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QuantumPackage/plugins/local/bi_ort_ints/three_body_ijmk.irp.f

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9.7 KiB
Fortran
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! ---
BEGIN_PROVIDER [ double precision, three_e_4_idx_direct_bi_ort , (mo_num, mo_num, mo_num, mo_num)]
&BEGIN_PROVIDER [ double precision, three_e_4_idx_exch13_bi_ort , (mo_num, mo_num, mo_num, mo_num)]
&BEGIN_PROVIDER [ double precision, three_e_4_idx_exch23_bi_ort , (mo_num, mo_num, mo_num, mo_num)]
&BEGIN_PROVIDER [ double precision, three_e_4_idx_cycle_1_bi_ort, (mo_num, mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator FOR THE DIRECT TERMS OF SINGLE EXCITATIONS AND BI ORTHO MOs
!
! three_e_4_idx_direct_bi_ort (m,j,k,i) = < m j k | -L | m j i > ::: notice that i is the RIGHT MO and k is the LEFT MO
! three_e_4_idx_exch13_bi_ort (m,j,k,i) = < m j k | -L | i j m > ::: notice that i is the RIGHT MO and k is the LEFT MO
! three_e_4_idx_exch23_bi_ort (m,j,k,i) = < m j k | -L | j m i > ::: notice that i is the RIGHT MO and k is the LEFT MO
! three_e_4_idx_cycle_1_bi_ort(m,j,k,i) = < m j k | -L | j i m > ::: notice that i is the RIGHT MO and k is the LEFT MO
!
! notice the -1 sign: in this way three_e_4_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
!
! three_e_4_idx_direct_bi_ort (m,j,k,i) : Lk Ri Imm Ijj + Lj Rj Imm Iki + Lm Rm Ijj Iki
! three_e_4_idx_exch13_bi_ort (m,j,k,i) : Lk Rm Imi Ijj + Lj Rj Imi Ikm + Lm Ri Ijj Ikm
! three_e_4_idx_exch23_bi_ort (m,j,k,i) : Lk Ri Imj Ijm + Lj Rm Imj Iki + Lm Rj Ijm Iki
! three_e_4_idx_cycle_1_bi_ort(m,j,k,i) : Lk Rm Imj Iji + Lj Ri Imj Ikm + Lm Rj Iji Ikm
!
END_DOC
implicit none
integer :: ipoint, i, j, k, m, n
double precision :: wall1, wall0
double precision :: tmp_loc_1, tmp_loc_2
double precision, allocatable :: tmp1(:,:,:), tmp2(:,:,:)
double precision, allocatable :: tmp_2d(:,:)
double precision, allocatable :: tmp_aux_1(:,:,:), tmp_aux_2(:,:)
print *, ' Providing the three_e_4_idx_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
! to reduce the number of operations
allocate(tmp_aux_1(n_points_final_grid,4,mo_num))
allocate(tmp_aux_2(n_points_final_grid,mo_num))
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (n, ipoint) &
!$OMP SHARED (mo_num, n_points_final_grid, &
!$OMP mos_l_in_r_array_transp, mos_r_in_r_array_transp, &
!$OMP int2_grad1_u12_bimo_t, final_weight_at_r_vector, &
!$OMP tmp_aux_1, tmp_aux_2)
!$OMP DO
do n = 1, mo_num
do ipoint = 1, n_points_final_grid
tmp_aux_1(ipoint,1,n) = int2_grad1_u12_bimo_t(ipoint,1,n,n) * final_weight_at_r_vector(ipoint)
tmp_aux_1(ipoint,2,n) = int2_grad1_u12_bimo_t(ipoint,2,n,n) * final_weight_at_r_vector(ipoint)
tmp_aux_1(ipoint,3,n) = int2_grad1_u12_bimo_t(ipoint,3,n,n) * final_weight_at_r_vector(ipoint)
tmp_aux_1(ipoint,4,n) = mos_l_in_r_array_transp(ipoint,n) * mos_r_in_r_array_transp(ipoint,n) * final_weight_at_r_vector(ipoint)
tmp_aux_2(ipoint,n) = mos_l_in_r_array_transp(ipoint,n) * mos_r_in_r_array_transp(ipoint,n)
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
! loops approach to break the O(N^4) scaling in memory
call set_multiple_levels_omp(.false.)
