diff --git a/toy_gwcosmo_v3/scripts/cosmology_functions/__init__.py b/toy_gwcosmo_v3/scripts/cosmology_functions/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..4bb6247dbbcd44b6a0d46398618a387446b61a17 --- /dev/null +++ b/toy_gwcosmo_v3/scripts/cosmology_functions/__init__.py @@ -0,0 +1,2 @@ +import cosmology_functions.priors +import cosmology_functions.cosmology diff --git a/toy_gwcosmo_v3/scripts/cosmology_functions/__pycache__/__init__.cpython-37.pyc b/toy_gwcosmo_v3/scripts/cosmology_functions/__pycache__/__init__.cpython-37.pyc new file mode 100644 index 0000000000000000000000000000000000000000..95ec65d740a3a50e8d345faf423c2e9384ca6e76 Binary files /dev/null and b/toy_gwcosmo_v3/scripts/cosmology_functions/__pycache__/__init__.cpython-37.pyc differ diff --git a/toy_gwcosmo_v3/scripts/cosmology_functions/__pycache__/__init__.cpython-38.pyc b/toy_gwcosmo_v3/scripts/cosmology_functions/__pycache__/__init__.cpython-38.pyc new file mode 100644 index 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0000000000000000000000000000000000000000..d5a3c4393ddd03c04c27ffbe401dad53641bfa03 --- /dev/null +++ b/toy_gwcosmo_v3/scripts/cosmology_functions/cosmology.py @@ -0,0 +1,92 @@ +import numpy as np +from scipy.interpolate import splrep, splev +from scipy.integrate import dblquad, quad, tplquad +from scipy.interpolate import splrep, splev +from scipy.interpolate import interp2d +import astropy.constants as const + +zmax = 10 # max redshift +H0 = 70 #Hubble constant +c = const.c.to('km/s').value #speed of light in km/s +omega_m = 0.3; omega_lambda = 0.7 #cosmological parameters +omega_k = 1- omega_lambda - omega_m + +@np.vectorize +def z_to_dl(z,H): + "distance as a function of z and H" + def E(z): + return np.sqrt((omega_m*(1+z)**(3) + omega_k*(1+z)**(2) + omega_lambda)) + + def I(z): + fact = lambda x: 1/E(x) + integral = quad(fact, 0, z) + return integral[0] + + dl = (c*(1+z) / H) * I(z) + return dl + +#make look up table objects with splrep and splev + +z_dl_grid = np.linspace(0.01, zmax, 1000) +dl_z_grid = z_to_dl(z_dl_grid,70) +spl_z_dl = splrep(z_dl_grid, dl_z_grid) +spl_dl_z = splrep(dl_z_grid, z_dl_grid) + +def fast_z_to_dl_v2(z,H): + spl_z = spl_z_dl[0] + spl_dl = spl_z_dl[1]*(70/H) + spl_degree = spl_z_dl[2] + return splev(z, (spl_z,spl_dl,spl_degree)) + +def fast_dl_to_z_v2(dl,H): + spl_dl = spl_dl_z[0]*(70/H) + spl_z = spl_dl_z[1] + spl_degree = spl_dl_z[2] + return splev(dl, (spl_dl,spl_z,spl_degree)) + +def dist_modulus(M,m): + 'Distance Modulus given Absolute Magnitude and ' + result = 10**((m - M - 25) /5) + return result + + +def z_MmH(M,m,H): + "redshift in function of absolute magnitude, apparent magnitude and H0" + result = fast_dl_to_z_v2(dist_modulus(M,m), H) + return result + + + +def app_mag(M,dl): + "apparent magnitude in function of absolute amgnitude and luminosity distance" + m = M + 5*(np.log10(dl))+25 + return m.flatten() + + +def abs_M(m,dl): + "absolute magnitude in function of apparent amgnitude and luminosity distance" + m = M + 5*(np.log10(dl))+25 + return m.flatten() + + +def M_z(chirp_M, z): + "Source Chirp mass in function of Chirp M and Redshift" + return chirp_M*(1+z) + +def Source_M(M_z,z): + "Source Mass frame" + Source_mass = M_z / (1+z) + return Source_mass + +def snr_Mz_z(redshifted_mass, z, H): + "SNR in function of redshifted chirp mass, distance, H0" + dl = fast_z_to_dl_v2(z,H) + return (2*redshifted_mass/dl) * (250/(2*2.8)) + + +def snr_M_z(source_mass, z, H): + "SNR in function of redshifted chirp mass, distance, H0" + dl = fast_z_to_dl_v2(z,H) + return (2*source_mass*(1+z)/dl) * (250/(2*2.8)) + + diff --git a/toy_gwcosmo_v3/scripts/cosmology_functions/priors.py b/toy_gwcosmo_v3/scripts/cosmology_functions/priors.py new file mode 100644 index 0000000000000000000000000000000000000000..f0b8b2be9056bceb700b0cfb37a054f0b33f9b24 --- /dev/null +++ b/toy_gwcosmo_v3/scripts/cosmology_functions/priors.py @@ -0,0 +1,47 @@ +import numpy as np +from scipy.interpolate import splrep, splev +from scipy.integrate import dblquad, quad, tplquad + +Mmin = 5 ; Mmax = 100 #chirp mass mass boundaries +zmax = 10 +omega_m = 0.3; omega_lambda = 0.7 #cosmological parameters +omega_k = 1- omega_lambda - omega_m + +@np.vectorize +def p_z(z): + "redshift probability distribution function for Omega_M = 0.3 ad Omega_Lambda = 0.7 (not