SimplexBuilder.cxx

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// @(#)root/minuit2:$Id$
// Authors: M. Winkler, F. James, L. Moneta, A. Zsenei   2003-2005

/**********************************************************************
 *                                                                    *
 * Copyright (c) 2005 LCG ROOT Math team,  CERN/PH-SFT                *
 *                                                                    *
 **********************************************************************/

#include "Minuit2/SimplexBuilder.h"
#include "Minuit2/FunctionMinimum.h"
#include "Minuit2/MnFcn.h"
#include "Minuit2/MinimumSeed.h"
#include "Minuit2/SimplexParameters.h"
#include "Minuit2/MinimumState.h"

#if defined(DEBUG) || defined(WARNINGMSG)
#include "Minuit2/MnPrint.h"
#endif


namespace ROOT {

   namespace Minuit2 {


//#define DEBUG 1

FunctionMinimum SimplexBuilder::Minimum(const MnFcn& mfcn, const GradientCalculator&, const MinimumSeed& seed, const MnStrategy&, unsigned int maxfcn, double minedm) const {
   // find the minimum using the Simplex method of Nelder and Mead (does not use function gradient)
   // method to find initial simplex is slightly different than in the orginal Fortran
   // Minuit since has not been proofed that one to be better

#ifdef DEBUG
   std::cout << "Running Simplex with maxfcn = " << maxfcn << " minedm = " << minedm << std::endl;
#endif

   const MnMachinePrecision& prec = seed.Precision();
   MnAlgebraicVector x = seed.Parameters().Vec();
   MnAlgebraicVector step = 10.*seed.Gradient().Gstep();

   unsigned int n = x.size();
   double wg = 1./double(n);
   double alpha = 1., beta = 0.5, gamma = 2., rhomin = 4., rhomax = 8.;
   double rho1 = 1. + alpha;
   //double rho2 = rho1 + alpha*gamma;
   //change proposed by david sachs (fnal)
   double rho2 = 1. + alpha*gamma;


   std::vector<std::pair<double, MnAlgebraicVector> > simpl; simpl.reserve(n+1);
   simpl.push_back(std::pair<double, MnAlgebraicVector>(seed.Fval(), x));

   unsigned int jl = 0, jh = 0;
   double amin = seed.Fval(), aming = seed.Fval();

   for(unsigned int i = 0; i < n; i++) {
      double dmin = 8.*prec.Eps2()*(fabs(x(i)) + prec.Eps2());
      if(step(i) < dmin) step(i) = dmin;
      x(i) += step(i);
      double tmp = mfcn(x);
      if(tmp < amin) {
         amin = tmp;
         jl = i+1;
      }
      if(tmp > aming) {
         aming = tmp;
         jh = i+1;
      }
      simpl.push_back(std::pair<double, MnAlgebraicVector>(tmp, x));
      x(i) -= step(i);
   }
   SimplexParameters simplex(simpl, jh, jl);

#ifdef DEBUG
   std::cout << "simplex initial parameters - min  " << jl << "  " << amin << " max " << jh << "  " << aming << std::endl;
   for (unsigned int i = 0; i < simplex.Simplex().size(); ++i)
      std::cout << " i = " << i << " x = " << simplex(i).second << " fval(x) = " << simplex(i).first << std::endl;
#endif

   double edmPrev = simplex.Edm();
   int niterations = 0;
   do {
      jl = simplex.Jl();
      jh = simplex.Jh();
      amin = simplex(jl).first;
      edmPrev = simplex.Edm();

#ifdef DEBUG
      std::cout << "\n\nsimplex iteration: edm =  " << simplex.Edm()
                << "\n--> Min Param is  " << jl << " pmin " << simplex(jl).second << " f(pmin) " << amin
                << "\n--> Max param is " << jh << "  " << simplex(jh).first << std::endl;

      //     std::cout << "ALL SIMPLEX PARAMETERS: "<< std::endl;
      //     for (unsigned int i = 0; i < simplex.Simplex().size(); ++i)
      //       std::cout << " i = " << i << " x = " << simplex(i).second << " fval(x) = " << simplex(i).first << std::endl;
#endif

      // trace the iterations (need to create a MinimunState although errors and gradient are not existing)
      if (TraceIter() ) TraceIteration(niterations, MinimumState(MinimumParameters(simplex(jl).second,simplex(jl).first), simplex.Edm(), mfcn.NumOfCalls()) );
      if (PrintLevel() > 1) MnPrint::PrintState(std::cout,simplex(jl).first, simplex.Edm(),mfcn.NumOfCalls(),"Simplex: Iteration # ", niterations);
      niterations++;


      MnAlgebraicVector pbar(n);
      for(unsigned int i = 0; i < n+1; i++) {
         if(i == jh) continue;
         pbar += (wg*simplex(i).second);
      }

