1044 lines
24 KiB
Fortran
1044 lines
24 KiB
Fortran
! Hessian
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! The hessian of the CI energy with respects to the orbital rotation is :
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! (C-c C-x C-l)
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! \begin{align*}
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! H_{pq,rs} &= \dfrac{\partial^2 E(x)}{\partial x_{pq}^2} \\
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! &= \mathcal{P}_{pq} \mathcal{P}_{rs} [ \frac{1}{2} \sum_u [\delta_{qr}(h_p^u \gamma_u^s + h_u^s \gamma_p^u)
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! + \delta_{ps}(h_r^u \gamma_u^q + h_u^q \gamma_r^u)]
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! -(h_p^s \gamma_r^q + h_r^q \gamma_p^s) \\
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! &+ \frac{1}{2} \sum_{tuv} [\delta_{qr}(v_{pt}^{uv} \Gamma_{uv}^{st} + v_{uv}^{st} \Gamma_{pt}^{uv})
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! + \delta_{ps}(v_{uv}^{qt} \Gamma_{rt}^{uv} + v_{rt}^{uv}\Gamma_{uv}^{qt})] \\
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! &+ \sum_{uv} (v_{pr}^{uv} \Gamma_{uv}^{qs} + v_{uv}^{qs} \Gamma_{pr}^{uv})
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! - \sum_{tu} (v_{pu}^{st} \Gamma_{rt}^{qu}+v_{pu}^{tr} \Gamma_{tr}^{qu}+v_{rt}^{qu}\Gamma_{pu}^{st} + v_{tr}^{qu}\Gamma_{pu}^{ts})
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! \end{align*}
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! With pq a permutation operator :
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! \begin{align*}
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! \mathcal{P}_{pq}= 1 - (p \leftrightarrow q)
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! \end{align*}
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! \begin{align*}
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! \mathcal{P}_{pq} \mathcal{P}_{rs} &= (1 - (p \leftrightarrow q))(1 - (r \leftrightarrow s)) \\
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! &= 1 - (p \leftrightarrow q) - (r \leftrightarrow s) + (p \leftrightarrow q, r \leftrightarrow s)
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! \end{align*}
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! Where p,q,r,s,t,u,v are general spatial orbitals
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! mo_num : the number of molecular orbitals
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! $$h$$ : One electron integrals
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! $$\gamma$$ : One body density matrix (state average in our case)
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! $$v$$ : Two electron integrals
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! $$\Gamma$$ : Two body density matrice (state average in our case)
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! The hessian is a 4D matrix of size mo_num, p,q,r,s,t,u,v take all the
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! values between 1 and mo_num (1 and mo_num include).
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! To do that we compute all the pairs (pq,rs)
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! Source :
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! Seniority-based coupled cluster theory
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! J. Chem. Phys. 141, 244104 (2014); https://doi.org/10.1063/1.4904384
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! Thomas M. Henderson, Ireneusz W. Bulik, Tamar Stein, and Gustavo E. Scuseria
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! *Compute the hessian of energy with respects to orbital rotations*
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! Provided:
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! | mo_num | integer | number of MOs |
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! | mo_one_e_integrals(mo_num,mo_num) | double precision | mono-electronic integrals |
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! | one_e_dm_mo(mo_num,mo_num) | double precision | one e- density matrix (state average) |
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! | two_e_dm_mo(mo_num,mo_num,mo_num) | double precision | two e- density matrix (state average) |
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! Input:
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! | n | integer | mo_num*(mo_num-1)/2 |
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! Output:
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! | H(n,n) | double precision | Hessian matrix |
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! | h_tmpr(mo_num,mo_num,mo_num,mo_num) | double precision | Complete hessian matrix before the tranformation |
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! | | | in n by n matrix |
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! Internal:
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! | hessian(mo_num,mo_num,mo_num,mo_num) | double precision | temporary array containing the hessian before |
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! | | | the permutations |
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! | p, q, r, s | integer | indexes of the hessian elements |
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! | t, u, v | integer | indexes for the sums |
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! | pq, rs | integer | indexes for the transformation of the hessian |
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! | | | (4D -> 2D) |
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! | t1,t2,t3 | double precision | t3 = t2 - t1, time to compute the hessian |
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! | t4,t5,t6 | double precision | t6 = t5 - t4, time to compute each element |
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! | tmp_bi_int_3(mo_num,mo_num,mo_num) | double precision | 3 indexes temporary array for the bielectronic integrals |
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! | tmp_2rdm_3(mo_num,mo_num,mo_num) | double precision | 3 indexes temporary array for the 2 body density matrix |
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! | ind_3(mo_num,mo_num,mo_num) | double precision | 3 indexes temporary array for matrix multiplication |
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! | tmp_accu(mo_num,mo_num) | double precision | temporary array |
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! | tmp_accu_sym(mo_num,mo_num) | double precision | temporary array |
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! Function:
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! | get_two_e_integral | double precision | bielectronic integrals |
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subroutine hessian_opt(n,H,h_tmpr)
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use omp_lib
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include 'constants.h'