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (k, i, j, m, n, ipoint, tmp_loc_1, tmp_loc_2, tmp_2d, tmp1, tmp2) &
!$OMP SHARED (mo_num, n_points_final_grid, &
!$OMP mos_l_in_r_array_transp, mos_r_in_r_array_transp, &
!$OMP int2_grad1_u12_bimo_t, final_weight_at_r_vector, &
!$OMP tmp_aux_1, tmp_aux_2, &
!$OMP three_e_4_idx_direct_bi_ort, three_e_4_idx_exch13_bi_ort, &
!$OMP three_e_4_idx_exch23_bi_ort, three_e_4_idx_cycle_1_bi_ort)
allocate(tmp_2d(mo_num,mo_num))
allocate(tmp1(n_points_final_grid,4,mo_num))
allocate(tmp2(n_points_final_grid,4,mo_num))
!$OMP DO
do k = 1, mo_num
! ---
do i = 1, mo_num
! ---
do n = 1, mo_num
do ipoint = 1, n_points_final_grid
tmp_loc_1 = mos_l_in_r_array_transp(ipoint,k) * mos_r_in_r_array_transp(ipoint,i)
tmp_loc_2 = tmp_aux_2(ipoint,n)
tmp1(ipoint,1,n) = int2_grad1_u12_bimo_t(ipoint,1,n,n) * tmp_loc_1 + int2_grad1_u12_bimo_t(ipoint,1,k,i) * tmp_loc_2
tmp1(ipoint,2,n) = int2_grad1_u12_bimo_t(ipoint,2,n,n) * tmp_loc_1 + int2_grad1_u12_bimo_t(ipoint,2,k,i) * tmp_loc_2
tmp1(ipoint,3,n) = int2_grad1_u12_bimo_t(ipoint,3,n,n) * tmp_loc_1 + int2_grad1_u12_bimo_t(ipoint,3,k,i) * tmp_loc_2
tmp1(ipoint,4,n) = int2_grad1_u12_bimo_t(ipoint,1,n,n) * int2_grad1_u12_bimo_t(ipoint,1,k,i) &
+ int2_grad1_u12_bimo_t(ipoint,2,n,n) * int2_grad1_u12_bimo_t(ipoint,2,k,i) &
+ int2_grad1_u12_bimo_t(ipoint,3,n,n) * int2_grad1_u12_bimo_t(ipoint,3,k,i)
enddo
enddo
call dgemm( 'T', 'N', mo_num, mo_num, 4*n_points_final_grid, 1.d0 &
, tmp_aux_1(1,1,1), 4*n_points_final_grid, tmp1(1,1,1), 4*n_points_final_grid &
, 0.d0, tmp_2d(1,1), mo_num)
do j = 1, mo_num
do m = 1, mo_num
three_e_4_idx_direct_bi_ort(m,j,k,i) = -tmp_2d(m,j)
enddo
enddo
! ---
do n = 1, mo_num
do ipoint = 1, n_points_final_grid
tmp_loc_1 = mos_l_in_r_array_transp(ipoint,k) * mos_r_in_r_array_transp(ipoint,n)
tmp_loc_2 = mos_l_in_r_array_transp(ipoint,n) * mos_r_in_r_array_transp(ipoint,i)
tmp1(ipoint,1,n) = int2_grad1_u12_bimo_t(ipoint,1,n,i) * tmp_loc_1 + int2_grad1_u12_bimo_t(ipoint,1,k,n) * tmp_loc_2
tmp1(ipoint,2,n) = int2_grad1_u12_bimo_t(ipoint,2,n,i) * tmp_loc_1 + int2_grad1_u12_bimo_t(ipoint,2,k,n) * tmp_loc_2
tmp1(ipoint,3,n) = int2_grad1_u12_bimo_t(ipoint,3,n,i) * tmp_loc_1 + int2_grad1_u12_bimo_t(ipoint,3,k,n) * tmp_loc_2
tmp1(ipoint,4,n) = int2_grad1_u12_bimo_t(ipoint,1,n,i) * int2_grad1_u12_bimo_t(ipoint,1,k,n) &
+ int2_grad1_u12_bimo_t(ipoint,2,n,i) * int2_grad1_u12_bimo_t(ipoint,2,k,n) &
+ int2_grad1_u12_bimo_t(ipoint,3,n,i) * int2_grad1_u12_bimo_t(ipoint,3,k,n)
tmp2(ipoint,1,n) = final_weight_at_r_vector(ipoint) * int2_grad1_u12_bimo_t(ipoint,1,i,n)
tmp2(ipoint,2,n) = final_weight_at_r_vector(ipoint) * int2_grad1_u12_bimo_t(ipoint,2,i,n)
