07-Jun-2023 07:02:39 test_opt_test(): MATLAB/Octave version 5.2.0 Test test_opt(). p00_title_test(): p00_title() prints the title for any problem. Problem Title 1: "The Fletcher-Powell helical valley function." 2: "The Biggs EXP6 function." 3: "The Gaussian function." 4: "The Powell badly scaled function." 5: "The Box 3-dimensional function." 6: "The variably dimensioned function." 7: "The Watson function." 8: "The Penalty Function #1." 9: "The Penalty Function #2." 10: "The Brown Badly Scaled Function." 11: "The Brown and Dennis Function." 12: "The Gulf R&D Function." 13: "The Trigonometric Function." 14: "The Extended Rosenbrock parabolic valley Function." 15: "The Extended Powell Singular Quartic Function." 16: "The Beale Function." 17: "The Wood Function." 18: "The Chebyquad Function" 19: "The Leon cubic valley function" 20: "The Gregory and Karney Tridiagonal Matrix Function" 21: "The Hilbert Matrix Function F = x'Ax" 22: "The De Jong Function F1" 23: "The De Jong Function F2" 24: "The De Jong Function F3, (discontinuous)" 25: "The De Jong Function F4 (with Gaussian noise)" 26: "The De Jong Function F5" 27: "The Schaffer Function F6" 28: "The Schaffer Function F7" 29: "The Goldstein Price Polynomial" 30: "The Branin RCOS Function" 31: "The Shekel SQRN5 Function" 32: "The Shekel SQRN7 Function" 33: "The Shekel SQRN10 Function" 34: "The Six-Hump Camel-Back Polynomial" 35: "The Shubert Function" 36: "The Stuckman Function" 37: "The Easom Function" 38: "The Bohachevsky Function #1" 39: "The Bohachevsky Function #2" 40: "The Bohachevsky Function #3" 41: "The Colville Polynomial" 42: "The Powell 3D Function" 43: "The Himmelblau function." p00_n_test(): p00_n() returns problem size or a minimum problem size. 1: N = 3 "The Fletcher-Powell helical valley function." 2: N = 6 "The Biggs EXP6 function." 3: N = 3 "The Gaussian function." 4: N = 2 "The Powell badly scaled function." 5: N = 3 "The Box 3-dimensional function." 6: Minimum N = 1 "The variably dimensioned function." 7: Minimum N = 2 "The Watson function." 8: Minimum N = 1 "The Penalty Function #1." 9: Minimum N = 1 "The Penalty Function #2." 10: N = 2 "The Brown Badly Scaled Function." 11: N = 4 "The Brown and Dennis Function." 12: N = 3 "The Gulf R&D Function." 13: Minimum N = 1 "The Trigonometric Function." 14: Minimum N = 1 "The Extended Rosenbrock parabolic valley Function." 15: Minimum N = 4 "The Extended Powell Singular Quartic Function." 16: N = 2 "The Beale Function." 17: N = 4 "The Wood Function." 18: Minimum N = 1 "The Chebyquad Function" 19: N = 2 "The Leon cubic valley function" 20: Minimum N = 1 "The Gregory and Karney Tridiagonal Matrix Function" 21: Minimum N = 1 "The Hilbert Matrix Function F = x'Ax" 22: N = 3 "The De Jong Function F1" 23: N = 2 "The De Jong Function F2" 24: N = 5 "The De Jong Function F3, (discontinuous)" 25: N = 30 "The De Jong Function F4 (with Gaussian noise)" 26: N = 2 "The De Jong Function F5" 27: N = 2 "The Schaffer Function F6" 28: N = 2 "The Schaffer Function F7" 29: N = 2 "The Goldstein Price Polynomial" 30: N = 2 "The Branin RCOS Function" 31: N = 4 "The Shekel SQRN5 Function" 32: N = 4 "The Shekel SQRN7 Function" 33: N = 4 "The Shekel SQRN10 Function" 34: N = 2 "The Six-Hump Camel-Back Polynomial" 35: N = 2 "The Shubert Function" 36: N = 2 "The Stuckman Function" 37: N = 2 "The Easom Function" 38: N = 2 "The Bohachevsky Function #1" 39: N = 2 "The Bohachevsky Function #2" 40: N = 2 "The Bohachevsky Function #3" 41: N = 4 "The Colville Polynomial" 42: N = 3 "The Powell 3D Function" 43: N = 2 "The Himmelblau function." p00_start_test(): p00_start() provides a starting point for minimization. 1: "The Fletcher-Powell helical valley function." Starting X = ( -1, 0, 0 ) 2: "The Biggs EXP6 function." Starting X = ( 1, 2, 1, 1, 1, 1 ) 3: "The Gaussian function." Starting X = ( 0.4, 1, 0 ) 4: "The Powell badly scaled function." Starting X = ( 0, 1 ) 5: "The Box 3-dimensional function." Starting X = ( 0, 10, 5 ) 6: "The variably dimensioned function." Starting X = ( 0.75, 0.5, 0.25, 0 ) 7: "The Watson function." Starting X = ( 0, 0, 0, 0 ) 8: "The Penalty Function #1." Starting X = ( 1, 2, 3, 4 ) 9: "The Penalty Function #2." Starting X = ( 0.5, 0.5, 0.5, 0.5 ) 10: "The Brown Badly Scaled Function." Starting X = ( 1, 1 ) 11: "The Brown and Dennis Function." Starting X = ( 25, 5, -5, -1 ) 12: "The Gulf R&D Function." Starting X = ( 40, 20, 1.2 ) 13: "The Trigonometric Function." Starting X = ( 0.25, 0.25, 0.25, 0.25 ) 14: "The Extended Rosenbrock parabolic valley Function." Starting X = ( -1.2, 1, -1.2, 1 ) 15: "The Extended Powell Singular Quartic Function." Starting X = ( 3, -1, 0, 1 ) 16: "The Beale Function." Starting X = ( 1, 1 ) 17: "The Wood Function." Starting X = ( -3, -1, -3, -1 ) 18: "The Chebyquad Function" Starting X = ( 0.2, 0.4, 0.6, 0.8 ) 19: "The Leon cubic valley function" Starting X = ( -1.2, -1 ) 20: "The Gregory and Karney Tridiagonal Matrix Function" Starting X = ( 0, 0, 0, 0 ) 21: "The Hilbert Matrix Function F = x'Ax" Starting X = ( 1, 1, 1, 1 ) 22: "The De Jong Function F1" Starting X = ( -5.12, 0, 5.12 ) 23: "The De Jong Function F2" Starting X = ( -2.048, 2.048 ) 24: "The De Jong Function F3, (discontinuous)" Starting X = ( -5.12, -2.56, 0, 2.56, 5.12 ) 25: "The De Jong Function F4 (with Gaussian noise)" Starting X = ( -1.28, -1.19172, -1.10345, -1.01517, -0.926897, -0.838621, -0.750345, -0.662069, -0.573793, -0.485517, -0.397241, -0.308966, -0.22069, -0.132414, -0.0441379, 0.0441379, 0.132414, 0.22069, 0.308966, 0.397241, 0.485517, 0.573793, 0.662069, 0.750345, 0.838621, 0.926897, 1.01517, 1.10345, 1.19172, 1.28 ) 26: "The De Jong Function F5" Starting X = ( -32.01, -32.02 ) 27: "The Schaffer Function F6" Starting X = ( -5, 10 ) 28: "The Schaffer Function F7" Starting X = ( -5, 10 ) 29: "The Goldstein Price Polynomial" Starting X = ( -0.5, 0.25 ) 30: "The Branin RCOS Function" Starting X = ( -1, 1 ) 31: "The Shekel SQRN5 Function" Starting X = ( 1, 3, 5, 6 ) 32: "The Shekel SQRN7 Function" Starting X = ( 1, 3, 5, 6 ) 33: "The Shekel SQRN10 Function" Starting X = ( 1, 3, 5, 6 ) 34: "The Six-Hump Camel-Back Polynomial" Starting X = ( -1.5, 0.5 ) 35: "The Shubert Function" Starting X = ( 0.5, 1 ) 36: "The Stuckman Function" Starting X = ( 0.5, 1 ) 37: "The Easom Function" Starting X = ( 0.5, 1 ) 38: "The Bohachevsky Function #1" Starting X = ( 0.5, 1 ) 39: "The Bohachevsky Function #2" Starting X = ( 0.6, 1.3 ) 40: "The Bohachevsky Function #3" Starting X = ( 0.5, 1 ) 41: "The Colville Polynomial" Starting X = ( 0.5, 1, -0.5, -1 ) 42: "The Powell 3D Function" Starting X = ( 0, 1, 2 ) 43: "The Himmelblau function." Starting X = ( -1.3, 2.7 ) p00_f_test(): p00_f() evaluates the objective function F(X). In this test, we evaluate F at a typical starting point. 1: "The Fletcher-Powell helical valley function." F(X_START) = 2500 2: "The Biggs EXP6 function." F(X_START) = 0.77907 3: "The Gaussian function." F(X_START) = 3.88811e-06 4: "The Powell badly scaled function." F(X_START) = 1.13526 5: "The Box 3-dimensional function." F(X_START) = 34.7325 6: "The variably dimensioned function." F(X_START) = 3222.19 7: "The Watson function." F(X_START) = 30 8: "The Penalty Function #1." F(X_START) = 885.063 9: "The Penalty Function #2." F(X_START) = 2.34001 10: "The Brown Badly Scaled Function." F(X_START) = 9.99998e+11 11: "The Brown and Dennis Function." F(X_START) = 7.92669e+06 12: "The Gulf R&D Function." F(X_START) = 1.20538 13: "The Trigonometric Function." F(X_START) = 0.0130531 14: "The Extended Rosenbrock parabolic valley Function." F(X_START) = 48.4 15: "The Extended Powell Singular Quartic Function." F(X_START) = 215 16: "The Beale Function." F(X_START) = 14.2031 17: "The Wood Function." F(X_START) = 19192 18: "The Chebyquad Function" F(X_START) = 0.0711839 19: "The Leon cubic valley function" F(X_START) = 57.8384 20: "The Gregory and Karney Tridiagonal Matrix Function" F(X_START) = 0 21: "The Hilbert Matrix Function F = x'Ax" F(X_START) = 5.07619 22: "The De Jong Function F1" F(X_START) = 52.4288 23: "The De Jong Function F2" F(X_START) = 469.952 24: "The De Jong Function F3, (discontinuous)" F(X_START) = -2 25: "The De Jong Function F4 (with Gaussian noise)" F(X_START) = 284.843 26: "The De Jong Function F5" F(X_START) = 0.002 27: "The Schaffer Function F6" F(X_START) = 0.868394 28: "The Schaffer Function F7" F(X_START) = 4.56376 29: "The Goldstein Price Polynomial" F(X_START) = 2738.74 30: "The Branin RCOS Function" F(X_START) = 60.3563 31: "The Shekel SQRN5 Function" F(X_START) = -0.167128 32: "The Shekel SQRN7 Function" F(X_START) = -0.215144 33: "The Shekel SQRN10 Function" F(X_START) = -0.270985 34: "The Six-Hump Camel-Back Polynomial" F(X_START) = 0.665625 35: "The Shubert Function" F(X_START) = -3.10442 36: "The Stuckman Function" F(X_START) = 82 37: "The Easom Function" F(X_START) = -4.50356e-06 38: "The Bohachevsky Function #1" F(X_START) = 2.55 39: "The Bohachevsky Function #2" F(X_START) = 4.23635 40: "The Bohachevsky Function #3" F(X_START) = 3.55 41: "The Colville Polynomial" F(X_START) = 239.775 42: "The Powell 3D Function" F(X_START) = 2.5 43: "The Himmelblau function." F(X_START) = 44.7122 p00_sol_test(): p00_sol() provides a local minimizer for any problem. 