add mo optimization
This commit is contained in:
parent
d6f7ec60f8
commit
b71888f459
|
|
@ -0,0 +1,62 @@
|
|||
#!/usr/bin/env bats
|
||||
|
||||
source $QP_ROOT/tests/bats/common.bats.sh
|
||||
source $QP_ROOT/quantum_package.rc
|
||||
|
||||
|
||||
function run() {
|
||||
thresh=2e-3
|
||||
test_exe scf || skip
|
||||
qp set_file $1
|
||||
qp edit --check
|
||||
qp reset -a
|
||||
qp run scf
|
||||
qp set_frozen_core
|
||||
qp set determinants n_states 2
|
||||
qp set determinants read_wf true
|
||||
qp set mo_two_e_ints io_mo_two_e_integrals None
|
||||
file="$(echo $1 | sed 's/.ezfio//g')"
|
||||
qp run cis
|
||||
qp run debug_gradient_list_opt > $file.debug_g.out
|
||||
err3="$(grep 'Max error:' $file.debug_g.out | awk '{print $3}')"
|
||||
qp run debug_hessian_list_opt > $file.debug_h1.out
|
||||
err1="$(grep 'Max error:' $file.debug_h1.out | awk '{print $3}')"
|
||||
qp run orb_opt > $file.opt1.out
|
||||
energy1="$(grep 'State average energy:' $file.opt1.out | tail -n 1 | awk '{print $4}')"
|
||||
qp set orbital_optimization optimization_method diag
|
||||
qp reset -d
|
||||
qp run scf
|
||||
qp run cis
|
||||
qp run debug_hessian_list_opt > $file.debug_h2.out
|
||||
err2="$(grep 'Max error_H:' $file.debug_h2.out | awk '{print $3}')"
|
||||
qp run orb_opt > $file.opt2.out
|
||||
energy2="$(grep 'State average energy:' $file.opt2.out | tail -n 1 | awk '{print $4}')"
|
||||
qp set orbital_optimization optimization_method full
|
||||
qp reset -d
|
||||
qp run scf
|
||||
eq $energy1 $2 $thresh
|
||||
eq $energy2 $3 $thresh
|
||||
eq $err1 0.0 1e-12
|
||||
eq $err2 0.0 1e-12
|
||||
eq $err3 0.0 1e-12
|
||||
}
|
||||
|
||||
@test "b2_stretched" {
|
||||
run b2_stretched.ezfio -48.9852901484277 -48.9852937541510
|
||||
}
|
||||
|
||||
@test "h2o" {
|
||||
run h2o.ezfio -75.9025622449206 -75.8691844585879
|
||||
}
|
||||
|
||||
@test "h2s" {
|
||||
run h2s.ezfio -398.576255809878 -398.574145943928
|
||||
}
|
||||
|
||||
@test "hbo" {
|
||||
run hbo.ezfio -99.9234823022109 -99.9234763597840
|
||||
}
|
||||
|
||||
@test "hco" {
|
||||
run hco.ezfio -113.204915552241 -113.204905207050
|
||||
}
|
||||
|
|
@ -0,0 +1,29 @@
|
|||
[optimization_method]
|
||||
type: character*(32)
|
||||
doc: Define the kind of hessian for the orbital optimization full : full hessian, diag : diagonal hessian, none : no hessian
|
||||
interface: ezfio,provider,ocaml
|
||||
default: full
|
||||
|
||||
[n_det_start]
|
||||
type: integer
|
||||
doc: Number of determinants after which the orbital optimization will start, n_det_start must be greater than 1. The algorithm does a cipsi until n_det > n_det_start and the optimization starts after
|
||||
interface: ezfio,provider,ocaml
|
||||
default: 5
|
||||
|
||||
[n_det_max_opt]
|
||||
type: integer
|
||||
doc: Maximal number of the determinants in the wf for the orbital optimization (to stop the optimization if n_det > n_det_max_opt)
|
||||
interface: ezfio,provider,ocaml
|
||||
default: 200000
|
||||
|
||||
[optimization_max_nb_iter]
|
||||
type: integer
|
||||
doc: Maximal number of iterations for the orbital optimization
|
||||
interface: ezfio,provider,ocaml
|
||||
default: 20
|
||||
|
||||
[thresh_opt_max_elem_grad]
|
||||
type: double precision
|
||||
doc: Threshold for the convergence, the optimization exits when the biggest element in the gradient is smaller than thresh_optimization_max_elem_grad
|
||||
interface: ezfio,provider,ocaml
|
||||
default: 1.e-5
|
||||
|
|
@ -0,0 +1,7 @@
|
|||
two_body_rdm
|
||||
hartree_fock
|
||||
cipsi
|
||||
davidson_undressed
|
||||
selectors_full
|
||||
generators_full
|
||||
utils_trust_region
|
||||
|
|
@ -0,0 +1,74 @@
|
|||
# Orbital optimization
|
||||
|
||||
## Methods
|
||||
Different methods are available:
|
||||
- full hessian
|
||||
```
|
||||
qp set orbital_optimization optimization_method full
|
||||
```
|
||||
- diagonal hessian
|
||||
```
|
||||
qp set orbital_optimization optimization_method diag
|
||||
```
|
||||
- identity matrix
|
||||
```
|
||||
qp set orbital_optimization optimization_method none
|
||||
```
|
||||
|
||||
After the optimization the ezfio contains the optimized orbitals
|
||||
|
||||
## For a fixed number of determinants
|
||||
To optimize the MOs for the actual determinants:
|
||||
```
|
||||
qp run orb_opt
|
||||
```
|
||||
|
||||
## For a complete optimization, i.e, with a larger and larger wave function
|
||||
To optimize the MOs with a larger and larger wave function:
|
||||
```
|
||||
qp run optimization
|
||||
```
|
||||
|
||||
The results are stored in the EZFIO in "mo_optimization/result_opt",
|
||||
with the following format:
|
||||
(1) (2) (3) (4)
|
||||
1: Number of determinants in the wf,
|
||||
2: Cispi energy before the optimization,
|
||||
3: Cipsi energy after the optimization,
|
||||
4: Energy difference between (2) and (3).
|
||||
|
||||
The optimization process if the following:
|
||||
- we do a first cipsi step to obtain a small number of determinants in the wf
|
||||
- we run an orbital optimization for this wf
|
||||
- we do a new cipsi step to double the number of determinants in the wf
|
||||
- we run an orbital optimization for this wf
|
||||
- ...
|
||||
- we do that until the energy difference between (2) and (3) is
|
||||
smaller than the targeted accuracy for the cispi (targeted_accuracy_cipsi in qp edit)
|
||||
or the wf is larger than a given size (n_det_max_opt in qp_edit)
|
||||
- after that you can reset your determinants (qp reset -d) and run a clean Cispi calculation
|
||||
|
||||
### End of the optimization
|
||||
You can choos the number of determinants after what the
|
||||
optimization will stop:
|
||||
```
|
||||
qp set orbital_optimization n_det_max_opt 1e5 # or any number
|
||||
```
|
||||
## Weight of the states
|
||||
You can change the weights of the differents states directly in qp edit.
|
||||
It will affect ths weights used in the orbital optimization.
|
||||
|
||||
# Tests
|
||||
To run the tests:
|
||||
```
|
||||
qp test
|
||||
```
|
||||
|
||||
# Org files
|
||||
The org files are stored in the directory org in order to avoid overwriting on user changes.
|
||||
The org files can be modified, to export the change to the source code, run
|
||||
```
|
||||
./TANGLE_org_mode.sh
|
||||
mv *.irp.f ../.
|
||||
```
|
||||
|
||||
|
|
@ -0,0 +1,12 @@
|
|||
BEGIN_PROVIDER [ logical, do_only_1h1p ]
|
||||
&BEGIN_PROVIDER [ logical, do_only_cas ]
|
||||
&BEGIN_PROVIDER [ logical, do_ddci ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! In the FCI case, all those are always false
|
||||
END_DOC
|
||||
do_only_1h1p = .False.
|
||||
do_only_cas = .False.
|
||||
do_ddci = .False.
|
||||
END_PROVIDER
|
||||
|
||||
|
|
@ -0,0 +1 @@
|
|||
logical, parameter :: debug=.False.
|
||||
|
|
@ -0,0 +1,78 @@
|
|||
! Debug the gradient
|
||||
|
||||
! *Program to check the gradient*
|
||||
|
||||
! The program compares the result of the first and last code for the
|
||||
! gradient.
|
||||
|
||||
! Provided:
|
||||
! | mo_num | integer | number of MOs |
|
||||
|
||||
! Internal:
|
||||
! | n | integer | number of orbitals pairs (p,q) p<q |
|
||||
! | v_grad(n) | double precision | Original gradient |
|
||||
! | v_grad2(n) | double precision | Gradient |
|
||||
! | i | integer | index |
|
||||
! | threshold | double precision | threshold for the errors |
|
||||
! | max_error | double precision | maximal error in the gradient |
|
||||
! | nb_error | integer | number of error in the gradient |
|
||||
|
||||
|
||||
program debug_gradient_list
|
||||
|
||||
implicit none
|
||||
|
||||
! Variables
|
||||
|
||||
double precision, allocatable :: v_grad(:), v_grad2(:)
|
||||
integer :: n,m
|
||||
integer :: i
|
||||
double precision :: threshold
|
||||
double precision :: max_error, max_elem, norm
|
||||
integer :: nb_error
|
||||
|
||||
m = dim_list_act_orb
|
||||
! Definition of n
|
||||
n = m*(m-1)/2
|
||||
|
||||
PROVIDE mo_two_e_integrals_in_map ! Vérifier pour suppression
|
||||
|
||||
! Allocation
|
||||
allocate(v_grad(n), v_grad2(n))
|
||||
|
||||
! Calculation
|
||||
|
||||
call diagonalize_ci ! Vérifier pour suppression
|
||||
|
||||
! Gradient
|
||||
call gradient_list_opt(n,m,list_act,v_grad,max_elem,norm)
|
||||
call first_gradient_list_opt(n,m,list_act,v_grad2)
|
||||
|
||||
|
||||
v_grad = v_grad - v_grad2
|
||||
nb_error = 0
|
||||
max_error = 0d0
|
||||
threshold = 1d-12
|
||||
|
||||
do i = 1, n
|
||||
if (ABS(v_grad(i)) > threshold) then
|
||||
print*,i,v_grad(i)
|
||||
nb_error = nb_error + 1
|
||||
|
||||
if (ABS(v_grad(i)) > max_error) then
|
||||
max_error = v_grad(i)
|
||||
endif
|
||||
|
||||
endif
|
||||
enddo
|
||||
|
||||
print*,''
|
||||
print*,'Check the gradient'
|
||||
print*,'Threshold:', threshold
|
||||
print*,'Nb error:', nb_error
|
||||
print*,'Max error:', max_error
|
||||
|
||||
! Deallocation
|
||||
deallocate(v_grad,v_grad2)
|
||||
|
||||
end program
|
||||
|
|
@ -0,0 +1,76 @@
|
|||
! Debug the gradient
|
||||
|
||||
! *Program to check the gradient*
|
||||
|
||||
! The program compares the result of the first and last code for the
|
||||
! gradient.
|
||||
|
||||
! Provided:
|
||||
! | mo_num | integer | number of MOs |
|
||||
|
||||
! Internal:
|
||||
! | n | integer | number of orbitals pairs (p,q) p<q |
|
||||
! | v_grad(n) | double precision | Original gradient |
|
||||
! | v_grad2(n) | double precision | Gradient |
|
||||
! | i | integer | index |
|
||||
! | threshold | double precision | threshold for the errors |
|
||||
! | max_error | double precision | maximal error in the gradient |
|
||||
! | nb_error | integer | number of error in the gradient |
|
||||
|
||||
|
||||
program debug_gradient
|
||||
|
||||
implicit none
|
||||
|
||||
! Variables
|
||||
|
||||
double precision, allocatable :: v_grad(:), v_grad2(:)
|
||||
integer :: n
|
||||
integer :: i
|
||||
double precision :: threshold
|
||||
double precision :: max_error, max_elem
|
||||
integer :: nb_error
|
||||
|
||||
! Definition of n
|
||||
n = mo_num*(mo_num-1)/2
|
||||
|
||||
PROVIDE mo_two_e_integrals_in_map ! Vérifier pour suppression
|
||||
|
||||
! Allocation
|
||||
allocate(v_grad(n), v_grad2(n))
|
||||
|
||||
! Calculation
|
||||
|
||||
call diagonalize_ci ! Vérifier pour suppression
|
||||
|
||||
! Gradient
|
||||
call first_gradient_opt(n,v_grad)
|
||||
call gradient_opt(n,v_grad2,max_elem)
|
||||
|
||||
v_grad = v_grad - v_grad2
|
||||
nb_error = 0
|
||||
max_error = 0d0
|
||||
threshold = 1d-12
|
||||
|
||||
do i = 1, n
|
||||
if (ABS(v_grad(i)) > threshold) then
|
||||
print*,v_grad(i)
|
||||
nb_error = nb_error + 1
|
||||
|
||||
if (ABS(v_grad(i)) > max_error) then
|
||||
max_error = v_grad(i)
|
||||
endif
|
||||
|
||||
endif
|
||||
enddo
|
||||
|
||||
print*,''
|
||||
print*,'Check the gradient'
|
||||
print*,'Threshold :', threshold
|
||||
print*,'Nb error :', nb_error
|
||||
print*,'Max error :', max_error
|
||||
|
||||
! Deallocation
|
||||
deallocate(v_grad,v_grad2)
|
||||
|
||||
end program
|
||||
|
|
@ -0,0 +1,147 @@
|
|||
! Debug the hessian
|
||||
|
||||
! *Program to check the hessian matrix*
|
||||
|
||||
! The program compares the result of the first and last code for the
|
||||
! hessian. First of all the 4D hessian and after the 2D hessian.
|
||||
|
||||
! Provided:
|
||||
! | mo_num | integer | number of MOs |
|
||||
! | optimization_method | string | Method for the orbital optimization: |
|
||||
! | | | - 'full' -> full hessian |
|
||||
! | | | - 'diag' -> diagonal hessian |
|
||||
! | dim_list_act_orb | integer | number of active MOs |
|
||||
! | list_act(dim_list_act_orb) | integer | list of the actives MOs |
|
||||
! | | | |
|
||||
|
||||
! Internal:
|
||||
! | m | integer | number of MOs in the list |
|
||||
! | | | (active MOs) |
|
||||
! | n | integer | number of orbitals pairs (p,q) p<q |
|
||||
! | | | n = m*(m-1)/2 |
|
||||
! | H(n,n) | double precision | Original hessian matrix (2D) |
|
||||
! | H2(n,n) | double precision | Hessian matrix (2D) |
|
||||
! | h_f(mo_num,mo_num,mo_num,mo_num) | double precision | Original hessian matrix (4D) |
|
||||
! | h_f2(mo_num,mo_num,mo_num,mo_num) | double precision | Hessian matrix (4D) |
|
||||
! | i,j,p,q,k | integer | indexes |
|
||||
! | threshold | double precision | threshold for the errors |
|
||||
! | max_error | double precision | maximal error in the 4D hessian |
|
||||
! | max_error_H | double precision | maximal error in the 2D hessian |
|
||||
! | nb_error | integer | number of errors in the 4D hessian |
|
||||
! | nb_error_H | integer | number of errors in the 2D hessian |
|
||||
|
||||
|
||||
program debug_hessian_list_opt
|
||||
|
||||
implicit none
|
||||
|
||||
! Variables
|
||||
|
||||
double precision, allocatable :: H(:,:),H2(:,:), h_f(:,:,:,:), h_f2(:,:,:,:)
|
||||
integer :: n,m
|
||||
integer :: i,j,k,l
|
||||
double precision :: max_error, max_error_H
|
||||
integer :: nb_error, nb_error_H
|
||||
double precision :: threshold
|
||||
|
||||
m = dim_list_act_orb !mo_num
|
||||
|
||||
! Definition of n
|
||||
n = m*(m-1)/2
|
||||
|
||||
PROVIDE mo_two_e_integrals_in_map ! Vérifier pour suppression
|
||||
|
||||
! Hessian
|
||||
if (optimization_method == 'full') then
|
||||
print*,'Use the full hessian matrix'
|
||||
allocate(H(n,n),H2(n,n))
|
||||
allocate(h_f(m,m,m,m),h_f2(m,m,m,m))
|
||||
|
||||
call hessian_list_opt(n,m,list_act,H,h_f)
|
||||
call first_hessian_list_opt(n,m,list_act,H2,h_f2)
|
||||
!call hessian_opt(n,H2,h_f2)
|
||||
|
||||
! Difference
|
||||
h_f = h_f - h_f2
|
||||
H = H - H2
|
||||
max_error = 0d0
|
||||
nb_error = 0
|
||||
threshold = 1d-12
|
||||
|
||||
do l = 1, m
|
||||
do k= 1, m
|
||||
do j = 1, m
|
||||
do i = 1, m
|
||||
if (ABS(h_f(i,j,k,l)) > threshold) then
|
||||
print*,h_f(i,j,k,l)
|
||||
nb_error = nb_error + 1
|
||||
if (ABS(h_f(i,j,k,l)) > ABS(max_error)) then
|
||||
max_error = h_f(i,j,k,l)
|
||||
endif
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
max_error_H = 0d0
|
||||
nb_error_H = 0
|
||||
|
||||
do j = 1, n
|
||||
do i = 1, n
|
||||
if (ABS(H(i,j)) > threshold) then
|
||||
print*, H(i,j)
|
||||
nb_error_H = nb_error_H + 1
|
||||
|
||||
if (ABS(H(i,j)) > ABS(max_error_H)) then
|
||||
max_error_H = H(i,j)
|
||||
endif
|
||||
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Deallocation
|
||||
deallocate(H, H2, h_f, h_f2)
|
||||
|
||||
else
|
||||
|
||||
print*, 'Use the diagonal hessian matrix'
|
||||
allocate(H(n,1),H2(n,1))
|
||||
call diag_hessian_list_opt(n,m,list_act,H)
|
||||
call first_diag_hessian_list_opt(n,m,list_act,H2)
|
||||
|
||||
H = H - H2
|
||||
|
||||
max_error_H = 0d0
|
||||
nb_error_H = 0
|
||||
|
||||
do i = 1, n
|
||||
if (ABS(H(i,1)) > threshold) then
|
||||
print*, H(i,1)
|
||||
nb_error_H = nb_error_H + 1
|
||||
|
||||
if (ABS(H(i,1)) > ABS(max_error_H)) then
|
||||
max_error_H = H(i,1)
|
||||
endif
|
||||
|
||||
endif
|
||||
enddo
|
||||
|
||||
endif
|
||||
|
||||
print*,''
|
||||
if (optimization_method == 'full') then
|
||||
print*,'Check of the full hessian'
|
||||
print*,'Threshold:', threshold
|
||||
print*,'Nb error:', nb_error
|
||||
print*,'Max error:', max_error
|
||||
print*,''
|
||||
else
|
||||
print*,'Check of the diagonal hessian'
|
||||
endif
|
||||
|
||||
print*,'Nb error_H:', nb_error_H
|
||||
print*,'Max error_H:', max_error_H
|
||||
|
||||
end program
|
||||
|
|
@ -0,0 +1,171 @@
|
|||
! Debug the hessian
|
||||
|
||||
! *Program to check the hessian matrix*
|
||||
|
||||
! The program compares the result of the first and last code for the
|
||||
! hessian. First of all the 4D hessian and after the 2D hessian.
|
||||
|
||||
! Provided:
|
||||
! | mo_num | integer | number of MOs |
|
||||
|
||||
! Internal:
|
||||
! | n | integer | number of orbitals pairs (p,q) p<q |
|
||||
! | H(n,n) | double precision | Original hessian matrix (2D) |
|
||||
! | H2(n,n) | double precision | Hessian matrix (2D) |
|
||||
! | h_f(mo_num,mo_num,mo_num,mo_num) | double precision | Original hessian matrix (4D) |
|
||||
! | h_f2(mo_num,mo_num,mo_num,mo_num) | double precision | Hessian matrix (4D) |
|
||||
! | method | integer | - 1: full hessian |
|
||||
! | | | - 2: diagonal hessian |
|
||||
! | i,j,p,q,k | integer | indexes |
|
||||
! | threshold | double precision | threshold for the errors |
|
||||
! | max_error | double precision | maximal error in the 4D hessian |
|
||||
! | max_error_H | double precision | maximal error in the 2D hessian |
|
||||
! | nb_error | integer | number of errors in the 4D hessian |
|
||||
! | nb_error_H | integer | number of errors in the 2D hessian |
|
||||
|
||||
|
||||
program debug_hessian
|
||||
|
||||
implicit none
|
||||
|
||||
! Variables
|
||||
|
||||
double precision, allocatable :: H(:,:),H2(:,:), h_f(:,:,:,:), h_f2(:,:,:,:)
|
||||
integer :: n
|
||||
integer :: i,j,k,l
|
||||
double precision :: max_error, max_error_H
|
||||
integer :: nb_error, nb_error_H
|
||||
double precision :: threshold
|
||||
|
||||
! Definition of n
|
||||
n = mo_num*(mo_num-1)/2
|
||||
|
||||
PROVIDE mo_two_e_integrals_in_map ! Vérifier pour suppression
|
||||
|
||||
! Allocation
|
||||
allocate(H(n,n),H2(n,n))
|
||||
allocate(h_f(mo_num,mo_num,mo_num,mo_num),h_f2(mo_num,mo_num,mo_num,mo_num))
|
||||
|
||||
! Calculation
|
||||
|
||||
! Hessian
|
||||
if (optimization_method == 'full') then
|
||||
|
||||
print*,'Use the full hessian matrix'
|
||||
call hessian_opt(n,H,h_f)
|
||||
call first_hessian_opt(n,H2,h_f2)
|
||||
|
||||
! Difference
|
||||
h_f = h_f - h_f2
|
||||
H = H - H2
|
||||
max_error = 0d0
|
||||
nb_error = 0
|
||||
threshold = 1d-12
|
||||
|
||||
do l = 1, mo_num
|
||||
do k= 1, mo_num
|
||||
do j = 1, mo_num
|
||||
do i = 1, mo_num
|
||||
if (ABS(h_f(i,j,k,l)) > threshold) then
|
||||
print*,h_f(i,j,k,l)
|
||||
nb_error = nb_error + 1
|
||||
if (ABS(h_f(i,j,k,l)) > ABS(max_error)) then
|
||||
max_error = h_f(i,j,k,l)
|
||||
endif
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
max_error_H = 0d0
|
||||
nb_error_H = 0
|
||||
|
||||
do j = 1, n
|
||||
do i = 1, n
|
||||
if (ABS(H(i,j)) > threshold) then
|
||||
print*, H(i,j)
|
||||
nb_error_H = nb_error_H + 1
|
||||
|
||||
if (ABS(H(i,j)) > ABS(max_error_H)) then
|
||||
max_error_H = H(i,j)
|
||||
endif
|
||||
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
|
||||
elseif (optimization_method == 'diag') then
|
||||
|
||||
print*, 'Use the diagonal hessian matrix'
|
||||
call diag_hessian_opt(n,H,h_f)
|
||||
call first_diag_hessian_opt(n,H2,h_f2)
|
||||
|
||||
h_f = h_f - h_f2
|
||||
max_error = 0d0
|
||||
nb_error = 0
|
||||
threshold = 1d-12
|
||||
|
||||
do l = 1, mo_num
|
||||
do k = 1, mo_num
|
||||
do j = 1, mo_num
|
||||
do i = 1, mo_num
|
||||
|
||||
if (ABS(h_f(i,j,k,l)) > threshold) then
|
||||
|
||||
print*,h_f(i,j,k,l)
|
||||
nb_error = nb_error + 1
|
||||
|
||||
if (ABS(h_f(i,j,k,l)) > ABS(max_error)) then
|
||||
max_error = h_f(i,j,k,l)
|
||||
endif
|
||||
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
h=H-H2
|
||||
|
||||
max_error_H = 0d0
|
||||
nb_error_H = 0
|
||||
|
||||
do j = 1, n
|
||||
do i = 1, n
|
||||
if (ABS(H(i,j)) > threshold) then
|
||||
print*, H(i,j)
|
||||
nb_error_H = nb_error_H + 1
|
||||
|
||||
if (ABS(H(i,j)) > ABS(max_error_H)) then
|
||||
max_error_H = H(i,j)
|
||||
endif
|
||||
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
|
||||
else
|
||||
print*,'Unknown optimization_method, please select full, diag'
|
||||
call abort
|
||||
endif
|
||||
|
||||
print*,''
|
||||
if (optimization_method == 'full') then
|
||||
print*,'Check the full hessian'
|
||||
else
|
||||
print*,'Check the diagonal hessian'
|
||||
endif
|
||||
|
||||
print*,'Threshold :', threshold
|
||||
print*,'Nb error :', nb_error
|
||||
print*,'Max error :', max_error
|
||||
print*,''
|
||||
print*,'Nb error_H :', nb_error_H
|
||||
print*,'Max error_H :', max_error_H
|
||||
|
||||
! Deallocation
|
||||
deallocate(H,H2,h_f,h_f2)
|
||||
|
||||
end program
|
||||
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
|
|
@ -0,0 +1,136 @@
|
|||
! Diagonalization of the hessian
|
||||
|
||||
! Just a matrix diagonalization using Lapack
|
||||
|
||||
! Input:
|
||||
! | n | integer | mo_num*(mo_num-1)/2 |
|
||||
! | H(n,n) | double precision | hessian |
|
||||
|
||||
! Output:
|
||||
! | e_val(n) | double precision | eigenvalues of the hessian |
|
||||
! | w(n,n) | double precision | eigenvectors of the hessian |
|
||||
|
||||
! Internal:
|
||||
! | nb_negative_nv | integer | number of negative eigenvalues |
|
||||
! | lwork | integer | for Lapack |
|
||||
! | work(lwork,n) | double precision | temporary array for Lapack |
|
||||
! | info | integer | if 0 -> ok, else problem in the diagonalization |
|
||||
! | i,j | integer | dummy indexes |
|
||||
|
||||
|
||||
subroutine diagonalization_hessian(n,H,e_val,w)
|
||||
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
! Variables
|
||||
|
||||
! in
|
||||
integer, intent(in) :: n
|
||||
double precision, intent(in) :: H(n,n)
|
||||
|
||||
! out
|
||||
double precision, intent(out) :: e_val(n), w(n,n)
|
||||
|
||||
! internal
|
||||
double precision, allocatable :: work(:,:)
|
||||
integer, allocatable :: key(:)
|
||||
integer :: info,lwork
|
||||
integer :: i,j
|
||||
integer :: nb_negative_vp
|
||||
double precision :: t1,t2,t3,max_elem
|
||||
|
||||
print*,''
|
||||
print*,'---Diagonalization_hessian---'
|
||||
|
||||
call wall_time(t1)
|
||||
|
||||
if (optimization_method == 'full') then
|
||||
! Allocation
|
||||
! For Lapack
|
||||
lwork=3*n-1
|
||||
|
||||
allocate(work(lwork,n))
|
||||
|
||||
! Calculation
|
||||
|
||||
! Copy the hessian matrix, the eigenvectors will be store in W
|
||||
W=H
|
||||
|
||||
! Diagonalization of the hessian
|
||||
call dsyev('V','U',n,W,size(W,1),e_val,work,lwork,info)
|
||||
|
||||
if (info /= 0) then
|
||||
print*, 'Error diagonalization : diagonalization_hessian'
|
||||
print*, 'info = ', info
|
||||
call ABORT
|
||||
endif
|
||||
|
||||
if (debug) then
|
||||
print *, 'vp Hess:'
|
||||
write(*,'(100(F10.5))') real(e_val(:))
|
||||
endif
|
||||
|
||||
! Number of negative eigenvalues
|
||||
max_elem = 0d0
|
||||
nb_negative_vp = 0
|
||||
do i = 1, n
|
||||
if (e_val(i) < 0d0) then
|
||||
nb_negative_vp = nb_negative_vp + 1
|
||||
if (e_val(i) < max_elem) then
|
||||
max_elem = e_val(i)
|
||||
endif
|
||||
!print*,'e_val < 0 :', e_val(i)
|
||||
endif
|
||||
enddo
|
||||
print*,'Number of negative eigenvalues:', nb_negative_vp
|
||||
print*,'Lowest eigenvalue:',max_elem
|
||||
|
||||
!nb_negative_vp = 0
|
||||
!do i = 1, n
|
||||
! if (e_val(i) < -thresh_eig) then
|
||||
! nb_negative_vp = nb_negative_vp + 1
|
||||
! endif
|
||||
!enddo
|
||||
!print*,'Number of negative eigenvalues <', -thresh_eig,':', nb_negative_vp
|
||||
|
||||
! Deallocation
|
||||
deallocate(work)
|
||||
|
||||
elseif (optimization_method == 'diag') then
|
||||
! Diagonalization of the diagonal hessian by hands
|
||||
allocate(key(n))
|
||||
|
||||
do i = 1, n
|
||||
e_val(i) = H(i,i)
|
||||
enddo
|
||||
|
||||
! Key list for dsort
|
||||
do i = 1, n
|
||||
key(i) = i
|
||||
enddo
|
||||
|
||||
! Sort of the eigenvalues
|
||||
call dsort(e_val, key, n)
|
||||
|
||||
! Eigenvectors
|
||||
W = 0d0
|
||||
do i = 1, n
|
||||
j = key(i)
|
||||
W(j,i) = 1d0
|
||||
enddo
|
||||
|
||||
deallocate(key)
|
||||
else
|
||||
print*,'Diagonalization_hessian, abort'
|
||||
call abort
|
||||
endif
|
||||
|
||||
call wall_time(t2)
|
||||
t3 = t2 - t1
|
||||
print*,'Time in diagonalization_hessian:', t3
|
||||
|
||||
print*,'---End diagonalization_hessian---'
|
||||
|
||||
end subroutine
|
||||
|
|
@ -0,0 +1,372 @@
|
|||
subroutine first_diag_hessian_list_opt(tmp_n,m,list,H)!, h_tmpr)
|
||||
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
!===========================================================================
|
||||
! Compute the diagonal hessian of energy with respects to orbital rotations
|
||||
!===========================================================================
|
||||
|
||||
!===========
|
||||
! Variables
|
||||
!===========
|
||||
|
||||
! in
|
||||
integer, intent(in) :: tmp_n, m, list(m)
|
||||
! tmp_n : integer, tmp_n = m*(m-1)/2
|
||||
|
||||
! out
|
||||
double precision, intent(out) :: H(tmp_n)!, h_tmpr(m,m,m,m)
|
||||
! H : n by n double precision matrix containing the 2D hessian
|
||||
|
||||
! internal
|
||||
double precision, allocatable :: hessian(:,:,:,:), tmp(:,:),h_tmpr(:,:,:,:)
|
||||
integer :: p,q, tmp_p,tmp_q
|
||||
integer :: r,s,t,u,v,tmp_r,tmp_s,tmp_t,tmp_u,tmp_v
|
||||
integer :: pq,rs,tmp_pq,tmp_rs
|
||||
double precision :: t1,t2,t3
|
||||
! hessian : mo_num 4D double precision matrix containing the hessian before the permutations
|
||||
! h_tmpr : mo_num 4D double precision matrix containing the hessian after the permutations
|
||||
! p,q,r,s : integer, indexes of the 4D hessian matrix
|
||||
! t,u,v : integer, indexes to compute hessian elements
|
||||
! pq,rs : integer, indexes for the conversion from 4D to 2D hessian matrix
|
||||
! t1,t2,t3 : double precision, t3 = t2 - t1, time to compute the hessian
|
||||
|
||||
! Function
|
||||
double precision :: get_two_e_integral
|
||||
! get_two_e_integral : double precision function, two e integrals
|
||||
|
||||
! Provided :
|
||||
! mo_one_e_integrals : mono e- integrals
|
||||
! get_two_e_integral : two e- integrals
|
||||
! one_e_dm_mo_alpha, one_e_dm_mo_beta : one body density matrix
|
||||
! two_e_dm_mo : two body density matrix
|
||||
|
||||
print*,'---first_diag_hess_list---'
|
||||
|
||||
!============
|
||||
! Allocation
|
||||
!============
|
||||
|
||||
allocate(hessian(m,m,m,m),tmp(tmp_n,tmp_n),h_tmpr(mo_num,mo_num,mo_num,mo_num))
|
||||
|
||||
!=============
|
||||
! Calculation
|
||||
!=============
|
||||
|
||||
! From Anderson et. al. (2014)
|
||||
! The Journal of Chemical Physics 141, 244104 (2014); doi: 10.1063/1.4904384
|
||||
|
||||
! LaTeX formula :
|
||||
|
||||
!\begin{align*}
|
||||
!H_{pq,rs} &= \dfrac{\partial^2 E(x)}{\partial x_{pq}^2} \\
|
||||
!&= \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)
|
||||
!+ \delta_{ps}(h_r^u \gamma_u^q + h_u^q \gamma_u^r)]
|
||||
!-(h_p^s \gamma_r^q + h_r^q \gamma_p^s) \\
|
||||
!&+ \frac{1}{2} \sum_{tuv} [\delta_{qr}(v_{pt}^{uv} \Gamma_{uv}^{st} +v_{uv}^{st} \Gamma_{pt}^{uv})
|
||||
!+ \delta_{ps}(v_{uv}^{qt} \Gamma_{rt}^{uv} + v_{rt}^{uv}\Gamma_{uv}^{qt})] \\
|
||||
!&+ \sum_{uv} (v_{pr}^{uv} \Gamma_{uv}^{qs} + v_{uv}^{qs} \Gamma_{ps}^{uv}) \\
|
||||
!&- \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})
|
||||
!\end{align*}
|
||||
|
||||
!================
|
||||
! Initialization
|
||||
!================
|
||||
hessian = 0d0
|
||||
|
||||
CALL wall_time(t1)
|
||||
|
||||
!========================
|
||||
! First line, first term
|
||||
!========================
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
if (q==r) then
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) + 0.5d0 * ( &
|
||||
mo_one_e_integrals(u,p) * one_e_dm_mo(u,s) &
|
||||
+ mo_one_e_integrals(s,u) * one_e_dm_mo(p,u))
|
||||
|
||||
enddo
|
||||
endif
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!=========================
|
||||
! First line, second term
|
||||
!=========================
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
if (p==s) then
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) + 0.5d0 * ( &
|
||||
mo_one_e_integrals(u,r) * one_e_dm_mo(u,q) &
|
||||
+ mo_one_e_integrals(q,u) * one_e_dm_mo(r,u))
|
||||
enddo
|
||||
endif
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!========================
|
||||
! First line, third term
|
||||
!========================
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) &
|
||||
- mo_one_e_integrals(s,p) * one_e_dm_mo(r,q) &
|
||||
- mo_one_e_integrals(q,r) * one_e_dm_mo(p,s)
|
||||
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!=========================
|
||||
! Second line, first term
|
||||
!=========================
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
if (q==r) then
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) + 0.5d0 * ( &
|
||||
get_two_e_integral(u,v,p,t,mo_integrals_map) * two_e_dm_mo(u,v,s,t) &
|
||||
+ get_two_e_integral(s,t,u,v,mo_integrals_map) * two_e_dm_mo(p,t,u,v))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!==========================
|
||||
! Second line, second term
|
||||
!==========================
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
if (p==s) then
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) + 0.5d0 * ( &
|
||||
get_two_e_integral(q,t,u,v,mo_integrals_map) * two_e_dm_mo(r,t,u,v) &
|
||||
+ get_two_e_integral(u,v,r,t,mo_integrals_map) * two_e_dm_mo(u,v,q,t))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!========================
|
||||
! Third line, first term
|
||||
!========================
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_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
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!=========================
|
||||
! Third line, second term
|
||||
!=========================
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_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
|
||||
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t2)
|
||||
t2 = t2 - t1
|
||||
print*, 'Time to compute the hessian :', t2
|
||||
|
||||
!==============
|
||||
! Permutations
|
||||
!==============
|
||||
|
||||
! Convert the hessian mo_num * mo_num * mo_num * mo_num matrix in a
|
||||
! 2D n * n matrix (n = mo_num*(mo_num-1)/2)
|
||||
! H(pq,rs) : p<q and r<s
|
||||
|
||||
do tmp_r = 1, m
|
||||
do tmp_s = 1, m
|
||||
do tmp_q = 1, m
|
||||
do tmp_p = 1, m
|
||||
|
||||
h_tmpr(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) - hessian(tmp_q,tmp_p,tmp_r,tmp_s) &
|
