root / src / Step_DIIS_all.f90 @ 2
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!C HEAT is never used, not even in call of Space(...) |
|---|---|
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!C Geom = input parameter vector (Geometry). |
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!C Grad = input gradient vector. |
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!C Geom_new = New Geometry. |
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|
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SUBROUTINE Step_diis_all(NGeomF,IGeom,Step,Geom,Grad,HP,HEAT,Hess,NCoord,allocation_flag,Tangent) |
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! IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
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|
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USE Io_module, only : IoOut |
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USE Path_module, only : Vfree |
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|
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IMPLICIT NONE |
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INTEGER, parameter :: KINT = kind(1) |
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INTEGER, parameter :: KREAL = kind(1.0d0) |
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|
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! INCLUDE 'SIZES' |
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|
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INTEGER(KINT) :: NGeomF,IGeom |
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REAL(KREAL) :: Geom_new(NCoord),Geom(NCoord),Grad(NCoord) |
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REAL(KREAL) :: Hess(NCoord*NCoord),Step(NCoord) |
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REAL(KREAL) :: HEAT,HP |
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LOGICAL :: allocation_flag |
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INTEGER(KINT), INTENT(IN) :: NCoord |
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REAL(KREAL), INTENT(INOUT) :: Tangent(Ncoord) |
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|
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!************************************************************************ |
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!* * |
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!* DIIS PERFORMS DIRECT INVERSION IN THE ITERATIVE SUBSPACE * |
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!* * |
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!* THIS INVOLVES SOLVING FOR C IN Geom(NEW) = Geom' - HG' * |
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!* * |
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!* WHERE Geom' = SUM(C(I)Geom(I), THE C COEFFICIENTES COMING FROM * |
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!* * |
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!* | B 1 | . | C | = | 0 | * |
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!* | 1 0 | |-L | | 1 | * |
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!* * |
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!* WHERE B(I,J) =GRAD(I)H(T)HGRAD(J) GRAD(I) = GRADIENT ON CYCLE I * |
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!* Hess = INVERSE HESSIAN * |
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!* * |
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!* REFERENCE * |
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!* * |
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!* P. CSASZAR, P. PULAY, J. MOL. STRUCT. (THEOCHEM), 114, 31 (1984) * |
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!* * |
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!************************************************************************ |
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!************************************************************************ |
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!* * |
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!* GEOMETRY OPTIMIZATION USING THE METHOD OF DIRECT INVERSION IN * |
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!* THE ITERATIVE SUBSPACE (GDIIS), COMBINED WITH THE BFGS OPTIMIZER * |
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!* (A VARIABLE METRIC METHOD) * |
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!* * |
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!* WRITTEN BY PETER L. CUMMINS, UNIVERSITY OF SYDNEY, AUSTRALIA * |
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!* * |
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!* REFERENCE * |
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!* * |
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!* "COMPUTATIONAL STRATEGIES FOR THE OPTIMIZATION OF EQUILIBRIUM * |
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!* GEOMETRIES AND TRANSITION-STATE STRUCTURES AT THE SEMIEMPIRICAL * |
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!* LEVEL", PETER L. CUMMINS, JILL E. GREADY, J. COMP. CHEM., 10, * |
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!* 939-950 (1989). * |
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!* * |
