Add mass_profile tools

* These tools are mainly use to calculate the total gravitational mass
  profile, as well as the intermediate products (e.g., surface
  brightness profile fitting, gas density profile, NFW fitting, etc.)
* There are additional tools for calculating the luminosity and flux.
* These tools mainly developed by Junhua GU, and contributed by
  Weitian (Aaron) LI, and Zhenghao ZHU.

1 files changed, 585 insertions, 0 deletions

diff --git a/mass_profile/fit_dbeta_sbp.cpp b/mass_profile/fit_dbeta_sbp.cpp
new file mode 100644
index 0000000..b74dc0c
--- /dev/null
+++ b/mass_profile/fit_dbeta_sbp.cpp
@@ -0,0 +1,585 @@
+/*
+  Perform a double-beta density model fitting to the surface brightness data
+  Author: Junhua Gu
+  Last modified: 2011.01.01
+  This code is distributed with no warrant
+*/
+
+
+#include <iostream>
+#include <fstream>
+#include <list>
+using namespace std;
+#include "vchisq.hpp"
+#include "dbeta.hpp"
+#include "beta_cfg.hpp"
+#include <data_sets/default_data_set.hpp>
+#include <methods/powell/powell_method.hpp>
+#include <core/freeze_param.hpp>
+#include <error_estimator/error_estimator.hpp>
+#include "spline.h"
+using namespace opt_utilities;
+//double s=5.63136645E20;
+const double kpc=3.086E21;//kpc in cm
+const double Mpc=kpc*1000;
+double dbeta_func(double r,
+		  double n01,double rc1,double beta1,
+		  double n02,double rc2,double beta2)
+{
+  
+  return abs(n01)*pow(1+r*r/rc1/rc1,-3./2.*abs(beta1))+abs(n02)*pow(1+r*r/rc2/rc2,-3./2.*abs(beta2));
+}
+
+
+  //calculate critical density from z, under following cosmological constants
+static double calc_critical_density(double z,
+				    const double H0=2.3E-18,
+				      const double Omega_m=.27)
+{
+  const double G=6.673E-8;//cm^3 g^-1 s^2
+  const double E=std::sqrt(Omega_m*(1+z)*(1+z)*(1+z)+1-Omega_m);
+  const double H=H0*E;    
+  return 3*H*H/8/pi/G;
+}
+
+
+//A class enclosing the spline interpolation method of cooling function
+//check spline.h for more detailed information
+//this class is a thin wrapper for the spline class defined in spline.h
+class spline_func_obj
+  :public func_obj<double,double>
+{
+  //has an spline object
+  spline<double> spl;
+public:
+  //This function is used to calculate the intepolated value
+  double do_eval(const double& x)
+  {
+    return spl.get_value(x);
+  }
+  
+  //we need this function, when this object is performing a clone of itself
+  spline_func_obj* do_clone()const
+  {
+    return new spline_func_obj(*this);
+  }
+
+public:
+  //add points to the spline object, after which the spline will be initialized
+  void add_point(double x,double y)
+  {
+    spl.push_point(x,y);
+  }
+  
+  //before getting the intepolated value, the spline should be initialzied by calling this function
+  void gen_spline()
+  {
+    spl.gen_spline(0,0);
+  }
+};
+
+int main(int argc,char* argv[])
+{
+  if(argc!=2)
+    {
+      cerr<<argv[0]<<" <configure file>"<<endl;
+      return -1;
