E-01 3 0.384466 0.785545E-01 0.250000 0.111046 4 0.316313 0.291321E-01 0.307532E-01 5 0.308413 0.302524E-02 0.517050E-02 6 0.306190 0.154779E-03 0.437571E-03 7 0.306048 0.128061E-05 0.361086E-05 8 0.306047 0.238790E-08 0.711827E-08 9 0.306047 0.435775E-11 Convergence criteria satisfied. Final X: 0.479119E-01 0.491845E-01 0.506087E-01 0.522230E-01 0.540831E-01 0.562733E-01 0.589321E-01 0.186397 0.154342 0.124625 Final F(X): 0.354584E-12 0.370086E-12 0.385789E-12 0.401700E-12 0.416549E-12 0.431516E-12 0.443097E-12 -0.156847E-12 -0.459771E-12 0.419823E-11 The exact solution is not known. Problem index 12 Variably dimensioned function. Problem size = 10 Use analytic jacobian Initial X: 0.900000 0.800000 0.700000 0.600000 0.500000 0.400000 0.300000 0.200000 0.100000 0.00000 Function value at initial X: -114172. -228344. -342516. -456687. -570859. -685031. -799203. -913375. -0.102755E+07 -0.114172E+07 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 1.68819 0.224021E+07 0.654195 1 2.09242 663823. 0.436204 2 2.42339 196726. 0.290913 3 2.66104 58314.0 0.194108 4 2.82516 17294.8 0.129654 5 2.93682 5135.41 0.868080E-01 6 3.01239 1528.90 0.584281E-01 7 3.06359 457.800 0.397783E-01 8 3.09859 138.716 0.277242E-01 9 3.12305 42.9381 0.201232E-01 10 3.14084 13.5494 0.149361E-01 11 3.15406 3.81502 0.824963E-02 12 3.16137 0.394721 0.102014E-02 13 3.16228 0.630962E-03 0.163462E-05 14 3.16228 0.259686E-11 Convergence criteria satisfied. Final X: 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 Final F(X): -0.132339E-12 -0.264677E-12 -0.397016E-12 -0.529354E-12 -0.661693E-12 -0.794032E-12 -0.926481E-12 -0.105882E-11 -0.119116E-11 -0.132350E-11 The exact solution X: 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 F(X): 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Problem index 12 Variably dimensioned function. Problem size = 10 Use finite difference jacobian Initial X: 0.900000 0.800000 0.700000 0.600000 0.500000 0.400000 0.300000 0.200000 0.100000 0.00000 Function value at initial X: -114172. -228344. -342516. -456687. -570859. -685031. -799203. -913375. -0.102755E+07 -0.114172E+07 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 1.68819 0.224021E+07 0.654210 1 2.09243 663799. 0.436218 2 2.42342 196706. 0.290925 3 2.66108 58301.5 0.194117 4 2.82521 17288.0 0.129661 5 2.93687 5131.94 0.868140E-01 6 3.01245 1527.21 0.584332E-01 7 3.06365 456.995 0.397833E-01 8 3.09865 138.341 0.277305E-01 9 3.12312 42.7650 0.201319E-01 10 3.14092 13.4680 0.149381E-01 11 3.15414 3.77256 0.819609E-02 12 3.16141 0.379855 0.982065E-03 13 3.16228 0.495889E-03 0.128468E-05 14 3.16228 0.248729E-08 Convergence criteria satisfied. Final X: 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 Final F(X): -0.126764E-09 -0.253528E-09 -0.380292E-09 -0.507056E-09 -0.633820E-09 -0.760584E-09 -0.887348E-09 -0.101411E-08 -0.114088E-08 -0.126764E-08 The exact solution X: 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 F(X): 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Problem index 13 Broyden tridiagonal function. Problem size = 10 Use analytic jacobian Initial X: -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 Function value at initial X: -2.