B d@sdZddlZddlZddlmZmZmZddlmZm Z e dZ ddZ dd d Z d d Zd dZddZddZddZdddZddZddZddZdd Zd!d"Zd#d$Zd%d&Zd'd(Zd)d*Zd+d,Zd-d.Zd/d0Zd1d2Z d3d4Z!d5d6Z"d7d8Z#d9d:Z$d;d<Z%d=d>Z&d?d@Z'e(e'Z)dAdBZ*dCdDZ+e(e+Z,dEdFZ-dGdHdIdHdJdHdKdHdLdHdMdHdNdHdOdHdPdHdQdHdRdHdSdHdTdHdUdHdVdHdWdHdXdHdYdHdZdHd[Z.d\d]Z/dd_d`Z0e(e0Z1ddddeZ2dfdgZ3dhdiZ4djdkZ5e(e5Z6dldmZ7dndoZ8ddqdrZ9ddsdtZ:ddudvZ;dwdxZe6Z?d{d|Z@d}d~ZAddZBdddZCdddZDdddZEdddZFdS)ziThis module contains convenience pN functions. This includes calculating conversions between quantities. N)bisectbrentqminimize) conversionslibutils lalsimulationcCstdtt|S)z= Return the nearest binary number larger than input_len. )intnumpyceillog2)Z input_lenr Z/work/yifan.wang/ringdown/master-ringdown-env/lib/python3.7/site-packages/pycbc/pnutils.pynearest_larger_binary_number$srffffff?cCstj|||dS)N)ref_mass)rchirp_distance)distmchirprr r rr)srcCs t||}t||}||fS)N)rZmtotal_from_mass1_mass2eta_from_mass1_mass2)mass1mass2m_totaletar r rmass1_mass2_to_mtotal_eta,s  rcCs t||}t||}||fS)N)rmass1_from_mtotal_etamass2_from_mtotal_eta)rrrrr r rmtotal_eta_to_mass1_mass21s  rcCs t||}t||}||fS)N)rZmchirp_from_mass1_mass2r)rrm_chirprr r rmass1_mass2_to_mchirp_eta6s  rcCs,t||}t||}t||}||fS)N)rZmtotal_from_mchirp_etarr)rrmtotalrrr r rmchirp_eta_to_mass1_mass2;s   r!cCs t||S)ai This function takes a value of mchirp and one component mass and returns the second component mass. As this is a cubic equation this requires finding the roots and returning the one that is real. Basically it can be shown that: m2^3 - a(m2 + m1) = 0 where a = Mc^5 / m1^3 this has 3 solutions but only one will be real. )rZmass2_from_mchirp_mass1)rrr r rmchirp_mass1_to_mass2Asr"FTcCstj||||dS)a This function takes values for eta and one component mass and returns the second component mass. Similar to mchirp_mass1_to_mass2 this requires finding the roots of a quadratic equation. Basically: eta m2^2 + (2 eta - 1)m1 m2 + \eta m1^2 = 0 This has two solutions which correspond to mass1 being the heavier mass or it being the lighter mass. By default the value corresponding to mass1 > mass2 is returned. Use the return_mass_heavier kwarg to invert this behaviour. )Zknown_is_secondary force_real)rZmass_from_knownmass_eta)rrZreturn_mass_heavierr#r r reta_mass1_to_mass2Rs r$cCs*t|}t||}t||}||fS)a This function takes a value of mchirp and the mass ratio mass1/mass2 and returns the two component masses. The map from q to eta is eta = (mass1*mass2)/(mass1+mass2)**2 = (q)/(1+q)**2 Then we can map from (mchirp,eta) to (mass1,mass2). )rZ eta_from_qZmass1_from_mchirp_etaZmass2_from_mchirp_eta)rqrrrr r rmchirp_q_to_mass1_mass2bs   r&cCs t|S)zused in calculating chirp times: see Cokelaer, arxiv.org:0706.4437 appendix 1, also lalinspiral/python/sbank/tau0tau3.py )rZ_a0)f_lowerr r rA0qsr(cCs t|S)z&another parameter used for chirp times)rZ_a3)r'r r rA3wsr)cCs$t|||}t|||}||fS)N)rZtau0_from_mass1_mass2Ztau3_from_mass1_mass2)rrr'tau0tau3r r rmass1_mass2_to_tau0_tau3{sr,cCs$t|||}t|||}||fS)N)rZmtotal_from_tau0_tau3Zeta_from_tau0_tau3)r*r+r'r rr r rtau0_tau3_to_mtotal_etasr-cCst|||\}}t||S)N)r-r)r*r+r'rrr