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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)
OPEN(UNIT=9,FILE='FOR009',STATUS='UNKNOWN',FORM='UNFORMATTED')
REWIND 9
OPEN(UNIT=10,FILE='FOR010',STATUS='UNKNOWN',FORM='UNFORMATTED')
REWIND 10
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
C------- modified by I. Cserny, June 21, 1995 -------
IF(INDEX(KEYWRD,' PREC') .NE. 0) TOL2=1.D-2
C----------------------------------------------------
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
FU = FU + (FX(IT)/(BU+EIGVAL(IT)))**2
FM = FM + (FX(IT)/(LAMDA+EIGVAL(IT)))**2
endif
FL = FL - d2max
FU = FU - d2max
FM = FM - d2max
c write(6,*)'bl,bu,lamda,fl,fu,fm from search2'
c write(6,668)bl,bu,lamda,fl,fu,fm
IF (ABS(XLAMDA-LAMDA).LT.sstoll) GOTO 570
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 550
C
570 CONTINUE
lamda0=-lamda
rscal=.true.
goto 776
C
1030 FORMAT(1X,'lamda that maximizes along ts modes = ',F15.5)
1031 FORMAT(1X,'lamda that minimizes along all modes = ',F15.5)
END
SUBROUTINE GETHES(XPARAM,IGTHES,NVAR,iloop,TOTIME)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
C GET THE HESSIAN. DEPENDING ON IGTHES WE GET IT FROM :
C
C 0 : DIAGONAL MATRIX, DGHSX*I (DEFAULT FOR MIN-SEARCH)
C 1 : CALCULATE IT NUMERICALLY (DEFAULT FOR TS-SEARCH)
C 2 : READ IN FROM FTN009
C 3 : CALCULATE IT BY DOUBLE NUMERICAL DIFFERENTIATION
C 4 : READ IN FROM FTN009 (DURING RESTART, PARTLY OR WHOLE,
C ALREADY DONE AT THIS POINT)
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 /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 /SIGMA2/ GNEXT1(MAXPAR), GMIN1(MAXPAR)
COMMON /NLLCOM/ HESS(MAXPAR,MAXPAR),BMAT(MAXPAR,MAXPAR),
*PMAT(MAXPAR**2)
COMMON /SCRACH/ PVEC(MAXPAR**2)
COMMON /TIMDMP/ TLEFT, TDUMP
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), EIGVAL(MAXPAR),TVEC(MAXPAR),SVEC(MAXPAR),
*FX(MAXPAR),HESSC(MAXHES),UC(MAXPAR**2)
DIMENSION XPARAM(*),tmp(150,150)
LOGICAL RESTRT,SCF1,LDUM
CHARACTER*241 KEYWRD,LINE
CHARACTER CHDOT*1,ZERO*1,NINE*1,CH*1
DATA CHDOT,ZERO,NINE /'.','0','9'/
DATA ICALCN,ZZERO,ONE,TWO /0,0.D0,1.D0,2.D0/
C
DATA DGHSS,DGHSA,DGHSD /1000.d0,500.d0,200.d0/
DATA XINC /1.d-3/
C DGHSX IS HESSIAN DIAGONAL FOR IGTHES=0 (STRETCHING, ANGLE,
C DIHEDRAL). THE VALUES SHOULD BE 'OPTIMUM' FOR CYCLOHEXANONE
C XINC IS STEPSIZE FOR HESSIAN CALCULATION. TESTS SHOWS THAT IT SHOULD
C BE IN THE RANGE 10(-2) TO 10(-4). 10(-3) APPEARS TO BE
C A REASONABLE COMPROMISE BETWEEN ACCURACY AND NUMERICAL PROBLEMS
IF (IGTHES.EQ.0) THEN
WRITE(6,60)
60 FORMAT(/,10X,'DIAGONAL MATRIX USED AS START HESSIAN',/)
DO 70 I=1,NVAR
DO 70 J=1,NVAR
HESS(I,J)=ZZERO
70 CONTINUE
IJ=1
DO 80 J=1,NUMATM
DO 80 I=1,3
IF (LOC(2,IJ).EQ.I.AND.LOC(1,IJ).EQ.J)THEN
IF (I.EQ.1)HESS(IJ,IJ)=DGHSS
IF (I.EQ.2)HESS(IJ,IJ)=DGHSA
IF (I.EQ.3)HESS(IJ,IJ)=DGHSD
IJ=IJ+1
ENDIF
80 CONTINUE
IJ=IJ-1
IF(IJ.NE.NVAR)WRITE(*,*)'ERROR IN IGTHES=0,IJ,NVAR',IJ,NVAR
ENDIF
C
IF (IGTHES.EQ.2) THEN
WRITE(6,100)
100 FORMAT(/,10X,'HESSIAN READ FROM DISK',/)
IPOW(9)=0
C USE DUMMY ARRAY FOR CALL EXCEPT FOR HESSIAN
C TEMPORARY SET NALPHA = 0, THEN WE CAN READ HESSIAN FROM RHF
C RUN FOR USE IN SAY UHF RUNS
C ALSO SAVE MODE, TO ALLOW FOLLOWING A DIFFERENT MODE THAN THE ONE
C CURRENTLY ON RESTART FILE
nxxx=nalpha
nalpha=0
mtmp=mode
CALL EFSAV(TDM,HESS,FDMY,GNEXT1,GMIN1,PMAT,IIDUM,J,BMAT,IPOW)
nalpha=nxxx
mode=mtmp
nstep=0
ENDIF
IF((IGTHES.EQ.1).OR.(IGTHES.EQ.3).OR.(IGTHES.EQ.4))THEN
C IF IGTHES IS .EQ. 4, THEN THIS IS A HESSIAN RESTART.
