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12 KiB
12 KiB
Ref: Integral-Direct and Parallel Implementation of the CCSD(T) Method: Algorithmic Developments and Large-Scale Applications László Gyevi-Nagy, Mihály Kállay, and Péter R. Nagy
- Chem. Theory Comput. 2020, 16, 1, 366–384
https://doi.org/10.1021/acs.jctc.9b00957
Dumb way
subroutine ccsd_par_t_space(nO,nV,t1,t2,energy)
implicit none
integer, intent(in) :: nO,nV
double precision, intent(in) :: t1(nO, nV)
double precision, intent(in) :: t2(nO, nO, nV, nV)
double precision, intent(out) :: energy
double precision, allocatable :: W(:,:,:,:,:,:)
double precision, allocatable :: V(:,:,:,:,:,:)
integer :: i,j,k,a,b,c
allocate(W(nO,nO,nO,nV,nV,nV))
allocate(V(nO,nO,nO,nV,nV,nV))
call form_w(nO,nV,t2,W)
call form_v(nO,nV,t1,W,V)
energy = 0d0
do c = 1, nV
do b = 1, nV
do a = 1, nV
do k = 1, nO
do j = 1, nO
do i = 1, nO
energy = energy + (4d0 * W(i,j,k,a,b,c) + W(i,j,k,b,c,a) + W(i,j,k,c,a,b)) * (V(i,j,k,a,b,c) - V(i,j,k,c,b,a)) / (cc_space_f_o(i) + cc_space_f_o(j) + cc_space_f_o(k) - cc_space_f_v(a) - cc_space_f_v(b) - cc_space_f_v(c)) !delta_ooovvv(i,j,k,a,b,c)
enddo
enddo
enddo
enddo
enddo
enddo
energy = energy / 3d0
deallocate(V,W)
endsubroutine form_w(nO,nV,t2,W)
implicit none
integer, intent(in) :: nO,nV
double precision, intent(in) :: t2(nO, nO, nV, nV)
double precision, intent(out) :: W(nO, nO, nO, nV, nV, nV)
integer :: i,j,k,l,a,b,c,d
W = 0d0
do c = 1, nV
print*,'W:',c,'/',nV
do b = 1, nV
do a = 1, nV
do k = 1, nO
do j = 1, nO
do i = 1, nO
do d = 1, nV
W(i,j,k,a,b,c) = W(i,j,k,a,b,c) &
! chem (bd|ai)
! phys <ba|di>
+ cc_space_v_vvvo(b,a,d,i) * t2(k,j,c,d) &
+ cc_space_v_vvvo(c,a,d,i) * t2(j,k,b,d) & ! bc kj
+ cc_space_v_vvvo(a,c,d,k) * t2(j,i,b,d) & ! prev ac ik
+ cc_space_v_vvvo(b,c,d,k) * t2(i,j,a,d) & ! prev ab ij
+ cc_space_v_vvvo(c,b,d,j) * t2(i,k,a,d) & ! prev bc kj
+ cc_space_v_vvvo(a,b,d,j) * t2(k,i,c,d) ! prev ac ik
enddo
do l = 1, nO
W(i,j,k,a,b,c) = W(i,j,k,a,b,c) &
! chem (ck|jl)
! phys <cj|kl>
- cc_space_v_vooo(c,j,k,l) * t2(i,l,a,b) &
- cc_space_v_vooo(b,k,j,l) * t2(i,l,a,c) & ! bc kj
- cc_space_v_vooo(b,i,j,l) * t2(k,l,c,a) & ! prev ac ik
- cc_space_v_vooo(a,j,i,l) * t2(k,l,c,b) & ! prev ab ij
- cc_space_v_vooo(a,k,i,l) * t2(j,l,b,c) & ! prev bc kj
- cc_space_v_vooo(c,i,k,l) * t2(j,l,b,a) ! prev ac ik
enddo
enddo
enddo
enddo
enddo
enddo
enddo
