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authorMichaŽl Baudin <michael.baudin@scilab.org>2009-09-25 16:55:29 +0200
committerMichaŽl Baudin <michael.baudin@scilab.org>2009-09-25 16:55:29 +0200
commit92019dd61338ef7da1e3645105c1e9298a59f6b6 (patch)
treefc8f6f5d989efac40d01f5566b1a55d16e2f4a6c /scilab_doc
parent83a775150fdacf3af12a5460b7dac6fbb470b63b (diff)
downloadscilab-92019dd61338ef7da1e3645105c1e9298a59f6b6.zip
scilab-92019dd61338ef7da1e3645105c1e9298a59f6b6.tar.gz
Updated Manual
Diffstat (limited to 'scilab_doc')
-rw-r--r--scilab_doc/neldermead/implementations.aux58
-rw-r--r--scilab_doc/neldermead/macros.aux27
-rw-r--r--scilab_doc/neldermead/macros.tex165
-rw-r--r--scilab_doc/neldermead/method-spendley.aux82
-rw-r--r--scilab_doc/neldermead/method-spendley.tex346
-rw-r--r--scilab_doc/neldermead/neldermead-simplex-so.aux28
-rw-r--r--scilab_doc/neldermead/neldermead-simplex-so.bbl63
-rw-r--r--scilab_doc/neldermead/neldermead-simplex-so.blg6
-rw-r--r--scilab_doc/neldermead/neldermead-simplex-so.log466
-rw-r--r--scilab_doc/neldermead/neldermead-simplex-so.out10
-rw-r--r--scilab_doc/neldermead/neldermead-simplex-so.pdfbin177631 -> 181032 bytes
-rw-r--r--scilab_doc/neldermead/neldermead-simplex-so.tex2
-rw-r--r--scilab_doc/neldermead/neldermead-simplex-so.toc10
-rw-r--r--scilab_doc/neldermead/neldermead-spendley-so.aux20
-rw-r--r--scilab_doc/neldermead/neldermead-spendley-so.bbl14
-rw-r--r--scilab_doc/neldermead/neldermead-spendley-so.blg4
-rw-r--r--scilab_doc/neldermead/neldermead-spendley-so.log552
-rw-r--r--scilab_doc/neldermead/neldermead-spendley-so.out10
-rw-r--r--scilab_doc/neldermead/neldermead-spendley-so.pdfbin0 -> 317287 bytes
-rw-r--r--scilab_doc/neldermead/neldermead-spendley-so.tex85
-rw-r--r--scilab_doc/neldermead/neldermead-spendley-so.toc10
-rw-r--r--scilab_doc/neldermead/neldermead.bib6
-rw-r--r--scilab_doc/neldermead/neldermead.tex4
-rw-r--r--scilab_doc/neldermead/nmbibliography.aux74
-rw-r--r--scilab_doc/neldermead/quad2-spendley-simplexcontours.pngbin18444 -> 5497 bytes
-rw-r--r--scilab_doc/neldermead/quad2bis-spendley-history-logfopt.pngbin11971 -> 3792 bytes
-rw-r--r--scilab_doc/neldermead/quad2bis-spendley-history-sigma.pngbin9722 -> 4237 bytes
-rw-r--r--scilab_doc/neldermead/quad2bis-spendley-simplexcontours.pngbin32301 -> 7315 bytes
-rw-r--r--scilab_doc/neldermead/rosenbrock.fixed.history.fbar.txt351
-rw-r--r--scilab_doc/neldermead/rosenbrock.fixed.history.fopt.txt351
-rw-r--r--scilab_doc/neldermead/rosenbrock.fixed.history.sigma.txt351
-rw-r--r--scilab_doc/neldermead/rosenbrock.fixed.history.simplex.txt3094
-rw-r--r--scilab_doc/neldermead/scripts/neldermead_dimensionnality.sce107
-rw-r--r--scilab_doc/neldermead/section-simplex.aux67
-rw-r--r--scilab_doc/neldermead/section-simplex.log26
-rw-r--r--scilab_doc/neldermead/section-simplex.tex52
-rw-r--r--scilab_doc/neldermead/spendley-dimension-nfevals.pngbin11047 -> 4496 bytes
-rw-r--r--scilab_doc/neldermead/spendley-steps-reflect.pngbin23005 -> 20971 bytes
-rw-r--r--scilab_doc/neldermead/spendley-steps-reflect.svg38
-rw-r--r--scilab_doc/neldermead/spendley-steps-reflect2.pngbin30191 -> 30169 bytes
-rw-r--r--scilab_doc/neldermead/spendley-steps-reflect2.svg14
-rw-r--r--scilab_doc/neldermead/test.pdf0
42 files changed, 6358 insertions, 135 deletions
diff --git a/scilab_doc/neldermead/implementations.aux b/scilab_doc/neldermead/implementations.aux
new file mode 100644
index 0000000..a8a5c92
--- /dev/null
+++ b/scilab_doc/neldermead/implementations.aux
@@ -0,0 +1,58 @@
1\relax
2\citation{MatlabFminsearch}
3\citation{Kelley1999}
4\citation{KelleyMethodsOptimizationMatlabCodes}
5\citation{589283}
6\@writefile{toc}{\contentsline {chapter}{\numberline {B}Implementations of the Nelder-Mead algorithm}{25}{appendix.B}}
7\@writefile{lof}{\addvspace {10\p@ }}
8\@writefile{lot}{\addvspace {10\p@ }}
9\@writefile{toc}{\contentsline {section}{\numberline {B.1}Matlab : fminsearch}{25}{section.B.1}}
10\@writefile{toc}{\contentsline {section}{\numberline {B.2}Kelley and the Nelder-Mead algorithm}{25}{section.B.2}}
11\citation{LolimotColletteURL}
12\citation{NelderMeadColletteURL}
13\citation{NumericalRecipes}
14\citation{GAMS-A19A20-Desc}
15\citation{GAMS-A19A20-Source}
16\citation{O'Neill1971AAF}
17\citation{O'NeillAS47}
18\citation{O'Neill1971AAF}
19\citation{Burkardtasa047}
20\@writefile{toc}{\contentsline {section}{\numberline {B.3}Nelder-Mead Scilab Toolbox : Lolimot}{27}{section.B.3}}
21\@writefile{toc}{\contentsline {section}{\numberline {B.4}Numerical Recipes}{27}{section.B.4}}
22\@writefile{toc}{\contentsline {section}{\numberline {B.5}NASHLIB : A19}{27}{section.B.5}}
23\@writefile{toc}{\contentsline {section}{\numberline {B.6}O'Neill implementations}{27}{section.B.6}}
24\citation{SurvivalBookOptim}
25\citation{Burkardtasa047}
26\citation{BurkardtNelderMeadMatlab}
27\@writefile{toc}{\contentsline {section}{\numberline {B.7}Burkardt implementations}{28}{section.B.7}}
28\citation{NAGE04CCF}
29\@writefile{toc}{\contentsline {section}{\numberline {B.8}NAG Fortran implementation}{29}{section.B.8}}
30\@writefile{toc}{\contentsline {section}{\numberline {B.9}GSL implementation}{29}{section.B.9}}
31\@setckpt{implementations}{
32\setcounter{page}{30}
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diff --git a/scilab_doc/neldermead/macros.aux b/scilab_doc/neldermead/macros.aux
new file mode 100644
index 0000000..5db44e4
--- /dev/null
+++ b/scilab_doc/neldermead/macros.aux
@@ -0,0 +1,27 @@
1\relax
2\@setckpt{macros}{
3\setcounter{page}{1}
4\setcounter{equation}{0}
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diff --git a/scilab_doc/neldermead/macros.tex b/scilab_doc/neldermead/macros.tex
index a205b7b..8c9af33 100644
--- a/scilab_doc/neldermead/macros.tex
+++ b/scilab_doc/neldermead/macros.tex
@@ -56,6 +56,171 @@
56% To highlight source code 56% To highlight source code
57\usepackage{listings} 57\usepackage{listings}
58 58
59\lstdefinelanguage{scilabscript}%
60 {morekeywords={abcd,abinv,abort,abs,acoshm,acosh,acosm,acos,addcolor,%
61 addf,addinter,addmenu,add_edge,add_node,adj2sp,adj_lists,aff2ab,%
62 amell,analpf,analyze,ans,apropos,arc_graph,arc_number,argn,arhnk,%
63 arl2,arma2p,armac,armax1,armax,arma,arsimul,artest,articul,ascii,%
64 asinhm,asinh,asinm,asin,atanhm,atanh,atanm,atan,augment,auread,%
65 auwrite,balanc,balreal,bandwr,basename,bdiag,besseli,besselj,%
66 besselk,bessely,best_match,bezout,bifish,bilin,binomial,black,%
67 bloc2exp,bloc2ss,bode,bool2s,boolean,boucle,break,bstap,buttmag,%
68 bvode,cainv,calerf,calfrq,call,canon,casc,case,ccontrg,cdfbet,%
69 cdfbin,cdfchi,cdfchn,cdffnc,cdff,cdfgam,cdfnbn,cdfnor,cdfpoi,%
70 cdft,ceil,center,cepstrum,chaintest,chain_struct,champ1,champ,%
71 chart,chdir,cheb1mag,cheb2mag,check_graph,check_io,chepol,chfact,%
72 chol,chsolve,circuit,classmarkov,clean,clearfun,clearglobal,%
73 clear,close,cls2dls,cmb_lin,cmndred,cmoment,code2str,coeff,coffg,%
74 coff,colcompr,colcomp,colinout,colormap,colregul,companion,comp,%
75 cond,conj,connex,contour2di,contour2d,contourf,contour,%
76 contract_edge,contrss,contr,cont_frm,cont_mat,convex_hull,convol,%
77 convstr,con_nodes,copfac,copy,correl,corr,coshm,cosh,cosm,cos,%
78 cotg,cothm,coth,covar,csim,cspect,ctr_gram,cumprod,cumsum,%
79 curblock,cycle_basis,czt,c_link,dasrt,dassl,datafit,date,dbphi,%
80 dcf,ddp,debug,dec2hex,deff,definedfields,degree,delbpt,%
81 delete_arcs,delete_nodes,delete,delip,delmenu,demos,denom,%
82 derivative,derivat,des2ss,des2tf,determ,detr,det,dft,dhinf,%
83 dhnorm,diag,diary,diff,diophant,dirname,dispbpt,dispfiles,disp,%
84 dlgamma,double,dragrect,drawaxis,drawlater,drawnow,draw,driver,%
85 dscr,dsearch,dsimul,dtsi,dt_ility,duplicate,edge_number,%
86 edit_curv,edit_graph_menus,edit_graph,edit,eigenmarkov,ell1mag,%
87 elseif,else,emptystr,endfunction,end,eqfir,eqiir,equil1,equil,%
88 ereduc,erfcx,erfc,erf,errbar,errcatch,errclear,error,eval3dp,%
89 eval3d,eval,evans,evstr,excel2sci,execstr,exec,exists,exit,expm,%
90 exp,external,eye,fac3d,factors,faurre,fchamp,fcontour2d,fcontour,%
91 fec,feedback,feval,ffilt,fftshift,fft,fgrayplot,figure,fileinfo,%
92 file,filter,findm,findobj,findx0BD,find_freq,find_path,find,%
93 findABCD,findAC,findBD,findBDK,findR,fit_dat,fix,floor,flts,foo,%
94 formatman,format,fort,for,fourplan,fplot2d,fplot3d1,fplot3d,%
95 fprintf,fprintfMat,frep2tf,freq,freson,frexp,frfit,frmag,fscanf,%
96 fscanfMat,fsfirlin,fsolve,fspecg,fstabst,fstair,ftest,ftuneq,%
97 fullrfk,fullrf,full,fun2string,funcprot,functions,function,%
98 funptr,fusee,gainplot,gamitg,gammaln,gamma,gcare,gcd,gcf,%
99 genfac3d,genlib,genmarkov,gen_net,geom3d,geomean,getblocklabel,%
100 getcolor,getcurblock,getcwd,getdate,getd,getenv,getfield,getfont,%
101 getf,getio,getlinestyle,getmark,getpid,getscicosvars,getsymbol,%
102 getvalue,getversion,get_function_path,get,gfare,gfrancis,girth,%
