BEGIN_PROVIDER  [ real, eplf_gamma ]
 implicit none
 BEGIN_DOC  
! Value of the gaussian for the EPLF
 END_DOC
 include 'constants.F'
 real            :: eps, N
! N = 0.1
! eps = -real(dlog(tiny(1.d0)))
! eplf_gamma = (4./3.*pi*density_value_p/N)**(2./3.) * eps
 N=0.001
 eps = 50.
 eplf_gamma = eps**2 *0.5d0*(4./9.*pi*density_value_p * N**(-1./3.))**(2./3.)
!eplf_gamma = 1.e10
!eplf_gamma = 1.e5
END_PROVIDER

BEGIN_PROVIDER [ double precision, ao_eplf_integral_matrix, (ao_num,ao_num) ]
 implicit none
 BEGIN_DOC  
! Array of all the <chi_i chi_j | exp(-gamma r^2)> for EPLF
 END_DOC
 integer :: i, j
 double precision :: ao_eplf_integral
 do i=1,ao_num
  do j=i,ao_num
    ao_eplf_integral_matrix(j,i) = ao_eplf_integral(j,i,dble(eplf_gamma),point)
    ao_eplf_integral_matrix(i,j) = ao_eplf_integral_matrix(j,i)
  enddo
 enddo
END_PROVIDER

BEGIN_PROVIDER [ double precision, mo_eplf_integral_matrix, (mo_num,mo_num) ]
 implicit none
 BEGIN_DOC  
! Array of all the <phi_i phi_j | exp(-gamma r^2)> for EPLF
 END_DOC
 integer :: i, j, k, l
 double precision :: t
 PROVIDE ao_eplf_integral_matrix
 PROVIDE mo_coef mo_coef_transp
 do i=1,mo_num
  do j=i,mo_num
    mo_eplf_integral_matrix(j,i) = 0.d0
  enddo


  do k=1,ao_num
   if (mo_coef(k,i) /= 0.) then
    do l=1,ao_num
     if (abs(ao_eplf_integral_matrix(l,k))>1.d-16) then
      t = mo_coef(k,i)*ao_eplf_integral_matrix(l,k)
      do j=i,mo_num
       mo_eplf_integral_matrix(j,i) += t*mo_coef_transp(j,l)
      enddo
     endif
    enddo
   endif

  enddo

 enddo

 do i=1,mo_num
  do j=i+1,mo_num
    mo_eplf_integral_matrix(i,j) = mo_eplf_integral_matrix(j,i)
  enddo
 enddo
END_PROVIDER

 BEGIN_PROVIDER [ double precision, eplf_up_up ]
&BEGIN_PROVIDER [ double precision, eplf_up_dn ]
 implicit none
 BEGIN_DOC  
! Value of the d_upup and d_updn quantities needed for EPLF
 END_DOC

 integer :: i, j

 eplf_up_up = 0.d0
 eplf_up_dn = 0.d0

 PROVIDE mo_coef_transp

 do i=1,mo_closed_num
  do j=1,mo_closed_num
    eplf_up_up += mo_value_p(i)* (  &
      mo_value_p(i)*mo_eplf_integral_matrix(j,j) - &
      mo_value_p(j)*mo_eplf_integral_matrix(j,i) )
    eplf_up_dn += mo_value_p(i)*mo_value_p(i)* &
        mo_eplf_integral_matrix(j,j)
  enddo
 enddo
 eplf_up_up *= 2.d0
 eplf_up_dn *= 2.d0 

 integer :: k,l,m,n,p,p2
 integer :: ik,il,jk,jl
 double precision :: phase,dtemp(2)
 integer :: exc(4), nactive, nactive2

 PROVIDE det
 PROVIDE elec_num_2
 PROVIDE mo_value_prod_p

 do k=1,det_num
  do l=k,det_num

   exc(1) = abs(det_exc(k,l,1))
   exc(2) = abs(det_exc(k,l,2))
   exc(3) = exc(1)+exc(2)
   exc(4) = det_exc(k,l,1)*det_exc(k,l,2)
   if (exc(4) /= 0) then
    exc(4) = exc(4)/abs(exc(4))
   else
    exc(4) = 1
   endif

   dtemp(1) = 0.d0
   dtemp(2) = 0.d0
   do p=1,2
     nactive  = elec_num_2(p) -mo_closed_num
     nactive2 = elec_num_2(p2)-mo_closed_num
     p2 = 1+mod(p,2)
     if ( exc(3) == 0 ) then
      ! Closed-open shell interactions
      do j=1,mo_closed_num
       do n=1,nactive
        ik = det(n,k,p)
        il = det(n,l,p)
        dtemp(1) += (  &
           mo_value_prod_p(il,ik)*mo_eplf_integral_matrix(j,j) - &
           mo_value_prod_p(j,ik)*mo_eplf_integral_matrix(j,il) )
        dtemp(2) += mo_value_prod_p(il,ik)*mo_eplf_integral_matrix(j,j) 
       enddo
      enddo

