add numerical recipes library

lib/nr/cpp/recipes/zriddr.cpp

@@ -0,0 +1,50 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+DP NR::zriddr(DP func(const DP), const DP x1, const DP x2, const DP xacc)
+{
+	const int MAXIT=60;
+	const DP UNUSED=-1.11e30;
+	int j;
+	DP ans,fh,fl,fm,fnew,s,xh,xl,xm,xnew;
+
+	fl=func(x1);
+	fh=func(x2);
+	if ((fl > 0.0 && fh < 0.0) || (fl < 0.0 && fh > 0.0)) {
+		xl=x1;
+		xh=x2;
+		ans=UNUSED;
+		for (j=0;j<MAXIT;j++) {
+			xm=0.5*(xl+xh);
+			fm=func(xm);
+			s=sqrt(fm*fm-fl*fh);
+			if (s == 0.0) return ans;
+			xnew=xm+(xm-xl)*((fl >= fh ? 1.0 : -1.0)*fm/s);
+			if (fabs(xnew-ans) <= xacc) return ans;
+			ans=xnew;
+			fnew=func(ans);
+			if (fnew == 0.0) return ans;
+			if (SIGN(fm,fnew) != fm) {
+				xl=xm;
+				fl=fm;
+				xh=ans;
+				fh=fnew;
+			} else if (SIGN(fl,fnew) != fl) {
+				xh=ans;
+				fh=fnew;
+			} else if (SIGN(fh,fnew) != fh) {
+				xl=ans;
+				fl=fnew;
+			} else nrerror("never get here.");
+			if (fabs(xh-xl) <= xacc) return ans;
+		}
+		nrerror("zriddr exceed maximum iterations");
+	}
+	else {
+		if (fl == 0.0) return x1;
+		if (fh == 0.0) return x2;
+		nrerror("root must be bracketed in zriddr.");
+	}
+	return 0.0;
+}