||||
- hessian(tmp_p,tmp_q,tmp_s,tmp_r) + hessian(tmp_q,tmp_p,tmp_s,tmp_r)
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!========================
|
||||
! 4D matrix -> 2D matrix
|
||||
!========================
|
||||
|
||||
! Convert the hessian mo_num * mo_num * mo_num * mo_num matrix in a
|
||||
! 2D n * n matrix (n = mo_num*(mo_num-1)/2)
|
||||
! H(pq,rs) : p<q and r<s
|
||||
|
||||
! 4D mo_num matrix to 2D n matrix
|
||||
do tmp_rs = 1, tmp_n
|
||||
call vec_to_mat_index(tmp_rs,tmp_r,tmp_s)
|
||||
do tmp_pq = 1, tmp_n
|
||||
call vec_to_mat_index(tmp_pq,tmp_p,tmp_q)
|
||||
tmp(tmp_pq,tmp_rs) = h_tmpr(tmp_p,tmp_q,tmp_r,tmp_s)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
do p = 1, tmp_n
|
||||
H(p) = tmp(p,p)
|
||||
enddo
|
||||
|
||||
! Display
|
||||
if (debug) then
|
||||
print*,'2D diag Hessian matrix'
|
||||
do tmp_pq = 1, tmp_n
|
||||
write(*,'(100(F10.5))') tmp(tmp_pq,:)
|
||||
enddo
|
||||
endif
|
||||
|
||||
!==============
|
||||
! Deallocation
|
||||
!==============
|
||||
|
||||
deallocate(hessian,h_tmpr,tmp)
|
||||
|
||||
print*,'---End first_diag_hess_list---'
|
||||
|
||||
end subroutine
|
||||
|
|
@ -0,0 +1,344 @@
|
|||
subroutine first_diag_hessian_opt(n,H, h_tmpr)
|
||||
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
!===========================================================================
|
||||
! Compute the diagonal hessian of energy with respects to orbital rotations
|
||||
!===========================================================================
|
||||
|
||||
!===========
|
||||
! Variables
|
||||
!===========
|
||||
|
||||
! in
|
||||
integer, intent(in) :: n
|
||||
! n : integer, n = mo_num*(mo_num-1)/2
|
||||
|
||||
! out
|
||||
double precision, intent(out) :: H(n,n), h_tmpr(mo_num,mo_num,mo_num,mo_num)
|
||||
! H : n by n double precision matrix containing the 2D hessian
|
||||
|
||||
! internal
|
||||
double precision, allocatable :: hessian(:,:,:,:)
|
||||
integer :: p,q
|
||||
integer :: r,s,t,u,v
|
||||
integer :: pq,rs
|
||||
double precision :: t1,t2,t3
|
||||
! hessian : mo_num 4D double precision matrix containing the hessian before the permutations
|
||||
! h_tmpr : mo_num 4D double precision matrix containing the hessian after the permutations
|
||||
! p,q,r,s : integer, indexes of the 4D hessian matrix
|
||||
! t,u,v : integer, indexes to compute hessian elements
|
||||
! pq,rs : integer, indexes for the conversion from 4D to 2D hessian matrix
|
||||
! t1,t2,t3 : double precision, t3 = t2 - t1, time to compute the hessian
|
||||
|
||||
! Function
|
||||
double precision :: get_two_e_integral
|
||||
! get_two_e_integral : double precision function, two e integrals
|
||||
|
||||
! Provided :
|
||||
! mo_one_e_integrals : mono e- integrals
|
||||
! get_two_e_integral : two e- integrals
|
||||
! one_e_dm_mo_alpha, one_e_dm_mo_beta : one body density matrix
|
||||
! two_e_dm_mo : two body density matrix
|
||||
|
||||
!============
|
||||
! Allocation
|
||||
!============
|
||||
|
||||
allocate(hessian(mo_num,mo_num,mo_num,mo_num))!,h_tmpr(mo_num,mo_num,mo_num,mo_num))
|
||||
|
||||
!=============
|
||||
! Calculation
|
||||
!=============
|
||||
|
||||
if (debug) then
|
||||
print*,'Enter in first_diag_hessien'
|
||||
endif
|
||||
|
||||
! From Anderson et. al. (2014)
|
||||
! The Journal of Chemical Physics 141, 244104 (2014); doi: 10.1063/1.4904384
|
||||
|
||||
! LaTeX formula :
|
||||
|
||||
!\begin{align*}
|
||||
!H_{pq,rs} &= \dfrac{\partial^2 E(x)}{\partial x_{pq}^2} \\
|
||||
!&= \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)
|
||||
!+ \delta_{ps}(h_r^u \gamma_u^q + h_u^q \gamma_u^r)]
|
||||
!-(h_p^s \gamma_r^q + h_r^q \gamma_p^s) \\
|
||||
!&+ \frac{1}{2} \sum_{tuv} [\delta_{qr}(v_{pt}^{uv} \Gamma_{uv}^{st} +v_{uv}^{st} \Gamma_{pt}^{uv})
|
||||
!+ \delta_{ps}(v_{uv}^{qt} \Gamma_{rt}^{uv} + v_{rt}^{uv}\Gamma_{uv}^{qt})] \\
|
||||
!&+ \sum_{uv} (v_{pr}^{uv} \Gamma_{uv}^{qs} + v_{uv}^{qs} \Gamma_{ps}^{uv}) \\
|
||||
!&- \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})
|
||||
!\end{align*}
|
||||
|
||||
!================
|
||||
! Initialization
|
||||
!================
|
||||
hessian = 0d0
|
||||
|
||||
CALL wall_time(t1)
|
||||
|
||||
!========================
|
||||
! First line, first term
|
||||
!========================
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
if (q==r) then
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
||||
mo_one_e_integrals(u,p) * one_e_dm_mo(u,s) &
|
||||
+ mo_one_e_integrals(s,u) * one_e_dm_mo(p,u))
|
||||
|
||||
enddo
|
||||
endif
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!=========================
|
||||
! First line, second term
|
||||
!=========================
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
if (p==s) then
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
||||
mo_one_e_integrals(u,r) * one_e_dm_mo(u,q) &
|
||||
+ mo_one_e_integrals(q,u) * one_e_dm_mo(r,u))
|
||||
enddo
|
||||
endif
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!========================
|
||||
! First line, third term
|
||||
!========================
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) &
|
||||
- mo_one_e_integrals(s,p) * one_e_dm_mo(r,q) &
|
||||
- mo_one_e_integrals(q,r) * one_e_dm_mo(p,s)
|
||||
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!=========================
|
||||
! Second line, first term
|
||||
!=========================
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
if (q==r) then
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
||||
get_two_e_integral(u,v,p,t,mo_integrals_map) * two_e_dm_mo(u,v,s,t) &
|
||||
+ get_two_e_integral(s,t,u,v,mo_integrals_map) * two_e_dm_mo(p,t,u,v))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!==========================
|
||||
! Second line, second term
|
||||
!==========================
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
if (p==s) then
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
||||
get_two_e_integral(q,t,u,v,mo_integrals_map) * two_e_dm_mo(r,t,u,v) &
|
||||
+ get_two_e_integral(u,v,r,t,mo_integrals_map) * two_e_dm_mo(u,v,q,t))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!========================
|
||||
! Third line, first term
|
||||
!========================
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
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
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!=========================
|
||||
! Third line, second term
|
||||
!=========================
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
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
|
||||
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t2)
|
||||
t2 = t2 - t1
|
||||
print*, 'Time to compute the hessian :', t2
|
||||
|
||||
!==============
|
||||
! Permutations
|
||||
!==============
|
||||
|
||||
! Convert the hessian mo_num * mo_num * mo_num * mo_num matrix in a
|
||||
! 2D n * n matrix (n = mo_num*(mo_num-1)/2)
|
||||
! H(pq,rs) : p<q and r<s
|
||||
|
||||
do r = 1, mo_num
|
||||
do s = 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
|
||||
|
||||
!========================
|
||||
! 4D matrix -> 2D matrix
|
||||
!========================
|
||||
|
||||
! Convert the hessian mo_num * mo_num * mo_num * mo_num matrix in a
|
||||
! 2D n * n matrix (n = mo_num*(mo_num-1)/2)
|
||||
! H(pq,rs) : p<q and r<s
|
||||
|
||||
! 4D mo_num matrix to 2D n matrix
|
||||
do rs = 1, n
|
||||
call vec_to_mat_index(rs,r,s)
|
||||
do pq = 1, n
|
||||
call vec_to_mat_index(pq,p,q)
|
||||
H(pq,rs) = h_tmpr(p,q,r,s)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Display
|
||||
if (debug) then
|
||||
print*,'2D diag Hessian matrix'
|
||||
do pq = 1, n
|
||||
write(*,'(100(F10.5))') H(pq,:)
|
||||
enddo
|
||||
endif
|
||||
|
||||
!==============
|
||||
! Deallocation
|
||||
!==============
|
||||
|
||||
deallocate(hessian)
|
||||
|
||||
if (debug) then
|
||||
print*,'Leave first_diag_hessien'
|
||||
endif
|
||||
|
||||
end subroutine
|
||||
|
|
@ -0,0 +1,125 @@
|
|||
! First gradient
|
||||
|
||||
subroutine first_gradient_list_opt(tmp_n,m,list,v_grad)
|
||||
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
!===================================================================
|
||||
! Compute the gradient of energy with respects to orbital rotations
|
||||
!===================================================================
|
||||
|
||||
! Check if read_wf = true, else :
|
||||
! qp set determinant read_wf true
|
||||
|
||||
! in
|
||||
integer, intent(in) :: tmp_n,m,list(m)
|
||||
! n : integer, n = m*(m-1)/2
|
||||
! m = list_size
|
||||
|
||||
! out
|
||||
double precision, intent(out) :: v_grad(tmp_n)
|
||||
! v_grad : double precision vector of length n containeing the gradient
|
||||
|
||||
! internal
|
||||
double precision, allocatable :: grad(:,:),A(:,:)
|
||||
double precision :: norm
|
||||
integer :: i,p,q,r,s,t,tmp_i,tmp_p,tmp_q,tmp_r,tmp_s,tmp_t
|
||||
! grad : double precision matrix containing the gradient before the permutation
|
||||
! A : double precision matrix containing the gradient after the permutation
|
||||
! norm : double precision number, the norm of the vector gradient
|
||||
! i,p,q,r,s,t : integer, indexes
|
||||
! istate : integer, the electronic state
|
||||
|
||||
! Function
|
||||
double precision :: get_two_e_integral, norm2
|
||||
! get_two_e_integral : double precision function that gives the two e integrals
|
||||
! norm2 : double precision function that gives the norm of a vector
|
||||
|
||||
! Provided :
|
||||
! mo_one_e_integrals : mono e- integrals
|
||||
! get_two_e_integral : two e- integrals
|
||||
! one_e_dm_mo : one body density matrix (state average)
|
||||
! two_e_dm_mo : two body density matrix (state average)
|
||||
|
||||
print*,'---first_gradient_list---'
|
||||
|
||||
!============
|
||||
! Allocation
|
||||
!============
|
||||
|
||||
allocate(grad(m,m),A(m,m))
|
||||
|
||||
!=============
|
||||
! Calculation
|
||||
!=============
|
||||
|
||||
v_grad = 0d0
|
||||
grad = 0d0
|
||||
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
!grad(tmp_p,tmp_q) = 0d0
|
||||
do r = 1, mo_num
|
||||
grad(tmp_p,tmp_q) = grad(tmp_p,tmp_q) + mo_one_e_integrals(p,r) * one_e_dm_mo(r,q) &
|
||||
- mo_one_e_integrals(r,q) * one_e_dm_mo(p,r)
|
||||
|
||||
enddo
|
||||
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
do t = 1, mo_num
|
||||
|
||||
grad(tmp_p,tmp_q) = grad(tmp_p,tmp_q) &
|
||||
+ get_two_e_integral(p,t,r,s,mo_integrals_map) * two_e_dm_mo(r,s,q,t) &
|
||||
- get_two_e_integral(r,s,q,t,mo_integrals_map) * two_e_dm_mo(p,t,r,s)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Conversion mo_num*mo_num matrix to mo_num(mo_num-1)/2 vector
|
||||
do tmp_i = 1, tmp_n
|
||||
call vec_to_mat_index(tmp_i,tmp_p,tmp_q)
|
||||
v_grad(tmp_i)=(grad(tmp_p,tmp_q) - grad(tmp_q,tmp_p))
|
||||
enddo
|
||||
|
||||
! Display, vector containing the gradient elements
|
||||
if (debug) then
|
||||
print*,'Vector containing the gradient :'
|
||||
write(*,'(100(F10.5))') v_grad(1:tmp_n)
|
||||
endif
|
||||
|
||||
! Norm of the vector
|
||||
norm = norm2(v_grad)
|
||||
print*, 'Norm : ', norm
|
||||
|
||||
! Matrix gradient
|
||||
A = 0d0
|
||||
do tmp_q = 1, m
|
||||
do tmp_p = 1, m
|
||||
A(tmp_p,tmp_q) = grad(tmp_p,tmp_q) - grad(tmp_q,tmp_p)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Display, matrix containting the gradient elements
|
||||
if (debug) then
|
||||
print*,'Matrix containing the gradient :'
|
||||
do tmp_i = 1, m
|
||||
write(*,'(100(E12.5))') A(tmp_i,1:m)
|
||||
enddo
|
||||
endif
|
||||
|
||||
!==============
|
||||
! Deallocation
|
||||
!==============
|
||||
|
||||
deallocate(grad,A)
|
||||
|
||||
print*,'---End first_gradient_list---'
|
||||
|
||||
end subroutine
|
||||
|
|
@ -0,0 +1,128 @@
|
|||
! First gradient
|
||||
|
||||
subroutine first_gradient_opt(n,v_grad)
|
||||
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
!===================================================================
|
||||
! Compute the gradient of energy with respects to orbital rotations
|
||||
!===================================================================
|
||||
|
||||
! Check if read_wf = true, else :
|
||||
! qp set determinant read_wf true
|
||||
|
||||
END_DOC
|
||||
|
||||
! in
|
||||
integer, intent(in) :: n
|
||||
! n : integer, n = mo_num*(mo_num-1)/2
|
||||
|
||||
! out
|
||||
double precision, intent(out) :: v_grad(n)
|
||||
! v_grad : double precision vector of length n containeing the gradient
|
||||
|
||||
! internal
|
||||
double precision, allocatable :: grad(:,:),A(:,:)
|
||||
double precision :: norm
|
||||
integer :: i,p,q,r,s,t
|
||||
integer :: istate
|
||||
! grad : double precision matrix containing the gradient before the permutation
|
||||
! A : double precision matrix containing the gradient after the permutation
|
||||
! norm : double precision number, the norm of the vector gradient
|
||||
! i,p,q,r,s,t : integer, indexes
|
||||
! istate : integer, the electronic state
|
||||
|
||||
! Function
|
||||
double precision :: get_two_e_integral, norm2
|
||||
! get_two_e_integral : double precision function that gives the two e integrals
|
||||
! norm2 : double precision function that gives the norm of a vector
|
||||
|
||||
! Provided :
|
||||
! mo_one_e_integrals : mono e- integrals
|
||||
! get_two_e_integral : two e- integrals
|
||||
! one_e_dm_mo : one body density matrix (state average)
|
||||
! two_e_dm_mo : two body density matrix (state average)
|
||||
|
||||
!============
|
||||
! Allocation
|
||||
!============
|
||||
|
||||
allocate(grad(mo_num,mo_num),A(mo_num,mo_num))
|
||||
|
||||
!=============
|
||||
! Calculation
|
||||
!=============
|
||||
|
||||
if (debug) then
|
||||
print*,'---first_gradient---'
|
||||
endif
|
||||
|
||||
v_grad = 0d0
|
||||
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
grad(p,q) = 0d0
|
||||
do r = 1, mo_num
|
||||
grad(p,q) = grad(p,q) + mo_one_e_integrals(p,r) * one_e_dm_mo(r,q) &
|
||||
- mo_one_e_integrals(r,q) * one_e_dm_mo(p,r)
|
||||
|
||||
enddo
|
||||
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
do t= 1, mo_num
|
||||
|
||||
grad(p,q) = grad(p,q) &
|
||||
+ get_two_e_integral(p,t,r,s,mo_integrals_map) * two_e_dm_mo(r,s,q,t) &
|
||||
- get_two_e_integral(r,s,q,t,mo_integrals_map) * two_e_dm_mo(p,t,r,s)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Conversion mo_num*mo_num matrix to mo_num(mo_num-1)/2 vector
|
||||
do i=1,n
|
||||
call vec_to_mat_index(i,p,q)
|
||||
v_grad(i)=(grad(p,q) - grad(q,p))
|
||||
enddo
|
||||
|
||||
! Display, vector containing the gradient elements
|
||||
if (debug) then
|
||||
print*,'Vector containing the gradient :'
|
||||
write(*,'(100(F10.5))') v_grad(1:n)
|
||||
endif
|
||||
|
||||
! Norm of the vector
|
||||
norm = norm2(v_grad)
|
||||
print*, 'Norm : ', norm
|
||||
|
||||
! Matrix gradient
|
||||
A = 0d0
|
||||
do q=1,mo_num
|
||||
do p=1,mo_num
|
||||
A(p,q) = grad(p,q) - grad(q,p)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Display, matrix containting the gradient elements
|
||||
if (debug) then
|
||||
print*,'Matrix containing the gradient :'
|
||||
do i = 1, mo_num
|
||||
write(*,'(100(E12.5))') A(i,1:mo_num)
|
||||
enddo
|
||||
endif
|
||||
|
||||
!==============
|
||||
! Deallocation
|
||||
!==============
|
||||
|
||||
deallocate(grad,A)
|
||||
|
||||
if (debug) then
|
||||
print*,'---End first_gradient---'
|
||||
endif
|
||||
|
||||
end subroutine
|
||||
|
|
@ -0,0 +1,365 @@
|
|||
subroutine first_hessian_list_opt(tmp_n,m,list,H,h_tmpr)
|
||||
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
!==================================================================
|
||||
! Compute the hessian of energy with respects to orbital rotations
|
||||
!==================================================================
|
||||
|
||||
!===========
|
||||
! Variables
|
||||
!===========
|
||||
|
||||
! in
|
||||
integer, intent(in) :: tmp_n, m, list(m)
|
||||
!tmp_n : integer, tmp_n = m*(m-1)/2
|
||||
|
||||
! out
|
||||
double precision, intent(out) :: H(tmp_n,tmp_n),h_tmpr(m,m,m,m)
|
||||
! H : n by n double precision matrix containing the 2D hessian
|
||||
|
||||
! internal
|
||||
double precision, allocatable :: hessian(:,:,:,:)
|
||||
integer :: p,q, tmp_p,tmp_q
|
||||
integer :: r,s,t,u,v,tmp_r,tmp_s,tmp_t,tmp_u,tmp_v
|
||||
integer :: pq,rs,tmp_pq,tmp_rs
|
||||
double precision :: t1,t2,t3,t4,t5,t6
|
||||
! hessian : mo_num 4D double precision matrix containing the hessian before the permutations
|
||||
! h_tmpr : mo_num 4D double precision matrix containing the hessian after the permutations
|
||||
! p,q,r,s : integer, indexes of the 4D hessian matrix
|
||||
! t,u,v : integer, indexes to compute hessian elements
|
||||
! pq,rs : integer, indexes for the conversion from 4D to 2D hessian matrix
|
||||
! t1,t2,t3 : double precision, t3 = t2 - t1, time to compute the hessian
|
||||
|
||||
! Funtion
|
||||
double precision :: get_two_e_integral
|
||||
! get_two_e_integral : double precision function, two e integrals
|
||||
|
||||
! Provided :
|
||||
! mo_one_e_integrals : mono e- integrals
|
||||
! get_two_e_integral : two e- integrals
|
||||
! one_e_dm_mo_alpha, one_e_dm_mo_beta : one body density matrix
|
||||
! two_e_dm_mo : two body density matrix
|
||||
|
||||
!============
|
||||
! Allocation
|
||||
!============
|
||||
|
||||
allocate(hessian(m,m,m,m))
|
||||
|
||||
!=============
|
||||
! Calculation
|
||||
!=============
|
||||
|
||||
print*,'---first_hess_list---'
|
||||
|
||||
! From Anderson et. al. (2014)
|
||||
! The Journal of Chemical Physics 141, 244104 (2014); doi: 10.1063/1.4904384
|
||||
|
||||
CALL wall_time(t1)
|
||||
|
||||
! Initialization
|
||||
hessian = 0d0
|
||||
|
||||
!========================
|
||||
! First line, first term
|
||||
!========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
if (q==r) then
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) + 0.5d0 * ( &
|
||||
mo_one_e_integrals(u,p) * one_e_dm_mo(u,s) &
|
||||
+ mo_one_e_integrals(s,u) * one_e_dm_mo(p,u))
|
||||
|
||||
enddo
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l1 1 :', t6
|
||||
|
||||
!=========================
|
||||
! First line, second term
|
||||
!=========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
if (p==s) then
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) + 0.5d0 * ( &
|
||||
mo_one_e_integrals(u,r) * one_e_dm_mo(u,q) &
|
||||
+ mo_one_e_integrals(q,u) * one_e_dm_mo(r,u))
|
||||
enddo
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l1 2 :', t6
|
||||
|
||||
!========================
|
||||
! First line, third term
|
||||
!========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) &
|
||||
- mo_one_e_integrals(s,p) * one_e_dm_mo(r,q)&
|
||||
- mo_one_e_integrals(q,r) * one_e_dm_mo(p,s)
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l1 3 :', t6
|
||||
|
||||
|
||||
!=========================
|
||||
! Second line, first term
|
||||
!=========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
if (q==r) then
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) + 0.5d0 * ( &
|
||||
get_two_e_integral(u,v,p,t,mo_integrals_map) * two_e_dm_mo(u,v,s,t) &
|
||||
+ get_two_e_integral(s,t,u,v,mo_integrals_map) * two_e_dm_mo(p,t,u,v))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l2 1 :', t6
|
||||
|
||||
!==========================
|
||||
! Second line, second term
|
||||
!==========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
if (p==s) then
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) + 0.5d0 * ( &
|
||||
get_two_e_integral(q,t,u,v,mo_integrals_map) * two_e_dm_mo(r,t,u,v) &
|
||||
+ get_two_e_integral(u,v,r,t,mo_integrals_map) * two_e_dm_mo(u,v,q,t))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l2 2 :', t6
|
||||
|
||||
!========================
|
||||
! Third line, first term
|
||||
!========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_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
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l3 1 :', t6
|
||||
|
||||
!=========================
|
||||
! Third line, second term
|
||||
!=========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_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
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l3 2 :', t6
|
||||
|
||||
CALL wall_time(t2)
|
||||
t3 = t2 -t1
|
||||
print*,'Time to compute the hessian : ', t3
|
||||
|
||||
!==============
|
||||
! Permutations
|
||||
!==============
|
||||
|
||||
! 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)
|
||||
|
||||
do tmp_s = 1, m
|
||||
do tmp_r = 1, m
|
||||
do tmp_q = 1, m
|
||||
do tmp_p = 1, m
|
||||
|
||||
h_tmpr(tmp_p,tmp_q,tmp_r,tmp_s) = (hessian(tmp_p,tmp_q,tmp_r,tmp_s) - hessian(tmp_q,tmp_p,tmp_r,tmp_s) &
|
||||
- hessian(tmp_p,tmp_q,tmp_s,tmp_r) + hessian(tmp_q,tmp_p,tmp_s,tmp_r))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!========================
|
||||
! 4D matrix to 2D matrix
|
||||
!========================
|
||||
|
||||
! Convert the hessian mo_num * mo_num * mo_num * mo_num matrix in a
|
||||
! 2D n * n matrix (n = mo_num*(mo_num-1)/2)
|
||||
! H(pq,rs) : p<q and r<s
|
||||
|
||||
! 4D mo_num matrix to 2D n matrix
|
||||
do tmp_pq = 1, tmp_n
|
||||
call vec_to_mat_index(tmp_pq,tmp_p,tmp_q)
|
||||
do tmp_rs = 1, tmp_n
|
||||
call vec_to_mat_index(tmp_rs,tmp_r,tmp_s)
|
||||
H(tmp_pq,tmp_rs) = h_tmpr(tmp_p,tmp_q,tmp_r,tmp_s)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Display
|
||||
if (debug) then
|
||||
print*,'2D Hessian matrix'
|
||||
do tmp_pq = 1, tmp_n
|
||||
write(*,'(100(F10.5))') H(tmp_pq,:)
|
||||
enddo
|
||||
endif
|
||||
|
||||
!==============
|
||||
! Deallocation
|
||||
!==============
|
||||
|
||||
deallocate(hessian)
|
||||
|
||||
print*,'---End first_hess_list---'
|
||||
|
||||
end subroutine
|
||||
|
|
@ -0,0 +1,360 @@
|
|||
subroutine first_hessian_opt(n,H,h_tmpr)
|
||||
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
!==================================================================
|
||||
! Compute the hessian of energy with respects to orbital rotations
|
||||
!==================================================================
|
||||
|
||||
!===========
|
||||
! Variables
|
||||
!===========
|
||||
|
||||
! in
|
||||
integer, intent(in) :: n
|
||||
!n : integer, n = mo_num*(mo_num-1)/2
|
||||
|
||||
! out
|
||||
double precision, intent(out) :: H(n,n),h_tmpr(mo_num,mo_num,mo_num,mo_num)
|
||||
! H : n by n double precision matrix containing the 2D hessian
|
||||
|
||||
! internal
|
||||
double precision, allocatable :: hessian(:,:,:,:)
|
||||
integer :: p,q
|
||||
integer :: r,s,t,u,v
|
||||
integer :: pq,rs
|
||||
double precision :: t1,t2,t3,t4,t5,t6
|
||||
! hessian : mo_num 4D double precision matrix containing the hessian before the permutations
|
||||
! h_tmpr : mo_num 4D double precision matrix containing the hessian after the permutations
|
||||
! p,q,r,s : integer, indexes of the 4D hessian matrix
|
||||
! t,u,v : integer, indexes to compute hessian elements
|
||||
! pq,rs : integer, indexes for the conversion from 4D to 2D hessian matrix
|
||||
! t1,t2,t3 : double precision, t3 = t2 - t1, time to compute the hessian
|
||||
|
||||
! Funtion
|
||||
double precision :: get_two_e_integral
|
||||
! get_two_e_integral : double precision function, two e integrals
|
||||
|
||||
! Provided :
|
||||
! mo_one_e_integrals : mono e- integrals
|
||||
! get_two_e_integral : two e- integrals
|
||||
! one_e_dm_mo_alpha, one_e_dm_mo_beta : one body density matrix
|
||||
! two_e_dm_mo : two body density matrix
|
||||
|
||||
!============
|
||||
! Allocation
|
||||
!============
|
||||
|
||||
allocate(hessian(mo_num,mo_num,mo_num,mo_num))
|
||||
|
||||
!=============
|
||||
! Calculation
|
||||
!=============
|
||||
|
||||
if (debug) then
|
||||
print*,'Enter in first_hess'
|
||||
endif
|
||||
|
||||
! From Anderson et. al. (2014)
|
||||
! The Journal of Chemical Physics 141, 244104 (2014); doi: 10.1063/1.4904384
|
||||
|
||||
CALL wall_time(t1)
|
||||
|
||||
! Initialization
|
||||
hessian = 0d0
|
||||
|
||||
!========================
|
||||
! First line, first term
|
||||
!========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
if (q==r) then
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
||||
mo_one_e_integrals(u,p) * one_e_dm_mo(u,s) &
|
||||
+ mo_one_e_integrals(s,u) * one_e_dm_mo(p,u))
|
||||
|
||||
enddo
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l1 1 :', t6
|
||||
|
||||
!=========================
|
||||
! First line, second term
|
||||
!=========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
if (p==s) then
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
||||
mo_one_e_integrals(u,r) * one_e_dm_mo(u,q) &
|
||||
+ mo_one_e_integrals(q,u) * one_e_dm_mo(r,u))
|
||||
enddo
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l1 2 :', t6
|
||||
|
||||
!========================
|
||||
! First line, third term
|
||||
!========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) &
|
||||
- mo_one_e_integrals(s,p) * one_e_dm_mo(r,q)&
|
||||
- mo_one_e_integrals(q,r) * one_e_dm_mo(p,s)
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l1 3 :', t6
|
||||
|
||||
|
||||
!=========================
|
||||
! Second line, first term
|
||||
!=========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do s = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do p = 1, mo_num
|
||||
|
||||
! do p = 1, mo_num
|
||||
! do q = 1, mo_num
|
||||
! do r = 1, mo_num
|
||||
! do s = 1, mo_num
|
||||
|
||||
if (q==r) then
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
||||
get_two_e_integral(u,v,p,t,mo_integrals_map) * two_e_dm_mo(u,v,s,t) &
|
||||
+ get_two_e_integral(s,t,u,v,mo_integrals_map) * two_e_dm_mo(p,t,u,v))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l2 1 :', t6
|
||||
|
||||
!==========================
|
||||
! Second line, second term
|
||||
!==========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do s = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do p = 1, mo_num
|
||||
|
||||
! do p = 1, mo_num
|
||||
! do q = 1, mo_num
|
||||
! do r = 1, mo_num
|
||||
! do s = 1, mo_num
|
||||
|
||||
if (p==s) then
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
||||
get_two_e_integral(q,t,u,v,mo_integrals_map) * two_e_dm_mo(r,t,u,v) &
|
||||
+ get_two_e_integral(u,v,r,t,mo_integrals_map) * two_e_dm_mo(u,v,q,t))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l2 2 :', t6
|
||||
|
||||
!========================
|
||||
! Third line, first term
|
||||
!========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do s = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do p = 1, mo_num
|
||||
|
||||
! 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
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l3 1 :', t6
|
||||
|
||||
!=========================
|
||||
! Third line, second term
|
||||
!=========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do s = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do p = 1, mo_num
|
||||
|
||||
! 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
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l3 2 :', t6
|
||||
|
||||
CALL wall_time(t2)
|
||||
t3 = t2 -t1
|
||||
print*,'Time to compute the hessian : ', t3
|
||||
|
||||
!==============
|
||||
! Permutations
|
||||
!==============
|
||||
|
||||
! 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)
|
||||
|
||||
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
|
||||
|
||||
!========================
|
||||
! 4D matrix to 2D matrix
|
||||
!========================
|
||||
|
||||
! Convert the hessian mo_num * mo_num * mo_num * mo_num matrix in a
|
||||
! 2D n * n matrix (n = mo_num*(mo_num-1)/2)
|
||||
! H(pq,rs) : p<q and r<s
|
||||
|
||||
! 4D mo_num matrix to 2D n matrix
|
||||
do pq = 1, n
|
||||
call vec_to_mat_index(pq,p,q)
|
||||
do rs = 1, n
|
||||
call vec_to_mat_index(rs,r,s)
|
||||
H(pq,rs) = h_tmpr(p,q,r,s)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Display
|
||||
if (debug) then
|
||||
print*,'2D Hessian matrix'
|
||||
do pq = 1, n
|
||||
write(*,'(100(F10.5))') H(pq,:)
|
||||
enddo
|
||||
endif
|
||||
|
||||
!==============
|
||||
! Deallocation
|
||||
!==============
|
||||
|
||||
deallocate(hessian)
|
||||
|
||||
if (debug) then
|
||||
print*,'Leave first_hess'
|
||||
endif
|
||||
|
||||
end subroutine
|
||||
|
|
@ -0,0 +1,381 @@
|
|||
! Gradient
|
||||
|
||||
! The gradient of the CI energy with respects to the orbital rotation
|
||||
! is:
|
||||
! (C-c C-x C-l)
|
||||
! $$
|
||||
! G(p,q) = \mathcal{P}_{pq} \left[ \sum_r (h_p^r \gamma_r^q - h_r^q \gamma_p^r) +
|
||||
! \sum_{rst}(v_{pt}^{rs} \Gamma_{rs}^{qt} - v_{rs}^{qt} \Gamma_{pt}^{rs})
|
||||
! \right]
|
||||
! $$
|
||||
|
||||
|
||||
! $$
|
||||
! \mathcal{P}_{pq}= 1 - (p \leftrightarrow q)
|
||||
! $$
|
||||
|
||||
! $$
|
||||
! G(p,q) = \left[
|
||||
! \sum_r (h_p^r \gamma_r^q - h_r^q \gamma_p^r) +
|
||||
! \sum_{rst}(v_{pt}^{rs} \Gamma_{rs}^{qt} - v_{rs}^{qt} \Gamma_{pt}^{rs})
|
||||
! \right] -
|
||||
! \left[
|
||||
! \sum_r (h_q^r \gamma_r^p - h_r^p \gamma_q^r) +
|
||||
! \sum_{rst}(v_{qt}^{rs} \Gamma_{rs}^{pt} - v_{rs}^{pt}
|
||||
! \Gamma_{qt}^{rs})
|
||||
! \right]
|
||||
! $$
|
||||
|
||||
! Where p,q,r,s,t are general spatial orbitals
|
||||
! mo_num : the number of molecular orbitals
|
||||
! $$h$$ : One electron integrals
|
||||
! $$\gamma$$ : One body density matrix (state average in our case)
|
||||
! $$v$$ : Two electron integrals
|
||||
! $$\Gamma$$ : Two body density matrice (state average in our case)
|
||||
|
||||
! The gradient is a mo_num by mo_num matrix, p,q,r,s,t take all the
|
||||
! values between 1 and mo_num (1 and mo_num include).
