Subroutine mctsglobalmin(ndim,funkmin_nongrad,f1dim_nongrad,
     &beta,betamin,betamax,ftol,fatbeta)
      implicit none
      integer ndim
      double precision beta(ndim),betamin(ndim),betamax(ndim),
     &ftol,fatbeta
!
      integer i,j,k,n,i2,icompete
      double precision ran2,ftol_relax,term1,term2,beta0(ndim),
     &fatbeta0,history(2000,ndim+3),discount
      external funkmin_nongrad,f1dim_nongrad
!-----------------------------------------------------
!the cost funcation value for the first initial guess must be provided!
      do i=1,ndim
        beta0(i)=beta(i)
        history(1,i)=beta(i)
      enddo
      fatbeta0=fatbeta
      history(1,ndim+1)=fatbeta
!entrance counter
      history(1,ndim+2)=1.0d0
!failure counter
      history(1,ndim+3)=0.0d0
!Is it a competition among different initial guesses?
      icompete=0
!j the total number of calls to nongradopt; k is the number of returns to the current best and reset
!to zero if a better minumum is found; n is the number of scouting points over the landscape of the cost function.
!The first initial guess provided by the user is always part of the set of scouting points.the rest consist of outcomes
!from calls to nongradopt if they are significantly different from the current best.
      j=0
      k=0
      n=1
      ftol_relax=ftol*1000.0d0
      discount=2.0d0
!relax the convergence criterion for scouting
30    call nongradopt(ndim,funkmin_nongrad,f1dim_nongrad,
     &beta,betamin,betamax,ftol_relax,fatbeta)
      call funkmin_generic(ndim,beta,fatbeta)
      if((fatbeta+1.0d0).eq.fatbeta.or.fatbeta.gt.fatbeta0)then
!failure
        if((fatbeta+1.0d0).ne.fatbeta)then
          if((fatbeta-fatbeta0).gt.10.0d0*ftol_relax)then
            if(icompete.eq.1)history(1,ndim+3)=history(1,ndim+3)+1.5d0
!even though fatbeta is much worse than fatbeta0, it is an output of optimization after all so
!include it in the set if it has not already been included in the set.
            i=1
            i2=1
40          if(dabs(history(i2,i)-beta(i)).gt.ftol_relax)then
              if(dabs(history(i2,ndim+1)-fatbeta).lt.ftol_relax)then
                history(i2,ndim+3)=history(i2,ndim+3)+1.0d0
                goto 60
              endif
              if(i2.ge.n)goto 50
              i2=i2+1
              i=1
              goto 40
            else
              if(i.ge.ndim)goto 60 
              i=i+1
              goto 40
            endif
50          n=n+1
            do i=1,ndim
              history(n,i)=beta(i)
            enddo
            history(n,ndim+1)=fatbeta
            history(n,ndim+2)=0.0d0
            history(n,ndim+3)=0.0d0
          else
!the difference is minimal even though fatbeta is larger than fatbeta0.
!Increment the counter for arriving at the same minimum.
            if(icompete.eq.1)history(1,ndim+3)=history(1,ndim+3)+1.0d0
            k=k+1
          endif
        else
          if(icompete.eq.1)history(1,ndim+3)=history(1,ndim+3)+2.0d0
        endif
60      do i=1,ndim
          beta(i)=beta0(i)
        enddo
        fatbeta=fatbeta0
      else
!success
        if((fatbeta0-fatbeta).lt.10.0d0*ftol_relax)then
!negligible improvement. Increment the counter for arriving at the same minimum.
!no increment for the set of central initial guesses
          if(icompete.eq.1)history(1,ndim+3)=history(1,ndim+3)+0.1d0
          k=k+1
        else
!reset the counter for arriving at a better minimum.
!Increment the set of central initial guesses
          if(dabs(discount-2.0d0).lt.ftol)then
            discount=dmax1(0.001d0,(fatbeta0-fatbeta)/1000.0d0)
          endif
          k=0
          n=n+1
          do i=1,ndim+3
            history(n,i)=history(1,i)
          enddo
          do i=1,ndim
            history(1,i)=beta(i)
          enddo
          history(1,ndim+1)=fatbeta
          history(1,ndim+2)=0.0d0
          history(1,ndim+3)=0.0d0
        endif
        do i=1,ndim
          beta0(i)=beta(i)
        enddo
        fatbeta0=fatbeta
      endif
      j=j+1
      if(j.lt.990.and.k.lt.3)then
!try different initial guesses
        if(ran2().gt.0.1d0)then
!guess around the best
          icompete=1
          term1=history(1,ndim+1)+
     &discount*history(1,ndim+2)*history(1,ndim+3)
          do i=2,n
            term2=history(i,ndim+1)+
     &discount*history(i,ndim+2)*history(i,ndim+3)
            if(term2.le.term1)then
              term1=term2
              do i2=1,ndim+3
                history(n+1,i2)=history(i,i2)
                history(i,i2)=history(1,i2)
                history(1,i2)=history(n+1,i2)
              enddo
            endif
          enddo
          term1=0.5d0*history(i,ndim+2)*history(i,ndim+3)
          history(1,ndim+2)=history(1,ndim+2)+1.0d0
          do i=1,ndim
            if(ran2().gt.0.5d0)then
              if((betamax(i)-history(1,i)).gt.
     &(betamax(i)-betamin(i))*1.0d-5)then
                beta(i)=history(1,i)+(ran2()**(4.0d0/(term1+1.0d0)))*
     &(betamax(i)-history(1,i))
              else
                beta(i)=betamax(i)-
     &(ran2()**4.0d0)*(betamax(i)-betamin(i))
              endif
            else
              if((history(1,i)-betamin(i)).gt.
     &(betamax(i)-betamin(i))*1.0d-5)then
                beta(i)=history(1,i)-(ran2()**(4.0d0/(term1+1.0d0)))*
     &(history(1,i)-betamin(i))
              else
                beta(i)=betamin(i)+
     &(ran2()**4.0d0)*(betamax(i)-betamin(i))
              endif
            endif
          enddo
        else
!completely random guess
          icompete=0
          do i=1,ndim
            beta(i)=betamin(i)+ran2()*(betamax(i)-betamin(i))
          enddo
        endif
        call funkmin_generic(ndim,beta,fatbeta)
        goto 30
      else
        if((ftol_relax-ftol).gt.ftol)then
          ftol_relax=ftol
          if(k.le.1)j=0
          goto 30
        endif
      endif
      return
      end subroutine mctsglobalmin
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