30-Mar-2019 21:53:26 test_opt_test MATLAB version Test test_opt. 30-Mar-2019 21:53:26 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. 30-Mar-2019 21:53:26 30-Mar-2019 21:53:26 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. 30-Mar-2019 21:53:26 30-Mar-2019 21:53:26 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. 30-Mar-2019 21:53:26 30-Mar-2019 21:53:26 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) = -4 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. 30-Mar-2019 21:53:26 30-Mar-2019 21:53:26 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 = ( 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 = ( 9.00315, 2.57578 ) F(X_MIN) = 95 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. 30-Mar-2019 21:53:26 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: 0.218418 0.956318 0.829509 G: -416.250383 91.160095 -260.964675 GDIF: -416.250385 91.160095 -260.964674 Problem 2: "The Biggs EXP6 function." X: 0.218418 0.956318 0.829509 0.561695 0.415307 0.066119 G: 1.479396 -0.937452 -7.853636 6.562406 0.117928 -7.501965 GDIF: 1.479396 -0.937452 -7.853636 6.562406 0.117928 -7.501965 Problem 3: "The Gaussian function." X: 0.218418 0.956318 0.829509 G: -0.833706 0.092006 0.214072 GDIF: -0.833706 0.092006 0.214072 Problem 4: "The Powell badly scaled function." X: 0.218418 0.956318 G: 39931471.678680 9120154.415360 GDIF: 39931471.627394 9120154.427120 Problem 5: "The Box 3-dimensional function." X: 0.218418 0.956318 0.829509 G: 0.828128 -0.695514 2.279768 GDIF: 0.828128 -0.695514 2.279768 Problem 6: "The variably dimensioned function." X: 0.218418 0.956318 0.829509 0.561695 G: -130.915708 -258.792453 -388.398614 -518.286786 GDIF: -130.915708 -258.792453 -388.398614 -518.286786 Problem 7: "The Watson function." X: 0.218418 0.956318 0.829509 0.561695 G: 121.461958 92.461770 60.487688 32.121454 GDIF: 121.461958 92.461770 60.487688 32.121454 Problem 8: "The Penalty Function #1." X: 0.218418 0.956318 0.829509 0.561695 G: 1.499065 6.563540 5.693208 3.855103 GDIF: 1.499065 6.563540 5.693208 3.855103 Problem 9: "The Penalty Function #2." X: 0.218418 0.956318 0.829509 0.561695 G: 12.709043 41.612770 24.063258 8.147119 GDIF: 12.709043 41.612770 24.063258 8.147119 Problem 10: "The Brown Badly Scaled Function." X: 0.218418 0.956318 G: -2000002.988928 1.130203 GDIF: -2000232.601592 0.000000 Problem 11: "The Brown and Dennis Function." X: 0.218418 0.956318 0.829509 0.561695 G: -1086892.411667 -4111378.118315 39776.583392 -15192.545488 GDIF: -1086892.431179 -4111378.136700 39776.616674 -15192.582914 Problem 12: "The Gulf R&D Function." X: 0.218418 0.956318 0.829509 G: -0.000000 -0.000000 0.000000 GDIF: 0.000000 0.000000 0.000000 Problem 13: "The Trigonometric Function." X: 0.218418 0.956318 0.829509 0.561695 G: 0.558937 8.325839 9.265787 6.697629 GDIF: 0.558937 8.325839 9.265787 6.697629 Problem 14: "The Extended Rosenbrock parabolic valley Function." X: 0.218418 0.956318 0.829509 0.561695 G: -80.946072 181.722205 41.595729 -25.278025 GDIF: -80.946072 181.722205 41.595729 -25.278025 Problem 15: "The Extended Powell Singular Quartic Function." X: 0.218418 0.956318 0.829509 0.561695 G: 17.945128 194.243939 5.454023 -1.060078 GDIF: 17.945128 194.243938 5.454023 -1.060078 Problem 16: "The Beale Function." X: 0.218418 0.956318 G: -1.163091 5.628668 GDIF: -1.163091 5.628668 Problem 17: "The Wood Function." X: 0.218418 0.956318 0.829509 0.561695 G: -80.946072 172.161390 37.402058 -32.468887 GDIF: -80.946072 172.161389 37.402058 -32.468887 Problem 18: "The Chebyquad Function" X: 0.218418 0.956318 0.829509 0.561695 G: -0.547793 -0.701756 0.909926 0.608409 GDIF: -0.547793 -0.701756 0.909926 0.608409 Problem 19: "The Leon cubic valley function" X: 0.218418 0.956318 G: -28.638471 189.179519 GDIF: -28.638471 189.179519 Problem 20: "The Gregory and Karney Tridiagonal Matrix Function" X: 0.218418 0.956318 0.829509 0.561695 G: -2.737899 0.864708 0.141005 0.293882 GDIF: -3.475799 1.729415 0.282011 0.587763 Problem 21: "The Hilbert Matrix Function F = x'Ax" X: 0.218418 0.956318 0.829509 0.561695 G: 2.227008 1.495396 1.142806 0.928724 GDIF: 2.227008 1.495396 1.142807 0.928724 Problem 22: "The De Jong Function F1" X: 0.218418 0.956318 0.829509 G: 0.436837 1.912635 1.659018 GDIF: 0.436837 1.912635 1.659018 Problem 23: "The De Jong Function F2" X: 0.218418 0.956318 G: -80.946072 181.722205 GDIF: -80.946072 181.722205 Problem 24: "The De Jong Function F3, (discontinuous)" X: 0.218418 0.956318 0.829509 0.561695 0.415307 G: 0.000000 0.000000 0.000000 0.000000 0.000000 GDIF: 0.000000 0.000000 0.000000 0.000000 0.000000 Problem 25: "The De Jong Function F4 (with Gaussian noise)" X: 0.218418 0.956318 0.829509 0.561695 0.415307 0.066119 0.257578 0.109957 0.043829 0.633966 0.061727 0.449539 0.401306 0.754673 0.797287 0.001838 0.897504 0.350752 0.094545 0.013617 0.859097 0.840847 0.123104 0.007512 0.260303 0.912484 0.113664 0.351629 0.822887 0.267132 G: 0.041680 6.996751 6.849280 2.835455 1.432643 0.006937 0.478501 0.042542 0.003031 10.191950 0.010349 4.360570 3.360711 24.069402 30.408516 0.000000 