|
||||
|
||||
! To do that we compute $$G(p,q)$$ for all the pairs (p,q).
|
||||
|
||||
! Source :
|
||||
! Seniority-based coupled cluster theory
|
||||
! J. Chem. Phys. 141, 244104 (2014); https://doi.org/10.1063/1.4904384
|
||||
! Thomas M. Henderson, Ireneusz W. Bulik, Tamar Stein, and Gustavo
|
||||
! E. Scuseria
|
||||
|
||||
! *Compute the gradient of energy with respects to orbital rotations*
|
||||
|
||||
! Provided:
|
||||
! | mo_num | integer | number of MOs |
|
||||
! | mo_one_e_integrals(mo_num,mo_num) | double precision | mono_electronic integrals |
|
||||
! | one_e_dm_mo(mo_num,mo_num) | double precision | one e- density matrix |
|
||||
! | two_e_dm_mo(mo_num,mo_num,mo_num,mo_num) | double precision | two e- density matrix |
|
||||
|
||||
! Input:
|
||||
! | n | integer | mo_num*(mo_num-1)/2 |
|
||||
|
||||
! Output:
|
||||
! | v_grad(n) | double precision | the gradient |
|
||||
! | max_elem | double precision | maximum element of the gradient |
|
||||
|
||||
! Internal:
|
||||
! | grad(mo_num,mo_num) | double precison | gradient before the tranformation in a vector |
|
||||
! | A((mo_num,mo_num) | doubre precision | gradient after the permutations |
|
||||
! | norm | double precision | norm of the gradient |
|
||||
! | p, q | integer | indexes of the element in the matrix grad |
|
||||
! | i | integer | index for the tranformation in a vector |
|
||||
! | r, s, t | integer | indexes dor the sums |
|
||||
! | t1, t2, t3 | double precision | t3 = t2 - t1, time to compute the gradient |
|
||||
! | t4, t5, t6 | double precission | t6 = t5 - t4, time to compute each element |
|
||||
! | tmp_bi_int_3(mo_num,mo_num,mo_num) | double precision | 3 indexes temporary array for the bi-electronic integrals |
|
||||
! | tmp_2rdm_3(mo_num,mo_num,mo_num) | double precision | 3 indexes temporary array for the two e- density matrix |
|
||||
! | tmp_accu(mo_num,mo_num) | double precision | temporary array |
|
||||
|
||||
! Function:
|
||||
! | get_two_e_integral | double precision | bi-electronic integrals |
|
||||
! | dnrm2 | double precision | (Lapack) norm |
|
||||
|
||||
|
||||
subroutine gradient_list_opt(n,m,list,v_grad,max_elem,norm)
|
||||
use omp_lib
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
! Variables
|
||||
|
||||
! in
|
||||
integer, intent(in) :: n,m,list(m)
|
||||
|
||||
! out
|
||||
double precision, intent(out) :: v_grad(n), max_elem, norm
|
||||
|
||||
! internal
|
||||
double precision, allocatable :: grad(:,:),A(:,:)
|
||||
integer :: i,p,q,r,s,t, tmp_p, tmp_q, tmp_i
|
||||
double precision :: t1,t2,t3,t4,t5,t6
|
||||
|
||||
double precision, allocatable :: tmp_accu(:,:), tmp_mo_one_e_integrals(:,:),tmp_one_e_dm_mo(:,:)
|
||||
double precision, allocatable :: tmp_bi_int_3(:,:,:), tmp_2rdm_3(:,:,:)
|
||||
|
||||
! Functions
|
||||
double precision :: get_two_e_integral, dnrm2
|
||||
|
||||
|
||||
print*,''
|
||||
print*,'---gradient---'
|
||||
|
||||
! Allocation of shared arrays
|
||||
allocate(grad(m,m),A(m,m))
|
||||
allocate(tmp_mo_one_e_integrals(m,mo_num),tmp_one_e_dm_mo(mo_num,m))
|
||||
|
||||
|
||||
! Initialization omp
|
||||
call omp_set_max_active_levels(1)
|
||||
|
||||
!$OMP PARALLEL &
|
||||
!$OMP PRIVATE( &
|
||||
!$OMP p,q,r,s,t,tmp_p,tmp_q, &
|
||||
!$OMP tmp_accu,tmp_bi_int_3, tmp_2rdm_3) &
|
||||
!$OMP SHARED(grad, one_e_dm_mo,m,list,mo_num,mo_one_e_integrals, &
|
||||
!$OMP mo_integrals_map,tmp_one_e_dm_mo, tmp_mo_one_e_integrals,t4,t5,t6) &
|
||||
!$OMP DEFAULT(SHARED)
|
||||
|
||||
! Allocation of private arrays
|
||||
allocate(tmp_accu(m,m))
|
||||
allocate(tmp_bi_int_3(mo_num,mo_num,m))
|
||||
allocate(tmp_2rdm_3(mo_num,mo_num,m))
|
||||
|
||||
! Initialization
|
||||
|
||||
!$OMP DO
|
||||
do tmp_q = 1, m
|
||||
do tmp_p = 1, m
|
||||
grad(tmp_p,tmp_q) = 0d0
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END DO
|
||||
|
||||
! Term 1
|
||||
|
||||
! Without optimization the term 1 is :
|
||||
|
||||
! do p = 1, mo_num
|
||||
! do q = 1, mo_num
|
||||
! do r = 1, mo_num
|
||||
! grad(p,q) = grad(p,q) &
|
||||
! + mo_one_e_integrals(p,r) * one_e_dm_mo(r,q) &
|
||||
! - mo_one_e_integrals(r,q) * one_e_dm_mo(p,r)
|
||||
! enddo
|
||||
! enddo
|
||||
! enddo
|
||||
|
||||
! Since the matrix multiplication A.B is defined like :
|
||||
! \begin{equation}
|
||||
! c_{ij} = \sum_k a_{ik}.b_{kj}
|
||||
! \end{equation}
|
||||
! The previous equation can be rewritten as a matrix multplication
|
||||
|
||||
|
||||
!****************
|
||||
! Opt first term
|
||||
!****************
|
||||
|
||||
!$OMP DO
|
||||
do r = 1, mo_num
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
tmp_mo_one_e_integrals(tmp_p,r) = mo_one_e_integrals(p,r)
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END DO
|
||||
|
||||
!$OMP DO
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do r = 1, mo_num
|
||||
tmp_one_e_dm_mo(r,tmp_q) = one_e_dm_mo(r,q)
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END DO
|
||||
|
||||
call dgemm('N','N',m,m,mo_num,1d0,&
|
||||
tmp_mo_one_e_integrals, size(tmp_mo_one_e_integrals,1),&
|
||||
tmp_one_e_dm_mo,size(tmp_one_e_dm_mo,1),0d0,tmp_accu,size(tmp_accu,1))
|
||||
|
||||
!$OMP DO
|
||||
do tmp_q = 1, m
|
||||
do tmp_p = 1, m
|
||||
|
||||
grad(tmp_p,tmp_q) = grad(tmp_p,tmp_q) + (tmp_accu(tmp_p,tmp_q) - tmp_accu(tmp_q,tmp_p))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END DO
|
||||
|
||||
!$OMP MASTER
|
||||
CALL wall_TIME(t4)
|
||||
!$OMP END MASTER
|
||||
|
||||
! call dgemm('N','N',mo_num,mo_num,mo_num,1d0,mo_one_e_integrals,&
|
||||
! mo_num,one_e_dm_mo,mo_num,0d0,tmp_accu,mo_num)
|
||||
!
|
||||
! !$OMP DO
|
||||
! do q = 1, mo_num
|
||||
! do p = 1, mo_num
|
||||
!
|
||||
! grad(p,q) = grad(p,q) + (tmp_accu(p,q) - tmp_accu(q,p))
|
||||
!
|
||||
! enddo
|
||||
! enddo
|
||||
! !$OMP END DO
|
||||
|
||||
!$OMP MASTER
|
||||
CALL wall_TIME(t5)
|
||||
t6 = t5-t4
|
||||
print*,'Gradient, first term (s) :', t6
|
||||
!$OMP END MASTER
|
||||
|
||||
! Term 2
|
||||
|
||||
! Without optimization the second term is :
|
||||
|
||||
! do p = 1, mo_num
|
||||
! do q = 1, mo_num
|
||||
! do r = 1, mo_num
|
||||
! do s = 1, mo_num
|
||||
! do t= 1, mo_num
|
||||
|
||||
! grad(p,q) = grad(p,q) &
|
||||
! + get_two_e_integral(p,t,r,s,mo_integrals_map) * two_e_dm_mo(r,s,q,t) &
|
||||
! - get_two_e_integral(r,s,q,t,mo_integrals_map) * two_e_dm_mo(p,t,r,s)
|
||||
! enddo
|
||||
! enddo
|
||||
! enddo
|
||||
! enddo
|
||||
! enddo
|
||||
|
||||
! Using the bielectronic integral properties :
|
||||
! get_two_e_integral(p,t,r,s,mo_integrals_map) = get_two_e_integral(r,s,p,t,mo_integrals_map)
|
||||
|
||||
! Using the two body matrix properties :
|
||||
! two_e_dm_mo(p,t,r,s) = two_e_dm_mo(r,s,p,t)
|
||||
|
||||
! t is one the right, we can put it on the external loop and create 3
|
||||
! indexes temporary array
|
||||
! r,s can be seen as one index
|
||||
|
||||
! By doing so, a matrix multiplication appears
|
||||
|
||||
|
||||
!*****************
|
||||
! Opt second term
|
||||
!*****************
|
||||
|
||||
!$OMP MASTER
|
||||
CALL wall_TIME(t4)
|
||||
!$OMP END MASTER
|
||||
|
||||
!$OMP DO
|
||||
do t = 1, mo_num
|
||||
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do s = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
|
||||
tmp_bi_int_3(r,s,tmp_p) = get_two_e_integral(r,s,p,t,mo_integrals_map)
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do s = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
|
||||
tmp_2rdm_3(r,s,tmp_q) = two_e_dm_mo(r,s,q,t)
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
call dgemm('T','N',m,m,mo_num*mo_num,1d0,tmp_bi_int_3,&
|
||||
mo_num*mo_num,tmp_2rdm_3,mo_num*mo_num,0d0,tmp_accu,size(tmp_accu,1))
|
||||
|
||||
!$OMP CRITICAL
|
||||
do tmp_q = 1, m
|
||||
do tmp_p = 1, m
|
||||
|
||||
grad(tmp_p,tmp_q) = grad(tmp_p,tmp_q) + tmp_accu(tmp_p,tmp_q) - tmp_accu(tmp_q,tmp_p)
|
||||
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END CRITICAL
|
||||
|
||||
enddo
|
||||
!$OMP END DO
|
||||
|
||||
!$OMP MASTER
|
||||
CALL wall_TIME(t5)
|
||||
t6 = t5-t4
|
||||
print*,'Gradient second term (s) : ', t6
|
||||
!$OMP END MASTER
|
||||
|
||||
! Deallocation of private arrays
|
||||
|
||||
deallocate(tmp_bi_int_3,tmp_2rdm_3,tmp_accu)
|
||||
|
||||
!$OMP END PARALLEL
|
||||
|
||||
call omp_set_max_active_levels(4)
|
||||
|
||||
! Permutation, 2D matrix -> vector, transformation
|
||||
! In addition there is a permutation in the gradient formula :
|
||||
! \begin{equation}
|
||||
! P_{pq} = 1 - (p <-> q)
|
||||
! \end{equation}
|
||||
|
||||
! We need a vector to use the gradient. Here the gradient is a
|
||||
! antisymetric matrix so we can transform it in a vector of length
|
||||
! mo_num*(mo_num-1)/2.
|
||||
|
||||
! Here we do these two things at the same time.
|
||||
|
||||
|
||||
do i=1,n
|
||||
call vec_to_mat_index(i,p,q)
|
||||
v_grad(i)=(grad(p,q) - grad(q,p))
|
||||
enddo
|
||||
|
||||
! Debug, diplay the vector containing the gradient elements
|
||||
if (debug) then
|
||||
print*,'Vector containing the gradient :'
|
||||
write(*,'(100(F10.5))') v_grad(1:n)
|
||||
endif
|
||||
|
||||
! Norm of the gradient
|
||||
! The norm can be useful.
|
||||
|
||||
norm = dnrm2(n,v_grad,1)
|
||||
print*, 'Gradient norm : ', norm
|
||||
|
||||
! Maximum element in the gradient
|
||||
! The maximum element in the gradient is very important for the
|
||||
! convergence criterion of the Newton method.
|
||||
|
||||
|
||||
! Max element of the gradient
|
||||
max_elem = 0d0
|
||||
do i = 1, n
|
||||
if (DABS(v_grad(i)) > DABS(max_elem)) then
|
||||
max_elem = v_grad(i)
|
||||
endif
|
||||
enddo
|
||||
|
||||
print*,'Max element in the gradient :', max_elem
|
||||
|
||||
! Debug, display the matrix containting the gradient elements
|
||||
if (debug) then
|
||||
! Matrix gradient
|
||||
A = 0d0
|
||||
do q=1,m
|
||||
do p=1,m
|
||||
A(p,q) = grad(p,q) - grad(q,p)
|
||||
enddo
|
||||
enddo
|
||||
print*,'Matrix containing the gradient :'
|
||||
do i = 1, m
|
||||
write(*,'(100(F10.5))') A(i,1:m)
|
||||
enddo
|
||||
endif
|
||||
|
||||
! Deallocation of shared arrays and end
|
||||
|
||||
deallocate(grad,A, tmp_mo_one_e_integrals,tmp_one_e_dm_mo)
|
||||
|
||||
print*,'---End gradient---'
|
||||
|
||||
end subroutine
|
||||
|
|
@ -0,0 +1,346 @@
|
|||
! Gradient
|
||||
|
||||
! The gradient of the CI energy with respects to the orbital rotation
|
||||
! is:
|
||||
! (C-c C-x C-l)
|
||||
! $$
|
||||
! G(p,q) = \mathcal{P}_{pq} \left[ \sum_r (h_p^r \gamma_r^q - h_r^q \gamma_p^r) +
|
||||
! \sum_{rst}(v_{pt}^{rs} \Gamma_{rs}^{qt} - v_{rs}^{qt} \Gamma_{pt}^{rs})
|
||||
! \right]
|
||||
! $$
|
||||
|
||||
|
||||
! $$
|
||||
! \mathcal{P}_{pq}= 1 - (p \leftrightarrow q)
|
||||
! $$
|
||||
|
||||
! $$
|
||||
! G(p,q) = \left[
|
||||
! \sum_r (h_p^r \gamma_r^q - h_r^q \gamma_p^r) +
|
||||
! \sum_{rst}(v_{pt}^{rs} \Gamma_{rs}^{qt} - v_{rs}^{qt} \Gamma_{pt}^{rs})
|
||||
! \right] -
|
||||
! \left[
|
||||
! \sum_r (h_q^r \gamma_r^p - h_r^p \gamma_q^r) +
|
||||
! \sum_{rst}(v_{qt}^{rs} \Gamma_{rs}^{pt} - v_{rs}^{pt}
|
||||
! \Gamma_{qt}^{rs})
|
||||
! \right]
|
||||
! $$
|
||||
|
||||
! Where p,q,r,s,t are general spatial orbitals
|
||||
! mo_num : the number of molecular orbitals
|
||||
! $$h$$ : One electron integrals
|
||||
! $$\gamma$$ : One body density matrix (state average in our case)
|
||||
! $$v$$ : Two electron integrals
|
||||
! $$\Gamma$$ : Two body density matrice (state average in our case)
|
||||
|
||||
! The gradient is a mo_num by mo_num matrix, p,q,r,s,t take all the
|
||||
! values between 1 and mo_num (1 and mo_num include).
|
||||
|
||||
! To do that we compute $$G(p,q)$$ for all the pairs (p,q).
|
||||
|
||||
! Source :
|
||||
! Seniority-based coupled cluster theory
|
||||
! J. Chem. Phys. 141, 244104 (2014); https://doi.org/10.1063/1.4904384
|
||||
! Thomas M. Henderson, Ireneusz W. Bulik, Tamar Stein, and Gustavo
|
||||
! E. Scuseria
|
||||
|
||||
! *Compute the gradient of energy with respects to orbital rotations*
|
||||
|
||||
! Provided:
|
||||
! | mo_num | integer | number of MOs |
|
||||
! | mo_one_e_integrals(mo_num,mo_num) | double precision | mono_electronic integrals |
|
||||
! | one_e_dm_mo(mo_num,mo_num) | double precision | one e- density matrix |
|
||||
! | two_e_dm_mo(mo_num,mo_num,mo_num,mo_num) | double precision | two e- density matrix |
|
||||
|
||||
! Input:
|
||||
! | n | integer | mo_num*(mo_num-1)/2 |
|
||||
|
||||
! Output:
|
||||
! | v_grad(n) | double precision | the gradient |
|
||||
! | max_elem | double precision | maximum element of the gradient |
|
||||
|
||||
! Internal:
|
||||
! | grad(mo_num,mo_num) | double precison | gradient before the tranformation in a vector |
|
||||
! | A((mo_num,mo_num) | doubre precision | gradient after the permutations |
|
||||
! | norm | double precision | norm of the gradient |
|
||||
! | p, q | integer | indexes of the element in the matrix grad |
|
||||
! | i | integer | index for the tranformation in a vector |
|
||||
! | r, s, t | integer | indexes dor the sums |
|
||||
! | t1, t2, t3 | double precision | t3 = t2 - t1, time to compute the gradient |
|
||||
! | t4, t5, t6 | double precission | t6 = t5 - t4, time to compute each element |
|
||||
! | tmp_bi_int_3(mo_num,mo_num,mo_num) | double precision | 3 indexes temporary array for the bi-electronic integrals |
|
||||
! | tmp_2rdm_3(mo_num,mo_num,mo_num) | double precision | 3 indexes temporary array for the two e- density matrix |
|
||||
! | tmp_accu(mo_num,mo_num) | double precision | temporary array |
|
||||
|
||||
! Function:
|
||||
! | get_two_e_integral | double precision | bi-electronic integrals |
|
||||
! | dnrm2 | double precision | (Lapack) norm |
|
||||
|
||||
|
||||
subroutine gradient_opt(n,v_grad,max_elem)
|
||||
use omp_lib
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
! Variables
|
||||
|
||||
! in
|
||||
integer, intent(in) :: n
|
||||
|
||||
! out
|
||||
double precision, intent(out) :: v_grad(n), max_elem
|
||||
|
||||
! internal
|
||||
double precision, allocatable :: grad(:,:),A(:,:)
|
||||
double precision :: norm
|
||||
integer :: i,p,q,r,s,t
|
||||
double precision :: t1,t2,t3,t4,t5,t6
|
||||
|
||||
double precision, allocatable :: tmp_accu(:,:)
|
||||
double precision, allocatable :: tmp_bi_int_3(:,:,:), tmp_2rdm_3(:,:,:)
|
||||
|
||||
! Functions
|
||||
double precision :: get_two_e_integral, dnrm2
|
||||
|
||||
|
||||
print*,''
|
||||
print*,'---gradient---'
|
||||
|
||||
! Allocation of shared arrays
|
||||
allocate(grad(mo_num,mo_num),A(mo_num,mo_num))
|
||||
|
||||
! Initialization omp
|
||||
call omp_set_max_active_levels(1)
|
||||
|
||||
!$OMP PARALLEL &
|
||||
!$OMP PRIVATE( &
|
||||
!$OMP p,q,r,s,t, &
|
||||
!$OMP tmp_accu, tmp_bi_int_3, tmp_2rdm_3) &
|
||||
!$OMP SHARED(grad, one_e_dm_mo, mo_num,mo_one_e_integrals, &
|
||||
!$OMP mo_integrals_map,t4,t5,t6) &
|
||||
!$OMP DEFAULT(SHARED)
|
||||
|
||||
! Allocation of private arrays
|
||||
allocate(tmp_accu(mo_num,mo_num))
|
||||
allocate(tmp_bi_int_3(mo_num,mo_num,mo_num))
|
||||
allocate(tmp_2rdm_3(mo_num,mo_num,mo_num))
|
||||
|
||||
! Initialization
|
||||
|
||||
!$OMP DO
|
||||
do q = 1, mo_num
|
||||
do p = 1,mo_num
|
||||
grad(p,q) = 0d0
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END DO
|
||||
|
||||
! Term 1
|
||||
|
||||
! Without optimization the term 1 is :
|
||||
|
||||
! do p = 1, mo_num
|
||||
! do q = 1, mo_num
|
||||
! do r = 1, mo_num
|
||||
! grad(p,q) = grad(p,q) &
|
||||
! + mo_one_e_integrals(p,r) * one_e_dm_mo(r,q) &
|
||||
! - mo_one_e_integrals(r,q) * one_e_dm_mo(p,r)
|
||||
! enddo
|
||||
! enddo
|
||||
! enddo
|
||||
|
||||
! Since the matrix multiplication A.B is defined like :
|
||||
! \begin{equation}
|
||||
! c_{ij} = \sum_k a_{ik}.b_{kj}
|
||||
! \end{equation}
|
||||
! The previous equation can be rewritten as a matrix multplication
|
||||
|
||||
|
||||
!****************
|
||||
! Opt first term
|
||||
!****************
|
||||
|
||||
!$OMP MASTER
|
||||
CALL wall_TIME(t4)
|
||||
!$OMP END MASTER
|
||||
|
||||
call dgemm('N','N',mo_num,mo_num,mo_num,1d0,mo_one_e_integrals,&
|
||||
mo_num,one_e_dm_mo,mo_num,0d0,tmp_accu,mo_num)
|
||||
|
||||
!$OMP DO
|
||||
do q = 1, mo_num
|
||||
do p = 1, mo_num
|
||||
|
||||
grad(p,q) = grad(p,q) + (tmp_accu(p,q) - tmp_accu(q,p))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END DO
|
||||
|
||||
!$OMP MASTER
|
||||
CALL wall_TIME(t5)
|
||||
t6 = t5-t4
|
||||
print*,'Gradient, first term (s) :', t6
|
||||
!$OMP END MASTER
|
||||
|
||||
! Term 2
|
||||
|
||||
! Without optimization the second term is :
|
||||
|
||||
! do p = 1, mo_num
|
||||
! do q = 1, mo_num
|
||||
! do r = 1, mo_num
|
||||
! do s = 1, mo_num
|
||||
! do t= 1, mo_num
|
||||
|
||||
! grad(p,q) = grad(p,q) &
|
||||
! + get_two_e_integral(p,t,r,s,mo_integrals_map) * two_e_dm_mo(r,s,q,t) &
|
||||
! - get_two_e_integral(r,s,q,t,mo_integrals_map) * two_e_dm_mo(p,t,r,s)
|
||||
! enddo
|
||||
! enddo
|
||||
! enddo
|
||||
! enddo
|
||||
! enddo
|
||||
|
||||
! Using the bielectronic integral properties :
|
||||
! get_two_e_integral(p,t,r,s,mo_integrals_map) = get_two_e_integral(r,s,p,t,mo_integrals_map)
|
||||
|
||||
! Using the two body matrix properties :
|
||||
! two_e_dm_mo(p,t,r,s) = two_e_dm_mo(r,s,p,t)
|
||||
|
||||
! t is one the right, we can put it on the external loop and create 3
|
||||
! indexes temporary array
|
||||
! r,s can be seen as one index
|
||||
|
||||
! By doing so, a matrix multiplication appears
|
||||
|
||||
|
||||
!*****************
|
||||
! Opt second term
|
||||
!*****************
|
||||
|
||||
!$OMP MASTER
|
||||
CALL wall_TIME(t4)
|
||||
!$OMP END MASTER
|
||||
|
||||
!$OMP DO
|
||||
do t = 1, mo_num
|
||||
|
||||
do p = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
|
||||
tmp_bi_int_3(r,s,p) = get_two_e_integral(r,s,p,t,mo_integrals_map)
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
do q = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
|
||||
tmp_2rdm_3(r,s,q) = two_e_dm_mo(r,s,q,t)
|
||||
|
||||
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)
|
||||
|
||||
!$OMP CRITICAL
|
||||
do q = 1, mo_num
|
||||
do p = 1, mo_num
|
||||
|
||||
grad(p,q) = grad(p,q) + tmp_accu(p,q) - tmp_accu(q,p)
|
||||
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END CRITICAL
|
||||
|
||||
enddo
|
||||
!$OMP END DO
|
||||
|
||||
!$OMP MASTER
|
||||
CALL wall_TIME(t5)
|
||||
t6 = t5-t4
|
||||
print*,'Gradient second term (s) : ', t6
|
||||
!$OMP END MASTER
|
||||
|
||||
! Deallocation of private arrays
|
||||
|
||||
deallocate(tmp_bi_int_3,tmp_2rdm_3,tmp_accu)
|
||||
|
||||
!$OMP END PARALLEL
|
||||
|
||||
call omp_set_max_active_levels(4)
|
||||
|
||||
! Permutation, 2D matrix -> vector, transformation
|
||||
! In addition there is a permutation in the gradient formula :
|
||||
! \begin{equation}
|
||||
! P_{pq} = 1 - (p <-> q)
|
||||
! \end{equation}
|
||||
|
||||
! We need a vector to use the gradient. Here the gradient is a
|
||||
! antisymetric matrix so we can transform it in a vector of length
|
||||
! mo_num*(mo_num-1)/2.