+    }
+  //initialize the parameters list
+  ifstream cfg_file(argv[1]);
+  assert(cfg_file.is_open());
+  cfg_map cfg=parse_cfg_file(cfg_file);
+  
+  //check the existence of following parameters
+  
+  const double z=cfg.z;
+
+  //initialize the radius list, sbp list and sbp error list
+  std::vector<double> radii;
+  std::vector<double> sbps;
+  std::vector<double> sbpe;
+  std::vector<double> radii_all;
+  std::vector<double> sbps_all;
+  std::vector<double> sbpe_all;
+  //read sbp and sbp error data
+  for(ifstream ifs(cfg.sbp_file.c_str());;)
+    {
+      assert(ifs.is_open());
+      double x,xe;
+      ifs>>x>>xe;
+      if(!ifs.good())
+	{
+	  break;
+	}
+      if(x/xe<2)
+	{
+	  break;
+	}
+      cerr<<x<<"\t"<<xe<<endl;
+      sbps.push_back(x);
+      sbpe.push_back(xe);
+      sbps_all.push_back(x);
+      sbpe_all.push_back(xe);
+    }
+
+  //read radius data
+  for(ifstream ifs(cfg.radius_file.c_str());;)
+    {
+      assert(ifs.is_open());
+      double x;
+      ifs>>x;
+      if(!ifs.good())
+	{
+	  break;
+	}
+      cerr<<x<<endl;
+      radii.push_back(x);
+      radii_all.push_back(x);
+    }
+  //initialize the cm/pixel value
+  double cm_per_pixel=cfg.cm_per_pixel;
+  double rmin=5*kpc/cm_per_pixel;
+  if(cfg.rmin_pixel>0)
+    {
+      rmin=cfg.rmin_pixel;
+    }
+  else
+    {
+      rmin=cfg.rmin_kpc*kpc/cm_per_pixel;
+    }
+  
+  cerr<<"rmin="<<rmin<<endl;
+  std::list<double> radii_tmp,sbps_tmp,sbpe_tmp;
+  radii_tmp.resize(radii.size());
+  sbps_tmp.resize(sbps.size());
+  sbpe_tmp.resize(sbpe.size());
+  copy(radii.begin(),radii.end(),radii_tmp.begin());
+  copy(sbps.begin(),sbps.end(),sbps_tmp.begin());
+  copy(sbpe.begin(),sbpe.end(),sbpe_tmp.begin());
+  for(list<double>::iterator i=radii_tmp.begin();i!=radii_tmp.end();)
+    {
+      if(*i<rmin)
+	{
+	  radii_tmp.pop_front();
+	  sbps_tmp.pop_front();
+	  sbpe_tmp.pop_front();
+	  i=radii_tmp.begin();
+	  continue;
+	}
+      ++i;
+    }
+  radii.resize(radii_tmp.size());
+  sbps.resize(sbps_tmp.size());
+  sbpe.resize(sbpe_tmp.size());
+  copy(radii_tmp.begin(),radii_tmp.end(),radii.begin());
+  copy(sbps_tmp.begin(),sbps_tmp.end(),sbps.begin());
+  copy(sbpe_tmp.begin(),sbpe_tmp.end(),sbpe.begin());
+
+  //read cooling function data
+  spline_func_obj cf;
+  for(ifstream ifs(cfg.cfunc_file.c_str());;)
+    {
+      assert(ifs.is_open());
+      double x,y,y1,y2;
+      ifs>>x>>y;
+      if(!ifs.good())
+	{
+	  break;
+	}
+      cerr<<x<<"\t"<<y<<endl;
+      if(x>radii.back())
+	{
+	  break;
+	}
+      //cf.add_point(x,y*2.1249719395939022e-68);//change with source
+      cf.add_point(x,y);//change with source
+    }
+  cf.gen_spline();
+  
+  //read temperature profile data
+  spline_func_obj Tprof;
+  int tcnt=0;
+  for(ifstream ifs1(cfg.T_file.c_str());;++tcnt)
+    {
+      assert(ifs1.is_open());
+      double x,y;
+      ifs1>>x>>y;
+      if(!ifs1.good())
+      {
+	break;
+      }
+      cerr<<x<<"\t"<<y<<endl;
