/// Fourier transform of NFW profile for satellites
double cosmology::uskofm(double k, double m, double z, double csbycdm)
{
double mvir,rvir, cvir, r200, c200;
modelNFWhalo(m,z,mvir,rvir,cvir,r200,c200);
c200=c200*csbycdm;
double rs=r200/c200;
double fac=log(1.+c200) - c200/(1.+c200);
double ci1,ci2;
double si1,si2;
double arg1=k*rs;
double arg2=(1.+c200)*k*rs;
double arg3=c200*k*rs;
ci1=gsl_sf_Ci(arg1);
ci2=gsl_sf_Ci(arg2);
si1=gsl_sf_Si(arg1);
si2=gsl_sf_Si(arg2);
double res1=sin(arg1)*(si2-si1);
res1-=sin(arg3)/arg2;
res1+=cos(arg1)*(ci2-ci1);
return res1/fac;
}
// FFT of NFW profile from White '01
double rho_NFW_fft(double k,
double M_vir,
double z,
int mode,
cosmo_info **cosmo){
double c_vir;
double R_vir;
double r_s;
double z_k;
double g_c;
double rho_o;
double x1;
double x2;
double Ci1;
double Ci2;
double Si1;
double Si2;
double r_val;
set_NFW_params(M_vir,z,mode,cosmo,&c_vir,&R_vir);
r_s =R_vir/c_vir;
z_k =k*r_s;
g_c =1./(log(1.+c_vir)-c_vir/(1.+c_vir));
rho_o=M_vir*g_c/(FOUR_PI*r_s*r_s*r_s);
x1 =1.+c_vir;
x2 =c_vir*z_k;
Ci1=gsl_sf_Ci((1.+c_vir)*z_k);
Si1=gsl_sf_Si((1.+c_vir)*z_k);
Ci2=gsl_sf_Ci( z_k);
Si2=gsl_sf_Si( z_k);
r_val=(FOUR_PI*rho_o*r_s*r_s*r_s/M_vir)*(cos(z_k)*(Ci1-Ci2)+
sin(z_k)*(Si1-Si2)-
sin(c_vir*z_k)/(z_k*(1.+c_vir)));
return(r_val);
}
/// The fourier transform of the NFW profile on a grid of k*rs and c
/// krsmin=10^-6 and krsmax=10.0^8.0
/// log(cmin)=0.0 and logcmax=2.5
void cosmology::ukinit()
{
double krsdiff=(krsmax-krsmin)/(Nuk-1.);
double cdiff=(cmax-cmin)/(Nuk-1.);
for(int i=0;i<Nuk;i++)
{
uk_krs[i]=krsmin+i*krsdiff;
uk_c [i]=cmin +i*cdiff;
}
/// Bilinear interpolation is not defined in GSL. So code this up yourself
//std::cout<<"# Start check here"<<std::endl;
for(int i=0;i<Nuk;i++)
{
double con=pow(10.,uk_c[i]);
double fac=log(1.+con) - con/(1.+con);
bool extrap=false;
double x_extrap,y_extrap;
for(int j=0;j<Nuk;j++)
{
double krs=pow(10.,uk_krs[j]);
// Do the cisi calculation only when u(k)>10^-6
// A log-linear interpolation for values below
if(!extrap)
{
double arg1=krs;
double arg2=(1.0+con)*krs;
double arg3=con*krs;
double ci1,ci2;
double si1,si2;
ci1=gsl_sf_Ci(arg1);
ci2=gsl_sf_Ci(arg2);
si1=gsl_sf_Si(arg1);
si2=gsl_sf_Si(arg2);
double res1=sin(arg1)*(si2-si1);
res1-=sin(arg3)/arg2;
res1+=cos(arg1)*(ci2-ci1);
if(res1/fac<=0.0){
std::cout<<"Some serious trouble here "<<res1<<" "<<fac<<" "<<krs<<" "<<con<<std::endl;
exit(0);
}
ukrsc[i][j]=log10(res1/fac);
//std::cout<<std::scientific;
//std::cout<<krs<<" "<<con<<" "<<res1/fac<<" "<<std::endl;
if (ukrsc[i][j] < -6.0) {
extrap=true;
x_extrap=uk_krs[j];
y_extrap=ukrsc[i][j];
}
}else{
ukrsc[i][j]=y_extrap-1.99*(uk_krs[j]-x_extrap);
//std::cout<<std::scientific;
//std::cout<<krs<<" "<<con<<" "<<pow(10.,ukrsc[i][j])<<" "<<std::endl;
}
}
//std::cout<<std::endl;
}
//exit(0);
uk_c_acc=gsl_interp_accel_alloc();
uk_krs_acc=gsl_interp_accel_alloc();
bool_inituk=true;
}
