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module_cosmodistances.cpp
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/**
* @file module_cosmodistances.cpp
* @Author Thomas Jalabert, EPFL (me@example.com)
* @date July 2015
* @version 0,1
* @brief Library for the computation of cosmological ratios
*
* compute the cosmological ratio of the distances between the lens and the source and the lens and the observer
*
*/
/// include header file
#include <string>
#include <stdio.h>
#include <math.h>
#include <cstring>
#include <stdlib.h>
#include "module_cosmodistances.h"
// Declare static functions that will only be used in this module
// The functions are defined further below
static double module_cosmodistances_cosmo_root(double z,cosmo_param C);
static double module_cosmodistances_sk(double x, double k);
static double module_cosmodistances_chi1(double z,cosmo_param C);
static double module_cosmodistances_chi2(double z1, double z2,cosmo_param C);
static double module_cosmodistances_chiz(double z,cosmo_param C);
static double module_cosmodistances_integral_chiz_ab(double a, double b,cosmo_param C);
// Function defintions
//==========================================================================================================
/** @brief Calculates ratio distance_(lens-source)/distance_(source)
* Calculates ratio distance_(lens-source)/distance_(source)
* @param nsetofimages number of set of images
* @param nImagesSet set of images
* @param z_lens redshift of lens
* @param source sources
* @param cosmoratio variable where result is stored
* @param cosmopar cosmological parameter
*/
void module_cosmodistances_lensSourceToSource( const int nsetofimages, int nImagesSet[], double z_lens, galaxy source[], double cosmoratio[], cosmo_param cosmopar){
//int imageCounter = 0; // Count the total number of images up to now
for(int i=0; i<nsetofimages; i++){
//printf("z_lens %f , imag.redshift %f \n" , z_lens,source[0].redshift);
cosmoratio[i]=module_cosmodistances_lensSourceToObserverSource(z_lens,source[i].redshift, cosmopar); /// lens efficiency (angular distance)
//imageCounter += (nImagesSet[i] - 1); // We add the number of images to skip to get to the next set
}
}
/** @brief Return the angular distance DA(observator(z=0),object(z)) (no unit)
* Multiply observerObject(z) by c/H0 to get the true value in Mpc.
* observerObject(z) * c/H0 = DA(0,z) = 1/(1+z) * Sk( integral( 0,z,c*dz/H(z) ) )
* @param z redshift of object
* @param cosmopar cosmological parameter
*/
double module_cosmodistances_observerObject(double z, cosmo_param cosmopar)
{
double g;
if (cosmopar.omegaX == 0.)
{
g = module_cosmodistances_cosmo_root(z,cosmopar);
// Reformulation of the Mattig relation of OL = OK = 0 (De Sitter)
return(2.*((1. - cosmopar.omegaM - g)*(1. - g)) / cosmopar.omegaM / cosmopar.omegaM / (1. + z) / (1. + z));
}
else
{
if (cosmopar.curvature != 0.)
return(module_cosmodistances_sk(module_cosmodistances_chi1(z,cosmopar)*sqrt(fabs(cosmopar.curvature)), cosmopar.curvature)
/ (1 + z) / sqrt(fabs(cosmopar.curvature)));
else
return(module_cosmodistances_chi1(z,cosmopar) / (1 + z));
}
}
/** @brief Return the angular distance DA(object(z1),object(z2)) divided by c/H0
* Return the angular distance DA(object(z1),object(z2)) divided by c/H0
* objectObject(z1,z2) * c/H0 = DA(z1,z2) = 1/(1+z2) * Sk( integral( z1,z2,c*dz/H(z) ) )
*
* @param z1 redshift of object 1
* @param z2 redshift of object 2
* @param cosmopar cosmological parameter
*/
double module_cosmodistances_objectObject(double z1, double z2, cosmo_param cosmopar)
{
double g1, g2;
if ( z1 >= z2 )
return 0.;
if (cosmopar.omegaX == 0.)