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implicit none
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! Variables
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! in
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integer, intent(in) :: n
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! out
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double precision, intent(out) :: H(n,n),h_tmpr(mo_num,mo_num,mo_num,mo_num)
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! internal
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double precision, allocatable :: hessian(:,:,:,:)!, h_tmpr(:,:,:,:)
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double precision, allocatable :: H_test(:,:)
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integer :: p,q
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integer :: r,s,t,u,v,k
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integer :: pq,rs
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double precision :: t1,t2,t3,t4,t5,t6
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! H_test : monum**2 by mo_num**2 double precision matrix to debug the H matrix
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double precision, allocatable :: tmp_bi_int_3(:,:,:), tmp_2rdm_3(:,:,:), ind_3(:,:,:)
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double precision, allocatable :: tmp_accu(:,:), tmp_accu_sym(:,:), tmp_accu_shared(:,:),tmp_accu_sym_shared(:,:)
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! Function
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double precision :: get_two_e_integral
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print*,''
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print*,'---hessian---'
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print*,'Use the full hessian'
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! Allocation of shared arrays
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allocate(hessian(mo_num,mo_num,mo_num,mo_num))!,h_tmpr(mo_num,mo_num,mo_num,mo_num))
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allocate(tmp_accu_shared(mo_num,mo_num),tmp_accu_sym_shared(mo_num,mo_num))
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! Calculations
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! OMP
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call omp_set_max_active_levels(1)
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!$OMP PARALLEL &
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!$OMP PRIVATE( &
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!$OMP p,q,r,s, tmp_accu, tmp_accu_sym, &
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!$OMP u,v,t, tmp_bi_int_3, tmp_2rdm_3, ind_3) &
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!$OMP SHARED(hessian,h_tmpr,H, mo_num,n, &
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!$OMP mo_one_e_integrals, one_e_dm_mo, &
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!$OMP two_e_dm_mo,mo_integrals_map,tmp_accu_sym_shared, tmp_accu_shared, &
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!$OMP t1,t2,t3,t4,t5,t6)&
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!$OMP DEFAULT(NONE)
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! Allocation of private arrays
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allocate(tmp_bi_int_3(mo_num,mo_num,mo_num))
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allocate(tmp_2rdm_3(mo_num,mo_num,mo_num), ind_3(mo_num,mo_num,mo_num))
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allocate(tmp_accu(mo_num,mo_num), tmp_accu_sym(mo_num,mo_num))
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! Initialization of the arrays
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!$OMP MASTER
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do q = 1, mo_num
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do p = 1, mo_num
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tmp_accu_shared(p,q) = 0d0
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enddo
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enddo
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!$OMP END MASTER
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!$OMP MASTER
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do q = 1, mo_num
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do p = 1, mo_num
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tmp_accu_sym(p,q) = 0d0
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enddo
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enddo
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!$OMP END MASTER
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!$OMP DO
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do s=1,mo_num
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do r=1,mo_num
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do q=1,mo_num
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do p=1,mo_num
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hessian(p,q,r,s) = 0d0
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enddo
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enddo
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enddo
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enddo
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!$OMP ENDDO
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!$OMP MASTER
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CALL wall_TIME(t1)
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!$OMP END MASTER
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! Line 1, term 1
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! Without optimization the term 1 of the line 1 is :
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! do p = 1, mo_num
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! do q = 1, mo_num
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! do r = 1, mo_num
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! do s = 1, mo_num
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! if (q==r) then
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! do u = 1, mo_num
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! hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
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! mo_one_e_integrals(u,p) * one_e_dm_mo(u,s) &
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! + mo_one_e_integrals(s,u) * one_e_dm_mo(p,u))
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! enddo
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! endif
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! enddo
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! enddo
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! enddo
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! enddo
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! We can write the formula as matrix multiplication.
