add numerical recipes library

lib/nr/ansi/recipes/gaulag.c

@@ -0,0 +1,43 @@
+
+#include <math.h>
+#define EPS 3.0e-14
+#define MAXIT 10
+
+void gaulag(float x[], float w[], int n, float alf)
+{
+	float gammln(float xx);
+	void nrerror(char error_text[]);
+	int i,its,j;
+	float ai;
+	double p1,p2,p3,pp,z,z1;
+
+	for (i=1;i<=n;i++) {
+		if (i == 1) {
+			z=(1.0+alf)*(3.0+0.92*alf)/(1.0+2.4*n+1.8*alf);
+		} else if (i == 2) {
+			z += (15.0+6.25*alf)/(1.0+0.9*alf+2.5*n);
+		} else {
+			ai=i-2;
+			z += ((1.0+2.55*ai)/(1.9*ai)+1.26*ai*alf/
+				(1.0+3.5*ai))*(z-x[i-2])/(1.0+0.3*alf);
+		}
+		for (its=1;its<=MAXIT;its++) {
+			p1=1.0;
+			p2=0.0;
+			for (j=1;j<=n;j++) {
+				p3=p2;
+				p2=p1;
+				p1=((2*j-1+alf-z)*p2-(j-1+alf)*p3)/j;
+			}
+			pp=(n*p1-(n+alf)*p2)/z;
+			z1=z;
+			z=z1-p1/pp;
+			if (fabs(z-z1) <= EPS) break;
+		}
+		if (its > MAXIT) nrerror("too many iterations in gaulag");
+		x[i]=z;
+		w[i] = -exp(gammln(alf+n)-gammln((float)n))/(pp*n*p2);
+	}
+}
+#undef EPS
+#undef MAXIT