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SUBROUTINE vegas(region,ndim,fxn,init,ncall,itmx,nprn,tgral,sd,
*chi2a)
INTEGER init,itmx,ncall,ndim,nprn,NDMX,MXDIM
REAL tgral,chi2a,sd,region(2*ndim),fxn,ALPH,TINY
PARAMETER (ALPH=1.5,NDMX=50,MXDIM=10,TINY=1.e-30)
EXTERNAL fxn
CU USES fxn,xran1,rebin
INTEGER i,idum,it,j,k,mds,nd,ndo,ng,npg,ia(MXDIM),kg(MXDIM)
REAL calls,dv2g,dxg,f,f2,f2b,fb,rc,ti,tsi,wgt,xjac,xn,xnd,xo,
*d(NDMX,MXDIM),di(NDMX,MXDIM),dt(MXDIM),dx(MXDIM),r(NDMX),x(MXDIM),
*xi(NDMX,MXDIM),xin(NDMX),xran1,rndn
EXTERNAL XRAN1
DOUBLE PRECISION schi,si,swgt
DATA idum/1/ ! DOES NOT AFFECT PREVIOUS SETTINGS
c
C GLOBAL
C
INTEGER NDIM1
REAL region1(2*MXDIM)
COMMON /VEGAS_PAR1/NG,NDIM1
COMMON /VEGAS_PAR2/region1,xi,xnd,dx
C
SAVE ! make variables static
c
if(init.le.0)then !enter here on a cold start
NDIM1=NDIM
do j=1,2*ndim
region1(j)=region(j)
enddo
mds=1
ndo=1
do 11 j=1,ndim
xi(1,j)=1.
11 continue
endif
c
if (init.le.1)then !enter here to inherit the grid but not the answers
si=0D0
swgt=0D0
schi=0D0
endif
c
if (init.le.2)then !enter here to inherit the grid and the answers
nd=NDMX
ng=1
c
if(mds.ne.0)then !setup for stratification
ng=(ncall/2.+0.25)**(1./ndim) !number of calls per dimension
mds=1
if((2*ng-NDMX).ge.0)then
mds=-1
npg=ng/NDMX+1
nd=ng/npg
ng=npg*nd
endif
endif
k=ng**ndim
npg=max(ncall/k,2)
calls=npg*k
cfax: returns the actual number of calls
ncall=int(calls)
dxg=1./ng
dv2g=(calls*dxg**ndim)**2/npg/npg/(npg-1.)
xnd=nd
dxg=dxg*xnd
xjac=1./calls
c WRITE (*,*) 'NG,NDIM,K ',NG,NDIM,K
c WRITE (*,*) 'NPG,CALLS,NCALL ',NPG,CALLS,NCALL
c WRITE (*,*) 'ND,DXG ',ND,DXG
do 12 j=1,ndim
dx(j)=region(j+ndim)-region(j)
xjac=xjac*dx(j)
12 continue
c-- do the binning if necessary
if(nd.ne.ndo)then
do 13 i=1,nd
r(i)=1.
13 continue
do 14 j=1,ndim
call rebin(ndo/xnd,nd,r,xin,xi(1,j))
14 continue
ndo=nd
endif
if(nprn.ge.0) write(*,200) ndim,calls,it,itmx,nprn,ALPH,mds,nd
endif
c
c MAIN ITERATION LOOP
c if init>=3 it enters here
c
do 28 it=1,itmx
ti=0.
tsi=0.
do 16 j=1,ndim
kg(j)=1
do 15 i=1,nd
d(i,j)=0.
di(i,j)=0.
15 continue
16 continue
10 continue
fb=0.
f2b=0.
do 19 k=1,npg
wgt=xjac
do 17 j=1,ndim
cfax: avoid random numbers exactly equal to 0. or 1.
303 rndn=xran1(idum)
if(rndn.eq.1e0.or.rndn.eq.0e0) goto 303
xn=(kg(j)-rndn)*dxg+1.
