""" hydro_mc is a python library and executable to perform masses conversions and Concentration fits of haloes in [Magenticum](http://www.magneticum.org) hydrodynamic simulations. These conversions are based on fits presented in the paper Ragagnin et al. (2020, in prep). To use this software, just download the content of this repository. You can use it as an executable via `python hydro_mc.py --help` or as a library inside your python project by including `import hydro_mc`. """ print('hydro_mc loading..') __author__="Antonio Ragagnin (c) 2019" __version__="0.1" import numpy as np import sys import re #start of fit parameters __mc_fit_parameters = {"vir": {"params": [1.503454114104443, -0.04283092691408333, 0.5157209989941997, 0.45445667750331026, -0.24856881467360964, 0.5544350140093234, -0.0048813484527866656, -0.12199409397642753, 0.11663423303800534, 0.05110946208460489, -0.07892747676338406, 0.24005903699741252, -0.1263499637381384, 0.6640188439939326, -0.0299567877892118, 0.3877956797872577], "pivots": {"M": 198759238503196.03, "a": 0.8771929824561403, "omega_m": 0.272, "omega_b": 0.0456, "sigma8": 0.809, "h0": 0.704}}, "200c": {"params": [1.2436364990990914, -0.04817261898156871, 0.20419215885982817, 0.6316820273466903, -0.24605297432854378, 0.560570072125268, -0.02627068018190943, -0.11775877953823762, 0.11193584169417208, 0.05634549061614718, -0.043822582719200295, 0.3524426183203193, -0.03879420539288709, 0.7673900896521332, -0.27569460666976725, 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"pivots": {"M": 68722326105291.2, "a": 0.8771929824561403, "omega_m": 0.272, "omega_b": 0.0456, "sigma8": 0.809, "h0": 0.704}}, "200m": {"params": [1.692410096240174, -0.040346034043160055, 0.9092242875122345, 0.2268328343963277, -0.2664240976376676, 0.5283845428748246, 0.015645163737334208, -0.11627375082296813, 0.11528658344781062, 0.05003254567973524, -0.09358485276497253, -0.04322554482713586, -0.06348838757477149, 0.6351347984085912, -0.40487997854959523, 0.3882554231750548], "pivots": {"M": 224397583007812.53, "a": 0.8771929824561403, "omega_m": 0.272, "omega_b": 0.0456, "sigma8": 0.809, "h0": 0.704}}} __mc_lite_fit_parameters = {"vir": {"params": [1.4985649929244846, -0.04754653951295999, 0.5199383344534508, 0.42335872983250744, -0.14123672388625216, 0.6530026638126829, -0.27667601800841235, 0.18958103942142024, 0.02371146453902725, 0.7637789994055261, -0.44859556264866146, 0.38803081506367154], "pivots": {"M": 198759238503196.03, "a": 0.8771929824561403, "omega_m": 0.272, "omega_b": 0.0456, "sigma8": 0.809, "h0": 0.704}}, "200c": {"params": [1.2382820777898689, -0.053413793724654476, 0.20072654857310923, 0.603607539963483, -0.1521899342583827, 0.6467505386837067, -0.24540931053697695, 0.3595828585445649, -0.14575941582538823, 0.7247582262393436, -0.07329103607606331, 0.3845164814226978], "pivots": {"M": 173960723876953.16, "a": 0.8771929824561403, "omega_m": 0.272, "omega_b": 0.0456, "sigma8": 0.809, "h0": 0.704}}, "500c": {"params": [0.8591961760288123, -0.05970360132842668, 0.18730552659285832, 0.6319223562569485, -0.13145810034048822, 0.6120793998567394, -0.2739015100800711, 0.33628042357787796, -0.04344994933928333, 0.8893178406086549, -0.4363827722023437, 0.3766897270799671], "pivots": {"M": 137038782293146.31, "a": 0.8771929824561403, "omega_m": 0.272, "omega_b": 0.0456, "sigma8": 0.809, "h0": 0.704}}, "2500c": {"params": [0.12248240026576206, -0.03731339714808029, 0.11023256345276963, 0.72734695998088, -0.17862618662088695, 0.5163267659318049, 