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powell.f
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powell.f
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SUBROUTINE powell(p,xi,xstep,xmin,n,np,mp,ftol,
1 iter,fret,iforwloc,itmax)
c p start point WITH n parameters
c xi eigen vectors
c xstep for normalization of point
c np, mp dimesions
c iter number of iterations
c fret value of objective FUNCTION
c iforwloc
INTEGER iter,n,np,mp,NMAX,ITMAX,itcnt,iforwloc
REAL fret,ftol,p(np),xi(mp,mp),func
PARAMETER (NMAX=500)
C USES func,linmin
INTEGER i,ibig,j,np1,ncom
REAL del,fp,fptt,t,pt(NMAX),ptt(NMAX),xit(NMAX),xerr
REAL xstep(np),xmin(np)
COMMON /myiter/itcnt
REAL pcom(NMAX),xicom(NMAX)
COMMON /f1com/ pcom,xicom,ncom
c WRITE(*,*)'Entering powell',itmax
ncom=n
itcnt=0
np1=np
DO 11 j=1,n
p(j)=(p(j)-xmin(j))/xstep(j)
pt(j)=p(j)
c WRITE(*,*)'p(j),xmin(j),xstep(j)',p(j),xmin(j),xstep(j),n,np,mp
11 CONTINUE
fp=func(p)
if (fp.lt.10) then
fret=fp
endif
WRITE(*,*)'initial fitness from powell',fret,fp
iter=0
1 iter=iter+1
IF(iter.GT.ITMAX) THEN
WRITE(*,*) 'test1, powell exceeding maximum iterations'
GOTO 99
ENDIF
fp=fret
ibig=0
del=0.
DO 13 i=1,n
DO 12 j=1,n
xit(j)=xi(j,i)
12 CONTINUE
fptt=fret
c WRITE(*,*)'linesearch parameter',i,iter
CALL linmin(p,xit,n,fret)
IF(ABS(fptt-fret).GT.del)THEN
del=ABS(fptt-fret)
ibig=i
ENDIF
c WRITE(*,*)' fptt,fret,del, #it', fptt,fret,del,itcnt
13 CONTINUE
c WRITE(*,*)'rel impr',2.*ABS(fp-fret)/(ABS(fp)+ABS(fret))
xerr=0
DO j=1,n
xerr=MAX(xerr,ABS(p(j)-pt(j)))
ENDDO
WRITE(*,*)'Largest step,Improvement in costfunction',
1 xerr,ABS(fp-fret)
IF(2.*ABS(fp-fret).LE.ftol*(ABS(fp)+ABS(fret)) .OR.
1 xerr.LT.0.01 ) GOTO 99
DO 14 j=1,n
ptt(j)=2.*p(j)-pt(j)
xit(j)=p(j)-pt(j)
pt(j)=p(j)
14 CONTINUE
fptt=func(ptt)
IF(fptt.GE.fp)GOTO 1
t=2.*(fp-2.*fret+fptt)*(fp-fret-del)**2-del*(fp-fptt)**2
IF(t.GE.0.)GOTO 1
WRITE(*,*)'linesearch stepest descend ',i,iter
CALL linmin(p,xit,n,fret)
DO 15 j=1,n
xi(j,ibig)=xi(j,n)
xi(j,n)=xit(j)
15 CONTINUE
IF(iter.EQ.ITMAX) THEN
WRITE(*,*) 'powell exceeding maximum iterations'
GOTO 99
ENDIF
GOTO 1
99 DO j=1,n
p(j)=P(j)*xstep(j)+xmin(j)
ENDDO
iforwloc=itcnt
END
c
c
c
c
SUBROUTINE linmin(p,xi,n,fret)
INTEGER n,NMAX
REAL fret,p(n),xi(n),TOL
PARAMETER (NMAX=500,TOL=1.e-4)
C U USES brentrec,f1dim,mnbrak
INTEGER j,ncom
REAL ax,bx,fa,fb,fx,xmin,xx,pcom(NMAX),xicom(NMAX),brentrec
COMMON /f1com/ pcom,xicom,ncom
REAL maxgain,xcormax
EXTERNAL f1dim
ncom=n
xcormax=0.
