add numerical recipes library

lib/nr/ansi/examples/xorthog.c

@@ -0,0 +1,64 @@
+
+/* Driver for routine orthog */
+
+#include <stdio.h>
+#include <math.h>
+#define NRANSI
+#include "nr.h"
+#include "nrutil.h"
+
+#define NP 64
+
+float func(float x)
+{
+	return 1.0/SQR(1.0+x);
+}
+
+int main(void)
+{
+	int i,n;
+	float amu0,check,xx,*a,*b,*x,*w,*anu,*alpha,*beta;
+
+	a=vector(1,NP);
+	b=vector(1,NP);
+	x=vector(1,NP);
+	w=vector(1,NP);
+	anu=vector(1,2*NP);
+	alpha=vector(1,2*NP-1);
+	beta=vector(1,2*NP-1);
+
+	/* Test with w[x] = -log x */
+	for (;;) {
+		printf("Enter N\n");
+		if (scanf("%d",&n) == EOF) break;
+		alpha[1]=0.5;
+		beta[1]=1.0;
+		for (i=2;i<=2*n-1;i++) {
+			alpha[i]=0.5;
+			beta[i]=1.0/(4.0*(4.0-1.0/((i-1)*(i-1))));
+		}
+		anu[1]=1.0;
+		anu[2] = -0.25;
+		for (i=2;i<=2*n-1;i++) anu[i+1] = -anu[i]*i*(i-1)/(2.0*(i+1)*(2*i-1));
+		orthog(n,anu,alpha,beta,a,b);
+		amu0=1.0;
+		gaucof(n,a,b,amu0,x,w);
+		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]);
+		for (check=0.0,i=1;i<=n;i++) check += w[i];
+		printf("\nCheck value: %15.7e  should be: %15.7e\n",check,amu0);
+		/* demonstrate the use of ORTHOG for an integral */
+		for (xx=0.0,i=1;i<=n;i++) xx += w[i]*func(x[i]);
+		printf("\nIntegral from orthog: %12.6f\n",xx);
+		printf("Actual value:         %12.6f\n",log(2.0));
+	}
+	free_vector(beta,1,2*NP-1);
+	free_vector(alpha,1,2*NP-1);
+	free_vector(anu,1,2*NP);
+	free_vector(w,1,NP);
+	free_vector(x,1,NP);
+	free_vector(b,1,NP);
+	free_vector(a,1,NP);
+	return 0;
+}
+#undef NRANSI