49.160714 3.106950 0.064228 0.000202 53.260553 52.315973 0.171634 0.000041 1.763752 79.014845 0.158596 4.869348 64.636688 2.287496 GDIF: 0.041680 6.996751 6.849280 2.835454 1.432643 0.006937 0.478501 0.042542 0.003031 10.191950 0.010348 4.360570 3.360712 24.069402 30.408516 0.000000 49.160714 3.106950 0.064228 0.000202 53.260553 52.315973 0.171634 0.000041 1.763752 79.014845 0.158596 4.869348 64.636688 2.287496 Repeat problem with P = 1.000000 X: -1.280000 -1.191724 -1.103448 -1.015172 -0.926897 -0.838621 -0.750345 -0.662069 -0.573793 -0.485517 -0.397241 -0.308966 -0.220690 -0.132414 -0.044138 0.044138 0.132414 0.220690 0.308966 0.397241 0.485517 0.573793 0.662069 0.750345 0.838621 0.926897 1.015172 1.103448 1.191724 1.280000 G: -8.388608 -13.539954 -16.122678 -16.739381 -15.926626 -14.154938 -11.828801 -9.286663 -6.800933 -4.577981 -2.758139 -1.415700 -0.558920 -0.130013 -0.005159 0.005503 0.157873 0.773889 2.241525 5.014798 9.613760 16.624502 26.699155 40.555888 58.978907 82.818458 112.990825 150.478330 196.329336 251.658240 GDIF: 13376863.992944 -15519344.518217 -8094602.544720 21361200.241489 -955982.543718 28677339.669230 -22036784.416731 -26493478.587529 -9399294.451087 25228163.989555 -54042285.034548 -32311832.524459 -13398971.037934 -20261623.537335 27185037.298673 -106728404.403304 -18882149.715052 -32096721.817002 -535998.882720 10424205.674965 -536706.816970 -34910720.258888 8138359.223979 23277373.778009 -25921263.954055 13307880.724684 3615020.414302 -7404770.264792 7280595.611185 21233359.438936 Problem 26: "The De Jong Function F5" X: 0.218418 0.956318 G: 0.000000 -0.000000 GDIF: 0.000000 -0.000000 Problem 27: "The Schaffer Function F6" X: 0.218418 0.956318 G: 0.205288 0.898826 GDIF: 0.205288 0.898826 Problem 28: "The Schaffer Function F7" X: 0.218418 0.956318 G: -1.640658 -7.183418 GDIF: -1.640658 -7.183418 Problem 29: "The Goldstein Price Polynomial" X: 0.218418 0.956318 G: -37314.459913 51534.589361 GDIF: -37314.460186 51534.589322 Problem 30: "The Branin RCOS Function" X: 0.218418 0.956318 G: -16.517562 -9.404444 GDIF: -16.517562 -9.404444 Problem 31: "The Shekel SQRN5 Function" X: 0.218418 0.956318 0.829509 0.561695 G: -1.467692 -0.087169 -0.323613 -0.825977 GDIF: -1.467692 -0.087169 -0.323613 -0.825977 Problem 32: "The Shekel SQRN7 Function" X: 0.218418 0.956318 0.829509 0.561695 G: -1.471670 -0.091191 -0.325455 -0.828763 GDIF: -1.471670 -0.091191 -0.325455 -0.828763 Problem 33: "The Shekel SQRN10 Function" X: 0.218418 0.956318 0.829509 0.561695 G: -1.477067 -0.092231 -0.330335 -0.830136 GDIF: -1.477067 -0.092231 -0.330335 -0.830136 Problem 34: "The Six-Hump Camel-Back Polynomial" X: 0.218418 0.956318 G: 2.617130 6.561379 GDIF: 2.617130 6.561379 Problem 35: "The Shubert Function" X: 0.218418 0.956318 G: -53.883152 42.611477 GDIF: -53.883152 42.611477 Problem 36: "The Stuckman Function" X: 0.218418 0.956318 G: 0.000000 0.000000 GDIF: 0.000000 0.000000 Problem 37: "The Easom Function" X: 0.218418 0.956318 G: -0.000005 -0.000003 GDIF: -0.000005 -0.000003 Problem 38: "The Bohachevsky Function #1" X: 0.218418 0.956318 G: 2.934565 1.202547 GDIF: 2.934565 1.202546 Problem 39: "The Bohachevsky Function #2" X: 0.218418 0.956318 G: 2.567607 4.747100 GDIF: 2.567607 4.747100 Problem 40: "The Bohachevsky Function #3" X: 0.218418 0.956318 G: 2.934565 10.382080 GDIF: 2.934565 10.382080 Problem 41: "The Colville Polynomial" X: 0.218418 0.956318 0.829509 0.561695 G: -80.946072 172.161390 37.402058 -32.468887 GDIF: -80.946072 172.161389 37.402058 -32.468887 Problem 42: "The Powell 3D Function" X: 0.218418 0.956318 0.829509 G: -0.618217 0.202459 -0.478821 GDIF: -0.618217 0.202459 -0.478821 Problem 43: "The Himmelblau function." X: 0.218418 0.956318 G: -20.467293 -42.434960 GDIF: -20.467292 -42.434959 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: 0.218418 0.956318 0.829509 H: Col: 1 2 3 Row 1 : 695.183 321.279 316.348 2 : 321.279 27.412 -72.2522 3 : 316.348 -72.2522 202 H (approximated): Col: 1 2 3 Row 1 : 695.19 321.279 316.347 2 : 321.279 27.4163 -72.2523 3 : 316.347 -72.2523 202.001 Problem 2 The Biggs EXP6 function. N = 6 X: 0.561695 0.415307 0.066119 0.257578 0.109957 0.043829 H: Col: 1 2 3 4 5 Row 1 : -0.347563 -0.107545 7.72601 0.525213 0.0244586 2 : -0.107545 2.12275 2.04606 -11.3721 -0.109786 3 : 7.72601 2.04606 12.9169 -14.015 -0.44614 4 : 0.525213 -11.3721 -14.015 15.2488 0.504308 5 : 0.0244586 -0.109786 -0.44614 0.504308 -0.340218 6 : -0.67303 2.96376 16.7654 -18.3504 10.6458 Col: 6 Row 1 : -0.67303 2 : 2.96376 3 : 16.7654 4 : -18.3504 5 : 10.6458 6 : 22.366 H (approximated): Col: 1 2 3 4 5 Row 1 : -0.34755 -0.107497 7.72604 0.525258 0.0244291 2 : -0.107497 2.12275 2.04605 -11.3721 -0.109802 3 : 7.72604 2.04605 12.917 -14.0151 -0.446162 4 : 0.525258 -11.3721 -14.0151 15.2487 0.504306 5 : 0.0244291 -0.109802 -0.446162 0.504306 -0.340121 6 : -0.673023 2.96375 16.7654 -18.3504 10.6458 Col: 6 Row 1 : -0.673023 2 : 2.96375 3 : 16.7654 4 : -18.3504 5 : 10.6458 6 : 22.366 Problem 3 The Gaussian function. N = 3 X: 0.633966 0.061727 0.449539 H: Col: 1 2 3 Row 1 : 