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

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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 
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! 
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!This subroutine calculates new coordinates given a Hessian, the forces 
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! and the old coordinates 
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! 
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!!!!!!!!!! 
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! v1.0 
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! Uses only basic RFO step 
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! 
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!!!!!!!!!! 
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! v 2.0 
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! We add the test of ADF here, so that it should be more efficient. 
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! This version uses HInv to decide wether it should work with the Hessian 
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! or its inverse. 
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! 
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! v 3.0 
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! Uses DIIS. Done by P. Dayal. 
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! 
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! v3.1 
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! Back to origins ! We remove the ADF test here to see what we loose... 
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! untill of course its replacement by something more efficient... and free :) 
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!!!!!!!!!!!!!!!!! 
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! 
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! Input: 
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!  NCoord: INTEGER(KINT), Number of degrees of freedom 
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!  IGeom : INTEGER(KINT), Index of the geometry along the path 
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!  Geom : REAL(KREAL)(NCOORD), Geometry expressed in full coordinates 
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!  Hess : REAL(KREAL)(Ncoord,NCoord), Hessian at the current geometry 
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! 
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! 
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! Output: 
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!  Step : REAL(KREAL)(Ncoord), Calculated step 
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! 
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! In/Out: 
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!  Tangent: REAL(KREAL)(Ncoord), Tangent to the path, at the current point 
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! if Tangent=0, then we are optimizing a minimum, tangent is not considered. 
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! Input: Expressed in full coordinates. 
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! Output: Replaced by the tangent expressed in Free vectors 
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! (Changes by PFL 3 Jan 2008) 
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!  Grad: READ(KREAL) (NCoord), Gradient at the current point 
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! Input: Expressed in full coordinates. 
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! PFL 18 Jan 2008: Grad is no longer changed on output > 
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! Output: Replaced by the gradient expressed in Free vector, in the subspace orthogonal to the tangent. 
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! < PFL 18 Jan 2008: Grad is no longer changed on output 
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 
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use Io_module, only : IoOut 
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use Path_module, only : NGeomF, Hinv,Coord,Vfree, NGintMax 
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! VFree(Ncoord,Ncoord) 
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IMPLICIT NONE 
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INTEGER, PARAMETER :: KINT=KIND(1) 
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INTEGER, PARAMETER :: KREAL=KIND(1.D0) 
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INTEGER(KINT), INTENT(IN) :: NCoord,IGeom 
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REAL(KREAL), INTENT(IN) :: Hess(NCoord,NCoord) 
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REAL(KREAL), INTENT(IN) :: Grad(NCoord),Geom(NCoord) 
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REAL(KREAL), INTENT(INOUT) :: Tangent(Ncoord) ! Destroyed on output 
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REAL(KREAL), INTENT(OUT) :: Step(NCoord) 
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INTEGER(KINT) :: NFree 
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REAL(KREAL), ALLOCATABLE :: eigval(:), eigvec(:,:), eigvli(:) 
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REAL(KREAL), ALLOCATABLE :: Tanf(:) 
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REAL(KREAL), ALLOCATABLE :: Grad_f(:),Step_f(:) ! NFree 
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REAL(KREAL), PARAMETER :: tiny=1e20, zero=0., dele3=1e6, eps=1e12 
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REAL(KREAL), PARAMETER :: crit=1e8 
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INTEGER(KINT) :: i, j, idx, k, isch 
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REAL(KREAL) :: grd, eval, norm 
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REAL(KREAL) :: dx 
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CHARACTER(120) :: fmt2 
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LOGICAL :: Debug 
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REAL(KREAL), ALLOCATABLE :: HFree(:,:) ! NFree,NFree 
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REAL(KREAL), ALLOCATABLE :: Htmp(:,:) ! NCoord,NFree 
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! LOGICAL, SAVE :: LFirst=.TRUE. 
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INTERFACE 
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function valid(string) result (isValid) 
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CHARACTER(*), intent(in) :: string 
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logical :: isValid 
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END function VALID 
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END INTERFACE 
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debug=valid("step_rfo_all") 
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if (debug) WRITE(*,*) "=========================== Entering Step_RFO_All ====================" 
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if (debug) WRITE(*,*) "=========================== IGeom=",IGeom," ====================" 
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! PFL 22.Nov.2007 > 
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! Nfree is equal to Ncoord1 only when optimizing in the plane 
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! orthogonal to the tangent. 