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!* MODIFIED BY JJPS TO CONFORM TO EXISTING MOPAC CONVENTIONS * |
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!* * |
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!************************************************************************ |
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|
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! MRESET = maximum number of iterations. |
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INTEGER(KINT), PARAMETER :: MRESET=15, M2=(MRESET+1)*(MRESET+1) !M2 = 256 |
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REAL(KREAL), ALLOCATABLE, SAVE :: GeomSet(:,:),GradSet(:,:),ERR(:,:) ! MRESET*NCoord |
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REAL(KREAL), SAVE :: ESET(MRESET) |
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REAL(KREAL), ALLOCATABLE, SAVE :: DXTMP(:,:),GSAVE(:,:) !NCoord, why DXTMP has SAVE attribute?? |
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REAL(KREAL) :: B(M2),BS(M2),BST(M2) |
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LOGICAL DEBUG, PRINT |
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INTEGER(KINT), ALLOCATABLE, SAVE :: MSET(:) |
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LOGICAL, ALLOCATABLE, SAVE :: FRST(:) |
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INTEGER(KINT) :: NDIIS, MPLUS, INV, ITERA, MM, NFree, I, J, K |
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INTEGER(KINT) :: JJ, KJ, JNV, II, IONE, IJ, INK,ITmp, Isch, Idx |
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REAL(KREAL) :: XMax, XNorm, S, DET, THRES, Norm |
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REAL(KREAL), PARAMETER :: eps=1e-12 |
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REAL(KREAL), PARAMETER :: crit=1e-8 |
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REAL(KREAL), ALLOCATABLE :: Tanf(:) ! NCoord |
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REAL(KREAL), ALLOCATABLE :: HFree(:) ! NFree*NFree |
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REAL(KREAL), ALLOCATABLE :: Htmp(:,:) ! NCoord,NFree |
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REAL(KREAL), ALLOCATABLE :: Grad_free(:),Grad_new_free_inter(:),Step_free(:) ! NFree |
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REAL(KREAL), ALLOCATABLE :: Geom_free(:),Geom_new_free_inter(:),Geom_new_free(:) ! NFree |
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REAL(KREAL), ALLOCATABLE, SAVE :: GeomSet_free(:,:),GradSet_free(:,:) |
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|
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DEBUG=.TRUE. |
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PRINT=.TRUE. |
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|
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IF (PRINT) WRITE(*,'(/,'' BEGIN GDIIS '')') |
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|
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! Initialization |
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IF (allocation_flag) THEN ! allocation_flag = .TRUE. at the begining and effective for all geometries in path. |
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! FRST(IGeom) will be set to False in Space, so no need to modify it here |
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IF (ALLOCATED(GeomSet)) THEN |
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IF (PRINT) WRITE(*,'(/,'' In FRST, GDIIS Dealloc '')') |
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DEALLOCATE(GeomSet,GradSet,ERR,DXTMP,GSave,GeomSet_free,GradSet_free) |
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RETURN |
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ELSE |
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! these allocated arrays need to be properly deallocated. |
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IF (PRINT) WRITE(*,'(/,'' In FRST, GDIIS Alloc '')') |
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ALLOCATE(GeomSet(NGeomF,MRESET*NCoord),GradSet(NGeomF,MRESET*NCoord),ERR(NGeomF,MRESET*NCoord)) |
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ALLOCATE(GeomSet_free(NGeomF,MRESET*NCoord),GradSet_free(NGeomF,MRESET*NCoord)) |
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ALLOCATE(DXTMP(NGeomF,NCoord),GSAVE(NGeomF,NCoord),MSET(NGeomF),FRST(NGeomF)) |
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DO I=1,NGeomF |
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FRST(I) = .TRUE. |
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GeomSet(I,:) = 0.d0 |
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GradSet(I,:) = 0.d0 |
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ERR(I,:) = 0.d0 |
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GeomSet_free(I,:) = 0.d0 |
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GradSet_free(I,:) = 0.d0 |
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DXTMP(I,:)=0.d0 |
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GSAVE(I,:)=0.d0 |
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END DO |
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MSET(:)=0 |