      MnAlgebraicVector pstar = (1. + alpha)*pbar - alpha*simplex(jh).second;
      double ystar = mfcn(pstar);

#ifdef DEBUG
      std::cout << " pbar = " << pbar << std::endl;
      std::cout << " pstar = " << pstar << " f(pstar) =  " << ystar << std::endl;
#endif

      if(ystar > amin) {
         if(ystar < simplex(jh).first) {
            simplex.Update(ystar, pstar);
            if(jh != simplex.Jh()) continue;
         }
         MnAlgebraicVector pstst = beta*simplex(jh).second + (1. - beta)*pbar;
         double ystst = mfcn(pstst);
#ifdef DEBUG
         std::cout << "Reduced simplex pstst = " << pstst << " f(pstst) =  " << ystst << std::endl;
#endif
         if(ystst > simplex(jh).first) break;
         simplex.Update(ystst, pstst);
         continue;
      }

      MnAlgebraicVector pstst = gamma*pstar + (1. - gamma)*pbar;
      double ystst = mfcn(pstst);
#ifdef DEBUG
      std::cout << " pstst = " << pstst << " f(pstst) =  " << ystst << std::endl;
#endif

      double y1 = (ystar - simplex(jh).first)*rho2;
      double y2 = (ystst - simplex(jh).first)*rho1;
      double rho = 0.5*(rho2*y1 - rho1*y2)/(y1 - y2);
      if(rho < rhomin) {
         if(ystst < simplex(jl).first) simplex.Update(ystst, pstst);
         else simplex.Update(ystar, pstar);
         continue;
      }
      if(rho > rhomax) rho = rhomax;
      MnAlgebraicVector prho = rho*pbar + (1. - rho)*simplex(jh).second;
      double yrho = mfcn(prho);
#ifdef DEBUG
      std::cout << " prho = " << prho << " f(prho) =  " << yrho << std::endl;
#endif
      if(yrho < simplex(jl).first && yrho < ystst) {
         simplex.Update(yrho, prho);
         continue;
      }
      if(ystst < simplex(jl).first) {
         simplex.Update(ystst, pstst);
         continue;
      }
      if(yrho > simplex(jl).first) {
         if(ystst < simplex(jl).first) simplex.Update(ystst, pstst);
         else simplex.Update(ystar, pstar);
         continue;
      }
      if(ystar > simplex(jh).first) {
         pstst = beta*simplex(jh).second + (1. - beta)*pbar;
         ystst = mfcn(pstst);
         if(ystst > simplex(jh).first) break;
         simplex.Update(ystst, pstst);
      }
#ifdef DEBUG
      std::cout << "End loop : edm = " << simplex.Edm() << "  pstst = " << pstst << " f(pstst) =  " << ystst << std::endl;
#endif
   } while( (simplex.Edm() > minedm || edmPrev > minedm )  && mfcn.NumOfCalls() < maxfcn);

   jl = simplex.Jl();
   jh = simplex.Jh();
   amin = simplex(jl).first;

   MnAlgebraicVector pbar(n);
   for(unsigned int i = 0; i < n+1; i++) {
      if(i == jh) continue;
      pbar += (wg*simplex(i).second);
   }
   double ybar = mfcn(pbar);
   if(ybar < amin) simplex.Update(ybar, pbar);
   else {
      pbar = simplex(jl).second;
      ybar = simplex(jl).first;
   }

   MnAlgebraicVector dirin = simplex.Dirin();
   //   Scale to sigmas on parameters werr^2 = dirin^2 * (up/edm)
   dirin *= sqrt(mfcn.Up()/simplex.Edm());

#ifdef DEBUG
   std::cout << "End simplex " << simplex.Edm() << "  pbar = " << pbar << " f(p) =  " << ybar << std::endl;
#endif


   MinimumState st(MinimumParameters(pbar, dirin, ybar), simplex.Edm(), mfcn.NumOfCalls());

   if (PrintLevel() > 1)
      MnPrint::PrintState(std::cout,st,"Simplex: Final iteration");
   if (TraceIter() ) TraceIteration(niterations, st);

   if(mfcn.NumOfCalls() > maxfcn) {
#ifdef WARNINGMSG
      MN_INFO_MSG("Simplex did not converge, #fcn calls exhausted.");
#endif
      return FunctionMinimum(seed, std::vector<MinimumState>(1, st), mfcn.Up(), FunctionMinimum::MnReachedCallLimit());
   }
   if(simplex.Edm() > minedm) {
#ifdef WARNINGMSG
      MN_INFO_MSG("Simplex did not converge, edm > minedm.");
#endif
      return FunctionMinimum(seed, std::vector<MinimumState>(1, st), mfcn.Up(), FunctionMinimum::MnAboveMaxEdm());
   }

   return FunctionMinimum(seed, std::vector<MinimumState>(1, st), mfcn.Up());
}

   }  // namespace Minuit2

}  // namespace ROOT