add numerical recipes library

lib/nr/k_and_r/recipes/savgol.c

@@ -0,0 +1,40 @@
+
+#include <math.h>
+#include "nrutil.h"
+
+void savgol(c,np,nl,nr,ld,m)
+float c[];
+int ld,m,nl,np,nr;
+{
+	void lubksb(),ludcmp();
+	int imj,ipj,j,k,kk,mm,*indx;
+	float d,fac,sum,**a,*b;
+
+	if (np < nl+nr+1 || nl < 0 || nr < 0 || ld > m || nl+nr < m)
+	nrerror("bad args in savgol");
+	indx=ivector(1,m+1);
+	a=matrix(1,m+1,1,m+1);
+	b=vector(1,m+1);
+	for (ipj=0;ipj<=(m << 1);ipj++) {
+		sum=(ipj ? 0.0 : 1.0);
+		for (k=1;k<=nr;k++) sum += pow((double)k,(double)ipj);
+		for (k=1;k<=nl;k++) sum += pow((double)-k,(double)ipj);
+		mm=IMIN(ipj,2*m-ipj);
+		for (imj = -mm;imj<=mm;imj+=2) a[1+(ipj+imj)/2][1+(ipj-imj)/2]=sum;
+	}
+	ludcmp(a,m+1,indx,&d);
+	for (j=1;j<=m+1;j++) b[j]=0.0;
+	b[ld+1]=1.0;
+	lubksb(a,m+1,indx,b);
+	for (kk=1;kk<=np;kk++) c[kk]=0.0;
+	for (k = -nl;k<=nr;k++) {
+		sum=b[1];
+		fac=1.0;
+		for (mm=1;mm<=m;mm++) sum += b[mm+1]*(fac *= k);
+		kk=((np-k) % np)+1;
+		c[kk]=sum;
+	}
+	free_vector(b,1,m+1);
+	free_matrix(a,1,m+1,1,m+1);
+	free_ivector(indx,1,m+1);
+}