r rtau0_tau3_to_mass1_mass2sr.c CsNt||\}}t||k||}t||k||}t|||\}} } || | fS)N)rr where!get_beta_sigma_from_aligned_spins) rrspin1zspin2z_rZ heavy_spinZ light_spinbetasigmagammar r r-mass1_mass2_spin1z_spin2z_to_beta_sigma_gammas r7c Csd||}d||}dd|d}||}dd||}|d||7}|dd|}|dd|d ||||7}||d ||7}d d |d |||} | d d|||7} ||| fS)a Calculate the various PN spin combinations from the masses and spins. See . Parameters ----------- eta : float or numpy.array Symmetric mass ratio of the input system(s) spin1z : float or numpy.array Spin(s) parallel to the orbit of the heaviest body(ies) spin2z : float or numpy.array Spin(s) parallel to the orbit of the smallest body(ies) Returns -------- beta : float or numpy.array The 1.5PN spin combination sigma : float or numpy.array The 2PN spin combination gamma : float or numpy.array The 2.5PN spin combination chis : float or numpy.array (spin1z + spin2z) / 2. g?gUUUUU"@gUUUUUU@gH@irg@@g@$@gjS2t@gHr@g98B@gqq/@r ) rr1r2ZchiSZchiAdeltaZspinspinr4r5r6r r rr0s  $ r0cCs |tjS)N)lalMSUN_SI)Z solar_massesr r rsolar_mass_to_kgsr=cCs |tjS)N)r;ZPC_SI)distancer r rparsecs_to_meterssr?cCs t|dS)Ng.A)r?)r>r r rmegaparsecs_to_meterssr@cCs t||S)N)rvelocity_to_frequency)vMr r rrAsrAcCs t||S)N)rfrequency_to_velocity)frCr r rrDsrDcCs t|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 )rZf_schwarzchild_isco)rCr r r f_SchwarzISCOsrFcCsHt||||}t||dd|d||d|||S)a Mass ratio dependent ISCO derived from estimates of the final spin of a merged black hole in a paper by Buonanno, Kidder, Lehner (arXiv:0709.3839). See also arxiv:0801.4297v2 eq.(5) Parameters ---------- m1 : float or numpy.array First component mass in solar mass units m2 : float or numpy.array Second component mass in solar mass units Returns ------- f : float or numpy.array Frequency in Hz r8gffffff@g@g?)r minimumrF)m1m2r%r r r f_BKLISCOsrJcCsddtj|tjS)a< Gravitational wave frequency corresponding to the light-ring orbit, equal to 1/(3**(3/2) pi M) : see InspiralBankGeneration.c Parameters ---------- M : float or numpy.array Total mass in solar mass units Returns ------- f : float or numpy.array Frequency in Hz g?g9B.@)r;PIMTSUN_SI)rCr r r f_LightRingsrMcCsddtjd|tjS)a Effective RingDown frequency studied in Pan et al. (arXiv:0704.1964) found to give good fit between stationary-phase templates and numerical relativity waveforms [NB equal-mass & nonspinning!] Equal to 1.07*omega_220/2*pi Parameters ---------- M : float or numpy.array Total mass in solar mass units Returns ------- f : float or numpy.array Frequency in Hz g‡-yracCst|d|dS)Nrr)rM)r`r r rrarbcCst|d|dS)Nrr)rN)r`r r rrarbcCst|d|dS)Nrr)rJ)r`r r rrarbcCst|d|dS)Nrr)rP)r`r r rrarbcCst|d|dS)Nrr)rQ)r`r r rrarbcCst|d|d|d|dS)Nrrr1r2)meco_frequency)r`r r rrascCs$t|d|d|d|ddddS)Nrrr1r2)qm1qm2)hybrid_meco_frequency)r`r r rrascCs td|d|d|d|dS)NZfIMRPhenomBFinalrrr1r2)r[)r`r r rras cCs td|d|d|d|dS)NZfIMRPhenomCFinalrrr1r2)r[)r`r r rras cCs td|d|d|d|dS)NZfIMRPhenomDPeakrrr1r2)r[)r`r r rras cCs td|d|d|d|dS)NZ fEOBNRv2RDrrr1r2)r[)r`r r rrascCs td|d|d|d|dS)NZ fEOBNRv2HMRDrrr1r2)r[)r`r r rrascCs td|d|d|d|dS)NZ fSEOBNRv1RDrrr1r2)r[)r`r r