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! In the case of a regular opt, NFree=Ncoord. 
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! Next line has been moved later 
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! NFree=Ncoord1 
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! < PFL 22.Nov.2007 
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IF (debug) THEN 
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WRITE(*,*) 'DBG Step_RFO_All Hess' 
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WRITE(*,*) 'DBG Step_RFO_All NCoord=',NCoord 
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Idx=min(12,NCoord) 
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DO I=1,NCoord 
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WRITE(*,'(12(1X,F10.4))') Hess(I,1:Idx) 
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END DO 
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WRITE(*,*) 'DBG Step_RFO_All Grad' 
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WRITE(*,'(12(1X,F10.4))') Grad(1:Idx) 
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WRITE(*,*) 'DBG Step_RFO_All Coord' 
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WRITE(*,'(12(1X,F10.4))') Geom(1:Idx) 
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WRITE(*,*) 'DBG Step_RFO_All Tangent' 
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WRITE(*,'(12(1X,F10.4))') tangent(1:Idx) 
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END IF 
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Call FreeMv(NCoord,Vfree) ! VFree(Ncoord,Ncoord) 
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! we orthogonalize Vfree to the tangent vector of this geom 
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! 2007/05/29 Only if Tangent/=0.d0 
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Norm=sqrt(dot_product(Tangent,Tangent)) 
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IF (Norm.GT.eps) THEN 
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ALLOCATE(Tanf(NCoord)) 
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! We normalize Tangent 
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Tangent=Tangent/Norm 
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! We convert Tangent into vfree only displacements 
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! This is useless for now (2007.Apr.23) as vfree=Id matrix 
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! but it will be usefull as soon as we introduce Constraints 
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DO I=1,NCoord 
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Tanf(I)=dot_product(reshape(vfree(:,I),(/NCoord/)),Tangent) 
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END DO 
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Tangent=0.d0 
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DO I=1,NCoord 
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Tangent=Tangent+Tanf(i)*vfree(:,I) 
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END DO 
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! first we substract Tangent from vfree 
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DO I=1,NCoord 
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Norm=dot_product(reshape(vfree(:,i),(/NCoord/)),Tangent) 
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Vfree(:,I)=vfree(:,i)Norm*Tangent 
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END DO 
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Idx=0. 
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! Schmidt orthogonalization of the vfree vectors 
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DO I=1,NCoord 
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! We substract the first vectors 
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! we do it twice as the Schmidt procedure is not numerically stable 
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DO isch=1,2 
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DO J=1,Idx 
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Norm=dot_product(reshape(vfree(:,I),(/NCoord/)),reshape(vfree(:,J),(/NCoord/))) 
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vfree(:,I)=vfree(:,I)Norm*vfree(:,J) 
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END DO 
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END DO 
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Norm=dot_product(reshape(vfree(:,I),(/NCoord/)),reshape(vfree(:,I),(/NCoord/))) 
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IF (Norm.GE.crit) THEN 
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idx=idx+1 
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vfree(:,idx)=vfree(:,i)/sqrt(Norm) 
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END IF 
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END DO 
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If (Idx/= NCoord1) THEN 
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WRITE(*,*) "Pb in orthogonalizing vfree to tangent for geom",IGeom 
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WRITE(Ioout,*) "Pb in orthogonalizing vfree to tangent for geom",IGeom 
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STOP 
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END IF 
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if (debug) WRITE(*,*) "Deallocating Tanf" 
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DEALLOCATE(Tanf) 
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NFree=Idx 
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ELSE ! Tangent =0, matches IF (Norm.GT.eps) THEN 
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if (debug) WRITE(*,*) "Tangent=0, using full displacement" 
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NFree=NCoord 
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END IF !IF (Norm.GT.eps) THEN 
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if (debug) WRITE(*,*) 'DBG Step_RFO_All NFree=',NFree 
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! We now calculate the new step 
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! we project the hessian onto the free vectors 
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ALLOCATE(hfree(NFree,NFree),htmp(NCoord,NFree),Grad_f(NFree),Step_f(NFree)) 
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DO J=1,NFree 