|
||||
|
||||
! Here we do these two things at the same time.
|
||||
|
||||
|
||||
do i=1,n
|
||||
call vec_to_mat_index(i,p,q)
|
||||
v_grad(i)=(grad(p,q) - grad(q,p))
|
||||
enddo
|
||||
|
||||
! Debug, diplay the vector containing the gradient elements
|
||||
if (debug) then
|
||||
print*,'Vector containing the gradient :'
|
||||
write(*,'(100(F10.5))') v_grad(1:n)
|
||||
endif
|
||||
|
||||
! Norm of the gradient
|
||||
! The norm can be useful.
|
||||
|
||||
norm = dnrm2(n,v_grad,1)
|
||||
print*, 'Gradient norm : ', norm
|
||||
|
||||
! Maximum element in the gradient
|
||||
! The maximum element in the gradient is very important for the
|
||||
! convergence criterion of the Newton method.
|
||||
|
||||
|
||||
! Max element of the gradient
|
||||
max_elem = 0d0
|
||||
do i = 1, n
|
||||
if (ABS(v_grad(i)) > ABS(max_elem)) then
|
||||
max_elem = v_grad(i)
|
||||
endif
|
||||
enddo
|
||||
|
||||
print*,'Max element in the gradient :', max_elem
|
||||
|
||||
! Debug, display the matrix containting the gradient elements
|
||||
if (debug) then
|
||||
! Matrix gradient
|
||||
A = 0d0
|
||||
do q=1,mo_num
|
||||
do p=1,mo_num
|
||||
A(p,q) = grad(p,q) - grad(q,p)
|
||||
enddo
|
||||
enddo
|
||||
print*,'Matrix containing the gradient :'
|
||||
do i = 1, mo_num
|
||||
write(*,'(100(F10.5))') A(i,1:mo_num)
|
||||
enddo
|
||||
endif
|
||||
|
||||
! Deallocation of shared arrays and end
|
||||
|
||||
deallocate(grad,A)
|
||||
|
||||
print*,'---End gradient---'
|
||||
|
||||
end subroutine
|
||||
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
|
|
@ -0,0 +1,141 @@
|
|||
! Dimensions of MOs
|
||||
|
||||
|
||||
BEGIN_PROVIDER [ integer, n_mo_dim ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Number of different pairs (i,j) of MOs we can build,
|
||||
! with i>j
|
||||
END_DOC
|
||||
|
||||
n_mo_dim = mo_num*(mo_num-1)/2
|
||||
|
||||
END_PROVIDER
|
||||
|
||||
BEGIN_PROVIDER [ integer, n_mo_dim_core ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Number of different pairs (i,j) of core MOs we can build,
|
||||
! with i>j
|
||||
END_DOC
|
||||
|
||||
n_mo_dim_core = dim_list_core_orb*(dim_list_core_orb-1)/2
|
||||
|
||||
END_PROVIDER
|
||||
|
||||
BEGIN_PROVIDER [ integer, n_mo_dim_act ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Number of different pairs (i,j) of active MOs we can build,
|
||||
! with i>j
|
||||
END_DOC
|
||||
|
||||
n_mo_dim_act = dim_list_act_orb*(dim_list_act_orb-1)/2
|
||||
|
||||
END_PROVIDER
|
||||
|
||||
BEGIN_PROVIDER [ integer, n_mo_dim_inact ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Number of different pairs (i,j) of inactive MOs we can build,
|
||||
! with i>j
|
||||
END_DOC
|
||||
|
||||
n_mo_dim_inact = dim_list_inact_orb*(dim_list_inact_orb-1)/2
|
||||
|
||||
END_PROVIDER
|
||||
|
||||
BEGIN_PROVIDER [ integer, n_mo_dim_virt ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Number of different pairs (i,j) of virtual MOs we can build,
|
||||
! with i>j
|
||||
END_DOC
|
||||
|
||||
n_mo_dim_virt = dim_list_virt_orb*(dim_list_virt_orb-1)/2
|
||||
|
||||
END_PROVIDER
|
||||
|
||||
! Energies/criterions
|
||||
|
||||
BEGIN_PROVIDER [ double precision, my_st_av_energy ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! State average CI energy
|
||||
END_DOC
|
||||
|
||||
!call update_st_av_ci_energy(my_st_av_energy)
|
||||
call state_average_energy(my_st_av_energy)
|
||||
|
||||
END_PROVIDER
|
||||
|
||||
! With all the MOs
|
||||
|
||||
BEGIN_PROVIDER [ double precision, my_gradient_opt, (n_mo_dim) ]
|
||||
&BEGIN_PROVIDER [ double precision, my_CC1_opt ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! - Gradient of the energy with respect to the MO rotations, for all the MOs.
|
||||
! - Maximal element of the gradient in absolute value
|
||||
END_DOC
|
||||
|
||||
double precision :: norm_grad
|
||||
|
||||
PROVIDE mo_two_e_integrals_in_map
|
||||
|
||||
call gradient_opt(n_mo_dim, my_gradient_opt, my_CC1_opt, norm_grad)
|
||||
|
||||
END_PROVIDER
|
||||
|
||||
BEGIN_PROVIDER [ double precision, my_hessian_opt, (n_mo_dim, n_mo_dim) ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! - Gradient of the energy with respect to the MO rotations, for all the MOs.
|
||||
! - Maximal element of the gradient in absolute value
|
||||
END_DOC
|
||||
|
||||
double precision, allocatable :: h_f(:,:,:,:)
|
||||
|
||||
PROVIDE mo_two_e_integrals_in_map
|
||||
|
||||
allocate(h_f(mo_num, mo_num, mo_num, mo_num))
|
||||
|
||||
call hessian_list_opt(n_mo_dim, my_hessian_opt, h_f)
|
||||
|
||||
END_PROVIDER
|
||||
|
||||
! With the list of active MOs
|
||||
! Can be generalized to any mo_class by changing the list/dimension
|
||||
|
||||
BEGIN_PROVIDER [ double precision, my_gradient_list_opt, (n_mo_dim_act) ]
|
||||
&BEGIN_PROVIDER [ double precision, my_CC2_opt ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! - Gradient of the energy with respect to the MO rotations, only for the active MOs !
|
||||
! - Maximal element of the gradient in absolute value
|
||||
END_DOC
|
||||
|
||||
double precision :: norm_grad
|
||||
|
||||
PROVIDE mo_two_e_integrals_in_map !one_e_dm_mo two_e_dm_mo mo_one_e_integrals
|
||||
|
||||
call gradient_list_opt(n_mo_dim_act, dim_list_act_orb, list_act, my_gradient_list_opt, my_CC2_opt, norm_grad)
|
||||
|
||||
END_PROVIDER
|
||||
|
||||
BEGIN_PROVIDER [ double precision, my_hessian_list_opt, (n_mo_dim_act, n_mo_dim_act) ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! - Gradient of the energy with respect to the MO rotations, only for the active MOs !
|
||||
! - Maximal element of the gradient in absolute value
|
||||
END_DOC
|
||||
|
||||
double precision, allocatable :: h_f(:,:,:,:)
|
||||
|
||||
PROVIDE mo_two_e_integrals_in_map
|
||||
|
||||
allocate(h_f(dim_list_act_orb, dim_list_act_orb, dim_list_act_orb, dim_list_act_orb))
|
||||
|
||||
call hessian_list_opt(n_mo_dim_act, dim_list_act_orb, list_act, my_hessian_list_opt, h_f)
|
||||
|
||||
END_PROVIDER
|
||||
|
|
@ -0,0 +1,22 @@
|
|||
! Orbital optimization program
|
||||
|
||||
! This is an optimization program for molecular orbitals. It produces
|
||||
! orbital rotations in order to lower the energy of a truncated wave
|
||||
! function.
|
||||
! This program just optimize the orbitals for a fixed number of
|
||||
! determinants. This optimization process must be repeated for different
|
||||
! number of determinants.
|
||||
|
||||
|
||||
|
||||
|
||||
! Main program : orb_opt_trust
|
||||
|
||||
|
||||
program orb_opt
|
||||
read_wf = .true. ! must be True for the orbital optimization !!!
|
||||
TOUCH read_wf
|
||||
io_mo_two_e_integrals = 'None'
|
||||
TOUCH io_mo_two_e_integrals
|
||||
call run_orb_opt_trust_v2
|
||||
end
|
||||
|
|
@ -0,0 +1,7 @@
|
|||
#!/bin/sh
|
||||
|
||||
list='ls *.org'
|
||||
for element in $list
|
||||
do
|
||||
emacs --batch $element -f org-babel-tangle
|
||||
done
|
||||
|
|
@ -0,0 +1,17 @@
|
|||
TODO:
|
||||
** TODO Keep under surveillance the performance of rotation matrix
|
||||
- is the fix ok ?
|
||||
** DONE Provider state_average_weight
|
||||
** DONE Diagonal hessian for orbital optimization with a list of MOs
|
||||
** DONE Something to force the step cancellation if R.R^T > treshold
|
||||
** TODO Iterative method to compute the rotation matrix
|
||||
- doesn't work actually
|
||||
** DONE Test trust region with polynomial functions
|
||||
** DONE Optimization/Localization program using the template
|
||||
** DONE Correction OMP hessian shared/private arrays
|
||||
** DONE State average energy
|
||||
** DONE Correction of Rho
|
||||
** TODO Check the PROVIDE/FREE/TOUCH
|
||||
** TODO research of lambda without the power 2
|
||||
** DONE Clean the OMP sections
|
||||
|
||||
|
|
@ -0,0 +1,79 @@
|
|||
* Debug the gradient
|
||||
|
||||
*Program to check the gradient*
|
||||
|
||||
The program compares the result of the first and last code for the
|
||||
gradient.
|
||||
|
||||
Provided:
|
||||
| mo_num | integer | number of MOs |
|
||||
|
||||
Internal:
|
||||
| n | integer | number of orbitals pairs (p,q) p<q |
|
||||
| v_grad(n) | double precision | Original gradient |
|
||||
| v_grad2(n) | double precision | Gradient |
|
||||
| i | integer | index |
|
||||
| threshold | double precision | threshold for the errors |
|
||||
| max_error | double precision | maximal error in the gradient |
|
||||
| nb_error | integer | number of error in the gradient |
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle debug_gradient_list_opt.irp.f
|
||||
program debug_gradient_list
|
||||
|
||||
implicit none
|
||||
|
||||
! Variables
|
||||
|
||||
double precision, allocatable :: v_grad(:), v_grad2(:)
|
||||
integer :: n,m
|
||||
integer :: i
|
||||
double precision :: threshold
|
||||
double precision :: max_error, max_elem, norm
|
||||
integer :: nb_error
|
||||
|
||||
m = dim_list_act_orb
|
||||
! Definition of n
|
||||
n = m*(m-1)/2
|
||||
|
||||
PROVIDE mo_two_e_integrals_in_map ! Vérifier pour suppression
|
||||
|
||||
! Allocation
|
||||
allocate(v_grad(n), v_grad2(n))
|
||||
|
||||
! Calculation
|
||||
|
||||
call diagonalize_ci ! Vérifier pour suppression
|
||||
|
||||
! Gradient
|
||||
call gradient_list_opt(n,m,list_act,v_grad,max_elem,norm)
|
||||
call first_gradient_list_opt(n,m,list_act,v_grad2)
|
||||
|
||||
|
||||
v_grad = v_grad - v_grad2
|
||||
nb_error = 0
|
||||
max_error = 0d0
|
||||
threshold = 1d-12
|
||||
|
||||
do i = 1, n
|
||||
if (ABS(v_grad(i)) > threshold) then
|
||||
print*,i,v_grad(i)
|
||||
nb_error = nb_error + 1
|
||||
|
||||
if (ABS(v_grad(i)) > max_error) then
|
||||
max_error = v_grad(i)
|
||||
endif
|
||||
|
||||
endif
|
||||
enddo
|
||||
|
||||
print*,''
|
||||
print*,'Check the gradient'
|
||||
print*,'Threshold:', threshold
|
||||
print*,'Nb error:', nb_error
|
||||
print*,'Max error:', max_error
|
||||
|
||||
! Deallocation
|
||||
deallocate(v_grad,v_grad2)
|
||||
|
||||
end program
|
||||
#+END_SRC
|
||||
|
|
@ -0,0 +1,77 @@
|
|||
* Debug the gradient
|
||||
|
||||
*Program to check the gradient*
|
||||
|
||||
The program compares the result of the first and last code for the
|
||||
gradient.
|
||||
|
||||
Provided:
|
||||
| mo_num | integer | number of MOs |
|
||||
|
||||
Internal:
|
||||
| n | integer | number of orbitals pairs (p,q) p<q |
|
||||
| v_grad(n) | double precision | Original gradient |
|
||||
| v_grad2(n) | double precision | Gradient |
|
||||
| i | integer | index |
|
||||
| threshold | double precision | threshold for the errors |
|
||||
| max_error | double precision | maximal error in the gradient |
|
||||
| nb_error | integer | number of error in the gradient |
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle debug_gradient_opt.irp.f
|
||||
program debug_gradient
|
||||
|
||||
implicit none
|
||||
|
||||
! Variables
|
||||
|
||||
double precision, allocatable :: v_grad(:), v_grad2(:)
|
||||
integer :: n
|
||||
integer :: i
|
||||
double precision :: threshold
|
||||
double precision :: max_error, max_elem
|
||||
integer :: nb_error
|
||||
|
||||
! Definition of n
|
||||
n = mo_num*(mo_num-1)/2
|
||||
|
||||
PROVIDE mo_two_e_integrals_in_map ! Vérifier pour suppression
|
||||
|
||||
! Allocation
|
||||
allocate(v_grad(n), v_grad2(n))
|
||||
|
||||
! Calculation
|
||||
|
||||
call diagonalize_ci ! Vérifier pour suppression
|
||||
|
||||
! Gradient
|
||||
call first_gradient_opt(n,v_grad)
|
||||
call gradient_opt(n,v_grad2,max_elem)
|
||||
|
||||
v_grad = v_grad - v_grad2
|
||||
nb_error = 0
|
||||
max_error = 0d0
|
||||
threshold = 1d-12
|
||||
|
||||
do i = 1, n
|
||||
if (ABS(v_grad(i)) > threshold) then
|
||||
print*,v_grad(i)
|
||||
nb_error = nb_error + 1
|
||||
|
||||
if (ABS(v_grad(i)) > max_error) then
|
||||
max_error = v_grad(i)
|
||||
endif
|
||||
|
||||
endif
|
||||
enddo
|
||||
|
||||
print*,''
|
||||
print*,'Check the gradient'
|
||||
print*,'Threshold :', threshold
|
||||
print*,'Nb error :', nb_error
|
||||
print*,'Max error :', max_error
|
||||
|
||||
! Deallocation
|
||||
deallocate(v_grad,v_grad2)
|
||||
|
||||
end program
|
||||
#+END_SRC
|
||||
|
|
@ -0,0 +1,148 @@
|
|||
* Debug the hessian
|
||||
|
||||
*Program to check the hessian matrix*
|
||||
|
||||
The program compares the result of the first and last code for the
|
||||
hessian. First of all the 4D hessian and after the 2D hessian.
|
||||
|
||||
Provided:
|
||||
| mo_num | integer | number of MOs |
|
||||
| optimization_method | string | Method for the orbital optimization: |
|
||||
| | | - 'full' -> full hessian |
|
||||
| | | - 'diag' -> diagonal hessian |
|
||||
| dim_list_act_orb | integer | number of active MOs |
|
||||
| list_act(dim_list_act_orb) | integer | list of the actives MOs |
|
||||
| | | |
|
||||
|
||||
Internal:
|
||||
| m | integer | number of MOs in the list |
|
||||
| | | (active MOs) |
|
||||
| n | integer | number of orbitals pairs (p,q) p<q |
|
||||
| | | n = m*(m-1)/2 |
|
||||
| H(n,n) | double precision | Original hessian matrix (2D) |
|
||||
| H2(n,n) | double precision | Hessian matrix (2D) |
|
||||
| h_f(mo_num,mo_num,mo_num,mo_num) | double precision | Original hessian matrix (4D) |
|
||||
| h_f2(mo_num,mo_num,mo_num,mo_num) | double precision | Hessian matrix (4D) |
|
||||
| i,j,p,q,k | integer | indexes |
|
||||
| threshold | double precision | threshold for the errors |
|
||||
| max_error | double precision | maximal error in the 4D hessian |
|
||||
| max_error_H | double precision | maximal error in the 2D hessian |
|
||||
| nb_error | integer | number of errors in the 4D hessian |
|
||||
| nb_error_H | integer | number of errors in the 2D hessian |
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle debug_hessian_list_opt.irp.f
|
||||
program debug_hessian_list_opt
|
||||
|
||||
implicit none
|
||||
|
||||
! Variables
|
||||
|
||||
double precision, allocatable :: H(:,:),H2(:,:), h_f(:,:,:,:), h_f2(:,:,:,:)
|
||||
integer :: n,m
|
||||
integer :: i,j,k,l
|
||||
double precision :: max_error, max_error_H
|
||||
integer :: nb_error, nb_error_H
|
||||
double precision :: threshold
|
||||
|
||||
m = dim_list_act_orb !mo_num
|
||||
|
||||
! Definition of n
|
||||
n = m*(m-1)/2
|
||||
|
||||
PROVIDE mo_two_e_integrals_in_map ! Vérifier pour suppression
|
||||
|
||||
! Hessian
|
||||
if (optimization_method == 'full') then
|
||||
print*,'Use the full hessian matrix'
|
||||
allocate(H(n,n),H2(n,n))
|
||||
allocate(h_f(m,m,m,m),h_f2(m,m,m,m))
|
||||
|
||||
call hessian_list_opt(n,m,list_act,H,h_f)
|
||||
call first_hessian_list_opt(n,m,list_act,H2,h_f2)
|
||||
!call hessian_opt(n,H2,h_f2)
|
||||
|
||||
! Difference
|
||||
h_f = h_f - h_f2
|
||||
H = H - H2
|
||||
max_error = 0d0
|
||||
nb_error = 0
|
||||
threshold = 1d-12
|
||||
|
||||
do l = 1, m
|
||||
do k= 1, m
|
||||
do j = 1, m
|
||||
do i = 1, m
|
||||
if (ABS(h_f(i,j,k,l)) > threshold) then
|
||||
print*,h_f(i,j,k,l)
|
||||
nb_error = nb_error + 1
|
||||
if (ABS(h_f(i,j,k,l)) > ABS(max_error)) then
|
||||
max_error = h_f(i,j,k,l)
|
||||
endif
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
max_error_H = 0d0
|
||||
nb_error_H = 0
|
||||
|
||||
do j = 1, n
|
||||
do i = 1, n
|
||||
if (ABS(H(i,j)) > threshold) then
|
||||
print*, H(i,j)
|
||||
nb_error_H = nb_error_H + 1
|
||||
|
||||
if (ABS(H(i,j)) > ABS(max_error_H)) then
|
||||
max_error_H = H(i,j)
|
||||
endif
|
||||
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Deallocation
|
||||
deallocate(H, H2, h_f, h_f2)
|
||||
|
||||
else
|
||||
|
||||
print*, 'Use the diagonal hessian matrix'
|
||||
allocate(H(n,1),H2(n,1))
|
||||
call diag_hessian_list_opt(n,m,list_act,H)
|
||||
call first_diag_hessian_list_opt(n,m,list_act,H2)
|
||||
|
||||
H = H - H2
|
||||
|
||||
max_error_H = 0d0
|
||||
nb_error_H = 0
|
||||
|
||||
do i = 1, n
|
||||
if (ABS(H(i,1)) > threshold) then
|
||||
print*, H(i,1)
|
||||
nb_error_H = nb_error_H + 1
|
||||
|
||||
if (ABS(H(i,1)) > ABS(max_error_H)) then
|
||||
max_error_H = H(i,1)
|
||||
endif
|
||||
|
||||
endif
|
||||
enddo
|
||||
|
||||
endif
|
||||
|
||||
print*,''
|
||||
if (optimization_method == 'full') then
|
||||
print*,'Check of the full hessian'
|
||||
print*,'Threshold:', threshold
|
||||
print*,'Nb error:', nb_error
|
||||
print*,'Max error:', max_error
|
||||
print*,''
|
||||
else
|
||||
print*,'Check of the diagonal hessian'
|
||||
endif
|
||||
|
||||
print*,'Nb error_H:', nb_error_H
|
||||
print*,'Max error_H:', max_error_H
|
||||
|
||||
end program
|
||||
#+END_SRC
|
||||
|
|
@ -0,0 +1,172 @@
|
|||
* Debug the hessian
|
||||
|
||||
*Program to check the hessian matrix*
|
||||
|
||||
The program compares the result of the first and last code for the
|
||||
hessian. First of all the 4D hessian and after the 2D hessian.
|
||||
|
||||
Provided:
|
||||
| mo_num | integer | number of MOs |
|
||||
|
||||
Internal:
|
||||
| n | integer | number of orbitals pairs (p,q) p<q |
|
||||
| H(n,n) | double precision | Original hessian matrix (2D) |
|
||||
| H2(n,n) | double precision | Hessian matrix (2D) |
|
||||
| h_f(mo_num,mo_num,mo_num,mo_num) | double precision | Original hessian matrix (4D) |
|
||||
| h_f2(mo_num,mo_num,mo_num,mo_num) | double precision | Hessian matrix (4D) |
|
||||
| method | integer | - 1: full hessian |
|
||||
| | | - 2: diagonal hessian |
|
||||
| i,j,p,q,k | integer | indexes |
|
||||
| threshold | double precision | threshold for the errors |
|
||||
| max_error | double precision | maximal error in the 4D hessian |
|
||||
| max_error_H | double precision | maximal error in the 2D hessian |
|
||||
| nb_error | integer | number of errors in the 4D hessian |
|
||||
| nb_error_H | integer | number of errors in the 2D hessian |
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle debug_hessian_opt.irp.f
|
||||
program debug_hessian
|
||||
|
||||
implicit none
|
||||
|
||||
! Variables
|
||||
|
||||
double precision, allocatable :: H(:,:),H2(:,:), h_f(:,:,:,:), h_f2(:,:,:,:)
|
||||
integer :: n
|
||||
integer :: i,j,k,l
|
||||
double precision :: max_error, max_error_H
|
||||
integer :: nb_error, nb_error_H
|
||||
double precision :: threshold
|
||||
|
||||
! Definition of n
|
||||
n = mo_num*(mo_num-1)/2
|
||||
|
||||
PROVIDE mo_two_e_integrals_in_map ! Vérifier pour suppression
|
||||
|
||||
! Allocation
|
||||
allocate(H(n,n),H2(n,n))
|
||||
allocate(h_f(mo_num,mo_num,mo_num,mo_num),h_f2(mo_num,mo_num,mo_num,mo_num))
|
||||
|
||||
! Calculation
|
||||
|
||||
! Hessian
|
||||
if (optimization_method == 'full') then
|
||||
|
||||
print*,'Use the full hessian matrix'
|
||||
call hessian_opt(n,H,h_f)
|
||||
call first_hessian_opt(n,H2,h_f2)
|
||||
|
||||
! Difference
|
||||
h_f = h_f - h_f2
|
||||
H = H - H2
|
||||
max_error = 0d0
|
||||
nb_error = 0
|
||||
threshold = 1d-12
|
||||
|
||||
do l = 1, mo_num
|
||||
do k= 1, mo_num
|
||||
do j = 1, mo_num
|
||||
do i = 1, mo_num
|
||||
if (ABS(h_f(i,j,k,l)) > threshold) then
|
||||
print*,h_f(i,j,k,l)
|
||||
nb_error = nb_error + 1
|
||||
if (ABS(h_f(i,j,k,l)) > ABS(max_error)) then
|
||||
max_error = h_f(i,j,k,l)
|
||||
endif
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
max_error_H = 0d0
|
||||
nb_error_H = 0
|
||||
|
||||
do j = 1, n
|
||||
do i = 1, n
|
||||
if (ABS(H(i,j)) > threshold) then
|
||||
print*, H(i,j)
|
||||
nb_error_H = nb_error_H + 1
|
||||
|
||||
if (ABS(H(i,j)) > ABS(max_error_H)) then
|
||||
max_error_H = H(i,j)
|
||||
endif
|
||||
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
|
||||
elseif (optimization_method == 'diag') then
|
||||
|
||||
print*, 'Use the diagonal hessian matrix'
|
||||
call diag_hessian_opt(n,H,h_f)
|
||||
call first_diag_hessian_opt(n,H2,h_f2)
|
||||
|
||||
h_f = h_f - h_f2
|
||||
max_error = 0d0
|
||||
nb_error = 0
|
||||
threshold = 1d-12
|
||||
|
||||
do l = 1, mo_num
|
||||
do k = 1, mo_num
|
||||
do j = 1, mo_num
|
||||
do i = 1, mo_num
|
||||
|
||||
if (ABS(h_f(i,j,k,l)) > threshold) then
|
||||
|
||||
print*,h_f(i,j,k,l)
|
||||
nb_error = nb_error + 1
|
||||
|
||||
if (ABS(h_f(i,j,k,l)) > ABS(max_error)) then
|
||||
max_error = h_f(i,j,k,l)
|
||||
endif
|
||||
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
h=H-H2
|
||||
|
||||
max_error_H = 0d0
|
||||
nb_error_H = 0
|
||||
|
||||
do j = 1, n
|
||||
do i = 1, n
|
||||
if (ABS(H(i,j)) > threshold) then
|
||||
print*, H(i,j)
|
||||
nb_error_H = nb_error_H + 1
|
||||
|
||||
if (ABS(H(i,j)) > ABS(max_error_H)) then
|
||||
max_error_H = H(i,j)
|
||||
endif
|
||||
|
||||
endif
|
||||
enddo
|
||||
enddo
|
||||
|
||||
else
|
||||
print*,'Unknown optimization_method, please select full, diag'
|
||||
call abort
|
||||
endif
|
||||
|
||||
print*,''
|
||||
if (optimization_method == 'full') then
|
||||
print*,'Check the full hessian'
|
||||
else
|
||||
print*,'Check the diagonal hessian'
|
||||
endif
|
||||
|
||||
print*,'Threshold :', threshold
|
||||
print*,'Nb error :', nb_error
|
||||
print*,'Max error :', max_error
|
||||
print*,''
|
||||
print*,'Nb error_H :', nb_error_H
|
||||
print*,'Max error_H :', max_error_H
|
||||
|
||||
! Deallocation
|
||||
deallocate(H,H2,h_f,h_f2)
|
||||
|
||||
end program
|
||||
#+END_SRC
|
||||
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
|
|
@ -0,0 +1,138 @@
|
|||
* Diagonalization of the hessian
|
||||
|
||||
Just a matrix diagonalization using Lapack
|
||||
|
||||
Input:
|
||||
| n | integer | mo_num*(mo_num-1)/2 |
|
||||
| H(n,n) | double precision | hessian |
|
||||
|
||||
Output:
|
||||
| e_val(n) | double precision | eigenvalues of the hessian |
|
||||
| w(n,n) | double precision | eigenvectors of the hessian |
|
||||
|
||||
Internal:
|
||||
| nb_negative_nv | integer | number of negative eigenvalues |
|
||||
| lwork | integer | for Lapack |
|
||||
| work(lwork,n) | double precision | temporary array for Lapack |
|
||||
| info | integer | if 0 -> ok, else problem in the diagonalization |
|
||||
| i,j | integer | dummy indexes |
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle diagonalization_hessian.irp.f
|
||||
subroutine diagonalization_hessian(n,H,e_val,w)
|
||||
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
! Variables
|
||||
|
||||
! in
|
||||
integer, intent(in) :: n
|
||||
double precision, intent(in) :: H(n,n)
|
||||
|
||||
! out
|
||||
double precision, intent(out) :: e_val(n), w(n,n)
|
||||
|
||||
! internal
|
||||
double precision, allocatable :: work(:,:)
|
||||
integer, allocatable :: key(:)
|
||||
integer :: info,lwork
|
||||
integer :: i,j
|
||||
integer :: nb_negative_vp
|
||||
double precision :: t1,t2,t3,max_elem
|
||||
|
||||
print*,''
|
||||
print*,'---Diagonalization_hessian---'
|
||||
|
||||
call wall_time(t1)
|
||||
|
||||
if (optimization_method == 'full') then
|
||||
! Allocation
|
||||
! For Lapack
|
||||
lwork=3*n-1
|
||||
|
||||
allocate(work(lwork,n))
|
||||
|
||||
! Calculation
|
||||
|
||||
! Copy the hessian matrix, the eigenvectors will be store in W
|
||||
W=H
|
||||
|
||||
! Diagonalization of the hessian
|
||||
call dsyev('V','U',n,W,size(W,1),e_val,work,lwork,info)
|
||||
|
||||
if (info /= 0) then
|
||||
print*, 'Error diagonalization : diagonalization_hessian'
|
||||
print*, 'info = ', info
|
||||
call ABORT
|
||||
endif
|
||||
|
||||
if (debug) then
|
||||
print *, 'vp Hess:'
|
||||
write(*,'(100(F10.5))') real(e_val(:))
|
||||
endif
|
||||
|
||||
! Number of negative eigenvalues
|
||||
max_elem = 0d0
|
||||
nb_negative_vp = 0
|
||||
do i = 1, n
|
||||
if (e_val(i) < 0d0) then
|
||||
nb_negative_vp = nb_negative_vp + 1
|
||||
if (e_val(i) < max_elem) then
|
||||
max_elem = e_val(i)
|
||||
endif
|
||||
!print*,'e_val < 0 :', e_val(i)
|
||||
endif
|
||||
enddo
|
||||
print*,'Number of negative eigenvalues:', nb_negative_vp
|
||||
print*,'Lowest eigenvalue:',max_elem
|
||||
|
||||
!nb_negative_vp = 0
|
||||
!do i = 1, n
|
||||
! if (e_val(i) < -thresh_eig) then
|
||||
! nb_negative_vp = nb_negative_vp + 1
|
||||
! endif
|
||||
!enddo
|
||||
!print*,'Number of negative eigenvalues <', -thresh_eig,':', nb_negative_vp
|
||||
|
||||
! Deallocation
|
||||
deallocate(work)
|
||||
|
||||
elseif (optimization_method == 'diag') then
|
||||
! Diagonalization of the diagonal hessian by hands
|
||||
allocate(key(n))
|
||||
|
||||
do i = 1, n
|
||||
e_val(i) = H(i,i)
|
||||
enddo
|
||||
|
||||
! Key list for dsort
|
||||
do i = 1, n
|
||||
key(i) = i
|
||||
enddo
|
||||
|
||||
! Sort of the eigenvalues
|
||||
call dsort(e_val, key, n)
|
||||
|
||||
! Eigenvectors
|
||||
W = 0d0
|
||||
do i = 1, n
|
||||
j = key(i)
|
||||
W(j,i) = 1d0
|
||||
enddo
|
||||
|
||||
deallocate(key)
|
||||
else
|
||||
print*,'Diagonalization_hessian, abort'
|
||||
call abort
|
||||
endif
|
||||
|
||||
call wall_time(t2)
|
||||
t3 = t2 - t1
|
||||
print*,'Time in diagonalization_hessian:', t3
|
||||
|
||||
print*,'---End diagonalization_hessian---'
|
||||
|
||||
end subroutine
|
||||
#+END_SRC
|
||||
|
||||
|
|
@ -0,0 +1,376 @@
|
|||
* First diagonal hessian
|
||||
|
||||
#+BEGIN_SRC f90 :comments :tangle first_diagonal_hessian_list_opt.irp.f
|
||||
subroutine first_diag_hessian_list_opt(tmp_n,m,list,H)!, h_tmpr)
|
||||
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
!===========================================================================
|
||||
! Compute the diagonal hessian of energy with respects to orbital rotations
|
||||
!===========================================================================
|
||||
|
||||
!===========
|
||||
! Variables
|
||||
!===========
|
||||
|
||||
! in
|
||||
integer, intent(in) :: tmp_n, m, list(m)
|
||||
! tmp_n : integer, tmp_n = m*(m-1)/2
|
||||
|
||||
! out
|
||||
double precision, intent(out) :: H(tmp_n)!, h_tmpr(m,m,m,m)
|
||||
! H : n by n double precision matrix containing the 2D hessian
|
||||
|
||||
! internal
|
||||
double precision, allocatable :: hessian(:,:,:,:), tmp(:,:),h_tmpr(:,:,:,:)
|
||||
integer :: p,q, tmp_p,tmp_q
|
||||
integer :: r,s,t,u,v,tmp_r,tmp_s,tmp_t,tmp_u,tmp_v
|
||||
integer :: pq,rs,tmp_pq,tmp_rs
|
||||
double precision :: t1,t2,t3
|
||||
! hessian : mo_num 4D double precision matrix containing the hessian before the permutations
|
||||
! h_tmpr : mo_num 4D double precision matrix containing the hessian after the permutations
|
||||
! p,q,r,s : integer, indexes of the 4D hessian matrix
|
||||
! t,u,v : integer, indexes to compute hessian elements
|
||||
! pq,rs : integer, indexes for the conversion from 4D to 2D hessian matrix
|
||||
! t1,t2,t3 : double precision, t3 = t2 - t1, time to compute the hessian
|
||||
|
||||
! Function
|
||||
double precision :: get_two_e_integral
|
||||
! get_two_e_integral : double precision function, two e integrals
|
||||
|
||||
! Provided :
|
||||
! mo_one_e_integrals : mono e- integrals
|
||||
! get_two_e_integral : two e- integrals
|
||||
! one_e_dm_mo_alpha, one_e_dm_mo_beta : one body density matrix
|
||||
! two_e_dm_mo : two body density matrix
|
||||
|
||||
print*,'---first_diag_hess_list---'
|
||||
|
||||
!============
|
||||
! Allocation
|
||||
!============
|
||||
|
||||
allocate(hessian(m,m,m,m),tmp(tmp_n,tmp_n),h_tmpr(mo_num,mo_num,mo_num,mo_num))
|
||||
|
||||
!=============
|
||||
! Calculation
|
||||
!=============
|
||||
|
||||
! From Anderson et. al. (2014)
|
||||
! The Journal of Chemical Physics 141, 244104 (2014); doi: 10.1063/1.4904384
|
||||
|
||||
! LaTeX formula :
|
||||
|
||||
