!&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& 
      subroutine fluorescencejmax()
      implicit none
      include '../testarea/LeafGasParams.h'
      include '../testarea/LeafGasHybridFit.h'
      integer i,ndim,k,j,iderivative,iwrong,n,icompete,i2,isitnaninf,
     &nave
      double precision beta(4),sumsquare0,beta0(4),sumsquarecp,
     &betacp(4),ftol,xtol,shortx(maxobs,2),shorty(maxobs),
     &xvar(maxobs,2),weitx(maxobs,2),weity(maxobs),
     &templflights0(maxobs),aparlights0(maxobs),termmin,termmax,
     &ftol_relax,term1,term2,ran2,discount,history(2000,10),upper,lower,
     &f1dim_flujmax,flujmax_pikaia
      parameter(ftol=1.0d-7,xtol=1.0d-7)
      external funkmin_flujmax,f1dim_flujmax,FCN_flujmax,flujmax_pikaia
!beta(1)=fjmax25
      beta(1)=univparams(8)
      betamin(1)=univparamsmin(8)
      betamax(1)=univparamsmax(8)
!beta(2)=phifactor
      beta(2)=univparams(11)
      betamin(2)=univparamsmin(11)
      betamax(2)=univparamsmax(11)
!beta(3)=thetafactor
      beta(3)=univparams(12)
      betamin(3)=univparamsmin(12)
      betamax(3)=univparamsmax(12)
      ndim=3
      ntotlights=0
      termmax=-1.0d+9
      termmin=1.0d+9
      do i=1,numALightcurves
        do j=1,nALightPoints(i)
          if(ALightchlflphips2(j,i).gt.0.0d0.and.
     &j.le.nstartalight(i))then
!Only points before nstartalight are used because these points are apparently limited by RuBP regeneration and therefore
!the electron transport equation applies.
            ntotlights=ntotlights+1
            templflights(ntotlights)=ALighttempleaf(j,i)
            if(templflights(ntotlights).lt.termmin)
     &termmin=templflights(ntotlights)
            if(templflights(ntotlights).gt.termmax)
     &termmax=templflights(ntotlights)
            aparlights(ntotlights)=ALightaPPFDlf(j,i)
            flphips2lights(ntotlights)=ALightchlflphips2(j,i)
            xvar(ntotlights,1)=aparlights(ntotlights)
            xvar(ntotlights,2)=templflights(ntotlights)
            weitx(ntotlights,1)=1.0d0
            weitx(ntotlights,2)=1.0d0
            weity(ntotlights)=1.0d0
            templflights0(ntotlights)=templflights(ntotlights)
            aparlights0(ntotlights)=aparlights(ntotlights)
          endif
        enddo
      enddo
      if((termmax-termmin).gt.2.0d0)then
        ndim=4
!beta(4)=ha_jmax
        beta(4)=univparams(17)
        betamin(4)=univparamsmin(17)
        betamax(4)=univparamsmax(17)
      endif
      if(ntotlights.lt.ndim)then
        ntotlights=0
        return
      endif
      isitbounded=1
      call funkmin_flujmax(ndim,beta,flujmaxfval)
      do i=1,ndim
        beta0(i)=beta(i)
        history(1,i)=beta(i)
      enddo
      sumsquare0=flujmaxfval
      history(1,ndim+1)=flujmaxfval
!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
      nave=1
      ftol_relax=ftol*1000.0d0
      discount=2.0d0
30    do i=1,ndim
        betacp(i)=beta(i)
      enddo
      sumsquarecp=flujmaxfval
      iderivative=0
      iwrong=0
      call odr_leastsquare(ndim,FCN_flujmax,beta,ntotlights,
     &xvar(1:ntotlights,1:2),2,flphips2lights,1,weitx(1:ntotlights,1:2),
     &weity,iderivative,shortx(1:ntotlights,1:2),shorty(1:ntotlights),
     &flujmaxfval,iwrong)
!after odr_leastsquare, forcing variables are destroyed. restore to the origninals
      do i=1,ntotlights
        templflights(i)=templflights0(i)
        aparlights(i)=aparlights0(i)
      enddo
      call funkmin_flujmax(ndim,beta,flujmaxfval)
      if(isitnaninf(flujmaxfval).eq.1.or.flujmaxfval.gt.sumsquarecp)then
        do i=1,ndim
          beta(i)=betacp(i)
        enddo
        flujmaxfval=sumsquarecp
      else
        do i=1,ndim
          betacp(i)=beta(i)
        enddo
        sumsquarecp=flujmaxfval
      endif
      call nongradopt(ndim,funkmin_flujmax,f1dim_flujmax,
     &beta,betamin,betamax,ftol_relax,flujmaxfval)
      if(isitnaninf(flujmaxfval).eq.1.or.flujmaxfval.gt.sumsquarecp)then
        do i=1,ndim
          beta(i)=betacp(i)
        enddo
        flujmaxfval=sumsquarecp
      endif
      if(flujmaxfval.gt.1.0d0)then
        term1=flujmaxfval*ftol_relax
      else
        term1=ftol_relax*10.0d0
      endif
      if(flujmaxfval.gt.sumsquare0)then
!failure
        if((flujmaxfval-sumsquare0).gt.term1)then
          if(icompete.eq.1)history(1,ndim+3)=history(1,ndim+3)+1.5d0
!even though flujmaxfval is much worse than sumsquare0, 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)-flujmaxfval).lt.term1)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)=flujmaxfval
          history(n,ndim+2)=0.0d0
          history(n,ndim+3)=0.0d0
!use average only when there is improvement
          nave=n
        else
!the difference is minimal even though flujmaxfval is larger than sumsquare0.