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END IF |
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allocation_flag = .FALSE. |
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END IF |
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|
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! Addded from here: |
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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 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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|
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! We normalize Tangent |
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Tangent=Tangent/Norm |
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|
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! We convert Tangent into Vfree only displacements. This is useless for now (2007.Apr.23) |
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! as Vfree=Id matrix 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 subtract 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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|
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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 subtract the first vectors, 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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|
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Print *, 'Idx=', Idx |
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IF (Idx/= NCoord-1) 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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|
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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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|
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if (debug) WRITE(*,*) 'DBG Step_DIIS_All, IGeom, NFree=', IGeom, NFree |
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|
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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_free(NFree),Grad_new_free_inter(NFree)) |
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ALLOCATE(Geom_free(NFree),Step_free(NFree),Geom_new_free_inter(NFree),Geom_new_free(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-1)*NCoord)+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-1)*NFree))=0.d0 |
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DO K=1,NCoord |
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HFree(I+((J-1)*NFree))=HFree(I+((J-1)*NFree))+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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|
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DO I=1,NFree |
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Grad_free(I)=dot_product(reshape(Vfree(:,I),(/NCoord/)),Grad) |
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Geom_free(I)=dot_product(reshape(Vfree(:,I),(/NCoord/)),Geom) |
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END DO |
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!Added Ends here.*********************************************** |
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|
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!C SPACE SIMPLY LOADS THE CURRENT VALUES OF Geom AND GRAD INTO |
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!C THE ARRAYS GeomSet AND GradSet |
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!C HEAT is never used, not even in Space_all(...) |
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|
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CALL Space_all(NGeomF,IGeom,MRESET,MSET,Geom,Grad,HEAT,NCoord,GeomSet,GradSet,ESET,FRST) |
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|
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IF (PRINT) WRITE(*,'(/,'' GDIIS after Space '')') |
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|
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DO J=1,MSet(IGeom) |
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DO K=1,NFree |
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GradSet_free(IGeom,((J-1)*NFree)+K)=dot_product(reshape(Vfree(:,K),(/NCoord/)),& |
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GradSet(IGeom,((J-1)*NCoord)+1:((J-1)*NCoord)+NCoord)) |
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GeomSet_free(IGeom,((J-1)*NFree)+K)=dot_product(reshape(Vfree(:,K),(/NCoord/)),& |
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GeomSet(IGeom,((J-1)*NCoord)+1:((J-1)*NCoord)+NCoord)) |
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END DO |
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END DO |
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!C |
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!C INITIALIZE SOME VARIABLES AND CONSTANTS |
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!C |
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NDIIS = MSET(IGeom) |
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MPLUS = MSET(IGeom) + 1 |
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MM = MPLUS * MPLUS |
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!C |