1: "The Fletcher-Powell helical valley function." Minimizing X = ( 1, 0, 0 ) F(X_MIN) = 0 2: "The Biggs EXP6 function." Minimizing X = ( 1, 10, 1, 5, 4, 3 ) F(X_MIN) = 1.44926e-32 3: "The Gaussian function." Exact minimizing solution not given. 4: "The Powell badly scaled function." Minimizing X = ( 1.09816e-05, 9.10615 ) F(X_MIN) = 1.45526e-13 5: "The Box 3-dimensional function." Minimizing X = ( 1, 10, 1 ) F(X_MIN) = 0 6: "The variably dimensioned function." Minimizing X = ( 1, 1, 1, 1 ) F(X_MIN) = 0 7: "The Watson function." Exact minimizing solution not given. 8: "The Penalty Function #1." Exact minimizing solution not given. 9: "The Penalty Function #2." Exact minimizing solution not given. 10: "The Brown Badly Scaled Function." Minimizing X = ( 1e+06, 2e-06 ) F(X_MIN) = 0 11: "The Brown and Dennis Function." Minimizing X = ( -11.5844, 13.1999, -0.4062, 0.240998 ) F(X_MIN) = 85822.4 12: "The Gulf R&D Function." Minimizing X = ( 50, 25, 1.5 ) F(X_MIN) = 8.4356e-31 13: "The Trigonometric Function." Exact minimizing solution not given. 14: "The Extended Rosenbrock parabolic valley Function." Minimizing X = ( 1, 1, 1, 1 ) F(X_MIN) = 0 15: "The Extended Powell Singular Quartic Function." Minimizing X = ( 0, 0, 0, 0 ) F(X_MIN) = 0 16: "The Beale Function." Minimizing X = ( 3, 0.5 ) F(X_MIN) = 0 17: "The Wood Function." Minimizing X = ( 1, 1, 1, 1 ) F(X_MIN) = 0 18: "The Chebyquad Function" Minimizing X = ( 0.102673, 0.406204, 0.593796, 0.897327 ) F(X_MIN) = 9.24962e-14 19: "The Leon cubic valley function" Minimizing X = ( 1, 1 ) F(X_MIN) = 0 20: "The Gregory and Karney Tridiagonal Matrix Function" Minimizing X = ( 4, 3, 2, 1 ) F(X_MIN) = -4 21: "The Hilbert Matrix Function F = x'Ax" Minimizing X = ( 0, 0, 0, 0 ) F(X_MIN) = 0 22: "The De Jong Function F1" Minimizing X = ( 0, 0, 0 ) F(X_MIN) = 0 23: "The De Jong Function F2" Minimizing X = ( 1, 1 ) F(X_MIN) = 0 24: "The De Jong Function F3, (discontinuous)" Minimizing X = ( -5, -5, -5, -5, -5 ) F(X_MIN) = -25 25: "The De Jong Function F4 (with Gaussian noise)" Minimizing X = ( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ) F(X_MIN) = 0 26: "The De Jong Function F5" Minimizing X = ( -32, -32 ) F(X_MIN) = 0.002 27: "The Schaffer Function F6" Minimizing X = ( 0, 0 ) F(X_MIN) = 0 28: "The Schaffer Function F7" Minimizing X = ( 0, 0 ) F(X_MIN) = 0 29: "The Goldstein Price Polynomial" Minimizing X = ( 0, -1 ) F(X_MIN) = 3 30: "The Branin RCOS Function" Minimizing X = ( 3.14159, 2.275 ) F(X_MIN) = 0.397887 31: "The Shekel SQRN5 Function" Minimizing X = ( 4, 4, 4, 4 ) F(X_MIN) = -10.1527 32: "The Shekel SQRN7 Function" Minimizing X = ( 4, 4, 4, 4 ) F(X_MIN) = -10.4023 33: "The Shekel SQRN10 Function" Minimizing X = ( 4, 4, 4, 4 ) F(X_MIN) = -10.5358 34: "The Six-Hump Camel-Back Polynomial" Minimizing X = ( -0.0898, 0.7126 ) F(X_MIN) = -1.03163 35: "The Shubert Function" Minimizing X = ( 0, 0 ) F(X_MIN) = 19.8758 36: "The Stuckman Function" Minimizing X = ( 8.2539, 6.03425 ) F(X_MIN) = 84 37: "The Easom Function" Minimizing X = ( 3.14159, 3.14159 ) F(X_MIN) = -1 38: "The Bohachevsky Function #1" Minimizing X = ( 0, 0 ) F(X_MIN) = 0 39: "The Bohachevsky Function #2" Minimizing X = ( 0, 0 ) F(X_MIN) = 0 40: "The Bohachevsky Function #3" Minimizing X = ( 0, 0 ) F(X_MIN) = 1 41: "The Colville Polynomial" Minimizing X = ( 1, 1, 1, 1 ) F(X_MIN) = 0 42: "The Powell 3D Function" Minimizing X = ( 1, 1, 1 ) F(X_MIN) = 1 43: "The Himmelblau function." Minimizing X = ( 3, 2 ) F(X_MIN) = 0 p00_gdif_test(): p00_gdif() estimates the gradient vector G with a finite difference estimate GDIF Problem 1: "The Fletcher-Powell helical valley function." X: 0.372555 0.043903 0.132028 G: -129.543 31.4394 -10.6688 GDIF: -129.543 31.4394 -10.6688 Problem 2: "The Biggs EXP6 function." X: 0.423159 0.259366 0.748379 0.216131 0.750508 0.464835 G: 0.127547 -0.00974717 -2.77505 2.79314 0.158027 -2.68896 GDIF: 0.127547 -0.00974717 -2.77505 2.79314 0.158027 -2.68896 Problem 3: "The Gaussian function." X: 0.313644 0.395977 0.373652 G: 0.209908 -0.278902 0.108544 GDIF: 0.209908 -0.278902 0.108544 Problem 4: "The Powell badly scaled function." X: 0.310471 0.124883 G: 965902 2.40133e+06 GDIF: 965902 2.40133e+06 Problem 5: "The Box 3-dimensional function." X: 0.0652914 0.877916 0.496622 G: -1.60488 0.723961 -0.280461 GDIF: -1.60488 0.723961 -0.280461 Problem 6: "The variably dimensioned function." X: 0.343723 0.30364 0.0143471 0.560049 G: -1253.67 -2506.11 -3759.04 -5010.31 GDIF: -1253.67 -2506.11 -3759.04 -5010.31 Problem 7: "The Watson function." X: 0.459914 0.0892906 0.81926 0.145135 G: 71.249 0.0374122 -6.87011 -14.3104 GDIF: 71.249 0.0374121 -6.87011 -14.3104 Problem 8: "The Penalty Function #1." X: 0.248269 0.290978 0.980123 0.559421 G: 1.16178 1.36165 4.58659 2.61786 GDIF: 1.16178 1.36165 4.58659 2.61786 Problem 9: "The Penalty Function #2." X: 0.122975 0.475417 0.333048 0.25808 G: -0.100922 0.154041 0.0719395 0.0278727 GDIF: -0.100922 0.154041 0.0719395 0.0278727 Problem 10: "The Brown Badly Scaled Function." X: 0.405434 0.0509175 G: -2e+06 -1.50317 GDIF: -2.00219e+06 0 Problem 11: "The Brown and Dennis Function." X: 0.181511 0.623477 0.542609 0.752966 G: -1.1988e+06 -4.52418e+06 31435.3 -9787.88 GDIF: -1.1988e+06 -4.52418e+06 31435.4 -9787.91 Problem 12: "The Gulf R&D Function." X: 0.818987 0.529748 0.537923 G: -0.411695 -0.00615122 1.1434 GDIF: -0.411695 -0.00615143 1.1434 Problem 13: "The Trigonometric Function." X: 0.0203032 0.711292 0.05864 0.423827 G: -0.570812 1.52936 -0.338591 1.2537 GDIF: -0.570812 1.52936 -0.338591 1.2537 Problem 14: "The Extended Rosenbrock parabolic valley Function." X: 0.00820892 0.743416 0.11272 0.240185 G: -4.42442 148.67 -12.0311 45.4959 GDIF: -4.42442 148.67 -12.0311 45.4959 Problem 15: "The Extended Powell Singular Quartic Function." X: 0.708629 0.591357 0.791257 0.822048 G: 13.186 128.549 7.48172 0.366268 GDIF: 13.186 128.549 7.48172 0.366268 Problem 16: "The Beale Function." X: 0.930805 0.894645 G: -2.46005 20.0381 GDIF: -2.46005 20.0381 Problem 17: "The Wood Function." X: 0.0341568 0.29242 0.321692 0.502972 G: -5.911 34.1164 -47.6208 47.8575 GDIF: -5.911 34.1164 -47.6208 47.8575 Problem 18: "The Chebyquad Function" X: 0.463654 0.369542 0.617482 0.247741 G: -0.436144 1.25556 -2.8322 2.59065 GDIF: -0.436144 1.25556 -2.8322 2.59065 Problem 19: "The Leon cubic valley function" X: 0.0727069 0.0970211 G: -2.1611 19.3274 GDIF: -2.1611 19.3274 Problem 20: "The Gregory and Karney Tridiagonal Matrix Function" X: 0.499215 0.655712 0.81935 0.647905 G: -2.1565 -0.00714188 0.335083 0.47646 GDIF: -2.31299 -0.0142837 0.670166 0.95292 Problem 21: "The Hilbert Matrix Function F = x'Ax" X: 0.234923 0.181104 0.230742 0.409964 G: 1.00976 0.635016 0.476119 0.38395 GDIF: 1.00976 0.635016 0.476119 0.38395 Problem 22: "The De Jong Function F1" X: 0.730645 0.801083 0.818664 G: 1.46129 1.60217 1.63733 GDIF: 1.46129 1.60217 1.63733 Problem 23: "The De Jong Function F2" X: 0.875314 0.673245 G: 32.2877 -18.5859 GDIF: 32.2877 -18.5859 Problem 24: "The De Jong Function F3, (discontinuous)" X: 0.721594 0.372544 0.977451 0.040763 0.359582 G: 0 0 0 0 0 GDIF: 0 0 0 0 0 Problem 25: "The De Jong Function F4 (with Gaussian noise)" X: 0.160963 0.303304 0.794202 0.845836 0.370806 0.521792 0.745202 0.498821 0.728691 0.323086 0.448758 0.676089 0.350216 0.450995 0.162555 0.0793543 0.754359 0.603612 0.886406 0.892115 0.844657 0.0672605 0.496656 0.744957 0.866686 0.314364 0.270314 0.0281734 0.345524 0.435064 G: 0.0166817 0.223217 6.01138 9.68231 1.01969 3.4096 11.5872 3.97177 13.9294 1.349 3.97639 14.8338 2.23362 5.13693 0.257721 0.031981 29.1906 15.8346 52.9311 56.8005 50.6197 0.0267771 11.2708 39.6885 65.1007 3.23098 2.13318 0.00250459 4.78511 9.88189 GDIF: 0.0166816 0.223217 6.01138 9.68231 1.01969 3.4096 11.5872 3.97177 13.9294 1.349 3.97639 14.8338 2.23362 5.13693 0.257721 0.0319809 29.1906 15.8346 52.9311 56.8005 50.6197 0.0267768 11.2708 39.6885 65.1007 3.23098 2.13318 0.00250436 4.78511 9.88189 Repeat problem with P = 1.000000 X: -1.28 -1.19172 -1.10345 -1.01517 -0.926897 -0.838621 -0.750345 -0.662069 -0.573793 -0.485517 -0.397241 -0.308966 -0.22069 -0.132414 -0.0441379 0.0441379 0.132414 0.22069 0.308966 0.397241 0.485517 0.573793 0.662069 0.750345 0.838621 0.926897 1.01517 1.10345 1.19172 1.28 G: -8.38861 -13.54 -16.1227 -16.7394 -15.9266 -14.1549 -11.8288 -9.28666 -6.80093 -4.57798 -2.75814 -1.4157 -0.55892 -0.130013 -0.00515926 0.00550321 0.157873 0.773889 2.24153 5.0148 9.61376 16.6245 26.6992 40.5559 58.9789 82.8185 112.991 150.478 196.329 251.658 GDIF: 1.45148e+07 -1.38754e+07 6.40375e+06 8.052e+06 1.14934e+07 -3.25919e+07 2.91857e+06 -3.13729e+07 -2.39473e+07 2.18637e+07 2.0198e+06 7.99446e+06 -1.84019e+07 4.38921e+07 7.44183e+07 2.72574e+07 -4.53985e+07 -8.35377e+07 1.72444e+07 -4.10913e+07 -2.70027e+07 2.04353e+07 -1.60415e+06 -1.62295e+07 3.49792e+07 -8.46577e+06 1.68934e+07 1.73363e+07 1.80717e+07 3.22248e+07 Problem 26: "The De Jong Function F5" X: 0.909548 0.736332 G: 2.67681e-10 -3.90514e-08 GDIF: 2.66721e-10 -3.90463e-08 Problem 27: "The Schaffer Function F6" X: 0.190164 0.805096 G: 0.228725 0.968353 GDIF: 0.228725 0.968353 Problem 28: "The Schaffer Function F7" X: 0.714982 0.288737 G: 6.93675 2.80133 GDIF: 6.93675 2.80133 Problem 29: "The Goldstein Price Polynomial" X: 