103 givens,glever,glist,global,glue,gpeche,graduate,grand,%
104 graphics_entities,graph_2_mat,graph_center,graph_complement,%
105 graph_diameter,graph_power,graph_simp,graph_sum,graph_union,%
106 graph-list,graycolormap,grayplot,graypolarplot,grep,group,%
107 gr_menu,gschur,gsort,gspec,gstacksize,gtild,g_margin,h2norm,halt,%
108 hamilton,hankelsv,hank,harmean,havewindow,help,hermit,hess,%
109 hex2dec,hilb,hinf,hist3d,histplot,horner,host,hotcolormap,%
110 householder,hrmt,htrianr,hypermat,h_cl,h_inf_st,h_inf,h_norm,%
111 iconvert,icon_edit,ieee,if,iirgroup,iirlp,iir,ilib_build,%
112 ilib_compile,ilib_for_link,ilib_gen_gateway,ilib_gen_loader,%
113 ilib_gen_Make,imag,impl,imrep2ss,imult,im_inv,inistate,input,%
114 int16,int2d,int32,int3d,int8,intc,intdec,integrate,interpln,%
115 interp,intersci,intersect,intg,intl,intppty,intsplin,inttrap,%
116 inttype,int,invr,invsyslin,inv_coeff,inv,iqr,isdef,isdir,isequal,%
117 iserror,isglobal,isinf,isnan,isoview,isreal,is_connex,jmat,%
118 justify,kalm,karmarkar,kernel,keyboard,knapsack,kpure,krac2,%
119 kroneck,kron,lasterror,lattn,lattp,lcf,lcmdiag,lcm,ldivf,ldiv,%
120 leastsq,legends,length,leqr,levin,lev,lex_sort,lft,lgfft,library,%
121 lib,lin2mu,lincos,lindquist,lines,line_graph,linfn,linf,link,%
122 linmeq,linpro,linsolve,linspace,lin,listfiles,list,lmisolver,%
123 lmitool,loadmatfile,loadplots,loadwave,load_graph,load,locate,%
124 log10,log1p,log2,logm,logspace,log,lotest,lqe,lqg2stan,lqg_ltr,%
125 lqg,lqr,lsq,lsslist,lstcat,lstsize,ltitr,ludel,lufact,luget,%
126 lusolve,lu,lyap,macglov,macr2lst,macrovar,macro,mad,make_graph,%
127 make_index,manedit,man,mapsound,markp2ss,matfile2sci,matrix,%
128 mat_2_graph,maxi,max_cap_path,max_clique,max_flow,max,mclearerr,%
129 mclose,meanf,mean,median,meof,mese,mesh2d,mfft,mfile2sci,mgeti,%
130 mgetl,mgetstr,mget,milk_drop,mine,mini,minreal,minss,%
131 min_lcost_cflow,min_lcost_flow1,min_lcost_flow2,min_qcost_flow,%
132 min_weight_tree,min,mlist,mode,modulo,moment,mopen,move,%
133 mps2linpro,mputl,mputstr,mput,mrfit,msd,mseek,mtell,mtlb_load,%
134 mtlb_mode,mtlb_save,mtlb_sparse,mu2lin,mulf,mvvacov,m_circle,%
135 names,nand2mean,nanmax,nanmeanf,nanmean,nanmedian,nanmin,%
136 nanstdev,nansum,narsimul,ndims,nearfloat,nehari,neighbors,%
137 netclose,netwindows,netwindow,newest,newfun,nextpow2,nf3d,nfreq,%
138 nlev,nnz,nodes_2_path,nodes_degrees,node_number,noisegen,norm,%
139 null,numdiff,numer,nyquist,obscont1,obscont,observer,obsvss,%
140 obsv_mat,obs_gram,odedc,odedi,odeoptions,ode_discrete,ode_root,%
141 ode,oldload,oldsave,ones,optim,orth,param3d1,param3d,%
142 paramfplot2d,parrot,part,pathconvert,path_2_nodes,pause,pbig,%
143 pdiv,pen2ea,pencan,penlaur,perctl,perfect_match,pertrans,pfss,%
144 phasemag,phc,pinv,pipe_network,playsnd,plot2d1,plot2d2,plot2d3,%
145 plot2d4,plot2d,plot3d1,plot3d2,plot3d3,plot3d,plotframe,%
146 plotprofile,plot_graph,plot,plzr,pmodulo,pol2des,pol2str,pol2tex,%
147 polarplot,polar,polfact,poly,portr3d,portrait,power,ppol,prbs_a,%
148 predecessors,predef,printf,printing,print,prod,profile,projsl,%
149 projspec,proj,psmall,pspect,pvm_addhosts,pvm_barrier,pvm_bcast,%
150 pvm_bufinfo,pvm_config,pvm_delhosts,pvm_error,pvm_exit,%
151 pvm_f772sci,pvm_getinst,pvm_gettid,pvm_get_timer,pvm_gsize,%
152 pvm_halt,pvm_joingroup,pvm_kill,pvm_lvgroup,pvm_mytid,pvm_parent,%
153 pvm_probe,pvm_recv,pvm_reduce,pvm_sci2f77,pvm_send,pvm_set_timer,%
154 pvm_spawn_independent,pvm_spawn,pvm_start,pvm_tasks,%
155 pvm_tidtohost,pvm,pwd,p_margin,qassign,qr,quapro,quart,quaskro,%
156 quit,randpencil,rand,range,rankqr,rank,rat,rcond,rdivf,read4b,%
157 readb,readc_,readmps,read,real,recur,reglin,regress,remezb,remez,%
158 repfreq,replot,residu,resume,return,riccati,riccsl,ricc,ric_desc,%
159 rlist,roots,rotate,round,routh_t,rowcompr,rowcomp,rowinout,%
160 rowregul,rowshuff,rpem,rref,rtitr,rubberbox,salesman,savewave,%
161 save_graph,save,scaling,scanf,schur,sci2exp,sci2for,sci2map,%
162 sciargs,scicosim,scicos,scifunc_block,sd2sci,secto3d,select,%
163 semidef,sensi,setbpt,seteventhandler,setfield,setmenu,%
164 setscicosvars,set,sfact,sgrid,shortest_path,showprofile,%
165 show_arcs,show_graph,show_nodes,sident,signm,sign,simp_mode,simp,%
166 sincd,sinc,sinc,sinhm,sinh,sinm,sin,size,sm2des,sm2ss,smooth,%
167 solve,sorder,sort,sound,sp2adj,spaninter,spanplus,spantwo,sparse,%
168 spchol,spcompack,specfact,spec,speye,spget,splin,split_edge,%
169 spones,sprand,sprintf,spzeros,sqroot,sqrtm,sqrt,squarewave,%
170 square,srfaur,srkf,ss2des,ss2ss,ss2tf,sscanf,sskf,ssprint,ssrand,%
171 stabil,stacksize,standard_define,standard_draw,standard_input,%
172 standard_origin,standard_output,startup,stdevf,stdev,steadycos,%
173 str2code,strange,strcat,strindex,strings,string,stripblanks,%
174 strong_connex,strong_con_nodes,strsubst,st_deviation,st_ility,%
175 subf,subgraph,subplot,successors,sum,supernode,sva,svd,svplot,%
176 sylm,sylv,sysconv,sysdiag,sysfact,syslin,syssize,systems,system,%
177 systmat,tabul,tangent,tanhm,tanh,tanm,tan,tdinit,testmatrix,%
178 texprint,tf2des,tf2ss,then,thrownan,timer,time_id,titlepage,%
179 tk_getdir,tk_getfile,tlist,toeplitz,tokenpos,tokens,trace,%
180 translatepaths,trans_closure,trans,trfmod,trianfml,tril,trimmean,%
181 trisolve,triu,trzeros,typename,typeof,type,uicontrol,uimenu,%
182 uint16,uint32,uint8,ui_observer,ulink,unglue,union,unique,unix_g,%
183 unix_s,unix_w,unix_x,unix,unobs,unsetmenu,user,varargin,%
184 varargout,variancef,variance,varn,warning,wavread,wavwrite,%
185 wcenter,wfir,what,whereami,whereis,where,while,whos,who_user,who,%
186 wiener,wigner,window,winsid,with_gtk,with_pvm,with_texmacs,%
187 with_tk,writb,write4b,write,xarcs,xarc,xarrows,xaxis,xbasc,%
188 xbasimp,xbasr,xchange,xclear,xclea,xclick,xclip,xdel,xend,xfarcs,%
189 xfarc,xfpolys,xfpoly,xfrect,xgetech,xgetfile,xgetmouse,xget,%
190 xgraduate,xgrid,xinfo,xinit,xlfont,xload,xname,xnumb,xpause,%
191 xpolys,xpoly,xrects,xrect,xrpoly,xs2fig,xs2gif,xs2ppm,xs2ps,%
192 xsave,xsegs,select,xsetech,xsetm,xset,xstringb,xstringl,xstring,%
193 xtape,xtitle,x_choices,x_choose,x_dialog,x_matrix,x_mdialog,%
194 x_message_modeless,x_message,yulewalk,zeropen,zeros,zgrid,zpbutt,%
195 zpch1,zpch2,zpell,mfprintf,mfscanf,mprintf,mscanf,msprintf,%
196 msscanf,mucomp,%
197 ABSBLK_f,AFFICH_f,ANDLOG_f,ANIMXY_f,BIGSOM_f,CLINDUMMY_f,CLKIN_f,%
198 CLKINV_f,CLKOUT_f,CLKOUTV_f,CLKSOM_f,CLKSOMV_f,CLKSPLIT_f,%
199 CLOCK_f,CLR_f,CLSS_f,CONST_f,COSBLK_f,CURV_f,DELAY_f,DELAYV_f,%
200 DEMUX_f,DLR_f,DLRADAPT_f,DLSS_f,EVENTSCOPE_f,EVTDLY_f,EVTGEN_f,%
201 EXPBLK_f,G_make,GAIN_f,GAINBLK_f,GENERAL_f,GENERIC_f,GENSIN_f,%
202 GENSQR_f,HALT_f,IFTHEL_f,IN_f,INTEGRAL_f,INTRP2BLK_f,INTRPLBLK_f,%
203 INVBLK_f,LOGBLK_f,LOOKUP_f,Matplot1,Matplot,MAX_f,MCLOCK_f,%
204 MFCLCK_f,MIN_f,MUX_f,NDcost,NEGTOPOS_f,OUT_f,POSTONEG_f,POWBLK_f,%
205 PROD_f,QUANT_f,RAND_f,READC_f,REGISTER_f,RELAY_f,RFILE_f,%
206 ScilabEval,Sfgrayplot,Sgrayplot,SAMPLEHOLD_f,SAT_f,SAWTOOTH_f,%
207 SCOPE_f,SCOPXY_f,SELECT_f,SINBLK_f,SOM_f,SPLIT_f,STOP_f,SUPER_f,%
208 TANBLK_f,TCLSS_f,TEXT_f,TIME_f,TK_EvalFile,TK_EvalStr,TK_GetVar,%
209 TK_SetVar,TRASH_f,WFILE_f,WRITEC_f,ZCROSS_f,%
210 \%asn,\%helps,\%k,\%sn},%
211 alsoletter=\%,% chmod
212 sensitive,%
213 morecomment=[l]//,%
214 morestring=[b]",%
215 morestring=[m]'%
216 numbers=none,%
217 basicstyle=\tiny,%
218 keywordstyle=\bfseries,%
219 commentstyle=\bfseries,%
220 showspaces=false,%
221 stringstyle=\bfseries
222 }[keywords,comments,strings]%
223
59\usepackage{algorithmic} 224\usepackage{algorithmic}
60 225
61% To allow one bibliograph by chapter 226% To allow one bibliograph by chapter
diff --git a/scilab_doc/neldermead/method-spendley.aux b/scilab_doc/neldermead/method-spendley.aux
new file mode 100644
index 0000000..5c36e0b
--- /dev/null
+++ b/scilab_doc/neldermead/method-spendley.aux
@@ -0,0 +1,82 @@
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40\newlabel{fig-spendley-numexp2-historysimplex}{{1.11}{11}{\rm \small Spendley et al. numerical experiment with $f(x_1,x_2) = a x_1^2 + x_2^2$ and $a=100$ -- History of simplex\relax }{figure.1.11}{}}
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42\newlabel{fig-spendley-numexp2-scaling}{{1.12}{11}{\rm \small Numerical experiment with Spendley's et al. method on a badly scaled quadratic function\relax }{figure.1.12}{}}
43\citation{HanNeumann2006}
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diff --git a/scilab_doc/neldermead/method-spendley.tex b/scilab_doc/neldermead/method-spendley.tex
index 335f142..a3725c0 100644
--- a/scilab_doc/neldermead/method-spendley.tex
+++ b/scilab_doc/neldermead/method-spendley.tex
@@ -1,9 +1,31 @@
1\chapter{Spendley's et al. method} 1\chapter{Spendley's et al. method}
2 2
3In this section, we present Spendley's et al. algorithm \cite{Spendley1962} for
4unconstrained optimization.
