B d"J@s"dZddlZddlZddlZddlmZddlZddlm Z m Z ddlm ZejdZejdZd d Zdd d ZddZddZddZddZddZddZddZddZddZd d!Zd"d#Zd$d%Z d&d'Z!d(d)Z"d*d+Z#d,d-Z$e%e$Z&dd/d0Z'e%e'Z(dd1d2Z)dd3d4Z*d5d6Z+d7d8Z,d9d:Z-d;d<Z.d=d>Z/d?d@Z0dAdBZ1dCdDZ2dEdFZ3ddGdHZ4dIdJZ5dKdLZ6dMdNZ7dOdPZ8ddRdSZ9ddUdVZ:ddWdXZ;dYdZZd_d`Z?dadbZ@dcddZAdedfZBdgdhZCdidjZDdkdlZEdmdnZFdodpZGdqdrZHdsdtZIdudvZJdwdxZKdydzZLd{d|ZMd}d~ZNddZOddZPddZQddZRddZSddZTddZUddZVdddZWdddZXiZYdddZZddZ[ddZ\ddZ]ddZ^dddZ_ddZ`dddZadddZbdddddZcdddddZddddZedddZfddZgddZhdddZidddZjdddZkddÄZlddńZmddDŽZnddɄZodd˄Zpdd̈́ZqddPdSddddddddd!d#d%d'd)d+ddd2d4d6d8d:d@dBdDdFdHdJdLdNdhdjdZd\d^d`dbdldndpdrdtdvdxd~dzd|ddddddddddddddddddddfdddddVdXgJZrdS)z This module provides a library of functions that calculate waveform parameters from other parameters. All exposed functions in this module's namespace return one parameter given a set of inputs. N)Detector)spherical_to_cartesiancartesian_to_spherical) neutron_starspykerr lalsimulationcGs*tdd|D}tj|}|||S)aApply numpy's broadcast rules to the given arguments. This will ensure that all of the arguments are numpy arrays and that they all have the same shape. See ``numpy.broadcast_arrays`` for more details. It also returns a boolean indicating whether any of the inputs were originally arrays. Parameters ---------- *args : The arguments to check. Returns ------- list : A list with length ``N+1`` where ``N`` is the number of given arguments. The first N values are the input arguments as ``ndarrays``s. The last value is a boolean indicating whether any of the inputs was an array. css|]}t|tjVqdS)N) isinstancenumpyZndarray).0argr ^/work/yifan.wang/ringdown/master-ringdown-env/lib/python3.7/site-packages/pycbc/conversions.py Iszensurearray..)anyr Zbroadcast_arraysappend)argsinput_is_arrayr r r ensurearray3s  rFcCs|s|jdkr|}|S)zTIf the given argument is a numpy array with shape (1,), just returns that value.r)sizeitem)r rr r r formatreturnOsrcCs |tjS)z/ Converts number of seconds to number of years )lalZYRJUL_SI)secr r r sec_to_year^srcCs8t||\}}}t|}||k}||||<t||S)z4Returns the larger of mass1 and mass2 (p = primary).)rcopyr)mass1mass2rmpmaskr r r primary_massjs   r cCsLt||\}}}|j|jkr$tdt|}||k}||||<t||S)z7Returns the smaller of mass1 and mass2 (s = secondary).z$mass1 and mass2 must have same shape)rshape ValueErrorrr)rrrmsrr r rsecondary_massss   r$cCs||S)z,Returns the total mass from mass1 and mass2.r )rrr r rmtotal_from_mass1_mass2~sr%cCst||t||S)z-Returns the mass ratio m1/m2, where m1 >= m2.)r r$)rrr r rq_from_mass1_mass2sr&cCst||t||S)z5Returns the inverse mass ratio m2/m1, where m1 >= m2.)r$r )rrr r rinvq_from_mass1_mass2sr'cCs||||dS)z6Returns the symmetric mass ratio from mass1 and mass2.g@r )rrr r reta_from_mass1_mass2sr(cCst||d||S)z,Returns the chirp mass from mass1 and mass2.g333333?)r()rrr r rmchirp_from_mass1_mass2sr)cCs||d|S)zReturns a component mass from the given total mass and mass ratio. If the mass ratio q is >= 1, the returned mass will be the primary (heavier) mass. If q < 1, the returned mass will be the secondary (lighter) mass. g?r )mtotalqr r rmass1_from_mtotal_qsr,cCs |d|S)zReturns a component mass from the given total mass and mass ratio. If the mass ratio q is >= 1, the returned mass will be the secondary (lighter) mass. If q < 1, the returned mass will be the primary (heavier) mass. g?r )r*r+r r rmass2_from_mtotal_qsr-cCsd|ddd|dS)zOReturns the primary mass from the total mass and symmetric mass ratio. g?g?g@r )r*etar r rmass1_from_mtotal_etasr/cCsd|ddd|dS)zQReturns the secondary mass from the total mass and symmetric mass ratio. g?g?g@r )r*r.r r rmass2_from_mtotal_etasr0cCs ||dS)zIReturns the total mass from the chirp mass and symmetric mass ratio. g333333?r )mchirpr.r r rmtotal_from_mchirp_etasr2cCst||}t||S)zKReturns the primary mass from the chirp mass and symmetric mass ratio. )r2r/)r1r.r*r r rmass1_from_mchirp_etas r3cCst||}t||S)zKReturns the primary mass from the chirp mass and symmetric mass ratio. )r2r0)r1r.r*r r rmass2_from_mchirp_etas r4cCsF|d|d}tdd| | |g}|t||j}|jS)awReturns the secondary mass from the chirp mass and primary mass. As this is a cubic equation this requires finding the roots and returning the one that