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594 lines
19 KiB
Org Mode
594 lines
19 KiB
Org Mode
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* 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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#+BEGIN_SRC f90 :comments org :tangle algo_trust.irp.f
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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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#+END_SRC
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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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#+BEGIN_SRC f90 :comments org :tangle algo_trust.irp.f
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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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#+END_SRC
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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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#+BEGIN_SRC f90 :comments org :tangle algo_trust.irp.f
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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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#+END_SRC
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** Template for MOs
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#+BEGIN_SRC f90 :comments org :tangle trust_region_template_mos.txt
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subroutine algo_trust_template(tmp_n, tmp_list_size, tmp_list)
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implicit none
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! Variables
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! In
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integer, intent(in) :: tmp_n, tmp_list_size, tmp_list(tmp_list_size)
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! Out
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! Rien ou un truc pour savoir si ça c'est bien passé
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! Internal
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double precision, allocatable :: e_val(:), W(:,:), tmp_R(:,:), R(:,:), tmp_x(:), tmp_m_x(:,:)
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double precision, allocatable :: prev_mos(:,:)
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double precision :: criterion, prev_criterion, criterion_model
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double precision :: delta, rho
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logical :: not_converged, cancel_step, must_exit, enforce_step_cancellation
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integer :: nb_iter, info, nb_sub_iter
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integer :: i,j,tmp_i,tmp_j
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allocate(W(tmp_n, tmp_n),e_val(tmp_n),tmp_x(tmp_n),tmp_m_x(tmp_list_size, tmp_list_size))
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allocate(tmp_R(tmp_list_size, tmp_list_size), R(mo_num, mo_num))
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allocate(prev_mos(ao_num, mo_num))
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! Provide the criterion, but unnecessary because it's done
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! automatically
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PROVIDE C_PROVIDER H_PROVIDER g_PROVIDER cc_PROVIDER
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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 ! Must start at 0.5
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not_converged = .True. ! Must be true
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! Compute the criterion before the loop
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prev_criterion = C_PROVIDER
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do while (not_converged)
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print*,''
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print*,'******************'
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print*,'Iteration', nb_iter
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print*,'******************'
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print*,''
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! The new hessian and gradient are computed at the end of the previous iteration
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! Diagonalization of the hessian
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call diagonalization_hessian(tmp_n, H_PROVIDER, e_val, W)
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cancel_step = .True. ! To enter in the loop just after
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nb_sub_iter = 0
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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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print*,'-----------------------------'
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print*,'Iteration:', nb_iter
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print*,'Sub iteration:', nb_sub_iter
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print*,'-----------------------------'
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! Hessian,gradient,Criterion -> x
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call trust_region_step_w_expected_e(tmp_n,tmp_n, H_PROVIDER, W, e_val, g_PROVIDER, &
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prev_criterion, rho, nb_iter, delta, criterion_model, tmp_x, must_exit)
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if (must_exit) then
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! if step_in_trust_region sets must_exit on true for numerical reasons
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print*,'trust_region_step_w_expected_e sent the message : Exit'
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exit
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endif
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! 1D tmp -> 2D tmp
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call vec_to_mat_v2(tmp_n, tmp_list_size, tmp_x, tmp_m_x)
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! Rotation submatrix (square matrix tmp_list_size by tmp_list_size)
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call rotation_matrix(tmp_m_x, tmp_list_size, tmp_R, tmp_list_size, tmp_list_size, info, enforce_step_cancellation)
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if (enforce_step_cancellation) then
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print*, 'Forces the step cancellation, too large error in the rotation matrix'
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rho = 0d0
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cycle
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endif
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! tmp_R to R, subspace to full space
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call sub_to_full_rotation_matrix(tmp_list_size, tmp_list, tmp_R, R)
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! Rotation of the MOs
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call apply_mo_rotation(R, prev_mos)
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! touch mo_coef
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call clear_mo_map ! Only if you are using the bi-electronic integrals
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! mo_coef becomes valid
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! And avoid the recomputation of the providers which depend of mo_coef
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TOUCH mo_coef C_PROVIDER H_PROVIDER g_PROVIDER cc_PROVIDER
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! To update the other parameters if needed
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call #update_parameters()
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! To enforce the program to provide new criterion after the update
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! of the parameters
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FREE C_PROVIDER
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PROVIDE C_PROVIDER
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criterion = C_PROVIDER
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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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! Cancellation of the step ?
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if (cancel_step) then
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! Replacement by the previous MOs
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mo_coef = prev_mos
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! call save_mos() ! depends of the time for 1 iteration
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! No need to clear_mo_map since we don't recompute the gradient and the hessian
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! mo_coef becomes valid
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! Avoid the recomputation of the providers which depend of mo_coef
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TOUCH mo_coef H_PROVIDER g_PROVIDER C_PROVIDER cc_PROVIDER
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else
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! The step is accepted:
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! criterion -> prev criterion
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! The replacement "criterion -> prev criterion" is already done
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! in trust_region_rho, so if the criterion does not have a reason
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! to change, it will change nothing for the criterion and will
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! force the program to provide the new hessian, gradient and
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! convergence criterion for the next iteration.