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -3.00000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 3.16228 4.58258 0.958176 1 2.23985 0.658075 0.194913 2 2.06250 0.296769E-01 0.983428E-02 3 2.05455 0.917963E-04 0.309819E-04 4 2.05452 0.106232E-08 0.357396E-09 5 2.05452 0.128037E-14 Convergence criteria satisfied. Final X: -0.570722 -0.681807 -0.702210 -0.705511 -0.704906 -0.701497 -0.691889 -0.665797 -0.596035 -0.416412 Final F(X): 0.00000 -0.666134E-15 0.888178E-15 -0.222045E-15 -0.444089E-15 0.00000 0.222045E-15 -0.222045E-15 -0.222045E-15 -0.111022E-15 The exact solution is not known. Problem index 13 Broyden tridiagonal function. Problem size = 10 Use finite difference jacobian Initial X: -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 Function value at initial X: -2.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -3.00000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 3.16228 4.58258 0.958091 1 2.23994 0.658339 0.194970 2 2.06253 0.297518E-01 0.985937E-02 3 2.05455 0.950527E-04 0.321382E-04 4 2.05452 0.111050E-07 0.388289E-08 5 2.05452 0.123786E-11 Convergence criteria satisfied. Final X: -0.570722 -0.681807 -0.702210 -0.705511 -0.704906 -0.701497 -0.691889 -0.665797 -0.596035 -0.416412 Final F(X): -0.905942E-13 -0.968114E-13 -0.937028E-13 -0.111244E-12 -0.161648E-12 -0.260902E-12 -0.419886E-12 -0.629496E-12 -0.752842E-12 -0.509925E-12 The exact solution is not known. Problem index 14 Broyden banded function. Problem size = 10 Use analytic jacobian Initial X: -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 Function value at initial X: -6.00000 -6.00000 -6.00000 -6.00000 -6.00000 -6.00000 -6.00000 -6.00000 -6.00000 -6.00000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 3.16228 18.9737 0.888024 1 2.27990 4.52299 0.397588 2 1.89643 0.747117 0.102640 3 1.80540 0.478399E-01 0.810123E-02 4 1.79910 0.312988E-03 0.560367E-04 5 1.79907 0.154777E-07 0.284621E-08 6 1.79907 0.140021E-14 Convergence criteria satisfied. Final X: -0.428303 -0.476596 -0.519652 -0.558099 -0.592506 -0.624504 -0.623239 -0.621394 -0.620454 -0.586469 Final F(X): 0.277556E-16 -0.111022E-15 -0.555112E-15 -0.333067E-15 -0.222045E-15 0.666134E-15 0.00000 0.888178E-15 0.444089E-15 -0.222045E-15 The exact solution is not known. Problem index 14 Broyden banded function. Problem size = 10 Use finite difference jacobian Initial X: -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 Function value at initial X: -6.00000 -6.00000 -6.00000 -6.00000 -6.00000 -6.00000 -6.00000 -6.00000 -6.00000 -6.00000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 3.16228 18.9737 0.887863 1 2.28006 4.52485 0.397605 2 1.89657 0.748216 0.102736 3 1.80543 0.481221E-01 0.814178E-02 4 1.79911 0.329684E-03 0.587115E-04 5 1.79907 