+#if 0
+      if(tcnt==0)
+	{
+	  Tprof.add_point(0,y);
+	}
+#endif
+      Tprof.add_point(x,y);
+    }
+
+
+  Tprof.gen_spline();
+  
+  default_data_set<std::vector<double>,std::vector<double> > ds;
+  ds.add_data(data<std::vector<double>,std::vector<double> >(radii,sbps,sbpe,sbpe,radii,radii));
+  
+  //initial fitter
+  fitter<vector<double>,vector<double>,vector<double>,double> f;
+  f.load_data(ds);
+  //initial the object, which is used to calculate projection effect
+  projector<double> a;
+  bool tie_beta=false;
+  if(cfg.param_map.find("beta")!=cfg.param_map.end()
+     &&cfg.param_map.find("beta1")==cfg.param_map.end()
+     &&cfg.param_map.find("beta2")==cfg.param_map.end())
+    {
+      dbeta2<double> dbetao;
+      a.attach_model(dbetao);
+      tie_beta=true;
+    }
+  else if((cfg.param_map.find("beta1")!=cfg.param_map.end()
+	   ||cfg.param_map.find("beta2")!=cfg.param_map.end())
+	  &&cfg.param_map.find("beta")==cfg.param_map.end())
+    {
+      dbeta<double> dbetao;
+      a.attach_model(dbetao);
+      tie_beta=false;
+    }
+  else
+    {
+      cerr<<"Error, cannot decide whether to tie beta together or let them vary freely!"<<endl;
+      assert(0);
+    }
+
+  //attach the cooling function
+  a.attach_cfunc(cf);
+  a.set_cm_per_pixel(cm_per_pixel);
+  
+  f.set_model(a);
+  //chi^2 statistic
+  vchisq<double> c;
+  c.verbose(true);
+  c.set_limit();
+  f.set_statistic(c);
+  //optimization method
+  f.set_opt_method(powell_method<double,std::vector<double> >());
+  //initialize the initial values
+  double n01=0;
+  double rc1=0;
+  double n02=0;
+  double rc2=0;
+  double beta=0;
+  double bkg=0;
+  if(tie_beta)
+    {
+      f.set_param_value("beta",.7);
+      f.set_param_lower_limit("beta",.3);
+      f.set_param_upper_limit("beta",1.4);
+    }
+  else
+    {
+      f.set_param_value("beta1",.7);
+      f.set_param_lower_limit("beta1",.3);
+      f.set_param_upper_limit("beta1",1.4);
+      f.set_param_value("beta2",.7);
+      f.set_param_lower_limit("beta2",.3);
+      f.set_param_upper_limit("beta2",1.4);
+    }
+  for(std::map<std::string,std::vector<double> >::iterator i=cfg.param_map.begin();
+      i!=cfg.param_map.end();++i)
+    {
+      std::string pname=i->first;
+      f.set_param_value(pname,i->second.at(0));
+      if(i->second.size()==3)
+	{
+	  double a1=i->second[1];
+	  double a2=i->second[2];
+	  double u=std::max(a1,a2);
+	  double l=std::min(a1,a2);
+	  f.set_param_upper_limit(pname,u);
+	  f.set_param_lower_limit(pname,l);
+	}
+      else
+	{
+	  if(pname=="beta"||pname=="beta1"||pname=="beta2")
+	    {
+	      f.set_param_lower_limit(pname,.3);
+	      f.set_param_upper_limit(pname,1.4);
+	    }
+	}
+    }
+
+
+  
+  //perform the fitting, first freeze beta1, beta2, rc1, and rc2
+  if(tie_beta)
+    {
+      f.set_param_modifier(freeze_param<std::vector<double>,std::vector<double>,std::vector<double>,std::string>("beta")+