!\begin{align*}
|
||||
!H_{pq,rs} &= \dfrac{\partial^2 E(x)}{\partial x_{pq}^2} \\
|
||||
!&= \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)
|
||||
!+ \delta_{ps}(h_r^u \gamma_u^q + h_u^q \gamma_u^r)]
|
||||
!-(h_p^s \gamma_r^q + h_r^q \gamma_p^s) \\
|
||||
!&+ \frac{1}{2} \sum_{tuv} [\delta_{qr}(v_{pt}^{uv} \Gamma_{uv}^{st} +v_{uv}^{st} \Gamma_{pt}^{uv})
|
||||
!+ \delta_{ps}(v_{uv}^{qt} \Gamma_{rt}^{uv} + v_{rt}^{uv}\Gamma_{uv}^{qt})] \\
|
||||
!&+ \sum_{uv} (v_{pr}^{uv} \Gamma_{uv}^{qs} + v_{uv}^{qs} \Gamma_{ps}^{uv}) \\
|
||||
!&- \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})
|
||||
!\end{align*}
|
||||
|
||||
!================
|
||||
! Initialization
|
||||
!================
|
||||
hessian = 0d0
|
||||
|
||||
CALL wall_time(t1)
|
||||
|
||||
!========================
|
||||
! First line, first term
|
||||
!========================
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
if (q==r) then
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) + 0.5d0 * ( &
|
||||
mo_one_e_integrals(u,p) * one_e_dm_mo(u,s) &
|
||||
+ mo_one_e_integrals(s,u) * one_e_dm_mo(p,u))
|
||||
|
||||
enddo
|
||||
endif
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!=========================
|
||||
! First line, second term
|
||||
!=========================
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
if (p==s) then
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) + 0.5d0 * ( &
|
||||
mo_one_e_integrals(u,r) * one_e_dm_mo(u,q) &
|
||||
+ mo_one_e_integrals(q,u) * one_e_dm_mo(r,u))
|
||||
enddo
|
||||
endif
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!========================
|
||||
! First line, third term
|
||||
!========================
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) &
|
||||
- mo_one_e_integrals(s,p) * one_e_dm_mo(r,q) &
|
||||
- mo_one_e_integrals(q,r) * one_e_dm_mo(p,s)
|
||||
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!=========================
|
||||
! Second line, first term
|
||||
!=========================
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
if (q==r) then
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) + 0.5d0 * ( &
|
||||
get_two_e_integral(u,v,p,t,mo_integrals_map) * two_e_dm_mo(u,v,s,t) &
|
||||
+ get_two_e_integral(s,t,u,v,mo_integrals_map) * two_e_dm_mo(p,t,u,v))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!==========================
|
||||
! Second line, second term
|
||||
!==========================
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
if (p==s) then
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) + 0.5d0 * ( &
|
||||
get_two_e_integral(q,t,u,v,mo_integrals_map) * two_e_dm_mo(r,t,u,v) &
|
||||
+ get_two_e_integral(u,v,r,t,mo_integrals_map) * two_e_dm_mo(u,v,q,t))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!========================
|
||||
! Third line, first term
|
||||
!========================
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_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
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!=========================
|
||||
! Third line, second term
|
||||
!=========================
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_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
|
||||
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t2)
|
||||
t2 = t2 - t1
|
||||
print*, 'Time to compute the hessian :', t2
|
||||
|
||||
!==============
|
||||
! Permutations
|
||||
!==============
|
||||
|
||||
! Convert the hessian mo_num * mo_num * mo_num * mo_num matrix in a
|
||||
! 2D n * n matrix (n = mo_num*(mo_num-1)/2)
|
||||
! H(pq,rs) : p<q and r<s
|
||||
|
||||
do tmp_r = 1, m
|
||||
do tmp_s = 1, m
|
||||
do tmp_q = 1, m
|
||||
do tmp_p = 1, m
|
||||
|
||||
h_tmpr(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) - hessian(tmp_q,tmp_p,tmp_r,tmp_s) &
|
||||
- hessian(tmp_p,tmp_q,tmp_s,tmp_r) + hessian(tmp_q,tmp_p,tmp_s,tmp_r)
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!========================
|
||||
! 4D matrix -> 2D matrix
|
||||
!========================
|
||||
|
||||
! Convert the hessian mo_num * mo_num * mo_num * mo_num matrix in a
|
||||
! 2D n * n matrix (n = mo_num*(mo_num-1)/2)
|
||||
! H(pq,rs) : p<q and r<s
|
||||
|
||||
! 4D mo_num matrix to 2D n matrix
|
||||
do tmp_rs = 1, tmp_n
|
||||
call vec_to_mat_index(tmp_rs,tmp_r,tmp_s)
|
||||
do tmp_pq = 1, tmp_n
|
||||
call vec_to_mat_index(tmp_pq,tmp_p,tmp_q)
|
||||
tmp(tmp_pq,tmp_rs) = h_tmpr(tmp_p,tmp_q,tmp_r,tmp_s)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
do p = 1, tmp_n
|
||||
H(p) = tmp(p,p)
|
||||
enddo
|
||||
|
||||
! Display
|
||||
if (debug) then
|
||||
print*,'2D diag Hessian matrix'
|
||||
do tmp_pq = 1, tmp_n
|
||||
write(*,'(100(F10.5))') tmp(tmp_pq,:)
|
||||
enddo
|
||||
endif
|
||||
|
||||
!==============
|
||||
! Deallocation
|
||||
!==============
|
||||
|
||||
deallocate(hessian,h_tmpr,tmp)
|
||||
|
||||
print*,'---End first_diag_hess_list---'
|
||||
|
||||
end subroutine
|
||||
#+END_SRC
|
||||
|
|
@ -0,0 +1,348 @@
|
|||
* First diagonal hessian
|
||||
|
||||
#+BEGIN_SRC f90 :comments :tangle first_diagonal_hessian_opt.irp.f
|
||||
subroutine first_diag_hessian_opt(n,H, h_tmpr)
|
||||
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
!===========================================================================
|
||||
! Compute the diagonal hessian of energy with respects to orbital rotations
|
||||
!===========================================================================
|
||||
|
||||
!===========
|
||||
! Variables
|
||||
!===========
|
||||
|
||||
! in
|
||||
integer, intent(in) :: n
|
||||
! n : integer, n = mo_num*(mo_num-1)/2
|
||||
|
||||
! out
|
||||
double precision, intent(out) :: H(n,n), h_tmpr(mo_num,mo_num,mo_num,mo_num)
|
||||
! H : n by n double precision matrix containing the 2D hessian
|
||||
|
||||
! internal
|
||||
double precision, allocatable :: hessian(:,:,:,:)
|
||||
integer :: p,q
|
||||
integer :: r,s,t,u,v
|
||||
integer :: pq,rs
|
||||
double precision :: t1,t2,t3
|
||||
! hessian : mo_num 4D double precision matrix containing the hessian before the permutations
|
||||
! h_tmpr : mo_num 4D double precision matrix containing the hessian after the permutations
|
||||
! p,q,r,s : integer, indexes of the 4D hessian matrix
|
||||
! t,u,v : integer, indexes to compute hessian elements
|
||||
! pq,rs : integer, indexes for the conversion from 4D to 2D hessian matrix
|
||||
! t1,t2,t3 : double precision, t3 = t2 - t1, time to compute the hessian
|
||||
|
||||
! Function
|
||||
double precision :: get_two_e_integral
|
||||
! get_two_e_integral : double precision function, two e integrals
|
||||
|
||||
! Provided :
|
||||
! mo_one_e_integrals : mono e- integrals
|
||||
! get_two_e_integral : two e- integrals
|
||||
! one_e_dm_mo_alpha, one_e_dm_mo_beta : one body density matrix
|
||||
! two_e_dm_mo : two body density matrix
|
||||
|
||||
!============
|
||||
! Allocation
|
||||
!============
|
||||
|
||||
allocate(hessian(mo_num,mo_num,mo_num,mo_num))!,h_tmpr(mo_num,mo_num,mo_num,mo_num))
|
||||
|
||||
!=============
|
||||
! Calculation
|
||||
!=============
|
||||
|
||||
if (debug) then
|
||||
print*,'Enter in first_diag_hessien'
|
||||
endif
|
||||
|
||||
! From Anderson et. al. (2014)
|
||||
! The Journal of Chemical Physics 141, 244104 (2014); doi: 10.1063/1.4904384
|
||||
|
||||
! LaTeX formula :
|
||||
|
||||
!\begin{align*}
|
||||
!H_{pq,rs} &= \dfrac{\partial^2 E(x)}{\partial x_{pq}^2} \\
|
||||
!&= \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)
|
||||
!+ \delta_{ps}(h_r^u \gamma_u^q + h_u^q \gamma_u^r)]
|
||||
!-(h_p^s \gamma_r^q + h_r^q \gamma_p^s) \\
|
||||
!&+ \frac{1}{2} \sum_{tuv} [\delta_{qr}(v_{pt}^{uv} \Gamma_{uv}^{st} +v_{uv}^{st} \Gamma_{pt}^{uv})
|
||||
!+ \delta_{ps}(v_{uv}^{qt} \Gamma_{rt}^{uv} + v_{rt}^{uv}\Gamma_{uv}^{qt})] \\
|
||||
!&+ \sum_{uv} (v_{pr}^{uv} \Gamma_{uv}^{qs} + v_{uv}^{qs} \Gamma_{ps}^{uv}) \\
|
||||
!&- \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})
|
||||
!\end{align*}
|
||||
|
||||
!================
|
||||
! Initialization
|
||||
!================
|
||||
hessian = 0d0
|
||||
|
||||
CALL wall_time(t1)
|
||||
|
||||
!========================
|
||||
! First line, first term
|
||||
!========================
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
if (q==r) then
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
||||
mo_one_e_integrals(u,p) * one_e_dm_mo(u,s) &
|
||||
+ mo_one_e_integrals(s,u) * one_e_dm_mo(p,u))
|
||||
|
||||
enddo
|
||||
endif
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!=========================
|
||||
! First line, second term
|
||||
!=========================
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
if (p==s) then
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
||||
mo_one_e_integrals(u,r) * one_e_dm_mo(u,q) &
|
||||
+ mo_one_e_integrals(q,u) * one_e_dm_mo(r,u))
|
||||
enddo
|
||||
endif
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!========================
|
||||
! First line, third term
|
||||
!========================
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) &
|
||||
- mo_one_e_integrals(s,p) * one_e_dm_mo(r,q) &
|
||||
- mo_one_e_integrals(q,r) * one_e_dm_mo(p,s)
|
||||
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!=========================
|
||||
! Second line, first term
|
||||
!=========================
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
if (q==r) then
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
||||
get_two_e_integral(u,v,p,t,mo_integrals_map) * two_e_dm_mo(u,v,s,t) &
|
||||
+ get_two_e_integral(s,t,u,v,mo_integrals_map) * two_e_dm_mo(p,t,u,v))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!==========================
|
||||
! Second line, second term
|
||||
!==========================
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
if (p==s) then
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
||||
get_two_e_integral(q,t,u,v,mo_integrals_map) * two_e_dm_mo(r,t,u,v) &
|
||||
+ get_two_e_integral(u,v,r,t,mo_integrals_map) * two_e_dm_mo(u,v,q,t))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!========================
|
||||
! Third line, first term
|
||||
!========================
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
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
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!=========================
|
||||
! Third line, second term
|
||||
!=========================
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
! Permutations
|
||||
if (((p==r) .and. (q==s)) .or. ((q==r) .and. (p==s)) &
|
||||
.or. ((p==s) .and. (q==r))) then
|
||||
|
||||
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
|
||||
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t2)
|
||||
t2 = t2 - t1
|
||||
print*, 'Time to compute the hessian :', t2
|
||||
|
||||
!==============
|
||||
! Permutations
|
||||
!==============
|
||||
|
||||
! Convert the hessian mo_num * mo_num * mo_num * mo_num matrix in a
|
||||
! 2D n * n matrix (n = mo_num*(mo_num-1)/2)
|
||||
! H(pq,rs) : p<q and r<s
|
||||
|
||||
do r = 1, mo_num
|
||||
do s = 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
|
||||
|
||||
!========================
|
||||
! 4D matrix -> 2D matrix
|
||||
!========================
|
||||
|
||||
! Convert the hessian mo_num * mo_num * mo_num * mo_num matrix in a
|
||||
! 2D n * n matrix (n = mo_num*(mo_num-1)/2)
|
||||
! H(pq,rs) : p<q and r<s
|
||||
|
||||
! 4D mo_num matrix to 2D n matrix
|
||||
do rs = 1, n
|
||||
call vec_to_mat_index(rs,r,s)
|
||||
do pq = 1, n
|
||||
call vec_to_mat_index(pq,p,q)
|
||||
H(pq,rs) = h_tmpr(p,q,r,s)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Display
|
||||
if (debug) then
|
||||
print*,'2D diag Hessian matrix'
|
||||
do pq = 1, n
|
||||
write(*,'(100(F10.5))') H(pq,:)
|
||||
enddo
|
||||
endif
|
||||
|
||||
!==============
|
||||
! Deallocation
|
||||
!==============
|
||||
|
||||
deallocate(hessian)
|
||||
|
||||
if (debug) then
|
||||
print*,'Leave first_diag_hessien'
|
||||
endif
|
||||
|
||||
end subroutine
|
||||
#+END_SRC
|
||||
|
|
@ -0,0 +1,127 @@
|
|||
* First gradient
|
||||
#+BEGIN_SRC f90 :comments org :tangle first_gradient_list_opt.irp.f
|
||||
subroutine first_gradient_list_opt(tmp_n,m,list,v_grad)
|
||||
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
!===================================================================
|
||||
! Compute the gradient of energy with respects to orbital rotations
|
||||
!===================================================================
|
||||
|
||||
! Check if read_wf = true, else :
|
||||
! qp set determinant read_wf true
|
||||
|
||||
! in
|
||||
integer, intent(in) :: tmp_n,m,list(m)
|
||||
! n : integer, n = m*(m-1)/2
|
||||
! m = list_size
|
||||
|
||||
! out
|
||||
double precision, intent(out) :: v_grad(tmp_n)
|
||||
! v_grad : double precision vector of length n containeing the gradient
|
||||
|
||||
! internal
|
||||
double precision, allocatable :: grad(:,:),A(:,:)
|
||||
double precision :: norm
|
||||
integer :: i,p,q,r,s,t,tmp_i,tmp_p,tmp_q,tmp_r,tmp_s,tmp_t
|
||||
! grad : double precision matrix containing the gradient before the permutation
|
||||
! A : double precision matrix containing the gradient after the permutation
|
||||
! norm : double precision number, the norm of the vector gradient
|
||||
! i,p,q,r,s,t : integer, indexes
|
||||
! istate : integer, the electronic state
|
||||
|
||||
! Function
|
||||
double precision :: get_two_e_integral, norm2
|
||||
! get_two_e_integral : double precision function that gives the two e integrals
|
||||
! norm2 : double precision function that gives the norm of a vector
|
||||
|
||||
! Provided :
|
||||
! mo_one_e_integrals : mono e- integrals
|
||||
! get_two_e_integral : two e- integrals
|
||||
! one_e_dm_mo : one body density matrix (state average)
|
||||
! two_e_dm_mo : two body density matrix (state average)
|
||||
|
||||
print*,'---first_gradient_list---'
|
||||
|
||||
!============
|
||||
! Allocation
|
||||
!============
|
||||
|
||||
allocate(grad(m,m),A(m,m))
|
||||
|
||||
!=============
|
||||
! Calculation
|
||||
!=============
|
||||
|
||||
v_grad = 0d0
|
||||
grad = 0d0
|
||||
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
!grad(tmp_p,tmp_q) = 0d0
|
||||
do r = 1, mo_num
|
||||
grad(tmp_p,tmp_q) = grad(tmp_p,tmp_q) + mo_one_e_integrals(p,r) * one_e_dm_mo(r,q) &
|
||||
- mo_one_e_integrals(r,q) * one_e_dm_mo(p,r)
|
||||
|
||||
enddo
|
||||
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
do t = 1, mo_num
|
||||
|
||||
grad(tmp_p,tmp_q) = grad(tmp_p,tmp_q) &
|
||||
+ get_two_e_integral(p,t,r,s,mo_integrals_map) * two_e_dm_mo(r,s,q,t) &
|
||||
- get_two_e_integral(r,s,q,t,mo_integrals_map) * two_e_dm_mo(p,t,r,s)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Conversion mo_num*mo_num matrix to mo_num(mo_num-1)/2 vector
|
||||
do tmp_i = 1, tmp_n
|
||||
call vec_to_mat_index(tmp_i,tmp_p,tmp_q)
|
||||
v_grad(tmp_i)=(grad(tmp_p,tmp_q) - grad(tmp_q,tmp_p))
|
||||
enddo
|
||||
|
||||
! Display, vector containing the gradient elements
|
||||
if (debug) then
|
||||
print*,'Vector containing the gradient :'
|
||||
write(*,'(100(F10.5))') v_grad(1:tmp_n)
|
||||
endif
|
||||
|
||||
! Norm of the vector
|
||||
norm = norm2(v_grad)
|
||||
print*, 'Norm : ', norm
|
||||
|
||||
! Matrix gradient
|
||||
A = 0d0
|
||||
do tmp_q = 1, m
|
||||
do tmp_p = 1, m
|
||||
A(tmp_p,tmp_q) = grad(tmp_p,tmp_q) - grad(tmp_q,tmp_p)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Display, matrix containting the gradient elements
|
||||
if (debug) then
|
||||
print*,'Matrix containing the gradient :'
|
||||
do tmp_i = 1, m
|
||||
write(*,'(100(E12.5))') A(tmp_i,1:m)
|
||||
enddo
|
||||
endif
|
||||
|
||||
!==============
|
||||
! Deallocation
|
||||
!==============
|
||||
|
||||
deallocate(grad,A)
|
||||
|
||||
print*,'---End first_gradient_list---'
|
||||
|
||||
end subroutine
|
||||
|
||||
#+END_SRC
|
||||
|
|
@ -0,0 +1,130 @@
|
|||
* First gradient
|
||||
#+BEGIN_SRC f90 :comments org :tangle first_gradient_opt.irp.f
|
||||
subroutine first_gradient_opt(n,v_grad)
|
||||
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
!===================================================================
|
||||
! Compute the gradient of energy with respects to orbital rotations
|
||||
!===================================================================
|
||||
|
||||
! Check if read_wf = true, else :
|
||||
! qp set determinant read_wf true
|
||||
|
||||
END_DOC
|
||||
|
||||
! in
|
||||
integer, intent(in) :: n
|
||||
! n : integer, n = mo_num*(mo_num-1)/2
|
||||
|
||||
! out
|
||||
double precision, intent(out) :: v_grad(n)
|
||||
! v_grad : double precision vector of length n containeing the gradient
|
||||
|
||||
! internal
|
||||
double precision, allocatable :: grad(:,:),A(:,:)
|
||||
double precision :: norm
|
||||
integer :: i,p,q,r,s,t
|
||||
integer :: istate
|
||||
! grad : double precision matrix containing the gradient before the permutation
|
||||
! A : double precision matrix containing the gradient after the permutation
|
||||
! norm : double precision number, the norm of the vector gradient
|
||||
! i,p,q,r,s,t : integer, indexes
|
||||
! istate : integer, the electronic state
|
||||
|
||||
! Function
|
||||
double precision :: get_two_e_integral, norm2
|
||||
! get_two_e_integral : double precision function that gives the two e integrals
|
||||
! norm2 : double precision function that gives the norm of a vector
|
||||
|
||||
! Provided :
|
||||
! mo_one_e_integrals : mono e- integrals
|
||||
! get_two_e_integral : two e- integrals
|
||||
! one_e_dm_mo : one body density matrix (state average)
|
||||
! two_e_dm_mo : two body density matrix (state average)
|
||||
|
||||
!============
|
||||
! Allocation
|
||||
!============
|
||||
|
||||
allocate(grad(mo_num,mo_num),A(mo_num,mo_num))
|
||||
|
||||
!=============
|
||||
! Calculation
|
||||
!=============
|
||||
|
||||
if (debug) then
|
||||
print*,'---first_gradient---'
|
||||
endif
|
||||
|
||||
v_grad = 0d0
|
||||
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
grad(p,q) = 0d0
|
||||
do r = 1, mo_num
|
||||
grad(p,q) = grad(p,q) + mo_one_e_integrals(p,r) * one_e_dm_mo(r,q) &
|
||||
- mo_one_e_integrals(r,q) * one_e_dm_mo(p,r)
|
||||
|
||||
enddo
|
||||
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
do t= 1, mo_num
|
||||
|
||||
grad(p,q) = grad(p,q) &
|
||||
+ get_two_e_integral(p,t,r,s,mo_integrals_map) * two_e_dm_mo(r,s,q,t) &
|
||||
- get_two_e_integral(r,s,q,t,mo_integrals_map) * two_e_dm_mo(p,t,r,s)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Conversion mo_num*mo_num matrix to mo_num(mo_num-1)/2 vector
|
||||
do i=1,n
|
||||
call vec_to_mat_index(i,p,q)
|
||||
v_grad(i)=(grad(p,q) - grad(q,p))
|
||||
enddo
|
||||
|
||||
! Display, vector containing the gradient elements
|
||||
if (debug) then
|
||||
print*,'Vector containing the gradient :'
|
||||
write(*,'(100(F10.5))') v_grad(1:n)
|
||||
endif
|
||||
|
||||
! Norm of the vector
|
||||
norm = norm2(v_grad)
|
||||
print*, 'Norm : ', norm
|
||||
|
||||
! Matrix gradient
|
||||
A = 0d0
|
||||
do q=1,mo_num
|
||||
do p=1,mo_num
|
||||
A(p,q) = grad(p,q) - grad(q,p)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Display, matrix containting the gradient elements
|
||||
if (debug) then
|
||||
print*,'Matrix containing the gradient :'
|
||||
do i = 1, mo_num
|
||||
write(*,'(100(E12.5))') A(i,1:mo_num)
|
||||
enddo
|
||||
endif
|
||||
|
||||
!==============
|
||||
! Deallocation
|
||||
!==============
|
||||
|
||||
deallocate(grad,A)
|
||||
|
||||
if (debug) then
|
||||
print*,'---End first_gradient---'
|
||||
endif
|
||||
|
||||
end subroutine
|
||||
|
||||
#+END_SRC
|
||||
|
|
@ -0,0 +1,370 @@
|
|||
* First hessian
|
||||
|
||||
#+BEGIN_SRC f90 :comments :tangle first_hessian_list_opt.irp.f
|
||||
subroutine first_hessian_list_opt(tmp_n,m,list,H,h_tmpr)
|
||||
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
!==================================================================
|
||||
! Compute the hessian of energy with respects to orbital rotations
|
||||
!==================================================================
|
||||
|
||||
!===========
|
||||
! Variables
|
||||
!===========
|
||||
|
||||
! in
|
||||
integer, intent(in) :: tmp_n, m, list(m)
|
||||
!tmp_n : integer, tmp_n = m*(m-1)/2
|
||||
|
||||
! out
|
||||
double precision, intent(out) :: H(tmp_n,tmp_n),h_tmpr(m,m,m,m)
|
||||
! H : n by n double precision matrix containing the 2D hessian
|
||||
|
||||
! internal
|
||||
double precision, allocatable :: hessian(:,:,:,:)
|
||||
integer :: p,q, tmp_p,tmp_q
|
||||
integer :: r,s,t,u,v,tmp_r,tmp_s,tmp_t,tmp_u,tmp_v
|
||||
integer :: pq,rs,tmp_pq,tmp_rs
|
||||
double precision :: t1,t2,t3,t4,t5,t6
|
||||
! hessian : mo_num 4D double precision matrix containing the hessian before the permutations
|
||||
! h_tmpr : mo_num 4D double precision matrix containing the hessian after the permutations
|
||||
! p,q,r,s : integer, indexes of the 4D hessian matrix
|
||||
! t,u,v : integer, indexes to compute hessian elements
|
||||
! pq,rs : integer, indexes for the conversion from 4D to 2D hessian matrix
|
||||
! t1,t2,t3 : double precision, t3 = t2 - t1, time to compute the hessian
|
||||
|
||||
! Funtion
|
||||
double precision :: get_two_e_integral
|
||||
! get_two_e_integral : double precision function, two e integrals
|
||||
|
||||
! Provided :
|
||||
! mo_one_e_integrals : mono e- integrals
|
||||
! get_two_e_integral : two e- integrals
|
||||
! one_e_dm_mo_alpha, one_e_dm_mo_beta : one body density matrix
|
||||
! two_e_dm_mo : two body density matrix
|
||||
|
||||
!============
|
||||
! Allocation
|
||||
!============
|
||||
|
||||
allocate(hessian(m,m,m,m))
|
||||
|
||||
!=============
|
||||
! Calculation
|
||||
!=============
|
||||
|
||||
print*,'---first_hess_list---'
|
||||
|
||||
! From Anderson et. al. (2014)
|
||||
! The Journal of Chemical Physics 141, 244104 (2014); doi: 10.1063/1.4904384
|
||||
|
||||
CALL wall_time(t1)
|
||||
|
||||
! Initialization
|
||||
hessian = 0d0
|
||||
|
||||
!========================
|
||||
! First line, first term
|
||||
!========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
if (q==r) then
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) + 0.5d0 * ( &
|
||||
mo_one_e_integrals(u,p) * one_e_dm_mo(u,s) &
|
||||
+ mo_one_e_integrals(s,u) * one_e_dm_mo(p,u))
|
||||
|
||||
enddo
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l1 1 :', t6
|
||||
|
||||
!=========================
|
||||
! First line, second term
|
||||
!=========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
if (p==s) then
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) + 0.5d0 * ( &
|
||||
mo_one_e_integrals(u,r) * one_e_dm_mo(u,q) &
|
||||
+ mo_one_e_integrals(q,u) * one_e_dm_mo(r,u))
|
||||
enddo
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l1 2 :', t6
|
||||
|
||||
!========================
|
||||
! First line, third term
|
||||
!========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) &
|
||||
- mo_one_e_integrals(s,p) * one_e_dm_mo(r,q)&
|
||||
- mo_one_e_integrals(q,r) * one_e_dm_mo(p,s)
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l1 3 :', t6
|
||||
|
||||
|
||||
!=========================
|
||||
! Second line, first term
|
||||
!=========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
if (q==r) then
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) + 0.5d0 * ( &
|
||||
get_two_e_integral(u,v,p,t,mo_integrals_map) * two_e_dm_mo(u,v,s,t) &
|
||||
+ get_two_e_integral(s,t,u,v,mo_integrals_map) * two_e_dm_mo(p,t,u,v))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l2 1 :', t6
|
||||
|
||||
!==========================
|
||||
! Second line, second term
|
||||
!==========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
if (p==s) then
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_s) + 0.5d0 * ( &
|
||||
get_two_e_integral(q,t,u,v,mo_integrals_map) * two_e_dm_mo(r,t,u,v) &
|
||||
+ get_two_e_integral(u,v,r,t,mo_integrals_map) * two_e_dm_mo(u,v,q,t))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l2 2 :', t6
|
||||
|
||||
!========================
|
||||
! Third line, first term
|
||||
!========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_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
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l3 1 :', t6
|
||||
|
||||
!=========================
|
||||
! Third line, second term
|
||||
!=========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do tmp_r = 1, m
|
||||
r = list(tmp_r)
|
||||
do tmp_s = 1, m
|
||||
s = list(tmp_s)
|
||||
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(tmp_p,tmp_q,tmp_r,tmp_s) = hessian(tmp_p,tmp_q,tmp_r,tmp_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
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l3 2 :', t6
|
||||
|
||||
CALL wall_time(t2)
|
||||
t3 = t2 -t1
|
||||
print*,'Time to compute the hessian : ', t3
|
||||
|
||||
!==============
|
||||
! Permutations
|
||||
!==============
|
||||
|
||||
! 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)
|
||||
|
||||
do tmp_s = 1, m
|
||||
do tmp_r = 1, m
|
||||
do tmp_q = 1, m
|
||||
do tmp_p = 1, m
|
||||
|
||||
h_tmpr(tmp_p,tmp_q,tmp_r,tmp_s) = (hessian(tmp_p,tmp_q,tmp_r,tmp_s) - hessian(tmp_q,tmp_p,tmp_r,tmp_s) &
|
||||
- hessian(tmp_p,tmp_q,tmp_s,tmp_r) + hessian(tmp_q,tmp_p,tmp_s,tmp_r))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
!========================
|
||||
! 4D matrix to 2D matrix
|
||||
!========================
|
||||
|
||||
! Convert the hessian mo_num * mo_num * mo_num * mo_num matrix in a
|
||||
! 2D n * n matrix (n = mo_num*(mo_num-1)/2)
|
||||
! H(pq,rs) : p<q and r<s
|
||||
|
||||
! 4D mo_num matrix to 2D n matrix
|
||||
do tmp_pq = 1, tmp_n
|
||||
call vec_to_mat_index(tmp_pq,tmp_p,tmp_q)
|
||||
do tmp_rs = 1, tmp_n
|
||||
call vec_to_mat_index(tmp_rs,tmp_r,tmp_s)
|
||||
H(tmp_pq,tmp_rs) = h_tmpr(tmp_p,tmp_q,tmp_r,tmp_s)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Display
|
||||
if (debug) then
|
||||
print*,'2D Hessian matrix'
|
||||
do tmp_pq = 1, tmp_n
|
||||
write(*,'(100(F10.5))') H(tmp_pq,:)
|
||||
enddo
|
||||
endif
|
||||
|
||||
!==============
|
||||
! Deallocation
|
||||
!==============
|
||||
|
||||
deallocate(hessian)
|
||||
|
||||
print*,'---End first_hess_list---'
|
||||
|
||||
end subroutine
|
||||
|
||||
#+END_SRC
|
||||
|
|
@ -0,0 +1,365 @@
|
|||
* First hessian
|
||||
|
||||
#+BEGIN_SRC f90 :comments :tangle first_hessian_opt.irp.f
|
||||
subroutine first_hessian_opt(n,H,h_tmpr)
|
||||
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
!==================================================================
|
||||
! Compute the hessian of energy with respects to orbital rotations
|
||||
!==================================================================
|
||||
|
||||
!===========
|
||||
! Variables
|
||||
!===========
|
||||
|
||||
! in
|
||||
integer, intent(in) :: n
|
||||
!n : integer, n = mo_num*(mo_num-1)/2
|
||||
|
||||
! out
|
||||
double precision, intent(out) :: H(n,n),h_tmpr(mo_num,mo_num,mo_num,mo_num)
|
||||