c write(*,*) k,kg(j),xn
ia(j)=max(min(int(xn),NDMX),1)
if(ia(j).gt.1)then
xo=xi(ia(j),j)-xi(ia(j)-1,j)
rc=xi(ia(j)-1,j)+(xn-ia(j))*xo
else
xo=xi(ia(j),j)
rc=(xn-ia(j))*xo
endif
x(j)=region(j)+rc*dx(j)
wgt=wgt*xo*xnd
17 continue
f=wgt*fxn(x,wgt)
f2=f*f
fb=fb+f
f2b=f2b+f2
do 18 j=1,ndim
di(ia(j),j)=di(ia(j),j)+f
if(mds.ge.0) d(ia(j),j)=d(ia(j),j)+f2
18 continue
19 continue
f2b=sqrt(f2b*npg)
f2b=(f2b-fb)*(f2b+fb)
if (f2b.le.0.) f2b=TINY
ti=ti+fb
tsi=tsi+f2b
if(mds.lt.0)then
do 21 j=1,ndim
d(ia(j),j)=d(ia(j),j)+f2b
21 continue
endif
c this is just a counter: total number of points thrown is ng**ndim
do 22 k=ndim,1,-1
kg(k)=mod(kg(k),ng)+1
if(kg(k).ne.1) goto 10
22 continue
c
c all points for this iteration have been thrown.
c now it calculates the results for this iteration
c and the cumulative result,chi^2
c
tsi=tsi*dv2g
wgt=1./tsi
si=si+dble(wgt)*dble(ti)
schi=schi+dble(wgt)*dble(ti)**2
swgt=swgt+dble(wgt)
tgral=si/swgt
chi2a=max((schi-si*tgral)/(it-.99d0),0.d0)
sd=sqrt(1./swgt)
tsi=sqrt(tsi)
if(nprn.ge.0)then
write(*,201) it,ti,tsi
if(nprn.ne.0)then
do 23 j=1,ndim
write(*,202) j,(xi(i,j),di(i,j),i=1+nprn/2,nd,nprn)
23 continue
endif
endif
c
c refines the grid after the iteration
c
do 25 j=1,ndim
xo=d(1,j)
xn=d(2,j)
d(1,j)=(xo+xn)/2.
dt(j)=d(1,j)
do 24 i=2,nd-1
rc=xo+xn
xo=xn
xn=d(i+1,j)
d(i,j)=(rc+xn)/3.
dt(j)=dt(j)+d(i,j)
24 continue
d(nd,j)=(xo+xn)/2.
dt(j)=dt(j)+d(nd,j)
25 continue
c-- slow down the evolution
do 27 j=1,ndim
rc=0.
do 26 i=1,nd
if(d(i,j).lt.TINY) d(i,j)=TINY
r(i)=((1.-d(i,j)/dt(j))/(log(dt(j))-log(d(i,j))))**ALPH
rc=rc+r(i)
26 continue
call rebin(rc/xnd,nd,r,xin,xi(1,j))
27 continue
c
28 continue !main iteration loop
c
return
c
c print out formats
c
200 FORMAT(/' input param. for vegas: ndim=',i3,' calls=',
*f8.0/24x,' it=',i5,' itmx=',i5/24x,' nprn=',i3,' alph=',
*f5.2/24x,' mds=',i3,' nd=',i4/)
c200 FORMAT(/' input parameters for vegas: ndim=',i3,' ncall=',
c *f8.0/28x,' it=',i5,' itmx=',i5/28x,' nprn=',i3,' alph=',
c *f5.2/28x,' mds=',i3,' nd=',i4/(30x,'xl(',i2,')= ',g11.4,' xu(',
c *i2,')= ',g11.4))
201 FORMAT(' iter. no.',I3,': ','integral =',g14.7,' +/- ',g9.2)
c201 FORMAT(/' iteration no.',I3,': ','integral =',g14.7,'+/- ',g9.2/
c *' all iterations: integral =',g14.7,'+/- ',g9.2,' chi**2/it',
c *'n =',g9.2)
202 FORMAT(/' data for axis ',I2/' X delta i ',
*' x delta i ',' x delta i ',/(1x,
*f7.5,1x,g11.4,5x,f7.5,1x,g11.4,5x,f7.5,1x,g11.4))
c
END
SUBROUTINE rebin(rc,nd,r,xin,xi)
INTEGER nd
PARAMETER (NDMX=50)
REAL rc,r(NDMX),xi(NDMX),xin(NDMX)
INTEGER i,k
REAL dr,xn,xo
k=0
xn=0.
dr=0.
do 11 i=1,nd-1
1 if(rc.gt.dr)then
k=k+1
dr=dr+r(k)
xo=xn
xn=xi(k)
goto 1
endif
dr=dr-rc
xin(i)=xn-(xn-xo)*dr/r(k)
11 continue
do 12 i=1,nd-1
xi(i)=xin(i)
12 continue
xi(nd)=1.
return
END
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