add numerical recipes library

lib/nr/ansi/examples/xpccheb.c

@@ -0,0 +1,69 @@
+
+/* Driver for routine pccheb */
+
+#include <stdio.h>
+#include <math.h>
+#define NRANSI
+#include "nr.h"
+#include "nrutil.h"
+
+#define NCHECK 15
+#define NFEW 13
+#define NMANY 17
+#define NMAX 100
+#define PI 3.14159265
+
+int main(void)
+{
+	int i,j;
+	float a=(-PI),b=PI,fac,f,sum,sume,py,py2,*c,*d,*e,*ee;
+
+	c=vector(0,NMAX-1);
+	d=vector(0,NMAX-1);
+	e=vector(0,NMAX-1);
+	ee=vector(0,NMAX-1);
+	/* put power series of cos(PI*y) into e */
+	fac=1.0;
+	e[0]=ee[0]=0.0;
+	for (j=0;j<NMANY;j++) {
+		i=j & 3;    /* tricky way to perform j % 4 */
+		if (i == 1 || i == 3) e[j]=0.0;
+		else if (i == 0) e[j]=1.0/fac;
+		else e[j] = -1.0/fac;
+		fac *= (j+1);
+		ee[j]=e[j];
+	}
+	pcshft((-2.0-b-a)/(b-a),(2.0-b-a)/(b-a),e,NMANY);
+	/* i.e., inverse of pcshft(a,b,...) which we do below */
+	pccheb(e,c,NMANY);
+	printf("Index, series, Chebyshev coefficients\n");
+	for (j=0;j<NMANY;j+=2)
+		printf("%3d %15.6e %15.6e\n",j,e[j],c[j]);
+	chebpc(c,d,NFEW);
+	pcshft(a,b,d,NFEW);
+	printf("Index, new series, coefficient ratios\n");
+	for (j=0;j<NFEW;j+=2) {
+		printf("%3d %15.6e %15.6e\n",
+			j,d[j],d[j]/(ee[j]+1.0e-30));
+	}
+	printf("      Point tested, function value, error power series, error Cheb.\n");
+	for (i=0;i<=NCHECK;i++) {
+		py=a+i*(b-a)/(float)NCHECK;
+		py2=py*py;
+		sum=sume=0.0;
+		fac=1.0;
+		for (j=0;j<NFEW;j+=2) {
+			sum += fac*d[j];
+			sume += fac*ee[j];
+			fac *= py2;
+		}
+		f=cos(py);
+		printf("check: %15.6e %15.6e %15.6e %15.6e\n",py,f,sume-f,sum-f);
+	}
+	free_vector(ee,0,NMAX-1);
+	free_vector(e,0,NMAX-1);
+	free_vector(d,0,NMAX-1);
+	free_vector(c,0,NMAX-1);
+	return 0;
+}
+#undef NRANSI