B d@4@sddlZddlZddlmZmZmZdZdZdZdZ iZ iZ iZ iZ dd Zd d Zd d ZddZddZddZd!ddZd"ddZeeddZd#ddZeje_d$dd ZdS)%N) _getspline _qnmomega _checkspingư>g{Gz?dFcCs$|dkrtd|dkr tddS)z1Checks that the spin weight is a supported value.)rzs must be either -2, -1, or 0rz only s=-2 is currently supportedN) ValueErrorNotImplementedError)sr ]/work/yifan.wang/ringdown/master-ringdown-env/lib/python3.7/site-packages/pykerr/harmonics.py_checkspinweightsrcCsTt|tdd|||t}tdd|||t}||d||}|dkrP|}|S)aReturns the angular separation constant for a Kerr BH. Parmeters --------- spin : float The dimensionless spin. Must be in [-0.9999, 0.9999]. l : int The l index. m : int The m index. n : int The overtone number (where n=0 is the fundamental mode). Returns ------- complex : The complex separation constant. almreZimy?r)rr_realm_splines_imalm_splinesconj)spinlmnZresplineZimsplinerr r r kerr_alm#srcCsd|d|d|dS)zLeaver's alpha coefficient for the Slm (Eq. 20 of Leaver). Note: we use jj in place of Leaver's n so as not to confuse with the overtone index. rrr )jjk1r r r _alpha@srcCs,||dd|||dd||S)zLeaver's beta coefficient for the Slm (Eq. 20 of Leaver). Note: we use jj in place of Leaver's n so as not to confuse with the overtone index. rrr )rrk2awalmtermr r r _betaIsr cCsd|||||S)zLeaver's gamma coefficient for the Slm (Eq. 20 of Leaver). Note: we use jj in place of Leaver's n so as not to confuse with the overtone index. rr )rrrrr r r r _gammaRsr!cCs|dkr |S|S)z/Convenience function to set tolerance defaults.Nr )argdefaultr r r _setdefault[sr$rTc Cs| rdyJ|dkr,tdt|d|||t} ntdt|d|||t} | |Stk rbYnXt|t}t|t}t|t }t j dt j |d} t | ||||||||dd } dt j t j| | jt | | d d d S) aCalculate the normalization constant for a spheroidal harmonic. The normalization is such that: .. math:: \int_{0}^{2\pi}\int_{0}^{\pi} |{}_{-s}S_{\ell m}(J,\theta,\phi)|^2 \sin(\theta)\mathrm{d}\theta \mathrm{d}\phi = 1 where :math:`J` is the spin of the black hole. The integral is calulcated using the trapezoidal rule. Parameters ---------- spin : float The dimensionless spin of the black hole. l : int The l index. Up to m=7 is supported. m : int The m index. All +/-m for the given l are supported. n : int The overtone number (where n=0 is the fundamental mode). Up to n=7 is supported. s : int, optional The spin number. Must be either 0, -1, or -2. Default is -2. npoints : int, optional The number of points to use in the integral. Default is 1000. tol : float, optional Tolerance used to determine when to stop the sum over coefficients :math:`c_n = a_n (1 + \cos(theta))^n` in the spheroidal harmonics (see Eq. 18 of Leaver). The sum stops when :math:`|c_n|` is less than the given value. If ``None`` (the default) will use :const:`pykerr.harmonics.TOL`. maxtol : float, optional Maximum allowed error in the sum over coefficients in the spheroidal harmonics. If no :math:`c_n` up to :math:`n` = ``max_recursion`` satisfies :math:`|c_n| <` ``tol``, then the sum will be done up to the smallest :math:`|c_n|` such that :math:`|c_n|` < ``maxtol``. If no :math:`|c_n|` is < ``maxtol``, then a ValueError will be raised. If set to ``None`` (the default), will use :const:`pykerr.harmonics.MAXTOL`. max_recursion : int, optional Maximum number of terms that will be used in the sum over coefficients in the spheroidal harmonics (see Eq. 18 of Leaver). If ``None`` (the default), will use :const:`pykerr.harmonics.MAX_RECURSION`. use_cache : bool, optional Use tabulated values in the cached data, if available. A cubic spline is used to interpolate to spins that are not in the cache. Default is True. rz s{}nmnormNzs{}norm)numF)r tolmaxtol max_recursion normalizerr)Zdxg)rformatabs_normnm_splines _norm_splinesKeyErrorr$TOLMAXTOL MAX_RECURSIONnumpyZlinspacepi spheroidalZtrapzrrealsin) rrrrr Znpointsr'r(r) use_cacheZsplineZthetasslmr r r slmnorm`s$5    "r:c # Cst|t}t|t}t| t} t|t|} t||||} t||||}||}dt ||}dt ||}d|d||d||||d|d||d| }d}d| }d}tj | t d}|d|d<t d|}t d||||}|}| ||}t tjtj}xt ||kr|| kr|||}|||<t ||}t |||||}t|||||}|||| |}|}|}|d7}qW|| krt |} || }t ||kr| d}trtd|t |||||||| t ||krPd t ||||||||}!trH|!d d tt|7}!t|!