! H : n by n double precision matrix containing the 2D hessian
|
||||
|
||||
! internal
|
||||
double precision, allocatable :: hessian(:,:,:,:)
|
||||
integer :: p,q
|
||||
integer :: r,s,t,u,v
|
||||
integer :: pq,rs
|
||||
double precision :: t1,t2,t3,t4,t5,t6
|
||||
! hessian : mo_num 4D double precision matrix containing the hessian before the permutations
|
||||
! h_tmpr : mo_num 4D double precision matrix containing the hessian after the permutations
|
||||
! p,q,r,s : integer, indexes of the 4D hessian matrix
|
||||
! t,u,v : integer, indexes to compute hessian elements
|
||||
! pq,rs : integer, indexes for the conversion from 4D to 2D hessian matrix
|
||||
! t1,t2,t3 : double precision, t3 = t2 - t1, time to compute the hessian
|
||||
|
||||
! Funtion
|
||||
double precision :: get_two_e_integral
|
||||
! get_two_e_integral : double precision function, two e integrals
|
||||
|
||||
! Provided :
|
||||
! mo_one_e_integrals : mono e- integrals
|
||||
! get_two_e_integral : two e- integrals
|
||||
! one_e_dm_mo_alpha, one_e_dm_mo_beta : one body density matrix
|
||||
! two_e_dm_mo : two body density matrix
|
||||
|
||||
!============
|
||||
! Allocation
|
||||
!============
|
||||
|
||||
allocate(hessian(mo_num,mo_num,mo_num,mo_num))
|
||||
|
||||
!=============
|
||||
! Calculation
|
||||
!=============
|
||||
|
||||
if (debug) then
|
||||
print*,'Enter in first_hess'
|
||||
endif
|
||||
|
||||
! From Anderson et. al. (2014)
|
||||
! The Journal of Chemical Physics 141, 244104 (2014); doi: 10.1063/1.4904384
|
||||
|
||||
CALL wall_time(t1)
|
||||
|
||||
! Initialization
|
||||
hessian = 0d0
|
||||
|
||||
!========================
|
||||
! First line, first term
|
||||
!========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
if (q==r) then
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
||||
mo_one_e_integrals(u,p) * one_e_dm_mo(u,s) &
|
||||
+ mo_one_e_integrals(s,u) * one_e_dm_mo(p,u))
|
||||
|
||||
enddo
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l1 1 :', t6
|
||||
|
||||
!=========================
|
||||
! First line, second term
|
||||
!=========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
if (p==s) then
|
||||
do u = 1, mo_num
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
||||
mo_one_e_integrals(u,r) * one_e_dm_mo(u,q) &
|
||||
+ mo_one_e_integrals(q,u) * one_e_dm_mo(r,u))
|
||||
enddo
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l1 2 :', t6
|
||||
|
||||
!========================
|
||||
! First line, third term
|
||||
!========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) &
|
||||
- mo_one_e_integrals(s,p) * one_e_dm_mo(r,q)&
|
||||
- mo_one_e_integrals(q,r) * one_e_dm_mo(p,s)
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l1 3 :', t6
|
||||
|
||||
|
||||
!=========================
|
||||
! Second line, first term
|
||||
!=========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do s = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do p = 1, mo_num
|
||||
|
||||
! do p = 1, mo_num
|
||||
! do q = 1, mo_num
|
||||
! do r = 1, mo_num
|
||||
! do s = 1, mo_num
|
||||
|
||||
if (q==r) then
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
||||
get_two_e_integral(u,v,p,t,mo_integrals_map) * two_e_dm_mo(u,v,s,t) &
|
||||
+ get_two_e_integral(s,t,u,v,mo_integrals_map) * two_e_dm_mo(p,t,u,v))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l2 1 :', t6
|
||||
|
||||
!==========================
|
||||
! Second line, second term
|
||||
!==========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do s = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do p = 1, mo_num
|
||||
|
||||
! do p = 1, mo_num
|
||||
! do q = 1, mo_num
|
||||
! do r = 1, mo_num
|
||||
! do s = 1, mo_num
|
||||
|
||||
if (p==s) then
|
||||
do t = 1, mo_num
|
||||
do u = 1, mo_num
|
||||
do v = 1, mo_num
|
||||
|
||||
hessian(p,q,r,s) = hessian(p,q,r,s) + 0.5d0 * ( &
|
||||
get_two_e_integral(q,t,u,v,mo_integrals_map) * two_e_dm_mo(r,t,u,v) &
|
||||
+ get_two_e_integral(u,v,r,t,mo_integrals_map) * two_e_dm_mo(u,v,q,t))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
endif
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l2 2 :', t6
|
||||
|
||||
!========================
|
||||
! Third line, first term
|
||||
!========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do s = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do p = 1, mo_num
|
||||
|
||||
! 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
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l3 1 :', t6
|
||||
|
||||
!=========================
|
||||
! Third line, second term
|
||||
!=========================
|
||||
|
||||
CALL wall_time(t4)
|
||||
|
||||
do s = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do p = 1, mo_num
|
||||
|
||||
! 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
|
||||
|
||||
CALL wall_time(t5)
|
||||
t6 = t5-t4
|
||||
print*,'l3 2 :', t6
|
||||
|
||||
CALL wall_time(t2)
|
||||
t3 = t2 -t1
|
||||
print*,'Time to compute the hessian : ', t3
|
||||
|
||||
!==============
|
||||
! Permutations
|
||||
!==============
|
||||
|
||||
! 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)
|
||||
|
||||
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
|
||||
|
||||
!========================
|
||||
! 4D matrix to 2D matrix
|
||||
!========================
|
||||
|
||||
! Convert the hessian mo_num * mo_num * mo_num * mo_num matrix in a
|
||||
! 2D n * n matrix (n = mo_num*(mo_num-1)/2)
|
||||
! H(pq,rs) : p<q and r<s
|
||||
|
||||
! 4D mo_num matrix to 2D n matrix
|
||||
do pq = 1, n
|
||||
call vec_to_mat_index(pq,p,q)
|
||||
do rs = 1, n
|
||||
call vec_to_mat_index(rs,r,s)
|
||||
H(pq,rs) = h_tmpr(p,q,r,s)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! Display
|
||||
if (debug) then
|
||||
print*,'2D Hessian matrix'
|
||||
do pq = 1, n
|
||||
write(*,'(100(F10.5))') H(pq,:)
|
||||
enddo
|
||||
endif
|
||||
|
||||
!==============
|
||||
! Deallocation
|
||||
!==============
|
||||
|
||||
deallocate(hessian)
|
||||
|
||||
if (debug) then
|
||||
print*,'Leave first_hess'
|
||||
endif
|
||||
|
||||
end subroutine
|
||||
|
||||
#+END_SRC
|
||||
|
|
@ -0,0 +1,393 @@
|
|||
* Gradient
|
||||
|
||||
The gradient of the CI energy with respects to the orbital rotation
|
||||
is:
|
||||
(C-c C-x C-l)
|
||||
$$
|
||||
G(p,q) = \mathcal{P}_{pq} \left[ \sum_r (h_p^r \gamma_r^q - h_r^q \gamma_p^r) +
|
||||
\sum_{rst}(v_{pt}^{rs} \Gamma_{rs}^{qt} - v_{rs}^{qt} \Gamma_{pt}^{rs})
|
||||
\right]
|
||||
$$
|
||||
|
||||
|
||||
$$
|
||||
\mathcal{P}_{pq}= 1 - (p \leftrightarrow q)
|
||||
$$
|
||||
|
||||
$$
|
||||
G(p,q) = \left[
|
||||
\sum_r (h_p^r \gamma_r^q - h_r^q \gamma_p^r) +
|
||||
\sum_{rst}(v_{pt}^{rs} \Gamma_{rs}^{qt} - v_{rs}^{qt} \Gamma_{pt}^{rs})
|
||||
\right] -
|
||||
\left[
|
||||
\sum_r (h_q^r \gamma_r^p - h_r^p \gamma_q^r) +
|
||||
\sum_{rst}(v_{qt}^{rs} \Gamma_{rs}^{pt} - v_{rs}^{pt}
|
||||
\Gamma_{qt}^{rs})
|
||||
\right]
|
||||
$$
|
||||
|
||||
Where p,q,r,s,t are general spatial orbitals
|
||||
mo_num : the number of molecular orbitals
|
||||
$$h$$ : One electron integrals
|
||||
$$\gamma$$ : One body density matrix (state average in our case)
|
||||
$$v$$ : Two electron integrals
|
||||
$$\Gamma$$ : Two body density matrice (state average in our case)
|
||||
|
||||
The gradient is a mo_num by mo_num matrix, p,q,r,s,t take all the
|
||||
values between 1 and mo_num (1 and mo_num include).
|
||||
|
||||
To do that we compute $$G(p,q)$$ for all the pairs (p,q).
|
||||
|
||||
Source :
|
||||
Seniority-based coupled cluster theory
|
||||
J. Chem. Phys. 141, 244104 (2014); https://doi.org/10.1063/1.4904384
|
||||
Thomas M. Henderson, Ireneusz W. Bulik, Tamar Stein, and Gustavo
|
||||
E. Scuseria
|
||||
|
||||
*Compute the gradient of energy with respects to orbital rotations*
|
||||
|
||||
Provided:
|
||||
| mo_num | integer | number of MOs |
|
||||
| mo_one_e_integrals(mo_num,mo_num) | double precision | mono_electronic integrals |
|
||||
| one_e_dm_mo(mo_num,mo_num) | double precision | one e- density matrix |
|
||||
| two_e_dm_mo(mo_num,mo_num,mo_num,mo_num) | double precision | two e- density matrix |
|
||||
|
||||
Input:
|
||||
| n | integer | mo_num*(mo_num-1)/2 |
|
||||
|
||||
Output:
|
||||
| v_grad(n) | double precision | the gradient |
|
||||
| max_elem | double precision | maximum element of the gradient |
|
||||
|
||||
Internal:
|
||||
| grad(mo_num,mo_num) | double precison | gradient before the tranformation in a vector |
|
||||
| A((mo_num,mo_num) | doubre precision | gradient after the permutations |
|
||||
| norm | double precision | norm of the gradient |
|
||||
| p, q | integer | indexes of the element in the matrix grad |
|
||||
| i | integer | index for the tranformation in a vector |
|
||||
| r, s, t | integer | indexes dor the sums |
|
||||
| t1, t2, t3 | double precision | t3 = t2 - t1, time to compute the gradient |
|
||||
| t4, t5, t6 | double precission | t6 = t5 - t4, time to compute each element |
|
||||
| tmp_bi_int_3(mo_num,mo_num,mo_num) | double precision | 3 indexes temporary array for the bi-electronic integrals |
|
||||
| tmp_2rdm_3(mo_num,mo_num,mo_num) | double precision | 3 indexes temporary array for the two e- density matrix |
|
||||
| tmp_accu(mo_num,mo_num) | double precision | temporary array |
|
||||
|
||||
Function:
|
||||
| get_two_e_integral | double precision | bi-electronic integrals |
|
||||
| dnrm2 | double precision | (Lapack) norm |
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle gradient_list_opt.irp.f
|
||||
subroutine gradient_list_opt(n,m,list,v_grad,max_elem,norm)
|
||||
use omp_lib
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
! Variables
|
||||
|
||||
! in
|
||||
integer, intent(in) :: n,m,list(m)
|
||||
|
||||
! out
|
||||
double precision, intent(out) :: v_grad(n), max_elem, norm
|
||||
|
||||
! internal
|
||||
double precision, allocatable :: grad(:,:),A(:,:)
|
||||
integer :: i,p,q,r,s,t, tmp_p, tmp_q, tmp_i
|
||||
double precision :: t1,t2,t3,t4,t5,t6
|
||||
|
||||
double precision, allocatable :: tmp_accu(:,:), tmp_mo_one_e_integrals(:,:),tmp_one_e_dm_mo(:,:)
|
||||
double precision, allocatable :: tmp_bi_int_3(:,:,:), tmp_2rdm_3(:,:,:)
|
||||
|
||||
! Functions
|
||||
double precision :: get_two_e_integral, dnrm2
|
||||
|
||||
|
||||
print*,''
|
||||
print*,'---gradient---'
|
||||
|
||||
! Allocation of shared arrays
|
||||
allocate(grad(m,m),A(m,m))
|
||||
allocate(tmp_mo_one_e_integrals(m,mo_num),tmp_one_e_dm_mo(mo_num,m))
|
||||
|
||||
|
||||
! Initialization omp
|
||||
call omp_set_max_active_levels(1)
|
||||
|
||||
!$OMP PARALLEL &
|
||||
!$OMP PRIVATE( &
|
||||
!$OMP p,q,r,s,t,tmp_p,tmp_q, &
|
||||
!$OMP tmp_accu,tmp_bi_int_3, tmp_2rdm_3) &
|
||||
!$OMP SHARED(grad, one_e_dm_mo,m,list,mo_num,mo_one_e_integrals, &
|
||||
!$OMP mo_integrals_map,tmp_one_e_dm_mo, tmp_mo_one_e_integrals,t4,t5,t6) &
|
||||
!$OMP DEFAULT(SHARED)
|
||||
|
||||
! Allocation of private arrays
|
||||
allocate(tmp_accu(m,m))
|
||||
allocate(tmp_bi_int_3(mo_num,mo_num,m))
|
||||
allocate(tmp_2rdm_3(mo_num,mo_num,m))
|
||||
#+END_SRC
|
||||
|
||||
** Calculation
|
||||
*** Initialization
|
||||
#+BEGIN_SRC f90 :comments org :tangle gradient_list_opt.irp.f
|
||||
!$OMP DO
|
||||
do tmp_q = 1, m
|
||||
do tmp_p = 1, m
|
||||
grad(tmp_p,tmp_q) = 0d0
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END DO
|
||||
#+END_SRC
|
||||
|
||||
*** Term 1
|
||||
|
||||
Without optimization the term 1 is :
|
||||
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
grad(p,q) = grad(p,q) &
|
||||
+ mo_one_e_integrals(p,r) * one_e_dm_mo(r,q) &
|
||||
- mo_one_e_integrals(r,q) * one_e_dm_mo(p,r)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
Since the matrix multiplication A.B is defined like :
|
||||
\begin{equation}
|
||||
c_{ij} = \sum_k a_{ik}.b_{kj}
|
||||
\end{equation}
|
||||
The previous equation can be rewritten as a matrix multplication
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle gradient_list_opt.irp.f
|
||||
!****************
|
||||
! Opt first term
|
||||
!****************
|
||||
|
||||
!$OMP DO
|
||||
do r = 1, mo_num
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
tmp_mo_one_e_integrals(tmp_p,r) = mo_one_e_integrals(p,r)
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END DO
|
||||
|
||||
!$OMP DO
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do r = 1, mo_num
|
||||
tmp_one_e_dm_mo(r,tmp_q) = one_e_dm_mo(r,q)
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END DO
|
||||
|
||||
call dgemm('N','N',m,m,mo_num,1d0,&
|
||||
tmp_mo_one_e_integrals, size(tmp_mo_one_e_integrals,1),&
|
||||
tmp_one_e_dm_mo,size(tmp_one_e_dm_mo,1),0d0,tmp_accu,size(tmp_accu,1))
|
||||
|
||||
!$OMP DO
|
||||
do tmp_q = 1, m
|
||||
do tmp_p = 1, m
|
||||
|
||||
grad(tmp_p,tmp_q) = grad(tmp_p,tmp_q) + (tmp_accu(tmp_p,tmp_q) - tmp_accu(tmp_q,tmp_p))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END DO
|
||||
|
||||
!$OMP MASTER
|
||||
CALL wall_TIME(t4)
|
||||
!$OMP END MASTER
|
||||
|
||||
! call dgemm('N','N',mo_num,mo_num,mo_num,1d0,mo_one_e_integrals,&
|
||||
! mo_num,one_e_dm_mo,mo_num,0d0,tmp_accu,mo_num)
|
||||
!
|
||||
! !$OMP DO
|
||||
! do q = 1, mo_num
|
||||
! do p = 1, mo_num
|
||||
!
|
||||
! grad(p,q) = grad(p,q) + (tmp_accu(p,q) - tmp_accu(q,p))
|
||||
!
|
||||
! enddo
|
||||
! enddo
|
||||
! !$OMP END DO
|
||||
|
||||
!$OMP MASTER
|
||||
CALL wall_TIME(t5)
|
||||
t6 = t5-t4
|
||||
print*,'Gradient, first term (s) :', t6
|
||||
!$OMP END MASTER
|
||||
#+END_SRC
|
||||
|
||||
*** Term 2
|
||||
|
||||
Without optimization the second term is :
|
||||
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
do t= 1, mo_num
|
||||
|
||||
grad(p,q) = grad(p,q) &
|
||||
+ get_two_e_integral(p,t,r,s,mo_integrals_map) * two_e_dm_mo(r,s,q,t) &
|
||||
- get_two_e_integral(r,s,q,t,mo_integrals_map) * two_e_dm_mo(p,t,r,s)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
Using the bielectronic integral properties :
|
||||
get_two_e_integral(p,t,r,s,mo_integrals_map) = get_two_e_integral(r,s,p,t,mo_integrals_map)
|
||||
|
||||
Using the two body matrix properties :
|
||||
two_e_dm_mo(p,t,r,s) = two_e_dm_mo(r,s,p,t)
|
||||
|
||||
t is one the right, we can put it on the external loop and create 3
|
||||
indexes temporary array
|
||||
r,s can be seen as one index
|
||||
|
||||
By doing so, a matrix multiplication appears
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle gradient_list_opt.irp.f
|
||||
!*****************
|
||||
! Opt second term
|
||||
!*****************
|
||||
|
||||
!$OMP MASTER
|
||||
CALL wall_TIME(t4)
|
||||
!$OMP END MASTER
|
||||
|
||||
!$OMP DO
|
||||
do t = 1, mo_num
|
||||
|
||||
do tmp_p = 1, m
|
||||
p = list(tmp_p)
|
||||
do s = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
|
||||
tmp_bi_int_3(r,s,tmp_p) = get_two_e_integral(r,s,p,t,mo_integrals_map)
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
do tmp_q = 1, m
|
||||
q = list(tmp_q)
|
||||
do s = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
|
||||
tmp_2rdm_3(r,s,tmp_q) = two_e_dm_mo(r,s,q,t)
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
call dgemm('T','N',m,m,mo_num*mo_num,1d0,tmp_bi_int_3,&
|
||||
mo_num*mo_num,tmp_2rdm_3,mo_num*mo_num,0d0,tmp_accu,size(tmp_accu,1))
|
||||
|
||||
!$OMP CRITICAL
|
||||
do tmp_q = 1, m
|
||||
do tmp_p = 1, m
|
||||
|
||||
grad(tmp_p,tmp_q) = grad(tmp_p,tmp_q) + tmp_accu(tmp_p,tmp_q) - tmp_accu(tmp_q,tmp_p)
|
||||
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END CRITICAL
|
||||
|
||||
enddo
|
||||
!$OMP END DO
|
||||
|
||||
!$OMP MASTER
|
||||
CALL wall_TIME(t5)
|
||||
t6 = t5-t4
|
||||
print*,'Gradient second term (s) : ', t6
|
||||
!$OMP END MASTER
|
||||
#+END_SRC
|
||||
|
||||
*** Deallocation of private arrays
|
||||
#+BEGIN_SRC f90 :comments org :tangle gradient_list_opt.irp.f
|
||||
deallocate(tmp_bi_int_3,tmp_2rdm_3,tmp_accu)
|
||||
|
||||
!$OMP END PARALLEL
|
||||
|
||||
call omp_set_max_active_levels(4)
|
||||
#+END_SRC
|
||||
|
||||
*** Permutation, 2D matrix -> vector, transformation
|
||||
In addition there is a permutation in the gradient formula :
|
||||
\begin{equation}
|
||||
P_{pq} = 1 - (p <-> q)
|
||||
\end{equation}
|
||||
|
||||
We need a vector to use the gradient. Here the gradient is a
|
||||
antisymetric matrix so we can transform it in a vector of length
|
||||
mo_num*(mo_num-1)/2.
|
||||
|
||||
Here we do these two things at the same time.
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle gradient_list_opt.irp.f
|
||||
do i=1,n
|
||||
call vec_to_mat_index(i,p,q)
|
||||
v_grad(i)=(grad(p,q) - grad(q,p))
|
||||
enddo
|
||||
|
||||
! Debug, diplay the vector containing the gradient elements
|
||||
if (debug) then
|
||||
print*,'Vector containing the gradient :'
|
||||
write(*,'(100(F10.5))') v_grad(1:n)
|
||||
endif
|
||||
#+END_SRC
|
||||
|
||||
*** Norm of the gradient
|
||||
The norm can be useful.
|
||||
#+BEGIN_SRC f90 :comments org :tangle gradient_list_opt.irp.f
|
||||
norm = dnrm2(n,v_grad,1)
|
||||
print*, 'Gradient norm : ', norm
|
||||
#+END_SRC
|
||||
|
||||
*** Maximum element in the gradient
|
||||
The maximum element in the gradient is very important for the
|
||||
convergence criterion of the Newton method.
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle gradient_list_opt.irp.f
|
||||
! Max element of the gradient
|
||||
max_elem = 0d0
|
||||
do i = 1, n
|
||||
if (DABS(v_grad(i)) > DABS(max_elem)) then
|
||||
max_elem = v_grad(i)
|
||||
endif
|
||||
enddo
|
||||
|
||||
print*,'Max element in the gradient :', max_elem
|
||||
|
||||
! Debug, display the matrix containting the gradient elements
|
||||
if (debug) then
|
||||
! Matrix gradient
|
||||
A = 0d0
|
||||
do q=1,m
|
||||
do p=1,m
|
||||
A(p,q) = grad(p,q) - grad(q,p)
|
||||
enddo
|
||||
enddo
|
||||
print*,'Matrix containing the gradient :'
|
||||
do i = 1, m
|
||||
write(*,'(100(F10.5))') A(i,1:m)
|
||||
enddo
|
||||
endif
|
||||
#+END_SRC
|
||||
|
||||
*** Deallocation of shared arrays and end
|
||||
#+BEGIN_SRC f90 :comments org :tangle gradient_list_opt.irp.f
|
||||
deallocate(grad,A, tmp_mo_one_e_integrals,tmp_one_e_dm_mo)
|
||||
|
||||
print*,'---End gradient---'
|
||||
|
||||
end subroutine
|
||||
|
||||
#+END_SRC
|
||||
|
||||
|
|
@ -0,0 +1,358 @@
|
|||
* Gradient
|
||||
|
||||
The gradient of the CI energy with respects to the orbital rotation
|
||||
is:
|
||||
(C-c C-x C-l)
|
||||
$$
|
||||
G(p,q) = \mathcal{P}_{pq} \left[ \sum_r (h_p^r \gamma_r^q - h_r^q \gamma_p^r) +
|
||||
\sum_{rst}(v_{pt}^{rs} \Gamma_{rs}^{qt} - v_{rs}^{qt} \Gamma_{pt}^{rs})
|
||||
\right]
|
||||
$$
|
||||
|
||||
|
||||
$$
|
||||
\mathcal{P}_{pq}= 1 - (p \leftrightarrow q)
|
||||
$$
|
||||
|
||||
$$
|
||||
G(p,q) = \left[
|
||||
\sum_r (h_p^r \gamma_r^q - h_r^q \gamma_p^r) +
|
||||
\sum_{rst}(v_{pt}^{rs} \Gamma_{rs}^{qt} - v_{rs}^{qt} \Gamma_{pt}^{rs})
|
||||
\right] -
|
||||
\left[
|
||||
\sum_r (h_q^r \gamma_r^p - h_r^p \gamma_q^r) +
|
||||
\sum_{rst}(v_{qt}^{rs} \Gamma_{rs}^{pt} - v_{rs}^{pt}
|
||||
\Gamma_{qt}^{rs})
|
||||
\right]
|
||||
$$
|
||||
|
||||
Where p,q,r,s,t are general spatial orbitals
|
||||
mo_num : the number of molecular orbitals
|
||||
$$h$$ : One electron integrals
|
||||
$$\gamma$$ : One body density matrix (state average in our case)
|
||||
$$v$$ : Two electron integrals
|
||||
$$\Gamma$$ : Two body density matrice (state average in our case)
|
||||
|
||||
The gradient is a mo_num by mo_num matrix, p,q,r,s,t take all the
|
||||
values between 1 and mo_num (1 and mo_num include).
|
||||
|
||||
To do that we compute $$G(p,q)$$ for all the pairs (p,q).
|
||||
|
||||
Source :
|
||||
Seniority-based coupled cluster theory
|
||||
J. Chem. Phys. 141, 244104 (2014); https://doi.org/10.1063/1.4904384
|
||||
Thomas M. Henderson, Ireneusz W. Bulik, Tamar Stein, and Gustavo
|
||||
E. Scuseria
|
||||
|
||||
*Compute the gradient of energy with respects to orbital rotations*
|
||||
|
||||
Provided:
|
||||
| mo_num | integer | number of MOs |
|
||||
| mo_one_e_integrals(mo_num,mo_num) | double precision | mono_electronic integrals |
|
||||
| one_e_dm_mo(mo_num,mo_num) | double precision | one e- density matrix |
|
||||
| two_e_dm_mo(mo_num,mo_num,mo_num,mo_num) | double precision | two e- density matrix |
|
||||
|
||||
Input:
|
||||
| n | integer | mo_num*(mo_num-1)/2 |
|
||||
|
||||
Output:
|
||||
| v_grad(n) | double precision | the gradient |
|
||||
| max_elem | double precision | maximum element of the gradient |
|
||||
|
||||
Internal:
|
||||
| grad(mo_num,mo_num) | double precison | gradient before the tranformation in a vector |
|
||||
| A((mo_num,mo_num) | doubre precision | gradient after the permutations |
|
||||
| norm | double precision | norm of the gradient |
|
||||
| p, q | integer | indexes of the element in the matrix grad |
|
||||
| i | integer | index for the tranformation in a vector |
|
||||
| r, s, t | integer | indexes dor the sums |
|
||||
| t1, t2, t3 | double precision | t3 = t2 - t1, time to compute the gradient |
|
||||
| t4, t5, t6 | double precission | t6 = t5 - t4, time to compute each element |
|
||||
| tmp_bi_int_3(mo_num,mo_num,mo_num) | double precision | 3 indexes temporary array for the bi-electronic integrals |
|
||||
| tmp_2rdm_3(mo_num,mo_num,mo_num) | double precision | 3 indexes temporary array for the two e- density matrix |
|
||||
| tmp_accu(mo_num,mo_num) | double precision | temporary array |
|
||||
|
||||
Function:
|
||||
| get_two_e_integral | double precision | bi-electronic integrals |
|
||||
| dnrm2 | double precision | (Lapack) norm |
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle gradient_opt.irp.f
|
||||
subroutine gradient_opt(n,v_grad,max_elem)
|
||||
use omp_lib
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
! Variables
|
||||
|
||||
! in
|
||||
integer, intent(in) :: n
|
||||
|
||||
! out
|
||||
double precision, intent(out) :: v_grad(n), max_elem
|
||||
|
||||
! internal
|
||||
double precision, allocatable :: grad(:,:),A(:,:)
|
||||
double precision :: norm
|
||||
integer :: i,p,q,r,s,t
|
||||
double precision :: t1,t2,t3,t4,t5,t6
|
||||
|
||||
double precision, allocatable :: tmp_accu(:,:)
|
||||
double precision, allocatable :: tmp_bi_int_3(:,:,:), tmp_2rdm_3(:,:,:)
|
||||
|
||||
! Functions
|
||||
double precision :: get_two_e_integral, dnrm2
|
||||
|
||||
|
||||
print*,''
|
||||
print*,'---gradient---'
|
||||
|
||||
! Allocation of shared arrays
|
||||
allocate(grad(mo_num,mo_num),A(mo_num,mo_num))
|
||||
|
||||
! Initialization omp
|
||||
call omp_set_max_active_levels(1)
|
||||
|
||||
!$OMP PARALLEL &
|
||||
!$OMP PRIVATE( &
|
||||
!$OMP p,q,r,s,t, &
|
||||
!$OMP tmp_accu, tmp_bi_int_3, tmp_2rdm_3) &
|
||||
!$OMP SHARED(grad, one_e_dm_mo, mo_num,mo_one_e_integrals, &
|
||||
!$OMP mo_integrals_map,t4,t5,t6) &
|
||||
!$OMP DEFAULT(SHARED)
|
||||
|
||||
! Allocation of private arrays
|
||||
allocate(tmp_accu(mo_num,mo_num))
|
||||
allocate(tmp_bi_int_3(mo_num,mo_num,mo_num))
|
||||
allocate(tmp_2rdm_3(mo_num,mo_num,mo_num))
|
||||
#+END_SRC
|
||||
|
||||
** Calculation
|
||||
*** Initialization
|
||||
#+BEGIN_SRC f90 :comments org :tangle gradient_opt.irp.f
|
||||
!$OMP DO
|
||||
do q = 1, mo_num
|
||||
do p = 1,mo_num
|
||||
grad(p,q) = 0d0
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END DO
|
||||
#+END_SRC
|
||||
|
||||
*** Term 1
|
||||
|
||||
Without optimization the term 1 is :
|
||||
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
grad(p,q) = grad(p,q) &
|
||||
+ mo_one_e_integrals(p,r) * one_e_dm_mo(r,q) &
|
||||
- mo_one_e_integrals(r,q) * one_e_dm_mo(p,r)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
Since the matrix multiplication A.B is defined like :
|
||||
\begin{equation}
|
||||
c_{ij} = \sum_k a_{ik}.b_{kj}
|
||||
\end{equation}
|
||||
The previous equation can be rewritten as a matrix multplication
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle gradient_opt.irp.f
|
||||
!****************
|
||||
! Opt first term
|
||||
!****************
|
||||
|
||||
!$OMP MASTER
|
||||
CALL wall_TIME(t4)
|
||||
!$OMP END MASTER
|
||||
|
||||
call dgemm('N','N',mo_num,mo_num,mo_num,1d0,mo_one_e_integrals,&
|
||||
mo_num,one_e_dm_mo,mo_num,0d0,tmp_accu,mo_num)
|
||||
|
||||
!$OMP DO
|
||||
do q = 1, mo_num
|
||||
do p = 1, mo_num
|
||||
|
||||
grad(p,q) = grad(p,q) + (tmp_accu(p,q) - tmp_accu(q,p))
|
||||
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END DO
|
||||
|
||||
!$OMP MASTER
|
||||
CALL wall_TIME(t5)
|
||||
t6 = t5-t4
|
||||
print*,'Gradient, first term (s) :', t6
|
||||
!$OMP END MASTER
|
||||
#+END_SRC
|
||||
|
||||
*** Term 2
|
||||
|
||||
Without optimization the second term is :
|
||||
|
||||
do p = 1, mo_num
|
||||
do q = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
do t= 1, mo_num
|
||||
|
||||
grad(p,q) = grad(p,q) &
|
||||
+ get_two_e_integral(p,t,r,s,mo_integrals_map) * two_e_dm_mo(r,s,q,t) &
|
||||
- get_two_e_integral(r,s,q,t,mo_integrals_map) * two_e_dm_mo(p,t,r,s)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
Using the bielectronic integral properties :
|
||||
get_two_e_integral(p,t,r,s,mo_integrals_map) = get_two_e_integral(r,s,p,t,mo_integrals_map)
|
||||
|
||||
Using the two body matrix properties :
|
||||
two_e_dm_mo(p,t,r,s) = two_e_dm_mo(r,s,p,t)
|
||||
|
||||
t is one the right, we can put it on the external loop and create 3
|
||||
indexes temporary array
|
||||
r,s can be seen as one index
|
||||
|
||||
By doing so, a matrix multiplication appears
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle gradient_opt.irp.f
|
||||
!*****************
|
||||
! Opt second term
|
||||
!*****************
|
||||
|
||||
!$OMP MASTER
|
||||
CALL wall_TIME(t4)
|
||||
!$OMP END MASTER
|
||||
|
||||
!$OMP DO
|
||||
do t = 1, mo_num
|
||||
|
||||
do p = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
|
||||
tmp_bi_int_3(r,s,p) = get_two_e_integral(r,s,p,t,mo_integrals_map)
|
||||
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
do q = 1, mo_num
|
||||
do s = 1, mo_num
|
||||
do r = 1, mo_num
|
||||
|
||||
tmp_2rdm_3(r,s,q) = two_e_dm_mo(r,s,q,t)
|
||||
|
||||
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)
|
||||
|
||||
!$OMP CRITICAL
|
||||
do q = 1, mo_num
|
||||
do p = 1, mo_num
|
||||
|
||||
grad(p,q) = grad(p,q) + tmp_accu(p,q) - tmp_accu(q,p)
|
||||
|
||||
enddo
|
||||
enddo
|
||||
!$OMP END CRITICAL
|
||||
|
||||
enddo
|
||||
!$OMP END DO
|
||||
|
||||
!$OMP MASTER
|
||||
CALL wall_TIME(t5)
|
||||
t6 = t5-t4
|
||||
print*,'Gradient second term (s) : ', t6
|
||||
!$OMP END MASTER
|
||||
#+END_SRC
|
||||
|
||||
*** Deallocation of private arrays
|
||||
#+BEGIN_SRC f90 :comments org :tangle gradient_opt.irp.f
|
||||
deallocate(tmp_bi_int_3,tmp_2rdm_3,tmp_accu)
|
||||
|
||||
!$OMP END PARALLEL
|
||||
|
||||
call omp_set_max_active_levels(4)
|
||||
#+END_SRC
|
||||
|
||||
*** Permutation, 2D matrix -> vector, transformation
|
||||
In addition there is a permutation in the gradient formula :
|
||||
\begin{equation}
|
||||
P_{pq} = 1 - (p <-> q)
|
||||
\end{equation}
|
||||
|
||||
We need a vector to use the gradient. Here the gradient is a
|
||||
antisymetric matrix so we can transform it in a vector of length
|
||||
mo_num*(mo_num-1)/2.
|
||||
|
||||
Here we do these two things at the same time.