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0.046829695425163395, -0.26786469607363345, 0.042821693277460486, 0.18179748839481427], "pivots": {"M": 68722326105291.2, "a": 0.8771929824561403, "omega_m": 0.272, "omega_b": 0.0456, "sigma8": 0.809, "h0": 0.704}}, "200m": {"params": [33.449928994127625, 1.0137672613631057, 0.3884270448825958, -0.6945245790633495, 0.07586049305592515, -0.35742671170676377, 0.13516778655853254, 0.07850133213044976, -0.32416434385441756, -0.014257525322939018, 0.44860092910474053, -0.4733572404757807, 0.17635892757694627, -0.7263246721102229, 0.001987326362323298, 0.24683192744384327], "pivots": {"M": 68722326105291.2, "a": 0.8771929824561403, "omega_m": 0.272, "omega_b": 0.0456, "sigma8": 0.809, "h0": 0.704}}} , "200m": {"vir": {"params": [32.91923993459246, 1.004998283710883, -0.24327974796307458, 0.146916873080803, 0.014085866496374992, 0.03403136832842445, -0.05495582811339603, -0.017709014761172495, 0.024922878675272438, -0.022277807902568742, -0.002687549490900499, 0.18766656690092864, -0.015980084879887904, 0.12354164631530422, -0.051383216549240274, -0.04852060193023841], "pivots": {"M": 224397583007812.53, "a": 0.8771929824561403, "omega_m": 0.272, "omega_b": 0.0456, "sigma8": 0.809, "h0": 0.704}}, "200c": {"params": [32.7092432548728, 1.0078543539776024, -0.4923401628810212, 0.317991173206413, 0.013757313724573065, 0.08830533446268542, -0.10310730596591498, -0.035138014465154285, 0.06273672319138414, -0.05014998021686202, -0.010943256393764618, 0.35758349293839736, -0.10227564269822434, 0.24551406258367856, 0.03345997504983831, -0.10235368375951033], "pivots": {"M": 224397583007812.53, "a": 0.8771929824561403, "omega_m": 0.272, "omega_b": 0.0456, "sigma8": 0.809, "h0": 0.704}}, "500c": {"params": [32.30590606420742, 1.0000540537767286, -0.4830289557913123, 0.4458649778490151, -0.013155061128686208, 0.21813115725504514, -0.15948649173162333, -0.06122690436674333, 0.12660113555523209, -0.07277092932568646, -0.04164041554251069, 0.4082628758536285, -0.17486998423199526, 0.47758038193650526, 0.013784564207430024, -0.1814127296908954], "pivots": {"M": 224397583007812.53, "a": 0.8771929824561403, "omega_m": 0.272, "omega_b": 0.0456, "sigma8": 0.809, "h0": 0.704}}, "2500c": {"params": [31.33382470213857, 0.9313085568714797, -0.23360541371644739, 0.7538862738599599, -0.1582096612458364, 0.6036429135207855, -0.11084469907190307, -0.09380588110396984, 0.23204562989471772, -0.04050734632304558, -0.19328155795275154, 0.5642713366169192, -0.29968357150510994, 0.6506712481038401, 0.026156355100851708, -0.3181591586420962], "pivots": {"M": 224397583007812.53, "a": 0.8771929824561403, "omega_m": 0.272, "omega_b": 0.0456, "sigma8": 0.809, "h0": 0.704}}} } #end of fit parameters __fit_parameter_names = ['A0','B0','C0','alpha_m','alpha_b','alpha_sigma','alpha_h','beta_m','beta_b','beta_sigma','beta_h','gamma_m','gamma_b','gamma_sigma','gamma_h','sigma'] __fit_parameter_lite_names = ['A0','B0','C0','alpha_m','alpha_b','alpha_sigma','alpha_h','gamma_m','gamma_b','gamma_sigma','gamma_h','sigma'] __fit_pivot_names = ['M','a','omega_m','omega_b','sigma8','h0'] __deltas = ['200c','500c','2500c','vir','200m'] def panic(x): sys.stderr.write(x+'\n') sys.exit(1) def printf(x): sys.stdout.write(x+'\n') def print_fit_params_and_pivots(table,is_lite=False): iparam=-1 fit_parameter_names = __fit_parameter_names if not is_lite else __fit_parameter_lite_names for parameter in fit_parameter_names: iparam+=1 print(' %s = %.3f'%(parameter, table['params'][iparam])) print('') for pivot in __fit_pivot_names: if pivot in table['pivots']: print(' %s_pivot = %.3f '%(pivot, table['pivots'][pivot])) def print_abc_equation(is_lite=False): print(' A = A0 + alpha_m * ln (Omega_m/Omega_m_pivot) + alpha_b * ln(Omega_b/Omega_b_pivot) + alpha_s * ln(sigma_8/sigma_8_pivot) + alpha_h * ln(h0/h0_pivot) ') if not is_lite: print(' B = B0 + beta_m * ln (Omega_m/Omega_m_pivot) + beta_b * ln(Omega_b/Omega_b_pivot) + beta_s * ln(sigma_8/sigma_8_pivot) + beta_h * ln(h0/h0_pivot) ') else: print (' B = B0') print(' C = C0 + gamma_m * ln (Omega_m/Omega_m_pivot) + gamma_b * ln(Omega_b/Omega_b_pivot) + gamma_s * ln(sigma_8/sigma_8_pivot) + gamma_h * ln(h0/h0_pivot) ') def set_fit_parameters(table, **kw): fit_parameter_values = [] for parameter_name in __fit_parameter_names: if parameter_name in kw and kw[parameter_name] is not None: value = kw[parameter_name] else: value = 0. fit_parameter_values.append(value) table['params']=fit_parameter_values for parameter_name in __fit_pivot_names: if 'pivot_'+parameter_name in kw and kw['pivot_'+parameter_name] is not None: table['pivots'][parameter_name]=kw['pivot_'+parameter_name] def fit_from_ragagnin2019_fit(table, pivots, use_lite_mc_fit=False, **kw): if not use_lite_mc_fit: norm, slopem, slopea, pim , pib, pis, pih, sim, sib, sis, sih, aim, aib, ais, aih, sigma = table else: norm, slopem, slopea, pim , pib, pis, pih, aim, aib, ais, aih, sigma = table logM, loga, logomega_m, logomega_b, logsigma8, logh0 = [np.log(np.array(kw[pivot]) / pivots[pivot]) if pivot in pivots else 0. for pivot in __fit_pivot_names] norm_2 = norm + pim* logomega_m +pib* logomega_b + pis * logsigma8 + pih * logh0 if not use_lite_mc_fit: slopem_2 = slopem +sim* logomega_m +sib* logomega_b + sis* logsigma8 + sih * logh0 else: slopem_2 = slopem slopea_2 = slopea + aim* logomega_m +aib* logomega_b + ais* logsigma8 + aih* logh0 return np.exp(norm_2 + logM*slopem_2 + loga*slopea_2) def concentration_from_mc_relation(delta, M, a, omega_m, omega_b, sigma8, h0, use_lite_mc_fit=False, use_lite_mc_dm_fit=False, show_fit_parameters=False, table=None, **kw): if use_lite_mc_dm_fit and not use_lite_mc_fit: raise Exception('If you activate use_lite_mc_dm_fit= you must also activate use_lite_mc_fit=True') if table is None: if use_lite_mc_fit and use_lite_mc_dm_fit: table = __mc_dm_lite_fit_parameters[delta] elif use_lite_mc_fit: table = __mc_lite_fit_parameters[delta] else: table = __mc_fit_parameters[delta] if show_fit_parameters: print(' MC relation fit: ') print(' ln(c_delta) = A + B ln(M_delta/Mp) + C ln(a/ap) ') use_lite_mc_fit and use_lite_mc_dm_fit and printf('\n Dark matter concentration with lite parametrisation: ') and print_abc_equation(is_lite=True) use_lite_mc_fit and not use_lite_mc_dm_fit and printf('\n Total matter oncentration with lite parameters: ') and print_abc_equation(is_lite=True) use_lite_mc_fit and not use_lite_mc_dm_fit and printf('\n Total matter oncentration: ') and print_abc_equation() print(' Delta = %s'% delta) print_fit_params_and_pivots(table,is_lite= use_lite_mc_fit) return fit_from_ragagnin2019_fit( table['params'], table['pivots'],use_lite_mc_fit=use_lite_mc_fit, M=M,a=a,omega_m=omega_m, omega_b=omega_b, sigma8=sigma8, h0=h0, **kw) def mass_from_mm_relation(delta_from, delta_to, M, a, omega_m, omega_b, sigma8, h0, show_fit_parameters=False, table=None, **kw): if show_fit_parameters: print_fit_params_and_pivots(__mm_fit_parameters[delta_from][delta_to]) if table is None: