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vide_public/c_tools/hod/hod_functions.c

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#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "header.h"
/* This file holds several useful functions for the HOD, such as the number of
* central and satellite halos, their second moment.
*
* This also intializes the HOD parameters.
*/
/* internal routines.
*/
double fixfunc1(double m);
double fixfunc2(double m);
double func_mlow(double m);
double func_mhi(double m);
double one_halo_from_file(double m);
/*****************
* DIFFERENT HOD PARAMETERIZATIONS: (1) Central galaxies
*
* This integer HOD.pdfc controls the parameterization of the central occupation.
* (I realize 'pdf' is not the right acronym, but it's a holdover from old code.)
*
* For soft central cutoffs, the PDF is the nearest integer distribution, AKA
* Bernoulli distribution.
*
* 0 = No galaxies, just halos. (always returns 1)
* 1 = Hard cutoff at M_min. Unity above M_min. (DEFAULT)
* 2 = Soft cutoff of the form 0.5*(1+erf((log10(m) - log10(HOD.M_min))/HOD.sigma_logM)
* 3 = Soft cutoff of the form N_cen = exp(-HOD.M_min/m)
* 4 = Hard cutoff, but N_cen -> 0 for M>M_min (i.e., blue galaxies)
* MaxCen*exp(-(lgM-lgM_min)**2/2/(sigma_logM)**2)
* NB! -> The value of N_cen(M_min) can be < 1. (It will== MaxCen)
* 5 = Hard Cutoff, Step function, but N_cen != 1, but some number < 1.
* 6 = Same as 4, but symmetric Gaussian around M_min (This is for mag bins.)
* 7 = A sqaure function. N_cen=1 for M_min <= m <= M_cen_max (for mag bin data)
* 8 = A sqaure function (like case 7) but with Gaussian cutoffs on either edge
* instead of sharp cutoffs.
*
* 9 = Magnitude bin model, but the upper mass cutoff is defined by the lower
* mass cutoff of the next-highest bin. (see function in ml_minimization.c)
*
* M_low is a parameter created to keep the integrals from having to go to M=0 for
* soft central cutoffs. N_cen(mlow) = 1.0E-3;
* If the value of sigma_logM gets above 1 or so, then M_low can be rediculously
* small, so I have placed a lower limit on M_low of 1.0E+7 Msol/h
*/
double N_cen(double m)
{
double x,f=1;
//return(one_halo_from_file(m));
if(HOD.color)
f=central_blue_fraction(m);
switch(HOD.pdfc) {
case -1:
return 0;
case 0:
return 1;
case 1:
if(m<HOD.M_min)return(0);
return(f*1.0);
break;
case 2:
return(f*HOD.MaxCen*0.5*(1+erf((log10(m) - log10(HOD.M_min))/HOD.sigma_logM)));
break;
case 3:
return(f*exp(-HOD.M_min/m));
break;
case 4:
if(m<HOD.M_min)return(0);
x = (log10(m) - log10(HOD.M_min))/HOD.sigma_logM;
return(f*HOD.MaxCen*exp(-x*x/2));
case 5:
if(m<HOD.M_min)return(0);
return(f*HOD.MaxCen);
case 6:
x = (log10(m) - log10(HOD.M_min))/HOD.sigma_logM;
return(f*HOD.MaxCen*exp(-x*x/2));
case 7:
if(m>=HOD.M_min && m<=HOD.M_cen_max)return(f);
return(0);
case 8:
if(m>=HOD.M_min && m<=HOD.M_cen_max)return(f);
if(m<HOD.M_low)return(0);
if(m<HOD.M_min)
x = (log10(m) - log10(HOD.M_min))/HOD.sigma_logM;
else
x = (log10(m) - log10(HOD.M_cen_max))/HOD.sigma_logM;
return(f*exp(-x*x/2));
default:
endrun("Illegal value of HOD.pdfc.");
}
return 0;
}
/*****************
* DIFFERENT HOD PARAMETERIZATIONS: (1) Satellite galaxies
*
* This integer HOD.pdfs controls the parameterization of the satellite occupation.