normalized)" + + def E(z): + return np.sqrt((omega_m*(1+z)**(3) + omega_k*(1+z)**(2) + omega_lambda)) + + def I(z): + fact = lambda x: 1/E(x) + integral = quad(fact, 0, z) + return integral[0] + result = (I(z))**(2) / E(z) + return result + +#Look up table grids using splrep and splev +z_grid = np.linspace(0,zmax,1000) +pz_grid = np.array([p_z(z) for z in z_grid]) +spl_z_pz = splrep(z_grid,pz_grid) + +def fast_p_z(z): + return splev(z, spl_z_pz) + + +def p_M(M, H): + "Schecter Function (B-band values) (not normalized)" + phi = (1.61/100)*(H/100)**3 + alpha = -1.21 + Mc = -19.66 + 5*np.log10(H/100) + return (2/5)*phi*(np.log(10))*((10**((2/5)*(Mc-M)))**(alpha+1))*(np.exp(-10**((2/5)*(Mc-M)))) + +@np.vectorize +def p_Chirp(M): + "Uniform Chirp mass prior betwee 5 and 100 Msol" + if M <= Mmax and M>=Mmin: + return 1 / (Mmax - Mmin) + else: + return 0 +# %% diff --git a/toy_gwcosmo_v3/scripts/likelihood_H0_v8.py b/toy_gwcosmo_v3/scripts/likelihood_H0_v8.py new file mode 100644 index 0000000000000000000000000000000000000000..f4f7dd5b03d0324bd5ce6da901eec736352d6650 --- /dev/null +++ b/toy_gwcosmo_v3/scripts/likelihood_H0_v8.py @@ -0,0 +1,251 @@ +#%% import libraries +import numpy as np +import pandas as pd +import time +from scipy.interpolate import splrep, splev +from scipy.integrate import dblquad, quad, tplquad +from tqdm import tqdm +import matplotlib.pyplot as plt +import bilby +import astropy.constants as const +from scipy.stats import norm +from scipy.special import erf + +from cosmology_functions import priors +from cosmology_functions import cosmology +np.random.seed(1) +#path to universe data frame files +path = "universes/" +path_plots = "plots/" + +#%% initial parameters +Nevent = 10 # the number of GW events +NH = 30 # the number of H0 vector values +H0 = 70 # the true H0 +h = H0 / 100 #hubble parameter +rho_th = 12 # the SNR threshold +Hvec = np.linspace(50,80,NH) # a vector of H0 values +mth = 24 # magnitude threshold +zmax = 10 # max redshift +c = const.c.to('km/s').value #speed of light in km/s +omega_m = 0.3; omega_lambda = 0.7 #cosmological parameters +omega_k = 1- omega_lambda - omega_m +Mmin = 1 ; Mmax = 100 #chirp mass Min and Max + +# read universe +universe = pd.read_csv(path+"small_uniform_universe.dat",skipinitialspace=True, usecols=['Absolute_M', 'Apparent_m', 'RA', 'dec', 'z', 'dist_lum']) +print('Universe read correctly') +print() +z_universe = universe.z +m_universe = universe.Apparent_m +dl_universe = universe.dist_lum +RA_universe = universe.RA +Dec_universe = universe.dec + +#%% initialize functions for likelihood analysis +@np.vectorize +def p_x_H0(z_sample, Mz_sample,Hvec, obs_rho, sigma_rho_sample = 1): + rho = cosmology.snr_Mz_z(Mz_sample, z_sample, Hvec) + prob_x = norm.pdf((obs_rho - rho)/sigma_rho_sample) + return prob_x + +@np.vectorize +def p_D_H0(z_sample, Mz_sample,Hvec, sigma_rho_sample = 1): + rho = cosmology.snr_Mz_z(Mz_sample, z_sample, Hvec) + rho_range = (rho_th - rho)/(np.sqrt(2)*sigma_rho_sample) + prob_D = 0.5*(1.0 - erf(rho_range)) + return prob_D + +#in catalogue +def p_x_H0_G(z_samples_cat, M_z_sample,Hvec, obs_rho, sigma_rho_sample = 1): + return np.array([sum(p_x_H0(z_samples_cat, M_z_sample,H, obs_rho, sigma_rho_sample = 1)) for H in tqdm(Hvec) ]) + +def p_D_H0_G(z_samples_cat, M_z_sample,Hvec, sigma_rho_sample = 1): + return np.array([sum(p_D_H0(z_samples_cat, M_z_sample, H, sigma_rho_sample = 1)) for H in tqdm(Hvec) ]) + +#out of catalgue +@np.vectorize +def p_x_H0_barG(M_z_sample, Hvec, obs_rho, sigma_rho_sample = 1): + return dblquad(lambda z, M: p_x_H0(z, M_z_sample, Hvec, obs_rho)*priors.fast_p_z(z)*priors.p_M(M,Hvec), -23,-5,lambda M:cosmology.z_MmH(M,mth,Hvec), lambda M:zmax, epsrel=1e-1, epsabs = 0)[0] + +@np.vectorize +def p_D_H0_barG(M_z_sample, Hvec,sigma_rho_sample = 1): + return dblquad(lambda z, M: p_D_H0(z, M_z_sample, Hvec)*priors.fast_p_z(z)*priors.p_M(M,Hvec), -23,-5,lambda M:cosmology.z_MmH(M,mth,Hvec), lambda M: zmax, epsrel=1e-1, epsabs = 0)[0] + +#weights for in and out of catalogue cases +@np.vectorize +def p_G_D_H(M_z_sample, Hvec,sigma_rho_sample = 1): + return dblquad(lambda z, M: p_D_H0(z, M_z_sample, Hvec)*priors.fast_p_z(z)*priors.p_M(M,Hvec), -23,-5,lambda M:0, lambda M: cosmology.z_MmH(M,mth,Hvec),epsrel=1e-1, epsabs = 0)[0] + +def p_D_tot(vec_P_G, vec_P_barG): + return vec_P_G + vec_P_barG + + +#%% GW event selection +def GW_events(Nevent): + "GW event selection for analysis of Nevents" + + #mass prior + prior_mass = bilby.core.prior.Uniform(Mmin, Mmax, "chirp_mass") + + #store parameters in empty list + event = [] + + i = 0 + while i < Nevent: + "Randomly select galaxy from universe and get parameters" + index = np.random.randint(0,len(z_universe)) + z_sample = z_universe.iloc[index] + RA_sample = RA_universe[index] + Dec_sample = Dec_universe[index] + app_m = m_universe.iloc[index] + dl_sample = dl_universe.iloc[index] + chirp_sample = prior_mass.sample() + Mz_sample = cosmology.M_z(chirp_sample,z_sample) + sigma_rho_sample = np.random.normal(0,1) + rho_sample = cosmology.snr_Mz_z(Mz_sample, z_sample, 70) + sigma_rho_sample + + + + if rho_sample >= rho_th: # did we detect this one? + if app_m <= mth: # is it in catalog? + #add some uncertainty to sky location + RA_sample_uncertainty = 10 #np.random.normal(0,3) #add uncertainties + Dec_sample_uncertainty = 10 #np.random.normal(0,3) #add uncertainties + temp_z = [] #initialize empty list to store redshifts of event sky location + for j in range(len(z_universe)): + #if dl_universe.iloc[j] > dl_sample - d_sample_uncertainty and dl_universe.iloc[j] < dl_sample + d_sample_uncertainty: + if RA_universe.iloc[j] > RA_sample - RA_sample_uncertainty and RA_universe.iloc[j] < RA_sample + RA_sample_uncertainty: + if Dec_universe.iloc[j] > Dec_sample - Dec_sample_uncertainty and Dec_universe.iloc[j] < Dec_sample + Dec_sample_uncertainty: + temp_z.append(z_universe.iloc[j]) + #print('Found {} galaxies within sky location'.format(j)) + z_catalog_event = temp_z + para = [ i+1 , z_catalog_event, + chirp_sample, dl_sample, rho_sample, Mz_sample, RA_sample, Dec_sample, app_m ] + event.append(para) + + print("-- N = {}".format(i+1)) + print('N_gal = {}, dl = {}, rho = {}, Mz = {}'.format( round(len(z_catalog_event),4), round(dl_sample,4), round(rho_sample,4), round(Mz_sample,4))) + print() + i += 1 + + + print('{} GW events stored '.format(Nevent)) + return event + +#compute event parameters +event = GW_events(Nevent) + + +#%% full Likelihood analysis +def full_likelihood_event(Nevent, NH, event_para): + "Likelihood analysis for each event stored in respective numerator and denominator" + #Initialize empty likelihood to store for each event + likelihood = np.zeros((Nevent, NH)) + event = event_para + like_funcs = [] + + for j in range(Nevent): + z_i = event[j][1] #get redshift associated with the host galaxy + rho = event[j][4] #get the current event SNR + Mz = event[j][5] #get source frame chirp mass + + print('Computing p_x_GH and p_D_GH, event {}'.format(j+1)) + p_x_G = p_x_H0_G(z_i, Mz, Hvec, rho) + p_D_G = p_D_H0_G(z_i, Mz, Hvec) + + print('Computing p_x_barH and p_D_barGH, event {}'.format(j+1)) + p_x_barG = np.array([p_x_H0_barG(Mz, H, rho) for H in tqdm(Hvec)]) + p_D_barG = np.array([p_D_H0_barG(Mz, H) for H in tqdm(Hvec)]) + + print('Computing p_G and p_barG, event {}'.format(j+1)) + num_p_G = np.array([p_G_D_H(Mz, H) for H in tqdm(Hvec)]) + den_pg = p_D_tot(num_p_G, p_D_barG ) + pG = num_p_G / den_pg + pbarG = 1 - pG + + + likelihood[j,:] = ((p_x_G / p_D_G)*pG) + ((p_x_barG / p_D_barG)*pbarG) + like_funcs.append([[p_x_G], [p_D_G], [pG], [p_x_barG], [p_D_barG], [pbarG]]) + return likelihood, like_funcs + +#Compute likelihoods numerator and denominator +likelihood, like_funcs = full_likelihood_event(Nevent, NH, event) + + + +#%% plot likelihood as gwcosmo +dH0 = Hvec[1] - Hvec[0] + + +import matplotlib.pyplot as plt +matplotlib.rcParams['font.family']= 'Times New Roman' +matplotlib.rcParams['font.sans-serif']= ['Bitstream Vera Sans'] +matplotlib.rcParams['text.usetex']= True +matplotlib.rcParams['mathtext.fontset']= 'stixsans' + +import seaborn as sns +sns.set_context('paper') +sns.set_style('ticks') +sns.set_palette('colorblind') +plt.style.use('default') +c=sns.color_palette('colorblind') + +fig, ax = plt.subplots(figsize=(10,10)) +Ltot = np.zeros(NH) #initialise combined posteriors numerator +N =Nevent +for j in range(N): + if j != 3 and j !