[Scilab-users] 'optim' vs 'Nelder-Mead' ... or difficulties to use 'optim'
paul.carrico at free.fr
paul.carrico at free.fr
Sun Jan 15 18:04:14 CET 2017
Hi Stephane,
You're right, I forgot my basis :-)
Nevertheless when I re-write the target function as the following, it
fails after some iterations and I do not understand the origin (??)
Paul
#######################################
function f=target(x)
val_lin = lineaire(x,1,2);
val_rac = racine(x,10,6);
// f = abs(val_lin - val_rac);
f = sqrt((val_lin - val_rac)^2);
printf("f = %g\n",f);
endfunction
######################################
Console message:
*********** qnbd (with bound cstr) ****************
dimension= 1, epsq= 0.2220446049250313E-15, verbosity level: imp= 3
max number of iterations allowed: iter= 1000
max number of calls to costf allowed: nap= 1000
------------------------------------------------
f = 23.6393
f = 25.1965
f = 22.0911
qnbd : iter= 1 f= 0.2363932D+02
qnbd : nbre fact 1 defact 0 total var factorisees 1
rlbd tp= 0.6440E+02 tmax= 0.1000E+11 dh0/dt=-0.6027E+00
f = 21.6468
f = 23.1924
f = 20.111
es t= 0.3318E+01 h=-0.1992E+01 dh/dt=-0.5981E+00 dfh/dt=-0.6005E+00 dt
0.3E+01
f = 4
f = 6.47214
f = 6
al_parameters,'qn','ar',nocf,niter,imp=3)
!--error 98
La variable retournée par la fonction Scilab passée en argument n'est
pas valide.
at line 36 of exec file called by :
RFACE/Rosembrock/fonctions_test.sce', -1
t= 0.6440E+02 h=-0.1992E+01 dh/dt=-0.5981E+00 dfh/dt= 0.0000E+00 dt
0.6E+02
qnbd : indqn= 0
Le 2017-01-15 12:59, Stéphane Mottelet a écrit :
> Hello
>
> Your target function is not differrentiable (Because of the absolute
> value). That explains why optim has some difficulties. Using a square
> instead should give the advantage to optim against nelder-mead.
>
> S.
>
>> Le 15 janv. 2017 à 11:39, paul.carrico at free.fr a écrit :
>>
>> Hi all
>>
>> Well, from a "macro" point of view, gradient based methods (order 1 method) should be more efficient than Nelder-Mead one (order 0) especially for 1D topic, shouldn't be?
>>
>> In the case here bellow, when I use 'Optim' it is not the case in comparison to 'NelderMead'... I don'y know what I'm doing wrong but I decide to frop off 'optim' in favor tp Nelder-Mead - nevertheless the later method requires much more iterations :-(
>>
>> I'll be interested by some feedback on such topic, either in the mailing list (or in MP in order to not pollute it).
>>
>> Paul
>> ########################################"
>> 'optim'
>> ########################################
>> mode(0)
>>
>> function f=lineaire(x, a2, b2)
>> f = a2*x+b2;
>> endfunction
>>
>> function g=racine(x, a1, b1)
>> g = sqrt(a1*x) + b1;
>> endfunction
>>
>> function f=target(x)
>> val_lin = lineaire(x,1,2);
>> val_rac = racine(x,10,6);
>> f = abs(val_lin - val_rac);
>> endfunction
>>
>> // Cost function :
>> function [f, g, ind]=cost(x, ind)
>> f = target(x);
>> // g = numderivative(target, x.');
>> // g = numderivative(target, x.',0.1,order = 2);
>> g = numderivative(target, x.',order = 2); // better but why ??? h automatic works better ???