is real. Basically it can be shown that: .. math:: m_2^3 - a(m_2 + m_1) = 0, where .. math:: a = \frac{\mathcal{M}^5}{m_1^3}. This has 3 solutions but only one will be real. rr)r rootsabsrealargmin)r1rar7Z real_rootr r r_mass2_from_mchirp_mass1sr<TcCsRt|d|d|||dg}|r2t|}|rB||S||SdS)aMReturns the other component mass given one of the component masses and the symmetric mass ratio. This requires finding the roots of the quadratic equation: .. math:: \eta m_2^2 + (2\eta - 1)m_1 m_2 + \eta m_1^2 = 0. This has two solutions which correspond to :math:`m_1` being the heavier mass or it being the lighter mass. By default, `known_mass` is assumed to be the heavier (primary) mass, and the smaller solution is returned. Use the `other_is_secondary` to invert. Parameters ---------- known_mass : float The known component mass. eta : float The symmetric mass ratio. known_is_secondary : {False, bool} Whether the known component mass is the primary or the secondary. If True, `known_mass` is assumed to be the secondary (lighter) mass and the larger solution is returned. Otherwise, the smaller solution is returned. Default is False. force_real : {True, bool} Force the returned mass to be real. Returns ------- float The other component mass. rg@N)r r7r9Zargmaxr:)Z known_massr.known_is_secondary force_realr7r r r_mass_from_knownmass_etas "$  r@cCst||d|dS)zSReturns the secondary mass from the primary mass and symmetric mass ratio. F)r>r?)mass_from_knownmass_eta)rr.r?r r rmass2_from_mass1_etasrBcCst||d|dS)zSReturns the primary mass from the secondary mass and symmetric mass ratio. T)r>r?)rA)rr.r?r r rmass1_from_mass2_etasrCcCs|d|dS)zReturns the symmetric mass ratio from the given mass ratio. This is given by: .. math:: \eta = \frac{q}{(1+q)^2}. Note that the mass ratio may be either < 1 or > 1. g?r=r )r+r r r eta_from_q#s rDcCs|dd|d|}|S)zBReturns the primary mass from the given chirp mass and mass ratio.g?g?g?r )r1r+rr r rmass1_from_mchirp_q0srEcCs|dd|d|}|S)zDReturns the secondary mass from the given chirp mass and mass ratio.g333333g?g?r )r1r+rr r rmass2_from_mchirp_q5srFcCsddtj|dS)zUsed in calculating chirp times: see Cokelaer, arxiv.org:0706.4437 appendix 1, also lalinspiral/python/sbank/tau0tau3.py. g@gp@gUUUUUU@)r pi)f_lowerr r r_a0:srIcCstjdtj|dS)z&Another parameter used for chirp timesg @g?)r rG)rHr r r_a3@srJcCs|tj}t||d|S)zcReturns :math:`\tau_0` from the total mass, symmetric mass ratio, and the given frequency. g?)rMTSUN_SIrI)r*r.rHr r rtau0_from_mtotal_etaEs rLcCs|tj}t||d|S)zcReturns :math:`\tau_0` from the total mass, symmetric mass ratio, and the given frequency. gUUUUUU?)rrKrJ)r*r.rHr r rtau3_from_mtotal_etaOs rMcCs||}t||}t|||S)zJReturns :math:`\tau_0` from the component masses and given frequency. )r(rL)rrrHr*r.r r rtau0_from_mass1_mass2Ys rNcCs||}t||}t|||S)zJReturns :math:`\tau_3` from the component masses and given frequency. )r(rM)rrrHr*r.r r rtau3_from_mass1_mass2as rOcCs*|t||t|}|s&|tj}|S)z/Returns total mass from :math:`\tau_0, \tau_3`.)rJrIrrK)tau0tau3rH in_secondsr*r r rmtotal_from_tau0_tau3is rScCs(t|||dd}|dt||}|S)z9Returns symmetric mass ratio from :math:`\tau_0, \tau_3`.T)rRgUUUUUU)rSrJ)rPrQrHr*r.r r reta_from_tau0_tau3ssrTcCs"t|||}t|||}t||S)z?Returns the primary mass from the given :math:`\tau_0, \tau_3`.)rSrTr/)rPrQrHr*r.r r rmass1_from_tau0_tau3{s  rUcCs"t|||}t|||}t||S)zAReturns the secondary mass from the given :math:`\tau_0, \tau_3`.)rSrTr0)rPrQrHr*r.r r rmass2_from_tau0_tau3s  rVcCst||||\}}}}}||}t||\}} ||k} ||  || <t||} |dd| d| d} dd| ddd| d| d|} td | | |S) z The effective lambda parameter The mass-weighted dominant effective lambda parameter defined in https://journals.aps.org/prd/pdf/10.1103/PhysRevD.91.043002 rg@g@g? g;;?)rr(r)rrZlambda1Zlambda2m1m2rZlsumZldiff_rr.p1p2r r r lambda_tildes ,r`cCsPt|}|dddf}|dddf}|dtj|}t|||}|S)zReturn the lambda parameter(s) corresponding to the input mass(es) interpolating from the mass-Lambda data for a particular EOS read in from an ASCII file. Nrrg?)r ZloadtxtpycbcZ cosmologyZredshiftZinterp)massZtov_fileZdistancedataZmass_from_fileZlambda_from_fileZmass_srclambdavr r rlambda_from_mass_tov_files  rf2Hc Cst||||\}}}}}yt||kr2|r2tdWn4tk