|d |}t|| d ||d| |d| |}"| r|"t|||||||| | d 9}"||"9}|d|dtd||9}|S)ag Calculate the spin-weighted spheroidal harmonic. See Eq. 18 of E. W. Leaver (1985) [`doi:10.1098/rspa.1985.0119` ]. Solutions for the angular separation constants :math:`A_{\ell m}` are from Berti, Cardoso, & Starinets CQG26, 163001 (2009) [arXiv:0905.2975]. Parameters ---------- theta : float The polar angle of the observer with respect to the black hole's spin. spin : float The dimensionless spin of the black hole. l : int The l index. Up to l=7 is supported. m : int The m index. All +/-m for the given l are supported. n : int The overtone number (where n=0 is the fundamental mode). Up to n=7 is supported. s : int, optional The spin number. Must be either 0, -1, or -2. Default is -2. phi : float, optional The azimuthal angle of the observer. Default is 0. tol : float, optional Tolerance used to determine when to stop the sum over coefficients :math:`c_n = a_n (1 + \cos(theta))^n` in the spheroidal harmonics (see Eq. 18 of Leaver). The sum stops when :math:`|c_n|` is less than the given value. If ``None`` (the default) will use :const:`pykerr.harmonics.TOL`. maxtol : float, optional Maximum allowed error in the sum over coefficients in the spheroidal harmonics. If no :math:`c_n` up to :math:`n` = ``max_recursion`` satisfies :math:`|c_n| <` ``tol``, then the sum will be done up to the smallest :math:`|c_n|` such that :math:`|c_n|` < ``maxtol``. If no :math:`|c_n|` is < ``maxtol``, then a ValueError will be raised. If set to ``None`` (the default), will use :const:`pykerr.harmonics.MAXTOL`. max_recursion : int, optional Maximum number of terms that will be used in the sum over coefficients in the spheroidal harmonics (see Eq. 18 of Leaver). If ``None`` (the default), will use :const:`pykerr.harmonics.MAX_RECURSION`. normalize : bool, optional Normalize the harmonic before returning. The normalization is such that the harmonic integrates to 1 over the unit sphere. use_cache : bool, optional If normalizing, use tabulated normalization constants in the cached data, if available. A cubic spline is used to interpolate to spins that are not in the cache. Otherwise, the normalization constant will be calculated on the fly by numerically integrating over theta. Default is True. Returns ------- slm : complex The value of the spheroidal harmonic. g?rrg?)ZdtypeyrzDid not get to target tolerance of {} for Slm. Actual tolerance is {}. Parameters: theta={}, spin={}, l={}, m={}, n={}, s={}, phi={}zMax recursion exceeded without satisfying maxtol. Smallest abs(term): {}. Parameters: theta={}, spin={}, l={}, m={}, n={}, s={}, phi={}.z Terms: {} Ny?)r r'r(r)r8r)r$r0r1r2rr3cosrrr,Zzeroscomplexrr infr!ZargminDEBUGloggingdebugr+joinmapstrr sumexpr:max)#thetarrrrr phir'r(r)r*r8uromegarrrrrZb_nZa0r9Zalpha0Zbeta0Za_nm1Za_nZc_nZalpha_nZbeta_nZgamma_nZa_np1ZminidxmsgZnormr r r _pyslmsl=    D      2 rN c Cs:t|||||||||| | | } t| tjr6| tj} | S)N)_npslm isinstancer3ZndarrayZastyper>) rIrrrrr rJr'r(r)r*r8outr r r r5@s   r5c syddlmWntk r,tdYnXy||Stk rt|}t|}t||}tfdd|D|j SXdS)aCalculate the spin-weighted spherical harmonic. Uses functions from lal. Parameters ---------- theta : float or array The polar angle. l : int The l index. m : int The m index. s : int, optional The spin number. Default is -2. phi : float or array, optional The azimuthal angle. Default is 0. Returns ------- complex : The value of the spherical harmonic. r)SpinWeightedSphericalHarmonicz[lalsuite must be installed to generate the spherical harmonics. Run `pip install lalsuite`.cs g|]\}}||qSr r ).0incrJ) _sphericalrrr r r qszspherical..N) ZlalrS ImportError TypeErrorr3Z atleast_1d broadcastarrayZreshapeshape)rIrrr rJZincphir )rVrrr r sphericalMs   r])rr%NNNT)rr;NNNTT)rr;NNNTT)rr;)rAr3Zqnmrrrr0r1r2r@rrr.r-rrrr r!r$r:rNZ frompyfuncrPr5__doc__r]r r r r s4    K