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focas_gradient.F90.BLAS3
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focas_gradient.F90.BLAS3
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!!
!@BEGIN LICENSE
!
! v2RDM-CASSCF by A. Eugene DePrince III, a plugin to:
!
! Psi4: an open-source quantum chemistry software package
!
! This program is free software; you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation; either version 2 of the License, or
! (at your option) any later version.
!
! This program is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License along
! with this program; if not, write to the Free Software Foundation, Inc.,
! 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
!
!@END LICENSE
!
!!
module focas_gradient
use focas_data
implicit none
contains
subroutine orbital_gradient(int1,int2,den1,den2)
implicit none
real(wp), intent(in) :: int1(:),int2(:),den1(:),den2(:)
integer :: omp_get_max_threads
real(wp) :: t0,t1
write(fid_,*)'************'
write(fid_,*)'new gradient'
write(fid_,*)'************'
! calculate inactive Fock matrix
t0=timer()
if ( df_vars_%use_df_teints == 0 ) then
call compute_f_i(int1,int2)
else
call compute_f_i_df(int1,int2)
endif
t1=timer()
write(fid_,'(a5,1x,f10.6)')'f_i',t1-t0
! calculate active Fock matrix
t0=timer()
if ( df_vars_%use_df_teints == 0 ) then
call compute_f_a(den1,int2)
else
call compute_f_a_df(den1,int2)
endif
t1=timer()
write(fid_,'(a5,1x,f10.6)')'f_a',t1-t0
! calculate auxiliary q matrix
t0=timer()
if ( df_vars_%use_df_teints == 0 ) then
call compute_q(den2,int2)
else
call compute_q_df(den2,int2)
endif
t1=timer()
write(fid_,'(a5,1x,f10.6)')'q',t1-t0
! calculate auxiliary z matrix
t0=timer()
call compute_z(den1)
t1=timer()
write(fid_,'(a5,1x,f10.6)')'z',t1-t0
write(fid_,*)
call flush(fid_)
! compute gradient
call compute_orbital_gradient()
! ! print the gradient
! if ( log_print_ == 1 ) call print_orbital_gradient()
return
end subroutine orbital_gradient
subroutine print_orbital_gradient()
implicit none
integer :: ij_pair,i,j,newline,i_class,j_class,j_class_start,j_start,i_sym
character(1) :: ityp,jtyp
! loop over rotation pairs
write(fid_,'(a)')'orbital gradient:'
newline=0
! the loop structure below cycles through the possible rotation pairs
! rotation pairs are sorted according to symmetry and for each irrep,
! the rotation pairs are sorted according to orbital classes: ad,ed,aa,ea
! for each pair j>i; for more details, see subroutine setup_rotation_indeces in focas_main.F90
ij_pair = 0
do i_sym = 1 , nirrep_
do i_class = 1 , 3
j_class_start = i_class + 1
if ( ( include_aa_rot_ == 1 ) .and. ( i_class == 2 ) ) j_class_start = i_class
do j_class = j_class_start , 3
do i = first_index_(i_sym,i_class) , last_index_(i_sym,i_class)
j_start = first_index_(i_sym,j_class)
if ( i_class == j_class ) j_start = i + 1
do j = j_start , last_index_(i_sym,j_class)
if ( i_class == 1 ) then
ityp = 'd'
jtyp = 'a'
if ( j_class == 3 ) jtyp = 'e'
else
ityp = 'a'
jtyp = 'a'
if ( j_class == 3 ) jtyp = 'e'
end if
ij_pair = ij_pair + 1
