add numerical recipes library

lib/nr/ansi/recipes/sfroid.c

@@ -0,0 +1,84 @@
+
+#include <stdio.h>
+#include <math.h>
+#define NRANSI
+#include "nrutil.h"
+#define NE 3
+#define M 41
+#define NB 1
+#define NSI NE
+#define NYJ NE
+#define NYK M
+#define NCI NE
+#define NCJ (NE-NB+1)
+#define NCK (M+1)
+#define NSJ (2*NE+1)
+
+int mm,n,mpt=M;
+float h,c2=0.0,anorm,x[M+1];
+
+int main(void)  /* Program sfroid */
+{
+	float plgndr(int l, int m, float x);
+	void solvde(int itmax, float conv, float slowc, float scalv[],
+		int indexv[], int ne, int nb, int m, float **y, float ***c, float **s);
+	int i,itmax,k,indexv[NE+1];
+	float conv,deriv,fac1,fac2,q1,slowc,scalv[NE+1];
+	float **y,**s,***c;
+
+	y=matrix(1,NYJ,1,NYK);
+	s=matrix(1,NSI,1,NSJ);
+	c=f3tensor(1,NCI,1,NCJ,1,NCK);
+	itmax=100;
+	conv=5.0e-6;
+	slowc=1.0;
+	h=1.0/(M-1);
+	printf("\nenter m n\n");
+	scanf("%d %d",&mm,&n);
+	if (n+mm & 1) {
+		indexv[1]=1;
+		indexv[2]=2;
+		indexv[3]=3;
+	} else {
+		indexv[1]=2;
+		indexv[2]=1;
+		indexv[3]=3;
+	}
+	anorm=1.0;
+	if (mm) {
+		q1=n;
+		for (i=1;i<=mm;i++) anorm = -0.5*anorm*(n+i)*(q1--/i);
+	}
+	for (k=1;k<=(M-1);k++) {
+		x[k]=(k-1)*h;
+		fac1=1.0-x[k]*x[k];
+		fac2=exp((-mm/2.0)*log(fac1));
+		y[1][k]=plgndr(n,mm,x[k])*fac2;
+		deriv = -((n-mm+1)*plgndr(n+1,mm,x[k])-
+			(n+1)*x[k]*plgndr(n,mm,x[k]))/fac1;
+		y[2][k]=mm*x[k]*y[1][k]/fac1+deriv*fac2;
+		y[3][k]=n*(n+1)-mm*(mm+1);
+	}
+	x[M]=1.0;
+	y[1][M]=anorm;
+	y[3][M]=n*(n+1)-mm*(mm+1);
+	y[2][M]=(y[3][M]-c2)*y[1][M]/(2.0*(mm+1.0));
+	scalv[1]=fabs(anorm);
+	scalv[2]=(y[2][M] > scalv[1] ? y[2][M] : scalv[1]);
+	scalv[3]=(y[3][M] > 1.0 ? y[3][M] : 1.0);
+	for (;;) {
+		printf("\nEnter c**2 or 999 to end.\n");
+		scanf("%f",&c2);
+		if (c2 == 999) {
+			free_f3tensor(c,1,NCI,1,NCJ,1,NCK);
+			free_matrix(s,1,NSI,1,NSJ);
+			free_matrix(y,1,NYJ,1,NYK);
+			return 0;
+		}
+		solvde(itmax,conv,slowc,scalv,indexv,NE,NB,M,y,c,s);
+		printf("\n %s %2d %s %2d %s %7.3f %s %10.6f\n",
+			"m =",mm,"  n =",n,"  c**2 =",c2,
+			" lamda =",y[3][1]+mm*(mm+1));
+	}
+}
+#undef NRANSI