rh||krd|sdtd|d|YnXt||\}}t||}t|||||} t| |S)aK Function that determines the remnant disk mass of an NS-BH system using the fit to numerical-relativity results discussed in Foucart, Hinderer & Nissanke, PRD 98, 081501(R) (2018). The BH spin may be misaligned with the orbital angular momentum. In such cases the ISSO is approximated following the approach of Stone, Loeb & Berger, PRD 87, 084053 (2013), which was originally devised for a previous NS-BH remnant mass fit of Foucart, PRD 86, 124007 (2012). Note: NS spin is assumed to be 0! Parameters ----------- mass1 : float The mass of the black hole, in solar masses. mass2 : float The mass of the neutron star, in solar masses. spin1a : float, optional The dimensionless magnitude of the spin of mass1. Default = 0. spin1pol : float, optional The tilt angle of the spin of mass1. Default = 0 (aligned w L). eos : str, optional Name of the equation of state being adopted. Default is '2H'. Returns ---------- remnant_mass: float The remnant mass in solar masses zRequire mass1 >= mass2zRequire mass1 >= mass2. z < ) rrr" TypeErrornsZinitialize_eosr(Z foucart18r) rrspin1aspin1poleosrZns_compactnessZ ns_b_massr.Z remnant_massr r r0remnant_mass_from_mass1_mass2_spherical_spin_eoss   rmc Cs$t|||\}}}t|||||dS)a Function that determines the remnant disk mass of an NS-BH system using the fit to numerical-relativity results discussed in Foucart, Hinderer & Nissanke, PRD 98, 081501(R) (2018). The BH spin may be misaligned with the orbital angular momentum. In such cases the ISSO is approximated following the approach of Stone, Loeb & Berger, PRD 87, 084053 (2013), which was originally devised for a previous NS-BH remnant mass fit of Foucart, PRD 86, 124007 (2012). Note: NS spin is assumed to be 0! Parameters ----------- mass1 : float The mass of the black hole, in solar masses. mass2 : float The mass of the neutron star, in solar masses. spin1x : float, optional The dimensionless x-component of the spin of mass1. Default = 0. spin1y : float, optional The dimensionless y-component of the spin of mass1. Default = 0. spin1z : float, optional The dimensionless z-component of the spin of mass1. Default = 0. eos: str, optional Name of the equation of state being adopted. Default is '2H'. Returns ---------- remnant_mass: float The remnant mass in solar masses )rl)_cartesian_to_sphericalrm) rrspin1xspin1yspin1zrlrjr]rkr r r0remnant_mass_from_mass1_mass2_cartesian_spin_eoss!rrcCs||||||S)zAReturns the effective spin from mass1, mass2, spin1z, and spin2z.r )rrrqspin2zr r rchi_effsrtcCs||||||S)zb Returns the aligned mass-weighted spin difference from mass1, mass2, spin1z, and spin2z. r )rrrqrsr r rchi_a srucCs.t||||||}t||||||}t||S)zeReturns the effective precession spin from mass1, mass2, spin1x, spin1y, spin2x, and spin2y. ) secondary_xi primary_xichi_p_from_xi1_xi2)rrrorpspin2xspin2yxi1xi2r r rchi_psr}cCsNtt||||t||||}tt||||t||||}||dtjS)z< Returns the angle between the in-plane perpendicular spins.r=)phi_from_spinx_spiny primary_spinsecondary_spinr rG)rrrorpryrzphi1phi2r r rphi_as rcCs&t||}t||}||dtjS)z5 Returns the sum of the in-plane perpendicular spins.r=)r~r rG)rorpryrzrrr r rphi_s"s  rcCs*|t|}|t|}t||||S)z@Returns the effective spin using spins in spherical coordinates.)r cosrt)rrspin1_a spin1_polarspin2_a spin2_polarrqrsr r rchi_eff_from_spherical)src Cs6t|||\}} } t|||\} } } t|||| | | S)zTReturns the effective precession spin using spins in spherical coordinates. )_spherical_to_cartesianr}) rrrZspin1_azimuthalrrZspin2_azimuthalrrorpr]ryrzr r rchi_p_from_spherical1s rcCs@t||||\}}}}}t|}||k}||||<t||S)z3Returns the dimensionless spin of the primary mass.)rrr)rrspin1spin2rsprr r rr=s   rcCs@t||||\}}}}}t|}||k}||||<t||S)z5Returns the dimensionless spin of the secondary mass.)rrr)rrrrrssrr r rrGs   rcCs&t||||}t||||}t||S)zHReturns the effective precession spin argument for the larger mass. )rchi_perp_from_spinx_spiny)rrrorpryrzspinxspinyr r rrwQsrwcCs*t||||}t||||}t||||S)zIReturns the effective precession spin argument for the smaller mass. )r"xi2_from_mass1_mass2_spin2x_spin2y)rrrorpryrzrrr r rrvYsrvcCs t||S)zReturns the effective precession spin argument for the larger mass. This function