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/*
Omega_D_effWEC for weak energy condition - RZA2 arXiv:1303.6193v2 - near clone of test_Omega_D
Copyright (C) 2014-2015 Boud Roukema, Jan Ostrowski
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2, or (at your option)
any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software Foundation,
Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
See also http://www.gnu.org/licenses/gpl.html
*/
#include <stdio.h>
#include <sys/types.h>
#include "config.h"
#include <math.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_statistics.h>
/* for malloc_usable_size if available */
#ifdef __GNUC__
#include <malloc.h>
#endif
#include "lib/inhomog.h"
/* int test_Omega_D(
struct rza_integrand_params_s rza_integrand_params,
*/
int main(void)
{
struct rza_integrand_params_s rza_integrand_params;
struct rza_integrand_params_s rza_integrand_params_sigma8;
struct background_cosm_params_s background_cosm_params;
int want_verbose = 0;
#define N_PLOT_T 3
#define N_PLOT_R 256
#define N_COSM_I 0
#define N_COSM 2
double R_domain_mod[N_PLOT_R];
/* double t_i = 0.004574998; */ /* for z=200, H_0=50, EdS */
/* double t_0 = 13.04; */ /* for z=200, H_0=50, EdS */
double t_i[N_COSM];
double t_0[N_COSM];
double t_background[N_COSM][N_PLOT_T];
double rza_Q_D[N_COSM][N_PLOT_R][N_PLOT_T];
double rza_R_D[N_COSM][N_PLOT_R][N_PLOT_T];
double a_D[N_COSM][N_PLOT_R][N_PLOT_T];
double dot_a_D[N_COSM][N_PLOT_R][N_PLOT_T];
double unphysical[N_COSM][N_PLOT_R][N_PLOT_T];
double H_D[N_COSM][N_PLOT_R][N_PLOT_T];
double Omm_D[N_COSM][N_PLOT_R][N_PLOT_T];
double OmQ_D[N_COSM][N_PLOT_R][N_PLOT_T];
double OmLam_D[N_COSM][N_PLOT_R][N_PLOT_T];
double OmR_D[N_COSM][N_PLOT_R][N_PLOT_T];
double delta_t;
double delta_ln_R;
double a_FLRW_expected;
double a_dot_FLRW_expected;
double H_FLRW_expected;
/* ordinary sigma^2 (e.g. \sigma_8^2) */
double sigmaIsq[N_COSM][N_PLOT_R][N_PLOT_T];
double sigmaIsq_err[N_COSM][N_PLOT_R][N_PLOT_T];
/* double sigmaIsq_grown[N_COSM][N_PLOT_R][N_PLOT_T]; */
double sigmaI_normalised[N_COSM][N_PLOT_R][N_PLOT_T];
double sigma8sq[N_COSM][N_PLOT_T];
double sigma8sq_err[N_COSM][N_PLOT_T];
/* double sigma8sq_grown[N_COSM][N_PLOT_T]; */
/* test mode: compare with RZA2 arXiv:1303.6193v2 */
int want_planar =0; /* cf RZA2 V.A */
int want_spherical = 0; /* cf RZA2 V.B.3 */
/* TODO: choose pseudo-tophat window function from RZA2 */
/* TODO: choose power spectrum from RZA2 */
const gsl_rng_type * T_gsl;
gsl_rng * r_gsl;
static unsigned long int local_gsl_seed=0;
/* long n_calls_invariants = 40000; */
long n_calls_invariants = 100000;
/* long n_calls_invariants = 500000; */
double n_sigma[3] =
/* {2.0, 2.0, 2.0}; */
/* {1.0, 1.0, 1.0}; */
{-1.0, -1.0, -1.0};
/* {0.0, -1.0, 0.0}; */
/* {-1.0, -1.0, -1.0}; */
/* {1.0, 0.0, 1.0}; */
/* {-1.0, 0.3333333333333, -0.037037037}; */
/* values for several different cases */
#define N_RZA2 27
double n_sigma_RZA2[N_RZA2][3]; /* =
{ {-1.0, 0.0, 0.0},
{1.0, 0.0, 0.0} }; */
int i_sigma,ii_sigma,iii_sigma; /* initialisation of n_sigma_RZA2 values */
int i_sigma_min = 0;
int i_sigma_max = 2;
int ii_sigma_min = -1;
int ii_sigma_max = 1;
int iii_sigma_min = -1;
int iii_sigma_max = 1;
int i_RZA2; /* iterate over RZA2 figure requirements */
int rza2_figures=1; /* Enable calculation for all RZA2 figures? plotting test?