5
6We begin by presenting a global overview of the algorithm.
7Then we present various geometric situations which might occur
8during the algorithm. In the second section, we present several
9numerical experiments which allow to get some insight of the behaviour
10of the algorithm on some simple situations. The two first cases
11are involving only 2 variables and are based on a quadratic function.
12The last numerical experiment explores the behaviour of the algorith
13when the number of variables increases.
14
3\section{Analysis} 15\section{Analysis}
4 16
17In this section, we present Spendley's et al algorithm for unconstrained optimization.
18This algorithm is based on the iterative update of a simplex.
19At each iteration, either a reflection of a shrink step is performed, so that
20the shape of the simplex does not change during the iterations.
21Then we present various geometric situations which might occur
22during the algorithm. This allows to understand when exactly a reflection
23or a shrink is performed in practice.
24
25\subsection{Algorithm}
26
5The simplex algorithms are based on the iterative update of 27The simplex algorithms are based on the iterative update of
6a \emph{simplex} made of $n+1$ points $S={x_i}_{i=1,n+1}$. Each point 28a \emph{simplex} made of $n+1$ points $S=\{x_i\}_{i=1,n+1}$. Each point
7in the simplex is called a \emph{vertex} and is associated with 29in the simplex is called a \emph{vertex} and is associated with
8a function value $f_i=f(x_i), i=1,n+1$. 30a function value $f_i=f(x_i), i=1,n+1$.
9 31
@@ -107,7 +129,7 @@ entirely determined from the initial simplex.
107\label{algo-spendley} 129\label{algo-spendley}
108\end{figure} 130\end{figure}
109 131
110\section{Geometric analysis} 132\subsection{Geometric analysis}
111 133
112The figure \ref{fig-spendley-moves} presents the various moves of the 134The figure \ref{fig-spendley-moves} presents the various moves of the
113simplex in the Spendley et al. algorithm. 135simplex in the Spendley et al. algorithm.
@@ -120,7 +142,7 @@ simplex in the Spendley et al. algorithm.
120\label{fig-spendley-moves} 142\label{fig-spendley-moves}
121\end{figure} 143\end{figure}
122 144
123The various situations in which these moves are chosen are 145The various situations in which these moves are performed are
124presented in figures \ref{fig-spendley-moves-reflect}, \ref{fig-spendley-moves-reflect2} 146presented in figures \ref{fig-spendley-moves-reflect}, \ref{fig-spendley-moves-reflect2}
125and \ref{fig-spendley-moves-shrink}. 147and \ref{fig-spendley-moves-shrink}.
126 148
@@ -136,7 +158,7 @@ a shrink step is necessary, as presented in figure \ref{fig-spendley-moves-shrin
136\begin{center} 158\begin{center}
137\includegraphics[width=10cm]{spendley-steps-reflect.png} 159\includegraphics[width=10cm]{spendley-steps-reflect.png}
138\end{center} 160\end{center}
139\caption{Spendley et al. simplex moves - reflection with respect to highest point} 161\caption{Spendley et al. simplex moves -- Reflection with respect to highest point}
140\label{fig-spendley-moves-reflect} 162\label{fig-spendley-moves-reflect}
141\end{figure} 163\end{figure}
142 164
@@ -144,7 +166,7 @@ a shrink step is necessary, as presented in figure \ref{fig-spendley-moves-shrin
144\begin{center} 166\begin{center}
145\includegraphics[width=10cm]{spendley-steps-reflect2.png} 167\includegraphics[width=10cm]{spendley-steps-reflect2.png}
146\end{center} 168\end{center}
147\caption{Spendley et al. simplex moves - reflection with respect to next-to-highest point. 169\caption{Spendley et al. simplex moves -- Reflection with respect to next-to-highest point.
148It may happen that the next iteration is a shrink step.} 170It may happen that the next iteration is a shrink step.}
149\label{fig-spendley-moves-reflect2} 171\label{fig-spendley-moves-reflect2}
150\end{figure} 172\end{figure}
@@ -161,13 +183,13 @@ optimum is searched.
161\begin{center} 183\begin{center}
162\includegraphics[width=10cm]{spendley-steps-shrink.png} 184\includegraphics[width=10cm]{spendley-steps-shrink.png}
163\end{center} 185\end{center}
164\caption{Spendley et al. simplex moves - shrink.} 186\caption{Spendley et al. simplex moves -- Shrink.}
165\label{fig-spendley-moves-shrink} 187\label{fig-spendley-moves-shrink}
166\end{figure} 188\end{figure}
167 189
168\subsection{Termination criteria} 190%% \subsection{Termination criteria}
169 191
170TODO... 192%% TODO...
171 193
172\section{Numerical experiments} 194\section{Numerical experiments}
173 195
@@ -191,6 +213,32 @@ with respect to the size of the initial simplex
191\end{eqnarray} 213\end{eqnarray}
192 214
193The initial simplex is a regular simplex with length unity. 215The initial simplex is a regular simplex with length unity.
216
217The following Scilab script performs the optimization.
218
219\lstset{language=scilabscript}
220\begin{lstlisting}
221function y = quadratic (x)
222 y = x(1)^2 + x(2)^2 - x(1) * x(2);
223endfunction
224nm = neldermead_new ();
225nm = neldermead_configure(nm,"-numberofvariables",2);
226nm = neldermead_configure(nm,"-function",quadratic);
227nm = neldermead_configure(nm,"-x0",[2.0 2.0]');
228nm = neldermead_configure(nm,"-maxiter",100);
229nm = neldermead_configure(nm,"-maxfunevals",300);
230nm = neldermead_configure(nm,"-tolxmethod","disabled");
231nm = neldermead_configure(nm,"-tolsimplexizerelative",1.e-8);
232nm = neldermead_configure(nm,"-simplex0method","spendley");
233nm = neldermead_configure(nm,"-method","fixed");
234nm = neldermead_configure(nm,"-verbose",1);
235nm = neldermead_configure(nm,"-verbosetermination",0);
236nm = neldermead_search(nm);
237neldermead_display(nm);
238nm = neldermead_destroy(nm);
239\end{lstlisting}
240
241
194The numerical results are presented in table \ref{fig-spendley-numexp1-table}. 242The numerical results are presented in table \ref{fig-spendley-numexp1-table}.
195 243
196\begin{figure}[htbp] 244\begin{figure}[htbp]
@@ -214,7 +262,6 @@ $f(x_1,x_2) = x_1^2 + x_2^2 - x_1 x_2$}
214\label{fig-spendley-numexp1-table} 262\label{fig-spendley-numexp1-table}
215\end{figure} 263\end{figure}
216 264
217
218The various simplices generated during the iterations are 265The various simplices generated during the iterations are
219presented in figure \ref{fig-spendley-numexp1-historysimplex}. 266presented in figure \ref{fig-spendley-numexp1-historysimplex}.
220The method use reflections in the early iterations. Then there 267The method use reflections in the early iterations. Then there
@@ -224,9 +271,9 @@ been discussed.
224 271
225\begin{figure} 272\begin{figure}
226\begin{center} 273\begin{center}
227\includegraphics[width=10cm]{quad2bis-spendley-simplexcontours.png} 274\includegraphics[width=15cm]{quad2bis-spendley-simplexcontours.png}
228\end{center} 275\end{center}
229\caption{Spendley et al. numerical experiment -- history of simplex} 276\caption{Spendley et al. numerical experiment -- History of simplex}
230\label{fig-spendley-numexp1-historysimplex} 277\label{fig-spendley-numexp1-historysimplex}
231\end{figure} 278\end{figure}
232 279
@@ -238,7 +285,7 @@ corresponds to a shrink in the algorithm.
238\begin{center} 285\begin{center}
239\includegraphics[width=10cm]{quad2bis-spendley-history-sigma.png} 286\includegraphics[width=10cm]{quad2bis-spendley-history-sigma.png}
240\end{center} 287\end{center}
241\caption{Spendley et al. numerical experiment -- history of length of simplex} 288\caption{Spendley et al. numerical experiment -- History of logarithm of the size of the simplex}
242\label{fig-spendley-numexp1-sigma} 289\label{fig-spendley-numexp1-sigma}
243\end{figure} 290\end{figure}
244 291
@@ -250,7 +297,7 @@ figure \ref{fig-spendley-numexp1-logfopt}.
250\begin{center} 297\begin{center}
251\includegraphics[width=10cm]{quad2bis-spendley-history-logfopt.png} 298\includegraphics[width=10cm]{quad2bis-spendley-history-logfopt.png}
252\end{center} 299\end{center}
253\caption{Spendley et al. numerical experiment -- history of logarithm of function} 300\caption{Spendley et al. numerical experiment -- History of logarithm of function}
254\label{fig-spendley-numexp1-logfopt} 301\label{fig-spendley-numexp1-logfopt}
255\end{figure} 302\end{figure}
256 303
@@ -269,6 +316,36 @@ to solve with the simplex algorithm.
269We set the maximum number of function evaluations to 400. 316We set the maximum number of function evaluations to 400.
270The initial simplex is a regular simplex with length unity. 317The initial simplex is a regular simplex with length unity.
271 318
319The following Scilab script uses the neldermead algorithm to perform the
320optimization.
