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