assumes it's given spins of the primary mass. )r)rorpr r rxi1_from_spin1x_spin1yasrcCsDt||}dd|d}ddd|}||d|t||S)zReturns the effective precession spin argument for the smaller mass. This function assumes it's given spins of the secondary mass. r=r6)r&r)rrryrzr+a1a2r r rrhs rcCst|d|dS)zCReturns the in-plane spin from the x/y components of the spin. r=)r sqrt)rrr r rrrsrcCs>t||}dd|d}ddd|}|d|||S)zUReturns the in-plane spin from mass1, mass2, and xi2 for the secondary mass. r=r6)r&)rrr|r+rrr r rchi_perp_from_mass1_mass2_xi2xs rcCs8t||\}}}t|}||k}||||<t||S)z8Returns effective precession spin from xi1 and xi2. )rrr)r{r|rr}rr r rrxs   rxcCs ||dS)zxReturns the angle between the x-component axis and the in-plane spin for the primary mass from phi_s and phi_a. g@r )rrr r rphi1_from_phi_a_phi_ssrcCs ||dS)zzReturns the angle between the x-component axis and the in-plane spin for the secondary mass from phi_s and phi_a. g@r )rrr r rphi2_from_phi_a_phi_ssrcCst||}|dtjS)zJReturns the angle between the x-component axis and the in-plane spin. r=)r Zarctan2rG)rrphir r rr~s r~cCs||d|||S)zReturns spin1z. g@r )rrrtrur r r%spin1z_from_mass1_mass2_chi_eff_chi_asrcCs||d|||S)zReturns spin2z. g@r )rrrtrur r r%spin2z_from_mass1_mass2_chi_eff_chi_asrcCst||}|t|S)z/Returns x-component spin for primary mass. )rr r)r{rrrr r rspin1x_from_xi1_phi_a_phi_ss rcCst||}|t|S)z/Returns y-component spin for primary mass. )rr sin)r{rrrr r rspin1y_from_xi1_phi_a_phi_ss rcCs$t|||}t||}|t|S)z1Returns x-component spin for secondary mass. )rrr r)rrr|rrchi_perprr r r'spin2x_from_mass1_mass2_xi2_phi_a_phi_ss  rcCs$t|||}t||}|t|S)z1Returns y-component spin for secondary mass. )rrr r)rrr|rrrrr r r'spin2y_from_mass1_mass2_xi2_phi_a_phi_ss  rcCs\t|}d}d}d}d}d}|||||d||d||d}t|d S) aDReturn the quadrupole moment of a neutron star given its lambda We use the relations defined here. https://arxiv.org/pdf/1302.4499.pdf. Note that the convention we use is that: .. math:: \mathrm{dquadmon} = \bar{Q} - 1. Where :math:`\bar{Q}` (dimensionless) is the reduced quadrupole moment. gE?ggj+?g0*D?gE>qgFn1 ?g@g@g@r)r logexp)rellZaiZbiciZdieiZln_quad_momentr r rdquadmon_from_lambdas 0rcCsBdtj|}|tj}d||dtjd}|||dS)aoReturns the dimensionless spin of a pulsar. Assumes the pulsar is a solid sphere when computing the moment of inertia. Parameters ---------- mass : float The mass of the pulsar, in solar masses. radius : float The assumed radius of the pulsar, in kilometers. freq : float The spin frequency of the pulsar, in Hz. r=g?i)r rGrrKC_SI)rcZradiusfreqomegamtZmominertr r rspin_from_pulsar_freqs rffffff?cCs|d||dS)zMReturns the chirp distance given the luminosity distance and chirp mass. g ڌ?g?r )distr1ref_massr r rchirp_distancesrcCs|d||dS)zKReturns the luminosity distance given a chirp distance and chirp mass. g ڌ?gr )rr1rr r r#distance_from_chirp_distance_mchirpsr geocentricc Csn|}|r d}||kr|S|tkr,t|t|<t|}|dkrN|||||St|}||||||SdS)aReturns the coalescence time of a signal in the given detector. Parameters ---------- detector_name : string The name of the detector, e.g., 'H1'. ra : float The right ascension of the signal, in radians. dec : float The declination of the signal, in radians. tc : float The GPS time of the coalescence of the signal in the `ref_frame`. ref_frame : {'geocentric', string} The reference frame that the given coalescence time is defined in. May specify 'geocentric', or a detector name; default is 'geocentric'. Returns ------- float : The GPS time of the coalescence in detector `detector_name`. rrN)_detector_cacherZtime_delay_from_earth_centerZtime_delay_from_detector) detector_nameradectcZ ref_framerelativeZref_timedetectorotherr r rdet_tc s rcCst|}||\}}||fS)zb Low-level function to be called from _optimal_dec_from_detector and _optimal_ra_from_detector)rZoptimal_orientation)rrdrrr r r!optimal_orientation_from_detector.srcCst||dS)aFor a given detector and GPS time, return the optimal orientation (directly overhead of the detector) in declination. Parameters ---------- detector_name : string The name of the detector, e.g., 'H1'. tc : float The GPS time of the coalescence of the signal in the `ref_frame`. Returns ------- float : The declination