[c@`s^ddlmZmZmZmZddlmZddlmZddl Z ddl m Z m Z m Z mZmZddlmZmZddlZdd lmZdd lmZdd lmZdd lmZdd lmZddlm Z ddlm!Z!ddddddddddg e!j"Z#idgd6Z$ej%ej&ej'j(dej&Z)ej&j(ej*Z+dde ej,j-dZ.e d d!Z/e d"d!Z0d#ej1j-ej2j-d$Z3ej4j(ej5ej6Z7d%e8fd&YZ9d'e:fd(YZ;ej<ed)e;fd*YZ=d+e=fd,YZ>d-e>fd.YZ?d/e=fd0YZ@d1e@fd2YZAd3e=fd4YZBd5eBfd6YZCd7e=fd8YZDd9e=fd:YZEd$d;ZFd<ZGx1e!j"D]&ZHeIe!eHZJeJd=re?eJd>eJd?d@eJdAdBeJdCdDejKeJdEej5dFeHdGeJdHZLdIZMeMjNeHeJdJeL_Onze>eJd>eJd?eJdKd@eJdAdBeJdCdDejKeJdEej5dFeHdGeJdHZLdLZMeMjNeHeJdJeL_OePe jQeReHeLqW[H[J[LdMe fdNYZSdS(Oi(tabsolute_importtdivisiontprint_functiontunicode_literalsi(tsix(tmapN(tsqrttpitexptlogtfloor(tABCMetatabstractmethodi(tscalar_inv_efuncs(t constants(tunits(t isiterable(t signature(t ScienceState(t parametersuFLRWu LambdaCDMu FlatLambdaCDMuwCDMuFlatwCDMu Flatw0waCDMuw0waCDMuwpwaCDMuw0wzCDMudefault_cosmologyuscipy.integrateu*g?g@g @ig @igN@gMbp?itCosmologyErrorcB`seZRS((t__name__t __module__(((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRVst CosmologycB`seZdZRS(uI Placeholder for when a more general Cosmology class is implemented. (RRt__doc__(((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRZstFLRWcB`seZdZddejdejdAdAdZdZdZ e dZ e dZ e d Z e d Ze d Ze d Ze d Ze dZe dZe dZe dZe dZe dZe dZe dZe dZe dZdZedZdZdZ dZ!dZ"dZ#dZ$d Z%d!Z&d"Z'd#Z(d$Z)d%Z*d&Z+d'Z,d(Z-d)Z.d*Z/d+Z0d,Z1d-Z2d.Z3d/Z4d0Z5d1Z6d2Z7d3Z8d4Z9d5Z:d6Z;d7Z<d8Z=d9Z>d:Z?d;Z@d<ZAd=ZBd>ZCd?ZDd@ZERS(Bu A class describing an isotropic and homogeneous (Friedmann-Lemaitre-Robertson-Walker) cosmology. This is an abstract base class -- you can't instantiate examples of this class, but must work with one of its subclasses such as `LambdaCDM` or `wCDM`. Parameters ---------- H0 : float or scalar `~astropy.units.Quantity` Hubble constant at z = 0. If a float, must be in [km/sec/Mpc] Om0 : float Omega matter: density of non-relativistic matter in units of the critical density at z=0. Note that this does not include massive neutrinos. Ode0 : float Omega dark energy: density of dark energy in units of the critical density at z=0. Tcmb0 : float or scalar `~astropy.units.Quantity`, optional Temperature of the CMB z=0. If a float, must be in [K]. Default: 0 [K]. Setting this to zero will turn off both photons and neutrinos (even massive ones). Neff : float, optional Effective number of Neutrino species. Default 3.04. m_nu : `~astropy.units.Quantity`, optional Mass of each neutrino species. If this is a scalar Quantity, then all neutrino species are assumed to have that mass. Otherwise, the mass of each species. The actual number of neutrino species (and hence the number of elements of m_nu if it is not scalar) must be the floor of Neff. Typically this means you should provide three neutrino masses unless you are considering something like a sterile neutrino. Ob0 : float or None, optional Omega baryons: density of baryonic matter in units of the critical density at z=0. If this is set to None (the default), any computation that requires its value will raise an exception. name : str, optional Name for this cosmological object. Notes ----- Class instances are static -- you can't change the values of the parameters. That is, all of the attributes above are read only. igRQ@gc C`st||_|jdkr-tdnt||_|dk rt||_|jdkrutdn|j|jkrtdn|j|j|_nd|_d|_t||_|jdkrtdn||_t j |dt j dt j|_ |j js3tdnt j |dt jt jt jdt j|_|jjstd n|jjd |_tj|jjt j|_|jjt} t j t| t j|_t| d } t j | t jt jd |_ t!t"|j|_#t$|_%|j#d kr|j jd kr|j|j#|_&t'|t j stdn|jt j(dt j)}|jr|jd kr|j#|_*d |_+qt,|_%d |_*|j#|_+|jt j-|j#|_.q|jj/d kr4tdn|jj0d kra|j#|_*d |_+qt,|_%t1||j#krd} t| nt1t j2|jd kd |_*|j#|j*|_+t j2|jd kd } || |_.n|j jd krt3|j jd|j j|_4d|j |_5|j%r|j.t6|j5} | j|_7|j7j8|_9|j4|j:d |_;qd|j|j4|_;n*d|_4t j dt j |_5d|_;d|j|j|j4|j;|_<|j=|_>d|_?dS(Ngu"Matter density can not be negativeu$Baryonic density can not be negativeu<Baryonic density can not be larger than total matter densityu1Effective number of neutrinos can not be negativetunittdtypeuTcmb0 is a non-scalar quantityuH0 is a non-scalar quantitygY@iiium_nu must be a Quantityt equivalenciesu,Invalid (negative) neutrino mass encounteredu$Unexpected number of neutrino massesigrv}+?gC?g?((@tfloatt_Om0t ValueErrort_Ode0tNonet_Ob0t_Odm0t_NefftnametutQuantitytKtnpt_Tcmb0tisscalartkmtstMpct_H0tvaluet_htconsttcttot_hubble_distancetH0units_to_invst sec_to_GyrtGyrt _hubble_timetcritdens_consttgtcmt_critical_density0tintR t _nneutrinostFalset _massivenut _neff_per_nut isinstanceteVt mass_energyt _nmasslessnut _nmassivenutTruetonest_massivenu_masstmintmaxtlentnonzerota_B_c2t_Ogamma0t_Tnu0tkB_evKt_nu_yttolistt _nu_y_listtnu_relative_densityt_Onu0t_Ok0t inv_efunct_inv_efunc_scalart_inv_efunc_scalar_args(tselftH0tOm0tOde0tTcmb0tNefftm_nutOb0R%tH0_stcd0valueterrstrtwtnu_y((s5lib/python2.7/site-packages/astropy/cosmology/core.pyt__init__s    $ 2 # !         %    % cC`s?|jdkr"dj|jjSdj|jj|jSdS(u* Helper function for constructing __repr__u{0}(u{0}(name="{1}", N(R%R!tformatt __class__R(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pyt _namelead+sc C`sId}|j|j|j|j|j|j|j|jt|j S(Nu[{0}H0={1:.3g}, Om0={2:.3g}, Ode0={3:.3g}, Tcmb0={4:.4g}, Neff={5:.3g}, m_nu={6}, Ob0={7:s})( RjRlR/RR R*R$Rbt_float_or_noneR"(R\tretstr((s5lib/python2.7/site-packages/astropy/cosmology/core.pyt__repr__3s!cC`s|jS(uB Return the Hubble constant as an `~astropy.units.Quantity` at z=0(R/(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR]>scC`s|jS(u5 Omega matter; matter density/critical density at z=0(R(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR^CscC`s|jS(u? Omega dark energy; dark energy density/critical density at z=0(R (R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR_HscC`s|jS(u> Omega baryon; baryonic matter density/critical density at z=0(R"(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRcMscC`s|jS(u? Omega dark matter; dark matter density/critical density at z=0(R#(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pytOdm0RscC`s|jS(uQ Omega curvature; the effective curvature density/critical density at z=0(RX(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pytOk0WscC`s|jS(u; Temperature of the CMB as `~astropy.units.Quantity` at z=0(R*(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR`]scC`s|jS(uK Temperature of the neutrino background as `~astropy.units.Quantity` at z=0(RQ(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pytTnu0bscC`s|jS(u% Number of effective neutrino species(R$(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRagscC`s|jjdkrtS|jS(u@ Does this cosmology have at least one massive neutrino species?i(RQR0R@RA(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pythas_massive_nulscC`s|jjdkrdS|jsGtjtj|jtj dtj S|jdkrutj|j tj dtj Stj tj|j|j j}tj|tj dtj S(u Mass of neutrino speciesiRN( RQR0R!RAR&R'R)tzerosRFRDRRJtappend(R\tnumass((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRbss   cC`s|jS(u: Dimensionless Hubble constant: h = H_0 / 100 [km/sec/Mpc](R1(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pythscC`s|jS(u) Hubble time as `~astropy.units.Quantity`(R9(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pyt hubble_timescC`s|jS(u- Hubble distance as `~astropy.units.Quantity`(R5(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pythubble_distancescC`s|jS(u5 Critical density as `~astropy.units.Quantity` at z=0(R=(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pytcritical_density0scC`s|jS(u< Omega gamma; the density/critical density of photons at z=0(RP(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pytOgamma0scC`s|jS(u; Omega