print(__mm_fit_parameters.keys()) print(__mm_fit_parameters[delta_from].keys()) table = __mm_fit_parameters[delta_from][delta_to] print(table) return fit_from_ragagnin2019_fit( table['params'], table['pivots'], M=M,a=a,omega_m=omega_m, omega_b=omega_b, sigma8=sigma8, h0=h0, **kw) def Omega(a, Omega_M, Omegar, Omegak, Omegal): return Omega_M * a**-3. / (Omega_M * a**-3. + Omegar * a**-4. + Omegak * a**-2. + Omegal) def delta_c(a, Omega_M, Omegar, Omegak, Omegal): Omegaz = Omega(a, Omega_M, Omegar, Omegak, Omegal) x = Omegaz -1. return (18. * np.pi **2. + 82. * x - 39. * x**2.) #/ Omegaz; def f_NFW(c): return (np.log(1.+c)-c/(1.+c)) def banach_caccioppoli(f,x0,accuracy=0.001): """ this function solves equation of the kind x=f(x) by iterations, given an initial value x=x0""" condition=True x1=x0 steps=0 while condition: steps+=1 x2 = f(x1) error = np.abs(x2-x1)/x2 condition = np.all(error>accuracy) x1=x2 return x2 print('a9') def critical_overdensity(delta, **args): if delta=='vir': if('a' not in args or args['a'] is None or 'omega_m' not in args or args['omega_m'] is None): raise Exception("You need to provide parameters a and omega_m if you use a delta==vir") return delta_c(args['a'], args['omega_m'], 0., 0., 1.- args['omega_m']) elif 'c' in delta: return float(delta[:-1]) else: raise Exception("Critical overdensity cannot be obtained from %s",delta) def cdelta1(delta2,delta1,cdelta1, f_NFW=f_NFW): return lambda cdelta2: cdelta1 * ( (delta1/delta2)*(f_NFW(cdelta2)/f_NFW(cdelta1)) )**(1./3.) def c2_bc(delta2, delta1, c1, f_NFW=f_NFW): c2 = banach_caccioppoli( cdelta1(delta2, delta1, c1, f_NFW = f_NFW), c1) return c2 def HK_func(x): log = np.log return(x*x*x*(log(1+1.0/x)-1.0/(1+x))); def HK_1(delta, delta_vir, cvir): log = np.log sqrt=np.sqrt a1 = 0.5116 a2 = -0.4283 a3 = -3.13E-3 a4 = -3.52E-5 f=delta/delta_vir*HK_func(1.0/cvir); p=a2+a3*log(f)+a4*log(f)*log(f); x1=1.0/sqrt(a1*(f**(2.*p))+0.5625)+2*f; return 1./x1 def convert_concentration(delta_from, delta_to, concentration, f_profile=None, c_hu_kratsov_2002=False, **kw): overdensity_from = critical_overdensity(delta_from, **kw) overdensity_to = critical_overdensity(delta_to, **kw) if not c_hu_kratsov_2002: if f_profile is None: f_profile = f_NFW return c2_bc(overdensity_to, overdensity_from, concentration, f_NFW=f_profile) else: return HK_1(overdensity_to, overdensity_from, concentration) def mass_from_m_and_c(delta_from, delta_to, concentration, **kw): c = concentration overdensity_from = critical_overdensity(delta_from, **kw) overdensity_to = critical_overdensity(delta_to, **kw) new_c = c2_bc(overdensity_to, overdensity_from, c) return kw['M'] * (overdensity_to/overdensity_from)*(new_c/c)**3. def mass_from_mc_relation(delta_from, delta_to, M, a, omega_m, omega_b, sigma8, h0, **kw): overdensity_from = critical_overdensity(delta_from, **kw) overdensity_to = critical_overdensity(delta_to, **kw) c = concentration_from_mc_relation(delta_from, M, a, omega_m, omega_b, sigma8, h0, **kw) new_c = c2_bc(overdensity_to, overdensity_from, c) M = M* (overdensity_to/overdensity_from)*(new_c/c)**3. return M def split_kv(a,d, names,prekey=''): for arg in a: if '=' not in arg: raise Exception('Values must be key/values separated by "=", found %s'%arg) k,v = arg.split('=') if k not in names: raise Exception('Parameter is not a valid key=value pair. Found "%s" but should be one of %s'%(k, ', '.join(names))) try: d[prekey+k]=float(v) except Exception as e: raise Exception('Value must be floats, in "%s" found "%s"'%(arg, v)) print('hydro_mc loaded..')