0.115400E-06 0.190352E-07 6 1.79907 0.346698E-10 Convergence criteria satisfied. Final X: -0.428303 -0.476596 -0.519652 -0.558099 -0.592506 -0.624504 -0.623239 -0.621394 -0.620454 -0.586469 Final F(X): -0.108887E-10 -0.119765E-10 -0.127736E-10 -0.134638E-10 -0.140947E-10 -0.144067E-10 -0.100300E-10 -0.711564E-11 -0.508171E-11 -0.350497E-11 The exact solution is not known. Problem index 15 Hammarling 2 by 2 matrix square root problem. Problem size = 4 Use analytic jacobian Initial X: 1.00000 0.00000 0.00000 1.00000 Function value at initial X: 0.999900 -1.00000 0.00000 0.999900 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 1.41421 1.73194 0.865968 1 0.866083 0.612291 0.828930 2 1.29889 0.385057 1.38441 3 2.62888 0.343606 2.67326 4 5.29546 0.332590 5.21887 5 10.5135 0.320659 9.71555 6 20.2290 0.283823 14.9034 7 35.1324 0.179626 12.3723 8 47.5047 0.384843E-01 2.46231 9 49.9670 0.588514E-03 0.329911E-01 10 50.0000 0.471121E-07 0.248306E-05 11 50.0000 0.111022E-15 Convergence criteria satisfied. Final X: 0.100000E-01 50.0000 -0.104562E-29 0.100000E-01 Final F(X): 0.00000 -0.111022E-15 -0.209123E-31 0.00000 The exact solution X: 0.100000E-01 50.0000 0.00000 0.100000E-01 F(X): 0.00000 0.00000 0.00000 0.00000 Problem index 15 Hammarling 2 by 2 matrix square root problem. Problem size = 4 Use finite difference jacobian Initial X: 1.00000 0.00000 0.00000 1.00000 Function value at initial X: 0.999900 -1.00000 0.00000 0.999900 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 1.41421 1.73194 0.865910 1 0.866141 0.612291 0.828798 2 1.29879 0.384982 1.38383 3 2.62816 0.343462 2.67106 4 5.29254 0.332335 5.21091 5 10.5026 0.320215 9.68953 6 20.1920 0.283191 14.8491 7 35.0411 0.179396 12.3817 8 47.4228 0.390666E-01 2.53671 9 49.9595 0.659816E-03 0.404525E-01 10 50.0000 0.120935E-06 0.441560E-04 11 50.0000 0.127998E-11 Convergence criteria satisfied. Final X: 0.100000E-01 50.0000 0.237363E-27 0.100000E-01 Final F(X): 0.769866E-12 -0.673017E-12 0.474726E-29 0.769866E-12 The exact solution X: 0.100000E-01 50.0000 0.00000 0.100000E-01 F(X): 0.00000 0.00000 0.00000 0.00000 Problem index 16 Hammarling 3 by 3 matrix square root problem. Problem size = 9 Use analytic jacobian Initial X: 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000 Function value at initial X: 0.999900 -1.00000 0.00000 0.00000 0.999900 0.00000 0.00000 0.00000 0.999900 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 1.73205 1.99985 0.999925 1 1.00008 0.661343 0.865787 2 1.32276 0.390090 1.39003 3 2.63186 0.343960 2.67399 4 5.29584 0.332612 5.21896 5 10.5136 0.320661 9.71556 6 20.2290 0.283823 14.9034 7 35.1324 0.179626 12.3723 8 47.5047 0.384843E-01 2.46231 9 49.9670 0.588514E-03 0.329911E-01 10 50.0000 0.471121E-07 0.248306E-05 11 50.0000 0.111022E-15 Convergence criteria satisfied. Final X: 0.100000E-01 50.0000 0.00000 -0.104562E-29 0.100000E-01 0.00000 0.00000 0.00000 0.100000E-01 Final F(X): 0.00000 -0.111022E-15 0.00000 -0.209123E-31 0.00000 0.00000 