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SUBROUTINE EF(XPARAM, NVAR, FUNCT)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
DOUBLE PRECISION LAMDA,LAMDA0
INCLUDE 'SIZES'
DIMENSION XPARAM(MAXPAR)
**********************************************************************
*
* EF IS A QUASI NEWTON RAPHSON OPTIMIZATION ROUTINE BASED ON
* Jacs Simons P-RFO algorithm as implemented by Jon Baker
* (J.COMP.CHEM. 7, 385). Step scaling to keep length within
* trust radius is taken from Culot et al. (Theo. Chim. Acta 82, 189)
* The trust radius can be updated dynamically according to Fletcher.
* Safeguards on valid step for TS searches based on actual/predicted
* function change and change in TS mode are own modifications
*
* ON ENTRY XPARAM = VALUES OF PARAMETERS TO BE OPTIMISED.
* NVAR = NUMBER OF PARAMETERS TO BE OPTIMISED.
*
* ON EXIT XPARAM = OPTIMISED PARAMETERS.
* FUNCT = HEAT OF FORMATION IN KCAL/MOL.
*
* Current version implementing combined NR, P-RFO and QA algorithm
* together with thrust radius update and step rejection was
* made october 1992 by F.Jensen, Odense, DK
*
**********************************************************************
C
COMMON /MESAGE/ IFLEPO,ISCF
COMMON /GEOVAR/ NDUM,LOC(2,MAXPAR), IDUMY, XARAM(MAXPAR)
COMMON /GEOM / GEO(3,NUMATM), XCOORD(3,NUMATM)
COMMON /GEOSYM/ NDEP,LOCPAR(MAXPAR),IDEPFN(MAXPAR),LOCDEP(MAXPAR)
COMMON /ISTOPE/ AMS(107)
COMMON /LAST / LAST
COMMON /KEYWRD/ KEYWRD
C ***** Modified by Jiro Toyoda at 1994-05-25 *****
C COMMON /TIME / TIME0
COMMON /TIMEC / TIME0
C ***************************** at 1994-05-25 *****
COMMON /GRADNT/ GRAD(MAXPAR),GNFINA
COMMON /MOLKST/ NUMAT,NAT(NUMATM),NFIRST(NUMATM),NMIDLE(NUMATM),
1 NLAST(NUMATM), NORBS, NELECS,NALPHA,NBETA,
2 NCLOSE,NOPEN,NDUMY,FRACT
COMMON /NUMCAL/ NUMCAL
COMMON /TIMDMP/ TLEFT, TDUMP
COMMON /SIGMA2/ GNEXT1(MAXPAR), GMIN1(MAXPAR)
CONVEX COMMON /NLLCOM/ HESS(MAXPAR,MAXPAR),BMAT(MAXPAR,MAXPAR),
CONVEX 1PMAT(MAXPAR*MAXPAR)
COMMON /NLLCOM/ HESS(MAXPAR,MAXPAR),BMAT(MAXPAR,MAXPAR),
1PMAT(MAXPAR**2)
CONVEX COMMON /SCRACH/ PVEC
COMMON /SCFTYP/ EMIN, LIMSCF
COMMON/OPTEF/OLDF(MAXPAR),D(MAXPAR),VMODE(MAXPAR),
$U(MAXPAR,MAXPAR),DD,rmin,rmax,omin,xlamd,xlamd0,skal,
$MODE,NSTEP,NEGREQ,IPRNT
COMMON/THREADS/NUM_THREADS
C ***** Modified by Jiro Toyoda at 1994-05-25 *****
C COMMON/FLUSH/NFLUSH
COMMON/FLUSHC/NFLUSH
C ***************************** at 1994-05-25 *****
DIMENSION IPOW(9), EIGVAL(MAXPAR),TVEC(MAXPAR),SVEC(MAXPAR),
1FX(MAXPAR),HESSC(MAXHES),UC(MAXPAR**2),oldfx(maxpar),
1oldeig(maxpar),
$oldhss(maxpar,maxpar),oldu(maxpar,maxpar),ooldf(maxpar)
DIMENSION BB(MAXPAR,MAXPAR)
LOGICAL RESTRT,SCF1,LIMSCF,LOG
LOGICAL LUPD,lts,lrjk,lorjk,rrscal,donr,gnmin
CHARACTER KEYWRD*241
EQUIVALENCE(IPOW(1),IHESS)
DATA ICALCN,ZERO,ONE,TWO /0,0.D0,1.D0,2.D0/
DATA tmone /1.0d-1/, TMTWO/1.0D-2/, TMSIX/1.0D-06/
data three/3.0d0/, four/4.0d0/,
1pt25/0.25d0/, pt5/0.50d0/, pt75/0.75d0/
data demin/2.0d-2/, gmin/5.0d0/
C GET ALL INITIALIZATION DATA
IF(ICALCN.NE.NUMCAL)
1CALL EFSTR(XPARAM,FUNCT,IHESS,NTIME,ILOOP,IGTHES,
$MXSTEP,IRECLC,IUPD,DMAX,DDMAX,dmin,TOL2,TOTIME,TIME1,TIME2,nvar,
$SCF1,LUPD,ldump,log,rrscal,donr,gnmin)
lts=.false.
if (negreq.eq.1) lts=.true.
lorjk=.false.
