B dx@sdZddlZddlZddlmZddlmZddl m Z m Z ddl m Z ddlmZmZd d d d d ddddddddddddddddddd d!d"d#gZd$d%d&d'd(d)d*d+d,d-d.d/d0d1d2d3d4d5d6d7d8d9d:d;dd?d@dAdBdCdDdEdFdGdHdIdJdKdLdMdNdOdPdQdRdSdTdUdVdWdXdYdZd[d\d]d^d_d`dadbdcdddedfdgdhdidjdkdldmdndodpdqdrdsdtdudvdwdxdydzd{d|d}d~dddddddddddddddddddddddddddddgxZGdd$d$eZGdd%d%eZGdd&d&eZGdd'd'eZGdd0d0eeZeZGdd1d1eeZeZGdd2d2eeZeZGdd3d3eeZeZGdd4d4eeZeZ Gdd5d5eeZ!e!Z"Gdd6d6eeZ#e#Z$Gdd7d7eeZ%e%Z&Gdd8d8eeZ'e'Z(Gdd9d9eeZ)e)Z*Gdd:d:eeZ+e+Z,Gdd;d;eeZ-e-Z.Gdd<dd>eeZ3e3Z4Gdd?d?eeZ5e5Z6Gdd(d(eZ7Gdd@d@ee7Z8e8Z9GddAdAee7Z:e:Z;GddBdBee7Ze>Z?GddDdDee7Z@e@ZAGddEdEee7ZBeBZCGddFdFee7ZDeDZEGddGdGee7ZFeFZGGdd)d)eZHGddHdHeeHZIeIZJGddIdIeeHZKeKZLGddJdJeeHZMeMZNGddKdKeeHZOeOZPGddLdLeeHZQeQZRGddMdMeeHZSeSZTGddNdNeeHZUeUZVGddOdOeeHZWeWZXGdd*d*eZYGddPdPeeYZZeZZ[GddQdQeeYZ\e\Z]GddRdReeYZ^e^Z_GddSdSeeYZ`e`ZaGddTdTeeYZbebZcGddUdUeeYZdedZeGddVdVeeYZfefZgGddWdWeeYZhehZiGdd+d+eZjGddXdXeejZkekZlGddYdYeejZmemZnGddZdZeejZoeoZpGdd[d[eejZqeqZrGdd,d,eZsGdd\d\eesZtetZuGdd]d]eesZvevZwGdd^d^eesZxexZyGdd_d_eesZzezZ{Gdd`d`eesZ|e|Z}GddadaeesZ~e~ZGdd-d-eZGddbdbeeZeZGddcdceeZeZGdddddeeZeZGddedeeeZeZGdd.d.eZdS)aK Implements projections--particularly sky projections defined in WCS Paper II [1]_. All angles are set and and displayed in degrees but internally computations are performed in radians. All functions expect inputs and outputs degrees. References ---------- .. [1] Calabretta, M.R., Greisen, E.W., 2002, A&A, 395, 1077 (Paper II) N)units)Model) ParameterInputParameterError) _projections) _to_radian _to_orig_unitZAZPZSZPZTANZSTGZSINZARCZZEAZAIRZCYPZCEAZCARZMERZSFLZPARZMOLZAITZCOPZCOEZCODZCOOZBONZPCOZTSCZCSCZQSCZHPXZXPH ProjectionPix2SkyProjectionSky2PixProjectionZenithal CylindricalPseudoCylindricalConic PseudoConicQuadCubeHEALPixAffineTransformation2D projcodesPix2Sky_ZenithalPerspectiveSky2Pix_ZenithalPerspective Pix2Sky_SlantZenithalPerspective Sky2Pix_SlantZenithalPerspectivePix2Sky_GnomonicSky2Pix_GnomonicPix2Sky_StereographicSky2Pix_StereographicPix2Sky_SlantOrthographicSky2Pix_SlantOrthographicPix2Sky_ZenithalEquidistantSky2Pix_ZenithalEquidistantPix2Sky_ZenithalEqualAreaSky2Pix_ZenithalEqualArea Pix2Sky_Airy Sky2Pix_AiryPix2Sky_CylindricalPerspectiveSky2Pix_CylindricalPerspectivePix2Sky_CylindricalEqualAreaSky2Pix_CylindricalEqualAreaPix2Sky_PlateCarreeSky2Pix_PlateCarreePix2Sky_MercatorSky2Pix_MercatorPix2Sky_SansonFlamsteedSky2Pix_SansonFlamsteedPix2Sky_ParabolicSky2Pix_ParabolicPix2Sky_MolleweideSky2Pix_MolleweidePix2Sky_HammerAitoffSky2Pix_HammerAitoffPix2Sky_ConicPerspectiveSky2Pix_ConicPerspectivePix2Sky_ConicEqualAreaSky2Pix_ConicEqualAreaPix2Sky_ConicEquidistantSky2Pix_ConicEquidistantPix2Sky_ConicOrthomorphicSky2Pix_ConicOrthomorphicPix2Sky_BonneEqualAreaSky2Pix_BonneEqualAreaPix2Sky_PolyconicSky2Pix_PolyconicPix2Sky_TangentialSphericalCubeSky2Pix_TangentialSphericalCubePix2Sky_COBEQuadSphericalCubeSky2Pix_COBEQuadSphericalCubePix2Sky_QuadSphericalCubeSky2Pix_QuadSphericalCubePix2Sky_HEALPixSky2Pix_HEALPixPix2Sky_HEALPixPolarSky2Pix_HEALPixPolar Pix2Sky_AZP Sky2Pix_AZP Pix2Sky_SZP Sky2Pix_SZP Pix2Sky_TAN Sky2Pix_TAN Pix2Sky_STG Sky2Pix_STG Pix2Sky_SIN Sky2Pix_SIN Pix2Sky_ARC Sky2Pix_ARC Pix2Sky_ZEA Sky2Pix_ZEA Pix2Sky_AIR Sky2Pix_AIR Pix2Sky_CYP Sky2Pix_CYP Pix2Sky_CEA Sky2Pix_CEA Pix2Sky_CAR Sky2Pix_CAR Pix2Sky_MER Sky2Pix_MER Pix2Sky_SFL Sky2Pix_SFL Pix2Sky_PAR Sky2Pix_PAR Pix2Sky_MOL Sky2Pix_MOL Pix2Sky_AIT Sky2Pix_AIT Pix2Sky_COP Sky2Pix_COP Pix2Sky_COE Sky2Pix_COE Pix2Sky_COD Sky2Pix_COD Pix2Sky_COO Sky2Pix_COO Pix2Sky_BON Sky2Pix_BON Pix2Sky_PCO Sky2Pix_PCO Pix2Sky_TSC Sky2Pix_TSC Pix2Sky_CSC Sky2Pix_CSC Pix2Sky_QSC Sky2Pix_QSC Pix2Sky_HPX Sky2Pix_HPX Pix2Sky_XPH Sky2Pix_XPHc@s6eZdZdZdejejZdZ e e j ddZ dS)r z#Base class for all sky projections.FcCsdS)zT Inverse projection--all projection models must provide an inverse. N)selfrri/work/yifan.wang/ringdown/master-ringdown-env/lib/python3.7/site-packages/astropy/modeling/projections.pyinversenszProjection.inverseN)__name__ __module__ __qualname____doc__udegnppiZr0 _separablepropertyabcabstractmethodrrrrrr es csHeZdZdZdZdZdZdZfddZe ddZ e dd Z Z S) r z'Base class for all Pix2Sky projections.Tcstj||d|_d|_dS)N)xy)phitheta)super__init__inputsoutputs)rargskwargs) __class__rrrszPix2SkyProjection.__init__cCs|jdtj|jdtjiS)Nrr)rrr)rrrr input_unitss zPix2SkyProjection.input_unitscCs|jdtj|jdtjiS)Nrr)rrr)rrrr return_unitss zPix2SkyProjection.return_units) rrrrn_inputs n_outputs_input_units_strict _input_units_allow_dimensionlessrrrr __classcell__rr)rrr vs  csHeZdZdZdZdZdZdZfddZe ddZ e dd Z Z S) r z'Base class for all Sky2Pix projections.rTcstj||d|_d|_dS)N)rr)rr)rrrr)rrr)rrrrszSky2PixProjection.__init__cCs|jdtj|jdtjiS)Nrr)rrr)rrrrrs zSky2PixProjection.input_unitscCs|jdtj|jdtjiS)Nrr)rrr)rrrrrs zSky2PixProjection.return_units) rrrrrrrrrrrrrrr)rrr s  c@seZdZdZdZdS)r aBase class for all Zenithal projections. Zenithal (or azimuthal) projections map the sphere directly onto a plane. All zenithal projections are specified by defining the radius as a function of native latitude, :math:`R_\theta`. The pixel-to-sky transformation