add numerical recipes library

lib/nr/cpp/recipes/sphoot.cpp

@@ -0,0 +1,63 @@
+#include <iostream>
+#include <iomanip>
+#include "nr.h"
+using namespace std;
+
+int m,n;
+DP c2,dx,gmma;
+
+int nvar;
+DP x1,x2;
+
+int main(void)	// Program sphoot
+{
+	const int N2=1;
+	bool check;
+	int i;
+	DP q1;
+	Vec_DP v(N2);
+
+	dx=1.0e-8;
+	nvar=3;
+	for (;;) {
+		cout << endl << "input m,n,c-squared (999 to end)" << endl;
+		cin >> m >> n >> c2;
+		if (c2 == 999) break;
+		if (n < m || m < 0) continue;
+		gmma=1.0;
+		q1=n;
+		for (i=1;i<=m;i++) gmma *= -0.5*(n+i)*(q1--/i);
+		v[0]=n*(n+1)-m*(m+1)+c2/2.0;
+		x1= -1.0+dx;
+		x2=0.0;
+		NR::newt(v,check,NR::shoot);
+		if (check) {
+			cout << "shoot failed; bad initial guess" << endl;
+		} else {
+			cout << "    " << "mu(m,n)" << endl;
+			cout << fixed << setprecision(6);
+			cout << setw(12) << v[0] << endl;
+		}
+	}
+	return 0;
+}
+
+void load(const DP x1, Vec_I_DP &v, Vec_O_DP &y)
+{
+	DP y1 = ((n-m & 1) != 0 ? -gmma : gmma);
+	y[2]=v[0];
+	y[1] = -(y[2]-c2)*y1/(2*(m+1));
+	y[0]=y1+y[1]*dx;
+}
+
+void score(const DP xf, Vec_I_DP &y, Vec_O_DP &f)
+{
+	f[0]=((n-m & 1) != 0 ? y[0] : y[1]);
+}
+
+void derivs(const DP x, Vec_I_DP &y, Vec_O_DP &dydx)
+{
+	dydx[0]=y[1];
+	dydx[1]=(2.0*x*(m+1.0)*y[1]-(y[2]-c2*x*x)*y[0])/(1.0-x*x);
+	dydx[2]=0.0;
+}