*
* 0 = halos only, no galaxies (always returns zero)
* 1 = power law: N_sat = pow(m/HOD.M1,HOD.alpha) [cut off at M_low]
* 2 = power law with soft cutoff: N_sat = pow((m-HOD.M_cut)/HOD.M1,alpha)
* 3 = power law with exp cutoff: N_sat = pow(m/HOD.M1,alpha)*exp(-M_cut/(m-M_min))
* 4 = broken power law with exp cutoff (alpha changes at some high mass value)
* 5 = broken power law (m-mcut)/m1 parameterization
* 6 = power with alternate exp cutoff: N_sat = pow(m/M1)*exp(-M_min/m)
* 7 = from Zheng's new paper lognormal cutoff power law
* 8 = power with Conroy exp cutoff: N_sat = pow(m/M1)*exp(-M_cut/m)
*
* The PDF is always assumed to be Poisson for satellite galaxies.
*/
double N_sat(double m)
{
double m1,f=1,n,nc;
if(HOD.color)
f = satellite_blue_fraction(m);
switch(HOD.pdfs) {
case 0:
return 0;
case 1:
if(m<HOD.M_min)return(0);
return(f*pow(m/HOD.M1,HOD.alpha));
break;
case 2:
if(m<HOD.M_low || m<HOD.M_cut)return(0);
return(f*pow((m-HOD.M_cut)/HOD.M1,HOD.alpha));
break;
case 3:
if(m<HOD.M_min)return(0);
return(f*exp(-HOD.M_cut/(m-HOD.M_min))*pow(m/HOD.M1,HOD.alpha));
break;
case 4:
if(m<HOD.M_min)return(0);
if(m<HOD.M_sat_break)
return(f*exp(-HOD.M_cut/(m-HOD.M_min))*pow(m/HOD.M1,HOD.alpha));
else
{
m1 = exp(log(HOD.M_sat_break) - HOD.alpha/HOD.alpha1*log(HOD.M_sat_break/HOD.M1));
return(f*exp(-HOD.M_cut/(m-HOD.M_min))*pow(m/m1,HOD.alpha1));
}
break;
case 5:
if(m<HOD.M_low || m<HOD.M_cut)return(0);
if(m<HOD.M_sat_break)
return(f*pow((m-HOD.M_cut)/HOD.M1,HOD.alpha));
else
{
m1 = HOD.M_sat_break*pow((HOD.M_sat_break-HOD.M_cut)/HOD.M1,-HOD.alpha/HOD.alpha1);
return(f*pow(m/m1,HOD.alpha1));
}
break;
case 6:
return(pow(m/HOD.M1,HOD.alpha)*exp(-HOD.M_min/m));
case 7:
if(m<HOD.M_low || m<HOD.M_cut)return(0);
return(0.5*(1+erf((log10(m) - log10(HOD.M_min))/HOD.sigma_logM))
*pow((m-HOD.M_cut)/HOD.M1,HOD.alpha));
break;
case 8:
n = (pow(m/HOD.M1,HOD.alpha)*exp(-HOD.M_cut/m));
if(m<HOD.M_min)
{
nc = N_cen(m);
if(n>nc)return(nc);
}
return(n);
case 9:
if(m<HOD.M_sat_break)
{
n = (pow(m/HOD.M1,HOD.alpha)*exp(-HOD.M_cut/m));
if(m<HOD.M_min)
{
nc = N_cen(m);
if(n>nc)return(nc);
}
return n;
}
m1 = (pow(HOD.M_sat_break/HOD.M1,HOD.alpha)*exp(-HOD.M_cut/HOD.M_sat_break));
n = m1*pow(m/HOD.M_sat_break,HOD.alpha1);
return n;
break;
case 10:
if(m<HOD.M_low)return(0);
return(0.5*(1+erf((log10(m) - log10(HOD.M_min))/HOD.sigma_logM))
*pow((m)/HOD.M1,HOD.alpha));
break;
case 11:
if(m<HOD.M_low)return(0);
return(f*exp(-HOD.M_cut/m)*pow(m/HOD.M1,HOD.alpha)*
0.5*(1+erf((log10(m) - log10(HOD.M_min))/HOD.sigma_logM)));
case 12: // Zheng et al. 2007
//if(m<HOD.M_low)return(0);
return(f*pow((m-HOD.M_cut)/HOD.M1,HOD.alpha)*
0.5*(1+erf((log10(m) - log10(HOD.M_min))/HOD.sigma_logM)));
break;
default:
endrun("Illegal value of HOD.pdfs.");
}
return 0;
}
/* If the sample is split up by color, this function
* returns the blue fraction at a given mass for satellite galaxies.
