08-Jan-2022 10:29:21 test_opt_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 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_title_test(): Normal end of execution. 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_n_test(): Normal end of execution. 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_start_test(): Normal end of execution. 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) = -5 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_f_test(): Normal end of execution. 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) = 2.55186e-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) = 9.49342e-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 = ( 9.42478, 2.475 ) 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 = ( 3.88437, 4.21761 ) F(X_MIN) = 97 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_sol_test(): Normal end of execution. 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: 0.792207 0.959492 0.655741 G: -116.017 159.145 -147.847 GDIF: -116.017 159.145 -147.847 Problem 2: "The Biggs EXP6 function." X: 0.0357117 0.849129 0.933993 0.678735 0.75774 0.743132 G: -6.33433 1.8079 4.88472 -1.29257 -2.20204 1.54946 GDIF: -6.33433 1.8079 4.88472 -1.29257 -2.20204 1.54946 Problem 3: "The Gaussian function." X: 0.392227 0.655478 0.171187 G: 0.343735 -0.141009 0.0821316 GDIF: 0.343735 -0.141009 0.0821316 Problem 4: "The Powell badly scaled function." X: 0.706046 0.0318328 G: 142454 3.15962e+06 GDIF: 142454 3.15962e+06 Problem 5: "The Box 3-dimensional function." X: 0.276923 0.0461714 0.0971318 G: 1.70914 -2.02666 1.7299 GDIF: 1.70914 -2.02666 1.7299 Problem 6: "The variably dimensioned function." X: 0.823458 0.694829 0.317099 0.950222 G: -118.213 -236.331 -354.947 -471.541 GDIF: -118.213 -236.331 -354.947 -471.541 Problem 7: "The Watson function." X: 0.0344461 0.438744 0.381558 0.765517 G: -15.6803 -10.2033 2.86411 7.82956 GDIF: -15.6803 -10.2033 2.86411 7.82956 Problem 8: "The Penalty Function #1." X: 0.7952 0.186873 0.489764 0.445586 G: 2.72174 0.639597 1.67632 1.52511 GDIF: 2.72174 0.639597 1.67632 1.52511 Problem 9: "The Penalty Function #2." X: 0.646313 0.709365 0.754687 0.276025 G: 36.0083 28.9061 20.5019 3.74927 GDIF: 36.0083 28.9061 20.5019 3.74927 Problem 10: "The Brown Badly Scaled Function." X: 0.679703 0.655098 G: -2e+06 -0.803314 GDIF: -2.00203e+06 0 Problem 11: "The Brown and Dennis Function." X: 0.162612 0.118998 0.498364 0.959744 G: -1.38164e+06 -5.1958e+06 30938.1 -7079.74 GDIF: -1.38164e+06 -5.1958e+06 30938.1 -7079.72 Problem 12: "The Gulf R&D Function." X: 0.340386 0.585268 0.223812 G: -3.19575 -0.00793714 3.73468 GDIF: -3.19575 -0.00793732 3.73468 Problem 13: "The Trigonometric Function." X: 0.751267 0.255095 0.505957 0.699077 G: 3.021 0.687004 2.80218 6.32925 GDIF: 3.021 0.687004 2.80218 6.32925 Problem 14: "The Extended Rosenbrock parabolic valley Function." X: 0.890903 0.959291 0.547216 0.138624 G: -59.2255 33.1166 34.2958 -32.1641 GDIF: -59.2255 33.1166 34.2958 -32.1641 Problem 15: "The Extended Powell Singular Quartic Function." X: 0.149294 0.257508 0.840717 0.254282 G: 5.40246 42.9391 28.9612 -5.81806 GDIF: 5.40246 42.9391 28.9612 -5.81806 Problem 16: "The Beale Function." X: 0.814285 0.243525 G: -7.72177 3.14484 GDIF: -7.72177 3.14484 Problem 17: "The Wood Function." X: 0.929264 0.349984 0.196595 0.251084 G: 190.747 -130.668 -16.6417 10.2397 GDIF: 190.747 -130.668 -16.6417 10.2397 Problem 18: "The Chebyquad Function" X: 0.616045 0.473289 0.35166 0.830829 G: -0.917018 0.867374 2.03545 -1.55809 GDIF: -0.917018 0.867374 2.03545 -1.55809 Problem 19: "The Leon cubic valley function" X: 0.585264 0.549724 G: -72.6076 69.8501 GDIF: -72.6076 69.8501 Problem 20: "The Gregory and Karney Tridiagonal Matrix Function" X: 0.917194 0.285839 0.7572 0.753729 G: -1.36865 -1.10272 0.474832 0.750258 GDIF: -0.737291 -2.20543 0.949665 1.50052 Problem 21: "The Hilbert Matrix Function F = x'Ax" X: 0.380446 0.567822 0.0758543 0.0539501 G: 1.40626 0.818501 0.585866 0.458051 GDIF: 1.40626 0.818501 0.585866 0.458051 Problem 22: "The De Jong Function F1" X: 0.530798 0.779167 0.934011 G: 1.0616 1.55833 1.86802 GDIF: 1.0616 1.55833 1.86802 Problem 23: "The De Jong Function F2" X: 0.129906 0.568824 G: -30.4208 110.39 GDIF: -30.4208 110.39 Problem 24: "The De Jong Function F3, (discontinuous)" X: 0.469391 0.0119021 0.337123 0.162182 0.794285 G: 0 0 0 0 0 GDIF: 0 0 0 0 0 Problem 25: "The De Jong Function F4 (with Gaussian noise)" X: 0.311215 0.528533 0.165649 0.601982 0.262971 0.654079 0.689215 0.748152 0.450542 0.0838214 0.228977 0.913337 0.152378 0.825817 0.538342 0.996135 0.0781755 0.442678 0.106653 0.961898 0.00463422 0.77491 0.817303 0.868695 0.0844358 0.399783 0.25987 0.800068 0.431414 0.910648 G: 0.120571 1.18115 0.0545438 3.49036 0.36371 6.71587 9.16687 13.4004 3.29236 0.0235572 0.528236 36.5708 0.18398 31.5384 9.3611 63.2607 0.0324879 6.24593 0.0921998 71.1995 8.36008e-06 40.9484 50.227 62.9322 