23.0411 -52.4058 -0.340601 2 : -52.4058 135.587 0.637746 3 : -0.340601 0.637746 -0.167435 H (approximated): Col: 1 2 3 Row 1 : 23.041 -52.4058 -0.3406 2 : -52.4058 135.587 0.637744 3 : -0.3406 0.637744 -0.16748 Problem 4 The Powell badly scaled function. N = 2 X: 0.401306 0.754673 H: Col: 1 2 Row 1 : 1.13906e+08 1.21122e+08 2 : 1.21122e+08 3.22093e+07 H (approximated): Col: 1 2 Row 1 : 1.13906e+08 1.21122e+08 2 : 1.21122e+08 3.22092e+07 Problem 5 The Box 3-dimensional function. N = 3 X: 0.797287 0.001838 0.897504 H: Col: 1 2 3 Row 1 : -1.29242 -4.16593 3.31195 2 : -4.16593 14.3681 -5.44545 3 : 3.31195 -5.44545 6.12801 H (approximated): Col: 1 2 3 Row 1 : -1.29245 -4.16594 3.31195 2 : -4.16594 14.3681 -5.44546 3 : 3.31195 -5.44546 6.12801 Problem 6 The variably dimensioned function. N = 4 X: 0.350752 0.094545 0.013617 0.859097 H: Col: 1 2 3 4 Row 1 : 433.544 863.088 1294.63 1726.18 2 : 863.088 1728.18 2589.26 3452.35 3 : 1294.63 2589.26 3885.9 5178.53 4 : 1726.18 3452.35 5178.53 6906.7 H (approximated): Col: 1 2 3 4 Row 1 : 433.585 863.085 1294.63 1726.18 2 : 863.085 1728.21 2589.27 3452.35 3 : 1294.63 2589.27 3885.9 5178.53 4 : 1726.18 3452.35 5178.53 6906.71 Problem 7 The Watson function. N = 4 X: 0.840847 0.123104 0.007512 0.260303 H: Col: 1 2 3 4 Row 1 : 419.563 107.218 33.6921 -7.22157 2 : 107.218 93.6921 52.7784 27.3018 3 : 33.6921 52.7784 47.6467 40.3167 4 : -7.22157 27.3018 40.3167 46.1526 H (approximated): Col: 1 2 3 4 Row 1 : 419.562 107.218 33.6921 -7.22179 2 : 107.218 93.6921 52.7783 27.3018 3 : 33.6921 52.7783 47.6459 40.3167 4 : -7.22179 27.3018 40.3167 46.1523 Problem 8 The Penalty Function #1. N = 4 X: 0.912484 0.113664 0.351629 0.822887 H: Col: 1 2 3 4 Row 1 : 12.2464 0.829733 2.56684 6.00697 2 : 0.829733 5.68871 0.31974 0.748262 3 : 2.56684 0.31974 6.57449 2.31481 4 : 6.00697 0.748262 2.31481 11.0025 H (approximated): Col: 1 2 3 4 Row 1 : 12.2463 0.829731 2.56684 6.00697 2 : 0.829731 5.68871 0.319741 0.748263 3 : 2.56684 0.319741 6.57449 2.31481 4 : 6.00697 0.748263 2.31481 11.0025 Problem 9 The Penalty Function #2. N = 4 X: 0.267132 0.692066 0.561662 0.861216 H: Col: 1 2 3 4 Row 1 : 44.6529 17.7478 9.60244 7.36187 2 : 17.7478 59.624 18.658 14.3044 3 : 9.60244 18.658 26.8543 7.7394 4 : 7.36187 14.3044 7.7394 14.3133 H (approximated): Col: 1 2 3 4 Row 1 : 44.6529 17.7478 9.60244 7.36188 2 : 17.7478 59.6239 18.658 14.3044 3 : 9.60244 18.658 26.8542 7.7394 4 : 7.36188 14.3044 7.7394 14.3133 Problem 10 The Brown Badly Scaled Function. N = 2 X: 0.453794 0.911977 H: Col: 1 2 Row 1 : 3.6634 -2.3446 2 : -2.3446 2.41186 H (approximated): Col: 1 2 Row 1 : 7.85382e+06 0 2 : 0 0 Problem 11 The Brown and Dennis Function. N = 4 X: 0.597917 0.188955 0.761492 0.396988 H: Col: 1 2 3 4 Row 1 : 100358 363049 -3200.99 333.505 2 : 363049 1.33386e+06 -10323.8 2193.46 3 : -3200.99 -10323.8 33819.7 -14522 4 : 333.505 2193.46 -14522 11700 H (approximated): Col: 1 2 3 4 Row 1 : 100386 363034 -3205.71 339.546 2 : 363034 1.33462e+06 -10316.2 2197.06 3 : -3205.71 -10316.2 33834.8 -14510.6 4 : 339.546 2197.06 -14510.6 11744.3 Problem 12 The Gulf R&D Function. N = 3 X: 0.185314 0.574366 0.367027 H: Col: 1 2 3 Row 1 : -0.00606336 -1.53412e-05 0.00399945 2 :-1.53412e-05 -4.27683e-08 9.06522e-06 3 : 0.00399945 9.06522e-06 -0.0024896 H (approximated): Col: 1 2 3 Row 1 : -0.00640013 0 0.00388579 2 : 0 -0.000152384 7.61921e-05 3 : 0.00388579 7.61921e-05 -0.00243815 Problem 13 The Trigonometric Function. N = 4 X: 0.617205 0.361529 0.212930 0.714471 H: Col: 1 2 3 4 Row 1 : 5.23588 1.20635 0.480848 4.88273 2 : 1.20635 5.12239 0.258676 2.87494 3 : 0.480848 0.258676 5.82458 1.44607 4 : 4.88273 2.87494 1.44607 23.912 H (approximated): Col: 1 2 3 4 Row 1 : 5.23588 1.20635 0.480848 4.88274 2 : 1.20635 5.12237 0.258677 2.87494 3 : 0.480848 0.258677 5.82459 1.44607 4 : 4.88274 2.87494 1.44607 23.912 Problem 14 The Extended Rosenbrock parabolic valley Function. N = 4 X: 0.117707 0.299329 0.825003 0.824660 H: Col: 1 2 3 4 Row 1 : -101.106 -47.0827 0 0 2 : -47.0827 200 0 0 3 : 0 0 488.892 -330.001 4 : 0 0 -330.001 200 H (approximated): Col: 1 2 3 4 Row 1 : -101.106 -47.0828 0 0 2 : -47.0828 200 0 0 3 : 0 0 488.892 -330.001 4 : 0 0 -330.001 200 Problem 15 The Extended Powell Singular Quartic Function. N = 4 X: 0.061862 0.710781 0.088283 0.777994 H: Col: 1 2 3 4 Row 1 : 63.5414 20 0 -61.5414 2 : 20 203.425 -6.84923 0 3 : 0 -6.84923 23.6985 -10 4 : -61.5414 0 -10 71.5414 H (approximated): Col: 1 2 3 4 Row 1 : 63.5413 20 0 -61.5415 2 : 20 203.425 -6.84921 0 3 : 0 -6.84921 23.6985 -10 4 : -61.5415 0 -10 71.5414 Problem 16 The Beale Function. N = 2 X: 0.745303 0.308675 H: Col: 1 2 Row 1 : 4.47698 2.72557 2 : 2.72557 11.5724 H (approximated): Col: 1 2 Row 1 : 4.47697 2.72558 2 : 2.72558 11.5724 Problem 17 The Wood Function. N = 4 X: 0.899373 0.763537 0.761731 0.406970 H: Col: 1 2 3 4 Row 1 : 667.232 -359.749 0 0 2 : -359.749 220.2 0 19.8 3 : 0 0 482.143 -274.223 4 : 0 19.8 -274.223 200.2 H (approximated): Col: 1 2 3 4 Row 1 : 667.232 -359.749 9.52401e-06 9.52401e-06 2 : -359.749 220.2 0 19.8 3 : 9.52401e-06 0 482.143 -274.223 