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! This program reads an old hessian, old forces, new

! forces and updates the hessian matrix inverse

! using the BFGS scheme.

! 

! This routines has been modified so that its input is now:

SUBROUTINE Hinvup_BFGS(Nfree,ds,dgrad,Hess)

  IMPLICIT NONE

  INTEGER, PARAMETER :: KINT=KIND(1)

  INTEGER, PARAMETER :: KREAL=KIND(1.D0)

  INTEGER(KINT), INTENT(IN) :: NFREE

  REAL(KREAL), INTENT(INOUT) :: Hess(Nfree,Nfree)

  REAL(KREAL), INTENT(IN) :: ds(Nfree)

  REAL(KREAL), INTENT(IN) :: dGrad(Nfree)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!

! This subroutine updates the inverse of the Hessian

! using a BFGS formula.

!

! input:

!  - nfree: number of coordinates

!  - ds: GeomOld-Geom (expressed in the optimization coord.)

!  - dgrad: GradOld-Grad  (expressed in the optimization coord.)

!

!  input/output:

!  - Hess: old Hessian in input, replaced by updated Hessian on output

!

!  Notations for the formula:

! s=Geom-GeomOld  

! y=Grad-GradOld

! W= (H)-1 ie the inverse matrix that we are updating

! W+=W - [s(yT)W+Wy(sT)]/(y,s)+ {1+[(y,Wy)/(y,s)]}(s(sT))/(y,s)

! 

!!!!!!!!!!!!!!!!

!

! Due to the dual properties, this routine is also called to compute

! the DFP update for the Hessian

!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

  REAL(KREAL), ALLOCATABLE  :: HessOld(:,:) , Wy(:)

  REAL(KREAL), ALLOCATABLE  :: Hup(:,:),ssT(:,:)

  REAL(KREAL), ALLOCATABLE  :: HupInt(:)

  REAL(KREAL), ALLOCATABLE  :: Num(:,:), Num2(:,:)

  REAL(KREAL) :: Phi, Num3, Den, Den2,NormDS

  CHARACTER(120) :: fmt,fmt2,Line

  INTEGER(KINT) :: i,j,k, Idx

  LOGICAL debug,valid

  EXTERNAL valid

  debug=valid("Hinvup_BFGS")

  if (debug) WRITE(*,*) "=========================== Entering Hinvup_BFGS ===================="

  ALLOCATE(HessOld(nfree,nfree), Hup(nfree,nfree), &

       HupInt(nfree),  &

       Num(nfree,nfree), Num2(nfree,nfree),Wy(Nfree),ssT(Nfree,nFree) )

  HessOld=Hess

  if (debug) THEN

     WRITE(*,*) 'DBG Hinvup_BFGS HessOld'

     Idx=min(12,Nfree)

     DO I=1,NFree

        WRITE(*,'(12(1X,F8.4))') HessOld(I,1:Idx)

     END DO

     WRITE(*,*) 'DBG Hinvup_BFGS ds'

     WRITE(*,'(12(1X,F8.4))') ds(1:Idx)

     WRITE(*,*) 'DBG Hinvup_BFGS dGrad'

     WRITE(*,'(12(1X,F8.4))') dGrad(1:Idx)

  END IF

  NormDS=sqrt(DOT_PRODUCT(DS,DS))

  if (NormDS>=1e-6) THEN

     IF (debug) WRITE(*,*) 'NormDS=',NormDS

     IF (debug) WRITE(*,*) 'DS=',DS

     IF (debug) WRITE(*,*) 'DGrad=',DGrad

     ! We calculate the denominator (DGrad,DS)

     den=DOT_PRODUCT(DGrad,DS)

     if (debug) WRITE(*,*) "(y,s)=(yT)s",den

     ! We calculate Wy

     Wy=0

     DO I=1,nfree

        DO J=1,NFree

           Wy(I)=Wy(I)+HessOld(i,j)*DGrad(j)

        END DO

     END DO

     if (debug) WRITE(*,*) "Wy=",Wy

     ! We calculate Num=Wy(sT)

     Num=0.

     DO I=1,Nfree

        DO J=1,Nfree

           Num(I,J)=Wy(i)*Ds(j)

        END DO

     END DO

     if (debug) THEN

        WRITE(*,*) "Wy(sT)"

        DO I=1,NFree

           WRITE(*,*) Num(I,:)

        END DO

     END if

     ! We calculate Num2=s(yT)

     Num2=0

     Do I=1,NFree

        DO J=1,NFree

           Num2(I,J)=Ds(i)*DGrad(j)

        END DO

     END DO

     if (debug) THEN

        WRITE(*,*) "s(yT)"

        DO I=1,NFree

           WRITE(*,*) Num2(I,:)

        END DO

     END if

     ! we add Num2*W to Num

     Do I=1,NFree

        DO J=1,NFree

           DO K=1,NFree

              Num(I,J)=Num(I,J)+Num2(I,K)*HessOld(K,J)

           END DO

        END DO

     END DO

     if (debug) THEN

        WRITE(*,*) "Num=s(yT)W+Wy(sT)"

        DO I=1,NFree

           WRITE(*,*) Num(I,:)

        END DO

     END if

     ! we calculate ssT

     ssT=0.

     DO I=1,Nfree

        DO J=1,NFree

           ssT(I,J)=Ds(I)*Ds(J)

        END DO

     END DO

     if (debug) THEN

        WRITE(*,*) "s(sT)"

        DO I=1,NFree

           WRITE(*,*) ssT(I,:)

        END DO

     END if

     !We add everything

     Hup=(1+DOT_PRODUCT(DGRAD,Wy)/Den)*ssT/Den-Num/Den

     Hess=HessOld+Hup

     if (debug) THEN

        WRITE(*,*) 'DBG Hinvup_BFGS Hup'

        Idx=min(12,Nfree)

        DO I=1,NFree

           WRITE(*,'(12(1X,F8.4))') Hup(I,1:Idx)

        END DO

        WRITE(*,*) 'DBG Hinvup_BFGS Hess new'

        Idx=min(12,Nfree)

        DO I=1,NFree

           WRITE(*,'(12(1X,F8.4))') Hess(I,1:Idx)

        END DO

     END IF

  ELSE

     Hess=HessOld

  END IF

  !     WRITE(*,*) 'New hess'

  !     DO I=1,nfree

  !        WRITE(*,fmt) Hess(i,:)

  !     END DO

  DEALLOCATE(HessOld, Wy,ssT, Hup,HupInt, Num, Num2 )

  if (debug) WRITE(*,*) "=========================== Hinvup_BFGS Over ===================="

END SUBROUTINE Hinvup_BFGS