0.0601978 6.64516 1.89537 57.3587 9.31408 90.6217 GDIF: 0.120571 1.18115 0.0545444 3.49036 0.363709 6.71587 9.16687 13.4004 3.29236 0.0235572 0.528236 36.5708 0.183981 31.5384 9.3611 63.2607 0.0324886 6.24593 0.0922002 71.1995 8.54348e-06 40.9484 50.227 62.9322 0.0601976 6.64516 1.89537 57.3587 9.31408 90.6217 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: -1.87428e+06 -1.309e+06 450547 1.16708e+07 -1.17826e+07 -8.06575e+06 3.79376e+07 -3.47012e+06 -5.41206e+06 1.75992e+07 -9.26867e+06 -6.55683e+07 -6.27249e+06 2.90967e+07 5.7978e+07 2.61969e+07 1.09272e+07 3.50895e+07 -7.40029e+06 1.29015e+07 1.1639e+06 -6.45415e+06 -4.70968e+06 -6.38448e+06 -4.69414e+07 4.0211e+07 9.71437e+06 -3.37305e+06 -2.26659e+07 2.21579e+07 Problem 26: "The De Jong Function F5" X: 0.521136 0.231594 G: 1.80258e-12 -1.14131e-08 GDIF: 9.56648e-12 -1.14256e-08 Problem 27: "The Schaffer Function F6" X: 0.488898 0.62406 G: 0.615846 0.786105 GDIF: 0.615846 0.786105 Problem 28: "The Schaffer Function F7" X: 0.679136 0.395515 G: 8.65882 5.04273 GDIF: 8.65882 5.04273 Problem 29: "The Goldstein Price Polynomial" X: 0.367437 0.987982 G: -31046 40567.7 GDIF: -31046 40567.7 Problem 30: "The Branin RCOS Function" X: 0.0377389 0.885168 G: -16.3541 -10.1099 GDIF: -16.3541 -10.1099 Problem 31: "The Shekel SQRN5 Function" X: 0.913287 0.796184 0.0987123 0.261871 G: -0.0711994 -0.162968 -0.703663 -0.577827 GDIF: -0.0711994 -0.162968 -0.703663 -0.577827 Problem 32: "The Shekel SQRN7 Function" X: 0.335357 0.679728 0.136553 0.721227 G: -0.548835 -0.269426 -0.709665 -0.234203 GDIF: -0.548835 -0.269426 -0.709665 -0.234203 Problem 33: "The Shekel SQRN10 Function" X: 0.106762 0.653757 0.494174 0.779052 G: -0.896226 -0.352355 -0.510864 -0.226807 GDIF: -0.896226 -0.352355 -0.510864 -0.226807 Problem 34: "The Six-Hump Camel-Back Polynomial" X: 0.715037 0.903721 G: 3.92695 5.29453 GDIF: 3.92695 5.29453 Problem 35: "The Shubert Function" X: 0.890923 0.334163 G: 35.9777 -0.0500692 GDIF: 35.9777 -0.0500689 Problem 36: "The Stuckman Function" X: 0.609867 0.617666 G: 0 0 GDIF: 0 0 Problem 37: "The Easom Function" X: 0.859442 0.805489 G: -3.59246e-05 -3.83217e-05 GDIF: -3.59246e-05 -3.83217e-05 Problem 38: "The Bohachevsky Function #1" X: 0.576722 0.182922 G: -0.966479 4.48446 GDIF: -0.966479 4.48446 Problem 39: "The Bohachevsky Function #2" X: 0.239932 0.886512 G: 0.794092 5.92214 GDIF: 0.794092 5.92214 Problem 40: "The Bohachevsky Function #3" X: 0.0286742 0.489901 G: 0.812188 3.55004 GDIF: 0.812188 3.55004 Problem 41: "The Colville Polynomial" X: 0.167927 0.978681 0.712694 0.500472 G: -65.5088 179.775 1.33986 -11.8557 GDIF: -65.5088 179.775 1.33986 -11.8557 Problem 42: "The Powell 3D Function" X: 0.471088 0.0596189 0.681972 G: 0.601881 -1.67094 -0.0934582 GDIF: 0.601881 -1.67094 -0.0934582 Problem 43: "The Himmelblau function." X: 0.0424311 0.0714455 G: -15.7595 -23.8404 GDIF: -15.7595 -23.8404 P00_GDIF_TEST Normal end of execution. 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: 0.52165 0.09673 0.818149 H: Col: 1 2 3 Row 1 : 33.8918 300.577 109.388 2 : 300.577 1788.96 -589.914 3 : 109.388 -589.914 202 H (approximated): Col: 1 2 3 Row 1 : 33.8922 300.577 109.388 2 : 300.577 1788.96 -589.914 3 : 109.388 -589.914 202 Problem 2 The Biggs EXP6 function. N = 6 X: 0.817547 0.72244 0.149865 0.659605 0.518595 0.972975 H: Col: 1 2 3 4 5 Row 1 : -0.130189 -0.373194 2.08371 0.774882 0.661098 2 : -0.373194 2.76022 3.4105 -6.60074 -3.17314 3 : 2.08371 3.4105 9.9151 -10.3902 -5.85223 4 : 0.774882 -6.60074 -10.3902 10.8996 6.29047 5 : 0.661098 -3.17314 -5.85223 6.29047 4.01961 6 : -0.901409 4.26448 11.5277 -12.1208 -4.1056 Col: 6 Row 1 : -0.901409 2 : 4.26448 3 : 11.5277 4 : -12.1208 5 : -4.1056 6 : 13.5482 H (approximated): Col: 1 2 3 4 5 Row 1 : -0.130184 -0.373196 2.08372 0.774876 0.661095 2 : -0.373196 2.76024 3.41051 -6.60073 -3.17314 3 : 2.08372 3.41051 9.9151 -10.3902 -5.85224 4 : 0.774876 -6.60073 -10.3902 10.8996 6.29047 5 : 0.661095 -3.17314 -5.85224 6.29047 4.01964 6 : -0.901404 4.26447 11.5277 -12.1208 -4.1056 Col: 6 Row 1 : -0.901404 2 : 4.26447 3 : 11.5277 4 : -12.1208 5 : -4.1056 6 : 13.5482 Problem 3 The Gaussian function. N = 3 X: 0.648991 0.800331 0.453798 H: Col: 1 2 3 Row 1 : 7.92493 -2.33112 0.5742 2 : -2.33112 1.42385 0.144578 3 : 0.5742 0.144578 0.745854 H (approximated): Col: 1 2 3 Row 1 : 7.92493 -2.33112 0.574199 2 : -2.33112 1.42386 0.144579 3 : 0.574199 0.144579 0.745859 Problem 4 The Powell badly scaled function. N = 2 X: 0.432392 0.825314 H: Col: 1 2 Row 1 : 1.36229e+08 1.42723e+08 2 : 1.42723e+08 3.73925e+07 H (approximated): Col: 1 2 Row 1 : 1.36229e+08 1.42723e+08 2 : 1.42723e+08 3.73925e+07 Problem 5 The Box 3-dimensional function. N = 3 X: 0.0834698 0.133171 0.173389 H: Col: 1 2 3 Row 1 : 6.43571 -6.50108 5.16498 2 : -6.50108 6.56629 -5.00236 3 : 5.16498 -5.00236 6.12801 H (approximated): Col: 1 2 3 Row 1 : 6.43571 -6.50108 5.16498 2 : -6.50108 6.56629 -5.00236 3 : 