c osmin is smallest step for which a ts-mode overlap less than omin
c will be rejected. for updated hessians there is little hope of
c better overlap by reducing the step below 0.005. for exact hessian
c the overlap should go toward one as the step become smaller, but
c don't allow very small steps
osmin=0.005d0
if(ireclc.eq.1)osmin=0.001d0
IF (SCF1) THEN
GNFINA=SQRT(DOT(GRAD,GRAD,NVAR))
IFLEPO=1
RETURN
ENDIF
C CHECK THAT GEOMETRY IS NOT ALREADY OPTIMIZED
RMX=SQRT(DOT(GRAD,GRAD,NVAR))
IF (RMX.LT.TOL2) THEN
IFLEPO=2
LAST=1
RETURN
ENDIF
C GET INITIAL HESSIAN. IF ILOOP IS .LE.0 THIS IS AN OPTIMIZATION RESTART
C AND HESSIAN SHOULD ALREADY BE AVAILABLE
IF (ILOOP .GT. 0) CALL GETHES(XPARAM,IGTHES,NVAR,iloop,TOTIME)
C START OF MAIN LOOP
C WE NOW HAVE GRADIENTS AND A HESSIAN. IF THIS IS THE FIRST
C TIME THROUGH DON'T UPDATE THE HESSIAN. FOR LATER LOOPS ALSO
C CHECK IF WE NEED TO RECALCULATE THE HESSIAN
IFLEPO=0
itime=0
10 CONTINUE
c store various things for possibly omin rejection
do 30 i=1,nvar
oldfx(i)=fx(i)
ooldf(i)=oldf(i)
oldeig(i)=eigval(i)
do 20 j=1,nvar
oldhss(i,j)=hess(i,j)
oldu(i,j)=u(i,j)
20 continue
30 continue
IF (IHESS.GE.IRECLC.AND.IFLEPO.NE.15) THEN
ILOOP=1
IHESS=0
if (igthes.ne.3)IGTHES=1
CALL GETHES(XPARAM,IGTHES,NVAR,iloop,TOTIME)
ENDIF
IF (IHESS.GT.0) CALL UPDHES(SVEC,TVEC,NVAR,IUPD)
IF(IPRNT.GE.2) call geout(6)
IF(IPRNT.GE.2) THEN
WRITE(6,'('' XPARAM '')')
WRITE(6,'(5(2I3,F10.4))')(LOC(1,I),LOC(2,I),XPARAM(I),I=1,NV
1AR)
WRITE(6,'('' GRADIENTS'')')
WRITE(6,'(3X,8F9.3)')(GRAD(I),I=1,NVAR)
ENDIF
C
C PRINT RESULTS IN CYCLE
GNFINA=SQRT(DOT(GRAD,GRAD,NVAR))
TIME2=SECOND()
if (itime.eq.0) time1=time0
TSTEP=TIME2-TIME1
IF (TSTEP.LT.ZERO)TSTEP=ZERO
TLEFT=TLEFT-TSTEP
TIME1=TIME2
itime=itime+1
IF (TLEFT .LT. TSTEP*TWO) GOTO 280
IF(LDUMP.EQ.0)THEN
WRITE(6,40)NSTEP+1,MIN(TSTEP,9999.99D0),
1MIN(TLEFT,9999999.9D0),MIN(GNFINA,999999.999D0),FUNCT
IF(LOG)WRITE(11,40)NSTEP+1,MIN(TSTEP,9999.99D0),
1MIN(TLEFT,9999999.9D0),MIN(GNFINA,999999.999D0),FUNCT
40 FORMAT(' CYCLE:',I4,' TIME:',F7.2,' TIME LEFT:',F9.1,
1' GRAD.:',F10.3,' HEAT:',G13.7)
IF ( NFLUSH.NE.0 ) THEN
IF ( MOD(NSTEP+1,NFLUSH).EQ.0) THEN
call flush(6)
call flush(11)
ENDIF
ENDIF
ELSE
WRITE(6,50)MIN(TLEFT,9999999.9D0),
1MIN(GNFINA,999999.999D0),FUNCT
IF(LOG)WRITE(11,50)MIN(TLEFT,9999999.9D0),
1MIN(GNFINA,999999.999D0),FUNCT
50 FORMAT(' RESTART FILE WRITTEN, TIME LEFT:',F9.1,
1' GRAD.:',F10.3,' HEAT:',G13.7)
IF ( NFLUSH.NE.0 ) THEN
IF ( MOD(NSTEP+1,NFLUSH).EQ.0) THEN
call flush(6)
call flush(11)
ENDIF
ENDIF
ENDIF
IHESS=IHESS+1
NSTEP=NSTEP+1
C
C TEST FOR CONVERGENCE
C
RMX=SQRT(DOT(GRAD,GRAD,NVAR))
IF (RMX.LT.TOL2)GOTO 250
OLDE = FUNCT
oldgn = rmx
DO 60 I=1,NVAR
OLDF(I)=GRAD(I)
60 CONTINUE
C
C if the optimization is in cartesian coordinates, we should remove
C translation and rotation modes. Possible problem if run is in
C internal but with exactly 3*natoms variable (i.e. dummy atoms
C are also optimized).
if (nvar.eq.3*numat) then
if (nstep.eq.1) write(6,70)
70 format(1x,'WARNING! EXACTLY 3N VARIABLES. EF ASSUMES THIS IS A',
$ ' CARTESIAN OPTIMIZATION.',/,1x,'IF THE OPTIMIZATION IS',
$ ' IN INTERNAL COORDINATES, EF WILL NOT WORK')
call prjfc(hess,xparam,nvar)
endif
IJ=0
DO 80 I=1,NVAR
DO 80 J=1,I
IJ=IJ+1
HESSC(IJ)=HESS(J,I)
80 CONTINUE
CONVEX CALL HQRII(HESSC,NVAR,NVAR,EIGVAL,UC)
CALL RSP(HESSC,NVAR,NVAR,EIGVAL,UC)
IJ=0
DO 90 I=1,NVAR
IF (ABS(EIGVAL(I)).LT.TMSIX) EIGVAL(I)=ZERO
DO 90 J=1,NVAR
IJ=IJ+1
U(J,I)=UC(IJ)
90 CONTINUE
IF (IPRNT.GE.3) CALL PRTHES(EIGVAL,NVAR)
IF (MXSTEP.EQ.0) nstep=0
IF (MXSTEP.EQ.0) GOTO 280
NEG=0
DO 100 I=1,NVAR
IF (EIGVAL(I) .LT. ZERO)NEG=NEG+1
100 CONTINUE
IF (IPRNT.GE.1)WRITE(6,110)NEG,(eigval(i),i=1,neg)
110 FORMAT(/,10X,'HESSIAN HAS',I3,' NEGATIVE EIGENVALUE(S)',6f7.1,/)
c if an eigenvalue has been zero out it is probably one of the T,R modes
c in a cartesian optimization. zero corresponding fx to allow formation
c of step without these contributions. a more safe criteria for deciding
c whether this actually is a cartesian optimization should be put in
c some day...