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! $$c_{p,s} = \sum_u a_{p,u} b_{u,s}$$
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!$OMP MASTER
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CALL wall_TIME(t4)
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!$OMP END MASTER
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call dgemm('T','N', mo_num, mo_num, mo_num, 1d0, mo_one_e_integrals,&
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size(mo_one_e_integrals,1), one_e_dm_mo, size(one_e_dm_mo,1),&
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0d0, tmp_accu_shared, size(tmp_accu_shared,1))
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!$OMP DO
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do s = 1, mo_num
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do p = 1, mo_num
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tmp_accu_sym_shared(p,s) = 0.5d0 * (tmp_accu_shared(p,s) + tmp_accu_shared(s,p))
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enddo
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enddo
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!$OMP END DO
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!$OMP DO
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do s = 1, mo_num
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do p = 1, mo_num
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do r = 1, mo_num
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hessian(p,r,r,s) = hessian(p,r,r,s) + tmp_accu_sym_shared(p,s)
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enddo
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enddo
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enddo
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!$OMP END DO
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!$OMP MASTER
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CALL wall_TIME(t5)
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t6=t5-t4
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print*,'l1 1',t6
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!$OMP END MASTER
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! Line 1, term 2
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! do p = 1, mo_num
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! do q = 1, mo_num
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! do r = 1, mo_num
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! do s = 1, mo_num
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! if (p==s) then
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! do u = 1, mo_num
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! hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
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! mo_one_e_integrals(u,r) * (one_e_dm_mo(u,q) &
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! + mo_one_e_integrals(q,u) * (one_e_dm_mo(r,u))
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! enddo
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! endif
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! enddo
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! enddo
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! enddo
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! enddo
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! We can write the formula as matrix multiplication.
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! $$c_{r,q} = \sum_u a_{r,u} b_{u,q}$$
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!$OMP MASTER
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CALL wall_TIME(t4)
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!$OMP END MASTER
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call dgemm('T','N', mo_num, mo_num, mo_num, 1d0, mo_one_e_integrals,&
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size(mo_one_e_integrals,1), one_e_dm_mo, size(one_e_dm_mo,1),&
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0d0, tmp_accu_shared, size(tmp_accu_shared,1))
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!$OMP DO
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do r = 1, mo_num
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do q = 1, mo_num
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tmp_accu_sym_shared(q,r) = 0.5d0 * (tmp_accu_shared(q,r) + tmp_accu_shared(r,q))
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enddo
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enddo
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!OMP END DO
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!$OMP DO
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do r = 1, mo_num
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do q = 1, mo_num
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do s = 1, mo_num
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hessian(s,q,r,s) = hessian(s,q,r,s) + tmp_accu_sym_shared(q,r)
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enddo
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enddo
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enddo
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!OMP END DO
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!$OMP MASTER
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CALL wall_TIME(t5)
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t6=t5-t4
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print*,'l1 2',t6
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!$OMP END MASTER
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! Line 1, term 3
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! Without optimization the third term is :
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! do p = 1, mo_num
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! do q = 1, mo_num
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! do r = 1, mo_num
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! do s = 1, mo_num
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! hessian(p,q,r,s) = hessian(p,q,r,s) &
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! - mo_one_e_integrals(s,p) * one_e_dm_mo(r,q) &
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! - mo_one_e_integrals(q,r) * one_e_dm_mo(p,s))
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! enddo
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! enddo
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! enddo
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! enddo
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! We can just re-order the indexes
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!$OMP MASTER
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CALL wall_TIME(t4)
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!$OMP END MASTER
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!$OMP DO
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do s = 1, mo_num
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do r = 1, mo_num
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do q = 1, mo_num
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do p = 1, mo_num
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hessian(p,q,r,s) = hessian(p,q,r,s) &
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- mo_one_e_integrals(s,p) * one_e_dm_mo(r,q)&
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- mo_one_e_integrals(q,r) * one_e_dm_mo(p,s)
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enddo
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enddo
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enddo
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enddo
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!$OMP END DO
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!$OMP MASTER
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CALL wall_TIME(t5)
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t6=t5-t4
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print*,'l1 3',t6
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!$OMP END MASTER
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! Line 2, term 1
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! Without optimization the fourth term is :
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! do p = 1, mo_num
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! do q = 1, mo_num
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! do r = 1, mo_num
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! do s = 1, mo_num
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! if (q==r) then
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! do t = 1, mo_num
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! do u = 1, mo_num
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! do v = 1, mo_num
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! hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
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! get_two_e_integral(u,v,p,t,mo_integrals_map) * two_e_dm_mo(u,v,s,t) &
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! + get_two_e_integral(s,t,u,v,mo_integrals_map) * two_e_dm_mo(p,t,u,v))
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! enddo
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! enddo
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! enddo
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! endif
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! enddo
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! enddo
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! enddo
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! enddo
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! Using bielectronic integral properties :
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! get_two_e_integral(s,t,u,v,mo_integrals_map) =
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! get_two_e_integral(u,v,s,t,mo_integrals_map)
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! Using the two electron density matrix properties :
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! two_e_dm_mo(p,t,u,v) = two_e_dm_mo(u,v,p,t)
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! With t on the external loop, using temporary arrays for each t and by
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! taking u,v as one variable a matrix multplication appears.
