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vegas.f
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1 C*******************************************************************
2 C
3 C
4 C
5 C
6 C*******************************************************************
7 C SUBROUTINE PERFORMS N-DIMENSIONAL MONTE CARLO INTEG'N
8 C - BY G.P. LEPAGE SEPT 1976/(REV)APR 1978
9 C*******************************************************************
10 C
11  SUBROUTINE vegas(FXN,AVGI,SD,CHI2A)
12  IMPLICIT REAL*8(a-h,o-z)
13  common/bveg1/xl(10),xu(10),acc,ndim,ncall,itmx,nprn
14  SAVE /bveg1/
15  common/bveg2/xi(50,10),si,si2,swgt,schi,ndo,it
16  SAVE /bveg2/
17  common/bveg3/f,ti,tsi
18  SAVE /bveg3/
19  EXTERNAL fxn
20  dimension d(50,10),di(50,10),xin(50),r(50),dx(10),dt(10),x(10)
21  1 ,kg(10),ia(10)
22  REAL*4 qran(10)
23  DATA ndmx/50/,alph/1.5d0/,one/1.d0/,mds/-1/
24 
25  SAVE d, di, xin, r, dx, dt, x, kg, ia, qran ! Uzhi
26  SAVE ndmx, alph, one, mds ! Uzhi
27 
28 C
29  ndo=1
30  DO 1 j=1,ndim
31 1 xi(1,j)=one
32 C
33  entry vegas1(fxn,avgi,sd,chi2a)
34 C - INITIALIZES CUMMULATIVE VARIABLES, BUT NOT GRID
35  it=0
36  si=0.
37  si2=si
38  swgt=si
39  schi=si
40 C
41  entry vegas2(fxn,avgi,sd,chi2a)
42 C - NO INITIALIZATION
43  nd=ndmx
44  ng=1
45  IF(mds.EQ.0) go to 2
46  ng=(ncall/2.)**(1./ndim)
47  mds=1
48  IF((2*ng-ndmx).LT.0) go to 2
49  mds=-1
50  npg=ng/ndmx+1
51  nd=ng/npg
52  ng=npg*nd
53 2 k=ng**ndim
54  npg=ncall/k
55  IF(npg.LT.2) npg=2
56  calls=npg*k
57  dxg=one/ng
58  dv2g=(calls*dxg**ndim)**2/npg/npg/(npg-one)
59  xnd=nd
60  ndm=nd-1
61  dxg=dxg*xnd
62  xjac=one/calls
63  DO 3 j=1,ndim
64 c***this is the line 50
65  dx(j)=xu(j)-xl(j)
66 3 xjac=xjac*dx(j)
67 C
68 C REBIN PRESERVING BIN DENSITY
69 C
70  IF(nd.EQ.ndo) go to 8
71  rc=ndo/xnd
72  DO 7 j=1,ndim
73  k=0
74  xn=0.
75  dr=xn
76  i=k
77 4 k=k+1
78  dr=dr+one
79  xo=xn
80  xn=xi(k,j)
81 5 IF(rc.GT.dr) go to 4
82  i=i+1
83  dr=dr-rc
84  xin(i)=xn-(xn-xo)*dr
85  IF(i.LT.ndm) go to 5
86  DO 6 i=1,ndm
87 6 xi(i,j)=xin(i)
88 7 xi(nd,j)=one
89  ndo=nd
90 C
91 8 CONTINUE
92  IF(nprn.NE.0) WRITE(16,200) ndim,calls,it,itmx,acc,mds,nd
93  1 ,(xl(j),xu(j),j=1,ndim)
94 C
95  entry vegas3(fxn,avgi,sd,chi2a)
96 C - MAIN INTEGRATION LOOP
97 9 it=it+1
98  ti=0.
99  tsi=ti
100  DO 10 j=1,ndim
101  kg(j)=1
102  DO 10 i=1,nd
103  d(i,j)=ti
104 10 di(i,j)=ti
105 C
106 11 fb=0.