      !- Open-closed shell interactions
      do m=1,nactive
       jk = det(m,k,p)
       jl = det(m,l,p)
       do i=1,mo_closed_num
         dtemp(1) += (  &
           mo_value_prod_p(i,i)*mo_eplf_integral_matrix(jl,jk) - &
           mo_value_prod_p(i,jl)*mo_eplf_integral_matrix(i,jk) )  
         dtemp(2) += mo_value_prod_p(i,i)*mo_eplf_integral_matrix(jl,jk) 
       enddo
      enddo

      !- Open-open shell interactions
      do m=1,nactive
       jk = det(m,k,p)
       jl = det(m,l,p)
       do n=1,nactive
         ik = det(n,k,p)
         il = det(n,l,p)
         dtemp(1) += (  &
           mo_value_prod_p(il,ik)*mo_eplf_integral_matrix(jl,jk) - &
           mo_value_prod_p(jl,ik)*mo_eplf_integral_matrix(il,jk) )
       enddo
       do n=1,nactive2
         ik = det(n,k,p2)
         il = det(n,l,p2)
         dtemp(2) += mo_value_prod_p(ik,il)*mo_eplf_integral_matrix(jl,jk) 
       enddo
      enddo
 
     else if ( (exc(3) == 1).and.(exc(p) == 1) ) then

     ! Sum over only the sigma-sigma interactions involving the excitation
      call get_single_excitation(k,l,ik,il,p)

      !- Open-closed shell interactions
      do j=1,mo_closed_num
       dtemp(1) += (  &
           mo_value_prod_p(il,ik)*mo_eplf_integral_matrix(j,j) - &
           mo_value_prod_p(j,ik)*mo_eplf_integral_matrix(j,il) )
       dtemp(2) += mo_value_prod_p(ik,il)*mo_eplf_integral_matrix(j,j)
      enddo

      !- Closed-open shell interactions
      do i=1,mo_closed_num
       dtemp(1) += (  &
           mo_value_prod_p(i,i)*mo_eplf_integral_matrix(jl,jk) - &
           mo_value_prod_p(i,jl)*mo_eplf_integral_matrix(i,jk) )  
       dtemp(2) += mo_value_prod_p(i,i)*mo_eplf_integral_matrix(jl,jk)
      enddo

      !- Open-open shell interactions
      do m=1,nactive
       jk = det(m,k,p)
       jl = det(m,l,p)
       dtemp(1) += (  &
           mo_value_prod_p(il,ik)*mo_eplf_integral_matrix(jl,jk) - &
           mo_value_prod_p(jl,ik)*mo_eplf_integral_matrix(il,jk) )
      enddo
      do m=1,nactive2
       jk = det(m,k,p2)
       jl = det(m,l,p2)
       dtemp(2) += mo_value_prod_p(ik,il)*mo_eplf_integral_matrix(jl,jk) 
      enddo

     else if ( (exc(3) == 2).and.(exc(p) == 2) ) then
    
     ! Consider only the double excitations of same-spin electrons
      call get_double_excitation(k,l,ik,il,jk,jl,p)
    
      dtemp(1) += (  &
             mo_value_prod_p(il,ik)*mo_eplf_integral_matrix(jl,jk) - &
             mo_value_prod_p(jl,ik)*mo_eplf_integral_matrix(il,jk) )
    
     else if ( (exc(3) == 2).and.(exc(p) == 1) ) then
    
     ! Consider only the double excitations of opposite-spin electrons
     call get_single_excitation(k,l,ik,il,p)
     call get_single_excitation(k,l,jk,jl,p2)
    
      dtemp(2) += mo_value_prod_p(ik,il)*mo_eplf_integral_matrix(jl,jk)
    