* This function is parameterized as a log-normal.
* See equation (11) in Zehavi et al Apj 2005, 360, 1
*
* if HOD.color == 1, returns blue fraction
* if HOD.color == 2, returns red fraction
*/
double satellite_blue_fraction(double m)
{
double x;
x = log10(m) - log10(HOD.M_low0);
x=(HOD.fblue0_sat*exp(-x*x/(2*HOD.sigma_fblue_sat*HOD.sigma_fblue_sat)));
if(x>1)x=1;
if(HOD.color==2)
return(1-x);
return(x);
}
/* If the sample is split up by color, this function
* returns the blue fraction at a given mass for central galaxies.
* This function is parameterized as a log-normal.
* See equation (11) in Zehavi et al Apj 2005, 360, 1
*
* if HOD.color == 1, returns blue fraction
* if HOD.color == 2, returns red fraction
*/
double central_blue_fraction(double m)
{
double x;
x = log10(m) - log10(HOD.M_low0);
x=(HOD.fblue0_cen*exp(-x*x/(2*HOD.sigma_fblue_cen*HOD.sigma_fblue_cen)));
if(x>1)x=1;
if(HOD.color==2)
return(1-x);
return(x);
}
/* If what is needed is the total number of galaxies in a halo.
*/
double N_avg(double m)
{
return(N_cen(m)+N_sat(m));
}
/* This is the <(N_sat-1)(N_sat)> moment, which is
* for the number of pairs of satellite galaxies.
* For a Poisson distribution, <N(N-1)> = N^2
*/
double moment_ss(double m)
{
double n,x;
n=N_sat(m);
return(n*n);
// sub-poisson model from millennium run
// doesn't seem to effect -20.5 stats much
x = 0.6 + 0.4*exp(-0.1/pow(n,1.5));
return(n*n*x*x);
}
/* This is a function to set the HOD parameters until
* I get some input code or batch file set up.
*
*/
void set_HOD_params()
{
int i,j=1;
double m,error=1.0,tol=1.0E-4,prev,s1,mlo;
/* If the mass function at M_max is undefined, reset M_max
*/
//LOCAL_DENSITY = -0.2;
if(LOCAL_DENSITY!=0)
{
HOD.M_max = 1.0E16;
while(dndM_interp(HOD.M_max)<=0)
{
HOD.M_max*=0.9;
}
fprintf(stderr,"NEW M_max= %e\n",HOD.M_max);
}
if(HOD.pdfc == 2 || HOD.pdfc == 3 || HOD.pdfc == 6 || HOD.pdfc == 8 || HOD.pdfc == 9)
SOFT_CENTRAL_CUTOFF=1;
/* Error trap both the galaxy density and M_min both left unspecified.
*/
if(HOD.M_min<=0 && GALAXY_DENSITY<=0 && HOD.free[0]==0)
endrun("ERROR: Must specify either M_min or GALAXY_DENSITY");
/* If the user has specified M_min and M1, calculate the galaxy density.