!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
60      do i=1,ndim
          beta(i)=beta0(i)
        enddo
        flujmaxfval=sumsquare0
      else
!success
        if((sumsquare0-flujmaxfval).lt.term1)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)+0.5d0
          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,(sumsquare0-flujmaxfval)/1000.0d0)
          endif
          k=0
          n=n+1
          do i=1,ndim
            history(n,i)=beta(i)
          enddo
          history(n,ndim+1)=flujmaxfval
          history(n,ndim+2)=0.0d0
          history(n,ndim+3)=0.0d0
        endif
        do i=1,ndim
          beta0(i)=beta(i)
        enddo
        sumsquare0=flujmaxfval
      endif
      j=j+1
      if(j.lt.200.and.k.lt.3)then
!first explore around the very first initial guess
        if(j.lt.10)then
          term1=0.05d0+dmin1(history(1,ndim+3)*0.1d0,0.9d0)
          history(1,ndim+2)=history(1,ndim+2)+1.0d0
          do i=1,ndim
            lower=history(1,i)-term1*(history(1,i)-betamin(i))
            upper=history(1,i)+term1*(betamax(i)-history(1,i))
            beta(i)=lower+ran2()*(upper-lower)
          enddo
          icompete=1
          goto 70
        endif
!try average
        if(n.gt.nave)then
          term1=1.0d0/(history(1,ndim+1)+1.0d-5)
          do i=2,n
            term1=term1+1.0d0/(history(i,ndim+1)+1.0d-5)
          enddo
          do i=1,ndim
            beta(i)=history(1,i)/(term1*(history(1,ndim+1)+1.0d-5))
            do icompete=2,n
              beta(i)=beta(i)+history(icompete,i)/
     &(term1*(history(icompete,ndim+1)+1.0d-5))
            enddo
          enddo
          nave=n
          icompete=0
          goto 70
        endif
!try different initial guesses
        if(ran2().gt.0.2d0)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=0.05d0+dmin1(history(1,ndim+2)*history(1,ndim+3)*
     &0.015d0,0.9d0)
          history(1,ndim+2)=history(1,ndim+2)+1.0d0
          do i=1,ndim
            lower=history(1,i)-term1*(history(1,i)-betamin(i))
            upper=history(1,i)+term1*(betamax(i)-history(1,i))
            beta(i)=lower+ran2()*(upper-lower)
          enddo
        else
!completely random guess
          do i=1,ndim
            beta(i)=betamin(i)+ran2()*(betamax(i)-betamin(i))
          enddo
          icompete=0
        endif
70      call funkmin_flujmax(ndim,beta,flujmaxfval)
        goto 30
      else
        if((ftol_relax-ftol).gt.ftol)then
          if(k.le.1)then
            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)=flujmaxfval
            history(1,ndim+2)=0.0d0
            history(1,ndim+3)=0.0d0
            do i=1,n
              do icompete=1,ndim
                betacp(icompete)=history(i,icompete)
              enddo
              sumsquarecp=history(i,ndim+1)
              call RepeatCompassSearch(ndim,betacp,sumsquarecp,
     &betamin,betamax,funkmin_flujmax,f1dim_flujmax,ftol_relax)
              call funkmin_flujmax(ndim,betacp,sumsquarecp)
              if(isitnaninf(sumsquarecp).eq.0.and.sumsquarecp.lt.