DO 120 I=1,NVAR
FX(I)=DOT(U(1,I),GRAD,NVAR)
if (abs(eigval(i)).eq.zero) fx(i)=zero
120 CONTINUE
c form geometry step d
130 CALL FORMD(EIGVAL,FX,NVAR,DMAX,osmin,LTS,lrjk,lorjk,rrscal,donr)
c if lorjk is true, then ts mode overlap is less than omin, reject prev step
if (lorjk) then
if (iprnt.ge.1)write(6,*)' Now undoing previous step'
dmax=odmax
dd=odd
olde=oolde
do i=1,nvar
fx(i)=oldfx(i)
oldf(i)=ooldf(i)
eigval(i)=oldeig(i)
do j=1,nvar
hess(i,j)=oldhss(i,j)
u(i,j)=oldu(i,j)
enddo
enddo
DO 140 I=1,NVAR
XPARAM(I)=XPARAM(I)-D(I)
K=LOC(1,I)
L=LOC(2,I)
GEO(L,K)=XPARAM(I)
140 CONTINUE
IF(NDEP.NE.0) CALL SYMTRY
dmax=min(dmax,dd)/two
odmax=dmax
odd=dd
nstep=nstep-1
if (dmax.lt.dmin) goto 230
if (iprnt.ge.1)write(6,*)
1' Finish undoing, now going for new step'
goto 130
endif
C
C FORM NEW TRIAL XPARAM AND GEO
C
DO 150 I=1,NVAR
XPARAM(I)=XPARAM(I)+D(I)
K=LOC(1,I)
L=LOC(2,I)
GEO(L,K)=XPARAM(I)
150 CONTINUE
IF(NDEP.NE.0) CALL SYMTRY
C
C COMPARE PREDICTED E-CHANGE WITH ACTUAL
C
depre=zero
imode=1
if (mode.ne.0)imode=mode
do 160 i=1,nvar
xtmp=xlamd
if (lts .and. i.eq.imode) xtmp=xlamd0
if (abs(xtmp-eigval(i)).lt.tmtwo) then
ss=zero
else
ss=skal*fx(i)/(xtmp-eigval(i))
endif
frodo=ss*fx(i) + pt5*ss*ss*eigval(i)
c write(6,88)i,fx(i),ss,xtmp,eigval(i),frodo
depre=depre+frodo
160 continue
c88 format(i3,f10.3,f10.6,f10.3,4f10.6)
C
C GET GRADIENT FOR NEW GEOMETRY
C
CALL COMPFG(XPARAM, .TRUE., FUNCT, .TRUE., GRAD, .TRUE.)
if(gnmin)gntest=sqrt(dot(grad,grad,nvar))
DEACT = FUNCT-OLDE
RATIO = DEACT/DEPRE
if(iprnt.ge.1)WRITE(6,170)DEACT,DEPRE,RATIO
170 FORMAT(5X,'ACTUAL, PREDICTED ENERGY CHANGE, RATIO',2F10.3,F10.5)
lrjk=.false.
C if this is a minimum search, don't allow the energy to raise
if (.not.lts .and. funct.gt.olde) then
if (iprnt.ge.1)write(6,180)funct,min(dmax,dd)/two
180 format(1x,'energy raises ',f10.4,' rejecting step, ',
$ 'reducing dmax to',f7.4)
lrjk=.true.
endif
if (gnmin .and. gntest.gt.oldgn) then
if (iprnt.ge.1)write(6,181)gntest,min(dmax,dd)/two
181 format(1x,'gradient norm raises ',f10.4,' rejecting step, ',
$ 'reducing dmax to',f7.4)
lrjk=.true.
endif
if (lts .and. (ratio.lt.rmin .or. ratio.gt.rmax) .and.
$(abs(depre).gt.demin .or. abs(deact).gt.demin)) then
if (iprnt.ge.1)write(6,190)min(dmax,dd)/two
190 format(1x,'unacceptable ratio,',
$ ' rejecting step, reducing dmax to',f7.4)
lrjk=.true.
endif
if (lrjk) then
DO 200 I=1,NVAR
XPARAM(I)=XPARAM(I)-D(I)
K=LOC(1,I)
L=LOC(2,I)
GEO(L,K)=XPARAM(I)
200 CONTINUE
IF(NDEP.NE.0) CALL SYMTRY
dmax=min(dmax,dd)/two
if (dmax.lt.dmin) goto 230
goto 130
endif
IF(IPRNT.GE.1)WRITE(6,210)DD
210 FORMAT(5X,'STEPSIZE USED IS',F9.5)
IF(IPRNT.GE.2) THEN
WRITE(6,'('' CALCULATED STEP'')')
WRITE(6,'(3X,8F9.5)')(D(I),I=1,NVAR)
ENDIF
C
C POSSIBLE USE DYNAMICAL TRUST RADIUS
odmax=dmax
odd=dd
oolde=olde
IF (LUPD .and. ( (RMX.gt.gmin) .or.
$ (abs(depre).gt.demin .or. abs(deact).gt.demin) ) ) THEN
c Fletcher recommend dmax=dmax/4 and dmax=dmax*2
c these are are a little more conservative since hessian is being updated
c don't reduce trust radius due to ratio for min searches
if (lts .and. ratio.le.tmone .or. ratio.ge.three)
$ dmax=min(dmax,dd)/two
if (lts .and. ratio.ge.pt75 .and. ratio.le.(four/three)
$ .and. dd.gt.(dmax-tmsix))
$ dmax=dmax*sqrt(two)
c allow wider limits for increasing trust radius for min searches
if (.not.lts .and. ratio.ge.pt5
$ .and. dd.gt.(dmax-tmsix))
$ dmax=dmax*sqrt(two)
c be brave if 0.90 < ratio < 1.10 ...
if (abs(ratio-one).lt.tmone) dmax=dmax*sqrt(two)
dmax=max(dmax,dmin-tmsix)
dmax=min(dmax,ddmax)
ENDIF
c allow stepsize up to 0.1 in the end-game where changes are less
c than demin and gradient is less than gmin
IF (LUPD .and. RMX.lt.gmin .and.