321
322\lstset{language=scilabscript}
323\begin{lstlisting}
324function y = quadratic (x)
325 y = 100 * x(1)^2 + x(2)^2;
326endfunction
327nm = nmplot_new ();
328nm = nmplot_configure(nm,"-numberofvariables",2);
329nm = nmplot_configure(nm,"-function",quadratic);
330nm = nmplot_configure(nm,"-x0",[10.0 10.0]');
331nm = nmplot_configure(nm,"-maxiter",400);
332nm = nmplot_configure(nm,"-maxfunevals",400);
333nm = nmplot_configure(nm,"-tolxmethod","disabled");
334nm = nmplot_configure(nm,"-tolsimplexizerelative",1.e-8);
335nm = nmplot_configure(nm,"-simplex0method","spendley");
336nm = nmplot_configure(nm,"-method","fixed");
337nm = nmplot_configure(nm,"-verbose",1);
338nm = nmplot_configure(nm,"-verbosetermination",0);
339nm = nmplot_configure(nm,"-simplexfn","rosenbrock.fixed.history.simplex.txt");
340nm = nmplot_configure(nm,"-fbarfn","rosenbrock.fixed.history.fbar.txt");
341nm = nmplot_configure(nm,"-foptfn","rosenbrock.fixed.history.fopt.txt");
342nm = nmplot_configure(nm,"-sigmafn","rosenbrock.fixed.history.sigma.txt");
343nm = nmplot_search(nm);
344nmplot_display(nm);
345nm = nmplot_destroy(nm);
346\end{lstlisting}
347
348
272The numerical results are presented in table \ref{fig-spendley-numexp1-table}, 349The numerical results are presented in table \ref{fig-spendley-numexp1-table},
273where the experiment is presented for $a=100$. One can check that the 350where the experiment is presented for $a=100$. One can check that the
274number of function evaluation is equal to its maximum limit, even if the value of the 351number of function evaluation is equal to its maximum limit, even if the value of the
@@ -307,9 +384,9 @@ which can vary its size, but not its shape.
307 384
308\begin{figure} 385\begin{figure}
309\begin{center} 386\begin{center}
310\includegraphics[width=10cm]{quad2-spendley-simplexcontours.png} 387\includegraphics[width=15cm]{quad2-spendley-simplexcontours.png}
311\end{center} 388\end{center}
312\caption{Spendley et al. numerical experiment with $f(x_1,x_2) = (a * x_1)^2 + x_2^2$ and $a=100$ -- history of simplex} 389\caption{Spendley et al. numerical experiment with $f(x_1,x_2) = a x_1^2 + x_2^2$ and $a=100$ -- History of simplex}
313\label{fig-spendley-numexp2-historysimplex} 390\label{fig-spendley-numexp2-historysimplex}
314\end{figure} 391\end{figure}
315 392
@@ -342,70 +419,160 @@ $10000.0$ & 400 & $56.08$ \\
342 419
343In this section, we try to study the convergence of the 420In this section, we try to study the convergence of the
344Spendley et al. algorithm with respect to the number of variables. 421Spendley et al. algorithm with respect to the number of variables.
345The function we try to minimize is the following quadratic 422The function we try to minimize is the following quadratic function
346in n-dimensions 423in $n$-dimensions
347\begin{eqnarray} 424\begin{eqnarray}
348\label{quadratic-sp-function3} 425\label{quadratic-sp-function3}
349f(x_1,x_2) = \sum_{i=1,n} x_i^2. 426f(\bx) = \sum_{i=1,n} x_i^2.
350\end{eqnarray} 427\end{eqnarray}
351 428
352The initial simplex is a regular simplex with length unity.
353The initial guess is at 0 so that this vertex is never updated 429The initial guess is at 0 so that this vertex is never updated
354during the iterations. 430during the iterations.
431The initial simplex is computed with a random number generator.
432The first vertex of the initial simplex is the origin.
433The other vertices are uniform in the $[-1,1]$ interval.
434for $i = 2, 2, \ldots , n+1$.
435An absolute termination criteria on the size of the simplex is used.
436More precisely, the method was stopped when $\sigma(Sk) \leq 10^{-8}$ is satisfied.
355 437
356For this test, we compute the rate of convergence as presented 438For this test, we compute the rate of convergence as presented
357in Han \& Neuman. This rate is defined as 439in Han \& Neuman \cite{HanNeumann2006}. This rate is defined as
358
359\begin{eqnarray} 440\begin{eqnarray}
360\label{rho-sp-rate-convergence} 441\label{rho-sp-rate-convergence}
361\rho(S_0,n) = \textrm{lim sup}_{k\rightarrow \infty} 442\rho(S_0,n) = \textrm{lim sup}_{k\rightarrow \infty}
362\left(\sum_{i=0,k-1} \frac{\sigma(S_{i+1}}{\sigma(S_i}\right)^{1/k} 443\left(\prod_{i=0,k-1} \frac{\sigma(S_{i+1})}{\sigma(S_i)}\right)^{1/k},
363\end{eqnarray} 444\end{eqnarray}
364 445where $k$ is the number of iterations.
365That definition can be viewed as the geometric mean of the ratio of the 446That definition can be viewed as the geometric mean of the ratio of the
366oriented lengths between successive simplices and the minimizer 0. 447oriented lengths between successive simplices and the minimizer 0.
367This definition implies 448This definition implies
368
369\begin{eqnarray} 449\begin{eqnarray}
370\label{rho-sp-rate-convergence2} 450\label{rho-sp-rate-convergence2}
371\rho(S_0,n) = \textrm{lim sup}_{k\rightarrow \infty} 451\rho(S_0,n) = \textrm{lim sup}_{k\rightarrow \infty}
372\left( \frac{\sigma(S_{k+1}}{\sigma(S_0}\right)^{1/k} 452\left(\frac{\sigma(S_k)}{\sigma(S_0)}\right)^{1/k},
453\end{eqnarray}
454
455If $k$ is the number of iterations required to obtain convergence, as
456indicated by the termination criteria, the rate of convergence is practically computed as
457\begin{eqnarray}
458\rho(S_0,n,k) = \left( \frac{\sigma(S_{k})}{\sigma(S_0)}\right)^{1/k}
373\end{eqnarray} 459\end{eqnarray}
374 460
375The figure \ref{fig-sp-numexp3-dimension} presents the results of this
376experiment for $n=1,20$.
377 461
378The number and kids of performed steps are presented in figure \ref{fig-sp-numexp3-nbsteps}. 462\lstset{language=scilabscript}
379It must be noticed that reflection step occurs rarely during the iterations : the algorithm mostly performs 463\begin{lstlisting}
380shrink steps. 464function y = quadratic (x)
465 y = x(:).' * x(:);
466endfunction
467//
468// myoutputcmd --
469// This command is called back by the Nelder-Mead
470// algorithm.
471// Arguments
472// state : the current state of the algorithm
473// "init", "iter", "done"
474// data : the data at the current state
475// This is a tlist with the following entries:
476// * x : the optimal vector of parameters
477// * fval : the minimum function value
478// * simplex : the simplex, as a simplex object
479// * iteration : the number of iterations performed
480// * funccount : the number of function evaluations
481// * step : the type of step in the previous iteration
482//
483function myoutputcmd ( state , data , step )
484 global STEP_COUNTER
485 STEP_COUNTER(step) = STEP_COUNTER(step) + 1
486endfunction
487
488// OptimizeHanNeumann --
489// Perform the optimization and returns the object
490// Arguments
491// N : the dimension
492function nm = OptimizeHanNeumann ( N )
493 global STEP_COUNTER
494 STEP_COUNTER("init") = 0;
495 STEP_COUNTER("done") = 0;
496 STEP_COUNTER("reflection") = 0;
497 STEP_COUNTER("expansion") = 0;
498 STEP_COUNTER("insidecontraction") = 0;
499 STEP_COUNTER("outsidecontraction") = 0;
500 STEP_COUNTER("expansion") = 0;
501 STEP_COUNTER("shrink") = 0;
502 STEP_COUNTER("reflectionnext") = 0;
503
504 x0 = zeros(N,1);
505 nm = neldermead_new ();
506 nm = neldermead_configure(nm,"-numberofvariables",N);
507 nm = neldermead_configure(nm,"-function",quadratic);
508 nm = neldermead_configure(nm,"-x0",x0);
509 nm = neldermead_configure(nm,"-maxiter",10000);
510 nm = neldermead_configure(nm,"-maxfunevals",10000);
511 nm = neldermead_configure(nm,"-tolxmethod","disabled");
512 nm = neldermead_configure(nm,"-tolsimplexizeabsolute",1.e-8);
513 nm = neldermead_configure(nm,"-tolsimplexizerelative",0);
514 nm = neldermead_configure(nm,"-simplex0method","given");
515 coords0(1,1:N) = zeros(1,N);
516 coords0(2:N+1,1:N) = 2 * rand(N,N) - 1;
517 nm = neldermead_configure(nm,"-coords0",coords0);
518 nm = neldermead_configure(nm,"-method","fixed");
519 nm = neldermead_configure(nm,"-verbose",0);
520 nm = neldermead_configure(nm,"-verbosetermination",0);
521 nm = neldermead_configure(nm,"-outputcommand",myoutputcmd);
522 //
523 // Perform optimization
524 //
525 nm = neldermead_search(nm);
526endfunction
527
528for N = 1:10
529 nm = OptimizeHanNeumann ( N );
530 niter = neldermead_get ( nm , "-iterations" );
531 funevals = neldermead_get ( nm , "-funevals" );
532 simplex0 = neldermead_get ( nm , "-simplex0" );
533 sigma0 = optimsimplex_size ( simplex0 , "sigmaplus" );
534 simplexopt = neldermead_get ( nm , "-simplexopt" );
535 sigmaopt = optimsimplex_size ( simplexopt , "sigmaplus" );
536 rho = ( sigmaopt / sigma0 ) ^ ( 1 / niter );
537 //mprintf ( "%d %d %d %e\n" , N , funevals , niter , rho );
538 mprintf("%d %s\n",N, strcat(string(STEP_COUNTER)," "))
539 nm = neldermead_destroy(nm);
540end
541
542\end{lstlisting}
543
544The figure \ref{fig-sp-numexp3-nbsteps} presents the type of
545steps which are performed for each number of variables.
546We see that the algorithm mostly performs shrink steps.
381 547
382\begin{figure}[htbp] 548\begin{figure}[htbp]
383\begin{center} 549\begin{center}
384\begin{tiny} 550\begin{tiny}
385\begin{tabular}{|l|l|l|l|} 551\begin{tabular}{|l|l|l|l|l|}
386\hline 552\hline
387$n$ & \# Reflections & \# Reflection & \#Shrink\\ 553$n$ & \#Iterations & \# Reflections & \# Reflection & \#Shrink\\
388 & / High & / Next to High & \\ 554 & & / High & / Next to High & \\
389\hline 555\hline
3901 & 0 & 0 & 27\\ 5561 & 27 & 0 & 0 & 26\\
3912 & 0 & 0 & 27\\ 5572 & 28 & 0 & 0 & 27\\
3923 & 1 & 0 & 27\\ 5583 & 30 & 2 & 0 & 27\\
3934 & 5 & 1 & 27\\ 5594 & 31 & 1 & 1 & 28\\
3945 & 0 & 0 & 27\\ 5605 & 29 & 0 & 0 & 28\\
3956 & 6 & 0 & 27\\ 5616 & 31 & 2 & 0 & 28\\
3967 & 4 & 0 & 27\\ 5627 & 29 & 0 & 0 & 28\\
3978 & 0 & 0 & 27\\ 5638 & 29 & 0 & 0 & 28\\
3989 & 12 & 1 & 27\\ 5649 & 29 & 0 & 0 & 28\\
39910 & 0 & 0 & 27\\ 56510 & 29 & 0 & 0 & 28\\
40011 & 0 & 0 & 27\\ 56611 & 29 & 0 & 0 & 28\\
40112 & 14 & 0 & 27\\ 56712 & 29 & 0 & 0 & 28\\
40213 & 0 & 0 & 27\\ 56813 & 31 & 0 & 2 & 28\\
40314 & 24 & 3 & 27\\ 56914 & 29 & 0 & 0 & 28\\
40415 & 0 & 0 & 27\\ 57015 & 29 & 0 & 0 & 28\\
40516 & 0 & 0 & 27\\ 57116 & 31 & 0 & 1 & 29\\
40617 & 21 & 0 & 27\\ 57217 & 30 & 0 & 0 & 29\\
40718 & 0 & 0 & 27\\ 57318 & 30 & 0 & 0 & 29\\
40819 & 28 & 0 & 27\\ 57419 & 31 & 0 & 1 & 29\\
57520 & 32 & 2 & 0 & 29\\
409\hline 576\hline
410\end{tabular} 577\end{tabular}
411\end{tiny} 578\end{tiny}
@@ -415,9 +582,12 @@ and kinds of steps performed}
415\label{fig-sp-numexp3-nbsteps} 582\label{fig-sp-numexp3-nbsteps}
416\end{figure} 583\end{figure}
417 584
418One can check that the number of function evaluations 585The figure \ref{fig-sp-numexp3-dimension} presents the number of function
586evaluations depending on the number of variables.