nu; the density/critical density of neutrinos at z=0(RW(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pytOnu0scK`st|dkr|St|jjj}i}xZ|D]R}yt||}|||}||krd}t|j|n||||>> from astropy.cosmology import Planck13 >>> newcos = Planck13.clone(name="Modified Planck 2013", Om0=0.35) iuObject did not have property corresponding to constructor argument '{}'; perhaps it is a user provided subclass that does not do souDUser provided argument '{}' not found in constructor for this object( RMRRiRtkeystgetattrtAttributeErrorRjRk(R\tkwargstarglisttargdicttargtvalRftnewarg((s5lib/python2.7/site-packages/astropy/cosmology/core.pytclones"    cC`stddS(u6 The dark energy equation of state. Parameters ---------- z : array-like Input redshifts. Returns ------- w : ndarray, or float if input scalar The dark energy equation of state Notes ----- The dark energy equation of state is defined as :math:`w(z) = P(z)/\rho(z)`, where :math:`P(z)` is the pressure at redshift z and :math:`\rho(z)` is the density at redshift z, both in units where c=1. This must be overridden by subclasses. uw(z) is not implementedN(tNotImplementedError(R\tz((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRgscC`sBt|rtj|}n|jd|d|j|dS(u Return the density parameter for non-relativistic matter at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Returns ------- Om : ndarray, or float if input scalar The density of non-relativistic matter relative to the critical density at each redshift. Notes ----- This does not include neutrinos, even if non-relativistic at the redshift of interest; see `Onu`. g?ii(RR)tasarrayRRY(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytOms cC`s`|jdkrtdnt|r<tj|}n|jd|d|j|dS(u Return the density parameter for baryonic matter at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Returns ------- Ob : ndarray, or float if input scalar The density of baryonic matter relative to the critical density at each redshift. Raises ------ ValueError If Ob0 is None. u)Baryon density not set for this cosmologyg?iiN(R"R!RRR)RRY(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytObs  cC`s`|jdkrtdnt|r<tj|}n|jd|d|j|dS(u5 Return the density parameter for dark matter at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Returns ------- Odm : ndarray, or float if input scalar The density of non-relativistic dark matter relative to the critical density at each redshift. Raises ------ ValueError If Ob0 is None. Notes ----- This does not include neutrinos, even if non-relativistic at the redshift of interest. uSBaryonic density not set for this cosmology, unclear meaning of dark matter densityg?iiN(R#R!RRR)RRY(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytOdm,s  cC`st|rOtj|}|jdkrbtjtj|jdtjSn|jdkrbdS|jd|d|j|dS(uN Return the equivalent density parameter for curvature at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Returns ------- Ok : ndarray, or float if input scalar The equivalent density parameter for curvature at each redshift. iRgg?i( RR)RRXRtt asanyarraytshapeRRY(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytOkKs %cC`st|rOtj|}|jdkrbtjtj|jdtjSn|jdkrbdS|j|j||j |dS(ua Return the density parameter for dark energy at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Returns ------- Ode : ndarray, or float if input scalar The density of non-relativistic matter relative to the critical density at each redshift. iRgi( RR)RR RtRRRtde_density_scaleRY(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytOdees %cC`sBt|rtj|}n|jd|d|j|dS(uW Return the density parameter for photons at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Returns ------- Ogamma : ndarray, or float if input scalar The energy density of photons relative to the critical density at each redshift. g?ii(RR)RRPRY(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytOgammas cC`s|t|rOtj|}|jdkrbtjtj|jdtjSn|jdkrbdS|j||j |S(u, Return the density parameter for neutrinos at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Returns ------- Onu : ndarray, or float if input scalar The energy density of neutrinos relative to the critical density at each redshift. Note that this includes their kinetic energy (if they have mass), so it is not equal to the commonly used :math:`\sum \frac{m_{\nu}}{94 eV}`, which does not include kinetic energy. iRg( RR)RRWRtRRRRRV(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytOnus %cC`s-t|rtj|}n|jd|S(u Return the CMB temperature at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Returns ------- Tcmb : `~astropy.units.Quantity` The temperature of the CMB in K. g?(RR)RR*(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytTcmbs cC`s-t|rtj|}n|jd|S(u  Return the neutrino temperature at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Returns ------- Tnu : `~astropy.units.Quantity` The temperature of the cosmic neutrino background in K. g?(RR)RRQ(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytTnus c C`sd}|jsYtj|r)||jS||jtjtj|jdtjSnd}d}d}tj|}|j dtj |dd}d||||}|j d|j }||j |S( uV Neutrino density function relative to the energy density in photons. Parameters ---------- z : array like Redshift Returns ------- f : ndarray, or float if z is scalar The neutrino density scaling factor relative to the density in photons at each redshift Notes ----- The density in neutrinos is given by .. math:: \rho_{\nu} \left(a\right) = 0.2271 \, N_{eff} \, f\left(m_{\nu} a / T_{\nu 0} \right) \, \rho_{\gamma} \left( a \right) where .. math:: f \left(y\right) = \frac{120}{7 \pi^4} \int_0^{\infty} \, dx \frac{x^2 \sqrt{x^2 + y^2}} {e^x + 1} assuming that all neutrino species have the same mass. If they have different masses, a similar term is calculated for each one. Note that f has the asymptotic behavior :math:`f(0) = 1`. This method returns :math:`0.2271 f` using an analytical fitting formula given in Komatsu et al. 2011, ApJS 192, 18. gC?RgHzG?g'|?gTN?g?taxisi(RAR)R+R$RIRRRRRSt expand_dimstsumRFRB( R\Rtprefactptinvptkt curr_nu_yt rel_mass_pertrel_mass((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRVs0   & cC`s!t|d}d|j|S(u1 Internal convenience function for w(z) integral.g?(RRg(R\tln1pzR((s5lib/python2.7/site-packages/astropy/cosmology/core.pyt _w_integrandsc C`sddlm}t|r{tj|}tjg|D])}||jdtd|d^q8}tjd|S||jdtd|d}td|SdS(u" Evaluates the redshift dependence of the dark energy density. Parameters ---------- z : array-like Input redshifts. Returns ------- I : ndarray, or float if input scalar The scaling of the energy density of dark energy with redshift. Notes ----- The scaling factor, I, is defined by :math:`\rho(z) = \rho_0 I`, and is given by .. math:: I = \exp \left( 3 \int_{a}^1 \frac{ da^{\prime} }{ a^{\prime} } \left[ 1 + w\left( a^{\prime} \right) \right] \right) It will generally helpful for subclasses to overload this method if the integral can be done analytically for the particular dark energy equation of state that they implement. i(tquadiiN( tscipy.integrateRRR)RtarrayRR R(R\RRtredshifttival((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR#s'  6#cC`st|rtj|}n|j|j|j}}}|jra|jd|j|}n|j|j }d|}tj |d|||||||j |S(u Function used to calculate H(z), the Hubble parameter. Parameters ---------- z : array-like Input redshifts. Returns ------- E : ndarray, or float if input scalar The redshift scaling of the Hubble constant. Notes ----- The return value, E, is defined such that :math:`H(z) = H_0 E`. It is not necessary to override this method, but if de_density_scale takes a particularly simple form, it may be advantageous to. ig?i( RR)RRR RXRARPRVRWRR(R\RR^R_RqtOrtzp1((s5lib/python2.7/site-packages/astropy/cosmology/core.pytefuncUs   !cC`st|rtj|}n|j|j|j}}}|jra|jd|j|}n|j|j }d|}|d|||||||j |dS(uInverse of efunc. Parameters ---------- z : array-like Input redshifts. Returns ------- E : ndarray, or float if input scalar The redshift scaling of the inverse Hubble constant. ig?ig( RR)RRR RXRARPRVRWR(R\RR^R_RqRR((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRYws   cC`s!