Chimie Théorique » Opt'n Path

SUBROUTINE Step_RFO_all(NCoord,Step,IGeom,Geom,Grad,Hess,Tangent)

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

!

!This subroutine calculates new coordinates given a Hessian, the forces

! and the old coordinates

!

!!!!!!!!!!

! v1.0

! Uses only basic RFO step

!

!!!!!!!!!!

! v 2.0

! We add the test of ADF here, so that it should be more efficient.

! This version uses HInv to decide wether it should work with the Hessian

! or its inverse.

!

! v 3.0

! Uses DIIS. Done by P. Dayal.

!

! v3.1

! Back to origins ! We remove the ADF test here to see what we loose...

! untill of course its replacement by something more efficient... and free :)

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

!

! Input:

!   - NCoord: INTEGER(KINT), Number of degrees of freedom

!   - IGeom : INTEGER(KINT), Index of the geometry along the path

!   - Geom  : REAL(KREAL)(NCOORD), Geometry expressed in full coordinates

!   - Hess  : REAL(KREAL)(Ncoord,NCoord), Hessian at the current geometry

!  

!

! Output:

!   - Step  : REAL(KREAL)(Ncoord), Calculated step

!

! In/Out:

!   - Tangent: REAL(KREAL)(Ncoord), Tangent to the path, at the current point

!             if Tangent=0, then we are optimizing a minimum,  tangent is not considered.

!               Input: Expressed in full coordinates.

!              Output: Replaced by the tangent expressed in Free vectors

! (Changes by PFL 3 Jan 2008)

!   -  Grad: READ(KREAL) (NCoord), Gradient at the current point

!               Input: Expressed in full coordinates.

! PFL 18 Jan 2008: Grad is no longer changed on output ->

!              Output: Replaced by the gradient expressed in Free vector, in the subspace orthogonal to the tangent.

! <- PFL 18 Jan 2008: Grad is no longer changed on output

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

  use Io_module, only : IoOut

  use Path_module, only : NGeomF, Hinv,Coord,Vfree, NGintMax

  ! VFree(Ncoord,Ncoord)

  IMPLICIT NONE

  INTEGER, PARAMETER :: KINT=KIND(1)

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

  INTEGER(KINT), INTENT(IN) :: NCoord,IGeom

  REAL(KREAL), INTENT(IN) :: Hess(NCoord,NCoord)

  REAL(KREAL), INTENT(IN) :: Grad(NCoord),Geom(NCoord)

  REAL(KREAL), INTENT(INOUT) :: Tangent(Ncoord) ! Destroyed on output

  REAL(KREAL), INTENT(OUT) :: Step(NCoord)

  INTEGER(KINT) :: NFree

  REAL(KREAL), ALLOCATABLE :: eigval(:), eigvec(:,:), eigvli(:)

  REAL(KREAL), ALLOCATABLE :: Tanf(:)

  REAL(KREAL), ALLOCATABLE :: Grad_f(:),Step_f(:) ! NFree

  REAL(KREAL), PARAMETER :: tiny=1e-20, zero=0., dele3=1e-6, eps=1e-12

  REAL(KREAL), PARAMETER :: crit=1e-8

  INTEGER(KINT) :: i, j, idx, k, isch

  REAL(KREAL) :: grd, eval, norm

  REAL(KREAL) :: dx

  CHARACTER(120) :: fmt2

  LOGICAL :: Debug

  REAL(KREAL), ALLOCATABLE :: HFree(:,:) ! NFree,NFree

  REAL(KREAL), ALLOCATABLE :: Htmp(:,:) ! NCoord,NFree

!  LOGICAL, SAVE :: LFirst=.TRUE.

  INTERFACE

     function valid(string) result (isValid)

       CHARACTER(*), intent(in) :: string

       logical                  :: isValid

     END function VALID

  END INTERFACE

  debug=valid("step_rfo_all")

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

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

! PFL 22.Nov.2007 ->

! Nfree is equal to Ncoord-1 only when optimizing in the plane

! orthogonal to the tangent. 

! In the case of a regular opt, NFree=Ncoord. 

! Next line has been moved later

!  NFree=Ncoord-1

! <- PFL 22.Nov.2007

  IF (debug) THEN

     WRITE(*,*) 'DBG Step_RFO_All Hess'

     WRITE(*,*) 'DBG Step_RFO_All NCoord=',NCoord

     Idx=min(12,NCoord)

     DO I=1,NCoord

        WRITE(*,'(12(1X,F10.4))') Hess(I,1:Idx)

     END DO

     WRITE(*,*) 'DBG Step_RFO_All Grad'

     WRITE(*,'(12(1X,F10.4))') Grad(1:Idx)

     WRITE(*,*) 'DBG Step_RFO_All Coord'

     WRITE(*,'(12(1X,F10.4))') Geom(1:Idx)

     WRITE(*,*) 'DBG Step_RFO_All Tangent'

     WRITE(*,'(12(1X,F10.4))') tangent(1:Idx)

  END IF

  Call FreeMv(NCoord,Vfree) ! VFree(Ncoord,Ncoord)

! we orthogonalize Vfree to the tangent vector of this geom

! 2007/05/29 Only if Tangent/=0.d0

  Norm=sqrt(dot_product(Tangent,Tangent))

  IF (Norm.GT.eps) THEN

     ALLOCATE(Tanf(NCoord))

     ! We normalize Tangent

     Tangent=Tangent/Norm

     ! We convert Tangent into vfree only displacements

     ! This is useless for now (2007.Apr.23) as vfree=Id matrix

     ! but it will be usefull as soon as we introduce Constraints

     DO I=1,NCoord

        Tanf(I)=dot_product(reshape(vfree(:,I),(/NCoord/)),Tangent)

     END DO

     Tangent=0.d0

     DO I=1,NCoord

        Tangent=Tangent+Tanf(i)*vfree(:,I)

     END DO

     ! first we substract Tangent from vfree

     DO I=1,NCoord

        Norm=dot_product(reshape(vfree(:,i),(/NCoord/)),Tangent)

        Vfree(:,I)=vfree(:,i)-Norm*Tangent

     END DO

     Idx=0.

