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SUBROUTINE DIIS(XP, XPARAM, GP, GRAD, HP, HEAT, HS, NVAR, FRST)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
DIMENSION XP(NVAR), XPARAM(NVAR), GP(NVAR),
1GRAD(NVAR), HS(NVAR*NVAR)
LOGICAL FRST
************************************************************************
* *
* DIIS PERFORMS DIRECT INVERSION IN THE ITERATIVE SUBSPACE *
* *
* THIS INVOLVES SOLVING FOR C IN XPARAM(NEW) = XPARAM' - HG' *
* *
* WHERE XPARAM' = SUM(C(I)XPARAM(I), THE C COEFFICIENTES COMING FROM *
* *
* | B 1 | . | C | = | 0 | *
* | 1 0 | |-L | | 1 | *
* *
* WHERE B(I,J) =GRAD(I)H(T)HGRAD(J) GRAD(I) = GRADIENT ON CYCLE I *
* H = INVERSE HESSIAN *
* *
* REFERENCE *
* *
* P. CSASZAR, P. PULAY, J. MOL. STRUCT. (THEOCHEM), 114, 31 (1984) *
* *
************************************************************************
************************************************************************
* *
* GEOMETRY OPTIMIZATION USING THE METHOD OF DIRECT INVERSION IN *
* THE ITERATIVE SUBSPACE (GDIIS), COMBINED WITH THE BFGS OPTIMIZER *
* (A VARIABLE METRIC METHOD) *
* *
* WRITTEN BY PETER L. CUMMINS, UNIVERSITY OF SYDNEY, AUSTRALIA *
* *
* REFERENCE *
* *
* "COMPUTATIONAL STRATEGIES FOR THE OPTIMIZATION OF EQUILIBRIUM *
* GEOMETRIES AND TRANSITION-STATE STRUCTURES AT THE SEMIEMPIRICAL *
* LEVEL", PETER L. CUMMINS, JILL E. GREADY, J. COMP. CHEM., 10, *
* 939-950 (1989). *
* *
* MODIFIED BY JJPS TO CONFORM TO EXISTING MOPAC CONVENTIONS *
* *
************************************************************************
COMMON /KEYWRD/ KEYWRD
PARAMETER (MRESET=15, M2=(MRESET+1)*(MRESET+1))
DIMENSION XSET(MRESET*MAXPAR),GSET(MRESET*MAXPAR), ESET(MRESET)
DIMENSION DX(MAXPAR),GSAVE(MAXPAR),
1 ERR(MRESET*MAXPAR),B(M2),BS(M2),BST(M2)
LOGICAL DEBUG, PRINT
CHARACTER*241 KEYWRD
DEBUG=.FALSE.
PRINT=(INDEX(KEYWRD,' DIIS').NE.0)
IF (PRINT) DEBUG=(INDEX(KEYWRD,'DEBUG').NE.0)
IF (PRINT) WRITE(6,'(/,'' ***** BEGIN GDIIS ***** '')')
C
C SPACE SIMPLY LOADS THE CURRENT VALUES OF XPARAM AND GNORM INTO
C THE ARRAYS XSET AND GSET
C
CALL SPACE(MRESET,MSET,XPARAM, GRAD, HEAT, NVAR, XSET, GSET, ESET
1, FRST)
C
C INITIALIZE SOME VARIABLES AND CONSTANTS
C
NDIIS = MSET
MPLUS = MSET + 1
MM = MPLUS * MPLUS
C
C COMPUTE THE APPROXIMATE ERROR VECTORS
C
INV=-NVAR
DO 30 I=1,MSET
INV = INV + NVAR
DO 30 J=1,NVAR
S = 0.D0
KJ=(J*(J-1))/2
DO 10 K=1,J
KJ = KJ+1
10 S = S - HS(KJ) * GSET(INV+K)
DO 20 K=J+1,NVAR
KJ = (K*(K-1))/2+J
20 S = S - HS(KJ) * GSET(INV+K)
30 ERR(INV+J) = S
C
C CONSTRUCT THE GDIIS MATRIX
C
DO 40 I=1,MM
40 B(I) = 1.D0
JJ=0
INV=-NVAR
DO 50 I=1,MSET
INV=INV+NVAR
JNV=-NVAR
DO 50 J=1,MSET
JNV=JNV+NVAR
JJ = JJ + 1
B(JJ)=0.D0
DO 50 K=1,NVAR
50 B(JJ) = B(JJ) + ERR(INV+K) * ERR(JNV+K)
C
DO 60 I=MSET-1,1,-1
DO 60 J=MSET,1,-1
60 B(I*MSET+J+I) = B(I*MSET+J)
DO 70 I=1,MPLUS
B(MPLUS*I) = 1.D0
70 B(MPLUS*MSET+I) = 1.D0
B(MM) = 0.D0
C
