add numerical recipes library

lib/nr/k_and_r/recipes/dfridr.c

@@ -0,0 +1,43 @@
+
+#include <math.h>
+#include "nrutil.h"
+#define CON 1.4
+#define CON2 (CON*CON)
+#define BIG 1.0e30
+#define NTAB 10
+#define SAFE 2.0
+
+float dfridr(func,x,h,err)
+float (*func)(),*err,h,x;
+{
+	int i,j;
+	float errt,fac,hh,**a,ans;
+
+	if (h == 0.0) nrerror("h must be nonzero in dfridr.");
+	a=matrix(1,NTAB,1,NTAB);
+	hh=h;
+	a[1][1]=((*func)(x+hh)-(*func)(x-hh))/(2.0*hh);
+	*err=BIG;
+	for (i=2;i<=NTAB;i++) {
+		hh /= CON;
+		a[1][i]=((*func)(x+hh)-(*func)(x-hh))/(2.0*hh);
+		fac=CON2;
+		for (j=2;j<=i;j++) {
+			a[j][i]=(a[j-1][i]*fac-a[j-1][i-1])/(fac-1.0);
+			fac=CON2*fac;
+			errt=FMAX(fabs(a[j][i]-a[j-1][i]),fabs(a[j][i]-a[j-1][i-1]));
+			if (errt <= *err) {
+				*err=errt;
+				ans=a[j][i];
+			}
+		}
+		if (fabs(a[i][i]-a[i-1][i-1]) >= SAFE*(*err)) break;
+	}
+	free_matrix(a,1,NTAB,1,NTAB);
+	return ans;
+}
+#undef CON
+#undef CON2
+#undef BIG
+#undef NTAB
+#undef SAFE