add numerical recipes library

lib/nr/k_and_r/recipes/sphoot.c

@@ -0,0 +1,65 @@
+
+#include <stdio.h>
+#include "nrutil.h"
+#define N2 1
+
+int m,n;
+float c2,dx,gmma;
+
+int nvar;
+float x1,x2;
+
+main()  /* Program sphoot */
+{
+	void newt(),shoot();
+	int check,i;
+	float q1,*v;
+
+	v=vector(1,N2);
+	dx=1.0e-4;
+	nvar=3;
+	for (;;) {
+		printf("input m,n,c-squared\n");
+		if (scanf("%d %d %f",&m,&n,&c2) == EOF) 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[1]=n*(n+1)-m*(m+1)+c2/2.0;
+		x1 = -1.0+dx;
+		x2=0.0;
+		newt(v,N2,&check,shoot);
+		if (check) {
+			printf("shoot failed; bad initial guess\n");
+		} else {
+			printf("\tmu(m,n)\n");
+			printf("%12.6f\n",v[1]);
+		}
+	}
+	free_vector(v,1,N2);
+	return 0;
+}
+
+void load(x1,v,y)
+float v[],x1,y[];
+{
+	float y1 = (n-m & 1 ? -gmma : gmma);
+	y[3]=v[1];
+	y[2] = -(y[3]-c2)*y1/(2*(m+1));
+	y[1]=y1+y[2]*dx;
+}
+
+void score(xf,y,f)
+float f[],xf,y[];
+{
+	f[1]=(n-m & 1 ? y[1] : y[2]);
+}
+
+void derivs(x,y,dydx)
+float dydx[],x,y[];
+{
+	dydx[1]=y[2];
+	dydx[2]=(2.0*x*(m+1.0)*y[2]-(y[3]-c2*x*x)*y[1])/(1.0-x*x);
+	dydx[3]=0.0;
+}
+#undef N2