*/
if(HOD.M_min>0 && HOD.M1>0)
{
HOD.M_low = -1;
if(SOFT_CENTRAL_CUTOFF)
HOD.M_low0 = HOD.M_low = exp(zbrent(func_mlow,log(HOD.M_min*1.0E-6),log(HOD.M_min*1.1),1.0E-5));
else
HOD.M_low0 = HOD.M_low = HOD.M_min;
GALAXY_DENSITY=qromo(func_galaxy_density,log(HOD.M_low),log(HOD.M_max),midpnt);
if(OUTPUT) {
fprintf(stdout,"M_low= %e\n",HOD.M_low);
fprintf(stdout,"ng= %e\n",GALAXY_DENSITY); }
}
/* If M_min<=0 then use the specified galaxy density to calculate M_min
*/
if(HOD.M_min<=0)
{
if(HOD.pdfc==7 && HOD.pdfc==8)
HOD.M_min=pow(10.0,zbrent(fixfunc1,8.0,log10(HOD.M_cen_max*0.99),1.0E-5));
else
HOD.M_min=pow(10.0,zbrent(fixfunc1,7.0,14.8,1.0E-5));
HOD.M_low = -1;
if(SOFT_CENTRAL_CUTOFF)
HOD.M_low = exp(zbrent(func_mlow,log(HOD.M_min)-5*HOD.sigma_logM*2.3,
log(HOD.M_min),1.0E-5));
else
HOD.M_low = HOD.M_min;
if(HOD.M_low<1.0E7)HOD.M_low=1.0E+7;
if(OUTPUT) {
fprintf(stdout,"M_min %e [ng= %e]\n",HOD.M_min,GALAXY_DENSITY);
fprintf(stdout,"M_low= %e\n",HOD.M_low); }
}
/* If M1<=0 then use the specified galaxy density to calculate M1
*/
if(HOD.M1<=0)
{
HOD.M_low = -1;
if(SOFT_CENTRAL_CUTOFF)
HOD.M_low = exp(zbrent(func_mlow,log(HOD.M_min)-5*HOD.sigma_logM*2.3,
log(HOD.M_min*1.1),1.0E-5));
else
HOD.M_low = HOD.M_min;
if(HOD.M_low<1.0E7)HOD.M_low=1.0E+7;
HOD.M1=pow(10.0,zbrent(fixfunc2,log10(HOD.M_low),15.8,1.0E-5));
if(OUTPUT) {
fprintf(stdout,"M1 %e [ng= %e]\n",HOD.M1,GALAXY_DENSITY);
fprintf(stdout,"M_min = %e M_low= %e\n",HOD.M_min,HOD.M_low); }
}
/* Set the number of halo mass bins we've got.
*/
NUM_POW2MASS_BINS=log(HOD.M_max/HOD.M_low)/LN_2+1;
if(HOD.pdfc==6)
HOD.M_hi = set_high_central_mass();
HOD.M_low0 = set_low_mass();
return;
}
/* If soft central cutoff, then put a lower limit on mass integrals
* that begins at the mass where N_cen=0.001.
*/
double func_mlow(double m)
{
/* Have a check in case the passed mass is equal to M_min, but the value of
* N_cen is < 0.001 (which might be the case for very small sigma_logM)
*/
if(fabs(exp(m)-HOD.M_min)<0.001*HOD.M_min)
if(N_cen(exp(m))<0.001)return(0);
// fprintf(stderr,"MLO %e %e %e %e %e\n",exp(m),N_cen(exp(m)),HOD.M_min,HOD.M_cen_max,HOD.M_low);
return(N_cen(exp(m))-0.001);
}
/* It is straightforward to calculate what M_low
* should be given the other parameters on N_cen.
*/
double set_low_mass()
{
double m;
if(!SOFT_CENTRAL_CUTOFF)return(HOD.M_min);
switch(HOD.pdfc){
case 8:
case 6:
m = log10(HOD.M_min) - sqrt(-2*HOD.sigma_logM*HOD.sigma_logM*log(0.001));
m = pow(10.0,m);
return(m);
case 9:
m = exp(zbrent(func_mlow,log(HOD.M_min)-5*HOD.sigma_logM*2.3,
log(HOD.M_min),1.0E-5));
return(m);
default:
m = exp(zbrent(func_mlow,log(HOD.M_min*1.0E-6),
log(HOD.M_min),1.0E-5));
return(m);
}
return(0);
}
/* If modeling magnitude bin samples, then there will be a high mass
* scale for central galaxies as well as a low mass scale. This finds
* the mass at which N_cen(m)=0.001, where m>M_min.
*/
double set_high_central_mass()
{
double m,n;
if(HOD.pdfc==7)
return(HOD.M_cen_max);
if(!(HOD.pdfc==6 || HOD.pdfc==8 || HOD.pdfc==9))
return(HOD.M_max);
m = HOD.M_min;
n = N_cen(m);
while(n>0.001)
{
m*=2;
n = N_cen(m);
if(m>HOD.M_max)return(HOD.M_max);
}
m = exp(zbrent(func_mhi,log(m/2),log(m),1.0E-5));
return(m);
}
double func_mhi(double m)
{
m=exp(m);
return(N_cen(m)-0.001);
}
/* This is a copy of the above function that can be called from any routine.