+			   freeze_param<std::vector<double>,std::vector<double>,std::vector<double>,std::string>("rc1")+
+			   freeze_param<std::vector<double>,std::vector<double>,std::vector<double>,std::string>("rc2")
+			   );
+    }
+  else
+    {
+      f.set_param_modifier(freeze_param<std::vector<double>,std::vector<double>,std::vector<double>,std::string>("beta1")+
+			   freeze_param<std::vector<double>,std::vector<double>,std::vector<double>,std::string>("beta2")+
+			   freeze_param<std::vector<double>,std::vector<double>,std::vector<double>,std::string>("rc1")+
+			   freeze_param<std::vector<double>,std::vector<double>,std::vector<double>,std::string>("rc2")
+			   );
+    }
+  
+  f.fit();
+  
+  f.clear_param_modifier();
+
+  //then perform the fitting, freeze beta1 and beta2
+  //f.set_param_modifier(freeze_param<std::vector<double>,std::vector<double>,std::vector<double>,std::string>("beta"));
+  //f.set_param_modifier(freeze_param<std::vector<double>,std::vector<double>,std::vector<double>,std::string>("bkg"));
+  f.fit();
+  //f.clear_param_modifier();
+
+  //finally thaw all parameters
+  f.fit();
+  double beta1=0;
+  double beta2=0;
+  
+  n01=f.get_param_value("n01");
+  rc1=f.get_param_value("rc1");
+  n02=f.get_param_value("n02");
+  rc2=f.get_param_value("rc2");
+  if(tie_beta)
+    {
+      beta=f.get_param_value("beta");
+      beta1=beta;
+      beta2=beta;
+    }
+  else
+    {
+      beta1=f.get_param_value("beta1");
+      beta2=f.get_param_value("beta2");
+    }
+  //output the params
+  ofstream param_output("dbeta_param.txt");
+  //output the datasets and fitting results
+  for(int i=0;i<f.get_num_params();++i)
+    {
+      if(f.get_param_info(i).get_name()=="rc1")
+	{
+	  cerr<<"rc1_kpc"<<"\t"<<abs(f.get_param_info(i).get_value())*cm_per_pixel/kpc<<endl;
+	  param_output<<"rc1_kpc"<<"\t"<<abs(f.get_param_info(i).get_value())*cm_per_pixel/kpc<<endl;
+	}
+      if(f.get_param_info(i).get_name()=="rc2")
+	{
+	  cerr<<"rc2_kpc"<<"\t"<<abs(f.get_param_info(i).get_value())*cm_per_pixel/kpc<<endl;
+	  param_output<<"rc2_kpc"<<"\t"<<abs(f.get_param_info(i).get_value())*cm_per_pixel/kpc<<endl;
+	}
+      cerr<<f.get_param_info(i).get_name()<<"\t"<<abs(f.get_param_info(i).get_value())<<endl;
+      param_output<<f.get_param_info(i).get_name()<<"\t"<<abs(f.get_param_info(i).get_value())<<endl;
+    }
+  cerr<<"chi square="<<f.get_statistic_value()/(radii.size()-f.get_model().get_num_free_params())<<endl;
+  param_output<<"chi square="<<f.get_statistic_value()/(radii.size()-f.get_model().get_num_free_params())<<endl;
+  
+  //c.verbose(false);
+  //f.set_statistic(c);
+  //f.fit();
+  std::vector<double> p=f.get_all_params();
+  f.clear_param_modifier();
+  std::vector<double> mv=f.eval_model(radii,p);
+  
+  
+  ofstream ofs_sbp("sbp_fit.qdp");
+  ofs_sbp<<"read serr 2"<<endl;
+  ofs_sbp<<"skip single"<<endl;
+  
+  ofs_sbp<<"line on 2"<<endl;
+  ofs_sbp<<"line on 3"<<endl;
+  ofs_sbp<<"line on 4"<<endl;
+  ofs_sbp<<"line on 5"<<endl;