587
588One can see that the number of function evaluations
419increases approximately linearily with the dimension of the problem in 589increases approximately linearily with the dimension of the problem in
420figure \ref{fig-sp-numexp3-fvn}. A rough rule of thumb is that, for $n=1,19$, 590figure \ref{fig-sp-numexp3-fvn}. A rough rule of thumb is that, for $n=1,20$,
421the number of function evaluations is equal to $30n$. 591the number of function evaluations is equal to $30n$.
422This test is in fact the best that we can expect from this algorithm : since 592This test is in fact the best that we can expect from this algorithm : since
423most iterations are shrink steps, most iterations improves the function value. 593most iterations are shrink steps, most iterations improves the function value.
@@ -427,27 +597,29 @@ most iterations are shrink steps, most iterations improves the function value.
427\begin{tiny} 597\begin{tiny}
428\begin{tabular}{|l|l|l|l|} 598\begin{tabular}{|l|l|l|l|}
429\hline 599\hline
430$n$ & Function evaluations & Iterations & $\rho(S_0,n)$\\ 600$n$ & Function & Iterations & $\rho(S_0,n)$\\
601 & Evaluations & & \\
431\hline 602\hline
4321 & 83 & 28 & 0.5125321059829373\\ 6031 & 81 & 27 & 0.513002 \\
4332 & 111 & 28 & 0.5125321059829373\\ 6042 & 112 & 28 & 0.512532 \\
4343 & 140 & 29 & 0.52448212766151725\\ 6053 & 142 & 29 & 0.524482 \\
4354 & 174 & 34 & 0.57669577295965202\\ 6064 & 168 & 28 & 0.512532 \\
4365 & 195 & 28 & 0.5125321059829373\\ 6075 & 206 & 31 & 0.534545 \\
4376 & 229 & 34 & 0.57669577295965202\\ 6086 & 232 & 29 & 0.512095 \\
4387 & 255 & 32 & 0.55719337129794622\\ 6097 & 262 & 30 & 0.523127 \\
4398 & 279 & 28 & 0.5125321059829373\\ 6108 & 292 & 30 & 0.523647 \\
4409 & 321 & 41 & 0.63352059021162177\\ 6119 & 321 & 30 & 0.523647 \\
44110 & 335 & 28 & 0.5125321059829373\\ 61210 & 348 & 29 & 0.512095 \\
44211 & 363 & 28 & 0.5125321059829373\\ 61311 & 377 & 29 & 0.512095 \\
44312 & 405 & 42 & 0.64044334488213628\\ 61412 & 406 & 29 & 0.512095 \\
44413 & 419 & 28 & 0.5125321059829373\\ 61513 & 435 & 29 & 0.512095 \\
44514 & 477 & 55 & 0.71157656804932146\\ 61614 & 464 & 29 & 0.512095 \\
44615 & 475 & 28 & 0.5125321059829373\\ 61715 & 493 & 29 & 0.512095 \\
44716 & 503 & 28 & 0.5125321059829373\\ 61816 & 540 & 30 & 0.511687 \\
44817 & 552 & 49 & 0.68253720379799854\\ 61917 & 570 & 30 & 0.511687 \\
44918 & 559 & 28 & 0.5125321059829373\\ 62018 & 600 & 30 & 0.511687 \\
45019 & 615 & 56 & 0.71591347660379834\\ 62119 & 630 & 30 & 0.511687 \\
62220 & 660 & 30 & 0.511687 \\
451\hline 623\hline
452\end{tabular} 624\end{tabular}
453\end{tiny} 625\end{tiny}
@@ -460,26 +632,16 @@ $n$ & Function evaluations & Iterations & $\rho(S_0,n)$\\
460\begin{center} 632\begin{center}
461\includegraphics[width=10cm]{spendley-dimension-nfevals.png} 633\includegraphics[width=10cm]{spendley-dimension-nfevals.png}
462\end{center} 634\end{center}
463\caption{Spendley et al. numerical experiment -- number of function evaluations 635\caption{Spendley et al. numerical experiment -- Number of function evaluations
464depending on the number of variables} 636depending on the number of variables}
465\label{fig-sp-numexp3-fvn} 637\label{fig-sp-numexp3-fvn}
466\end{figure} 638\end{figure}
467 639
468The figure \ref{fig-nm-numexp3-rho} presents the rate of convergence 640The table \ref{fig-sp-numexp3-dimension} also shows the interesting
469depending on the number of variables. The figure shows that 641fact that the convergence rate is almost constant and
470the rate of convergence rapidly gets close to 1 when the number 642very close to 1. This is a consequence of the shrink steps,
471of variables increases. That shows that the rate of convergence 643which are dividing the size of the simplex at each iterations by 2.
472is slower and slower as the number of variables increases, as 644Therefore, the convergence rate is close to $1/2$.
473explained by Han \& Neuman.
474
475\begin{figure}
476\begin{center}
477\includegraphics[width=10cm]{spendley-dimension-rho.png}
478\end{center}
479\caption{Spendley et al. numerical experiment -- rate of convergence
480depending on the number of variables}
481\label{fig-sp-numexp3-rho}
482\end{figure}
483 645
484\section{Conclusion} 646\section{Conclusion}
485 647
@@ -492,4 +654,8 @@ This limitation occurs with even moderate badly scaled
492functions and generates a very slow method in these 654functions and generates a very slow method in these
493cases. 655cases.
494 656
657In the last experiment, we have explored what happens when the number of
658iterations is increasing. The rate of convergence in this case is close to $1/2$
659and the number of function evaluations is a linear function of the number
660of variables (approximately $30n$ in this case).
495 661
diff --git a/scilab_doc/neldermead/neldermead-simplex-so.aux b/scilab_doc/neldermead/neldermead-simplex-so.aux
new file mode 100644
index 0000000..3d3a282
--- /dev/null
+++ b/scilab_doc/neldermead/neldermead-simplex-so.aux
@@ -0,0 +1,28 @@
1\relax
2\ifx\hyper@anchor\@undefined
3\global \let \oldcontentsline\contentsline
4\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
5\global \let \oldnewlabel\newlabel
6\gdef \newlabel#1#2{\newlabelxx{#1}#2}
7\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
8\AtEndDocument{\let \contentsline\oldcontentsline
9\let \newlabel\oldnewlabel}
10\else
11\global \let \hyper@last\relax
12\fi
13
14\@input{section-simplex.aux}
15\bibstyle{plain}
16\bibdata{neldermead}
17\bibcite{Box1965}{{1}{}{{}}{{}}}
18\bibcite{Fan2002}{{2}{}{{}}{{}}}
19\bibcite{Kelley1999}{{3}{}{{}}{{}}}
20\bibcite{lagarias:112}{{4}{}{{}}{{}}}
21\bibcite{nla.cat-vn1060620}{{5}{}{{}}{{}}}
22\bibcite{citeulike:3009487}{{6}{}{{}}{{}}}
23\bibcite{parkinson1972}{{7}{}{{}}{{}}}
24\bibcite{NumericalRecipes}{{8}{}{{}}{{}}}
25\bibcite{Spendley1962}{{9}{}{{}}{{}}}
26\bibcite{Torczon89multi-directionalsearch}{{10}{}{{}}{{}}}
27\@writefile{toc}{\contentsline {chapter}{Bibliography}{9}{equation.1.3.19}}
28\global\NAT@numberstrue
diff --git a/scilab_doc/neldermead/neldermead-simplex-so.bbl b/scilab_doc/neldermead/neldermead-simplex-so.bbl
new file mode 100644
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@@ -0,0 +1,63 @@
1\begin{thebibliography}{10}
2
3\bibitem{Box1965}
4M.~J. Box.
5\newblock A new method of constrained optimization and a comparison with other
6 methods.
7\newblock {\em The Computer Journal}, pages 42--52, 1965.
8
9\bibitem{Fan2002}
10Ellen Fan.
11\newblock Global optimization of lennard-jones atomic clusters.
12\newblock Technical report, McMaster University, February 2002.
13
14\bibitem{Kelley1999}
15C.~T. Kelley.
16\newblock {\em Iterative Methods for Optimization}, volume~19.
17\newblock SIAM Frontiers in Applied Mathematics, 1999.
18\newblock \url{http://www.siam.org/books/textbooks/fr18_book.pdf}.
19
20\bibitem{lagarias:112}
21Jeffrey~C. Lagarias, James~A. Reeds, Margaret~H. Wright, and Paul~E. Wright.
22\newblock Convergence properties of the nelder--mead simplex method in low
23 dimensions.
24\newblock {\em SIAM Journal on Optimization}, 9(1):112--147, 1998.
25\newblock \url{http://link.aip.org/link/?SJE/9/112/1}.
26
27\bibitem{nla.cat-vn1060620}
28J.~C. Nash.
29\newblock {\em Compact numerical methods for computers : linear algebra and
30 function minimisation}.
31\newblock Hilger, Bristol, 1979.
32
33\bibitem{citeulike:3009487}
34J.~A. Nelder and R.~Mead.
35\newblock A simplex method for function minimization.
36\newblock {\em The Computer Journal}, 7(4):308--313, January 1965.
37\newblock \url{http://dx.doi.org/10.1093/comjnl/7.4.308}.
38
39\bibitem{parkinson1972}
40Parkinson and Hutchinson.
41\newblock An investigation into the efficiency of variants on the simplex
42 method.
43\newblock {\em F. A. Lootsma, editor, Numerical Methods for Non-linear
44 Optimization}, pages 115--135, 1972.
45
46\bibitem{NumericalRecipes}
47W.~H. Press, Saul~A. Teukolsky, William~T. Vetterling, and Brian~P. Flannery.
48\newblock {\em Numerical Recipes in C, Second Edition}.
49\newblock 1992.
50
51\bibitem{Spendley1962}
52W.~Spendley, G.~R. Hext, and F.~R. Himsworth.
53\newblock Sequential application of simplex designs in optimisation and
54 evolutionary operation.
55\newblock {\em Technometrics}, 4(4):441--461, 1962.
56
57\bibitem{Torczon89multi-directionalsearch}
58Virginia~Joanne Torczon.
59\newblock Multi-directional search: A direct search algorithm for parallel
60 machines.
61\newblock Technical report, Rice University, 1989.