rrascCs td|d|d|d|dS)NZ fSEOBNRv1Peakrrr1r2)r[)r`r r rrascCs td|d|d|d|dS)NZ fSEOBNRv2RDrrr1r2)r[)r`r r rrascCs td|d|d|d|dS)NZ fSEOBNRv2Peakrrr1r2)r[)r`r r rrascCs td|d|d|d|dS)NZ fSEOBNRv4RDrrr1r2)r[)r`r r rrascCs td|d|d|d|dS)NZ fSEOBNRv4Peakrrr1r2)r[)r`r r rras)Z SchwarzISCOZ LightRingZERDZBKLISCOZFRDZLRDZMECOZ HybridMECOZIMRPhenomBFinalZIMRPhenomCFinalZIMRPhenomDPeakZ EOBNRv2RDZ EOBNRv2HMRDZ SEOBNRv1RDZ SEOBNRv1PeakZ SEOBNRv2RDZ SEOBNRv2PeakZ SEOBNRv4RDZ SEOBNRv4PeakcCs||||d}t||S)a Returns the result of evaluating the frequency cutoff function specified by 'name' on a template with given parameters. Parameters ---------- name : string Name of the cutoff function m1 : float or numpy.array First component mass in solar masses m2 : float or numpy.array Second component mass in solar masses s1z : float or numpy.array First component dimensionless spin S_1/m_1^2 projected onto L s2z : float or numpy.array Second component dimensionless spin S_2/m_2^2 projected onto L Returns ------- f : float or numpy.array Frequency in Hz )rrr1r2)named_frequency_cutoffs)namerHrIrTrUparamsr r rfrequency_cutoff_from_namesrjSEOBNRv4cCst|t|t|t|t|f\}}}}}|dkrbt||||}t|tj|tj||}n|dkrt|tj|tj|||}nt|dkrt||tj|tj||}nL|dks|dkrt||||}t ||tj|tj|d}n t d||dS) z>Wrapper of lalsimulation template duration approximate formulaSEOBNRv2Z IMRPhenomDrkSPAtmpltTaylorF2z#I can't calculate a duration for %sg?) rRrZSimIMRPhenomBComputeChiZ!SimIMRSEOBNRv2ChirpTimeSingleSpinr;r<ZSimIMRPhenomDChirpTime SimIMRSEOBNRv4ROMTimeOfFrequencyZ(SimInspiralTaylorF2ReducedSpinComputeChiZ'SimInspiralTaylorF2ReducedSpinChirpTime RuntimeError)rHrIrTrUf_low approximantchiZ time_lengthr r r_get_imr_durations&  rudrnc  sGddd} | } | _| _| _| _yt|ddit| d}Wnttfk r^YnX|dkrddlm t } t t |t | |} t fd d | D} n|d krtd } t t |t | |} t fd d | D} nh|dkrftd} t t |t d| |} t fdd | D} ntd|d|| | fS)zCompute the time-frequency evolution of an inspiral signal. Return a tuple of time and frequency vectors tracking the evolution of an inspiral signal in the time-frequency plane. c@s eZdZdS)zget_inspiral_tf..ParamsN)__name__ __module__ __qualname__r r r rParams!sr{ __builtins__N)ri)rnrmr)findchirp_chirptimecs&g|]}ttt|qSr )rR).0rE)r}rr pn_2orderr r 5sz#get_inspiral_tf..)rlZSEOBNRv2_ROM_DoubleSpinZSEOBNRv2_ROM_DoubleSpin_HIrlc s.g|]&}t|ttttqSr )rZ,SimIMRSEOBNRv2ROMDoubleSpinHITimeOfFrequencyr=rR)r~rE)rrspin1spin2r rr>s)rkZ SEOBNRv4_ROMrkg+?c s.g|]&}t|ttttqSr )rrpr=rR)r~rE)rrrrr rrGsz Approximant z not supported)rrr1r2evaldict NameError TypeErrorZpycbc.waveform.spa_tmpltr}rFr Zlogspacelog10arrayr_ ValueError)ZtcrrrrrrZn_pointsrrsr{riZf_highZtrack_fZtrack_tr )r}rrrrrrget_inspiral_tfsD        rcCs||}||||}|||||}||d}d|d||d}d|||d} d||||d||d||||d||} d |} d |d} d } d d |dt|dd}d }ddt|dddt|dd|ddttjdd}| d|dd||d7} |d| dd| d7}|d|dd|dd|d|d |t|dd7}| | | |||fS)!zL Return the center-of-mass energy coefficients up to 3.0pN (2.5pN spin) g@g@\@gS@g(@gS@g @g@T@g0@gggg rg8@g%gX@#g@@gqqM@ 4i`ig0u@i i)powr;rK)rHrIchi1chi2mtotrrtchisymr4sigma12sigmaqmZenergy0energy2energy3energy4energy5energy6r r r_energy_coeffsRs& " D @rcs:t||||\}fdd}t|ddS)a Returns