of the signal, in radians. r)r)rrr r roptimal_dec_from_detector6srcCst||dS)aFor a given detector and GPS time, return the optimal orientation (directly overhead of the detector) in right ascension. Parameters ---------- detector_name : string The name of the detector, e.g., 'H1'. tc : float The GPS time of the coalescence of the signal in the `ref_frame`. Returns ------- float : The declination of the signal, in radians. r)r)rrr r roptimal_ra_from_detectorIsrc Cs^t|t}|rt|g}tjddtd|}WdQRXd|t|<|rZ|d}|S)ahReturns SNR computed from the given log likelihood ratio(s). This is defined as `sqrt(2*loglr)`.If the log likelihood ratio is < 0, returns 0. Parameters ---------- loglr : array or float The log likelihood ratio(s) to evaluate. Returns ------- array or float The SNRs computed from the log likelihood ratios. ignore)invalidr=Ngr)r floatr arrayZerrstaterisnan)ZloglrZ singlevalZsnrsr r rsnr_from_loglrcs  rbothc Cst|||||\}}}}}}|dkp*|dk}|dkp:|dk}g} |rft|||||} | t| ||rt|||||} | t| ||r|s| d} | S)aReturn the f0 and the tau for one or more overtones of an l, m mode. Parameters ---------- mass : float or array Mass of the black hole (in solar masses). spin : float or array Dimensionless spin of the final black hole. l : int or array l-index of the harmonic. m : int or array m-index of the harmonic. n : int or array Overtone(s) to generate, where n=0 is the fundamental mode. Default is 0. which : {'both', 'f0', 'tau'}, optional What to return; 'both' returns both frequency and tau, 'f0' just frequency, 'tau' just tau. Default is 'both'. Returns ------- f0 : float or array Returned if ``which`` is 'both' or 'f0'. The frequency of the QNM(s), in Hz. tau : float or array Returned if ``which`` is 'both' or 'tau'. The damping time of the QNM(s), in seconds. rf0taur)rrZqnmfreqrrZqnmtau) rcspinlmnwhichrZgetf0ZgettauoutZf0sZtausr r r get_lm_f0tausrc Csii}}x|D]}d}t|dt|dt|d}}} xPt| D]D} t||||| \} } | |||t|| <| |||t|| <qJWqW||fS)aReturns a dictionary of all of the frequencies and damping times for the requested modes. Parameters ---------- mass : float or array Mass of the black hole (in solar masses). spin : float or array Dimensionless spin of the final black hole. modes : list of str The modes to get. Each string in the list should be formatted 'lmN', where l (m) is the l (m) index of the harmonic and N is the number of overtones to generate (note, N is not the index of the overtone). Returns ------- f0 : dict Dictionary mapping the modes to the frequencies. The dictionary keys are 'lmn' string, where l (m) is the l (m) index of the harmonic and n is the index of the overtone. For example, '220' is the l = m = 2 mode and the 0th overtone. tau : dict Dictionary mapping the modes to the damping times. The keys are the same as ``f0``. z{}{}{}rrr=)intrangerformatr8) rcrmodesrrZlmnkeyrrZnmodesrZtmp_f0Ztmp_taur r rget_lm_f0tau_allmodess  (rr=cCst|||||ddS)ahReturns QNM frequency for the given mass and spin and mode. Parameters ---------- final_mass : float or array Mass of the black hole (in solar masses). final_spin : float or array Dimensionless spin of the final black hole. l : int or array, optional l-index of the harmonic. Default is 2. m : int or array, optional m-index of the harmonic. Default is 2. n : int or array Overtone(s) to generate, where n=0 is the fundamental mode. Default is 0. Returns ------- float or array The frequency of the QNM(s), in Hz. r)rr)r) final_mass final_spinrrrr r rfreq_from_final_mass_spinsrcCst|||||ddS)asReturns QNM damping time for the given mass and spin and mode. Parameters ---------- final_mass : float or array Mass of the black hole (in solar masses). final_spin : float or array Dimensionless spin of the final black hole. l : int or array, optional l-index of the harmonic. Default is 2. m : int or array, optional m-index of the harmonic. Default is 2. n : int or array Overtone(s) to generate, where n=0 is the fundamental mode. Default is 0. Returns ------- float or array The damping time of the QNM(s), in seconds. r)rr)r)rrrrrr r rtau_from_final_mass_spinsr)gffffff?g\m?gV-߿)g333333ӿgEJ@g0L F%Ϳ)g?gX9v@gbX9޿)g_vO?gg@gzG޿))r=r=)r=r)r6r6)rXrX)gAf?gn4@gaTR'?)g333333?g8gDioͿgQ?)gd`T?gBig48E?)gffffff@ggw#?c