0.778111 0.421669 G: 305.417 -786.796 GDIF: 305.417 -786.796 Problem 30: "The Branin RCOS Function" X: 0.754833 0.800477 G: -17.9517 -8.14355 GDIF: -17.9517 -8.14355 Problem 31: "The Shekel SQRN5 Function" X: 0.730721 0.754001 0.361571 0.218526 G: -0.299151 -0.274464 -0.703915 -0.861598 GDIF: -0.299151 -0.274464 -0.703915 -0.861598 Problem 32: "The Shekel SQRN7 Function" X: 0.554223 0.397186 0.886094 0.146326 G: -0.401723 -0.542254 -0.106201 -0.763217 GDIF: -0.401723 -0.542254 -0.106201 -0.763217 Problem 33: "The Shekel SQRN10 Function" X: 0.0953509 0.929339 0.880772 0.600274 G: -1.27685 -0.108923 -0.17728 -0.567442 GDIF: -1.27685 -0.108923 -0.17728 -0.567442 Problem 34: "The Six-Hump Camel-Back Polynomial" X: 0.254825 0.410289 G: 2.31204 -1.92242 GDIF: 2.31204 -1.92242 Problem 35: "The Shubert Function" X: 0.938033 0.653429 G: -27.007 59.2821 GDIF: -27.007 59.2821 Problem 36: "The Stuckman Function" X: 0.242871 0.248952 G: 0 0 GDIF: 0 0 Problem 37: "The Easom Function" X: 0.433156 0.209733 G: -5.30097e-07 -6.04611e-07 GDIF: -5.30097e-07 -6.04611e-07 Problem 38: "The Bohachevsky Function #1" X: 0.221571 0.53327 G: 2.9004 4.17388 GDIF: 2.9004 4.17388 Problem 39: "The Bohachevsky Function #2" X: 0.9899 0.967756 G: 2.22677 5.35039 GDIF: 2.22677 5.35039 Problem 40: "The Bohachevsky Function #3" X: 0.738539 0.32222 G: 3.24919 11.1911 GDIF: 3.24919 11.1911 Problem 41: "The Colville Polynomial" X: 0.462484 0.159005 0.297818 0.207707 G: 9.07861 -43.6528 -14.1641 -11.2341 GDIF: 9.07861 -43.6528 -14.1641 -11.2341 Problem 42: "The Powell 3D Function" X: 0.031559 0.557198 0.501679 G: -0.643686 -0.0695216 -0.790525 GDIF: -0.643686 -0.0695216 -0.790525 Problem 43: "The Himmelblau function." X: 0.951259 0.521465 G: -47.9817 -31.1969 GDIF: -47.9817 -31.1969 p00_hdif_test(): p00_hdif() approximates the Hessian H with a finite difference estimate HDIF. Problem 1 The Fletcher-Powell helical valley function. N = 3 X: 0.41046 0.517534 0.0272666 H: Col: 1 2 3 Row 1 : 1725.35 -184.36 377.559 2 : -184.36 -467.039 -299.445 3 : 377.559 -299.445 202 H (approximated): Col: 1 2 3 Row 1 : 1725.35 -184.36 377.559 2 : -184.36 -467.041 -299.445 3 : 377.559 -299.445 202 Problem 2 The Biggs EXP6 function. N = 6 X: 0.505446 0.648883 0.289662 0.299227 0.294147 0.507719 H: Col: 1 2 3 4 5 Row 1 : 0.224782 -0.464095 0.270687 2.00197 1.09819 2 : -0.464095 0.702067 2.06808 -4.22443 -0.99046 3 : 0.270687 2.06808 13.7494 -12.7005 -4.65218 4 : 2.00197 -4.22443 -12.7005 11.7619 4.14373 5 : 1.09819 -0.99046 -4.65218 4.14373 1.81052 6 : -2.65415 2.44213 15.5294 -14.2886 -2.81037 Col: 6 Row 1 : -2.65415 2 : 2.44213 3 : 15.5294 4 : -14.2886 5 : -2.81037 6 : 17.6441 H (approximated): Col: 1 2 3 4 5 Row 1 : 0.224795 -0.464095 0.270682 2.00198 1.0982 2 : -0.464095 0.70211 2.06808 -4.22443 -0.990454 3 : 0.270682 2.06808 13.7494 -12.7005 -4.65217 4 : 2.00198 -4.22443 -12.7005 11.7619 4.14372 5 : 1.0982 -0.990454 -4.65217 4.14372 1.81055 6 : -2.65415 2.44214 15.5294 -14.2886 -2.81037 Col: 6 Row 1 : -2.65415 2 : 2.44214 3 : 15.5294 4 : -14.2886 5 : -2.81037 6 : 17.6441 Problem 3 The Gaussian function. N = 3 X: 0.448951 0.656069 0.27485 H: Col: 1 2 3 Row 1 : 8.75281 -2.02661 0.332945 2 : -2.02661 1.12138 0.0918943 3 : 0.332945 0.0918943 0.527764 H (approximated): Col: 1 2 3 Row 1 : 8.75281 -2.02661 0.332945 2 : -2.02661 1.12138 0.0918942 3 : 0.332945 0.0918942 0.527765 Problem 4 The Powell badly scaled function. N = 2 X: 0.605601 0.16301 H: Col: 1 2 Row 1 : 5.31448e+06 3.94677e+07 2 : 3.94677e+07 7.33505e+07 H (approximated): Col: 1 2 Row 1 : 5.31448e+06 3.94677e+07 2 : 3.94677e+07 7.33505e+07 Problem 5 The Box 3-dimensional function. N = 3 X: 0.643976 0.0173335 0.617976 H: Col: 1 2 3 Row 1 : -0.185703 -4.62216 3.63357 2 : -4.62216 12.5278 -5.39089 3 : 3.63357 -5.39089 6.12801 H (approximated): Col: 1 2 3 Row 1 : -0.185737 -4.62216 3.63357 2 : -4.62216 12.5278 -5.3909 3 : 3.63357 -5.3909 6.128 Problem 6 The variably dimensioned function. N = 4 X: 0.698916 0.349901 0.00862616 0.198338 H: Col: 1 2 3 4 Row 1 : 730.724 1457.45 2186.17 2914.89 2 : 1457.45 2916.89 4372.34 5829.79 3 : 2186.17 4372.34 6560.51 8744.68 4 : 2914.89 5829.79 8744.68 11661.6 H (approximated): Col: 1 2 3 4 Row 1 : 730.702 1457.44 2186.17 2914.89 2 : 1457.44 2916.9 4372.34 5829.79 3 : 2186.17 4372.34 6560.47 8744.69 4 : 2914.89 5829.79 8744.69 11661.6 Problem 7 The Watson function. N = 4 X: 0.755788 0.570591 0.728483 0.782183 H: Col: 1 2 3 4 Row 1 : 808.298 393.755 242.259 145.432 2 : 393.755 302.259 205.432 137.485 3 : 242.259 205.432 157.83 116.847 4 : 145.432 137.485 116.847 95.1297 H (approximated): Col: 1 2 3 4 Row 1 : 808.299 393.754 242.259 145.432 2 : 393.754 302.259 205.433 137.485 3 : 242.259 205.433 157.83 116.847 4 : 145.432 137.485 116.847 95.1288 Problem 8 The Penalty Function #1. N = 4 X: 0.361933 0.469963 0.551941 0.44696 H: Col: 1 2 3 4 Row 1 : 3.47307 1.36076 1.59812 1.29415 2 : 1.36076 4.19203 2.07513 1.68043 3 : 1.59812 2.07513 4.86222 1.97356 4 : 1.29415 1.68043 1.97356 4.02329 H (approximated): Col: 1 2 3 4 Row 1 : 3.47307 1.36076 1.59812 1.29415 2 : 1.36076 4.19202 2.07513 1.68044 3 : 1.59812 2.07513 4.86222 1.97356 4 : 1.29415 1.68044 1.97356 4.02329 Problem 9 The Penalty Function #2. N = 4 X: 0.707556 0.395621 0.205908 0.616953 H: Col: 1 2 3 4 Row 1 : 97.0817 26.8727 9.32426 13.9689 2 : 26.8727 34.5194 3.91016 5.85791 3 : 9.32426 3.91016 16.8569 2.03257 4 : 13.9689 5.85791 2.03257 10.7951 H (approximated): Col: 1 2 3 4 Row 1 : 97.0817 26.8727 9.32427 13.9689 2 : 26.8727 34.5194 3.91016 5.85791 3 : 9.32427 3.91016 16.8569 2.03257 4 : 13.9689 5.85791 2.03257 10.7951 Problem 10 The Brown Badly Scaled Function. N = 2 X: 0.448152 0.583679 H: Col: 1 2 Row 1 : 2.68136 -2.95369 2 : -2.95369 2.40168 H (approximated): Col: 1 2 Row 1 :-2.61794e+06 0 2 : 0 0 Problem 11 The Brown and Dennis Function. N = 4 X: 0.0103533 0.498526 0.823829 0.394238 H: Col: 1 2 3 4 Row 1 : 97671.4 353111 -3298.65 342.462 2 : 353111 1.29734e+06 -10624.3 2279.13 3 : -3298.65 -10624.3 32954.9 -14101.1 4 : 342.462 2279.13 -14101.1 11443.7 H (approximated): Col: 1 2 3 4 Row 1 : 97709.3 353138 -3315.57 329.559 2 : 353138 1.29814e+06 -10615.8 2276.95 3 : -3315.57 -10615.8 32916 -14091.2 4 : 329.559 2276.95 -14091.2 11424.7 Problem 12 The Gulf R&D Function. N = 3 X: 0.64889 0.150404 0.830349 H: Col: 1 2 3 Row 1 :-1.82323e-06 -3.81605e-08 4.07702e-06 2 :-3.81605e-08 -8.06373e-10 8.01959e-08 3 : 4.07702e-06 8.01959e-08 -8.71819e-06 H (approximated): Col: 1 2 3 Row 1 : 0.000457152 0 0 2 : 0 0 -0.000114288 3 : 0 -0.000114288 0 Problem 13 The Trigonometric Function. N = 4 X: 0.45309 0.257153 0.428211 0.881215 H: Col: 1 2 3 4 Row 1 : 6.07522 0.254597 1.36521 4.13474 2 : 0.254597 6.79422 0.635037 2.10844 3 : 1.36521 0.635037 9.25577 5.11598 4 : 4.13474 2.10844 5.11598 35.7686 H (approximated): Col: 1 2 3 4 Row 1 : 6.07527 0.254596 1.36521 4.13474 2 : 0.254596 6.79426 0.635037 2.10844 3 : 1.36521 0.635037 9.25587 5.11599 4 : 4.13474 2.10844 5.11599 35.7687 Problem 14 The Extended Rosenbrock parabolic valley Function. N = 4 X: 0.76103 0.0856564 0.408696 0.179427 H: Col: 1 2 3 4 Row 1 : 662.737 -304.412 0 0 2 : -304.412 200 0 0 3 : 0 0 130.668 -163.478 4 : 0 0 -163.478 200 H (approximated): Col: 1 2 3 4 Row 1 : 662.737 -304.412 0 0 2 : -304.412 200 0 0 3 : 0 0 130.668 -163.478 4 : 0 0 -163.478 200 Problem 15 The Extended Powell Singular Quartic Function. N = 4 X: 0.237713 0.144005 0.955415 0.588691 H: Col: 1 2 3 4 Row 1 : 16.7823 20 0 -14.7823 2 : 20 237.46 -74.92 0 3 : 0 -74.92 159.84 -10 4 : -14.7823 0 -10 24.7823 H (approximated): Col: 1 2 3 4 Row 1 : 16.7823 20 0 -14.7823 2 : 20 237.46 -74.92 0 3 : 0 -74.92 159.84 -10 4 : -14.7823 0 -10 24.7823 Problem 16 The Beale Function. N = 2 X: 0.0848425 0.177121 H: Col: 1 2 Row 1 : 5.20857 4.66073 2 : 4.66073 1.21017 H (approximated): Col: 1 2 Row 1 : 5.20853 4.66074 2 : 4.66074 1.21004 Problem 17 The Wood Function. N = 4 X: 0.0222628 0.0897757 0.275503 0.636379 H: Col: 1 2 3 4 Row 1 : -33.3155 -8.90512 0 0 2 : -8.90512 220.2 0 19.8 3 : 0 0 -145.122 -99.1811 4 : 0 19.8 -99.1811 200.2 H (approximated): Col: 1 2 3 4 Row 1 : -33.3153 -8.90517 -3.8096e-05 -3.8096e-05 2 : -8.90517 220.2 0 19.8 3 : -3.8096e-05 0 -145.122 -99.1811 4 : -3.8096e-05 19.8 -99.1811 200.2 Problem 18 The Chebyquad Function N = 4 X: 0.125943 0.334535 0.307624 0.91384 H: Col: 1 2 3 4 Row 1 : -28.5473 -3.60551 -2.56619 1.74562 2 : -3.60551 6.91572 11.5097 4.04205 3 : -2.56619 11.5097 3.7605 5.37813 4 : 1.74562 4.04205 5.37813 23.0814 H (approximated): Col: 1 2 3 4 Row 1 : -28.5473 -3.60551 -2.56619 1.74562 2 : -3.60551 6.91572 11.5097 4.04205 3 : -2.56619 11.5097 3.76049 5.37813 4 : 1.74562 4.04205 5.37813 23.0814 Problem 19 The Leon cubic valley function N = 2 X: 0.215155 0.561998 H: Col: 1 2 Row 1 : -136.671 -27.775 2 : -27.775 200 H (approximated): Col: 1 2 Row 1 : -136.671 -27.775 2 : -27.775 200 Problem 20 The Gregory and Karney Tridiagonal Matrix Function N = 4 X: 0.516002 0.00151227 0.312822 0.80863 H: Col: 1 2 3 4 Row 1 : 2 -2 0 0 2 : -2 4 -2 0 3 : 0 -2 4 -2 4 : 0 0 -2 4 H (approximated): Col: 1 2 3 4 Row 1 : 1.99999 -2 1.1905e-06 1.1905e-06 2 : -2 4 -2 -1.1905e-06 3 : 1.1905e-06 -2 4 -2 4 : 1.1905e-06 -1.1905e-06 -2 4 Problem 21 The Hilbert Matrix Function F = x'Ax N = 4 X: 0.150621 