DO 11 j=1,n
pcom(j)=p(j)
xicom(j)=xi(j)
xcormax=MAX(xcormax,ABS(xicom(j)))
11 CONTINUE
IF (xcormax.LT.0.1) THEN
DO j=1,n
xicom(j)=xicom(j)*0.1/xcormax
ENDDO
ENDIF
ax=0.
xx=1.
c WRITE(*,*)'search direction', (xicom(j),j=1,n),xcormax
fa=fret
CALL mnbrak(ax,xx,bx,fa,fx,fb,f1dim)
c WRITE(*,*)'calling brent'
maxgain=0.
DO j=1,n
maxgain=MAX(maxgain,ABS(xicom(j)*(ax-bx)))
ENDDO
c WRITE(*,*)'gain?', maxgain
IF (maxgain.GT.0.05) THEN
fret=brentrec(ax,xx,bx,fa,fx,fb,f1dim,TOL,xmin)
ELSE
xmin=(ax+bx)/2
ENDIF
IF (xmin.NE.0) THEN
DO 12 j=1,n
xi(j)=xmin*xi(j)
p(j)=p(j)+xi(j)
12 CONTINUE
ENDIF
c write(*,*)'exit linmin'
END
c
c
c
FUNCTION brentrec(ax,bx,cx,fa,fb,fc,f,tol,xmin)
INTEGER ITMAX
REAL brentrec,ax,bx,cx,tol,xmin,f,CGOLD,ZEPS,fa,fb,fc
EXTERNAL f
c pg PARAMETER (ITMAX=10,CGOLD=.3819660,ZEPS=1.0e-10)
PARAMETER (ITMAX=5,CGOLD=.3819660,ZEPS=1.0e-10)
INTEGER iter
REAL a,b,d,e,etemp,fu,fv,fw,fx,p,q,r,tol1,tol2,u,v,w,x,xm
c WRITE(*,*)'ax,bx,cx',ax,bx,cx
a=MIN(ax,cx)
b=MAX(ax,cx)
v=bx
w=v
x=v
e=0.
c fx=f(x)
c WRITE(*,*)'x,bx,fx,fb',x,bx,fx,fb
c peters additions
fx=fb
w=a
fw=fa
v=b
fv=fc
c fv=fx
c fw=fx
DO 11 iter=1,ITMAX
xm=0.5*(a+b)
tol1=tol*ABS(x)+ZEPS
tol2=2.*tol1
tol2=2*(tol*ABS(x)+ZEPS+0.01)
IF(ABS(x-xm).LE.(tol2-.5*(b-a))) GOTO 3
IF(ABS(e).GT.tol1) THEN
r=(x-w)*(fx-fv)
q=(x-v)*(fx-fw)
p=(x-v)*q-(x-w)*r
q=2.*(q-r)
IF(q.GT.0.) p=-p
q=ABS(q)
etemp=e
e=d
IF(ABS(p).GE.ABS(.5*q*etemp)
* .OR.p.LE.q*(a-x).OR.p.GE.q*(b-x))
* GOTO 1
d=p/q
u=x+d
IF(u-a.LT.tol2 .OR. b-u.LT.tol2) d=SIGN(tol1,xm-x)
GOTO 2
ENDIF
1 IF(x.GE.xm) THEN
e=a-x
ELSE
e=b-x
ENDIF
d=CGOLD*e
2 IF(ABS(d).GE.tol1) THEN
u=x+d
ELSE
u=x+SIGN(tol1,d)
ENDIF
fu=f(u)
IF(fu.LE.fx) THEN
IF(u.GE.x) THEN
a=x
ELSE
b=x
ENDIF
v=w
fv=fw
w=x
fw=fx
x=u
fx=fu
ELSE
IF(u.LT.x) THEN
a=u
ELSE
b=u
ENDIF
IF(fu.LE.fw .OR. w.EQ.x) THEN
v=w
fv=fw
w=u
fw=fu
ELSE IF(fu.LE.fv .OR. v.EQ.x .OR. v.EQ.w) THEN
v=u
fv=fu
ENDIF
ENDIF
11 CONTINUE
c WRITE(*,*) 'brentrec exceed maximum iterations'
3 xmin=x
brentrec=fx
END
c
c
c
SUBROUTINE mnbrak(ax,bx,cx,fa,fb,fc,func)
