root / src / Step_GDIIS_Simple_Err.f90 @ 7
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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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SUBROUTINE Step_GDIIS_Simple_Err(NewGeom,Geom,NewGrad,GRAD,HP,HEAT,Hess,NCoord,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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|
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! INCLUDE 'SIZES' |
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|
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INTEGER(KINT) :: NCoord |
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REAL(KREAL) :: NewGeom(NCoord), Geom(NCoord), NewGrad(NCoord), GRAD(NCoord), Hess(NCoord*NCoord) |
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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 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 = 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) :: ESET(MRESET) |
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REAL(KREAL), ALLOCATABLE, SAVE :: DX(:), GSAVE(:) !NCoord |
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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, I, J, K |
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INTEGER(KINT) :: 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 Step_GDIIS_Simple_Err '')') |
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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(GeomSet)) THEN |
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IF (PRINT) WRITE(*,'(/,'' In FRST, Step_GDIIS_Simple_Err Dealloc '')') |
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DEALLOCATE(GeomSet,GradSet,ERR,DX,GSave) |
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RETURN |
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ELSE |
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IF (PRINT) WRITE(*,'(/,'' In FRST, Step_GDIIS_Simple_Err alloc '')') |
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ALLOCATE(GeomSet(MRESET*NCoord), GradSet(MRESET*NCoord), ERR(MRESET*NCoord)) |
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ALLOCATE(DX(NCoord),GSAVE(NCoord)) |
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END IF |
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END IF |
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|
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! SPACE SIMPLY LOADS THE CURRENT VALUES OF Geom AND GRAD INTO THE ARRAYS GeomSet AND GradSet |
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! HEAT is never used, not even in Space(...) |
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CALL SPACE(MRESET,MSET,Geom,Grad,HEAT,NCoord,GeomSet,GradSet,ESET,FRST) |
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|
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IF (PRINT) WRITE(*,'(/,'' Step_GDIIS_Simple_Err after Space '')') |
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|
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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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! CONSTRUCT THE GDIIS MATRIX: |
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! B_ij calculations from <B_ij=(g_i-g_j)(R_i-R_j)> |
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JJ=0 |
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INV=-NCoord |
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DO I=1,MSET |
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INV=INV+NCoord |
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JNV=-NCoord |
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DO J=1,MSET |
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JNV=JNV+NCoord |
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JJ = JJ + 1 |
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B(JJ)=0.D0 |
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DO K=1, NCoord |
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B(JJ) = B(JJ) + (((GradSet(INV+K)-GradSet(JNV+K))*(GeomSet(INV+K)-GeomSet(JNV+K)))/2.D0) |
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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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! 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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|
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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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! OUTPUT THE GDIIS MATRIX: |
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WRITE(*,'(/5X,'' Step_GDIIS_Simple_Err 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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|
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! SCALE DIIS MATRIX BEFORE INVERSION: |
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DO 160 I=1,MPLUS |
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II = MPLUS * (I-1) + I |
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160 GSAVE(I) = 1.D0 / DSQRT(1.D-20+DABS(B(II))) |
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GSAVE(MPLUS) = 1.D0 |
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DO 170 I=1,MPLUS |
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DO 170 J=1,MPLUS |
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IJ = MPLUS * (I-1) + J |
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170 B(IJ) = B(IJ) * GSAVE(I) * GSAVE(J) |
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|
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IF (DEBUG) THEN |
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! OUTPUT SCALED GDIIS MATRIX: |
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WRITE(*,'(/5X,'' Step_GDIIS_Simple_Err 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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|
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ENDIF ! matches IF (DEBUG) THEN |
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|
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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 190 I=1,MPLUS |
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DO 190 J=1,MPLUS |
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IJ = MPLUS * (I-1) + J |
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190 B(IJ) = B(IJ) * GSAVE(I) * GSAVE(J) |
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! COMPUTE THE INTERMEDIATE INTERPOLATED PARAMETER AND GRADIENT VECTORS: |
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DO 200 K=1,NCoord |
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NewGeom(K) = 0.D0 |
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NewGrad(K) = 0.D0 |
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DO 200 I=1,MSET |
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INK = (I-1) * NCoord + K |
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!Print *, 'B(',MPLUS*MSET+I,')=', B(MPLUS*MSET+I)
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NewGeom(K) = NewGeom(K) + B(MPLUS*MSET+I) * GeomSet(INK) |
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200 NewGrad(K) = NewGrad(K) + B(MPLUS*MSET+I) * GradSet(INK) |
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HP=0.D0 |
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DO 210 I=1,MSET |
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210 HP=HP+B(MPLUS*MSET+I)*ESET(I) |
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DO 220 K=1,NCoord |
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220 DX(K) = Geom(K) - NewGeom(K) |
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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,''Step_GDIIS_Simple_Err 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**(-NCoord), 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 230 K=1,MM |
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230 B(K) = BS(K) |
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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 240 K=1,NCoord |
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NewGeom(K) = Geom(K) |
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240 NewGrad(K) = GRAD(K) |
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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(NCoord,Reshape(Hess,(/NCoord,NCoord/)),Hess_inv,NCoord) ! 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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!Geom=0.d0 |
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!DO I=1, NCoord |
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! Geom(:) = Geom(:) + Hess_inv(:,I)*NewGrad(I) |
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!END DO |
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!Geom(:) = NewGeom(:) - Geom(:) ! now Geom 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 = Geom - Geom_old |
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IF (PRINT) WRITE(*,'(/,'' END Step_GDIIS_Simple_Err '',/)') |
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|
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END SUBROUTINE Step_GDIIS_Simple_Err |