* In this clone: use this for the BAO scale for + and - fluctuations
*/
int n_rza2; /* either N_RZA2 or an override */
/* BAO scale: sqrt(90*123) \approx 105; /0.5 = h^{-1} */
double R_domain_lower_BKS00 =
0.5 * 1.0/0.67*INHOMOG_A_SCALE_FACTOR_INITIAL / INHOMOG_A_SCALE_FACTOR_NOW;
double R_domain_upper_BKS00 =
0.5 * 100.0/0.67*INHOMOG_A_SCALE_FACTOR_INITIAL / INHOMOG_A_SCALE_FACTOR_NOW;
#define EIGHT_MPC_H100 8.0
/* n_calls_invariants = 300000; */
/*
{ { {1.1178, 0.1758, 0.000103667, 0.663858},
{1.02825, 0.241843, -6.35389e-05, 0.710868} },
{ {1.31723, 0.290207, -0.0105453, 0},
{1.06082, 0.744882, -0.004969, 0} } };
*/
/* n_calls_invariants = 10000;
{ { {1.11369, 0.175526, 3.59408e-05, 0.663589},
{1.02291, 0.245114, -8.68882e-05, 0.713223} },
{ {1.30339, 0.288883, -0.0113041, 0 },
{1.05623, 0.737999, -0.00639778, 0 } } };
*/
/* int I_invariant; */
int i_t, i_R; /* counters in time and length scale */
int i_EdS;
gsl_rng_env_setup();
T_gsl = gsl_rng_default;
gsl_rng_default_seed += 2467 + local_gsl_seed;
local_gsl_seed = gsl_rng_default_seed;
r_gsl = gsl_rng_alloc (T_gsl); /* this gets reallocated each time the
function gets called */
/* cf BKS00 Table 1, Fig 1 : final FLRW comoving units 16 Mpc, 100 Mpc */
/*
R_domain_lower_BKS00 = 0.08;
R_domain_upper_BKS00 = 0.5;
*/
rza_integrand_params.w_type = 1; /* test standard spherical domains */
rza_integrand_params.delta_R = DELTA_R_DEFAULT; /* if(2==rza_integrand_params.w_type) */
/* 'B' = BBKS (BKS version); 'e' = EisHu98 short formula set ;
'E' = EisHu98 full formula set */
rza_integrand_params.pow_spec_type = 'E';
/* possible overrides: this may make expected_a_D_Omegas cause failure */
/* RZA2 Fig 2 :
physical radii approx 0.125 Mpc, 0.5 Mpc;
final FLRW comoving diameters (2R) approx 50 Mpc, 200 Mpc */
/* R_domain_lower_BKS00 = 0.5 * 20.0*INHOMOG_A_SCALE_FACTOR_INITIAL / INHOMOG_A_SCALE_FACTOR_NOW; */
/* R_domain_lower_BKS00 = 0.5 * 50.0*INHOMOG_A_SCALE_FACTOR_INITIAL / INHOMOG_A_SCALE_FACTOR_NOW; */
/* R_domain_lower_BKS00 = 33.8 *INHOMOG_A_SCALE_FACTOR_INITIAL / INHOMOG_A_SCALE_FACTOR_NOW; */
/* TODO: use the constants in inhomog.h */
/* R_domain_lower_BKS00 = 0.5 * 25.0/(1.0+z_initial); */
/* R_domain_upper_BKS00 = 0.5 * 100.0*INHOMOG_A_SCALE_FACTOR_INITIAL / INHOMOG_A_SCALE_FACTOR_NOW; */
/* R_domain_upper_BKS00 = 0.5 * 200.0*INHOMOG_A_SCALE_FACTOR_INITIAL / INHOMOG_A_SCALE_FACTOR_NOW; */
if(rza2_figures){
n_rza2 = N_RZA2;
i_RZA2=0;
/* assign initial invariants I, II, III in terms of sigma's */
for(i_sigma=i_sigma_min; i_sigma <= i_sigma_max; i_sigma++){
for(ii_sigma=ii_sigma_min; ii_sigma <= ii_sigma_max; ii_sigma++){
for(iii_sigma=iii_sigma_min; iii_sigma <= iii_sigma_max; iii_sigma++){
n_sigma_RZA2[i_RZA2][0] = (double)i_sigma;
n_sigma_RZA2[i_RZA2][1] = (double)ii_sigma;
n_sigma_RZA2[i_RZA2][2] = (double)iii_sigma;
i_RZA2++;
};
};
}; /* for(i_sigma=i_sigma_min; i_sigma < i_sigma_max; i_sigma++) */
if(i_RZA2 != n_rza2){
printf("Error in assigning initial I, II, III values. Correct the code, please.\n");
exit(1);
};
}else{
n_rza2 = 1;
};
for(i_RZA2=0; i_RZA2<n_rza2; i_RZA2++){
if(rza2_figures){