is defined as: .. math:: \phi &= \arg(-y, x) \\ R_\theta &= \sqrt{x^2 + y^2} and the inverse (sky-to-pixel) is defined as: .. math:: x &= R_\theta \sin \phi \\ y &= R_\theta \cos \phi FN)rrrrrrrrrr scsheZdZdZeddZedeedZej ej ffdd Z ej ddZe d d Z ed d ZZS) ru Zenithal perspective projection - pixel to sky. Corresponds to the ``AZP`` projection in FITS WCS. .. math:: \phi &= \arg(-y \cos \gamma, x) \\ \theta &= \left\{\genfrac{}{}{0pt}{}{\psi - \omega}{\psi + \omega + 180^{\circ}}\right. where: .. math:: \psi &= \arg(\rho, 1) \\ \omega &= \sin^{-1}\left(\frac{\rho \mu}{\sqrt{\rho^2 + 1}}\right) \\ \rho &= \frac{R}{\frac{180^{\circ}}{\pi}(\mu + 1) + y \sin \gamma} \\ R &= \sqrt{x^2 + y^2 \cos^2 \gamma} Parameters -------------- mu : float Distance from point of projection to center of sphere in spherical radii, μ. Default is 0. gamma : float Look angle γ in degrees. Default is 0°. g)default)rgettersetterc stj||f|dS)N)rr)rmugammar)rrrrsz$Pix2Sky_ZenithalPerspective.__init__cCst|dkrtddS)Nz:Zenithal perspective projection is not defined for mu = -1)ranyr)rvaluerrrrszPix2Sky_ZenithalPerspective.mucCst|jj|jjS)N)rrrr)rrrrrsz#Pix2Sky_ZenithalPerspective.inversecCst|||t|S)N)rZazpx2sr )clsrrrrrrrevaluatesz$Pix2Sky_ZenithalPerspective.evaluate)rrrrrrr rrrr validatorrr classmethodrrrr)rrrs  c@sNeZdZdZeddZedeedZej ddZe ddZ e d d Z d S) ru8 Zenithal perspective projection - sky to pixel. Corresponds to the ``AZP`` projection in FITS WCS. .. math:: x &= R \sin \phi \\ y &= -R \sec \gamma \cos \theta where: .. math:: R = \frac{180^{\circ}}{\pi} \frac{(\mu + 1) \cos \theta}{(\mu + \sin \theta) + \cos \theta \cos \phi \tan \gamma} Parameters ---------- mu : float Distance from point of projection to center of sphere in spherical radii, μ. Default is 0. gamma : float Look angle γ in degrees. Default is 0°. g)r)rrrcCst|dkrtddS)Nrz:Zenithal perspective projection is not defined for mu = -1)rrr)rrrrrrszSky2Pix_ZenithalPerspective.mucCst|jj|jjS)N)rLrrr)rrrrrsz#Sky2Pix_ZenithalPerspective.inversecCst|||t|S)N)rZazps2xr )rrrrrrrrrsz$Sky2Pix_ZenithalPerspective.evaluateN)rrrrrrr rrrrrrrrrrrrs   c@sXeZdZdZddZededZedeedZ edeedZ e dd Z e d d Zd S) ru Slant zenithal perspective projection - pixel to sky. Corresponds to the ``SZP`` projection in FITS WCS. Parameters -------------- mu : float Distance from point of projection to center of sphere in spherical radii, μ. Default is 0. phi0 : float The longitude φ₀ of the reference point, in degrees. Default is 0°. theta0 : float The latitude θ₀ of the reference point, in