{
g1 = module_cosmodistances_cosmo_root(z1,cosmopar);
g2 = module_cosmodistances_cosmo_root(z2,cosmopar);
// Mattig relation for a De Sitter Universe
return(2.*((1. - cosmopar.omegaM - g1*g2)*(g1 - g2))
/ cosmopar.omegaM / cosmopar.omegaM / (1. + z1) / (1. + z2) / (1. + z2));
}
else
{
if ( cosmopar.curvature != 0. )
return(module_cosmodistances_sk(module_cosmodistances_chi2(z1, z2,cosmopar)*sqrt(fabs(cosmopar.curvature)), cosmopar.curvature)
/ (1 + z2) / sqrt(fabs(cosmopar.curvature)));
else
return(module_cosmodistances_chi2(z1, z2,cosmopar) / (1 + z2));
}
}
/****************************************************************/
/** @brief Return the lens efficacity E=DA(LS) / DA(OS)
* If zl > zs, return 0.
*
* @param zl redshift lens
* @param zs redshift source
* @param cosmopar cosmological parameter
*/
double module_cosmodistances_lensSourceToObserverSource(double zl, double zs, cosmo_param cosmopar)
{
if ( zl >= zs ){
printf("*******************\nWarning, a source is between the lens and the observer\n*******************\n");
printf("Zl: %f , ZS: %f \n", zl, zs);
return (0.);
}
return (module_cosmodistances_objectObject(zl, zs, cosmopar) / module_cosmodistances_observerObject(zs, cosmopar));
}
/** @brief Calculate square root
*
* @param z redshift
* @param C cosmological parameter
*/
// Calculate square root
static double module_cosmodistances_cosmo_root(double z,cosmo_param C)
{
return(sqrt(1. + C.omegaM*z));
}
// Calculate S_k for cosmology
/** @brief Calculate S_k for cosmology
*
* @param x
* @param k curvature
*/
static double module_cosmodistances_sk(double x, double k)
{
if (k > 0)
return(sin(x));
else if (k < 0)
return(sinh(x));
else
return(x);
}
/** @brief Return 1 / H(z) multiplied by H0
* chiz(z) / H0 = 1 / H(z) = 1/H0/(1+z)/sqrt( sum(i, Omega_i*(1+z)^(3*(w_i + 1) ) )
*
* @param z redshift
* @param C cosmological parameter
*/
static double module_cosmodistances_chiz(double z,cosmo_param C)
{
double x;
double yy, yyy, y4;
double r0, e1, e2, frac;
x = 1 + z;
switch (C.model) //TV CPL Model
{
case(1):
x = -x * x * C.curvature + x * x * x * C.omegaM + C.omegaX * pow(x, 3 * (1 + C.wX + C.wa)) * exp(-3 * C.wa * z / x);
break;
case(2): //TV Cardassian (wx is q, wa is n)
yy = pow ( (1.+C.curvature)/C.omegaM ,C.wX);
yyy = (yy - 1.) * pow( x,3.*C.wX*(C.wa-1.) );
y4 = pow(1.+yyy,1./C.wX);
x = -x * x * C.curvature + x * x * x * C.omegaM*y4;
break;
case(3): //TV Interacting DE Model (wa is delta)
yy = C.omegaX*pow( x,3.*(1.+C.wX) );
yyy = ( C.omegaM/(C.wa+3.*C.wX) ) * ( C.wa*pow(x,3.*(1.+C.wX)) + 3.*C.wX*pow(x,(3.-C.wa)) );
x = -x * x * C.curvature + yy +yyy;
break;
case(4): //TV Holographic Ricci Scale with CPL
r0 = C.omegaM/(1.-C.omegaM);
e1 = (3./2.)*( (1.+r0+C.wX+4*C.wa)/(1.+r0+3.*C.wa) );
e2 = (-1./2.)*( (1.+r0-3.*C.wX)/(1.+r0+3.*C.wa) ) ;
frac = ( 1.+r0+3.*C.wa*(x-1.)/x )/(1.+r0) ;
yy = pow(x,e1);
yyy = pow(frac,e2);
x = (yy*yyy)*(yy*yyy);
break;
default:
printf("ERROR: Unknown cosmological model %d\n", C.model);
exit(-1);
}
if ( x <= 0 )