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! $$c_{p,s} = \sum_{uv} a_{p,uv} b_{uv,s}$$
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! There is a kroenecker delta $$\delta_{qr}$$, so we juste compute the
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! terms like : hessian(p,r,r,s)
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!$OMP MASTER
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call wall_TIME(t4)
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!$OMP END MASTER
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!$OMP DO
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do t = 1, mo_num
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do p = 1, mo_num
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do v = 1, mo_num
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do u = 1, mo_num
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tmp_bi_int_3(u,v,p) = get_two_e_integral(u,v,p,t,mo_integrals_map)
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enddo
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enddo
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enddo
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do p = 1, mo_num ! error, the p might be replace by a s
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! it's a temporary array, the result by replacing p and s will be the same
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do v = 1, mo_num
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do u = 1, mo_num
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tmp_2rdm_3(u,v,p) = two_e_dm_mo(u,v,p,t)
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enddo
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enddo
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enddo
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call dgemm('T','N', mo_num, mo_num, mo_num*mo_num, 1.d0, &
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tmp_bi_int_3, mo_num*mo_num, tmp_2rdm_3, mo_num*mo_num, &
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0.d0, tmp_accu, size(tmp_accu,1))
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do p = 1, mo_num
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do s = 1, mo_num
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tmp_accu_sym(s,p) = 0.5d0 * (tmp_accu(p,s)+tmp_accu(s,p))
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enddo
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enddo
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!$OMP CRITICAL
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do s = 1, mo_num
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do r = 1, mo_num
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do p = 1, mo_num
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hessian(p,r,r,s) = hessian(p,r,r,s) + tmp_accu_sym(p,s)
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enddo
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enddo
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enddo
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!$OMP END CRITICAL
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enddo
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!$OMP END DO
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!$OMP MASTER
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call wall_TIME(t5)
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t6=t5-t4
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print*,'l2 1', t6
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!$OMP END MASTER
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! Line 2, term 2
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! do p = 1, mo_num
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! do q = 1, mo_num
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! do r = 1, mo_num
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! do s = 1, mo_num
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! if (p==s) then
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! do t = 1, mo_num
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! do u = 1, mo_num
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! do v = 1, mo_num
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! hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
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! get_two_e_integral(q,t,u,v,mo_integrals_map) * two_e_dm_mo(r,t,u,v) &
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! + get_two_e_integral(u,v,r,t,mo_integrals_map) * two_e_dm_mo(u,v,q,t))
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! enddo
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! enddo
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! enddo
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! endif
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! enddo
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! enddo
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! enddo
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! enddo
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! Using the two electron density matrix properties :
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! get_two_e_integral(q,t,u,v,mo_integrals_map) =
|
|
! get_two_e_integral(u,v,q,t,mo_integrals_map)
|
|
|
|
! Using the two electron density matrix properties :
|
|
! two_e_dm_mo(r,t,u,v) = two_e_dm_mo(u,v,r,t)
|
|
|
|
! With t on the external loop, using temporary arrays for each t and by
|
|
! taking u,v as one variable a matrix multplication appears.