degrees. Default is 90°. cCst|dkrtd|S)Nrz8Zenithal perspective projection is not defined for mu=-1)rasarrayr ValueError)rrrr _validate_mu8sz-Pix2Sky_SlantZenithalPerspective._validate_mug)rr)rrrgV@cCst|jj|jj|jjS)N)rrrphi0theta0)rrrrrBsz(Pix2Sky_SlantZenithalPerspective.inversecCst|||t|t|S)N)rZszpx2sr )rrrrrrrrrrGsz)Pix2Sky_SlantZenithalPerspective.evaluateN)rrrrrrrr rrrrrrrrrrrr#s  c@sXeZdZdZddZededZedeedZ edeedZ e ddZ e d d Zd S) ru Zenithal perspective projection - sky to pixel. Corresponds to the ``SZP`` projection in FITS WCS. Parameters ---------- mu : float distance from point of projection to center of sphere in spherical radii, μ. Default is 0. phi0 : float The longitude φ₀ of the reference point, in degrees. Default is 0°. theta0 : float The latitude θ₀ of the reference point, in degrees. Default is 90°. cCst|dkrtd|S)Nrz8Zenithal perspective projection is not defined for mu=-1)rrrr)rrrrresz-Sky2Pix_SlantZenithalPerspective._validate_mug)rr)rrrcCst|jj|jj|jjS)N)rrrrr)rrrrrnsz(Sky2Pix_SlantZenithalPerspective.inversecCst|||t|t|S)N)rZszps2xr )rrrrrrrrrrssz)Sky2Pix_SlantZenithalPerspective.evaluateN)rrrrrrrr rrrrrrrrrrrrPs  c@s(eZdZdZeddZeddZdS)rz Gnomonic projection - pixel to sky. Corresponds to the ``TAN`` projection in FITS WCS. See `Zenithal` for a definition of the full transformation. .. math:: \theta = \tan^{-1}\left(\frac{180^{\circ}}{\pi R_\theta}\right) cCstS)N)r)rrrrrszPix2Sky_Gnomonic.inversecCs t||S)N)rZtanx2s)rrrrrrrszPix2Sky_Gnomonic.evaluateN)rrrrrrrrrrrrr|s  c@s(eZdZdZeddZeddZdS)rz Gnomonic Projection - sky to pixel. Corresponds to the ``TAN`` projection in FITS WCS. See `Zenithal` for a definition of the full transformation. .. math:: R_\theta = \frac{180^{\circ}}{\pi}\cot \theta cCstS)N)r)rrrrrszSky2Pix_Gnomonic.inversecCs t||S)N)rZtans2x)rrrrrrrszSky2Pix_Gnomonic.evaluateN)rrrrrrrrrrrrrs  c@s(eZdZdZeddZeddZdS)ra Stereographic Projection - pixel to sky. Corresponds to the ``STG`` projection in FITS WCS. See `Zenithal` for a definition of the full transformation. .. math:: \theta = 90^{\circ} - 2 \tan^{-1}\left(\frac{\pi R_\theta}{360^{\circ}}\right) cCstS)N)r)rrrrrszPix2Sky_Stereographic.inversecCs t||S)N)rZstgx2s)rrrrrrrszPix2Sky_Stereographic.evaluateN)rrrrrrrrrrrrrs  c@s(eZdZdZeddZeddZdS)ra  Stereographic Projection - sky to pixel. Corresponds to the ``STG`` projection in FITS WCS. See `Zenithal` for a definition of the full transformation. .. math:: R_\theta = \frac{180^{\circ}}{\pi}\frac{2 \cos \theta}{1 + \sin \theta} cCstS)N)r)rrrrrszSky2Pix_Stereographic.inversecCs