endsubroutine form_v(nO,nV,t1,w,v)
implicit none
integer, intent(in) :: nO,nV
double precision, intent(in) :: t1(nO, nV)
double precision, intent(in) :: W(nO, nO, nO, nV, nV, nV)
double precision, intent(out) :: V(nO, nO, nO, nV, nV, nV)
integer :: i,j,k,a,b,c
V = 0d0
do c = 1, nV
do b = 1, nV
do a = 1, nV
do k = 1, nO
do j = 1, nO
do i = 1, nO
V(i,j,k,a,b,c) = V(i,j,k,a,b,c) + W(i,j,k,a,b,c) &
+ cc_space_v_vvoo(b,c,j,k) * t1(i,a) &
+ cc_space_v_vvoo(a,c,i,k) * t1(j,b) &
+ cc_space_v_vvoo(a,b,i,j) * t1(k,c)
enddo
enddo
enddo
enddo
enddo
enddo
endBetter way
Main
subroutine ccsd_par_t_space_v2(nO,nV,t1,t2,f_o,f_v,v_vvvo,v_vvoo,v_vooo,energy)
implicit none
integer, intent(in) :: nO,nV
double precision, intent(in) :: t1(nO,nV), f_o(nO), f_v(nV)
double precision, intent(in) :: t2(nO,nO,nV,nV)
double precision, intent(in) :: v_vvvo(nV,nV,nV,nO), v_vvoo(nV,nV,nO,nO), v_vooo(nV,nO,nO,nO)
double precision, intent(out) :: energy
double precision, allocatable :: W(:,:,:,:,:,:)
double precision, allocatable :: V(:,:,:,:,:,:)
double precision, allocatable :: W_ijk(:,:,:), V_ijk(:,:,:)
double precision, allocatable :: X_vvvo(:,:,:,:), X_ovoo(:,:,:,:), X_vvoo(:,:,:,:)
double precision, allocatable :: T_vvoo(:,:,:,:), T_ovvo(:,:,:,:), T_vo(:,:)
integer :: i,j,k,l,a,b,c,d
double precision :: e,ta,tb, delta, delta_ijk
!allocate(W(nV,nV,nV,nO,nO,nO))
!allocate(V(nV,nV,nV,nO,nO,nO))
allocate(W_ijk(nV,nV,nV), V_ijk(nV,nV,nV))
allocate(X_vvvo(nV,nV,nV,nO), X_ovoo(nO,nV,nO,nO), X_vvoo(nV,nV,nO,nO))
allocate(T_vvoo(nV,nV,nO,nO), T_ovvo(nO,nV,nV,nO), T_vo(nV,nO))
! Temporary arrays
!$OMP PARALLEL &
!$OMP SHARED(nO,nV,T_vvoo,T_ovvo,T_vo,X_vvvo,X_ovoo,X_vvoo, &
!$OMP t1,t2,v_vvvo,v_vooo,v_vvoo) &
!$OMP PRIVATE(a,b,c,d,i,j,k,l) &
!$OMP DEFAULT(NONE)
!v_vvvo(b,a,d,i) * t2(k,j,c,d) &
!X_vvvo(d,b,a,i) * T_vvoo(d,c,k,j)
!$OMP DO collapse(3)
do i = 1, nO
do a = 1, nV
do b = 1, nV
do d = 1, nV
X_vvvo(d,b,a,i) = v_vvvo(b,a,d,i)
enddo
enddo
enddo
enddo
!$OMP END DO nowait
!$OMP DO collapse(3)
do j = 1, nO
do k = 1, nO
do c = 1, nV
do d = 1, nV
T_vvoo(d,c,k,j) = t2(k,j,c,d)
enddo
enddo
enddo
enddo
!$OMP END DO nowait
!v_vooo(c,j,k,l) * t2(i,l,a,b) &
!X_ovoo(l,c,j,k) * T_ovvo(l,a,b,i) &
!$OMP DO collapse(3)
do k = 1, nO
do j = 1, nO
do c = 1, nV
do l = 1, nO
X_ovoo(l,c,j,k) = v_vooo(c,j,k,l)
enddo
enddo
enddo
enddo
!$OMP END DO nowait
!$OMP DO collapse(3)
do i = 1, nO
do b = 1, nV
do a = 1, nV