$ (abs(depre).lt.demin .and. abs(deact).lt.demin) )
$ dmax=max(dmax,tmone)
if(iprnt.ge.1)WRITE(6,220)DMAX
220 FORMAT(5X,'CURRENT TRUST RADIUS = ',F7.5)
230 if (dmax.lt.dmin) then
write(6,240)dmin
240 format(/,5x,'TRUST RADIUS NOW LESS THAN ',F7.5,' OPTIMIZATION',
$ ' TERMINATING',/,5X,
1' GEOMETRY MAY NOT BE COMPLETELY OPTIMIZED')
goto 270
endif
C CHECK STEPS AND ENOUGH TIME FOR ANOTHER PASS
if (nstep.ge.mxstep) goto 280
C IN USER UNFRIENDLY ENVIROMENT, SAVE RESULTS EVERY 1 CPU HRS
ITTEST=AINT((TIME2-TIME0)/TDUMP)
IF (ITTEST.GT.NTIME) THEN
LDUMP=1
NTIME=MAX(ITTEST,(NTIME+1))
IPOW(9)=2
TT0=SECOND()-TIME0
CALL EFSAV(TT0,HESS,FUNCT,GRAD,XPARAM,PMAT,-NSTEP,NSTEP,BMAT,I
1POW)
ELSE
LDUMP=0
ENDIF
C RETURN FOR ANOTHER CYCLE
GOTO 10
C
C ****** OPTIMIZATION TERMINATION ******
C
250 CONTINUE
WRITE(6,260)RMX,TOL2
260 FORMAT(/,5X,'RMS GRADIENT =',F9.5,' IS LESS THAN CUTOFF =',
1F9.5,//)
270 IFLEPO=15
LAST=1
C SAVE HESSIAN ON FILE 9
IPOW(9)=2
TT0=SECOND()-TIME0
CALL EFSAV(TT0,HESS,FUNCT,GRAD,XPARAM,PMAT,-NSTEP,NSTEP,BMAT,I
1POW)
C CALL COMPFG TO CALCULATE ENERGY FOR FIXING MO-VECTOR BUG
CALL COMPFG(XPARAM, .TRUE., FUNCT, .TRUE., GRAD, .FALSE.)
RETURN
280 CONTINUE
C WE RAN OUT OF TIME or too many iterations. DUMP RESULTS
IF (TLEFT .LT. TSTEP*TWO) THEN
WRITE(6,290)
290 FORMAT(/,5X,'NOT ENOUGH TIME FOR ANOTHER CYCLE')
ENDIF
IF (nstep.ge.mxstep) THEN
WRITE(6,300)
300 FORMAT(/,5X,'EXCESS NUMBER OF OPTIMIZATION CYCLES')
ENDIF
IPOW(9)=1
TT0=SECOND()-TIME0
CALL EFSAV(TT0,HESS,FUNCT,GRAD,XPARAM,PMAT,-NSTEP,NSTEP,BMAT,I
1POW)
STOP
END
SUBROUTINE EFSAV(TT0,HESS,FUNCT,GRAD,XPARAM,PMAT,IL,JL,BMAT,IPOW)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
CHARACTER ELEMNT*2, KEYWRD*241, KOMENT*81, TITLE*81
DIMENSION HESS(MAXPAR,*),GRAD(*),BMAT(MAXPAR,*),IPOW(9),
1 XPARAM(*), PMAT(*)
**********************************************************************
*
* EFSAV STORES AND RETRIEVE DATA USED IN THE EF GEOMETRY
* OPTIMISATION. VERY SIMILAR TO POWSAV.
*
* ON INPUT HESS = HESSIAN MATRIX, PARTIAL OR WHOLE.
* GRAD = GRADIENTS.
* XPARAM = CURRENT STATE OF PARAMETERS.
* IL = INDEX OF HESSIAN,
* JL = CYCLE NUMBER REACHED SO-FAR.
* BMAT = "B" MATRIX!
* IPOW = INDICES AND FLAGS.
* IPOW(9)= 0 FOR RESTORE, 1 FOR DUMP, 2 FOR SILENT DUMP
*
**********************************************************************
COMMON /GEOVAR/ NVAR,LOC(2,MAXPAR), IDUMY, DUMY(MAXPAR)
COMMON /ELEMTS/ ELEMNT(107)
COMMON /GEOSYM/ NDEP,LOCPAR(MAXPAR),IDEPFN(MAXPAR),
1 LOCDEP(MAXPAR)
COMMON/OPTEF/OLDF(MAXPAR),D(MAXPAR),VMODE(MAXPAR),
$U(MAXPAR,MAXPAR),DD,rmin,rmax,omin,xlamd,xlamd0,skal,
$MODE,NSTEP,NEGREQ,IPRNT
COMMON /TITLES/ KOMENT,TITLE
COMMON /GEOKST/ NATOMS,LABELS(NUMATM),
1 NA(NUMATM),NB(NUMATM),NC(NUMATM)
COMMON /GEOM / GEO(3,NUMATM), XCOORD(3,NUMATM)
COMMON /LOCVAR/ LOCVAR(2,MAXPAR)
COMMON /NUMSCF/ NSCF
COMMON /KEYWRD/ KEYWRD
COMMON /VALVAR/ VALVAR(MAXPAR),NUMVAR
COMMON /DENSTY/ P(MPACK), PA(MPACK), PB(MPACK)
COMMON /ALPARM/ ALPARM(3,MAXPAR),X0, X1, X2, JLOOP
COMMON /MOLKST/ NUMAT,NAT(NUMATM),NFIRST(NUMATM),NMIDLE(NUMATM),
1 NLAST(NUMATM), NORBS, NELECS,NALPHA,NBETA,
2 NCLOSE,NOPEN,NDUMY,FRACT
COMMON /PATH / LATOM,LPARAM,REACT(200)
C aoyama editted
CHARACTER INF*80 ,OUTF*80,RESF*80,DENF*80,LOGF*80,ARCF*80,
+ GPTF*80,SYBF*80,ERR0*80,ERR1*80
COMMON /DECKS/ INF,OUTF,RESF,DENF,LOGF,ARCF,GPTF,SYBF,ERR0,ERR1
integer RESLEN,DENLEN
IF(len_trim(RESF)==0) THEN
RESF='FOR009'
ENDIF
IF(len_trim(DENF)==0) THEN
DENF='FOR010'
ENDIF
RESLEN=len_trim(RESF)
DENLEN=len_trim(DENF)