5.16498 -5.00236 6.12801 Problem 6 The variably dimensioned function. N = 4 X: 0.390938 0.83138 0.803364 0.0604712 H: Col: 1 2 3 4 Row 1 : 340.359 676.717 1015.08 1353.43 2 : 676.717 1355.43 2030.15 2706.87 3 : 1015.08 2030.15 3047.23 4060.3 4 : 1353.43 2706.87 4060.3 5415.74 H (approximated): Col: 1 2 3 4 Row 1 : 340.355 676.718 1015.07 1353.43 2 : 676.718 1355.44 2030.15 2706.87 3 : 1015.07 2030.15 3047.23 4060.3 4 : 1353.43 2706.87 4060.3 5415.74 Problem 7 The Watson function. N = 4 X: 0.399258 0.526876 0.416799 0.65686 H: Col: 1 2 3 4 Row 1 : 350.778 133.964 55.561 5.16134 2 : 133.964 115.561 65.1613 29.963 3 : 55.561 65.1613 50.3078 34.0502 4 : 5.16134 29.963 34.0502 31.8775 H (approximated): Col: 1 2 3 4 Row 1 : 350.778 133.964 55.561 5.16132 2 : 133.964 115.561 65.1614 29.963 3 : 55.561 65.1614 50.308 34.0502 4 : 5.16132 29.963 34.0502 31.8775 Problem 8 The Penalty Function #1. N = 4 X: 0.627973 0.291984 0.431651 0.0154871 H: Col: 1 2 3 4 Row 1 : 4.8195 1.46687 2.16852 0.077804 2 : 1.46687 2.34673 1.00828 0.036176 3 : 2.16852 1.00828 3.15527 0.0534803 4 : 0.077804 0.036176 0.0534803 1.66661 H (approximated): Col: 1 2 3 4 Row 1 : 4.8195 1.46687 2.16852 0.077804 2 : 1.46687 2.34673 1.00828 0.0361759 3 : 2.16852 1.00828 3.15527 0.0534803 4 : 0.077804 0.0361759 0.0534803 1.66661 Problem 9 The Penalty Function #2. N = 4 X: 0.984064 0.167168 0.106216 0.37241 H: Col: 1 2 3 4 Row 1 : 175.851 15.7924 6.68951 11.7272 2 : 15.7924 39.4354 0.852289 1.49412 3 : 6.68951 0.852289 25.3099 0.632896 4 : 11.7272 1.49412 0.632896 13.584 H (approximated): Col: 1 2 3 4 Row 1 : 175.851 15.7924 6.68951 11.7272 2 : 15.7924 39.4354 0.852322 1.49413 3 : 6.68951 0.852322 25.3099 0.632889 4 : 11.7272 1.49413 0.632889 13.584 Problem 10 The Brown Badly Scaled Function. N = 2 X: 0.198118 0.489688 H: Col: 1 2 Row 1 : 2.47959 -3.61194 2 : -3.61194 2.0785 H (approximated): Col: 1 2 Row 1 :-5.23588e+06 0 2 : 0 0 Problem 11 The Brown and Dennis Function. N = 4 X: 0.339493 0.95163 0.920332 0.052677 H: Col: 1 2 3 4 Row 1 : 86390.6 314881 -3320.25 661.833 2 : 314881 1.16286e+06 -11093 3219.08 3 : -3320.25 -11093 29191 -13200.8 4 : 661.833 3219.08 -13200.8 10197.6 H (approximated): Col: 1 2 3 4 Row 1 : 86404.4 314899 -3315.57 659.119 2 : 314899 1.16376e+06 -11095.2 3205.71 3 : -3315.57 -11095.2 29240.9 -13192.4 4 : 659.119 3205.71 -13192.4 10266.3 Problem 12 The Gulf R&D Function. N = 3 X: 0.737858 0.269119 0.422836 H: Col: 1 2 3 Row 1 : -11.5862 -0.148646 37.2011 2 : -0.148646 -0.00230689 0.319901 3 : 37.2011 0.319901 -94.4807 H (approximated): Col: 1 2 3 Row 1 : -11.5862 -0.148613 37.201 2 : -0.148613 -0.00213338 0.31993 3 : 37.201 0.31993 -94.4809 Problem 13 The Trigonometric Function. N = 4 X: 0.547871 0.942737 0.417744 0.983052 H: Col: 1 2 3 4 Row 1 : 11.8689 3.90705 1.73628 5.80397 2 : 3.90705 20.7345 3.9531 11.5924 3 : 1.73628 3.9531 16.709 5.45649 4 : 5.80397 11.5924 5.45649 47.9423 H (approximated): Col: 1 2 3 4 Row 1 : 11.8689 3.90704 1.73624 5.80397 2 : 3.90704 20.7347 3.95314 11.5924 3 : 1.73624 3.95314 16.7091 5.45648 4 : 5.80397 11.5924 5.45648 47.9424 Problem 14 The Extended Rosenbrock parabolic valley Function. N = 4 X: 0.301455 0.701099 0.666339 0.539126 H: Col: 1 2 3 4 Row 1 : -169.389 -120.582 0 0 2 : -120.582 200 0 0 3 : 0 0 319.158 -266.536 4 : 0 0 -266.536 200 H (approximated): Col: 1 2 3 4 Row 1 : -169.39 -120.582 0 0 2 : -120.582 200 0 0 3 : 0 0 319.159 -266.536 4 : 0 0 -266.536 200 Problem 15 The Extended Powell Singular Quartic Function. N = 4 X: 0.698106 0.666528 0.178132 0.128014 H: Col: 1 2 3 4 Row 1 : 41.0005 20 0 -39.0005 2 : 20 201.155 -2.31032 0 3 : 0 -2.31032 14.6206 -10 4 : -39.0005 0 -10 49.0005 H (approximated): Col: 1 2 3 4 Row 1 : 41.0002 20 0 -39.0005 2 : 20 201.155 -2.3103 3.8096e-05 3 : 0 -2.3103 14.6206 -9.99994 4 : -39.0005 3.8096e-05 -9.99994 49.0006 Problem 16 The Beale Function. N = 2 X: 0.99908 0.171121 H: Col: 1 2 Row 1 : 5.23867 0.0118544 2 : 0.0118544 10.7075 H (approximated): Col: 1 2 Row 1 : 5.23866 0.0118526 2 : 0.0118526 10.7075 Problem 17 The Wood Function. N = 4 X: 0.0326008 0.5612 0.881867 0.669175 H: Col: 1 2 3 4 Row 1 : -221.205 -13.0403 0 0 2 : -13.0403 220.2 0 19.8 3 : 0 0 601 -317.472 4 : 0 19.8 -317.472 200.2 H (approximated): Col: 1 2 3 4 Row 1 : -221.205 -13.0404 0 0 2 : -13.0404 220.2 0 19.8 3 : 0 0 601 -317.472 4 : 0 19.8 -317.472 200.2 Problem 18 The Chebyquad Function N = 4 X: 0.190433 0.368917 0.460726 0.981638 H: Col: 1 2 3 4 Row 1 : 2.14939 4.24015 -0.0169581 17.4811 2 : 4.24015 -3.83772 6.09253 13.4932 3 : -0.0169581 6.09253 -6.43931 -3.82028 4 : 17.4811 13.4932 -3.82028 204.332 H (approximated): Col: 1 2 3 4 Row 1 : 2.14939 4.24015 -0.0169575 17.4811 2 : 4.24015 -3.83772 6.09253 13.4932 3 : -0.0169575 6.09253 -6.43932 -3.82028 4 : 17.4811 13.4932 -3.82028 204.332 Problem 19 The Leon cubic valley function N = 2 X: 0.156405 0.855523 H: Col: 1 2 Row 1 : -156.774 -14.6775 2 : -14.6775 200 H (approximated): Col: 