C USE GNEXT1 AND DUMMY FOR CALLS TO COMPFG DURING HESSIAN
C CALCULATION
IF (IGTHES.EQ.1)WRITE(6,190)
190 FORMAT(/,10X,'HESSIAN CALCULATED NUMERICALLY',/)
IF (IGTHES.EQ.3)WRITE(6,191)
191 FORMAT(/,10X,'HESSIAN CALCULATED DOUBLE NUMERICALLY',/)
IF(IPRNT.GE.5)WRITE(6,'(I3,12(8F9.4,/3X))')
1 0,(Grad(IF),IF=1,NVAR)
TIME1=SECOND()
TSTORE=TIME1
DO 210 I=ILOOP,NVAR
XPARAM(I)=XPARAM(I) + XINC
CALL COMPFG(XPARAM, .TRUE., DUMMY, .TRUE., GNEXT1, .TRUE.)
IF(IPRNT.GE.5)WRITE(6,'(I3,12(8F9.4,/3X))')
1 I,(GNEXT1(IF),IF=1,NVAR)
XPARAM(I)=XPARAM(I) - XINC
if (igthes.eq.3) then
XPARAM(I)=XPARAM(I) - XINC
CALL COMPFG(XPARAM, .TRUE., DUMMY, .TRUE., GMIN1, .TRUE.)
IF(IPRNT.GE.5)WRITE(6,'(I3,12(8F9.4,/3X))')
1 -I,(GMIN1(IF),IF=1,NVAR)
XPARAM(I)=XPARAM(I) + XINC
DO 199 J=1,NVAR
199 HESS(I,J)= (GNEXT1(J)-GMIN1(J))/(XINC+XINC)
else
DO 200 J=1,NVAR
200 HESS(I,J)= (GNEXT1(J)-GRAD(J))/XINC
endif
TIME2=SECOND()
TSTEP=TIME2-TIME1
TLEFT=TLEFT-TSTEP
TIME1=TIME2
IF( TLEFT .LT. TSTEP*TWO) THEN
C
C STORE PARTIAL HESSIAN PATRIX
C STORE GRADIENTS FOR GEOMETRY AND ILOOP AS POSITIVE
WRITE(6,'(A)')' NOT ENOUGH TIME TO COMPLETE HESSIAN'
WRITE(6,'(A,I4)')' STOPPING IN HESSIAN AT COORDINATE:',I
IPOW(9)=1
TT0=SECOND()-TIME0
CALL EFSAV(TT0,HESS,FUNCT,GRAD,XPARAM,PMAT,I,NSTEP,BMAT,
1IPOW)
STOP
ENDIF
210 CONTINUE
C fix last entry in geo array, this is currently at value-xinc
K=LOC(1,nvar)
L=LOC(2,nvar)
GEO(L,K)=XPARAM(nvar)
IF(NDEP.NE.0) CALL SYMTRY
c add all time used back to tleft, this will then be subtracted
c again in main ef routine
TIME2=SECOND()
TSTEP=TIME2-TSTORE
TLEFT=TLEFT+TSTEP
ENDIF
C
C SYMMETRIZE HESSIAN
DO 220 I=1,NVAR
C$DIR NO_RECURRENCE
DO 220 J=1,I-1
HESS(I,J)=(HESS(I,J)+HESS(J,I))/TWO
HESS(J,I)=HESS(I,J)
220 CONTINUE
RETURN
END
C*MODULE BLAS1 *DECK IDAMAX
INTEGER FUNCTION IDAMAX(N,DX,INCX)
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
DIMENSION DX(1)
C
C FINDS THE INDEX OF ELEMENT HAVING MAX. ABSOLUTE VALUE.
C JACK DONGARRA, LINPACK, 3/11/78.
C
IDAMAX = 0
IF( N .LT. 1 ) RETURN
IDAMAX = 1
IF(N.EQ.1)RETURN
IF(INCX.EQ.1)GO TO 20
C
C CODE FOR INCREMENT NOT EQUAL TO 1
C
IX = 1
RMAX = ABS(DX(1))
IX = IX + INCX
DO 10 I = 2,N
IF(ABS(DX(IX)).LE.RMAX) GO TO 5
IDAMAX = I
RMAX = ABS(DX(IX))
5 IX = IX + INCX
10 CONTINUE
RETURN
C
C CODE FOR INCREMENT EQUAL TO 1
C
20 RMAX = ABS(DX(1))
DO 30 I = 2,N
IF(ABS(DX(I)).LE.RMAX) GO TO 30
IDAMAX = I
RMAX = ABS(DX(I))
30 CONTINUE
RETURN
END
SUBROUTINE OVERLP(dmax,osmin,NEWMOD,NVAR,lorjk)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
COMMON/OPTEF/OLDF(MAXPAR),D(MAXPAR),VMODE(MAXPAR),
$U(MAXPAR,MAXPAR),DD,rmin,rmax,omin,xlamd,xlamd0,skal,
$MODE,NSTEP,NEGREQ,IPRNT
dimension xo(maxpar)
logical lorjk,first
data first/.true./
C
C ON THE FIRST STEP SIMPLY DETERMINE WHICH MODE TO FOLLOW
C
c IF(NSTEP.EQ.1) THEN
IF(first) THEN
first=.false.
IF(MODE.GT.NVAR)THEN
WRITE(6,*)'ERROR!! MODE IS LARGER THAN NVAR',MODE
STOP
ENDIF
IT=MODE
if (iprnt.ge.1) WRITE(6,40) MODE
40 FORMAT(5X,'HESSIAN MODE FOLLOWING SWITCHED ON'/
1 ' FOLLOWING MODE ',I3)
C
ELSE
C
C ON SUBSEQUENT STEPS DETERMINE WHICH HESSIAN EIGENVECTOR HAS
C THE GREATEST OVERLAP WITH THE MODE WE ARE FOLLOWING
C
IT=1
lorjk=.false.