|j}|j||d|S(u# Integrand of the lookback time. Parameters ---------- z : float Input redshift. Returns ------- I : float The integrand for the lookback time References ---------- Eqn 30 from Hogg 1999. g?(R[RZ(R\Rtargs((s5lib/python2.7/site-packages/astropy/cosmology/core.pyt_lookback_time_integrand_scalars cC`s=t|r"dtj|}n d|}|j||S(u: Integrand of the lookback time. Parameters ---------- z : float or array-like Input redshift. Returns ------- I : float or array The integrand for the lookback time References ---------- Eqn 30 from Hogg 1999. g?(RR)RRY(R\RR((s5lib/python2.7/site-packages/astropy/cosmology/core.pytlookback_time_integrands  cC`s%|j}d|d|j||S(u2 Integrand of the absorption distance. Parameters ---------- z : float Input redshift. Returns ------- X : float The integrand for the absorption distance References ---------- See Hogg 1999 section 11. g?i(R[RZ(R\RR((s5lib/python2.7/site-packages/astropy/cosmology/core.pyt_abs_distance_integrand_scalars cC`sAt|r"dtj|}n d|}|d|j|S(uD Integrand of the absorption distance. Parameters ---------- z : float or array Input redshift. Returns ------- X : float or array The integrand for the absorption distance References ---------- See Hogg 1999 section 11. g?i(RR)RRY(R\RR((s5lib/python2.7/site-packages/astropy/cosmology/core.pytabs_distance_integrands  cC`s|j|j|S(u  Hubble parameter (km/s/Mpc) at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Returns ------- H : `~astropy.units.Quantity` Hubble parameter at each input redshift. (R/R(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytHscC`s*t|rtj|}ndd|S(uA Scale factor at redshift ``z``. The scale factor is defined as :math:`a = 1 / (1 + z)`. Parameters ---------- z : array-like Input redshifts. Returns ------- a : ndarray, or float if input scalar Scale factor at each input redshift. g?(RR)R(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pyt scale_factors c`s6ddlmfd}jt||S(u Lookback time in Gyr to redshift ``z``. The lookback time is the difference between the age of the Universe now and the age at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Must be 1D or scalar Returns ------- t : `~astropy.units.Quantity` Lookback time in Gyr to each input redshift. See Also -------- z_at_value : Find the redshift corresponding to a lookback time. i(Rc`sjd|dS(Ni(R(tred(RR\(s5lib/python2.7/site-packages/astropy/cosmology/core.pyt(s(RRR9tvectorize_if_needed(R\Rtf((RR\s5lib/python2.7/site-packages/astropy/cosmology/core.pyt lookback_timescC`s |j|tjjtjS(u The lookback distance is the light travel time distance to a given redshift. It is simply c * lookback_time. It may be used to calculate the proper distance between two redshifts, e.g. for the mean free path to ionizing radiation. Parameters ---------- z : array-like Input redshifts. Must be 1D or scalar Returns ------- d : `~astropy.units.Quantity` Lookback distance in Mpc (RR2R3R4R&R.(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytlookback_distance+sc`s6ddlmfd}jt||S(u Age of the universe in Gyr at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Must be 1D or scalar. Returns ------- t : `~astropy.units.Quantity` The age of the universe in Gyr at each input redshift. See Also -------- z_at_value : Find the redshift corresponding to an age. i(Rc`sj|tjdS(Ni(RR)tinf(R(RR\(s5lib/python2.7/site-packages/astropy/cosmology/core.pyRQs (RRR9R(R\RR((RR\s5lib/python2.7/site-packages/astropy/cosmology/core.pytage>scC`s|j|j|dS(u" Critical density in grams per cubic cm at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Returns ------- rho : `~astropy.units.Quantity` Critical density in g/cm^3 at each input redshift. i(R=R(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytcritical_densityUscC`s|jd|S(u Comoving line-of-sight distance in Mpc at a given redshift. The comoving distance along the line-of-sight between two objects remains constant with time for objects in the Hubble flow. Parameters ---------- z : array-like Input redshifts. Must be 1D or scalar. Returns ------- d : `~astropy.units.Quantity` Comoving distance in Mpc to each input redshift. i(t_comoving_distance_z1z2(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytcomoving_distanceesc`s9ddlmfd}jt|||S(u Comoving line-of-sight distance in Mpc between objects at redshifts z1 and z2. The comoving distance along the line-of-sight between two objects remains constant with time for objects in the Hubble flow. Parameters ---------- z1, z2 : array-like, shape (N,) Input redshifts. Must be 1D or scalar. Returns ------- d : `~astropy.units.Quantity` Comoving distance in Mpc between each input redshift. i(Rc`s j||djdS(NRi(RZR[(tz1tz2(RR\(s5lib/python2.7/site-packages/astropy/cosmology/core.pyRs(RRR5R(R\RRR((RR\s5lib/python2.7/site-packages/astropy/cosmology/core.pyRzscC`s|jd|S(u Comoving transverse distance in Mpc at a given redshift. This value is the transverse comoving distance at redshift ``z`` corresponding to an angular separation of 1 radian. This is the same as the comoving distance if omega_k is zero (as in the current concordance lambda CDM model). Parameters ---------- z : array-like Input redshifts. Must be 1D or scalar. Returns ------- d : `~astropy.units.Quantity` Comoving transverse distance in Mpc at each input redshift. Notes ----- This quantity also called the 'proper motion distance' in some texts. i(t"_comoving_transverse_distance_z1z2(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytcomoving_transverse_distancescC`s|j}|j||}|dkr+|Stt|}|j}|dkru||tj||j|jS||tj||j|jSdS(uComoving transverse distance in Mpc between two redshifts. This value is the transverse comoving distance at redshift ``z2`` as seen from redshift ``z1`` corresponding to an angular separation of 1 radian. This is the same as the comoving distance if omega_k is zero (as in the current concordance lambda CDM model). Parameters ---------- z1, z2 : array-like, shape (N,) Input redshifts. Must be 1D or scalar. Returns ------- d : `~astropy.units.Quantity` Comoving transverse distance in Mpc between input redshift. Notes ----- This quantity is also called the 'proper motion distance' in some texts. iN( RXRRtabsR5R)tsinhR0tsin(R\RRRqtdctsqrtOk0tdh((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRs    #cC`s3t|rtj|}n|j|d|S(uB Angular diameter distance in Mpc at a given redshift. This gives the proper (sometimes called 'physical') transverse distance corresponding to an angle of 1 radian for an object at redshift ``z``. Weinberg, 1972, pp 421-424; Weedman, 1986, pp 65-67; Peebles, 1993, pp 325-327. Parameters ---------- z : array-like Input redshifts. Must be 1D or scalar. Returns ------- d : `~astropy.units.Quantity` Angular diameter distance in Mpc at each input redshift. g?(RR)RR(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytangular_diameter_distances cC`s3t|rtj|}nd||j|S(u Luminosity distance in Mpc at redshift ``z``. This is the distance to use when converting between the bolometric flux from an object at redshift ``z`` and its bolometric luminosity. Parameters ---------- z : array-like Input redshifts. Must be 1D or scalar. Returns ------- d : `~astropy.units.Quantity` Luminosity distance in Mpc at each input redshift. See Also -------- z_at_value : Find the redshift corresponding to a luminosity distance. References ---------- Weinberg, 1972, pp 420-424; Weedman, 1986, pp 60-62. g?