Cst||\}}}t||f\}}}|j}|}|}t|j} xht| jD]Z} || || tj} yd| ||d|} Wnt k rtj } YnX| | | <qPW| |} t | |S)aReturns the final spin based on the given frequency and damping time. .. note:: Currently, only (l,m) = (2,2), (3,3), (4,4), (2,1) are supported. Any other indices will raise a ``KeyError``. Parameters ---------- f0 : float or array Frequency of the QNM (in Hz). tau : float or array Damping time of the QNM (in seconds). l : int, optional l-index of the harmonic. Default is 2. m : int, optional m-index of the harmonic. Default is 2. Returns ------- float or array The spin of the final black hole. If the combination of frequency and damping times give an unphysical result, ``numpy.nan`` will be returned. g?) r_berti_spin_constantsr!ravelr zerosrrrGr"nanreshaper) rrrrrr;bc origshapeZspinsiiQsr r rfinal_spin_from_f0_tau s    rcCsJt||||d}t||f\}}}||d||dtj|tjS)aReturns the final mass (in solar masses) based on the given frequency and damping time. .. note:: Currently, only (l,m) = (2,2), (3,3), (4,4), (2,1) are supported. Any other indices will raise a ``KeyError``. Parameters ---------- f0 : float or array Frequency of the QNM (in Hz). tau : float or array Damping time of the QNM (in seconds). l : int, optional l-index of the harmonic. Default is 2. m : int, optional m-index of the harmonic. Default is 2. Returns ------- float or array The mass of the final black hole. If the combination of frequency and damping times give an unphysical result, ``numpy.nan`` will be returned. )rrrr=)r_berti_mass_constantsr rGrrK)rrrrrr;rrr r rfinal_mass_from_f0_tauLsrc Cslt||||d}t||||d}t||\}}}tj||dk<tj|t|dk<t||||d} t| |S)a^Returns the QNM frequency (in Hz) of a chosen new (l,m) mode from the given current (l,m) mode. Parameters ---------- f0 : float or array Frequency of the current QNM (in Hz). tau : float or array Damping time of the current QNM (in seconds). current_l : int, optional l-index of the current QNM. current_m : int, optional m-index of the current QNM. new_l : int, optional l-index of the new QNM to convert to. new_m : int, optional m-index of the new QNM to convert to. Returns ------- float or array The frequency of the new (l, m) QNM mode. If the combination of frequency and damping time provided for the current (l, m) QNM mode correspond to an unphysical Kerr black hole mass and/or spin, ``numpy.nan`` will be returned. )rrrgx#?)rrrr rr8rr) rr current_l current_mnew_lnew_mrcrrZnew_f0r r rfreqlmn_from_other_lmnksrc Cslt||||d}t||||d}t||\}}}tj||dk<tj|t|dk<t||||d} t| |S)ahReturns the QNM damping time (in seconds) of a chosen new (l,m) mode from the given current (l,m) mode. Parameters ---------- f0 : float or array Frequency of the current QNM (in Hz). tau : float or array Damping time of the current QNM (in seconds). current_l : int, optional l-index of the current QNM. current_m : int, optional m-index of the current QNM. new_l : int, optional l-index of the new QNM to convert to. new_m : int, optional m-index of the new QNM to convert to. Returns ------- float or array The daming time of the new (l, m) QNM mode. If the combination of frequency and damping time provided for the current (l, m) QNM mode correspond to an unphysical Kerr black hole mass and/or spin, ``numpy.nan`` will be returned. )rrrgx#?)rrrr rr8rr) rrrrrrrcrrZnew_taur r rtaulmn_from_other_lmnsr SEOBNRv4PHMc  Cs6||||||||f} t| } | d} | dj} dd| ddD} | \}}}}}}}}t|jtj} t|jtj}xt| jD]}t||}t||}tt t||||||g}tt t||||||g}|dkrddl m }y,|j |t j|t j||dd d g| d }Wntk r>wYnX|d dt j| |<|d }|d d ||<|ddkr ||d9<q|dkrt||||tt|\}}}|||| |<|||<qt||||tt|\}}}|||| |<|||<qW| | } || }t| | t|| fS)a}Estimates the final mass and spin from the given initial parameters. This uses the fits used by either the NRSur7dq4 or EOBNR models for converting from initial parameters to final, depending on the ``approximant`` argument. Parameters ---------- mass1 : float The mass of one of the components, in solar masses. mass2 : float The mass of the other component, in solar masses. spin1x : float, optional The dimensionless x-component of the spin of mass1. Default is 0. spin1y : float, optional The dimensionless y-component of the spin of mass1. Default