the velocity of the minimum energy cutoff for 3.5pN (2.5pN spin) Parameters ---------- m1 : float First component mass in solar masses m2 : float Second component mass in solar masses chi1 : float First component dimensionless spin S_1/m_1^2 projected onto L chi2 : float Second component dimensionless spin S_2/m_2^2 projected onto L Returns ------- v : float Velocity (dimensionless) c sDd||d|d|d|dd|S)Ng@g@g@g@g@g @r )rB)rrrrrr reprimeszmeco_velocity..eprimeg?g?)rr)rHrIrrr3rr )rrrrrr meco_velocitynsrcCstt||||||S)zNReturns the frequency of the minimum energy cutoff for 3.5pN (2.5pN spin) )rAr)rHrIrrr r r_meco_frequencysrcCs||}||||}|||||}||d}d|d||d}d|||d} d||||d||d||||d||} d } d d d |} d tj|} dd|d||d| | }dtjdd|d|dd||dd||dd|||d}dd|d||d|||}d}tjdd d!|d"||}| | | |||||fS)#z= Returns the dt/dv coefficients up to 3.5pN (2.5pN spin) g@g@\@gS@g(@gS@g @g@T@g0@g?gaah?g8@g@ggUGAg,TAgPAg/AgaaX?g1g@g(Ag@gE@glxAg@g@l@gq= ף6@gZd;Od@g{Nz@gG`@g[[@ghmgBhAg4RA)r;rK)rHrIrrrrrtrr4rrZdtdv0dtdv2dtdv3dtdv4dtdv5dtdv6dtdv6logdtdv7r r r _dtdv_coeffss" "$V("rcsVt||||\}fdd}|ddkrNt|ddSdSdS)Ncsb}||dt|}||}||}||}||}|||dS)Ng@g?)r log)rBx)rrrrrrrr r dtdv_funcs    z(_dtdv_cutoff_velocity..dtdv_funcg?gg?)rr)rHrIrrr3rr )rrrrrrrr_dtdv_cutoff_velocitys   rrocCszd}d}||krtdn |dkr&|}||kr8tdn |dkrD|}d}d} ||} ||| } || } || } || | }|| | }t||\}}t|d}|dkrd|d<|dkrd|d<|dkrdd ||d<|d krd|d <|d krd d |||d|d <|dkr$d|d<|dkrfdddtjtj|d||d|||d<dd||}dd||}d|}|d| | }| dd| | }| dd| | }dd|d | | dd|d}dd|d | | dd|d}dd|dd ||d!| | d"d#|d$||d}dd|dd ||d!| | d"d#|d$||d}|d kr|d ||||7<|d kr2|d |||d||7<|d ||||||||||||7<|dkrP|||||d<|dkrv|d||||7<|S)%zZ Return the energy coefficients. This assumes that the system has aligned spins only. rwz8pN coeffiecients of that order have not been implementedrog?r8rrgUUUUUUg"@rr9g@TgL@g8@g%gqqM@gUUUUU@gUUUUU?g{?gUUUUUU@g@g@g&@gN@gg$@g@@gv@g@g=@g(@ggC@g@)rrr Zzerosr;rK)rHrIrTrU phase_order spin_orderZimplemented_phase_orderZimplemented_spin_orderZqmdef1Zqmdef2rCdmZm1MZm2Mr3recofZESO15s1ZESO15s2ZESS2ZEQM2s1ZEQM2s1LZEQM2s2LZESO25s1ZESO25s2ZESO35s1ZESO35s2r r renergy_coefficientssl        8((DD  $<  rc Csht||||||}t||\}} d| } d} x2tdt|dD]} | || d|| 7} q@W| | S)Nggrr8g@)rrr arangelen) rBrrrTrUrrrr3rampeir r renergysrcs*t||||||fdd}t|ddS)NcsDd}x:tdtdD]$}|||d||d7}qW|S)Nrr8g?r)r rr)rBder)rr rtests$zmeco2..testgMbP?g?)rr)rHrIrTrUrrrr )rrmeco2s rcCstt||||t||||S)N)minrr)rHrIrrr r rt2_cutoff_velocitysrcCstt||||||S)N)rAr)rHrIrrr r rt2_cutoff_frequencysrcCs0d||dd|dd||ddS)z@Return the function whose first root defines the Kerr light ringr8rrgUUUUUU?r )rBrtr r rkerr_lightring(srcCs,|dkrttddddSttdd|dSdS)z*Return the velocity at the Kerr light ringgx#?rg?)argsN)rr)rtr r rkerr_lightring_velocity-src Cs~tjd}|d|d|d|d|d|df\}} } } } } |d|df\}}t|t|f\}}t||}|d|df\}}|||}|d|df\}}|d|df\}}|d|df\}}|||||}ddd |d|| d td|| d|| d |d || d }||d | |d d|||| d d|d|d||d ||||d ||| dd|||d|d||||d|d||||| d|dd||dd|dd|ddd|d|||d|d||||dd|d ||||||dd|d ||||||d!d"|d#|||d!d"||| |d d d$|d%|||d d%|d$|||d&d'|d(||||d&d(|d'||||d)|||| }|S)*aReturn hybrid MECO energy. Return the hybrid energy [eq. (6)] whose minimum defines the hybrid