(RR)RR(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytluminosity_distances cC`s6tj|}tj|}|j||d|S(u Angular diameter distance between objects at 2 redshifts. Useful for gravitational lensing. Parameters ---------- z1, z2 : array-like, shape (N,) Input redshifts. z2 must be large than z1. Returns ------- d : `~astropy.units.Quantity`, shape (N,) or single if input scalar The angular diameter distance between each input redshift pair. g?(R)RR(R\RR((s5lib/python2.7/site-packages/astropy/cosmology/core.pytangular_diameter_distance_z1z2 sc`s/ddlmfd}t||S(up Absorption distance at redshift ``z``. This is used to calculate the number of objects with some cross section of absorption and number density intersecting a sightline per unit redshift path. Parameters ---------- z : array-like Input redshifts. Must be 1D or scalar. Returns ------- d : float or ndarray Absorption distance (dimensionless) at each input redshift. References ---------- Hogg 1999 Section 11. (astro-ph/9905116) Bahcall, John N. and Peebles, P.J.E. 1969, ApJ, 156L, 7B i(Rc`sjd|dS(Ni(R(R(RR\(s5lib/python2.7/site-packages/astropy/cosmology/core.pyR7s(RRR(R\RR((RR\s5lib/python2.7/site-packages/astropy/cosmology/core.pytabsorption_distancescC`s<dtjt|j|jd}tj|tjS(u Distance modulus at redshift ``z``. The distance modulus is defined as the (apparent magnitude - absolute magnitude) for an object at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Must be 1D or scalar. Returns ------- distmod : `~astropy.units.Quantity` Distance modulus at each input redshift, in magnitudes See Also -------- z_at_value : Find the redshift corresponding to a distance modulus. g@g9@(R)tlog10RRR0R&R'tmag(R\RR((s5lib/python2.7/site-packages/astropy/cosmology/core.pytdistmod:s)cC`s|j}|dkr.d t|j|dS|jj}|j|j}dt|dd|tjd}||tj d|||d}t t |||}|dkr||dt t |tj |S||dt t |tj |Sd S( u Comoving volume in cubic Mpc at redshift ``z``. This is the volume of the universe encompassed by redshifts less than ``z``. For the case of omega_k = 0 it is a sphere of radius `comoving_distance` but it is less intuitive if omega_k is not 0. Parameters ---------- z : array-like Input redshifts. Must be 1D or scalar. Returns ------- V : `~astropy.units.Quantity` Comoving volume in :math:`Mpc^3` at each input redshift. ig@g@ig@iig?NgUUUUUU?( RXRRR5R0RR&R.R)RRtarcsinhtarcsin(R\RRqRtdmtterm1tterm2tterm3((s5lib/python2.7/site-packages/astropy/cosmology/core.pytcomoving_volumeVs   %' )cC`sN|j}|j|}d|}|||dtj|j|tjS(uDifferential comoving volume at redshift z. Useful for calculating the effective comoving volume. For example, allows for integration over a comoving volume that has a sensitivity function that changes with redshift. The total comoving volume is given by integrating differential_comoving_volume to redshift z and multiplying by a solid angle. Parameters ---------- z : array-like Input redshifts. Returns ------- dV : `~astropy.units.Quantity` Differential comoving volume per redshift per steradian at each input redshift.g?g@(R5RR&R'Rt steradian(R\RRtdaR((s5lib/python2.7/site-packages/astropy/cosmology/core.pytdifferential_comoving_volumexs   !cC`s$|j|jtjttjS(u Separation in transverse comoving kpc corresponding to an arcminute at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Must be 1D or scalar. Returns ------- d : `~astropy.units.Quantity` The distance in comoving kpc corresponding to an arcmin at each input redshift. (RR4R&tkpctarcmin_in_radianstarcmin(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytkpc_comoving_per_arcminscC`s$|j|jtjttjS(u Separation in transverse proper kpc corresponding to an arcminute at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Must be 1D or scalar. Returns ------- d : `~astropy.units.Quantity` The distance in proper kpc corresponding to an arcmin at each input redshift. (RR4R&RRR(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytkpc_proper_per_arcminscC`s$tj|j|jtjtS(u Angular separation in arcsec corresponding to a comoving kpc at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Must be 1D or scalar. Returns ------- theta : `~astropy.units.Quantity` The angular separation in arcsec corresponding to a comoving kpc at each input redshift. (R&tarcsecRR4Rtarcsec_in_radians(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytarcsec_per_kpc_comovingscC`s$tj|j|jtjtS(u Angular separation in arcsec corresponding to a proper kpc at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Must be 1D or scalar. Returns ------- theta : `~astropy.units.Quantity` The angular separation in arcsec corresponding to a proper kpc at each input redshift. (R&RRR4RR(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pytarcsec_per_kpc_propersN(FRRRR&R'RDR!RiRlRotpropertyR]R^R_RcRpRqR`RrRaRsRbRwRxRyRzR{R|RR RgRRRRRRRRRRVRRRRYRRRRRRRRRRRRRRRRRRRRRRRRR(((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR_s~5!   =          G 2 "               %      "    t LambdaCDMcB`sYeZdZddejdejd d dZdZdZ dZ dZ RS( utFLRW cosmology with a cosmological constant and curvature. This has no additional attributes beyond those of FLRW. Parameters ---------- H0 : float or `~astropy.units.Quantity` Hubble constant at z = 0. If a float, must be in [km/sec/Mpc] Om0 : float Omega matter: density of non-relativistic matter in units of the critical density at z=0. Ode0 : float Omega dark energy: density of the cosmological constant in units of the critical density at z=0. Tcmb0 : float or scalar `~astropy.units.Quantity`, optional Temperature of the CMB z=0. If a float, must be in [K]. Default: 0 [K]. Setting this to zero will turn off both photons and neutrinos (even massive ones). Neff : float, optional Effective number of Neutrino species. Default 3.04. m_nu : `~astropy.units.Quantity`, optional Mass of each neutrino species. If this is a scalar Quantity, then all neutrino species are assumed to have that mass. Otherwise, the mass of each species. The actual number of neutrino species (and hence the number of elements of m_nu if it is not scalar) must be the floor of Neff. Typically this means you should provide three neutrino masses unless you are considering something like a sterile neutrino. Ob0 : float or None, optional Omega baryons: density of baryonic matter in units of the critical density at z=0. If this is set to None (the default), any computation that requires its value will raise an exception. name : str, optional Name for this cosmological object. Examples -------- >>> from astropy.cosmology import LambdaCDM >>> cosmo = LambdaCDM(H0=70, Om0=0.3, Ode0=0.7) The comoving distance in Mpc at redshift z: >>> z = 0.5 >>> dc = cosmo.comoving_distance(z) igRQ@gc C`stj|||||||d|d||jjdkrgtj|_|j|j|j f|_ n|j stj |_|j|j|j |j |jf|_ n?tj|_|j|j|j |j |j|j|jf|_ dS(NR%Rci(RRiR*R0R tlcdm_inv_efunc_norelRZRR RXR[RAtlcdm_inv_efunc_nomnuRPRWtlcdm_inv_efuncRBRFRU( R\R]R^R_R`RaRbRcR%((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRis$     cC`s=tj|rdSdtjtj|jdtjSdS(uEReturns dark energy equation of state at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Returns ------- w : ndarray, or float if input scalar The dark energy equation of state Notes ------ The dark energy equation of state is defined as :math:`w(z) = P(z)/\rho(z)`, where :math:`P(z)` is the pressure