151 lines
3.1 KiB
C++
151 lines
3.1 KiB
C++
#include <cmath>
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#include <limits>
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#include "nr.h"
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using namespace std;
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void NR::bessjy(const DP x, const DP xnu, DP &rj, DP &ry, DP &rjp, DP &ryp)
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{
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const int MAXIT=10000;
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const DP EPS=numeric_limits<DP>::epsilon();
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const DP FPMIN=numeric_limits<DP>::min()/EPS;
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const DP XMIN=2.0, PI=3.141592653589793;
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DP a,b,br,bi,c,cr,ci,d,del,del1,den,di,dlr,dli,dr,e,f,fact,fact2,
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fact3,ff,gam,gam1,gam2,gammi,gampl,h,p,pimu,pimu2,q,r,rjl,
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rjl1,rjmu,rjp1,rjpl,rjtemp,ry1,rymu,rymup,rytemp,sum,sum1,
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temp,w,x2,xi,xi2,xmu,xmu2;
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int i,isign,l,nl;
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if (x <= 0.0 || xnu < 0.0)
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nrerror("bad arguments in bessjy");
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nl=(x < XMIN ? int(xnu+0.5) : MAX(0,int(xnu-x+1.5)));
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xmu=xnu-nl;
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xmu2=xmu*xmu;
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xi=1.0/x;
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xi2=2.0*xi;
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w=xi2/PI;
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isign=1;
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h=xnu*xi;
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if (h < FPMIN) h=FPMIN;
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b=xi2*xnu;
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d=0.0;
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c=h;
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for (i=0;i<MAXIT;i++) {
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b += xi2;
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d=b-d;
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if (fabs(d) < FPMIN) d=FPMIN;
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c=b-1.0/c;
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if (fabs(c) < FPMIN) c=FPMIN;
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d=1.0/d;
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del=c*d;
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h=del*h;
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if (d < 0.0) isign = -isign;
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if (fabs(del-1.0) <= EPS) break;
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}
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if (i >= MAXIT)
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nrerror("x too large in bessjy; try asymptotic expansion");
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rjl=isign*FPMIN;
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rjpl=h*rjl;
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rjl1=rjl;
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rjp1=rjpl;
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fact=xnu*xi;
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for (l=nl-1;l>=0;l--) {
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rjtemp=fact*rjl+rjpl;
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fact -= xi;
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rjpl=fact*rjtemp-rjl;
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rjl=rjtemp;
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}
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if (rjl == 0.0) rjl=EPS;
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f=rjpl/rjl;
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if (x < XMIN) {
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x2=0.5*x;
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pimu=PI*xmu;
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fact = (fabs(pimu) < EPS ? 1.0 : pimu/sin(pimu));
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d = -log(x2);
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e=xmu*d;
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fact2 = (fabs(e) < EPS ? 1.0 : sinh(e)/e);
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beschb(xmu,gam1,gam2,gampl,gammi);
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ff=2.0/PI*fact*(gam1*cosh(e)+gam2*fact2*d);
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e=exp(e);
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p=e/(gampl*PI);
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q=1.0/(e*PI*gammi);
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pimu2=0.5*pimu;
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fact3 = (fabs(pimu2) < EPS ? 1.0 : sin(pimu2)/pimu2);
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r=PI*pimu2*fact3*fact3;
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c=1.0;
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d = -x2*x2;
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sum=ff+r*q;
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sum1=p;
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for (i=1;i<=MAXIT;i++) {
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ff=(i*ff+p+q)/(i*i-xmu2);
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c *= (d/i);
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p /= (i-xmu);
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q /= (i+xmu);
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del=c*(ff+r*q);
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sum += del;
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del1=c*p-i*del;
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sum1 += del1;
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if (fabs(del) < (1.0+fabs(sum))*EPS) break;
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}
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if (i > MAXIT)
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nrerror("bessy series failed to converge");
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rymu = -sum;
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ry1 = -sum1*xi2;
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rymup=xmu*xi*rymu-ry1;
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rjmu=w/(rymup-f*rymu);
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} else {
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a=0.25-xmu2;
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p = -0.5*xi;
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q=1.0;
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br=2.0*x;
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bi=2.0;
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fact=a*xi/(p*p+q*q);
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cr=br+q*fact;
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ci=bi+p*fact;
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den=br*br+bi*bi;
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dr=br/den;
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di = -bi/den;
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dlr=cr*dr-ci*di;
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dli=cr*di+ci*dr;
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temp=p*dlr-q*dli;
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q=p*dli+q*dlr;
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p=temp;
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for (i=1;i<MAXIT;i++) {
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a += 2*i;
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bi += 2.0;
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dr=a*dr+br;
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di=a*di+bi;
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if (fabs(dr)+fabs(di) < FPMIN) dr=FPMIN;
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fact=a/(cr*cr+ci*ci);
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cr=br+cr*fact;
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ci=bi-ci*fact;
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if (fabs(cr)+fabs(ci) < FPMIN) cr=FPMIN;
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den=dr*dr+di*di;
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dr /= den;
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di /= -den;
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dlr=cr*dr-ci*di;
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dli=cr*di+ci*dr;
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temp=p*dlr-q*dli;
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q=p*dli+q*dlr;
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p=temp;
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if (fabs(dlr-1.0)+fabs(dli) <= EPS) break;
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}
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if (i >= MAXIT) nrerror("cf2 failed in bessjy");
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gam=(p-f)/q;
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rjmu=sqrt(w/((p-f)*gam+q));
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rjmu=SIGN(rjmu,rjl);
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rymu=rjmu*gam;
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rymup=rymu*(p+q/gam);
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ry1=xmu*xi*rymu-rymup;
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}
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fact=rjmu/rjl;
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rj=rjl1*fact;
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rjp=rjp1*fact;
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for (i=1;i<=nl;i++) {
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rytemp=(xmu+i)*xi2*ry1-rymu;
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rymu=ry1;
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ry1=rytemp;
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}
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ry=rymu;
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ryp=xnu*xi*rymu-ry1;
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}
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