add numerical recipes library

lib/nr/cpp/recipes/memcof.cpp

@@ -0,0 +1,40 @@
+#include <cmath>
+#include "nr.h"
+using namespace std;
+
+void NR::memcof(Vec_I_DP &data, DP &xms, Vec_O_DP &d)
+{
+	int k,j,i;
+	DP p=0.0;
+
+	int n=data.size();
+	int m=d.size();
+	Vec_DP wk1(n),wk2(n),wkm(m);
+	for (j=0;j<n;j++) p += SQR(data[j]);
+	xms=p/n;
+	wk1[0]=data[0];
+	wk2[n-2]=data[n-1];
+	for (j=1;j<n-1;j++) {
+		wk1[j]=data[j];
+		wk2[j-1]=data[j];
+	}
+	for (k=0;k<m;k++) {
+		DP num=0.0,denom=0.0;
+		for (j=0;j<(n-k-1);j++) {
+			num += (wk1[j]*wk2[j]);
+			denom += (SQR(wk1[j])+SQR(wk2[j]));
+		}
+		d[k]=2.0*num/denom;
+		xms *= (1.0-SQR(d[k]));
+		for (i=0;i<k;i++)
+			d[i]=wkm[i]-d[k]*wkm[k-1-i];
+		if (k == m-1)
+			return;
+		for (i=0;i<=k;i++) wkm[i]=d[i];
+		for (j=0;j<(n-k-2);j++) {
+			wk1[j] -= (wkm[k]*wk2[j]);
+			wk2[j]=wk2[j+1]-wkm[k]*wk1[j+1];
+		}
+	}
+	nrerror("never get here in memcof.");
+}