TOVLP=DOT(U(1,1),VMODE,NVAR)
TOVLP=ABS(TOVLP)
c xo(1)=tovlp
DO 10 I=2,NVAR
OVLP=DOT(U(1,I),VMODE,NVAR)
OVLP=ABS(OVLP)
c xo(i)=ovlp
IF(OVLP.GT.TOVLP) THEN
TOVLP=OVLP
IT=I
ENDIF
10 CONTINUE
C
if (iprnt.ge.5) then
do j=1,5
xxx=0.d0
do i=1,nvar
if (xo(i).gt.xxx)ix=i
if (xo(i).gt.xxx)xxx=xo(i)
enddo
xo(ix)=0.d0
write(6,*)'overlaps',ix,xxx
enddo
endif
if(iprnt.ge.1)WRITE(6,30) IT,TOVLP
if (tovlp.lt.omin) then
if (dmax.gt.osmin) then
lorjk=.true.
if (iprnt.ge.1)write(6,31)omin
return
else
if (iprnt.ge.1)write(6,32)omin,dmax,osmin
endif
endif
ENDIF
30 FORMAT(5X,'OVERLAP OF CURRENT MODE',I3,' WITH PREVIOUS MODE IS ',
$ F6.3)
31 FORMAT(5X,'OVERLAP LESS THAN OMIN',
1F6.3,' REJECTING PREVIOUS STEP')
32 FORMAT(5X,'OVERLAP LESS THAN OMIN',F6.3,' BUT TRUST RADIUS',F6.3,
$ ' IS LESS THAN',F6.3,/,5X,' ACCEPTING STEP')
C
C SAVE THE EIGENVECTOR IN VMODE
C
DO 20 I=1,NVAR
VMODE(I)=U(I,IT)
20 CONTINUE
C
NEWMOD=IT
RETURN
C
END
SUBROUTINE PRJFC(F,xparam,nvar)
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
INCLUDE 'SIZES'
C
C CALCULATES PROJECTED FORCE CONSTANT MATRIX (F).
C THIS ROUTINE CAME ORIGINALLY FROM POLYRATE. IT IS USED BY PERMISSION
C OF D. TRUHLAR. THE CURRENT VERSION IS LIFTED FROM GAMESS AND
C ADAPTED BY F.JENSEN, ODENSE, DK
C IF WE ARE AT A STATIONARY POINT (STPT=.T.), I.E. GNORM .LT. 10,
C THEN THE ROTATIONAL AND TRANSLATIONAL MODES ARE PROJECTED OUT
C AND THEIR FREQUENCIES BECOME IDENTICAL ZERO. IF NOT AT A STATIONARY
C POINT THEN THE MASS-WEIGHTED GRADIENT IS ALSO PROJECTED OUT AND
C THE CORRESPONDING FREQUENCY BECOME ZERO.
C ************************************************
C X : MASS-WEIGHTED COORDINATE
C DX: NORMALIZED MASS-WEIGHTED GRADIENT VECTOR
C F : MASS-WEIGHTED FORCE CONSTANT MATRIX
C RM: INVERSION OF SQUARE ROOT OF MASS
C P, COF: BUFFER
C
COMMON /ATMASS/ ATMASS(NUMATM)
DIMENSION X(MAXPAR),RM(MAXPAR),F(MAXPAR,MAXPAR),
* P(MAXPAR,MAXPAR),COF(MAXPAR,MAXPAR)
DIMENSION TENS(3,3,3),ROT(3,3),SCR(3,3),ISCR(6),CMASS(3)
dimension coord(3,numatm),dx(maxpar),xparam(maxpar)
DIMENSION DETX(2)
EQUIVALENCE (DET,DETX(1))
PARAMETER (ZERO=0.0d+00, ONE=1.0d+00, EPS=1.0d-14,
* CUT5=1.0d-05, CUT8=1.0d-08)
C
C TOTALLY ASYMMETRIC CARTESIAN TENSOR.
DATA TENS/ 0.0d+00, 0.0d+00, 0.0d+00,
X 0.0d+00, 0.0d+00, -1.0d+00,
X 0.0d+00, 1.0d+00, 0.0d+00,
Y 0.0d+00, 0.0d+00, 1.0d+00,
Y 0.0d+00, 0.0d+00, 0.0d+00,
Y -1.0d+00, 0.0d+00, 0.0d+00,
Z 0.0d+00, -1.0d+00, 0.0d+00,
Z 1.0d+00, 0.0d+00, 0.0d+00,
Z 0.0d+00, 0.0d+00, 0.0d+00 /
C
natm=nvar/3
nc1=nvar
ij=1
do 2 i=1,natm
coord(1,i)=xparam(ij)
coord(2,i)=xparam(ij+1)
coord(3,i)=xparam(ij+2)
ij=ij+3
2 continue
C CALCULATE 1/SQRT(MASS)
L=0
DO 3 I=1,NATM
TMP=ONE/SQRT(ATMASS(I))
DO 3 J=1,3
L=L+1
3 RM(L)=TMP
C PREPARE GRADIENT
DO 4 I=1,NC1
4 DX(I)=ZERO
C FIND CMS AND CALCULATED MASS WEIGHTED COORDINATES
totm=zero
cmass(1)=zero
cmass(2)=zero
cmass(3)=zero
DO 6 I=1,NATM
TOTM=TOTM+ATMASS(I)
DO 6 J=1,3
CMASS(J)=CMASS(J)+ATMASS(I)*COORD(J,I)
6 CONTINUE
DO 7 J=1,3
7 CMASS(J)=CMASS(J)/TOTM
L=0
DO 8 I=1,NATM
DO 8 J=1,3
TMP=SQRT(ATMASS(I))
L=L+1
X(L)=TMP*(COORD(J,I)-CMASS(J))
8 CONTINUE
c WRITE(6,9020)
c CALL prsq(f,nc1,nc1,maxpar,1)
c9020 FORMAT(/1X,'ENTER THE SUBROUTINE <PRJFC>'//
c * 1X,'UNPROJECTED FORCE CONSTANT MATRIX (HARTREE/BOHR**2)')
c WRITE(6,*)' MASS-WEIGHTED COORDINATES AND CORRESPONDING GRADIENT'
c DO 9 I=1,NC1
c9 WRITE(6,*)X(I),DX(I)
C
C 2. COMPUTE INERTIA TENSOR.
