local real gdisk(real rad)
{
real x;
x = 0.5 * alpha * rad;
return - alpha*alpha * mdisk * x *
(bessi0(x) * bessk0(x) - bessi1(x) * bessk1(x));
}
void potential_double(int *ndim,double *pos,double *acc,double *pot,double *time)
{
double apar, qpar, spar, ppar, lpar, rpar, rcyl;
int i;
// 20070312 bwillett added ppar - the plummer denominator: r + rc = sqrt(x^2+y^2+z^2) + rc
// 20070312 bwillett added lpar - the logarithmic argument: R^2 + (z/q)^2 + d^2
// 20070427 bwillett added rpar - the spherical radius: r + rc - rc = ppar - plu_rc
// 20070501 bwillett added apar - a + qpar
// 20070507 bwillett took out pow statements
// 20070507 bwillett used hypot from math.h
rcyl = hypot(pos[X],pos[Y]);
ppar = sqrt ((pos[X]*pos[X])+(pos[Y]*pos[Y])+(pos[Z]*pos[Z])) + plu_rc;
rpar = ppar - plu_rc;
lpar = (rcyl*rcyl) + ((pos[Z]/q)*(pos[Z]/q)) + (d*d);
// This is only valid for 3 dimensions, and is in (x,y,z)
// Recall F_mu = -grad_mu U
// So a_mu = -grad_mu Phi
// I did these derivatives in Mathematica, and will try to keep it consistent with the conventions written above
acc[X] = - ( ( (2.0*vhalo*vhalo*pos[X])/(lpar) ) + ( (plu_mass*pos[X])/(rpar*ppar*ppar) ) );
acc[Y] = - ( ( (2.0*vhalo*vhalo*pos[Y])/(lpar) ) + ( (plu_mass*pos[Y])/(rpar*ppar*ppar) ) );
acc[Z] = - ( ( (2.0*vhalo*vhalo*pos[Z])/(lpar) ) + ( (plu_mass*pos[Z])/(rpar*ppar*ppar) ) );
// Copied from expdisk.c
double r2, r, arg, i0, k0, i1, k1, f;
double alpha;
alpha = 1.0/a;
r = rpar;
r2 = r*r;
arg = 0.5*alpha*r;
//printf("%f %f %f %f %f\n", a, mass, r, r2, x);
i0=bessi0(arg);
k0=bessk0(arg);
i1=bessi1(arg);
k1=bessk1(arg);
// 20080928 - willeb added exponential disk to acceleration field
*pot = -mass*arg*(i0*k1-i1*k0);
f = -0.5*alpha*alpha*alpha*mass*(i0*k0-i1*k1);
acc[X] += f*pos[X];
acc[Y] += f*pos[Y];
acc[Z] += f*pos[Z];
// 20080928 - willeb added bulge and halo to potential
*pot += (-(plu_mass)/ppar);
*pot += (vhalo*vhalo*log(lpar));
}
float bessk(int n, float x)
{
float bessk0(float x);
float bessk1(float x);
void nrerror(char error_text[]);
int j;
float bk,bkm,bkp,tox;
if (n < 2) nrerror("Index n less than 2 in bessk");
tox=2.0/x;
bkm=bessk0(x);
bk=bessk1(x);
for (j=1;j<n;j++) {
bkp=bkm+j*tox*bk;
bkm=bk;
bk=bkp;
}
return bk;
}
void potential_dummy_for_c(void)
{
double a,b,c;
int spline();
double bessi0(), bessk0(), bessi1(), bessk1();
void get_atable();
void read_image();
error("potential.c: Cannot call dummy_for_c - included to fool linkers");
(void) spline();
(void) bessi0();
(void) bessk0();
(void) bessi1();
(void) sqr(1.0);
stropen("/dev/null","w");
#ifndef NO_IMAGE
read_image();
#endif
get_atable();
}
static double pbar_PropagatorInfiniteR(double rSrc, double zSrc, double ek)
{
double distance;
double propagator,kspal,kv,kd,cn,knL;
int n,i;
if (rSrc==0.) return 0;
distance= sqrt(SQR(rSrc) + SQR(zSrc));
// n_terms_infinite_sum=1000000;
// if (distance<L_dif/100.) return 1./(4.*M_PI*Kdif*distance);
propagator=0.;
kspal= 2.*h*Gtot/Kdif;
kv=Vdif/(2.*Kdif);
kd= (kspal + 2.*kv);
for (n=0; ; n++)
{ double dPropagator;
// if(n<=lastK) knL=kn[n]; else
{
knL= (n+0.5)*M_PI; cn=1;
if(kd)
{ int nn;
if(kd>0) nn=n+1; else nn=n;
for(i=0; i<10; ++i) knL = nn*M_PI - atan(2.*knL/(kd*L_dif));
}
// kn[n]=knL;
// lastK=n;
}
cn= 1. - sin(2.*knL)/(2.*knL);
dPropagator=bessk0(sqrt(SQR(knL/L_dif)+SQR(kv))*rSrc);
propagator+=dPropagator*sin(knL*(L_dif-zSrc)/L_dif)*sin(knL)/cn;
if(fabs(dPropagator) <= 0.1*Eps*fabs(propagator)) break;
}
return propagator*exp(-kv*zSrc)/(2.*M_PI*Kdif*L_dif);
}
int main(void)
{
char txt[MAXSTR];
int i,nval;
float val,x;
FILE *fp;
if ((fp = fopen("fncval.dat","r")) == NULL)
nrerror("Data file fncval.dat not found\n");
fgets(txt,MAXSTR,fp);
while (strncmp(txt,"Modified Bessel Function K0",27)) {
fgets(txt,MAXSTR,fp);
if (feof(fp)) nrerror("Data not found in fncval.dat\n");
}
fscanf(fp,"%d %*s",&nval);
printf("\n%s\n",txt);
printf("%5s %13s %18s \n","x","actual","bessk0(x)");
for (i=1;i<=nval;i++) {
fscanf(fp,"%f %f",&x,&val);
printf("%6.2f %16.7e %16.7e\n",x,val,bessk0(x));
}
fclose(fp);
return 0;
}