write(fid_,'(a,a,a,a,i3,a,i3,a,1x,es10.3,4x)',advance='no')jtyp,'-',ityp,' (',j,',',i,')',orbital_gradient_(ij_pair)
newline = newline + 1
if ( mod(newline,4) == 0 ) write(fid_,*)
end do
end do
end do
end do
end do
if ( mod(newline,4) /= 0 ) write(fid_,*)
write(fid_,'(a,1x,es10.3)')'gradient norm:',grad_norm_
call flush(fid_)
return
end subroutine print_orbital_gradient
subroutine compute_orbital_gradient()
! subroutine to compute the orbital gradient without explicit storage
! of the generalized Fock matrix
implicit none
integer :: grad_ind
integer :: a_sym,t_sym
integer :: i,t,u,a
integer :: ia,it
real(wp) :: ddot
orbital_gradient_ = 0.0_wp
! ********************************
! external - doubly-occupied pairs
! ********************************
do a_sym = 1 , nirrep_
grad_ind = rot_pair_%pair_offset(a_sym,rot_pair_%ext_doc_type)
do i = first_index_(a_sym,1) , last_index_(a_sym,1)
do a = first_index_(a_sym,3) , last_index_(a_sym,3)
grad_ind = grad_ind + 1
ia = ints_%gemind(i,a)
orbital_gradient_(grad_ind) = 4.0_wp*(fock_i_(ia)+fock_a_(ia))
end do
end do
end do
! ******************************
! acitve - doubly-occupied pairs
! ******************************
do t_sym = 1 , nirrep_
grad_ind = rot_pair_%pair_offset(t_sym,rot_pair_%act_doc_type)
do i = first_index_(t_sym,1) , last_index_(t_sym,1)
do t = first_index_(t_sym,2) , last_index_(t_sym,2)
grad_ind = grad_ind + 1
it = ints_%gemind(i,t)
orbital_gradient_(grad_ind) = 4.0_wp*(fock_i_(it)+fock_a_(it)) - 2.0_wp * ( q_(t - ndoc_tot_,i) + z_(t - ndoc_tot_,i))
end do
end do
end do
! ***********************
! external - active pairs
! ***********************
do a_sym = 1 , nirrep_
grad_ind = rot_pair_%pair_offset(a_sym,rot_pair_%ext_act_type)
do t = first_index_(a_sym,2) , last_index_(a_sym,2)
do a = first_index_(a_sym,3) , last_index_(a_sym,3)
grad_ind = grad_ind + 1
orbital_gradient_(grad_ind) = 2.0_wp * ( q_(t - ndoc_tot_,a) + z_(t - ndoc_tot_,a))
end do
end do
end do
! *********************
! active - active pairs
! *********************
if ( include_aa_rot_ == 1 ) then
do t_sym = 1 , nirrep_
grad_ind = rot_pair_%pair_offset(t_sym,rot_pair_%act_act_type)
do u = first_index_(t_sym,2) , last_index_(t_sym,2)
do t = u + 1 , last_index_(t_sym,2)
grad_ind = grad_ind + 1
orbital_gradient_(grad_ind) = 2.0_wp * ( q_(u - ndoc_tot_,t) + &
& z_(u - ndoc_tot_,t) - q_(t - ndoc_tot_,u) - z_(t - ndoc_tot_,u))
end do
end do
end do
end if
grad_norm_ = sqrt(ddot(rot_pair_%n_tot,orbital_gradient_,1,orbital_gradient_,1))
return
end subroutine compute_orbital_gradient
subroutine compute_z(den1)
implicit none
! function to compute contraction of the density with the inactive Fock matrix according to
! z(m,t) = sum_u { den1(tu) * f_i(mu) } t,u \in A m \in D,A,E
real(wp), intent(in) :: den1(:)
integer :: t,u,tu_den,mu_int,t_sym,m,m_class
real(wp) :: val
! initialize output
z_ = 0.0_wp
! loop over symmetries for t
do t_sym = 1 , nirrep_
! loop over u indeces
do t = first_index_(t_sym,2) , last_index_(t_sym,2)
! loop over classes for m
do m_class = 1 , 3
! loop over m indeces