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle gradient_opt.irp.f
|
||||
do i=1,n
|
||||
call vec_to_mat_index(i,p,q)
|
||||
v_grad(i)=(grad(p,q) - grad(q,p))
|
||||
enddo
|
||||
|
||||
! Debug, diplay the vector containing the gradient elements
|
||||
if (debug) then
|
||||
print*,'Vector containing the gradient :'
|
||||
write(*,'(100(F10.5))') v_grad(1:n)
|
||||
endif
|
||||
#+END_SRC
|
||||
|
||||
*** Norm of the gradient
|
||||
The norm can be useful.
|
||||
#+BEGIN_SRC f90 :comments org :tangle gradient_opt.irp.f
|
||||
norm = dnrm2(n,v_grad,1)
|
||||
print*, 'Gradient norm : ', norm
|
||||
#+END_SRC
|
||||
|
||||
*** Maximum element in the gradient
|
||||
The maximum element in the gradient is very important for the
|
||||
convergence criterion of the Newton method.
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle gradient_opt.irp.f
|
||||
! Max element of the gradient
|
||||
max_elem = 0d0
|
||||
do i = 1, n
|
||||
if (ABS(v_grad(i)) > ABS(max_elem)) then
|
||||
max_elem = v_grad(i)
|
||||
endif
|
||||
enddo
|
||||
|
||||
print*,'Max element in the gradient :', max_elem
|
||||
|
||||
! Debug, display the matrix containting the gradient elements
|
||||
if (debug) then
|
||||
! Matrix gradient
|
||||
A = 0d0
|
||||
do q=1,mo_num
|
||||
do p=1,mo_num
|
||||
A(p,q) = grad(p,q) - grad(q,p)
|
||||
enddo
|
||||
enddo
|
||||
print*,'Matrix containing the gradient :'
|
||||
do i = 1, mo_num
|
||||
write(*,'(100(F10.5))') A(i,1:mo_num)
|
||||
enddo
|
||||
endif
|
||||
#+END_SRC
|
||||
|
||||
*** Deallocation of shared arrays and end
|
||||
#+BEGIN_SRC f90 :comments org :tangle gradient_opt.irp.f
|
||||
deallocate(grad,A)
|
||||
|
||||
print*,'---End gradient---'
|
||||
|
||||
end subroutine
|
||||
|
||||
#+END_SRC
|
||||
|
||||
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
|
|
@ -0,0 +1,308 @@
|
|||
* Providers
|
||||
** Dimensions of MOs
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle my_providers.irp.f
|
||||
BEGIN_PROVIDER [ integer, n_mo_dim ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Number of different pairs (i,j) of MOs we can build,
|
||||
! with i>j
|
||||
END_DOC
|
||||
|
||||
n_mo_dim = mo_num*(mo_num-1)/2
|
||||
|
||||
END_PROVIDER
|
||||
#+END_SRC
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle my_providers.irp.f
|
||||
BEGIN_PROVIDER [ integer, n_mo_dim_core ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Number of different pairs (i,j) of core MOs we can build,
|
||||
! with i>j
|
||||
END_DOC
|
||||
|
||||
n_mo_dim_core = dim_list_core_orb*(dim_list_core_orb-1)/2
|
||||
|
||||
END_PROVIDER
|
||||
#+END_SRC
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle my_providers.irp.f
|
||||
BEGIN_PROVIDER [ integer, n_mo_dim_act ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Number of different pairs (i,j) of active MOs we can build,
|
||||
! with i>j
|
||||
END_DOC
|
||||
|
||||
n_mo_dim_act = dim_list_act_orb*(dim_list_act_orb-1)/2
|
||||
|
||||
END_PROVIDER
|
||||
#+END_SRC
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle my_providers.irp.f
|
||||
BEGIN_PROVIDER [ integer, n_mo_dim_inact ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Number of different pairs (i,j) of inactive MOs we can build,
|
||||
! with i>j
|
||||
END_DOC
|
||||
|
||||
n_mo_dim_inact = dim_list_inact_orb*(dim_list_inact_orb-1)/2
|
||||
|
||||
END_PROVIDER
|
||||
#+END_SRC
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle my_providers.irp.f
|
||||
BEGIN_PROVIDER [ integer, n_mo_dim_virt ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Number of different pairs (i,j) of virtual MOs we can build,
|
||||
! with i>j
|
||||
END_DOC
|
||||
|
||||
n_mo_dim_virt = dim_list_virt_orb*(dim_list_virt_orb-1)/2
|
||||
|
||||
END_PROVIDER
|
||||
#+END_SRC
|
||||
|
||||
** Energies/criterions
|
||||
#+BEGIN_SRC f90 :comments org :tangle my_providers.irp.f
|
||||
BEGIN_PROVIDER [ double precision, my_st_av_energy ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! State average CI energy
|
||||
END_DOC
|
||||
|
||||
!call update_st_av_ci_energy(my_st_av_energy)
|
||||
call state_average_energy(my_st_av_energy)
|
||||
|
||||
END_PROVIDER
|
||||
#+END_SRC
|
||||
|
||||
** Gradient/hessian
|
||||
*** Orbital optimization
|
||||
**** With all the MOs
|
||||
#+BEGIN_SRC f90 :comments org :tangle my_providers.irp.f
|
||||
BEGIN_PROVIDER [ double precision, my_gradient_opt, (n_mo_dim) ]
|
||||
&BEGIN_PROVIDER [ double precision, my_CC1_opt ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! - Gradient of the energy with respect to the MO rotations, for all the MOs.
|
||||
! - Maximal element of the gradient in absolute value
|
||||
END_DOC
|
||||
|
||||
double precision :: norm_grad
|
||||
|
||||
PROVIDE mo_two_e_integrals_in_map
|
||||
|
||||
call gradient_opt(n_mo_dim, my_gradient_opt, my_CC1_opt, norm_grad)
|
||||
|
||||
END_PROVIDER
|
||||
#+END_SRC
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle my_providers.irp.f
|
||||
BEGIN_PROVIDER [ double precision, my_hessian_opt, (n_mo_dim, n_mo_dim) ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! - Gradient of the energy with respect to the MO rotations, for all the MOs.
|
||||
! - Maximal element of the gradient in absolute value
|
||||
END_DOC
|
||||
|
||||
double precision, allocatable :: h_f(:,:,:,:)
|
||||
|
||||
PROVIDE mo_two_e_integrals_in_map
|
||||
|
||||
allocate(h_f(mo_num, mo_num, mo_num, mo_num))
|
||||
|
||||
call hessian_list_opt(n_mo_dim, my_hessian_opt, h_f)
|
||||
|
||||
END_PROVIDER
|
||||
#+END_SRC
|
||||
|
||||
**** With the list of active MOs
|
||||
Can be generalized to any mo_class by changing the list/dimension
|
||||
#+BEGIN_SRC f90 :comments org :tangle my_providers.irp.f
|
||||
BEGIN_PROVIDER [ double precision, my_gradient_list_opt, (n_mo_dim_act) ]
|
||||
&BEGIN_PROVIDER [ double precision, my_CC2_opt ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! - Gradient of the energy with respect to the MO rotations, only for the active MOs !
|
||||
! - Maximal element of the gradient in absolute value
|
||||
END_DOC
|
||||
|
||||
double precision :: norm_grad
|
||||
|
||||
PROVIDE mo_two_e_integrals_in_map !one_e_dm_mo two_e_dm_mo mo_one_e_integrals
|
||||
|
||||
call gradient_list_opt(n_mo_dim_act, dim_list_act_orb, list_act, my_gradient_list_opt, my_CC2_opt, norm_grad)
|
||||
|
||||
END_PROVIDER
|
||||
#+END_SRC
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle my_providers.irp.f
|
||||
BEGIN_PROVIDER [ double precision, my_hessian_list_opt, (n_mo_dim_act, n_mo_dim_act) ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! - Gradient of the energy with respect to the MO rotations, only for the active MOs !
|
||||
! - Maximal element of the gradient in absolute value
|
||||
END_DOC
|
||||
|
||||
double precision, allocatable :: h_f(:,:,:,:)
|
||||
|
||||
PROVIDE mo_two_e_integrals_in_map
|
||||
|
||||
allocate(h_f(dim_list_act_orb, dim_list_act_orb, dim_list_act_orb, dim_list_act_orb))
|
||||
|
||||
call hessian_list_opt(n_mo_dim_act, dim_list_act_orb, list_act, my_hessian_list_opt, h_f)
|
||||
|
||||
END_PROVIDER
|
||||
#+END_SRC
|
||||
|
||||
*** Orbital localization
|
||||
**** Gradient
|
||||
***** Core MOs
|
||||
#+BEGIN_SRC f90 :comments org
|
||||
!:tangle my_providers.irp.f
|
||||
BEGIN_PROVIDER [ double precision, my_gradient_loc_core, (n_mo_dim_core) ]
|
||||
&BEGIN_PROVIDER [ double precision, my_CC_loc_core ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! - Gradient of the MO localization with respect to the MO rotations for the core MOs
|
||||
! - Maximal element of the gradient in absolute value
|
||||
END_DOC
|
||||
|
||||
double precision :: norm_grad
|
||||
|
||||
!PROVIDE something ?
|
||||
|
||||
call gradient_localization(n_mo_dim_core, dim_list_core_orb, list_core, my_gradient_loc_core, my_CC_loc_core , norm_grad)
|
||||
|
||||
END_PROVIDER
|
||||
#+END_SRC
|
||||
|
||||
***** Active MOs
|
||||
#+BEGIN_SRC f90 :comments org
|
||||
!:tangle my_providers.irp.f
|
||||
BEGIN_PROVIDER [ double precision, my_gradient_loc_act, (n_mo_dim_act) ]
|
||||
&BEGIN_PROVIDER [ double precision, my_CC_loc_act ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! - Gradient of the MO localization with respect to the MO rotations for the active MOs
|
||||
! - Maximal element of the gradient in absolute value
|
||||
END_DOC
|
||||
|
||||
double precision :: norm_grad
|
||||
|
||||
!PROVIDE something ?
|
||||
|
||||
call gradient_localization(n_mo_dim_act, dim_list_act_orb, list_act, my_gradient_loc_act, my_CC_loc_act , norm_grad)
|
||||
|
||||
END_PROVIDER
|
||||
#+END_SRC
|
||||
|
||||
***** Inactive MOs
|
||||
#+BEGIN_SRC f90 :comments org !
|
||||
:tangle my_providers.irp.f
|
||||
BEGIN_PROVIDER [ double precision, my_gradient_loc_inact, (n_mo_dim_inact) ]
|
||||
&BEGIN_PROVIDER [ double precision, my_CC_loc_inact ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! - Gradient of the MO localization with respect to the MO rotations for the inactive MOs
|
||||
! - Maximal element of the gradient in absolute value
|
||||
END_DOC
|
||||
|
||||
double precision :: norm_grad
|
||||
|
||||
!PROVIDE something ?
|
||||
|
||||
call gradient_localization(n_mo_dim_inact, dim_list_inact_orb, list_inact, my_gradient_loc_inact, my_CC_loc_inact , norm_grad)
|
||||
|
||||
END_PROVIDER
|
||||
#+END_SRC
|
||||
|
||||
***** Virtual MOs
|
||||
#+BEGIN_SRC f90 :comments org
|
||||
!:tangle my_providers.irp.f
|
||||
BEGIN_PROVIDER [ double precision, my_gradient_loc_virt, (n_mo_dim_virt) ]
|
||||
&BEGIN_PROVIDER [ double precision, my_CC_loc_virt ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! - Gradient of the MO localization with respect to the MO rotations for the virtual MOs
|
||||
! - Maximal element of the gradient in absolute value
|
||||
END_DOC
|
||||
|
||||
double precision :: norm_grad
|
||||
|
||||
!PROVIDE something ?
|
||||
|
||||
call gradient_localization(n_mo_dim_virt, dim_list_virt_orb, list_virt, my_gradient_loc_virt, my_CC_loc_virt , norm_grad)
|
||||
|
||||
END_PROVIDER
|
||||
#+END_SRC
|
||||
|
||||
**** Hessian
|
||||
***** Core MOs
|
||||
#+BEGIN_SRC f90 :comments org
|
||||
!:tangle my_providers.irp.f
|
||||
BEGIN_PROVIDER [ double precision, my_hessian_loc_core, (n_mo_dim_core) ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! - Hessian of the MO localization with respect to the MO rotations for the core MOs
|
||||
END_DOC
|
||||
|
||||
!PROVIDE something ?
|
||||
|
||||
call hessian_localization(n_mo_dim_core, dim_list_core_orb, list_core, my_hessian_loc_core)
|
||||
|
||||
END_PROVIDER
|
||||
#+END_SRC
|
||||
|
||||
***** Active MOs
|
||||
#+BEGIN_SRC f90 :comments org
|
||||
!:tangle my_providers.irp.f
|
||||
BEGIN_PROVIDER [ double precision, my_hessian_loc_act, (n_mo_dim_act) ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! - Hessian of the MO localization with respect to the MO rotations for the active MOs
|
||||
END_DOC
|
||||
|
||||
!PROVIDE something ?
|
||||
|
||||
call hessian_localization(n_mo_dim_act, dim_list_act_orb, list_act, my_hessian_loc_act)
|
||||
|
||||
END_PROVIDER
|
||||
#+END_SRC
|
||||
|
||||
***** Inactive MOs
|
||||
#+BEGIN_SRC f90 :comments org
|
||||
!:tangle my_providers.irp.f
|
||||
BEGIN_PROVIDER [ double precision, my_hessian_loc_inact, (n_mo_dim_inact) ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! - Hessian of the MO localization with respect to the MO rotations for the inactive MOs
|
||||
END_DOC
|
||||
|
||||
!PROVIDE something ?
|
||||
|
||||
call hessian_localization(n_mo_dim_inact, dim_list_inact_orb, list_inact, my_hessian_loc_inact)
|
||||
|
||||
END_PROVIDER
|
||||
#+END_SRC
|
||||
|
||||
***** Virtual MOs
|
||||
#+BEGIN_SRC f90 :comments org
|
||||
!:tangle my_providers.irp.f
|
||||
BEGIN_PROVIDER [ double precision, my_hessian_loc_virt, (n_mo_dim_virt) ]
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! - Hessian of the MO localization with respect to the MO rotations for the virtual MOs
|
||||
END_DOC
|
||||
|
||||
!PROVIDE something ?
|
||||
|
||||
call hessian_localization(n_mo_dim_virt, dim_list_virt_orb, list_virt, my_hessian_loc_virt)
|
||||
|
||||
END_PROVIDER
|
||||
#+END_SRC
|
||||
|
||||
|
|
@ -0,0 +1,91 @@
|
|||
#+BEGIN_SRC f90 :comments org :tangle optimization.irp.f
|
||||
program optimization
|
||||
|
||||
read_wf = .true. ! must be True for the orbital optimization !!!
|
||||
TOUCH read_wf
|
||||
call run_optimization
|
||||
|
||||
end
|
||||
#+END_SRC
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle optimization.irp.f
|
||||
subroutine run_optimization
|
||||
|
||||
implicit none
|
||||
|
||||
double precision :: e_cipsi, e_opt, delta_e
|
||||
integer :: nb_iter,i
|
||||
logical :: not_converged
|
||||
character (len=100) :: filename
|
||||
|
||||
PROVIDE psi_det psi_coef mo_two_e_integrals_in_map
|
||||
|
||||
not_converged = .True.
|
||||
nb_iter = 0
|
||||
|
||||
! To start from the wf
|
||||
N_det_max = max(n_det,5)
|
||||
TOUCH N_det_max
|
||||
|
||||
open(unit=10, file=trim(ezfio_filename)//'/mo_optimization/result_opt')
|
||||
write(10,*) " Ndet E_cipsi E_opt Delta_e"
|
||||
call state_average_energy(e_cipsi)
|
||||
write(10,'(I10, 3F15.7)') n_det, e_cipsi, e_cipsi, 0d0
|
||||
close(10)
|
||||
|
||||
do while (not_converged)
|
||||
print*,''
|
||||
print*,'======================'
|
||||
print*,' Cipsi step:', nb_iter
|
||||
print*,'======================'
|
||||
print*,''
|
||||
print*,'********** cipsi step **********'
|
||||
! cispi calculation
|
||||
call run_stochastic_cipsi
|
||||
|
||||
! State average energy after the cipsi step
|
||||
call state_average_energy(e_cipsi)
|
||||
|
||||
print*,''
|
||||
print*,'********** optimization step **********'
|
||||
! orbital optimization
|
||||
call run_orb_opt_trust_v2
|
||||
|
||||
! State average energy after the orbital optimization
|
||||
call state_average_energy(e_opt)
|
||||
|
||||
print*,''
|
||||
print*,'********** diff step **********'
|
||||
! Gain in energy
|
||||
delta_e = e_opt - e_cipsi
|
||||
print*, 'Gain in energy during the orbital optimization:', delta_e
|
||||
|
||||
open(unit=10, file=trim(ezfio_filename)//'/mo_optimization/result_opt', position='append')
|
||||
write(10,'(I10, 3F15.7)') n_det, e_cipsi, e_opt, delta_e
|
||||
close(10)
|
||||
|
||||
! Exit
|
||||
if (delta_e > 1d-12) then
|
||||
print*, 'WARNING, something wrong happened'
|
||||
print*, 'The gain (delta_e) in energy during the optimization process'
|
||||
print*, 'is > 0, but it must be < 0'
|
||||
print*, 'The program will exit'
|
||||
exit
|
||||
endif
|
||||
|
||||
if (n_det > n_det_max_opt) then
|
||||
print*, 'The number of determinants in the wf > n_det_max_opt'
|
||||
print*, 'The program will exit'
|
||||
exit
|
||||
endif
|
||||
|
||||
! To double the number of determinants in the wf
|
||||
N_det_max = int(dble(n_det * 2)*0.9)
|
||||
TOUCH N_det_max
|
||||
|
||||
nb_iter = nb_iter + 1
|
||||
enddo
|
||||
|
||||
end
|
||||
|
||||
#+END_SRC
|
||||
|
|
@ -0,0 +1,349 @@
|
|||
* Orbital optimization program
|
||||
|
||||
This is an optimization program for molecular orbitals. It produces
|
||||
orbital rotations in order to lower the energy of a truncated wave
|
||||
function.
|
||||
This program just optimize the orbitals for a fixed number of
|
||||
determinants. This optimization process must be repeated for different
|
||||
number of determinants.
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle orb_opt.irp.f
|
||||
#+END_SRC
|
||||
|
||||
* Main program : orb_opt_trust
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle orb_opt.irp.f
|
||||
program orb_opt
|
||||
read_wf = .true. ! must be True for the orbital optimization !!!
|
||||
TOUCH read_wf
|
||||
io_mo_two_e_integrals = 'None'
|
||||
TOUCH io_mo_two_e_integrals
|
||||
call run_orb_opt_trust_v2
|
||||
end
|
||||
#+END_SRC
|
||||
|
||||
* Subroutine : run_orb_opt_trust
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle run_orb_opt_trust_v2.irp.f
|
||||
|
||||
#+END_SRC
|
||||
|
||||
Subroutine to optimize the MOs using a trust region algorithm:
|
||||
- choice of the method
|
||||
- initialization
|
||||
- optimization until convergence
|
||||
|
||||
The optimization use the trust region algorithm, the different parts
|
||||
are explained in the corresponding subroutine files.
|
||||
|
||||
qp_edit:
|
||||
| thresh_opt_max_elem_grad |
|
||||
| optimization_max_nb_iter |
|
||||
| optimization_method |
|
||||
|
||||
Provided:
|
||||
| mo_num | integer | number of MOs |
|
||||
| ao_num | integer | number of AOs |
|
||||
| N_states | integer | number of states |
|
||||
| ci_energy(N_states) | double precision | CI energies |
|
||||
| state_average_weight(N_states) | double precision | Weight of the different states |
|
||||
|
||||
Variables:
|
||||
| m | integer | number of active MOs |
|
||||
| tmp_n | integer | m*(m-1)/2, number of MO parameters |
|
||||
| tmp_n2 | integer | m*(m-1)/2 or 1 if the hessian is diagonal |
|
||||
| v_grad(tmp_n) | double precision | gradient |
|
||||
| H(tmp_n,tmp_n) | double precision | hessian (2D) |
|
||||
| h_f(m,m,m,m) | double precision | hessian (4D) |
|
||||
| e_val(m) | double precision | eigenvalues of the hessian |
|
||||
| w(m,m) | double precision | eigenvectors of the hessian |
|
||||
| x(m) | double precision | step given by the trust region |
|
||||
| m_x(m,m) | double precision | step given by the trust region after |
|
||||
| tmp_R(m,m) | double precision | rotation matrix for active MOs |
|
||||
| R(mo_num,mo_num) | double precision | full rotation matrix |
|
||||
| prev_mos(ao_num,mo_num) | double precision | previous MOs (before the rotation) |
|
||||
| new_mos(ao_num,mo_num) | double precision | new MOs (after the roration) |
|
||||
| delta | double precision | radius of the trust region |
|
||||
| rho | double precision | agreement between the model and the exact function |
|
||||
| max_elem | double precision | maximum element in the gradient |
|
||||
| i | integer | index |
|
||||
| tmp_i,tmp_j | integer | indexes in the subspace containing only |
|
||||
| | | the active MOs |
|
||||
| converged | logical | convergence of the algorithm |
|
||||
| cancel_step | logical | if the step must be cancelled |
|
||||
| nb_iter | integer | number of iterations (accepted) |
|
||||
| nb_diag | integer | number of diagonalizations of the CI matrix |
|
||||
| nb_cancel | integer | number of cancelled steps for the actual iteration |
|
||||
| nb_cancel_tot | integer | total number of cancel steps |
|
||||
| info | integer | if 0 ok, else problem in the diagonalization of |
|
||||
| | | the hessian with the Lapack routine |
|
||||
| criterion | double precision | energy at a given step |
|
||||
| prev_criterion | double precision | energy before the rotation |
|
||||
| criterion_model | double precision | estimated energy after the rotation using |
|
||||
| | | a Taylor series |
|
||||
| must_exit | logical | To exit the trust region algorithm when |
|
||||
| | | criterion - criterion_model is too small |
|
||||
| enforce_step_cancellation | logical | To force the cancellation of the step if the |
|
||||
| | | error in the rotation matrix is too large |
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle run_orb_opt_trust_v2.irp.f
|
||||
subroutine run_orb_opt_trust_v2
|
||||
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
BEGIN_DOC
|
||||
! Orbital optimization
|
||||
END_DOC
|
||||
|
||||
! Variables
|
||||
|
||||
double precision, allocatable :: R(:,:)
|
||||
double precision, allocatable :: H(:,:),h_f(:,:,:,:)
|
||||
double precision, allocatable :: v_grad(:)
|
||||
double precision, allocatable :: prev_mos(:,:),new_mos(:,:)
|
||||
integer :: info
|
||||
integer :: n
|
||||
integer :: i,j,p,q,k
|
||||
double precision :: max_elem_grad, delta, rho, norm_grad, normalization_factor
|
||||
logical :: cancel_step
|
||||
integer :: nb_iter, nb_diag, nb_cancel, nb_cancel_tot, nb_sub_iter
|
||||
double precision :: t1, t2, t3
|
||||
double precision :: prev_criterion, criterion, criterion_model
|
||||
logical :: not_converged, must_exit, enforce_step_cancellation
|
||||
integer :: m, tmp_n, tmp_i, tmp_j, tmp_k, tmp_n2
|
||||
integer,allocatable :: tmp_list(:), key(:)
|
||||
double precision, allocatable :: tmp_m_x(:,:),tmp_R(:,:), tmp_x(:), W(:,:), e_val(:)
|
||||
|
||||
PROVIDE mo_two_e_integrals_in_map ci_energy psi_det psi_coef
|
||||
#+END_SRC
|
||||
|
||||
** Allocation
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle run_orb_opt_trust_v2.irp.f
|
||||
allocate(R(mo_num,mo_num)) ! rotation matrix
|
||||
allocate(prev_mos(ao_num,mo_num), new_mos(ao_num,mo_num)) ! old and new MOs
|
||||
|
||||
! Definition of m and tmp_n
|
||||
m = dim_list_act_orb
|
||||
tmp_n = m*(m-1)/2
|
||||
|
||||
allocate(tmp_list(m))
|
||||
allocate(tmp_R(m,m), tmp_m_x(m,m), tmp_x(tmp_n))
|
||||
allocate(e_val(tmp_n),key(tmp_n),v_grad(tmp_n))
|
||||
|
||||
#+END_SRC
|
||||
|
||||
** Method
|
||||
There are three different methods :
|
||||
- the "full" hessian, which uses all the elements of the hessian
|
||||
matrix"
|
||||
- the "diagonal" hessian, which uses only the diagonal elements of the
|
||||
hessian
|
||||
- without the hessian (hessian = identity matrix)
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle run_orb_opt_trust_v2.irp.f
|
||||
!Display the method
|
||||
print*, 'Method :', optimization_method
|
||||
if (optimization_method == 'full') then
|
||||
print*, 'Full hessian'
|
||||
allocate(H(tmp_n,tmp_n), h_f(m,m,m,m),W(tmp_n,tmp_n))
|
||||
tmp_n2 = tmp_n
|
||||
elseif (optimization_method == 'diag') then
|
||||
print*,'Diagonal hessian'
|
||||
allocate(H(tmp_n,1),W(tmp_n,1))
|
||||
tmp_n2 = 1
|
||||
elseif (optimization_method == 'none') then
|
||||
print*,'No hessian'
|
||||
allocate(H(tmp_n,1),W(tmp_n,1))
|
||||
tmp_n2 = 1
|
||||
else
|
||||
print*,'Unknown optimization_method, please select full, diag or none'
|
||||
call abort
|
||||
endif
|
||||
print*, 'Absolute value of the hessian:', absolute_eig
|
||||
#+END_SRC
|
||||
|
||||
** Calculations
|
||||
*** Algorithm
|
||||
|
||||
Here is the main algorithm of the optimization:
|
||||
- First of all we initialize some parameters and we compute the
|
||||
criterion (the ci energy) before doing any MO rotations
|
||||
- We compute the gradient and the hessian for the active MOs
|
||||
- We diagonalize the hessian
|
||||
- We compute a step and loop to reduce the radius of the
|
||||
trust region (and the size of the step by the way) until the step is
|
||||
accepted
|
||||
- We repeat the process until the convergence
|
||||
NB: the convergence criterion can be changed
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle run_orb_opt_trust_v2.irp.f
|
||||
! Loop until the convergence of the optimization
|
||||
! call diagonalize_ci
|
||||
|
||||
!### Initialization ###
|
||||
nb_iter = 0
|
||||
rho = 0.5d0
|
||||
not_converged = .True.