=8 : + ax.plot(Hvec,likelihood[j,:]/(np.sum(likelihood[j,:])*dH0),color=c[np.random.randint(9)], alpha=0.5, label='event {}'.format(j + 1)) + Ltot += np.log(likelihood[j,:]/(np.sum(likelihood[j,:])*dH0)) + + +#plt.title(r' $Ngal = {}, dL = {}, \rho = {}, Mz = {}$'.format( round(len(event[j][2]),2), round(event[j][4] ,2), round(event[j][5],2), round(event[j][6],2))) +plt.title(r'$Nevent = {}$'.format(10)) +plt.axvline(70,ls='--', color='k',alpha=0.8, label = r'$H_0 = 70$ (km s$^{-1}$ Mpc$^{-1}$)') +plt.plot(Hvec,np.exp(Ltot)/(np.sum((np.exp(Ltot)))*dH0), linewidth = 1.5, label='Posterior',c='red') +plt.xlim(Hvec[0],Hvec[-1]) +plt.ylim(0.001,0.1) +plt.xticks(fontsize=14) +plt.yticks(fontsize=14) +plt.xlabel(r'$H_0$ (km s$^{-1}$ Mpc$^{-1}$)',fontsize=16) +plt.ylabel(r'$p(H_0)$ (km$^{-1}$ s Mpc)', fontsize=16) +plt.legend(loc='upper right',fontsize=15) +plt.tight_layout() +plt.grid(True, alpha =0.3) +#plt.savefig(path_plots+'likelihood_H0_full_analysis_Nevent_better_8_test_2.png', dpi = 800) +plt.show() + + +#%% plot signle event +def plot_single_event_likelihoods(j): + dH0 = Hvec[1] - Hvec[0] + + pxgh =like_funcs[j][0][0] / sum(like_funcs[j][0][0]*dH0) + pdgh = like_funcs[j][1][0] / sum(like_funcs[j][1][0]*dH0) + pxbargh = like_funcs[j][3][0] / sum(like_funcs[j][3][0]*dH0) + pdbargh =like_funcs[j][4][0] / sum(like_funcs[j][4][0]*dH0) + pg = like_funcs[j][2][0] / sum(like_funcs[j][2][0]*dH0) + pbarg = like_funcs[j][5][0] / sum(like_funcs[j][5][0]*dH0) + x = Hvec + fig, axs = plt.subplots(3, 2) + plt.suptitle(r' $Ngal = {}, dL = {}, \rho = {}, Mz = {}$'.format( round(len(event[j][1]),2), round(event[j][3] ,2), round(event[j][4],2), round(event[j][5],2))) + axs[0, 0].plot(x, pxgh) + axs[0, 0].set_title(r'$p(\rho|G,H)$') + axs[1, 0].plot(x, pxbargh) + axs[1, 0].set_title(r'$p(\rho|\bar{G},H)$') + axs[0, 1].plot(x, pdgh) + axs[0, 1].set_title(r'$p(D|G,H)$') + axs[1, 1].plot(x, pdbargh) + axs[1, 1].set_title(r'$p(D|\bar{G},H)$') + axs[2, 0].plot(x, pg) + axs[2, 0].set_title(r'$p(G|D,H)$') + axs[2, 1].plot(x, pbarg) + axs[2, 1].set_title(r'$p(\bar{G}|D,H)$') + + plt.tight_layout() + plt.savefig(path_plots+'likelihood_H0_v7_test_subplots_test_2.png',dpi=800) + return plt.show() + +plot_single_event_likelihoods(7) +# %% diff --git a/toy_gwcosmo_v3/scripts/make_universe.py b/toy_gwcosmo_v3/scripts/make_universe.py new file mode 100644 index 0000000000000000000000000000000000000000..d0e2f4094093df134162d5fe3021c476bdc5dc4f --- /dev/null +++ b/toy_gwcosmo_v3/scripts/make_universe.py @@ -0,0 +1,162 @@ +# Author: Federico Stachurski +#Procedure: generate data frame of glaxies with corresponding redshift, RA, dec, luminosity distance, apparent magnitude +# and absolute magnitude, given initial cosmological parameters and maximum distance in comoving volume. +#Input: -N number of galaxies, -d max comoving distance, -H) hubble constant to use +#Output: data frame of galaxies +#Date: 11/12/2020 + +#%% import libraries +import numpy as np +import scipy.stats +import matplotlib.pyplot as plt +import astropy.constants as const +from scipy.integrate import dblquad, quad +import numpy.random as rn +from tqdm import tqdm +from math import e +import random +from scipy.stats import multivariate_normal +np.random.seed(2) +import time +import pandas as pd +from astropy import units as u +from astropy.coordinates import SkyCoord +from scipy.stats import loguniform +import argparse + +# Construct the argument parser +ap = argparse.ArgumentParser() + +# Add the arguments to the parser +ap.add_argument("-N", "--Ngal", required=True, + help="number of galaxies in universe") +ap.add_argument("-d", "--co_dist_max", required=True, + help="maximum comoving distance to generate universe in Gpc", default = 1) +ap.add_argument("-H0", "--Hubble", required=True, + help="Hubble constant to use") +ap.add_argument("-Name", "--Universe_Name", required=True, + help="Filename to save dataframe") + +args = vars(ap.parse_args()) +N = int(args['Ngal']) +dmax = float(args['co_dist_max']) +H0 = float(args['Hubble']) +Name = args['Universe_Name'] + + +# set constants +c = const.c.to('km/s').value #speed of light in km/s #Hubble constant (km/s/Mpc) +h=H0/100 #Hubble parameter 0.7 +dmax = dmax*1000 #Mpc + + +omega_m = 0.3 +omega_lambda = 0.7 +omega_k = 1- omega_lambda - omega_m + +print('Generating universe with {} galaxies, max comoving distance of {} Mpc and H0 = {}'.format(N, dmax, H0)) + +#%% initialise functions +def z_to_dl(z,H): + "distance as a function of z and H" + def E(z): + return np.sqrt((omega_m*(1+z)**(3) + omega_k*(1+z)**(2) + omega_lambda)) + + def