0.00000 0.00000 0.00000 The exact solution X: 0.100000E-01 50.0000 0.00000 0.00000 0.100000E-01 0.00000 0.00000 0.00000 0.100000E-01 F(X): 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Problem index 16 Hammarling 3 by 3 matrix square root problem. Problem size = 9 Use finite difference jacobian Initial X: 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000 Function value at initial X: 0.999900 -1.00000 0.00000 0.00000 0.999900 0.00000 0.00000 0.00000 0.999900 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 1.73205 1.99985 0.999850 1 1.00015 0.661362 0.865657 2 1.32266 0.390021 1.38945 3 2.63115 0.343816 2.67179 4 5.29292 0.332357 5.21100 5 10.5027 0.320217 9.68954 6 20.1921 0.283191 14.8491 7 35.0411 0.179396 12.3817 8 47.4228 0.390666E-01 2.53671 9 49.9595 0.659816E-03 0.404525E-01 10 50.0000 0.120935E-06 0.441560E-04 11 50.0000 0.149366E-11 Convergence criteria satisfied. Final X: 0.100000E-01 50.0000 0.00000 0.237363E-27 0.100000E-01 0.00000 0.00000 0.00000 0.100000E-01 Final F(X): 0.769866E-12 -0.673017E-12 0.00000 0.474726E-29 0.769866E-12 0.00000 0.00000 0.00000 0.769866E-12 The exact solution X: 0.100000E-01 50.0000 0.00000 0.00000 0.100000E-01 0.00000 0.00000 0.00000 0.100000E-01 F(X): 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Problem index 17 Dennis and Schnabel 2 by 2 example. Problem size = 2 Use analytic jacobian Initial X: 1.00000 5.00000 Function value at initial X: 3.00000 17.0000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 5.09902 17.2627 2.12867 1 3.67848 4.53125 0.753901 2 3.09328 0.568366 0.126230 3 3.00265 0.159341E-01 0.374908E-02 4 3.00000 0.140556E-04 0.331293E-05 5 3.00000 0.109779E-10 Convergence criteria satisfied. Final X: -0.182953E-11 3.00000 Final F(X): 0.00000 0.109779E-10 The exact solution X: 0.00000 3.00000 F(X): 0.00000 0.00000 Problem index 17 Dennis and Schnabel 2 by 2 example. Problem size = 2 Use finite difference jacobian Initial X: 1.00000 5.00000 Function value at initial X: 3.00000 17.0000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 5.09902 17.2627 2.12869 1 3.67865 4.53247 0.753997 2 3.09336 0.568845 0.126321 3 3.00267 0.160032E-01 0.376499E-02 4 3.00000 0.155077E-04 0.365489E-05 5 3.00000 0.130556E-08 Convergence criteria satisfied. Final X: -0.217593E-09 3.00000 Final F(X): 0.00000 0.130556E-08 The exact solution X: 0.00000 3.00000 F(X): 0.00000 0.00000 Problem index 18 Sample problem 18. Problem size = 2 Use analytic jacobian Initial X: 2.00000 2.00000 Function value at initial X: 1.96337 0.981684 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 2.82843 2.19511 5.32630 1 2.62653 1.55700 1.99169 2 0.645098 0.787591E-01 0.465756 3 0.191419 0.153270E-01 0.163859 4 0.886679E-01 0.402719E-03 0.454769E-02 5 0.885494E-01 0.819916E-08 0.518210E-03 6 0.890676E-01 0.476970E-10 0.897789E-01 7 0.711277E-03 0.382412E-12 0.711277E-03 8 0.647032E-09 0.00000 0.00000 9 0.647032E-09 0.00000 Convergence criteria satisfied. Final X: 0.537641E-09 -0.359989E-09 Final F(X): 0.00000 -0.00000 The exact solution X: 0.00000 0.00000 F(X): 0.00000 0.00000 Problem index 18 Sample problem 18. Problem size = 2 Use finite difference jacobian Initial X: 2.00000 2.00000 Function value at initial X: 1.96337 0.981684 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 2.82843 2.19511 5.32542 1 2.62570 1.55622 1.98987 2 0.646078 0.790397E-01 0.466206 3 0.191927 0.153958E-01 0.164325 4 0.887877E-01 0.406722E-03 0.458679E-02 5 0.886672E-01 0.869174E-08 0.461053E-03 6 0.882062E-01 0.444310E-10 0.888982E-01 7 0.692034E-03 0.349948E-12 0.692035E-03 8 0.649433E-09 0.00000 0.00000 9 0.649433E-09 0.00000 Convergence criteria satisfied. Final X: -0.505680E-09 -0.407493E-09 Final F(X): -0.00000 0.00000 The exact solution X: 0.00000 0.00000 F(X): 0.00000 0.00000 Problem index 19 Sample problem 19. Problem size = 2 Use analytic jacobian Initial X: 3.00000 3.00000 Function value at initial X: 54.0000 54.0000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 4.24264 76.3675 1.41421 1 2.82843 22.6274 0.942809 2 1.88562 6.70442 0.628539 3 1.25708 1.98649 0.419026 4 0.838052 0.588591 0.279351 5 0.558702 0.174397 0.186234 6 0.372468 0.516733E-01 0.124156 7 0.248312 0.153106E-01 0.827706E-01 8 0.165541 0.453648E-02 0.551804E-01 9 0.110361 0.134414E-02 0.367869E-01 10 0.735739E-01 0.398264E-03 0.245246E-01 11 0.490493E-01 0.118004E-03 0.163498E-01 12 0.326995E-01 0.349642E-04 0.108998E-01 13 0.217997E-01 0.103598E-04 0.726656E-02 14 0.145331E-01 0.306956E-05 0.484437E-02 15 0.968874E-02 0.909499E-06 0.322958E-02 16 0.645916E-02 0.269481E-06 0.215305E-02 17 0.430611E-02 0.798463E-07 0.143537E-02 18 0.287074E-02 0.236581E-07 0.956913E-03 19 0.191383E-02 0.700982E-08 0.637942E-03 20 0.127588E-02 0.207698E-08 0.425295E-03 21 0.850589E-03 0.615403E-09 0.283530E-03 22 0.567059E-03 0.182342E-09 0.189020E-03 23 0.378040E-03 0.540271E-10 0.126013E-03 24 0.252026E-03 0.160080E-10 0.840088E-04 25 0.168018E-03 0.474312E-11 0.560059E-04 26 0.112012E-03 0.140537E-11 0.373372E-04 27 0.746745E-04 0.416406E-12 0.248915E-04 28 0.497830E-04 0.123379E-12 0.165943E-04 29 0.331887E-04 0.365569E-13 0.110629E-04 30 0.221258E-04 0.108317E-13 0.737526E-05 31 0.147505E-04 0.320938E-14 0.491684E-05 32 0.983368E-05 0.950929E-15 0.327789E-05 33 0.655579E-05 0.281757E-15 0.218526E-05 34 0.437052E-05 0.834834E-16 0.145684E-05 35 0.291368E-05 0.247358E-16 0.971227E-06 36 0.194245E-05 0.732914E-17 Convergence criteria satisfied. Final X: 0.137352E-05 0.137352E-05 Final F(X): 0.518248E-17 0.518248E-17 The exact solution X: 0.00000 0.00000 F(X): 0.00000 0.00000 Problem index 19 Sample problem 19. Problem size = 2 Use finite difference jacobian Initial X: 3.00000 3.00000 Function value at initial X: 54.0000 54.0000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 4.24264 76.3675 1.41409 1 2.82855 22.6304 0.942757 2 1.88580 6.70632 0.628525 3 1.25727 1.98741 0.419031 4 0.838240 0.588986 0.279363 5 0.558877 0.174561 0.186248 6 0.372628 