/// 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);
}
scalar sasfit_ff_pearl_necklace(scalar q, sasfit_param * param)
{
scalar qR,ql,qA,Psi,L,Mr,mr,ms,beta,Sr,Sp,Sm,sinqA_qA,sinql2_ql2,A;
SASFIT_ASSERT_PTR(param); // assert pointer param is valid
SASFIT_CHECK_COND1((q < 0.0), param, "q(%lg) < 0",q);
SASFIT_CHECK_COND1((R < 0.0), param, "R(%lg) < 0",R); // modify condition to your needs
SASFIT_CHECK_COND1((L < 0.0), param, "L(%lg) < 0",L); // modify condition to your needs
SASFIT_CHECK_COND1((NU < 0.0), param, "nu(%lg) < 0",NU); // modify condition to your needs
SASFIT_CHECK_COND1((B < 0.0), param, "b(%lg) < 0",B); // modify condition to your needs
SASFIT_CHECK_COND1((NP < 0.0), param, "Np(%lg) < 0",NP); // modify condition to your needs
// insert your code here
A=l+2.*R;
qR = q*R;
ql = q*l;
qA = q*A;
mr=l/B; // number of monomers in rod-like segment
ms=4.0*M_PI*gsl_pow_3(R)/(3.*NU);
Mr=NP-1.0;
if (qR==0.0) {
Psi = 1;
} else {
Psi=3.*(sin(qR)-qR*cos(qR))/gsl_pow_3(qR);
}
if (ql == 0.0) {
L=1.0;
sinql2_ql2= 1.0;
} else {
L=gsl_sf_Si(ql)/(ql);
sinql2_ql2 = sin(ql/2.0)*2/ql;
}
if (qA == 0.0) {
sinqA_qA=1.;
} else {
sinqA_qA=sin(qA)/(qA);
}
if (q==0) {
beta = 1.0;
} else if (A==2*R) {
if (R==0) {
beta = 1;
} else {
beta = sin(q*R)/(q*R);
}
} else {
beta=(gsl_sf_Si(q*(A-R))-gsl_sf_Si(qR))/(ql);
}
Sp=2*pow(ms,2)*pow(Psi,2)*((NP/(1-sinqA_qA))-(NP/2)-((1-pow(fabs(sinqA_qA),NP))/pow(1-sinqA_qA,2))*sinqA_qA);
Sr=pow(mr,2)*(Mr*(2*L-pow(sinql2_ql2,2))+(2*Mr*pow(beta,2)/(1-sinqA_qA))- 2*pow(beta,2)*(1-pow(fabs(sinqA_qA),Mr))/pow(1-sinqA_qA,2));
Sm=mr*beta*ms*Psi*4*(((NP-1)/(1-sinqA_qA))-((1-pow(fabs(sinqA_qA),NP-1))/pow(1-sinqA_qA,2))*sinqA_qA);
return (Sp+Sr+Sm)/pow(Mr*mr+NP*ms,2);
}
scalar sasfit_ff_very_long_cyl_w_gauss_chains(scalar q, sasfit_param * param)
{
scalar Pp, Pcs, Fc, w, Scc, Ssc, J1x_x;
scalar R, Rg, d, Nagg, H, r_core, r_chains;
SASFIT_ASSERT_PTR(param);
sasfit_get_param(param, 7, &R, &Rg, &d, &Nagg, &H, &r_core, &r_chains);
SASFIT_CHECK_COND1((H <= 0.0), param, "H(%lg) < 0", H);
if (q == 0.0) return Pp = 1.0;
Pp =(2.0*gsl_sf_Si(q*H)/(q*H)-pow(sin(q*H*0.5)/(q*H*0.5),2.0));
w = sasfit_rwbrush_w(q, Rg);
Fc = sasfit_gauss_fc(q, Rg);
Scc = w*w*pow(gsl_sf_bessel_J0(q*(R+d*Rg)),2.);
if (q*R == 0)
{
J1x_x = 0.5;
} else
{
J1x_x = gsl_sf_bessel_J1(q*R)/(q*R);
}
Ssc = w*2.*J1x_x*gsl_sf_bessel_J0(q*(R+d*Rg));
Pcs = pow(r_core*2.*J1x_x,2.)