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DO I=1,NCoord 
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Htmp(I,J)=0.d0 
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DO K=1,NCoord 
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Htmp(I,J)=htmp(I,J)+Hess(I,K)*vfree(K,J) 
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END DO 
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END DO 
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END DO 
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DO J=1,NFree 
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DO I=1,NFree 
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HFree(i,j)=0.d0 
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DO K=1,NCoord 
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HFree(i,j)=hfree(i,j)+vfree(k,i)*htmp(k,j) 
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END DO 
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END DO 
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END DO 
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! We diagonalize the hessian or its inverse 
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ALLOCATE(eigval(NFree), eigvec(NFree,NFree), eigvli(NFree)) 
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call Jacobi(Hfree,NFree,eigvli,eigvec,NFree) 
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if (debug) THEN 
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WRITE(*,*) 'Eigensystem, Step_RFO_all.f90, L225' 
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fmt2='(I5,":",F8.3," ", (1X,F10.4))' 
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WRITE(fmt2(19:20),'(I2)') min(NFree,99) 
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DO I=1,NFree 
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WRITE(*,fmt2) I,Eigvli(I),eigvec(:,I) 
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END DO 
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END IF 
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! We inverse the eigenvalues if Hess corresponds to Hessian inverse 
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IF (Hinv) THEN 
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do J=1,NFree 
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if (abs(eigvli(j)) <= tiny) eigvli(j) = zero 
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eigval(j) = sign (eigvli(j)**2 / (dele3 + abs(eigvli(j))**3), eigvli(j)) 
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if (abs(eigval(j)) <= tiny) eigval(j) = zero 
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end do 
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ELSE 
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eigval=eigvli 
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END IF 
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call trie(NFree,eigval,eigvec,NFree) 
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DO I=1,NFree 
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Grad_f(I)=dot_product(reshape(vfree(:,I),(/NCoord/)),grad) 
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END DO 
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! We now construct the step 
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Step_f=0.d0 
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DO I=1,NFree 
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grd= dot_product(grad_f,reshape(eigvec(:,i),(/NFree/))) 
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eval = 0.5 * (abs(eigval(i)) + sqrt (eigval(i)**2 + 4.*grd**2)) 
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dx = (grd) / eval 
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step_f = step_f + dx * eigvec(:,i) 
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if (debug) write (*,*) i,eigval(i),eval,grd,dx 
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END DO 
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Step=0.d0 
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! PFL 04 Apr 2008 > 
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! Grad is once again modified 
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! Grad=0.d0 
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DO I=1,NFree 
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Step=Step+ step_f(i)*vfree(:,i) 
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! Grad=Grad+ Grad_f(i)*vfree(:,i) 
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END DO 
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! < PFL 04 Apr 2008 
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if (debug) WRITE(*,*) "Deallocataing Eigval" 
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DEALLOCATE(eigval) 
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if (debug) WRITE(*,*) "Deallocataing Eigvec" 
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DEALLOCATE(eigvec) 
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if (debug) WRITE(*,*) "Deallocataing Eigvli" 
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DEALLOCATE(eigvli) 
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if (debug) WRITE(*,*) "Deallocataing hfree" 
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DEALLOCATE(hfree) 
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if (debug) WRITE(*,*) "Deallocataing htmp" 
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DEALLOCATE(htmp) 
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if (debug) WRITE(*,*) "Deallocataing grad_f" 
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DEALLOCATE(grad_f) 
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if (debug) WRITE(*,*) "Deallocataing step_f" 
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DEALLOCATE(step_f) 
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if (debug) THEN 
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WRITE(*,*) 'DBG Step_RFO_All Step' 
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WRITE(*,'(12(1X,F8.4))') Step(1:Idx) 
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END IF 
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if (debug) WRITE(*,*) "=========================== Step_RFO_All Over ====================" 
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END SUBROUTINE STEP_RFO_ALL 
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