+  ofs_sbp<<"line on 7"<<endl;
+  ofs_sbp<<"ls 2 on 7"<<endl;
+  ofs_sbp<<"ls 2 on 3"<<endl;
+  ofs_sbp<<"ls 2 on 4"<<endl;
+  ofs_sbp<<"ls 2 on 5"<<endl;
+  
+
+
+  ofs_sbp<<"!LAB  POS Y  4.00"<<endl;
+  ofs_sbp<<"!LAB  ROT"<<endl;
+  ofs_sbp<<"win 1"<<endl;
+  ofs_sbp<<"yplot 1 2 3 4 5"<<endl;
+  ofs_sbp<<"loc 0 0 1 1"<<endl;
+  ofs_sbp<<"vie .1 .4 .9 .9"<<endl;
+  ofs_sbp<<"la y cnt/s/pixel/cm^2"<<endl;
+  ofs_sbp<<"log x"<<endl;
+  ofs_sbp<<"log y"<<endl;
+  ofs_sbp<<"r x "<<(radii[1]+radii[0])/2*cm_per_pixel/kpc<<" "<<(radii[sbps.size()-2]+radii[sbps.size()-1])/2*cm_per_pixel/kpc<<endl;
+  ofs_sbp<<"win 2"<<endl;
+  ofs_sbp<<"yplot 6 7"<<endl;
+  ofs_sbp<<"loc 0 0 1 1"<<endl;
+  ofs_sbp<<"vie .1 .1 .9 .4"<<endl;
+  ofs_sbp<<"la x radius (kpc)"<<endl;
+  ofs_sbp<<"la y chi"<<endl;
+  ofs_sbp<<"log x"<<endl;
+  ofs_sbp<<"log y off"<<endl;
+  ofs_sbp<<"r x "<<(radii[1]+radii[0])/2*cm_per_pixel/kpc<<" "<<(radii[sbps.size()-2]+radii[sbps.size()-1])/2*cm_per_pixel/kpc<<endl;
+  for(int i=1;i<sbps.size();++i)
+    {
+      double x=(radii[i]+radii[i-1])/2;
+      double y=sbps[i-1];
+      double ye=sbpe[i-1];
+      double ym=mv[i-1];
+      ofs_sbp<<x*cm_per_pixel/kpc<<"\t"<<y<<"\t"<<ye<<endl;
+    }
+  ofs_sbp<<"no no no"<<endl;
+  for(int i=1;i<sbps.size();++i)
+    {
+      double x=(radii[i]+radii[i-1])/2;
+      double y=sbps[i-1];
+      double ye=sbpe[i-1];
+      double ym=mv[i-1];
+      ofs_sbp<<x*cm_per_pixel/kpc<<"\t"<<ym<<"\t"<<0<<endl;
+    }
+  //bkg
+  ofs_sbp<<"no no no"<<endl;
+  double bkg_level=abs(f.get_param_value("bkg"));
+  for(int i=0;i<sbps.size();++i)
+    {
+      double x=(radii[i]+radii[i-1])/2;
+      ofs_sbp<<x*cm_per_pixel/kpc<<"\t"<<bkg_level<<"\t0"<<endl;
+    }
+  //rc1
+  ofs_sbp<<"no no no"<<endl;
+  double rc1_kpc=abs(f.get_param_value("rc1")*cm_per_pixel/kpc);
+  double max_sbp=*max_element(sbps.begin(),sbps.end());
+  double min_sbp=*min_element(sbps.begin(),sbps.end());
+  for(double x=min_sbp;x<=max_sbp;x+=(max_sbp-min_sbp)/100)
+    {
+      ofs_sbp<<rc1_kpc<<"\t"<<x<<"\t"<<"0"<<endl;
+    }
+  //rc2
+  ofs_sbp<<"no no no"<<endl;
+  double rc2_kpc=abs(f.get_param_value("rc2")*cm_per_pixel/kpc);
+  for(double x=min_sbp;x<=max_sbp;x+=(max_sbp-min_sbp)/100)
+    {
+      ofs_sbp<<rc2_kpc<<"\t"<<x<<"\t"<<"0"<<endl;
+    }
+  //resid
+  ofs_sbp<<"no no no"<<endl;
+  for(int i=1;i<sbps.size();++i)
+    {
+      double x=(radii[i]+radii[i-1])/2;
+      double y=sbps[i-1];
+      double ye=sbpe[i-1];
+      double ym=mv[i-1];
+      ofs_sbp<<x*cm_per_pixel/kpc<<"\t"<<(ym-sbps[i-1])/sbpe[i-1]<<"\t"<<1<<endl;
+    }
+  //zero level in resid map
+  ofs_sbp<<"no no no"<<endl;
+  for(int i=1;i<sbps.size();++i)
+    {
+      double x=(radii[i]+radii[i-1])/2;
+      double y=sbps[i-1];
+      double ye=sbpe[i-1];
+      double ym=mv[i-1];
+      ofs_sbp<<x*cm_per_pixel/kpc<<"\t"<<0<<"\t"<<0<<endl;
+    }
+
+
+  mv=f.eval_model_raw(radii,p);
+  ofstream ofs_rho("rho_fit.qdp");
