/* Finer Multi-Candidates Latin Hypercube Search (Multi-dimensional Grid Search)      */
/* Switching between deterministic and stochastic search  with flexible focus ratios. */
new; cls;
xmin={1,0,0};
xmax={10,10,10};
nc=10;             /* This number can be very big even in GAUSS Light. */
nn=2;
status={1,0,0};
p={0.2,0.1,0.1};      
fn f(x)=sin(x[1])-cos(x[2])-x[3];
print fLHSsearch(xmin,xmax,nc,nn,status,p,&f);


/*
**  LHSCH03m.txt - Finer Switching Multi-Candidates Latin Hypercube Search
** (Multi-dimensional Grid Search). Switching search types with flexible focus ratio.
** (C) Copyright 2005 Yosuke Amijima. All Rights Reserved.
**
**  Purpose:    Gets maximum values of function f(x) between xmin and xmax initially.
**
**  Format:     xstarstar=fLHSsearch(xmin,xmax,nc,nn,status,p,&f);
**
**  Input:      xmin     vector,    nn x 1 vector of initial minimum values to search
**
**              xmax     vector,    nn x 1 vector of initial maximum values to search
**
**              nc       scalar,    number of initial segments(i.e. nc^dim candidates)
**
**              nn       scalar,    number of segments
**
**              status   vector,    0 if deterministic, 1 if stochastic search
**                                 (the number of rows of this is the number of steps to focus in)
**
**              p        vector,    focus ratios in each step (the last one is void)
**
**              &f       pointer to a procedure of objective function f(x) to be maximized
**
**
**  Output:  xstarstar   vector,    nn x 1 vector of maximum values
**
**  Notice:     This algorithm is very powerful even in GAUSS Light. Initial partition does not
**              depends on any matrix expansion. Parameter nc could be very big.
**              If you have some trouble to run, start over GAUSS again.
*/
proc fLHSsearch(xmin,xmax,nc,nn,status,p,&f);
   local dim,y1,y2,y3,range0,range,step,xmin0,zmax0,zmax,zmaxj,xstar,i,j,k,index,x,z,d,U,nsteps,c,xstarstar;
   local f:proc;
/* indexing */
   dim=rows(xmin);
   y1=dimindex0(nn,dim);      /* location index      */
   y2=dimindex0(nn+1,dim);    /* sub-location index  */
   y3=dimindex0(nn,dim)+1;    /* stochastic index beginning from 1 */
/* initial step settings */
   zmax0=-1e256;
   xmin0=xmin;
   range0=(xmax-xmin)/nc;
/* main */
   nsteps=rows(status);        /* # of steps to focus in */
   d=1/(nn);
   c=0;
   do while c<=nc^dim-1;
      xmin=xmin0'+locounter(nc,dim,c)'.*range0'; xmin=xmin';
      range=range0;
      step=range/nn;
      zmax=f(xmin); 
      xstar=xmin;
      k=1;
      do while k<=nsteps;
         print;
         j=1;
         do while j<=nn^dim;
            if status[k]==0;                                          /* deterministic search */
               /* regular grid including endpoints(allow overlaps) */
               x=xmin'+y1[j,.].*step'+y2.*step'/nn;
            elseif status[k]==1;                                      /* stochastic search    */
               /* LHS before scaling by parameter vector 'step' */
               U=(d*y3-d*(y3-1)).*rndu(nn^dim,dim)+d*(y3-1);
               /* [     location       ] + [ U(0,1) inside each cube]  */ 
               x=xmin'+(y3[j,.]-1).*step'+U.*step';
            else;
               errorlog "ERROR: Elements of 'steps' must be 0 or 1.";
               retp(".");
            endif;
         /* calculation f(x) in each hypercube */
            z=zeros(nn^dim,1);
            i=1;
            do while i<=nn^dim;
               z[i]=f(x[i,.]');
               i=i+1;
            endo;
            zmaxj=maxc(z);
         /* uptate xstar if larger solution zmaxj is found */
            if zmax<zmaxj;
               index=maxindc(z);
               xstar=x[index,.]';
               zmax=zmaxj;
            endif;
                  /* just counting */
                  if j%50==0;
                     call sleep(1);
                  endif;
                  print/lz "candidate" c+1 "/" nc^dim "   step" k "   " j "       /" nn^dim;
            j=j+1;
         endo;
      /* update step length for next step to focus in */
         range=range*p[k];                               /* focus ratios are changing */
         xmin=xstar-1/2*range;
         step=range/nn;
         k=k+1;
      endo;
      /* update if larger zmax is found for each candidate */
      if zmax0<zmax;
         xstarstar=xstar;
         zmax0=zmax;
      endif;
      c=c+1;
   endo;
   retp(xstarstar);
endp;

proc locounter(nc,dim,i);
   local x,j;
   if (nc^dim-1)==(nc^dim-2);
      errorlog "ERROR: Overflow in digit. Reduce the number of nc";
      retp(".");
   endif;
   if i>nc^dim-1;
      errorlog "ERROR: Parameter i must be 0<=i<=nn^dim-1.";
      retp(".");
   endif;
   x=zeros(dim,1);
   j=dim;
   do until j==1;
      x[j]=floor(i/(nc^(j-1)));
      i=i-(x[j]*(nc^(j-1)));
      j=j-1;
   endo;
   x[1]=i;
   retp(x);
endp;

/*
**  dimindex0.txt - Dimension Indexing.
** (C) Copyright 2005 Yosuke Amijima. All Rights Reserved.
**
**  Purpose:    Gets index numbers for given dimension in a very easy way.
**
**  Format:     y=dimindex0(nn,dim);
**
**  Input:      nn       scalar,    max number of index  (0,1,2,3,...,nn-1) beginning from 0
**
**              dim      scalar,    dimension            (1,...,dim)
**
**
**  Output:     y        matrix ,   (nn^dim) x (dim) of resulting index matrix
**
*/
proc dimindex0(nn,dim);
   local x,b,n,z,y;
/* convert x(base 10) to y(base b) */
   x=seqa(1,1,nn^dim-1); 
   b=nn;
   n=maxc(log(x)/log(b))+1;
   z=reshape(b,n,rows(x));
   y=rev(recserrc(x,z))';
/* adjustments */
   y=zeros(1,dim)|y;           /* insert 0's at the 1st row  */
   retp(y);
endp;