* (But this one integrates over dlogm).
*/
double func_halo_density(double m)
{
double n1;
m=exp(m);
n1=dndM_interp(m);
return(n1*m);
}
/* This is a copy of the above function that can be called from any routine.
* (But this one integrates over dlogm
*/
double func_galaxy_density(double m)
{
double n1,n2,m0;
m=exp(m);
n1=dndM_interp(m);
n2=N_avg(m);
return(n1*n2*m);
}
double func_mean_halo_mass(double m)
{
double n1,n2,m0;
m=exp(m);
n1=dndM_interp(m);
n2=N_avg(m);
return(n1*n2*m*m);
}
/* This is the equation for zbrent to solve. What value
* of M_min gives the correct galaxy density?
* For HODs that have sharp central cutoffs, use M_min as the lower
* limit of the integration. For soft cutoffs, first find M_low.
*/
double fixfunc1(double m)
{
double n,mlo;
HOD.M_min=m=pow(10.0,m);
HOD.M_low=0;
if(SOFT_CENTRAL_CUTOFF)
mlo = (zbrent(func_mlow,log(HOD.M_min)-5*HOD.sigma_logM*2.3,log(HOD.M_min),1.0E-5));
else
mlo = log(HOD.M_min);
if(exp(mlo)<1.0E7)mlo=log(1.0E+7);
n=qromo(func_galaxy_density,mlo,log(HOD.M_max),midpnt);
// fprintf(stderr,"MMIN %e %e %e %e %e %e\n",m,exp(mlo),n,GALAXY_DENSITY,N_sat(2*m),N_cen(m));
return(GALAXY_DENSITY-n);
}
/* This function is sent to zbrent to determine what M1 is based
* on the number density. Both M_min and M_low have already been specified.
*/
double fixfunc2(double m)
{
double n;
HOD.M1=m=pow(10.0,m);
n=qromo(func_galaxy_density,log(HOD.M_low),log(HOD.M_max),midpnt);
return(GALAXY_DENSITY-n);
}
/* This function is to be passed to qromo to integrate the number density
* of satellite galaxies.
*/
double func_satfrac(double m)
{
m=exp(m);
return(N_sat(m)*dndM_interp(m)*m);
}
/* This function is to be passed to qromo to integrate the number density
* of satellite galaxies.
*/
double func_satellite_density(double m)
{
m=exp(m);
return(N_sat(m)*dndM_interp(m)*m);
}
/* This function is to be passed to qromo to integrate the number density
* of satellite galaxies.
*/
double func_central_density(double m)
{
m=exp(m);
return(N_cen(m)*dndM_interp(m)*m);
}
/* Calculates the average mass of a halo in the HOD.
*/
double number_weighted_halo_mass()
{
double funcxx1();
return(qromo(funcxx1,log(HOD.M_low),log(HOD.M_max),midpnt)/GALAXY_DENSITY);
}
double funcxx1(double m)
{
m=exp(m);
return(m*N_avg(m)*dndM_interp(m)*m);
}
/* Calculates the average mass of a halo in the HOD
* (weighted by central galaxies).
*/
double number_weighted_central_mass()
{
double funcxx2();
return(qromo(funcxx2,log(HOD.M_low),log(HOD.M_max),midpnt)/
qromo(func_central_density,log(HOD.M_low),log(HOD.M_max),midpnt));
}
double funcxx2(double m)
{
m=exp(m);
return(m*N_cen(m)*dndM_interp(m)*m);
}
double one_halo_from_file(double m)
{
static double *x, *y, *z;
static int n, flag = 1;
FILE *fp;
int i;
double a;
if(flag)
{
muh(0);
fp = openfile("ncen.dat");
muh(0);
n = filesize(fp);
x = dvector(1,n);
y = dvector(1,n);
z = dvector(1,n);
for(i=1;i<=n;++i)
fscanf(fp,"%lf %lf",&x[i],&y[i]);
spline(x,y,n,1.0E+30,1.0E+30,z);
flag = 0;
muh(0);
}
if(log10(m)<x[1])return 0;
splint(x,y,z,n,log10(m),&a);
//printf("%e %e\n",m,pow(10.0,a));
if(a>0) return 1;
return pow(10.0,a);
}
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