add numerical recipes library

2025-09-12 18:55:25 +09:00
parent d4dff245bd
commit 2c75620ec9
1344 changed files with 63869 additions and 0 deletions
--- a/lib/nr/cpp/recipes/bessik.cpp
+++ b/lib/nr/cpp/recipes/bessik.cpp
@@ -0,0 +1,121 @@
+#include <cmath>
+#include <limits>
+#include "nr.h"
+using namespace std;
+
+void NR::bessik(const DP x, const DP xnu, DP &ri, DP &rk, DP &rip, DP &rkp)
+{
+	const int MAXIT=10000;
+	const DP EPS=numeric_limits<DP>::epsilon();
+	const DP FPMIN=numeric_limits<DP>::min()/EPS;
+	const DP XMIN=2.0, PI=3.141592653589793;
+	DP a,a1,b,c,d,del,del1,delh,dels,e,f,fact,fact2,ff,gam1,gam2,
+		gammi,gampl,h,p,pimu,q,q1,q2,qnew,ril,ril1,rimu,rip1,ripl,
+		ritemp,rk1,rkmu,rkmup,rktemp,s,sum,sum1,x2,xi,xi2,xmu,xmu2;
+	int i,l,nl;
+
+	if (x <= 0.0 || xnu < 0.0) nrerror("bad arguments in bessik");
+	nl=int(xnu+0.5);
+	xmu=xnu-nl;
+	xmu2=xmu*xmu;
+	xi=1.0/x;
+	xi2=2.0*xi;
+	h=xnu*xi;
+	if (h < FPMIN) h=FPMIN;
+	b=xi2*xnu;
+	d=0.0;
+	c=h;
+	for (i=0;i<MAXIT;i++) {
+		b += xi2;
+		d=1.0/(b+d);
+		c=b+1.0/c;
+		del=c*d;
+		h=del*h;
+		if (fabs(del-1.0) <= EPS) break;
+	}
+	if (i >= MAXIT)
+		nrerror("x too large in bessik; try asymptotic expansion");
+	ril=FPMIN;
+	ripl=h*ril;
+	ril1=ril;
+	rip1=ripl;
+	fact=xnu*xi;
+	for (l=nl-1;l >= 0;l--) {
+		ritemp=fact*ril+ripl;
+		fact -= xi;
+		ripl=fact*ritemp+ril;
+		ril=ritemp;
+	}
+	f=ripl/ril;
+	if (x < XMIN) {
+		x2=0.5*x;
+		pimu=PI*xmu;
+		fact = (fabs(pimu) < EPS ? 1.0 : pimu/sin(pimu));
+		d = -log(x2);
+		e=xmu*d;
+		fact2 = (fabs(e) < EPS ? 1.0 : sinh(e)/e);
+		beschb(xmu,gam1,gam2,gampl,gammi);
+		ff=fact*(gam1*cosh(e)+gam2*fact2*d);
+		sum=ff;
+		e=exp(e);
+		p=0.5*e/gampl;
+		q=0.5/(e*gammi);
+		c=1.0;
+		d=x2*x2;
+		sum1=p;
+		for (i=1;i<=MAXIT;i++) {
+			ff=(i*ff+p+q)/(i*i-xmu2);
+			c *= (d/i);
+			p /= (i-xmu);
+			q /= (i+xmu);
+			del=c*ff;
+			sum += del;
+			del1=c*(p-i*ff);
+			sum1 += del1;
+			if (fabs(del) < fabs(sum)*EPS) break;
+		}
+		if (i > MAXIT) nrerror("bessk series failed to converge");
+		rkmu=sum;
+		rk1=sum1*xi2;
+	} else {
+		b=2.0*(1.0+x);
+		d=1.0/b;
+		h=delh=d;
+		q1=0.0;
+		q2=1.0;
+		a1=0.25-xmu2;
+		q=c=a1;
+		a = -a1;
+		s=1.0+q*delh;
+		for (i=1;i<MAXIT;i++) {
+			a -= 2*i;
+			c = -a*c/(i+1.0);
+			qnew=(q1-b*q2)/a;
+			q1=q2;
+			q2=qnew;
+			q += c*qnew;
+			b += 2.0;
+			d=1.0/(b+a*d);
+			delh=(b*d-1.0)*delh;
+			h += delh;
+			dels=q*delh;
+			s += dels;
+			if (fabs(dels/s) <= EPS) break;
+		}
+		if (i >= MAXIT) nrerror("bessik: failure to converge in cf2");
+		h=a1*h;
+		rkmu=sqrt(PI/(2.0*x))*exp(-x)/s;
+		rk1=rkmu*(xmu+x+0.5-h)*xi;
+	}
+	rkmup=xmu*xi*rkmu-rk1;
+	rimu=xi/(f*rkmu-rkmup);
+	ri=(rimu*ril1)/ril;
+	rip=(rimu*rip1)/ril;
+	for (i=1;i <= nl;i++) {
+		rktemp=(xmu+i)*xi2*rk1+rkmu;
+		rkmu=rk1;
+		rk1=rktemp;
+	}
+	rk=rkmu;
+	rkp=xnu*xi*rkmu-rk1;
+}