4 : 9.52401e-06 19.8 -274.223 200.2 Problem 18 The Chebyquad Function N = 4 X: 0.938749 0.562088 0.017820 0.501103 H: Col: 1 2 3 4 Row 1 : 109.846 -14.7105 -31.1127 -8.97823 2 : -14.7105 -9.54222 0.832467 4.75854 3 : -31.1127 0.832467 223.201 -11.5224 4 : -8.97823 4.75854 -11.5224 -11.1572 H (approximated): Col: 1 2 3 4 Row 1 : 109.846 -14.7105 -31.1127 -8.97823 2 : -14.7105 -9.54222 0.832467 4.75854 3 : -31.1127 0.832467 223.201 -11.5224 4 : -8.97823 4.75854 -11.5224 -11.1572 Problem 19 The Leon cubic valley function N = 2 X: 0.041909 0.368851 H: Col: 1 2 Row 1 : -16.5406 -1.05383 2 : -1.05383 200 H (approximated): Col: 1 2 Row 1 : -16.5406 -1.0538 2 : -1.0538 200 Problem 20 The Gregory and Karney Tridiagonal Matrix Function N = 4 X: 0.271724 0.858573 0.029037 0.017442 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 : 2.00001 -2 0 0 2 : -2 4 -2 0 3 : 0 -2 4 -2 4 : 0 0 -2 4.00001 Problem 21 The Hilbert Matrix Function F = x'Ax N = 4 X: 0.152384 0.114319 0.353907 0.119308 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 0.666664 0.5 0.4 3 : 0.666667 0.5 0.399999 0.333333 4 : 0.5 0.4 0.333333 0.285713 Problem 22 The De Jong Function F1 N = 3 X: 0.206653 0.212924 0.612948 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 -2.97625e-07 2 : 0 2 -2.97625e-07 3 :-2.97625e-07 -2.97625e-07 2 Problem 23 The De Jong Function F2 N = 2 X: 0.809519 0.587090 H: Col: 1 2 Row 1 : 553.55 -323.808 2 : -323.808 200 H (approximated): Col: 1 2 Row 1 : 553.55 -323.808 2 : -323.808 200 Problem 24 The De Jong Function F3, (discontinuous) N = 5 X: 0.215492 0.768056 0.723297 0.448019 0.855176 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: 0.945017 0.909057 0.519726 0.030195 0.481067 0.292313 0.902640 0.667842 0.412278 0.156948 0.833282 0.964404 0.740790 0.456099 0.653561 0.406827 0.540539 0.832281 0.145756 0.717128 0.775651 0.362262 0.531111 0.379977 0.269285 0.877418 0.761285 0.913675 0.135794 0.291195 H: Col: 1 2 3 4 5 Row 1 : 10.7167 0 0 0 0 2 : 0 19.8332 0 0 0 3 : 0 0 9.72413 0 0 4 : 0 0 0 0.0437623 0 5 : 0 0 0 0 13.8855 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 : 6.15217 0 0 0 0 7 : 0 68.4397 0 0 0 8 : 0 0 42.8172 0 0 9 : 0 0 0 18.3571 0 10 : 0 0 0 0 2.95594 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 : 91.6553 0 0 0 0 12 : 0 133.931 0 0 0 13 : 0 0 85.6081 0 0 14 : 0 0 0 34.9484 0 15 : 0 0 0 0 76.8857 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 : 31.7776 0 0 0 0 17 : 0 59.6051 0 0 0 18 : 0 0 149.621 0 0 19 : 0 0 0 4.8438 0 20 : 0 0 0 0 123.426 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 : 151.612 0 0 0 0 22 : 0 34.6456 0 0 0 23 : 0 0 77.8537 0 0 24 : 0 0 0 41.5821 0 25 : 0 0 0 0 21.7544 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 : 240.197 0 0 0 0 27 : 0 187.776 0 0 0 28 : 0 0 280.493 0 0 29 : 0 0 0 6.41713 0 30 : 0 0 0 0 30.5261 H (approximated): Col: 1 2 3 4 5 Row 1 : 10.7166 0 0 0 0 2 : 0 19.8331 0 0 0 3 : 0 0 9.72393 0 0 4 : 0 0 0 0.0432771 0 5 : 0 0 0 0 13.8852 6 :-7.61921e-05 0 0 0 -7.61921e-05 7 : 0 0 0 0 0 8 : 0 0 7.61921e-05 0 0 9 : 0 0 0 0 0 10 :-7.61921e-05 0 0 0 0 11 : 7.61921e-05 0 0 7.61921e-05 0 12 :-7.61921e-05 0 7.61921e-05 0 7.61921e-05 13 : 0 0 7.61921e-05 0 7.61921e-05 14 : 7.61921e-05 0 0 0 0 15 : 0 0 0 0 0 16 : 0 0 0 0 0 17 : 0 0 -7.61921e-05 0 -7.61921e-05 18 :-7.61921e-05 0 -0.000152384 0 -0.000152384 19 :-7.61921e-05 0 0 0 0 20 : 0 0 0 0 0 21 : 7.61921e-05 0 7.61921e-05 0 7.61921e-05 22 : 7.61921e-05 0 7.61921e-05 0 7.61921e-05 23 :-7.61921e-05 0 -7.61921e-05 0 -7.61921e-05 24 :-7.61921e-05 0 -7.61921e-05 0 -7.61921e-05 25 : 0 0 0 0 0 26 : 7.61921e-05 0 7.61921e-05 0 7.61921e-05 27 : 0 0 0 0 0 28 : 7.61921e-05 0 0 0 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 0 0 -7.61921e-05 2 : 0 0 0 0 0 3 : 0 0 7.61921e-05 0 0 4 : 0 0 0 0 0 5 :-7.61921e-05 0 0 0 0 6 : 6.15205 0 7.61921e-05 -7.61921e-05 7.61921e-05 7 : 0 68.44 0 0 0 8 : 7.61921e-05 0 42.8172 0 -7.61921e-05 9 :-7.61921e-05 0 0 18.3568 0 10 : 7.61921e-05 0 -7.61921e-05 0 2.95564 11 :-7.61921e-05 0 -7.61921e-05 0 0 12 : 0.000152384 0 0 7.61921e-05 0 13 : 7.61921e-05 0 7.61921e-05 7.61921e-05 0 14 : 0 0 -7.61921e-05 0 -7.61921e-05 15 : 0 0 0 0 0 16 : 0 0 0 0 0 17 :-0.000152384 0 0 -7.61921e-05 7.61921e-05 18 :-0.000152384 0 7.61921e-05 -0.000152384 0.000152384 19 : 7.61921e-05 0 7.61921e-05 0 0 20 :-7.61921e-05 0 0 0 0 21 : 0 0 -7.61921e-05 7.61921e-05 -7.61921e-05 22 : 7.61921e-05 0 -7.61921e-05 7.61921e-05 -7.61921e-05 23 :-7.61921e-05 0 7.61921e-05 -7.61921e-05 7.61921e-05 24 :-7.61921e-05 0 7.61921e-05 -7.61921e-05 7.61921e-05 25 : 0 0 0 0 0 26 : 0 0 -7.61921e-05 7.61921e-05 -7.61921e-05 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: 11 12 13 14 15 Row 1 : 7.61921e-05 -7.61921e-05 0 7.61921e-05 0 2 : 0 0 0 0 0 3 : 0 7.61921e-05 7.61921e-05 0 0 4 : 7.61921e-05 0 0 0 0 5 : 0 7.61921e-05 7.61921e-05 0 0 6 :-7.61921e-05 0.000152384 7.61921e-05 0 0 7 : 0 0 0 0 0 8 :-7.61921e-05 0 7.61921e-05 -7.61921e-05 0 9 : 0 7.61921e-05 7.61921e-05 0 0 10 : 0 0 0 -7.61921e-05 0 11 : 91.6551 -0.000152384 0 7.61921e-05 0 12 :-0.000152384 133.931 0 -7.61921e-05 