62
63\end{thebibliography}
diff --git a/scilab_doc/neldermead/neldermead-simplex-so.blg b/scilab_doc/neldermead/neldermead-simplex-so.blg
new file mode 100644
index 0000000..6f8acfe
--- /dev/null
+++ b/scilab_doc/neldermead/neldermead-simplex-so.blg
@@ -0,0 +1,6 @@
1This is BibTeX, Version 0.99cThe top-level auxiliary file: neldermead-simplex-so.aux
2A level-1 auxiliary file: section-simplex.aux
3The style file: plain.bst
4Database file #1: neldermead.bib
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diff --git a/scilab_doc/neldermead/neldermead-simplex-so.out b/scilab_doc/neldermead/neldermead-simplex-so.out
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@@ -0,0 +1,10 @@
1\BOOKMARK [0][-]{chapter.1}{Simplex theory}{}
2\BOOKMARK [1][-]{section.1.1}{The simplex}{chapter.1}
3\BOOKMARK [1][-]{section.1.2}{The size of the simplex}{chapter.1}
4\BOOKMARK [1][-]{section.1.3}{The initial simplex}{chapter.1}
5\BOOKMARK [2][-]{subsection.1.3.1}{Importance of the initial simplex}{section.1.3}
6\BOOKMARK [2][-]{subsection.1.3.2}{Spendley's et al simplex}{section.1.3}
7\BOOKMARK [2][-]{subsection.1.3.3}{Simplex along the axes}{section.1.3}
8\BOOKMARK [2][-]{subsection.1.3.4}{Randomized bounds}{section.1.3}
9\BOOKMARK [2][-]{subsection.1.3.5}{Pfeffer's method}{section.1.3}
10\BOOKMARK [0][-]{equation.1.3.19}{Bibliography}{}
diff --git a/scilab_doc/neldermead/neldermead-simplex-so.pdf b/scilab_doc/neldermead/neldermead-simplex-so.pdf
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@@ -48,7 +48,7 @@ $$\fbox{$
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diff --git a/scilab_doc/neldermead/neldermead-simplex-so.toc b/scilab_doc/neldermead/neldermead-simplex-so.toc
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@@ -0,0 +1,10 @@
1\contentsline {chapter}{\numberline {1}Simplex theory}{3}{chapter.1}
2\contentsline {section}{\numberline {1.1}The simplex}{3}{section.1.1}
3\contentsline {section}{\numberline {1.2}The size of the simplex}{4}{section.1.2}
4\contentsline {section}{\numberline {1.3}The initial simplex}{4}{section.1.3}
5\contentsline {subsection}{\numberline {1.3.1}Importance of the initial simplex}{5}{subsection.1.3.1}
6\contentsline {subsection}{\numberline {1.3.2}Spendley's et al simplex}{6}{subsection.1.3.2}
7\contentsline {subsection}{\numberline {1.3.3}Simplex along the axes}{6}{subsection.1.3.3}
8\contentsline {subsection}{\numberline {1.3.4}Randomized bounds}{7}{subsection.1.3.4}
9\contentsline {subsection}{\numberline {1.3.5}Pfeffer's method}{8}{subsection.1.3.5}
10\contentsline {chapter}{Bibliography}{9}{equation.1.3.19}
diff --git a/scilab_doc/neldermead/neldermead-spendley-so.aux b/scilab_doc/neldermead/neldermead-spendley-so.aux
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diff --git a/scilab_doc/neldermead/neldermead-spendley-so.bbl b/scilab_doc/neldermead/neldermead-spendley-so.bbl
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@@ -0,0 +1,14 @@
1\begin{thebibliography}{1}
2
3\bibitem{HanNeumann2006}
4Lixing Han and Michael Neumann.
5\newblock Effect of dimensionality on the nelder-mead simplex method.
6\newblock {\em Optimization Methods and Software}, 21(1):1--16, 2006.
7
8\bibitem{Spendley1962}
9W.~Spendley, G.~R. Hext, and F.~R. Himsworth.
10\newblock Sequential application of simplex designs in optimisation and
11 evolutionary operation.
12\newblock {\em Technometrics}, 4(4):441--461, 1962.
13
14\end{thebibliography}
diff --git a/scilab_doc/neldermead/neldermead-spendley-so.blg b/scilab_doc/neldermead/neldermead-spendley-so.blg
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diff --git a/scilab_doc/neldermead/neldermead-spendley-so.log b/scilab_doc/neldermead/neldermead-spendley-so.log
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diff --git a/scilab_doc/neldermead/neldermead-spendley-so.out b/scilab_doc/neldermead/neldermead-spendley-so.out
new file mode 100644
index 0000000..8a243e4
--- /dev/null
+++ b/scilab_doc/neldermead/neldermead-spendley-so.out
@@ -0,0 +1,10 @@
1\BOOKMARK [0][-]{chapter.1}{Spendley's et al. method}{}
2\BOOKMARK [1][-]{section.1.1}{Analysis}{chapter.1}
3\BOOKMARK [2][-]{subsection.1.1.1}{Algorithm}{section.1.1}
4\BOOKMARK [2][-]{subsection.1.1.2}{Geometric analysis}{section.1.1}
5\BOOKMARK [1][-]{section.1.2}{Numerical experiments}{chapter.1}
6\BOOKMARK [2][-]{subsection.1.2.1}{Quadratic function}{section.1.2}
7\BOOKMARK [2][-]{subsection.1.2.2}{Badly scaled quadratic function}{section.1.2}
8\BOOKMARK [2][-]{subsection.1.2.3}{Sensitivity to dimension}{section.1.2}
9\BOOKMARK [1][-]{section.1.3}{Conclusion}{chapter.1}
10\BOOKMARK [0][-]{section.1.3}{Bibliography}{}
diff --git a/scilab_doc/neldermead/neldermead-spendley-so.pdf b/scilab_doc/neldermead/neldermead-spendley-so.pdf
new file mode 100644
index 0000000..454e180
--- /dev/null
+++ b/scilab_doc/neldermead/neldermead-spendley-so.pdf
Binary files differ
diff --git a/scilab_doc/neldermead/neldermead-spendley-so.tex b/scilab_doc/neldermead/neldermead-spendley-so.tex
new file mode 100644
index 0000000..d062a3c
--- /dev/null
+++ b/scilab_doc/neldermead/neldermead-spendley-so.tex
@@ -0,0 +1,85 @@
1%
2% neldermead.tex --
3% Some notes about Nelder-Mead algorithms.
4%
5% Copyright 2008-2009 Michael Baudin
6%
7\documentclass[12pt]{report}
8
9\include{macros}
10
11\begin{document}
12%% User defined page headers
13\pagestyle{fancyplain}
14\renewcommand{\chaptermark}[1]{\markboth{\chaptername\ \thechapter. #1}{}}
15\renewcommand{\sectionmark}[1]{\markright{\thesection. #1}}
16\lhead[]{\fancyplain{}{\bfseries\leftmark}}
17\rhead[]{\fancyplain{}{\bfseries\thepage}}
18\cfoot{}
19
20%% User defined figure legends
21\makeatletter
22\def\figurename{{\protect\sc \protect\small\bfseries Fig.}}
23\def\f@ffrench{\protect\figurename\space{\protect\small\bf \thefigure}\space}
24\let\fnum@figure\f@ffrench%
25\let\captionORI\caption
26\def\caption#1{\captionORI{\rm\small #1}}
27\makeatother
28
29%% First page
30\thispagestyle{empty}
31{
32\begin{center}
33%% Comment for DVI
34\includegraphics[height=40mm]{scilab_logo}
35\vskip4cm
36
37%% Empty space between the box and the text
38\fboxsep6mm
39%% Box thickness
40\fboxrule1.3pt
41\Huge
42$$\fbox{$
43 \begin{array}{c}
44 \textbf{Nelder-Mead}\\
45 \textbf{Toolbox Manual}\\
46 \textbf{-- Spendley et al. algorithm --}\\
47 \end{array}
48 $}
49$$
50\end{center}
51\vskip4cm
52
53\normalsize
54
55\begin{flushright}
56Version 0.2 \\
57September 2009
58\end{flushright}
59
60\begin{flushright}
61Micha\"el BAUDIN
62\end{flushright}
63
64\clearpage
65
66%% Table of contents
67\renewcommand{\baselinestretch}{1.30}\small \normalsize
68
69\tableofcontents
70
71\renewcommand{\baselinestretch}{1.18}\small \normalsize
72
73\include{method-spendley}
74
75\clearpage
76
77
78%% Bibliography
79
80\addcontentsline{toc}{chapter}{Bibliography}
81\bibliographystyle{plain}
82\bibliography{neldermead}
83
84\end{document}
85
diff --git a/scilab_doc/neldermead/neldermead-spendley-so.toc b/scilab_doc/neldermead/neldermead-spendley-so.toc
new file mode 100644
index 0000000..b73ff29
--- /dev/null
+++ b/scilab_doc/neldermead/neldermead-spendley-so.toc
@@ -0,0 +1,10 @@
1\contentsline {chapter}{\numberline {1}Spendley's et al. method}{3}{chapter.1}
2\contentsline {section}{\numberline {1.1}Analysis}{3}{section.1.1}
3\contentsline {subsection}{\numberline {1.1.1}Algorithm}{3}{subsection.1.1.1}
4\contentsline {subsection}{\numberline {1.1.2}Geometric analysis}{4}{subsection.1.1.2}
5\contentsline {section}{\numberline {1.2}Numerical experiments}{6}{section.1.2}
6\contentsline {subsection}{\numberline {1.2.1}Quadratic function}{7}{subsection.1.2.1}
7\contentsline {subsection}{\numberline {1.2.2}Badly scaled quadratic function}{9}{subsection.1.2.2}
8\contentsline {subsection}{\numberline {1.2.3}Sensitivity to dimension}{12}{subsection.1.2.3}
9\contentsline {section}{\numberline {1.3}Conclusion}{15}{section.1.3}
10\contentsline {chapter}{Bibliography}{16}{section.1.3}
diff --git a/scilab_doc/neldermead/neldermead.bib b/scilab_doc/neldermead/neldermead.bib
index d2835e9..0ee9803 100644
--- a/scilab_doc/neldermead/neldermead.bib
+++ b/scilab_doc/neldermead/neldermead.bib
@@ -212,9 +212,6 @@ publisher= {}}
212 ISSN = {0010-4620}, 212 ISSN = {0010-4620},
213 bibdate = {Fri Sep 29 08:51:24 MDT 2000}, 213 bibdate = {Fri Sep 29 08:51:24 MDT 2000},
214 bibsource = {http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_04/}, 214 bibsource = {http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_04/},
215 note={\url{http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_04/100416.sgm.abs.html},
216 \url{http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_04/tiff/416.tif},
217 \url{http://www3.oup.co.uk/computer_journal/hdb/Volume_10/Issue_04/tiff/417.tif}},
218 acknowledgement = ack-nhfb, 215 acknowledgement = ack-nhfb,
219} 216}
220 217
@@ -258,8 +255,7 @@ publisher= {}}
258 institution = {Department of Mechanical Engineering, Link\"oping University}, 255 institution = {Department of Mechanical Engineering, Link\"oping University},
259 year = {2001}, 256 year = {2001},
260 note={\url{https://polopoly.liu.se/content/1/c6/10/99/74/phdthesis.pdf}, 257 note={\url{https://polopoly.liu.se/content/1/c6/10/99/74/phdthesis.pdf},
261 \url{http://www.iei.liu.se/machine/johan-olvander/home"l=en}, 258 \url{http://www.iei.liu.se/machine/johan-olvander}}
262 \url{http://www.machine.ikp.liu.se/index.html?/staff/johan/index.html}}
263} 259}
264 260
265@article{Box1965, 261@article{Box1965,
diff --git a/scilab_doc/neldermead/neldermead.tex b/scilab_doc/neldermead/neldermead.tex
index 1b927df..c44550a 100644
--- a/scilab_doc/neldermead/neldermead.tex
+++ b/scilab_doc/neldermead/neldermead.tex
@@ -32,7 +32,7 @@
32\begin{center} 32\begin{center}
33%% Comment for DVI 33%% Comment for DVI
34\includegraphics[height=40mm]{scilab_logo} 34\includegraphics[height=40mm]{scilab_logo}
35\vskip5cm 35\vskip4cm
36 36
37%% Empty space between the box and the text 37%% Empty space between the box and the text
38\fboxsep6mm 38\fboxsep6mm
@@ -47,7 +47,7 @@ $$\fbox{$
47 $} 47 $}
48$$ 48$$
49\end{center} 49\end{center}
50\vskip8cm 50\vskip4cm
51 51
52\normalsize 52\normalsize
53 53
diff --git a/scilab_doc/neldermead/nmbibliography.aux b/scilab_doc/neldermead/nmbibliography.aux
new file mode 100644
index 0000000..833387c
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diff --git a/scilab_doc/neldermead/quad2-spendley-simplexcontours.png b/scilab_doc/neldermead/quad2-spendley-simplexcontours.png
index 990ed24..d89d92c 100644
--- a/scilab_doc/neldermead/quad2-spendley-simplexcontours.png
+++ b/scilab_doc/neldermead/quad2-spendley-simplexcontours.png
Binary files differ
diff --git a/scilab_doc/neldermead/quad2bis-spendley-history-logfopt.png b/scilab_doc/neldermead/quad2bis-spendley-history-logfopt.png
index f819f4b..509d56a 100644
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diff --git a/scilab_doc/neldermead/quad2bis-spendley-history-sigma.png b/scilab_doc/neldermead/quad2bis-spendley-history-sigma.png
index bf093f7..0d20c54 100644
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diff --git a/scilab_doc/neldermead/quad2bis-spendley-simplexcontours.png b/scilab_doc/neldermead/quad2bis-spendley-simplexcontours.png
index 309d738..0ba04df6 100644
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diff --git a/scilab_doc/neldermead/rosenbrock.fixed.history.fbar.txt b/scilab_doc/neldermead/rosenbrock.fixed.history.fbar.txt
new file mode 100644
index 0000000..b3c781d
--- /dev/null
+++ b/scilab_doc/neldermead/rosenbrock.fixed.history.fbar.txt
@@ -0,0 +1,351 @@
1//
2// rosenbrock.fixed.history.fbar.txt--
3// History of the function value average during Nelder-Mead algorithm.