do m = first_index_(t_sym,m_class) , last_index_(t_sym,m_class)
! initialize contraction value
val = 0.0_wp
do u = first_index_(t_sym,2) , last_index_(t_sym,2)
! integral/density addressing
tu_den = dens_%gemind(t,u)
mu_int = ints_%gemind(m,u)
val = val + den1(tu_den) * fock_i_(mu_int)
end do ! end u loop
z_( t - ndoc_tot_ , m ) = val
end do ! end m loop
end do ! end m_class loop
end do ! end t loop
end do ! end t_sym loop
return
end subroutine compute_z
subroutine compute_q_df(den2,int2)
implicit none
! this subroutine computes the "auxiliary Q" matrix according to Eq. 12.5.14 in Helgaker on page 622
! Q(v,m) = \SUM[w,x,y \in A] { d2(vw|xy) * g(mw|xy) }
! Because only those D2 elements with all four indeces \in A are nonzero, we have v \in A
! Also, m is a general orbital index && sym_m == sym_v
! Integrals are stored in 3-index format. Instead of doing many ddots, the set of integrals
! (mw|xy) is computed using dgemm g(mw|xy) = sum_Q xy_df(xy,Q) * mw_df(Q,mw)
! this requires extra storage but not too much: g ~ nact^3 xy_df ~ nQ*nirrep*nact^2 mw_df ~ nQ*nact
real(wp), intent(in) :: den2(:),int2(:)
integer :: mw_sym,x_sym,y_sym,w_sym,m_sym,m_class,m,v,w,x,y,mdf,wdf,xdf,ydf
integer :: xy_den,vw_den
integer(ip) :: mw,xy,nQ
integer :: den_ind,den_sym_offset,int_col,int_row,y_last
integer :: imw,ixy
integer :: max_nmopi,max_ngempi,error
real(wp) :: val,int_val,ddot
real(wp) :: v_mw(df_vars_%nQ)
type sym_block
real(wp), allocatable :: mw_df(:,:)
real(wp), allocatable :: xy_df(:,:)
real(wp), allocatable :: ints(:,:)
end type sym_block
type(sym_block) :: df_q(nirrep_)
nQ = int(df_vars_%nQ,kind=ip)
max_nmopi = maxval(nactpi_)
max_ngempi = max_nmopi * max_nmopi
error = allocate_df_q()
! initialize
q_ = 0.0_wp
! loop over symmetries for m
do m_sym = 1 , nirrep_
! loop over classes for m
do m_class = 1 , 3
! loop over orbital index m
do m = first_index_(m_sym,m_class) , last_index_(m_sym,m_class)
! m index in df order
mdf = df_vars_%class_to_df_map(m)
! *************************************
! gather df integrals (:|mw) and (:|xy)
! *************************************
do w_sym = 1 , nirrep_
if ( nactpi_(w_sym) == 0 ) cycle
imw = 0
mw_sym = group_mult_tab_(m_sym,w_sym)
do w = first_index_(w_sym,2) , last_index_(w_sym,2)
wdf = df_vars_%class_to_df_map(w)
mw = df_pq_index(wdf,mdf)
imw = imw + 1
call dcopy(nQ,int2(mw+1:mw+nQ),1,df_q(w_sym)%mw_df(:,imw),1)
end do ! end w loop
ixy = 0
do x_sym = 1 , nirrep_
y_sym = group_mult_tab_(x_sym,mw_sym)
if ( y_sym > x_sym ) cycle
do x = first_index_(x_sym,2) , last_index_(x_sym,2)
xdf = df_vars_%class_to_df_map(x)
y_last = last_index_(y_sym,2)
if ( y_sym == x_sym ) y_last = x
do y = first_index_(y_sym,2) , y_last
ydf = df_vars_%class_to_df_map(y)
xy = df_pq_index(xdf,ydf)
ixy = ixy + 1
call dcopy(df_vars_%nQ,int2(xy+1:xy+nQ),1,df_q(w_sym)%xy_df(:,ixy),1)
end do ! end y loop
end do ! end x loop
end do ! end x_sym loop
if ( ixy == 0 ) cycle
! *******************************************************************************************
! multiply 3-index integral matrices to get the 4-index integrals (xy|mw) for all w,x,y \in A
