add numerical recipes library

lib/nr/k_and_r/recipes/rtsafe.c

@@ -0,0 +1,55 @@
+
+#include <math.h>
+#define MAXIT 100
+
+float rtsafe(funcd,x1,x2,xacc)
+float x1,x2,xacc;
+void (*funcd)();
+{
+	void nrerror();
+	int j;
+	float df,dx,dxold,f,fh,fl;
+	float temp,xh,xl,rts;
+
+	(*funcd)(x1,&fl,&df);
+	(*funcd)(x2,&fh,&df);
+	if ((fl > 0.0 && fh > 0.0) || (fl < 0.0 && fh < 0.0))
+		nrerror("Root must be bracketed in rtsafe");
+	if (fl == 0.0) return x1;
+	if (fh == 0.0) return x2;
+	if (fl < 0.0) {
+		xl=x1;
+		xh=x2;
+	} else {
+		xh=x1;
+		xl=x2;
+	}
+	rts=0.5*(x1+x2);
+	dxold=fabs(x2-x1);
+	dx=dxold;
+	(*funcd)(rts,&f,&df);
+	for (j=1;j<=MAXIT;j++) {
+		if ((((rts-xh)*df-f)*((rts-xl)*df-f) > 0.0)
+			|| (fabs(2.0*f) > fabs(dxold*df))) {
+			dxold=dx;
+			dx=0.5*(xh-xl);
+			rts=xl+dx;
+			if (xl == rts) return rts;
+		} else {
+			dxold=dx;
+			dx=f/df;
+			temp=rts;
+			rts -= dx;
+			if (temp == rts) return rts;
+		}
+		if (fabs(dx) < xacc) return rts;
+		(*funcd)(rts,&f,&df);
+		if (f < 0.0)
+			xl=rts;
+		else
+			xh=rts;
+	}
+	nrerror("Maximum number of iterations exceeded in rtsafe");
+	return 0.0;
+}
+#undef MAXIT