+ Nagg*(Nagg-1.)*pow(r_chains,2.0)*Scc*((Nagg < 1) ? 0 : 1)
+ 2.*Nagg*r_chains*r_core*Ssc;
// sasfit_out("Cyl_Fc:%lf \n",pow(r_chains,2.0)*Nagg*Fc);
return Pp*Pcs
+ pow(r_chains,2.0)*Nagg*Fc;
}
/*
* form factor of a spherical Cylinder with radius R, height L and scattering
* length density eta
*/
scalar sasfit_ff_long_cyl(scalar q, sasfit_param * param)
{
scalar mu, sigma, pi_mu, G1, G2, I_sp, Sum, V, omega;
scalar R, L, eta;
SASFIT_ASSERT_PTR(param);
sasfit_get_param(param, 4, &R, &L, EMPTY, &eta);
SASFIT_CHECK_COND1((q < 0.0), param, "q(%lg) < 0",q);
SASFIT_CHECK_COND1((R < 0.0), param, "R(%lg) < 0",R);
SASFIT_CHECK_COND1((L < 0.0), param, "L(%lg) < 0",L);
if (R == 0.0) return 0.0;
if (L == 0.0) return 0.0;
mu = L*q;
sigma = 2.0*R*q;
V = M_PI*R*R*L;
if (R==0 || L==0) return 0;
if (q==0) return V*V*eta*eta;
pi_mu = gsl_sf_Si(mu)+cos(mu)/mu+sin(mu)/mu/mu;
G1 = 2.0/(0.5*sigma) * gsl_sf_bessel_J1(0.5*sigma);
G2 = 8.0/sigma/sigma * gsl_sf_bessel_Jn(2,sigma);
// I_sp = 3.0 * (sin(sigma*0.5)-0.5*sigma*cos(0.5*sigma)) / pow(sigma/2.0,3);
// I_sp = I_sp*I_sp;
omega = 8/gsl_pow_2(sigma)*(3*gsl_sf_bessel_Jn(2,sigma)+gsl_sf_bessel_J0(sigma)-1);
// Sum = 2.0/mu * (pi_mu*G1*G1 - 1.0/mu*(2.0*G2-I_sp) - sin(mu)/mu/mu);
Sum = 2.0/mu * (pi_mu*G1*G1 - omega/mu - sin(mu)/mu/mu);
return eta*eta *V*V* Sum;
}
/* Int_0^mu dy cos(a*y) log(abs(b*y)) =
(1/a) * (log(|b*mu|)*sin(a*mu) - Si(a*mu) ) */
double FC_FUNC(intcoslog, INTCOSLOG)(double *mu, double *a, double *b)
{
if(fabs(*a)>0.0){
return (1.0/(*a)) * (log((*b)*(*mu))*sin((*a)*(*mu)) - gsl_sf_Si((*a)*(*mu)) );
}else{
return (*mu)*(log((*mu)*(*b)) - 1.0);
}
}
scalar sasfit_ff_Rod_Exp_Profile(scalar q, sasfit_param * param)
{
scalar Psh, Fsh, Fsh1, Fsh2, Fc, Pc, Vc, V, S, Nagg, b_c, b_sh, Pcs, Pp, Plocal;
scalar eta_out_in;
scalar Rc, n_agg, Vsh, rho_c, rho_sh, rho_solv, xsolv_core, t, alpha, H;
sasfit_param subParam;
SASFIT_ASSERT_PTR(param);
sasfit_get_param(param, 10, EMPTY, EMPTY, &Vsh, &rho_c, &rho_sh, &rho_solv, EMPTY, &t, &alpha, &H);
switch( param->kernelSelector )
{
case ROD_EXP:
Rc = param->p[0];
n_agg = param->p[1];
xsolv_core = param->p[6];
eta_out_in = 0.0;