OPEN(UNIT=9,FILE=RESF(1:RESLEN),STATUS='UNKNOWN',
+ FORM='UNFORMATTED')
REWIND 9
OPEN(UNIT=10,FILE=DENF(1:DENLEN),STATUS='UNKNOWN',
+ FORM='UNFORMATTED')
REWIND 10
C OPEN(UNIT=9,FILE='FOR009',STATUS='UNKNOWN',FORM='UNFORMATTED')
C REWIND 9
C OPEN(UNIT=10,FILE='FOR010',STATUS='UNKNOWN',FORM='UNFORMATTED')
C REWIND 10
C end aoyama editted
IR=9
IF(IPOW(9) .EQ. 1 .OR. IPOW(9) .EQ. 2) THEN
FUNCT1=SQRT(DOT(GRAD,GRAD,NVAR))
IF(IPOW(9).EQ.1)THEN
WRITE(6,'(//10X,''CURRENT VALUE OF GRADIENT NORM =''
1 ,F12.6)')FUNCT1
WRITE(6,'(/10X,''CURRENT VALUE OF GEOMETRY'',/)')
CALL GEOUT(6)
ENDIF
C
C IPOW(1) AND IPOW(9) ARE USED ALREADY, THE REST ARE FREE FOR USE
C
IPOW(8)=NSCF
WRITE(IR)IPOW,IL,JL,FUNCT,TT0
WRITE(IR)(XPARAM(I),I=1,NVAR)
WRITE(IR)( GRAD(I),I=1,NVAR)
WRITE(IR)((HESS(J,I),J=1,NVAR),I=1,NVAR)
WRITE(IR)((BMAT(J,I),J=1,NVAR),I=1,NVAR)
WRITE(IR)(OLDF(I),I=1,NVAR),(D(I),I=1,NVAR),(VMODE(I),I=1,NVAR)
WRITE(IR)DD,MODE,NSTEP,NEGREQ
LINEAR=(NVAR*(NVAR+1))/2
WRITE(IR)(PMAT(I),I=1,LINEAR)
LINEAR=(NORBS*(NORBS+1))/2
WRITE(10)(PA(I),I=1,LINEAR)
IF(NALPHA.NE.0)WRITE(10)(PB(I),I=1,LINEAR)
IF(LATOM .NE. 0) THEN
WRITE(IR)((ALPARM(J,I),J=1,3),I=1,NVAR)
WRITE(IR)JLOOP,X0, X1, X2
ENDIF
CLOSE(9)
CLOSE(10)
RETURN
ELSE
C# WRITE(6,'(//10X,'' READING DATA FROM DISK''/)')
READ(IR,END=10,ERR=10)IPOW,IL,JL,FUNCT,TT0
NSCF=IPOW(8)
I=TT0/1000000
TT0=TT0-I*1000000
WRITE(6,'(//10X,''TOTAL TIME USED SO FAR:'',
1 F13.2,'' SECONDS'')')TT0
WRITE(6,'( 10X,'' FUNCTION:'',F17.6)')FUNCT
READ(IR)(XPARAM(I),I=1,NVAR)
READ(IR)( GRAD(I),I=1,NVAR)
READ(IR)((HESS(J,I),J=1,NVAR),I=1,NVAR)
READ(IR)((BMAT(J,I),J=1,NVAR),I=1,NVAR)
READ(IR)(OLDF(I),I=1,NVAR),(D(I),I=1,NVAR),(VMODE(I),I=1,NVAR)
READ(IR)DD,MODE,NSTEP,NEGREQ
LINEAR=(NVAR*(NVAR+1))/2
READ(IR)(PMAT(I),I=1,LINEAR)
LINEAR=(NORBS*(NORBS+1))/2
C READ DENSITY MATRIX
READ(10)(PA(I),I=1,LINEAR)
IF(NALPHA.NE.0)READ(10)(PB(I),I=1,LINEAR)
IF(LATOM.NE.0) THEN
READ(IR)((ALPARM(J,I),J=1,3),I=1,NVAR)
READ(IR)JLOOP,X0, X1, X2
IL=IL+1
ENDIF
CLOSE(9)
CLOSE(10)
RETURN
10 WRITE(6,'(//10X,''NO RESTART FILE EXISTS!'')')
STOP
ENDIF
END
SUBROUTINE EFSTR(XPARAM,FUNCT,IHESS,NTIME,ILOOP,IGTHES,MXSTEP,
$IRECLC,IUPD,DMAX,DDMAX,dmin,TOL2,TOTIME,TIME1,TIME2,nvar,
$SCF1,LUPD,ldump,log,rrscal,donr,gnmin)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
DIMENSION XPARAM(*)
C
COMMON /ISTOPE/ AMS(107)
COMMON /LAST / LAST
COMMON /KEYWRD/ KEYWRD
COMMON /TIMEX / TIME0
COMMON /GRADNT/ GRAD(MAXPAR),GNFINA
COMMON /MOLKST/ NUMAT,NAT(NUMATM),NFIRST(NUMATM),NMIDLE(NUMATM),
1 NLAST(NUMATM), NORBS, NELECS,NALPHA,NBETA,
2 NCLOSE,NOPEN,NDUMY,FRACT
COMMON /NUMCAL/ NUMCAL
COMMON /SCFTYP/ EMIN, LIMSCF
COMMON /NLLCOM/ HESS(MAXPAR,MAXPAR),BMAT(MAXPAR,MAXPAR),
*PMAT(MAXPAR**2)
COMMON/OPTEF/OLDF(MAXPAR),D(MAXPAR),VMODE(MAXPAR),
$U(MAXPAR,MAXPAR),DD,rmin,rmax,omin,xlamd,xlamd0,skal,
$MODE,NSTEP,NEGREQ,IPRNT
DIMENSION IPOW(9)
LOGICAL RESTRT,SCF1,LDUM,LUPD,log,rrscal,donr,gnmin
C ***** Added by Jiro Toyoda at 1994-05-25 *****
LOGICAL LIMSCF
C ***************************** at 1994-05-25 *****
CHARACTER*241 KEYWRD,LINE
CHARACTER CHDOT*1,ZERO*1,NINE*1,CH*1
DATA CHDOT,ZERO,NINE /'.','0','9'/
DATA ICALCN,ZZERO /0,0.D0/
C GET ALL INITIALIZATION DATA
NVAR=ABS(NVAR)
LDUMP=0
ICALCN=NUMCAL
LUPD=(INDEX(KEYWRD,' NOUPD') .EQ. 0)
RESTRT=(INDEX(KEYWRD,'RESTART') .NE. 0)
LOG = INDEX(KEYWRD,'NOLOG').EQ.0
SCF1=(INDEX(KEYWRD,'1SCF') .NE. 0)
NSTEP=0
IHESS=0
LAST=0
NTIME=0
ILOOP=1
IMIN=INDEX(KEYWRD,' EF')
IF(IMIN.NE.0) THEN
MODE=0
IGTHES=0
IUPD =2
NEGREQ=0
ddmax=0.5d0
ENDIF
LIMSCF=.FALSE.