DO 10 I=1,3
DO 10 J=1,3
10 ROT(I,J)=ZERO
DO 20 I=1,NATM
L=3*(I-1)+1
ROT(1,1)=ROT(1,1)+X(L+1)**2+X(L+2)**2
ROT(1,2)=ROT(1,2)-X(L)*X(L+1)
ROT(1,3)=ROT(1,3)-X(L)*X(L+2)
ROT(2,2)=ROT(2,2)+X(L)**2+X(L+2)**2
ROT(2,3)=ROT(2,3)-X(L+1)*X(L+2)
20 ROT(3,3)=ROT(3,3)+X(L)**2+X(L+1)**2
ROT(2,1)=ROT(1,2)
ROT(3,1)=ROT(1,3)
ROT(3,2)=ROT(2,3)
C
CHECK THE INERTIA TENSOR.
CHK=ROT(1,1)*ROT(2,2)*ROT(3,3)
IF(ABS(CHK).GT.CUT8) GO TO 21
c WRITE(6,23)
c 23 FORMAT(/1X,'MATRIX OF INERTIA MOMENT')
c CALL PRSQ(ROT,3,3,3,3)
IF(ABS(ROT(1,1)).GT.CUT8) GO TO 11
C X=0
IF(ABS(ROT(2,2)).GT.CUT8) GO TO 12
C X,Y=0
IF(ABS(ROT(3,3)).GT.CUT8) GO TO 13
WRITE(6,14) ROT(1,1),ROT(2,2),ROT(3,3)
14 FORMAT(1X,'EVERY DIAGONAL ELEMENTS ARE ZERO ?',3F20.10)
RETURN
C
C* 1. X,Y=0 BUT Z.NE.0
13 ROT(3,3)=ONE/ROT(3,3)
GO TO 22
C Y.NE.0
12 IF(ABS(ROT(3,3)).GT.CUT8) GO TO 15
C* 2. X,Z=0 BUT Y.NE.0
ROT(2,2)=ONE/ROT(2,2)
GO TO 22
C X.NE.0
11 IF(ABS(ROT(2,2)).GT.CUT8) GO TO 16
IF(ABS(ROT(3,3)).GT.CUT8) GO TO 17
C* 3. Y,Z=0 BUT X.NE.0
ROT(1,1)=ONE/ROT(1,1)
GO TO 22
C* 4. X,Y.NE.0 BUT Z=0
16 DET=ROT(1,1)*ROT(2,2)-ROT(1,2)*ROT(2,1)
TRP=ROT(1,1)
ROT(1,1)=ROT(2,2)/DET
ROT(2,2)=TRP/DET
ROT(1,2)=-ROT(1,2)/DET
ROT(2,1)=-ROT(2,1)/DET
GO TO 22
C* 5. X,Z.NE.0 BUT Y=0
17 DET=ROT(1,1)*ROT(3,3)-ROT(1,3)*ROT(3,1)
TRP=ROT(1,1)
ROT(1,1)=ROT(3,3)/DET
ROT(3,3)=TRP/DET
ROT(1,3)=-ROT(1,3)/DET
ROT(3,1)=-ROT(3,1)/DET
GO TO 22
C* 6. Y,Z.NE.0 BUT X=0
15 DET=ROT(3,3)*ROT(2,2)-ROT(3,2)*ROT(2,3)
TRP=ROT(3,3)
ROT(3,3)=ROT(2,2)/DET
ROT(2,2)=TRP/DET
ROT(3,2)=-ROT(3,2)/DET
ROT(2,3)=-ROT(2,3)/DET
GO TO 22
21 CONTINUE
C
C.DEBUG.
c CALL PRSQ(TENS(1,1,1),3,3,3,3)
c CALL PRSQ(TENS(1,1,2),3,3,3,3)
c CALL PRSQ(TENS(1,1,3),3,3,3,3)
c CALL PRSQ(ROT,3,3,3,3)
C
C 4. COMPUTE INVERSION MATRIX OF ROT.
C CALL MXLNEQ(ROT,3,3,DET,JRNK,EPS,SCR,+0)
C IF(JRNK.LT.3) STOP 1
INFO=0
CALL DGEFA(ROT,3,3,ISCR,INFO)
IF(INFO.NE.0) STOP
DET=ZERO
CALL DGEDI(ROT,3,3,ISCR,DETX,SCR,1)
C
22 CONTINUE
c WRITE (6,702)
c 702 FORMAT(/1X,'INVERSE MATRIX OF MOMENT OF INERTIA.')
c CALL PRSQ(ROT,3,3,3,3)
C
C 5. TOTAL MASS ---> TOTM.
C
C 6. COMPUTE P MATRIX
C ----------------
DO 100 IP=1,NATM
INDX=3*(IP-1)
DO 100 JP=1,IP
JNDX=3*(JP-1)
DO 70 IC=1,3
JEND=3
IF(JP.EQ.IP) JEND=IC
DO 70 JC=1,JEND
SUM=ZERO
DO 50 IA=1,3
DO 50 IB=1,3
IF(TENS(IA,IB,IC).EQ.0) GO TO 50
DO 30 JA=1,3
DO 30 JB=1,3
IF(TENS(JA,JB,JC).EQ.0) GO TO 30
SUM=SUM+TENS(IA,IB,IC)*TENS(JA,JB,JC)*ROT(IA,JA)*
& X(INDX+IB)*X(JNDX+JB)
30 CONTINUE
50 CONTINUE
II=INDX+IC
JJ=JNDX+JC
P(II,JJ)=SUM+DX(II)*DX(JJ)
IF(IC.EQ.JC) P(II,JJ)=P(II,JJ)+ONE/(RM(II)*RM(JJ)*TOTM)
70 CONTINUE
100 CONTINUE
C
C 7. COMPUTE DELTA(I,J)-P(I,J)
DO 110 I=1,NC1
DO 110 J=1,I
P(I,J)=-P(I,J)
IF(I.EQ.J) P(I,J) = ONE +P(I,J)
110 CONTINUE
C
C 8. NEGLECT SMALLER VALUES THAN 10**-8.