|
||||
tmp_list = list_act ! Optimization of the active MOs
|
||||
nb_cancel_tot = 0
|
||||
|
||||
! Renormalization of the weights of the states
|
||||
call state_weight_normalization
|
||||
|
||||
! Compute the criterion before the loop
|
||||
call state_average_energy(prev_criterion)
|
||||
|
||||
do while (not_converged)
|
||||
print*,''
|
||||
print*,'******************'
|
||||
print*,'Iteration', nb_iter
|
||||
print*,'******************'
|
||||
print*,''
|
||||
|
||||
! Gradient
|
||||
call gradient_list_opt(tmp_n, m, tmp_list, v_grad, max_elem_grad, norm_grad)
|
||||
|
||||
! Hessian
|
||||
if (optimization_method == 'full') then
|
||||
! Full hessian
|
||||
call hessian_list_opt(tmp_n, m, tmp_list, H, h_f)
|
||||
|
||||
! Diagonalization of the hessian
|
||||
call diagonalization_hessian(tmp_n, H, e_val, w)
|
||||
|
||||
elseif (optimization_method == 'diag') then
|
||||
! Diagonal hessian
|
||||
call diag_hessian_list_opt(tmp_n, m, tmp_list, H)
|
||||
else
|
||||
! Identity matrix
|
||||
do tmp_i = 1, tmp_n
|
||||
H(tmp_i,1) = 1d0
|
||||
enddo
|
||||
endif
|
||||
|
||||
if (optimization_method /= 'full') then
|
||||
! Sort
|
||||
do tmp_i = 1, tmp_n
|
||||
key(tmp_i) = tmp_i
|
||||
e_val(tmp_i) = H(tmp_i,1)
|
||||
enddo
|
||||
call dsort(e_val,key,tmp_n)
|
||||
|
||||
! Eigenvalues and eigenvectors
|
||||
do tmp_i = 1, tmp_n
|
||||
w(tmp_i,1) = dble(key(tmp_i))
|
||||
enddo
|
||||
|
||||
endif
|
||||
|
||||
! Init before the internal loop
|
||||
cancel_step = .True. ! To enter in the loop just after
|
||||
nb_cancel = 0
|
||||
nb_sub_iter = 0
|
||||
|
||||
! Loop to reduce the trust radius until the criterion decreases and rho >= thresh_rho
|
||||
do while (cancel_step)
|
||||
print*,''
|
||||
print*,'-----------------------------'
|
||||
print*,'Iteration: ', nb_iter
|
||||
print*,'Sub iteration:', nb_sub_iter
|
||||
print*,'Max elem grad:', max_elem_grad
|
||||
print*,'-----------------------------'
|
||||
|
||||
! Hessian,gradient,Criterion -> x
|
||||
call trust_region_step_w_expected_e(tmp_n,tmp_n2,H,W,e_val,v_grad,prev_criterion,rho,nb_iter,delta,criterion_model,tmp_x,must_exit)
|
||||
|
||||
if (must_exit) then
|
||||
print*,'step_in_trust_region sends: Exit'
|
||||
exit
|
||||
endif
|
||||
|
||||
! 1D tmp -> 2D tmp
|
||||
call vec_to_mat_v2(tmp_n, m, tmp_x, tmp_m_x)
|
||||
|
||||
! Rotation matrix for the active MOs
|
||||
call rotation_matrix(tmp_m_x, m, tmp_R, m, m, info, enforce_step_cancellation)
|
||||
|
||||
! Security to ensure an unitary transformation
|
||||
if (enforce_step_cancellation) then
|
||||
print*, 'Step cancellation, too large error in the rotation matrix'
|
||||
rho = 0d0
|
||||
cycle
|
||||
endif
|
||||
|
||||
! tmp_R to R, subspace to full space
|
||||
call sub_to_full_rotation_matrix(m, tmp_list, tmp_R, R)
|
||||
|
||||
! MO rotations
|
||||
call apply_mo_rotation(R, prev_mos)
|
||||
|
||||
! Update of the energy before the diagonalization of the hamiltonian
|
||||
call clear_mo_map
|
||||
TOUCH mo_coef psi_det psi_coef ci_energy two_e_dm_mo
|
||||
call state_average_energy(criterion)
|
||||
|
||||
! Criterion -> step accepted or rejected
|
||||
call trust_region_is_step_cancelled(nb_iter, prev_criterion, criterion, criterion_model, rho, cancel_step)
|
||||
|
||||
! Cancellation of the step if necessary
|
||||
if (cancel_step) then
|
||||
mo_coef = prev_mos
|
||||
call save_mos()
|
||||
nb_cancel = nb_cancel + 1
|
||||
nb_cancel_tot = nb_cancel_tot + 1
|
||||
else
|
||||
! Diagonalization of the hamiltonian
|
||||
FREE ci_energy! To enforce the recomputation
|
||||
call diagonalize_ci
|
||||
call save_wavefunction_unsorted
|
||||
|
||||
! Energy obtained after the diagonalization of the CI matrix
|
||||
call state_average_energy(prev_criterion)
|
||||
endif
|
||||
|
||||
nb_sub_iter = nb_sub_iter + 1
|
||||
enddo
|
||||
call save_mos() !### depend of the time for 1 iteration
|
||||
|
||||
! To exit the external loop if must_exit = .True.
|
||||
if (must_exit) then
|
||||
exit
|
||||
endif
|
||||
|
||||
! Step accepted, nb iteration + 1
|
||||
nb_iter = nb_iter + 1
|
||||
|
||||
! External loop exit conditions
|
||||
if (DABS(max_elem_grad) < thresh_opt_max_elem_grad) then
|
||||
print*,'Converged: DABS(max_elem_grad) < thresh_opt_max_elem_grad'
|
||||
not_converged = .False.
|
||||
endif
|
||||
if (nb_iter >= optimization_max_nb_iter) then
|
||||
print*,'Not converged: nb_iter >= optimization_max_nb_iter'
|
||||
not_converged = .False.
|
||||
endif
|
||||
|
||||
if (.not. not_converged) then
|
||||
print*,'#############################'
|
||||
print*,' End of the optimization'
|
||||
print*,'#############################'
|
||||
endif
|
||||
enddo
|
||||
|
||||
#+END_SRC
|
||||
|
||||
** Deallocation, end
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle run_orb_opt_trust_v2.irp.f
|
||||
deallocate(v_grad,H,R,W,e_val)
|
||||
deallocate(prev_mos,new_mos)
|
||||
if (optimization_method == 'full') then
|
||||
deallocate(h_f)
|
||||
endif
|
||||
|
||||
end
|
||||
#+END_SRC
|
||||
|
||||
|
|
@ -0,0 +1,73 @@
|
|||
* State average energy
|
||||
|
||||
Calculation of the state average energy from the integrals and the
|
||||
density matrices.
|
||||
|
||||
\begin{align*}
|
||||
E = \sum_{ij} h_{ij} \gamma_{ij} + \frac{1}{2} v_{ij}^{kl} \Gamma_{ij}^{kl}
|
||||
\end{align*}
|
||||
$h_{ij}$: mono-electronic integral
|
||||
$\gamma_{ij}$: one electron density matrix
|
||||
$v_{ij}^{kl}$: bi-electronic integral
|
||||
$\Gamma_{ij}^{kl}$: two electrons density matrix
|
||||
|
||||
TODO: OMP version
|
||||
|
||||
PROVIDED:
|
||||
| mo_one_e_integrals | double precision | mono-electronic integrals |
|
||||
| get_two_e_integral | double precision | bi-electronic integrals |
|
||||
| one_e_dm_mo | double precision | one electron density matrix |
|
||||
| two_e_dm_mo | double precision | two electrons density matrix |
|
||||
| nuclear_repulsion | double precision | nuclear repulsion |
|
||||
| mo_num | integer | number of MOs |
|
||||
|
||||
Output:
|
||||
| energy | double precision | state average energy |
|
||||
|
||||
Internal:
|
||||
| mono_e | double precision | mono-electronic energy |
|
||||
| bi_e | double precision | bi-electronic energy |
|
||||
| i,j,k,l | integer | indexes to loop over the MOs |
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle state_average_energy.irp.f
|
||||
subroutine state_average_energy(energy)
|
||||
|
||||
implicit none
|
||||
|
||||
double precision, intent(out) :: energy
|
||||
|
||||
double precision :: get_two_e_integral
|
||||
double precision :: mono_e, bi_e
|
||||
integer :: i,j,k,l
|
||||
|
||||
! mono electronic part
|
||||
mono_e = 0d0
|
||||
do j = 1, mo_num
|
||||
do i = 1, mo_num
|
||||
mono_e = mono_e + mo_one_e_integrals(i,j) * one_e_dm_mo(i,j)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! bi electronic part
|
||||
bi_e = 0d0
|
||||
do l = 1, mo_num
|
||||
do k = 1, mo_num
|
||||
do j = 1, mo_num
|
||||
do i = 1, mo_num
|
||||
bi_e = bi_e + get_two_e_integral(i,j,k,l,mo_integrals_map) * two_e_dm_mo(i,j,k,l)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! State average energy
|
||||
energy = mono_e + 0.5d0 * bi_e + nuclear_repulsion
|
||||
|
||||
! Check
|
||||
!call print_energy_components
|
||||
|
||||
print*,'State average energy:', energy
|
||||
!print*,ci_energy
|
||||
|
||||
end
|
||||
#+END_SRC
|
||||
|
|
@ -0,0 +1,31 @@
|
|||
#+BEGIN_SRC f90 :comments org :tangle state_weight_normalization.irp.f
|
||||
subroutine state_weight_normalization
|
||||
|
||||
implicit none
|
||||
|
||||
BEGIN_DOC
|
||||
! Renormalization of the state weights or enforcing state average
|
||||
! weights for orbital optimization
|
||||
END_DOC
|
||||
|
||||
integer :: i
|
||||
double precision :: normalization_factor
|
||||
|
||||
! To normalize the sum of the state weights
|
||||
normalization_factor = 0d0
|
||||
do i = 1, N_states
|
||||
normalization_factor = normalization_factor + state_average_weight(i)
|
||||
enddo
|
||||
normalization_factor = 1d0 / normalization_factor
|
||||
|
||||
do i = 1, N_states
|
||||
state_average_weight(i) = state_average_weight(i) * normalization_factor
|
||||
enddo
|
||||
TOUCH state_average_weight
|
||||
|
||||
print*, 'Number of states:', N_states
|
||||
print*, 'State average weights:'
|
||||
print*, state_average_weight(:)
|
||||
|
||||
end
|
||||
#+END_SRC
|
||||
|
|
@ -0,0 +1,16 @@
|
|||
Subroutine toupdate the parameters.
|
||||
Ex: TOUCH mo_coef ...
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle update_parameters.irp.f
|
||||
subroutine update_parameters()
|
||||
|
||||
implicit none
|
||||
|
||||
!### TODO
|
||||
! Touch yours parameters
|
||||
call clear_mo_map
|
||||
TOUCH mo_coef psi_det psi_coef
|
||||
call diagonalize_ci
|
||||
call save_wavefunction_unsorted
|
||||
end
|
||||
#+END_SRC
|
||||
|
|
@ -0,0 +1,26 @@
|
|||
* Update the CI state average energy
|
||||
|
||||
Computes the state average energy
|
||||
\begin{align*}
|
||||
E =\sum_{i=1}^{N_{states}} E_i . w_i
|
||||
\end{align*}
|
||||
|
||||
$E_i$: energy of state i
|
||||
$w_i$: weight of state i
|
||||
|
||||
#+BEGIN_SRC f90 :comments org :tangle update_st_av_ci_energy.irp.f
|
||||
subroutine update_st_av_ci_energy(energy)
|
||||
|
||||
implicit none
|
||||
|
||||
double precision, intent(out) :: energy
|
||||
integer :: i
|
||||
|
||||
energy = 0d0
|
||||
do i = 1, N_states
|
||||
energy = energy + ci_energy(i) * state_average_weight(i)
|
||||
enddo
|
||||
|
||||
print*, 'ci_energy :', energy
|
||||
end
|
||||
#+END_SRC
|
||||
|
|
@ -0,0 +1,317 @@
|
|||
! Subroutine : run_orb_opt_trust
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
! Subroutine to optimize the MOs using a trust region algorithm:
|
||||
! - choice of the method
|
||||
! - initialization
|
||||
! - optimization until convergence
|
||||
|
||||
! The optimization use the trust region algorithm, the different parts
|
||||
! are explained in the corresponding subroutine files.
|
||||
|
||||
! qp_edit:
|
||||
! | thresh_opt_max_elem_grad |
|
||||
! | optimization_max_nb_iter |
|
||||
! | optimization_method |
|
||||
|
||||
! Provided:
|
||||
! | mo_num | integer | number of MOs |
|
||||
! | ao_num | integer | number of AOs |
|
||||
! | N_states | integer | number of states |
|
||||
! | ci_energy(N_states) | double precision | CI energies |
|
||||
! | state_average_weight(N_states) | double precision | Weight of the different states |
|
||||
|
||||
! Variables:
|
||||
! | m | integer | number of active MOs |
|
||||
! | tmp_n | integer | m*(m-1)/2, number of MO parameters |
|
||||
! | tmp_n2 | integer | m*(m-1)/2 or 1 if the hessian is diagonal |
|
||||
! | v_grad(tmp_n) | double precision | gradient |
|
||||
! | H(tmp_n,tmp_n) | double precision | hessian (2D) |
|
||||
! | h_f(m,m,m,m) | double precision | hessian (4D) |
|
||||
! | e_val(m) | double precision | eigenvalues of the hessian |
|
||||
! | w(m,m) | double precision | eigenvectors of the hessian |
|
||||
! | x(m) | double precision | step given by the trust region |
|
||||
! | m_x(m,m) | double precision | step given by the trust region after |
|
||||
! | tmp_R(m,m) | double precision | rotation matrix for active MOs |
|
||||
! | R(mo_num,mo_num) | double precision | full rotation matrix |
|
||||
! | prev_mos(ao_num,mo_num) | double precision | previous MOs (before the rotation) |
|
||||
! | new_mos(ao_num,mo_num) | double precision | new MOs (after the roration) |
|
||||
! | delta | double precision | radius of the trust region |
|
||||
! | rho | double precision | agreement between the model and the exact function |
|
||||
! | max_elem | double precision | maximum element in the gradient |
|
||||
! | i | integer | index |
|
||||
! | tmp_i,tmp_j | integer | indexes in the subspace containing only |
|
||||
! | | | the active MOs |
|
||||
! | converged | logical | convergence of the algorithm |
|
||||
! | cancel_step | logical | if the step must be cancelled |
|
||||
! | nb_iter | integer | number of iterations (accepted) |
|
||||
! | nb_diag | integer | number of diagonalizations of the CI matrix |
|
||||
! | nb_cancel | integer | number of cancelled steps for the actual iteration |
|
||||
! | nb_cancel_tot | integer | total number of cancel steps |
|
||||
! | info | integer | if 0 ok, else problem in the diagonalization of |
|
||||
! | | | the hessian with the Lapack routine |
|
||||
! | criterion | double precision | energy at a given step |
|
||||
! | prev_criterion | double precision | energy before the rotation |
|
||||
! | criterion_model | double precision | estimated energy after the rotation using |
|
||||
! | | | a Taylor series |
|
||||
! | must_exit | logical | To exit the trust region algorithm when |
|
||||
! | | | criterion - criterion_model is too small |
|
||||
! | enforce_step_cancellation | logical | To force the cancellation of the step if the |
|
||||
! | | | error in the rotation matrix is too large |
|
||||
|
||||
|
||||
subroutine run_orb_opt_trust_v2
|
||||
|
||||
include 'constants.h'
|
||||
|
||||
implicit none
|
||||
|
||||
BEGIN_DOC
|
||||
! Orbital optimization
|
||||
END_DOC
|
||||
|
||||
! Variables
|
||||
|
||||
double precision, allocatable :: R(:,:)
|
||||
double precision, allocatable :: H(:,:),h_f(:,:,:,:)
|
||||
double precision, allocatable :: v_grad(:)
|
||||
double precision, allocatable :: prev_mos(:,:),new_mos(:,:)
|
||||
integer :: info
|
||||
integer :: n
|
||||
integer :: i,j,p,q,k
|
||||
double precision :: max_elem_grad, delta, rho, norm_grad, normalization_factor
|
||||
logical :: cancel_step
|
||||
integer :: nb_iter, nb_diag, nb_cancel, nb_cancel_tot, nb_sub_iter
|
||||
double precision :: t1, t2, t3
|
||||
double precision :: prev_criterion, criterion, criterion_model
|
||||
logical :: not_converged, must_exit, enforce_step_cancellation
|
||||
integer :: m, tmp_n, tmp_i, tmp_j, tmp_k, tmp_n2
|
||||
integer,allocatable :: tmp_list(:), key(:)
|
||||
double precision, allocatable :: tmp_m_x(:,:),tmp_R(:,:), tmp_x(:), W(:,:), e_val(:)
|
||||
|
||||
PROVIDE mo_two_e_integrals_in_map ci_energy psi_det psi_coef
|
||||
|
||||
! Allocation
|
||||
|
||||
|
||||
allocate(R(mo_num,mo_num)) ! rotation matrix
|
||||
allocate(prev_mos(ao_num,mo_num), new_mos(ao_num,mo_num)) ! old and new MOs
|
||||
|
||||
! Definition of m and tmp_n
|
||||
m = dim_list_act_orb
|
||||
tmp_n = m*(m-1)/2
|
||||
|
||||
allocate(tmp_list(m))
|
||||
allocate(tmp_R(m,m), tmp_m_x(m,m), tmp_x(tmp_n))
|
||||
allocate(e_val(tmp_n),key(tmp_n),v_grad(tmp_n))
|
||||
|
||||
! Method
|
||||
! There are three different methods :
|
||||
! - the "full" hessian, which uses all the elements of the hessian
|
||||
! matrix"
|
||||
! - the "diagonal" hessian, which uses only the diagonal elements of the
|
||||
! hessian
|
||||
! - without the hessian (hessian = identity matrix)
|
||||
|
||||
|
||||
!Display the method
|
||||
print*, 'Method :', optimization_method
|
||||
if (optimization_method == 'full') then
|
||||
print*, 'Full hessian'
|
||||
allocate(H(tmp_n,tmp_n), h_f(m,m,m,m),W(tmp_n,tmp_n))
|
||||
tmp_n2 = tmp_n
|
||||
elseif (optimization_method == 'diag') then
|
||||
print*,'Diagonal hessian'
|
||||
allocate(H(tmp_n,1),W(tmp_n,1))
|
||||
tmp_n2 = 1
|
||||
elseif (optimization_method == 'none') then
|
||||
print*,'No hessian'
|
||||
allocate(H(tmp_n,1),W(tmp_n,1))
|
||||
tmp_n2 = 1
|
||||
else
|
||||
print*,'Unknown optimization_method, please select full, diag or none'
|
||||
call abort
|
||||
endif
|
||||
print*, 'Absolute value of the hessian:', absolute_eig
|
||||
|
||||
! Algorithm
|
||||
|
||||
! Here is the main algorithm of the optimization:
|
||||
! - First of all we initialize some parameters and we compute the
|
||||
! criterion (the ci energy) before doing any MO rotations
|
||||
! - We compute the gradient and the hessian for the active MOs
|
||||
! - We diagonalize the hessian
|
||||
! - We compute a step and loop to reduce the radius of the
|
||||
! trust region (and the size of the step by the way) until the step is
|
||||
! accepted
|
||||
! - We repeat the process until the convergence
|
||||
! NB: the convergence criterion can be changed
|
||||
|
||||
|
||||
! Loop until the convergence of the optimization
|
||||
! call diagonalize_ci
|
||||
|
||||
!### Initialization ###
|
||||
nb_iter = 0
|
||||
rho = 0.5d0
|
||||
not_converged = .True.
|
||||
tmp_list = list_act ! Optimization of the active MOs
|
||||
nb_cancel_tot = 0
|
||||
|
||||
! Renormalization of the weights of the states
|
||||
call state_weight_normalization
|
||||
|
||||
! Compute the criterion before the loop
|
||||
call state_average_energy(prev_criterion)
|
||||
|
||||
do while (not_converged)
|
||||
print*,''
|
||||
print*,'******************'
|
||||
print*,'Iteration', nb_iter
|
||||
print*,'******************'
|
||||
print*,''
|
||||
|
||||
! Gradient
|
||||
call gradient_list_opt(tmp_n, m, tmp_list, v_grad, max_elem_grad, norm_grad)
|
||||
|
||||
! Hessian
|
||||
if (optimization_method == 'full') then
|
||||
! Full hessian
|
||||
call hessian_list_opt(tmp_n, m, tmp_list, H, h_f)
|
||||
|
||||
! Diagonalization of the hessian
|
||||
call diagonalization_hessian(tmp_n, H, e_val, w)
|
||||
|
||||
elseif (optimization_method == 'diag') then
|
||||
! Diagonal hessian
|
||||
call diag_hessian_list_opt(tmp_n, m, tmp_list, H)
|
||||
else
|
||||
! Identity matrix
|
||||
do tmp_i = 1, tmp_n
|
||||
H(tmp_i,1) = 1d0
|
||||
enddo
|
||||
endif
|
||||
|
||||
if (optimization_method /= 'full') then
|
||||
! Sort
|
||||
do tmp_i = 1, tmp_n
|
||||
key(tmp_i) = tmp_i
|
||||
e_val(tmp_i) = H(tmp_i,1)
|
||||
enddo
|
||||
call dsort(e_val,key,tmp_n)
|
||||
|
||||
! Eigenvalues and eigenvectors
|
||||
do tmp_i = 1, tmp_n
|
||||
w(tmp_i,1) = dble(key(tmp_i))
|
||||
enddo
|
||||
|
||||
endif
|
||||
|
||||
! Init before the internal loop
|
||||
cancel_step = .True. ! To enter in the loop just after
|
||||
nb_cancel = 0
|
||||
nb_sub_iter = 0
|
||||
|
||||
! Loop to reduce the trust radius until the criterion decreases and rho >= thresh_rho
|
||||
do while (cancel_step)
|
||||
print*,''
|
||||
print*,'-----------------------------'
|
||||
print*,'Iteration: ', nb_iter
|
||||
print*,'Sub iteration:', nb_sub_iter
|
||||
print*,'Max elem grad:', max_elem_grad
|
||||
print*,'-----------------------------'
|
||||
|
||||
! Hessian,gradient,Criterion -> x
|
||||
call trust_region_step_w_expected_e(tmp_n,tmp_n2,H,W,e_val,v_grad,prev_criterion,rho,nb_iter,delta,criterion_model,tmp_x,must_exit)
|
||||
|
||||
if (must_exit) then
|
||||
print*,'step_in_trust_region sends: Exit'
|
||||
exit
|
||||
endif
|
||||
|
||||
! 1D tmp -> 2D tmp
|
||||
call vec_to_mat_v2(tmp_n, m, tmp_x, tmp_m_x)
|
||||
|
||||
! Rotation matrix for the active MOs
|
||||
call rotation_matrix(tmp_m_x, m, tmp_R, m, m, info, enforce_step_cancellation)
|
||||
|
||||
! Security to ensure an unitary transformation
|
||||
if (enforce_step_cancellation) then
|
||||
print*, 'Step cancellation, too large error in the rotation matrix'
|
||||
rho = 0d0
|
||||
cycle
|
||||
endif
|
||||
|
||||
! tmp_R to R, subspace to full space
|
||||
call sub_to_full_rotation_matrix(m, tmp_list, tmp_R, R)
|
||||
|
||||
! MO rotations
|
||||
call apply_mo_rotation(R, prev_mos)
|
||||
|
||||
! Update of the energy before the diagonalization of the hamiltonian
|
||||
call clear_mo_map
|
||||
TOUCH mo_coef psi_det psi_coef ci_energy two_e_dm_mo
|
||||
call state_average_energy(criterion)
|
||||
|
||||
! Criterion -> step accepted or rejected
|
||||
call trust_region_is_step_cancelled(nb_iter, prev_criterion, criterion, criterion_model, rho, cancel_step)
|
||||
|
||||
! Cancellation of the step if necessary
|
||||
if (cancel_step) then
|
||||
mo_coef = prev_mos
|
||||
call save_mos()
|
||||
nb_cancel = nb_cancel + 1
|
||||
nb_cancel_tot = nb_cancel_tot + 1
|
||||
else
|
||||
! Diagonalization of the hamiltonian
|
||||
FREE ci_energy! To enforce the recomputation
|
||||
call diagonalize_ci
|
||||
call save_wavefunction_unsorted
|
||||
|
||||
! Energy obtained after the diagonalization of the CI matrix
|
||||
call state_average_energy(prev_criterion)
|
||||
endif
|
||||
|
||||
nb_sub_iter = nb_sub_iter + 1
|
||||
enddo
|
||||
call save_mos() !### depend of the time for 1 iteration
|
||||
|
||||
! To exit the external loop if must_exit = .True.
|
||||
if (must_exit) then
|
||||
exit
|
||||
endif
|
||||
|
||||
! Step accepted, nb iteration + 1
|
||||
nb_iter = nb_iter + 1
|
||||
|
||||
! External loop exit conditions
|
||||
if (DABS(max_elem_grad) < thresh_opt_max_elem_grad) then
|
||||
print*,'Converged: DABS(max_elem_grad) < thresh_opt_max_elem_grad'
|
||||
not_converged = .False.
|
||||
endif
|
||||
if (nb_iter >= optimization_max_nb_iter) then
|
||||
print*,'Not converged: nb_iter >= optimization_max_nb_iter'
|
||||
not_converged = .False.
|
||||
endif
|
||||
|
||||
if (.not. not_converged) then
|
||||
print*,'#############################'
|
||||
print*,' End of the optimization'
|
||||
print*,'#############################'
|
||||
endif
|
||||
enddo
|
||||
|
||||
! Deallocation, end
|
||||
|
||||
|
||||
deallocate(v_grad,H,R,W,e_val)
|
||||
deallocate(prev_mos,new_mos)
|
||||
if (optimization_method == 'full') then
|
||||
deallocate(h_f)
|
||||
endif
|
||||
|
||||
end
|
||||
|
|
@ -0,0 +1,9 @@
|
|||
subroutine save_energy(E,pt2)
|
||||
implicit none
|
||||
BEGIN_DOC
|
||||
! Saves the energy in |EZFIO|.
|
||||
END_DOC
|
||||
double precision, intent(in) :: E(N_states), pt2(N_states)
|
||||
call ezfio_set_fci_energy(E(1:N_states))
|
||||
call ezfio_set_fci_energy_pt2(E(1:N_states)+pt2(1:N_states))
|
||||
end
|
||||
|
|
@ -0,0 +1,72 @@
|
|||
! State average energy
|
||||
|
||||
! Calculation of the state average energy from the integrals and the
|
||||
! density matrices.
|
||||
|
||||
! \begin{align*}
|
||||
! E = \sum_{ij} h_{ij} \gamma_{ij} + \frac{1}{2} v_{ij}^{kl} \Gamma_{ij}^{kl}
|
||||
! \end{align*}
|
||||
! $h_{ij}$: mono-electronic integral
|
||||
! $\gamma_{ij}$: one electron density matrix
|
||||
! $v_{ij}^{kl}$: bi-electronic integral
|
||||
! $\Gamma_{ij}^{kl}$: two electrons density matrix
|
||||
|
||||
! TODO: OMP version
|
||||
|
||||
! PROVIDED:
|
||||
! | mo_one_e_integrals | double precision | mono-electronic integrals |
|
||||
! | get_two_e_integral | double precision | bi-electronic integrals |
|
||||
! | one_e_dm_mo | double precision | one electron density matrix |
|
||||
! | two_e_dm_mo | double precision | two electrons density matrix |
|
||||
! | nuclear_repulsion | double precision | nuclear repulsion |
|
||||
! | mo_num | integer | number of MOs |
|
||||
|
||||
! Output:
|
||||
! | energy | double precision | state average energy |
|
||||
|
||||
! Internal:
|
||||
! | mono_e | double precision | mono-electronic energy |
|
||||
! | bi_e | double precision | bi-electronic energy |
|
||||
! | i,j,k,l | integer | indexes to loop over the MOs |
|
||||
|
||||
|
||||
subroutine state_average_energy(energy)
|
||||
|
||||
implicit none
|
||||
|
||||
double precision, intent(out) :: energy
|
||||
|
||||
double precision :: get_two_e_integral
|
||||
double precision :: mono_e, bi_e
|
||||
integer :: i,j,k,l
|
||||
|
||||
! mono electronic part
|
||||
mono_e = 0d0
|
||||
do j = 1, mo_num
|
||||
do i = 1, mo_num
|
||||
mono_e = mono_e + mo_one_e_integrals(i,j) * one_e_dm_mo(i,j)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! bi electronic part
|
||||
bi_e = 0d0
|
||||
do l = 1, mo_num
|
||||
do k = 1, mo_num
|
||||
do j = 1, mo_num
|
||||
do i = 1, mo_num
|
||||
bi_e = bi_e + get_two_e_integral(i,j,k,l,mo_integrals_map) * two_e_dm_mo(i,j,k,l)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! State average energy
|
||||
energy = mono_e + 0.5d0 * bi_e + nuclear_repulsion
|
||||
|
||||
! Check
|
||||
!call print_energy_components
|
||||
|
||||
print*,'State average energy:', energy
|
||||
!print*,ci_energy
|
||||
|
||||
end
|
||||
|
|
@ -0,0 +1,29 @@
|
|||
subroutine state_weight_normalization
|
||||
|
||||
implicit none
|
||||
|
||||
BEGIN_DOC
|
||||
! Renormalization of the state weights or enforcing state average
|
||||
! weights for orbital optimization
|
||||
END_DOC
|
||||
|
||||
integer :: i
|
||||
double precision :: normalization_factor
|
||||
|
||||
! To normalize the sum of the state weights
|
||||
normalization_factor = 0d0
|
||||
do i = 1, N_states
|
||||
normalization_factor = normalization_factor + state_average_weight(i)
|
||||
enddo
|
||||
normalization_factor = 1d0 / normalization_factor
|
||||
|
||||
do i = 1, N_states
|
||||
state_average_weight(i) = state_average_weight(i) * normalization_factor
|
||||
enddo
|
||||
TOUCH state_average_weight
|
||||
|
||||
print*, 'Number of states:', N_states
|
||||
print*, 'State average weights:'
|
||||
print*, state_average_weight(:)
|
||||
|
||||
end
|
||||
|
|
@ -0,0 +1,15 @@
|
|||
! Subroutine toupdate the parameters.
|
||||
! Ex: TOUCH mo_coef ...
|
||||
|
||||
|
||||
subroutine update_parameters()
|
||||
|
||||
implicit none
|
||||
|
||||
!### TODO
|
||||
! Touch yours parameters
|
||||
call clear_mo_map
|
||||
TOUCH mo_coef psi_det psi_coef
|
||||
call diagonalize_ci
|
||||
call save_wavefunction_unsorted
|
||||
end
|
||||
|
|
@ -0,0 +1,25 @@
|
|||
! Update the CI state average energy
|
||||
|
||||
! Computes the state average energy
|
||||
! \begin{align*}
|
||||
! E =\sum_{i=1}^{N_{states}} E_i . w_i
|
||||
! \end{align*}
|
||||
|
||||
! $E_i$: energy of state i
|
||||
! $w_i$: weight of state i
|
||||
|
||||
|
||||
subroutine update_st_av_ci_energy(energy)
|
||||
|
||||
implicit none
|
||||
|
||||
double precision, intent(out) :: energy
|
||||
integer :: i
|
||||
|
||||
energy = 0d0
|
||||
do i = 1, N_states
|
||||
energy = energy + ci_energy(i) * state_average_weight(i)
|
||||
enddo
|
||||
|
||||
print*, 'ci_energy :', energy
|
||||
end
|
||||
Loading…
Reference in New Issue