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! But in the case of orbital optimization we diagonalize the CI
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! matrix after the "FREE" statement, so the criterion will change
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FREE C_PROVIDER H_PROVIDER g_PROVIDER cc_PROVIDER
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PROVIDE C_PROVIDER H_PROVIDER g_PROVIDER cc_PROVIDER
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prev_criterion = C_PROVIDER
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endif
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nb_sub_iter = nb_sub_iter + 1
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enddo
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! call save_mos() ! depends of the time for 1 iteration
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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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! Step accepted, nb iteration + 1
|
|||
|
nb_iter = nb_iter + 1
|
|||
|
|
|||
|
! Provide the convergence criterion
|
|||
|
! Provide the gradient and the hessian for the next iteration
|
|||
|
PROVIDE cc_PROVIDER
|
|||
|
|
|||
|
! To exit
|
|||
|
if (dabs(cc_PROVIDER) < thresh_opt_max_elem_grad) then
|
|||
|
not_converged = .False.
|
|||
|
endif
|
|||
|
|
|||
|
if (nb_iter > optimization_max_nb_iter) then
|
|||
|
not_converged = .False.
|
|||
|
endif
|
|||
|
|
|||
|
if (delta < thresh_delta) then
|
|||
|
not_converged = .False.
|
|||
|
endif
|
|||
|
|
|||
|
enddo
|
|||
|
|
|||
|
! Save the final MOs
|
|||
|
call save_mos()
|
|||
|
|
|||
|
! Diagonalization of the hessian
|
|||
|
! (To see the eigenvalues at the end of the optimization)
|
|||
|
call diagonalization_hessian(tmp_n, H_PROVIDER, e_val, W)
|
|||
|
|
|||
|
deallocate(e_val, W, tmp_R, R, tmp_x, prev_mos)
|
|||
|
|
|||
|
end
|
|||
|
#+END_SRC
|
|||
|
|
|||
|
** Cartesian version
|
|||
|
#+BEGIN_SRC f90 :comments org :tangle trust_region_template_xyz.txt
|
|||
|
subroutine algo_trust_cartesian_template(tmp_n)
|
|||
|
|
|||
|
implicit none
|
|||
|
|
|||
|
! Variables
|
|||
|
|
|||
|
! In
|
|||
|
integer, intent(in) :: tmp_n
|
|||
|
|
|||
|
! Out
|
|||
|
! Rien ou un truc pour savoir si ça c'est bien passé
|
|||
|
|
|||
|
! Internal
|
|||
|
double precision, allocatable :: e_val(:), W(:,:), tmp_x(:)
|
|||
|
double precision :: criterion, prev_criterion, criterion_model
|
|||
|
double precision :: delta, rho
|
|||
|
logical :: not_converged, cancel_step, must_exit
|
|||
|
integer :: nb_iter, nb_sub_iter
|
|||
|
integer :: i,j
|
|||
|
|
|||
|
allocate(W(tmp_n, tmp_n),e_val(tmp_n),tmp_x(tmp_n))
|
|||
|
|
|||
|
PROVIDE C_PROVIDER X_PROVIDER H_PROVIDER g_PROVIDER
|
|||
|
|
|||
|
! Initialization
|
|||
|
delta = 0d0
|
|||
|
nb_iter = 0 ! Must start at 0 !!!
