add numerical recipes library

lib/nr/cpp/recipes/selip.cpp

@@ -0,0 +1,64 @@
+#include "nr.h"
+
+DP NR::selip(const int k, Vec_I_DP &arr)
+{
+	const int M=64;
+	const DP BIG=1.0e30;
+	int i,j,jl,jm,ju,kk,mm,nlo,nxtmm;
+	DP ahi,alo,sum;
+	Vec_INT isel(M+2);
+	Vec_DP sel(M+2);
+
+	int n=arr.size();
+	if (k < 0 || k > n-1) nrerror("bad input to selip");
+	kk=k;
+	ahi=BIG;
+	alo = -BIG;
+	for (;;) {
+		mm=nlo=0;
+		sum=0.0;
+		nxtmm=M+1;
+		for (i=0;i<n;i++) {
+			if (arr[i] >= alo && arr[i] <= ahi) {
+				mm++;
+				if (arr[i] == alo) nlo++;
+				if (mm <= M) sel[mm-1]=arr[i];
+				else if (mm == nxtmm) {
+					nxtmm=mm+mm/M;
+					sel[(i+2+mm+kk) % M]=arr[i];
+				}
+				sum += arr[i];
+			}
+		}
+		if (kk < nlo) {
+			return alo;
+		}
+		else if (mm < M+1) {
+			shell(mm,sel);
+			ahi = sel[kk];
+			return ahi;
+		}
+		sel[M]=sum/mm;
+		shell(M+1,sel);
+		sel[M+1]=ahi;
+		for (j=0;j<M+2;j++) isel[j]=0;
+		for (i=0;i<n;i++) {
+			if (arr[i] >= alo && arr[i] <= ahi) {
+				jl=0;
+				ju=M+2;
+				while (ju-jl > 1) {
+					jm=(ju+jl)/2;
+					if (arr[i] >= sel[jm-1]) jl=jm;
+					else ju=jm;
+				}
+				isel[ju-1]++;
+			}
+		}
+		j=0;
+		while (kk >= isel[j]) {
+			alo=sel[j];
+			kk -= isel[j++];
+		}
+		ahi=sel[j];
+	}
+}