178 lines
4.0 KiB
C
178 lines
4.0 KiB
C
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#include <stdio.h>
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#include <math.h>
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#include "nrutil.h"
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#define ALPH 1.5
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#define NDMX 50
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#define MXDIM 10
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#define TINY 1.0e-30
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extern long idum;
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void vegas(regn,ndim,fxn,init,ncall,itmx,nprn,tgral,sd,chi2a)
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float (*fxn)(),*chi2a,*sd,*tgral,regn[];
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int init,itmx,ndim,nprn;
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unsigned long ncall;
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{
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float ran2();
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void rebin();
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static int i,it,j,k,mds,nd,ndo,ng,npg,ia[MXDIM+1],kg[MXDIM+1];
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static float calls,dv2g,dxg,f,f2,f2b,fb,rc,ti,tsi,wgt,xjac,xn,xnd,xo;
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static float d[NDMX+1][MXDIM+1],di[NDMX+1][MXDIM+1],dt[MXDIM+1],
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dx[MXDIM+1], r[NDMX+1],x[MXDIM+1],xi[MXDIM+1][NDMX+1],xin[NDMX+1];
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static double schi,si,swgt;
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if (init <= 0) {
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mds=ndo=1;
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for (j=1;j<=ndim;j++) xi[j][1]=1.0;
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}
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if (init <= 1) si=swgt=schi=0.0;
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if (init <= 2) {
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nd=NDMX;
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ng=1;
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if (mds) {
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ng=(int)pow(ncall/2.0+0.25,1.0/ndim);
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mds=1;
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if ((2*ng-NDMX) >= 0) {
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mds = -1;
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npg=ng/NDMX+1;
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nd=ng/npg;
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ng=npg*nd;
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}
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}
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for (k=1,i=1;i<=ndim;i++) k *= ng;
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npg=IMAX(ncall/k,2);
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calls=(float)npg * (float)k;
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dxg=1.0/ng;
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for (dv2g=1,i=1;i<=ndim;i++) dv2g *= dxg;
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dv2g=SQR(calls*dv2g)/npg/npg/(npg-1.0);
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xnd=nd;
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dxg *= xnd;
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xjac=1.0/calls;
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for (j=1;j<=ndim;j++) {
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dx[j]=regn[j+ndim]-regn[j];
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xjac *= dx[j];
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}
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if (nd != ndo) {
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for (i=1;i<=IMAX(nd,ndo);i++) r[i]=1.0;
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for (j=1;j<=ndim;j++) rebin(ndo/xnd,nd,r,xin,xi[j]);
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ndo=nd;
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}
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if (nprn >= 0) {
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printf("%s: ndim= %3d ncall= %8.0f\n",
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" Input parameters for vegas",ndim,calls);
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printf("%28s it=%5d itmx=%5d\n"," ",it,itmx);
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printf("%28s nprn=%3d ALPH=%5.2f\n"," ",nprn,ALPH);
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printf("%28s mds=%3d nd=%4d\n"," ",mds,nd);
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for (j=1;j<=ndim;j++) {
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printf("%30s xl[%2d]= %11.4g xu[%2d]= %11.4g\n",
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" ",j,regn[j],j,regn[j+ndim]);
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}
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}
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}
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for (it=1;it<=itmx;it++) {
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ti=tsi=0.0;
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for (j=1;j<=ndim;j++) {
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kg[j]=1;
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for (i=1;i<=nd;i++) d[i][j]=di[i][j]=0.0;
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}
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for (;;) {
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fb=f2b=0.0;
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for (k=1;k<=npg;k++) {
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wgt=xjac;
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for (j=1;j<=ndim;j++) {
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xn=(kg[j]-ran2(&idum))*dxg+1.0;
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ia[j]=IMAX(IMIN((int)(xn),NDMX),1);
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if (ia[j] > 1) {
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xo=xi[j][ia[j]]-xi[j][ia[j]-1];
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rc=xi[j][ia[j]-1]+(xn-ia[j])*xo;
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} else {
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xo=xi[j][ia[j]];
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rc=(xn-ia[j])*xo;
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}
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x[j]=regn[j]+rc*dx[j];
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wgt *= xo*xnd;
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}
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f=wgt*(*fxn)(x,wgt);
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f2=f*f;
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fb += f;
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f2b += f2;
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for (j=1;j<=ndim;j++) {
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di[ia[j]][j] += f;
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if (mds >= 0) d[ia[j]][j] += f2;
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}
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}
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f2b=sqrt(f2b*npg);
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f2b=(f2b-fb)*(f2b+fb);
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if (f2b <= 0.0) f2b=TINY;
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ti += fb;
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tsi += f2b;
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if (mds < 0) {
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for (j=1;j<=ndim;j++) d[ia[j]][j] += f2b;
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}
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for (k=ndim;k>=1;k--) {
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kg[k] %= ng;
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if (++kg[k] != 1) break;
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}
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if (k < 1) break;
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}
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tsi *= dv2g;
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wgt=1.0/tsi;
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si += wgt*ti;
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schi += wgt*ti*ti;
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swgt += wgt;
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*tgral=si/swgt;
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*chi2a=(schi-si*(*tgral))/(it-0.9999);
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if (*chi2a < 0.0) *chi2a = 0.0;
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*sd=sqrt(1.0/swgt);
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tsi=sqrt(tsi);
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if (nprn >= 0) {
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printf("%s %3d : integral = %14.7g +/- %9.2g\n",
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" iteration no.",it,ti,tsi);
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printf("%s integral =%14.7g+/-%9.2g chi**2/IT n = %9.2g\n",
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" all iterations: ",*tgral,*sd,*chi2a);
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if (nprn) {
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for (j=1;j<=ndim;j++) {
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printf(" DATA FOR axis %2d\n",j);
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printf("%6s%13s%11s%13s%11s%13s\n",
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"X","delta i","X","delta i","X","delta i");
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for (i=1+nprn/2;i<=nd;i += nprn+2) {
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printf("%8.5f%12.4g%12.5f%12.4g%12.5f%12.4g\n",
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xi[j][i],di[i][j],xi[j][i+1],
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di[i+1][j],xi[j][i+2],di[i+2][j]);
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}
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}
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}
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}
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for (j=1;j<=ndim;j++) {
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xo=d[1][j];
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xn=d[2][j];
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d[1][j]=(xo+xn)/2.0;
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dt[j]=d[1][j];
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for (i=2;i<nd;i++) {
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rc=xo+xn;
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xo=xn;
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xn=d[i+1][j];
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d[i][j] = (rc+xn)/3.0;
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dt[j] += d[i][j];
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}
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d[nd][j]=(xo+xn)/2.0;
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dt[j] += d[nd][j];
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}
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for (j=1;j<=ndim;j++) {
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rc=0.0;
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for (i=1;i<=nd;i++) {
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if (d[i][j] < TINY) d[i][j]=TINY;
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r[i]=pow((1.0-d[i][j]/dt[j])/
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(log(dt[j])-log(d[i][j])),ALPH);
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rc += r[i];
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}
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rebin(rc/xnd,nd,r,xin,xi[j]);
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}
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}
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}
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#undef ALPH
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#undef NDMX
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#undef MXDIM
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#undef TINY
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