! *******************************************************************************************
call dgemm('t','n',ixy,imw,df_vars_%nQ, &
& 1.0_wp,df_q(w_sym)%xy_df(:,1:ixy),df_vars_%nQ,&
& df_q(w_sym)%mw_df(:,1:imw),df_vars_%nQ,&
& 0.0_wp,df_q(w_sym)%ints,nirrep_*max_ngempi)
end do ! end w_sym loop
! loop over orbital index v
#ifdef OMP
!$omp parallel shared(m_class,nQ,m_sym,m,mdf,first_index_,last_index_,df_vars_,den2,int2,dens_,q_) num_threads(nthread_use_)
!$omp do private(ixy,imw,val,v,w_sym,mw_sym,den_sym_offset,w,vw_den,x_sym,y_sym,x,y,xy_den,den_ind,int_val)
#endif
do v = first_index_(m_sym,2) , last_index_(m_sym,2)
! initialize matrix element
val = 0.0_wp
! loop over symmetries for w
do w_sym = 1 , nirrep_
imw = 0
! symmetry of mw geminal
mw_sym = group_mult_tab_(m_sym,w_sym)
! vw density offset
den_sym_offset = dens_%offset(mw_sym)
! loop over w orbital index
do w = first_index_(w_sym,2) , last_index_(w_sym,2)
ixy = 0
imw = imw + 1
! vw geminal index for density
vw_den = dens_%gemind(v,w)
! loop over x_sym
do x_sym = 1 , nirrep_
! figure out symmetry of y
y_sym = group_mult_tab_(mw_sym,x_sym)
if ( y_sym == x_sym ) then
! loop over x orbital index
do x = first_index_(x_sym,2) , last_index_(x_sym,2)
! ***********************************************
! loop over y orbital index (x>y) --> factor of 2
! ***********************************************
do y = first_index_(y_sym,2) , x - 1
ixy = ixy + 1
! xy geminal index and density index
xy_den = dens_%gemind(x,y)
den_ind = pq_index(vw_den,xy_den) + den_sym_offset
! update matrix element
val = val + 2.0_wp * df_q(w_sym)%ints(ixy,imw) * den2(den_ind)
end do ! end y loop
! **********************
! x == y --> factor of 1
! **********************
xy_den = dens_%gemind(x,x)
den_ind = pq_index(vw_den,xy_den) + den_sym_offset
ixy = ixy + 1
! xy geminal index in df order
xy = df_pq_index(xdf,xdf)
! update matrix element
val = val + df_q(w_sym)%ints(ixy,imw) * den2(den_ind)
end do ! end x loop
elseif ( y_sym < x_sym) then
! loop over x orbital index
do x = first_index_(x_sym,2) , last_index_(x_sym,2)
! ***********************************************
! loop over y orbital index (x>y) --> factor of 2
! ***********************************************
do y = first_index_(y_sym,2) , last_index_(y_sym,2)
! xy geminal index and density index
xy_den = dens_%gemind(x,y)
den_ind = pq_index(vw_den,xy_den) + den_sym_offset
ixy = ixy + 1
! update matrix element
val = val + 2.0_wp * df_q(w_sym)%ints(ixy,imw) * den2(den_ind)
end do ! end y loop
end do ! end x loop
endif
end do ! end x_sym loop
end do ! end w loop
end do ! end w_sym loop
! save matrix element
q_( v - ndoc_tot_ , m ) = val
end do ! end v loop
#ifdef OMP
!$omp end do nowait
!$omp end parallel
#endif
end do ! end m loop
end do ! end m_class loop
end do ! end m_sym loop
error = deallocate_df_q()
return
contains
integer function allocate_df_q()
implicit none
integer :: w_sym
do w_sym = 1 , nirrep_
if ( nactpi_(w_sym) == 0 ) cycle
allocate(df_q(w_sym)%mw_df(df_vars_%nQ,nactpi_(w_sym)))
