cd v:\cursos\pos\otimiza\aulas help steepdes Unconstrained optimization using steep descent. [xo,Ot,nS]=steepdes(S,x0,ip,G,method,Lb,Ub,problem,tol,mxit) S: objective function x0: initial point ip: (0) no plot (default), (>0) plot figure ip with pause, (<0) plot figure ip G: gradient vector function method: line-search method: (0) quadratic+cubic (default), (1) cubic Lb, Ub: lower and upper bound vectors to plot (default = x0*(1+/-2)) problem: (-1): minimum (default), (1): maximum tol: tolerance (default = 1e-4) mxit: maximum number of iterations (default = 50*(1+4*~(ip>0))) xo: optimal point Ot: optimal value of S nS: number of objective function evaluations type test10 function S=test(x) % Edgar & Himmelblau, 1988 % x0 = [1, 2]' % xo = [0, 0]' % S(xo) = 0 S=4*x(1).^2-2.*x(1).*x(2)+x(2).^2; type gtest10 function G=test(x) % Gradient of Edgar & Himmelblau, 1988 % x0 = [1, 1]' % xo = [0, 0]' % S(xo) = 0 G(1)=8*x(1)-2*x(2); G(2)=-2*x(1)+2*x(2); [xo,Ot,nS]=steepdes('test10',[1 1],1,'gtest10') Pause: hit any key to continue... Directional Iteration Func-count f(x) Step-size derivative 1 0 3 0.166667 -36 Warning: Divide by zero. > In C:\Apps\Matlab\toolbox\optim\cubici2.m at line 12 In C:\Apps\Matlab\toolbox\optim\searchq.m at line 65 In v:\cursos\pos\otimiza\aulas\fminusub.m at line 283 In v:\cursos\pos\otimiza\aulas\fminunc1.m at line 220 In v:\cursos\pos\otimiza\aulas\varmetr.m at line 115 In v:\cursos\pos\otimiza\aulas\steepdes.m at line 51 Warning: Divide by zero. > In C:\Apps\Matlab\toolbox\optim\cubici2.m at line 16 In C:\Apps\Matlab\toolbox\optim\searchq.m at line 65 In v:\cursos\pos\otimiza\aulas\fminusub.m at line 283 In v:\cursos\pos\otimiza\aulas\fminunc1.m at line 220 In v:\cursos\pos\otimiza\aulas\varmetr.m at line 115 In v:\cursos\pos\otimiza\aulas\steepdes.m at line 51 Pause: hit any key to continue... 2 4 0.75 0.125 0 Pause: hit any key to continue... 3 9 0.21 0.6 0.45 Warning: Divide by zero. > In C:\Apps\Matlab\toolbox\optim\cubici2.m at line 12 In C:\Apps\Matlab\toolbox\optim\searchq.m at line 71 In v:\cursos\pos\otimiza\aulas\fminusub.m at line 283 In v:\cursos\pos\otimiza\aulas\fminunc1.m at line 220 In v:\cursos\pos\otimiza\aulas\varmetr.m at line 115 In v:\cursos\pos\otimiza\aulas\steepdes.m at line 51 Warning: Divide by zero. > In C:\Apps\Matlab\toolbox\optim\cubici2.m at line 16 In C:\Apps\Matlab\toolbox\optim\searchq.m at line 71 In v:\cursos\pos\otimiza\aulas\fminusub.m at line 283 In v:\cursos\pos\otimiza\aulas\fminunc1.m at line 220 In v:\cursos\pos\otimiza\aulas\varmetr.m at line 115 In v:\cursos\pos\otimiza\aulas\steepdes.m at line 51 Pause: hit any key to continue... 4 13 0.0138057 0.117834 7.7e-016 Warning: Divide by zero. > In C:\Apps\Matlab\toolbox\optim\cubici2.m at line 12 In C:\Apps\Matlab\toolbox\optim\searchq.m at line 34 In v:\cursos\pos\otimiza\aulas\fminusub.m at line 283 In v:\cursos\pos\otimiza\aulas\fminunc1.m at line 220 In v:\cursos\pos\otimiza\aulas\varmetr.m at line 115 In v:\cursos\pos\otimiza\aulas\steepdes.m at line 51 Warning: Divide by zero. > In C:\Apps\Matlab\toolbox\optim\cubici2.m at line 16 In C:\Apps\Matlab\toolbox\optim\searchq.m at line 34 In v:\cursos\pos\otimiza\aulas\fminusub.m at line 283 In v:\cursos\pos\otimiza\aulas\fminunc1.m at line 220 In v:\cursos\pos\otimiza\aulas\varmetr.m at line 115 In v:\cursos\pos\otimiza\aulas\steepdes.m at line 51 Pause: hit any key to continue... 5 18 0.00142354 0.792857 0.00781 Pause: hit any key to continue... 6 22 0.000107465 0.118106 -8.57e-017 Pause: hit any key to continue... 7 27 1.20867e-005 0.782782 6.09e-005 Optimization terminated successfully: Current search direction is a descent direction, and magnitude of directional derivative in search direction less than 2*options.TolFun Pause: hit any key to continue... xo = 0.0019 0.0006 Ot = 1.2087e-005 nS = 28 help fminunc FMINUNC Finds the minimum of a function of several variables. X=FMINUNC(FUN,X0) starts at the point X0 and finds a minimum X of the function described in FUN. X0 can be a scalar, vector or matrix. The function FUN (usually an M-file or inline object) should return a scalar function value F evaluated at X when called with feval: F=feval(FUN,X). See the examples below for more about FUN. X=FMINUNC(FUN,X0,OPTIONS) minimizes with the default optimization parameters replaced by values in the structure OPTIONS, an argument created with the OPTIMSET function. See OPTIMSET for details. Used options are Display, TolX, TolFun, DerivativeCheck, Diagnostics, GradObj, HessPattern, LineSearchType, Hessian, HessUpdate, MaxFunEvals, MaxIter, DiffMinChange and DiffMaxChange, LargeScale, MaxPCGIter, PrecondBandWidth, TolPCG, TypicalX. Use the GradObj option to specify that FUN can be called with two output arguments where the second, G, is the partial derivatives of the function df/dX, at the point X: [F,G] = feval(FUN,X). Use Hessian to specify that FUN can be called with three output arguments where the second, G, is the partial derivatives of the function df/dX, and the third H is the 2nd partial derivatives of the function (the Hessian) at the point X: [F,G,H] = feval(FUN,X). The Hessian is only used by the large-scale method, not the line-search method. X=FMINUNC(FUN,X0,OPTIONS,P1,P2,...) passes the problem-dependent parameters P1,P2,... directly to the function FUN, e.g. FUN would be called using feval as in: feval(FUN,X,P1,P2,...). Pass an empty matrix for OPTIONS to use the default values. [X,FVAL]=FMINUNC(FUN,X0,...) returns the value of the objective function FUN at the solution X. [X,FVAL,EXITFLAG]=FMINUNC(FUN,X0,...) returns a string EXITFLAG that describes the exit condition of FMINUNC. If EXITFLAG is: > 0 then FMINUNC converged to a solution X. 0 then the maximum number of function evaluations was reached. < 0 then FMINUNC did not converge to a solution. [X,FVAL,EXITFLAG,OUTPUT]=FMINUNC(FUN,X0,...) returns a structure OUTPUT with the number of iterations taken in OUTPUT.iterations, the number of function evaluations in OUTPUT.funcCount, the algorithm used in OUTPUT.algorithm, the number of CG iterations (if used) in OUTPUT.cgiterations, and the first-order optimality (if used) in OUTPUT.firstorderopt. [X,FVAL,EXITFLAG,OUTPUT,GRAD]=FMINUNC(FUN,X0,...) returns the value of the gradient of FUN at the solution X. [X,FVAL,EXITFLAG,OUTPUT,GRAD,HESSIAN]=FMINUNC(FUN,X0,...) returns the value of the Hessian of the objective function FUN at the solution X. Examples Minimize the one dimensional function f(x) = sin(x) + 3: To use an M-file, i.e. FUN = 'myfun', create a file myfun.m: function f = myfun(x) f = sin(x)+3; Then call FMINUNC to find a minimum of FUN near 2: x = fminunc('myfun',2) To minimize this function with the gradient provided, modify the m-file myfun.m so the gradient is the second output argument: function [f,g]= myfun(x) f = sin(x) + 3; g = cos(x); and indicate the gradient value is available by creating an options structure with OPTIONS.GradObj set to 'on' (using OPTIMSET): options = optimset('GradObj','on'); x = fminunc('myfun',2,options); To minimize the function f(x) = sin(x) + 3 using an inline object: f = inline('sin(x)+3'); x = fminunc(f,2); To use inline objects for the function and gradient, FUN is a cell array of two inline objects where the first is the objective and the second is the gradient of the objective: options = optimset('GradObj','on'); x = fminunc({ inline('sin(x)+3'), inline('cos(x)') } ,2,options); [xo,Ot,nS]=steepdes('test10',[1 1],1) Pause: hit any key to continue... Directional Iteration Func-count f(x) Step-size derivative 1 2 3 0.166667 -36 Pause: hit any key to continue... 2 8 0.75 0.125 -4.66e-007 Pause: hit any key to continue... 3 15 0.1875 0.5 -1.67e-008 Pause: hit any key to continue... 4 21 0.046875 0.125 2.08e-009 Pause: hit any key to continue... 5 28 0.0117187 0.5 -1.15e-008 Pause: hit any key to continue... 6 34 0.00292968 0.125 -3.01e-008 Pause: hit any key to continue... 7 41 0.000732417 0.500001 -1.02e-008 Pause: hit any key to continue... 8 47 0.000183103 0.125 -3.75e-008 Pause: hit any key to continue... 9 54 4.57711e-005 0.500016 -1e-008 Pause: hit any key to continue... 10 60 1.14416e-005 0.125 -3.75e-008 Optimization terminated successfully: Current search direction is a descent direction, and magnitude of directional derivative in search direction less than 2*options.TolFun Pause: hit any key to continue... xo = 0.0010 0.0028 Ot = 6.2115e-006 nS = 61 [xo,Ot,nS]=steepdes('test10',[1 1],1,'gtest10',1) Pause: hit any key to continue... Directional Iteration Func-count f(x) Step-size derivative 1 0 3 0.166667 -36 Pause: hit any key to continue... 2 1 1 0.166667 12 Pause: hit any key to continue... 3 2 0.444444 0.166667 1.33 Pause: hit any key to continue... 4 3 0.234568 0.166667 -0.296 Pause: hit any key to continue... 5 4 0.113964 0.233333 -0.194 Pause: hit any key to continue... 6 5 0.0822687 0.359333 0.33 Pause: hit any key to continue... 7 6 0.256428 0.359333 2.02 Pause: hit any key to continue... 8 7 0.0174369 0.12306 5.97e-016 Pause: hit any key to continue... 9 8 0.0118302 0.12306 -0.0396 Pause: hit any key to continue... 10 9 0.000150807 0.640029 -0.00349 Pause: hit any key to continue... 11 10 0.000564359 0.849067 0.0016 Pause: hit any key to continue... 12 11 7.64959e-005 0.238351 -5.42e-020 Pause: hit any key to continue... 13 12 0.000241774 0.572055 0.00102 Pause: hit any key to continue... 14 13 3.8802e-005 0.17228 -2.71e-020 Optimization terminated successfully: Current search direction is a descent direction, and magnitude of directional derivative in search direction less than 2*options.TolFun Pause: hit any key to continue... xo = -0.0014 0.0036 Ot = 3.0004e-005 nS = 14 [xo,Ot,nS]=steepdes('test1',[-1.2 1],1,'gtest1') Pause: hit any key to continue... Directional Iteration Func-count f(x) Step-size derivative 1 0 24.2 0.001 -5.42e+004 Pause: hit any key to continue... 2 4 4.12814 0.000786792 -68.5 Pause: hit any key to continue... 3 10 2.51901 0.474636 -3.52 Pause: hit any key to continue... 4 11 1334.32 1.81761 2.64e+003 Pause: hit any key to continue... 5 12 14.6767 0.454632 86.6 Pause: hit any key to continue... 6 13 2.39681 0.0873426 1.38 Pause: hit any key to continue... 7 18 2.18924 0.00259764 -0.0586 Pause: hit any key to continue... 8 23 2.05632 0.0506328 0.025 Pause: hit any key to continue... 9 27 1.9435 0.00324456 0.0115 Pause: hit any key to continue... 10 32 1.85496 0.0318887 -0.0072 Pause: hit any key to continue... 11 36 1.77328 0.0038722 -0.0112 Pause: hit any key to continue... 12 41 1.70345 0.0235929 -0.00453 Pause: hit any key to continue... 13 45 1.63651 0.00453985 -0.0145 Pause: hit any key to continue... 14 50 1.57699 0.018776 -0.00249 Pause: hit any key to continue... 15 54 1.51869 0.0052898 -0.0106 Pause: hit any key to continue... 16 59 1.46567 0.0155433 -0.00115 Pause: hit any key to continue... 17 63 1.41297 0.00616508 -0.0074 Pause: hit any key to continue... 18 68 1.36427 0.0131905 -0.000179 Pause: hit any key to continue... 19 72 1.3153 0.00722181 -0.0051 Pause: hit any key to continue... 20 76 1.26948 0.0113785 -0.000206 Pause: hit any key to continue... 21 80 1.22289 0.00855135 0.00296 Pause: hit any key to continue... 22 84 1.17882 0.00990883 -0.000124 Pause: hit any key to continue... 23 88 1.13349 0.0102947 -0.00223 Pause: hit any key to continue... 24 92 1.09014 0.00869839 6.03e-005 Pause: hit any key to continue... 25 97 1.04491 0.0127083 -0.00259 Pause: hit any key to continue... 26 101 1.00112 0.00765536 -0.001 Pause: hit any key to continue... 27 106 0.954494 0.0163651 -0.00364 Pause: hit any key to continue... 28 110 0.90861 0.00672118 -0.00179 Pause: hit any key to continue... 29 115 0.857986 0.0227281 -0.0158 Pause: hit any key to continue... 30 119 0.806848 0.00584408 -0.0038 Pause: hit any key to continue... 31 124 0.745361 0.0376699 -0.0624 Pause: hit any key to continue... 32 128 0.67918 0.0049208 -0.0142 Pause: hit any key to continue... 33 134 0.37907 0.195478 -2.39 Pause: hit any key to continue... 34 138 0.30518 0.00280425 -0.989 Pause: hit any key to continue... 35 142 0.255314 0.108733 -0.122 Pause: hit any key to continue... 36 146 0.237502 0.00248565 -0.000378 Pause: hit any key to continue... 37 151 0.223127 0.0560455 -0.000576 Pause: hit any key to continue... 38 155 0.211859 0.00238209 -0.000367 Pause: hit any key to continue... 39 160 0.202105 0.0455429 -0.000579 Pause: hit any key to continue... 40 164 0.193909 0.00230943 -0.000175 Pause: hit any key to continue... 41 169 0.186563 0.0391765 -0.000364 Pause: hit any key to continue... 42 173 0.180147 0.00225356 -9.63e-005 Pause: hit any key to continue... 43 178 0.174274 0.0348427 -0.000233 Pause: hit any key to continue... 44 182 0.169019 0.0022082 -5.89e-005 Pause: hit any key to continue... 45 187 0.164141 0.0316664 -0.000156 Pause: hit any key to continue... 46 191 0.159702 0.00217008 -3.87e-005 Pause: hit any key to continue... 47 196 0.155541 0.0292183 -0.000109 Pause: hit any key to continue... 48 200 0.151708 0.00213722 -2.69e-005 Pause: hit any key to continue... 49 205 0.148087 0.0272614 -7.96e-005 Pause: hit any key to continue... 50 209 0.144721 0.00210838 -1.95e-005 Pause: hit any key to continue... 51 214 0.141522 0.0256536 -5.97e-005 Maximum number of iterations exceeded; increase options.MaxIter Pause: hit any key to continue... Warning steepdesc: reached maximum number of iterations! xo = 0.6301 0.3902 Ot = 0.1415 nS = 215 help steepdes Unconstrained optimization using steep descent. [xo,Ot,nS]=steepdes(S,x0,ip,G,method,Lb,Ub,problem,tol,mxit) S: objective function x0: initial point ip: (0) no plot (default), (>0) plot figure ip with pause, (<0) plot figure ip G: gradient vector function method: line-search method: (0) quadratic+cubic (default), (1) cubic Lb, Ub: lower and upper bound vectors to plot (default = x0*(1+/-2)) problem: (-1): minimum (default), (1): maximum tol: tolerance (default = 1e-4) mxit: maximum number of iterations (default = 50*(1+4*~(ip>0))) xo: optimal point Ot: optimal value of S nS: number of objective function evaluations [xo,Ot,nS]=steepdes('test1',[-1.2 1],-1,'gtest1',[],[],[],[],[],2000) Directional Iteration Func-count f(x) Step-size derivative 1 0 24.2 0.001 -5.42e+004 2 4 4.12814 0.000786792 -68.5 3 10 2.51901 0.474636 -3.52 4 11 1334.32 1.81761 2.64e+003 5 12 14.6767 0.454632 86.6 6 13 2.39681 0.0873426 1.38 7 18 2.18924 0.00259764 -0.0586 8 23 2.05632 0.0506328 0.025 9 27 1.9435 0.00324456 0.0115 10 32 1.85496 0.0318887 -0.0072 11 36 1.77328 0.0038722 -0.0112 12 41 1.70345 0.0235929 -0.00453 13 45 1.63651 0.00453985 -0.0145 14 50 1.57699 0.018776 -0.00249 15 54 1.51869 0.0052898 -0.0106 16 59 1.46567 0.0155433 -0.00115 17 63 1.41297 0.00616508 -0.0074 18 68 1.36427 0.0131905 -0.000179 19 72 1.3153 0.00722181 -0.0051 20 76 1.26948 0.0113785 -0.000206 21 80 1.22289 0.00855135 0.00296 22 84 1.17882 0.00990883 -0.000124 23 88 1.13349 0.0102947 -0.00223 24 92 1.09014 0.00869839 6.03e-005 25 97 1.04491 0.0127083 -0.00259 26 101 1.00112 0.00765536 -0.001 27 106 0.954494 0.0163651 -0.00364 28 110 0.90861 0.00672118 -0.00179 29 115 0.857986 0.0227281 -0.0158 30 119 0.806848 0.00584408 -0.0038 31 124 0.745361 0.0376699 -0.0624 32 128 0.67918 0.0049208 -0.0142 33 134 0.37907 0.195478 -2.39 34 138 0.30518 0.00280425 -0.989 35 142 0.255314 0.108733 -0.122 36 146 0.237502 0.00248565 -0.000378 37 151 0.223127 0.0560455 -0.000576 38 155 0.211859 0.00238209 -0.000367 39 160 0.202105 0.0455429 -0.000579 40 164 0.193909 0.00230943 -0.000175 41 169 0.186563 0.0391765 -0.000364 42 173 0.180147 0.00225356 -9.63e-005 43 178 0.174274 0.0348427 -0.000233 44 182 0.169019 0.0022082 -5.89e-005 45 187 0.164141 0.0316664 -0.000156 46 191 0.159702 0.00217008 -3.87e-005 47 196 0.155541 0.0292183 -0.000109 48 200 0.151708 0.00213722 -2.69e-005 49 205 0.148087 0.0272614 -7.96e-005 50 209 0.144721 0.00210838 -1.95e-005 51 214 0.141522 0.0256536 -5.97e-005 52 218 0.138528 0.00208269 -1.46e-005 53 223 0.135668 0.0243039 -4.59e-005 54 227 0.132975 0.00205956 -1.12e-005 55 232 0.130394 0.023151 -3.61e-005 56 236 0.127951 0.00203854 -8.8e-006 57 241 0.125603 0.0221522 -2.88e-005 58 245 0.12337 0.00201928 -7.04e-006 59 250 0.121218 0.0212766 -2.34e-005 60 254 0.119166 0.00200151 -5.72e-006 61 259 0.117183 0.0205012 -1.93e-005 62 263 0.115286 0.00198505 -4.71e-006 63 268 0.113449 0.0198085 -1.6e-005 64 272 0.111687 0.0019697 -3.93e-006 65 277 0.109978 0.0191852 -1.35e-005 66 281 0.108336 0.00195534 -3.31e-006 67 286 0.10674 0.0186205 -1.15e-005 68 290 0.105203 0.00194185 -2.81e-006 69 295 0.103707 0.018106 -9.8e-006 70 299 0.102264 0.00192914 -2.41e-006 71 304 0.100858 0.0176348 -8.45e-006 72 308 0.0994988 0.00191713 -2.08e-006 73 313 0.0981734 0.0172012 -7.33e-006 74 317 0.0968906 0.00190574 -1.81e-006 75 322 0.095638 0.0168006 -6.4e-006 76 326 0.094424 0.00189493 -1.58e-006 77 331 0.0932376 0.0164291 -5.62e-006 78 335 0.0920864 0.00188463 -1.39e-006 79 340 0.0909603 0.0160833 -4.96e-006 80 344 0.0898663 0.0018748 -1.23e-006 81 349 0.0887954 0.0157606 -4.4e-006 82 353 0.087754 0.00186541 -1.09e-006 83 358 0.0867338 0.0154584 -3.91e-006 84 362 0.0857407 0.00185641 -9.72e-007 85 367 0.0847672 0.0151748 -3.5e-006 86 371 0.0838187 0.00184779 -8.7e-007 87 376 0.0828883 0.014908 -3.14e-006 88 380 0.0819812 0.0018395 -7.81e-007 89 385 0.0810908 0.0146563 -2.82e-006 90 389 0.080222 0.00183154 -7.04e-007 91 394 0.0793688 0.0144185 -2.55e-006 92 398 0.0785356 0.00182387 -6.37e-007 93 403 0.077717 0.0141932 -2.31e-006 94 407 0.0769171 0.00181647 -5.77e-007 95 412 0.0761309 0.0139796 -2.1e-006 96 416 0.075362 0.00180933 -5.25e-007 97 421 0.074606 0.0137766 -1.91e-006 98 425 0.0738663 0.00180244 -4.79e-007 99 430 0.0731385 0.0135834 -1.74e-006 100 434 0.0724261 0.00179577 -4.38e-007 101 439 0.071725 0.0133993 -1.6e-006 102 443 0.0710382 0.00178931 -4.01e-007 103 448 0.0703621 0.0132235 -1.46e-006 104 452 0.0696995 0.00178306 -3.68e-007 105 457 0.0690469 0.0130555 -1.34e-006 106 461 0.0684071 0.001777 -3.39e-007 107 466 0.0677768 0.0128947 -1.24e-006 108 470 0.0671585 0.00177111 -3.12e-007 109 475 0.0665492 0.0127407 -1.14e-006 110 479 0.0659512 0.0017654 -2.88e-007 111 484 0.0653618 0.0125929 -1.06e-006 112 488 0.0647831 0.00175985 -2.67e-007 113 493 0.0642125 0.012451 -9.77e-007 114 497 0.0636521 0.00175445 -2.47e-007 115 502 0.0630994 0.0123147 -9.06e-007 116 506 0.0625564 0.00174919 -2.29e-007 117 511 0.0620206 0.0121835 -8.41e-007 118 515 0.0614941 0.00174408 -2.13e-007 119 520 0.0609744 0.0120571 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8179 0.00021473 0.00484285 -2.61e-013 1822 8183 0.000214192 0.00129481 -8.34e-014 1823 8188 0.000213655 0.00484228 -2.58e-013 1824 8192 0.000213119 0.00129476 -8.08e-014 1825 8197 0.000212584 0.00484172 -2.56e-013 1826 8201 0.000212051 0.0012947 -7.74e-014 1827 8206 0.00021152 0.00484116 -2.54e-013 1828 8210 0.000210989 0.00129464 -7.79e-014 1829 8215 0.00021046 0.0048406 -2.51e-013 1830 8219 0.000209933 0.00129459 -7.83e-014 1831 8224 0.000209407 0.00484004 -2.47e-013 1832 8228 0.000208882 0.00129453 -7.63e-014 1833 8233 0.000208358 0.00483948 -2.45e-013 1834 8237 0.000207836 0.00129448 -7.8e-014 1835 8242 0.000207315 0.00483893 -2.43e-013 1836 8246 0.000206796 0.00129442 -7.51e-014 1837 8251 0.000206278 0.00483838 -2.41e-013 1838 8255 0.000205761 0.00129437 -7.25e-014 1839 8260 0.000205246 0.00483783 -2.39e-013 1840 8264 0.000204732 0.00129431 -7.14e-014 1841 8269 0.000204219 0.00483728 -2.35e-013 1842 8273 0.000203707 0.00129426 -7.56e-014 1843 8278 0.000203197 0.00483673 -2.33e-013 1844 8282 0.000202689 0.0012942 -6.71e-014 1845 8287 0.000202181 0.00483618 -2.31e-013 1846 8291 0.000201675 0.00129415 -7.15e-014 1847 8296 0.00020117 0.00483563 -2.28e-013 1848 8300 0.000200667 0.00129409 -6.92e-014 1849 8305 0.000200164 0.00483509 -2.26e-013 1850 8309 0.000199663 0.00129404 -6.88e-014 1851 8314 0.000199164 0.00483455 -2.23e-013 1852 8318 0.000198665 0.00129398 -6.69e-014 1853 8323 0.000198168 0.00483401 -2.22e-013 1854 8327 0.000197672 0.00129393 -7.01e-014 1855 8332 0.000197178 0.00483347 -2.19e-013 1856 8336 0.000196685 0.00129387 -6.57e-014 1857 8341 0.000196193 0.00483293 -2.17e-013 1858 8345 0.000195702 0.00129382 -6.79e-014 1859 8350 0.000195212 0.00483239 -2.14e-013 1860 8354 0.000194724 0.00129377 -6.49e-014 1861 8359 0.000194237 0.00483186 -2.13e-013 1862 8363 0.000193752 0.00129371 -6.59e-014 1863 8368 0.000193267 0.00483133 -2.09e-013 1864 8372 0.000192784 0.00129366 -6.34e-014 Optimization terminated successfully: Current search direction is a descent direction, and magnitude of directional derivative in search direction less than 2*options.TolFun xo = 0.9861 0.9724 Ot = 1.9247e-004 nS = 8373 [xo,Ot,nS]=steepdes('test1',[-1.2 1],-1,'gtest1',[],[],[],[],[],5) Directional Iteration Func-count f(x) Step-size derivative 1 0 24.2 0.001 -5.42e+004 2 4 4.12814 0.000786792 -68.5 3 10 2.51901 0.474636 -3.52 4 11 1334.32 1.81761 2.64e+003 5 12 14.6767 0.454632 86.6 6 13 2.39681 0.0873426 1.38 Maximum number of iterations exceeded; increase options.MaxIter Warning steepdesc: reached maximum number of iterations! xo = -0.5040 0.2173 Ot = 2.3968 nS = 14 [xo,Ot,nS]=steepdes('test1',[-1.2 1],-1,'gtest1',[],[],[],[],[],5) Directional Iteration Func-count f(x) Step-size derivative 1 0 24.2 0.001 -5.42e+004 2 4 4.12814 0.000786792 -68.5 3 10 2.51901 0.474636 -3.52 4 11 1334.32 1.81761 2.64e+003 5 12 14.6767 0.454632 86.6 6 13 2.39681 0.0873426 1.38 Maximum number of iterations exceeded; increase options.MaxIter Warning steepdesc: reached maximum number of iterations! xo = -0.5040 0.2173 Ot = 2.3968 nS = 14 help fminunc FMINUNC Finds the minimum of a function of several variables. X=FMINUNC(FUN,X0) starts at the point X0 and finds a minimum X of the function described in FUN. X0 can be a scalar, vector or matrix. The function FUN (usually an M-file or inline object) should return a scalar function value F evaluated at X when called with feval: F=feval(FUN,X). See the examples below for more about FUN. X=FMINUNC(FUN,X0,OPTIONS) minimizes with the default optimization parameters replaced by values in the structure OPTIONS, an argument created with the OPTIMSET function. See OPTIMSET for details. Used options are Display, TolX, TolFun, DerivativeCheck, Diagnostics, GradObj, HessPattern, LineSearchType, Hessian, HessUpdate, MaxFunEvals, MaxIter, DiffMinChange and DiffMaxChange, LargeScale, MaxPCGIter, PrecondBandWidth, TolPCG, TypicalX. Use the GradObj option to specify that FUN can be called with two output arguments where the second, G, is the partial derivatives of the function df/dX, at the point X: [F,G] = feval(FUN,X). Use Hessian to specify that FUN can be called with three output arguments where the second, G, is the partial derivatives of the function df/dX, and the third H is the 2nd partial derivatives of the function (the Hessian) at the point X: [F,G,H] = feval(FUN,X). The Hessian is only used by the large-scale method, not the line-search method. X=FMINUNC(FUN,X0,OPTIONS,P1,P2,...) passes the problem-dependent parameters P1,P2,... directly to the function FUN, e.g. FUN would be called using feval as in: feval(FUN,X,P1,P2,...). Pass an empty matrix for OPTIONS to use the default values. [X,FVAL]=FMINUNC(FUN,X0,...) returns the value of the objective function FUN at the solution X. [X,FVAL,EXITFLAG]=FMINUNC(FUN,X0,...) returns a string EXITFLAG that describes the exit condition of FMINUNC. If EXITFLAG is: > 0 then FMINUNC converged to a solution X. 0 then the maximum number of function evaluations was reached. < 0 then FMINUNC did not converge to a solution. [X,FVAL,EXITFLAG,OUTPUT]=FMINUNC(FUN,X0,...) returns a structure OUTPUT with the number of iterations taken in OUTPUT.iterations, the number of function evaluations in OUTPUT.funcCount, the algorithm used in OUTPUT.algorithm, the number of CG iterations (if used) in OUTPUT.cgiterations, and the first-order optimality (if used) in OUTPUT.firstorderopt. [X,FVAL,EXITFLAG,OUTPUT,GRAD]=FMINUNC(FUN,X0,...) returns the value of the gradient of FUN at the solution X. [X,FVAL,EXITFLAG,OUTPUT,GRAD,HESSIAN]=FMINUNC(FUN,X0,...) returns the value of the Hessian of the objective function FUN at the solution X. Examples Minimize the one dimensional function f(x) = sin(x) + 3: To use an M-file, i.e. FUN = 'myfun', create a file myfun.m: function f = myfun(x) f = sin(x)+3; Then call FMINUNC to find a minimum of FUN near 2: x = fminunc('myfun',2) To minimize this function with the gradient provided, modify the m-file myfun.m so the gradient is the second output argument: function [f,g]= myfun(x) f = sin(x) + 3; g = cos(x); and indicate the gradient value is available by creating an options structure with OPTIONS.GradObj set to 'on' (using OPTIMSET): options = optimset('GradObj','on'); x = fminunc('myfun',2,options); To minimize the function f(x) = sin(x) + 3 using an inline object: f = inline('sin(x)+3'); x = fminunc(f,2); To use inline objects for the function and gradient, FUN is a cell array of two inline objects where the first is the objective and the second is the gradient of the objective: options = optimset('GradObj','on'); x = fminunc({ inline('sin(x)+3'), inline('cos(x)') } ,2,options); op=optimset('fminunc') op = ActiveConstrTol: [] DerivativeCheck: 'off' Diagnostics: 'off' DiffMaxChange: 0.1000 DiffMinChange: 1.0000e-008 Display: 'final' GoalsExactAchieve: [] GradConstr: [] GradObj: 'off' Hessian: 'off' HessMult: [] HessPattern: 'sparse(ones(numberOfVariables))' HessUpdate: 'bfgs' Jacobian: [] JacobMult: [] JacobPattern: [] LargeScale: 'on' LevenbergMarquardt: [] LineSearchType: 'quadcubic' MaxFunEvals: '100*numberOfVariables' MaxIter: 400 MaxPCGIter: 'max(1,floor(numberOfVariables/2))' MeritFunction: [] MinAbsMax: [] Preconditioner: [] PrecondBandWidth: 0 ShowStatusWindow: [] TolCon: [] TolFun: 1.0000e-006 TolPCG: 0.1000 TolX: 1.0000e-006 TypicalX: 'ones(numberOfVariables,1)' what M-files in the current directory v:\cursos\pos\otimiza\aulas CATALIS extrat minlp2 test0 EXTRATOR fmincon1 minlp3 test1 LUCRO fminunc1 minlp4 test10 MINQUA fminusub minlp5 test11 MODELO fun minlp6 test12 Minqua44 func44 minlpn test13 Modelo44 gmilp1 modelagem test14 OPT_RES gminlp1 naturais test15 PLANOS gminlp2 newton test16 READ2 gminlp3 newton_h test17 SEMIDEF gminlp4 newtont test18 SMODELO gminlp5 nlconst test19 aurea gminlp6 nlp_internal test1m bandem1 gmodelagem pareto18 test2 bfgs gmurray pareto19 test20 bracket grad pareto20 test21 buscarnd grg pareto21 test22 cgrad gtest1 powell test23 checkbounds gtest10 qpsub test3 coggins gtest12 refino test4 compdir gtest13 restr test5 complex gtest2 restr1 test6 dados_ex6_44 gtest9 restr14 test7 dfp hkjeeves restr15 test8 dual htest1 restr16 test9 ex2_karm htest2 restr17 teste_buscarnd ex_karma interior restr20 univar ex_qp1 karmarkar restr21 varmetr ex_qp2 lmarqua rosembr visual ex_qp3 lp_nlp set1 writearq ex_swarm milp setoptim xplot exmilp milp1 sol_extrat exmilp2 milprog sqp exmilprog minlp steepdes exmilprog2 minlp1 swarm setoptim what M-files in the current directory v:\cursos\pos\otimiza\aulas CATALIS extrat minlp2 test0 EXTRATOR fmincon1 minlp3 test1 LUCRO fminunc1 minlp4 test10 MINQUA fminusub minlp5 test11 MODELO fun minlp6 test12 Minqua44 func44 minlpn test13 Modelo44 gmilp1 modelagem test14 OPT_RES gminlp1 naturais test15 PLANOS gminlp2 newton test16 READ2 gminlp3 newton_h test17 SEMIDEF gminlp4 newtont test18 SMODELO gminlp5 nlconst test19 aurea gminlp6 nlp_internal test1m bandem1 gmodelagem pareto18 test2 bfgs gmurray pareto19 test20 bracket grad pareto20 test21 buscarnd grg pareto21 test22 cgrad gtest1 powell test23 checkbounds gtest10 qpsub test3 coggins gtest12 refino test4 compdir gtest13 restr test5 complex gtest2 restr1 test6 dados_ex6_44 gtest9 restr14 test7 dfp hkjeeves restr15 test8 dual htest1 restr16 test9 ex2_karm htest2 restr17 teste_buscarnd ex_karma interior restr20 univar ex_qp1 karmarkar restr21 varmetr ex_qp2 lmarqua rosembr visual ex_qp3 lp_nlp set1 writearq ex_swarm milp setoptim xplot exmilp milp1 sol_extrat exmilp2 milprog sqp exmilprog minlp steepdes exmilprog2 minlp1 swarm op=setoptim Warning: One or more output arguments not assigned during call to 'setoptim'. op Warning: Reference to uninitialized variable op. help setoptim funcao setoptim Permite a edicao dos parametros do optimset setoptim() - carrega o default do matlab e escreve o vetor options no workspace setoptim([],optv) - o padrao na abertura e dado por optv setoptim([],[],OKcallback) - o callback do botao ok pode ser inserido neste caso o default e escrever no workspace clear all who setoptim who Your variables are: opt opt opt = DerivativeCheck: 'off' Diagnostics: 'off' Display: 'final' GradObj: 'off' Hessian: 'off' HessUpdate: 'steepdesc' LargeScale: 'off' LineSearchType: 'quadcubic' DiffMaxChange: 0.1000 DiffMinChange: 1.0000e-008 MaxIter: 400 PrecondBandWidth: 0 TolFun: 1.0000e-006 TolPCG: 0.1000 TolX: 1.0000e-006 opt opt = DerivativeCheck: 'off' Diagnostics: 'off' Display: 'iter' GradObj: 'off' Hessian: 'off' HessUpdate: 'steepdesc' LargeScale: 'off' LineSearchType: 'quadcubic' DiffMaxChange: 0.1000 DiffMinChange: 1.0000e-008 MaxIter: 400 PrecondBandWidth: 0 TolFun: 1.0000e-006 TolPCG: 0.1000 TolX: 1.0000e-006 help fminunc FMINUNC Finds the minimum of a function of several variables. X=FMINUNC(FUN,X0) starts at the point X0 and finds a minimum X of the function described in FUN. X0 can be a scalar, vector or matrix. The function FUN (usually an M-file or inline object) should return a scalar function value F evaluated at X when called with feval: F=feval(FUN,X). See the examples below for more about FUN. X=FMINUNC(FUN,X0,OPTIONS) minimizes with the default optimization parameters replaced by values in the structure OPTIONS, an argument created with the OPTIMSET function. See OPTIMSET for details. Used options are Display, TolX, TolFun, DerivativeCheck, Diagnostics, GradObj, HessPattern, LineSearchType, Hessian, HessUpdate, MaxFunEvals, MaxIter, DiffMinChange and DiffMaxChange, LargeScale, MaxPCGIter, PrecondBandWidth, TolPCG, TypicalX. Use the GradObj option to specify that FUN can be called with two output arguments where the second, G, is the partial derivatives of the function df/dX, at the point X: [F,G] = feval(FUN,X). Use Hessian to specify that FUN can be called with three output arguments where the second, G, is the partial derivatives of the function df/dX, and the third H is the 2nd partial derivatives of the function (the Hessian) at the point X: [F,G,H] = feval(FUN,X). The Hessian is only used by the large-scale method, not the line-search method. X=FMINUNC(FUN,X0,OPTIONS,P1,P2,...) passes the problem-dependent parameters P1,P2,... directly to the function FUN, e.g. FUN would be called using feval as in: feval(FUN,X,P1,P2,...). Pass an empty matrix for OPTIONS to use the default values. [X,FVAL]=FMINUNC(FUN,X0,...) returns the value of the objective function FUN at the solution X. [X,FVAL,EXITFLAG]=FMINUNC(FUN,X0,...) returns a string EXITFLAG that describes the exit condition of FMINUNC. If EXITFLAG is: > 0 then FMINUNC converged to a solution X. 0 then the maximum number of function evaluations was reached. < 0 then FMINUNC did not converge to a solution. [X,FVAL,EXITFLAG,OUTPUT]=FMINUNC(FUN,X0,...) returns a structure OUTPUT with the number of iterations taken in OUTPUT.iterations, the number of function evaluations in OUTPUT.funcCount, the algorithm used in OUTPUT.algorithm, the number of CG iterations (if used) in OUTPUT.cgiterations, and the first-order optimality (if used) in OUTPUT.firstorderopt. [X,FVAL,EXITFLAG,OUTPUT,GRAD]=FMINUNC(FUN,X0,...) returns the value of the gradient of FUN at the solution X. [X,FVAL,EXITFLAG,OUTPUT,GRAD,HESSIAN]=FMINUNC(FUN,X0,...) returns the value of the Hessian of the objective function FUN at the solution X. Examples Minimize the one dimensional function f(x) = sin(x) + 3: To use an M-file, i.e. FUN = 'myfun', create a file myfun.m: function f = myfun(x) f = sin(x)+3; Then call FMINUNC to find a minimum of FUN near 2: x = fminunc('myfun',2) To minimize this function with the gradient provided, modify the m-file myfun.m so the gradient is the second output argument: function [f,g]= myfun(x) f = sin(x) + 3; g = cos(x); and indicate the gradient value is available by creating an options structure with OPTIONS.GradObj set to 'on' (using OPTIMSET): options = optimset('GradObj','on'); x = fminunc('myfun',2,options); To minimize the function f(x) = sin(x) + 3 using an inline object: f = inline('sin(x)+3'); x = fminunc(f,2); To use inline objects for the function and gradient, FUN is a cell array of two inline objects where the first is the objective and the second is the gradient of the objective: options = optimset('GradObj','on'); x = fminunc({ inline('sin(x)+3'), inline('cos(x)') } ,2,options); [X,So]=FMINUNC('test1',[-1.2 1],opt) Directional Iteration Func-count f(x) Step-size derivative 1 2 24.2 0.001 -5.42e+004 2 8 4.12814 0.000786792 -68.5 3 16 2.51863 0.474743 -3.51 4 19 1204.75 1.76646 2.44e+003 5 22 13.2979 0.437951 79.8 6 25 2.39442 0.0854245 1.24 7 32 2.19589 0.00259144 -0.0497 8 39 2.0661 0.0496021 0.0175 9 45 1.95527 0.00322052 0.0074 10 52 1.86758 0.0316857 -0.00711 11 58 1.78648 0.00383452 -0.0112 12 65 1.71693 0.0235769 -0.00441 13 71 1.65017 0.00448926 -0.0146 14 78 1.59071 0.0188227 -0.00245 15 84 1.53244 0.00522511 -0.0108 16 91 1.47937 0.0156139 -0.00117 17 97 1.42662 0.00608381 -0.00758 18 104 1.37782 0.0132697 -0.000231 19 110 1.32875 0.00711992 -0.00527 20 116 1.2828 0.0114597 -0.000194 21 122 1.23609 0.00842267 0.00364 22 128 1.19188 0.0099871 -0.000116 23 134 1.14642 0.0101287 -0.00209 24 140 1.10292 0.00877406 -3.09e-005 25 146 1.05755 0.0124852 -0.00255 26 152 1.01362 0.00772814 -0.000946 27 159 0.966872 0.0160433 -0.00318 28 165 0.920869 0.00679083 -0.00169 29 172 0.870187 0.0221976 -0.0152 30 178 0.819017 0.00591172 -0.00356 31 185 0.757785 0.0364212 -0.0596 32 191 0.692054 0.00499089 -0.0128 33 199 0.393156 0.192634 -2.49 Maximum number of function evaluations exceeded; increase options.MaxFunEvals X = 0.4427 0.1935 So = 0.3112 eps ans = 2.2204e-016 help newton Unconstrained optimization using Newton. [xo,Ot,nS]=newton(S,x0,ip,G,H,Lb,Ub,problem,tol,mxit) S: objective function x0: initial point ip: (0) no plot (default), (>0) plot figure ip with pause, (<0) plot figure ip G: gradient vector function H: Hessian matrix function Lb, Ub: lower and upper bound vectors to plot (default = x0*(1+/-2)) problem: (-1): minimum (default), (1): maximum tol: tolerance (default = 1e-4) mxit: maximum number of iterations (default = 50*(1+4*~(ip>0))) xo: optimal point Ot: optimal value of S nS: number of objective function evaluations type newton function [xo,Ot,nS]=newton(S,x0,ip,G,H,Lb,Ub,problem,tol,mxit) % Unconstrained optimization using Newton. % % [xo,Ot,nS]=newton(S,x0,ip,G,H,Lb,Ub,problem,tol,mxit) % % S: objective function % x0: initial point % ip: (0) no plot (default), (>0) plot figure ip with pause, (<0) plot figure ip % G: gradient vector function % H: Hessian matrix function % Lb, Ub: lower and upper bound vectors to plot (default = x0*(1+/-2)) % problem: (-1): minimum (default), (1): maximum % tol: tolerance (default = 1e-4) % mxit: maximum number of iterations (default = 50*(1+4*~(ip>0))) % xo: optimal point % Ot: optimal value of S % nS: number of objective function evaluations % Copyright (c) 2001 by LASIM-DEQUI-UFRGS % $Revision: 1.0 $ $Date: 2001/07/16 08:10:12 $ % Argimiro R. Secchi (arge@enq.ufrgs.br) if nargin < 2, error('newton requires two input arguments!'); end if nargin < 3 | isempty(ip), ip=0; end if nargin < 4 | isempty(G), grad=0; else grad=1; end if nargin < 5 | isempty(H), hes=0; if ~grad, error('Newton: numerical gradient not allowed with numerical Hessian!'); end else hes=1; end if nargin < 6 | isempty(Lb), Lb=-x0-~x0; end if nargin < 7 | isempty(Ub), Ub=2*x0+~x0; end if nargin < 8 | isempty(problem), problem=-1; end if nargin < 9 | isempty(tol), tol=1e-4; end if nargin < 10 | isempty(mxit), mxit=50*(1+4*~(ip>0)); end x0=x0(:); y0=feval(S,x0)*problem; n=size(x0,1); if ~grad, d=1e-5*abs(x0)+1e-5*ones(n,1); CHG=0.01*d; gr=d; end if ip & n == 2, figure(abs(ip)); [X1,X2]=meshgrid(Lb(1):(Ub(1)-Lb(1))/20:Ub(1),Lb(2):(Ub(2)-Lb(2))/20:Ub(2)); [n1,n2]=size(X1); f=zeros(n1,n2); for i=1:n1, for j=1:n2, f(i,j)=feval(S,[X1(i,j);X2(i,j)]); end end mxf=max(max(f)); mnf=min(min(f)); df=mnf+(mxf-mnf)*(2.