DO 120 I=1,NC1
DO 120 J=1,I
IF(ABS(P(I,J)).LT.CUT8) P(I,J)=ZERO
P(J,I)=P(I,J)
120 CONTINUE
C
C.DEBUG.
c WRITE(6,703)
c 703 FORMAT(/1X,'PROJECTION MATRIX')
c CALL PRSQ(P,NC1,NC1,NC1)
c CALL PRSQ(P,NC1,NC1,maxpar,3)
C
C 10. POST AND PREMULTIPLY F BY P.
C USE COF FOR SCRATCH.
DO 150 I=1,NC1
DO 150 J=1,NC1
SUM=ZERO
DO 140 K=1,NC1
140 SUM=SUM+F(I,K)*P(K,J)
150 COF(I,J)=SUM
C
C 11. COMPUTE P*F*P.
DO 200 I=1,NC1
DO 200 J=1,NC1
SUM=ZERO
DO 190 K=1,NC1
190 SUM=SUM+P(I,K)*COF(K,J)
200 F(I,J)=SUM
C
c WRITE(6,9030)
c CALL prsq(f,nc1,nc1,maxpar,1)
c9030 FORMAT(/1X,'LEAVE THE SUBROUTINE <PRJFC>'//
c * 1X,'PROJECTED FORCE CONSTANT MATRIX (HARTREE/BOHR**2)')
RETURN
END
SUBROUTINE PRTHES(EIGVAL,NVAR)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
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 EIGVAL(MAXPAR)
IF (IPRNT.GE.4) THEN
WRITE(6,*)' '
WRITE(6,*)' HESSIAN MATRIX'
LOW=1
NUP=8
540 NUP=MIN(NUP,NVAR)
WRITE(6,1000) (I,I=LOW,NUP)
DO 550 I=1,NVAR
WRITE(6,1010) I,(HESS(I,J),J=LOW,NUP)
550 CONTINUE
NUP=NUP+8
LOW=LOW+8
IF(LOW.LE.NVAR) GOTO 540
ENDIF
WRITE(6,*)' '
WRITE(6,*)' HESSIAN EIGENVALUES AND -VECTORS'
LOW=1
NUP=8
560 NUP=MIN(NUP,NVAR)
WRITE(6,1000) (I,I=LOW,NUP)
WRITE(6,1020) (EIGVAL(I),I=LOW,NUP)
DO 570 I=1,NVAR
WRITE(6,1030) I,(U(I,J),J=LOW,NUP)
570 CONTINUE
NUP=NUP+8
LOW=LOW+8
IF(LOW.LE.NVAR) GOTO 560
1000 FORMAT(/,3X,8I9)
1010 FORMAT(1X,I3,8F9.1)
1020 FORMAT(/,4X,8F9.1,/)
1030 FORMAT(1X,I3,8F9.4)
RETURN
END
SUBROUTINE UPDHES(SVEC,TVEC,NVAR,IUPD)
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
INCLUDE 'SIZES'
DIMENSION TVEC(*),SVEC(*)
LOGICAL FIRST
COMMON/OPTEF/OLDF(MAXPAR),D(MAXPAR),VMODE(MAXPAR),
$U(MAXPAR,MAXPAR),DD,rmin,rmax,omin,xlamd,xlamd0,skal,
$MODE,NSTEP,NEGREQ,IPRNT
CONVEX COMMON /NLLCOM/ HESS(MAXPAR,MAXPAR*3)
COMMON /NLLCOM/ HESS(MAXPAR,MAXPAR), BMAT(MAXPAR,MAXPAR),
. PMAT(MAXPAR**2)
COMMON /GRADNT/ GRAD(MAXPAR),GNFINA
C
DATA ZERO/0.0D0/
C
C UPDATING OF THE HESSIAN
C DEPENDS ON CURRENT GRADIENTS, OLD GRADIENTS AND THE
C CORRECTION VECTOR USED ON THE LAST CYCLE
C SVEC & TVEC ARE FOR TEMPORARY STORAGE
C
C 2 UPDATING PROCEDURES ARE POSSIBLE
C (I) THE POWELL UPDATE
C THIS PRESERVES THE SYMMETRIC CHARACTER OF THE HESSIAN
C WHILST ALLOWING ITS EIGENVALUE STRUCTURE TO CHANGE.
C IT IS THE DEFAULT UPDATE FOR A TRANSITION STATE SEARCH
C (II) THE BFGS UPDATE
C THIS UPDATE HAS THE IMPORTANT CHARACTERISTIC OF RETAINING
C POSITIVE DEFINITENESS (NOTE: THIS IS NOT RIGOROUSLY
C GUARANTEED, BUT CAN BE CHECKED FOR BY THE PROGRAM).
C IT IS THE DEFAULT UPDATE FOR A MINIMUM SEARCH
C
C SWITCH : IUPD
C IUPD = 0 : SKIP UPDATE
C IUPD = 1 : POWELL
C IUPD = 2 : BFGS
C
IF (.NOT. FIRST) THEN
FIRST=.TRUE.
