add numerical recipes library

lib/nr/k_and_r/recipes/dbrent.c

@@ -0,0 +1,91 @@
+
+#include <math.h>
+#include "nrutil.h"
+#define ITMAX 100
+#define ZEPS 1.0e-10
+#define MOV3(a,b,c, d,e,f) (a)=(d);(b)=(e);(c)=(f);
+
+float dbrent(ax,bx,cx,f,df,tol,xmin)
+float (*df)(),(*f)(),*xmin,ax,bx,cx,tol;
+{
+	int iter,ok1,ok2;
+	float a,b,d,d1,d2,du,dv,dw,dx,e=0.0;
+	float fu,fv,fw,fx,olde,tol1,tol2,u,u1,u2,v,w,x,xm;
+
+	a=(ax < cx ? ax : cx);
+	b=(ax > cx ? ax : cx);
+	x=w=v=bx;
+	fw=fv=fx=(*f)(x);
+	dw=dv=dx=(*df)(x);
+	for (iter=1;iter<=ITMAX;iter++) {
+		xm=0.5*(a+b);
+		tol1=tol*fabs(x)+ZEPS;
+		tol2=2.0*tol1;
+		if (fabs(x-xm) <= (tol2-0.5*(b-a))) {
+			*xmin=x;
+			return fx;
+		}
+		if (fabs(e) > tol1) {
+			d1=2.0*(b-a);
+			d2=d1;
+			if (dw != dx) d1=(w-x)*dx/(dx-dw);
+			if (dv != dx) d2=(v-x)*dx/(dx-dv);
+			u1=x+d1;
+			u2=x+d2;
+			ok1 = (a-u1)*(u1-b) > 0.0 && dx*d1 <= 0.0;
+			ok2 = (a-u2)*(u2-b) > 0.0 && dx*d2 <= 0.0;
+			olde=e;
+			e=d;
+			if (ok1 || ok2) {
+				if (ok1 && ok2)
+					d=(fabs(d1) < fabs(d2) ? d1 : d2);
+				else if (ok1)
+					d=d1;
+				else
+					d=d2;
+				if (fabs(d) <= fabs(0.5*olde)) {
+					u=x+d;
+					if (u-a < tol2 || b-u < tol2)
+						d=SIGN(tol1,xm-x);
+				} else {
+					d=0.5*(e=(dx >= 0.0 ? a-x : b-x));
+				}
+			} else {
+				d=0.5*(e=(dx >= 0.0 ? a-x : b-x));
+			}
+		} else {
+			d=0.5*(e=(dx >= 0.0 ? a-x : b-x));
+		}
+		if (fabs(d) >= tol1) {
+			u=x+d;
+			fu=(*f)(u);
+		} else {
+			u=x+SIGN(tol1,d);
+			fu=(*f)(u);
+			if (fu > fx) {
+				*xmin=x;
+				return fx;
+			}
+		}
+		du=(*df)(u);
+		if (fu <= fx) {
+			if (u >= x) a=x; else b=x;
+			MOV3(v,fv,dv, w,fw,dw)
+			MOV3(w,fw,dw, x,fx,dx)
+			MOV3(x,fx,dx, u,fu,du)
+		} else {
+			if (u < x) a=u; else b=u;
+			if (fu <= fw || w == x) {
+				MOV3(v,fv,dv, w,fw,dw)
+				MOV3(w,fw,dw, u,fu,du)
+			} else if (fu < fv || v == x || v == w) {
+				MOV3(v,fv,dv, u,fu,du)
+			}
+		}
+	}
+	nrerror("Too many iterations in routine dbrent");
+	return 0.0;
+}
+#undef ITMAX
+#undef ZEPS
+#undef MOV3