is 0. spin1z : float, optional The dimensionless z-component of the spin of mass1. Default is 0. spin2x : float, optional The dimensionless x-component of the spin of mass2. Default is 0. spin2y : float, optional The dimensionless y-component of the spin of mass2. Default is 0. spin2z : float, optional The dimensionless z-component of the spin of mass2. Default is 0. approximant : str, optional The waveform approximant to use for the fit function. If "NRSur7dq4", the NRSur7dq4Remnant fit in lalsimulation will be used. If "SEOBNRv4", the ``XLALSimIMREOBFinalMassSpin`` function in lalsimulation will be used. Otherwise, ``XLALSimIMREOBFinalMassSpinPrec`` from lalsimulation will be used, with the approximant name passed as the approximant in that function ("SEOBNRv4PHM" will work with this function). Default is "SEOBNRv4PHM". f_ref : float, optional The reference frequency for the spins. Only used by the NRSur7dq4 fit. Default (-1) will use the default reference frequency for the approximant. Returns ------- final_mass : float The final mass, in solar masses. final_spin : float The dimensionless final spin. rrcSsg|] }|qSr )r)r r;r r r sz*get_final_from_initial..NZ NRSur7dq4)nrfitsZNRSur7dq4RemnantZ FinalMassZ FinalSpin)f_refr=g?ZSEOBNRv4)rr!r fullrrrrlistmaprrZ eval_nrfitrMSUN_SI RuntimeErrorsumlalsimZSimIMREOBFinalMassSpingetattrZSimIMREOBFinalMassSpinPrecrr)rrrorprqryrzrs approximantrrrrrrrr[r\rrrresZsfr]fmfsr r rget_final_from_initialsR/              rc Cs t|||||||||| d dS)a*Estimates the final mass from the given initial parameters. This uses the fits used by either the NRSur7dq4 or EOBNR models for converting from initial parameters to final, depending on the ``approximant`` argument. Parameters ---------- mass1 : float The mass of one of the components, in solar masses. mass2 : float The mass of the other component, in solar masses. spin1x : float, optional The dimensionless x-component of the spin of mass1. Default is 0. spin1y : float, optional The dimensionless y-component of the spin of mass1. Default is 0. spin1z : float, optional The dimensionless z-component of the spin of mass1. Default is 0. spin2x : float, optional The dimensionless x-component of the spin of mass2. Default is 0. spin2y : float, optional The dimensionless y-component of the spin of mass2. Default is 0. spin2z : float, optional The dimensionless z-component of the spin of mass2. Default is 0. approximant : str, optional The waveform approximant to use for the fit function. If "NRSur7dq4", the NRSur7dq4Remnant fit in lalsimulation will be used. If "SEOBNRv4", the ``XLALSimIMREOBFinalMassSpin`` function in lalsimulation will be used. Otherwise, ``XLALSimIMREOBFinalMassSpinPrec`` from lalsimulation will be used, with the approximant name passed as the approximant in that function ("SEOBNRv4PHM" will work with this function). Default is "SEOBNRv4PHM". f_ref : float, optional The reference frequency for the spins. Only used by the NRSur7dq4 fit. Default (-1) will use the default reference frequency for the approximant. Returns ------- float The final mass, in solar masses. )rr)r) rrrorprqryrzrsrrr r rfinal_mass_from_initials- rc Cs t|||||||||| d dS)a'Estimates the final spin from the given initial parameters. This uses the fits used by either the NRSur7dq4 or EOBNR models for converting from initial parameters to final, depending on the ``approximant`` argument. Parameters ---------- mass1 : float The mass of one of the components, in solar masses. mass2 : float The mass of the other component, in solar masses. spin1x : float, optional The dimensionless x-component of the spin of mass1. Default is 0. spin1y : float, optional The dimensionless y-component of the spin of mass1. Default is 0. spin1z : float, optional The dimensionless z-component of the spin of mass1. Default is 0. spin2x : float, optional The dimensionless x-component of the spin of mass2. Default is 0. spin2y : float, optional The dimensionless y-component of the spin of mass2. Default is 0. spin2z : float, optional The dimensionless z-component of the spin of mass2. Default is 0. approximant : str, optional The waveform approximant to use for