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!C COMPUTE THE APPROXIMATE ERROR VECTORS |
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!C |
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INV=-NFree |
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DO 30 I=1,MSET(IGeom) |
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INV = INV + NFree |
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DO 30 J=1,NFree |
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S = 0.D0 |
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KJ=(J*(J-1))/2 |
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DO 10 K=1,J |
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KJ = KJ+1 |
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10 S = S - HFree(KJ) * GradSet_free(IGeom,INV+K) |
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DO 20 K=J+1,NFree |
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KJ = (K*(K-1))/2+J |
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20 S = S - HFree(KJ) * GradSet_free(IGeom,INV+K) |
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30 ERR(IGeom,INV+J) = S |
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|
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!C |
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!C CONSTRUCT THE GDIIS MATRIX |
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!C |
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DO 40 I=1,MM |
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40 B(I) = 1.D0 |
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|
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JJ=0 |
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INV=-NFree |
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DO 50 I=1,MSET(IGeom) |
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INV=INV+NFree |
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JNV=-NFree |
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DO 50 J=1,MSET(IGeom) |
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JNV=JNV+NFree |
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JJ = JJ + 1 |
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B(JJ)=0.D0 |
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DO 50 K=1,NFree |
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!Print *, 'B(',JJ,')=', B(JJ) + ERR(IGeom,INV+K) * ERR(IGeom,JNV+K)
|
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50 B(JJ) = B(JJ) + ERR(IGeom,INV+K) * ERR(IGeom,JNV+K) |
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|
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! The following shifting is required to correct indices of B_ij elements in the GDIIS matrix. |
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! The correction is needed because the last coloumn of the matrix contains all 1 and one zero. |
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DO 60 I=MSET(IGeom)-1,1,-1 |
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DO 60 J=MSET(IGeom),1,-1 |
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60 B(I*MSET(IGeom)+J+I) = B(I*MSET(IGeom)+J) |
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|
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! For the last row and last column of GEDIIS matrix: |
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DO 70 I=1,MPLUS |
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B(MPLUS*I) = 1.D0 |
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70 B(MPLUS*MSET(IGeom)+I) = 1.D0 |
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B(MM) = 0.D0 |
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!C |
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!C ELIMINATE ERROR VECTORS WITH THE LARGEST NORM |
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!C |
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80 CONTINUE |
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DO 90 I=1,MM |
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90 BS(I) = B(I) |
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|
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IF (NDIIS .EQ. MSET(IGeom)) GO TO 140 |
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DO 130 II=1,MSET(IGeom)-NDIIS |
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XMAX = -1.D10 |
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ITERA = 0 |
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DO 110 I=1,MSET(IGeom) |
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XNORM = 0.D0 |
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INV = (I-1) * MPLUS |
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DO 100 J=1,MSET(IGeom) |
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100 XNORM = XNORM + ABS(B(INV + J)) |
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IF (XMAX.LT.XNORM .AND. XNORM.NE.1.0D0) THEN |
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XMAX = XNORM |
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ITERA = I |
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IONE = INV + I |
| 292 |
ENDIF |
| 293 |
110 CONTINUE |
| 294 |
|
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DO 120 I=1,MPLUS |