+  ofstream ofs_rho_data("rho_fit.dat");
+  ofstream ofs_entropy("entropy.qdp");
+  ofs_rho<<"la x radius (kpc)"<<endl;
+  ofs_rho<<"la y density (cm\\u-3\\d)"<<endl;
+  /*
+  for(int i=1;i<sbps.size();++i)
+    {
+      double x=(radii[i]+radii[i-1])/2;
+      double ym=mv[i-1];
+      ofs_rho<<x*cm_per_pixel/kpc<<"\t"<<ym<<endl;
+    }
+  */
+  
+  double lower,upper;
+  double dr=1;
+  //calculate the mass profile
+  const double G=6.673E-8;//cm^3 g^-1 s^-2
+  static const double mu=1.4074;
+  static const double mp=1.67262158E-24;//g
+  static const double M_sun=1.98892E33;//g
+  static const double k=1.38E-16;
+
+  ofstream ofs_mass("mass_int.qdp");
+  ofstream ofs_mass_dat("mass_int.dat");
+  ofstream ofs_overdensity("overdensity.qdp");
+  ofstream ofs_gas_mass("gas_mass_int.qdp");
+  //ofs_mass<<"la x radius (kpc)"<<endl;
+  //ofs_mass<<"la y mass enclosed (solar mass)"<<endl;
+  //ofs_overdensity<<"la x radius (kpc)"<<endl;
+  //ofs_overdensity<<"la y overdensity"<<endl;
+  double gas_mass=0;
+  for(double r=1;r<200000;r+=dr)
+    {
+      dr=r/100;
+      double r1=r+dr;
+      double r_cm=r*cm_per_pixel;
+      double r1_cm=r1*cm_per_pixel;
+      double dr_cm=dr*cm_per_pixel;
+      double V_cm3=4./3.*pi*(dr_cm*(r1_cm*r1_cm+r_cm*r_cm+r_cm*r1_cm));
+      double ne=dbeta_func(r,n01,rc1,beta1,
+			   n02,rc2,beta2);//cm^3
+
+      double dmgas=V_cm3*ne*mu*mp/M_sun;
+      gas_mass+=dmgas;
+      
+      ofs_gas_mass<<r*cm_per_pixel/kpc<<"\t"<<gas_mass<<endl;
+      double ne_beta1=dbeta_func(r,n01,rc1,beta1,
+				 0,rc2,beta2);
+
+      double ne_beta2=dbeta_func(r,0,rc1,beta1,
+				 n02,rc2,beta2);
+
+      double ne1=dbeta_func(r1,n01,rc1,beta1,
+			    n02,rc2,beta2);//cm^3
+      
+      double T_keV=Tprof(r);
+      double T1_keV=Tprof(r1);
+      
+      double T_K=T_keV*11604505.9;
+      double T1_K=T1_keV*11604505.9;
+
+      double dlnT=log(T1_keV/T_keV);
+      double dlnr=log(r+dr)-log(r);
+      double dlnn=log(ne1/ne);
+
+      double r_kpc=r_cm/kpc;
+      double r_Mpc=r_cm/Mpc;
+      //double M=-r_cm*T_K*k/G/mu/mp*(dlnT/dlnr+dlnn/dlnr);
+      //ref:http://adsabs.harvard.edu/abs/2012MNRAS.422.3503W
+      //Walker et al. 2012
+      double M=-3.68E13*M_sun*T_keV*r_Mpc*(dlnT/dlnr+dlnn/dlnr);
+      double rho=M/(4./3.*pi*r_cm*r_cm*r_cm);
+      
+      double S=T_keV/pow(ne,2./3.);
+      //cout<<r<<"\t"<<M/M_sun<<endl;
+      //cout<<r<<"\t"<<T_keV<<endl;
+
+      ofs_rho<<r*cm_per_pixel/kpc<<"\t"<<ne<<"\t"<<ne_beta1<<"\t"<<ne_beta2<<endl;
+      ofs_rho_data<<r*cm_per_pixel/kpc<<"\t"<<ne<<endl;
+      ofs_entropy<<r*cm_per_pixel/kpc<<"\t"<<S<<endl;
+#if 0
+      if(r*cm_per_pixel/kpc<5)
+	{
+	  continue;
+	}
+#endif
+      ofs_mass<<r*cm_per_pixel/kpc<<"\t"<<M/M_sun<<endl;
+      if(r<radii.back())
+	{
+	  ofs_mass_dat<<r*cm_per_pixel/kpc<<"\t0\t"<<M/M_sun<<"\t"<<M/M_sun*.1<<endl;	  
+	}
+      ofs_overdensity<<r*cm_per_pixel/kpc<<"\t"<<rho/calc_critical_density(z)<<endl;
+      
+    }
+}