107  f2b=fb
108  k=0
109 12 k=k+1
110  CALL aran9(qran,ndim)
111  wgt=xjac
112  DO 15 j=1,ndim
113  xn=(kg(j)-qran(j))*dxg+one
114 c*****this is the line 100
115  ia(j)=xn
116  IF(ia(j).GT.1) go to 13
117  xo=xi(ia(j),j)
118  rc=(xn-ia(j))*xo
119  go to 14
120 13 xo=xi(ia(j),j)-xi(ia(j)-1,j)
121  rc=xi(ia(j)-1,j)+(xn-ia(j))*xo
122 14 x(j)=xl(j)+rc*dx(j)
123  wgt=wgt*xo*xnd
124 15 CONTINUE
125 C
126  f=wgt
127  f=f*fxn(x,wgt)
128  f2=f*f
129  fb=fb+f
130  f2b=f2b+f2
131  DO 16 j=1,ndim
132  di(ia(j),j)=di(ia(j),j)+f
133 16 IF(mds.GE.0) d(ia(j),j)=d(ia(j),j)+f2
134  IF(k.LT.npg) go to 12
135 C
136  f2b=dsqrt(f2b*npg)
137  f2b=(f2b-fb)*(f2b+fb)
138  ti=ti+fb
139  tsi=tsi+f2b
140  IF(mds.GE.0) go to 18
141  DO 17 j=1,ndim
142 17 d(ia(j),j)=d(ia(j),j)+f2b
143 18 k=ndim
144 19 kg(k)=mod(kg(k),ng)+1
145  IF(kg(k).NE.1) go to 11
146  k=k-1
147  IF(k.GT.0) go to 19
148 C
149 C FINAL RESULTS FOR THIS ITERATION
150 C
151  tsi=tsi*dv2g
152  ti2=ti*ti
153  wgt=ti2/(tsi+1.0d-37)
154  si=si+ti*wgt
155  si2=si2+ti2
156  swgt=swgt+wgt
157  swgt=swgt+1.0d-37
158  si2=si2+1.0d-37
159  schi=schi+ti2*wgt
160  avgi=si/(swgt)
161  sd=swgt*it/(si2)
162  chi2a=sd*(schi/swgt-avgi*avgi)/(it-.999)
163  sd=dsqrt(one/sd)
164 C****this is the line 150
165  IF(nprn.EQ.0) go to 21
166  tsi=dsqrt(tsi)
167  WRITE(16,201) it,ti,tsi,avgi,sd,chi2a
168  IF(nprn.GE.0) go to 21
169  DO 20 j=1,ndim
170 20 WRITE(16,202) j,(xi(i,j),di(i,j),d(i,j),i=1,nd)
171 C
172 C REFINE GRID
173 C
174 21 DO 23 j=1,ndim
175  xo=d(1,j)
176  xn=d(2,j)
177  d(1,j)=(xo+xn)/2.
178  dt(j)=d(1,j)
179  DO 22 i=2,ndm
180  d(i,j)=xo+xn
181  xo=xn
182  xn=d(i+1,j)
183  d(i,j)=(d(i,j)+xn)/3.
184 22 dt(j)=dt(j)+d(i,j)
185  d(nd,j)=(xn+xo)/2.
186 23 dt(j)=dt(j)+d(nd,j)
187 C
188  DO 28 j=1,ndim
189  rc=0.
190  DO 24 i=1,nd
191  r(i)=0.
192  IF (dt(j).GE.1.0d18) THEN
193  WRITE(6,*) '************** A SINGULARITY >1.0D18'
194 C WRITE(5,1111)
195 C1111 FORMAT(1X,'**************IMPORTANT NOTICE***************')
196 C WRITE(5,1112)
197 C1112 FORMAT(1X,'THE INTEGRAND GIVES RISE A SINGULARITY >1.0D18')
198 C WRITE(5,1113)
199 C1113 FORMAT(1X,'PLEASE CHECK THE INTEGRAND AND THE LIMITS')
200 C WRITE(5,1114)
201 C1114 FORMAT(1X,'**************END NOTICE*************')
202  END IF
203  IF(d(i,j).LE.1.0d-18) go to 24
204  xo=dt(j)/d(i,j)
205  r(i)=((xo-one)/xo/dlog(xo))**alph
206 24 rc=rc+r(i)
207  rc=rc/xnd
208  k=0
209  xn=0.
210  dr=xn
211  i=k
212 25 k=k+1
213  dr=dr+r(k)
214  xo=xn
215 c****this is the line 200
216  xn=xi(k,j)
217 26 IF(rc.GT.dr) go to 25
218  i=i+1
219  dr=dr-rc
220  xin(i)=xn-(xn-xo)*dr/(r(k)+1.0d-30)
221  IF(i.LT.ndm) go to 26
222  DO 27 i=1,ndm
223 27 xi(i,j)=xin(i)
224 28 xi(nd,j)=one
225 C
226  IF(it.LT.itmx.AND.acc*dabs(avgi).LT.sd) go to 9
227 200 FORMAT('0INPUT PARAMETERS FOR VEGAS: NDIM=',i3,' NCALL=',f8.0
228  1 /28x,' IT=',i5,' ITMX=',i5/28x,' ACC=',g9.3
229  2 /28x,' MDS=',i3,' ND=',i4/28x,' (XL,XU)=',
230  3 (t40,'( ',g12.6,' , ',g12.6,' )'))
231 201 FORMAT(///' INTEGRATION BY VEGAS' / '0ITERATION NO.',i3,
232  1 ': INTEGRAL =',g14.8/21x,'STD DEV =',g10.4 /
233  2 ' ACCUMULATED RESULTS: INTEGRAL =',g14.8 /
234  3 24x,'STD DEV =',g10.4 / 24x,'CHI**2 PER IT''N =',g10.4)
235 202 FORMAT('0DATA FOR AXIS',i2 / ' ',6x,'X',7x,' DELT I ',
236  1 2x,' CONV''CE ',11x,'X',7x,' DELT I ',2x,' CONV''CE '
237  2 ,11x,'X',7x,' DELT I ',2x,' CONV''CE ' /
238  2 (' ',3g12.4,5x,3g12.4,5x,3g12.4))
239  RETURN
240  END