|
|
! $$c_{q,r} = \sum_uv a_{q,uv} b_{uv,r}$$
|
|
|
|
! There is a kroenecker delta $$\delta_{ps}$$, so we juste compute the
|
|
! terms like : hessian(s,q,r,s)
|
|
|
|
|
|
!******************************
|
|
! Opt Second line, second term
|
|
!******************************
|
|
|
|
!$OMP MASTER
|
|
CALL wall_TIME(t4)
|
|
!$OMP END MASTER
|
|
|
|
!$OMP DO
|
|
do t = 1, mo_num
|
|
|
|
do q = 1, mo_num
|
|
do v = 1, mo_num
|
|
do u = 1, mo_num
|
|
|
|
tmp_bi_int_3(u,v,q) = get_two_e_integral(u,v,q,t,mo_integrals_map)
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
do r = 1, mo_num
|
|
do v = 1, mo_num
|
|
do u = 1, mo_num
|
|
|
|
tmp_2rdm_3(u,v,r) = two_e_dm_mo(u,v,r,t)
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
call dgemm('T','N', mo_num, mo_num, mo_num*mo_num, 1.d0, &
|
|
tmp_bi_int_3 , mo_num*mo_num, tmp_2rdm_3, mo_num*mo_num, &
|
|
0.d0, tmp_accu, size(tmp_accu,1))
|
|
|
|
do r = 1, mo_num
|
|
do q = 1, mo_num
|
|
|
|
tmp_accu_sym(q,r) = 0.5d0 * (tmp_accu(q,r) + tmp_accu(r,q))
|
|
|
|
enddo
|
|
enddo
|
|
|
|
!$OMP CRITICAL
|
|
do r = 1, mo_num
|
|
do q = 1, mo_num
|
|
do s = 1, mo_num
|
|
|
|
hessian(s,q,r,s) = hessian(s,q,r,s) + tmp_accu_sym(q,r)
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
!$OMP END CRITICAL
|
|
|
|
enddo
|
|
!$OMP END DO
|
|
|
|
!$OMP MASTER
|
|
CALL wall_TIME(t5)
|
|
t6=t5-t4
|
|
print*,'l2 2',t6
|
|
!$OMP END MASTER
|
|
|
|
! Line 3, term 1
|
|
|
|
! do p = 1, mo_num
|
|
! do q = 1, mo_num
|
|
! do r = 1, mo_num
|
|
! do s = 1, mo_num
|
|
|
|
! do u = 1, mo_num
|
|
! do v = 1, mo_num
|
|
|
|
! hessian(p,q,r,s) = hessian(p,q,r,s) &
|
|
! + get_two_e_integral(u,v,p,r,mo_integrals_map) * two_e_dm_mo(u,v,q,s) &
|
|
! + get_two_e_integral(q,s,u,v,mo_integrals_map) * two_e_dm_mo(p,r,u,v)
|
|
|
|
! enddo
|
|
! enddo
|
|
|
|
! enddo
|
|
! enddo
|
|
! enddo
|
|
! enddo
|
|
|
|
! Using the two electron density matrix properties :
|
|
! get_two_e_integral(u,v,p,r,mo_integrals_map) =
|
|
! get_two_e_integral(p,r,u,v,mo_integrals_map)
|
|
|
|
! Using the two electron density matrix properties :
|
|
! two_e_dm_mo(u,v,q,s) = two_e_dm_mo(q,s,u,v)
|
|
|
|
! With v on the external loop, using temporary arrays for each v and by
|
|
! taking p,r and q,s as one dimension a matrix multplication
|
|
! appears. $$c_{pr,qs} = \sum_u a_{pr,u} b_{u,qs}$$
|
|
|
|
! Part 1
|
|
|
|
!$OMP MASTER
|
|
call wall_TIME(t4)
|
|
!$OMP END MASTER
|
|
|
|
!--------
|
|
! part 1
|
|
! get_two_e_integral(u,v,p,r,mo_integrals_map) * two_e_dm_mo(u,v,q,s)
|
|
!--------
|
|
|
|
!$OMP DO
|
|
do v = 1, mo_num
|
|
|
|
do u = 1, mo_num
|
|
do r = 1, mo_num
|
|
do p = 1, mo_num
|
|
|
|
tmp_bi_int_3(p,r,u) = get_two_e_integral(p,r,u,v,mo_integrals_map)
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
do s = 1, mo_num
|
|
do q = 1, mo_num
|
|
do u = 1, mo_num
|
|
|
|
tmp_2rdm_3(u,q,s) = two_e_dm_mo(q,s,u,v)
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
do s = 1, mo_num
|
|
|
|
call dgemm('N','N',mo_num*mo_num, mo_num, mo_num, 1d0, tmp_bi_int_3,&
|
|
size(tmp_bi_int_3,1)*size(tmp_bi_int_3,2), tmp_2rdm_3(1,1,s),&
|
|
size(tmp_2rdm_3,1), 0d0, ind_3, size(ind_3,1) * size(ind_3,2))
|
|
|
|
!$OMP CRITICAL
|
|
do r = 1, mo_num
|
|
do q = 1, mo_num
|
|
do p = 1, mo_num
|
|
hessian(p,q,r,s) = hessian(p,q,r,s) + ind_3(p,r,q)
|
|
enddo
|
|
enddo
|
|
enddo
|
|
!$OMP END CRITICAL
|
|
|
|
enddo
|
|
|
|
enddo
|
|
!$OMP END DO
|
|
|
|
|
|
|
|
