add numerical recipes library

lib/nr/ansi/examples/xmrqmin.c

@@ -0,0 +1,91 @@
+
+/* Driver for routine mrqmin */
+
+#include <stdio.h>
+#include <math.h>
+#define NRANSI
+#include "nr.h"
+#include "nrutil.h"
+
+#define NPT 100
+#define MA 6
+#define SPREAD 0.001
+
+int main(void)
+{
+	long idum=(-911);
+	int i,*ia,iter,itst,j,k,mfit=MA;
+	float alamda,chisq,ochisq,*x,*y,*sig,**covar,**alpha;
+	static float a[MA+1]=
+		{0.0,5.0,2.0,3.0,2.0,5.0,3.0};
+	static float gues[MA+1]=
+		{0.0,4.5,2.2,2.8,2.5,4.9,2.8};
+
+	ia=ivector(1,MA);
+	x=vector(1,NPT);
+	y=vector(1,NPT);
+	sig=vector(1,NPT);
+	covar=matrix(1,MA,1,MA);
+	alpha=matrix(1,MA,1,MA);
+	/* First try a sum of two Gaussians */
+	for (i=1;i<=NPT;i++) {
+		x[i]=0.1*i;
+		y[i]=0.0;
+		for (j=1;j<=MA;j+=3) {
+			y[i] += a[j]*exp(-SQR((x[i]-a[j+1])/a[j+2]));
+		}
+		y[i] *= (1.0+SPREAD*gasdev(&idum));
+		sig[i]=SPREAD*y[i];
+	}
+	for (i=1;i<=mfit;i++) ia[i]=1;
+	for (i=1;i<=MA;i++) a[i]=gues[i];
+	for (iter=1;iter<=2;iter++) {
+		alamda = -1;
+		mrqmin(x,y,sig,NPT,a,ia,MA,covar,alpha,&chisq,fgauss,&alamda);
+		k=1;
+		itst=0;
+		for (;;) {
+			printf("\n%s %2d %17s %10.4f %10s %9.2e\n","Iteration #",k,
+				"chi-squared:",chisq,"alamda:",alamda);
+			printf("%8s %8s %8s %8s %8s %8s\n",
+				"a[1]","a[2]","a[3]","a[4]","a[5]","a[6]");
+			for (i=1;i<=6;i++) printf("%9.4f",a[i]);
+			printf("\n");
+			k++;
+			ochisq=chisq;
+			mrqmin(x,y,sig,NPT,a,ia,MA,covar,alpha,&chisq,fgauss,&alamda);
+			if (chisq > ochisq)
+				itst=0;
+			else if (fabs(ochisq-chisq) < 0.1)
+				itst++;
+			if (itst < 4) continue;
+			alamda=0.0;
+			mrqmin(x,y,sig,NPT,a,ia,MA,covar,alpha,&chisq,fgauss,&alamda);
+			printf("\nUncertainties:\n");
+			for (i=1;i<=6;i++) printf("%9.4f",sqrt(covar[i][i]));
+			printf("\n");
+			printf("\nExpected results:\n");
+			printf(" %7.2f %8.2f %8.2f %8.2f %8.2f %8.2f\n",
+				5.0,2.0,3.0,2.0,5.0,3.0);
+			break;
+		}
+		if (iter == 1) {
+			printf("press return to continue with constraint\n");
+			(void) getchar();
+			printf("holding a[2] and a[5] constant\n");
+			for (j=1;j<=MA;j++) a[j] += 0.1;
+			a[2]=2.0;
+			ia[2]=0;
+			a[5]=5.0;
+			ia[5]=0;
+		}
+	}
+	free_matrix(alpha,1,MA,1,MA);
+	free_matrix(covar,1,MA,1,MA);
+	free_vector(sig,1,NPT);
+	free_vector(y,1,NPT);
+	free_vector(x,1,NPT);
+	free_ivector(ia,1,MA);
+	return 0;
+}
+#undef NRANSI