add numerical recipes library

lib/nr/cpp/recipes/dfridr.cpp

@@ -0,0 +1,36 @@
+#include <cmath>
+#include <limits>
+#include "nr.h"
+using namespace std;
+
+DP NR::dfridr(DP func(const DP), const DP x, const DP h, DP &err)
+{
+	const int NTAB=10;
+	const DP CON=1.4, CON2=(CON*CON);
+	const DP BIG=numeric_limits<DP>::max();
+	const DP SAFE=2.0;
+	int i,j;
+	DP errt,fac,hh,ans;
+	Mat_DP a(NTAB,NTAB);
+
+	if (h == 0.0) nrerror("h must be nonzero in dfridr.");
+	hh=h;
+	a[0][0]=(func(x+hh)-func(x-hh))/(2.0*hh);
+	err=BIG;
+	for (i=1;i<NTAB;i++) {
+		hh /= CON;
+		a[0][i]=(func(x+hh)-func(x-hh))/(2.0*hh);
+		fac=CON2;
+		for (j=1;j<=i;j++) {
+			a[j][i]=(a[j-1][i]*fac-a[j-1][i-1])/(fac-1.0);
+			fac=CON2*fac;
+			errt=MAX(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;
+	}
+	return ans;
+}