! With v on the external loop, using temporary arrays for each v and by
|
|
! taking q,s and p,r as one dimension a matrix multplication
|
|
! appears. $$c_{qs,pr} = \sum_u a_{qs,u}*b_{u,pr}$$
|
|
|
|
! Part 2
|
|
|
|
!--------
|
|
! part 2
|
|
! get_two_e_integral(q,s,u,v,mo_integrals_map) * two_e_dm_mo(p,r,u,v)
|
|
!--------
|
|
|
|
!$OMP DO
|
|
do v = 1, mo_num
|
|
|
|
do u = 1, mo_num
|
|
do s = 1, mo_num
|
|
do q = 1, mo_num
|
|
|
|
tmp_bi_int_3(q,s,u) = get_two_e_integral(q,s,u,v,mo_integrals_map)
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
do r = 1, mo_num
|
|
do p = 1, mo_num
|
|
do u = 1, mo_num
|
|
|
|
tmp_2rdm_3(u,p,r) = two_e_dm_mo(p,r,u,v)
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
do r = 1, mo_num
|
|
call dgemm('N','N', mo_num*mo_num, mo_num, mo_num, 1d0, tmp_bi_int_3,&
|
|
size(tmp_bi_int_3,1)*size(tmp_bi_int_3,2), tmp_2rdm_3(1,1,r),&
|
|
size(tmp_2rdm_3,1), 0d0, ind_3, size(ind_3,1) * size(ind_3,2))
|
|
|
|
!$OMP CRITICAL
|
|
do s = 1, mo_num
|
|
do q = 1, mo_num
|
|
do p = 1, mo_num
|
|
hessian(p,q,r,s) = hessian(p,q,r,s) + ind_3(q,s,p)
|
|
enddo
|
|
enddo
|
|
enddo
|
|
!$OMP END CRITICAL
|
|
|
|
enddo
|
|
|
|
enddo
|
|
!$OMP END DO
|
|
|
|
!$OMP MASTER
|
|
call wall_TIME(t5)
|
|
t6 = t5 - t4
|
|
print*,'l3 1', t6
|
|
!$OMP END MASTER
|
|
|
|
! Line 3, term 2
|
|
|
|
! do p = 1, mo_num
|
|
! do q = 1, mo_num
|
|
! do r = 1, mo_num
|
|
! do s = 1, mo_num
|
|
|
|
! do t = 1, mo_num
|
|
! do u = 1, mo_num
|
|
|
|
! hessian(p,q,r,s) = hessian(p,q,r,s) &
|
|
! - get_two_e_integral(s,t,p,u,mo_integrals_map) * two_e_dm_mo(r,t,q,u) &
|
|
! - get_two_e_integral(t,s,p,u,mo_integrals_map) * two_e_dm_mo(t,r,q,u) &
|
|
! - get_two_e_integral(q,u,r,t,mo_integrals_map) * two_e_dm_mo(p,u,s,t) &
|
|
! - get_two_e_integral(q,u,t,r,mo_integrals_map) * two_e_dm_mo(p,u,t,s)
|
|
|
|
! enddo
|
|
! enddo
|
|
|
|
! enddo
|
|
! enddo
|
|
! enddo
|
|
! enddo
|
|
|
|
! With q on the external loop, using temporary arrays for each p and q,
|
|
! and taking u,v as one variable, a matrix multiplication appears:
|
|
! $$c_{r,s} = \sum_{ut} a_{r,ut} b_{ut,s}$$
|
|
|
|
! Part 1
|
|
|
|
!--------
|
|
! Part 1
|
|
! - get_two_e_integral(s,t,p,u,mo_integrals_map) * two_e_dm_mo(r,t,q,u)
|
|
!--------
|
|
|
|
!$OMP MASTER
|
|
CALL wall_TIME(t4)
|
|
!$OMP END MASTER
|
|
|
|
!$OMP DO
|
|
do q = 1, mo_num
|
|
|
|
do r = 1, mo_num
|
|
do t = 1, mo_num
|
|
do u = 1, mo_num
|
|
|
|
tmp_2rdm_3(u,t,r) = two_e_dm_mo(q,u,r,t)
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
do p = 1, mo_num
|
|
|
|
do s = 1, mo_num
|
|
do t = 1, mo_num
|
|
do u = 1, mo_num
|
|
|
|
tmp_bi_int_3(u,t,s) = - get_two_e_integral(u,s,t,p,mo_integrals_map)
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
call dgemm('T','N', mo_num, mo_num, mo_num*mo_num, 1d0, tmp_bi_int_3,&
|
|
mo_num*mo_num, tmp_2rdm_3, mo_num*mo_num, 0d0, tmp_accu, mo_num)
|
|
|
|
!$OMP CRITICAL
|
|
do s = 1, mo_num
|
|
do r = 1, mo_num
|
|
|
|
hessian(p,q,r,s) = hessian(p,q,r,s) + tmp_accu(s,r)
|
|
|
|
enddo
|
|
enddo
|
|
!$OMP END CRITICAL
|
|
|
|
enddo
|
|
|
|
enddo
|
|
!$OMP END DO
|
|
|
|
|
|
|
|
! With q on the external loop, using temporary arrays for each p and q,
|
|
! and taking u,v as one variable, a matrix multiplication appears:
|
|
! $$c_{r,s} = \sum_{ut} a_{r,ut} b_{ut,s}$$
|
|
|
|
! Part 2
|
|
|
|
!--------
|
|
! Part 2
|
|
!- get_two_e_integral(t,s,p,u,mo_integrals_map) * two_e_dm_mo(t,r,q,u)
|
|
!--------
|
|
|
|
!$OMP DO
|
|