4//
5// Copyright (C) 2008-2009 - INRIA - Michael Baudin
6//
7history = [
80 1.095833e+004
90 1.095833e+004
101 1.095833e+004
112 9.831672e+003
123 9.035590e+003
134 8.016591e+003
145 7.299587e+003
156 6.388247e+003
167 5.750322e+003
178 4.946639e+003
189 4.387793e+003
1910 3.691768e+003
2011 3.212000e+003
2112 2.623633e+003
2213 2.222944e+003
2314 1.742234e+003
2415 1.420625e+003
2516 1.047573e+003
2617 8.050417e+002
2718 5.396472e+002
2819 3.761952e+002
2920 2.184584e+002
3021 1.340852e+002
3122 8.400610e+001
3223 7.871178e+001
3324 6.633892e+001
3425 4.943542e+001
3526 4.461691e+001
3627 4.341508e+001
3728 4.133672e+001
3829 3.962772e+001
3930 3.926530e+001
4031 3.824133e+001
4132 3.802633e+001
4233 3.734488e+001
4334 3.643189e+001
4435 3.564642e+001
4536 3.507595e+001
4637 3.418645e+001
4738 3.395850e+001
4839 3.296497e+001
4940 3.264594e+001
5041 3.199494e+001
5142 3.121641e+001
5243 3.046138e+001
5344 3.002537e+001
5445 2.916632e+001
5546 2.907283e+001
5647 2.810974e+001
5748 2.768669e+001
5849 2.706612e+001
5950 2.642206e+001
6051 2.569747e+001
6152 2.539593e+001
6253 2.456731e+001
6354 2.448677e+001
6455 2.400067e+001
6556 2.314856e+001
6657 2.255843e+001
6758 2.204884e+001
6859 2.135469e+001
6960 2.118761e+001
7061 2.038943e+001
7162 2.020487e+001
7263 1.974921e+001
7364 1.903156e+001
7465 1.847188e+001
7566 1.809675e+001
7667 1.743303e+001
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194185 1.991958e+000
195186 1.947327e+000
196187 1.898733e+000
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200191 1.782761e+000
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203194 1.648709e+000
204195 1.602017e+000
205196 1.587197e+000
206197 1.534004e+000
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209200 1.442523e+000
210201 1.404235e+000
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215206 1.256950e+000
216207 1.227066e+000
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220211 1.087548e+000
221212 1.055639e+000
222213 1.054371e+000
223214 1.040143e+000
224215 1.020205e+000
225216 1.004351e+000
226217 9.897657e-001
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229220 9.439480e-001
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236227 8.574658e-001
237228 8.388369e-001
238229 8.343181e-001
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240231 8.053054e-001
241232 7.904029e-001
242233 7.800191e-001
243234 7.634912e-001
244235 7.584593e-001
245236 7.403059e-001
246237 7.341618e-001
247238 7.213603e-001
248239 7.077257e-001
249240 6.932988e-001
250241 6.850161e-001
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252243 6.681715e-001
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254245 6.405856e-001
255246 6.282597e-001
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263254 5.417393e-001
264255 5.323068e-001
265256 5.188311e-001
266257 5.147504e-001
267258 4.996493e-001
268259 4.956062e-001
269260 4.858570e-001
270261 4.731736e-001
271262 4.617990e-001
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273264 4.414675e-001
274265 4.394878e-001
275266 4.248624e-001
276267 4.191938e-001
277268 4.099202e-001
278269 3.993379e-001
279270 3.884389e-001
280271 3.832084e-001
281272 3.706840e-001
282273 3.703673e-001
283274 3.631947e-001
284275 3.493616e-001
285276 3.405636e-001
286277 3.320823e-001
287278 3.216589e-001
288279 3.185294e-001
289280 3.064806e-001
290281 3.045385e-001
291282 2.978416e-001
292283 2.861094e-001
293284 2.777871e-001
294285 2.714068e-001
295286 2.614590e-001
296287 2.604306e-001
297288 2.488574e-001
298289 2.452899e-001
299290 2.390686e-001
300291 2.294375e-001
301292 2.215907e-001
302293 2.173115e-001
303294 2.078393e-001
304295 2.004868e-001
305296 1.992788e-001
306297 1.946021e-001
307298 1.928778e-001
308299 1.895392e-001
309300 1.861805e-001
310301 1.824355e-001
311302 1.804147e-001
312303 1.762634e-001
313304 1.758770e-001
314305 1.730636e-001
315306 1.688922e-001
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317308 1.628391e-001
318309 1.592129e-001
319310 1.577175e-001
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326317 1.376355e-001
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329320 1.315527e-001
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331322 1.258562e-001
332323 1.228742e-001
333324 1.210913e-001
334325 1.177030e-001
335326 1.172581e-001
336327 1.134634e-001
337328 1.118580e-001
338329 1.094013e-001
339330 1.068057e-001
340331 1.039427e-001
341332 1.026850e-001
342333 9.941561e-002
343334 9.914817e-002
344335 9.721673e-002
345336 9.380842e-002
346337 9.147062e-002
347338 8.940027e-002
348339 8.665613e-002
349340 8.592373e-002
350340 8.592373e-002
351]
diff --git a/scilab_doc/neldermead/rosenbrock.fixed.history.fopt.txt b/scilab_doc/neldermead/rosenbrock.fixed.history.fopt.txt
new file mode 100644
index 0000000..b03c4a9
--- /dev/null
+++ b/scilab_doc/neldermead/rosenbrock.fixed.history.fopt.txt
@@ -0,0 +1,351 @@
1//
2// rosenbrock.fixed.history.fopt.txt--
3// History of the function value optimum during Nelder-Mead algorithm.
4//
5// Copyright (C) 2008-2009 - INRIA - Michael Baudin
6//
7history = [
80 1.010000e+004
90 1.010000e+004
101 1.010000e+004
112 8.750429e+003
123 8.256340e+003
134 7.043005e+003
145 6.599417e+003
156 5.522319e+003
167 5.129230e+003
178 4.188368e+003
189 3.845780e+003
1910 3.041155e+003
2011 2.749066e+003
2112 2.080677e+003
2213 1.839089e+003
2314 1.306937e+003
2415 1.115848e+003
2516 7.199326e+002
2617 5.793442e+002
2718 3.196649e+002
2819 2.295766e+002
2920 1.061338e+002
3021 6.654541e+001
3122 6.654541e+001
3223 6.654541e+001
3324 4.222055e+001
3425 4.222055e+001
3526 4.222055e+001
3627 4.222055e+001
3728 3.852425e+001
3829 3.852425e+001
3930 3.852425e+001
4031 3.703384e+001
4132 3.703384e+001
4233 3.647991e+001
4334 3.578192e+001
4435 3.467743e+001
4536 3.467743e+001
4637 3.311343e+001
4738 3.311343e+001
4839 3.178792e+001
4940 3.178792e+001
5041 3.116041e+001
5142 3.070091e+001
5243 2.952282e+001
5344 2.952282e+001
5445 2.812373e+001
5546 2.812373e+001
5647 2.696313e+001
5748 2.696313e+001
5849 2.626203e+001
5950 2.604102e+001
6051 2.478935e+001
6152 2.478935e+001
6253 2.355517e+001
6354 2.355517e+001
6455 2.333105e+001
6556 2.255947e+001
6657 2.178478e+001
6758 2.178478e+001
6859 2.047701e+001
6960 2.047701e+001
7061 1.940773e+001
7162 1.940773e+001
7263 1.911002e+001
7364 1.857694e+001
7465 1.772866e+001
7566 1.772866e+001
7667 1.658580e+001
7768 1.658580e+001
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7970 1.568142e+001
8071 1.531013e+001
8172 1.501554e+001
8273 1.409367e+001
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8475 1.311571e+001
8576 1.311571e+001
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8980 1.243410e+001
9081 1.237624e+001
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9586 1.137578e+001
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9788 1.087981e+001
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9990 1.044347e+001
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10192 1.006676e+001
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112103 8.424336e+000
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119110 7.220927e+000
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121112 6.848642e+000
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126117 6.282943e+000
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140131 4.639334e+000
141132 4.565049e+000
142133 4.482366e+000
143134 4.457397e+000
144135 4.340304e+000
145136 4.340304e+000
146137 4.213148e+000
147138 4.213148e+000
148139 4.160277e+000
149140 4.100898e+000
150141 4.013616e+000
151142 4.003553e+000
152143 3.881861e+000
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155146 3.765011e+000
156147 3.707541e+000
157148 3.663067e+000
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160151 3.449738e+000
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162153 3.343194e+000
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177168 2.664453e+000
178169 2.627596e+000
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187178 2.235668e+000
188179 2.159801e+000
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190181 2.064673e+000
191182 2.064673e+000
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197188 1.838668e+000
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205196 1.543855e+000
206197 1.469340e+000
207198 1.469340e+000
208199 1.448497e+000
209200 1.409731e+000
210201 1.354477e+000
211202 1.354477e+000
212203 1.275363e+000
213204 1.275363e+000
214205 1.211155e+000
215206 1.211155e+000
216207 1.185712e+000
217208 1.161852e+000
218209 1.101999e+000
219210 1.101999e+000
220211 1.033191e+000
221212 1.033191e+000
222213 1.033191e+000
223214 1.023047e+000
224215 1.004377e+000
225216 9.856302e-001
226217 9.792895e-001
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229220 9.219758e-001
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236227 8.447277e-001
237228 8.173404e-001
238229 8.173404e-001
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243234 7.440957e-001
244235 7.440957e-001
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246237 7.192851e-001
247238 7.056913e-001
248239 6.982008e-001
249240 6.760044e-001
250241 6.760044e-001
251242 6.500439e-001
252243 6.500439e-001
253244 6.439030e-001
254245 6.278099e-001
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256247 6.093023e-001
257248 5.859561e-001
258249 5.859561e-001
259250 5.625722e-001
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261252 5.552815e-001
262253 5.429149e-001
263254 5.270215e-001
264255 5.269839e-001
265256 5.024879e-001
266257 5.024879e-001
267258 4.816807e-001
268259 4.816807e-001
269260 4.732402e-001
270261 4.646000e-001
271262 4.475568e-001
272263 4.475568e-001
273264 4.255999e-001
274265 4.255999e-001
275266 4.073693e-001
276267 4.073693e-001
277268 3.977791e-001
278269 3.928653e-001
279270 3.746723e-001
280271 3.746723e-001
281272 3.552920e-001
282273 3.552920e-001
283274 3.531546e-001
284275 3.396381e-001
285276 3.288980e-001
286277 3.277107e-001
287278 3.083679e-001
288279 3.083679e-001
289280 2.915643e-001
290281 2.915643e-001
291282 2.882770e-001
292283 2.784870e-001
293284 2.665972e-001
294285 2.665972e-001
295286 2.486437e-001
296287 2.486437e-001
297288 2.344167e-001
298289 2.344167e-001
299290 2.299797e-001
300291 2.239161e-001
301292 2.108764e-001
302293 2.108764e-001
303294 1.954996e-001
304295 1.954996e-001
305296 1.954996e-001
306297 1.892086e-001
307298 1.892086e-001
308299 1.854836e-001
309300 1.838492e-001
310301 1.779736e-001
311302 1.779736e-001
312303 1.713951e-001
313304 1.713951e-001
314305 1.695333e-001
315306 1.657483e-001
316307 1.617358e-001
317308 1.610331e-001
318309 1.548699e-001
319310 1.548699e-001
320311 1.489357e-001
321312 1.489357e-001
322313 1.467864e-001
323314 1.439330e-001
324315 1.396331e-001
325316 1.396331e-001
326317 1.334114e-001
327318 1.334114e-001
328319 1.281212e-001
329320 1.281212e-001
330321 1.256846e-001
331322 1.237627e-001
332323 1.191754e-001
333324 1.191754e-001
334325 1.135978e-001
335326 1.135978e-001
336327 1.089519e-001
337328 1.089519e-001
338329 1.062277e-001
339330 1.052375e-001
340331 1.003627e-001
341332 1.003627e-001
342333 9.542932e-002
343334 9.542932e-002
344335 9.456841e-002
345336 9.142752e-002
346337 8.841594e-002
347338 8.835734e-002
348339 8.319509e-002
349340 8.319509e-002
350340 8.319509e-002
351]
diff --git a/scilab_doc/neldermead/rosenbrock.fixed.history.sigma.txt b/scilab_doc/neldermead/rosenbrock.fixed.history.sigma.txt
new file mode 100644
index 0000000..ab0d540
--- /dev/null
+++ b/scilab_doc/neldermead/rosenbrock.fixed.history.sigma.txt
@@ -0,0 +1,351 @@
1//
2// rosenbrock.fixed.history.sigma.txt--
3// History of the maximum of oriented length during Nelder-Mead algorithm.