I(z): + fact = lambda x: 1/E(x) + integral = quad(fact, 0, z) + return integral[0] + dl = np.zeros(len(z)) + for i in range(len(z)): + dl[i] = (c / H) * I(z[i]) + return dl + +def dl_to_z(d,H): + "computes redshifts from a look up table using z_to_dl" + z_grid = np.linspace(0,2,1000) + dl = z_to_dl(z_grid,70) + redshifts = np.interp(d, dl, z_grid) + #v_pec=np.random.normal(0,200,len(d)) + obs_redshifts = redshifts #(v_pec/c)*(1+redshifts) + return obs_redshifts + +def luminosity_dist(d,z): + "computes the luminsoity distance as distance x (1+z)" + dl = d*(1+z) + return dl + +def app_mag(M,dl): + print('Computing apparent magnitudes from absolute Magnitudes and luminosity distances') + m = M + 5*(np.log10(dl))+25 + return m.flatten() + +def p_M(M): #Schecter Function (B-band values) + phi = (1.61/100)*h**3 + alpha = -1.21 + Mc = -19.66 + 5*np.log10(h) + return (2/5)*phi*(np.log(10))*((10**((2/5)*(Mc-M)))**(alpha+1))*(e**(-10**((2/5)*(Mc-M)))) + +def draw_dist(N): + print('Sampling Distances') + def d_sample(n): + x_sample = np.random.uniform(-dmax,dmax, N)#np.random.multivariate_normal(x_cluster_means, x_cluster_cov,size=1) + y_sample = np.random.uniform(-dmax,dmax, N)#np.random.multivariate_normal(y_cluster_means, y_cluster_cov,size=1) + z_sample = np.random.uniform(-dmax,dmax, N)#np.random.multivariate_normal(z_cluster_means, z_cluster_cov,size=1) + d_comoving = np.sqrt(x_sample**(2) + y_sample**(2) + z_sample**(2) ) + return d_comoving[d_comoving < dmax] + + d_com = d_sample(N) + temp = len(d_com) + while True: + if temp < N: + rem = int(N - temp) + d_com = np.hstack((d_com,d_sample(rem))) + temp = temp + len(d_com) + else: + d_com = d_com[:N] + break + return d_com + + +def draw_RA_Dec(N): + print('Sampling Ra and Dec') + #sample RA + ra_obs = np.random.uniform(-180,180,N) + + #sample declinations + P = np.random.uniform(0,1,N) + dec = np.arcsin(2*P-1) + return ra_obs, dec + + +def draw_M(N): + print('Sampling Absolute magnitudes from Schecter Function') + M_grid = np.linspace(-23,-5,10000) + cdf_M = np.zeros(len(M_grid)) + for i in range(len(M_grid )): + cdf_M[i] = quad(lambda z: p_M(z), -23, M_grid[i])[0] + cdf_M = cdf_M/np.max(cdf_M) + t = rn.random(N) + M_sample = np.interp(t,cdf_M,M_grid) + return M_sample + +#%% run functions +start = time.time() +comoving_dist = draw_dist(N) +RA_samples, dec_samples = draw_RA_Dec(N) +print("Computing redshifts") +z_samples = dl_to_z(comoving_dist,H0) +print("Computing luminosty distances") +dl_samples = luminosity_dist(comoving_dist,z_samples) +M_samples = draw_M(N) +print("Computing apparent magnitudes") +m_samples = app_mag(M_samples,dl_samples) +end = time.time() +print("Universe was generated in {} seconds ({} minutes)".format((end-start), (end-start)/60)) +#save universe as a data frame .dat file +print('Saving galaxies in Data Frame ') +output_df = pd.DataFrame({'RA': RA_samples, 'dec': dec_samples, \ + 'dist_lum': dl_samples, 'z': z_samples,\ + 'Apparent_m': m_samples, 'Absolute_M': M_samples } ) +output_df.to_csv(Name +'.dat') +print("Universe Complete") diff --git a/toy_gwcosmo_v3/scripts/make_universe_clustered.py b/toy_gwcosmo_v3/scripts/make_universe_clustered.py new file mode 100644 index 0000000000000000000000000000000000000000..68f267ffcda6261b7bd68c1bf88764a41f2cd2f0 --- /dev/null +++ b/toy_gwcosmo_v3/scripts/make_universe_clustered.py @@ -0,0 +1,189 @@ +# Author: Federico Stachurski +#Procedure: generate data frame of glaxies with corresponding redshift, RA, dec, luminosity distance, apparent magnitude +# and absolute magnitude, given initial cosmological parameters and maximum distance in comoving volume. +#Input: -N number of galaxies, -d max comoving distance, -H) hubble constant to use +#Output: data frame of galaxies +#Date: 11/12/2020 + +#%% import libraries +import numpy as np +import scipy.stats +import matplotlib.pyplot as plt +import astropy.constants as const +from scipy.integrate import dblquad, quad +import numpy.random as rn +from tqdm import tqdm +from math import e +import random +from scipy.stats import multivariate_normal +np.random.seed(2) +import time +import pandas as pd +from astropy import units as u +from astropy.coordinates import SkyCoord +from scipy.stats import loguniform +import argparse + +# Construct the argument parser +ap = argparse.ArgumentParser() + +# Add