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SUBROUTINE LINMIN(XPARAM,ALPHA,PVECT,NVAR,FUNCT,OKF,IC, DOTT)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
DIMENSION XPARAM(NVAR),PVECT(NVAR),GRAD(MAXPAR)
COMMON /GRAVEC/ COSINE
COMMON /NUMCAL/ NUMCAL
C*********************************************************************
C
C LINMIN DOES A LINE MINIMISATION.
C
C ON INPUT: XPARAM = STARTING COORDINATE OF SEARCH.
C ALPHA = STEP SIZE FOR INITIATING SEARCH.
C PVECT = DIRECTION OF SEARCH.
C NVAR = NUMBER OF VARIABLES IN XPARAM.
C FUNCT = INITIAL VALUE OF THE FUNCTION TO BE MINIMIZED.
C ISOK = NOT IMPORTANT.
C COSINE = COSINE OF ANGLE OF CURRENT AND PREVIOUS GRADIENT.
C
C ON OUTPUT: XPARAM = COORDINATE OF MINIMUM OF FUNCTI0N.
C ALPHA = NEW STEP SIZE, USED IN NEXT CALL OF LINMIN.
C FUNCT = FINAL, MINIMUM VALUE OF THE FUNCTION.
C OKF = TRUE IF LINMIN IMPROVED FUNCT, FALSE OTHERWISE.
C
C**********************************************************************
COMMON /KEYWRD/ KEYWRD
C
C THE FOLLOWING COMMON IS USED TO FIND OUT IF A NON-VARIATIONALLY
C OPTIMIZED WAVE-FUNCTION IS BEING USED.
C
COMMON /MOLKST/ NUMAT,NAT(NUMATM),NFIRST(NUMATM),NMIDLE(NUMATM),
1 NLAST(NUMATM), NORBS, NELECS,NALPHA,NBETA,
2 NCLOSE,NOPEN,NDUMY,FRACT
CHARACTER KEYWRD*241
DIMENSION PHI(3), VT(4)
DIMENSION XSTOR(MAXPAR), XPAREF(MAXPAR)
INTEGER LEFT,RIGHT,CENTER
LOGICAL PRINT,OKF, HALFE, DIIS
SAVE ICALCN, PRINT, HALFE, XMAXM, I
SAVE MAXLIN, YMAXST
DATA ICALCN /0/
IF (ICALCN.NE.NUMCAL) THEN
HALFE =(INDEX(KEYWRD,'C.I.') .NE. 0 .OR. NCLOSE.NE.NOPEN)
IF(INDEX(KEYWRD,'GNORM') .NE. 0)
1DROP=DROP*MIN(READA(KEYWRD,INDEX(KEYWRD,'GNORM')),1.D0)
XMAXM = 0.4D0
DELTA2 = 0.001D0
IF(INDEX(KEYWRD,'NOTH') .EQ. 0) THEN
DELTA1 = 0.5D0
ELSE
DELTA1 = 0.1D0
ENDIF
ALPHA = 1.D0
MAXLIN = 15
IF(NVAR.EQ.1)THEN
PVECT(1)=0.01D0
DROP=0.01D0
ALPHA=1.D0
DELTA1 = 0.00005D0
DELTA2 = 0.00001D0
IF(INDEX(KEYWRD,'PREC') .NE. 0) DELTA1=0.0000005D0
MAXLIN=30
ENDIF
COSINE=99.99D0
C
YMAXST = 0.4D0
PRINT=(INDEX(KEYWRD,'LINMIN') .NE. 0)
ICALCN=NUMCAL
ENDIF
DO 10 I=1,NVAR
XPAREF(I)=XPARAM(I)
10 CONTINUE
XMAXM=0.D0
DO 20 I=1,NVAR
PABS=ABS(PVECT(I))
20 XMAXM=MAX(XMAXM,PABS)
XMAXM=YMAXST/XMAXM
IF(NVAR.EQ.1)
1CALL COMPFG(XPARAM, .TRUE., FUNCT,.TRUE.,GRAD,.FALSE.)