MECO up to 3.5PN (including the 3PN spin-spin) Parameters ---------- m1 : float Mass of the primary object in solar masses. m2 : float Mass of the secondary object in solar masses. chi1: float Dimensionless spin of the primary object. chi2: float Dimensionless spin of the secondary object. qm1: float Quadrupole-monopole term of the primary object (1 for black holes). qm2: float Quadrupole-monopole term of the secondary object (1 for black holes). Returns ------- h_E: float The hybrid energy as a function of v rrr9rrrwgg?g@gUUUUUU?g@r8g(@g3@g @g8@gqq?g^@gS@gF@g@g@gi@gX@g`c@gA@g@@grq?g5@gL@g;@g4@g?@g"@gC@g@r@g@T@g@g@gv@g@)r pirRsqrt)rBrHrIrrrdreZpi_sqZv2Zv3Zv4Zv5Zv6Zv7Zchi1_sqZchi2_sqrCZM_2ZM_4rZeta2Zeta3Zm1_2Zm1_4Zm2_2Zm2_4rtZKerrZh_Er r r hybridEnergy6s& 4  :rc Csd|dkr d}|dkrd}||||||}t|d}ttd||||||fd|fgdjS)aReturn the velocity of the hybrid MECO Parameters ---------- m1 : float Mass of the primary object in solar masses. m2 : float Mass of the secondary object in solar masses. chi1: float Dimensionless spin of the primary object. chi2: float Dimensionless spin of the secondary object. qm1: {None, float}, optional Quadrupole-monopole term of the primary object (1 for black holes). If None, will be set to qm1 = 1. qm2: {None, float}, optional Quadrupole-monopole term of the secondary object (1 for black holes). If None, will be set to qm2 = 1. Returns ------- v: float The velocity (dimensionless) of the hybrid MECO Nr8g{Gz?g?g?)rZbounds)rrrritem)rHrIrrrdrertZvmaxr r rhybrid_meco_velocityzs rcCs4|dkr d}|dkrd}tt||||||||S)aReturn the frequency of the hybrid MECO Parameters ---------- m1 : float Mass of the primary object in solar masses. m2 : float Mass of the secondary object in solar masses. chi1: float Dimensionless spin of the primary object. chi2: float Dimensionless spin of the secondary object. qm1: {None, float}, optional Quadrupole-monopole term of the primary object (1 for black holes). If None, will be set to qm1 = 1. qm2: {None, float}, optional Quadrupole-monopole term of the secondary object (1 for black holes). If None, will be set to qm2 = 1. Returns ------- f: float The frequency (in Hz) of the hybrid MECO Nr8)rAr)rHrIrrrdrer r rrfs rfc  CsPt|||| | |||tj|tj|| \} } } }}}}| | | ||||d}|S)aConverts J-frame parameters into L0 frame. Parameters ---------- mass1 : float The mass of the first component object in the binary (in solar masses) mass2 : float The mass of the second component object in the binary (in solar masses) f_ref : float The reference frequency. thetajn : float Angle between the line of sight and the total angular momentume J. phijl : float Azimuthal angle of L on its cone about J. spin1_a : float The dimensionless spin magnitude :math:`|\vec{{s}}_1/m^2_1|`. spin2_a : float The dimensionless spin magnitude :math:`|\vec{{s}}_2/m^2_2|`. spin1_polar : float Angle between L and the spin magnitude of the larger object. spin2_polar : float Angle betwen L and the spin magnitude of the smaller object. spin12_deltaphi : float Difference between the azimuthal angles of the spin of the larger object (S1) and the spin of