ITS=INDEX(KEYWRD,' TS')
IF(ITS.NE.0) THEN
MODE=1
IGTHES=1
IUPD =1
NEGREQ=1
rmin=0.0d0
rmax=4.0d0
omin=0.8d0
ddmax=0.3d0
ENDIF
rrscal=.false.
I=INDEX(KEYWRD,' RSCAL')
IF(I.NE.0) rrscal=.true.
donr=.true.
I=INDEX(KEYWRD,' NONR')
IF(I.NE.0) donr=.false.
gnmin=.false.
I=INDEX(KEYWRD,' GNMIN')
IF(I.NE.0) gnmin=.true.
IPRNT=0
IP=INDEX(KEYWRD,' PRNT=')
IF(IP.NE.0) IPRNT=READA(KEYWRD,IP)
IF(IPRNT.GT.5)IPRNT=5
IF(IPRNT.LT.0)IPRNT=0
MXSTEP=100
I=INDEX(KEYWRD,' CYCLES=')
IF(I.NE.0) MXSTEP=READA(KEYWRD,I)
IF (I.NE.0 .AND. MXSTEP.EQ.0 .AND. IP.EQ.0) IPRNT=3
IRECLC=999999
I=INDEX(KEYWRD,' RECALC=')
IF(I.NE.0) IRECLC=READA(KEYWRD,I)
I=INDEX(KEYWRD,' IUPD=')
IF(I.NE.0) IUPD=READA(KEYWRD,I)
I=INDEX(KEYWRD,' MODE=')
IF(I.NE.0) MODE=READA(KEYWRD,I)
DMIN=1.0D-3
I=INDEX(KEYWRD,' DDMIN=')
IF(I.NE.0) DMIN=READA(KEYWRD,I)
DMAX=0.2D0
I=INDEX(KEYWRD,' DMAX=')
IF(I.NE.0) DMAX=READA(KEYWRD,I)
I=INDEX(KEYWRD,' DDMAX=')
IF(I.NE.0) DDMAX=READA(KEYWRD,I)
TOL2=1.D+0
IF(INDEX(KEYWRD,' PREC') .NE. 0) TOL2=5.D-2
I=INDEX(KEYWRD,' GNORM=')
IF(I.NE.0) TOL2=READA(KEYWRD,I)
IF(INDEX(KEYWRD,' LET').EQ.0.AND.TOL2.LT.0.01D0)THEN
WRITE(6,'(/,A)')' GNORM HAS BEEN SET TOO LOW, RESET TO 0
1.01. SPECIFY LET AS KEYWORD TO ALLOW GNORM LESS THAN 0.01'
TOL2=0.01D0
ENDIF
I=INDEX(KEYWRD,' HESS=')
IF(I.NE.0) IGTHES=READA(KEYWRD,I)
I=INDEX(KEYWRD,' RMIN=')
IF(I.NE.0) RMIN=READA(KEYWRD,I)
I=INDEX(KEYWRD,' RMAX=')
IF(I.NE.0) RMAX=READA(KEYWRD,I)
I=INDEX(KEYWRD,' OMIN=')
IF(I.NE.0) OMIN=READA(KEYWRD,I)
TIME1=TIME0
TIME2=TIME1
C DONE WITH ALL INITIALIZING STUFF.
C CHECK THAT OPTIONS REQUESTED ARE RESONABLE
IF(NVAR.GT.(3*NUMAT-6) .and. numat.ge.3)WRITE(6,25)
25 FORMAT(/,'*** WARNING! MORE VARIABLES THAN DEGREES OF FREEDOM',
1/)
IF((ITS.NE.0).AND.(IUPD.EQ.2))THEN
WRITE(6,*)' TS SEARCH AND BFGS UPDATE WILL NOT WORK'
STOP
ENDIF
IF((ITS.NE.0).AND.(IGTHES.EQ.0))THEN
WRITE(6,*)' TS SEARCH REQUIRE BETTER THAN DIAGONAL HESSIAN'
STOP
ENDIF
IF((IGTHES.LT.0).OR.(IGTHES.GT.3))THEN
WRITE(6,*)' UNRECOGNIZED HESS OPTION',IGTHES
STOP
ENDIF
IF((OMIN.LT.0.d0).OR.(OMIN.GT.1.d0))THEN
WRITE(6,*)' OMIN MUST BE BETWEEN 0 AND 1',OMIN
STOP
ENDIF
IF (RESTRT) THEN
C
C RESTORE DATA. I INDICATES (HESSIAN RESTART OR OPTIMIZATION
C RESTART). IF I .GT. 0 THEN HESSIAN RESTART AND I IS LAST
C STEP CALCULATED IN THE HESSIAN. IF I .LE. 0 THEN J (NSTEP)
C IN AN OPTIMIZATION HAS BEEN DONE.