C ELIMINATE ERROR VECTORS WITH THE LARGEST NORM
C
80 CONTINUE
DO 90 I=1,MM
90 BS(I) = B(I)
IF (NDIIS .EQ. MSET) GO TO 140
DO 130 II=1,MSET-NDIIS
XMAX = -1.D10
ITERA = 0
DO 110 I=1,MSET
XNORM = 0.D0
INV = (I-1) * MPLUS
DO 100 J=1,MSET
100 XNORM = XNORM + ABS(B(INV + J))
IF (XMAX.LT.XNORM .AND. XNORM.NE.1.0D0) THEN
XMAX = XNORM
ITERA = I
IONE = INV + I
ENDIF
110 CONTINUE
DO 120 I=1,MPLUS
INV = (I-1) * MPLUS
DO 120 J=1,MPLUS
JNV = (J-1) * MPLUS
IF (J.EQ.ITERA) B(INV + J) = 0.D0
B(JNV + I) = B(INV + J)
120 CONTINUE
B(IONE) = 1.0D0
130 CONTINUE
140 CONTINUE
C
IF (DEBUG) THEN
C
C OUTPUT THE GDIIS MATRIX
C
WRITE(*,'(/5X,'' GDIIS MATRIX'')')
IJ = 0
DO 150 I=1,MPLUS
DO 150 J=1,I
IJ = IJ + 1
150 BST(IJ) = B( MPLUS * (J-1) + I)
CALL VECPRT(BST,MPLUS)
ENDIF
C
C SCALE DIIS MATRIX BEFORE INVERSION
C
DO 160 I=1,MPLUS
II = MPLUS * (I-1) + I
160 GSAVE(I) = 1.D0 / DSQRT(1.D-20+DABS(B(II)))
GSAVE(MPLUS) = 1.D0
DO 170 I=1,MPLUS
DO 170 J=1,MPLUS
IJ = MPLUS * (I-1) + J
170 B(IJ) = B(IJ) * GSAVE(I) * GSAVE(J)
C
IF (DEBUG) THEN
C
C OUTPUT SCALED GDIIS MATRIX
C
WRITE(*,'(/5X,'' GDIIS MATRIX (SCALED)'')')
IJ = 0
DO 180 I=1,MPLUS
DO 180 J=1,I
IJ = IJ + 1
180 BST(IJ) = B( MPLUS * (J-1) + I)
CALL VECPRT(BST,MPLUS)
ENDIF
C
C INVERT THE GDIIS MATRIX
C
CALL MINV(B,MPLUS,DET)
C
DO 190 I=1,MPLUS
DO 190 J=1,MPLUS
IJ = MPLUS * (I-1) + J
190 B(IJ) = B(IJ) * GSAVE(I) * GSAVE(J)
C
C COMPUTE THE INTERMEDIATE INTERPOLATED PARAMETER AND GRADIENT
C VECTORS
C
DO 200 K=1,NVAR
XP(K) = 0.D0
GP(K) = 0.D0
DO 200 I=1,MSET
INK = (I-1) * NVAR + K
XP(K) = XP(K) + B(MPLUS*MSET+I) * XSET(INK)
200 GP(K) = GP(K) + B(MPLUS*MSET+I) * GSET(INK)
HP=0.D0
DO 210 I=1,MSET
210 HP=HP+B(MPLUS*MSET+I)*ESET(I)
C
DO 220 K=1,NVAR
220 DX(K) = XPARAM(K) - XP(K)
XNORM = SQRT(DOT(DX,DX,NVAR))
IF (PRINT) THEN
WRITE (6,'(/10X,''DEVIATION IN X '',F7.4,8X,''DETERMINANT '',
1 G9.3)') XNORM,DET
WRITE(6,'(10X,''GDIIS COEFFICIENTS'')')
WRITE(6,'(10X,5F12.5)') (B(MPLUS*MSET+I),I=1,MSET)
ENDIF
C
C THE FOLLOWING TOLERENCES FOR XNORM AND DET ARE SOMEWHAT ARBITRARY!
C
THRES = MAX(10.D0**(-NVAR), 1.D-25)
IF (XNORM.GT.2.D0 .OR. DABS(DET).LT. THRES) THEN
IF (PRINT) WRITE(6,'(10X,''THE DIIS MATRIX IS ILL CONDITIONED''
1, /10X,'' - PROBABLY, VECTORS ARE LINEARLY DEPENDENT - '',
2 /10X,''THE DIIS STEP WILL BE REPEATED WITH A SMALLER SPACE'')')
DO 230 K=1,MM
230 B(K) = BS(K)
NDIIS = NDIIS - 1
IF (NDIIS .GT. 0) GO TO 80
IF (PRINT) WRITE(*,'(10X,''NEWTON-RAPHSON STEP TAKEN'')')
DO 240 K=1,NVAR
XP(K) = XPARAM(K)
240 GP(K) = GRAD(K)
C
ENDIF
IF (PRINT) WRITE(6,'(/,'' ***** END GDIIS ***** '',/)')
C
RETURN
END
SUBROUTINE SPACE(MRESET, MSET, XPARAM, GRAD, HEAT, NVAR,
1XSET, GSET, ESET, FRST)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
DIMENSION XPARAM(NVAR), GRAD(NVAR)
DIMENSION XSET(MRESET*NVAR),GSET(MRESET*NVAR), ESET(MRESET)
LOGICAL FRST
C
C UPDATE PARAMETER AND GRADIENT SUBSPACE
C
IF(FRST)THEN
NRESET=MIN(NVAR/2,MRESET)
FRST=.FALSE.