do q = 1, mo_num
|
|
|
|
do r = 1, mo_num
|
|
do t = 1, mo_num
|
|
do u = 1, mo_num
|
|
|
|
tmp_2rdm_3(u,t,r) = two_e_dm_mo(q,u,t,r)
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
do p = 1, mo_num
|
|
|
|
do s = 1, mo_num
|
|
do t = 1, mo_num
|
|
do u = 1, mo_num
|
|
|
|
tmp_bi_int_3(u,t,s) = - get_two_e_integral(u,t,s,p,mo_integrals_map)
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
call dgemm('T','N', mo_num, mo_num, mo_num*mo_num, 1d0, tmp_bi_int_3,&
|
|
mo_num*mo_num, tmp_2rdm_3, mo_num*mo_num, 0d0, tmp_accu, mo_num)
|
|
|
|
!$OMP CRITICAL
|
|
do s = 1, mo_num
|
|
do r = 1, mo_num
|
|
|
|
hessian(p,q,r,s) = hessian(p,q,r,s) + tmp_accu(s,r)
|
|
|
|
enddo
|
|
enddo
|
|
!$OMP END CRITICAL
|
|
|
|
enddo
|
|
|
|
enddo
|
|
!$OMP END DO
|
|
|
|
|
|
|
|
! With q on the external loop, using temporary arrays for each p and q,
|
|
! and taking u,v as one variable, a matrix multiplication appears:
|
|
! $$c_{r,s} = \sum_{ut} a_{r,ut} b_{ut,s}$$
|
|
|
|
! Part 3
|
|
|
|
!--------
|
|
! Part 3
|
|
!- get_two_e_integral(q,u,r,t,mo_integrals_map) * two_e_dm_mo(p,u,s,t)
|
|
!--------
|
|
|
|
!$OMP DO
|
|
do q = 1, mo_num
|
|
|
|
do r = 1, mo_num
|
|
do t = 1, mo_num
|
|
do u = 1, mo_num
|
|
|
|
tmp_bi_int_3(u,t,r) = - get_two_e_integral(u,q,t,r,mo_integrals_map)
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
do p = 1, mo_num
|
|
|
|
do s = 1, mo_num
|
|
do t = 1, mo_num
|
|
do u = 1, mo_num
|
|
|
|
tmp_2rdm_3(u,t,s) = two_e_dm_mo(p,u,s,t)
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
call dgemm('T','N', mo_num, mo_num, mo_num*mo_num, 1d0, tmp_2rdm_3,&
|
|
mo_num*mo_num, tmp_bi_int_3, mo_num*mo_num, 0d0, tmp_accu, mo_num)
|
|
|
|
!$OMP CRITICAL
|
|
do s = 1, mo_num
|
|
do r = 1, mo_num
|
|
|
|
hessian(p,q,r,s) = hessian(p,q,r,s) + tmp_accu(s,r)
|
|
|
|
enddo
|
|
enddo
|
|
!$OMP END CRITICAL
|
|
|
|
enddo
|
|
|
|
enddo
|
|
!$OMP END DO
|
|
|
|
|
|
|
|
! With q on the external loop, using temporary arrays for each p and q,
|
|
! and taking u,v as one variable, a matrix multiplication appears:
|
|
! $$c_{r,s} = \sum_{ut} a_{r,ut} b_{ut,s}$$
|
|
|
|
! Part 4
|
|
|
|
!--------
|
|
! Part 4
|
|
! - get_two_e_integral(q,u,t,r,mo_integrals_map) * two_e_dm_mo(p,u,t,s)
|
|
!--------
|
|
|
|
!$OMP DO
|
|
do q = 1, mo_num
|
|
|
|
do r = 1, mo_num
|
|
do t = 1, mo_num
|
|
do u = 1, mo_num
|
|
|
|
tmp_bi_int_3(u,t,r) = - get_two_e_integral(u,t,r,q,mo_integrals_map)
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
do p = 1, mo_num
|
|
|
|
do s = 1, mo_num
|
|
do t = 1, mo_num
|
|
do u = 1, mo_num
|
|
|
|
tmp_2rdm_3(u,t,s) = two_e_dm_mo(p,u,t,s)
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
call dgemm('T','N', mo_num, mo_num, mo_num*mo_num, 1d0, tmp_2rdm_3,&
|
|
mo_num*mo_num, tmp_bi_int_3, mo_num*mo_num, 0d0, tmp_accu, mo_num)
|
|
|
|
!$OMP CRITICAL
|
|
do s = 1, mo_num
|
|
do r = 1, mo_num
|
|
|
|
hessian(p,q,r,s) = hessian(p,q,r,s) + tmp_accu(s,r)
|
|
|
|
enddo
|
|
enddo
|
|
!$OMP END CRITICAL
|
|
|
|
enddo
|
|
|
|
enddo
|
|
!$OMP END DO
|
|
|
|
!$OMP MASTER
|
|
call wall_TIME(t5)
|
|
t6 = t5-t4
|
|
print*,'l3 2',t6
|
|
!$OMP END MASTER
|
|
|
|
!$OMP MASTER
|
|
CALL wall_TIME(t2)
|
|
t3 = t2 -t1
|
|
print*,'Time to compute the hessian : ', t3
|
|
!$OMP END MASTER
|
|
|
|
! Deallocation of private arrays
|
|
! In the omp section !
|
|
|
|
deallocate(tmp_bi_int_3, tmp_2rdm_3, tmp_accu, tmp_accu_sym, ind_3)
|
|
|
|
! Permutations
|
|