FIN=FUNCT
SSQLST=FUNCT
DIIS=IC.EQ.1.AND.NVAR.GT.1
PHI(1)=FUNCT
ALPHA=1.D0
VT(1)=0.0D00
VT(2)=ALPHA
IF (VT(2).GT.XMAXM) VT(2)=XMAXM
FMAX=FUNCT
FMIN=FUNCT
ALPHA=VT(2)
DO 30 I=1,NVAR
30 XPARAM(I)=XPAREF(I)+ALPHA*PVECT(I)
CALL COMPFG(XPARAM, .TRUE., PHI(2),.TRUE.,GRAD,.FALSE.)
IF(PHI(2).GT.FMAX) FMAX=PHI(2)
IF(PHI(2).LT.FMIN) FMIN=PHI(2)
CALL EXCHNG (PHI(2),SQSTOR,ENERGY,ESTOR,XPARAM,XSTOR,
1ALPHA,ALFS,NVAR)
IF(DIIS)GOTO 190
IF(NVAR.GT.1)THEN
C
C CALCULATE A NEW ALPHA BASED ON THIEL'S FORMULA
C
ALPHA=-ALPHA**2*DOTT/(2.D0*(PHI(2)-SSQLST-ALPHA*DOTT))
IF(ALPHA.GT.2.D0)ALPHA=2.D0
ELSE
IF(PHI(2).LT.PHI(1))THEN
ALPHA=2*ALPHA
ELSE
ALPHA=-ALPHA
ENDIF
ENDIF
C# IF(PRINT)WRITE(6,'(3(A,F12.6))')' ESTIMATED DROP:',DOTT*0.5D0,
C# 1' ACTUAL: ',PHI(2)-SSQLST, ' PREDICTED ALPHA',ALPHA
OKF=OKF.OR.PHI(2).LT.SSQLST
IF(DELTA1.GT.0.3D0)THEN
C
C THIEL'S TESTS # 18 AND 19
C
IF(OKF.AND.ALPHA.LT.2.D0)GOTO 190
ENDIF
VT(3)=ALPHA
IF (VT(3).LE.1.D0) THEN
LEFT=3
CENTER=1
RIGHT=2
ELSE
LEFT=1
CENTER=2
RIGHT=3
ENDIF
DO 40 I=1,NVAR
40 XPARAM(I)=XPAREF(I)+ALPHA*PVECT(I)
CALL COMPFG (XPARAM, .TRUE., FUNCT,.TRUE.,GRAD,.FALSE.)
IF(FUNCT.GT.FMAX) FMAX=FUNCT
IF(FUNCT.LT.FMIN) FMIN=FUNCT
IF (FUNCT.LT.SQSTOR) CALL EXCHNG (FUNCT,SQSTOR,ENERGY,
1ESTOR,XPARAM,XSTOR,ALPHA,ALFS,NVAR)
OKF=(OKF.OR.FUNCT.LT.FIN)
PHI(3)=FUNCT
IF (PRINT)WRITE (6,50) VT(1),PHI(1),PHI(1)-FIN,
1 VT(2),PHI(2),PHI(2)-FIN,
2 VT(3),PHI(3),PHI(3)-FIN
50 FORMAT ( ' ---QLINMN ',/5X, 'LEFT ...',F17.8,2F17.11/5X,
1 'CENTER ...',F17.8,2F17.11,/5X, 'RIGHT ...',F17.8,2F17.11,/)
DO 180 ICTR=3,MAXLIN
ALPHA=VT(2)-VT(3)
BETA=VT(3)-VT(1)
GAMMA=VT(1)-VT(2)
IF(ABS(ALPHA*BETA*GAMMA) .GT. 1.D-4)THEN
ALPHA=-(PHI(1)*ALPHA+PHI(2)*BETA+PHI(3)*GAMMA)/(ALPHA*BETA*G
1AMM A)
ELSE
C
C FINISH BECAUSE TWO POINTS CALCULATED ARE VERY CLOSE TOGETHER
C
GOTO 190
ENDIF
BETA=((PHI(1)-PHI(2))/GAMMA)-ALPHA*(VT(1)+VT(2))
IF (ALPHA) 60,60,90
60 IF (PHI(RIGHT).GT.PHI(LEFT)) GO TO 70
ALPHA=3.0D00*VT(RIGHT)-2.0D00*VT(CENTER)
GO TO 80
70 ALPHA=3.0D00*VT(LEFT)-2.0D00*VT(CENTER)
80 S=ALPHA-ALPOLD
IF (ABS(S).GT.XMAXM) S=SIGN(XMAXM,S)*(1+0.01D0*(XMAXM/S))
ALPHA=S+ALPOLD
GO TO 100
90 ALPHA=-BETA/(2.0D00*ALPHA)
S=ALPHA-ALPOLD
XXM=2.0D00*XMAXM
IF (ABS(S).GT.XXM) S=SIGN(XXM,S)*(1+0.01D0*(XXM/S))
ALPHA=S+ALPOLD
100 CONTINUE
C
C FINISH IF CALCULATED POINT IS NEAR TO POINT ALREADY CALCULATED
C
DO 110 I=1,3
110 IF (ABS(ALPHA-VT(I)).LT.DELTA1*(1.D0+VT(I)).AND.OKF) GOTO 190
DO 120 I=1,NVAR
120 XPARAM(I)=XPAREF(I)+ALPHA*PVECT(I)
FUNOLD=FUNCT
CALL COMPFG (XPARAM, .TRUE., FUNCT,.TRUE.,GRAD,.FALSE.)