0 13 : 0 0 85.6082 0 0 14 : 7.61921e-05 -7.61921e-05 0 34.9481 0 15 : 0 0 0 0 76.8857 16 : 0 0 0 0 0 17 : 0 0 -7.61921e-05 7.61921e-05 0 18 :-7.61921e-05 7.61921e-05 0 7.61921e-05 0 19 :-7.61921e-05 7.61921e-05 7.61921e-05 -7.61921e-05 0 20 : 0 0 -7.61921e-05 0 0 21 : 7.61921e-05 -7.61921e-05 -7.61921e-05 0 0 22 : 7.61921e-05 -7.61921e-05 0 0 0 23 :-7.61921e-05 7.61921e-05 0 0 0 24 :-7.61921e-05 7.61921e-05 0 0 0 25 : 0 0 0 0 0 26 : 7.61921e-05 -7.61921e-05 -7.61921e-05 0 0 27 : 0 0 0 0 0 28 : 7.61921e-05 -7.61921e-05 0 7.61921e-05 0 29 : 0 0 0 0 0 30 : 0 0 0 0 0 Col: 16 17 18 19 20 Row 1 : 0 0 -7.61921e-05 -7.61921e-05 0 2 : 0 0 0 0 0 3 : 0 -7.61921e-05 -0.000152384 0 0 4 : 0 0 0 0 0 5 : 0 -7.61921e-05 -0.000152384 0 0 6 : 0 -0.000152384 -0.000152384 7.61921e-05 -7.61921e-05 7 : 0 0 0 0 0 8 : 0 0 7.61921e-05 7.61921e-05 0 9 : 0 -7.61921e-05 -0.000152384 0 0 10 : 0 7.61921e-05 0.000152384 0 0 11 : 0 0 -7.61921e-05 -7.61921e-05 0 12 : 0 0 7.61921e-05 7.61921e-05 0 13 : 0 -7.61921e-05 0 7.61921e-05 -7.61921e-05 14 : 0 7.61921e-05 7.61921e-05 -7.61921e-05 0 15 : 0 0 0 0 0 16 : 31.7776 0 0 0 0 17 : 0 59.605 -7.61921e-05 -7.61921e-05 0 18 : 0 -7.61921e-05 149.621 0 -7.61921e-05 19 : 0 -7.61921e-05 0 4.84399 -7.61921e-05 20 : 0 0 -7.61921e-05 -7.61921e-05 123.425 21 : 0 7.61921e-05 0 -7.61921e-05 0 22 : 0 7.61921e-05 7.61921e-05 0 0 23 : 0 -7.61921e-05 -7.61921e-05 0 0 24 : 0 -7.61921e-05 -7.61921e-05 0 0 25 : 0 0 0 0 0 26 : 0 7.61921e-05 0 -7.61921e-05 0 27 : 0 0 0 0 0 28 : 0 7.61921e-05 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 : 7.61921e-05 7.61921e-05 -7.61921e-05 -7.61921e-05 0 2 : 0 0 0 0 0 3 : 7.61921e-05 7.61921e-05 -7.61921e-05 -7.61921e-05 0 4 : 0 0 0 0 0 5 : 7.61921e-05 7.61921e-05 -7.61921e-05 -7.61921e-05 0 6 : 0 7.61921e-05 -7.61921e-05 -7.61921e-05 0 7 : 0 0 0 0 0 8 :-7.61921e-05 -7.61921e-05 7.61921e-05 7.61921e-05 0 9 : 7.61921e-05 7.61921e-05 -7.61921e-05 -7.61921e-05 0 10 :-7.61921e-05 -7.61921e-05 7.61921e-05 7.61921e-05 0 11 : 7.61921e-05 7.61921e-05 -7.61921e-05 -7.61921e-05 0 12 :-7.61921e-05 -7.61921e-05 7.61921e-05 7.61921e-05 0 13 :-7.61921e-05 0 0 0 0 14 : 0 0 0 0 0 15 : 0 0 0 0 0 16 : 0 0 0 0 0 17 : 7.61921e-05 7.61921e-05 -7.61921e-05 -7.61921e-05 0 18 : 0 7.61921e-05 -7.61921e-05 -7.61921e-05 0 19 :-7.61921e-05 0 0 0 0 20 : 0 0 0 0 0 21 : 151.612 -7.61921e-05 7.61921e-05 7.61921e-05 0 22 :-7.61921e-05 34.6454 7.61921e-05 7.61921e-05 0 23 : 7.61921e-05 7.61921e-05 77.8536 -7.61921e-05 0 24 : 7.61921e-05 7.61921e-05 -7.61921e-05 41.582 0 25 : 0 0 0 0 21.7544 26 :-7.61921e-05 -7.61921e-05 7.61921e-05 7.61921e-05 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 : 7.61921e-05 0 7.61921e-05 0 0 2 : 0 0 0 0 0 3 : 7.61921e-05 0 0 0 0 4 : 0 0 0 0 0 5 : 7.61921e-05 0 0 0 0 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 :-7.61921e-05 0 -7.61921e-05 0 0 9 : 7.61921e-05 0 0 0 0 10 :-7.61921e-05 0 0 0 0 11 : 7.61921e-05 0 7.61921e-05 0 0 12 :-7.61921e-05 0 -7.61921e-05 0 0 13 :-7.61921e-05 0 0 0 0 14 : 0 0 7.61921e-05 0 0 15 : 0 0 0 0 0 16 : 0 0 0 0 0 17 : 7.61921e-05 0 7.61921e-05 0 0 18 : 0 0 7.61921e-05 0 0 19 :-7.61921e-05 0 0 0 0 20 : 0 0 0 0 0 21 :-7.61921e-05 0 0 0 0 22 :-7.61921e-05 0 0 0 0 23 : 7.61921e-05 0 0 0 0 24 : 7.61921e-05 0 0 0 0 25 : 0 0 0 0 0 26 : 240.197 0 -7.61921e-05 0 0 27 : 0 187.776 -7.61921e-05 0 0 28 :-7.61921e-05 -7.61921e-05 280.493 0 0 29 : 0 0 0 6.41689 0 30 : 0 0 0 0 30.5262 Repeat problem with P = 1.000000 X: -1.280000 -1.191724 -1.103448 -1.015172 -0.926897 -0.838621 -0.750345 -0.662069 -0.573793 -0.485517 -0.397241 -0.308966 -0.220690 -0.132414 -0.044138 0.044138 0.132414 0.220690 0.308966 0.397241 0.485517 0.573793 0.662069 0.750345 0.838621 0.926897 1.015172 1.103448 1.191724 1.280000 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 :-3.07048e+10 3.31957e+08 -2.77561e+09 -8.22986e+09 -3.29802e+09 2 : 3.31957e+08 3.36311e+09 6.01677e+08 7.66099e+08 -5.24215e+09 3 :-2.77561e+09 6.01677e+08 -8.05815e+10 2.41868e+10 -1.5229e+08 4 :-8.22986e+09 7.66099e+08 2.41868e+10 3.78977e+10 -2.61599e+09 5 :-3.29802e+09 -5.24215e+09 -1.5229e+08 -2.61599e+09 2.16917e+10 6 : 1.76193e+10 -7.20313e+09 4.55641e+09 -9.19001e+09 -1.31644e+10 7 :-5.03621e+09 6.51069e+09 -1.63426e+10 -1.70094e+10 1.29782e+10 8 :-7.33743e+09 1.30828e+10 5.60634e+09 5.35131e+09 -3.13846e+09 9 : 1.09117e+09 -6.83044e+09 -4.66636e+09 -7.31431e+09 2.27566e+10 10 : 1.38939e+09 1.45162e+10 -3.24384e+09 -4.59843e+09 1.90077e+10 11 : 5.52087e+09 -5.90552e+09 1.08457e+10 -8.62188e+09 -1.83275e+10 12 :-1.12382e+10 -8.98719e+09 -1.39693e+10 1.65677e+08 -2.03402e+09 13 :-2.13065e+08 -1.03876e+10 -2.91775e+10 -1.20506e+10 -1.19218e+09 14 : 9.2695e+09 1.17811e+10 -2.08903e+09 -6.39257e+09 -6.77569e+09 15 :-1.17814e+10 9.60108e+09 9.3599e+09 6.65326e+09 -6.18189e+09 16 : 6.43978e+09 1.5996e+10 -7.96586e+09 -1.35877e+10 2.24159e+09 17 :-2.79601e+09 -4.40176e+08 -8.92408e+09 7.05418e+09 1.07714e+10 18 : 1.98253e+09 -1.68972e+10 1.85348e+10 -6.87712e+09 1.58285e+10 19 : 2.81911e+09 -5.84329e+07 -6.2954e+09 9.89757e+09 3.93951e+09 20 : -5.006e+07 3.56306e+09 