the arguments to the parser +ap.add_argument("-N", "--Ngal", required=True, + help="number of galaxies in universe") +ap.add_argument("-d", "--co_dist_max", required=True, + help="maximum comoving distance to generate universe in Gpc", default = 1) +ap.add_argument("-H0", "--Hubble", required=True, + help="Hubble constant to use") +ap.add_argument("-Name", "--Universe_Name", required=True, + help="Filename to save dataframe") + +args = vars(ap.parse_args()) +N = int(args['Ngal']) +dmax = float(args['co_dist_max']) +H0 = float(args['Hubble']) +Name = args['Universe_Name'] + + +# set constants +c = const.c.to('km/s').value #speed of light in km/s #Hubble constant (km/s/Mpc) +h=H0/100 #Hubble parameter 0.7 +dmax = dmax*1000 #Mpc + + +omega_m = 0.3 +omega_lambda = 0.7 +omega_k = 1- omega_lambda - omega_m + +print('Generating universe with {} galaxies, max comoving distance of {} Mpc and H0 = {}'.format(N, dmax, H0)) + +#%% initialise functions +def z_to_dl(z,H): + "distance as a function of z and H" + def E(z): + return np.sqrt((omega_m*(1+z)**(3) + omega_k*(1+z)**(2) + omega_lambda)) + + def I(z): + fact = lambda x: 1/E(x) + integral = quad(fact, 0, z) + return integral[0] + dl = np.zeros(len(z)) + for i in range(len(z)): + dl[i] = (c / H) * I(z[i]) + return dl + +def dl_to_z(d,H): + "computes redshifts from a look up table using z_to_dl" + z_grid = np.linspace(0,2,1000) + dl = z_to_dl(z_grid,70) + redshifts = np.interp(d, dl, z_grid) + #v_pec=np.random.normal(0,200,len(d)) + obs_redshifts = redshifts #(v_pec/c)*(1+redshifts) + return obs_redshifts + +def luminosity_dist(d,z): #luminosity distance + "computes the luminsoity distance as distance x (1+z)" + dl = d*(1+z) + return dl + +def app_mag(M,dl): #apparent magnitude + print('Computing apparent magnitudes from absolute Magnitudes and luminosity distances') + m = M + 5*(np.log10(dl))+25 + return m.flatten() + +def p_M(M): #Schecter Function (B-band values) + phi = (1.61/100)*h**3 + alpha = -1.21 + Mc = -19.66 + 5*np.log10(h) + return (2/5)*phi*(np.log(10))*((10**((2/5)*(Mc-M)))**(alpha+1))*(e**(-10**((2/5)*(Mc-M)))) + + + + +def draw_RA_dec_dist(N, N_clu): + print('Sampling Right Ascencions, Declinations and co-moving Distances') + N_gal_clu = int(N/N_clu) + dist_max = dmax*1e-3 + sigma = 0.1 + mean = np.random.uniform(-dist_max,dist_max,(N_clu,3)) + # cov = np.diagflat(np.random.uniform(0,sigma, 3)) + # cov = np.sqrt(cov*cov.T) + + def cluster(N_gal_clu,mean,cov): + x,y,z = np.random.multivariate_normal(mean,cov,N_gal_clu).T + return x,y,z + + for i in range(N_clu): + cov = np.diagflat(np.random.uniform(0,sigma, 3)) + cov = np.sqrt(cov*cov.T) + #print(cov) + if i == 0: + dx,dy,dz = cluster(N_gal_clu,mean[i,:],cov) + else: + temp_x,temp_y,temp_z = cluster(N_gal_clu,mean[i,:],cov) + dx = np.vstack((dx,temp_x)) + dy = np.vstack((dy,temp_y)) + dz = np.vstack((dz,temp_z)) + + d_comoving = np.sqrt(dx**(2) + dy**(2) + dz**(2) ) + indicies = np.where(d_comoving <= dist_max) + #convert into spherical coordinates + def cart2spher(x,y,z): + coordinates = SkyCoord(x=x, y=y, z=z, unit = 'Gpc', representation_type='cartesian') + coordinates.representation_type = 'spherical' + RA = coordinates.ra.value + dec = coordinates.dec.value + distance = coordinates.distance.value + return RA.flatten(), dec.flatten(), distance.flatten() + + RA, dec, co_dist = cart2spher(dx[indicies],dy[indicies],dz[indicies]) + return RA.flatten(), dec.flatten(), co_dist.flatten()*1e3, mean.flatten()*1e3, dx.flatten()*1e3, dy.flatten()*1e3, dz.flatten()*1e3 + + +# def draw_RA_Dec(N): +# print('Sampling Ra and Dec') +# #sample RA +# ra_obs = np.random.uniform(0,180,N) + +# #sample declinations +# P = np.random.uniform(0,1,N) +# dec = np.arcsin(2*P-1) +# return ra_obs, dec + + +def draw_M(N): + print('Sampling Absolute magnitudes from Schecter Function') + M_grid = np.linspace(-23,-5,10000) + cdf_M = np.zeros(len(M_grid)) + for i in range(len(M_grid )): + cdf_M[i] = quad(lambda z: p_M(z), -23, M_grid[i])[0] + cdf_M = cdf_M/np.max(cdf_M) + t = rn.random(N) + M_sample = np.interp(t,cdf_M,M_grid) + return M_sample + +#%% run functions +start = time.time() +RA_samples, dec_samples, comoving_dist, means, dx, dy, dz = draw_RA_dec_dist(N,20) + +# RA_samples, dec_samples = draw_RA_Dec(N) +print("Computing redshifts") +z_samples = dl_to_z(comoving_dist,H0) +print("Computing