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3.3 KiB
3.3 KiB
Predicted energy : e_model
Compute the energy predicted by the Taylor series
The energy is predicted using a Taylor expansion truncated at te 2nd order :
\begin{align*} E_{k+1} = E_{k} + \textbf{g}_k^{T} \cdot \textbf{x}_{k+1} + \frac{1}{2} \cdot \textbf{x}_{k+1}^T \cdot \textbf{H}_{k} \cdot \textbf{x}_{k+1} + \mathcal{O}(\textbf{x}_{k+1}^2) \end{align*}Input:
n | integer | m*(m-1)/2 |
n2 | integer | m*(m-1)/2 or 1 if the hessian is diagonal |
v_grad(n) | double precision | gradient |
H(n,n) | double precision | hessian |
x(n) | double precision | Step in the trust region |
prev_energy | double precision | previous energy |
Output:
e_model | double precision | predicted energy after the rotation of the MOs |
Internal:
part_1 | double precision | v_grad^T.x |
part_2 | double precision | 1/2 . x^T.H.x |
part_2a | double precision | H.x |
i,j | integer | indexes |
Function:
ddot | double precision | dot product (Lapack) |
subroutine trust_region_expected_e(n,n2,v_grad,H,x,prev_energy,e_model)
include 'pi.h'
!BEGIN_DOC
! Compute the expected criterion/energy after the application of the step x
!END_DOC
implicit none
! Variables
! in
integer, intent(in) :: n,n2
double precision, intent(in) :: v_grad(n),H(n,n2),x(n)
double precision, intent(in) :: prev_energy
! out
double precision, intent(out) :: e_model
! internal
double precision :: part_1, part_2, t1,t2,t3
double precision, allocatable :: part_2a(:)
integer :: i,j
!Function
double precision :: ddot
print*,''
print*,'---Trust_e_model---'
call wall_time(t1)
! Allocation
allocate(part_2a(n))
Calculations
part_1 corresponds to the product g.x part_2a corresponds to the product H.x part_2 corresponds to the product 0.5*(x^T.H.x)
TODO: remove the dot products
! Product v_grad.x
part_1 = ddot(n,v_grad,1,x,1)
!if (debug) then
! print*,'g.x : ', part_1
!endif
! Product H.x
if (n == n2) then
call dgemv('N',n,n,1d0,H,size(H,1),x,1,0d0,part_2a,1)
else
! If the hessian is diagonal
do i = 1, n
part_2a(i) = H(i,1) * x(i)
enddo
endif
! Product 1/2 . x^T.H.x
part_2 = 0.5d0 * ddot(n,x,1,part_2a,1)
!if (debug) then
! print*,'1/2*x^T.H.x : ', part_2
!endif
! Sum
e_model = prev_energy + part_1 + part_2
! Writing the predicted energy
print*, 'prev_energy: ', prev_energy
print*, 'Predicted energy after the rotation:', e_model
print*, 'Previous energy - predicted energy: ', prev_energy - e_model
! Can be deleted, already in another subroutine
if (DABS(prev_energy - e_model) < 1d-12 ) then
print*,'WARNING: ABS(prev_energy - e_model) < 1d-12'
endif
! Deallocation
deallocate(part_2a)
call wall_time(t2)
t3 = t2 - t1
print*,'Time in trust e model:', t3
print*,'---End trust_e_model---'
end subroutine