4.97805e+08 -8.11736e+09 -2.21671e+09 21 : 1.47928e+10 1.27672e+10 -1.33827e+10 -5.80112e+09 3.69646e+09 22 :-1.18394e+10 -8.28522e+09 -7.29086e+09 -1.94937e+10 -1.43027e+10 23 :-1.04078e+09 -1.50562e+10 -1.08231e+10 -9.71266e+09 -1.41936e+09 24 : 3.2272e+09 4.61984e+09 -6.60179e+09 -2.43553e+10 3.06134e+08 25 :-1.33303e+09 3.23673e+09 -1.92478e+10 1.10479e+10 -9.75017e+09 26 :-6.38063e+09 5.39602e+08 -1.39204e+10 8.22885e+09 -1.09364e+10 27 : 1.12581e+10 -1.13247e+10 7.05296e+09 -1.29575e+10 1.56375e+10 28 :-3.00398e+09 -6.53127e+09 -1.47578e+09 1.8802e+09 -1.97207e+10 29 :-3.86028e+08 -8.33672e+09 7.61399e+09 7.87904e+09 7.79853e+08 30 :-5.42683e+09 -3.98527e+09 -6.14347e+09 -1.36086e+10 8.63181e+09 Col: 6 7 8 9 10 Row 1 : 1.76193e+10 -5.03621e+09 -7.33743e+09 1.09117e+09 1.38939e+09 2 :-7.20313e+09 6.51069e+09 1.30828e+10 -6.83044e+09 1.45162e+10 3 : 4.55641e+09 -1.63426e+10 5.60634e+09 -4.66636e+09 -3.24384e+09 4 :-9.19001e+09 -1.70094e+10 5.35131e+09 -7.31431e+09 -4.59843e+09 5 :-1.31644e+10 1.29782e+10 -3.13846e+09 2.27566e+10 1.90077e+10 6 :-1.90148e+10 1.91086e+10 -5.1413e+08 1.72754e+10 8.60111e+09 7 : 1.91086e+10 1.77934e+10 -1.74554e+10 1.9461e+10 3.61382e+09 8 : -5.1413e+08 -1.74554e+10 -4.55488e+10 -1.28171e+10 1.48423e+10 9 : 1.72754e+10 1.9461e+10 -1.28171e+10 -8.58641e+10 -3.82129e+08 10 : 8.60111e+09 3.61382e+09 1.48423e+10 -3.82129e+08 -1.50136e+10 11 : 6.05186e+09 8.74091e+09 -1.07547e+10 -4.71697e+09 -5.23088e+09 12 :-6.66582e+09 -1.20474e+10 4.81638e+09 2.08755e+09 -1.5084e+10 13 : 1.69303e+10 -1.22627e+10 6.44581e+09 5.21629e+09 -8.4617e+09 14 : 3.06774e+09 2.61173e+09 -4.79066e+09 8.65924e+09 -1.10433e+10 15 : 9.14071e+09 1.50878e+10 -2.05806e+09 -7.9931e+09 5.99268e+09 16 :-1.20168e+10 -8.00462e+09 -2.15625e+10 1.75991e+10 1.26166e+10 17 :-6.26748e+09 -8.47844e+09 -8.29938e+09 2.49392e+09 2.66909e+10 18 :-1.44838e+09 4.68301e+09 -6.03574e+09 9.70133e+09 -7.97774e+09 19 :-6.32634e+09 -4.66687e+09 6.53413e+09 -9.38179e+09 -2.78833e+09 20 : 1.32348e+09 7.46214e+09 6.41661e+09 1.29943e+10 1.7131e+09 21 :-4.79968e+09 1.25906e+09 1.10239e+10 3.0636e+09 8.7953e+09 22 : 7.42939e+09 2.41005e+09 -2.09587e+09 -6.05885e+09 -7.34671e+09 23 : 9.02343e+09 -1.69322e+10 -3.66231e+09 1.97841e+09 -3.71434e+09 24 :-2.02252e+10 -1.02785e+10 6.3511e+09 -2.34282e+10 -5.81162e+09 25 :-1.97176e+10 -4.79572e+09 -1.914e+10 -4.56683e+09 3.03112e+09 26 : 5.57728e+09 1.74857e+10 1.05999e+10 -8.70657e+09 -7.58045e+09 27 :-5.92606e+09 -5.73735e+09 -1.75502e+09 -1.16717e+10 -1.75006e+10 28 : 5.95475e+09 6.30289e+08 1.11226e+10 4.06734e+09 -4.9996e+09 29 : -9.7878e+09 -1.72526e+10 2.11543e+09 2.06301e+10 1.86886e+09 30 :-5.85987e+09 1.14051e+10 -5.35091e+09 7.12596e+09 7.40071e+09 Col: 11 12 13 14 15 Row 1 : 5.52087e+09 -1.12382e+10 -2.13065e+08 9.2695e+09 -1.17814e+10 2 :-5.90552e+09 -8.98719e+09 -1.03876e+10 1.17811e+10 9.60108e+09 3 : 1.08457e+10 -1.39693e+10 -2.91775e+10 -2.08903e+09 9.3599e+09 4 :-8.62188e+09 1.65677e+08 -1.20506e+10 -6.39257e+09 6.65326e+09 5 :-1.83275e+10 -2.03402e+09 -1.19218e+09 -6.77569e+09 -6.18189e+09 6 : 6.05186e+09 -6.66582e+09 1.69303e+10 3.06774e+09 9.14071e+09 7 : 8.74091e+09 -1.20474e+10 -1.22627e+10 2.61173e+09 1.50878e+10 8 :-1.07547e+10 4.81638e+09 6.44581e+09 -4.79066e+09 -2.05806e+09 9 :-4.71697e+09 2.08755e+09 5.21629e+09 8.65924e+09 -7.9931e+09 10 :-5.23088e+09 -1.5084e+10 -8.4617e+09 -1.10433e+10 5.99268e+09 11 : 2.41631e+10 1.76749e+10 -1.46175e+10 -1.44846e+10 2.35849e+09 12 : 1.76749e+10 -1.93308e+09 1.28938e+10 -1.38853e+10 -4.41524e+09 13 :-1.46175e+10 1.28938e+10 -2.17291e+10 -5.25117e+09 2.3072e+09 14 :-1.44846e+10 -1.38853e+10 -5.25117e+09 -1.28942e+11 -1.0295e+10 15 : 2.35849e+09 -4.41524e+09 2.3072e+09 -1.0295e+10 2.85583e+10 16 : 8.10533e+09 1.19001e+10 8.25196e+08 -2.60859e+08 1.22767e+09 17 :-1.38497e+10 1.34263e+10 -1.12973e+10 1.57059e+09 3.51581e+09 18 :-1.02126e+09 -8.05283e+09 -5.85028e+09 3.55693e+08 1.3188e+10 19 :-1.39269e+10 2.31603e+09 8.44379e+08 8.86097e+09 -4.25825e+09 20 : 7.97553e+09 -1.94055e+10 1.01146e+10 1.25578e+10 -1.46582e+10 21 :-8.33971e+09 -2.23274e+09 -8.39396e+09 -1.69184e+10 -7.36401e+09 22 : 1.8447e+10 7.81e+09 -2.52881e+09 4.06654e+09 2.12485e+09 23 :-2.14593e+10 4.58949e+09 -1.51836e+10 6.56239e+09 -8.18548e+09 24 :-1.21657e+10 3.30317e+09 1.27456e+10 1.04641e+10 1.31821e+10 25 : 4.63943e+09 1.00415e+10 -2.93781e+10 -1.05135e+09 -9.63303e+09 26 : 1.36203e+10 3.47409e+09 -1.32162e+10 -1.17744e+10 -1.19902e+10 27 :-1.15114e+10 -1.31261e+10 -1.13832e+10 2.52454e+10 -1.71288e+10 28 : 1.11069e+10 9.8258e+08 8.60663e+08 8.93354e+09 -3.03955e+09 29 : 1.65928e+10 2.85804e+09 -6.41958e+09 1.44398e+10 8.78126e+09 30 :-1.56707e+09 -1.61752e+10 1.9573e+09 1.06868e+09 2.2871e+09 Col: 16 17 18 19 20 Row 1 : 6.43978e+09 -2.79601e+09 1.98253e+09 2.81911e+09 -5.006e+07 2 : 1.5996e+10 -4.40176e+08 -1.68972e+10 -5.84329e+07 3.56306e+09 3 :-7.96586e+09 -8.92408e+09 1.85348e+10 -6.2954e+09 4.97805e+08 4 :-1.35877e+10 7.05418e+09 -6.87712e+09 9.89757e+09 -8.11736e+09 5 : 2.24159e+09 1.07714e+10 1.58285e+10 3.93951e+09 -2.21671e+09 6 :-1.20168e+10 -6.26748e+09 -1.44838e+09 -6.32634e+09 1.32348e+09 7 :-8.00462e+09 -8.47844e+09 4.68301e+09 -4.66687e+09 7.46214e+09 8 :-2.15625e+10 -8.29938e+09 -6.03574e+09 6.53413e+09 6.41661e+09 9 : 1.75991e+10 2.49392e+09 9.70133e+09 -9.38179e+09 1.29943e+10 10 : 1.26166e+10 2.66909e+10 -7.97774e+09 -2.78833e+09 1.7131e+09 11 : 8.10533e+09 -1.38497e+10 -1.02126e+09 -1.39269e+10 7.97553e+09 12 : 1.19001e+10 1.34263e+10 -8.05283e+09 2.31603e+09 -1.94055e+10 13 : 8.25196e+08 -1.12973e+10 -5.85028e+09 8.44379e+08 1.01146e+10 14 :-2.60859e+08 1.57059e+09 3.55693e+08 8.86097e+09 1.25578e+10 15 : 1.22767e+09 3.51581e+09 1.3188e+10 -4.25825e+09 -1.46582e+10 16 :-7.39792e+10 -1.39474e+10 -4.57623e+09 1.95493e+09 1.45527e+10 17 :-1.39474e+10 2.78819e+09 -4.84677e+08 -1.05209e+09 1.41871e+10 18 :-4.57623e+09 -4.84677e+08 -3.93805e+10 -6.03436e+09 -6.0333e+09 19 : 1.95493e+09 -1.05209e+09 -6.03436e+09 -1.40853e+10 2.27072e+10 20 : 1.45527e+10 1.41871e+10 -6.0333e+09 2.27072e+10 -9.81594e+09 21 :-8.57575e+09 5.58732e+08 8.11518e+09 5.67831e+09 -5.61504e+09 22 :-1.54375e+10 -2.38874e+10 4.26958e+09 -1.7222e+10 -2.19923e+09 23 :-5.13708e+09 -3.90971e+09 2.51906e+09 -1.31118e+10 1.03991e+10 24 : 4.71203e+09 4.87922e+09 2.38143e+09 1.92991e+09 8.63743e+09 25 : 7.73789e+09 -3.26244e+08 -2.60852e+09 1.17876e+10 -3.61692e+09 26 :-5.69329e+09 -3.40724e+08 4.65169e+09 -1.24046e+08 -1.46693e+10 27 : 5.63478e+09 -1.87394e+10 7.82845e+09 2.30451e+10 -1.28422e+09 28 :-6.65068e+09 4.54614e+09 2.2836e+09 8.45384e+07 -9.3787e+09 29 :-1.03521e+10 -2.01925e+09 9.37187e+09 -1.61676e+08 1.01504e+10 30 :-4.43462e+09 8.56259e+09 2.40419e+10 4.70852e+09 -1.1012e+10 Col: 21 22 23 24 25 Row 1 : 1.47928e+10 -1.18394e+10 -1.04078e+09 3.2272e+09 -1.33303e+09 2 : 1.27672e+10 -8.28522e+09 -1.50562e+10 4.61984e+09 3.23673e+09 3 :-1.33827e+10 -7.29086e+09 -1.08231e+10 -6.60179e+09 -1.92478e+10 4 :-5.80112e+09 -1.94937e+10 -9.71266e+09 -2.43553e+10 1.10479e+10 5 : 3.69646e+09 -1.43027e+10 -1.41936e+09 3.06134e+08 -9.75017e+09 6 :-4.79968e+09 7.42939e+09 9.02343e+09 -2.02252e+10 -1.97176e+10 7 : 1.25906e+09 2.41005e+09 -1.69322e+10 -1.02785e+10 -4.79572e+09 8 : 1.10239e+10 -2.09587e+09 -3.66231e+09 6.3511e+09 -1.914e+10 9 : 3.0636e+09 -6.05885e+09 1.97841e+09 -2.34282e+10 -4.56683e+09 10 : 8.7953e+09 -7.34671e+09 -3.71434e+09 -5.81162e+09 3.03112e+09 11 :-8.33971e+09 1.8447e+10 -2.14593e+10 -1.21657e+10 4.63943e+09 12 :-2.23274e+09 7.81e+09 4.58949e+09 3.30317e+09 1.00415e+10 13 :-8.39396e+09 -2.52881e+09 -1.51836e+10 1.27456e+10 -2.93781e+10 14 :-1.69184e+10 4.06654e+09 6.56239e+09 1.04641e+10 -1.05135e+09 15 :-7.36401e+09 2.12485e+09 -8.18548e+09 1.31821e+10 -9.63303e+09 16 :-8.57575e+09 -1.54375e+10 -5.13708e+09 4.71203e+09 7.73789e+09 17 : 5.58732e+08 -2.38874e+10 -3.90971e+09 4.87922e+09 -3.26244e+08 18 : 8.11518e+09 4.26958e+09 2.51906e+09 2.38143e+09 -2.60852e+09 19 : 5.67831e+09 -1.7222e+10 -1.31118e+10 1.92991e+09 1.17876e+10 20 :-5.61504e+09 -2.19923e+09 1.03991e+10 8.63743e+09 -3.61692e+09 21 : 5.50779e+10 -3.6254e+09 1.24674e+10 3.41132e+09 -9.48257e+09 22 : -3.6254e+09 -3.95603e+10 -3.83663e+09 1.08222e+10 8.53075e+09 23 : 1.24674e+10 -3.83663e+09 7.64736e+10 1.86672e+10 -1.17755e+10 24 : 3.41132e+09 1.08222e+10 1.86672e+10 5.59184e+10 -1.16968e+10 25 :-9.48257e+09 8.53075e+09 -1.17755e+10 -1.16968e+10 -2.67059e+10 26 :-1.20477e+10 -1.74244e+10 2.46477e+09 -4.67202e+09 1.34007e+10 27 : 8.71423e+08 -9.31578e+09 9.09955e+08 6.65594e+09 -1.53074e+09 28 : 1.00676e+10 9.536e+09 -9.64798e+09 -5.8335e+09 -4.26719e+09 29 : 2.95975e+08 -6.28741e+09 3.68105e+09 5.7211e+09 -8.23047e+09 30 :-4.60108e+08 5.86947e+09 -1.57339e+09 3.11376e+09 3.18203e+09 Col: 26 27 28 29 30 Row 1 :-6.38063e+09 1.12581e+10 -3.00398e+09 -3.86028e+08 -5.42683e+09 2 : 5.39602e+08 -1.13247e+10 -6.53127e+09 -8.33672e+09 -3.98527e+09 3 :-1.39204e+10 7.05296e+09 -1.47578e+09 7.61399e+09 -6.14347e+09 4 : 8.22885e+09 -1.29575e+10 1.8802e+09 7.87904e+09 -1.36086e+10 5 :-1.09364e+10 1.56375e+10 -1.97207e+10 7.79853e+08 8.63181e+09 6 : 5.57728e+09 -5.92606e+09 5.95475e+09 -9.7878e+09 -5.85987e+09 7 : 1.74857e+10 -5.73735e+09 6.30289e+08 -1.72526e+10 1.14051e+10 8 : 1.05999e+10 -1.75502e+09 1.11226e+10 2.11543e+09 -5.35091e+09 9 :-8.70657e+09 -1.16717e+10 4.06734e+09 2.06301e+10 7.12596e+09 10 :-7.58045e+09 -1.75006e+10 -4.9996e+09 1.86886e+09 7.40071e+09 11 : 1.36203e+10 -1.15114e+10 1.11069e+10 1.65928e+10 -1.56707e+09 12 : 3.47409e+09 -1.31261e+10 9.8258e+08 2.85804e+09 -1.61752e+10 13 :-1.32162e+10 -1.13832e+10 8.60663e+08 -6.41958e+09 1.9573e+09 14 :-1.17744e+10 2.52454e+10 8.93354e+09 1.44398e+10 1.06868e+09 15 :-1.19902e+10 -1.71288e+10 -3.03955e+09 8.78126e+09 2.2871e+09 16 :-5.69329e+09 5.63478e+09 -6.65068e+09 -1.03521e+10 -4.43462e+09 17 :-3.40724e+08 -1.87394e+10 4.54614e+09 -2.01925e+09 8.56259e+09 18 : 4.65169e+09 7.82845e+09 2.2836e+09 9.37187e+09 2.40419e+10 19 :-1.24046e+08 2.30451e+10 8.45384e+07 -1.61676e+08 4.70852e+09 20 :-1.46693e+10 -1.28422e+09 -9.3787e+09 1.01504e+10 -1.1012e+10 21 :-1.20477e+10 8.71423e+08 1.00676e+10 2.95975e+08 -4.60108e+08 22 :-1.74244e+10 -9.31578e+09 9.536e+09 -6.28741e+09 5.86947e+09 23 : 2.46477e+09 9.09955e+08 -9.64798e+09 3.68105e+09 -1.57339e+09 24 :-4.67202e+09 6.65594e+09 -5.8335e+09 5.7211e+09 3.11376e+09 25 : 1.34007e+10 -1.53074e+09 -4.26719e+09 -8.23047e+09 3.18203e+09 26 :-2.25516e+10 -5.25905e+09 -9.71362e+09 8.96552e+09 1.9515e+10 27 :-5.25905e+09 -1.85946e+10 1.90313e+10 1.23447e+10 -1.60326e+10 28 :-9.71362e+09 1.90313e+10 -2.2377e+10 -9.97568e+09 7.52439e+09 29 : 8.96552e+09 1.23447e+10 -9.97568e+09 3.54656e+10 2.42007e+09 30 : 1.9515e+10 -1.60326e+10 7.52439e+09 2.42007e+09 1.50031e+10 Problem 26 The De Jong Function F5 N = 2 X: 0.118211 0.771781 H: Col: 1 2 Row 1 : 0 0 2 : 0 0 H (approximated): Col: 1 2 Row 1 : 9.30079e-09 2.3252e-09 2 : 2.3252e-09 -9.30079e-08 Problem 27 The Schaffer Function F6 N = 2 X: 0.320633 0.877413 H: Col: 1 2 Row 1 : 0.830927 -0.520346 2 : -0.520346 -0.402851 H (approximated): Col: 1 2 Row 1 : 0.830927 -0.520346 2 : -0.520346 -0.402854 Problem 28 The Schaffer Function F7 N = 2 X: 0.679476 0.949176 H: Col: 1 2 Row 1 : -45.9253 -70.9999 2 : -70.9999 -94.2808 H (approximated): Col: 1 2 Row 1 : -45.9254 -71 2 : -71 -94.2809 Problem 29 The Goldstein Price Polynomial N = 2 X: 0.793361 0.021366 H: Col: 1 2 Row 1 : -4602.99 4432.79 2 : 4432.79 -8277.57 H (approximated): Col: 1 2 Row 1 : -4602.99 4432.79 2 : 4432.79 -8277.58 Problem 30 The Branin RCOS Function N = 2 X: 0.102278 0.991406 H: Col: 1 2 Row 1 : -2.14799 3.13025 2 : 3.13025 2 H (approximated): Col: 1 2 Row 1 : -2.14801 3.13024 2 : 3.13024 2.00004 Problem 31 The Shekel SQRN5 Function N = 4 X: 0.563260 0.704528 0.994146 0.604334 H: Col: 1 2 3 4 Row 1 : -1.00412 -4.0404 -0.0812913 -5.41002 2 : -4.0404 2.2331 -0.0554413 -3.6608 3 : -0.0812913 -0.0554413 4.96509 -0.0738354 4 : -5.41002 -3.6608 -0.0738354 0.0656652 H (approximated): Col: 1 2 3 4 Row 1 : -1.0041 -4.0404 -0.0812922 -5.41002 2 : -4.0404 2.23309 -0.0554404 -3.6608 3 : -0.0812922 -0.0554404 4.96509 -0.0738349 4 : -5.41002 -3.6608 -0.0738349 0.0656775 Problem 32 The Shekel SQRN7 Function N = 4 X: 0.046145 0.562029 0.021515 0.609135 H: Col: 1 2 3 4 Row 1 : -0.175254 -0.24006 -0.533769 -0.214035 2 : -0.24006 0.234145 -0.245878 -0.0992186 3 : -0.533769 -0.245878 -0.201798 -0.219348 4 : -0.214035 -0.0992186 -0.219348 0.256973 H (approximated): Col: 1 2 3 4 Row 1 : -0.175252 -0.24006 -0.533769 -0.214035 2 : -0.24006 0.234144 -0.245878 -0.0992187 3 : -0.533769 -0.245878 -0.201798 -0.219349 4 : -0.214035 -0.0992187 -0.219349 0.256973 Problem 33 The Shekel SQRN10 Function N = 4 X: 0.728789 0.748407 0.469634 0.135194 H: Col: 1 2 3 4 Row 1 : 0.840369 -0.216614 -0.454609 -0.738531 2 : -0.216614 0.873481 -0.420901 -0.685296 3 : -0.454609 -0.420901 0.188846 -1.44173 4 : -0.738531 -0.685296 -1.44173 -1.27496 H (approximated): Col: 1 2 3 4 Row 1 : 0.840355 -0.216615 -0.45461 -0.738533 2 : -0.216615 0.873478 -0.420902 -0.685294 3 : -0.45461 -0.420902 0.188844 -1.44173 4 : -0.738533 -0.685294 -1.44173 -1.27496 Problem 34 The Six-Hump Camel-Back Polynomial N = 2 X: 0.202348 0.860120 H: Col: 1 2 Row 1 : 6.98496 1 2 : 1 27.5107 H (approximated): Col: 1 2 Row 1 : 6.98496 1 2 : 1 27.5107 Problem 35 The Shubert Function N = 2 X: 0.040624 0.773973 H: Col: 1 2 Row 1 : -46.9153 -250.078 2 : -250.078 -419.891 H (approximated): Col: 1 2 Row 1 : -46.9158 -250.078 2 : -250.078 -419.89 Problem 36 The Stuckman Function N = 2 X: 0.218418 0.956318 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: 0.829509 0.561695 H: Col: 1 2 Row 1 :-2.90291e-05 -5.60947e-05 2 :-5.60947e-05 -6.00506e-05 H (approximated): Col: 1 2 Row 1 :-2.90291e-05 -5.60947e-05 2 :-5.60947e-05 -6.00506e-05 Problem 38 The Bohachevsky Function #1 N = 2 X: 0.415307 0.066119 H: Col: 1 2 Row 1 : -17.0828 0 2 : 0 46.5882 H (approximated): Col: 1 2 Row 1 : -17.0828 0 2 : 0 46.5882 Problem 39 The Bohachevsky Function #2 N = 2 X: 0.257578 0.109957 H: Col: 1 2 Row 1 : -1.78451 -22.8526 2 : -22.8526 -2.72801 H (approximated): Col: 1 2 Row 1 : -1.78451 -22.8526 2 : -22.8526 -2.72801 Problem 40 The Bohachevsky Function #3 N = 2 X: 0.043829 0.633966 H: Col: 1 2 Row 1 : 26.4066 0 2 : 0 21.754 H (approximated): Col: 1 2 Row 1 : 26.4066 -1.1905e-06 2 : -1.1905e-06 21.754 Problem 41 The Colville Polynomial N = 4 X: 0.061727 0.449539 0.401306 0.754673 H: Col: 1 2 3 4 Row 1 : -173.243 -24.6909 0 0 2 : -24.6909 220.2 0 19.8 3 : 0 0 -95.752 -144.47 4 : 0 19.8 -144.47 200.2 H (approximated): Col: 1 2 3 4 Row 1 : -173.243 -24.6909 0 0 2 : -24.6909 220.2 0 19.8 3 : 0 0 -95.7519 -144.47 4 : 0 19.8 -144.47 200.2 Problem 42 The Powell 3D Function N = 3 X: 0.797287 0.001838 0.897504 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 : -0.412723 0.412723 0 2 : 0.412723 -0.40758 -1.57078 3 : 0 -1.57078 0 Problem 43 The Himmelblau function. N = 2 X: 0.350752 0.094545 H: Col: 1 2 Row 1 : -40.1455 1.78119 2 : 1.78119 -24.4897 H (approximated): Col: 1 2 Row 1 : -40.1447 1.78152 2 : 1.78152 -24.49 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) = -4 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. 30-Mar-2019 21:53:27