>> // g = numderivative(target, x.',order = 4);
>> // g = numderivative(target, x.',0.1, order = 4);
>> endfunction
>>
>> // optimisation avec optim
>> initial_parameters = [50]
>> lower_bounds = [0];
>> upper_bounds = [1000];
>> nocf = 1000; // number of call of f
>> niter = 1000; // number of iterations
>> [fopt, xopt, gopt, work, iters, evals, err] = optim(cost,'b',lower_bounds,upper_bounds,initial_parameters,'qn','ar',nocf,niter,imp=3);
>> xopt
>> fopt
>> err
>>
>> // traçage courbes
>> x = linspace(0,50,1000)';
>> plot_raci = racine(x,10,6);
>> plot_lin = lineaire(x,1,2);
>>
>> scf(1);
>> drawlater();
>> xgrid(3);
>> f = gcf();
>> //f
>> f.figure_size = [1000, 1000];
>> f.background = color(255,255,255);
>> a = gca();
>> //a
>> a.font_size = 2;
>> a.x_label.text = "X axis" ;
>> a.x_location="bottom";
>> a.x_label.font_angle=0;
>> a.x_label.font_size = 4;
>> a.y_label.text = "Y axis";
>> a.y_location="left";
>> a.y_label.font_angle=-90;
>> a.Y_label.font_size = 4;
>> a.title.text = "Title";
>> a.title.font_size = 5;
>> a.line_style = 1;
>>
>> // début des courbes
>> plot(x,plot_lin);
>> e1 = gce();
>> p1 = e1.children;
>> p1.thickness = 1;
>> p1.line_style = 1;
>> p1.foreground = 3;
>>
>> plot(x,plot_raci);
>> e2 = gce();
>> p2 = e2.children;
>> p2.thickness = 1;
>> p2.line_style = 1;
>> p2.foreground = 2;
>> drawnow();
>>
>> #######################################
>> Nelder Mead
>> #######################################
>> mode(0)
>>
>> function f=lineaire(x, a2, b2)
>> f = a2*x+b2;
>> endfunction
>>
>> function g=racine(x, a1, b1)
>> g = sqrt(a1*x) + b1;
>> endfunction
>>
>> function [f, index]=target(x, index)
>> val_lin = lineaire(x,1,2);
>> val_rac = racine(x,10,6);
>> f = abs(val_lin - val_rac);
>> endfunction
>>
>> // optimisation avec optim
>> initial_parameters = [50]
>> lower_bounds = [0];
>> upper_bounds = [1000];
>>
>> nm = neldermead_new ();
>> nm = neldermead_configure(nm,"-numberofvariables",1);
>> nm = neldermead_configure(nm,"-function",target);
>> nm = neldermead_configure(nm,"-x0",initial_parameters);
>> nm = neldermead_configure(nm,"-maxiter",1000);
>> nm = neldermead_configure(nm,"-maxfunevals",1000);
>> nm = neldermead_configure(nm,"-tolfunrelative",10*%eps);
>> nm = neldermead_configure(nm,"-tolxrelative",10*%eps);
>> nm = neldermead_configure(nm,"-method","box");
>> nm = neldermead_configure(nm,"-boundsmin",lower_bounds);
>> nm = neldermead_configure(nm,"-boundsmax", upper_bounds);
>> nm = neldermead_search(nm);
>> nm = neldermead_restart(nm);
>> xopt = neldermead_get(nm,"-xopt")
>> fopt = neldermead_get(nm,"-fopt")
>> nm = neldermead_destroy(nm);
>>
>> // traçage courbes
>> x = linspace(0,50,1000)';
>> a1 = 10; b1 = 6; // b1 > b2 here
>> a2 = 1; b2 = 2;
>>
>> plot_raci = racine(x,a1,b1);
>> plot_lin = lineaire(x,a2,b2);
>>
>> scf(1);
>> drawlater();
>> xgrid(3);
>> f = gcf();
>> //f
>> f.figure_size = [1000, 1000];
>> f.background = color(255,255,255);
>> a = gca();
>> //a
>> a.font_size = 2;
>> a.x_label.text = "X axis" ;
>> a.x_location="bottom";
>> a.x_label.font_angle=0;
>> a.x_label.font_size = 4;
>> a.y_label.text = "Y axis";
>> a.y_location="left";
>> a.y_label.font_angle=-90;
>> a.Y_label.font_size = 4;
>> a.title.text = "Title";
>> a.title.font_size = 5;
>> a.line_style = 1;
>>
>> // début des courbes
>> plot(x,plot_lin);
>> e1 = gce();
>> p1 = e1.children;
>> p1.thickness = 1;
>> p1.line_style = 1;
>> p1.foreground = 3;
>>
>> plot(x,plot_raci);
>> e2 = gce();
>> p2 = e2.children;
>> p2.thickness = 1;
>> p2.line_style = 1;
>> p2.foreground = 2;
>> drawnow();
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