0.754909 0.311375 0.24356 H: Col: 1 2 3 4 Row 1 : 2 1 0.666667 0.5 2 : 1 0.666667 0.5 0.4 3 : 0.666667 0.5 0.4 0.333333 4 : 0.5 0.4 0.333333 0.285714 H (approximated): Col: 1 2 3 4 Row 1 : 2 1 0.666667 0.5 2 : 1 0.666669 0.5 0.4 3 : 0.666667 0.5 0.400001 0.333334 4 : 0.5 0.4 0.333334 0.285713 Problem 22 The De Jong Function F1 N = 3 X: 0.91075 0.883759 0.217085 H: Col: 1 2 3 Row 1 : 2 0 0 2 : 0 2 0 3 : 0 0 2 H (approximated): Col: 1 2 3 Row 1 : 1.99999 2.381e-06 0 2 : 2.381e-06 1.99999 0 3 : 0 0 2 Problem 23 The De Jong Function F2 N = 2 X: 0.61067 0.212056 H: Col: 1 2 Row 1 : 364.679 -244.268 2 : -244.268 200 H (approximated): Col: 1 2 Row 1 : 364.679 -244.268 2 : -244.268 200 Problem 24 The De Jong Function F3, (discontinuous) N = 5 X: 0.954515 0.58664 0.58726 0.974247 0.801179 H: Col: 1 2 3 4 5 Row 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 0 0 0 0 0 4 : 0 0 0 0 0 5 : 0 0 0 0 0 H (approximated): Col: 1 2 3 4 5 Row 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 0 0 0 0 0 4 : 0 0 0 0 0 5 : 0 0 0 0 0 Problem 25 The De Jong Function F4 (with Gaussian noise) N = 30 X: 0.0241616 0.374987 0.114483 0.147922 0.697066 0.893389 0.782544 0.751662 0.883319 0.550413 0.685514 0.165997 0.332703 0.236485 0.163636 0.851865 0.128532 0.79192 0.597409 0.859554 0.708321 0.917073 0.538454 0.858527 0.69712 0.688412 0.604203 0.290386 0.5121 0.266983 H: Col: 1 2 3 4 5 Row 1 : 0.00700538 0 0 0 0 2 : 0 3.37476 0 0 0 3 : 0 0 0.471831 0 0 4 : 0 0 0 1.05029 0 5 : 0 0 0 0 29.1541 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0 0 0 0 0 10 : 0 0 0 0 0 11 : 0 0 0 0 0 12 : 0 0 0 0 0 13 : 0 0 0 0 0 14 : 0 0 0 0 0 15 : 0 0 0 0 0 16 : 0 0 0 0 0 17 : 0 0 0 0 0 18 : 0 0 0 0 0 19 : 0 0 0 0 0 20 : 0 0 0 0 0 21 : 0 0 0 0 0 22 : 0 0 0 0 0 23 : 0 0 0 0 0 24 : 0 0 0 0 0 25 : 0 0 0 0 0 26 : 0 0 0 0 0 27 : 0 0 0 0 0 28 : 0 0 0 0 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 6 7 8 9 10 Row 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 0 0 0 0 0 4 : 0 0 0 0 0 5 : 0 0 0 0 0 6 : 57.4664 0 0 0 0 7 : 0 51.4395 0 0 0 8 : 0 0 54.2396 0 0 9 : 0 0 0 84.2672 0 10 : 0 0 0 0 36.3546 11 : 0 0 0 0 0 12 : 0 0 0 0 0 13 : 0 0 0 0 0 14 : 0 0 0 0 0 15 : 0 0 0 0 0 16 : 0 0 0 0 0 17 : 0 0 0 0 0 18 : 0 0 0 0 0 19 : 0 0 0 0 0 20 : 0 0 0 0 0 21 : 0 0 0 0 0 22 : 0 0 0 0 0 23 : 0 0 0 0 0 24 : 0 0 0 0 0 25 : 0 0 0 0 0 26 : 0 0 0 0 0 27 : 0 0 0 0 0 28 : 0 0 0 0 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 11 12 13 14 15 Row 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 0 0 0 0 0 4 : 0 0 0 0 0 5 : 0 0 0 0 0 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0 0 0 0 0 10 : 0 0 0 0 0 11 : 62.0308 0 0 0 0 12 : 0 3.9679 0 0 0 13 : 0 0 17.2678 0 0 14 : 0 0 0 9.39542 0 15 : 0 0 0 0 4.81982 16 : 0 0 0 0 0 17 : 0 0 0 0 0 18 : 0 0 0 0 0 19 : 0 0 0 0 0 20 : 0 0 0 0 0 21 : 0 0 0 0 0 22 : 0 0 0 0 0 23 : 0 0 0 0 0 24 : 0 0 0 0 0 25 : 0 0 0 0 0 26 : 0 0 0 0 0 27 : 0 0 0 0 0 28 : 0 0 0 0 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 16 17 18 19 20 Row 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 0 0 0 0 0 4 : 0 0 0 0 0 5 : 0 0 0 0 0 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0 0 0 0 0 10 : 0 0 0 0 0 11 : 0 0 0 0 0 12 : 0 0 0 0 0 13 : 0 0 0 0 0 14 : 0 0 0 0 0 15 : 0 0 0 0 0 16 : 139.33 0 0 0 0 17 : 0 3.37018 0 0 0 18 : 0 0 135.462 0 0 19 : 0 0 0 81.3728 0 20 : 0 0 0 0 177.32 21 : 0 0 0 0 0 22 : 0 0 0 0 0 23 : 0 0 0 0 0 24 : 0 0 0 0 0 25 : 0 0 0 0 0 26 : 0 0 0 0 0 27 : 0 0 0 0 0 28 : 0 0 0 0 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 21 22 23 24 25 Row 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 0 0 0 0 0 4 : 0 0 0 0 0 5 : 0 0 0 0 0 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0 0 0 0 0 10 : 0 0 0 0 0 11 : 0 0 0 0 0 12 : 0 0 0 0 0 13 : 0 0 0 0 0 14 : 0 0 0 0 0 15 : 0 0 0 0 0 16 : 0 0 0 0 0 17 : 0 0 0 0 0 18 : 0 0 0 0 0 19 : 0 0 0 0 0 20 : 0 0 0 0 0 21 : 126.433 0 0 0 0 22 : 0 222.03 0 0 0 23 : 0 0 80.0215 0 0 24 : 0 0 0 212.276 0 25 : 0 0 0 0 145.793 26 : 0 0 0 0 0 27 : 0 0 0 0 0 28 : 0 0 0 0 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 26 27 28 29 30 Row 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 0 0 0 0 0 4 : 0 0 0 0 0 5 : 0 0 0 0 0 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0 0 0 0 0 10 : 0 0 0 0 0 11 : 0 0 0 0 0 12 : 0 0 0 0 0 13 : 0 0 0 0 0 14 : 0 0 0 0 0 15 : 0 0 0 0 0 16 : 0 0 0 0 0 17 : 0 0 0 0 0 18 : 0 0 0 0 0 19 : 0 0 0 0 0 20 : 0 0 0 0 0 21 : 0 0 0 0 0 22 : 0 0 0 0 0 23 : 0 0 0 0 0 24 : 0 0 0 0 0 25 : 0 0 0 0 0 26 : 147.86 0 0 0 0 27 : 0 118.28 0 0 0 28 : 0 0 28.3329 0 0 29 : 0 0 0 91.2619 0 30 : 0 0 0 0 25.6608 H (approximated): Col: 1 2 3 4 5 Row 1 : 0.00792397 0 0.000152384 0.000152384 0.000152384 2 : 0 3.37561 0 0 0 3 : 0.000152384 0 0.472391 0 0.000152384 4 : 0.000152384 0 0 1.05084 0.000152384 5 : 0.000152384 0 0.000152384 0.000152384 29.1547 6 : 0 0 0 0 0 7 : 0.000152384 0.000152384 0 0 0 8 : 0.000152384 0 0.000152384 0 0.000152384 9 : 0.000152384 0.000152384 0 0 0 10 : 0 0 0 0 0 11 : 0.000152384 0.000152384 0 0 0 12 : 0 0 0 0 0 13 : 0 0 -0.000152384 -0.000152384 -0.000152384 14 :-0.000152384 -0.000152384 0 0 0 15 : 0 0 0 0 0 16 :-0.000152384 -0.000152384 -0.000152384 -0.000152384 -0.000152384 17 : 0.000152384 0.000152384 0 0 0 18 : 0.000152384 0 0 0 0 19 : 0 0 0.000152384 0.000152384 0.000152384 20 : 0 0 -0.000152384 -0.000152384 -0.000152384 21 : 0 0 7.61921e-05 7.61921e-05 7.61921e-05 22 : 0 0 7.61921e-05 7.61921e-05 7.61921e-05 23 : 0 0 0 0 0 24 : 0 0 0 0 0 25 : 0 0 0 0 0 26 : 0 0 0 0 0 27 : 0 0 0 0 0 28 : 0 0 0 0 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 6 7 8 9 10 Row 1 : 0 0.000152384 0.000152384 0.000152384 0 2 : 0 0.000152384 0 0.000152384 0 3 : 0 0 0.000152384 0 0 4 : 0 0 0 0 0 5 : 0 0 0.000152384 0 0 6 : 57.4671 -0.000152384 0 -0.000152384 0 7 :-0.000152384 51.44 0 -0.000152384 0 8 : 0 0 54.2396 0 0 9 :-0.000152384 -0.000152384 0 84.2678 0 10 : 0 0 0 0 36.3546 11 :-0.000152384 -0.000152384 0 0 0 12 : 0 0 0 0 0 13 : 0 -0.000152384 0 0 0 14 : 0.000152384 0.000152384 0 0 0 15 : 0 0 0 0 0 16 : 0.000152384 0 0 -0.000152384 0 17 :-0.000152384 -0.000152384 0 0 0 18 : 0 -0.000152384 0 -0.000152384 0 19 : 0 0.000152384 0 0.000152384 0 20 : 0 -0.000152384 0 -0.000152384 0 21 : 0 7.61921e-05 0 7.61921e-05 0 22 : 0 7.61921e-05 0 7.61921e-05 0 23 : 0 0 0 0 0 24 : 0 0 0 0 0 25 : 0 0 0 0 0 26 : 0 0 0 0 0 27 : 0 0 0 0 0 28 : 0 0 0 0 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 11 12 13 14 15 Row 1 : 0.000152384 0 0 -0.000152384 0 2 : 0.000152384 0 0 -0.000152384 0 3 : 0 0 -0.000152384 0 0 4 : 0 0 -0.000152384 0 0 5 : 0 0 -0.000152384 0 0 6 :-0.000152384 0 0 0.000152384 0 7 :-0.000152384 0 -0.000152384 0.000152384 0 8 : 0 0 0 0 0 9 : 0 0 0 0 0 10 : 0 0 0 0 0 11 : 62.0313 0 0 0.000152384 0 12 : 0 3.96869 0 0 0 13 : 0 0 17.2682 0 0 14 : 0.000152384 0 0 9.396 0 15 : 0 0 0 0 4.82082 16 : 0 0 -0.000152384 0 0 17 :-0.000152384 0 0 0.000152384 0 18 :-0.000152384 0 -0.000152384 0.000152384 0 19 : 0.000152384 0 0.000152384 -0.000152384 0 20 :-0.000152384 0 -0.000152384 0.000152384 0 21 : 7.61921e-05 0 7.61921e-05 -7.61921e-05 0 22 : 7.61921e-05 0 7.61921e-05 -7.61921e-05 0 23 : 0 0 0 0 0 24 : 0 0 0 0 0 25 : 0 0 0 0 0 26 : 0 0 0 0 0 27 : 0 0 0 0 0 28 : 0 0 0 0 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 16 17 18 19 20 Row 1 :-0.000152384 0.000152384 0.000152384 0 0 2 :-0.000152384 0.000152384 0 0 0 3 :-0.000152384 0 0 0.000152384 -0.000152384 4 :-0.000152384 0 0 0.000152384 -0.000152384 5 :-0.000152384 0 0 0.000152384 -0.000152384 6 : 0.000152384 -0.000152384 0 0 0 7 : 0 -0.000152384 -0.000152384 0.000152384 -0.000152384 8 : 0 0 0 0 0 9 :-0.000152384 0 -0.000152384 0.000152384 -0.000152384 10 : 0 0 0 0 0 11 : 0 -0.000152384 -0.000152384 0.000152384 -0.000152384 12 : 0 0 0 0 0 13 :-0.000152384 0 -0.000152384 0.000152384 -0.000152384 14 : 0 0.000152384 0.000152384 -0.000152384 0.000152384 15 : 0 0 0 0 0 16 : 139.33 0 0 0 0 17 : 0 3.37074 -0.000152384 0.000152384 -0.000152384 18 : 0 -0.000152384 135.462 0.000152384 -0.000152384 19 : 0 0.000152384 0.000152384 81.3731 0.000152384 20 : 0 -0.000152384 -0.000152384 0.000152384 177.32 21 : 0 7.61921e-05 7.61921e-05 -7.61921e-05 7.61921e-05 22 : 0 7.61921e-05 7.61921e-05 -7.61921e-05 7.61921e-05 23 : 0 0 0 0 0 24 : 0 0 0 0 0 25 : 0 0 0 0 0 26 : 0 0 0 0 0 27 : 0 0 0 0 0 28 : 0 0 0 0 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 21 22 23 24 25 Row 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 7.61921e-05 7.61921e-05 0 0 0 4 : 7.61921e-05 7.61921e-05 0 0 0 5 : 7.61921e-05 7.61921e-05 0 0 0 6 : 0 0 0 0 0 7 : 7.61921e-05 7.61921e-05 0 0 0 8 : 0 0 0 0 0 9 : 7.61921e-05 7.61921e-05 0 0 0 10 : 0 0 0 0 0 11 : 7.61921e-05 7.61921e-05 0 0 0 12 : 0 0 0 0 0 13 : 7.61921e-05 7.61921e-05 0 0 0 14 :-7.61921e-05 -7.61921e-05 0 0 0 15 : 0 0 0 0 0 16 : 0 0 0 0 0 17 : 7.61921e-05 7.61921e-05 0 0 0 18 : 7.61921e-05 7.61921e-05 0 0 0 19 :-7.61921e-05 -7.61921e-05 0 0 0 20 : 7.61921e-05 7.61921e-05 0 0 0 21 : 126.434 0 0 0 0 22 : 0 222.03 0 -7.61921e-05 0 23 : 0 0 80.0215 7.61921e-05 0 24 : 0 -7.61921e-05 7.61921e-05 212.276 0 25 : 0 0 0 0 145.793 26 : 0 0 0 0 0 27 : 0 0 0 0 0 28 : 0 0 0 0 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 26 27 28 29 30 Row 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 0 0 0 0 0 4 : 0 0 0 0 0 5 : 0 0 0 0 0 