add numerical recipes library

lib/nr/k_and_r/recipes/hypgeo.c

@@ -0,0 +1,43 @@
+
+#include <math.h>
+#include "complex.h"
+#include "nrutil.h"
+#define EPS 1.0e-6
+
+fcomplex aa,bb,cc,z0,dz;
+
+int kmax,kount;
+float *xp,**yp,dxsav;
+
+fcomplex hypgeo(a,b,c,z)
+fcomplex a,b,c,z;
+{
+	void bsstep(),hypdrv(),hypser(),odeint();
+	int nbad,nok;
+	fcomplex ans,y[3];
+	float *yy;
+
+	kmax=0;
+	if (z.r*z.r+z.i*z.i <= 0.25) {
+		hypser(a,b,c,z,&ans,&y[2]);
+		return ans;
+	}
+	else if (z.r < 0.0) z0=Complex(-0.5,0.0);
+	else if (z.r <= 1.0) z0=Complex(0.5,0.0);
+	else z0=Complex(0.0,z.i >= 0.0 ? 0.5 : -0.5);
+	aa=a;
+	bb=b;
+	cc=c;
+	dz=Csub(z,z0);
+	hypser(aa,bb,cc,z0,&y[1],&y[2]);
+	yy=vector(1,4);
+	yy[1]=y[1].r;
+	yy[2]=y[1].i;
+	yy[3]=y[2].r;
+	yy[4]=y[2].i;
+	odeint(yy,4,0.0,1.0,EPS,0.1,0.0001,&nok,&nbad,hypdrv,bsstep);
+	y[1]=Complex(yy[1],yy[2]);
+	free_vector(yy,1,4);
+	return y[1];
+}
+#undef EPS