IR-egdZddlZddlZddlmZddlmZddl m Z ddl m Z ddl mZmZgd ZGd d e ZGd d e ZGdde ZGdde ZdS)z$ Models that have physical origins. N) constants)units)AstropyUserWarning)Fittable1DModel)InputParameterError Parameter) BlackBodyDrude1D Plummer1DNFWceZdZdZeddejdZedddZd Z d ej iZ ej ej d zejzejzejzz Zej ej d zejzejzejzz ej ej d zejzejzejzz d Zfd ZdZedZdZedZedZedZxZS)r aY Blackbody model using the Planck function. Parameters ---------- temperature : `~astropy.units.Quantity` ['temperature'] Blackbody temperature. scale : float or `~astropy.units.Quantity` ['dimensionless'] Scale factor. If dimensionless, input units will assumed to be in Hz and output units in (erg / (cm ** 2 * s * Hz * sr). If not dimensionless, must be equivalent to either (erg / (cm ** 2 * s * Hz * sr) or erg / (cm ** 2 * s * AA * sr), in which case the result will be returned in the requested units and the scale will be stripped of units (with the float value applied). Notes ----- Model formula: .. math:: B_{\nu}(T) = A \frac{2 h \nu^{3} / c^{2}}{exp(h \nu / k T) - 1} Examples -------- >>> from astropy.modeling import models >>> from astropy import units as u >>> bb = models.BlackBody(temperature=5000*u.K) >>> bb(6000 * u.AA) # doctest: +FLOAT_CMP .. plot:: :include-source: import numpy as np import matplotlib.pyplot as plt from astropy.modeling.models import BlackBody from astropy import units as u from astropy.visualization import quantity_support bb = BlackBody(temperature=5778*u.K) wav = np.arange(1000, 110000) * u.AA flux = bb(wav) with quantity_support(): plt.figure() plt.semilogx(wav, flux) plt.axvline(bb.nu_max.to(u.AA, equivalencies=u.spectral()).value, ls='--') plt.show() g@rzBlackbody temperaturedefaultminunit description?z Scale factorrrrTx)SNUSLAMc|dd}t|dr|jtjse|j}||jt jdtjzstd||j |d<||_ n |j|_ tj |i|S)Nscalerrz8scale units not dimensionless or in surface brightness: )gethasattrr is_equivalentudimensionless_unscaled _native_unitsspectral_densityAA ValueErrorvalue _output_unitssuper__init__)selfargskwargsr output_units __class__s @lib/python3.11/site-packages/astropy/modeling/physical_models.pyr(zBlackBody.__init__cs 7D)) 5& ! ! 4%**B*B $+ +  4!:L--"A$6q14x$@$@ !:+7:: $kF7O!-D  !%!3D uww0000c.t|tjs tj|tj}n|}t|tjs!tj||jd}n|}tjtjtjz5tj|tjtj }tj|tj}dddn #1swxYwYtj |dkrtd|tj tj|rtj |dkrtjdt"t$j|zt$j|zz }tj|} dt$jz|dzzt$jd z| zz tjz } |jjCt5|d s||jjz}|tjj}|| |jtj|z} t5|d r| S| jS) aEvaluate the model. Parameters ---------- x : float, `~numpy.ndarray`, or `~astropy.units.Quantity` ['frequency'] Frequency at which to compute the blackbody. If no units are given, this defaults to Hz (or AA if `scale` was initialized with units equivalent to erg / (cm ** 2 * s * AA * sr)). temperature : float, `~numpy.ndarray`, or `~astropy.units.Quantity` Temperature of the blackbody. If no units are given, this defaults to Kelvin. scale : float, `~numpy.ndarray`, or `~astropy.units.Quantity` ['dimensionless'] Desired scale for the blackbody. Returns ------- y : number or ndarray Blackbody spectrum. The units are determined from the units of ``scale``. .. note:: Use `numpy.errstate` to suppress Numpy warnings, if desired. .. warning:: Output values might contain ``nan`` and ``inf``. Raises ------ ValueError Invalid temperature. ZeroDivisionError Wavelength is zero (when converting to frequency). r)dtypeNrz Temperature should be positive: z4Input contains invalid wavelength/frequency value(s)g@rr) isinstancerQuantityK input_unitsadd_enabled_equivalenciesspectral temperatureHznpfloat64anyr$allisfinitewarningswarnrconsthk_Bexpm1csrrrrtor r%r&r") r)rr9rin_tempin_xfreqtemp log_boltzboltzm1bb_nuys r.evaluatezBlackBody.evaluate{sjN+qz22 "jac22GG!G!QZ(( :a!1#!677DDD ( )G H H , ,:dAD ;;;D:gqs++D , , , , , , , , , , , , , , , 6$(   HFFFGG Gvbk$''(( BF419,=,=  MF"    GdNei$&67 (9%%eg a'57A:+?@14G :? &5&)) 0 /HHQ566N@)rBrDr9rCrUs r.nu_maxzBlackBody.nu_maxs 59$t'77%'AAr/)__name__ __module__ __qualname____doc__r rr5r9r _input_units_allow_dimensionlessr8input_units_equivalenciesr`rarbr:rGr!r#rSr(rQpropertyr6rZrdrgri __classcell__r-s@r.r r s11h)AAC5LK Icqn E E EE (,$"%jajll 3EQT1Wqs]QT1AD89M ua!# ,qt34q13-45 111110XXXt**X*$$$ : :X ://X/BBXBBBBBr/r ceZdZdZeddZeddZeddZedZ edZ e d Z d Z e d Zd Zee_ddZdS)r a? Drude model based one the behavior of electons in materials (esp. metals). Parameters ---------- amplitude : float Peak value x_0 : float Position of the peak fwhm : float Full width at half maximum Model formula: .. math:: f(x) = A \frac{(fwhm/x_0)^2}{((x/x_0 - x_0/x)^2 + (fwhm/x_0)^2} Examples -------- .. plot:: :include-source: import numpy as np import matplotlib.pyplot as plt from astropy.modeling.models import Drude1D fig, ax = plt.subplots() # generate the curves and plot them x = np.arange(7.5 , 12.5 , 0.1) dmodel = Drude1D(amplitude=1.0, fwhm=1.0, x_0=10.0) ax.plot(x, dmodel(x)) ax.set_xlabel('x') ax.set_ylabel('F(x)') plt.show() rz Peak ValuerrzPosition of the peakzFull width at half maximumcH|||z dzz||z ||z z dz||z dzzz S)z7 One dimensional Drude model function. r)r amplitudex_0fwhms r.rQzDrude1D.evaluate(sE s q  "C#'!a'4#:!*;; = r/c||z dz||z ||z z dz||z dzzz }d|z|zd|z ||dz|dzz z| |z d|z z ||z ||z z zd|dzz|dzz z zzz}d|z|z|z d|z z}|||gS)z5 Drude1D model function derivatives. rrr2rv)rrwrxry d_amplituded_x_0d_fwhms r. fit_derivzDrude1D.fit_deriv3s cza'AGcAg,=!+CtczVWFW+WX   S6D!G#%R#XA%!c'C!G*;<47{S!V+-  i-+-4[IUF++r/cP|jjdS|jd|jjiSNr)rx input_unitrTrUs r.r6zDrude1D.input_unitsJs( 8  &4 A 344r/ct||jd||jd||jddS)Nr)rxryrw)rToutputsrWs r.rZz'Drude1D._parameter_units_for_data_unitsPs;t{1~. A/%dl1o6   r/cP|jjdS|jd|jjiSr)rwrrrUs r. return_unitszDrude1D.return_unitsWs( >  &4 Q!455r/cTtj|dkrtddS)zEnsure `x_0` is not 0.rz!0 is not an allowed value for x_0N)r;r=r)r)vals r._x_0_validatorzDrude1D._x_0_validator]s4 6#(   K%&IJJ J K Kr/2c8|j}||jz}||z ||zfS)zTuple defining the default ``bounding_box`` limits, ``(x_low, x_high)``. Parameters ---------- factor : float The multiple of FWHM used to define the limits. )rxry)r)factorx0dxs r. bounding_boxzDrude1D.bounding_boxds*X di Rb!!r/N)r)rjrkrlrmr rwrxry staticmethodrQrrpr6rZrr _validatorrrvr/r.r r s&&P #<@@@I )C-C D D DC 9S.J K K KD  \ ,,\,,55X5    66X6 KKK $CN " " " " " "r/r ceZdZdZeddZeddZedZedZ e dZ d Z d S) r aOne dimensional Plummer density profile model. Parameters ---------- mass : float Total mass of cluster. r_plum : float Scale parameter which sets the size of the cluster core. Notes ----- Model formula: .. math:: \rho(r)=\frac{3M}{4\pi a^3}(1+\frac{r^2}{a^2})^{-5/2} References ---------- .. [1] https://ui.adsabs.harvard.edu/abs/1911MNRAS..71..460P