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INV = (I-1) * MPLUS |
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DO 120 J=1,MPLUS |
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JNV = (J-1) * MPLUS |
| 299 |
IF (J.EQ.ITERA) B(INV + J) = 0.D0 |
| 300 |
B(JNV + I) = B(INV + J) |
| 301 |
!Print *,'B(JNV + I)=',B(JNV + I) |
| 302 |
120 CONTINUE |
| 303 |
B(IONE) = 1.0D0 |
| 304 |
130 CONTINUE |
| 305 |
140 CONTINUE |
| 306 |
!C |
| 307 |
!C OUTPUT THE GDIIS MATRIX |
| 308 |
!C |
| 309 |
IF (DEBUG) THEN |
| 310 |
WRITE(*,'(/5X,'' GDIIS MATRIX'')') |
| 311 |
ITmp=min(12,MPLUS) |
| 312 |
DO IJ=1,MPLUS |
| 313 |
WRITE(*,'(12(F12.4,1X))') B((IJ-1)*MPLUS+1:(IJ-1)*MPLUS+ITmp) |
| 314 |
END DO |
| 315 |
ENDIF |
| 316 |
!C |
| 317 |
!C SCALE DIIS MATRIX BEFORE INVERSION |
| 318 |
!C |
| 319 |
DO 160 I=1,MPLUS |
| 320 |
II = MPLUS * (I-1) + I |
| 321 |
!Print *, 'B(',II,')=', B(II)
|
| 322 |
!Print *, 'GSave(',IGeom,',',I,')=', 1.D0 / DSQRT(1.D-20+DABS(B(II)))
|
| 323 |
160 GSAVE(IGeom,I) = 1.D0 / DSQRT(1.D-20+DABS(B(II))) |
| 324 |
|
| 325 |
GSAVE(IGeom,MPLUS) = 1.D0 |
| 326 |
!Print *, 'GSave(',IGeom,',',MPlus,')=1.D0'
|
| 327 |
|
| 328 |
DO 170 I=1,MPLUS |
| 329 |
DO 170 J=1,MPLUS |
| 330 |
IJ = MPLUS * (I-1) + J |
| 331 |
170 B(IJ) = B(IJ) * GSAVE(IGeom,I) * GSAVE(IGeom,J) |
| 332 |
!C |
| 333 |
!C OUTPUT SCALED GDIIS MATRIX |
| 334 |
!C |
| 335 |
IF (DEBUG) THEN |
| 336 |
WRITE(*,'(/5X,'' GDIIS MATRIX (SCALED)'')') |
| 337 |
ITmp=min(12,MPLUS) |
| 338 |
DO IJ=1,MPLUS |
| 339 |
WRITE(*,'(12(F12.4,1X))') B((IJ-1)*MPLUS+1:(IJ-1)*MPLUS+ITmp) |
| 340 |
END DO |
| 341 |
ENDIF |
| 342 |
!C |
| 343 |
!C INVERT THE GDIIS MATRIX B |
| 344 |
!C |
| 345 |
CALL MINV(B,MPLUS,DET) ! matrix inversion. |
| 346 |
|
| 347 |
DO 190 I=1,MPLUS |
| 348 |
DO 190 J=1,MPLUS |
| 349 |
IJ = MPLUS * (I-1) + J |
| 350 |
!Print *, 'B(',IJ,')=', B(IJ)
|
| 351 |
!Print *, 'GSAVE(',IGeom,',',I,')=', GSAVE(IGeom,I)
|
| 352 |
!Print *, 'GSAVE(',IGeom,',',J,')=', GSAVE(IGeom,J)
|
| 353 |
!Print *, 'B(',IJ,')=', B(IJ) * GSAVE(I) * GSAVE(J)
|
| 354 |
190 B(IJ) = B(IJ) * GSAVE(IGeom,I) * GSAVE(IGeom,J) |
| 355 |
!C |
| 356 |
!C COMPUTE THE INTERMEDIATE INTERPOLATED PARAMETER AND GRADIENT VECTORS |
| 357 |
!C |
| 358 |
!Print *, 'MSET(',IGeom,')=', MSET(IGeom), ' MPLUS=', MPLUS
|
| 359 |
DO 200 K=1,NFree |
| 360 |
Geom_new_free_inter(K) = 0.D0 |
| 361 |
Grad_new_free_inter(K) = 0.D0 |
| 362 |
DO 200 I=1,MSET(IGeom) |
| 363 |
INK = (I-1) * NFree + K |
| 364 |
Geom_new_free_inter(K) = Geom_new_free_inter(K) + B(MPLUS*MSET(IGeom)+I) * GeomSet_free(IGeom,INK) |
| 365 |
!Print *, 'Geom_new_free_inter(',K,')=', Geom_new_free_inter(K)
|
| 366 |
!Print *, 'B(MPLUS*MSET(',IGeom,')+',I,')=', B(MPLUS*MSET(IGeom)+I)
|
| 367 |
!Print *, 'GeomSet_free(',IGeom,',',INK,')=', GeomSet_free(IGeom,INK)
|
| 368 |
200 Grad_new_free_inter(K) = Grad_new_free_inter(K) + B(MPLUS*MSET(IGeom)+I) * GradSet_free(IGeom,INK) |
| 369 |
HP=0.D0 |
| 370 |
DO 210 I=1,MSET(IGeom) |
| 371 |
210 HP=HP+B(MPLUS*MSET(IGeom)+I)*ESET(I) |
| 372 |
DO 220 K=1,NFree |
| 373 |
220 DXTMP(IGeom,K) = Geom_free(K) - Geom_new_free_inter(K) |
| 374 |
XNORM = SQRT(DOT_PRODUCT(DXTMP(IGeom,1:NFree),DXTMP(IGeom,1:NFree))) |
| 375 |
IF (PRINT) THEN |
| 376 |
WRITE (6,'(/10X,''DEVIATION IN X '',F10.6, 8X,''DETERMINANT '',G9.3)') XNORM,DET |
| 377 |
WRITE(*,'(10X,''GDIIS COEFFICIENTS'')') |
| 378 |
WRITE(*,'(10X,5F12.5)') (B(MPLUS*MSET(IGeom)+I),I=1,MSET(IGeom)) |
| 379 |
ENDIF |
| 380 |
|
| 381 |
!C THE FOLLOWING TOLERENCES FOR XNORM AND DET ARE SOMEWHAT ARBITRARY! |
| 382 |
THRES = MAX(10.D0**(-NFree), 1.D-25) |
| 383 |
IF (XNORM.GT.2.D0 .OR. DABS(DET).LT. THRES) THEN |
| 384 |
IF (PRINT)THEN |
| 385 |
WRITE(*,*) "THE DIIS MATRIX IS ILL CONDITIONED" |
| 386 |
WRITE(*,*) " - PROBABLY, VECTORS ARE LINEARLY DEPENDENT - " |
| 387 |
WRITE(*,*) "THE DIIS STEP WILL BE REPEATED WITH A SMALLER SPACE" |
| 388 |
END IF |
| 389 |
DO 230 K=1,MM |
| 390 |
230 B(K) = BS(K) |
| 391 |
NDIIS = NDIIS - 1 |
| 392 |
IF (NDIIS .GT. 0) GO TO 80 |
| 393 |
IF (PRINT) WRITE(*,'(10X,''NEWTON-RAPHSON STEP TAKEN'')') |
| 394 |
DO 240 K=1,NFree |
| 395 |
Geom_new_free_inter(K) = Geom_free(K) |
| 396 |
240 Grad_new_free_inter(K) = Grad_free(K) |
| 397 |
ENDIF ! matches IF (XNORM.GT.2.D0 .OR. DABS(DET).LT. THRES) THEN, L378 |
| 398 |
|
| 399 |
! q_{m+1} = q'_{m+1} - H^{-1}g'_{m+1}
|
| 400 |
Geom_new_free=0.d0 |
| 401 |
DO I = 1, NFree |
| 402 |
DO J = 1, NFree |
| 403 |
! If Hinv=.False., then we need to invert Hess |
| 404 |
!Geom_new_free(:) = Geom_new_free(:) + HFree(:,I)*Grad_new_free_inter(I) |
| 405 |
Geom_new_free(J) = Geom_new_free(J) + HFree(I+((J-1)*NFree))*Grad_new_free_inter(I) |
| 406 |
END DO |
| 407 |
END DO |
| 408 |
Geom_new_free(:) = Geom_new_free_inter(:) - Geom_new_free(:) |
| 409 |
|
| 410 |
Step_free = Geom_new_free - Geom_free |
| 411 |
|
| 412 |
Step = 0.d0 |
| 413 |
DO I=1,NFree |
| 414 |
Step = Step + Step_free(I)*Vfree(:,I) |
| 415 |
END DO |
| 416 |
|
| 417 |
DEALLOCATE(Hfree,Htmp,Grad_free,Grad_new_free_inter,Step_free,Geom_free) |
| 418 |
DEALLOCATE(Geom_new_free_inter,Geom_new_free) |
| 419 |
|
| 420 |
IF (PRINT) WRITE(*,'(/,'' END GDIIS '',/)') |
| 421 |
|
| 422 |
END SUBROUTINE Step_diis_all |