IF(IPRNT.GE.2) THEN
IF (IUPD.EQ.0)WRITE(6,90)
IF (IUPD.EQ.1)WRITE(6,80)
IF (IUPD.EQ.2)WRITE(6,120)
ENDIF
ENDIF
IF(IUPD.EQ.0) RETURN
CONVEX DO 10 I=1,NVAR
CONVEX TVEC(I)=ZERO
CONVEX DO 10 J=1,NVAR
CONVEX TVEC(I)=TVEC(I) + HESS(I,J)*D(J)
CONVEX 10 CONTINUE
DO 5 I=1,NVAR
TVEC(I)=ZERO
5 CONTINUE
DO 10 J=1,NVAR
DO 10 I=1,NVAR
TVEC(I)=TVEC(I) + HESS(I,J)*D(J)
10 CONTINUE
C
IF(IUPD.EQ.1) THEN
C
C (I) POWELL UPDATE
C
DO 20 I=1,NVAR
TVEC(I)=GRAD(I)-OLDF(I)-TVEC(I)
sVEC(I)=GRAD(I)-OLDF(I)
20 CONTINUE
DDS=DD*DD
DDTD=DOT(TVEC,D,NVAR)
DDTD=DDTD/DDS
C
CONVEX DO 40 I=1,NVAR
CONVEX DO 30 J=1,I
CONVEX TEMP=TVEC(I)*D(J) + D(I)*TVEC(J) - D(I)*DDTD*D(J)
CONVEX HESS(I,J)=HESS(I,J)+TEMP/DDS
CONVEX HESS(J,I)=HESS(I,J)
CONVEX 30 CONTINUE
CONVEX 40 CONTINUE
DO 40 I=2,NVAR
C$DIR NO_RECURRENCE
DO 30 J=1,I-1
TEMP=TVEC(I)*D(J) + D(I)*TVEC(J) - D(I)*DDTD*D(J)
HESS(I,J)=HESS(I,J)+TEMP/DDS
HESS(J,I)=HESS(I,J)
30 CONTINUE
40 CONTINUE
DO 45 I=1,NVAR
TEMP=D(I)*(2.0D0*TVEC(I) - D(I)*DDTD)
HESS(I,I)=HESS(I,I)+TEMP/DDS
45 CONTINUE
C
ENDIF
IF (IUPD.EQ.2) THEN
C
C (II) BFGS UPDATE
C
DO 50 I=1,NVAR
SVEC(I)=GRAD(I)-OLDF(I)
50 CONTINUE
DDS=DOT(SVEC,D,NVAR)
C
C IF DDS IS NEGATIVE, RETENTION OF POSITIVE DEFINITENESS IS NOT
C GUARANTEED. PRINT A WARNING AND SKIP UPDATE THIS CYCLE.
C
cfrj With the current level shift technique I think the Hessian should
cfrj be allowed to aquire negative eigenvalues. Without updating the
cfrj optimization has the potential of stalling
cfrj IF(DDS.LT.ZERO) THEN
cfrj WRITE(6,100)
cfrj WRITE(6,110)
cfrj RETURN
cfrj ENDIF
C
DDTD=DOT(D,TVEC,NVAR)
C
CONVEX DO 70 I=1,NVAR
CONVEX DO 60 J=1,I
CONVEX TEMP= (SVEC(I)*SVEC(J))/DDS - (TVEC(I)*TVEC(J))/DDTD
CONVEX HESS(I,J)=HESS(I,J)+TEMP
CONVEX HESS(J,I)=HESS(I,J)
CONVEX 60 CONTINUE
CONVEX 70 CONTINUE
DO 70 I=2,NVAR
C$DIR NO_RECURRENCE
DO 60 J=1,I-1
TEMP= (SVEC(I)*SVEC(J))/DDS - (TVEC(I)*TVEC(J))/DDTD
HESS(I,J)=HESS(I,J)+TEMP
HESS(J,I)=HESS(I,J)
60 CONTINUE
70 CONTINUE
DO 75 I=1,NVAR
TEMP= (SVEC(I)*SVEC(I))/DDS - (TVEC(I)*TVEC(I))/DDTD
HESS(I,I)=HESS(I,I)+TEMP
75 CONTINUE
ENDIF
C
RETURN
C
80 FORMAT(/,5X,'HESSIAN IS BEING UPDATED USING THE POWELL UPDATE',/)
90 FORMAT(/,5X,'HESSIAN IS NOT BEING UPDATED',/)
c 100 FORMAT(5X,'WARNING! HEREDITARY POSITIVE DEFINITENESS ENDANGERED')
c 110 FORMAT(5X,'UPDATE SKIPPED THIS CYCLE')
120 FORMAT(/,5X,'HESSIAN IS BEING UPDATED USING THE BFGS UPDATE',/)
END
C*MODULE BLAS1 *DECK DAXPY
SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY)
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
DIMENSION DX(1),DY(1)
C
C CONSTANT TIMES A VECTOR PLUS A VECTOR.
C DY(I) = DY(I) + DA * DX(I)
C USES UNROLLED LOOPS FOR INCREMENTS EQUAL TO ONE.
C JACK DONGARRA, LINPACK, 3/11/78.
C
IF(N.LE.0)RETURN
IF (DA .EQ. 0.0D+00) RETURN
IF(INCX.EQ.1.AND.INCY.EQ.1)GO TO 20
C
C CODE FOR UNEQUAL INCREMENTS OR EQUAL INCREMENTS
C NOT EQUAL TO 1
C
IX = 1
IY = 1
IF(INCX.LT.0)IX = (-N+1)*INCX + 1
IF(INCY.LT.0)IY = (-N+1)*INCY + 1
DO 10 I = 1,N
DY(IY) = DY(IY) + DA*DX(IX)
IX = IX + INCX
IY = IY + INCY
10 CONTINUE
RETURN
C
C CODE FOR BOTH INCREMENTS EQUAL TO 1
C
C
C CLEAN-UP LOOP
C
20 M = MOD(N,4)
IF( M .EQ. 0 ) GO TO 40
DO 30 I = 1,M
DY(I) = DY(I) + DA*DX(I)
30 CONTINUE
IF( N .LT. 4 ) RETURN
40 MP1 = M + 1
DO 50 I = MP1,N,4
DY(I) = DY(I) + DA*DX(I)
DY(I + 1) = DY(I + 1) + DA*DX(I + 1)
DY(I + 2) = DY(I + 2) + DA*DX(I + 2)
DY(I + 3) = DY(I + 3) + DA*DX(I + 3)
50 CONTINUE
RETURN
END
C ***********************************************************************
c below are math routines needed for prjfc. they are basicly just
c matrix diagonalization routines and should at some point be replaced
c with the diagonalization routine used in the rest of the program.
c the routines below have been lifted from GAMESS
C ***********************************************************************
SUBROUTINE DGEDI(A,LDA,N,IPVT,DET,WORK,JOB)
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
DIMENSION A(LDA,1),DET(2),WORK(1),IPVT(1)
C
C DGEDI COMPUTES THE DETERMINANT AND INVERSE OF A MATRIX
C USING THE FACTORS COMPUTED BY DGECO OR DGEFA.