do l = 1, nO
T_ovvo(l,a,b,i) = t2(i,l,a,b)
enddo
enddo
enddo
enddo
!$OMP END DO nowait
!v_vvoo(b,c,j,k) * t1(i,a) &
!X_vvoo(b,c,k,j) * T1_vo(a,i) &
!$OMP DO collapse(3)
do j = 1, nO
do k = 1, nO
do c = 1, nV
do b = 1, nV
X_vvoo(b,c,k,j) = v_vvoo(b,c,j,k)
enddo
enddo
enddo
enddo
!$OMP END DO nowait
!$OMP DO collapse(1)
do i = 1, nO
do a = 1, nV
T_vo(a,i) = t1(i,a)
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
call wall_time(ta)
energy = 0d0
do i = 1, nO
do j = 1, nO
do k = 1, nO
delta_ijk = f_o(i) + f_o(j) + f_o(k)
call form_w_ijk(nO,nV,i,j,k,T_vvoo,T_ovvo,X_vvvo,X_ovoo,W_ijk)
call form_v_ijk(nO,nV,i,j,k,T_vo,X_vvoo,W_ijk,V_ijk)
!$OMP PARALLEL &
!$OMP SHARED(energy,nV,i,j,k,W_ijk,V_ijk,f_o,f_v,delta_ijk) &
!$OMP PRIVATE(a,b,c,e,delta) &
!$OMP DEFAULT(NONE)
e = 0d0
!$OMP DO
do c = 1, nV
do b = 1, nV
do a = 1, nV
delta = 1d0 / (delta_ijk - f_v(a) - f_v(b) - f_v(c))
!energy = energy + (4d0 * W(i,j,k,a,b,c) + W(i,j,k,b,c,a) + W(i,j,k,c,a,b)) * (V(i,j,k,a,b,c) - V(i,j,k,c,b,a)) / (cc_space_f_o(i) + cc_space_f_o(j) + cc_space_f_o(k) - cc_space_f_v(a) - cc_space_f_v(b) - cc_space_f_v(c)) !delta_ooovvv(i,j,k,a,b,c)
e = e + (4d0 * W_ijk(a,b,c) + W_ijk(b,c,a) + W_ijk(c,a,b)) &
* (V_ijk(a,b,c) - V_ijk(c,b,a)) * delta
enddo
enddo
enddo
!$OMP END DO
!$OMP CRITICAL
energy = energy + e
!$OMP END CRITICAL
!$OMP END PARALLEL
enddo
enddo
call wall_time(tb)
write(*,'(F12.2,A5,F12.2,A2)') dble(i)/dble(nO)*100d0, '% in ', tb - ta, ' s'
enddo
energy = energy / 3d0
deallocate(W_ijk,V_ijk,X_vvvo,X_ovoo,T_vvoo,T_ovvo,T_vo)
!deallocate(V,W)
endW_ijk
subroutine form_w_ijk(nO,nV,i,j,k,T_vvoo,T_ovvo,X_vvvo,X_ovoo,W)
implicit none
integer, intent(in) :: nO,nV,i,j,k
!double precision, intent(in) :: t2(nO,nO,nV,nV)
double precision, intent(in) :: T_vvoo(nV,nV,nO,nO), T_ovvo(nO,nV,nV,nO)
double precision, intent(in) :: X_vvvo(nV,nV,nV,nO), X_ovoo(nO,nV,nO,nO)
double precision, intent(out) :: W(nV,nV,nV)!,nO,nO,nO)
integer :: l,a,b,c,d
!W = 0d0
!do i = 1, nO
! do j = 1, nO
! do k = 1, nO
!$OMP PARALLEL &
!$OMP SHARED(nO,nV,i,j,k,T_vvoo,T_ovvo,X_vvvo,X_ovoo,W) &
!$OMP PRIVATE(a,b,c,d,l) &
!$OMP DEFAULT(NONE)
!$OMP DO collapse(2)
do c = 1, nV
do b = 1, nV
do a = 1, nV
W(a,b,c) = 0d0
do d = 1, nV
!W(i,j,k,a,b,c) = W(i,j,k,a,b,c) &
W(a,b,c) = W(a,b,c) &
! chem (bd|ai)
! phys <ba|di>
!+ cc_space_v_vvvo(b,a,d,i) * t2(k,j,c,d) &
!+ cc_space_v_vvvo(c,a,d,i) * t2(j,k,b,d) & ! bc kj