if (Rc == 0.0) return 0.0;
V = M_PI *Rc*Rc * H;
S = 2. * M_PI *Rc*H;
Nagg = n_agg*S;
if (Nagg == 0.0) return 0;
Vc = V * (1.-xsolv_core) / Nagg;
break;
case ROD_EXP_RC:
Rc = param->p[0];
Vc = param->p[1];
eta_out_in = param->p[6];
xsolv_core = 0.0;
if (Rc == 0.0) return 0.0;
SASFIT_CHECK_COND1((Vc <= 0.0), param, "Vcore(%lg) <= 0", Vc);
V = M_PI *Rc*Rc * H;
S = 2. * M_PI *Rc*H;
Nagg = V * (1.-xsolv_core)/ Vc;
break;
case ROD_EXP_NAGG:
n_agg = param->p[0];
Vc = param->p[1];
eta_out_in = param->p[6];
xsolv_core = 0.0;
SASFIT_CHECK_COND1((n_agg < 0.0), param, "n_agg(%lg) < 0", n_agg);
if ( n_agg==0.0 ) return 0.0;
// wrong equation Rc = sqrt(n_agg*Vc/(1.-xsolv_core)/M_PI);
// Solve[{Vc/(1 - xsolv)*nagg*2*Pi*Rc*H == Pi*Rc^2*H}, {Rc}]
// here the total volume of the rod is given by V == Vc/(1 - xsolv)*nagg*2*Pi*Rc*H == Pi*Rc^2*H
// {{Rc -> 0}, {Rc -> -((2 nagg Vc)/(-1 + xsolv))}}
Rc = 2.0*n_agg*Vc/(1.0-xsolv_core);
S = 2. * M_PI *Rc*H;
Nagg = n_agg*H;
if (Nagg == 0.0) return 0;
break;
default:
SASFIT_ERR_UNKNOWN_KERNEL(param, "kernel");
break;
}
Fc = sasfit_rod_fc(q, Rc);
Pc = Fc * Fc;
b_c = Vc * (rho_c - rho_solv);
b_sh = Vsh * (rho_sh - rho_solv);
if (b_sh==0.0)
{
Fsh = Psh = 0.0;
} else
{
//Fsh = ROD_Exp_ave(interp,q,Rc,eta_out_in,t,alpha,error);
sasfit_init_param( &subParam );
subParam.p[0] = Rc;
subParam.p[1] = eta_out_in;
subParam.p[2] = t;
subParam.p[3] = alpha;
subParam.p[MAXPAR-1] = q;
Fsh1 = sasfit_integrate(Rc, Rc+t, sasfit_Rod_Exp_ave_core, &subParam);
subParam.p[MAXPAR-1] = 0.0;
Fsh2 = sasfit_integrate(Rc, Rc+t, sasfit_Rod_Exp_ave_core, &subParam);
SASFIT_CHECK_SUB_ERR(param, subParam);
Fsh = Fsh1/Fsh2;
Psh = Fsh*Fsh;
}
Pcs = Nagg*Nagg * b_c*b_c * Pc +
Nagg*(Nagg-1.0) * b_sh * b_sh * Psh * ((Nagg < 1) ? 0 : 1) +
// Nagg*Nagg * b_sh * b_sh * Psh +
2.0*Nagg*Nagg * b_c * b_sh * Fc * Fsh;
Pp =(2.0*gsl_sf_Si(q*H)/(q*H)-pow(sin(q*H*0.5)/(q*H*0.5),2.0));
Plocal =(2.0*gsl_sf_Si(q*t)/(q*t)-pow(sin(q*t*0.5)/(q*t*0.5),2.0));
return Pp*Pcs + Nagg*b_sh*b_sh*Plocal;
}
double FC_FUNC_(oct_sine_integral, OCT_SINE_INTEGRAL)
(const double *x)
{
return gsl_sf_Si(*x);
}
/// 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;
}