^(([0:10]/10).^2)-1); [v,h]=contour(X1,X2,f,df); hold on; % clabel(v,h); h1=plot(x0(1),x0(2),'ro'); legend(h1,'start point'); if ip > 0, disp('Pause: hit any key to continue...'); pause; end end xo=x0; yo=y0; it=0; nS=1; while it < mxit, if ~grad, y=yo; % Finite difference perturbation levels % First check perturbation level is not less than search direction. j=find(10*abs(CHG)>abs(d)); CHG(j)=-0.1*d(j); % Ensure within user-defined limits for i=1:n xo(i)=xo(i)+CHG(i); yo=feval(S,xo)*problem; gr(i)=(yo-y)/CHG(i); if yo > y, y=yo; else xo(i)=xo(i)-CHG(i); end end % Try to set difference to 1e-8 for next iteration % Add eps for machines that can't handle divide by zero. CHG=1e-8./(gr+eps); yo=y; nS=nS+n; else gr=feval(G,xo)*problem; gr=gr(:); end if ~hes, if problem == 1, fun={S,G}; else fun={inline(['-feval(''' S ''',x)']),inline(['-feval(''' G ''',x)'])}; end; Hstr=sparse(ones(n)); % dense matrix only group=color(Hstr,(n+1)*ones(n,1)-colmmd(Hstr)'); he=full(sfd(xo,gr,Hstr,group,[],[{['fun_then_grad']},{['newton']},fun])); else he=feval(H,xo)*problem; end d=-he\gr; stepsize=1; x=xo+d; yo=feval(S,x)*problem; nS=nS+1; while yo < y0, stepsize=-0.5*stepsize; x=xo+stepsize*d; yo=feval(S,x)*problem; nS=nS+1; end xo=x; it=it+1; if norm(xo-x0) < tol*(0.1+norm(x0)) & abs(yo-y0) < tol*(0.1+abs(y0)), break; end if ip & n == 2, plot([x0(1) xo(1)],[x0(2) xo(2)],'r'); if ip > 0, disp('Pause: hit any key to continue...'); pause; end end x0=xo; y0=yo; end Ot=yo*problem; if it == mxit, disp('Warning Newton: reached maximum number of iterations!'); elseif ip & n == 2, h2=plot(xo(1),xo(2),'r*'); legend([h1,h2],'start point','optimum'); end help newton Unconstrained optimization using Newton. [xo,Ot,nS]=newton(S,x0,ip,G,H,Lb,Ub,problem,tol,mxit) S: objective function x0: initial point ip: (0) no plot (default), (>0) plot figure ip with pause, (<0) plot figure ip G: gradient vector function H: Hessian matrix function Lb, Ub: lower and upper bound vectors to plot (default = x0*(1+/-2)) problem: (-1): minimum (default), (1): maximum tol: tolerance (default = 1e-4) mxit: maximum number of iterations (default = 50*(1+4*~(ip>0))) xo: optimal point Ot: optimal value of S nS: number of objective function evaluations type htest10 ??? Error using ==> type htest10.m: File not found. what M-files in the current directory v:\cursos\pos\otimiza\aulas CATALIS extrat minlp2 test0 EXTRATOR fmincon1 minlp3 test1 LUCRO fminunc1 minlp4 test10 MINQUA fminusub minlp5 test11 MODELO fun minlp6 test12 Minqua44 func44 minlpn test13 Modelo44 gmilp1 modelagem test14 OPT_RES gminlp1 naturais test15 PLANOS gminlp2 newton test16 READ2 gminlp3 newton_h test17 SEMIDEF gminlp4 newtont test18 SMODELO gminlp5 nlconst test19 aurea gminlp6 nlp_internal test1m bandem1 gmodelagem pareto18 test2 bfgs gmurray pareto19 test20 bracket grad pareto20 test21 buscarnd grg pareto21 test22 cgrad gtest1 powell test23 checkbounds gtest10 qpsub test3 coggins gtest12 refino test4 compdir gtest13 restr test5 complex gtest2 restr1 test6 dados_ex6_44 gtest9 restr14 test7 dfp hkjeeves restr15 test8 dual htest1 restr16 test9 ex2_karm htest2 restr17 teste_buscarnd ex_karma interior restr20 univar ex_qp1 karmarkar restr21 varmetr ex_qp2 lmarqua rosembr visual ex_qp3 lp_nlp set1 writearq ex_swarm milp setoptim xplot exmilp milp1 sol_extrat exmilp2 milprog sqp exmilprog minlp steepdes exmilprog2 minlp1 swarm edit htest10 File 'htest10' not found. edit gtest10 disp(sprintf('%d',feature('SessionTool'))) 0 ; dbstatus dbstack dbstack ; disp(which('gtest10')); v:\cursos\pos\otimiza\aulas\gtest10.m mdbstatus 'v:\cursos\pos\otimiza\aulas\gtest10.m' eval( 'if exist(''Gradient'',''var''), mauifunc(Gradient), end', ''); eval( 'if exist(''function'',''var''), mauifunc(function), end', ''); disp(which('htest10')); disp(char(which('htest10','-all'))); eval( 'if exist(''Edgar'',''var''), mauifunc(Edgar), end', ''); eval( 'if exist(''test'',''var''), mauifunc(test), end', ''); disp(which('htest10')); disp(char(which('htest10','-all'))); eval( 'if exist(''function'',''var''), mauifunc(function), end', ''); eval( 'if exist(''Hessian'',''var''), mauifunc(Hessian), end', ''); ; cd(cd) [xo,Ot,nS]=newton('test10',[1 1],1,'gtest10','htest10') Pause: hit any key to continue... Pause: hit any key to continue... xo = 1.0e-031 * 0.1233 0.3287 Ot = 8.7781e-064 nS = 3 [xo,Ot,nS]=newton('test10',[1 1],1,'gtest10') Pause: hit any key to continue... Pause: hit any key to continue... xo = 1.0e-031 * 0.1233 0.3287 Ot = 8.7781e-064 nS = 3 [xo,Ot,nS]=newton('test10',[1 1],1) ??? Error using ==> newton Newton: numerical gradient not allowed with numerical Hessian! [xo,Ot,nS]=newton('test1',[-1.2 1],1,'gtest1','htest1') Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... 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Pause: hit any key to continue... xo = 1.0000 1.0000 Ot = 2.1254e-024 nS = 35 help test9 Himmelblau, 1972 x0 = [1, 1]' xo = [3, 2]', xo = [3.58443, -1.84813]', xo = [-3.7793, -3.2832]' e xo = [-2.8051, 3.1313]' S(xo) = 0 local maximum: xo = [-0.2708, -0.9230]', S(xo) = 181.6 [xo,Ot,nS]=newton('test1',[-1.2 1],-1,'gtest1','htest1') xo = 1.0000 1.0000 Ot = 2.1254e-024 nS = 35 [xo,Ot,nS]=newton('test1',[-1.2 1],-1,'gtest1') xo = 1.0000 1.0000 Ot = 4.5475e-024 nS = 35 type htest1 function H=test(x) % Hessian of Rosenbrock, 1960 % x0 = [-1.2, 1]' % xo = [1, 1]' % S(xo) = 0 H(1,1)=100*(12*x(1)^2-4*x(2))+2; H(1,2)=-400*x(1); H(2,1)=H(1,2); H(2,2)=200; type gtest1 function G=test(x) % Gradient of Rosenbrock, 1960 % x0 = [-1.2, 1]' % xo = [1, 1]' % S(xo) = 0 G(1)=100*(4*x(1)^3-4*x(1)*x(2))+2*x(1)-2; G(2)=100*(2*x(2)-2*x(1)^2); help test9 Himmelblau, 1972 x0 = [1, 1]' xo = [3, 2]', xo = [3.58443, -1.84813]', xo = [-3.7793, -3.2832]' e xo = [-2.8051, 3.1313]' S(xo) = 0 local maximum: xo = [-0.2708, -0.9230]', S(xo) = 181.6 type htest9 ??? Error using ==> type htest9.m: File not found. edit gtest9 disp(sprintf('%d',feature('SessionTool'))) 0 ; dbstatus dbstack dbstack ; disp(which('gtest9')); v:\cursos\pos\otimiza\aulas\gtest9.m mdbstatus 'v:\cursos\pos\otimiza\aulas\gtest9.m' eval( 'if exist(''function'',''var''), mauifunc(function), end', ''); disp(which('htest9')); disp(char(which('htest9','-all'))); eval( 'if exist(''maximum'',''var''), mauifunc(maximum), end', ''); eval( 'if exist(''Gradient'',''var''), mauifunc(Gradient), end', ''); eval( 'if exist(''H'',''var''), mauifunc(H), end', ''); eval( 'if exist(''H'',''var''), mauifunc(H), end', ''); eval( 'if exist(''Hessian'',''var''), mauifunc(Hessian), end', ''); eval( 'if exist(''function'',''var''), mauifunc(function), end', ''); eval( 'if exist(''H'',''var''), mauifunc(H), end', ''); eval( 'if exist(''test'',''var''), mauifunc(test), end', ''); eval( 'if exist(''of'',''var''), mauifunc(of), end', ''); eval( 'if exist(''Hessian'',''var''), mauifunc(Hessian), end', ''); eval( 'if exist(''function'',''var''), mauifunc(function), end', ''); disp(which('htest9')); disp(char(which('htest9','-all'))); ; cd(cd) [xo,Ot,nS]=newton('test9',[1 1],1,'gtest9','htest9') Pause: hit any key to continue... Error in ==> v:\cursos\pos\otimiza\aulas\newton.m On line 87 ==> disp('Pause: hit any key to continue...'); pause; [xo,Ot,nS]=newton('test9',[1 1],1,'gtest9','htest9') Pause: hit any key to continue... Error in ==> v:\cursos\pos\otimiza\aulas\newton.m On line 87 ==> disp('Pause: hit any key to continue...'); pause; help newton Unconstrained optimization using Newton. [xo,Ot,nS]=newton(S,x0,ip,G,H,Lb,Ub,problem,tol,mxit) S: objective function x0: initial point ip: (0) no plot (default), (>0) plot figure ip with pause, (<0) plot figure ip G: gradient vector function H: Hessian matrix function Lb, Ub: lower and upper bound vectors to plot (default = x0*(1+/-2)) problem: (-1): minimum (default), (1): maximum tol: tolerance (default = 1e-4) mxit: maximum number of iterations (default = 50*(1+4*~(ip>0))) xo: optimal point Ot: optimal value of S nS: number of objective function evaluations [xo,Ot,nS]=newton('test9',[1 1],1,'gtest9','htest9',[-5 -5],[5 5]) Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 3.3852 0.0739 Ot = 13.3119 nS = 14 [xo,Ot,nS]=newton('test9',[0 -1],1,'gtest9','htest9',[-5 -5],[5 5]) Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 3.0000 2.0000 Ot = 1.7668e-026 nS = 25 [xo,Ot,nS]=newton('test9',[0 1],1,'gtest9','htest9',[-5 -5],[5 5]) Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 0.0867 2.8843 Ot = 67.7192 nS = 6 [xo,Ot,nS]=newton('test9',[0 0],1,'gtest9','htest9',[-5 -5],[5 5]) Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 3.0000 2.0000 Ot = 2.0274e-028 nS = 39 [xo,Ot,nS]=newton('test9',[-1 -1],1,'gtest9','htest9',[-5 -5],[5 5]) Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 3.5844 -1.8481 Ot = 9.3808e-016 nS = 12 type test9 function S=test(x) % Himmelblau, 1972 % x0 = [1, 1]' % xo = [3, 2]', xo = [3.58443, -1.84813]', xo = [-3.7793, -3.2832]' e xo = [-2.8051, 3.1313]' % S(xo) = 0 % local maximum: xo = [-0.2708, -0.9230]', S(xo) = 181.6 S=(x(1).^2+x(2)-11).^2+(x(1)+x(2).^2-7).^2; [xo,Ot,nS]=newton('test9',[-0.3 -1],1,'gtest9','htest9',[-5 -5],[5 5]) Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = -2.8051 3.1313 Ot = 1.5723e-019 nS = 25 [xo,Ot,nS]=newton('test9',[-0.27 -0.9],1,'gtest9','htest9',[-5 -5],[5 5]) Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 0.0867 2.8843 Ot = 67.7192 nS = 35 edit newton disp(sprintf('%d',feature('SessionTool'))) 0 ; dbstatus dbstack dbstack ; disp(which('newton')); v:\cursos\pos\otimiza\aulas\newton.m mdbstatus 'v:\cursos\pos\otimiza\aulas\newton.m' eval( 'if exist(''Date'',''var''), mauifunc(Date), end', ''); eval( 'if exist(''lower'',''var''), mauifunc(lower), end', ''); eval( 'if exist(''gradient'',''var''), mauifunc(gradient), end', ''); eval( 'if exist(''initial'',''var''), mauifunc(initial), end', ''); eval( 'if exist(''function'',''var''), mauifunc(function), end', ''); disp(which('newton_mod')); disp(char(which('newton_mod','-all'))); eval( 'if exist(''iterations'',''var''), mauifunc(iterations), end', ''); eval( 'if exist(''plot'',''var''), mauifunc(plot), end', ''); eval( 'if exist(''pause'',''var''), mauifunc(pause), end', ''); eval( 'if exist(''problem'',''var''), mauifunc(problem), end', ''); eval( 'if exist(''xo'',''var''), mauifunc(xo), end', ''); 0.0867 2.8843 eval( 'if exist(''full'',''var''), mauifunc(full), end', ''); eval( 'if exist(''sparse'',''var''), mauifunc(sparse), end', ''); eval( 'if exist(''fun'',''var''), mauifunc(fun), end', ''); disp(which('newton_mod')); disp(char(which('newton_mod','-all'))); eval( 'if exist(''sparse'',''var''), mauifunc(sparse), end', ''); [xo,Ot,nS]=newton('test9',[-1 0],1,'gtest9','htest9',[-5 -5],[5 5]) Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = -3.7793 -3.2832 Ot = 1.5393e-019 nS = 12 [xo,Ot,nS]=newton('test9',[1 1],1,'gtest9','htest9',[-5 -5],[5 5]) Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 3.3852 0.0739 Ot = 13.3119 nS = 14 [xo,Ot,nS]=newton_mod('test9',[1 1],1,'gtest9','htest9',[-5 -5],[5 5]) ??? Undefined function or variable 'newton_mod'. cd(cd) [xo,Ot,nS]=newton_mod('test9',[1 1],1,'gtest9','htest9',[-5 -5],[5 5]) Pause: hit any key to continue... he = 26 -8 -8 10 ans = 29.3137 6.6863 Pause: hit any key to continue... he = 7.9980 -13.4082 -13.4082 -21.6785 ans = 13.1586 -26.8391 Pause: hit any key to continue... he = -25.5884 -12.0089 -12.0089 11.1993 ans = -29.1615 14.7724 Pause: hit any key to continue... he = -56.7454 -14.2568 -14.2568 8.1476 ans = -59.7394 11.1417 Pause: hit any key to continue... he = -110.3762 -14.7991 -14.7991 11.5275 ans = -112.1471 13.2984 Pause: hit any key to continue... he = -96.7294 -13.8983 -13.8983 12.3413 ans = -98.4725 14.0845 Pause: hit any key to continue... he = -95.8109 -13.8363 -13.8363 12.3937 ans = -97.5522 14.1349 xo = 3.3852 0.0739 Ot = 13.3119 nS = 14 H=[ -95.8109 -13.8363 -13.8363 12.3937] H = -95.8109 -13.8363 -13.8363 12.3937 eig(H) ans = -97.5521 14.1349 eig(H+eye(2)*(100)) ans = 2.4479 114.1349 eval( 'if exist(''sparse'',''var''), mauifunc(sparse), end', ''); eval( 'if exist(''full'',''var''), mauifunc(full), end', ''); eig([0 1;1 0]) ans = -1.0000 1.0000 eval( 'if exist(''inline'',''var''), mauifunc(inline), end', ''); eval( 'if exist(''color'',''var''), mauifunc(color), end', ''); eval( 'if exist(''sfd'',''var''), mauifunc(sfd), end', ''); eval( 'if exist(''H'',''var''), mauifunc(H), end', ''); -95.8109 -13.8363 -13.8363 12.3937 eval( 'if exist(''n'',''var''), mauifunc(n), end', ''); eval( 'if exist(''group'',''var''), mauifunc(group), end', ''); eval( 'if exist(''Hstr'',''var''), mauifunc(Hstr), end', ''); eval( 'if exist(''fun'',''var''), mauifunc(fun), end', ''); eval( 'if exist(''else'',''var''), mauifunc(else), end', ''); eval( 'if exist(''fun'',''var''), mauifunc(fun), end', ''); eval( 'if exist(''problem'',''var''), mauifunc(problem), end', ''); disp(which('newton_mod')); v:\cursos\pos\otimiza\aulas\newton_mod.m clear 'v:\cursos\pos\otimiza\aulas\newton_mod.m' eval( 'if exist(''fun'',''var''), mauifunc(fun), end', ''); eval( 'if exist(''sparse'',''var''), mauifunc(sparse), end', ''); cd(cd) [xo,Ot,nS]=newton_mod('test9',[1 1],1,'gtest9','htest9',[-5 -5],[5 5]) Pause: hit any key to continue... he = 1026 -8 -8 1010 ans = 1.0e+003 * 1.0293 1.0067 Pause: hit any key to continue... he = 1.0e+003 * 1.0254 -0.0082 -0.0082 1.0094 ans = 1.0e+003 * 1.0288 1.0060 Pause: hit any key to continue... he = 1.0e+003 * 1.0247 -0.0083 -0.0083 1.0089 ans = 1.0e+003 * 1.0283 1.0053 Pause: hit any key to continue... he = 1.0e+003 * 1.0241 -0.0085 -0.0085 1.0083 ans = 1.0e+003 * 1.0278 1.0046 Pause: hit any key to continue... he = 1.0e+003 * 1.0234 -0.0087 -0.0087 1.0077 ans = 1.0e+003 * 1.0273 1.0039 Pause: hit any key to continue... he = 1.0e+003 * 1.0227 -0.0088 -0.0088 1.0072 ans = 1.0e+003 * 1.0267 1.0032 Pause: hit any key to continue... he = 1.0e+003 * 1.0220 -0.0090 -0.0090 1.0066 ans = 1.0e+003 * 1.0261 1.0024 Pause: hit any key to continue... he = 1.0e+003 * 1.0213 -0.0092 -0.0092 1.0059 ans = 1.0e+003 * 1.0256 1.0016 Pause: hit any key to continue... he = 1.0e+003 * 1.0205 -0.0094 -0.0094 1.0053 ans = 1.0e+003 * 1.0250 1.0009 Pause: hit any key to continue... he = 1.0e+003 * 1.0197 -0.0095 -0.0095 1.0047 ans = 1.0e+003 * 1.0243 1.0001 Pause: hit any key to continue... he = 1.0e+003 * 1.0189 -0.0097 -0.0097 1.0041 ans = 1.0e+003 * 1.0237 0.9993 Pause: hit any key to continue... he = 1.0e+003 * 1.0181 -0.0099 -0.0099 1.0034 ans = 1.0e+003 * 1.0231 0.9985 Pause: hit any key to continue... he = 1.0e+003 * 1.0173 -0.0100 -0.0100 1.0028 ans = 1.0e+003 * 1.0224 0.9977 Pause: hit any key to continue... he = 1.0e+003 * 1.0165 -0.0102 -0.0102 1.0021 ans = 1.0e+003 * 1.0218 0.9968 Pause: hit any key to continue... he = 1.0e+003 * 1.0156 -0.0104 -0.0104 1.0015 ans = 1.0e+003 * 1.0211 0.9960 Pause: hit any key to continue... he = 1.0e+003 * 1.0147 -0.0106 -0.0106 1.0008 ans = 1.0e+003 * 1.0204 0.9951 Pause: hit any key to continue... he = 1.0e+003 * 1.0138 -0.0107 -0.0107 1.0001 ans = 1.0e+003 * 1.0197 0.9942 Pause: hit any key to continue... he = 1.0e+003 * 1.0129 -0.0109 -0.0109 0.9995 ans = 1.0e+003 * 1.0190 0.9934 Pause: hit any key to continue... he = 1.0e+003 * 1.0119 -0.0111 -0.0111 0.9988 ans = 1.0e+003 * 1.0183 0.9925 Pause: hit any key to continue... he = 1.0e+003 * 1.0110 -0.0113 -0.0113 0.9981 ans = 1.0e+003 * 1.0175 0.9916 Pause: hit any key to continue... he = 1.0e+003 * 1.0100 -0.0114 -0.0114 0.9974 ans = 1.0e+003 * 1.0168 0.9907 Pause: hit any key to continue... he = 1.0e+003 * 1.0090 -0.0116 -0.0116 0.9967 ans = 1.0e+003 * 1.0160 0.9897 Pause: hit any key to continue... he = 1.0e+003 * 1.0080 -0.0118 -0.0118 0.9960 ans = 1.0e+003 * 1.0152 0.9888 Pause: hit any key to continue... he = 1.0e+003 * 1.0070 -0.0120 -0.0120 0.9953 ans = 1.0e+003 * 1.0145 0.9879 Pause: hit any key to continue... he = 1.0e+003 * 1.0059 -0.0121 -0.0121 0.9946 ans = 1.0e+003 * 1.0137 0.9869 Pause: hit any key to continue... he = 1.0e+003 * 1.0049 -0.0123 -0.0123 0.9939 ans = 1.0e+003 * 1.0129 0.9859 Pause: hit any key to continue... he = 1.0e+003 * 1.0038 -0.0125 -0.0125 0.9932 ans = 1.0e+003 * 1.0121 0.9850 Pause: hit any key to continue... he = 1.0e+003 * 1.0027 -0.0126 -0.0126 0.9926 ans = 1.0e+003 * 1.0113 0.9840 Pause: hit any key to continue... he = 1.0e+003 * 1.0016 -0.0128 -0.0128 0.9919 ans = 1.0e+003 * 1.0104 0.9830 Pause: hit any key to continue... he = 1.0e+003 * 1.0005 -0.0130 -0.0130 0.9912 ans = 1.0e+003 * 1.0096 0.9820 Pause: hit any key to continue... he = 999.3781 -13.1424 -13.1424 990.4686 ans = 1.0e+003 * 1.0088 0.9810 Pause: hit any key to continue... he = 998.2415 -13.3074 -13.3074 989.7794 ans = 1.0e+003 * 1.0080 0.9800 Pause: hit any key to continue... he = 997.0941 -13.4711 -13.4711 989.0934 ans = 1.0e+003 * 1.0071 0.9790 Pause: hit any key to continue... he = 995.9369 -13.6335 -13.6335 988.4112 ans = 1.0e+003 * 1.0063 0.9780 Pause: hit any key to continue... he = 994.7706 -13.7944 -13.7944 987.7335 ans = 1.0e+003 * 1.0055 0.9770 Pause: hit any key to continue... he = 993.5962 -13.9537 -13.9537 987.0606 ans = 1.0e+003 * 1.0047 0.9760 Pause: hit any key to continue... he = 992.4145 -14.1114 -14.1114 986.3932 ans = 1.0e+003 * 1.0038 0.9750 Pause: hit any key to continue... he = 991.2265 -14.2674 -14.2674 985.7318 ans = 1.0e+003 * 1.0030 0.9739 Pause: hit any key to continue... he = 990.0331 -14.4216 -14.4216 985.0769 ans = 1.0e+003 * 1.0022 0.9729 Pause: hit any key to continue... he = 988.8353 -14.5740 -14.5740 984.4290 ans = 1.0e+003 * 1.0014 0.9719 Pause: hit any key to continue... he = 987.6341 -14.7245 -14.7245 983.7886 ans = 1.0e+003 * 1.0006 0.9709 Pause: hit any key to continue... he = 986.4305 -14.8729 -14.8729 983.1561 ans = 999.7561 969.8305 Pause: hit any key to continue... he = 985.2255 -15.0194 -15.0194 982.5319 ans = 998.9583 968.7991 Pause: hit any key to continue... he = 984.0201 -15.1637 -15.1637 981.9166 ans = 998.1685 967.7682 Pause: hit any key to continue... he = 982.8154 -15.3058 -15.3058 981.3104 ans = 997.3872 966.7386 Pause: hit any key to continue... he = 981.6124 -15.4458 -15.4458 980.7138 ans = 996.6154 965.7108 Pause: hit any key to continue... he = 980.4120 -15.5835 -15.5835 980.1271 ans = 995.8537 964.6855 Pause: hit any key to continue... he = 979.2154 -15.7188 -15.7188 979.5506 ans = 963.6633 995.1027 Pause: hit any key to continue... he = 978.0235 -15.8518 -15.8518 978.9847 ans = 962.6450 994.3632 Pause: hit any key to continue... he = 976.8373 -15.9824 -15.9824 978.4296 ans = 961.6312 993.6357 Pause: hit any key to continue... Warning Newton: reached maximum number of iterations! xo = 2.2194 1.8082 Ot = 20.4814 nS = 101 help newton Unconstrained optimization using Newton. [xo,Ot,nS]=newton(S,x0,ip,G,H,Lb,Ub,problem,tol,mxit) S: objective function x0: initial point ip: (0) no plot (default), (>0) plot figure ip with pause, (<0) plot figure ip G: gradient vector function H: Hessian matrix function Lb, Ub: lower and upper bound vectors to plot (default = x0*(1+/-2)) problem: (-1): minimum (default), (1): maximum tol: tolerance (default = 1e-4) mxit: maximum number of iterations (default = 50*(1+4*~(ip>0))) xo: optimal point Ot: optimal value of S nS: number of objective function evaluations [xo,Ot,nS]=newton_mod('test9',[1 1],1,'gtest9','htest9',[-5 -5],[5 5],[],[],500) Pause: hit any key to continue... he = 1026 -8 -8 1010 ans = 1.0e+003 * 1.0293 1.0067 Pause: hit any key to continue... he = 1.0e+003 * 1.0254 -0.0082 -0.0082 1.0094 ans = 1.0e+003 * 1.0288 1.0060 Pause: hit any key to continue... he = 1.0e+003 * 1.0247 -0.0083 -0.0083 1.0089 ans = 1.0e+003 * 1.0283 1.0053 Pause: hit any key to continue... he = 1.0e+003 * 1.0241 -0.0085 -0.0085 1.0083 ans = 1.0e+003 * 1.0278 1.0046 Pause: hit any key to continue... he = 1.0e+003 * 1.0234 -0.0087 -0.0087 1.0077 ans = 1.0e+003 * 1.0273 1.0039 Pause: hit any key to continue... he = 1.0e+003 * 1.0227 -0.0088 -0.0088 1.0072 ans = 1.0e+003 * 1.0267 1.0032 Pause: hit any key to continue... he = 1.0e+003 * 1.0220 -0.0090 -0.0090 1.0066 ans = 1.0e+003 * 1.0261 1.0024 Pause: hit any key to continue... he = 1.0e+003 * 1.0213 -0.0092 -0.0092 1.0059 ans = 1.0e+003 * 1.0256 1.0016 Pause: hit any key to continue... he = 1.0e+003 * 1.0205 -0.0094 -0.0094 1.0053 ans = 1.0e+003 * 1.0250 1.0009 Pause: hit any key to continue... he = 1.0e+003 * 1.0197 -0.0095 -0.0095 1.0047 ans = 1.0e+003 * 1.0243 1.0001 Pause: hit any key to continue... he = 1.0e+003 * 1.0189 -0.0097 -0.0097 1.0041 ans = 1.0e+003 * 1.0237 0.9993 Pause: hit any key to continue... he = 1.0e+003 * 1.0181 -0.0099 -0.0099 1.0034 ans = 1.0e+003 * 1.0231 0.9985 Pause: hit any key to continue... he = 1.0e+003 * 1.0173 -0.0100 -0.0100 1.0028 ans = 1.0e+003 * 1.0224 0.9977 Pause: hit any key to continue... he = 1.0e+003 * 1.0165 -0.0102 -0.0102 1.0021 ans = 1.0e+003 * 1.0218 0.9968 Pause: hit any key to continue... he = 1.0e+003 * 1.0156 -0.0104 -0.0104 1.0015 ans = 1.0e+003 * 1.0211 0.9960 Pause: hit any key to continue... he = 1.0e+003 * 1.0147 -0.0106 -0.0106 1.0008 ans = 1.0e+003 * 1.0204 0.9951 Pause: hit any key to continue... he = 1.0e+003 * 1.0138 -0.0107 -0.0107 1.0001 ans = 1.0e+003 * 1.0197 0.9942 Pause: hit any key to continue... he = 1.0e+003 * 1.0129 -0.0109 -0.0109 0.9995 ans = 1.0e+003 * 1.0190 0.9934 Pause: hit any key to continue... he = 1.0e+003 * 1.0119 -0.0111 -0.0111 0.9988 ans = 1.0e+003 * 1.0183 0.9925 Pause: hit any key to continue... he = 1.0e+003 * 1.0110 -0.0113 -0.0113 0.9981 ans = 1.0e+003 * 1.0175 0.9916 Pause: hit any key to continue... he = 1.0e+003 * 1.0100 -0.0114 -0.0114 0.9974 ans = 1.0e+003 * 1.0168 0.9907 Pause: hit any key to continue... he = 1.0e+003 * 1.0090 -0.0116 -0.0116 0.9967 ans = 1.0e+003 * 1.0160 0.9897 Pause: hit any key to continue... he = 1.0e+003 * 1.0080 -0.0118 -0.0118 0.9960 ans = 1.0e+003 * 1.0152 0.9888 Pause: hit any key to continue... he = 1.0e+003 * 1.0070 -0.0120 -0.0120 0.9953 ans = 1.0e+003 * 1.0145 0.9879 Pause: hit any key to continue... he = 1.0e+003 * 1.0059 -0.0121 -0.0121 0.9946 ans = 1.0e+003 * 1.0137 0.9869 Pause: hit any key to continue... he = 1.0e+003 * 1.0049 -0.0123 -0.0123 0.9939 ans = 1.0e+003 * 1.0129 0.9859 Pause: hit any key to continue... he = 1.0e+003 * 1.0038 -0.0125 -0.0125 0.9932 ans = 1.0e+003 * 1.0121 0.9850 Pause: hit any key to continue... he = 1.0e+003 * 1.0027 -0.0126 -0.0126 0.9926 ans = 1.0e+003 * 1.0113 0.9840 Pause: hit any key to continue... he = 1.0e+003 * 1.0016 -0.0128 -0.0128 0.9919 ans = 1.0e+003 * 1.0104 0.9830 Pause: hit any key to continue... he = 1.0e+003 * 1.0005 -0.0130 -0.0130 0.9912 ans = 1.0e+003 * 1.0096 0.9820 Pause: hit any key to continue... he = 999.3781 -13.1424 -13.1424 990.4686 ans = 1.0e+003 * 1.0088 0.9810 Pause: hit any key to continue... he = 998.2415 -13.3074 -13.3074 989.7794 ans = 1.0e+003 * 1.0080 0.9800 Pause: hit any key to continue... he = 997.0941 -13.4711 -13.4711 989.0934 ans = 1.0e+003 * 1.0071 0.9790 Pause: hit any key to continue... he = 995.9369 -13.6335 -13.6335 988.4112 ans = 1.0e+003 * 1.0063 0.9780 Pause: hit any key to continue... he = 994.7706 -13.7944 -13.7944 987.7335 ans = 1.0e+003 * 1.0055 0.9770 Pause: hit any key to continue... he = 993.5962 -13.9537 -13.9537 987.0606 ans = 1.0e+003 * 1.0047 0.9760 Pause: hit any key to continue... he = 992.4145 -14.1114 -14.1114 986.3932 ans = 1.0e+003 * 1.0038 0.9750 Pause: hit any key to continue... he = 991.2265 -14.2674 -14.2674 985.7318 ans = 1.0e+003 * 1.0030 0.9739 Pause: hit any key to continue... he = 990.0331 -14.4216 -14.4216 985.0769 ans = 1.0e+003 * 1.0022 0.9729 Pause: hit any key to continue... he = 988.8353 -14.5740 -14.5740 984.4290 ans = 1.0e+003 * 1.0014 0.9719 Pause: hit any key to continue... he = 987.6341 -14.7245 -14.7245 983.7886 ans = 1.0e+003 * 1.0006 0.9709 Pause: hit any key to continue... he = 986.4305 -14.8729 -14.8729 983.1561 ans = 999.7561 969.8305 Pause: hit any key to continue... he = 985.2255 -15.0194 -15.0194 982.5319 ans = 998.9583 968.7991 Pause: hit any key to continue... he = 984.0201 -15.1637 -15.1637 981.9166 ans = 998.1685 967.7682 Pause: hit any key to continue... he = 982.8154 -15.3058 -15.3058 981.3104 ans = 997.3872 966.7386 Pause: hit any key to continue... he = 981.6124 -15.4458 -15.4458 980.7138 ans = 996.6154 965.7108 Pause: hit any key to continue... he = 980.4120 -15.5835 -15.5835 980.1271 ans = 995.8537 964.6855 Pause: hit any key to continue... he = 979.2154 -15.7188 -15.7188 979.5506 ans = 963.6633 995.1027 Pause: hit any key to continue... he = 978.0235 -15.8518 -15.8518 978.9847 ans = 962.6450 994.3632 Pause: hit any key to continue... he = 976.8373 -15.9824 -15.9824 978.4296 ans = 961.6312 993.6357 Pause: hit any key to continue... he = 975.6578 -16.1106 -16.1106 977.8856 ans = 960.6226 992.9208 Pause: hit any key to continue... he = 974.4859 -16.2363 -16.2363 977.3529 ans = 959.6200 992.2189 Pause: hit any key to continue... he = 973.3225 -16.3595 -16.3595 976.8318 ans = 958.6238 991.5305 Pause: hit any key to continue... he = 972.1687 -16.4802 -16.4802 976.3223 ans = 957.6350 990.8560 Pause: hit any key to continue... he = 971.0252 -16.5983 -16.5983 975.8246 ans = 956.6540 990.1958 Pause: hit any key to continue... he = 969.8928 -16.7139 -16.7139 975.3390 ans = 955.6816 989.5502 Pause: hit any key to continue... he = 968.7725 -16.8269 -16.8269 974.8654 ans = 954.7184 988.9194 Pause: hit any key to continue... he = 967.6649 -16.9374 -16.9374 974.4039 ans = 953.7651 988.3037 Pause: hit any key to continue... he = 966.5709 -17.0452 -17.0452 973.9547 ans = 952.8223 987.7033 Pause: hit any key to continue... he = 965.4910 -17.1505 -17.1505 973.5178 ans = 951.8906 987.1182 Pause: hit any key to continue... he = 964.4260 -17.2532 -17.2532 973.0931 ans = 950.9705 986.5486 Pause: hit any key to continue... he = 963.3765 -17.3533 -17.3533 972.6806 ans = 950.0625 985.9946 Pause: hit any key to continue... he = 962.3431 -17.4508 -17.4508 972.2803 ans = 949.1673 985.4561 Pause: hit any key to continue... he = 961.3262 -17.5458 -17.5458 971.8922 ans = 948.2853 984.9331 Pause: hit any key to continue... he = 960.3264 -17.6382 -17.6382 971.5162 ans = 947.4170 984.4257 Pause: hit any key to continue... he = 959.3441 -17.7281 -17.7281 971.1522 ans = 946.5628 983.9336 Pause: hit any key to continue... he = 958.3797 -17.8155 -17.8155 970.8001 ans = 945.7230 983.4568 Pause: hit any key to continue... he = 957.4335 -17.9004 -17.9004 970.4598 ans = 944.8981 982.9952 Pause: hit any key to continue... he = 956.5059 -17.9829 -17.9829 970.1311 ans = 944.0884 982.5486 Pause: hit any key to continue... he = 955.5971 -18.0629 -18.0629 969.8139 ans = 943.2942 982.1168 Pause: hit any key to continue... he = 954.7073 -18.1406 -18.1406 969.5080 ans = 942.5157 981.6996 Pause: hit any key to continue... he = 953.8368 -18.2158 -18.2158 969.2133 ans = 941.7532 981.2969 Pause: hit any key to continue... he = 952.9855 -18.2888 -18.2888 968.9295 ans = 941.0068 980.9082 Pause: hit any key to continue... he = 952.1537 -18.3594 -18.3594 968.6564 ans = 940.2767 980.5335 Pause: hit any key to continue... he = 951.3415 -18.4278 -18.4278 968.3940 ans = 939.5630 980.1725 Pause: hit any key to continue... he = 950.5487 -18.4940 -18.4940 968.1419 ans = 938.8658 979.8247 Pause: hit any key to continue... he = 949.7754 -18.5580 -18.5580 967.8999 ans = 938.1852 979.4901 Pause: hit any key to continue... he = 949.0216 -18.6199 -18.6199 967.6678 ans = 937.5211 979.1682 Pause: hit any key to continue... he = 948.2871 -18.6797 -18.6797 967.4453 ans = 936.8736 978.8589 Pause: hit any key to continue... he = 947.5720 -18.7374 -18.7374 967.2324 ans = 936.2427 978.5617 Pause: hit any key to continue... he = 946.8759 -18.7932 -18.7932 967.0286 ans = 935.6282 978.2763 Pause: hit any key to continue... he = 946.1988 -18.8470 -18.8470 966.8337 ans = 935.0300 978.0025 Pause: hit any key to continue... he = 945.5405 -18.8989 -18.8989 966.6476 ans = 934.4482 977.7400 Pause: hit any key to continue... he = 944.9008 -18.9489 -18.9489 966.4700 ans = 933.8824 977.4883 Pause: hit any key to continue... he = 944.2793 -18.9971 -18.9971 966.3005 ans = 933.3326 977.2473 Pause: hit any key to continue... he = 943.6760 -19.0436 -19.0436 966.1391 ans = 932.7986 977.0165 Pause: hit any key to continue... he = 943.0905 -19.0883 -19.0883 965.9854 ans = 932.2802 976.7957 Pause: hit any key to continue... he = 942.5225 -19.1314 -19.1314 965.8392 ans = 931.7771 976.5846 Pause: hit any key to continue... he = 941.9717 -19.1728 -19.1728 965.7003 ans = 931.2892 976.3828 Pause: hit any key to continue... he = 941.4378 -19.2127 -19.2127 965.5684 ans = 930.8161 976.1901 Pause: hit any key to continue... he = 940.9205 -19.2510 -19.2510 965.4433 ans = 930.3577 976.0061 Pause: hit any key to continue... he = 940.4195 -19.2878 -19.2878 965.3247 ans = 929.9137 975.8305 Pause: hit any key to continue... he = 939.9343 -19.3232 -19.3232 965.2125 ans = 929.4837 975.6631 Pause: hit any key to continue... he = 939.4648 -19.3572 -19.3572 965.1064 ans = 929.0676 975.5036 Pause: hit any key to continue... he = 939.0104 -19.3899 -19.3899 965.0062 ans = 928.6650 975.3516 Pause: hit any key to continue... he = 938.5709 -19.4212 -19.4212 964.9116 ans = 928.2755 975.2070 Pause: hit any key to continue... he = 938.1459 -19.4512 -19.4512 964.8225 ans = 927.8990 975.0694 Pause: hit any key to continue... he = 937.7350 -19.4801 -19.4801 964.7386 ans = 927.5351 974.9386 Pause: hit any key to continue... he = 937.3379 -19.5077 -19.5077 964.6598 ans = 927.1835 974.8143 Pause: hit any key to continue... he = 936.9543 -19.5342 -19.5342 964.5859 ans = 926.8439 974.6963 Pause: hit any key to continue... he = 936.5836 -19.5596 -19.5596 964.5166 ans = 926.5159 974.5843 Pause: hit any key to continue... he = 936.2256 -19.5839 -19.5839 964.4518 ans = 926.1993 974.4781 Pause: hit any key to continue... he = 935.8800 -19.6072 -19.6072 964.3913 ans = 925.8938 974.3775 Pause: hit any key to continue... he = 935.5463 -19.6295 -19.6295 964.3348 ans = 925.5990 974.2822 Pause: hit any key to continue... he = 935.2243 -19.6509 -19.6509 964.2824 ans = 925.3146 974.1920 Pause: hit any key to continue... he = 934.9135 -19.6713 -19.6713 964.2336 ans = 925.0404 974.1068 Pause: hit any key to continue... he = 934.6136 -19.6908 -19.6908 964.1885 ans = 924.7760 974.0262 Pause: hit any key to continue... he = 934.3244 -19.7095 -19.7095 964.1469 ans = 924.5211 973.9502 Pause: hit any key to continue... he = 934.0454 -19.7273 -19.7273 964.1085 ans = 924.2754 973.8785 Pause: hit any key to continue... he = 933.7763 -19.7444 -19.7444 964.0733 ans = 924.0387 973.8109 Pause: hit any key to continue... he = 933.5169 -19.7607 -19.7607 964.0411 ans = 923.8107 973.7473 Pause: hit any key to continue... he = 933.2667 -19.7762 -19.7762 964.0118 ans = 923.5910 973.6875 Pause: hit any key to continue... he = 933.0256 -19.7911 -19.7911 963.9852 ans = 923.3795 973.6314 Pause: hit any key to continue... he = 932.7931 -19.8053 -19.8053 963.9613 ans = 923.1758 973.5786 Pause: hit any key to continue... he = 932.5691 -19.8188 -19.8188 963.9398 ans = 922.9796 973.5292 Pause: hit any key to continue... he = 932.3531 -19.8317 -19.8317 963.9207 ans = 922.7908 973.4830 Pause: hit any key to continue... he = 932.1450 -19.8440 -19.8440 963.9038 ans = 922.6091 973.4398 Pause: hit any key to continue... he = 931.9445 -19.8557 -19.8557 963.8891 ans = 922.4342 973.3995 Pause: hit any key to continue... he = 931.7513 -19.8669 -19.8669 963.8765 ans = 922.2658 973.3619 Pause: hit any key to continue... he = 931.5651 -19.8776 -19.8776 963.8657 ans = 922.1039 973.3269 Pause: hit any key to continue... he = 931.3857 -19.8877 -19.8877 963.8568 ans = 921.9480 973.2945 Pause: hit any key to continue... he = 931.2128 -19.8973 -19.8973 963.8497 ans = 921.7981 973.2644 Pause: hit any key