root / src / Step_DIIS.f90 @ 6
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!C HEAT is never used, not even in call of Space(...) |
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!C XPARAM = input parameter vector (Geometry). |
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!C Grad = input gradient vector. |
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SUBROUTINE Step_DIIS(XP,XPARAM,GP,GRAD,HP,HEAT,Hess,NVAR,FRST) |
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!SUBROUTINE DIIS(XPARAM,STEP,GRAD,HP,HEAT,Hess,NVAR,FRST) |
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! IMPLICIT DOUBLE PRECISION (A-H,O-Z) |
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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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! INCLUDE 'SIZES' |
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|
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INTEGER(KINT) :: NVAR |
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REAL(KREAL) :: XP(NVAR), XPARAM(NVAR), GP(NVAR), GRAD(NVAR), Hess(NVAR*NVAR) |
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!REAL(KREAL) :: Hess_inv(NVAR,NVAR),XPARAM_old(NVAR),STEP(NVAR) |
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REAL(KREAL) :: HEAT, HP |
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LOGICAL :: FRST |
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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 XPARAM(NEW) = XPARAM' - HG' * |
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!* * |
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!* WHERE XPARAM' = SUM(C(I)XPARAM(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 = 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 :: XSET(:),GSET(:),ERR(:) ! MRESET*NVAR |
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REAL(KREAL) :: ESET(MRESET) |
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REAL(KREAL), ALLOCATABLE, SAVE :: DX(:),GSAVE(:) !NVAR |
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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), SAVE :: MSET |
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INTEGER(KINT) :: NDIIS, MPLUS, INV, ITERA, MM |
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INTEGER(KINT) :: I,J,K, JJ, KJ, JNV, II, IONE, IJ, INK,ITmp |
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REAL(KREAL) :: XMax, XNorm, S, DET, THRES |
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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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!XPARAM_old = XPARAM |
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|
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! Initialization |
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IF (FRST) THEN |
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! FRST will be set to False in Space, so no need to modify it here |
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IF (ALLOCATED(XSET)) THEN |
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IF (PRINT) WRITE(*,'(/,'' In FRST, GDIIS Dealloc '')') |
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DEALLOCATE(XSet,GSET,ERR,DX,GSave) |
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RETURN |
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ELSE |
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IF (PRINT) WRITE(*,'(/,'' In FRST, GDIIS alloc '')') |
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ALLOCATE(XSet(MRESET*NVAR), GSet(MRESET*NVAR), ERR(MRESET*NVAR)) |
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ALLOCATE(DX(NVAR),GSAVE(NVAR)) |
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END IF |
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END IF |
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!C |
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!C SPACE SIMPLY LOADS THE CURRENT VALUES OF XPARAM AND GRAD INTO |
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!C THE ARRAYS XSET AND GSET |
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!C |
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!C HEAT is never used, not even in Space(...) |
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CALL SPACE(MRESET,MSET,XPARAM,GRAD,HEAT,NVAR,XSET,GSET,ESET,FRST) |
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|
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IF (PRINT) WRITE(*,'(/,'' GDIIS after Space '')') |
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! INITIALIZE SOME VARIABLES AND CONSTANTS: |
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NDIIS = MSET |
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MPLUS = MSET + 1 |
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MM = MPLUS * MPLUS |
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|
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! COMPUTE THE APPROXIMATE ERROR VECTORS: |
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INV=-NVAR |
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DO 30 I=1,MSET |
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INV = INV + NVAR |
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DO 30 J=1,NVAR |
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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 - Hess(KJ) * GSET(INV+K) |
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DO 20 K=J+1,NVAR |
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KJ = (K*(K-1))/2+J |
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20 S = S - Hess(KJ) * GSET(INV+K) |
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30 ERR(INV+J) = S |
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! CONSTRUCT THE GDIIS MATRIX: |
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! initialization (not really needed) |
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DO I=1,MM |
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B(I) = 1.D0 |
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END DO |
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|
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! B_ij calculations from <e_i|e_j> |
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JJ=0 |
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INV=-NVAR |
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DO 50 I=1,MSET |
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INV=INV+NVAR |
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JNV=-NVAR |
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DO 50 J=1,MSET |
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JNV=JNV+NVAR |
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JJ = JJ + 1 |
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B(JJ)=0.D0 |
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DO 50 K=1,NVAR |
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50 B(JJ) = B(JJ) + ERR(INV+K) * ERR(JNV+K) |
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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-1,1,-1 |
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DO 60 J=MSET,1,-1 |
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60 B(I*MSET+J+I) = B(I*MSET+J) |
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! For last row and last column of GDIIS 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+I) = 1.D0 |
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B(MM) = 0.D0 |
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|
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! ELIMINATE ERROR VECTORS WITH THE LARGEST NORM: |
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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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IF (NDIIS .EQ. MSET) GO TO 140 |
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DO 130 II=1,MSET-NDIIS |
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XMAX = -1.D10 |
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ITERA = 0 |
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DO 110 I=1,MSET |
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XNORM = 0.D0 |
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INV = (I-1) * MPLUS |
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DO 100 J=1,MSET |
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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 |
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ENDIF |
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110 CONTINUE |
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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 |
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IF (J.EQ.ITERA) B(INV + J) = 0.D0 |