C
IPOW(9)=0
mtmp=mode
CALL EFSAV(TT0,HESS,FUNCT,GRAD,XPARAM,PMAT,I,J,BMAT,IPOW)
mode=mtmp
K=TT0/1000000.D0
TIME0=TIME0-TT0+K*1000000.D0
ILOOP=I
IF (I .GT. 0) THEN
IGTHES=4
NSTEP=J
WRITE(6,'(10X,''RESTARTING HESSIAN AT POINT'',I4)')ILOOP
IF(NSTEP.NE.0)WRITE(6,'(10X,''IN OPTIMIZATION STEP'',I4)'
1)NSTEP
ELSE
NSTEP=J
WRITE(6,'(//10X,''RESTARTING OPTIMIZATION AT STEP'',I4)')
1NSTEP
DO 26 I=1,NVAR
26 GRAD(I)=ZZERO
CALL COMPFG(XPARAM, .TRUE., FUNCT, .TRUE., GRAD, .TRUE.)
ENDIF
ELSE
C NOT A RESTART, WE NEED TO GET THE GRADIENTS
DO 30 I=1,NVAR
30 GRAD(I)=ZZERO
CALL COMPFG(XPARAM, .TRUE., FUNCT, .TRUE., GRAD, .TRUE.)
ENDIF
return
end
SUBROUTINE FORMD(EIGVAL,FX,NVAR,DMAX,
1osmin,ts,lrjk,lorjk,rrscal,donr)
C This version forms geometry step by either pure NR, P-RFO or QA
C algorithm, under the condition that the steplength is less than dmax
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
DOUBLE PRECISION LAMDA,lamda0
INCLUDE 'SIZES'
logical ts,rscal,frodo1,frodo2,lrjk,lorjk,rrscal,donr
DIMENSION EIGVAL(MAXPAR),FX(MAXPAR)
COMMON/OPTEF/OLDF(MAXPAR),D(MAXPAR),VMODE(MAXPAR),
$U(MAXPAR,MAXPAR),DD,rmin,rmax,omin,xlamd,xlamd0,skal,
$MODE,NSTEP,NEGREQ,IPRNT
DATA ZERO/0.0D0/, HALF/0.5D0/, TWO/2.0D+00/, TOLL/1.0D-8/
DATA STEP/5.0D-02/, TEN/1.0D+1/, ONE/1.0D+0/, BIG/1.0D+3/
DATA FOUR/4.0D+00/
DATA TMTWO/1.0D-2/, TMSIX/1.0D-06/, SFIX/1.0D+01/, EPS/1.0D-12/
C
MAXIT=999
NUMIT=0
SKAL=ONE
rscal=rrscal
it=0
jt=1
if (ts) then
IF(MODE.NE.0) THEN
CALL OVERLP(dmax,osmin,NEWMOD,NVAR,lorjk)
if (lorjk) return
C
C ON RETURN FROM OVERLP, NEWMOD IS THE TS MODE
C
IF(NEWMOD.NE.MODE .and. iprnt.ge.1) WRITE(6,1000) MODE,NEWMOD
1000 FORMAT(5X,'WARNING! MODE SWITCHING. WAS FOLLOWING MODE ',I3,
$ ' NOW FOLLOWING MODE ',I3)
MODE=NEWMOD
IT=MODE
ELSE
IT=1
ENDIF
eigit=eigval(it)
IF (IPRNT.GE.1) THEN
WRITE(6,900)IT,EIGIT
WRITE(6,910)(U(I,IT),I=1,NVAR)
900 FORMAT(/,5X,'TS MODE IS NUMBER',I3,' WITH EIGENVALUE',F9.1,/,
*5X,'AND COMPONENTS',/)
910 FORMAT(5X,8F9.4)
ENDIF
endif
if (it.eq.1) jt=2
eone=eigval(jt)
ssmin=max(abs(eone)*eps,(ten*eps))
ssmax=max(big,abs(eone))
ssmax=ssmax*big
sstoll=toll
d2max=dmax*dmax
c write(6,*)'from formd, eone, ssmin, ssmax, sstoll',
c $eone,ssmin,ssmax,sstoll
C SOLVE ITERATIVELY FOR LAMDA
C INITIAL GUESS FOR LAMDA IS ZERO EXCEPT NOTE THAT
C LAMDA SHOULD BE LESS THAN EIGVAL(1)
C START BY BRACKETING ROOT, THEN HUNT IT DOWN WITH BRUTE FORCE BISECT.
C
frodo1=.false.
frodo2=.false.
LAMDA=ZERO
lamda0=zero
if (ts .and. eigit.lt.zero .and. eone.ge.zero .and. donr) then
if (iprnt.ge.1) then
write(6,*)' ts search, correct hessian, trying pure NR step'
endif
goto 776
endif
if (.not.ts .and. eone.ge.zero .and. donr) then
if (iprnt.ge.1) then
write(6,*)' min search, correct hessian, trying pure NR step'
endif
goto 776
endif
5 if (ts) then
lamda0=eigval(it)+sqrt(eigval(it)**2+four*fx(it)**2)
lamda0=lamda0*half
if (iprnt.ge.1)WRITE(6,1030) LAMDA0
endif
SSTEP = STEP
IF(EONE.LE.ZERO) LAMDA=EONE-SSTEP
IF(EONE.GT.ZERO) SSTEP=EONE
BL = LAMDA - SSTEP
BU = LAMDA + SSTEP*HALF
20 FL = ZERO
FU = ZERO
DO 30 I = 1,NVAR
if (i.eq.it) goto 30
FL = FL + (FX(I)*FX(I))/(BL-EIGVAL(I))
FU = FU + (FX(I)*FX(I))/(BU-EIGVAL(I))
30 CONTINUE
FL = FL - BL
FU = FU - BU
c write(6,*)'bl,bu,fl,fu from brack'
c write(6,668)bl,bu,fl,fu
c668 format(6f20.15)
IF (FL*FU .LT. ZERO) GOTO 40
BL = BL - (EONE-BL)
BU = BU + HALF*(EONE-BU)
IF (BL.LE.-SSMAX) then
BL = -SSMAX
frodo1=.true.