at redshift z and :math:`\rho(z)` is the density at redshift z, both in units where c=1. Here this is :math:`w(z) = -1`. gRN(R)R+RIRRR(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRg'scC`s9tj|rdStjtj|jdtjSdS(u Evaluates the redshift dependence of the dark energy density. Parameters ---------- z : array-like Input redshifts. Returns ------- I : ndarray, or float if input scalar The scaling of the energy density of dark energy with redshift. Notes ----- The scaling factor, I, is defined by :math:`\rho(z) = \rho_0 I`, and in this case is given by :math:`I = 1`. g?RN(R)R+RIRRR(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRBscC`st|rtj|}n|j|j|j}}}|jra|jd|j|}n|j|j }d|}tj |d||||||S(u Function used to calculate H(z), the Hubble parameter. Parameters ---------- z : array-like Input redshifts. Returns ------- E : ndarray, or float if input scalar The redshift scaling of the Hubble constant. Notes ----- The return value, E, is defined such that :math:`H(z) = H_0 E`. g?i( RR)RRR RXRARPRVRWR(R\RR^R_RqRR((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRZs   cC`st|rtj|}n|j|j|j}}}|jra|jd|j|}n|j|j }d|}|d||||||dS(u Function used to calculate :math:`\frac{1}{H_z}`. Parameters ---------- z : array-like Input redshifts. Returns ------- E : ndarray, or float if input scalar The inverse redshift scaling of the Hubble constant. Notes ----- The return value, E, is defined such that :math:`H_z = H_0 / E`. ig?ig( RR)RRR RXRARPRVRW(R\RR^R_RqRR((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRYzs   N( RRRR&R'RDR!RiRgRRRY(((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRs4!   t FlatLambdaCDMcB`sPeZdZddejdejdddZdZdZ dZ RS( uFLRW cosmology with a cosmological constant and no curvature. This has no additional attributes beyond those of FLRW. Parameters ---------- H0 : float or `~astropy.units.Quantity` Hubble constant at z = 0. If a float, must be in [km/sec/Mpc] Om0 : float Omega matter: density of non-relativistic matter in units of the critical density at z=0. Tcmb0 : float or scalar `~astropy.units.Quantity`, optional Temperature of the CMB z=0. If a float, must be in [K]. Default: 0 [K]. Setting this to zero will turn off both photons and neutrinos (even massive ones). Neff : float, optional Effective number of Neutrino species. Default 3.04. m_nu : `~astropy.units.Quantity`, optional Mass of each neutrino species. If this is a scalar Quantity, then all neutrino species are assumed to have that mass. Otherwise, the mass of each species. The actual number of neutrino species (and hence the number of elements of m_nu if it is not scalar) must be the floor of Neff. Typically this means you should provide three neutrino masses unless you are considering something like a sterile neutrino. Ob0 : float or None, optional Omega baryons: density of baryonic matter in units of the critical density at z=0. If this is set to None (the default), any computation that requires its value will raise an exception. name : str, optional Name for this cosmological object. Examples -------- >>> from astropy.cosmology import FlatLambdaCDM >>> cosmo = FlatLambdaCDM(H0=70, Om0=0.3) The comoving distance in Mpc at redshift z: >>> z = 0.5 >>> dc = cosmo.comoving_distance(z) igRQ@gc C`stj|||d|||d|d|d|j|j|j|_d|_|jjdkrt j |_ |j|jf|_ ns|j st j|_ |j|j|j|jf|_ n9t j|_ |j|j|j|j|j|jf|_ dS(NgR%Rcg?i(RRiRRPRWR RXR*R0R tflcdm_inv_efunc_norelRZR[RAtflcdm_inv_efunc_nomnutflcdm_inv_efuncRBRFRU(R\R]R^R`RaRbRcR%((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRis $        cC`st|rtj|}n|j|j}}|jrW|jd|j|}n|j|j}d|}tj |d||||S(u Function used to calculate H(z), the Hubble parameter. Parameters ---------- z : array-like Input redshifts. Returns ------- E : ndarray, or float if input scalar The redshift scaling of the Hubble constant. Notes ----- The return value, E, is defined such that :math:`H(z) = H_0 E`. ig?i( RR)RRR RARPRVRWR(R\RR^R_RR((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRs   cC`st|rtj|}n|j|j}}|jrW|jd|j|}n|j|j}d|}|d||||dS(uFunction used to calculate :math:`\frac{1}{H_z}`. Parameters ---------- z : array-like Input redshifts. Returns ------- E : ndarray, or float if input scalar The inverse redshift scaling of the Hubble constant. Notes ----- The return value, E, is defined such that :math:`H_z = H_0 / E`. g?ig( RR)RRR RARPRVRW(R\RR^R_RR((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRYs   c C`sCd}|j|j|j|j|j|j|jt|jS(NuM{0}H0={1:.3g}, Om0={2:.3g}, Tcmb0={3:.4g}, Neff={4:.3g}, m_nu={5}, Ob0={6:s})( RjRlR/RR*R$RbRmR"(R\Rn((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRosN( RRRR&R'RDR!RiRRYRo(((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRs /! twCDMcB`steZdZdddejdejd d dZedZ dZ dZ d Z d Z d ZRS( u=FLRW cosmology with a constant dark energy equation of state and curvature. This has one additional attribute beyond those of FLRW. Parameters ---------- H0 : float or `~astropy.units.Quantity` Hubble constant at z = 0. If a float, must be in [km/sec/Mpc] Om0 : float Omega matter: density of non-relativistic matter in units of the critical density at z=0. Ode0 : float Omega dark energy: density of dark energy in units of the critical density at z=0. w0 : float, optional Dark energy equation of state at all redshifts. This is pressure/density for dark energy in units where c=1. A cosmological constant has w0=-1.0. Tcmb0 : float or scalar `~astropy.units.Quantity`, optional Temperature of the CMB z=0. If a float, must be in [K]. Default: 0 [K]. Setting this to zero will turn off both photons and neutrinos (even massive ones). Neff : float, optional Effective number of Neutrino species. Default 3.04. m_nu : `~astropy.units.Quantity`, optional Mass of each neutrino species. If this is a scalar Quantity, then all neutrino species are assumed to have that mass. Otherwise, the mass of each species. The actual number of neutrino species (and hence the number of elements of m_nu if it is not scalar) must be the floor of Neff. Typically this means you should provide three neutrino masses unless you are considering something like a sterile neutrino. Ob0 : float or None, optional Omega baryons: density of baryonic matter in units of the critical density at z=0. If this is set to None (the default), any computation that requires its value will raise an exception. name : str, optional Name for this cosmological object. Examples -------- >>> from astropy.cosmology import wCDM >>> cosmo = wCDM(H0=70, Om0=0.3, Ode0=0.7, w0=-0.9) The comoving distance in Mpc at redshift z: >>> z = 0.5 >>> dc = cosmo.comoving_distance(z) gigRQ@gc C`s tj|||||||d| d|t||_|jjdkr|tj|_|j |j |j |jf|_ n|j stj|_|j |j |j |j|j|jf|_ nEtj|_|j |j |j |j|j|j|j|jf|_ dS(NR%Rci(RRiRt_w0R*R0R twcdm_inv_efunc_norelRZRR RXR[RAtwcdm_inv_efunc_nomnuRPRWtwcdm_inv_efuncRBRFRU( R\R]R^R_tw0R`RaRbRcR%((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRics"$      cC`s|jS(u Dark energy equation of state(R(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR|scC`sCtj|r|jS|jtjtj|jdtjSdS(uFReturns dark energy equation of state at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Returns ------- w : ndarray, or float if input scalar The dark energy equation of state Notes ------ The dark energy equation of state is defined as :math:`w(z) = P(z)/\rho(z)`, where :math:`P(z)` is the pressure at redshift z and :math:`\rho(z)` is the density at redshift z, both in units where c=1. Here this is :math:`w(z) = w_0`. RN(R)R+RRIRRR(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRgscC`s5t|rtj|}nd|dd|jS(u Evaluates