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0 0 0 0 0 10 : 0 0 0 0 0 11 : 0 0 0 0 0 12 : 0 0 0 0 0 13 : 0 0 0 0 0 14 : 0 0 0 0 0 15 : 0 0 0 0 0 16 : 0 0 0 0 0 17 : 0 0 0 0 0 18 : 0 0 0 0 0 19 : 0 0 0 0 0 20 : 0 0 0 0 0 21 : 0 0 0 0 0 22 : 0 0 0 0 0 23 : 0 0 0 0 0 24 : 0 0 0 0 0 25 : 0 0 0 0 0 26 : 147.86 0 0 0 0 27 : 0 118.28 0 0 0 28 : 0 0 28.3334 0 0 29 : 0 0 0 91.2622 0 30 : 0 0 0 0 25.6606 Repeat problem with P = 1.000000 X: -1.28 -1.19172 -1.10345 -1.01517 -0.926897 -0.838621 -0.750345 -0.662069 -0.573793 -0.485517 -0.397241 -0.308966 -0.22069 -0.132414 -0.0441379 0.0441379 0.132414 0.22069 0.308966 0.397241 0.485517 0.573793 0.662069 0.750345 0.838621 0.926897 1.01517 1.10345 1.19172 1.28 H: Col: 1 2 3 4 5 Row 1 : 19.6608 0 0 0 0 2 : 0 34.085 0 0 0 3 : 0 0 43.8335 0 0 4 : 0 0 0 49.4676 0 5 : 0 0 0 0 51.5482 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0 0 0 0 0 10 : 0 0 0 0 0 11 : 0 0 0 0 0 12 : 0 0 0 0 0 13 : 0 0 0 0 0 14 : 0 0 0 0 0 15 : 0 0 0 0 0 16 : 0 0 0 0 0 17 : 0 0 0 0 0 18 : 0 0 0 0 0 19 : 0 0 0 0 0 20 : 0 0 0 0 0 21 : 0 0 0 0 0 22 : 0 0 0 0 0 23 : 0 0 0 0 0 24 : 0 0 0 0 0 25 : 0 0 0 0 0 26 : 0 0 0 0 0 27 : 0 0 0 0 0 28 : 0 0 0 0 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 6 7 8 9 10 Row 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 0 0 0 0 0 4 : 0 0 0 0 0 5 : 0 0 0 0 0 6 : 50.6365 0 0 0 0 7 : 0 47.2935 0 0 0 8 : 0 0 42.0802 0 0 9 : 0 0 0 35.5578 0 10 : 0 0 0 0 28.2872 11 : 0 0 0 0 0 12 : 0 0 0 0 0 13 : 0 0 0 0 0 14 : 0 0 0 0 0 15 : 0 0 0 0 0 16 : 0 0 0 0 0 17 : 0 0 0 0 0 18 : 0 0 0 0 0 19 : 0 0 0 0 0 20 : 0 0 0 0 0 21 : 0 0 0 0 0 22 : 0 0 0 0 0 23 : 0 0 0 0 0 24 : 0 0 0 0 0 25 : 0 0 0 0 0 26 : 0 0 0 0 0 27 : 0 0 0 0 0 28 : 0 0 0 0 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 11 12 13 14 15 Row 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 0 0 0 0 0 4 : 0 0 0 0 0 5 : 0 0 0 0 0 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0 0 0 0 0 10 : 0 0 0 0 0 11 : 20.8297 0 0 0 0 12 : 0 13.7462 0 0 0 13 : 0 0 7.59781 0 0 14 : 0 0 0 2.94561 0 15 : 0 0 0 0 0.350668 16 : 0 0 0 0 0 17 : 0 0 0 0 0 18 : 0 0 0 0 0 19 : 0 0 0 0 0 20 : 0 0 0 0 0 21 : 0 0 0 0 0 22 : 0 0 0 0 0 23 : 0 0 0 0 0 24 : 0 0 0 0 0 25 : 0 0 0 0 0 26 : 0 0 0 0 0 27 : 0 0 0 0 0 28 : 0 0 0 0 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 16 17 18 19 20 Row 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 0 0 0 0 0 4 : 0 0 0 0 0 5 : 0 0 0 0 0 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0 0 0 0 0 10 : 0 0 0 0 0 11 : 0 0 0 0 0 12 : 0 0 0 0 0 13 : 0 0 0 0 0 14 : 0 0 0 0 0 15 : 0 0 0 0 0 16 : 0.374046 0 0 0 0 17 : 0 3.57682 0 0 0 18 : 0 0 10.52 0 0 19 : 0 0 0 21.7648 0 20 : 0 0 0 0 37.8722 21 : 0 0 0 0 0 22 : 0 0 0 0 0 23 : 0 0 0 0 0 24 : 0 0 0 0 0 25 : 0 0 0 0 0 26 : 0 0 0 0 0 27 : 0 0 0 0 0 28 : 0 0 0 0 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 21 22 23 24 25 Row 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 0 0 0 0 0 4 : 0 0 0 0 0 5 : 0 0 0 0 0 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0 0 0 0 0 10 : 0 0 0 0 0 11 : 0 0 0 0 0 12 : 0 0 0 0 0 13 : 0 0 0 0 0 14 : 0 0 0 0 0 15 : 0 0 0 0 0 16 : 0 0 0 0 0 17 : 0 0 0 0 0 18 : 0 0 0 0 0 19 : 0 0 0 0 0 20 : 0 0 0 0 0 21 : 59.4032 0 0 0 0 22 : 0 86.919 0 0 0 23 : 0 0 120.981 0 0 24 : 0 0 0 162.149 0 25 : 0 0 0 0 210.985 26 : 0 0 0 0 0 27 : 0 0 0 0 0 28 : 0 0 0 0 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 26 27 28 29 30 Row 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 0 0 0 0 0 4 : 0 0 0 0 0 5 : 0 0 0 0 0 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0 0 0 0 0 10 : 0 0 0 0 0 11 : 0 0 0 0 0 12 : 0 0 0 0 0 13 : 0 0 0 0 0 14 : 0 0 0 0 0 15 : 0 0 0 0 0 16 : 0 0 0 0 0 17 : 0 0 0 0 0 18 : 0 0 0 0 0 19 : 0 0 0 0 0 20 : 0 0 0 0 0 21 : 0 0 0 0 0 22 : 0 0 0 0 0 23 : 0 0 0 0 0 24 : 0 0 0 0 0 25 : 0 0 0 0 0 26 : 268.051 0 0 0 0 27 : 0 333.906 0 0 0 28 : 0 0 409.113 0 0 29 : 0 0 0 494.232 0 30 : 0 0 0 0 589.824 H (approximated): Col: 1 2 3 4 5 Row 1 : 2.43992e+10 -7.07665e+09 1.09491e+10 1.29531e+10 -7.46525e+08 2 :-7.07665e+09 1.82314e+10 1.95275e+09 2.69839e+09 -9.1188e+09 3 : 1.09491e+10 1.95275e+09 5.5489e+10 -4.55267e+09 4.66082e+09 4 : 1.29531e+10 2.69839e+09 -4.55267e+09 1.19698e+11 1.46683e+10 5 :-7.46525e+08 -9.1188e+09 4.66082e+09 1.46683e+10 9.93822e+10 6 : 1.72621e+10 -3.51593e+09 1.92657e+10 -1.25877e+10 -3.61646e+09 7 :-5.17716e+08 1.72358e+10 5.86515e+09 2.08529e+09 -3.05875e+09 8 : 1.40141e+09 1.3216e+10 -8.81852e+09 -1.05592e+10 6.30162e+09 9 :-2.91603e+08 -6.6672e+09 -2.25907e+09 2.16257e+09 2.0125e+10 10 :-1.15147e+10 -1.28749e+10 -9.24841e+09 -1.49808e+10 2.75873e+10 11 : 1.97756e+09 1.52285e+10 1.05668e+10 -1.72385e+10 -1.86101e+10 12 : 1.44762e+10 -1.48585e+10 -3.70832e+09 5.7963e+09 -6.0684e+09 13 : 7.23003e+09 -3.08593e+10 -4.32977e+09 4.2202e+09 -1.08153e+10 14 :-1.56819e+10 1.76938e+10 -3.70416e+07 4.39192e+09 -9.31036e+09 15 :-2.25954e+09 -1.31007e+10 -5.66229e+08 1.59659e+10 2.96599e+09 16 : 1.08423e+10 5.61588e+09 1.32951e+09 3.94669e+09 -3.08015e+09 17 : 3.12536e+09 1.18705e+09 7.2211e+08 -2.78784e+09 2.59462e+09 18 :-9.00309e+09 -5.02887e+09 1.616e+10 1.07267e+10 -2.90624e+08 19 : 2.84477e+09 5.60069e+08 1.49753e+10 9.0805e+09 2.49925e+09 20 : 1.66687e+10 -4.3878e+09 6.68223e+09 -1.42759e+10 5.16123e+08 21 :-2.65023e+09 9.54958e+09 1.03502e+10 8.33709e+09 -1.25048e+10 22 : 1.27275e+10 -2.1292e+10 -6.40373e+09 -2.81974e+09 -7.87927e+09 23 :-7.12974e+09 -1.04011e+10 9.40471e+09 1.0355e+09 -1.30898e+10 24 : 1.30302e+10 2.74779e+09 -6.51934e+09 5.23199e+09 -4.69665e+09 25 : 1.77196e+09 6.70047e+09 -1.32979e+10 6.04738e+09 -8.76418e+07 26 : 6.27327e+09 -6.60037e+08 3.21902e+09 3.47919e+09 8.06831e+09 27 :-4.50361e+09 1.41524e+10 -1.34626e+10 -3.05856e+08 -3.30392e+09 28 :-5.20117e+08 -1.34791e+09 2.20564e+10 5.14901e+09 -2.8001e+09 29 : 5.93898e+09 -1.19343e+10 -4.61166e+09 -3.55803e+08 -2.17934e+09 30 : 1.64814e+09 1.16544e+09 6.96233e+09 -1.36064e+10 9.46092e+09 Col: 6 7 8 9 10 Row 1 : 1.72621e+10 -5.17716e+08 1.40141e+09 -2.91603e+08 -1.15147e+10 2 :-3.51593e+09 1.72358e+10 1.3216e+10 -6.6672e+09 -1.28749e+10 3 : 1.92657e+10 5.86515e+09 -8.81852e+09 -2.25907e+09 -9.24841e+09 4 :-1.25877e+10 2.08529e+09 -1.05592e+10 2.16257e+09 -1.49808e+10 5 :-3.61646e+09 -3.05875e+09 6.30162e+09 2.0125e+10 2.75873e+10 6 : 3.18667e+10 -1.07505e+09 -1.00952e+10 -9.15427e+09 2.52648e+10 7 :-1.07505e+09 6.86376e+10 5.75154e+09 -2.482e+09 -1.17544e+10 8 :-1.00952e+10 5.75154e+09 -7.67355e+10 -2.22899e+10 -3.50503e+09 9 :-9.15427e+09 -2.482e+09 -2.22899e+10 -3.39969e+10 -7.53244e+09 10 : 2.52648e+10 -1.17544e+10 -3.50503e+09 -7.53244e+09 -9.1094e+09 11 : -6.3652e+08 9.46495e+09 -2.16188e+10 4.64966e+09 1.15784e+10 12 :-1.39192e+10 -7.79672e+08 -1.5609e+10 1.03381e+10 -9.96405e+08 13 :-1.56407e+09 6.68068e+09 1.32115e+10 7.53916e+09 7.35108e+09 14 : 4.14007e+08 -8.95699e+09 -2.9095e+09 6.94826e+09 -6.13164e+09 15 :-2.07731e+10 1.25179e+10 -3.43729e+09 -5.15064e+09 6.43214e+09 16 : 4.84928e+09 -1.14125e+09 -3.50716e+09 1.53798e+09 7.54122e+09 17 :-4.21172e+09 -1.99941e+09 -4.32797e+09 6.29379e+09 -1.88538e+09 18 : -4.2077e+09 -9.92098e+09 3.88031e+09 9.12121e+09 -2.025e+10 19 : 1.4845e+10 -1.03624e+10 -2.9128e+09 -1.81297e+10 -9.77305e+08 20 :-7.81837e+09 -1.12946e+08 -3.81444e+09 1.08377e+10 1.85064e+10 21 :-1.79797e+10 1.99678e+09 -1.8199e+10 -1.8823e+10 1.46084e+10 22 : 6.68406e+09 4.8602e+09 -9.76736e+09 -2.79938e+10 -1.44638e+10 23 : 1.67567e+09 9.62106e+09 1.45598e+10 -6.22857e+09 6.68523e+09 24 :-1.12924e+10 1.09425e+10 -2.08972e+09 1.38671e+10 3.17132e+09 25 : 8.8103e+09 4.2131e+09 1.64003e+09 8.07454e+09 5.03193e+09 26 : 1.55437e+10 -3.36362e+09 2.20282e+09 -9.48724e+09 9.36775e+09 27 :-1.14498e+08 -9.08876e+09 1.00012e+10 1.79438e+08 6.7048e+09 28 : 1.23251e+10 3.50794e+09 -2.72074e+09 -1.52529e+09 1.18076e+10 29 :-4.46913e+09 2.36069e+08 2.65934e+09 4.40505e+09 -2.23506e+08 30 :-4.35114e+09 5.2497e+09 1.27461e+09 9.16671e+09 6.89718e+09 Col: 11 12 13 14 15 Row 1 : 1.97756e+09 1.44762e+10 7.23003e+09 -1.56819e+10 -2.25954e+09 2 : 1.52285e+10 -1.48585e+10 -3.08593e+10 1.76938e+10 -1.31007e+10 3 : 1.05668e+10 -3.70832e+09 -4.32977e+09 -3.70416e+07 -5.66229e+08 4 :-1.72385e+10 5.7963e+09 4.2202e+09 4.39192e+09 1.59659e+10 5 :-1.86101e+10 -6.0684e+09 -1.08153e+10 -9.31036e+09 2.96599e+09 6 : -6.3652e+08 -1.39192e+10 -1.56407e+09 4.14007e+08 -2.07731e+10 7 : 9.46495e+09 -7.79672e+08 6.68068e+09 -8.95699e+09 1.25179e+10 8 :-2.16188e+10 -1.5609e+10 1.32115e+10 -2.9095e+09 -3.43729e+09 9 : 4.64966e+09 1.03381e+10 7.53916e+09 6.94826e+09 -5.15064e+09 10 : 1.15784e+10 -9.96405e+08 7.35108e+09 -6.13164e+09 6.43214e+09 11 :-4.14056e+10 -7.83163e+08 -3.22286e+09 5.39374e+09 1.1617e+10 12 :-7.83163e+08 1.12279e+11 6.39334e+09 -1.47826e+10 -4.90865e+09 13 :-3.22286e+09 6.39334e+09 4.97114e+09 7.8842e+09 -2.01153e+10 14 : 5.39374e+09 -1.47826e+10 7.8842e+09 -2.51876e+10 -9.27167e+09 15 : 1.1617e+10 -4.90865e+09 -2.01153e+10 -9.27167e+09 -2.65507e+10 16 :-1.50951e+10 -2.75566e+09 -1.58975e+10 2.11256e+10 1.32483e+10 17 : 1.55561e+10 6.57886e+09 1.28652e+10 5.77537e+08 3.95047e+07 18 : 1.54167e+10 -3.03951e+09 3.55999e+09 -1.88819e+10 9.40976e+09 19 : 1.00897e+10 9.10961e+09 5.62406e+09 1.4093e+10 -1.58152e+10 20 : 1.35071e+10 -7.30724e+09 -1.80972e+10 -9.56852e+09 -7.1305e+08 21 :-2.96266e+09 