rzTotal mass of clusterrtz7Scale parameter which sets the size of the cluster corecVd|zdtjz|dzzz d||z dzzdzzS)z9 Evaluate plummer density profile model. r2r\rrgr;r_)rmassr_plums r.rQzPlummer1D.evaluates< X!be)fai/ 0AV8I4Iv3V V r/cddtjz|dzz||z dzdzdzzz }d|z|dzzd|z|dzzz dtjz|dzzd||z dzzdzzz }||gS) z. Plummer1D model derivatives. r2r\rrg@ g @r)rrrd_massd_r_plums r.rzPlummer1D.fit_derivs q25y619,1v:!2Ca2GU1STUHq!tOa$h&:: Y "qAJ1+<'<%&H H !!r/c\|jj}|jj}||dS|jd|iSr)rrrrT)r) mass_unit r_plum_units r.r6zPlummer1D.input_unitss7I( k,  !44 A ,,r/c~||jd||jddzz||jddS)Nrr2)rr)rrTrWs r.rZz)Plummer1D._parameter_units_for_data_unitssC a1K A4OST4TT!$+a.1   r/N) rjrkrlrmr rrrrQrrpr6rZrvr/r.r r ss, 9S.E F F FD YMF   \ ""\"--X-     r/r ceZdZdZeddejdZedddZedddZ d Z ej ej ej ej e j d d ffd Zd ZdZedZdZedZdZedZedZedZedZdZedZedZdZxZS)r u Navarro–Frenk–White (NFW) profile - model for radial distribution of dark matter. Parameters ---------- mass : float or `~astropy.units.Quantity` ['mass'] Mass of NFW peak within specified overdensity radius. concentration : float Concentration of the NFW profile. redshift : float Redshift of the NFW profile. massfactor : tuple or str Mass overdensity factor and type for provided profiles: Tuple version: ("virial",) : virial radius ("critical", N) : radius where density is N times that of the critical density ("mean", N) : radius where density is N times that of the mean density String version: "virial" : virial radius "Nc" : radius where density is N times that of the critical density (e.g. "200c") "Nm" : radius where density is N times that of the mean density (e.g. "500m") cosmo : :class:`~astropy.cosmology.Cosmology` Background cosmology for density calculation. If None, the default cosmology will be used. Notes ----- Model formula: .. math:: \rho(r)=\frac{\delta_c\rho_{c}}{r/r_s(1+r/r_s)^2} References ---------- .. [1] https://arxiv.org/pdf/astro-ph/9508025 .. [2] https://en.wikipedia.org/wiki/Navarro%E2%80%93Frenk%E2%80%93White_profile .. [3] https://en.wikipedia.org/wiki/Virial_mass rz-Peak mass within specified overdensity radiusr ConcentrationrgRedshiftT)criticalNc x|ddlm}|}||||t |t js t j|t j}n|}|||| ||tj d|||d|dS)Nr)default_cosmologyr concentrationredshiftrv) astropy.cosmologyrr_density_deltar3rr4M_sun _radius_s _density_sr'r() r)rrr massfactorcosmor+rin_massr-s r.r(z NFW.__init__s = ; ; ; ; ; ;%))++E Jx888$ ++ jqw//GGG t]+++ m,,,    LR     r/cbt|dr|}ntj|tj}|||||jz }||||tjd|zdzzz }t|dr|S|jS)a3 One dimensional NFW profile function. Parameters ---------- r : float or `~astropy.units.Quantity` ['length'] Radial position of density to be calculated for the NFW profile. mass : float or `~astropy.units.Quantity` ['mass'] Mass of NFW peak within specified overdensity radius. concentration : float Concentration of the NFW profile. redshift : float Redshift of the NFW profile. Returns ------- density : float or `~astropy.units.Quantity` ['density'] NFW profile mass density at location ``r``. The density units are: [``mass`` / ``r`` ^3] Notes ----- .. warning:: Output values might contain ``nan`` and ``inf``. rrr) rrr4kpcrrHrrr%)r)rrrrin_rradius_reduceddensitys r.rQz NFW.evaluates8 1f   (DD:a''Dt] C C F Fty Q QQ //$ 66 ajoo>1D D  4  !N= r/ct|tr|ddkrd}|d}n`|ddkrt|d}d}n)|ddkrt|d}d}nt