the redshift dependence of the dark energy density. Parameters ---------- z : array-like Input redshifts. Returns ------- I : ndarray, or float if input scalar The scaling of the energy density of dark energy with redshift. Notes ----- The scaling factor, I, is defined by :math:`\rho(z) = \rho_0 I`, and in this case is given by :math:`I = \left(1 + z\right)^{3\left(1 + w_0\right)}` g?g@(RR)RR(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRs cC`st|rtj|}n|j|j|j|jf\}}}}|jrn|jd|j |}n|j|j }d|}tj |d|||||||dd|S(u Function used to calculate H(z), the Hubble parameter. Parameters ---------- z : array-like Input redshifts. Returns ------- E : ndarray, or float if input scalar The redshift scaling of the Hubble constant. Notes ----- The return value, E, is defined such that :math:`H(z) = H_0 E`. g?ig@( RR)RRR RXRRARPRVRWR(R\RR^R_RqRRR((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRs *  !cC`st|rtj|}n|j|j|j|jf\}}}}|jrn|jd|j |}n|j|j }d|}|d|||||||dd|dS(u Function used to calculate :math:`\frac{1}{H_z}`. Parameters ---------- z : array-like Input redshifts. Returns ------- E : ndarray, or float if input scalar The inverse redshift scaling of the Hubble constant. Notes ----- The return value, E, is defined such that :math:`H_z = H_0 / E`. g?ig@g( RR)RRR RXRRARPRVRW(R\RR^R_RqRRR((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRYs *  c C`sOd}|j|j|j|j|j|j|j|j|jt |j  S(Nug{0}H0={1:.3g}, Om0={2:.3g}, Ode0={3:.3g}, w0={4:.3g}, Tcmb0={5:.4g}, Neff={6:.3g}, m_nu={7}, Ob0={8:s})( RjRlR/RR RR*R$RbRmR"(R\Rn((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRosN(RRRR&R'RDR!RiRRRgRRRYRo(((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR's:$    tFlatwCDMcB`sSeZdZdddejdejd d dZdZdZ dZ RS( uFLRW cosmology with a constant dark energy equation of state and no spatial curvature. This has one additional attribute beyond those of FLRW. Parameters ---------- H0 : float or `~astropy.units.Quantity` Hubble constant at z = 0. If a float, must be in [km/sec/Mpc] Om0 : float Omega matter: density of non-relativistic matter in units of the critical density at z=0. w0 : float, optional Dark energy equation of state at all redshifts. This is pressure/density for dark energy in units where c=1. A cosmological constant has w0=-1.0. Tcmb0 : float or scalar `~astropy.units.Quantity`, optional Temperature of the CMB z=0. If a float, must be in [K]. Default: 0 [K]. Setting this to zero will turn off both photons and neutrinos (even massive ones). Neff : float, optional Effective number of Neutrino species. Default 3.04. m_nu : `~astropy.units.Quantity`, optional Mass of each neutrino species. If this is a scalar Quantity, then all neutrino species are assumed to have that mass. Otherwise, the mass of each species. The actual number of neutrino species (and hence the number of elements of m_nu if it is not scalar) must be the floor of Neff. Typically this means you should provide three neutrino masses unless you are considering something like a sterile neutrino. Ob0 : float or None, optional Omega baryons: density of baryonic matter in units of the critical density at z=0. If this is set to None (the default), any computation that requires its value will raise an exception. name : str, optional Name for this cosmological object. Examples -------- >>> from astropy.cosmology import FlatwCDM >>> cosmo = FlatwCDM(H0=70, Om0=0.3, w0=-0.9) The comoving distance in Mpc at redshift z: >>> z = 0.5 >>> dc = cosmo.comoving_distance(z) gigRQ@gc C`stj|||d||||d|d|d|j|j|j|_d|_|jjdkrt j |_ |j|j|j f|_ n|jst j|_ |j|j|j|j|j f|_ n?t j|_ |j|j|j|j|j|j|j f|_ dS(NgR%Rcg?i(RRiRRPRWR RXR*R0R tfwcdm_inv_efunc_norelRZRR[RAtfwcdm_inv_efunc_nomnutfwcdm_inv_efuncRBRFRU( R\R]R^RR`RaRbRcR%((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRi0s$!           cC`st|rtj|}n|j|j|j}}}|jra|jd|j|}n|j|j }d|}tj |d|||||dd|S(u Function used to calculate H(z), the Hubble parameter. Parameters ---------- z : array-like Input redshifts. Returns ------- E : ndarray, or float if input scalar The redshift scaling of the Hubble constant. Notes ----- The return value, E, is defined such that :math:`H(z) = H_0 E`. g?ig@i( RR)RRR RRARPRVRWR(R\RR^R_RRR((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRKs   cC`st|rtj|}n|j|j|j}}}|jra|jd|j|}n|j|j }d|}|d|||||dd|dS(u Function used to calculate :math:`\frac{1}{H_z}`. Parameters ---------- z : array-like Input redshifts. Returns ------- E : ndarray, or float if input scalar The inverse redshift scaling of the Hubble constant. Notes ----- The return value, E, is defined such that :math:`H_z = H_0 / E`. g?ig@g( RR)RRR RRARPRVRW(R\RR^R_RRR((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRYis   c C`sId}|j|j|j|j|j|j|j|jt|j S(NuY{0}H0={1:.3g}, Om0={2:.3g}, w0={3:.3g}, Tcmb0={4:.4g}, Neff={5:.3g}, m_nu={6}, Ob0={7:s})( RjRlR/RRR*R$RbRmR"(R\Rn((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRos!N( RRRR&R'RDR!RiRRYRo(((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRs 6$  tw0waCDMcB`steZdZddddejdejd d dZedZ edZ dZ d Z d Z RS( u~ FLRW cosmology with a CPL dark energy equation of state and curvature. The equation for the dark energy equation of state uses the CPL form as described in Chevallier & Polarski Int. J. Mod. Phys. D10, 213 (2001) and Linder PRL 90, 91301 (2003): :math:`w(z) = w_0 + w_a (1-a) = w_0 + w_a z / (1+z)`. Parameters ---------- H0 : float or `~astropy.units.Quantity` Hubble constant at z = 0. If a float, must be in [km/sec/Mpc] Om0 : float Omega matter: density of non-relativistic matter in units of the critical density at z=0. Ode0 : float Omega dark energy: density of dark energy in units of the critical density at z=0. w0 : float, optional Dark energy equation of state at z=0 (a=1). This is pressure/density for dark energy in units where c=1. wa : float, optional Negative derivative of the dark energy equation of state with respect to the scale factor. A cosmological constant has w0=-1.0 and wa=0.0. Tcmb0 : float or scalar `~astropy.units.Quantity`, optional Temperature of the CMB z=0. If a float, must be in [K]. Default: 0 [K]. Setting this to zero will turn off both photons and neutrinos (even massive ones). Neff : float, optional Effective number of Neutrino species. Default 3.04. m_nu : `~astropy.units.Quantity`, optional Mass of each neutrino species. If this is a scalar Quantity, then all neutrino species are assumed to have that mass. Otherwise, the mass of each species. The actual number of neutrino species (and hence the number of elements of m_nu if it is not scalar) must be the floor of Neff. Typically this means you should provide three neutrino masses unless you are considering something like a sterile neutrino. Ob0 : float or None, optional Omega baryons: density of baryonic matter in units of the critical density at z=0. If this is set to None (the default), any computation that requires its value will raise an exception. name : str, optional Name for this cosmological object. Examples -------- >>> from astropy.cosmology import w0waCDM >>> cosmo = w0waCDM(H0=70, Om0=0.3, Ode0=0.7, w0=-0.9, wa=0.2) The comoving distance in Mpc at redshift z: >>> z = 0.5 >>> dc = cosmo.comoving_distance(z) ggigRQ@c C`s,tj|||||||d| d| t||_t||_|jjdkrtj|_ |j |j |j |j|jf|_ n|jstj|_ |j |j |j |j|j|j|jf|_ nKtj|_ |j |j |j |j|j|j|j|j|jf |_ dS(NR%Rci(RRiRRt_waR*R0R tw0wacdm_inv_efunc_norelRZRR RXR[RAtw0wacdm_inv_efunc_nomnuRPRWtw0wacdm_inv_efuncRBRFRU( R\R]R^R_RtwaR`RaRbRcR%((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRis&$       cC`s|jS(u% Dark energy equation of state at z=0(R(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRscC`s|jS(u> Negative derivative of dark energy equation of state w.r.t. a(R(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRscC`s8t|rtj|}n|j|j|d|S(unReturns dark energy equation of state at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Returns ------- w : ndarray, or float if input scalar The dark energy equation of state Notes ------ The dark energy equation of state is defined as :math:`w(z) = P(z)/\rho(z)`, where :math:`P(z)` is the pressure at redshift z and :math:`\rho(z)` is the density at redshift z, both in units where c=1. Here this is :math:`w(z) = w_0 + w_a (1 - a) = w_0 + w_a \frac{z}{1+z}`. g?