C
C ON ENTRY
C
C A DOUBLE PRECISION(LDA, N)
C THE OUTPUT FROM DGECO OR DGEFA.
C
C LDA INTEGER
C THE LEADING DIMENSION OF THE ARRAY A .
C
C N INTEGER
C THE ORDER OF THE MATRIX A .
C
C IPVT INTEGER(N)
C THE PIVOT VECTOR FROM DGECO OR DGEFA.
C
C WORK DOUBLE PRECISION(N)
C WORK VECTOR. CONTENTS DESTROYED.
C
C JOB INTEGER
C = 11 BOTH DETERMINANT AND INVERSE.
C = 01 INVERSE ONLY.
C = 10 DETERMINANT ONLY.
C
C ON RETURN
C
C A INVERSE OF ORIGINAL MATRIX IF REQUESTED.
C OTHERWISE UNCHANGED.
C
C DET DOUBLE PRECISION(2)
C DETERMINANT OF ORIGINAL MATRIX IF REQUESTED.
C OTHERWISE NOT REFERENCED.
C DETERMINANT = DET(1) * 10.0**DET(2)
C WITH 1.0 .LE. ABS(DET(1)) .LT. 10.0
C OR DET(1) .EQ. 0.0 .
C
C ERROR CONDITION
C
C A DIVISION BY ZERO WILL OCCUR IF THE INPUT FACTOR CONTAINS
C A ZERO ON THE DIAGONAL AND THE INVERSE IS REQUESTED.
C IT WILL NOT OCCUR IF THE SUBROUTINES ARE CALLED CORRECTLY
C AND IF DGECO HAS SET RCOND .GT. 0.0 OR DGEFA HAS SET
C INFO .EQ. 0 .
C
C LINPACK. THIS VERSION DATED 08/14/78 .
C CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB.
C
C SUBROUTINES AND FUNCTIONS
C
C BLAS DAXPY,DSCAL,DSWAP
C FORTRAN ABS,MOD
C
C COMPUTE DETERMINANT
C
IF (JOB/10 .EQ. 0) GO TO 70
DET(1) = 1.0D+00
DET(2) = 0.0D+00
TEN = 10.0D+00
DO 50 I = 1, N
IF (IPVT(I) .NE. I) DET(1) = -DET(1)
DET(1) = A(I,I)*DET(1)
C ...EXIT
IF (DET(1) .EQ. 0.0D+00) GO TO 60
10 IF (ABS(DET(1)) .GE. 1.0D+00) GO TO 20
DET(1) = TEN*DET(1)
DET(2) = DET(2) - 1.0D+00
GO TO 10
20 CONTINUE
30 IF (ABS(DET(1)) .LT. TEN) GO TO 40
DET(1) = DET(1)/TEN
DET(2) = DET(2) + 1.0D+00
GO TO 30
40 CONTINUE
50 CONTINUE
60 CONTINUE
70 CONTINUE
C
C COMPUTE INVERSE(U)
C
IF (MOD(JOB,10) .EQ. 0) GO TO 150
DO 100 K = 1, N
A(K,K) = 1.0D+00/A(K,K)
T = -A(K,K)
CALL DSCAL(K-1,T,A(1,K),1)
KP1 = K + 1
IF (N .LT. KP1) GO TO 90
DO 80 J = KP1, N
T = A(K,J)
A(K,J) = 0.0D+00
CALL DAXPY(K,T,A(1,K),1,A(1,J),1)
80 CONTINUE
90 CONTINUE
100 CONTINUE
C
C FORM INVERSE(U)*INVERSE(L)
C
NM1 = N - 1
IF (NM1 .LT. 1) GO TO 140
DO 130 KB = 1, NM1
K = N - KB
KP1 = K + 1
DO 110 I = KP1, N
WORK(I) = A(I,K)
A(I,K) = 0.0D+00
110 CONTINUE
DO 120 J = KP1, N
T = WORK(J)
CALL DAXPY(N,T,A(1,J),1,A(1,K),1)
120 CONTINUE
L = IPVT(K)
IF (L .NE. K) CALL DSWAP(N,A(1,K),1,A(1,L),1)
130 CONTINUE
140 CONTINUE
150 CONTINUE
RETURN
END
SUBROUTINE DGEFA(A,LDA,N,IPVT,INFO)
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
DIMENSION A(LDA,1),IPVT(1)
C
C DGEFA FACTORS A DOUBLE PRECISION MATRIX BY GAUSSIAN ELIMINATION.
C
C DGEFA IS USUALLY CALLED BY DGECO, BUT IT CAN BE CALLED
C DIRECTLY WITH A SAVING IN TIME IF RCOND IS NOT NEEDED.
C (TIME FOR DGECO) = (1 + 9/N)*(TIME FOR DGEFA) .
C
C ON ENTRY
C
C A DOUBLE PRECISION(LDA, N)
C THE MATRIX TO BE FACTORED.
C
C LDA INTEGER
C THE LEADING DIMENSION OF THE ARRAY A .
C
C N INTEGER
C THE ORDER OF THE MATRIX A .