|
|||
|
rho = 0.5d0 ! Must start at 0.5
|
|||
|
not_converged = .True. ! Must be true
|
|||
|
|
|||
|
! Compute the criterion before the loop
|
|||
|
prev_criterion = C_PROVIDER
|
|||
|
|
|||
|
do while (not_converged)
|
|||
|
|
|||
|
print*,''
|
|||
|
print*,'******************'
|
|||
|
print*,'Iteration', nb_iter
|
|||
|
print*,'******************'
|
|||
|
print*,''
|
|||
|
|
|||
|
if (nb_iter > 0) then
|
|||
|
PROVIDE H_PROVIDER g_PROVIDER
|
|||
|
endif
|
|||
|
|
|||
|
! Diagonalization of the hessian
|
|||
|
call diagonalization_hessian(tmp_n, H_PROVIDER, e_val, W)
|
|||
|
|
|||
|
cancel_step = .True. ! To enter in the loop just after
|
|||
|
nb_sub_iter = 0
|
|||
|
|
|||
|
! Loop to Reduce the trust radius until the criterion decreases and rho >= thresh_rho
|
|||
|
do while (cancel_step)
|
|||
|
|
|||
|
print*,'-----------------------------'
|
|||
|
print*,'Iteration:', nb_iter
|
|||
|
print*,'Sub iteration:', nb_sub_iter
|
|||
|
print*,'-----------------------------'
|
|||
|
|
|||
|
! Hessian,gradient,Criterion -> x
|
|||
|
call trust_region_step_w_expected_e(tmp_n,tmp_n, H_PROVIDER, W, e_val, g_PROVIDER, &
|
|||
|
prev_criterion, rho, nb_iter, delta, criterion_model, tmp_x, must_exit)
|
|||
|
|
|||
|
if (must_exit) then
|
|||
|
! if step_in_trust_region sets must_exit on true for numerical reasons
|
|||
|
print*,'trust_region_step_w_expected_e sent the message : Exit'
|
|||
|
exit
|
|||
|
endif
|
|||
|
|
|||
|
! New coordinates, check the sign
|
|||
|
X_PROVIDER = X_PROVIDER - tmp_x
|
|||
|
|
|||
|
! touch X_PROVIDER
|
|||
|
TOUCH X_PROVIDER H_PROVIDER g_PROVIDER cc_PROVIDER
|
|||
|
|
|||
|
! To update the other parameters if needed
|
|||
|
call #update_parameters()
|
|||
|
|
|||
|
! New criterion
|
|||
|
PROVIDE C_PROVIDER ! Unnecessary
|
|||
|
criterion = C_PROVIDER
|
|||
|
|
|||
|
! Criterion -> step accepted or rejected
|
|||
|
call trust_region_is_step_cancelled(nb_iter, prev_criterion, criterion, criterion_model, rho, cancel_step)
|
|||
|
|
|||
|
! Cancel the previous step
|
|||
|
if (cancel_step) then
|
|||
|
! Replacement by the previous coordinates, check the sign
|
|||
|
X_PROVIDER = X_PROVIDER + tmp_x
|
|||
|
|
|||
|
! Avoid the recomputation of the hessian and the gradient
|
|||
|
TOUCH X_PROVIDER H_PROVIDER g_PROVIDER C_PROVIDER cc_PROVIDER
|
|||
|
endif
|
|||
|
|
|||
|
nb_sub_iter = nb_sub_iter + 1
|
|||
|
enddo
|
|||
|
|
|||
|
! 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
|
|||
|
|
|||
|
PROVIDE cc_PROVIDER
|
|||
|
|
|||
|
! To exit
|
|||
|
if (dabs(cc_PROVIDER) < thresh_opt_max_elem_grad) then
|
|||
|
not_converged = .False.
|
|||
|
endif
|
|||
|
|
|||
|
if (nb_iter > optimization_max_nb_iter) then
|
|||
|
not_converged = .False.
|
|||
|
endif
|
|||
|
|
|||
|
if (delta < thresh_delta) then
|
|||
|
not_converged = .False.
|
|||
|
endif
|
|||
|
|
|||
|
enddo
|
|||
|
|
|||
|
deallocate(e_val, W, tmp_x)
|
|||
|
|
|||
|
end
|
|||
|
#+END_SRC
|
|||
|
|
|||
|
** Script template
|
|||
|
#+BEGIN_SRC bash :tangle script_template_mos.sh
|
|||
|
#!/bin/bash
|
|||
|
|
|||
|
your_file=
|
|||
|
|
|||
|
your_C_PROVIDER=
|
|||
|
your_H_PROVIDER=
|
|||
|
your_g_PROVIDER=
|
|||
|
your_cc_PROVIDER=
|
|||
|
|
|||
|
sed "s/C_PROVIDER/$your_C_PROVIDER/g" trust_region_template_mos.txt > $your_file
|
|||
|
sed -i "s/H_PROVIDER/$your_H_PROVIDER/g" $your_file
|
|||
|
sed -i "s/g_PROVIDER/$your_g_PROVIDER/g" $your_file
|
|||
|
sed -i "s/cc_PROVIDER/$your_cc_PROVIDER/g" $your_file
|
|||
|
#+END_SRC
|
|||
|
|
|||
|
#+BEGIN_SRC bash :tangle script_template_xyz.sh
|
|||
|
#!/bin/bash
|
|||
|
|
|||
|
your_file=
|
|||
|
|
|||
|
your_C_PROVIDER=
|
|||
|
your_X_PROVIDER=
|
|||
|
your_H_PROVIDER=
|
|||
|
your_g_PROVIDER=
|
|||
|
your_cc_PROVIDER=
|
|||
|
|
|||
|
sed "s/C_PROVIDER/$your_C_PROVIDER/g" trust_region_template_xyz.txt > $your_file
|
|||
|
sed -i "s/X_PROVIDER/$your_X_PROVIDER/g" $your_file
|
|||
|
sed -i "s/H_PROVIDER/$your_H_PROVIDER/g" $your_file
|
|||
|
sed -i "s/g_PROVIDER/$your_g_PROVIDER/g" $your_file
|
|||
|
sed -i "s/cc_PROVIDER/$your_cc_PROVIDER/g" $your_file
|
|||
|
#+END_SRC
|
|||
|
|