luminosty distances") +dl_samples = luminosity_dist(comoving_dist,z_samples) +M_samples = draw_M(len(RA_samples)) +print("Computing apparent magnitudes") +m_samples = app_mag(M_samples,dl_samples) +end = time.time() +print("Universe was generated in {} seconds ({} minutes)".format((end-start), (end-start)/60)) +#save universe as a data frame .dat file +print('Saving galaxies in Data Frame ') +output_df = pd.DataFrame({'RA': RA_samples, 'dec': dec_samples, \ + 'dist_lum': dl_samples, 'z': z_samples,\ + 'Apparent_m': m_samples, 'Absolute_M': M_samples} ) +output_df.to_csv("universes\ "+Name+".dat") +print("Universe Complete") +output_df = pd.DataFrame({ 'Cluster_means': means }) +output_df.to_csv("universes\ "+Name+"_means.dat") + +output_df = pd.DataFrame({ 'dx': dx, 'dy': dy, 'dz': dz} ) +output_df.to_csv("universes\ "+Name+"_cartesian_coordinates.dat") diff --git a/toy_gwcosmo_v3/scripts/plot_universe.py b/toy_gwcosmo_v3/scripts/plot_universe.py new file mode 100644 index 0000000000000000000000000000000000000000..1dbe339795d46ec49becd40a1eb25fd9fb8b5e83 --- /dev/null +++ b/toy_gwcosmo_v3/scripts/plot_universe.py @@ -0,0 +1,207 @@ +#%% +import numpy as np +import matplotlib.pyplot as plt +import pandas as pd +from scipy.integrate import dblquad, quad +from astropy import units as u +from astropy.coordinates import SkyCoord +import astropy.constants as const +plt.style.use('default') +path = "universes" +data = pd.read_csv(path+"/universe_uniform.dat",skipinitialspace=True, usecols=['Absolute_M', 'Apparent_m', 'RA', 'dec', 'z', 'dist_lum']) +#means = pd.read_csv(path+"universe_clustered_means.dat",skipinitialspace=True, usecols=['Cluster_means']) +#dist_cartesian = pd.read_csv(path+"universe_clustered_cartesian_coordinates.dat",skipinitialspace=True, usecols=['dx', 'dy', 'dz']) + + +print(data.Apparent_m) +print(data.Absolute_M) +print(data.RA) +print(data.dec) +print(data.z) +#print(data.dist_lum) +#print(means.Cluster_means) +zmax = 1 # max redshift +c = const.c.to('km/s').value #speed of light in km/s +omega_m = 0.3; omega_lambda = 0.7 #cosmological parameters +omega_k = 1- omega_lambda - omega_m +#%% retrieve mean locations in RA and Dec from means +means_pos = np.array(means.Cluster_means) +def cart2spher(x,y,z): + coordinates = SkyCoord(x=x, y=y, z=z, unit = 'Mpc', representation_type='cartesian') + coordinates.representation_type = 'spherical' + RA = coordinates.ra.value + dec = coordinates.dec.value + distance = coordinates.distance.value + return RA.flatten(), dec.flatten(), distance.flatten() + +Ra_mean, Dec_mean, dist_mean = cart2spher(means_pos[0::3],means_pos[1::3],means_pos[2::3]) +print(Ra_mean) +@np.vectorize +def p_z(z): + "redshift probability distribution function for Omega_M = 1" + + def E(z): + return np.sqrt((omega_m*(1+z)**(3) + omega_k*(1+z)**(2) + omega_lambda)) + + def I(z): + fact = lambda x: 1/E(x) + integral = quad(fact, 0, z) + return integral[0] + norm = quad(lambda z: I(z) / E(z), 0, zmax)[0] + result = (1/norm) * (I(z))**(2) / E(z) + return result + +def z_to_dl(z,H): + "distance as a function of z and H" + + def E(z): + return np.sqrt((omega_m*(1+z)**(3) + omega_k*(1+z)**(2) + omega_lambda)) + + def I(z): + fact = lambda x: 1/E(x) + integral = quad(fact, 0, z) + return integral[0] + + dl = (c*(1+z) / H) * I(z) + return dl + +@np.vectorize +def dl_to_z(dl,H): + "redshifts from a look up table using z_to_dl" + + z_grid = np.linspace(0,zmax,10000) + dl_grid = np.zeros(len(z_grid)) + for i in range(len(z_grid)): + dl_grid[i] = z_to_dl(z_grid[i],H) + redshifts = np.interp(dl, dl_grid, z_grid) + return redshifts +# for i in range(len(mean_pos)): +# pos_x = means_pos[i] +# pos_y = means_pos[i+1] +# pos_z = means_pos[i+2] +# cart2spher(pos_x, pos_y, pos_) + +z_means = dl_to_z(dist_mean, 70) +print(z_means) +# %% plot apparent magnitudes +plt.title(r'Apparent Magnitudes') +plt.xlabel(r'$m$') +plt.ylabel(r'$p(m)$') +plt.hist(data.Apparent_m[::1], density=True,bins=100) +#plt.savefig('plots\catalog_mapp.png',dpi=800) +# %% plot absolute magnitudes +plt.title(r'Absolute Magnitudes') +plt.xlabel(r'$M$') +plt.ylabel(r'$p(M)$') +plt.xlim([-5, -22.5]) +plt.hist(data.Absolute_M[::1], density=True,bins=100) +#plt.savefig('plots\catalog_Mabs.png',dpi=800) +# %% plot luminosity distance +plt.title(r'Luminosity