add numerical recipes library

lib/nr/ansi/examples/xgaujac.c

@@ -0,0 +1,51 @@
+
+/* Driver for routine gaujac */
+
+#include <stdio.h>
+#include <math.h>
+#define NRANSI
+#include "nr.h"
+#include "nrutil.h"
+
+#define NP 64
+#define PIBY2 1.5707963
+
+float func(float ak,float x)
+{
+	return 1.0/sqrt(1.0-ak*ak*(1.0+x)/2.0);
+}
+
+int main(void)
+{
+	int i,n;
+	float ak,alf=(-0.5),bet=(-0.5),checkw,checkx,xx,*x,*w;
+
+	x=vector(1,NP);
+	w=vector(1,NP);
+	for (;;) {
+		printf("Enter N\n");
+		if (scanf("%d",&n) == EOF) break;
+		gaujac(x,w,n,alf,bet);
+		printf("%3s %10s %14s\n","#","x(i)","w(i)");
+		for (i=1;i<=n;i++) printf("%3d %14.6e %14.6e\n",i,x[i],w[i]);
+		checkx=checkw=0.0;
+		for (i=1;i<=n;i++) {
+			checkx += x[i];
+			checkw += w[i];
+		}
+		printf("\nCheck value: %15.7e  should be: %15.7e\n",
+			checkx,n*(bet-alf)/(alf+bet+2*n));
+		printf("\nCheck value: %15.7e  should be: %15.7e\n",
+			checkw,exp(gammln(1.0+alf)+gammln(1.0+bet)-
+			gammln(2.0+alf+bet))*pow(2.0,alf+bet+1.0));
+		/* demonstrate the use of GAUJAC for an integral */
+		ak=0.5;
+		for (xx=0.0,i=1;i<=n;i++) xx += w[i]*func(ak,x[i]);
+		printf("\nIntegral from gaujac: %12.6f\n",xx);
+		printf("Actual value:         %12.6f\n",2.0*ellf(PIBY2,ak));
+	}
+	free_vector(w,1,NP);
+	free_vector(x,1,NP);
+	return 0;
+}
+#undef NRANSI