0.517401E-01 0.124170 7 0.248459 0.153378E-01 0.827826E-01 8 0.165676 0.454756E-02 0.551902E-01 9 0.110486 0.134871E-02 0.367947E-01 10 0.736910E-01 0.400169E-03 0.245306E-01 11 0.491604E-01 0.118808E-03 0.163543E-01 12 0.328061E-01 0.353071E-04 0.109033E-01 13 0.219028E-01 0.105075E-04 0.726911E-02 14 0.146337E-01 0.313374E-05 0.484628E-02 15 0.978742E-02 0.937573E-06 0.323102E-02 16 0.655640E-02 0.281836E-06 0.215418E-02 17 0.440222E-02 0.853132E-07 0.143630E-02 18 0.296592E-02 0.260903E-07 0.957767E-03 19 0.200815E-02 0.809825E-08 0.638821E-03 20 0.136933E-02 0.256760E-08 0.426305E-03 21 0.943029E-03 0.838639E-09 0.284783E-03 22 0.658245E-03 0.285209E-09 0.190630E-03 23 0.467615E-03 0.102250E-09 0.128085E-03 24 0.339530E-03 0.391413E-10 0.866142E-04 25 0.252916E-03 0.161782E-10 0.591628E-04 26 0.193753E-03 0.727355E-11 0.409933E-04 27 0.152760E-03 0.356474E-11 0.289298E-04 28 0.123830E-03 0.189880E-11 0.208588E-04 29 0.102971E-03 0.109181E-11 0.153912E-04 30 0.875801E-04 0.671764E-12 0.116252E-04 31 0.759549E-04 0.438195E-12 0.898070E-05 32 0.669742E-04 0.300416E-12 0.708500E-05 33 0.598892E-04 0.214805E-12 0.569762E-05 34 0.541916E-04 0.159146E-12 0.466167E-05 35 0.495299E-04 0.121507E-12 0.387336E-05 36 0.456565E-04 0.951720E-13 0.326286E-05 37 0.423937E-04 0.761909E-13 0.278238E-05 38 0.396113E-04 0.621523E-13 0.239861E-05 39 0.372127E-04 0.515315E-13 0.208795E-05 40 0.351247E-04 0.433351E-13 The Newton iteration did not converge. Final X: 0.248369E-04 0.248369E-04 Final F(X): 0.306425E-13 0.306425E-13 The exact solution X: 0.00000 0.00000 F(X): 0.00000 0.00000 Problem index 20 Scalar problem f(x) = x * ( x - 5 ) * ( x - 5 ). Problem size = 1 Use analytic jacobian Initial X: 1.00000 Function value at initial X: 16.0000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 1.00000 16.0000 1.00000 1 0.00000 0.00000 0.500000 0.00000 2 0.00000 0.00000 Convergence criteria satisfied. Final X: 0.00000 Final F(X): 0.00000 The exact solution X: 0.00000 F(X): 0.00000 Problem index 20 Scalar problem f(x) = x * ( x - 5 ) * ( x - 5 ). Problem size = 1 Use finite difference jacobian Initial X: 1.00000 Function value at initial X: 16.0000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 1.00000 16.0000 1.00018 1 0.175026E-03 0.437595E-02 0.500000 0.175006E-03 2 0.192532E-07 0.481331E-06 0.192525E-07 3 0.770255E-12 0.192564E-10 Convergence criteria satisfied. Final X: -0.770255E-12 Final F(X): -0.192564E-10 The exact solution X: 5.00000 F(X): 0.00000 Problem index 21 Freudenstein-Roth function. Problem size = 2 Use analytic jacobian Initial X: 0.500000 -2.00000 Function value at initial X: 19.5000 -4.50000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 2.06155 20.0125 6.12311 1 6.75817 10.6604 0.632495 14.2133 2 20.7763 9.75627 9.59540 3 11.2664 8.89440 0.500000 6.13320 4 17.3367 8.62497 0.228279 9.16836 5 8.29574 10.3058 0.241175 15.3197 6 23.4555 11.3903 16.6944 7 6.99067 12.9017 11.3736 8 18.1568 8.59872 6.57215 9 11.6463 