!+ cc_space_v_vvvo(a,c,d,k) * t2(j,i,b,d) & ! prev ac ik
!+ cc_space_v_vvvo(b,c,d,k) * t2(i,j,a,d) & ! prev ab ij
!+ cc_space_v_vvvo(c,b,d,j) * t2(i,k,a,d) & ! prev bc kj
!+ cc_space_v_vvvo(a,b,d,j) * t2(k,i,c,d) ! prev ac ik
+ X_vvvo(d,b,a,i) * T_vvoo(d,c,k,j) &
+ X_vvvo(d,c,a,i) * T_vvoo(d,b,j,k) & ! bc kj
+ X_vvvo(d,a,c,k) * T_vvoo(d,b,j,i) & ! prev ac ik
+ X_vvvo(d,b,c,k) * T_vvoo(d,a,i,j) & ! prev ab ij
+ X_vvvo(d,c,b,j) * T_vvoo(d,a,i,k) & ! prev bc kj
+ X_vvvo(d,a,b,j) * T_vvoo(d,c,k,i) ! prev ac ik
enddo
enddo
enddo
enddo
!$OMP END DO nowait
!$OMP DO collapse(2)
do c = 1, nV
do b = 1, nV
do a = 1, nV
do l = 1, nO
!W(i,j,k,a,b,c) = W(i,j,k,a,b,c) &
W(a,b,c) = W(a,b,c) &
! chem (ck|jl)
! phys <cj|kl>
!- cc_space_v_vooo(c,j,k,l) * t2(i,l,a,b) &
!- cc_space_v_vooo(b,k,j,l) * t2(i,l,a,c) & ! bc kj
!- cc_space_v_vooo(b,i,j,l) * t2(k,l,c,a) & ! prev ac ik
!- cc_space_v_vooo(a,j,i,l) * t2(k,l,c,b) & ! prev ab ij
!- cc_space_v_vooo(a,k,i,l) * t2(j,l,b,c) & ! prev bc kj
!- cc_space_v_vooo(c,i,k,l) * t2(j,l,b,a) ! prev ac ik
- X_ovoo(l,c,j,k) * T_ovvo(l,a,b,i) &
- X_ovoo(l,b,k,j) * T_ovvo(l,a,c,i) & ! bc kj
- X_ovoo(l,b,i,j) * T_ovvo(l,c,a,k) & ! prev ac ik
- X_ovoo(l,a,j,i) * T_ovvo(l,c,b,k) & ! prev ab ij
- X_ovoo(l,a,k,i) * T_ovvo(l,b,c,j) & ! prev bc kj
- X_ovoo(l,c,i,k) * T_ovvo(l,b,a,j) ! prev ac ik
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
! enddo
! enddo
!enddo
endV_ijk
subroutine form_v_ijk(nO,nV,i,j,k,T_vo,X_vvoo,w,v)
implicit none
integer, intent(in) :: nO,nV,i,j,k
!double precision, intent(in) :: t1(nO,nV)
double precision, intent(in) :: T_vo(nV,nO)
double precision, intent(in) :: X_vvoo(nV,nV,nO,nO)
double precision, intent(in) :: W(nV,nV,nV)!,nO,nO,nO)
double precision, intent(out) :: V(nV,nV,nV)!,nO,nO,nO)
integer :: a,b,c
!V = 0d0
!do i = 1, nO
! do j = 1, nO
! do k = 1, nO
!$OMP PARALLEL &
!$OMP SHARED(nO,nV,i,j,k,T_vo,X_vvoo,W,V) &
!$OMP PRIVATE(a,b,c) &
!$OMP DEFAULT(NONE)
!$OMP DO collapse(2)
do c = 1, nV
do b = 1, nV
do a = 1, nV
!V(i,j,k,a,b,c) = V(i,j,k,a,b,c) + W(i,j,k,a,b,c) &
V(a,b,c) = W(a,b,c) &
!+ cc_space_v_vvoo(b,c,j,k) * t1(i,a) &
!+ cc_space_v_vvoo(a,c,i,k) * t1(j,b) &
!+ cc_space_v_vvoo(a,b,i,j) * t1(k,c)
+ X_vvoo(b,c,k,j) * T_vo(a,i) &
+ X_vvoo(a,c,k,i) * T_vo(b,j) &
+ X_vvoo(a,b,j,i) * T_vo(c,k)
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
! enddo
! enddo
!enddo
end