1.30718e+10 7.40615e+09 1.02703e+09 -1.78258e+10 22 :-1.94273e+09 -7.1545e+09 -2.63184e+09 1.02948e+10 -2.55283e+10 23 : 1.07333e+10 -4.32442e+09 7.36517e+09 -4.76505e+09 1.18082e+10 24 :-8.09853e+09 7.39771e+09 6.63091e+09 1.0789e+09 5.61973e+09 25 :-6.22588e+09 -7.34994e+09 2.60882e+09 1.62126e+09 1.62637e+10 26 : 1.65384e+10 1.13023e+10 7.92425e+09 -4.5616e+09 9.22631e+09 27 : 1.3729e+10 1.25362e+09 5.43582e+09 5.82685e+09 1.90098e+09 28 : 7.2986e+09 -1.11594e+09 -1.11228e+10 3.3087e+09 1.02362e+10 29 : 7.46291e+09 -6.46206e+09 -3.25075e+09 1.54875e+09 6.71335e+09 30 :-1.08994e+10 -5.11673e+09 7.2912e+09 7.74956e+08 4.12134e+08 Col: 16 17 18 19 20 Row 1 : 1.08423e+10 3.12536e+09 -9.00309e+09 2.84477e+09 1.66687e+10 2 : 5.61588e+09 1.18705e+09 -5.02887e+09 5.60069e+08 -4.3878e+09 3 : 1.32951e+09 7.2211e+08 1.616e+10 1.49753e+10 6.68223e+09 4 : 3.94669e+09 -2.78784e+09 1.07267e+10 9.0805e+09 -1.42759e+10 5 :-3.08015e+09 2.59462e+09 -2.90624e+08 2.49925e+09 5.16123e+08 6 : 4.84928e+09 -4.21172e+09 -4.2077e+09 1.4845e+10 -7.81837e+09 7 :-1.14125e+09 -1.99941e+09 -9.92098e+09 -1.03624e+10 -1.12946e+08 8 :-3.50716e+09 -4.32797e+09 3.88031e+09 -2.9128e+09 -3.81444e+09 9 : 1.53798e+09 6.29379e+09 9.12121e+09 -1.81297e+10 1.08377e+10 10 : 7.54122e+09 -1.88538e+09 -2.025e+10 -9.77305e+08 1.85064e+10 11 :-1.50951e+10 1.55561e+10 1.54167e+10 1.00897e+10 1.35071e+10 12 :-2.75566e+09 6.57886e+09 -3.03951e+09 9.10961e+09 -7.30724e+09 13 :-1.58975e+10 1.28652e+10 3.55999e+09 5.62406e+09 -1.80972e+10 14 : 2.11256e+10 5.77537e+08 -1.88819e+10 1.4093e+10 -9.56852e+09 15 : 1.32483e+10 3.95047e+07 9.40976e+09 -1.58152e+10 -7.1305e+08 16 :-1.06447e+10 -1.13124e+10 -1.45113e+10 -8.27537e+07 6.58789e+09 17 :-1.13124e+10 1.32892e+10 7.0556e+09 -8.12916e+09 -2.89385e+09 18 :-1.45113e+10 7.0556e+09 5.15264e+10 8.21668e+08 2.57084e+09 19 :-8.27537e+07 -8.12916e+09 8.21668e+08 2.34466e+10 -1.35408e+09 20 : 6.58789e+09 -2.89385e+09 2.57084e+09 -1.35408e+09 8.68757e+10 21 : 2.02178e+10 -3.90217e+08 -6.20672e+09 1.30736e+10 7.62842e+09 22 : -6.7e+09 3.87769e+08 1.09567e+09 -6.73446e+08 3.1042e+09 23 :-1.34079e+09 -1.9481e+10 1.04567e+10 -1.19459e+09 1.00125e+09 24 : 3.474e+09 -8.71767e+09 -2.43422e+10 -1.14308e+10 -8.14302e+08 25 :-5.68612e+09 1.70531e+10 4.11172e+09 -6.10873e+09 5.97694e+09 26 : 7.70965e+09 -1.51059e+10 8.70716e+09 -3.96211e+09 -6.17931e+09 27 :-7.29477e+08 7.27107e+09 1.16829e+10 7.92493e+09 -5.69342e+09 28 :-9.30194e+09 -3.55137e+09 -3.45212e+09 -8.93143e+09 -1.05165e+10 29 :-3.10884e+08 -2.81879e+10 -4.17287e+09 1.29292e+10 4.47516e+09 30 : 4.65541e+09 -4.69683e+09 -1.28342e+09 -6.06248e+09 -1.93814e+10 Col: 21 22 23 24 25 Row 1 :-2.65023e+09 1.27275e+10 -7.12974e+09 1.30302e+10 1.77196e+09 2 : 9.54958e+09 -2.1292e+10 -1.04011e+10 2.74779e+09 6.70047e+09 3 : 1.03502e+10 -6.40373e+09 9.40471e+09 -6.51934e+09 -1.32979e+10 4 : 8.33709e+09 -2.81974e+09 1.0355e+09 5.23199e+09 6.04738e+09 5 :-1.25048e+10 -7.87927e+09 -1.30898e+10 -4.69665e+09 -8.76418e+07 6 :-1.79797e+10 6.68406e+09 1.67567e+09 -1.12924e+10 8.8103e+09 7 : 1.99678e+09 4.8602e+09 9.62106e+09 1.09425e+10 4.2131e+09 8 : -1.8199e+10 -9.76736e+09 1.45598e+10 -2.08972e+09 1.64003e+09 9 : -1.8823e+10 -2.79938e+10 -6.22857e+09 1.38671e+10 8.07454e+09 10 : 1.46084e+10 -1.44638e+10 6.68523e+09 3.17132e+09 5.03193e+09 11 :-2.96266e+09 -1.94273e+09 1.07333e+10 -8.09853e+09 -6.22588e+09 12 : 1.30718e+10 -7.1545e+09 -4.32442e+09 7.39771e+09 -7.34994e+09 13 : 7.40615e+09 -2.63184e+09 7.36517e+09 6.63091e+09 2.60882e+09 14 : 1.02703e+09 1.02948e+10 -4.76505e+09 1.0789e+09 1.62126e+09 15 :-1.78258e+10 -2.55283e+10 1.18082e+10 5.61973e+09 1.62637e+10 16 : 2.02178e+10 -6.7e+09 -1.34079e+09 3.474e+09 -5.68612e+09 17 :-3.90217e+08 3.87769e+08 -1.9481e+10 -8.71767e+09 1.70531e+10 18 :-6.20672e+09 1.09567e+09 1.04567e+10 -2.43422e+10 4.11172e+09 19 : 1.30736e+10 -6.73446e+08 -1.19459e+09 -1.14308e+10 -6.10873e+09 20 : 7.62842e+09 3.1042e+09 1.00125e+09 -8.14302e+08 5.97694e+09 21 :-3.78149e+10 9.80235e+09 2.67451e+09 2.9086e+09 4.20254e+09 22 : 9.80235e+09 -2.83692e+10 -3.69988e+09 -1.83178e+10 -1.44298e+10 23 : 2.67451e+09 -3.69988e+09 6.2949e+09 6.09606e+09 2.31732e+10 24 : 2.9086e+09 -1.83178e+10 6.09606e+09 6.56395e+09 -6.7038e+09 25 : 4.20254e+09 -1.44298e+10 2.31732e+10 -6.7038e+09 -1.05568e+11 26 :-1.07229e+10 1.07015e+09 1.81941e+10 1.89627e+10 4.96075e+09 27 :-1.00128e+10 -1.1884e+10 -4.84221e+09 -1.41747e+10 -2.34034e+09 28 :-8.26065e+09 1.00294e+10 5.60867e+09 -2.6053e+09 -1.32025e+10 29 :-3.14474e+09 -1.78093e+09 2.29439e+10 1.13852e+09 -1.57102e+10 30 : 1.35005e+09 5.76629e+09 1.09758e+10 1.22559e+09 -6.99349e+09 Col: 26 27 28 29 30 Row 1 : 6.27327e+09 -4.50361e+09 -5.20117e+08 5.93898e+09 1.64814e+09 2 :-6.60037e+08 1.41524e+10 -1.34791e+09 -1.19343e+10 1.16544e+09 3 : 3.21902e+09 -1.34626e+10 2.20564e+10 -4.61166e+09 6.96233e+09 4 : 3.47919e+09 -3.05856e+08 5.14901e+09 -3.55803e+08 -1.36064e+10 5 : 8.06831e+09 -3.30392e+09 -2.8001e+09 -2.17934e+09 9.46092e+09 6 : 1.55437e+10 -1.14498e+08 1.23251e+10 -4.46913e+09 -4.35114e+09 7 :-3.36362e+09 -9.08876e+09 3.50794e+09 2.36069e+08 5.2497e+09 8 : 2.20282e+09 1.00012e+10 -2.72074e+09 2.65934e+09 1.27461e+09 9 :-9.48724e+09 1.79438e+08 -1.52529e+09 4.40505e+09 9.16671e+09 10 : 9.36775e+09 6.7048e+09 1.18076e+10 -2.23506e+08 6.89718e+09 11 : 1.65384e+10 1.3729e+10 7.2986e+09 7.46291e+09 -1.08994e+10 12 : 1.13023e+10 1.25362e+09 -1.11594e+09 -6.46206e+09 -5.11673e+09 13 : 7.92425e+09 5.43582e+09 -1.11228e+10 -3.25075e+09 7.2912e+09 14 : -4.5616e+09 5.82685e+09 3.3087e+09 1.54875e+09 7.74956e+08 15 : 9.22631e+09 1.90098e+09 1.02362e+10 6.71335e+09 4.12134e+08 16 : 7.70965e+09 -7.29477e+08 -9.30194e+09 -3.10884e+08 4.65541e+09 17 :-1.51059e+10 7.27107e+09 -3.55137e+09 -2.81879e+10 -4.69683e+09 18 : 8.70716e+09 1.16829e+10 -3.45212e+09 -4.17287e+09 -1.28342e+09 19 :-3.96211e+09 7.92493e+09 -8.93143e+09 1.29292e+10 -6.06248e+09 20 :-6.17931e+09 -5.69342e+09 -1.05165e+10 4.47516e+09 -1.93814e+10 21 :-1.07229e+10 -1.00128e+10 -8.26065e+09 -3.14474e+09 1.35005e+09 22 : 1.07015e+09 -1.1884e+10 1.00294e+10 -1.78093e+09 5.76629e+09 23 : 1.81941e+10 -4.84221e+09 5.60867e+09 2.29439e+10 1.09758e+10 24 : 1.89627e+10 -1.41747e+10 -2.6053e+09 1.13852e+09 1.22559e+09 25 : 4.96075e+09 -2.34034e+09 -1.32025e+10 -1.57102e+10 -6.99349e+09 26 : 8.96525e+09 4.03899e+09 1.12548e+09 -1.72841e+10 6.16852e+09 27 : 4.03899e+09 3.60802e+10 3.52175e+09 -1.073e+10 5.09257e+09 28 : 1.12548e+09 3.52175e+09 -5.25148e+10 -1.17035e+10 -1.12373e+10 29 :-1.72841e+10 -1.073e+10 -1.17035e+10 -4.75508e+10 -1.82488e+09 30 : 6.16852e+09 5.09257e+09 -1.12373e+10 -1.82488e+09 3.17513e+09 Problem 26 The De Jong Function F5 N = 2 X: 0.747375 0.836482 H: Col: 1 2 Row 1 : 0 0 2 : 0 0 H (approximated): Col: 1 2 Row 1 :-9.30079e-09 0 2 : 0 -1.39512e-07 Problem 27 The Schaffer Function F6 N = 2 X: 0.932551 0.912798 H: Col: 1 2 Row 1 : -0.692323 -1.055 2 : -1.055 -0.647147 H (approximated): Col: 1 2 Row 1 : -0.692329 -1.055 2 : -1.055 -0.647147 Problem 28 The Schaffer Function F7 N = 2 X: 0.0110354 0.929986 H: Col: 1 2 Row 1 : -9.18729 -0.921562 2 : -0.921562 -86.8392 H (approximated): Col: 1 2 Row 1 : -9.18748 -0.921546 2 : -0.921546 -86.8393 Problem 29 The Goldstein Price Polynomial N = 2 X: 0.157055 0.932945 H: Col: 1 2 Row 1 : 59277.8 -110049 2 : -110049 129309 H (approximated): Col: 1 2 Row 1 : 59277.8 -110049 2 : -110049 129309 Problem 30 The Branin RCOS Function N = 2 X: 0.939462 0.442184 H: Col: 1 2 Row 1 : 0.129481 2.69764 2 : 2.69764 2 H (approximated): Col: 1 2 Row 1 : 0.129222 2.69766 2 : 2.69766 1.99974 Problem 31 The Shekel SQRN5 Function N = 4 X: 0.625572 0.673998 0.441291 0.0976529 H: Col: 1 2 3 4 Row 1 : 0.520443 -0.251939 -0.431066 -0.695769 2 : -0.251939 0.589932 -0.375507 -0.60613 3 : -0.431066 -0.375507 0.1668 -1.03771 4 : -0.695769 -0.60613 -1.03771 -0.865964 H (approximated): Col: 1 2 3 4 Row 1 : 0.520449 -0.25194 -0.431068 -0.69577 2 : -0.25194 0.589938 -0.375505 -0.606129 3 : -0.431068 -0.375505 0.166808 -1.03771 4 : -0.69577 -0.606129 -1.03771 -0.865958 Problem 32 The Shekel SQRN7 Function N = 4 X: 0.116516 0.0434305 0.769686 0.312855 H: Col: 1 2 3 4 Row 1 : -0.0990738 -0.478512 -0.115933 -0.343823 2 : -0.478512 -0.175377 -0.12552 -0.37246 3 : -0.115933 -0.12552 0.312134 -0.0902948 4 : -0.343823 -0.37246 -0.0902948 0.0751239 H (approximated): Col: 1 2 3 4 Row 1 : -0.0990782 -0.478512 -0.115933 -0.343823 2 : -0.478512 -0.175381 -0.12552 -0.372461 3 : -0.115933 -0.12552 0.31213 -0.0902944 4 : -0.343823 -0.372461 -0.0902944 0.0751206 Problem 33 The Shekel SQRN10 Function N = 4 X: 0.548096 0.494725 0.88548 0.713279 H: Col: 1 2 3 4 Row 1 : -0.289562 -4.25035 -0.966108 -2.41251 2 : -4.25035 -1.23874 -1.07869 -2.6973 3 : -0.966108 -1.07869 3.2664 -0.612713 4 : -2.41251 -2.6973 -0.612713 1.98202 H (approximated): Col: 1 2 3 4 Row 1 : -0.289558 -4.25035 -0.966104 -2.41251 2 : -4.25035 -1.23874 -1.07869 -2.6973 3 : -0.966104 -1.07869 3.2664 -0.612713 4 : -2.41251 -2.6973 -0.612713 1.98202 Problem 34 The Six-Hump Camel-Back Polynomial N = 2 X: 0.461855 0.148386 H: Col: 1 2 Row 1 : 3.07959 1 2 : 1 -6.94311 H (approximated): Col: 1 2 Row 1 : 3.07959 1 2 : 1 -6.94311 Problem 35 The Shubert Function N = 2 X: 0.629636 0.626675 H: Col: 1 2 Row 1 : -75.777 