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B(JNV + I) = B(INV + J) |
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120 CONTINUE |
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B(IONE) = 1.0D0 |
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130 CONTINUE |
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140 CONTINUE |
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|
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IF (DEBUG) THEN |
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|
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! OUTPUT THE GDIIS MATRIX: |
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WRITE(*,'(/5X,'' GDIIS MATRIX'')') |
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ITmp=min(12,MPLUS) |
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DO IJ=1,MPLUS |
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WRITE(*,'(12(F10.4,1X))') B((IJ-1)*MPLUS+1:(IJ-1)*MPLUS+ITmp) |
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END DO |
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ENDIF |
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! SCALE DIIS MATRIX BEFORE INVERSION: |
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|
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DO I=1,MPLUS |
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II = MPLUS * (I-1) + I |
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GSAVE(I) = 1.D0 / DSQRT(1.D-20+DABS(B(II))) |
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END DO |
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|
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GSAVE(MPLUS) = 1.D0 |
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DO I=1,MPLUS |
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DO J=1,MPLUS |
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IJ = MPLUS * (I-1) + J |
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B(IJ) = B(IJ) * GSAVE(I) * GSAVE(J) |
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END DO |
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END DO |
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IF (DEBUG) THEN |
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! OUTPUT SCALED GDIIS MATRIX: |
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WRITE(*,'(/5X,'' GDIIS MATRIX (SCALED)'')') |
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ITmp=min(12,MPLUS) |
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DO IJ=1,MPLUS |
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WRITE(*,'(12(F10.4,1X))') B((IJ-1)*MPLUS+1:(IJ-1)*MPLUS+ITmp) |
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END DO |
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ENDIF ! matches IF (DEBUG) THEN |
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! INVERT THE GDIIS MATRIX B: |
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CALL MINV(B,MPLUS,DET) ! matrix inversion. |
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DO I=1,MPLUS |
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DO J=1,MPLUS |
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IJ = MPLUS * (I-1) + J |
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B(IJ) = B(IJ) * GSAVE(I) * GSAVE(J) |
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END DO |
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END DO |
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|
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! COMPUTE THE INTERMEDIATE INTERPOLATED PARAMETER AND GRADIENT VECTORS: |
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DO K=1,NVAR |
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XP(K) = 0.D0 |
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GP(K) = 0.D0 |
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DO I=1,MSET |
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INK = (I-1) * NVAR + K |
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!Print *, 'B(',MPLUS*MSET+I,')=', B(MPLUS*MSET+I)
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XP(K) = XP(K) + B(MPLUS*MSET+I) * XSET(INK) |
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GP(K) = GP(K) + B(MPLUS*MSET+I) * GSET(INK) |
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END DO |
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END DO |
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HP=0.D0 |
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DO I=1,MSET |
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HP=HP+B(MPLUS*MSET+I)*ESET(I) |
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END DO |
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|
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DO K=1,NVAR |
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DX(K) = XPARAM(K) - XP(K) |
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END DO |
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XNORM = SQRT(DOT_PRODUCT(DX,DX)) |
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IF (PRINT) THEN |
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WRITE (6,'(/10X,''DEVIATION IN X '',F7.4,8X,''DETERMINANT '',G9.3)') XNORM,DET |
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WRITE(*,'(10X,''GDIIS COEFFICIENTS'')') |
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WRITE(*,'(10X,5F12.5)') (B(MPLUS*MSET+I),I=1,MSET) |
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ENDIF |
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|
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! THE FOLLOWING TOLERENCES FOR XNORM AND DET ARE SOMEWHAT ARBITRARY! |
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THRES = MAX(10.D0**(-NVAR), 1.D-25) |
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IF (XNORM.GT.2.D0 .OR. DABS(DET).LT. THRES) THEN |
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IF (PRINT)THEN |
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WRITE(*,*) "THE DIIS MATRIX IS ILL CONDITIONED" |
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WRITE(*,*) " - PROBABLY, VECTORS ARE LINEARLY DEPENDENT - " |
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WRITE(*,*) "THE DIIS STEP WILL BE REPEATED WITH A SMALLER SPACE" |
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END IF |
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DO K=1,MM |
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B(K) = BS(K) |
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END DO |
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NDIIS = NDIIS - 1 |
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IF (NDIIS .GT. 0) GO TO 80 |
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IF (PRINT) WRITE(*,'(10X,''NEWTON-RAPHSON STEP TAKEN'')') |
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DO K=1,NVAR |
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XP(K) = XPARAM(K) |
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GP(K) = GRAD(K) |
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END DO |
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ENDIF ! matches IF (XNORM.GT.2.D0 .OR. DABS(DET).LT. THRES) THEN |
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|
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! q_{m+1} = q'_{m+1} - H^{-1}g'_{m+1}
|
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! Hess is a symmetric matrix. |
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!Hess_inv = 1.d0 ! to be deleted. |
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!Call GenInv(NVAR,Reshape(Hess,(/NVAR,NVAR/)),Hess_inv,NVAR) ! Implemented in Mat_util.f90 |
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! H^{-1}g'_{m+1}
|
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!Print *, 'Hess_inv=' |
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!Print *, Hess_inv |
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!XPARAM=0.d0 |
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!DO I=1, NVAR |
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!XPARAM(:) = XPARAM(:) + Hess_inv(:,I)*GP(I) |
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!END DO |
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!XPARAM(:) = XP(:) - XPARAM(:) ! now XPARAM is a new geometry. |
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|
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!STEP is the difference between the new and old geometry and thus "step": |
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!STEP = XPARAM - XPARAM_old |
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|
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IF (PRINT) WRITE(*,'(/,'' END GDIIS '',/)') |
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|
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END SUBROUTINE Step_DIIS |