1 2 Row 1 : -156.775 -14.6774 2 : -14.6774 200 Problem 20 The Gregory and Karney Tridiagonal Matrix Function N = 4 X: 0.644765 0.376272 0.190924 0.428253 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 : 2 -2 0 -1.1905e-06 2 : -2 4 -2 0 3 : 0 -2 4 -2 4 : -1.1905e-06 0 -2 4 Problem 21 The Hilbert Matrix Function F = x'Ax N = 4 X: 0.482022 0.120612 0.589507 0.226188 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 0.333333 4 : 0.5 0.4 0.333333 0.285713 Problem 22 The De Jong Function F1 N = 3 X: 0.384619 0.582986 0.251806 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 : 2 0 -5.9525e-07 2 : 0 2 0 3 : -5.9525e-07 0 2 Problem 23 The De Jong Function F2 N = 2 X: 0.290441 0.617091 H: Col: 1 2 Row 1 : -143.609 -116.176 2 : -116.176 200 H (approximated): Col: 1 2 Row 1 : -143.609 -116.176 2 : -116.176 200 Problem 24 The De Jong Function F3, (discontinuous) N = 5 X: 0.265281 0.824376 0.982663 0.730249 0.343877 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: 0.584069 0.107769 0.906308 0.879654 0.817761 0.260728 0.594356 0.0225126 0.425259 0.312719 0.161485 0.178766 0.422886 0.0942293 0.598524 0.470924 0.695949 0.699888 0.638531 0.0336038 0.0688061 0.3196 0.530864 0.654446 0.407619 0.819981 0.718359 0.968649 0.531334 0.325146 H: Col: 1 2 3 4 5 Row 1 : 4.09364 0 0 0 0 2 : 0 0.27874 0 0 0 3 : 0 0 29.5702 0 0 4 : 0 0 0 37.142 0 5 : 0 0 0 0 40.1239 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 : 4.89449 0 0 0 0 7 : 0 29.6738 0 0 0 8 : 0 0 0.0486544 0 0 9 : 0 0 0 19.5313 0 10 : 0 0 0 0 11.7352 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 : 3.44221 0 0 0 0 12 : 0 4.60186 0 0 0 13 : 0 0 27.8978 0 0 14 : 0 0 0 1.4917 0 15 : 0 0 0 0 64.4815 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 : 42.5798 0 0 0 0 17 : 0 98.8065 0 0 0 18 : 0 0 105.806 0 0 19 : 0 0 0 92.9605 0 20 : 0 0 0 0 0.271012 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 : 1.19304 0 0 0 0 22 : 0 26.966 0 0 0 23 : 0 0 77.7815 0 0 24 : 0 0 0 123.35 0 25 : 0 0 0 0 49.846 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 : 209.779 0 0 0 0 27 : 0 167.197 0 0 0 28 : 0 0 315.263 0 0 29 : 0 0 0 98.2459 0 30 : 0 0 0 0 38.0591 H (approximated): Col: 1 2 3 4 5 Row 1 : 4.09365 0 0 -7.61921e-05 7.61921e-05 2 : 0 0.278558 -7.61921e-05 -7.61921e-05 0 3 : 0 -7.61921e-05 29.5698 0 -7.61921e-05 4 :-7.61921e-05 -7.61921e-05 0 37.1418 -7.61921e-05 5 : 7.61921e-05 0 -7.61921e-05 -7.61921e-05 40.124 6 :-7.61921e-05 0 0 0 7.61921e-05 7 : 0 0 7.61921e-05 0 0 8 :-7.61921e-05 0 0 7.61921e-05 7.61921e-05 9 : 0 0 0 0 0 10 : 0 -7.61921e-05 0 7.61921e-05 0 11 :-7.61921e-05 7.61921e-05 0 -7.61921e-05 7.61921e-05 12 : 0 7.61921e-05 0 -7.61921e-05 0 13 : 0 0 0 0 0 14 :-7.61921e-05 0 0 7.61921e-05 7.61921e-05 15 : 0 -7.61921e-05 7.61921e-05 7.61921e-05 0 16 : 0 0 7.61921e-05 0 0 17 :-7.61921e-05 0 7.61921e-05 0 7.61921e-05 18 :-7.61921e-05 7.61921e-05 0 0 7.61921e-05 19 : 0 0 0 0 0 20 : 0 0 0 0 0 21 : 0 0 0 0 0 22 : 0 7.61921e-05 0 -7.61921e-05 0 23 : 7.61921e-05 -7.61921e-05 0 0 -7.61921e-05 24 : 0 7.61921e-05 0 -7.61921e-05 0 25 :-7.61921e-05 7.61921e-05 0 0 7.61921e-05 26 :-7.61921e-05 7.61921e-05 0 0 7.61921e-05 27 : 0 0 0 0 0 28 : 0 7.61921e-05 0 -7.61921e-05 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 6 7 8 9 10 Row 1 :-7.61921e-05 0 -7.61921e-05 0 0 2 : 0 0 0 0 -7.61921e-05 3 : 0 7.61921e-05 0 0 0 4 : 0 0 7.61921e-05 0 7.61921e-05 5 : 7.61921e-05 0 7.61921e-05 0 0 6 : 4.89458 0 0 0 0 7 : 0 29.6738 -7.61921e-05 0 0 8 : 0 -7.61921e-05 0.0484581 0 7.61921e-05 9 : 0 0 0 19.5311 -7.61921e-05 10 : 0 0 7.61921e-05 -7.61921e-05 11.7351 11 :-7.61921e-05 0 -7.61921e-05 0 -7.61921e-05 12 : 0 0 -7.61921e-05 0 -7.61921e-05 13 : 0 0 0 7.61921e-05 7.61921e-05 14 : 0 -7.61921e-05 7.61921e-05 0 7.61921e-05 15 : 0 0 0 0 7.61921e-05 16 : 0 0 -7.61921e-05 0 0 17 :-7.61921e-05 0 -7.61921e-05 0 0 18 : 0 -7.61921e-05 -7.61921e-05 7.61921e-05 0 19 : 0 0 0 0 0 20 : 0 0 0 0 0 21 : 0 0 0 0 0 22 : 0 0 -7.61921e-05 0 -7.61921e-05 23 : 0 7.61921e-05 7.61921e-05 0 7.61921e-05 24 : 0 0 -7.61921e-05 0 -7.61921e-05 25 : 0 -7.61921e-05 -7.61921e-05 7.61921e-05 0 26 : 0 -7.61921e-05 -7.61921e-05 7.61921e-05 0 27 : 0 0 0 0 0 28 : 0 -7.61921e-05 0 0 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 11 12 13 14 15 Row 1 :-7.61921e-05 0 0 -7.61921e-05 0 2 : 7.61921e-05 7.61921e-05 0 0 -7.61921e-05 3 : 0 0 0 0 7.61921e-05 4 :-7.61921e-05 -7.61921e-05 0 7.61921e-05 7.61921e-05 5 : 7.61921e-05 0 0 7.61921e-05 0 6 :-7.61921e-05 0 0 0 0 7 : 0 0 0 -7.61921e-05 0 8 :-7.61921e-05 -7.61921e-05 0 7.61921e-05 0 9 : 0 0 7.61921e-05 0 0 10 :-7.61921e-05 -7.61921e-05 7.61921e-05 7.61921e-05 7.61921e-05 11 : 3.44205 7.61921e-05 0 -7.61921e-05 -7.61921e-05 12 : 7.61921e-05 4.6017 0 -7.61921e-05 -7.61921e-05 13 : 0 0 27.8976 0 0 14 :-7.61921e-05 -7.61921e-05 0 1.49154 0 15 :-7.61921e-05 -7.61921e-05 0 0 64.4813 16 : 0 0 0 -7.61921e-05 0 17 : 0 0 0 -7.61921e-05 0 18 : 0 7.61921e-05 -7.61921e-05 -7.61921e-05 -7.61921e-05 19 : 0 0 0 0 0 20 : 0 0 0 0 0 21 : 0 0 0 0 0 22 : 7.61921e-05 7.61921e-05 0 -7.61921e-05 -7.61921e-05 23 : 0 -7.61921e-05 0 7.61921e-05 7.61921e-05 24 : 7.61921e-05 7.61921e-05 0 -7.61921e-05 -7.61921e-05 25 : 0 7.61921e-05 -7.61921e-05 -7.61921e-05 -7.61921e-05 26 : 0 7.61921e-05 -7.61921e-05 -7.61921e-05 -7.61921e-05 27 : 0 0 0 0 0 28 : 7.61921e-05 0 0 0 -7.61921e-05 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 16 17 18 19 20 Row 1 : 0 -7.61921e-05 -7.61921e-05 0 0 2 : 0 0 7.61921e-05 0 0 3 : 7.61921e-05 7.61921e-05 0 0 0 4 : 0 0 0 0 0 5 : 0 7.61921e-05 7.61921e-05 0 0 6 : 0 -7.61921e-05 0 0 0 7 : 0 0 -7.61921e-05 0 0 8 :-7.61921e-05 -7.61921e-05 -7.61921e-05 0 0 9 : 0 0 7.61921e-05 0 0 10 : 0 0 0 0 0 11 : 0 0 0 0 0 12 : 0 0 7.61921e-05 0 0 13 : 0 0 -7.61921e-05 0 0 14 :-7.61921e-05 -7.61921e-05 -7.61921e-05 0 0 15 : 0 0 -7.61921e-05 0 0 16 : 42.5798 0 0 0 0 17 : 0 98.8065 -7.61921e-05 0 0 18 : 0 -7.61921e-05 105.806 0 0 19 : 0 0 0 92.9604 0 20 : 0 0 0 0 0.270939 21 : 0 0 0 0 0 22 : 0 0 7.61921e-05 0 0 23 : 0 7.61921e-05 0 0 0 24 : 0 0 7.61921e-05 0 0 25 : 0 -7.61921e-05 -7.61921e-05 0 0 26 : 0 -7.61921e-05 -7.61921e-05 0 0 27 : 0 0 0 0 0 28 : 0 0 7.61921e-05 0 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 21 22 23 24 25 Row 1 : 0 0 7.61921e-05 0 -7.61921e-05 2 : 0 7.61921e-05 -7.61921e-05 7.61921e-05 7.61921e-05 3 : 0 0 0 0 0 4 : 0 -7.61921e-05 0 -7.61921e-05 0 5 : 0 0 -7.61921e-05 0 7.61921e-05 6 : 0 0 0 0 0 7 : 0 0 7.61921e-05 0 -7.61921e-05 8 : 0 -7.61921e-05 7.61921e-05 -7.61921e-05 -7.61921e-05 9 : 0 0 0 0 7.61921e-05 10 : 0 -7.61921e-05 7.61921e-05 -7.61921e-05 0 11 : 0 7.61921e-05 0 7.61921e-05 0 12 : 0 7.61921e-05 -7.61921e-05 7.61921e-05 7.61921e-05 13 : 0 0 0 0 -7.61921e-05 14 : 0 -7.61921e-05 7.61921e-05 -7.61921e-05 -7.61921e-05 15 : 0 -7.61921e-05 7.61921e-05 -7.61921e-05 -7.61921e-05 16 : 0 0 0 0 0 17 : 0 0 7.61921e-05 0 -7.61921e-05 18 : 0 7.61921e-05 0 7.61921e-05 -7.61921e-05 19 : 0 0 0 0 0 20 : 0 0 0 0 0 21 : 1.19286 0 0 0 0 22 : 0 26.9659 -7.61921e-05 7.61921e-05 7.61921e-05 23 : 0 -7.61921e-05 77.7814 -7.61921e-05 0 24 : 0 7.61921e-05 -7.61921e-05 123.35 0 25 : 0 7.61921e-05 0 0 49.8461 26 : 0 7.61921e-05 0 0 -7.61921e-05 27 : 0 0 0 0 0 28 : 0 0 -7.61921e-05 7.61921e-05 7.61921e-05 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 26 27 28 29 30 Row 1 :-7.61921e-05 0 0 0 0 2 : 7.61921e-05 0 7.61921e-05 0 0 3 : 0 0 0 0 0 4 : 0 0 -7.61921e-05 0 0 5 : 7.61921e-05 0 0 0 0 6 : 0 0 0 0 0 7 :-7.61921e-05 0 -7.61921e-05 0 0 8 :-7.61921e-05 0 0 0 0 9 : 7.61921e-05 0 0 0 0 10 : 0 0 0 0 0 11 : 0 0 7.61921e-05 0 0 12 : 7.61921e-05 0 0 0 0 13 :-7.61921e-05 0 0 0 0 14 :-7.61921e-05 0 0 0 0 15 :-7.61921e-05 0 -7.61921e-05 0 0 16 : 0 0 0 0 0 17 :-7.61921e-05 0 0 0 0 18 :-7.61921e-05 0 7.61921e-05 0 0 19 : 0 0 0 0 0 20 : 0 0 0 0 0 21 : 0 0 0 0 0 22 : 7.61921e-05 0 0 0 0 23 : 0 0 -7.61921e-05 0 0 24 : 0 0 7.61921e-05 0 0 25 :-7.61921e-05 0 7.61921e-05 0 0 26 : 209.779 0 0 0 0 27 : 0 167.196 0 0 0 28 : 0 0 315.262 0 0 29 : 0 0 0 98.2454 0 30 : 0 0 0 0 38.0588 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 :-3.09658e+09 1.03417e+09 -1.40671e+09 9.7896e+09 1.63221e+09 2 : 1.03417e+09 -7.4476e+09 -4.86926e+09 6.66382e+07 -4.71584e+09 3 :-1.40671e+09 -4.86926e+09 -8.87262e+09 9.20442e+09 1.80474e+10 4 : 9.7896e+09 6.66382e+07 9.20442e+09 -5.2376e+10 -5.74587e+09 5 : 1.63221e+09 -4.71584e+09 1.80474e+10 -5.74587e+09 -1.33504e+09 6 : 1.89774e+10 -8.98297e+09 -9.8333e+09 1.03547e+10 -1.57111e+10 7 :-3.78851e+08 2.72902e+09 6.80472e+09 8.80557e+09 -4.4826e+09 8 :-8.43341e+09 8.09349e+09 1.97601e+10 -1.10611e+10 -5.96736e+09 9 : 1.86382e+08 -3.63302e+09 -4.1645e+09 2.64847e+09 -4.16687e+09 10 : 7.05301e+09 -8.41143e+08 4.02869e+09 9.03469e+09 -7.24353e+09 11 :-9.75879e+09 3.59267e+08 2.39715e+09 9.51569e+09 -7.69989e+09 12 :-9.51653e+09 -7.22288e+09 1.46561e+10 1.17528e+10 5.74923e+09 13 : 1.09899e+09 -1.6485e+10 -6.93381e+09 7.872e+09 2.90647e+09 14 : 3.55279e+09 3.41078e+09 -6.46721e+09 1.15987e+10 3.87411e+09 15 :-3.56892e+08 6.6617e+08 1.00298e+10 5.9063e+09 2.53484e+09 16 : 1.55058e+09 -4.66612e+09 -6.77105e+08 2.52562e+09 -1.76153e+10 17 : 6.80333e+09 -1.23574e+10 5.50348e+09 3.30027e+09 2.62206e+09 18 : 1.3597e+10 -3.69504e+09 -3.53519e+09 -7.06397e+09 1.07638e+10 19 :-1.16061e+09 2.06814e+10 7.04175e+09 6.37051e+09 -1.08675e+10 20 :-5.46657e+09 -5.49448e+09 -2.6681e+09 6.82201e+09 8.62922e+09 21 : 1.44859e+10 -2.62664e+09 4.50987e+09 -1.30605e+09 -1.46155e+10 22 :-8.32489e+09 -2.33003e+09 2.08528e+10 -1.84264e+10 -1.51272e+10 23 :-1.53004e+10 1.52413e+10 1.03631e+10 -1.38118e+09 4.21157e+09 24 : 2.46421e+09 -2.23555e+10 1.04818e+10 -1.13478e+10 -1.24267e+10 25 : -4.4002e+09 -1.16452e+10 8.00999e+09 7.92514e+08 -5.5394e+09 26 : 1.49268e+09 -1.33799e+10 -7.02812e+08 -4.28888e+09 -7.2456e+08 27 : 7.05695e+09 8.02879e+09 9.0924e+09 2.26523e+10 -1.11337e+10 28 : 1.59773e+09 -1.91098e+09 2.64969e+10 1.70928e+10 