     &flujmaxfval)then
                do icompete=1,ndim
                  beta(icompete)=betacp(icompete)
                enddo
                flujmaxfval=sumsquarecp
              endif
            enddo
            do i=1,ndim
              beta0(i)=beta(i)
            enddo
            sumsquare0=flujmaxfval
            j=0
            icompete=1
          else
            icompete=0
          endif
          ftol_relax=ftol
          goto 30
        endif
      endif

      goto 110

      call RepeatCompassSearch(ndim,beta,flujmaxfval,betamin,
     &betamax,funkmin_flujmax,f1dim_flujmax,xtol)
      call funkmin_flujmax(ndim,beta,flujmaxfval)
      if(isitnaninf(flujmaxfval).eq.1.or.flujmaxfval.gt.sumsquare0)then
        do i=1,ndim
          beta(i)=beta0(i)
        enddo
        flujmaxfval=sumsquare0
      else
        do i=1,ndim
          beta0(i)=beta(i)
        enddo
        sumsquare0=flujmaxfval
      endif
      do i=1,ndim
        betacp(i)=(beta(i)-betamin(i))/(betamax(i)-betamin(i))
      enddo
      call pikaia(flujmax_pikaia,ndim,gacontrol,betacp,flujmaxfval,i)
      if(i.eq.0)then
        do i=1,ndim
          betacp(i)=betamin(i)+betacp(i)*(betamax(i)-betamin(i))
        enddo
        call funkmin_flujmax(ndim,betacp,flujmaxfval)
        if(isitnaninf(flujmaxfval).eq.0.and.flujmaxfval.lt.sumsquare0)
     &then
          do i=1,ndim
            beta(i)=betacp(i)
            beta0(i)=betacp(i)
          enddo
          sumsquare0=flujmaxfval
        endif
      endif
      flujmaxfval=sumsquare0
      iderivative=0
      iwrong=0
      call odr_leastsquare(ndim,FCN_flujmax,beta,ntotlights,
     &xvar(1:ntotlights,1:2),2,flphips2lights,1,weitx(1:ntotlights,1:2),
     &weity,iderivative,shortx(1:ntotlights,1:2),shorty(1:ntotlights),
     &flujmaxfval,iwrong)
!after odr_leastsquare, forcing variables are destroyed. restore to the origninals
      do i=1,ntotlights
        templflights(i)=templflights0(i)
        aparlights(i)=aparlights0(i)
      enddo
      call funkmin_flujmax(ndim,beta,flujmaxfval)
      if(isitnaninf(flujmaxfval).eq.1.or.flujmaxfval.gt.sumsquare0)then
        do i=1,ndim
          beta(i)=beta0(i)
        enddo
        flujmaxfval=sumsquare0
      endif
      j=0
100   sumsquare0=flujmaxfval
      do i=1,ndim
        beta0(i)=beta(i)
      enddo
      call nongradopt(ndim,funkmin_flujmax,f1dim_flujmax,
     &beta,betamin,betamax,ftol,flujmaxfval)
      call funkmin_flujmax(ndim,beta,flujmaxfval)
      if(flujmaxfval.eq.sumsquare0)return
      if(isitnaninf(flujmaxfval).eq.1.or.flujmaxfval.gt.sumsquare0)then
        do i=1,ndim
          beta(i)=beta0(i)
        enddo
        flujmaxfval=sumsquare0
      endif
      sumsquarecp=flujmaxfval
      do i=1,ndim
        betacp(i)=beta(i)
      enddo
      call RepeatCompassSearch(ndim,betacp,sumsquarecp,betamin,
     &betamax,funkmin_flujmax,f1dim_flujmax,xtol)
      call funkmin_flujmax(ndim,betacp,sumsquarecp)
      if(flujmaxfval.eq.sumsquarecp)return
      if(isitnaninf(sumsquarecp).eq.0.and.flujmaxfval.gt.sumsquarecp)
     &then
        do i=1,ndim
          beta(i)=betacp(i)
        enddo
        flujmaxfval=sumsquarecp
      endif
      j=j+1
      if(j.le.2.and.(sumsquare0-flujmaxfval).gt.ftol)goto 100
!
!------------------------------------------------------
110   call funkmin_flujmax(ndim,beta,flujmaxfval)
      return
      END subroutine fluorescencejmax