add numerical recipes library

lib/nr/k_and_r/recipes/mrqmin.c

@@ -0,0 +1,57 @@
+
+#include "nrutil.h"
+
+void mrqmin(x,y,sig,ndata,a,ia,ma,covar,alpha,chisq,funcs,alamda)
+float **alpha,**covar,*alamda,*chisq,a[],sig[],x[],y[];
+int ia[],ma,ndata;
+void (*funcs)();
+{
+	void covsrt(),gaussj(),mrqcof();
+	int j,k,l;
+	static int mfit;
+	static float ochisq,*atry,*beta,*da,**oneda;
+
+	if (*alamda < 0.0) {
+		atry=vector(1,ma);
+		beta=vector(1,ma);
+		da=vector(1,ma);
+		for (mfit=0,j=1;j<=ma;j++)
+			if (ia[j]) mfit++;
+		oneda=matrix(1,mfit,1,1);
+		*alamda=0.001;
+		mrqcof(x,y,sig,ndata,a,ia,ma,alpha,beta,chisq,funcs);
+		ochisq=(*chisq);
+		for (j=1;j<=ma;j++) atry[j]=a[j];
+	}
+	for (j=1;j<=mfit;j++) {
+		for (k=1;k<=mfit;k++) covar[j][k]=alpha[j][k];
+		covar[j][j]=alpha[j][j]*(1.0+(*alamda));
+		oneda[j][1]=beta[j];
+	}
+	gaussj(covar,mfit,oneda,1);
+	for (j=1;j<=mfit;j++) da[j]=oneda[j][1];
+	if (*alamda == 0.0) {
+		covsrt(covar,ma,ia,mfit);
+		covsrt(alpha,ma,ia,mfit);
+		free_matrix(oneda,1,mfit,1,1);
+		free_vector(da,1,ma);
+		free_vector(beta,1,ma);
+		free_vector(atry,1,ma);
+		return;
+	}
+	for (j=0,l=1;l<=ma;l++)
+		if (ia[l]) atry[l]=a[l]+da[++j];
+	mrqcof(x,y,sig,ndata,atry,ia,ma,covar,da,chisq,funcs);
+	if (*chisq < ochisq) {
+		*alamda *= 0.1;
+		ochisq=(*chisq);
+		for (j=1;j<=mfit;j++) {
+			for (k=1;k<=mfit;k++) alpha[j][k]=covar[j][k];
+			beta[j]=da[j];
+		}
+		for (l=1;l<=ma;l++) a[l]=atry[l];
+	} else {
+		*alamda *= 10.0;
+		*chisq=ochisq;
+	}
+}