1.77598e+10 29 : 5.35539e+09 -1.8469e+09 4.10063e+09 7.36058e+09 8.95886e+09 30 : 2.64872e+09 6.99189e+09 -2.69376e+09 6.24664e+09 1.47039e+10 Col: 6 7 8 9 10 Row 1 : 1.89774e+10 -3.78851e+08 -8.43341e+09 1.86382e+08 7.05301e+09 2 :-8.98297e+09 2.72902e+09 8.09349e+09 -3.63302e+09 -8.41143e+08 3 : -9.8333e+09 6.80472e+09 1.97601e+10 -4.1645e+09 4.02869e+09 4 : 1.03547e+10 8.80557e+09 -1.10611e+10 2.64847e+09 9.03469e+09 5 :-1.57111e+10 -4.4826e+09 -5.96736e+09 -4.16687e+09 -7.24353e+09 6 :-3.04613e+10 -1.28935e+10 4.14588e+09 8.18961e+09 -1.31154e+10 7 :-1.28935e+10 5.66422e+10 -1.06336e+10 -6.17969e+08 -2.21497e+10 8 : 4.14588e+09 -1.06336e+10 -5.52047e+09 1.31173e+10 5.97349e+09 9 : 8.18961e+09 -6.17969e+08 1.31173e+10 7.19435e+10 -1.19999e+10 10 :-1.31154e+10 -2.21497e+10 5.97349e+09 -1.19999e+10 3.17189e+10 11 : 2.42954e+10 -2.10851e+10 9.0562e+09 9.57916e+09 2.41697e+09 12 : 1.00792e+10 9.80212e+09 -2.09103e+09 -1.41015e+10 1.51494e+09 13 :-7.38423e+09 1.0664e+10 -9.18461e+09 -5.58834e+09 -6.51396e+09 14 :-8.04159e+09 8.2147e+09 6.99942e+09 -7.80874e+09 -1.00292e+10 15 : 1.0577e+10 1.29309e+10 1.22201e+09 -4.11685e+09 1.53322e+10 16 : 1.32208e+10 -2.60491e+09 2.38356e+10 8.04325e+08 9.1577e+09 17 : 1.83658e+10 3.92435e+09 1.57592e+10 1.43281e+10 2.36195e+09 18 : 1.17478e+10 2.78259e+10 1.36453e+09 1.62787e+10 5.99916e+09 19 : 2.72034e+10 1.25118e+10 -1.1153e+10 -1.22723e+10 1.4266e+09 20 :-8.59197e+09 -8.11806e+09 -9.1994e+09 -6.43151e+09 -1.2719e+10 21 :-9.02775e+09 2.63594e+10 -1.42324e+10 -1.61655e+10 7.25849e+09 22 :-2.03981e+08 4.62368e+09 -1.04301e+09 -8.76954e+09 5.50455e+09 23 :-2.32825e+10 1.12539e+09 6.24996e+09 1.03813e+10 -9.91436e+09 24 : 1.58541e+07 -6.55057e+09 9.80022e+09 -9.80483e+09 -3.45501e+09 25 :-6.47029e+09 1.37824e+10 3.52182e+09 1.3251e+10 8.93763e+09 26 : 1.17765e+10 1.16828e+10 1.3066e+10 4.57948e+09 1.30847e+10 27 : 1.28893e+10 -1.02557e+10 -1.5841e+10 -5.67291e+08 -9.89688e+09 28 : 8.87719e+09 -1.73953e+10 -3.48195e+09 -4.68944e+09 7.65007e+09 29 :-2.14574e+10 1.23171e+10 -4.38654e+09 3.64053e+09 -1.4741e+10 30 : 3.35229e+09 -2.00176e+09 6.53405e+09 3.93657e+09 7.63375e+09 Col: 11 12 13 14 15 Row 1 :-9.75879e+09 -9.51653e+09 1.09899e+09 3.55279e+09 -3.56892e+08 2 : 3.59267e+08 -7.22288e+09 -1.6485e+10 3.41078e+09 6.6617e+08 3 : 2.39715e+09 1.46561e+10 -6.93381e+09 -6.46721e+09 1.00298e+10 4 : 9.51569e+09 1.17528e+10 7.872e+09 1.15987e+10 5.9063e+09 5 :-7.69989e+09 5.74923e+09 2.90647e+09 3.87411e+09 2.53484e+09 6 : 2.42954e+10 1.00792e+10 -7.38423e+09 -8.04159e+09 1.0577e+10 7 :-2.10851e+10 9.80212e+09 1.0664e+10 8.2147e+09 1.29309e+10 8 : 9.0562e+09 -2.09103e+09 -9.18461e+09 6.99942e+09 1.22201e+09 9 : 9.57916e+09 -1.41015e+10 -5.58834e+09 -7.80874e+09 -4.11685e+09 10 : 2.41697e+09 1.51494e+09 -6.51396e+09 -1.00292e+10 1.53322e+10 11 : 2.82769e+09 -1.07795e+10 1.11577e+10 1.46998e+10 -4.42157e+09 12 :-1.07795e+10 -2.22266e+09 -1.14737e+10 4.0579e+09 -3.47483e+09 13 : 1.11577e+10 -1.14737e+10 -1.82659e+10 1.9006e+10 1.93327e+08 14 : 1.46998e+10 4.0579e+09 1.9006e+10 -5.09113e+10 -1.55345e+10 15 :-4.42157e+09 -3.47483e+09 1.93327e+08 -1.55345e+10 -6.2769e+10 16 :-5.74347e+09 1.21873e+10 -8.29282e+09 1.75393e+10 8.55979e+09 17 :-1.32328e+10 -3.21034e+08 -2.16146e+09 -4.38211e+09 4.38179e+09 18 :-9.80099e+09 -1.12906e+09 1.31411e+10 -8.3621e+08 -3.82989e+09 19 :-2.89452e+10 2.72187e+07 2.33573e+10 -1.2902e+10 1.01957e+10 20 :-8.41256e+09 1.48132e+10 7.6443e+09 -1.46211e+10 -2.98978e+09 21 : 9.94721e+09 8.1402e+09 -9.2652e+09 1.63888e+10 -1.16268e+10 22 : 1.7753e+10 -5.23169e+09 -5.49541e+09 -7.57403e+09 -8.46585e+09 23 : 7.11801e+09 -1.36472e+10 7.36061e+09 -1.09367e+10 -2.40138e+09 24 : 6.33375e+09 -3.45797e+09 1.853e+10 2.50493e+09 -2.20864e+10 25 : 5.54901e+09 4.28868e+09 -3.98455e+09 8.82011e+09 -1.21257e+10 26 : 1.14164e+10 -4.64297e+09 1.08447e+10 3.09481e+08 2.14885e+10 27 : 7.43263e+09 -7.13102e+09 7.16426e+09 -8.92253e+09 -7.55732e+09 28 : 3.78765e+08 2.82091e+09 6.27236e+09 3.06291e+09 -1.31924e+10 29 :-1.58392e+10 3.60682e+09 3.01499e+09 9.77561e+09 4.27218e+09 30 : 1.45721e+10 4.29915e+09 -3.68204e+09 -1.30384e+10 -5.65213e+09 Col: 16 17 18 19 20 Row 1 : 1.55058e+09 6.80333e+09 1.3597e+10 -1.16061e+09 -5.46657e+09 2 :-4.66612e+09 -1.23574e+10 -3.69504e+09 2.06814e+10 -5.49448e+09 3 :-6.77105e+08 5.50348e+09 -3.53519e+09 7.04175e+09 -2.6681e+09 4 : 2.52562e+09 3.30027e+09 -7.06397e+09 6.37051e+09 6.82201e+09 5 :-1.76153e+10 2.62206e+09 1.07638e+10 -1.08675e+10 8.62922e+09 6 : 1.32208e+10 1.83658e+10 1.17478e+10 2.72034e+10 -8.59197e+09 7 :-2.60491e+09 3.92435e+09 2.78259e+10 1.25118e+10 -8.11806e+09 8 : 2.38356e+10 1.57592e+10 1.36453e+09 -1.1153e+10 -9.1994e+09 9 : 8.04325e+08 1.43281e+10 1.62787e+10 -1.22723e+10 -6.43151e+09 10 : 9.1577e+09 2.36195e+09 5.99916e+09 1.4266e+09 -1.2719e+10 11 :-5.74347e+09 -1.32328e+10 -9.80099e+09 -2.89452e+10 -8.41256e+09 12 : 1.21873e+10 -3.21034e+08 -1.12906e+09 2.72187e+07 