REAL ax,bx,cx,fa,fb,fc,func,GOLD,GLIMIT,TINY
EXTERNAL func
PARAMETER (GOLD=1.618034, GLIMIT=100., TINY=1.e-20)
REAL dum,fu,q,r,u,ulim
c WRITE(*,*)'mnbrak fa entry',fa
c fa=func(ax)
c WRITE(*,*)'mnbrak fb calle',fa,bx
fb=func(bx)
c WRITE(*,*)'mnbrak fb called',fb,fa
IF(fb.GT.fa)THEN
dum=ax
ax=bx
bx=dum
dum=fb
fb=fa
fa=dum
ENDIF
cx=bx+GOLD*(bx-ax)
fc=func(cx)
c WRITE(*,*)'mnbrak fc called',fa,fb,fc,ax,ab,ac
1 IF(fb.GE.fc)THEN
r=(bx-ax)*(fb-fc)
q=(bx-cx)*(fb-fa)
u=bx-((bx-cx)*q-(bx-ax)*r)/(2.*SIGN(MAX(ABS(q-r),TINY),q-r))
ulim=bx+GLIMIT*(cx-bx)
IF((bx-u)*(u-cx).GT.0.)THEN
fu=func(u)
IF(fu.LT.fc)THEN
ax=bx
fa=fb
bx=u
fb=fu
RETURN
ELSE IF(fu.GT.fb)THEN
cx=u
fc=fu
RETURN
ENDIF
u=cx+GOLD*(cx-bx)
fu=func(u)
ELSE IF((cx-u)*(u-ulim).GT.0.)THEN
fu=func(u)
IF(fu.LT.fc)THEN
bx=cx
cx=u
u=cx+GOLD*(cx-bx)
fb=fc
fc=fu
fu=func(u)
ENDIF
ELSE IF((u-ulim)*(ulim-cx).GE.0.)THEN
u=ulim
fu=func(u)
ELSE
u=cx+GOLD*(cx-bx)
fu=func(u)
ENDIF
ax=bx
bx=cx
cx=u
fa=fb
fb=fc
fc=fu
GOTO 1
ENDIF
RETURN
END
c
c
FUNCTION f1dim(x)
REAL f1dim,func,x
INTEGER j,ncom, NMAX
PARAMETER (NMAX=500)
REAL pcom(NMAX),xicom(NMAX),xt(NMAX)
COMMON /f1com/ pcom,xicom,ncom
DO 11 j=1,ncom
xt(j)=pcom(j)+x*xicom(j)
c WRITE(*,*),xt(j),pcom(j),x,xicom(j)
11 CONTINUE
f1dim=func(xt)
END
FUNCTION func(xt)
INCLUDE 'comopt.h'
REAL func
INTEGER i,nmax
PARAMETER (NMAX=500)
INTEGER j,ncom,itcnt
REAL pcom(NMAX),xicom(NMAX),xt(NMAX),xtt(Nmax)
COMMON /f1com/ pcom,xicom,ncom
COMMON /myiter/itcnt
DO i=1,ncom
xtt(i)=xt(i)*df(i)+fmin(i)
IF ((xtt(i).LT.fmin(i)).OR.
1 (xtt(i).GT.fmax(i))) THEN
c IF ((xtt(i).LT.fmin(i)*xonel).OR.
c 1 (xtt(i).GT.fmax(i)*xoneu)) THEN
c WRITE(*,*)'Powell: model rejected, parameter',i
c WRITE(*,*)'xtt(i),fmin(i),fmax(i)'
c WRITE(*,*)xtt(i),xt(i),fmin(i),fmax(i)
func=100000000
RETURN
ENDIF
ENDDO
CALL setmodelreal(xtt)
c WRITE(80,*) func,itcnt
c WRITE(80,*) (xtt(i),i=1,ncom)
c CALL flush(80)
CALL forw2
CALL cost(func)
itcnt=itcnt+1
c WRITE(80,*) func,itcnt
c WRITE(80,*) (xtt(i),i=1,ncom)
c CALL flush(80)
END