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qp2/src/utils_trust_region/algo_trust.irp.f

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2023-04-18 13:01:25 +02:00
! Algorithm for the trust region
! step_in_trust_region:
! Computes the step in the trust region (delta)
! (automatically sets at the iteration 0 and which evolves during the
! process in function of the evolution of rho). The step is computing by
! constraining its norm with a lagrange multiplier.
! Since the calculation of the step is based on the Newton method, an
! estimation of the gain in energy is given using the Taylors series
! truncated at the second order (criterion_model).
! If (DABS(criterion-criterion_model) < 1d-12) then
! must_exit = .True.
! else
! must_exit = .False.
! This estimation of the gain in energy is used by
! is_step_cancel_trust_region to say if the step is accepted or cancelled.
! If the step must be cancelled, the calculation restart from the same
! hessian and gradient and recomputes the step but in a smaller trust
! region and so on until the step is accepted. If the step is accepted
! the hessian and the gradient are recomputed to produce a new step.
! Example:
! !### Initialization ###
! delta = 0d0
! nb_iter = 0 ! Must start at 0 !!!
! rho = 0.5d0
! not_converged = .True.
!
! ! ### TODO ###
! ! Compute the criterion before the loop
! call #your_criterion(prev_criterion)
!
! do while (not_converged)
! ! ### TODO ##
! ! Call your gradient
! ! Call you hessian
! call #your_gradient(v_grad) (1D array)
! call #your_hessian(H) (2D array)
!
! ! ### TODO ###
! ! Diagonalization of the hessian
! call diagonalization_hessian(n,H,e_val,w)
!
! cancel_step = .True. ! To enter in the loop just after
! ! Loop to Reduce the trust radius until the criterion decreases and rho >= thresh_rho
! do while (cancel_step)
!
! ! Hessian,gradient,Criterion -> x
! call trust_region_step_w_expected_e(tmp_n,W,e_val,v_grad,prev_criterion,rho,nb_iter,delta,criterion_model,tmp_x,must_exit)
!
! if (must_exit) then
! ! ### Message ###
! ! if step_in_trust_region sets must_exit on true for numerical reasons
! print*,'algo_trust1 sends the message : Exit'
! !### exit ###
! endif
!
! !### TODO ###
! ! Compute x -> m_x
! ! Compute m_x -> R
! ! Apply R and keep the previous MOs...
! ! Update/touch
! ! Compute the new criterion/energy -> criterion
!
! call #your_routine_1D_to_2D_antisymmetric_array(x,m_x)
! call #your_routine_2D_antisymmetric_array_to_rotation_matrix(m_x,R)
! call #your_routine_to_apply_the_rotation_matrix(R,prev_mos)
!
! TOUCH #your_variables
!
! call #your_criterion(criterion)
!
! ! Criterion -> step accepted or rejected
! call trust_region_is_step_cancelled(nb_iter,prev_criterion, criterion, criterion_model,rho,cancel_step)
!
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! !### TODO ###
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! !if (cancel_step) then
! ! Cancel the previous step (mo_coef = prev_mos if you keep them...)
! !endif
! #if (cancel_step) then
! #mo_coef = prev_mos
! #endif
!
! 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
!
! ! ### TODO ###
! !if (###Conditions###) then
! ! no_converged = .False.
! !endif
! #if (#your_conditions) then
! # not_converged = .False.
! #endif
!
! enddo
! Variables:
! Input:
! | n | integer | m*(m-1)/2 |
! | m | integer | number of mo in the mo_class |
! | H(n,n) | double precision | Hessian |
! | v_grad(n) | double precision | Gradient |
! | W(n,n) | double precision | Eigenvectors of the hessian |
! | e_val(n) | double precision | Eigenvalues of the hessian |
! | criterion | double precision | Actual criterion |
! | prev_criterion | double precision | Value of the criterion before the first iteration/after the previous iteration |
! | rho | double precision | Given by is_step_cancel_trus_region |
! | | | Agreement between the real function and the Taylor series (2nd order) |
! | nb_iter | integer | Actual number of iterations |
! Input/output:
! | delta | double precision | Radius of the trust region |
! Output:
! | criterion_model | double precision | Predicted criterion after the rotation |
! | x(n) | double precision | Step |
! | must_exit | logical | If the program must exit the loop |
subroutine trust_region_step_w_expected_e(n,n2,H,W,e_val,v_grad,prev_criterion,rho,nb_iter,delta,criterion_model,x,must_exit)
include 'pi.h'
!BEGIN_DOC
! Compute the step and the expected criterion/energy after the step
!END_DOC
implicit none
! in
integer, intent(in) :: n,n2, nb_iter
double precision, intent(in) :: H(n,n2), W(n,n2), v_grad(n)
double precision, intent(in) :: rho, prev_criterion
! inout
double precision, intent(inout) :: delta, e_val(n)
! out
double precision, intent(out) :: criterion_model, x(n)
logical, intent(out) :: must_exit
! internal
integer :: info
must_exit = .False.
call trust_region_step(n,n2,nb_iter,v_grad,rho,e_val,W,x,delta)
call trust_region_expected_e(n,n2,v_grad,H,x,prev_criterion,criterion_model)
! exit if DABS(prev_criterion - criterion_model) < 1d-12
if (DABS(prev_criterion - criterion_model) < thresh_model) then
print*,''
print*,'###############################################################################'
print*,'DABS(prev_criterion - criterion_model) <', thresh_model, 'stop the trust region'
print*,'###############################################################################'
print*,''
must_exit = .True.
endif
if (delta < thresh_delta) then
print*,''
print*,'##############################################'
print*,'Delta <', thresh_delta, 'stop the trust region'
print*,'##############################################'
print*,''
must_exit = .True.
endif
! Add after the call to this subroutine, a statement:
! "if (must_exit) then
! exit
! endif"
! in order to exit the optimization loop
end subroutine
! Variables:
! Input:
! | nb_iter | integer | actual number of iterations |
! | prev_criterion | double precision | criterion before the application of the step x |
! | criterion | double precision | criterion after the application of the step x |
! | criterion_model | double precision | predicted criterion after the application of x |
! Output:
! | rho | double precision | Agreement between the predicted criterion and the real new criterion |
! | cancel_step | logical | If the step must be cancelled |
subroutine trust_region_is_step_cancelled(nb_iter,prev_criterion, criterion, criterion_model,rho,cancel_step)
include 'pi.h'
!BEGIN_DOC
! Compute if the step should be cancelled
!END_DOC
implicit none
! in
double precision, intent(in) :: prev_criterion, criterion, criterion_model
! inout
integer, intent(inout) :: nb_iter
! out
logical, intent(out) :: cancel_step
double precision, intent(out) :: rho
! Computes rho
call trust_region_rho(prev_criterion,criterion,criterion_model,rho)
if (nb_iter == 0) then
nb_iter = 1 ! in order to enable the change of delta if the first iteration is cancelled
endif
! If rho < thresh_rho -> give something in output to cancel the step
if (rho >= thresh_rho) then !0.1d0) then
! The step is accepted
cancel_step = .False.
else
! The step is rejected
cancel_step = .True.
print*, '***********************'
print*, 'Step cancel : rho <', thresh_rho
print*, '***********************'
endif
end subroutine