add numerical recipes library

lib/nr/k_and_r/recipes/sphfpt.c

@@ -0,0 +1,80 @@
+
+#include <stdio.h>
+#include <math.h>
+#include "nrutil.h"
+#define N1 2
+#define N2 1
+#define NTOT (N1+N2)
+#define DXX 1.0e-4
+
+int m,n;
+float c2,dx,gmma;
+
+int nn2,nvar;
+float x1,x2,xf;
+
+main()  /* Program sphfpt */
+{
+	void newt(),shootf();
+	int check,i;
+	float q1,*v1,*v2,*v;
+
+	v=vector(1,NTOT);
+	v1=v;
+	v2 = &v[N2];
+	nvar=NTOT;
+	nn2=N2;
+	dx=DXX;
+	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);
+		v1[1]=n*(n+1)-m*(m+1)+c2/2.0;
+		v2[2]=v1[1];
+		v2[1]=gmma*(1.0-(v2[2]-c2)*dx/(2*(m+1)));
+		x1 = -1.0+dx;
+		x2=1.0-dx;
+		xf=0.0;
+		newt(v,NTOT,&check,shootf);
+		if (check) {
+			printf("shootf failed; bad initial guess\n");
+		} else {
+			printf("\tmu(m,n)\n");
+			printf("%12.6f\n",v[1]);
+		}
+	}
+	free_vector(v,1,NTOT);
+	return 0;
+}
+
+void load1(x1,v1,y)
+float v1[],x1,y[];
+{
+	float y1 = (n-m & 1 ? -gmma : gmma);
+	y[3]=v1[1];
+	y[2] = -(y[3]-c2)*y1/(2*(m+1));
+	y[1]=y1+y[2]*dx;
+}
+
+void load2(x2,v2,y)
+float v2[],x2,y[];
+{
+	y[3]=v2[2];
+	y[1]=v2[1];
+	y[2]=(y[3]-c2)*y[1]/(2*(m+1));
+}
+
+void score(xf,y,f)
+float f[],xf,y[];
+{
+	int i;
+
+	for (i=1;i<=3;i++) f[i]=y[i];
+}
+#undef N1
+#undef N2
+#undef NTOT
+#undef DXX