add numerical recipes library

lib/nr/cpp/recipes/sfroid.cpp

@@ -0,0 +1,74 @@
+#include <iostream>
+#include <iomanip>
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+const int M=40;
+int mm,n,mpt=M+1;
+DP h,c2=0.0,anorm;
+Vec_DP *x_p;
+
+int main(void)	// Program sfroid
+{
+	const int NE=3,NB=1,NYJ=NE,NYK=M+1;
+	int i,itmax,k;
+	DP conv,deriv,fac1,fac2,q1,slowc;
+	Vec_INT indexv(NE);
+	Vec_DP scalv(NE);
+	Mat_DP y(NYJ,NYK);
+
+	x_p=new Vec_DP(M+1);
+	Vec_DP &x=*x_p;
+	itmax=100;
+	conv=1.0e-14;
+	slowc=1.0;
+	h=1.0/M;
+	cout << endl << "Enter m n" << endl;
+	cin >> mm >> n;
+	if ((n+mm & 1) != 0) {
+		indexv[0]=0;
+		indexv[1]=1;
+		indexv[2]=2;
+	} else {
+		indexv[0]=1;
+		indexv[1]=0;
+		indexv[2]=2;
+	}
+	anorm=1.0;
+	if (mm != 0) {
+		q1=n;
+		for (i=1;i<=mm;i++) anorm = -0.5*anorm*(n+i)*(q1--/i);
+	}
+	for (k=0;k<M;k++) {
+		x[k]=k*h;
+		fac1=1.0-x[k]*x[k];
+		fac2=exp((-mm/2.0)*log(fac1));
+		y[0][k]=NR::plgndr(n,mm,x[k])*fac2;
+		deriv = -((n-mm+1)*NR::plgndr(n+1,mm,x[k])-
+			(n+1)*x[k]*NR::plgndr(n,mm,x[k]))/fac1;
+		y[1][k]=mm*x[k]*y[0][k]/fac1+deriv*fac2;
+		y[2][k]=n*(n+1)-mm*(mm+1);
+	}
+	x[M]=1.0;
+	y[0][M]=anorm;
+	y[2][M]=n*(n+1)-mm*(mm+1);
+	y[1][M]=(y[2][M]-c2)*y[0][M]/(2.0*(mm+1.0));
+	scalv[0]=fabs(anorm);
+	scalv[1]=(y[1][M] > scalv[0] ? y[1][M] : scalv[0]);
+	scalv[2]=(y[2][M] > 1.0 ? y[2][M] : 1.0);
+	for (;;) {
+		cout << endl << "Enter c**2 or 999 to end" << endl;
+		cin >> c2;
+		if (c2 == 999) {
+			delete x_p;
+			return 0;
+		}
+		NR::solvde(itmax,conv,slowc,scalv,indexv,NB,y);
+		cout << endl << " m = " << setw(3) << mm;
+		cout << "  n = " << setw(3) << n << "  c**2 = ";
+		cout << fixed << setprecision(3) << setw(7) << c2;
+		cout << " lamda = " << setprecision(6) << (y[2][0]+mm*(mm+1));
+		cout << endl;
+	}
+}