{
printf("ERROR : H^2(z)<=0 produced (z,omegaM,omegaX,wX,wa) = (%.3lf,%.3lf,%.3lf,%.3lf,%.3lf)\n",
z, C.omegaM, C.omegaX, C.wX, C.wa );
exit(-1);
}
return( 1. / sqrt(x) );
}
/** @brief Return the proper distance Dp(0,z) divided by c/H0
* chi1(z) * c/H0 = Dp(0,z) = integral( 0, z, c*dz / H(z) )
*
* @param z redshift
* @param C cosmological parameter
*/
static double module_cosmodistances_chi1(double z,cosmo_param C)
{
double rez;
rez = module_cosmodistances_integral_chiz_ab(0., z,C);
return rez;
}
/** @brief Return the proper distance Dp(z1,z2) divided by c/H0
* chi2(z) * c/H0 = Dp(z1,z2) = integral( z1, z2, c*dz / H(z) )
*
* @param zl redshift lens
* @param zs redshift source
* @param C cosmological parameter
*/
static double module_cosmodistances_chi2(double z1, double z2,cosmo_param C)
{
double rez;
rez = module_cosmodistances_integral_chiz_ab(z1, z2,C);
return rez;
}
/** @brief compute the integral of H0/H(z) by trapezes method
* compute the integral of H0/H(z) by trapezes method
* @param a,b, cosmologicalparameters cosmopar
*
* @param a
* @param b
* @param C cosmological parameter
*/
static double module_cosmodistances_integral_chiz_ab(double a, double b,cosmo_param C)
{
int i,nit;
double res, epsilon=1.e-5; /// accuracy of the integration
nit=(b-a)/epsilon;
res=epsilon*(module_cosmodistances_chiz(a,C)+module_cosmodistances_chiz(b,C))/2.;
for(i=1;i<nit;i++)
{
res=res+epsilon*module_cosmodistances_chiz(a+i*epsilon,C);
}
return res;
}
/** @brief Debug function to print the calculated output of the functions
* Debug function to print the calculated output of the functions
*/
// Debug function to print the calculated output of the functions
int module_cosmodistances_debug(int runmode[], double strongLensingRatios_lensSourceToSource[], double weakLensingRatios_lensSourceToSource[], double weakLensing_observerSource[], int numberCleanLens, double cleanlensRatios_lensSourceToSource[], double cleanlens_observerSource[], std::string DEBUG)
{
if (strcasecmp(DEBUG.c_str(), "True") == 0) // If we are in debug mode
{
if (runmode[0] == 1 or runmode[1] == 1) // If we have strong lensing
{
printf("DEBUG: Strong lensing cosmo ratios D_LS/D_OS for first 2 sets: %lf, %lf\n\n", strongLensingRatios_lensSourceToSource[0], strongLensingRatios_lensSourceToSource[1]);
};
if (runmode[2] == 1) // We have weak lensing
{
printf("DEBUG: Weak lensing D_LS/D_OS for first 2 arclets: %lf, %lf. Weak lensing D_OS for first 2 arclets: %lf, %lf.\n\n", weakLensingRatios_lensSourceToSource[0], weakLensingRatios_lensSourceToSource[1], weakLensing_observerSource[0], weakLensing_observerSource[1]);
};
if (numberCleanLens > 0) // We have cleanlens mode
{
printf("DEBUG: Cleanlens D_LS/D_OS for first 2 sources: %lf, %lf. Cleanlens D_OS for first 2 sources: %lf, %lf.\n\n", cleanlensRatios_lensSourceToSource[0], cleanlensRatios_lensSourceToSource[1], cleanlens_observerSource[0], cleanlens_observerSource[1]);
};
};
return 0;
}

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