1.48132e+10 13 :-8.29282e+09 -2.16146e+09 1.31411e+10 2.33573e+10 7.6443e+09 14 : 1.75393e+10 -4.38211e+09 -8.3621e+08 -1.2902e+10 -1.46211e+10 15 : 8.55979e+09 4.38179e+09 -3.82989e+09 1.01957e+10 -2.98978e+09 16 : 4.85037e+10 1.38881e+10 1.89258e+09 6.95281e+09 2.1679e+10 17 : 1.38881e+10 1.65012e+10 2.01463e+10 -2.82688e+09 -1.65427e+10 18 : 1.89258e+09 2.01463e+10 6.53684e+10 1.81989e+10 1.41384e+10 19 : 6.95281e+09 -2.82688e+09 1.81989e+10 2.64943e+10 -1.48808e+10 20 : 2.1679e+10 -1.65427e+10 1.41384e+10 -1.48808e+10 3.79922e+10 21 : 7.46626e+09 -1.64984e+10 8.83972e+08 -2.22965e+10 1.64966e+09 22 : 1.55712e+10 -3.77208e+09 -2.06252e+09 -9.58147e+08 -1.89731e+10 23 : 2.23269e+10 1.47953e+10 7.13602e+09 1.1764e+10 -4.81705e+09 24 : 8.27458e+09 3.40533e+09 -9.06371e+09 -3.40809e+10 -3.5226e+09 25 :-2.41713e+08 -5.02546e+09 1.62367e+10 4.11324e+09 -8.37799e+09 26 : 1.5983e+10 -1.87131e+09 -1.28447e+10 7.59378e+09 -2.92295e+09 27 : 7.3831e+08 1.46312e+10 1.06837e+10 1.77768e+10 -1.73885e+10 28 :-7.11961e+08 -9.11867e+09 -4.77038e+09 -4.27909e+09 3.87219e+07 29 : 5.30394e+09 -9.40991e+09 1.87548e+10 -1.39241e+10 7.75745e+09 30 : 4.04052e+09 -3.53536e+09 5.78486e+08 1.47643e+10 1.16489e+10 Col: 21 22 23 24 25 Row 1 : 1.44859e+10 -8.32489e+09 -1.53004e+10 2.46421e+09 -4.4002e+09 2 :-2.62664e+09 -2.33003e+09 1.52413e+10 -2.23555e+10 -1.16452e+10 3 : 4.50987e+09 2.08528e+10 1.03631e+10 1.04818e+10 8.00999e+09 4 :-1.30605e+09 -1.84264e+10 -1.38118e+09 -1.13478e+10 7.92514e+08 5 :-1.46155e+10 -1.51272e+10 4.21157e+09 -1.24267e+10 -5.5394e+09 6 :-9.02775e+09 -2.03981e+08 -2.32825e+10 1.58541e+07 -6.47029e+09 7 : 2.63594e+10 4.62368e+09 1.12539e+09 -6.55057e+09 1.37824e+10 8 :-1.42324e+10 -1.04301e+09 6.24996e+09 9.80022e+09 3.52182e+09 9 :-1.61655e+10 -8.76954e+09 1.03813e+10 -9.80483e+09 1.3251e+10 10 : 7.25849e+09 5.50455e+09 -9.91436e+09 -3.45501e+09 8.93763e+09 11 : 9.94721e+09 1.7753e+10 7.11801e+09 6.33375e+09 5.54901e+09 12 : 8.1402e+09 -5.23169e+09 -1.36472e+10 -3.45797e+09 4.28868e+09 13 : -9.2652e+09 -5.49541e+09 7.36061e+09 1.853e+10 -3.98455e+09 14 : 1.63888e+10 -7.57403e+09 -1.09367e+10 2.50493e+09 8.82011e+09 15 :-1.16268e+10 -8.46585e+09 -2.40138e+09 -2.20864e+10 -1.21257e+10 16 : 7.46626e+09 1.55712e+10 2.23269e+10 8.27458e+09 -2.41713e+08 17 :-1.64984e+10 -3.77208e+09 1.47953e+10 3.40533e+09 -5.02546e+09 18 : 8.83972e+08 -2.06252e+09 7.13602e+09 -9.06371e+09 1.62367e+10 19 :-2.22965e+10 -9.58147e+08 1.1764e+10 -3.40809e+10 4.11324e+09 20 : 1.64966e+09 -1.89731e+10 -4.81705e+09 -3.5226e+09 -8.37799e+09 21 : 1.63082e+10 -3.52573e+09 -2.66035e+09 1.06943e+10 -1.19466e+10 22 :-3.52573e+09 2.92222e+10 -8.59051e+09 -1.30954e+09 -6.14416e+09 23 :-2.66035e+09 -8.59051e+09 -4.76692e+10 3.84547e+09 3.96448e+09 24 : 1.06943e+10 -1.30954e+09 3.84547e+09 7.4076e+10 -1.06322e+10 25 :-1.19466e+10 -6.14416e+09 3.96448e+09 -1.06322e+10 -6.73244e+10 26 : 1.72029e+10 -2.57555e+10 1.48302e+10 1.2128e+10 8.42073e+09 27 : 8.10658e+09 3.95518e+09 -6.62488e+09 1.23323e+10 4.51735e+09 28 : 1.66787e+10 1.61283e+10 -1.56938e+10 8.12263e+09 -6.94794e+09 29 : 1.09349e+10 -9.21224e+08 4.31733e+09 4.3071e+09 5.21725e+09 30 : 3.43363e+09 -4.54516e+09 -6.2854e+09 1.19855e+09 7.31122e+08 Col: 26 27 28 29 30 Row 1 : 1.49268e+09 7.05695e+09 1.59773e+09 5.35539e+09 2.64872e+09 2 :-1.33799e+10 8.02879e+09 -1.91098e+09 -1.8469e+09 6.99189e+09 3 :-7.02812e+08 9.0924e+09 2.64969e+10 4.10063e+09 -2.69376e+09 4 :-4.28888e+09 2.26523e+10 1.70928e+10 7.36058e+09 6.24664e+09 5 : -7.2456e+08 -1.11337e+10 1.77598e+10 8.95886e+09 1.47039e+10 6 : 1.17765e+10 1.28893e+10 8.87719e+09 -2.14574e+10 3.35229e+09 7 : 1.16828e+10 -1.02557e+10 -1.73953e+10 1.23171e+10 -2.00176e+09 8 : 1.3066e+10 -1.5841e+10 -3.48195e+09 -4.38654e+09 6.53405e+09 9 : 4.57948e+09 -5.67291e+08 -4.68944e+09 3.64053e+09 3.93657e+09 10 : 1.30847e+10 -9.89688e+09 7.65007e+09 -1.4741e+10 7.63375e+09 11 : 1.14164e+10 7.43263e+09 3.78765e+08 -1.58392e+10 1.45721e+10 12 :-4.64297e+09 -7.13102e+09 2.82091e+09 3.60682e+09 4.29915e+09 13 : 1.08447e+10 7.16426e+09 6.27236e+09 3.01499e+09 -3.68204e+09 14 : 3.09481e+08 -8.92253e+09 3.06291e+09 9.77561e+09 -1.30384e+10 15 : 2.14885e+10 -7.55732e+09 -1.31924e+10 4.27218e+09 -5.65213e+09 16 : 1.5983e+10 7.3831e+08 -7.11961e+08 5.30394e+09 4.04052e+09 17 :-1.87131e+09 1.46312e+10 -9.11867e+09 -9.40991e+09 -3.53536e+09 18 :-1.28447e+10 1.06837e+10 -4.77038e+09 1.87548e+10 5.78486e+08 19 : 7.59378e+09 1.77768e+10 -4.27909e+09 -1.39241e+10 1.47643e+10 20 :-2.92295e+09 -1.73885e+10 3.87219e+07 7.75745e+09 1.16489e+10 21 : 1.72029e+10 8.10658e+09 1.66787e+10 1.09349e+10 3.43363e+09 22 :-2.57555e+10 3.95518e+09 1.61283e+10 -9.21224e+08 -4.54516e+09 23 : 1.48302e+10 -6.62488e+09 -1.56938e+10 4.31733e+09 -6.2854e+09 24 : 1.2128e+10 1.23323e+10 8.12263e+09 4.3071e+09 1.19855e+09 25 : 8.42073e+09 4.51735e+09 -6.94794e+09 5.21725e+09 7.31122e+08 26 :-1.97681e+08 8.77401e+09 7.66005e+09 