n_sigma[0]= n_sigma_RZA2[i_RZA2][0];
n_sigma[1]= n_sigma_RZA2[i_RZA2][1];
n_sigma[2]= n_sigma_RZA2[i_RZA2][2];
};
background_cosm_params.flatFLRW = 1;
for(i_EdS=N_COSM_I; i_EdS<N_COSM; i_EdS++){
background_cosm_params.EdS = i_EdS;
printf("background_cosm_params.EdS = %d\n",
background_cosm_params.EdS);
background_cosm_params.recalculate_t_0 = 1; /* initially recalculate for this test */
background_cosm_params.Theta2p7 = 2.726/2.7; /* e.g. arXiv:0911.1955 */
if(1 == background_cosm_params.EdS){
background_cosm_params.H_0 = 50.0;
background_cosm_params.Omm_0 = 1.0;
background_cosm_params.OmLam_0 = 0.0;
background_cosm_params.Ombary_0 = 0.088;
/* Planck: Ade et al 2013 arXiv:1303.5076v3, Table 2 */
background_cosm_params.sigma8 = 0.83;
t_i[i_EdS] = t_EdS(&background_cosm_params,
(double)INHOMOG_A_SCALE_FACTOR_INITIAL,
want_verbose);
}else if(1 == background_cosm_params.flatFLRW){
/*
WMAP:
background_cosm_params.H_0 = 70.0;
background_cosm_params.OmLam_0 = 0.73;
*/
/*
Planck:
*/
background_cosm_params.H_0 = 67.0;
background_cosm_params.OmLam_0 = 0.68;
background_cosm_params.Ombary_0 = 0.044;
/* Planck: Ade et al 2013 arXiv:1303.5076v3, Table 2 */
background_cosm_params.sigma8 = 0.83;
/*
background_cosm_params.H_0 = 50.0;
background_cosm_params.OmLam_0 = 0.001;
*/
background_cosm_params.Omm_0 = 1.0 - background_cosm_params.OmLam_0;
t_i[i_EdS] = t_flatFLRW(&background_cosm_params,
(double)INHOMOG_A_SCALE_FACTOR_INITIAL,
want_verbose);
}else{
printf("No other options for background_cosm_params so far in program.\n");
exit(1);
};
background_cosm_params.recalculate_t_0 = 1;
printf("\nOmega_D_effWEC:\n");
t_0[i_EdS] = background_cosm_params.t_0;
delta_t = (t_0[i_EdS]-t_i[i_EdS])/((double)(N_PLOT_T-1));
delta_ln_R = (log(R_domain_upper_BKS00) - log(R_domain_lower_BKS00))/(double)(N_PLOT_R-1);
/* random (50:50) choice of + or - fluctuations, independently for
each of the three invariants */
/* not used in RZA2 article:
for(I_invariant=0; I_invariant<3; I_invariant++){
if(gsl_rng_uniform(r_gsl) > 0.5)
n_sigma[I_invariant] = -n_sigma[I_invariant];
};
*/
for(i_t=0; i_t<N_PLOT_T; i_t++){
t_background[i_EdS][i_t] = t_i[i_EdS] + (double)i_t * delta_t;
};
/* allow nested openmp if possible - so that the invariants can be calculated in parallel */
/* #ifdef _OPENMP
omp_set_nested(1);
#endif
*/
#pragma omp parallel \
default(shared) \
private(i_R, \
rza_integrand_params_sigma8) \
firstprivate(rza_integrand_params, \
background_cosm_params)
{
#pragma omp for schedule(dynamic)
for(i_R=0; i_R<N_PLOT_R; i_R++){
switch(rza_integrand_params.w_type)
{
case 1:
default:
R_domain_mod[i_R] = exp( log(R_domain_lower_BKS00) + ((double)i_R)* delta_ln_R );
rza_integrand_params.R_domain = R_domain_mod[i_R];
break;
case 2: /* shell-shaped domains */
R_domain_mod[i_R] = exp( log(R_domain_lower_BKS00) + ((double)i_R)* delta_ln_R );
rza_integrand_params.R_domain_1 = R_domain_mod[i_R] -
0.5*rza_integrand_params.delta_R;
rza_integrand_params.R_domain_2 = R_domain_mod[i_R] +
0.5*rza_integrand_params.delta_R;
break;
};
/* calculate the first invariant, i.e. same as for FLRW linear theory */