8.33917 0.250000 6.32313 10 17.9116 8.62131 0.177083 7.38820 11 10.6005 8.85844 0.250000 11.6005 12 22.1043 10.5464 0.478684 9.08139 13 13.0896 8.67955 0.500000 7.04478 14 20.0800 9.63412 0.139455 11.5430 15 8.67281 10.4934 0.500000 15.1652 16 23.6827 11.5485 16.5811 17 7.31820 12.6749 11.5913 18 18.7128 8.80631 6.00759 19 12.7555 8.15638 0.250000 6.87777 20 19.5806 9.23803 0.112156 11.2001 21 8.51749 10.2105 0.500000 15.6603 22 24.0219 11.7903 16.4316 23 7.79061 12.3750 11.9436 24 19.5509 9.15845 10.7766 25 8.90068 9.83084 0.500000 8.44402 26 17.2344 8.49399 0.500000 9.11718 27 8.24440 10.1271 0.249371 15.6661 28 23.7509 11.5966 16.5492 29 7.41481 12.6110 11.6596 30 18.8806 8.87304 5.86447 31 13.0638 8.12588 0.250000 7.03188 32 20.0442 9.44430 0.916651E-01 10.6129 33 9.54513 9.66723 0.500000 9.07165 34 18.5125 8.90026 0.500000 6.87515 35 11.7008 8.68852 0.250000 6.35042 36 17.9915 8.77376 0.201324 7.83806 37 10.2384 9.24929 0.250000 10.5268 38 20.6654 9.78492 0.500000 10.2274 39 10.5350 9.35186 0.500000 10.6761 40 21.1128 10.0350 0.500000 The Newton iteration did not converge. Final X: 21.1089 -0.405682 Final F(X): 9.80988 -2.11378 The exact solution X: 5.00000 4.00000 F(X): 0.00000 0.00000 Problem index 21 Freudenstein-Roth function. Problem size = 2 Use finite difference jacobian Initial X: 0.500000 -2.00000 Function value at initial X: 19.5000 -4.50000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 2.06155 20.0125 6.12311 1 6.75817 10.6599 0.632637 14.2105 2 20.7734 9.75477 9.59873 3 11.2603 8.89606 0.500000 6.13015 4 17.3276 8.62261 0.228647 9.16378 5 8.29122 10.3077 0.240297 15.3088 6 23.4400 11.3796 16.7038 7 6.96674 12.9189 11.3554 8 18.1139 8.58356 6.62413 9 11.5524 8.36001 0.250000 6.27621 10 17.7703 8.57842 0.181993 7.62758 11 10.2258 8.99779 0.250000 11.1141 12 21.2399 10.0556 0.500000 9.60400 13 11.7165 8.92418 0.500000 6.35825 14 18.0135 8.86340 0.217739 8.17428 15 9.93099 9.53970 0.250000 9.60392 16 19.4334 9.25128 0.500000 11.8988 17 7.69688 10.9003 0.500000 13.9868 18 21.5088 10.1594 9.11901 19 12.4619 8.63744 0.500000 6.73095 20 19.1363 9.20150 0.167693 6.42941 21 12.7600 8.60938 0.250000 6.88002 22 19.5848 9.38585 0.151141 12.0830 23 7.66633 11.0698 0.500000 13.7098 24 21.1994 9.98500 9.30449 25 11.9720 8.72597 0.500000 6.48601 26 18.3991 8.93692 0.194675 7.32059 27 11.1501 8.98509 0.250000 6.07503 28 17.1611 8.60225 0.237160 4.54029 29 12.6624 8.52154 0.111400 6.83118 30 19.4385 9.29271 0.148797 12.1305 31 7.47831 11.1368 0.500000 13.5698 32 20.8669 9.80429 9.52997 33 11.4205 8.85344 0.500000 6.21023 34 17.5687 8.68593 0.221563 8.89257 35 8.79127 10.0195 0.250000 8.15242 36 16.8319 8.42477 0.500000 4.45798 37 12.4159 8.39650 0.104935 6.70795 38 19.0686 9.09274 0.150329 6.22665 39 12.8929 8.43852 0.250000 6.94644 40 19.7856 9.42103 0.129852 The Newton iteration did not converge. Final X: 19.7791 -0.506679 Final F(X): 9.20612 -2.00078 The exact solution X: 5.00000 4.00000 F(X): 0.00000 0.00000 Problem index 