allocate(df_q(w_sym)%xy_df(df_vars_%nQ,nirrep_*max_ngempi))
allocate(df_q(w_sym)%ints(nirrep_*max_ngempi,max_nmopi))
end do
allocate_df_q = 0
end function allocate_df_q
integer function deallocate_df_q()
integer :: w_sym
do w_sym = 1 , nirrep_
if (allocated(df_q(w_sym)%mw_df)) deallocate(df_q(w_sym)%mw_df)
if (allocated(df_q(w_sym)%xy_df)) deallocate(df_q(w_sym)%xy_df)
if (allocated(df_q(w_sym)%ints)) deallocate(df_q(w_sym)%ints)
end do
deallocate_df_q = 0
end function deallocate_df_q
end subroutine compute_q_df
subroutine compute_q(den2,int2)
implicit none
! this subroutine computes the "auxiliary Q" matrix according to Eq. 12.5.14 in Helgaker on page 622
! Q(v,m) = \SUM[w,x,y \in A] { d2(vw|xy) * g(mw|xy) }
! Because only those D2 elements with all four indeces \in A are nonzero, we have v \in A
! Also, m is a general orbital index && sym_m == sym_v
real(wp), intent(in) :: den2(:),int2(:)
integer :: mw_sym,x_sym,y_sym,w_sym,m_sym,m_class,m,v,w,x,y
integer :: xy_den,xy_int,mw,vw
integer :: den_ind,den_sym_offset,int_ind,int_sym_offset
real(wp) :: val
! initialize
q_ = 0.0_wp
! loop irreps for m and v
do m_sym = 1 , nirrep_
! loop over irreps for w
do w_sym = 1, nirrep_
! mw//vw symmetry
mw_sym = group_mult_tab_(m_sym,w_sym)
! offsets for integral/density addressing
den_sym_offset = dens_%offset(mw_sym)
int_sym_offset = ints_%offset(mw_sym)
! loop over irreps for x
do x_sym = 1 , nirrep_
! correspoing irrep for y
y_sym = group_mult_tab_(x_sym,mw_sym)
! at this point, we have mw_sym == xy_sym && m_sym == v_sym
! loop over m_class
do m_class = 1 , 3
! loop over v indeces
do m = first_index_(m_sym,m_class) , last_index_(m_sym,m_class)
! loop over v \in A
do v = first_index_(m_sym,2) , last_index_(m_sym,2)
! initialize q matrix element
val = 0.0_wp
! loop over w indeces
do w = first_index_(w_sym,2) , last_index_(w_sym,2)
! save geminal indeces for integral/density addressing
mw = ints_%gemind(m,w)
vw = dens_%gemind(v,w)
! loop over x indeces
do x = first_index_(x_sym,2) , last_index_(x_sym,2)
! loop over y indeces
do y = first_index_(y_sym,2) , last_index_(y_sym,2)
! save geminal indeces for integral/density addressing
xy_int = ints_%gemind(x,y)
xy_den = dens_%gemind(x,y)
! integral/density addresses
int_ind = pq_index(xy_int,mw) + int_sym_offset
den_ind = pq_index(xy_den,vw) + den_sym_offset
! update temporary value
val = val + den2(den_ind) * int2(int_ind)
end do ! end y loop
end do ! end x loop
end do ! end w loop
! update q matrix element
q_( v - ndoc_tot_ , m ) = q_( v - ndoc_tot_ , m ) + val
end do ! end v loop
end do ! end m loop
end do ! end m_class loop
end do ! end x_sym loop
end do ! end w_sym loop
end do ! end m_sym loop
return
end subroutine compute_q
subroutine compute_f_a_df(den1,int2)
implicit none
! this subroutine computes the "active fock matrix" according to Eq. 12.5.13 in Helgaker on page 622
! F_a(m|n) = h(m|n) + SUM[v,w \in A] { g(mn|vw) - 0.5 g(mw|vn) }
! Apart from the symmetry constraint m_sym == n_sym and m >= n, m and n can belong to either of the three
! orbital classes.