rza_integrand_params.background_cosm_params =
background_cosm_params;
sigma_sq_invariant_I(rza_integrand_params,
n_calls_invariants,
want_verbose,
(double*)&(sigmaIsq[i_EdS][i_R][0]),
(double*)&(sigmaIsq_err[i_EdS][i_R][0]));
/* calculate sigma_8^2 using the first invariant, i.e. same
as for FLRW linear theory */
if(0==i_R){
rza_integrand_params_sigma8 = rza_integrand_params;
rza_integrand_params_sigma8.R_domain = 0.5 * EIGHT_MPC_H100/
(background_cosm_params.H_0/100.0) *
INHOMOG_A_SCALE_FACTOR_INITIAL / INHOMOG_A_SCALE_FACTOR_NOW;
sigma_sq_invariant_I(rza_integrand_params_sigma8,
n_calls_invariants,
want_verbose,
(double*)&(sigma8sq[i_EdS][0]),
(double*)&(sigma8sq_err[i_EdS][0]));
};
Omega_D(&rza_integrand_params,
background_cosm_params,
(double*)&(t_background[i_EdS][0]), (int)N_PLOT_T,
n_sigma,
n_calls_invariants,
want_planar, /* cf RZA2 V.A */
want_spherical,
want_verbose,
(double*)&(rza_Q_D[i_EdS][i_R][0]),
(double*)&(rza_R_D[i_EdS][i_R][0]),
(double*)&(a_D[i_EdS][i_R][0]),
(double*)&(dot_a_D[i_EdS][i_R][0]),
(int*)&(unphysical[i_EdS][i_R][0]),
(double*)&(H_D[i_EdS][i_R][0]),
(double*)&(Omm_D[i_EdS][i_R][0]),
(double*)&(OmQ_D[i_EdS][i_R][0]),
(double*)&(OmLam_D[i_EdS][i_R][0]),
(double*)&(OmR_D[i_EdS][i_R][0])
);
}; /* for(i_R=0; i_R<N_PLOT_R; i_R++) */
}; /* #pragma omp parallel */
/* normalise the sigma_I^2 estimates according to FLRW linear
theory */
for(i_R=0; i_R<N_PLOT_R; i_R++){
for(i_t=0; i_t<N_PLOT_T; i_t++){
sigmaI_normalised[i_EdS][i_R][i_t] =
sqrt(sigmaIsq[i_EdS][i_R][0])
/ sqrt(sigma8sq[i_EdS][0])
* background_cosm_params.sigma8;
/* * growth_FLRW(&background_cosm_params,
t_background[i_EdS][i_t],
want_verbose)/
growth_FLRW(&background_cosm_params,
t_background[i_EdS][0],
want_verbose)
*/
};
};
for(i_t=0; i_t<N_PLOT_T; i_t++){
for(i_R=0; i_R<N_PLOT_R; i_R++){
a_FLRW_expected = exp(log(t_background[i_EdS][i_t]/t_i[i_EdS])*(2.0/3.0))
* INHOMOG_A_SCALE_FACTOR_INITIAL;
H_FLRW_expected = 2.0/(3.0*t_background[i_EdS][i_t]);
a_dot_FLRW_expected = H_FLRW_expected * a_FLRW_expected;
(void)a_dot_FLRW_expected; /* avoid compile warning */
/* printf("test_scale_factor_D: Warning: curvature backreaction inferred\n");
printf("from Hamilton constraint; not calculated directly.\n"); */
/*
OmR_D[i_EdS][i_R][i_t] =
1.0 - Omm_D[i_EdS][i_R][i_t]
- OmQ_D[i_EdS][i_R][i_t]
- OmLam_D[i_EdS][i_R][i_t];
*/
printf(/*nsig=*/" %4.1f %4.1f %4.1f: tB2 R : a_D H_D : %g %g : %g %g : %g %g %g : %g : %g %g\n",
n_sigma[0],
n_sigma[1],
n_sigma[2],
t_background[i_EdS][i_t],
R_domain_mod[i_R],
a_D[i_EdS][i_R][i_t],
H_D[i_EdS][i_R][i_t],
Omm_D[i_EdS][i_R][i_t],
OmQ_D[i_EdS][i_R][i_t],
/* OmLam_D[i_EdS][i_R][i_t], */
OmR_D[i_EdS][i_R][i_t],
sigmaI_normalised[i_EdS][i_R][i_t],
Omm_D[i_EdS][i_R][i_t] + OmQ_D[i_EdS][i_R][i_t] + OmR_D[i_EdS][i_R][i_t],
Omm_D[i_EdS][i_R][i_t] + 2.0* OmQ_D[i_EdS][i_R][i_t] + (2.0/3.0)*OmR_D[i_EdS][i_R][i_t]
);
}; /* for(i_R=0; i_R<N_PLOT_R; i_R++) */
}; /* for(i_t=0; i_t<N_PLOT_T; i_t++) */
}; /* for(i_EdS=0; i_EdS<N_COSM; i_EdS++) */
}; /* for(i_RZA2=0; i_RZA2<n_rza2; i_RZA2++) */
gsl_rng_free(r_gsl);
return 0;
}
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