! As we mentioned before there are two permutation operator in the
|
|
! formula :
|
|
! Hessian(p,q,r,s) = P_pq P_rs [...]
|
|
! => Hessian(p,q,r,s) = (p,q,r,s) - (q,p,r,s) - (p,q,s,r) + (q,p,s,r)
|
|
|
|
|
|
!$OMP MASTER
|
|
CALL wall_TIME(t4)
|
|
!$OMP END MASTER
|
|
|
|
!$OMP DO
|
|
do s = 1, mo_num
|
|
do r = 1, mo_num
|
|
do q = 1, mo_num
|
|
do p = 1, mo_num
|
|
|
|
h_tmpr(p,q,r,s) = (hessian(p,q,r,s) - hessian(q,p,r,s) - hessian(p,q,s,r) + hessian(q,p,s,r))
|
|
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
!$OMP END DO
|
|
|
|
!$OMP MASTER
|
|
call wall_TIME(t5)
|
|
t6 = t5-t4
|
|
print*,'Time for permutations :',t6
|
|
!$OMP END MASTER
|
|
|
|
! 4D -> 2D matrix
|
|
! We need a 2D matrix for the Newton method's. Since the Hessian is
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! "antisymmetric" : $$H_{pq,rs} = -H_{rs,pq}$$
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! We can write it as a 2D matrix, N by N, with N = mo_num(mo_num-1)/2
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! with p<q and r<s
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!$OMP MASTER
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CALL wall_TIME(t4)
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!$OMP END MASTER
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!$OMP DO
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do rs = 1, n
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call vec_to_mat_index(rs,r,s)
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do pq = 1, n
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call vec_to_mat_index(pq,p,q)
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H(pq,rs) = h_tmpr(p,q,r,s)
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enddo
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enddo
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!$OMP END DO
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!$OMP MASTER
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call wall_TIME(t5)
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t6 = t5-t4
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print*,'4D -> 2D :',t6
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!$OMP END MASTER
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!$OMP END PARALLEL
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call omp_set_max_active_levels(4)
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! Display
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if (debug) then
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print*,'2D Hessian matrix'
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do pq = 1, n
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write(*,'(100(F10.5))') H(pq,:)
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enddo
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endif
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! Deallocation of shared arrays, end
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deallocate(hessian)!,h_tmpr)
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! h_tmpr is intent out in order to debug the subroutine
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! It's why we don't deallocate it
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print*,'---End hessian---'
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end subroutine
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