to continue... he = 931.0463 -19.9065 -19.9065 963.8442 ans = 921.6539 973.2366 Pause: hit any key to continue... he = 930.8859 -19.9153 -19.9153 963.8403 ans = 921.5151 973.2110 Pause: hit any key to continue... he = 930.7313 -19.9236 -19.9236 963.8378 ans = 921.3817 973.1874 Pause: hit any key to continue... he = 930.5824 -19.9315 -19.9315 963.8368 ans = 921.2533 973.1658 Pause: hit any key to continue... he = 930.4389 -19.9390 -19.9390 963.8371 ans = 921.1299 973.1461 Pause: hit any key to continue... he = 930.3007 -19.9461 -19.9461 963.8386 ans = 921.0112 973.1281 Pause: hit any key to continue... he = 930.1675 -19.9528 -19.9528 963.8414 ans = 920.8970 973.1119 Pause: hit any key to continue... he = 930.0392 -19.9593 -19.9593 963.8452 ans = 920.7872 973.0972 Pause: hit any key to continue... he = 929.9155 -19.9653 -19.9653 963.8501 ans = 920.6816 973.0840 Pause: hit any key to continue... he = 929.7964 -19.9711 -19.9711 963.8560 ans = 920.5801 973.0723 Pause: hit any key to continue... he = 929.6816 -19.9766 -19.9766 963.8629 ans = 920.4824 973.0620 Pause: hit any key to continue... he = 929.5710 -19.9818 -19.9818 963.8706 ans = 920.3885 973.0530 Pause: hit any key to continue... he = 929.4643 -19.9867 -19.9867 963.8791 ans = 920.2982 973.0452 Pause: hit any key to continue... he = 929.3616 -19.9913 -19.9913 963.8884 ans = 920.2114 973.0386 Pause: hit any key to continue... he = 929.2625 -19.9957 -19.9957 963.8985 ans = 920.1279 973.0331 Pause: hit any key to continue... he = 929.1670 -19.9998 -19.9998 963.9092 ans = 920.0476 973.0286 Pause: hit any key to continue... he = 929.0750 -20.0038 -20.0038 963.9205 ans = 919.9703 973.0252 Pause: hit any key to continue... he = 928.9862 -20.0075 -20.0075 963.9325 ans = 919.8961 973.0226 Pause: hit any key to continue... he = 928.9006 -20.0109 -20.0109 963.9450 ans = 919.8246 973.0210 Pause: hit any key to continue... he = 928.8181 -20.0142 -20.0142 963.9580 ans = 919.7559 973.0202 Pause: hit any key to continue... he = 928.7385 -20.0173 -20.0173 963.9714 ans = 919.6898 973.0202 Pause: hit any key to continue... he = 928.6618 -20.0202 -20.0202 963.9854 ans = 919.6262 973.0209 Pause: hit any key to continue... he = 928.5877 -20.0230 -20.0230 963.9997 ans = 919.5650 973.0224 Pause: hit any key to continue... he = 928.5163 -20.0256 -20.0256 964.0144 ans = 919.5062 973.0245 Pause: hit any key to continue... he = 928.4474 -20.0280 -20.0280 964.0294 ans = 919.4496 973.0272 Pause: hit any key to continue... he = 928.3808 -20.0302 -20.0302 964.0448 ans = 919.3951 973.0305 Pause: hit any key to continue... he = 928.3166 -20.0323 -20.0323 964.0605 ans = 919.3427 973.0344 Pause: hit any key to continue... he = 928.2547 -20.0343 -20.0343 964.0764 ans = 919.2922 973.0388 Pause: hit any key to continue... he = 928.1948 -20.0362 -20.0362 964.0925 ans = 919.2437 973.0437 Pause: hit any key to continue... he = 928.1370 -20.0379 -20.0379 964.1089 ans = 919.1969 973.0490 Pause: hit any key to continue... he = 928.0812 -20.0395 -20.0395 964.1255 ans = 919.1519 973.0548 Pause: hit any key to continue... he = 928.0273 -20.0410 -20.0410 964.1422 ans = 919.1086 973.0609 Pause: hit any key to continue... he = 927.9753 -20.0424 -20.0424 964.1591 ans = 919.0669 973.0675 Pause: hit any key to continue... he = 927.9250 -20.0437 -20.0437 964.1761 ans = 919.0267 973.0744 Pause: hit any key to continue... he = 927.8764 -20.0449 -20.0449 964.1933 ans = 918.9881 973.0816 Pause: hit any key to continue... he = 927.8294 -20.0460 -20.0460 964.2105 ans = 918.9508 973.0891 Pause: hit any key to continue... he = 927.7839 -20.0470 -20.0470 964.2278 ans = 918.9149 973.0969 Pause: hit any key to continue... he = 927.7400 -20.0479 -20.0479 964.2452 ans = 918.8803 973.1049 Pause: hit any key to continue... he = 927.6975 -20.0487 -20.0487 964.2627 ans = 918.8470 973.1132 Pause: hit any key to continue... he = 927.6564 -20.0495 -20.0495 964.2802 ans = 918.8149 973.1217 Pause: hit any key to continue... he = 927.6167 -20.0502 -20.0502 964.2977 ans = 918.7839 973.1304 Pause: hit any key to continue... he = 927.5782 -20.0508 -20.0508 964.3152 ans = 918.7541 973.1393 Pause: hit any key to continue... he = 927.5410 -20.0514 -20.0514 964.3327 ans = 918.7253 973.1484 Pause: hit any key to continue... he = 927.5049 -20.0519 -20.0519 964.3502 ans = 918.6976 973.1576 Pause: hit any key to continue... he = 927.4700 -20.0523 -20.0523 964.3677 ans = 918.6708 973.1669 Pause: hit any key to continue... he = 927.4362 -20.0527 -20.0527 964.3852 ans = 918.6450 973.1764 Pause: hit any key to continue... he = 927.4035 -20.0531 -20.0531 964.4026 ans = 918.6201 973.1860 Pause: hit any key to continue... he = 927.3718 -20.0534 -20.0534 964.4200 ans = 918.5961 973.1957 Pause: hit any key to continue... he = 927.3410 -20.0536 -20.0536 964.4374 ans = 918.5729 973.2055 Pause: hit any key to continue... he = 927.3112 -20.0538 -20.0538 964.4546 ans = 918.5505 973.2154 Pause: hit any key to continue... he = 927.2824 -20.0539 -20.0539 964.4719 ans = 918.5289 973.2253 Pause: hit any key to continue... he = 927.2543 -20.0540 -20.0540 964.4890 ans = 918.5080 973.2353 Pause: hit any key to continue... he = 927.2272 -20.0541 -20.0541 964.5060 ans = 918.4878 973.2454 Pause: hit any key to continue... he = 927.2008 -20.0542 -20.0542 964.5230 ans = 918.4684 973.2555 Pause: hit any key to continue... he = 927.1752 -20.0542 -20.0542 964.5399 ans = 918.4495 973.2656 Pause: hit any key to continue... he = 927.1504 -20.0541 -20.0541 964.5567 ans = 918.4314 973.2757 Pause: hit any key to continue... he = 927.1263 -20.0541 -20.0541 964.5734 ans = 918.4138 973.2859 Pause: hit any key to continue... he = 927.1029 -20.0540 -20.0540 964.5899 ans = 918.3968 973.2960 Pause: hit any key to continue... he = 927.0802 -20.0539 -20.0539 964.6064 ans = 918.3803 973.3062 Pause: hit any key to continue... he = 927.0581 -20.0538 -20.0538 964.6227 ans = 918.3644 973.3164 Pause: hit any key to continue... he = 927.0366 -20.0536 -20.0536 964.6390 ans = 918.3491 973.3265 Pause: hit any key to continue... he = 927.0158 -20.0534 -20.0534 964.6551 ans = 918.3342 973.3367 Pause: hit any key to continue... he = 926.9955 -20.0532 -20.0532 964.6711 ans = 918.3198 973.3468 Pause: hit any key to continue... he = 926.9758 -20.0530 -20.0530 964.6870 ans = 918.3058 973.3569 Pause: hit any key to continue... he = 926.9566 -20.0528 -20.0528 964.7027 ans = 918.2923 973.3670 Pause: hit any key to continue... he = 926.9380 -20.0525 -20.0525 964.7183 ans = 918.2792 973.3770 Pause: hit any key to continue... he = 926.9198 -20.0522 -20.0522 964.7338 ans = 918.2666 973.3870 Pause: hit any key to continue... he = 926.9021 -20.0519 -20.0519 964.7492 ans = 918.2543 973.3970 Pause: hit any key to continue... he = 926.8849 -20.0516 -20.0516 964.7644 ans = 918.2424 973.4069 Pause: hit any key to continue... he = 926.8682 -20.0513 -20.0513 964.7794 ans = 918.2309 973.4168 Pause: hit any key to continue... he = 926.8519 -20.0510 -20.0510 964.7944 ans = 918.2197 973.4266 Pause: hit any key to continue... he = 926.8360 -20.0507 -20.0507 964.8092 ans = 918.2088 973.4363 Pause: hit any key to continue... he = 926.8205 -20.0503 -20.0503 964.8238 ans = 918.1983 973.4460 Pause: hit any key to continue... he = 926.8054 -20.0499 -20.0499 964.8384 ans = 918.1881 973.4557 Pause: hit any key to continue... he = 926.7907 -20.0496 -20.0496 964.8527 ans = 918.1782 973.4653 Pause: hit any key to continue... he = 926.7764 -20.0492 -20.0492 964.8670 ans = 918.1686 973.4748 Pause: hit any key to continue... he = 926.7624 -20.0488 -20.0488 964.8811 ans = 918.1592 973.4842 Pause: hit any key to continue... he = 926.7487 -20.0484 -20.0484 964.8950 ans = 918.1502 973.4936 Pause: hit any key to continue... he = 926.7354 -20.0480 -20.0480 964.9088 ans = 918.1414 973.5029 Pause: hit any key to continue... he = 926.7224 -20.0476 -20.0476 964.9225 ans = 918.1328 973.5122 Pause: hit any key to continue... he = 926.7098 -20.0472 -20.0472 964.9360 ans = 918.1245 973.5213 Pause: hit any key to continue... he = 926.6974 -20.0468 -20.0468 964.9494 ans = 918.1164 973.5304 Pause: hit any key to continue... he = 926.6853 -20.0464 -20.0464 964.9627 ans = 918.1085 973.5395 Pause: hit any key to continue... he = 926.6735 -20.0460 -20.0460 964.9758 ans = 918.1008 973.5484 Pause: hit any key to continue... he = 926.6620 -20.0456 -20.0456 964.9887 ans = 918.0934 973.5573 Pause: hit any key to continue... he = 926.6507 -20.0452 -20.0452 965.0015 ans = 918.0862 973.5661 Pause: hit any key to continue... he = 926.6397 -20.0447 -20.0447 965.0142 ans = 918.0791 973.5748 Pause: hit any key to continue... he = 926.6289 -20.0443 -20.0443 965.0267 ans = 918.0722 973.5834 Pause: hit any key to continue... he = 926.6184 -20.0439 -20.0439 965.0391 ans = 918.0655 973.5920 Pause: hit any key to continue... he = 926.6081 -20.0434 -20.0434 965.0514 ans = 918.0590 973.6004 Pause: hit any key to continue... he = 926.5980 -20.0430 -20.0430 965.0635 ans = 918.0527 973.6088 Pause: hit any key to continue... he = 926.5881 -20.0426 -20.0426 965.0755 ans = 918.0465 973.6171 Pause: hit any key to continue... he = 926.5785 -20.0421 -20.0421 965.0873 ans = 918.0405 973.6254 Pause: hit any key to continue... he = 926.5691 -20.0417 -20.0417 965.0990 ans = 918.0346 973.6335 Pause: hit any key to continue... he = 926.5598 -20.0413 -20.0413 965.1106 ans = 918.0289 973.6416 Pause: hit any key to continue... he = 926.5508 -20.0409 -20.0409 965.1220 ans = 918.0233 973.6495 Pause: hit any key to continue... he = 926.5420 -20.0404 -20.0404 965.1333 ans = 918.0178 973.6574 Pause: hit any key to continue... he = 926.5333 -20.0400 -20.0400 965.1445 ans = 918.0125 973.6653 Pause: hit any key to continue... he = 926.5248 -20.0396 -20.0396 965.1555 ans = 918.0073 973.6730 Pause: hit any key to continue... he = 926.5165 -20.0391 -20.0391 965.1664 ans = 918.0022 973.6807 Pause: hit any key to continue... he = 926.5083 -20.0387 -20.0387 965.1772 ans = 917.9973 973.6882 Pause: hit any key to continue... he = 926.5003 -20.0383 -20.0383 965.1878 ans = 917.9924 973.6957 Pause: hit any key to continue... he = 926.4925 -20.0379 -20.0379 965.1983 ans = 917.9877 973.7031 Pause: hit any key to continue... he = 926.4848 -20.0374 -20.0374 965.2087 ans = 917.9831 973.7105 Pause: hit any key to continue... he = 926.4773 -20.0370 -20.0370 965.2190 ans = 917.9786 973.7177 Pause: hit any key to continue... he = 926.4699 -20.0366 -20.0366 965.2291 ans = 917.9742 973.7249 Pause: hit any key to continue... he = 926.4627 -20.0362 -20.0362 965.2391 ans = 917.9699 973.7320 Pause: hit any key to continue... he = 926.4556 -20.0358 -20.0358 965.2490 ans = 917.9657 973.7390 Pause: hit any key to continue... he = 926.4486 -20.0354 -20.0354 965.2588 ans = 917.9615 973.7459 Pause: hit any key to continue... he = 926.4418 -20.0350 -20.0350 965.2684 ans = 917.9575 973.7527 Pause: hit any key to continue... he = 926.4351 -20.0346 -20.0346 965.2780 ans = 917.9536 973.7595 Pause: hit any key to continue... he = 926.4285 -20.0342 -20.0342 965.2874 ans = 917.9497 973.7662 Pause: hit any key to continue... he = 926.4221 -20.0338 -20.0338 965.2967 ans = 917.9459 973.7728 Pause: hit any key to continue... he = 926.4157 -20.0334 -20.0334 965.3059 ans = 917.9422 973.7794 Pause: hit any key to continue... he = 926.4095 -20.0330 -20.0330 965.3149 ans = 917.9386 973.7858 Pause: hit any key to continue... he = 926.4034 -20.0326 -20.0326 965.3239 ans = 917.9350 973.7922 Pause: hit any key to continue... he = 926.3974 -20.0322 -20.0322 965.3327 ans = 917.9316 973.7985 Pause: hit any key to continue... he = 926.3915 -20.0318 -20.0318 965.3414 ans = 917.9282 973.8048 Pause: hit any key to continue... he = 926.3857 -20.0314 -20.0314 965.3501 ans = 917.9248 973.8109 Pause: hit any key to continue... he = 926.3800 -20.0311 -20.0311 965.3586 ans = 917.9215 973.8170 Pause: hit any key to continue... he = 926.3744 -20.0307 -20.0307 965.3670 ans = 917.9183 973.8230 Pause: hit any key to continue... he = 926.3689 -20.0303 -20.0303 965.3753 ans = 917.9152 973.8290 Pause: hit any key to continue... he = 926.3635 -20.0300 -20.0300 965.3834 ans = 917.9121 973.8349 Pause: hit any key to continue... he = 926.3582 -20.0296 -20.0296 965.3915 ans = 917.9091 973.8407 Pause: hit any key to continue... he = 926.3530 -20.0292 -20.0292 965.3995 ans = 917.9061 973.8464 Pause: hit any key to continue... he = 926.3479 -20.0289 -20.0289 965.4074 ans = 917.9032 973.8520 Pause: hit any key to continue... he = 926.3428 -20.0285 -20.0285 965.4152 ans = 917.9004 973.8576 Pause: hit any key to continue... he = 926.3379 -20.0282 -20.0282 965.4229 ans = 917.8976 973.8632 Pause: hit any key to continue... he = 926.3330 -20.0278 -20.0278 965.4304 ans = 917.8948 973.8686 Pause: hit any key to continue... he = 926.3282 -20.0275 -20.0275 965.4379 ans = 917.8921 973.8740 Pause: hit any key to continue... he = 926.3235 -20.0272 -20.0272 965.4453 ans = 917.8895 973.8793 Pause: hit any key to continue... he = 926.3189 -20.0268 -20.0268 965.4526 ans = 917.8869 973.8846 Pause: hit any key to continue... he = 926.3143 -20.0265 -20.0265 965.4598 ans = 917.8843 973.8898 Pause: hit any key to continue... he = 926.3098 -20.0262 -20.0262 965.4669 ans = 917.8818 973.8949 Pause: hit any key to continue... he = 926.3054 -20.0258 -20.0258 965.4739 ans = 917.8794 973.9000 Pause: hit any key to continue... he = 926.3011 -20.0255 -20.0255 965.4809 ans = 917.8770 973.9050 Pause: hit any key to continue... he = 926.2968 -20.0252 -20.0252 965.4877 ans = 917.8746 973.9099 Pause: hit any key to continue... he = 926.2926 -20.0249 -20.0249 965.4944 ans = 917.8722 973.9148 Pause: hit any key to continue... he = 926.2885 -20.0246 -20.0246 965.5011 ans = 917.8700 973.9196 Pause: hit any key to continue... he = 926.2844 -20.0243 -20.0243 965.5077 ans = 917.8677 973.9244 Pause: hit any key to continue... he = 926.2804 -20.0240 -20.0240 965.5142 ans = 917.8655 973.9291 Pause: hit any key to continue... he = 926.2764 -20.0237 -20.0237 965.5206 ans = 917.8633 973.9337 Pause: hit any key to continue... he = 926.2726 -20.0234 -20.0234 965.5269 ans = 917.8612 973.9383 Pause: hit any key to continue... he = 926.2687 -20.0231 -20.0231 965.5331 ans = 917.8591 973.9428 Pause: hit any key to continue... he = 926.2650 -20.0228 -20.0228 965.5393 ans = 917.8570 973.9472 Pause: hit any key to continue... he = 926.2613 -20.0225 -20.0225 965.5454 ans = 917.8550 973.9517 Pause: hit any key to continue... he = 926.2576 -20.0222 -20.0222 965.5513 ans = 917.8530 973.9560 Pause: hit any key to continue... he = 926.2540 -20.0219 -20.0219 965.5573 ans = 917.8510 973.9603 Pause: hit any key to continue... he = 926.2505 -20.0216 -20.0216 965.5631 ans = 917.8491 973.9645 Pause: hit any key to continue... he = 926.2470 -20.0214 -20.0214 965.5689 ans = 917.8472 973.9687 Pause: hit any key to continue... he = 926.2436 -20.0211 -20.0211 965.5746 ans = 917.8453 973.9729 Pause: hit any key to continue... he = 926.2402 -20.0208 -20.0208 965.5802 ans = 917.8435 973.9769 Pause: hit any key to continue... he = 926.2369 -20.0206 -20.0206 965.5857 ans = 917.8417 973.9810 Pause: hit any key to continue... he = 926.2336 -20.0203 -20.0203 965.5912 ans = 917.8399 973.9849 Pause: hit any key to continue... he = 926.2304 -20.0200 -20.0200 965.5966 ans = 917.8381 973.9889 Pause: hit any key to continue... he = 926.2272 -20.0198 -20.0198 965.6019 ans = 917.8364 973.9927 Pause: hit any key to continue... he = 926.2241 -20.0195 -20.0195 965.6072 ans = 917.8347 973.9966 Pause: hit any key to continue... he = 926.2210 -20.0193 -20.0193 965.6124 ans = 917.8330 974.0003 Pause: hit any key to continue... he = 926.2179 -20.0190 -20.0190 965.6175 ans = 917.8314 974.0041 Pause: hit any key to continue... he = 926.2149 -20.0188 -20.0188 965.6225 ans = 917.8298 974.0077 Pause: hit any key to continue... he = 926.2120 -20.0185 -20.0185 965.6275 ans = 917.8282 974.0114 Pause: hit any key to continue... he = 926.2091 -20.0183 -20.0183 965.6325 ans = 917.8266 974.0149 Pause: hit any key to continue... he = 926.2062 -20.0181 -20.0181 965.6373 ans = 917.8251 974.0185 Pause: hit any key to continue... he = 926.2034 -20.0178 -20.0178 965.6421 ans = 917.8235 974.0220 Pause: hit any key to continue... he = 926.2006 -20.0176 -20.0176 965.6468 ans = 917.8220 974.0254 Pause: hit any key to continue... he = 926.1979 -20.0174 -20.0174 965.6515 ans = 917.8206 974.0288 Pause: hit any key to continue... he = 926.1952 -20.0171 -20.0171 965.6561 ans = 917.8191 974.0322 Pause: hit any key to continue... he = 926.1925 -20.0169 -20.0169 965.6607 ans = 917.8177 974.0355 Pause: hit any key to continue... he = 926.1899 -20.0167 -20.0167 965.6651 ans = 917.8163 974.0388 Pause: hit any key to continue... he = 926.1873 -20.0165 -20.0165 965.6696 ans = 917.8149 974.0420 Pause: hit any key to continue... he = 926.1847 -20.0163 -20.0163 965.6739 ans = 917.8135 974.0452 Pause: hit any key to continue... he = 926.1822 -20.0161 -20.0161 965.6782 ans = 917.8122 974.0483 Pause: hit any key to continue... he = 926.1798 -20.0159 -20.0159 