Distance') +plt.xlabel(r'$d_{L}$') +plt.ylabel(r'$p(d_{L})$') +plt.hist(data.dist_lum[::1], density=True,bins=100) +#plt.savefig('plots\catalog_dl.png',dpi=800) +# %% plot redshifts +plt.title(r'Redshifts') +plt.xlabel(r'$z$') +plt.ylabel(r'$p(z)$') +plt.hist(data.z[::1], density=True,bins=100) +plt.savefig('plots\catalog_redshifts.png',dpi=800) +# %% plot right ascencions +plt.title(r'Right Ascencion') +plt.xlabel(r'$RA$') +plt.ylabel(r'$p(RA)$') +plt.hist(data.RA[::1], density=True,bins=100) +#plt.savefig('plots\catalog_RA.png',dpi=800) +# %% plot declinations +plt.title(r'Declination') +plt.xlabel(r'$\delta$') +plt.ylabel(r'$p(\delta)$') +plt.hist(data.dec[::1], density=True,bins=100) +#plt.savefig('plots\catalog_dec.png',dpi=800) + +#%% plot redshift distribution +def p_z(z): + "redshift probability distribution function for Omega_M = 1" + omega_m = 0.3; omega_lambda = 0.7 #cosmological parameters + omega_k = 1- omega_lambda - omega_m + def E(z): + return np.sqrt((omega_m*(1+z)**(3) + omega_k*(1+z)**(2) + omega_lambda)) + + def I(z): + fact = lambda x: 1/E(x) + integral = quad(fact, 0, z) + return integral[0] + + return (I(z))**(2) / E(z) + +norm = quad(lambda z: p_z(z), 0, np.max(data.z))[0] +z_sort = np.sort(data.z[::10]) +pz = np.array([p_z(z) for z in z_sort])*(1/norm) +#%% + +fig = plt.subplots() +plt.title(r'Redshifts $\Omega_{m} = 0.3$, $\Omega_{\Lambda} = 0.7$') +plt.xlabel(r'$z$') +plt.ylabel(r'$p(z)$') +weights = np.ones_like(z_sort)/float(len(z_sort)) +hist,bins = np.histogram(z_sort,density=True) +plt.hist(z_sort,density = True,bins=100) +plt.plot(z_sort,pz, '--k', linewidth=2, label=r'$p(z) = \frac{dVc}{dz}$') +plt.legend() +#plt.savefig('Redshift_Hogg_clustered.png',dpi=800) + + +# %% cone plot of redshift and RA +plt.style.use('default') +fig = plt.figure() +ax = fig.add_subplot(111, polar=True) +c = ax.scatter( data.RA[::20]*(np.pi/180),data.z[::20], c='b', s=0.1, cmap='hsv', alpha=0.5) +#c = ax.scatter( Ra_mean*(np.pi/180),z_means, c='r', s=30, cmap='hsv', alpha=1) +plt.savefig('plots\Redshift_RA_clustered.png',dpi=800) +plt.show() +# %% cone plot of redshift and dec +plt.style.use('default') +fig = plt.figure() +ax = fig.add_subplot(111, polar=True) +c = ax.scatter(data.dec[::20]*(np.pi/180), data.z[::20], c='b', s=0.1, cmap='hsv', alpha=1) +ax.set_thetamin(-90) +ax.set_thetamax(90) +plt.show() + + + + + + + + +#%% plot clustered universe x-y +plt.title('XY plane') +plt.ylabel('$d_{y} \\ [Mpc]$') +plt.xlabel('$d_{x} \\ [Mpc]$') +plt.xlim([-3500, 3500]) +plt.ylim([-3500, 3500]) +plt.scatter(dist_cartesian.dx[::10], dist_cartesian.dy[::10],s = 0.1,alpha=0.5) +plt.scatter(means_pos[0::3], means_pos[1::3], s = 20, c='black') +plt.savefig('plots\XY.png',dpi=800) +#%% plot clustered universe x-z +plt.title('XZ plane') +plt.ylabel('$d_{z} \\ [Mpc]$') +plt.xlabel('$d_{x} \\ [Mpc]$') +plt.xlim([-3500, 3500]) +plt.ylim([-3500, 3500]) +plt.scatter(dist_cartesian.dx[::10], dist_cartesian.dz[::10],s = 0.1, alpha=0.5) +plt.scatter(means_pos[0::3], means_pos[2::3], s = 20, c='black') +plt.savefig('plots\XZ.png',dpi=800) +#%% plot clustered universe y-z +plt.title('YZ plane') +plt.ylabel('$d_{z} \\ [Mpc]$') +plt.xlabel('$d_{y} \\ [Mpc]$') +plt.xlim([-3500, 3500]) +plt.ylim([-3500, 3500]) +plt.scatter(dist_cartesian.dy[::10], dist_cartesian.dz[::10],s = 0.1 ,alpha=0.5) +plt.scatter(means_pos[1::3], means_pos[2::3], s = 20, c='black') +plt.savefig('plots\YZ.png',dpi=800) +# %% diff --git a/toy_gwcosmo_v3/scripts/universes/small_uniform_universe.dat b/toy_gwcosmo_v3/scripts/universes/small_uniform_universe.dat new file mode 100644 index 0000000000000000000000000000000000000000..67525278cbbe5b289ad754061902070c00e4dc9b --- /dev/null +++ b/toy_gwcosmo_v3/scripts/universes/small_uniform_universe.dat @@ -0,0 +1,100001 @@ +,RA,dec,dist_lum,z,Apparent_m,Absolute_M +0,61.079253130154854,1.1283694643605588,516.4611963259046,0.1113567629767098,19.869544921020214,-18.69564356348928 +1,156.48979584941708,-0.5581614092092733,3961.6946922177895,0.6596481658562351,37.832640928877474,-5.156764089181962 +2,15.051462781502522,1.0280251590431824,5901.500039157011,0.9125686427764078,27.848794772872058,-16.00601729883684 +3,-49.625694946003335,0.580101047462329,2654.4119303159996,0.4735478705038575,34.232611209417946,-7.887230393738533 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