add numerical recipes library

lib/nr/ansi/recipes/powell.c

@@ -0,0 +1,60 @@
+
+#include <math.h>
+#define NRANSI
+#include "nrutil.h"
+#define TINY 1.0e-25
+#define ITMAX 200
+
+void powell(float p[], float **xi, int n, float ftol, int *iter, float *fret,
+	float (*func)(float []))
+{
+	void linmin(float p[], float xi[], int n, float *fret,
+		float (*func)(float []));
+	int i,ibig,j;
+	float del,fp,fptt,t,*pt,*ptt,*xit;
+
+	pt=vector(1,n);
+	ptt=vector(1,n);
+	xit=vector(1,n);
+	*fret=(*func)(p);
+	for (j=1;j<=n;j++) pt[j]=p[j];
+	for (*iter=1;;++(*iter)) {
+		fp=(*fret);
+		ibig=0;
+		del=0.0;
+		for (i=1;i<=n;i++) {
+			for (j=1;j<=n;j++) xit[j]=xi[j][i];
+			fptt=(*fret);
+			linmin(p,xit,n,fret,func);
+			if (fptt-(*fret) > del) {
+				del=fptt-(*fret);
+				ibig=i;
+			}
+		}
+		if (2.0*(fp-(*fret)) <= ftol*(fabs(fp)+fabs(*fret))+TINY) {
+			free_vector(xit,1,n);
+			free_vector(ptt,1,n);
+			free_vector(pt,1,n);
+			return;
+		}
+		if (*iter == ITMAX) nrerror("powell exceeding maximum iterations.");
+		for (j=1;j<=n;j++) {
+			ptt[j]=2.0*p[j]-pt[j];
+			xit[j]=p[j]-pt[j];
+			pt[j]=p[j];
+		}
+		fptt=(*func)(ptt);
+		if (fptt < fp) {
+			t=2.0*(fp-2.0*(*fret)+fptt)*SQR(fp-(*fret)-del)-del*SQR(fp-fptt);
+			if (t < 0.0) {
+				linmin(p,xit,n,fret,func);
+				for (j=1;j<=n;j++) {
+					xi[j][ibig]=xi[j][n];
+					xi[j][n]=xit[j];
+				}
+			}
+		}
+	}
+}
+#undef ITMAX
+#undef NRANSI