4//
5// Copyright (C) 2008-2009 - INRIA - Michael Baudin
6//
7history = [
80 1.000000e+000
90 1.000000e+000
101 1.000000e+000
112 1.000000e+000
123 1.000000e+000
134 1.000000e+000
145 1.000000e+000
156 1.000000e+000
167 1.000000e+000
178 1.000000e+000
189 1.000000e+000
1910 1.000000e+000
2011 1.000000e+000
2112 1.000000e+000
2213 1.000000e+000
2314 1.000000e+000
2415 1.000000e+000
2516 1.000000e+000
2617 1.000000e+000
2718 1.000000e+000
2819 1.000000e+000
2920 1.000000e+000
3021 1.000000e+000
3122 1.000000e+000
3223 1.000000e+000
3324 1.000000e+000
3425 5.000000e-001
3526 2.500000e-001
3627 2.500000e-001
3728 2.500000e-001
3829 1.250000e-001
3930 1.250000e-001
4031 1.250000e-001
4132 1.250000e-001
4233 1.250000e-001
4334 1.250000e-001
4435 1.250000e-001
4536 1.250000e-001
4637 1.250000e-001
4738 1.250000e-001
4839 1.250000e-001
4940 1.250000e-001
5041 1.250000e-001
5142 1.250000e-001
5243 1.250000e-001
5344 1.250000e-001
5445 1.250000e-001
5546 1.250000e-001
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351]
diff --git a/scilab_doc/neldermead/rosenbrock.fixed.history.simplex.txt b/scilab_doc/neldermead/rosenbrock.fixed.history.simplex.txt
new file mode 100644
index 0000000..2a35824
--- /dev/null
+++ b/scilab_doc/neldermead/rosenbrock.fixed.history.simplex.txt
@@ -0,0 +1,3094 @@
1//
2// rosenbrock.fixed.history.simplex.txt--
3// History of the simplex during Nelder-Mead algorithm.
4//
5// Copyright (C) 2008-2009 - INRIA - Michael Baudin
6//
7history = list()
8// Iteration #0
9history($+1) = [
10// Vertex #1
111.000000e+001 1.000000e+001
12// Vertex #2
131.096593e+001 1.025882e+001
14// Vertex #3
151.025882e+001 1.096593e+001
16]
17// Iteration #0
18history($+1) = [
19// Vertex #1
201.000000e+001 1.000000e+001
21// Vertex #2
221.025882e+001 1.096593e+001
23// Vertex #3
241.096593e+001 1.025882e+001
25]
26// Iteration #1
27history($+1) = [
28// Vertex #1
291.000000e+001 1.000000e+001
30// Vertex #2
311.025882e+001 1.096593e+001
32// Vertex #3
331.096593e+001 1.025882e+001
34]
35// Iteration #2
36history($+1) = [
37// Vertex #1
389.292893e+000 1.070711e+001
39// Vertex #2
401.000000e+001 1.000000e+001
41// Vertex #3
421.025882e+001 1.096593e+001
43]
44// Iteration #3
45history($+1) = [
46// Vertex #1
479.034074e+000 9.741181e+000
48// Vertex #2
499.292893e+000 1.070711e+001
50// Vertex #3
511.000000e+001 1.000000e+001
52]
53// Iteration #4
54history($+1) = [
55// Vertex #1
568.326967e+000 1.044829e+001
57// Vertex #2
589.034074e+000 9.741181e+000
59// Vertex #3
609.292893e+000 1.070711e+001
61]
62// Iteration #5
63history($+1) = [
64// Vertex #1
658.068148e+000 9.482362e+000
66// Vertex #2
678.326967e+000 1.044829e+001
68// Vertex #3
699.034074e+000 9.741181e+000
70]
71// Iteration #6
72history($+1) = [
73// Vertex #1
747.361042e+000 1.018947e+001
75// Vertex #2
768.068148e+000 9.482362e+000
77// Vertex #3
788.326967e+000 1.044829e+001
79]
80// Iteration #7
81history($+1) = [
82// Vertex #1
837.102223e+000 9.223543e+000
84// Vertex #2
857.361042e+000 1.018947e+001
86// Vertex #3
878.068148e+000 9.482362e+000
88]
89// Iteration #8
90history($+1) = [
91// Vertex #1
926.395116e+000 9.930650e+000
93// Vertex #2
947.102223e+000 9.223543e+000
95// Vertex #3
967.361042e+000 1.018947e+001
97]
98// Iteration #9
99history($+1) = [
100// Vertex #1
1016.136297e+000 8.964724e+000
102// Vertex #2
1036.395116e+000 9.930650e+000
104// Vertex #3
1057.102223e+000 9.223543e+000
106]
107// Iteration #10
108history($+1) = [
109// Vertex #1
1105.429190e+000 9.671831e+000
111// Vertex #2
1126.136297e+000 8.964724e+000
113// Vertex #3
1146.395116e+000 9.930650e+000
115]
116// Iteration #11
117history($+1) = [
118// Vertex #1
1195.170371e+000 8.705905e+000
120// Vertex #2
1215.429190e+000 9.671831e+000
122// Vertex #3
1236.136297e+000 8.964724e+000
124]
125// Iteration #12
126history($+1) = [
127// Vertex #1
1284.463264e+000 9.413012e+000
129// Vertex #2
1305.170371e+000 8.705905e+000
131// Vertex #3
1325.429190e+000 9.671831e+000
133]
134// Iteration #13
135history($+1) = [
136// Vertex #1
1374.204445e+000 8.447086e+000
138// Vertex #2
1394.463264e+000 9.413012e+000
140// Vertex #3
1415.170371e+000 8.705905e+000
142]
143// Iteration #14
144history($+1) = [
145// Vertex #1
1463.497338e+000 9.154193e+000
147// Vertex #2
1484.204445e+000 8.447086e+000
149// Vertex #3
1504.463264e+000 9.413012e+000
151]
152// Iteration #15
153history($+1) = [
154// Vertex #1
1553.238519e+000 8.188267e+000
156// Vertex #2
1573.497338e+000 9.154193e+000
158// Vertex #3
1594.204445e+000 8.447086e+000
160]
161// Iteration #16
162history($+1) = [
163// Vertex #1
1642.531412e+000 8.895373e+000
165// Vertex #2
1663.238519e+000 8.188267e+000
167// Vertex #3
1683.497338e+000 9.154193e+000
169]
170// Iteration #17
171history($+1) = [
172// Vertex #1
1732.272593e+000 7.929448e+000
174// Vertex #2
1752.531412e+000 8.895373e+000
176// Vertex #3
1773.238519e+000 8.188267e+000
178]
179// Iteration #18
180history($+1) = [
181// Vertex #1
1821.565487e+000 8.636554e+000
183// Vertex #2
1842.272593e+000 7.929448e+000
185// Vertex #3
1862.531412e+000 8.895373e+000
187]
188// Iteration #19
189history($+1) = [
190// Vertex #1
1911.306668e+000 7.670629e+000
192// Vertex #2
1931.565487e+000 8.636554e+000
194// Vertex #3
1952.272593e+000 7.929448e+000
196]
197// Iteration #20
198history($+1) = [
199// Vertex #1
2005.995608e-001 8.377735e+000
201// Vertex #2
2021.306668e+000 7.670629e+000
203// Vertex #3
2041.565487e+000 8.636554e+000
205]
206// Iteration #21
207history($+1) = [
208// Vertex #1
2093.407417e-001 7.411810e+000
210// Vertex #2
2115.995608e-001 8.377735e+000
212// Vertex #3
2131.306668e+000 7.670629e+000
214]
215// Iteration #22
216history($+1) = [
217// Vertex #1
2183.407417e-001 7.411810e+000
219// Vertex #2
220-3.663650e-001 8.118916e+000
221// Vertex #3
2225.995608e-001 8.377735e+000
223]
224// Iteration #23
225history($+1) = [
226// Vertex #1
2273.407417e-001 7.411810e+000
228// Vertex #2
229-3.663650e-001 8.118916e+000
230// Vertex #3
231-6.251841e-001 7.152991e+000
232]
233// Iteration #24
234history($+1) = [
235// Vertex #1
2368.192269e-002 6.445884e+000
237// Vertex #2
2383.407417e-001 7.411810e+000
239// Vertex #3
240-6.251841e-001 7.152991e+000
241]
242// Iteration #25
243history($+1) = [
244// Vertex #1
2458.192269e-002 6.445884e+000
246// Vertex #2
2472.113322e-001 6.928847e+000
248// Vertex #3
249-2.716307e-001 6.799437e+000
250]
251// Iteration #26
252history($+1) = [
253// Vertex #1
2548.192269e-002 6.445884e+000
255// Vertex #2
256-9.485400e-002 6.622660e+000
257// Vertex #3
2581.466275e-001 6.687365e+000
259]
260