965.6825 ans = 917.8108 974.0514 Pause: hit any key to continue... he = 926.1773 -20.0157 -20.0157 965.6867 ans = 917.8095 974.0545 Pause: hit any key to continue... he = 926.1749 -20.0154 -20.0154 965.6908 ans = 917.8082 974.0575 Pause: hit any key to continue... he = 926.1725 -20.0152 -20.0152 965.6949 ans = 917.8070 974.0605 Pause: hit any key to continue... he = 926.1702 -20.0151 -20.0151 965.6990 ans = 917.8057 974.0634 Pause: hit any key to continue... he = 926.1679 -20.0149 -20.0149 965.7029 ans = 917.8045 974.0664 Pause: hit any key to continue... he = 926.1656 -20.0147 -20.0147 965.7069 ans = 917.8033 974.0692 Pause: hit any key to continue... he = 926.1634 -20.0145 -20.0145 965.7107 ans = 917.8021 974.0721 Pause: hit any key to continue... he = 926.1612 -20.0143 -20.0143 965.7146 ans = 917.8009 974.0748 Pause: hit any key to continue... he = 926.1590 -20.0141 -20.0141 965.7183 ans = 917.7997 974.0776 Pause: hit any key to continue... he = 926.1568 -20.0139 -20.0139 965.7221 ans = 917.7986 974.0803 Pause: hit any key to continue... he = 926.1547 -20.0137 -20.0137 965.7257 ans = 917.7975 974.0830 Pause: hit any key to continue... he = 926.1526 -20.0136 -20.0136 965.7294 ans = 917.7963 974.0857 Pause: hit any key to continue... he = 926.1506 -20.0134 -20.0134 965.7330 ans = 917.7952 974.0883 Pause: hit any key to continue... he = 926.1485 -20.0132 -20.0132 965.7365 ans = 917.7942 974.0909 Pause: hit any key to continue... he = 926.1465 -20.0130 -20.0130 965.7400 ans = 917.7931 974.0934 Pause: hit any key to continue... he = 926.1446 -20.0129 -20.0129 965.7434 ans = 917.7921 974.0959 Pause: hit any key to continue... he = 926.1426 -20.0127 -20.0127 965.7468 ans = 917.7910 974.0984 Pause: hit any key to continue... he = 926.1407 -20.0125 -20.0125 965.7502 ans = 917.7900 974.1009 Pause: hit any key to continue... he = 926.1388 -20.0124 -20.0124 965.7535 ans = 917.7890 974.1033 Pause: hit any key to continue... he = 926.1369 -20.0122 -20.0122 965.7567 ans = 917.7880 974.1057 Pause: hit any key to continue... he = 926.1351 -20.0120 -20.0120 965.7599 ans = 917.7870 974.1080 Pause: hit any key to continue... he = 926.1333 -20.0119 -20.0119 965.7631 ans = 917.7861 974.1103 Pause: hit any key to continue... he = 926.1315 -20.0117 -20.0117 965.7662 ans = 917.7851 974.1126 Pause: hit any key to continue... he = 926.1297 -20.0116 -20.0116 965.7693 ans = 917.7842 974.1149 xo = 2.9979 2.0049 Ot = 3.6446e-004 nS = 639 eval( 'if exist(''inline'',''var''), mauifunc(inline), end', ''); disp(which('newton_mod')); v:\cursos\pos\otimiza\aulas\newton_mod.m clear 'v:\cursos\pos\otimiza\aulas\newton_mod.m' eval( 'if exist(''group'',''var''), mauifunc(group), end', ''); cd(cd) [xo,Ot,nS]=newton_mod('test9',[1 1],1,'gtest9','htest9',[-5 -5],[5 5],[],[],500) Pause: hit any key to continue... he = 126 -8 -8 110 ans = 129.3137 106.6863 Pause: hit any key to continue... he = 120.1333 -9.5251 -9.5251 104.3186 ans = 124.6055 99.8464 Pause: hit any key to continue... he = 112.4694 -11.2040 -11.2040 97.2491 ans = 118.4034 91.3151 Pause: hit any key to continue... he = 102.5933 -13.0279 -13.0279 88.7098 ans = 110.4134 80.8896 Pause: hit any key to continue... he = 90.1336 -14.9658 -14.9658 78.8311 ans = 100.4796 68.4851 Pause: hit any key to continue... he = 74.9865 -16.9422 -16.9422 68.1994 ans = 88.8717 54.3142 Pause: hit any key to continue... he = 57.9144 -18.7917 -18.7917 58.2843 ans = 39.3067 76.8920 Pause: hit any key to continue... he = 42.0193 -20.1710 -20.1710 51.9690 ans = 26.2187 67.7696 Pause: hit any key to continue... he = 34.3611 -20.5429 -20.5429 52.7100 ans = 21.0371 66.0340 Pause: hit any key to continue... he = 33.7509 -20.3041 -20.3041 56.5590 ans = 21.8674 68.4425 Pause: hit any key to continue... he = 30.3654 -20.3938 -20.3938 57.8122 ans = 19.5076 68.6701 Pause: hit any key to continue... he = 30.6892 -20.2091 -20.2091 60.0913 ans = 20.3996 70.3808 Pause: hit any key to continue... he = 28.3109 -20.2884 -20.2884 60.6993 ans = 18.5461 70.4641 Pause: hit any key to continue... he = 29.2894 -20.1162 -20.1162 62.3064 ans = 19.7750 71.8208 Pause: hit any key to continue... he = 27.0175 -20.2274 -20.2274 62.3953 ans = 17.8355 71.5773 Pause: hit any key to continue... he = 28.7168 -20.0344 -20.0344 63.7652 ans = 19.6238 72.8582 Pause: hit any key to continue... he = 26.0139 -20.2031 -20.2031 63.3879 ans = 17.1806 72.2212 Pause: hit any key to continue... he = 26.6982 -20.1402 -20.1402 63.7470 ans = 17.8587 72.5864 Pause: hit any key to continue... he = 27.6184 -20.0324 -20.0324 64.5252 ans = 18.8353 73.3083 Pause: hit any key to continue... he = 26.0448 -20.1271 -20.1271 64.3490 ans = 17.4137 72.9800 Pause: hit any key to continue... he = 27.6667 -19.9773 -19.9773 65.1993 ans = 19.0237 73.8422 Pause: hit any key to continue... he = 25.3722 -20.1371 -20.1371 64.6626 ans = 16.8849 73.1499 Pause: hit any key to continue... he = 26.0600 -20.0801 -20.0801 64.9417 ans = 17.5517 73.4501 Pause: hit any key to continue... he = 27.0267 -19.9902 -19.9902 65.4561 ans = 18.5139 73.9688 Pause: hit any key to continue... he = 26.6742 -20.0145 -20.0145 65.3771 ans = 18.1858 73.8656 Pause: hit any key to continue... he = 25.9900 -20.0558 -20.0558 65.2987 ans = 17.5636 73.7251 Pause: hit any key to continue... he = 26.1750 -20.0391 -20.0391 65.3906 ans = 17.7466 73.8190 Pause: hit any key to continue... he = 26.4462 -20.0089 -20.0089 65.5975 ans = 18.0297 74.0141 Pause: hit any key to continue... he = 25.9775 -20.0375 -20.0375 65.5392 ans = 17.6020 73.9148 Pause: hit any key to continue... he = 26.1066 -20.0260 -20.0260 65.6015 ans = 17.7293 73.9788 Pause: hit any key to continue... he = 26.2991 -20.0052 -20.0052 65.7405 ans = 17.9287 74.1109 Pause: hit any key to continue... he = 25.9719 -20.0255 -20.0255 65.6955 ans = 17.6289 74.0385 Pause: hit any key to continue... he = 26.0637 -20.0174 -20.0174 65.7384 ans = 17.7192 74.0829 Pause: hit any key to continue... he = 26.2025 -20.0028 -20.0028 65.8330 ans = 17.8618 74.1737 Pause: hit any key to continue... he = 25.9710 -20.0174 -20.0174 65.7979 ans = 17.6490 74.1200 Pause: hit any key to continue... he = 26.0370 -20.0117 -20.0117 65.8278 ans = 17.7137 74.1511 Pause: hit any key to continue... he = 26.1381 -20.0014 -20.0014 65.8928 ans = 17.8167 74.2141 Pause: hit any key to continue... he = 25.9729 -20.0120 -20.0120 65.8654 ans = 17.6644 74.1740 Pause: hit any key to continue... he = 26.0207 -20.0079 -20.0079 65.8864 ans = 17.7111 74.1960 Pause: hit any key to continue... he = 26.0947 -20.0006 -20.0006 65.9314 ans = 17.7861 74.2400 Pause: hit any key to continue... he = 25.9761 -20.0083 -20.0083 65.9101 ans = 17.6763 74.2099 Pause: hit any key to continue... he = 26.0109 -20.0054 -20.0054 65.9249 ans = 17.7102 74.2256 Pause: hit any key to continue... he = 26.0653 -20.0001 -20.0001 65.9562 ans = 17.7650 74.2566 Pause: hit any key to continue... he = 26.0440 -20.0015 -20.0015 65.9521 ans = 17.7451 74.2509 Pause: hit any key to continue... he = 26.0050 -20.0037 -20.0037 65.9502 ans = 17.7101 74.2451 Pause: hit any key to continue... he = 26.0455 -19.9999 -19.9999 65.9723 ans = 17.7506 74.2672 xo = 2.9995 2.0007 Ot = 9.3290e-006 nS = 115 eval( 'if exist(''problem'',''var''), mauifunc(problem), end', ''); eval( 'if exist(''G'',''var''), mauifunc(G), end', ''); eval( 'if exist(''inline'',''var''), mauifunc(inline), end', ''); eval( 'if exist(''ones'',''var''), mauifunc(ones), end', ''); eval( 'if exist(''Hstr'',''var''), mauifunc(Hstr), end', ''); eval( 'if exist(''xo'',''var''), mauifunc(xo), end', ''); 2.9995 2.0007 eval( 'if exist(''problem'',''var''), mauifunc(problem), end', ''); eval( 'if exist(''sfd'',''var''), mauifunc(sfd), end', ''); eval( 'if exist(''color'',''var''), mauifunc(color), end', ''); disp(which('newton_mod')); v:\cursos\pos\otimiza\aulas\newton_mod.m clear 'v:\cursos\pos\otimiza\aulas\newton_mod.m' eval( 'if exist(''else'',''var''), mauifunc(else), end', ''); [xo,Ot,nS]=newton_mod('test9',[1 1],1,'gtest9','htest9',[-5 -5],[5 5],[],[],500) Pause: hit any key to continue... he = 76 -8 -8 60 ans = 79.3137 56.6863 Pause: hit any key to continue... he = 64.9804 -10.8114 -10.8114 48.3732 ans = 70.3089 43.0446 Pause: hit any key to continue... he = 45.6406 -14.5770 -14.5770 28.0904 ans = 53.8799 19.8511 Pause: hit any key to continue... he = 1.3096 -21.0930 -21.0930 -21.3199 ans = 13.9309 -33.9412 Pause: hit any key to continue... he = -12.3837 -21.7398 -21.7398 -18.7371 ans = 6.4103 -37.5310 Pause: hit any key to continue... he = -34.4905 -22.2815 -22.2815 -8.6280 ans = -47.3213 4.2028 Pause: hit any key to continue... he = -38.4616 -22.2655 -22.2655 -5.3765 ans = -49.6573 5.8191 Pause: hit any key to continue... he = -33.0487 -22.2335 -22.2335 -9.0046 ans = -46.3023 4.2490 Pause: hit any key to continue... he = -37.1017 -22.2202 -22.2202 -5.7028 ans = -48.6090 5.8045 Pause: hit any key to continue... he = -35.7140 -22.2129 -22.2129 -6.6364 ans = -47.7231 5.3727 Pause: hit any key to continue... he = -36.4765 -22.2147 -22.2147 -6.0884 ans = -48.1963 5.6314 Pause: hit any key to continue... he = -36.1163 -22.2133 -22.2133 -6.3376 ans = -47.9688 5.5148 Pause: hit any key to continue... he = -36.3011 -22.2139 -22.2139 -6.2075 ans = -48.0845 5.5760 Pause: hit any key to continue... he = -35.9367 -22.2125 -22.2125 -6.4621 ans = -47.8563 5.4574 Pause: hit any key to continue... he = -36.6857 -22.2147 -22.2147 -5.9310 ans = -48.3261 5.7093 Pause: hit any key to continue... he = -35.2703 -22.2083 -22.2083 -6.9025 ans = -47.4377 5.2649 Pause: hit any key to continue... he = -36.0528 -22.2096 -22.2096 -6.3298 ans = -47.9145 5.5319 Pause: hit any key to continue... he = -36.2371 -22.2102 -22.2102 -6.2001 ans = -48.0300 5.5927 Pause: hit any key to continue... he = -36.1462 -22.2099 -22.2099 -6.2635 ans = -47.9728 5.5631 Pause: hit any key to continue... he = -36.1233 -22.2098 -22.2098 -6.2795 ans = -47.9584 5.5556 xo = 3.1424 2.4101 Ot = 5.4562 nS = 146 ; help lmarquadt lmarquadt.m not found. what M-files in the current directory v:\cursos\pos\otimiza\aulas CATALIS extrat minlp sqp EXTRATOR fmincon1 minlp1 steepdes LUCRO fminunc1 minlp2 swarm MINQUA fminusub minlp3 test0 MODELO fun minlp4 test1 Minqua44 func44 minlp5 test10 Modelo44 gmilp1 minlp6 test11 OPT_RES gminlp1 minlpn test12 PLANOS gminlp2 modelagem test13 READ2 gminlp3 naturais test14 SEMIDEF gminlp4 newton test15 SMODELO gminlp5 newton_h test16 aurea gminlp6 newton_mod test17 bandem1 gmodelagem newtont test18 bfgs gmurray nlconst test19 bracket grad nlp_internal test1m buscarnd grg pareto18 test2 cgrad gtest1 pareto19 test20 checkbounds gtest10 pareto20 test21 coggins gtest12 pareto21 test22 compdir gtest13 powell test23 complex gtest2 qpsub test3 dados_ex6_44 gtest9 refino test4 dfp hkjeeves restr test5 dual htest1 restr1 test6 ex2_karm htest10 restr14 test7 ex_karma htest2 restr15 test8 ex_qp1 htest9 restr16 test9 ex_qp2 interior restr17 teste_buscarnd ex_qp3 karmarkar restr20 univar ex_swarm lmarqua restr21 varmetr exmilp lp_nlp rosembr visual exmilp2 milp set1 writearq exmilprog milp1 setoptim xplot exmilprog2 milprog sol_extrat help lmarqua Unconstrained optimization using Levenberg-Marquardt. [xo,Ot,nS]=lmarqua(S,x0,ip,G,H,Lb,Ub,problem,tol,mxit) S: objective function x0: initial point ip: (0) no plot (default), (>0) plot figure ip with pause, (<0) plot figure ip G: gradient vector function H: Hessian matrix function Lb, Ub: lower and upper bound vectors to plot (default = x0*(1+/-2)) problem: (-1): minimum (default), (1): maximum tol: tolerance (default = 1e-4) mxit: maximum number of iterations (default = 50*(1+4*~(ip>0))) xo: optimal point Ot: optimal value of S nS: number of objective function evaluations edit lmarqua disp(sprintf('%d',feature('SessionTool'))) 0 ; dbstatus dbstack dbstack ; disp(which('lmarqua')); v:\cursos\pos\otimiza\aulas\lmarqua.m mdbstatus 'v:\cursos\pos\otimiza\aulas\lmarqua.m' eval( 'if exist(''ver'',''var''), mauifunc(ver), end', ''); eval( 'if exist(''beta'',''var''), mauifunc(beta), end', ''); eval( 'if exist(''beta'',''var''), mauifunc(beta), end', ''); eval( 'if exist(''test9'',''var''), mauifunc(test9), end', ''); eval( 'if exist(''problem'',''var''), mauifunc(problem), end', ''); help lmarqua Unconstrained optimization using Levenberg-Marquardt. [xo,Ot,nS]=lmarqua(S,x0,ip,G,H,Lb,Ub,problem,tol,mxit) S: objective function x0: initial point ip: (0) no plot (default), (>0) plot figure ip with pause, (<0) plot figure ip G: gradient vector function H: Hessian matrix function Lb, Ub: lower and upper bound vectors to plot (default = x0*(1+/-2)) problem: (-1): minimum (default), (1): maximum tol: tolerance (default = 1e-4) mxit: maximum number of iterations (default = 50*(1+4*~(ip>0))) xo: optimal point Ot: optimal value of S nS: number of objective function evaluations [xo,Ot,nS]=lmarqua('test9',[1 1],1,'gtest9','htest9',[-5 -5],[5 5],[],[],500) Pause: hit any key to continue... ans = -2.9314 -25.5588 beta = -64.4902 Pause: hit any key to continue... ans = -29.6164 -0.1264 beta = -2.7810 beta = -5.5620 beta = -11.1240 Pause: hit any key to continue... ans = -157.4775 -31.0168 Pause: hit any key to continue... ans = -118.2633 -36.1111 Pause: hit any key to continue... ans = -108.9717 -43.3909 Pause: hit any key to continue... ans = -107.5196 -47.3114 Pause: hit any key to continue... ans = -107.5481 -49.3506 Pause: hit any key to continue... ans = -107.7266 -50.3871 Pause: hit any key to continue... ans = -107.8524 -50.9086 Pause: hit any key to continue... ans = -107.9236 -51.1699 Pause: hit any key to continue... ans = -107.9612 -51.3007 Pause: hit any key to continue... ans = -107.9805 -51.3661 Pause: hit any key to continue... ans = -107.9902 -51.3988 xo = 3.0001 1.9998 Ot = 8.6448e-007 nS = 18 edit newton_mod dbstack ; disp(which('newton_mod')); v:\cursos\pos\otimiza\aulas\newton_mod.m mdbstatus 'v:\cursos\pos\otimiza\aulas\newton_mod.m' eval( 'if exist(''upper'',''var''), mauifunc(upper), end', ''); eval( 'if exist(''stepsize'',''var''), mauifunc(stepsize), end', ''); disp(which('newton_mod')); v:\cursos\pos\otimiza\aulas\newton_mod.m clear 'v:\cursos\pos\otimiza\aulas\newton_mod.m' eval( 'if exist(''stepsize'',''var''), mauifunc(stepsize), end', ''); eval( 'if exist(''yo'',''var''), mauifunc(yo), end', ''); eval( 'if exist(''while'',''var''), mauifunc(while), end', ''); [xo,Ot,nS]=newton_mod('test9',[1 1],1,'gtest9','htest9',[-5 -5],[5 5],[],[],500) Pause: hit any key to continue... he = -24 -8 -8 -40 ans = -20.6863 -43.3137 Pause: hit any key to continue... he = -102.8367 -17.2857 -17.2857 -65.8520 ans = -109.6577 -59.0311 Pause: hit any key to continue... he = -118.3120 -18.8407 -18.8407 -73.6481 ans = -125.1980 -66.7621 Pause: hit any key to continue... he = -123.1445 -19.4462 -19.4462 -77.7657 ans = -130.3376 -70.5726 Pause: hit any key to continue... he = -124.5120 -19.7119 -19.7119 -80.1103 ans = -132.0001 -72.6222 Pause: hit any key to continue... he = -124.7466 -19.8390 -19.8390 -81.5168 ans = -132.4709 -73.7924 Pause: hit any key to continue... he = -124.6497 -19.9049 -19.9049 -82.3919 ans = -132.5490 -74.4926 Pause: hit any key to continue... he = -124.4896 -19.9415 -19.9415 -82.9497 ans = -132.5129 -74.9264 Pause: hit any key to continue... he = -124.3468 -19.9630 -19.9630 -83.3107 ans = -132.4559 -75.2016 Pause: hit any key to continue... he = -124.2382 -19.9762 -19.9762 -83.5463 ans = -132.4055 -75.3790 Pause: hit any key to continue... he = -124.1609 -19.9845 -19.9845 -83.7010 ans = -132.3674 -75.4944 Pause: hit any key to continue... he = -124.1077 -19.9899 -19.9899 -83.8027 ans = -132.3404 -75.5700 Pause: hit any key to continue... he = -124.0717 -19.9934 -19.9934 -83.8698 ans = -132.3218 -75.6197 Pause: hit any key to continue... he = -124.0475 -19.9956 -19.9956 -83.9140 ans = -132.3092 -75.6524 Pause: hit any key to continue... he = -124.0315 -19.9971 -19.9971 -83.9432 ans = -132.3008 -75.6739 Pause: hit any key to continue... he = -124.0208 -19.9981 -19.9981 -83.9625 ans = -132.2952 -75.6881 xo = 3.0002 1.9995 Ot = 4.2951e-006 nS = 17 eval( 'if exist(''full'',''var''), mauifunc(full), end', ''); eval( 'if exist(''feval'',''var''), mauifunc(feval), end', ''); eval( 'if exist(''fun'',''var''), mauifunc(fun), end', ''); eval( 'if exist(''xo'',''var''), mauifunc(xo), end', ''); 3.0002 1.9995 eval( 'if exist(''color'',''var''), mauifunc(color), end', ''); eval( 'if exist(''sparse'',''var''), mauifunc(sparse), end', ''); disp(which('newton_mod')); v:\cursos\pos\otimiza\aulas\newton_mod.m clear 'v:\cursos\pos\otimiza\aulas\newton_mod.m' eval( 'if exist(''ones'',''var''), mauifunc(ones), end', ''); [xo,Ot,nS]=newton_mod('test9',[1 1],1,'gtest9','htest9',[-5 -5],[5 5],[],[],500) Pause: hit any key to continue... he = -974 -8 -8 -990 ans = -970.6863 -993.3137 Pause: hit any key to continue... Error in ==> v:\cursos\pos\otimiza\aulas\newton_mod.m On line 164 ==> disp('Pause: hit any key to continue...'); pause; [xo,Ot,nS]=newton_mod('test9',[1 1],1,'gtest9','htest9',[-5 -5],[5 5],[],[],500) Pause: hit any key