d |dd  |dkrd}|}n|d dks|d dkr2t|dd }|d }nt d |d n(#t t f$rt d |dwxYw|dkrW||dz }dtj dzzd|zzd|dzzz }|| |z|_ n]|dkr|| |z|_ n9|dkr3|| |z||z|_ |j S)z* Calculate density delta. rvirialNrrrFmeanmz Massfactor 'z,' not one of 'critical', 'mean', or 'virial'z Massfactor z/ string not of the form '#m', '#c', or 'virial'z not a tuple or stringrg2@rgT@gC@) r3tuplelowerfloatr$AttributeError TypeErrorOmr;r_critical_density density_delta)r)rrrdeltamasstypeOm_cd_cs r.rzNFW._density_deltaHs j% ( (* R !}""$$00%a=..00A$$&&*44jm,,A$$&&&00jm,, *:a=***  R ##%%11 E)//11HH^))++s22jn6J6J6L6LPS6S6S!*QrT"233E)"~3355HH$2j222#I. R R R Pj P P PQQQ R x  88H%%+D/D4K/$q.@C!$u'='=h'G'G!GD   __!&)?)?)I)I!ID   __..x888588H;M;MM  !!s B0F %F/cBtjd|z|d|zz z S)z Dimensionless volume integral of the NFW profile, used as an intermediate step in some calculations for this model. Notes ----- Model formula: .. math:: A_{NFW} = [\ln(1+y) - \frac{y}{1+y}] r)r;log)rPs r.A_NFWz NFW.A_NFWs#vcAg!sQw-00r/ct|tjs tj|tj}n|}|dtjz|||dzz||zz |_|jS)z= Calculate scale density of the NFW profile. @r2) r3rr4rr;r_rr density_sr)rrrs r.rzNFW._density_ss $ ++ jqw//GGG! e nnWm449 :jj'' ( ~r/c|jS)zf Scale density of the NFW profile. Often written in the literature as :math:`\rho_s`. )rrUs r. rho_scalez NFW.rho_scales ~r/ct|tjs tj|tj}n|}d|zdtjz|jzz dz|z |_|jtj S)z< Calculate scale radius of the NFW profile. g@rgUUUUUU?) r3rr4rr;r_rradius_srHrrs r.rz NFW._radius_ssy $ ++ jqw//GGGGmbe d.@ @ Ay Q  }&&&r/c|jS)z2 Scale radius of the NFW profile. )rrUs r.r_szNFW.r_ss }r/c |j|jzS)zn Mass factor defined virial radius of the NFW profile (R200c for M200c, Rvir for Mvir, etc.). )rrrUs r.r_virialz NFW.r_virials x$,,,r/c|jdzS)z6 Radius of maximum circular velocity. g7L@)rrUs r.r_maxz NFW.r_maxs x'!!r/c6||jS)z, Maximum circular velocity. )circular_velocityrrUs r.v_maxz NFW.v_maxs %%dj111r/c tt|dr|}ntj|tj}t j|jtj |j dz|jj tj dzzz z|j z }||j |j z }t j|dz| |j|zz|| |jzz }| tjtj z S)a Circular velocities of the NFW profile. Parameters ---------- r : float or `~astropy.units.Quantity` ['length'] Radial position of velocity to be calculated for the NFW profile. Returns ------- velocity : float or `~astropy.units.Quantity` ['speed'] NFW profile circular velocity at location ``r``. The velocity units are: [km / s] Notes ----- Model formula: .. math:: v_{circ}(r)^2 = \frac{1}{x}\frac{\ln(1+cx)-(cx)/(1+cx)}{\ln(1+c)-c/(1+c)} .. math:: x = r/r_s .. warning:: Output values might contain ``nan`` and ``inf``. rr2r)rrr4rr;sqrtrrBGrHrrbrrrkm)r)rr v_profilereduced_radiusvelocitys r.rzNFW.circular_velocitys 8 1f   (DD:a''DG IgjjA!#q&)@ABB Cm    0 0 ; ;; 7 \DJJt'9N'JKK K 4+= > >> @   {{14!#:&&&r/c4|jdtjiSr)rTrrrUs r.r6zNFW.input_unitss A&&r/c|jj5|jdtj|j|jddzz iS|jd|jj|j|jddzz iS)Nrr2)rrrrrr6rTrUs r.rzNFW.return_unitssn 9> !LOQWt/? A/OST/T%TU U Q$2B4;q>2RVW2W!W r/c"tjdddS)Nr)rrrWs r.rZz#NFW._parameter_units_for_data_units(s$DIIIr/) rjrkrlrmr rrrrrrnr4rrr(rQrrrrrprrrrrrrr6rrZrqrrs@r.r r s ((Z 9  WC    DIcsPPPMy#:FFFH(,$QZ di 0 0#+!$ ! ! ! ! ! ! F/!/!/!b="="="~ 1 1\ 1*X ''',X --X- ""X" 22X2 3'3'3'j''X'XJJJJJJJr/r )rmr@numpyr;astropyrrBrrastropy.utils.exceptionsrcorer parametersrr __all__r r r r rvr/r.rsr &&&&&&777777!!!!!!66666666 6 6 6cBcBcBcBcBcBcBcBLu"u"u"u"u"ou"u"u"p? ? ? ? ? ? ? ? DtJtJtJtJtJ/tJtJtJtJtJr/