     endif
   enddo

   phase = dble(exc(4))
   eplf_up_up += phase * det_coef(k)*det_coef(l) * dtemp(1) 
   eplf_up_dn += phase * det_coef(k)*det_coef(l) * dtemp(2)
   if (k /= l) then
    eplf_up_up += phase * det_coef(k)*det_coef(l) * dtemp(1)
    eplf_up_dn += phase * det_coef(k)*det_coef(l) * dtemp(2)
   endif

  enddo
 enddo
 
END_PROVIDER


BEGIN_PROVIDER [ real, eplf_value_p ]
 implicit none
 BEGIN_DOC  
! Value of the EPLF at the current point.
 END_DOC
 double precision :: aa, ab
 double precision, parameter :: eps = tiny(1.d0)

 aa = eplf_up_up
 ab = eplf_up_dn
 if ( (aa > 0.d0).and.(ab > 0.d0) ) then
   aa = min(1.d0,aa)
   ab = min(1.d0,ab)
   aa = -dlog(aa)
   aa = dsqrt(aa)
   ab = -dlog(ab)
   ab = dsqrt(ab)
   eplf_value_p = (aa-ab)/(aa+ab+eps)
 else
   eplf_value_p = 0.d0
 endif

END_PROVIDER


!double precision function ao_eplf_integral_primitive_oneD_numeric(a,xa,i,b,xb,j,gmma,xr)
! implicit none
! include 'constants.F'
!
! real, intent(in)    :: a,b,gmma ! Exponents
! real, intent(in)    :: xa,xb,xr ! Centers
! integer, intent(in) :: i,j   ! Powers of xa and xb
! integer,parameter :: Npoints=10000
! real :: x, xmin, xmax, dx
!
! ASSERT (a>0.)
! ASSERT (b>0.)
! ASSERT (i>=0)
! ASSERT (j>=0)
!
! xmin = min(xa,xb)
! xmax = max(xa,xb)
! xmin = min(xmin,xr) - 10.
! xmax = max(xmax,xr) + 10.
! dx = (xmax-xmin)/real(Npoints)
!
! real :: dtemp
! dtemp = 0.
! x = xmin
! integer :: k
! do k=1,Npoints
!  dtemp += &
!   (x-xa)**i * (x-xb)**j * exp(-(a*(x-xa)**2+b*(x-xb)**2+gmma*(x-xr)**2))
!  x = x+dx
! enddo
! ao_eplf_integral_primitive_oneD_numeric = dtemp*dx
!
!end function
!
!double precision function ao_eplf_integral_numeric(i,j,gmma,center)
! implicit none
! integer, intent(in) :: i, j
! integer :: p,q,k
! double precision :: integral
! double precision :: ao_eplf_integral_primitive_oneD_numeric
! real :: gmma, center(3), c
!
! 
!  ao_eplf_integral_numeric = 0.d0
!  do q=1,ao_prim_num(j)
!   do p=1,ao_prim_num(i)
!    c = ao_coef(i,p)*ao_coef(j,q)
!    integral =                              &
!    ao_eplf_integral_primitive_oneD_numeric(   &
!     ao_expo(i,p),                          &
!     nucl_coord(ao_nucl(i),1),              &
!     ao_power(i,1),                         &
!     ao_expo(j,q),                          &
!     nucl_coord(ao_nucl(j),1),              &
!     ao_power(j,1),                         &
!     gmma,                                  &
!     center(1))   *                         &
!    ao_eplf_integral_primitive_oneD_numeric(   &
!     ao_expo(i,p),                          &
!     nucl_coord(ao_nucl(i),2),              &
!     ao_power(i,2),                         &
!     ao_expo(j,q),                          &
!     nucl_coord(ao_nucl(j),2),              &
!     ao_power(j,2),                         &
!     gmma,                                  &
!     center(2))   *                         &
!    ao_eplf_integral_primitive_oneD_numeric(   &
!     ao_expo(i,p),                          &
!     nucl_coord(ao_nucl(i),3),              &
!     ao_power(i,3),                         &
!     ao_expo(j,q),                          &
!     nucl_coord(ao_nucl(j),3),              &
!     ao_power(j,3),                         &
!     gmma,                                  &
!     center(3))
!    ao_eplf_integral_numeric = ao_eplf_integral_numeric + c*integral
!   enddo
!  enddo
!  
!end function
 

double precision function ao_eplf_integral_primitive_oneD(a,xa,i,b,xb,j,gmma,xr)
  implicit none
  include 'constants.F'
 
  real, intent(in)    :: a,b ! Exponents
  double precision , intent(in) :: gmma  ! eplf_gamma 
  real, intent(in)    :: xa,xb,xr ! Centers
  integer, intent(in) :: i,j   ! Powers of xa and xb
  integer :: ii, jj, kk
 