to continue... he = -974 -8 -8 -990 ans = -970.6863 -993.3137 Pause: hit any key to continue... he = -975.3044 -8.3397 -8.3397 -991.1171 ans = -971.7190 -994.7025 Pause: hit any key to continue... he = -976.6830 -8.6823 -8.6823 -992.2699 ans = -972.8094 -996.1435 Pause: hit any key to continue... he = -978.1366 -9.0273 -9.0273 -993.4559 ans = -973.9572 -997.6353 Pause: hit any key to continue... he = -979.6656 -9.3743 -9.3743 -994.6726 ans = -975.1616 -999.1766 Pause: hit any key to continue... he = -981.2700 -9.7224 -9.7224 -995.9170 ans = 1.0e+003 * -0.9764 -1.0008 Pause: hit any key to continue... he = -982.9492 -10.0713 -10.0713 -997.1859 ans = 1.0e+003 * -0.9777 -1.0024 Pause: hit any key to continue... he = -984.7021 -10.4202 -10.4202 -998.4759 ans = 1.0e+003 * -0.9791 -1.0041 Pause: hit any key to continue... he = -986.5268 -10.7685 -10.7685 -999.7832 ans = 1.0e+003 * -0.9805 -1.0058 Pause: hit any key to continue... he = 1.0e+003 * -0.9884 -0.0111 -0.0111 -1.0011 ans = 1.0e+003 * -0.9820 -1.0076 Pause: hit any key to continue... he = 1.0e+003 * -0.9904 -0.0115 -0.0115 -1.0024 ans = 1.0e+003 * -0.9835 -1.0094 Pause: hit any key to continue... he = 1.0e+003 * -0.9924 -0.0118 -0.0118 -1.0038 ans = 1.0e+003 * -0.9850 -1.0112 Pause: hit any key to continue... he = 1.0e+003 * -0.9945 -0.0121 -0.0121 -1.0051 ans = 1.0e+003 * -0.9865 -1.0130 Pause: hit any key to continue... he = 1.0e+003 * -0.9966 -0.0125 -0.0125 -1.0064 ans = 1.0e+003 * -0.9881 -1.0149 Pause: hit any key to continue... he = 1.0e+003 * -0.9988 -0.0128 -0.0128 -1.0078 ans = 1.0e+003 * -0.9897 -1.0169 Pause: hit any key to continue... he = 1.0e+003 * -1.0010 -0.0131 -0.0131 -1.0091 ans = 1.0e+003 * -0.9913 -1.0188 Pause: hit any key to continue... he = 1.0e+003 * -1.0033 -0.0135 -0.0135 -1.0104 ans = 1.0e+003 * -0.9929 -1.0208 Pause: hit any key to continue... he = 1.0e+003 * -1.0056 -0.0138 -0.0138 -1.0117 ans = 1.0e+003 * -0.9945 -1.0227 Pause: hit any key to continue... he = 1.0e+003 * -1.0079 -0.0141 -0.0141 -1.0129 ans = 1.0e+003 * -0.9961 -1.0247 Pause: hit any key to continue... he = 1.0e+003 * -1.0102 -0.0144 -0.0144 -1.0141 ans = 1.0e+003 * -0.9977 -1.0267 Pause: hit any key to continue... he = 1.0e+003 * -1.0126 -0.0147 -0.0147 -1.0154 ans = 1.0e+003 * -0.9992 -1.0287 Pause: hit any key to continue... he = 1.0e+003 * -1.0149 -0.0149 -0.0149 -1.0165 ans = 1.0e+003 * -1.0008 -1.0307 Pause: hit any key to continue... he = 1.0e+003 * -1.0172 -0.0152 -0.0152 -1.0177 ans = 1.0e+003 * -1.0022 -1.0327 Pause: hit any key to continue... he = 1.0e+003 * -1.0196 -0.0155 -0.0155 -1.0188 ans = 1.0e+003 * -1.0346 -1.0037 Pause: hit any key to continue... he = 1.0e+003 * -1.0219 -0.0157 -0.0157 -1.0198 ans = 1.0e+003 * -1.0366 -1.0051 Pause: hit any key to continue... he = 1.0e+003 * -1.0241 -0.0160 -0.0160 -1.0208 ans = 1.0e+003 * -1.0386 -1.0064 Pause: hit any key to continue... he = 1.0e+003 * -1.0264 -0.0162 -0.0162 -1.0218 ans = 1.0e+003 * -1.0405 -1.0077 Pause: hit any key to continue... he = 1.0e+003 * -1.0285 -0.0164 -0.0164 -1.0228 ans = 1.0e+003 * -1.0424 -1.0089 Pause: hit any key to continue... he = 1.0e+003 * -1.0307 -0.0167 -0.0167 -1.0237 ans = 1.0e+003 * -1.0442 -1.0101 Pause: hit any key to continue... he = 1.0e+003 * -1.0328 -0.0169 -0.0169 -1.0245 ans = 1.0e+003 * -1.0460 -1.0113 Pause: hit any key to continue... he = 1.0e+003 * -1.0348 -0.0171 -0.0171 -1.0253 ans = 1.0e+003 * -1.0478 -1.0123 Pause: hit any key to continue... he = 1.0e+003 * -1.0368 -0.0173 -0.0173 -1.0261 ans = 1.0e+003 * -1.0495 -1.0134 Pause: hit any key to continue... he = 1.0e+003 * -1.0387 -0.0174 -0.0174 -1.0268 ans = 1.0e+003 * -1.0512 -1.0143 Pause: hit any key to continue... he = 1.0e+003 * -1.0406 -0.0176 -0.0176 -1.0275 ans = 1.0e+003 * -1.0528 -1.0152 Pause: hit any key to continue... he = 1.0e+003 * -1.0424 -0.0178 -0.0178 -1.0281 ans = 1.0e+003 * -1.0544 -1.0161 Pause: hit any key to continue... he = 1.0e+003 * -1.0441 -0.0179 -0.0179 -1.0287 ans = 1.0e+003 * -1.0559 -1.0169 Pause: hit any key to continue... he = 1.0e+003 * -1.0457 -0.0181 -0.0181 -1.0293 ans = 1.0e+003 * -1.0574 -1.0177 Pause: hit any key to continue... he = 1.0e+003 * -1.0473 -0.0182 -0.0182 -1.0298 ans = 1.0e+003 * -1.0588 -1.0184 Pause: hit any key to continue... he = 1.0e+003 * -1.0488 -0.0183 -0.0183 -1.0303 ans = 1.0e+003 * -1.0601 -1.0190 Pause: hit any key to continue... he = 1.0e+003 * -1.0503 -0.0185 -0.0185 -1.0308 ans = 1.0e+003 * -1.0614 -1.0197 Pause: hit any key to continue... he = 1.0e+003 * -1.0516 -0.0186 -0.0186 -1.0312 ans = 1.0e+003 * -1.0626 -1.0202 Pause: hit any key to continue... he = 1.0e+003 * -1.0530 -0.0187 -0.0187 -1.0316 ans = 1.0e+003 * -1.0638 -1.0208 Pause: hit any key to continue... he = 1.0e+003 * -1.0542 -0.0188 -0.0188 -1.0320 ans = 1.0e+003 * -1.0649 -1.0213 Pause: hit any key to continue... he = 1.0e+003 * -1.0554 -0.0189 -0.0189 -1.0323 ans = 1.0e+003 * -1.0660 -1.0217 Pause: hit any key to continue... he = 1.0e+003 * -1.0565 -0.0190 -0.0190 -1.0326 ans = 1.0e+003 * -1.0670 -1.0222 Pause: hit any key to continue... he = 1.0e+003 * -1.0575 -0.0190 -0.0190 -1.0329 ans = 1.0e+003 * -1.0679 -1.0226 Pause: hit any key to continue... he = 1.0e+003 * -1.0585 -0.0191 -0.0191 -1.0332 ans = 1.0e+003 * -1.0688 -1.0229 Pause: hit any key to continue... he = 1.0e+003 * -1.0595 -0.0192 -0.0192 -1.0334 ans = 1.0e+003 * -1.0696 -1.0233 Pause: hit any key to continue... he = 1.0e+003 * -1.0604 -0.0193 -0.0193 -1.0337 ans = 1.0e+003 * -1.0704 -1.0236 Pause: hit any key to continue... he = 1.0e+003 * -1.0612 -0.0193 -0.0193 -1.0339 ans = 1.0e+003 * -1.0712 -1.0239 Pause: hit any key to continue... he = 1.0e+003 * -1.0620 -0.0194 -0.0194 -1.0341 ans = 1.0e+003 * -1.0719 -1.0241 Pause: hit any key to continue... he = 1.0e+003 * -1.0627 -0.0194 -0.0194 -1.0342 ans = 1.0e+003 * -1.0726 -1.0244 Pause: hit any key to continue... he = 1.0e+003 * -1.0634 -0.0195 -0.0195 -1.0344 ans = 1.0e+003 * -1.0732 -1.0246 Pause: hit any key to continue... he = 1.0e+003 * -1.0641 -0.0195 -0.0195 -1.0345 ans = 1.0e+003 * -1.0738 -1.0248 Pause: hit any key to continue... he = 1.0e+003 * -1.0647 -0.0196 -0.0196 -1.0346 ans = 1.0e+003 * -1.0743 -1.0250 Pause: hit any key to continue... he = 1.0e+003 * -1.0653 -0.0196 -0.0196 -1.0347 ans = 1.0e+003 * -1.0748 -1.0252 Pause: hit any key to continue... he = 1.0e+003 * -1.0658 -0.0196 -0.0196 -1.0348 ans = 1.0e+003 * -1.0753 -1.0253 Pause: hit any key to continue... he = 1.0e+003 * -1.0663 -0.0197 -0.0197 -1.0349 ans = 1.0e+003 * -1.0758 -1.0255 Pause: hit any key to continue... he = 1.0e+003 * -1.0668 -0.0197 -0.0197 -1.0350 ans = 1.0e+003 * -1.0762 -1.0256 Pause: hit any key to continue... he = 1.0e+003 * -1.0672 -0.0197 -0.0197 -1.0351 ans = 1.0e+003 * -1.0766 -1.0257 Pause: hit any key to continue... he = 1.0e+003 * -1.0676 -0.0198 -0.0198 -1.0351 ans = 1.0e+003 * -1.0770 -1.0258 Pause: hit any key to continue... he = 1.0e+003 * -1.0680 -0.0198 -0.0198 -1.0352 ans = 1.0e+003 * -1.0773 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0684 -0.0198 -0.0198 -1.0352 ans = 1.0e+003 * -1.0776 -1.0260 Pause: hit any key to continue... he = 1.0e+003 * -1.0687 -0.0198 -0.0198 -1.0353 ans = 1.0e+003 * -1.0779 -1.0261 Pause: hit any key to continue... he = 1.0e+003 * -1.0690 -0.0198 -0.0198 -1.0353 ans = 1.0e+003 * -1.0782 -1.0261 Pause: hit any key to continue... he = 1.0e+003 * -1.0693 -0.0199 -0.0199 -1.0353 ans = 1.0e+003 * -1.0785 -1.0262 Pause: hit any key to continue... he = 1.0e+003 * -1.0696 -0.0199 -0.0199 -1.0354 ans = 1.0e+003 * -1.0787 -1.0262 Pause: hit any key to continue... he = 1.0e+003 * -1.0699 -0.0199 -0.0199 -1.0354 ans = 1.0e+003 * -1.0789 -1.0263 Pause: hit any key to continue... he = 1.0e+003 * -1.0701 -0.0199 -0.0199 -1.0354 ans = 1.0e+003 * -1.0791 -1.0263 Pause: hit any key to continue... he = 1.0e+003 * -1.0703 -0.0199 -0.0199 -1.0354 ans = 1.0e+003 * -1.0793 -1.0264 Pause: hit any key to continue... he = 1.0e+003 * -1.0705 -0.0199 -0.0199 -1.0354 ans = 1.0e+003 * -1.0795 -1.0264 Pause: hit any key to continue... he = 1.0e+003 * -1.0707 -0.0199 -0.0199 -1.0354 ans = 1.0e+003 * -1.0797 -1.0264 Pause: hit any key to continue... he = 1.0e+003 * -1.0709 -0.0200 -0.0200 -1.0354 ans = 1.0e+003 * -1.0799 -1.0264 Pause: hit any key to continue... he = 1.0e+003 * -1.0711 -0.0200 -0.0200 -1.0354 ans = 1.0e+003 * -1.0800 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0712 -0.0200 -0.0200 -1.0354 ans = 1.0e+003 * -1.0802 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0714 -0.0200 -0.0200 -1.0354 ans = 1.0e+003 * -1.0803 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0715 -0.0200 -0.0200 -1.0354 ans = 1.0e+003 * -1.0804 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0717 -0.0200 -0.0200 -1.0354 ans = 1.0e+003 * -1.0805 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0718 -0.0200 -0.0200 -1.0353 ans = 1.0e+003 * -1.0806 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0719 -0.0200 -0.0200 -1.0353 ans = 1.0e+003 * -1.0807 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0720 -0.0200 -0.0200 -1.0353 ans = 1.0e+003 * -1.0808 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0721 -0.0200 -0.0200 -1.0353 ans = 1.0e+003 * -1.0809 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0722 -0.0200 -0.0200 -1.0353 ans = 1.0e+003 * -1.0810 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0723 -0.0200 -0.0200 -1.0353 ans = 1.0e+003 * -1.0811 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0724 -0.0200 -0.0200 -1.0352 ans = 1.0e+003 * -1.0811 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0725 -0.0200 -0.0200 -1.0352 ans = 1.0e+003 * -1.0812 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0725 -0.0200 -0.0200 -1.0352 ans = 1.0e+003 * -1.0812 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0726 -0.0200 -0.0200 -1.0352 ans = 1.0e+003 * -1.0813 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0727 -0.0200 -0.0200 -1.0352 ans = 1.0e+003 * -1.0814 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0727 -0.0200 -0.0200 -1.0351 ans = 1.0e+003 * -1.0814 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0728 -0.0200 -0.0200 -1.0351 ans = 1.0e+003 * -1.0815 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0728 -0.0200 -0.0200 -1.0351 ans = 1.0e+003 * -1.0815 -1.0265 Pause: hit any key to continue... he = 1.0e+003 * -1.0729 -0.0200 -0.0200 -1.0351 ans = 1.0e+003 * -1.0815 -1.0264 Pause: hit any key to continue... he = 1.0e+003 * -1.0729 -0.0200 -0.0200 -1.0351 ans = 1.0e+003 * -1.0816 -1.0264 Pause: hit any key to continue... he = 1.0e+003 * -1.0730 -0.0200 -0.0200 -1.0350 ans = 1.0e+003 * -1.0816 -1.0264 Pause: hit any key to continue... he = 1.0e+003 * -1.0730 -0.0200 -0.0200 -1.0350 ans = 1.0e+003 * -1.0816 -1.0264 Pause: hit any key to continue... he = 1.0e+003 * -1.0731 -0.0200 -0.0200 -1.0350 ans = 1.0e+003 * -1.0817 -1.0264 Pause: hit any key to continue... he = 1.0e+003 * -1.0731 -0.0200 -0.0200 -1.0350 ans = 1.0e+003 * -1.0817 -1.0264 Pause: hit any key to continue... he = 1.0e+003 * -1.0732 -0.0200 -0.0200 -1.0350 ans = 1.0e+003 * -1.0817 -1.0264 Pause: hit any key to continue... he = 1.0e+003 * -1.0732 -0.0200 -0.0200 -1.0349 ans = 1.0e+003 * -1.0818 -1.0264 Pause: hit any key to continue... he = 1.0e+003 * -1.0732 -0.0200 -0.0200 -1.0349 ans = 1.0e+003 * -1.0818 -1.0264 Pause: hit any key to continue... he = 1.0e+003 * -1.0733 -0.0200 -0.0200 -1.0349 ans = 1.0e+003 * -1.0818 -1.0263 Pause: hit any key to continue... he = 1.0e+003 * -1.0733 -0.0200 -0.0200 -1.0349 ans = 1.0e+003 * -1.0818 -1.0263 Pause: hit any key to continue... he = 1.0e+003 * -1.0733 -0.0200 -0.0200 -1.0349 ans = 1.0e+003 * -1.0818 -1.0263 Pause: hit any key to continue... he = 1.0e+003 * -1.0733 -0.0200 -0.0200 -1.0348 ans = 1.0e+003 * -1.0819 -1.0263 Pause: hit any key to continue... he = 1.0e+003 * -1.0734 -0.0200 -0.0200 -1.0348 ans = 1.0e+003 * -1.0819 -1.0263 Pause: hit any key to continue... he = 1.0e+003 * -1.0734 -0.0200 -0.0200 -1.0348 ans = 1.0e+003 * -1.0819 -1.0263 Pause: hit any key to continue... he = 1.0e+003 * -1.0734 -0.0200 -0.0200 -1.0348 ans = 1.0e+003 * -1.0819 -1.0263 Pause: hit any key to continue... he = 1.0e+003 * -1.0734 -0.0200 -0.0200 -1.0348 ans = 1.0e+003 * -1.0819 -1.0263 Pause: hit any key to continue... he = 1.0e+003 * -1.0734 -0.0200 -0.0200 -1.0348 ans = 1.0e+003 * -1.0819 -1.0263 Pause: hit any key to continue... he = 1.0e+003 * -1.0735 -0.0200 -0.0200 -1.0347 ans = 1.0e+003 * -1.0820 -1.0262 Pause: hit any key to continue... he = 1.0e+003 * -1.0735 -0.0200 -0.0200 -1.0347 ans = 1.0e+003 * -1.0820 -1.0262 Pause: hit any key to continue... he = 1.0e+003 * -1.0735 -0.0200 -0.0200 -1.0347 ans = 1.0e+003 * -1.0820 -1.0262 Pause: hit any key to continue... he = 1.0e+003 * -1.0735 -0.0200 -0.0200 -1.0347 ans = 1.0e+003 * -1.0820 -1.0262 Pause: hit any key to continue... he = 1.0e+003 * -1.0735 -0.0200 -0.0200 -1.0347 ans = 1.0e+003 * -1.0820 -1.0262 Pause: hit any key to continue... he = 1.0e+003 * -1.0736 -0.0200 -0.0200 -1.0347 ans = 1.0e+003 * -1.0820 -1.0262 Pause: hit any key to continue... he = 1.0e+003 * -1.0736 -0.0200 -0.0200 -1.0346 ans = 1.0e+003 * -1.0820 -1.0262 Pause: hit any key to continue... he = 1.0e+003 * -1.0736 -0.0200 -0.0200 -1.0346 ans = 1.0e+003 * -1.0820 -1.0262 Pause: hit any key to continue... he = 1.0e+003 * -1.0736 -0.0200 -0.0200 -1.0346 ans = 1.0e+003 * -1.0820 -1.0262 Pause: hit any key to continue... he = 1.0e+003 * -1.0736 -0.0200 -0.0200 -1.0346 ans = 1.0e+003 * -1.0821 -1.0261 Pause: hit any key to continue... he = 1.0e+003 * -1.0736 -0.0200 -0.0200 -1.0346 ans = 1.0e+003 * -1.0821 -1.0261 Pause: hit any key to continue... he = 1.0e+003 * -1.0736 -0.0200 -0.0200 -1.0346 ans = 1.0e+003 * -1.0821 -1.0261 Pause: hit any key to continue... he = 1.0e+003 * -1.0736 -0.0200 -0.0200 -1.0346 ans = 1.0e+003 * -1.0821 -1.0261 Pause: hit any key to continue... he = 1.0e+003 * -1.0737 -0.0200 -0.0200 -1.0345 ans = 1.0e+003 * -1.0821 -1.0261 Pause: hit any key to continue... he = 1.0e+003 * -1.0737 -0.0200 -0.0200 -1.0345 ans = 1.0e+003 * -1.0821 -1.0261 Pause: hit any key to continue... he = 1.0e+003 * -1.0737 -0.0200 -0.0200 -1.0345 ans = 1.0e+003 * -1.0821 -1.0261 Pause: hit any key to continue... he = 1.0e+003 * -1.0737 -0.0200 -0.0200 -1.0345 ans = 1.0e+003 * -1.0821 -1.0261 Pause: hit any key to continue... he = 1.0e+003 * -1.0737 -0.0200 -0.0200 -1.0345 ans = 1.0e+003 * -1.0821 -1.0261 Pause: hit any key to continue... he = 1.0e+003 * -1.0737 -0.0200 -0.0200 -1.0345 ans = 1.0e+003 * -1.0821 -1.0261 Pause: hit any key to continue... he = 1.0e+003 * -1.0737 -0.0200 -0.0200 -1.0345 ans = 1.0e+003 * -1.0821 -1.0261 Pause: hit any key to continue... he = 1.0e+003 * -1.0737 -0.0200 -0.0200 -1.0345 ans = 1.0e+003 * -1.0821 -1.0260 Pause: hit any key to continue... he = 1.0e+003 * -1.0737 -0.0200 -0.0200 -1.0344 ans = 1.0e+003 * -1.0821 -1.0260 Pause: hit any key to continue... he = 1.0e+003 * -1.0737 -0.0200 -0.0200 -1.0344 ans = 1.0e+003 * -1.0821 -1.0260 Pause: hit any key to continue... he = 1.0e+003 * -1.0737 -0.0200 -0.0200 -1.0344 ans = 1.0e+003 * -1.0821 -1.0260 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0344 ans = 1.0e+003 * -1.0821 -1.0260 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0344 ans = 1.0e+003 * -1.0822 -1.0260 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0344 ans = 1.0e+003 * -1.0822 -1.0260 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0344 ans = 1.0e+003 * -1.0822 -1.0260 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0344 ans = 1.0e+003 * -1.0822 -1.0260 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0344 ans = 1.0e+003 * -1.0822 -1.0260 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0344 ans = 1.0e+003 * -1.0822 -1.0260 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0343 ans = 1.0e+003 * -1.0822 -1.0260 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0343 ans = 1.0e+003 * -1.0822 -1.0260 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0343 ans = 1.0e+003 * -1.0822 -1.0260 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0343 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0343 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0343 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0343 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0343 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0343 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0343 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0343 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0738 -0.0200 -0.0200 -1.0343 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0739 -0.0200 -0.0200 -1.0343 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0739 -0.0200 -0.0200 -1.0342 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0739 -0.0200 -0.0200 -1.0342 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0739 -0.0200 -0.0200 -1.0342 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0739 -0.0200 -0.0200 -1.0342 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0739 -0.0200 -0.0200 -1.0342 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0739 -0.0200 -0.0200 -1.0342 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0739 -0.0200 -0.0200 -1.0342 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0739 -0.0200 -0.0200 -1.0342 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0739 -0.0200 -0.0200 -1.0342 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0739 -0.0200 -0.0200 -1.0342 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0739 -0.0200 -0.0200 -1.0342 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0739 -0.0200 -0.0200 -1.0342 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0739 -0.0200 -0.0200 -1.0342 ans = 1.0e+003 * -1.0822 -1.0259 Pause: hit any key to continue... he = 1.0e+003 * -1.0739 -0.0200 -0.0200 -1.0342 ans = 1.0e+003 * -1.0822 -1.0258 Pause: hit any key to continue... he = 1.0e+003 * -1.0739 -0.0200 -0.0200 -1.0342 ans = 1.0e+003 * -1.0822 -1.0258 Pause: hit any key to continue... he = 1.0e+003 * -1.0739 -0.0200 -0.0200 -1.0342 ans = 1.0e+003 * -1.0822 -1.0258 Pause: hit any key to continue... he = 1.0e+003 * -1.0739 -0.0200 -0.0200 -1.0342 ans = 1.0e+003 * -1.0822 -1.0258 xo = 2.9985 2.0035 Ot = 1.8317e-004 nS = 172 eval( 'if exist(''G'',''var''), mauifunc(G), end', ''); eval( 'if exist(''ver'',''var''), mauifunc(ver), end', ''); eval( 'if exist(''gr'',''var''), mauifunc(gr), end', ''); eval( 'if exist(''heuristica'',''var''), mauifunc(heuristica), end', ''); eval( 'if exist(''xo'',''var''), mauifunc(xo), end', ''); 2.9985 2.0035 eval( 'if exist(''sparse'',''var''), mauifunc(sparse), end', ''); eval( 'if exist(''sparse'',''var''), mauifunc(sparse), end', ''); disp(which('lmarqua')); v:\cursos\pos\otimiza\aulas\lmarqua.m clear 'v:\cursos\pos\otimiza\aulas\lmarqua.m' eval( 'if exist(''optimum'',''var''), mauifunc(optimum), end', ''); ; cd(cd) [xo,Ot,nS]=lmarqua('test9',[1 1],1,'gtest9','htest9',[-5 -5],[5 5],[],[],500) Pause: hit any key to continue... beta = -64.4902 Pause: hit any key to continue... beta = -2.7810 beta = -5.5620 beta = -11.1240 Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 3.0001 1.9998 Ot = 8.6448e-007 nS = 18 [xo,Ot,nS]=lmarqua('test9',[3 0],1,'gtest9','htest9',[-5 -5],[5 5],[],[],500) Pause: hit any key to continue... Pause: hit any key to continue... beta = -26.1685 Pause: hit any key to continue... beta = -11.9302 Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 3.5844 -1.8483 Ot = 6.7236e-007 nS = 18 help lsqnonlin LSQNONLIN Solves non-linear least squares problems. LSQNONLIN solves problems of the form: min sum {FUN(X).^2} where X and the values returned by FUN can be x vectors or matrices. X=LSQNONLIN(FUN,X0) starts at the matrix X0 and finds a minimum to the sum of squares of the functions described in FUN. FUN is usually an M-file which returns a vector of objective functions: F=FUN(X). NOTE: FUN should return FUN(X) and not the sum-of-squares sum(FUN(X).^2)). (FUN(X) is summed and squared implicitly in the algorithm.) See below for more options for FUN. X=LSQNONLIN(FUN,X0,LB,UB) defines a set of lower and upper bounds on the design variables, X, so that the solution is in the range LB <= X <= UB. Use empty matrices for LB and UB if no bounds exist. Set LB(i) = -inf if X(i) is unbounded below; set UB(i) = inf if X(i) is unbounded above. X=LSQNONLIN(FUN,X0,LB,UB,OPTIONS) minimizes with the default optimization parameters replaced by values in the structure OPTIONS, an argument created with the OPTIMSET function. See OPTIMSET for details. Used options are Display, TolX, TolFun, DerivativeCheck, Diagnostics, Jacobian, JacobPattern, LineSearchType, LevenbergMarquardt, MaxFunEvals, MaxIter, DiffMinChange and DiffMaxChange, LargeScale, MaxPCGIter, PrecondBandWidth, TolPCG, TypicalX. Use the Jacobian option to specify that FUN may be called with two output arguments where the second, J, is the Jacobian matrix: [F,J] = feval(FUN,X). If FUN returns a vector (matrix) of m components when X has length n, then J is an m-by-n matrix where J(i,j) is the partial derivative of F(i) with respect to x(j). (Note that the Jacobian J is the transpose of the gradient of F.) X=LSQNONLIN(FUN,X0,LB,UB,OPTIONS,P1,P2,..) passes the problem-dependent parameters P1,P2,... directly to the functions FUN: FUN(X,P1,P2,...). Pass an empty matrix for OPTIONS to use the default values. [X,RESNORM]=LSQNONLIN(FUN,X0,...) returns the value of the squared 2-norm of the residual at X: sum(FUN(X).^2). [X,RESNORM,RESIDUAL]=LSQNONLIN(FUN,X0,...) returns the value of the residual at the solution X: RESIDUAL = FUN(X). [X,RESNORM,RESIDUAL,EXITFLAG]=LSQNONLIN(FUN,X0,...) returns a string EXITFLAG that describes the exit condition of LSQNONLIN. If EXITFLAG is: > 0 then LSQNONLIN converged to a solution X. 0 then the maximum number of function evaluations was reached. < 0 then LSQNONLIN did not converge to a solution. [X,RESNORM,RESIDUAL,EXITFLAG,OUTPUT]=LSQNONLIN(FUN,X0,...) returns a structure OUTPUT with the number of iterations taken in OUTPUT.iterations, the number of function evaluations in OUTPUT.funcCount, the algorithm used in OUTPUT.algorithm, the number of CG iterations (if used) in OUTPUT.cgiterations, and the first-order optimality (if used) in OUTPUT.firstorderopt. [X,RESNORM,RESIDUAL,EXITFLAG,OUTPUT,LAMBDA]=LSQNONLIN(FUN,X0,...) returns the set of Lagrangian multipliers, LAMBDA, at the solution: LAMBDA.lower for LB and LAMBDA.upper for UB. [X,RESNORM,RESIDUAL,EXITFLAG,OUTPUT,LAMBDA,JACOBIAN]=LSQNONLIN(FUN,X0,...) returns the Jacobian of FUN at X. type test1 function S=test(x) % Rosenbrock, 1960 % x0 = [-1.2, 1]' % xo = [1, 1]' % S(xo) = 0 % x0=[-0.8 0], d=[8 5] (busca Coggins) S=100*(x(2)-x(1).^2).^2+(1-x(1)).^2; help lsqnonlin LSQNONLIN Solves non-linear least squares problems. LSQNONLIN solves problems of the form: min sum {FUN(X).^2} where X and the values returned by FUN can be x vectors or matrices. X=LSQNONLIN(FUN,X0) starts at the matrix X0 and finds a minimum to the sum of squares of the functions described in FUN. FUN is usually an M-file which returns a vector of objective functions: F=FUN(X). NOTE: FUN should return FUN(X) and not the sum-of-squares sum(FUN(X).^2)). (FUN(X) is summed and squared implicitly in the algorithm.) See below for more options for FUN. X=LSQNONLIN(FUN,X0,LB,UB) defines a set of lower and upper bounds on the design variables, X, so that the solution is in the range LB <= X <= UB. Use empty matrices for LB and UB if no bounds exist. Set LB(i) = -inf if X(i) is unbounded below; set UB(i) = inf if X(i) is unbounded above. X=LSQNONLIN(FUN,X0,LB,UB,OPTIONS) minimizes with the default optimization parameters replaced by values in the structure OPTIONS, an argument created with the OPTIMSET function. See OPTIMSET for details. Used options are Display, TolX, TolFun, DerivativeCheck, Diagnostics, Jacobian, JacobPattern, LineSearchType, LevenbergMarquardt, MaxFunEvals, MaxIter, DiffMinChange and DiffMaxChange, LargeScale, MaxPCGIter, PrecondBandWidth, TolPCG, TypicalX. Use the Jacobian option to specify that FUN may be called with two output arguments where the second, J, is the Jacobian matrix: [F,J] = feval(FUN,X). If FUN returns a vector (matrix) of m components when X has length n, then J is an m-by-n matrix where J(i,j) is the partial derivative of F(i) with respect to x(j). (Note that the Jacobian J is the transpose of the gradient of F.) X=LSQNONLIN(FUN,X0,LB,UB,OPTIONS,P1,P2,..) passes the problem-dependent parameters P1,P2,... directly to the functions FUN: FUN(X,P1,P2,...). Pass an empty matrix for OPTIONS to use the default values. [X,RESNORM]=LSQNONLIN(FUN,X0,...) returns the value of the squared 2-norm of the residual at X: sum(FUN(X).^2). [X,RESNORM,RESIDUAL]=LSQNONLIN(FUN,X0,...) returns the value of the residual at the solution X: RESIDUAL = FUN(X). [X,RESNORM,RESIDUAL,EXITFLAG]=LSQNONLIN(FUN,X0,...) returns a string EXITFLAG that describes the exit condition of LSQNONLIN. If EXITFLAG is: > 0 then LSQNONLIN converged to a solution X. 0 then the maximum number of function evaluations was reached. < 0 then LSQNONLIN did not converge to a solution. [X,RESNORM,RESIDUAL,EXITFLAG,OUTPUT]=LSQNONLIN(FUN,X0,...) returns a structure OUTPUT with the number of iterations taken in OUTPUT.iterations, the number of function evaluations in OUTPUT.funcCount, the algorithm used in OUTPUT.algorithm, the number of CG iterations (if used) in OUTPUT.cgiterations, and the first-order optimality (if used) in OUTPUT.firstorderopt. [X,RESNORM,RESIDUAL,EXITFLAG,OUTPUT,LAMBDA]=LSQNONLIN(FUN,X0,...) returns the set of Lagrangian multipliers, LAMBDA, at the solution: LAMBDA.lower for LB and LAMBDA.upper for UB. [X,RESNORM,RESIDUAL,EXITFLAG,OUTPUT,LAMBDA,JACOBIAN]=LSQNONLIN(FUN,X0,...) returns the Jacobian of FUN at X. edit test1 disp(sprintf('%d',feature('SessionTool'))) 0 ; dbstatus dbstack dbstack ; disp(which('test1')); v:\cursos\pos\otimiza\aulas\test1.m mdbstatus 'v:\cursos\pos\otimiza\aulas\test1.m' disp(which('test1gn')); disp(char(which('test1gn','-all'))); eval( 'if exist(''Rosenbrock'',''var''), mauifunc(Rosenbrock), end', ''); eval( 'if exist(''Rosenbrock'',''var''), mauifunc(Rosenbrock), end', ''); disp(which('test1gn')); disp(char(which('test1gn','-all'))); eval( 'if exist(''Rosenbrock'',''var''), mauifunc(Rosenbrock), end', ''); eval( 'if exist(''function'',''var''), mauifunc(function), end', ''); disp(which('test1gn')); disp(char(which('test1gn','-all'))); eval( 'if exist(''F'',''var''), mauifunc(F), end', ''); [X,So]=LSQNONLIN('test1gn',[-1.2 1]) ??? Cannot find function 'test1gn'. Error in ==> C:\Apps\Matlab\toolbox\optim\lsqnonlin.m On line 156 ==> fuser = feval(funfcn{3},x,varargin{:}); cd(cd) [X,So]=LSQNONLIN('test1gn',[-1.2 1]) Optimization terminated successfully: First-order optimality less than OPTIONS.TolFun, and no zero curvature detected X = 1 1 So = 0 [X,So,res,flag,out]=LSQNONLIN('test1gn',[-1.2 1]) Optimization terminated successfully: First-order optimality less than OPTIONS.TolFun, and no zero curvature detected X = 1 1 So = 0 res = 0 0 flag = 1 out = firstorderopt: 0 iterations: 24 funcCount: 73 cgiterations: 16 algorithm: 'large-scale: trust-region reflective Newton' setoptim opt opt = DerivativeCheck: 'off' Diagnostics: 'off' Display: 'iter' Jacobian: 'off' LargeScale: 'off' LevenbergMarquardt: 'on' LineSearchType: 'quadcubic' DiffMaxChange: 0.1000 DiffMinChange: 1.0000e-008 MaxIter: 400 PrecondBandWidth: 0 TolFun: 1.0000e-006 TolPCG: 0.1000 TolX: 1.0000e-006 [X,So,res,flag,out]=LSQNONLIN('test1gn',[-1.2 1],[],[],opt) Directional Iteration Func-count Residual Step-size derivative Lambda 1 2 24.2 1 -48.4 2 8 23.4818 0.0177 -32.8 396.104 3 15 3.95987 1.73 -0.0379 144.96 4 21 3.68265 24.8 -0.0114 2.86802 5 27 3.16413 1.01 -0.39 1.08482 6 33 2.67191 0.47 -0.349 2.42026 7 39 2.11661 0.829 -0.145 2.74926 8 45 1.64771 0.696 -0.113 3.29128 9 51 1.23729 0.697 -0.0923 3.77489 10 57 0.85261 1 0.0788 4.0076 11 64 0.388178 1.64 -0.103 1.43066 12 70 0.261568 0.812 -0.0261 1.52417 13 77 0.101376 1.68 -0.033 0.483768 14 83 0.0510359 1 0.000804 0.503873 15 90 0.00398951 1.97 -0.00726 0.102066 16 96 0.000774445 1.01 -0.000158 0.102429 17 103 1.68711e-005 1.27 -1.66e-006 0.0450451 18 109 2.24699e-007 1.09 -1.13e-009 0.0215718 19 115 5.54212e-010 1.06 -1.66e-013 0.0104935 20 121 3.65112e-013 1.02 -1.67e-017 0.00518259 Optimization terminated successfully: Search direction less than tolX X = 1.0000 1.0000 So = 1.2328e-016 res = 1.0e-007 * -0.0045 0.1109 flag = 1 out = iterations: 20 funcCount: 122 stepsize: 1 cgiterations: [] firstorderopt: [] algorithm: 'medium-scale: Levenberg-Marquardt, line-search' ; help cgrad Unconstrained optimization using conjugate gradients (Fletcher-Reeves). [xo,Ot,nS]=cgrad(S,x0,ip,G,method,Lb,Ub,problem,tol,mxit) S: objective function x0: initial point ip: (0) no plot (default), (>0) plot figure ip with pause, (<0) plot figure ip G: gradient vector function method: line-search method: (0) Coggins (default), (1): Golden Section Lb, Ub: lower and upper bound vectors to plot (default = x0*(1+/-2)) problem: (-1): minimum (default), (1): maximum tol: tolerance (default = 1e-4) mxit: maximum number of iterations (default = 50*(1+4*~(ip>0))) xo: optimal point Ot: optimal value of S nS: number of objective function evaluations [xo,Ot,nS]=cgrad('test10',[1 1],1,'gtest10') Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 1.0e-015 * -0.1698 -0.5848 Ot = 2.5873e-031 nS = 37 [xo,Ot,nS]=steepdes('test10',[1 1],1,'gtest10') Pause: hit any key to continue... Directional Iteration Func-count f(x) Step-size derivative 1 0 3 0.166667 -36 Warning: Divide by zero. > In C:\Apps\Matlab\toolbox\optim\cubici2.m at line 12 In C:\Apps\Matlab\toolbox\optim\searchq.m at line 65 In v:\cursos\pos\otimiza\aulas\fminusub.m at line 283 In v:\cursos\pos\otimiza\aulas\fminunc1.m at line 220 In v:\cursos\pos\otimiza\aulas\varmetr.m at line 115 In v:\cursos\pos\otimiza\aulas\steepdes.m at line 51 Warning: Divide by zero. > In C:\Apps\Matlab\toolbox\optim\cubici2.m at line 16 In C:\Apps\Matlab\toolbox\optim\searchq.m at line 65 In v:\cursos\pos\otimiza\aulas\fminusub.m at line 283 In v:\cursos\pos\otimiza\aulas\fminunc1.m at line 220 In v:\cursos\pos\otimiza\aulas\varmetr.m at line 115 In v:\cursos\pos\otimiza\aulas\steepdes.m at line 51 Pause: hit any key to continue... 2 4 0.75 0.125 0 Pause: hit any key to continue... 3 9 0.21 0.6 0.45 Warning: Divide by zero. > In C:\Apps\Matlab\toolbox\optim\cubici2.m at line 12 In C:\Apps\Matlab\toolbox\optim\searchq.m at line 71 In v:\cursos\pos\otimiza\aulas\fminusub.m at line 283 In v:\cursos\pos\otimiza\aulas\fminunc1.m at line 220 In v:\cursos\pos\otimiza\aulas\varmetr.m at line 115 In v:\cursos\pos\otimiza\aulas\steepdes.m at line 51 Warning: Divide by zero. > In C:\Apps\Matlab\toolbox\optim\cubici2.m at line 16 In C:\Apps\Matlab\toolbox\optim\searchq.m at line 71 In v:\cursos\pos\otimiza\aulas\fminusub.m at line 283 In v:\cursos\pos\otimiza\aulas\fminunc1.m at line 220 In v:\cursos\pos\otimiza\aulas\varmetr.m at line 115 In v:\cursos\pos\otimiza\aulas\steepdes.m at line 51 Pause: hit any key to continue... 4 13 0.0138057 0.117834 7.7e-016 Warning: Divide by zero. > In C:\Apps\Matlab\toolbox\optim\cubici2.m at line 12 In C:\Apps\Matlab\toolbox\optim\searchq.m at line 34 In v:\cursos\pos\otimiza\aulas\fminusub.m at line 283 In v:\cursos\pos\otimiza\aulas\fminunc1.m at line 220 In v:\cursos\pos\otimiza\aulas\varmetr.m at line 115 In v:\cursos\pos\otimiza\aulas\steepdes.m at line 51 Warning: Divide by zero. > In C:\Apps\Matlab\toolbox\optim\cubici2.m at line 16 In C:\Apps\Matlab\toolbox\optim\searchq.m at line 34 In v:\cursos\pos\otimiza\aulas\fminusub.m at line 283 In v:\cursos\pos\otimiza\aulas\fminunc1.m at line 220 In v:\cursos\pos\otimiza\aulas\varmetr.m at line 115 In v:\cursos\pos\otimiza\aulas\steepdes.m at line 51 Pause: hit any key to continue... 5 18 0.00142354 0.792857 0.00781 Pause: hit any key to continue... 6 22 0.000107465 0.118106 -8.57e-017 Pause: hit any key to continue... 7 27 1.20867e-005 0.782782 6.09e-005 Optimization terminated successfully: Current search direction is a descent direction, and magnitude of directional derivative in search direction less than 2*options.TolFun Pause: hit any key to continue... xo = 0.0019 0.0006 Ot = 1.2087e-005 nS = 28 [xo,Ot,nS]=newton('test10',[1 1],1,'gtest10') Pause: hit any key to continue... Pause: hit any key to continue... xo = 1.0e-031 * 0.1233 0.3287 Ot = 8.7781e-064 nS = 3 [xo,Ot,nS]=cgrad('test1',[-1.2 1],1,'gtest1') Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 1.0000 1.0000 Ot = 3.1054e-010 nS = 507 [xo,Ot,nS]=newton('test1',[-1.2 1],1,'gtest1') Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 1.0000 1.0000 Ot = 4.5475e-024 nS = 35 help powell Unconstrained optimization using Powell. [xo,Ot,nS]=powell(S,x0,ip,method,Lb,Ub,problem,tol,mxit) S: objective function x0: initial point ip: (0): no plot (default), (>0) plot figure ip with pause, (<0) plot figure ip method: (0) Coggins (default), (1): Golden Section Lb, Ub: lower and upper bound vectors to plot (default = x0*(1+/-2)) problem: (-1): minimum (default), (1): maximum tol: tolerance (default = 1e-4) mxit: maximum number of stages (default = 50*(1+4*~(ip>0))) xo: optimal point Ot: optimal value of S nS: number of objective function evaluations [xo,Ot,nS]=powell('test1',[-1.2 1],1) Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... 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Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 1.0000 1.0000 Ot = 1.7272e-011 nS = 503 [xo,Ot,nS]=powell('test10',[-1.2 1],1) Pause: hit any key to continue... Error in ==> v:\cursos\pos\otimiza\aulas\powell.m On line 73 ==> disp('Pause: hit any key to continue...'); pause; [xo,Ot,nS]=powell('test10',[1 1],1) Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 1.0e-018 * 0 0.2367 Ot = 5.6023e-038 nS = 64 [xo,Ot,nS]=cgrad('test10',[1 1],1) Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... Pause: hit any key to continue... xo = 1.0e-012 * -0.0356 -0.1426 Ot = 1.5245e-026 nS = 45 quit