add numerical recipes library

lib/nr/k_and_r/recipes/newt.c

@@ -0,0 +1,88 @@
+
+#include <math.h>
+#include "nrutil.h"
+#define MAXITS 200
+#define TOLF 1.0e-4
+#define TOLMIN 1.0e-6
+#define TOLX 1.0e-7
+#define STPMX 100.0
+
+int nn;
+float *fvec;
+void (*nrfuncv)();
+#define FREERETURN {free_vector(fvec,1,n);free_vector(xold,1,n);\
+	free_vector(p,1,n);free_vector(g,1,n);free_matrix(fjac,1,n,1,n);\
+	free_ivector(indx,1,n);return;}
+
+void newt(x,n,check,vecfunc)
+float x[];
+int *check,n;
+void (*vecfunc)();
+{
+	float fmin();
+	void fdjac(),lnsrch(),lubksb(),ludcmp();
+	int i,its,j,*indx;
+	float d,den,f,fold,stpmax,sum,temp,test,**fjac,*g,*p,*xold;
+
+	indx=ivector(1,n);
+	fjac=matrix(1,n,1,n);
+	g=vector(1,n);
+	p=vector(1,n);
+	xold=vector(1,n);
+	fvec=vector(1,n);
+	nn=n;
+	nrfuncv=vecfunc;
+	f=fmin(x);
+	test=0.0;
+	for (i=1;i<=n;i++)
+		if (fabs(fvec[i]) > test) test=fabs(fvec[i]);
+	if (test < 0.01*TOLF) {
+		*check=0;
+		FREERETURN
+	}
+	for (sum=0.0,i=1;i<=n;i++) sum += SQR(x[i]);
+	stpmax=STPMX*FMAX(sqrt(sum),(float)n);
+	for (its=1;its<=MAXITS;its++) {
+		fdjac(n,x,fvec,fjac,vecfunc);
+		for (i=1;i<=n;i++) {
+			for (sum=0.0,j=1;j<=n;j++) sum += fjac[j][i]*fvec[j];
+			g[i]=sum;
+		}
+		for (i=1;i<=n;i++) xold[i]=x[i];
+		fold=f;
+		for (i=1;i<=n;i++) p[i] = -fvec[i];
+		ludcmp(fjac,n,indx,&d);
+		lubksb(fjac,n,indx,p);
+		lnsrch(n,xold,fold,g,p,x,&f,stpmax,check,fmin);
+		test=0.0;
+		for (i=1;i<=n;i++)
+			if (fabs(fvec[i]) > test) test=fabs(fvec[i]);
+		if (test < TOLF) {
+			*check=0;
+			FREERETURN
+		}
+		if (*check) {
+			test=0.0;
+			den=FMAX(f,0.5*n);
+			for (i=1;i<=n;i++) {
+				temp=fabs(g[i])*FMAX(fabs(x[i]),1.0)/den;
+				if (temp > test) test=temp;
+			}
+			*check=(test < TOLMIN ? 1 : 0);
+			FREERETURN
+		}
+		test=0.0;
+		for (i=1;i<=n;i++) {
+			temp=(fabs(x[i]-xold[i]))/FMAX(fabs(x[i]),1.0);
+			if (temp > test) test=temp;
+		}
+		if (test < TOLX) FREERETURN
+	}
+	nrerror("MAXITS exceeded in newt");
+}
+#undef MAXITS
+#undef TOLF
+#undef TOLMIN
+#undef TOLX
+#undef STPMX
+#undef FREERETURN