! v and w belong to the active orbital class
real(wp), intent(in) :: den1(:),int2(:)
integer :: m_class,n_class,m_sym,m,n,v,w,w_sym,mdf,ndf,wdf,vdf
integer :: den_ind,mn_fock
integer(ip) :: mn,vw,mw,nQ
integer :: max_nmopi,max_nactpi
integer :: m_dgemm,n_dgemm,k_dgemm,mc_l,mc_f
integer :: df_ind,error,mn_J
integer :: coulomb_ind,exchange_row,exchange_col
real(wp) :: val,ival,dval,ddot
real(wp) :: v_mn(df_vars_%nQ),v_mw(df_vars_%nQ)
type df_int_block
real(wp), allocatable :: df_int(:,:)
end type df_int_block
type w_sym_block
type(df_int_block), allocatable :: w_irr(:)
end type w_sym_block
type m_sym_block
type(w_sym_block), allocatable :: m_irr(:)
end type m_sym_block
type int_block
real(wp), allocatable :: ints(:,:)
end type int_block
type(int_block) :: Km(nirrep_)
type(int_block) :: Jm(nirrep_)
type(m_sym_block) :: mw_df
type(w_sym_block) :: vw_df
type(df_int_block) :: mn_df
nQ = int(df_vars_%nQ,kind=ip)
max_nmopi = maxval(trans_%nmopi)
max_nactpi = maxval(nactpi_)
error = allocate_df_fa()
! *****************************
! collect all mw df vectors
! m is a general orbital index
! w is an active orbital index
! this adds nQ*nact*nmo storage
! *****************************
do m_sym = 1 , nirrep_
do w_sym = 1 , nirrep_
df_ind = 0
do m_class = 1 , 3
do m = first_index_(m_sym,m_class) , last_index_(m_sym,m_class)
mdf = df_vars_%class_to_df_map(m)
do w = first_index_(w_sym,2) , last_index_(w_sym,2)
wdf = df_vars_%class_to_df_map(w)
mw = df_pq_index(mdf,wdf)
df_ind = df_ind + 1
call dcopy(df_vars_%nQ,int2(mw+1:mw+nQ),1,mw_df%m_irr(m_sym)%w_irr(w_sym)%df_int(:,df_ind),1)
end do
end do
end do
end do
end do
! ******************************************
! collect all vw df vectors
! v&w are both active orbital indeces
! this adds nQ*nact*(nact+1)/2 extra storage
! ******************************************
do w_sym = 1 ,nirrep_
df_ind = 0
do w = first_index_(w_sym,2) , last_index_(w_sym,2)
wdf = df_vars_%class_to_df_map(w)
do v = first_index_(w_sym,2) , w
vdf = df_vars_%class_to_df_map(v)
vw = df_pq_index(vdf,wdf)
df_ind = df_ind + 1
call dcopy(df_vars_%nQ,int2(vw+1:vw+nQ),1,vw_df%w_irr(w_sym)%df_int(:,df_ind),1)
end do
end do
end do
! initialize
fock_a_ = 0.0_wp
! loop over orbital classes for m
do m_class = 1 , 3
! loop over irreps (m_sym == n_sym for F(m,n) != 0)
do m_sym = 1 , nirrep_
! loop over m indeces
do m = first_index_(m_sym,m_class) , last_index_(m_sym,m_class)
! orbital index in df order
mdf = df_vars_%class_to_df_map(m)
! **********************************
! gather ALL df integrals for this m
! this adds nQ*nmo extra storage
! **********************************