(RR)RRR(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRgs cC`s^t|rtj|}nd|}|dd|j|jtjd|j||S(uL Evaluates the redshift dependence of the dark energy density. Parameters ---------- z : array-like Input redshifts. Returns ------- I : ndarray, or float if input scalar The scaling of the energy density of dark energy with redshift. Notes ----- The scaling factor, I, is defined by :math:`\\rho(z) = \\rho_0 I`, and in this case is given by .. math:: I = \left(1 + z\right)^{3 \left(1 + w_0 + w_a\right)} \exp \left(-3 w_a \frac{z}{1+z}\right) g?iii(RR)RRRR(R\RR((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR s   c C`sUd}|j|j|j|j|j|j|j|j|j|j t |j  S(Nus{0}H0={1:.3g}, Om0={2:.3g}, Ode0={3:.3g}, w0={4:.3g}, wa={5:.3g}, Tcmb0={6:.4g}, Neff={7:.3g}, m_nu={8}, Ob0={9:s})( RjRlR/RR RRR*R$RbRmR"(R\Rn((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRo- s N(RRRR&R'RDR!RiRRRRgRRo(((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRs> $  t Flatw0waCDMcB`sDeZdZddddejdejdddZdZRS(u FLRW cosmology with a CPL dark energy equation of state and no curvature. The equation for the dark energy equation of state uses the CPL form as described in Chevallier & Polarski Int. J. Mod. Phys. D10, 213 (2001) and Linder PRL 90, 91301 (2003): :math:`w(z) = w_0 + w_a (1-a) = w_0 + w_a z / (1+z)`. Parameters ---------- H0 : float or `~astropy.units.Quantity` Hubble constant at z = 0. If a float, must be in [km/sec/Mpc] Om0 : float Omega matter: density of non-relativistic matter in units of the critical density at z=0. w0 : float, optional Dark energy equation of state at z=0 (a=1). This is pressure/density for dark energy in units where c=1. wa : float, optional Negative derivative of the dark energy equation of state with respect to the scale factor. A cosmological constant has w0=-1.0 and wa=0.0. Tcmb0 : float or scalar `~astropy.units.Quantity`, optional Temperature of the CMB z=0. If a float, must be in [K]. Default: 0 [K]. Setting this to zero will turn off both photons and neutrinos (even massive ones). Neff : float, optional Effective number of Neutrino species. Default 3.04. m_nu : `~astropy.units.Quantity`, optional Mass of each neutrino species. If this is a scalar Quantity, then all neutrino species are assumed to have that mass. Otherwise, the mass of each species. The actual number of neutrino species (and hence the number of elements of m_nu if it is not scalar) must be the floor of Neff. Typically this means you should provide three neutrino masses unless you are considering something like a sterile neutrino. Ob0 : float or None, optional Omega baryons: density of baryonic matter in units of the critical density at z=0. If this is set to None (the default), any computation that requires its value will raise an exception. name : str, optional Name for this cosmological object. Examples -------- >>> from astropy.cosmology import Flatw0waCDM >>> cosmo = Flatw0waCDM(H0=70, Om0=0.3, w0=-0.9, wa=0.2) The comoving distance in Mpc at redshift z: >>> z = 0.5 >>> dc = cosmo.comoving_distance(z) ggigRQ@c C`s8tj|||dd|d|d|d|d|d| d|d |j|j|j|_d|_|jjd krt j |_ |j|j|j |j f|_n|jst j|_ |j|j|j|j|j |j f|_nEt j|_ |j|j|j|j|j|j|j |j f|_dS( NgRRR`RaRbR%Rcg?i(RRiRRPRWR RXR*R0R tfw0wacdm_inv_efunc_norelRZRRR[RAtfw0wacdm_inv_efunc_nomnutfw0wacdm_inv_efuncRBRFRU( R\R]R^RRR`RaRbRcR%((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRiu s&'           c C`sId}|j|j|j|j|j|j|j|jt|j S(NuY{0}H0={1:.3g}, Om0={2:.3g}, w0={3:.3g}, Tcmb0={4:.4g}, Neff={5:.3g}, m_nu={6}, Ob0={7:s})( RjRlR/RRR*R$RbRmR"(R\Rn((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRo s!N( RRRR&R'RDR!RiRo(((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR7 s< $twpwaCDMc B`seZdZdddddejdejd d dZedZ edZ edZ d Z d Z d ZRS( u FLRW cosmology with a CPL dark energy equation of state, a pivot redshift, and curvature. The equation for the dark energy equation of state uses the CPL form as described in Chevallier & Polarski Int. J. Mod. Phys. D10, 213 (2001) and Linder PRL 90, 91301 (2003), but modified to have a pivot redshift as in the findings of the Dark Energy Task Force (Albrecht et al. arXiv:0901.0721 (2009)): :math:`w(a) = w_p + w_a (a_p - a) = w_p + w_a( 1/(1+zp) - 1/(1+z) )`. Parameters ---------- H0 : float or `~astropy.units.Quantity` Hubble constant at z = 0. If a float, must be in [km/sec/Mpc] Om0 : float Omega matter: density of non-relativistic matter in units of the critical density at z=0. Ode0 : float Omega dark energy: density of dark energy in units of the critical density at z=0. wp : float, optional Dark energy equation of state at the pivot redshift zp. This is pressure/density for dark energy in units where c=1. wa : float, optional Negative derivative of the dark energy equation of state with respect to the scale factor. A cosmological constant has wp=-1.0 and wa=0.0. zp : float, optional Pivot redshift -- the redshift where w(z) = wp Tcmb0 : float or scalar `~astropy.units.Quantity`, optional Temperature of the CMB z=0. If a float, must be in [K]. Default: 0 [K]. Setting this to zero will turn off both photons and neutrinos (even massive ones). Neff : float, optional Effective number of Neutrino species. Default 3.04. m_nu : `~astropy.units.Quantity`, optional Mass of each neutrino species. If this is a scalar Quantity, then all neutrino species are assumed to have that mass. Otherwise, the mass of each species. The actual number of neutrino species (and hence the number of elements of m_nu if it is not scalar) must be the floor of Neff. Typically this means you should provide three neutrino masses unless you are considering something like a sterile neutrino. Ob0 : float or None, optional Omega baryons: density of baryonic matter in units of the critical density at z=0. If this is set to None (the default), any computation that requires its value will raise an exception. name : str, optional Name for this cosmological object. Examples -------- >>> from astropy.cosmology import wpwaCDM >>> cosmo = wpwaCDM(H0=70, Om0=0.3, Ode0=0.7, wp=-0.9, wa=0.2, zp=0.4) The comoving distance in Mpc at redshift z: >>> z = 0.5 >>> dc = cosmo.comoving_distance(z) ggigRQ@c C`sUtj||||||| d| d| t||_t||_t||_dd|j} |jjdkrtj |_ |j |j |j |j| |jf|_n|jstj|_ |j |j |j |j|j|j| |jf|_nNtj|_ |j |j |j |j|j|j|j|j| |jf |_dS(NR%Rcg?i(RRiRt_wpRt_zpR*R0R twpwacdm_inv_efunc_norelRZRR RXR[RAtwpwacdm_inv_efunc_nomnuRPRWtwpwacdm_inv_efuncRBRFRU( R\R]R^R_twpRtzpR`RaRbRcR%tapiv((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRi s*$       cC`s|jS(u7 Dark energy equation of state at the pivot redshift zp(R(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR scC`s|jS(u> Negative derivative of dark energy equation of state w.r.t. a(R(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR scC`s|jS(u$ The pivot redshift, where w(z) = wp(R(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR scC`sMt|rtj|}ndd|j}|j|j|dd|S(uReturns dark energy equation of state at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Returns ------- w : ndarray, or float if input scalar The dark energy equation of state Notes ------ The dark energy equation of state is defined as :math:`w(z) = P(z)/\rho(z)`, where :math:`P(z)` is the pressure at redshift z and :math:`\rho(z)` is the density at redshift z, both in units where c=1. Here this is :math:`w(z) = w_p + w_a (a_p - a)` where :math:`a = 1/1+z` and :math:`a_p = 1 / 1 + z_p`. g?