endif
IF (abs(eone-bu).le.ssmin) then
BU = EONE-SSMIN
frodo2=.true.
endif
IF (frodo1.and.frodo2) THEN
WRITE(6,*)'NUMERICAL PROBLEMS IN BRACKETING LAMDA',
$ EONE,BL,BU,FL,FU
write(6,*)' going for fixed step size....'
goto 450
ENDIF
GOTO 20
40 CONTINUE
NCNT = 0
XLAMDA = ZERO
50 CONTINUE
FL = ZERO
FU = ZERO
FM = ZERO
LAMDA = HALF*(BL+BU)
DO 60 I = 1,NVAR
if (i.eq.it) goto 60
FL = FL + (FX(I)*FX(I))/(BL-EIGVAL(I))
FU = FU + (FX(I)*FX(I))/(BU-EIGVAL(I))
FM = FM + (FX(I)*FX(I))/(LAMDA-EIGVAL(I))
60 CONTINUE
FL = FL - BL
FU = FU - BU
FM = FM - LAMDA
c write(6,*)'bl,bu,lamda,fl,fu,fm from search'
c write(6,668)bl,bu,lamda,fl,fu,fm
IF (ABS(XLAMDA-LAMDA).LT.sstoll) GOTO 776
NCNT = NCNT + 1
IF (NCNT.GT.1000) THEN
WRITE(6,*)'TOO MANY ITERATIONS IN LAMDA BISECT',
$ BL,BU,LAMDA,FL,FU
STOP
ENDIF
XLAMDA = LAMDA
IF (FM*FU.LT.ZERO) BL = LAMDA
IF (FM*FL.LT.ZERO) BU = LAMDA
GOTO 50
C
776 if (iprnt.ge.1) WRITE(6,1031) LAMDA
C
C CALCULATE THE STEP
C
DO 310 I=1,NVAR
D(I)=ZERO
310 CONTINUE
DO 330 I=1,NVAR
if (lamda.eq.zero .and. abs(eigval(i)).lt.tmtwo) then
temp=zero
else
TEMP=FX(I)/(LAMDA-EIGVAL(I))
endif
if (i.eq.it) then
TEMP=FX(IT)/(LAMDA0-EIGVAL(IT))
endif
if (iprnt.ge.5) write(6,*)'formd, delta step',i,temp
DO 320 J=1,NVAR
D(J)=D(J)+TEMP*U(J,I)
320 CONTINUE
330 CONTINUE
dd=sqrt(dot(d,d,nvar))
if(lamda.eq.zero .and. lamda0.eq.zero .and.iprnt.ge.1)
1 write(6,777)dd
777 format(1x,'pure NR-step has length',f10.5)
if(lamda.ne.zero .and. lamda0.ne.-lamda .and.iprnt.ge.1)
1write(6,778)dd
778 format(1x,'P-RFO-step has length',f10.5)
if (dd.lt.(dmax+tmsix)) then
xlamd=lamda
xlamd0=lamda0
return
endif
if (lamda.eq.zero .and. lamda0.eq.zero) goto 5
if (rscal) then
SKAL=DMAX/DD
DO 160 I=1,NVAR
D(I)=D(I)*SKAL
160 CONTINUE
DD=SQRT(DOT(D,D,NVAR))
IF(IPRNT.GE.1)WRITE(6,170)SKAL
170 FORMAT(5X,'CALCULATED STEP SIZE TOO LARGE, SCALED WITH',F9.5)
xlamd=lamda
xlamd0=lamda0
return
endif
450 LAMDA=ZERO
frodo1=.false.
frodo2=.false.
SSTEP = STEP
IF(EONE.LE.ZERO) LAMDA=EONE-SSTEP
if (ts .and. -eigit.lt.eone) lamda=-eigit-sstep
IF(EONE.GT.ZERO) SSTEP=EONE
BL = LAMDA - SSTEP
BU = LAMDA + SSTEP*HALF
520 FL = ZERO
FU = ZERO
DO 530 I = 1,NVAR
if (i.eq.it) goto 530
FL = FL + (FX(I)/(BL-EIGVAL(I)))**2
FU = FU + (FX(I)/(BU-EIGVAL(I)))**2
530 CONTINUE
if (ts) then
FL = FL + (FX(IT)/(BL+EIGVAL(IT)))**2
FU = FU + (FX(IT)/(BU+EIGVAL(IT)))**2
endif
FL = FL - d2max
FU = FU - d2max
c write(6,*)'bl,bu,fl,fu from brack2'
c write(6,668)bl,bu,fl,fu
IF (FL*FU .LT. ZERO) GOTO 540
BL = BL - (EONE-BL)
BU = BU + HALF*(EONE-BU)
IF (BL.LE.-SSMAX) then
BL = -SSMAX
frodo1=.true.
endif
IF (abs(eone-bu).le.ssmin) then
BU = EONE-SSMIN
frodo2=.true.
endif
IF (frodo1.and.frodo2) THEN
WRITE(6,*)'NUMERICAL PROBLEMS IN BRACKETING LAMDA',
$ EONE,BL,BU,FL,FU
write(6,*)' going for fixed level shifted NR step...'
c both lamda searches failed, go for fixed level shifted nr
c this is unlikely to produce anything useful, but maybe we're lucky
lamda=eone-sfix
lamda0=eigit+sfix
rscal=.true.
goto 776
ENDIF
GOTO 520
540 CONTINUE
NCNT = 0
XLAMDA = ZERO
550 CONTINUE
FL = ZERO
FU = ZERO
FM = ZERO
LAMDA = HALF*(BL+BU)
DO 560 I = 1,NVAR
if (i.eq.it) goto 560
FL = FL + (FX(I)/(BL-EIGVAL(I)))**2
FU = FU + (FX(I)/(BU-EIGVAL(I)))**2
FM = FM + (FX(I)/(LAMDA-EIGVAL(I)))**2
560 CONTINUE
if (ts) then
FL = FL + (FX(IT)/(BL+EIGVAL(IT)))**2