df_ind = 0
! this used to include all classes
do n_class = 1 , m_class
do n = first_index_(m_sym,n_class) , last_index_(m_sym,n_class)
ndf = df_vars_%class_to_df_map(n)
mn = df_pq_index(mdf,ndf)
df_ind = df_ind + 1
call dcopy(df_vars_%nQ,int2(mn+1:mn+nQ),1,mn_df%df_int(:,df_ind),1)
end do
end do
! *******************************************************
! form ALL exchange/coulomb integrals for this value of m
! this adds 2 * nact*nact*nmo extra storage
! *******************************************************
do w_sym = 1 , nirrep_
if ( nactpi_(w_sym) == 0 ) cycle
mc_f = ( trans_%class_to_irrep_map(m) - 1 ) * nactpi_(w_sym)
mc_l = mc_f + nactpi_(w_sym)
m_dgemm = nactpi_(w_sym) * trans_%nmopi(m_sym)
n_dgemm = nactpi_(w_sym)
k_dgemm = df_vars_%nQ
if ( ( m_dgemm > 0 ) .and. ( n_dgemm > 0 ) ) then
call dgemm('t','n',m_dgemm,n_dgemm,k_dgemm,1.0_wp, &
& mw_df%m_irr(m_sym)%w_irr(w_sym)%df_int,k_dgemm, &
& mw_df%m_irr(m_sym)%w_irr(w_sym)%df_int(:,mc_f+1:mc_l),k_dgemm, &
& 0.0_wp,Km(w_sym)%ints(1:m_dgemm,1:n_dgemm),m_dgemm)
end if
m_dgemm = nactpi_(w_sym) * ( nactpi_(w_sym) + 1 ) /2
n_dgemm = df_ind !trans_%nmopi(m_sym)
if ( ( m_dgemm > 0 ) .and. ( n_dgemm > 0 ) ) then
! vw --> df_int [ nQ , na*(na+1)/2 ]
! mn --> df_int [ nQ , max_nmo ]
! Jm --> [ na*(na+1)/2 , max_nmo ]
call dgemm('t','n',m_dgemm,n_dgemm,k_dgemm,1.0_wp,vw_df%w_irr(w_sym)%df_int, &
& k_dgemm,mn_df%df_int(:,1:n_dgemm),k_dgemm,0.0_wp, &
& Jm(w_sym)%ints(:,1:n_dgemm),m_dgemm)
end if
end do
! loop over n indeces ( m_class == n_class && m >= n && m_sym == n_sym )
#ifdef OMP
!$omp parallel shared(m_sym,m_class,m,nirrep_,first_index_,trans_,den1,Jm,Km,nactpi_) num_threads(nthread_use_)
!$omp do private(n,mn_J,val,den_ind,w_sym,coulomb_ind,exchange_col,w,exchange_row,v)
#endif
do n = first_index_(m_sym,m_class) , m
mn_J = trans_%class_to_irrep_map(n)
! initialize Fock matrix element
val = 0.0_wp
! loop over irreps for v
den_ind = 0
do w_sym = 1 , nirrep_
coulomb_ind = 0
exchange_col = 0
! loop over w indeces
do w = 1, nactpi_(w_sym) !first_index_(w_sym,2) , last_index_(w_sym,2)
exchange_row = df_ga_index(n,first_index_(w_sym,2),w_sym) - 1
exchange_col = exchange_col + 1
! *** w > v --> factor of 2
! loop over v indeces
do v = 1 , w - 1 !first_index_(w_sym,2) , w - 1
den_ind = den_ind + 1
coulomb_ind = coulomb_ind + 1
exchange_row = exchange_row + 1
! :: d1(v|w) * [ 2 * g(mn|vw) - g(mw|wn) ]
val = val + den1(den_ind) * ( 2.0_wp * Jm(w_sym)%ints(coulomb_ind,mn_J) - &
& Km(w_sym)%ints(exchange_row,exchange_col) )
end do ! end v loop
! **** w == v --> factor of 1
den_ind = den_ind + 1