(RR)RRRR(R\RR((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRg s cC`sst|rtj|}nd|}dd|j}|dd|j||jtjd|j||S(ur Evaluates the redshift dependence of the dark energy density. Parameters ---------- z : array-like Input redshifts. Returns ------- I : ndarray, or float if input scalar The scaling of the energy density of dark energy with redshift. Notes ----- The scaling factor, I, is defined by :math:`\\rho(z) = \\rho_0 I`, and in this case is given by .. math:: a_p = \frac{1}{1 + z_p} I = \left(1 + z\right)^{3 \left(1 + w_p + a_p w_a\right)} \exp \left(-3 w_a \frac{z}{1+z}\right) g?g@g(RR)RRRRR(R\RRR((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR+ s   c C`s[d}|j|j|j|j|j|j|j|j|j|j |j t |j  S(Nu{0}H0={1:.3g}, Om0={2:.3g}, Ode0={3:.3g}, wp={4:.3g}, wa={5:.3g}, zp={6:.3g}, Tcmb0={7:.4g}, Neff={8:.3g}, m_nu={9}, Ob0={10:s})( RjRlR/RR RRRR*R$RbRmR"(R\Rn((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRoL s N(RRRR&R'RDR!RiRRRRRgRRo(((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR sE   !tw0wzCDMcB`steZdZddddejdejd d dZedZ edZ dZ d Z d Z RS( u FLRW cosmology with a variable dark energy equation of state and curvature. The equation for the dark energy equation of state uses the simple form: :math:`w(z) = w_0 + w_z z`. This form is not recommended for z > 1. Parameters ---------- H0 : float or `~astropy.units.Quantity` Hubble constant at z = 0. If a float, must be in [km/sec/Mpc] Om0 : float Omega matter: density of non-relativistic matter in units of the critical density at z=0. Ode0 : float Omega dark energy: density of dark energy in units of the critical density at z=0. w0 : float, optional Dark energy equation of state at z=0. This is pressure/density for dark energy in units where c=1. wz : float, optional Derivative of the dark energy equation of state with respect to z. A cosmological constant has w0=-1.0 and wz=0.0. Tcmb0 : float or scalar `~astropy.units.Quantity`, optional Temperature of the CMB z=0. If a float, must be in [K]. Default: 0 [K]. Setting this to zero will turn off both photons and neutrinos (even massive ones). Neff : float, optional Effective number of Neutrino species. Default 3.04. m_nu : `~astropy.units.Quantity`, optional Mass of each neutrino species. If this is a scalar Quantity, then all neutrino species are assumed to have that mass. Otherwise, the mass of each species. The actual number of neutrino species (and hence the number of elements of m_nu if it is not scalar) must be the floor of Neff. Typically this means you should provide three neutrino masses unless you are considering something like a sterile neutrino. Ob0 : float or None, optional Omega baryons: density of baryonic matter in units of the critical density at z=0. If this is set to None (the default), any computation that requires its value will raise an exception. name : str, optional Name for this cosmological object. Examples -------- >>> from astropy.cosmology import w0wzCDM >>> cosmo = w0wzCDM(H0=70, Om0=0.3, Ode0=0.7, w0=-0.9, wz=0.2) The comoving distance in Mpc at redshift z: >>> z = 0.5 >>> dc = cosmo.comoving_distance(z) ggigRQ@c C`s,tj|||||||d| d| t||_t||_|jjdkrtj|_ |j |j |j |j|jf|_ n|jstj|_ |j |j |j |j|j|j|jf|_ nKtj|_ |j |j |j |j|j|j|j|j|jf |_ dS(NR%Rci(RRiRRt_wzR*R0R tw0wzcdm_inv_efunc_norelRZRR RXR[RAtw0wzcdm_inv_efunc_nomnuRPRWtw0wzcdm_inv_efuncRBRFRU( R\R]R^R_RtwzR`RaRbRcR%((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRi s&$       cC`s|jS(u% Dark energy equation of state at z=0(R(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR scC`s|jS(u9 Derivative of the dark energy equation of state w.r.t. z(R(R\((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR  scC`s0t|rtj|}n|j|j|S(uWReturns dark energy equation of state at redshift ``z``. Parameters ---------- z : array-like Input redshifts. Returns ------- w : ndarray, or float if input scalar The dark energy equation of state Notes ------ The dark energy equation of state is defined as :math:`w(z) = P(z)/\rho(z)`, where :math:`P(z)` is the pressure at redshift z and :math:`\rho(z)` is the density at redshift z, both in units where c=1. Here this is given by :math:`w(z) = w_0 + w_z z`. (RR)RRR(R\R((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRg s cC`sZt|rtj|}nd|}|dd|j|jtjd|j|S(u? Evaluates the redshift dependence of the dark energy density. Parameters ---------- z : array-like Input redshifts. Returns ------- I : ndarray, or float if input scalar The scaling of the energy density of dark energy with redshift. Notes ----- The scaling factor, I, is defined by :math:`\\rho(z) = \\rho_0 I`, and in this case is given by .. math:: I = \left(1 + z\right)^{3 \left(1 + w_0 - w_z\right)} \exp \left(-3 w_z z\right) g?g@g(RR)RRRR(R\RR((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR s   c C`sUd}|j|j|j|j|j|j|j|j|j|j t |j  S(Nur{0}H0={1:.3g}, Om0={2:.3g}, Ode0={3:.3g}, w0={4:.3g}, wz={5:.3g} Tcmb0={6:.4g}, Neff={7:.3g}, m_nu={8}, Ob0={9:s})( RjRlR/RR RRR*R$RbRmR"(R\Rn((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRo sN(RRRR&R'RDR!RiRRR RgRRo(((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRV s@    cC`s8|dkrt|Sdj|d|}|j|S(uA Helper function to format a variable that can be a float or Noneu{0:.{digits}g}tdigitsN(R!tstrRj(txR tfmtstr((s5lib/python2.7/site-packages/astropy/cosmology/core.pyRm s  cG`s6ttt|r(tj||S||SdS(u7 Helper function to vectorize functions on array inputsN(tanyRRR)t vectorize(tfuncR((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR suflatuH0uOm0R`uTcmb0RauNeffRbum_nuR%RcuOb0u1{} instance of FlatLambdaCDM cosmology (from {})u referenceuOde0u-{} instance of LambdaCDM cosmology (from {})tdefault_cosmologycB`s2eZdZdZedZedZRS(uT The default cosmology to use. To change it:: >>> from astropy.cosmology import default_cosmology, WMAP7 >>> with default_cosmology.set(WMAP7): ... # WMAP7 cosmology in effect Or, you may use a string:: >>> with default_cosmology.set('WMAP7'): ... # WMAP7 cosmology in effect uWMAP9cC`sh|dkrd}nOyttjt|}Wn2tk rcdj|tj}t |nX|S(u4 Return a cosmology instance from a string. u no_defaultu-Unknown cosmology '{}'. Valid cosmologies: {}N( R!R~tsystmodulesRRRjRt availableR(RtcosmoR-((s5lib/python2.7/site-packages/astropy/cosmology/core.pytget_cosmology_from_string@ s   cC`sW|dkrd}nt|tjr4|j|St|trG|StddS(NuPlanck15u9default_cosmology must be a string or Cosmology instance.(R!RCRt string_typesRRt TypeError(tclsR0((s5lib/python2.7/site-packages/astropy/cosmology/core.pytvalidateO s   (RRRt_valuet staticmethodRt classmethodR(((s5lib/python2.7/site-packages/astropy/cosmology/core.pyR1 s (Tt __future__RRRRtexternRtextern.six.movesRRtmathRRRR R tabcR R tnumpyR)tR RR2RR&tutilsRtutils.compat.funcsigsRt utils.stateRRRt__all__t__doctest_requires__R,R-R.R4R6R8R7tGR0R:RRtsigma_sbR3ROtk_BRDR(RRt ExceptionRtobjectRt add_metaclassRRRRRRRRRRmRtkeyR~tparR'RtdocstrRjRtsetattrRRR(((s5lib/python2.7/site-packages/astropy/cosmology/core.pyts|" (   ''c