double precision function sigmoidfunc(y0,a,b,c,x0,x)
      implicit none
      double precision y0,a,b,c,x0,x,term,crit
      parameter(crit=300.0d0)
      if((-(x-x0)/b).lt.crit)then
        term=dexp(-(x-x0)/b)
        sigmoidfunc=y0+a*(1.0d0/(1.0d0+term))**c
      else
        term=dexp((x-x0)/b)
        sigmoidfunc=y0+a*(term/(1.0d0+term))**c
      endif
      return
      end
!-------------------------------------------------------------------
      subroutine gradsigmoidfunc(y0,a,b,c,x0,x,grad)
      implicit none
      double precision y0,a,b,c,x0,x,grad(6),term,crit
      parameter(crit=300.0d0)
!      a<->grad(1)
!      b<->grad(2)
!      c<->grad(3)
!      x0<->grad(4)
!      y0<->grad(5)
!      x<->grad(6)
      grad(5)=1.0d0
      if((-(x-x0)/b).lt.crit)then
        term=dexp(-(x-x0)/b)
        grad(1)=(1.0d0/(1.0d0+term))**c
        grad(6)=(a*c*term/b)*(1.0d0/(1.0d0+term))**(1.0d0+c)
        grad(4)=-(a*c*term/b)*(1.0d0/(1.0d0+term))**(1.0d0+c)
        grad(2)=-(a*c*term*(x-x0)/(b*b))*
     &           (1.0d0/(1.0d0+term))**(1.0d0+c)
        grad(3)=-(a*dlog(1.0d0+term))*(1.0d0/(1.0d0+term))**c
      else
        term=(x-x0)/b
        grad(1)=(dexp(term)/(1.0d0+dexp(term)))**c
        grad(6)=(a*c/b)*(dexp(term*c/(c+1.0d0))/
     &              (1.0d0+dexp(term)))**(c+1.0d0)
        grad(4)=-(a*c/b)*(dexp(term*c/(c+1))/
     &              (1.0d0+dexp(term)))**(c+1.0d0)
        grad(2)=-(a*c*(x-x0)/(b*b))*
     &    (dexp(term*c/(c+1.0d0))/(1.0d0+dexp(term)))**(1.0d0+c)
        grad(3)=-a*(dlog(1.0d0+dexp(term))-term)*
     &           (dexp(term)/(1.0d0+dexp(term)))**c
      endif
      return
      end
!--------------------------------------------------------------------
      double precision function twoexpfunc(y0,a1,b1,c1,x01,
     &a2,b2,c2,x02,x)
      implicit none
      double precision y0,a1,b1,c1,x01,a2,b2,c2,x02,x,sigmoidfunc
      twoexpfunc=y0+sigmoidfunc(0.0d0,a1,b1,c1,x01,x)-
     &sigmoidfunc(0.0d0,a2,b2,c2,x02,x)
      return
      end
!---------------------------------------------------------------------
      subroutine gradtwoexp(y0,a1,b1,c1,x01,a2,b2,c2,x02,x,grad)
      implicit none
      double precision y0,a1,b1,c1,x01,a2,b2,c2,x02,x,grad(10),grad6(6)
      integer i
!      a1<->grad(1)
!      b1<->grad(2)
!      c1<->grad(3)
!      x01<->grad(4)
!      y0<->grad(5)
!      x<->grad(6)
!      a2<->grad(7)
!      b2<->grad(8)
!      c2<->grad(9)
!      x02<->grad(10)
      call gradsigmoidfunc(y0,a1,b1,c1,x01,x,grad6)
      do i=1,6
        grad(i)=grad6(i)
      enddo
      call gradsigmoidfunc(0.0d0,a2,b2,c2,x02,x,grad6)
      grad(6)=grad(6)-grad6(6)
      do i=1,4
        grad(6+i)=-grad6(i)
      enddo
      return
      end
!------------------------------------------------------------------------------
      subroutine proxyinflpoints(b1,c1,x01,b2,c2,x02,xinfl1,xinfl2)
! the approximate inflection points. The exact analytical solution
! is difficult to find
      implicit none
      double precision b1,c1,x01,b2,c2,x02,xinfl1,xinfl2
      xinfl1=x01+b1*dlog(c1)
      xinfl2=x02+b2*dlog(c2)
      end
!------------------------------------------------------------------------------
      double precision function sigmoidcurvat(y0,a,b,c,x0,x)
      implicit none
      double precision y0,a,b,c,x0,x,term,yp,ypp,crit
      parameter(crit=300.0d0)
      if((-(x-x0)/b).lt.crit)then
        term=dexp(-(x-x0)/b)
        yp=(a*c*term/b)*(1.0d0/(1.0d0+term))**(c+1.0d0)
        ypp=(a*c/(b*b))*term*(c*term-1.0d0)*
     &      (1.0d0/(1.0d0+term))**(c+2)
      else
        term=(x-x0)/b
        yp=(a*c/b)*(dexp(term*c/(c+1))/
     &              (1.0d0+dexp(term)))**(c+1.0d0)
        ypp=(a*c/(b*b))*(c-dexp(term))*(dexp(term*c/(c+2))/
     &          (1.0d0+dexp(term)))**(c+2)
      endif
      sigmoidcurvat=dabs(ypp/((1.0d0+yp*yp)**1.5d0))
      return
      end
!------------------------------------------------------------------------------
      double precision function twoexpcurvat(y0,a1,b1,c1,x01,
     &a2,b2,c2,x02,x)
      implicit none
      double precision y0,a1,b1,c1,x01,a2,b2,c2,x02,x,a,b,c,x0,
     &term,yp,ypp,crit
      parameter(crit=300.0d0)

! first part
      a=a1
      b=b1
      c=c1
      x0=x01
      if((-(x-x0)/b).lt.crit)then    
        term=dexp(-(x-x0)/b)
        yp=(a*c*term/b)*(1.0d0/(1.0d0+term))**(c+1.0d0)
        ypp=(a*c/(b*b))*term*(c*term-1.0d0)*
     &      (1.0d0/(1.0d0+term))**(c+2)
      else
        term=(x-x0)/b
        yp=(a*c/b)*(dexp(term*c/(c+1))/
     &              (1.0d0+dexp(term)))**(c+1.0d0)
        ypp=(a*c/(b*b))*(c-dexp(term))*(dexp(term*c/(c+2))/
     &          (1.0d0+dexp(term)))**(c+2)
      endif

! second part
      a=a2
      b=b2
      c=c2
      x0=x02
      if((-(x-x0)/b).lt.crit)then    
        term=dexp(-(x-x0)/b)
        yp=yp-(a*c*term/b)*(1.0d0/(1.0d0+term))**(c+1.0d0)
        ypp=ypp-(a*c/(b*b))*term*(c*term-1.0d0)*
     &      (1.0d0/(1.0d0+term))**(c+2)
      else
        term=(x-x0)/b
        yp=yp-(a*c/b)*(dexp(term*c/(c+1))/
     &              (1.0d0+dexp(term)))**(c+1.0d0)
        ypp=ypp-(a*c/(b*b))*(c-dexp(term))*(dexp(term*c/(c+2))/
     &          (1.0d0+dexp(term)))**(c+2)
      endif
      twoexpcurvat=dabs(ypp/((1.0d0+yp*yp)**1.5d0))
      return
      end
!-----------------------------------------------------------------------