1.72292e+09 -1.89474e+10 27 : 8.77401e+09 -1.95039e+10 -4.50007e+09 -1.63647e+10 8.20867e+09 28 : 7.66005e+09 -4.50007e+09 -8.18046e+10 -4.15539e+09 3.02849e+09 29 : 1.72292e+09 -1.63647e+10 -4.15539e+09 7.76386e+08 1.50546e+09 30 :-1.89474e+10 8.20867e+09 3.02849e+09 1.50546e+09 -4.95262e+10 Problem 26 The De Jong Function F5 N = 2 X: 0.34014 0.918927 H: Col: 1 2 Row 1 : 0 0 2 : 0 0 H (approximated): Col: 1 2 Row 1 :-9.30079e-09 0 2 : 0 -1.58113e-07 Problem 27 The Schaffer Function F6 N = 2 X: 0.456267 0.442497 H: Col: 1 2 Row 1 : 1.03003 -0.458322 2 : -0.458322 1.05812 H (approximated): Col: 1 2 Row 1 : 1.03003 -0.458322 2 : -0.458322 1.05813 Problem 28 The Schaffer Function F7 N = 2 X: 0.454186 0.945282 H: Col: 1 2 Row 1 : 36.0738 65.9958 2 : 65.9958 141.719 H (approximated): Col: 1 2 Row 1 : 36.0738 65.9958 2 : 65.9958 141.719 Problem 29 The Goldstein Price Polynomial N = 2 X: 0.219119 0.882403 H: Col: 1 2 Row 1 : 52140.8 -92279.6 2 : -92279.6 111611 H (approximated): Col: 1 2 Row 1 : 52141.1 -92279.5 2 : -92279.5 111611 Problem 30 The Branin RCOS Function N = 2 X: 0.0198754 0.341765 H: Col: 1 2 Row 1 : -1.65929 3.17283 2 : 3.17283 2 H (approximated): Col: 1 2 Row 1 : -1.65916 3.17283 2 : 3.17283 1.99989 Problem 31 The Shekel SQRN5 Function N = 4 X: 0.766027 0.342804 0.618806 0.453021 H: Col: 1 2 3 4 Row 1 : 1.26082 -0.851117 -0.494008 -0.708541 2 : -0.851117 -0.824557 -1.38598 -1.98851 3 : -0.494008 -1.38598 0.760124 -1.15371 4 : -0.708541 -1.98851 -1.15371 -0.0908522 H (approximated): Col: 1 2 3 4 Row 1 : 1.26082 -0.851118 -0.494009 -0.70854 2 : -0.851118 -0.824558 -1.38598 -1.98851 3 : -0.494009 -1.38598 0.760128 -1.15371 4 : -0.70854 -1.98851 -1.15371 -0.0908471 Problem 32 The Shekel SQRN7 Function N = 4 X: 0.0101626 0.599081 0.601568 0.649417 H: Col: 1 2 3 4 Row 1 : -1.07671 -0.74599 -0.740774 -0.652126 2 : -0.74599 0.45839 -0.300909 -0.265307 3 : -0.740774 -0.300909 0.463229 -0.263083 4 : -0.652126 -0.265307 -0.263083 0.529952 H (approximated): Col: 1 2 3 4 Row 1 : -1.07672 -0.74599 -0.740772 -0.652127 2 : -0.74599 0.458383 -0.300912 -0.265308 3 : -0.740772 -0.300912 0.463217 -0.263083 4 : -0.652127 -0.265308 -0.263083 0.529947 Problem 33 The Shekel SQRN10 Function N = 4 X: 0.342721 0.493299 0.701774 0.887803 H: Col: 1 2 3 4 Row 1 : -1.52059 -2.74658 -1.61811 -0.609681 2 : -2.74658 -0.0756446 -1.2471 -0.470619 3 : -1.61811 -1.2471 1.30693 -0.277394 4 : -0.609681 -0.470619 -0.277394 1.9369 H (approximated): Col: 1 2 3 4 Row 1 : -1.52057 -2.74658 -1.61811 -0.609682 2 : -2.74658 -0.0756444 -1.24711 -0.470614 3 : -1.61811 -1.24711 1.30692 -0.277394 4 : -0.609682 -0.470614 -0.277394 1.9369 Problem 34 The Six-Hump Camel-Back Polynomial N = 2 X: 0.0550578 0.098362 H: Col: 1 2 Row 1 : 7.9237 1 2 : 1 -7.5356 H (approximated): Col: 1 2 Row 1 : 7.9237 1 2 : 1 -7.5356 Problem 35 The Shubert Function N = 2 X: 0.649783 0.764071 H: Col: 1 2 Row 1 : -269.333 172.765 2 : 172.765 -244.847 H (approximated): Col: 1 2 Row 1 : -269.333 172.765 2 : 172.765 -244.847 Problem 36 The Stuckman Function N = 2 X: 0.133475 0.672651 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: 0.202585 0.868515 H: Col: 1 2 Row 1 :-1.86374e-05 -1.22079e-05 2 :-1.22079e-05 -4.42812e-06 H (approximated): Col: 1 2 Row 1 :-1.86375e-05 -1.22079e-05 2 :-1.22079e-05 -4.42814e-06 Problem 38 The Bohachevsky Function #1 N = 2 X: 0.751157 0.41938 H: Col: 1 2 Row 1 : 20.6363 0 2 : 0 37.429 H (approximated): Col: 1 2 Row 1 : 20.6363 1.1905e-06 2 : 1.1905e-06 37.429 Problem 39 The Bohachevsky Function #2 N = 2 X: 0.000231065 0.149464 H: Col: 1 2 Row 1 : -6.06367 -0.0737486 2 : -0.0737486 -10.3354 H (approximated): Col: 1 2 Row 1 : -6.06367 -0.0737485 2 : -0.0737485 -10.3354 Problem 40 The Bohachevsky Function #3 N = 2 X: 0.273834 0.872425 H: Col: 1 2 Row 1 : -20.5668 0 2 : 0 9.10891 H (approximated): Col: 1 2 Row 1 : -20.5668 0 2 : 0 9.10892 Problem 41 The Colville Polynomial N = 4 X: 0.601251 0.321188 0.284293 0.435316 H: Col: 1 2 3 4 Row 1 : 307.328 -240.5 0 0 2 : -240.5 220.2 0 19.8 3 : 0 0 -67.4253 -102.346 4 : 0 19.8 -102.346 200.2 H (approximated): Col: 1 2 3 4 Row 1 : 307.328 -240.5 -1.9048e-05 1.9048e-05 2 : -240.5 220.2 -1.9048e-05 19.8 3 : -1.9048e-05 -1.9048e-05 -67.4253 -102.345 4 : 1.9048e-05 19.8 -102.345 200.2 Problem 42 The Powell 3D Function N = 3 X: 0.903759 0.925106 0.505292 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 : 1.99431 -1.99423 -0.000226195 2 : -1.99423 2.41623 -0.392908 3 :-0.000226195 -0.392908 1.41467 Problem 43 The Himmelblau function. N = 2 X: 0.627582 0.719264 H: Col: 1 2 Row 1 : -34.3966 5.38738 2 : 5.38738 -17.2816 H (approximated): Col: 1 2 Row 1 : -34.3967 5.38769 2 : 5.38769 -17.2816 P00_HDIF_TEST Normal end of execution. 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) = -16 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 GRADIENT_METHOD_TEST Normal end of execution. test_opt_test(): Normal end of execution. 08-Jan-2022 10:29:22