the smaller object (S2). Returns ------- dict : Dictionary of: * inclination : float Inclination (rad), defined as the angle between the orbital angular momentum L and the line-of-sight at the reference frequency. * spin1x : float The x component of the first binary component's dimensionless spin. * spin1y : float The y component of the first binary component's dimensionless spin. * spin1z : float The z component of the first binary component's dimensionless spin. * spin2x : float The x component of the second binary component's dimensionless spin. * spin2y : float The y component of the second binary component's dimensionless spin. * spin2z : float The z component of the second binary component's dimensionless spin. ) inclinationspin1xspin1yr1spin2xspin2yr2)rZ2SimInspiralTransformPrecessingNewInitialConditionsr;r<)rrf_refphirefthetajnphijlspin1_aspin2_a spin1_polar spin2_polarspin12_deltaphirrrr1rrr2outr r rjframe_to_l0frames= rc  CsDt|||||| | |||| \} } } }}}}| | | ||||d}|S)aConverts L0-frame parameters to J-frame. Parameters ---------- mass1 : float The mass of the first component object in the binary (in solar masses) mass2 : float The mass of the second component object in the binary (in solar masses) f_ref : float The reference frequency. phiref : float The orbital phase at ``f_ref``. inclination : float Inclination (rad), defined as the angle between the orbital angular momentum L and the line-of-sight at the reference frequency. spin1x : float The x component of the first binary component's dimensionless spin. spin1y : float The y component of the first binary component's dimensionless spin. spin1z : float The z component of the first binary component's dimensionless spin. spin2x : float The x component of the second binary component's dimensionless spin. spin2y : float The y component of the second binary component's dimensionless spin. spin2z : float The z component of the second binary component's dimensionless spin. Returns ------- dict : Dictionary of: * thetajn : float Angle between the line of sight and the total angular momentume J. * phijl : float Azimuthal angle of L on its cone about J. * spin1_a : float The dimensionless spin magnitude :math:`|\vec{{s}}_1/m^2_1|`. * spin2_a : float The dimensionless spin magnitude :math:`|\vec{{s}}_2/m^2_2|`. * spin1_polar : float Angle between L and the spin magnitude of the larger object. * spin2_polar : float Angle betwen L and the spin magnitude of the smaller object. * spin12_deltaphi : float Difference between the azimuthal angles of the spin of the larger object (S1) and the spin of the smaller object (S2). )rrrrrrr)rZ$SimInspiralTransformPrecessingWvf2PE)rrrrrrrr1rrr2rrZs1polZs2polZ s12_deltaphirrrr r rl0frame_to_jframe s@r)r)FT)rk)rvrwrn)rrroro)rrroro)rrroro)NN)NN)rrrrrrrr)rrrrrrrr)G__doc__r;r Zscipy.optimizerrrZpycbcrrZimport_optionalrrrrrrr!r"r$r&r(r)r,r-r.r7r0r=r?r@rArDrFrJrMrNrPrQrXZ vectorizerZr[r]r^r_rgrjruZget_imr_durationrrrrrcrrrrrrrZt4_cutoff_velocityZt4_cutoff_frequencyrrrrrfrrr r r rs    '       8  K  D ' ! 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