  ASSERT (a>0.)
  ASSERT (b>0.)
  ASSERT (i>=0)
  ASSERT (j>=0)
 
  double precision :: alpha, beta, delta, c
  alpha = a*xa*xa + b*xb*xb + gmma*xr*xr
  delta = a*xa    + b*xb    + gmma*xr
  beta  = a       + b       + gmma
  c = alpha-delta**2/beta
  
  if ( c > 32.d0 ) then   ! Cut-off on exp(-32)
   ao_eplf_integral_primitive_oneD = 0.d0
   return
  endif

  double precision :: u,v,w
  c = exp(-c) 
  w = 1.d0/sqrt(beta)
  u=delta/beta-xa
  v=delta/beta-xb

  double precision :: fact2, binom, f, ac
  ac = 0.d0
  integer :: istart(0:1)
  istart = (/ 0, 1 /)
  do ii=0,i
   do jj=istart(mod(ii,2)),j,2
     kk=(ii+jj)/2
     f=binom(ii,i)*binom(jj,j)*fact2(ii+jj-1)
     ac += u**(i-ii)*v**(j-jj)*w**(ii+jj)*f/dble(2**kk)
   enddo
  enddo
  ao_eplf_integral_primitive_oneD = dsqrt_pi*w*c*ac
 
end function


double precision function ao_eplf_integral(i,j,gmma,center)
 implicit none
 integer, intent(in) :: i, j
 real, intent(in)    :: center(3)
 double precision, intent(in) :: gmma
!DEC$ ATTRIBUTES FORCEINLINE
 integer :: p,q,k
 double precision :: integral
 double precision :: ao_eplf_integral_primitive_oneD
 double precision :: buffer(100)


 ASSERT(i>0)
 ASSERT(j>0)
 ASSERT(ao_prim_num_max < 100)
 ASSERT(i<=ao_num)
 ASSERT(j<=ao_num)

 ao_eplf_integral = 0.d0
 do p=1,ao_prim_num_max
   buffer(p) = 0.d0
 enddo

 do q=1,ao_prim_num(j)
  do p=1,ao_prim_num(i)
   integral =                              &
   ao_eplf_integral_primitive_oneD(        &
    ao_expo(i,p),                          &
    nucl_coord(ao_nucl(i),1),              &
    ao_power(i,1),                         &
    ao_expo(j,q),                          &
    nucl_coord(ao_nucl(j),1),              &
    ao_power(j,1),                         &
    gmma,                                  &
    center(1))
   if (integral /= 0.d0) then
     integral *=                             &
      ao_eplf_integral_primitive_oneD(       &
      ao_expo(i,p),                          &
      nucl_coord(ao_nucl(i),2),              &
      ao_power(i,2),                         &
      ao_expo(j,q),                          &
      nucl_coord(ao_nucl(j),2),              &
      ao_power(j,2),                         &
      gmma,                                  &
      center(2))
     if (integral /= 0.d0) then
      integral *=                             &
       ao_eplf_integral_primitive_oneD(       &
       ao_expo(i,p),                          &
       nucl_coord(ao_nucl(i),3),              &
       ao_power(i,3),                         &
       ao_expo(j,q),                          &
       nucl_coord(ao_nucl(j),3),              &
       ao_power(j,3),                         &
       gmma,                                  &
       center(3))
      buffer(p) += integral*ao_coef(i,p)*ao_coef(j,q)
     endif
   endif
  enddo
 enddo
 do p=1,ao_prim_num_max
   ao_eplf_integral += buffer(p)
 enddo
 
end function

double precision function mo_eplf_integral(i,j)
  implicit none
  integer :: i, j, k, l
  PROVIDE ao_eplf_integral_matrix
  PROVIDE mo_coef
  mo_eplf_integral = 0.d0
 
   do k=1,ao_num
     if (mo_coef(k,i) /= 0.) then
       do l=1,ao_num
        mo_eplf_integral +=  &
          mo_coef(k,i)*mo_coef(l,j)*ao_eplf_integral_matrix(k,l)
       enddo
     endif
   enddo
 
end function