IF(FUNCT.GT.FMAX) FMAX=FUNCT
IF(FUNCT.LT.FMIN) FMIN=FUNCT
IF (FUNCT.LT.SQSTOR) CALL EXCHNG (FUNCT,SQSTOR,ENERGY,ESTOR,
1 XPARAM,XSTOR,ALPHA,ALFS,NVAR)
OKF=OKF .OR. (FUNCT.LT.FIN)
IF (PRINT) WRITE(6,130) VT(LEFT),PHI(LEFT), PHI(LEFT)-FIN,
1 VT(CENTER),PHI(CENTER),PHI(CENTER)-FIN,
2 VT(RIGHT),PHI(RIGHT),PHI(RIGHT)-FIN,
3 ALPHA,FUNCT,FUNCT-FIN
130 FORMAT (5X,'LEFT ...',F17.8,2F17.11,/5X,'CENTER ...',
1F17.8,2F17.11,/5X,'RIGHT ...',F17.8,2F17.11,/5X,
2 'NEW ...',F17.8,2F17.11,/)
C
C TEST TO EXIT FROM LINMIN IF NOT DROPPING IN VALUE OF FUNCTION FAST.
C
IF(ABS(FUNOLD-FUNCT) .LT. DELTA2 .AND. OKF) GOTO 190
ALPOLD=ALPHA
IF ((ALPHA.GT.VT(RIGHT)).OR.(ALPHA.GT.VT(CENTER)
1 .AND.FUNCT.LT.PHI(CENTER)).OR.(ALPHA.GT.VT(LEFT)
2 .AND.ALPHA.LT.VT(CENTER).AND.FUNCT.GT.PHI(CENTER)))
3 GOTO 140
VT(RIGHT)=ALPHA
PHI(RIGHT)=FUNCT
GO TO 150
140 VT(LEFT)=ALPHA
PHI(LEFT)=FUNCT
150 IF (VT(CENTER).LT.VT(RIGHT)) GO TO 160
I=CENTER
CENTER=RIGHT
RIGHT=I
160 IF (VT(LEFT).LT.VT(CENTER)) GO TO 170
I=LEFT
LEFT=CENTER
CENTER=I
170 IF (VT(CENTER).LT.VT(RIGHT)) GO TO 180
I=CENTER
CENTER=RIGHT
RIGHT=I
180 CONTINUE
190 CONTINUE
C
C IC=1 IF THE LAST POINT CALCULATED WAS THE BEST POINT, IC=2 OTHERWISE
C
IC=2
IF(ABS(ESTOR-ENERGY).LT.1.D-12)IC=1
CALL EXCHNG (SQSTOR,FUNCT,ESTOR,ENERGY,XSTOR,XPARAM,
1 ALFS,ALPHA,NVAR)
OKF = (FUNCT.LT.SSQLST.OR.DIIS)
IF (FUNCT.GE.SSQLST) RETURN
IF (ALPHA) 200,220,220
200 ALPHA=-ALPHA
DO 210 I=1,NVAR
210 PVECT(I)=-PVECT(I)
220 CONTINUE
RETURN
C
C
END
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