tmp2(ipoint,3,n) = final_weight_at_r_vector(ipoint) * int2_grad1_u12_bimo_t(ipoint,3,i,n)
tmp2(ipoint,4,n) = final_weight_at_r_vector(ipoint) * mos_l_in_r_array_transp(ipoint,i) * mos_r_in_r_array_transp(ipoint,n)
enddo
enddo
! ---
call dgemm( 'T', 'N', mo_num, mo_num, 4*n_points_final_grid, 1.d0 &
, tmp1(1,1,1), 4*n_points_final_grid, tmp_aux_1(1,1,1), 4*n_points_final_grid &
, 0.d0, tmp_2d(1,1), mo_num)
do j = 1, mo_num
do m = 1, mo_num
three_e_4_idx_exch13_bi_ort(m,j,k,i) = -tmp_2d(m,j)
enddo
enddo
! ---
call dgemm( 'T', 'N', mo_num, mo_num, 4*n_points_final_grid, 1.d0 &
, tmp1(1,1,1), 4*n_points_final_grid, tmp2(1,1,1), 4*n_points_final_grid &
, 0.d0, tmp_2d(1,1), mo_num)
do j = 1, mo_num
do m = 1, mo_num
three_e_4_idx_cycle_1_bi_ort(m,i,k,j) = -tmp_2d(m,j)
enddo
enddo
! ---
enddo ! i
! ---
do j = 1, mo_num
do n = 1, mo_num
do ipoint = 1, n_points_final_grid
tmp_loc_1 = final_weight_at_r_vector(ipoint) * mos_l_in_r_array_transp(ipoint,j) * mos_r_in_r_array_transp(ipoint,n)
tmp_loc_2 = final_weight_at_r_vector(ipoint) * mos_l_in_r_array_transp(ipoint,n) * mos_r_in_r_array_transp(ipoint,j)
tmp1(ipoint,1,n) = int2_grad1_u12_bimo_t(ipoint,1,n,j) * tmp_loc_1 + int2_grad1_u12_bimo_t(ipoint,1,j,n) * tmp_loc_2
tmp1(ipoint,2,n) = int2_grad1_u12_bimo_t(ipoint,2,n,j) * tmp_loc_1 + int2_grad1_u12_bimo_t(ipoint,2,j,n) * tmp_loc_2
tmp1(ipoint,3,n) = int2_grad1_u12_bimo_t(ipoint,3,n,j) * tmp_loc_1 + int2_grad1_u12_bimo_t(ipoint,3,j,n) * tmp_loc_2
tmp1(ipoint,4,n) = int2_grad1_u12_bimo_t(ipoint,1,n,j) * int2_grad1_u12_bimo_t(ipoint,1,j,n) &
+ int2_grad1_u12_bimo_t(ipoint,2,n,j) * int2_grad1_u12_bimo_t(ipoint,2,j,n) &
+ int2_grad1_u12_bimo_t(ipoint,3,n,j) * int2_grad1_u12_bimo_t(ipoint,3,j,n)
tmp2(ipoint,1,n) = int2_grad1_u12_bimo_t(ipoint,1,k,n)
tmp2(ipoint,2,n) = int2_grad1_u12_bimo_t(ipoint,2,k,n)
tmp2(ipoint,3,n) = int2_grad1_u12_bimo_t(ipoint,3,k,n)
tmp2(ipoint,4,n) = final_weight_at_r_vector(ipoint) * mos_l_in_r_array_transp(ipoint,k) * mos_r_in_r_array_transp(ipoint,n)
enddo
enddo
call dgemm( 'T', 'N', mo_num, mo_num, 4*n_points_final_grid, 1.d0 &
, tmp1(1,1,1), 4*n_points_final_grid, tmp2(1,1,1), 4*n_points_final_grid &
, 0.d0, tmp_2d(1,1), mo_num)
do i = 1, mo_num
do m = 1, mo_num
three_e_4_idx_exch23_bi_ort(m,j,k,i) = -tmp_2d(m,i)
enddo
enddo
enddo ! j
! ---
enddo !k
!$OMP END DO
deallocate(tmp_2d)
deallocate(tmp1)
deallocate(tmp2)
!$OMP END PARALLEL
deallocate(tmp_aux_1)
deallocate(tmp_aux_2)
call wall_time(wall1)
print *, ' wall time for three_e_4_idx_bi_ort', wall1 - wall0
call print_memory_usage()
END_PROVIDER
! ---
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