C
C ON RETURN
C
C A AN UPPER TRIANGULAR MATRIX AND THE MULTIPLIERS
C WHICH WERE USED TO OBTAIN IT.
C THE FACTORIZATION CAN BE WRITTEN A = L*U WHERE
C L IS A PRODUCT OF PERMUTATION AND UNIT LOWER
C TRIANGULAR MATRICES AND U IS UPPER TRIANGULAR.
C
C IPVT INTEGER(N)
C AN INTEGER VECTOR OF PIVOT INDICES.
C
C INFO INTEGER
C = 0 NORMAL VALUE.
C = K IF U(K,K) .EQ. 0.0 . THIS IS NOT AN ERROR
C CONDITION FOR THIS SUBROUTINE, BUT IT DOES
C INDICATE THAT DGESL OR DGEDI WILL DIVIDE BY ZERO
C IF CALLED. USE RCOND IN DGECO FOR A RELIABLE
C INDICATION OF SINGULARITY.
C
C LINPACK. THIS VERSION DATED 08/14/78 .
C CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB.
C
C SUBROUTINES AND FUNCTIONS
C
C BLAS DAXPY,DSCAL,IDAMAX
C
C GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING
C
INFO = 0
NM1 = N - 1
IF (NM1 .LT. 1) GO TO 70
DO 60 K = 1, NM1
KP1 = K + 1
C
C FIND L = PIVOT INDEX
C
L = IDAMAX(N-K+1,A(K,K),1) + K - 1
IPVT(K) = L
C
C ZERO PIVOT IMPLIES THIS COLUMN ALREADY TRIANGULARIZED
C
IF (A(L,K) .EQ. 0.0D+00) GO TO 40
C
C INTERCHANGE IF NECESSARY
C
IF (L .EQ. K) GO TO 10
T = A(L,K)
A(L,K) = A(K,K)
A(K,K) = T
10 CONTINUE
C
C COMPUTE MULTIPLIERS
C
T = -1.0D+00/A(K,K)
CALL DSCAL(N-K,T,A(K+1,K),1)
C
C ROW ELIMINATION WITH COLUMN INDEXING
C
DO 30 J = KP1, N
T = A(L,J)
IF (L .EQ. K) GO TO 20
A(L,J) = A(K,J)
A(K,J) = T
20 CONTINUE
CALL DAXPY(N-K,T,A(K+1,K),1,A(K+1,J),1)
30 CONTINUE
GO TO 50
40 CONTINUE
INFO = K
50 CONTINUE
60 CONTINUE
70 CONTINUE
IPVT(N) = N
IF (A(N,N) .EQ. 0.0D+00) INFO = N
RETURN
END
C*MODULE BLAS1 *DECK DSCAL
SUBROUTINE DSCAL(N,DA,DX,INCX)
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
DIMENSION DX(*)
C
C SCALES A VECTOR BY A CONSTANT.
C DX(I) = DA * DX(I)
C USES UNROLLED LOOPS FOR INCREMENT EQUAL TO ONE.
C JACK DONGARRA, LINPACK, 3/11/78.
C
IF(N.LE.0)RETURN
IF(INCX.EQ.1)GO TO 20
C
C CODE FOR INCREMENT NOT EQUAL TO 1
C
NINCX = N*INCX
DO 10 I = 1,NINCX,INCX
DX(I) = DA*DX(I)
10 CONTINUE
RETURN
C
C CODE FOR INCREMENT EQUAL TO 1
C
C
C CLEAN-UP LOOP
C
20 M = MOD(N,5)
IF( M .EQ. 0 ) GO TO 40
DO 30 I = 1,M
DX(I) = DA*DX(I)
30 CONTINUE
IF( N .LT. 5 ) RETURN
40 MP1 = M + 1
DO 50 I = MP1,N,5
DX(I) = DA*DX(I)
DX(I + 1) = DA*DX(I + 1)
DX(I + 2) = DA*DX(I + 2)
DX(I + 3) = DA*DX(I + 3)
DX(I + 4) = DA*DX(I + 4)
50 CONTINUE
RETURN
END
C*MODULE BLAS1 *DECK DSWAP
SUBROUTINE DSWAP (N,DX,INCX,DY,INCY)
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
DIMENSION DX(*),DY(*)
C
C INTERCHANGES TWO VECTORS.
C DX(I) <==> DY(I)
C USES UNROLLED LOOPS FOR INCREMENTS EQUAL ONE.
C JACK DONGARRA, LINPACK, 3/11/78.
C
IF(N.LE.0)RETURN
IF(INCX.EQ.1.AND.INCY.EQ.1)GO TO 20
C
C CODE FOR UNEQUAL INCREMENTS OR EQUAL INCREMENTS NOT EQUAL
C TO 1
C
IX = 1
IY = 1
IF(INCX.LT.0)IX = (-N+1)*INCX + 1
IF(INCY.LT.0)IY = (-N+1)*INCY + 1
DO 10 I = 1,N
DTEMP = DX(IX)
DX(IX) = DY(IY)
DY(IY) = DTEMP
IX = IX + INCX
IY = IY + INCY
10 CONTINUE
RETURN
C
C CODE FOR BOTH INCREMENTS EQUAL TO 1
C
C
C CLEAN-UP LOOP
C
20 M = MOD(N,3)
IF( M .EQ. 0 ) GO TO 40
DO 30 I = 1,M
DTEMP = DX(I)
DX(I) = DY(I)
DY(I) = DTEMP
30 CONTINUE
IF( N .LT. 3 ) RETURN
40 MP1 = M + 1
DO 50 I = MP1,N,3
DTEMP = DX(I)
DX(I) = DY(I)
DY(I) = DTEMP
DTEMP = DX(I + 1)
DX(I + 1) = DY(I + 1)
DY(I + 1) = DTEMP
DTEMP = DX(I + 2)
DX(I + 2) = DY(I + 2)
DY(I + 2) = DTEMP
50 CONTINUE
RETURN
END
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