22 Boggs function. Problem size = 2 Use analytic jacobian Initial X: 1.00000 0.00000 Function value at initial X: 2.00000 0.00000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 1.00000 2.00000 2.00000 1 2.23607 2.00000 2.23607 2 0.993014E-15 1.41421 0.500000 1.41421 3 1.41421 1.41421 0.666034 4 0.848081 0.385407 0.325243 5 0.944389 0.743607E-01 0.108191 6 0.991408 0.888549E-02 0.160390E-01 7 0.999815 0.184924E-03 0.344720E-03 8 1.00000 0.846982E-07 0.157723E-06 9 1.00000 0.177638E-13 Convergence criteria satisfied. Final X: 0.279421E-13 1.00000 Final F(X): 0.177636E-13 -0.967835E-16 The exact solution X: 0.00000 1.00000 F(X): 0.00000 -0.612323E-16 Problem index 22 Boggs function. Problem size = 2 Use finite difference jacobian Initial X: 1.00000 0.00000 Function value at initial X: 2.00000 0.00000 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 1.00000 2.00000 1.99951 1 2.23552 1.99975 2.23175 2 0.377094E-02 1.41067 0.500000 1.40688 3 1.41043 1.39737 0.661994 4 0.848580 0.379839 0.322375 5 0.945049 0.731067E-01 0.106737 6 0.991629 0.864963E-02 0.156252E-01 7 0.999823 0.176818E-03 0.329526E-03 8 1.00000 0.105215E-06 0.195889E-06 9 1.00000 0.165518E-10 Convergence criteria satisfied. Final X: 0.260022E-10 1.00000 Final F(X): 0.165518E-10 0.267943E-14 The exact solution X: 0.00000 1.00000 F(X): 0.00000 -0.612323E-16 Problem index 23 Chandrasekhar function. Problem size = 10 Use analytic jacobian Initial X: 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 Function value at initial X: -0.705512E-01 -0.157865 -0.220050 -0.269231 -0.309872 -0.344333 -0.374076 -0.400089 -0.423079 -0.443574 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 3.16228 1.02037 1.59629 1 4.67614 0.112333 0.199051 2 4.85605 0.190225E-02 0.338525E-02 3 4.85907 0.541257E-06 0.960176E-06 4 4.85907 0.429236E-13 Convergence criteria satisfied. Final X: 1.09674 1.23348 1.34236 1.43565 1.51787 1.59149 1.65811 1.71884 1.77454 1.82587 Final F(X): -0.222045E-15 -0.888178E-15 -0.244249E-14 -0.466294E-14 -0.732747E-14 -0.106581E-13 -0.137668E-13 -0.182077E-13 -0.217604E-13 -0.255351E-13 An exact solution is not given. Problem index 23 Chandrasekhar function. Problem size = 10 Use finite difference jacobian Initial X: 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 Function value at initial X: -0.705512E-01 -0.157865 -0.220050 -0.269231 -0.309872 -0.344333 -0.374076 -0.400089 -0.423079 -0.443574 Iteration ||X|| ||F(X)|| Damping ||dX|| 0 3.16228 1.02037 1.59629 1 4.67614 0.112330 0.199047 2 4.85605 0.190124E-02 0.338347E-02 3 4.85907 0.524065E-06 0.929579E-06 4 4.85907 0.451265E-11 Convergence criteria satisfied. Final X: 1.09674 1.23348 1.34236 1.43565 1.51787 1.59149 1.65811 1.71884 1.77454 1.82587 Final F(X): 0.126565E-13 0.101696E-12 0.264899E-12 0.492717E-12 0.775824E-12 0.110356E-11 0.146838E-11 0.186295E-11 0.228173E-11 0.271805E-11 An exact solution is not given. TEST_NONLIN_TEST Normal end of execution. 17 September 2021 11:54:16.702 PM