MSET=0
ENDIF
C
IF (MSET .EQ. NRESET) THEN
DO 10 I=1,MSET-1
MI = NVAR*(I-1)
NI = NVAR*I
ESET(I)=ESET(I+1)
DO 10 K=1,NVAR
XSET(MI+K) = XSET(NI+K)
10 GSET(MI+K) = GSET(NI+K)
MSET=NRESET-1
ENDIF
C
C STORE THE CURRENT POINT
C
DO 20 K=1,NVAR
NMK = NVAR*MSET+K
XSET(NMK) = XPARAM(K)
20 GSET(NMK) = GRAD(K)
MSET=MSET+1
ESET(MSET)=HEAT
C
RETURN
END
SUBROUTINE MINV(A,N,D)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
DIMENSION A(*)
**********************************************************************
*
* INVERT A MATRIX USING GAUSS-JORDAN METHOD. PART OF DIIS
* A - INPUT MATRIX (MUST BE A GENERAL MATRIX), DESTROYED IN
* COMPUTATION AND REPLACED BY RESULTANT INVERSE.
* N - ORDER OF MATRIX A
* D - RESULTANT DETERMINANT
*
**********************************************************************
DIMENSION M(MAXPAR), L(MAXPAR)
C
C SEARCH FOR LARGEST ELEMENT
C
D=1.0D0
NK=-N
DO 180 K=1,N
NK=NK+N
L(K)=K
M(K)=K
KK=NK+K
BIGA=A(KK)
DO 20 J=K,N
IZ=N*(J-1)
DO 20 I=K,N
IJ=IZ+I
10 IF (ABS(BIGA).LT.ABS(A(IJ)))THEN
BIGA=A(IJ)
L(K)=I
M(K)=J
ENDIF
20 CONTINUE
C
C INTERCHANGE ROWS
C
J=L(K)
IF (J-K) 50,50,30
30 KI=K-N
DO 40 I=1,N
KI=KI+N
HOLD=-A(KI)
JI=KI-K+J
A(KI)=A(JI)
40 A(JI)=HOLD
C
C INTERCHANGE COLUMNS
C
50 I=M(K)
IF (I-K) 80,80,60
60 JP=N*(I-1)
DO 70 J=1,N
JK=NK+J
JI=JP+J
HOLD=-A(JK)
A(JK)=A(JI)
70 A(JI)=HOLD
C
C DIVIDE COLUMN BY MINUS PIVOT (VALUE OF PIVOT ELEMENT IS
C CONTAINED IN BIGA)
C
80 IF (BIGA) 100,90,100
90 D=0.0D0
RETURN
100 DO 120 I=1,N
IF (I-K) 110,120,110
110 IK=NK+I
A(IK)=A(IK)/(-BIGA)
120 CONTINUE
C REDUCE MATRIX
DO 150 I=1,N
IK=NK+I
HOLD=A(IK)
IJ=I-N
DO 150 J=1,N
IJ=IJ+N
IF (I-K) 130,150,130
130 IF (J-K) 140,150,140
140 KJ=IJ-I+K
A(IJ)=HOLD*A(KJ)+A(IJ)
150 CONTINUE
C
C DIVIDE ROW BY PIVOT
C
KJ=K-N
DO 170 J=1,N
KJ=KJ+N
IF (J-K) 160,170,160
160 A(KJ)=A(KJ)/BIGA
170 CONTINUE
C
C PRODUCT OF PIVOTS
C
D=MAX(-1.D25,MIN(1.D25,D))
D=D*BIGA
C
C REPLACE PIVOT BY RECIPROCAL
C
A(KK)=1.0D0/BIGA
180 CONTINUE
C
C FINAL ROW AND COLUMN INTERCHANGE
C
K=N
190 K=(K-1)
IF (K) 260,260,200
200 I=L(K)
IF (I-K) 230,230,210
210 JQ=N*(K-1)
JR=N*(I-1)
DO 220 J=1,N
JK=JQ+J
HOLD=A(JK)
JI=JR+J
A(JK)=-A(JI)
220 A(JI)=HOLD
230 J=M(K)
IF (J-K) 190,190,240
240 KI=K-N
DO 250 I=1,N
KI=KI+N
HOLD=A(KI)
JI=KI-K+J
A(KI)=-A(JI)
250 A(JI) =HOLD
GO TO 190
260 RETURN
END
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