the fit function. If "NRSur7dq4", the NRSur7dq4Remnant fit in lalsimulation will be used. If "SEOBNRv4", the ``XLALSimIMREOBFinalMassSpin`` function in lalsimulation will be used. Otherwise, ``XLALSimIMREOBFinalMassSpinPrec`` from lalsimulation will be used, with the approximant name passed as the approximant in that function ("SEOBNRv4PHM" will work with this function). Default is "SEOBNRv4PHM". f_ref : float, optional The reference frequency for the spins. Only used by the NRSur7dq4 fit. Default (-1) will use the default reference frequency for the approximant. Returns ------- float The dimensionless final spin. )rr)r) rrrorprqryrzrsrrr r rfinal_spin_from_initialDs- rcCs|d|tjtjS)a Calculate the gravitational-wave frequency from the total mass and invariant velocity. Parameters ---------- v : float Invariant velocity M : float Binary total mass Returns ------- f : float Gravitational-wave frequency g@)rrKPI)vMr r rvelocity_to_frequency~srcCstj|tj|dS)a) Calculate the invariant velocity from the total mass and gravitational-wave frequency. Parameters ---------- f: float Gravitational-wave frequency M: float Binary total mass Returns ------- v : float or numpy.array Invariant velocity gUUUUUU?)rrrK)frr r rfrequency_to_velocitysr cCs td|S)a Innermost stable circular orbit (ISCO) for a test particle orbiting a Schwarzschild black hole Parameters ---------- M : float or numpy.array Total mass in solar mass units Returns ------- f : float or numpy.array Frequency in Hz g>, p ?)r)rr r rf_schwarzchild_iscosr c Csd}t||}|tjj9}dtjjtjj||tjjdd}d|}dtjj|||||d}d||||d} ||| fS) a9Calculate the coefficents needed to compute the shift in t(f) and phi(f) due to non-linear tides. Parameters ---------- amplitude: float Amplitude of effect n: float Growth dependence of effect m1: float Mass of component 1 m2: float Mass of component 2 Returns ------- f_ref : float Reference frequency used to define A and n t_of_f_factor: float The constant factor needed to compute t(f) phi_of_f_factor: float The constant factor needed to compute phi(f) gY@g3333333@g@g?g@gg@g)r)rrZG_SIrr) amplituderr[r\rZmcr;rZ t_of_f_factorphi_of_f_factorr r r nltides_coefss  *$rc Cst||||||\}}}}}}}t|j}t||||\}} } ||k} | |  || ||| d|| <||k} | |  || ||| d|| <t||S)aCalculate the gravitational-wave phase shift bwtween f and f_coalescence = infinity due to non-linear tides. To compute the phase shift between e.g. f_low and f_isco, call this function twice and compute the difference. Parameters ---------- f: float or numpy.array Frequency from which to compute phase f0: float or numpy.array Frequency that NL effects switch on amplitude: float or numpy.array Amplitude of effect n: float or numpy.array Growth dependence of effect m1: float or numpy.array Mass of component 1 m2: float or numpy.array Mass of component 2 Returns ------- delta_phi: float or numpy.array Phase in radians g@)rr rr!rr) r rr rr[r\rZ delta_phirr]r rr r rnltides_gw_phase_differences &&rc Csjt|||||\}}}}}}t|j|}t||||||}t||}t||||||} t| ||S)aCalculate the gravitational-wave phase shift bwtween f_low and f_isco due to non-linear tides. Parameters ---------- f_low: float Frequency from which to compute phase. If the other arguments are passed as numpy arrays then the value of f_low is duplicated for all elements in the array f0: float or numpy.array Frequency that NL effects switch on amplitude: float or numpy.array Amplitude of effect n: float or numpy.array Growth dependence of effect m1: float or numpy.array Mass of component 1 m2: float or numpy.array Mass of component 2 Returns ------- delta_phi: float or numpy.array Phase in radians )rr rr!rr r) Zf_lowrr rr[r\rZphi_lZf_iscoZphi_ir r rnltides_gw_phase_diff_iscos rmass2_from_mchirp_mass1rA)F)FT)T)T)F)ra)rararg)rarararg)r)r)rF)rr)r=r=r)r=r=r)r=r=)r=r=)rararararararr)rararararararr)rararararararr)s__doc__rr rZpycbc.detectorrZpycbc.cosmologyrbZ coordinatesrrrrnrriZlibutilsZimport_optionalrrrrrr r$r%r&r'r(r)r,r-r/r0r2r3r4r<Z vectorizerr@rArBrCrDrErFrIrJrLrMrNrOrSrTrUrVr`rfrmrrrtrur}rrrrrrrwrvrrrrrxrrr~rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr r rrr__all__r r r rs2            )         / ,           %" 0&   , &% Z 0 8***