     ! Schmidt orthogonalization of the vfree vectors

     DO I=1,NCoord

        ! We substract the first vectors

        ! we do it twice as the Schmidt procedure is not numerically stable

        DO isch=1,2

           DO J=1,Idx

              Norm=dot_product(reshape(vfree(:,I),(/NCoord/)),reshape(vfree(:,J),(/NCoord/)))

              vfree(:,I)=vfree(:,I)-Norm*vfree(:,J)

           END DO

        END DO

        Norm=dot_product(reshape(vfree(:,I),(/NCoord/)),reshape(vfree(:,I),(/NCoord/)))

        IF (Norm.GE.crit) THEN

           idx=idx+1

           vfree(:,idx)=vfree(:,i)/sqrt(Norm)

        END IF

     END DO

     If (Idx/= NCoord-1) THEN

        WRITE(*,*) "Pb in orthogonalizing vfree to tangent for geom",IGeom

        WRITE(Ioout,*) "Pb in orthogonalizing vfree to tangent for geom",IGeom

        STOP

     END IF

     if (debug) WRITE(*,*) "Deallocating Tanf"

     DEALLOCATE(Tanf)

     NFree=Idx

  ELSE ! Tangent =0, matches IF (Norm.GT.eps) THEN

     if (debug) WRITE(*,*) "Tangent=0, using full displacement"

     NFree=NCoord

  END IF !IF (Norm.GT.eps) THEN

  if (debug) WRITE(*,*) 'DBG Step_RFO_All NFree=',NFree

! We now calculate the new step

! we project the hessian onto the free vectors

     ALLOCATE(hfree(NFree,NFree),htmp(NCoord,NFree),Grad_f(NFree),Step_f(NFree))

     DO J=1,NFree

        DO I=1,NCoord

           Htmp(I,J)=0.d0

           DO K=1,NCoord

              Htmp(I,J)=htmp(I,J)+Hess(I,K)*vfree(K,J)

           END DO

        END DO

     END DO

     DO J=1,NFree

        DO I=1,NFree

           HFree(i,j)=0.d0

           DO K=1,NCoord

              HFree(i,j)=hfree(i,j)+vfree(k,i)*htmp(k,j)

           END DO

        END DO

     END DO

! We diagonalize the hessian or its inverse

  ALLOCATE(eigval(NFree), eigvec(NFree,NFree), eigvli(NFree)) 

  call Jacobi(Hfree,NFree,eigvli,eigvec,NFree)

  if (debug) THEN

     WRITE(*,*) 'Eigensystem, Step_RFO_all.f90, L225'

     fmt2='(I5,":",F8.3," -",  (1X,F10.4))'

     WRITE(fmt2(19:20),'(I2)') min(NFree,99)

     DO I=1,NFree

        WRITE(*,fmt2) I,Eigvli(I),eigvec(:,I)

     END DO

  END IF

  ! We inverse the eigenvalues if Hess corresponds to Hessian inverse

  IF (Hinv) THEN

     do J=1,NFree

        if (abs(eigvli(j)) <= tiny) eigvli(j) = zero

        eigval(j) = sign (eigvli(j)**2 / (dele3 + abs(eigvli(j))**3), eigvli(j))

        if (abs(eigval(j)) <= tiny) eigval(j) = zero

     end do

  ELSE

     eigval=eigvli

  END IF

  call trie(NFree,eigval,eigvec,NFree)

  DO I=1,NFree

     Grad_f(I)=dot_product(reshape(vfree(:,I),(/NCoord/)),grad)

  END DO

  ! We now construct the step

  Step_f=0.d0

  DO I=1,NFree

     grd= dot_product(grad_f,reshape(eigvec(:,i),(/NFree/)))

     eval = 0.5 * (abs(eigval(i)) + sqrt (eigval(i)**2 + 4.*grd**2))

     dx   = (-grd) / eval

     step_f = step_f + dx * eigvec(:,i)

     if (debug) write (*,*) i,eigval(i),eval,grd,dx

  END DO

  Step=0.d0

! PFL 04 Apr 2008 -> 

! Grad is once again modified

!  Grad=0.d0

  DO I=1,NFree

     Step=Step+ step_f(i)*vfree(:,i)

!     Grad=Grad+ Grad_f(i)*vfree(:,i)

  END DO

! <- PFL 04 Apr 2008

  if (debug) WRITE(*,*) "Deallocataing Eigval"

  DEALLOCATE(eigval) 

  if (debug) WRITE(*,*) "Deallocataing Eigvec"

  DEALLOCATE(eigvec) 

  if (debug) WRITE(*,*) "Deallocataing Eigvli"

  DEALLOCATE(eigvli) 

  if (debug) WRITE(*,*) "Deallocataing hfree"

  DEALLOCATE(hfree) 

  if (debug) WRITE(*,*) "Deallocataing htmp"

  DEALLOCATE(htmp) 

  if (debug) WRITE(*,*) "Deallocataing grad_f"

  DEALLOCATE(grad_f) 

  if (debug) WRITE(*,*) "Deallocataing step_f"

  DEALLOCATE(step_f) 

  if (debug) THEN

     WRITE(*,*) 'DBG Step_RFO_All Step'

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

  END IF

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

END SUBROUTINE STEP_RFO_ALL