508.521 2 : 508.521 -76.3314 H (approximated): Col: 1 2 Row 1 : -75.7769 508.521 2 : 508.521 -76.3313 Problem 36 The Stuckman Function N = 2 X: 0.138132 0.58407 H: Col: 1 2 Row 1 : 0 0 2 : 0 0 H (approximated): Col: 1 2 Row 1 : 0 0 2 : 0 0 Problem 37 The Easom Function N = 2 X: 0.666667 0.191613 H: Col: 1 2 Row 1 :-3.84471e-06 -6.66061e-06 2 :-6.66061e-06 -8.27752e-06 H (approximated): Col: 1 2 Row 1 :-3.84473e-06 -6.66061e-06 2 :-6.66061e-06 -8.27753e-06 Problem 38 The Bohachevsky Function #1 N = 2 X: 0.759262 0.631652 H: Col: 1 2 Row 1 : 19.1285 0 2 : 0 -1.27358 H (approximated): Col: 1 2 Row 1 : 19.1285 0 2 : 0 -1.27358 Problem 39 The Bohachevsky Function #2 N = 2 X: 0.597279 0.147598 H: Col: 1 2 Row 1 : -3.92559 20.7488 2 : 20.7488 -6.53438 H (approximated): Col: 1 2 Row 1 : -3.92559 20.7488 2 : 20.7488 -6.53438 Problem 40 The Bohachevsky Function #3 N = 2 X: 0.262722 0.276293 H: Col: 1 2 Row 1 : -18.9616 0 2 : 0 153.372 H (approximated): Col: 1 2 Row 1 : -18.9616 0 2 : 0 153.372 Problem 41 The Colville Polynomial N = 4 X: 0.728016 0.81698 0.110778 0.773853 H: Col: 1 2 3 4 Row 1 : 311.217 -291.206 0 0 2 : -291.206 220.2 0 19.8 3 : 0 0 -263.333 -39.88 4 : 0 19.8 -39.88 200.2 H (approximated): Col: 1 2 3 4 Row 1 : 311.217 -291.206 0 0 2 : -291.206 220.2 -3.8096e-05 19.8 3 : 0 -3.8096e-05 -263.334 -39.88 4 : 0 19.8 -39.88 200.2 Problem 42 The Powell 3D Function N = 3 X: 0.461749 0.537902 0.0216419 H: Col: 1 2 3 Row 1 : 0 0 0 2 : 0 0 0 3 : 0 0 0 H (approximated): Col: 1 2 3 Row 1 : 1.90688 -1.91388 -0.0245112 2 : -1.91388 1.9197 -1.55248 3 : -0.0245112 -1.55248 -0.0114526 Problem 43 The Himmelblau function. N = 2 X: 0.975278 0.754463 H: Col: 1 2 Row 1 : -27.5681 6.91896 2 : 6.91896 -15.2683 H (approximated): Col: 1 2 Row 1 : -27.5681 6.91892 2 : 6.91892 -15.2677 gradient_method_test(): For each problem, take a few steps of the gradient method. Problem 1 The Fletcher-Powell helical valley function. N = 3 Starting F(X) = 2500 Reject step, F = 3.53485e+08, S = 1 Reject step, F = 2.194e+07, S = 0.25 Reject step, F = 1.33348e+06, S = 0.0625 Reject step, F = 74367.1, S = 0.015625 Reject step, F = 2953.78, S = 0.00390625 New F(X) = 665.014, S = 0.000976562 New F(X) = 104.929, S = 0.00195312 New F(X) = 36.5365, S = 0.00390625 Reject step, F = 283.827, S = 0.0078125 New F(X) = 8.63696, S = 0.00195312 New F(X) = 5.41798, S = 0.00390625 Problem 2 The Biggs EXP6 function. N = 6 Starting F(X) = 0.77907 Reject step, F = 49.1877, S = 1 Reject step, F = 2.90414, S = 0.25 New F(X) = 0.611655, S = 0.0625 New F(X) = 0.570841, S = 0.125 Reject step, F = 3.07621, S = 0.25 New F(X) = 0.427907, S = 0.0625 New F(X) = 0.424486, S = 0.125 Reject step, F = 1.56095, S = 0.25 New F(X) = 0.350655, S = 0.0625 Problem 3 The Gaussian function. N = 3 Starting F(X) = 3.88811e-06 Reject step, F = 0.000147137, S = 1 New F(X) = 2.43372e-06, S = 0.25 Reject step, F = 1.61414e-05, S = 0.5 New F(X) = 3.84032e-08, S = 0.125 New F(X) = 2.83687e-08, S = 0.25 Reject step, F = 1.22509e-07, S = 0.5 New F(X) = 1.1893e-08, S = 0.125 New F(X) = 1.17948e-08, S = 0.25 Problem 4 The Powell badly scaled function. N = 2 Starting F(X) = 1.13526 Reject step, F = 6.45814e+16, S = 1 Reject step, F = 2.8499e+15, S = 0.25 Reject step, F = 1.61592e+14, S = 0.0625 Reject step, F = 9.8491e+12, S = 0.015625 Reject step, F = 6.11686e+11, S = 0.00390625 Reject step, F = 3.81696e+10, S = 0.000976562 Reject step, F = 2.38458e+09, S = 0.000244141 Reject step, F = 1.49003e+08, S = 6.10352e-05 Reject step, F = 9.30788e+06, S = 1.52588e-05 Reject step, F = 580596, S = 3.8147e-06 Reject step, F = 36002.1, S = 9.53674e-07 Repeated step reductions do not help. Problem abandoned. Problem 5 The Box 3-dimensional function. N = 3 Starting F(X) = 34.7325 Reject step, F = 1.99301e+14, S = 1 Reject step, F = 6654.07, S = 0.25 New F(X) = 9.95623, S = 0.0625 New F(X) = 9.59798, S = 0.125 Reject step, F = 55.2168, S = 0.25 New F(X) = 2.34354, S = 0.0625 New F(X) = 1.52119, S = 0.125 Reject step, F = 2.73449, S = 0.25 New F(X) = 0.839371, S = 0.0625 Problem 6 The variably dimensioned function. N = 4 Starting F(X) = 3222.19 Reject step, F = 6.80908e+18, S = 1 Reject step, F = 2.65511e+16, S = 0.25 Reject step, F = 1.02986e+14, S = 0.0625 Reject step, F = 3.91044e+11, S = 0.015625 Reject step, F = 1.36098e+09, S = 0.00390625 Reject step, F = 3.23154e+06, S = 0.000976562 New F(X) = 637.237, S = 0.000244141 New F(X) = 38.189, S = 0.000488281 New F(X) = 0.618963, S = 0.000976562 New F(X) = 0.333017, S = 0.00195312 New F(X) = 0.119057, S = 0.00390625 Problem 7 The Watson function. N = 4 Starting F(X) = 30 Reject step, F = 4.01347e+09, S = 1 Reject step, F = 1.42856e+07, S = 0.25 Reject step, F = 38072.7, S = 0.0625 Reject step, F = 32.378, S = 0.015625 New F(X) = 6.39124, S = 0.00390625 New F(X) = 2.70405, S = 0.0078125 New F(X) = 1.138, S = 0.015625 New F(X) = 0.857861, S = 0.03125 Reject step, F = 2.19693, S = 0.0625 New F(X) = 0.734496, S = 0.015625 Problem 8 The Penalty Function #1. N = 4 Starting F(X) = 885.063 Reject step, F = 1.7449e+11, S = 1 Reject step, F = 6.14873e+08, S = 0.25 Reject step, F = 1.54503e+06, S = 0.0625 New F(X) = 479.863, S = 0.015625 Reject step, F = 4447.8, S = 0.03125 New F(X) = 3.82063, S = 0.0078125 New F(X) = 2.09932, S = 0.015625 New F(X) = 0.790816, S = 0.03125 New F(X) = 0.192804, S = 0.0625 Problem 9 The Penalty Function #2. N = 4 Starting F(X) = 2.34001 Reject step, F = 753818, S = 1 Reject step, F = 1478.08, S = 0.25 New F(X) = 0.517244, S = 0.0625 New F(X) = 0.470693, S = 0.125 Reject step, F = 0.573029, S = 0.25 New F(X) = 0.398558, S = 0.0625 New F(X) = 0.3876, S = 0.125 Reject step, F = 0.527121, S = 0.25 New F(X) = 0.325491, S = 0.0625 Problem 10 The Brown Badly Scaled Function. N = 2 Starting F(X) = 9.99998e+11 Reject step, F = 5.00003e+12, S = 1 New F(X) = 4.99999e+11, S = 0.25 Reject step, F = 1.5625e+34, S = 0.5 Reject step, F = 9.76567e+32, S = 0.125 Reject step, F = 6.10355e+31, S = 0.03125 Reject step, F = 3.81472e+30, S = 0.0078125 Reject step, F = 2.3842e+29, S = 0.00195312 Reject step, F = 1.49013e+28, S = 0.000488281 Reject step, F = 9.31328e+26, S = 0.00012207 Reject step, F = 5.8208e+25, S = 3.05176e-05 Reject step, F = 3.638e+24, S = 7.62939e-06 Reject step, F = 2.27375e+23, S = 1.90735e-06 Reject step, F = 1.42108e+22, S = 4.76837e-07 Repeated step reductions do not help. Problem abandoned. Problem 11 The Brown and Dennis Function. N = 4 Starting F(X) = 7.92669e+06 Reject step, F = 2.41869e+28, S = 1 Reject step, F = 9.44783e+25, S = 0.25 Reject step, F = 3.69025e+23, S = 0.0625 Reject step, F = 1.44103e+21, S = 0.015625 Reject step, F = 5.62158e+18, S = 0.00390625 Reject step, F = 2.1844e+16, S = 0.000976562 Reject step, F = 8.35789e+13, S = 0.000244141 Reject step, F = 3.02247e+11, S = 6.10352e-05 Reject step, F = 9.54527e+08, S = 1.52588e-05 New F(X) = 4.91737e+06, S = 3.8147e-06 Reject step, F = 2.31819e+07, S = 7.62939e-06 New F(X) = 2.41183e+06, S = 1.90735e-06 New F(X) = 2.17692e+06, S = 3.8147e-06 New F(X) = 1.80533e+06, S = 7.62939e-06 New F(X) = 1.31682e+06, S = 1.52588e-05 Problem 12 The Gulf R&D Function. N = 3 Starting F(X) = 1.20538 Reject step, F = 32.835, S = 1 Reject step, F = 31.8463, S = 0.25 Reject step, F = 8.08284, S = 0.0625 Reject step, F = 1.38377, S = 0.015625 New F(X) = 1.13451, S = 0.00390625 New F(X) = 1.12838, S = 0.0078125 Reject step, F = 1.1298, S = 0.015625 New F(X) = 1.12698, S = 0.00390625 New F(X) = 1.12623, S = 0.0078125 New F(X) = 1.12494, S = 0.015625 Problem 13 The Trigonometric Function. N = 4 Starting F(X) = 0.0130531 New F(X) = 0.00543699, S = 1 Reject step, F = 0.0126427, S = 2 New F(X) = 0.00364804, S = 0.5 New F(X) = 0.00281509, S = 1 Reject step, F = 0.00389188, S = 2 New F(X) = 0.00216898, S = 0.5 New F(X) = 0.00150748, S = 1 Problem 14 The Extended Rosenbrock parabolic valley Function. N = 4 Starting F(X) = 48.4 Reject step, F = 4.20965e+11, S = 1 Reject step, F = 1.51723e+09, S = 0.25 Reject step, F = 4.15758e+06, S = 0.0625 Reject step, F = 1087.09, S = 0.015625 Reject step, F = 299.282, S = 0.00390625 New F(X) = 10.2022, S = 0.000976562 New F(X) = 10.094, S = 0.00195312 Reject step, F = 25.4617, S = 0.00390625 New F(X) = 8.22808, S = 0.000976562 New F(X) = 8.21617, S = 0.00195312 Reject step, F = 8.25558, S = 0.00390625 New F(X) = 8.20227, S = 0.000976562 Problem 15 The Extended Powell Singular Quartic Function. N = 4 Starting F(X) = 215 Reject step, F = 1.42163e+12, S = 1 Reject step, F = 5.33939e+09, S = 0.25 Reject step, F = 1.77586e+07, S = 0.0625 Reject step, F = 34089.1, S = 0.015625 New F(X) = 31.1898, S = 0.00390625 New F(X) = 19.3828, S = 0.0078125 Reject step, F = 22.8878, S = 0.015625 New F(X) = 14.7456, S = 0.00390625 New F(X) = 11.2532, S = 0.0078125 New F(X) = 7.99787, S = 0.015625 Problem 16 The Beale Function. N = 2 Starting F(X) = 14.2031 Reject step, F = 3.66842e+08, S = 1 Reject step, F = 44499.3, S = 0.25 New F(X) = 4.76686, S = 0.0625 New F(X) = 2.72086, S = 0.125 New F(X) = 1.93345, S = 0.25 Reject step, F = 12579, S = 0.5 Reject step, F = 3.15478, S = 0.125 New F(X) = 0.702596, S = 0.03125 New F(X) = 0.423079, S = 0.0625 Problem 17 The Wood Function. N = 4 Starting F(X) = 19192 Reject step, F = 3.30367e+18, S = 1 Reject step, F = 1.28635e+16, S = 0.25 Reject step, F = 4.96052e+13, S = 0.0625 Reject step, F = 1.83968e+11, S = 0.015625 Reject step, F = 5.80056e+08, S = 0.00390625 Reject step, F = 849067, S = 0.000976562 New F(X) = 160.276, S = 0.000244141 New F(X) = 130.004, S = 0.000488281 New F(X) = 88.6572, S = 0.000976562 New F(X) = 49.6193, S = 0.00195312 New F(X) = 34.7912, S = 0.00390625 Problem 18 The Chebyquad Function N = 4 Starting F(X) = 0.0711839 Reject step, F = 1032.51, S = 1 Reject step, F = 0.0905045, S = 0.25 New F(X) = 0.0385551, S = 0.0625 New F(X) = 0.00447472, S = 0.125 Reject step, F = 0.0678796, S = 0.25 New F(X) = 0.000710858, S = 0.0625 New F(X) = 0.000119982, S = 0.125 New F(X) = 7.6066e-05, S = 0.25 Problem 19 The Leon cubic valley function N = 2 Starting F(X) = 57.8384 Reject step, F = 6.38402e+18, S = 1 Reject step, F = 1.50613e+15, S = 0.25 Reject step, F = 3.20081e+11, S = 0.0625 Reject step, F = 4.36975e+07, S = 0.015625 Reject step, F = 1323.19, S = 0.00390625 Reject step, F = 91.9179, S = 0.000976562 New F(X) = 5.32434, S = 0.000244141 New F(X) = 4.06994, S = 0.000488281 New F(X) = 4.06922, S = 0.000976562 Reject step, F = 4.20001, S = 0.00195312 New F(X) = 4.05256, S = 0.000488281 New F(X) = 4.05105, S = 0.000976562 Problem 20 The Gregory and Karney Tridiagonal Matrix Function N = 4 Starting F(X) = 0 Reject step, F = 0, S = 1 New F(X) = -0.75, S = 0.25 New F(X) = -1.4375, S = 0.5 New F(X) = -2.3125, S = 1 New F(X) = -3.0625, S = 2 Reject step, F = 16.9375, S = 4 New F(X) = -3.125, S = 1 Problem 21 The Hilbert Matrix Function F = x'Ax N = 4 Starting F(X) = 5.07619 Reject step, F = 19.9153, S = 1 New F(X) = 0.403688, S = 0.25 New F(X) = 0.142298, S = 0.5 Reject step, F = 0.338863, S = 1 New F(X) = 0.0591186, S = 0.25 New F(X) = 0.0387393, S = 0.5 New F(X) = 0.0213893, S = 1 Problem 22 The De Jong Function F1 N = 3 Starting F(X) = 52.4288 Reject step, F = 52.4288, S = 1 New F(X) = 13.1072, S = 0.25 New F(X) = 0, S = 0.5 Terminate because of zero gradient. Problem 23 The De Jong Function F2 N = 2 Starting F(X) = 469.952 Reject step, F = 9.64271e+14, S = 1 Reject step, F = 3.71125e+12, S = 0.25 Reject step, F = 1.36504e+10, S = 0.0625 Reject step, F = 4.12828e+07, S = 0.015625 Reject step, F = 38979.1, S = 0.00390625 Reject step, F = 559.458, S = 0.000976562 New F(X) = 28.2592, S = 0.000244141 New F(X) = 6.26485, S = 0.000488281 New F(X) = 6.23854, S = 0.000976562 Reject step, F = 6.85596, S = 0.00195312 New F(X) = 6.14669, S = 0.000488281 New F(X) = 6.1442, S = 0.000976562 Problem 24 The De Jong Function F3, (discontinuous) N = 5 Starting F(X) = -2 Terminate because of zero gradient. Problem 25 The De Jong Function F4 (with Gaussian noise) N = 30 Starting F(X) = 284.843 Reject step, F = 1.79661e+11, S = 1 Reject step, F = 6.55246e+08, S = 0.25 Reject step, F = 1.92382e+06, S = 0.0625 Reject step, F = 1931.93, S = 0.015625 New F(X) = 43.2751, S = 0.00390625 New F(X) = 22.0326, S = 0.0078125 New F(X) = 10.0258, S = 0.015625 New F(X) = 3.74085, S = 0.03125 New F(X) = 1.1543, S = 0.0625 Problem 26 The De Jong Function F5 N = 2 Starting F(X) = 0.002 Reject step, F = 0.002, S = 1 Reject step, F = 0.002, S = 0.25 Reject step, F = 0.002, S = 0.0625 Reject step, F = 0.002, S = 0.015625 Reject step, F = 0.002, S = 0.00390625 Reject step, F = 0.002, S = 0.000976562 Reject step, F = 0.002, S = 0.000244141 Reject step, F = 0.002, S = 6.10352e-05 Reject step, F = 0.002, S = 1.52588e-05 Reject step, F = 0.002, S = 3.8147e-06 Reject step, F = 0.002, S = 9.53674e-07 Repeated step reductions do not help. Problem abandoned. Problem 27 The Schaffer Function F6 N = 2 Starting F(X) = 0.868394 New F(X) = 0.720791, S = 1 New F(X) = 0.16564, S = 2 Reject step, F = 0.726596, S = 4 New F(X) = 0.134207, S = 1 Reject step, F = 0.1548, S = 2 New F(X) = 0.127459, S = 0.5 New F(X) = 0.127105, S = 1 Problem 28 The Schaffer Function F7 N = 2 Starting F(X) = 4.56376 Reject step, F = 7.63075, S = 1 Reject step, F = 5.68423, S = 0.25 New F(X) = 3.58955, S = 0.0625 New F(X) = 3.47981, S = 0.125 Reject step, F = 3.77236, S = 0.25 New F(X) = 3.41225, S = 0.0625 New F(X) = 3.41115, S = 0.125 Reject step, F = 3.41547, S = 0.25 New F(X) = 3.41024, S = 0.0625 Problem 29 The Goldstein Price Polynomial N = 2 Starting F(X) = 2738.74 Reject step, F = 2.83955e+36, S = 1 Reject step, F = 4.33329e+31, S = 0.25 Reject step, F = 6.61493e+26, S = 0.0625 Reject step, F = 1.01098e+22, S = 0.015625 Reject step, F = 1.54971e+17, S = 0.00390625 Reject step, F = 2.3406e+12, S = 0.000976562 Reject step, F = 2.28075e+07, S = 0.000244141 New F(X) = 41.6044, S = 6.10352e-05 New F(X) = 32.8631, S = 0.00012207 New F(X) = 30.4646, S = 0.000244141 New F(X) = 28.8325, S = 0.000488281 New F(X) = 24.4628, S = 0.000976562 Problem 30 The Branin RCOS Function N = 2 Starting F(X) = 60.3563 New F(X) = 2.31441, S = 1 Reject step, F = 2868.71, S = 2 Reject step, F = 96.4597, S = 0.5 Reject step, F = 4.45963, S = 0.125 New F(X) = 1.39707, S = 0.03125 New F(X) = 1.2446, S = 0.0625 New F(X) = 1.12647, S = 0.125 Reject step, F = 2.05597, S = 0.25 New F(X) = 1.01744, S = 0.0625 Problem 31 The Shekel SQRN5 Function N = 4 Starting F(X) = -0.167128 New F(X) = -0.170213, S = 1 New F(X) = -0.176862, S = 2 New F(X) = -0.192492, S = 4 New F(X) = -0.238518, S = 8 New F(X) = -0.608952, S = 16 Problem 32 The Shekel SQRN7 Function N = 4 Starting F(X) = -0.215144 New F(X) = -0.219776, S = 1 New F(X) = -0.229882, S = 2 New F(X) = -0.254334, S = 4 New F(X) = -0.332969, S = 8 New F(X) = -1.61138, S = 16 Problem 33 The Shekel SQRN10 Function N = 4 Starting F(X) = -0.270985 New F(X) = -0.277271, S = 1 New F(X) = -0.291109, S = 2 New F(X) = -0.325399, S = 4 New F(X) = -0.446838, S = 8 New F(X) = -2.12675, S = 16 Problem 34 The Six-Hump Camel-Back Polynomial N = 2 Starting F(X) = 0.665625 Reject step, F = 1110.77, S = 1 Reject step, F = 6.97285, S = 0.25 New F(X) = -0.0842702, S = 0.0625 Reject step, F = -0.0528379, S = 0.125 New F(X) = -0.176424, S = 0.03125 New F(X) = -0.214842, S = 0.0625 Reject step, F = -0.213341, S = 0.125 New F(X) = -0.215414, S = 0.03125 New F(X) = -0.215455, S = 0.0625 Problem 35 The Shubert Function N = 2 Starting F(X) = -3.10442 Reject step, F = 105.929, S = 1 Reject step, F = -2.66027, S = 0.25 Reject step, F = 7.35794, S = 0.0625 New F(X) = -17.8712, S = 0.015625 Reject step, F = 32.6487, S = 0.03125 Reject step, F = -7.26875, S = 0.0078125 Reject step, F = -11.5614, S = 0.00195312 New F(X) = -28.4214, S = 0.000488281 New F(X) = -32.3787, S = 0.000976562 Reject step, F = -31.314, S = 0.00195312 New F(X) = -32.7401, S = 0.000488281 New F(X) = -32.7658, S = 0.000976562 Problem 36 The Stuckman Function N = 2 Starting F(X) = 8 Terminate because of zero gradient. Problem 37 The Easom Function N = 2 Starting F(X) = -4.50356e-06 New F(X) = -4.50417e-06, S = 1 New F(X) = -4.50538e-06, S = 2 New F(X) = -4.50781e-06, S = 4 New F(X) = -4.51266e-06, S = 8 New F(X) = -4.5224e-06, S = 16 Problem 38 The Bohachevsky Function #1 N = 2 Starting F(X) = 2.55 Reject step, F = 24.0165, S = 1 New F(X) = 1.49112, S = 0.25 New F(X) = 0.453987, S = 0.5 Reject step, F = 3.66745, S = 1 Reject step, F = 1.20011, S = 0.25 New F(X) = 0.418581, S = 0.0625 Reject step, F = 0.441209, S = 0.125 New F(X) = 0.413065, S = 0.03125 New F(X) = 0.412982, S = 0.0625 Problem 39 The Bohachevsky Function #2 N = 2 Starting F(X) = 4.23635 Reject step, F = 12.9053, S = 1 New F(X) = 0.47813, S = 0.25 Reject step, F = 1.21855, S = 0.5 Reject step, F = 0.549567, S = 0.125 New F(X) = 0.461668, S = 0.03125 New F(X) = 0.460761, S = 0.0625 Reject step, F = 0.462524, S = 0.125 New F(X) = 0.460323, S = 0.03125 New F(X) = 0.46031, S = 0.0625 Problem 40 The Bohachevsky Function #3 N = 2 Starting F(X) = 3.55 Reject step, F = 25.0165, S = 1 New F(X) = 2.49112, S = 0.25 New F(X) = 1.45399, S = 0.5 Reject step, F = 4.66745, S = 1 Reject step, F = 2.20011, S = 0.25 New F(X) = 1.41858, S = 0.0625 Reject step, F = 1.44121, S = 0.125 New F(X) = 1.41307, S = 0.03125 New F(X) = 1.41298, S = 0.0625 Problem 41 The Colville Polynomial N = 4 Starting F(X) = 239.775 Reject step, F = 2.91811e+11, S = 1 Reject step, F = 1.1019e+09, S = 0.25 Reject step, F = 3.80455e+06, S = 0.0625 Reject step, F = 11429.3, S = 0.015625 New F(X) = 59.3805, S = 0.00390625 Reject step, F = 66.579, S = 0.0078125 New F(X) = 40.7969, S = 0.00195312 Reject step, F = 51.299, S = 0.00390625 New F(X) = 21.6407, S = 0.000976562 New F(X) = 13.1751, S = 0.00195312 New F(X) = 11.9598, S = 0.00390625 Problem 42 The Powell 3D Function N = 3 Starting F(X) = 2.5 Reject step, F = 3.81991, S = 1 New F(X) = 1.77695, S = 0.25 Reject step, F = 3.02853, S = 0.5 New F(X) = 1.21714, S = 0.125 New F(X) = 1.12113, S = 0.25 Reject step, F = 1.47114, S = 0.5 New F(X) = 1.05896, S = 0.125 New F(X) = 1.02273, S = 0.25 Problem 43 The Himmelblau function. N = 2 Starting F(X) = 44.7122 Reject step, F = 1.77972e+06, S = 1 Reject step, F = 10956.3, S = 0.25 Reject step, F = 72.551, S = 0.0625 New F(X) = 22.184, S = 0.015625 New F(X) = 0.311905, S = 0.03125 Reject step, F = 3.05292, S = 0.0625 New F(X) = 0.00276039, S = 0.015625 Reject step, F = 0.0049786, S = 0.03125 New F(X) = 0.000496512, S = 0.0078125 New F(X) = 1.51994e-05, S = 0.015625 test_opt_test(): Normal end of execution. 07-Jun-2023 07:02:41