t||S)N)rZstgs2x)rrrrrrrszSky2Pix_Stereographic.evaluateN)rrrrrrrrrrrrrs  c@s<eZdZdZeddZeddZeddZe ddZ dS) ru Slant orthographic projection - pixel to sky. Corresponds to the ``SIN`` projection in FITS WCS. See `Zenithal` for a definition of the full transformation. The following transformation applies when :math:`\xi` and :math:`\eta` are both zero. .. math:: \theta = \cos^{-1}\left(\frac{\pi}{180^{\circ}}R_\theta\right) The parameters :math:`\xi` and :math:`\eta` are defined from the reference point :math:`(\phi_c, \theta_c)` as: .. math:: \xi &= \cot \theta_c \sin \phi_c \\ \eta &= - \cot \theta_c \cos \phi_c Parameters ---------- xi : float Obliqueness parameter, ξ. Default is 0.0. eta : float Obliqueness parameter, η. Default is 0.0. g)rcCst|jj|jjS)N)rxireta)rrrrrsz!Pix2Sky_SlantOrthographic.inversecCst||||S)N)rZsinx2s)rrrrrrrrrsz"Pix2Sky_SlantOrthographic.evaluateN) rrrrrrrrrrrrrrrrs    c@s<eZdZdZeddZeddZeddZe ddZ dS) ra) Slant orthographic projection - sky to pixel. Corresponds to the ``SIN`` projection in FITS WCS. See `Zenithal` for a definition of the full transformation. The following transformation applies when :math:`\xi` and :math:`\eta` are both zero. .. math:: R_\theta = \frac{180^{\circ}}{\pi}\cos \theta But more specifically are: .. math:: x &= \frac{180^\circ}{\pi}[\cos \theta \sin \phi + \xi(1 - \sin \theta)] \\ y &= \frac{180^\circ}{\pi}[\cos \theta \cos \phi + \eta(1 - \sin \theta)] g)rcCst|jj|jjS)N)rrrr)rrrrr!sz!Sky2Pix_SlantOrthographic.inversecCst||||S)N)rZsins2x)rrrrrrrrr%sz"Sky2Pix_SlantOrthographic.evaluateN) rrrrrrrrrrrrrrrr s    c@s(eZdZdZeddZeddZdS)r z Zenithal equidistant projection - pixel to sky. Corresponds to the ``ARC`` projection in FITS WCS. See `Zenithal` for a definition of the full transformation. .. math:: \theta = 90^\circ - R_\theta cCstS)N)r!)rrrrr8sz#Pix2Sky_ZenithalEquidistant.inversecCs t||S)N)rZarcx2s)rrrrrrr<sz$Pix2Sky_ZenithalEquidistant.evaluateN)rrrrrrrrrrrrr -s  c@s(eZdZdZeddZeddZdS)r!z Zenithal equidistant projection - sky to pixel. Corresponds to the ``ARC`` projection in FITS WCS. See `Zenithal` for a definition of the full transformation. .. math:: R_\theta = 90^\circ - \theta cCstS)N)r )rrrrrOsz#Sky2Pix_ZenithalEquidistant.inversecCs t||S)N)rZarcs2x)rrrrrrrSsz$Sky2Pix_ZenithalEquidistant.evaluateN)rrrrrrrrrrrrr!Ds  c@s(eZdZdZeddZeddZdS)r"a Zenithal equidistant projection - pixel to sky. Corresponds to the ``ZEA`` projection in FITS WCS. See `Zenithal` for a definition of the full transformation. .. math:: \theta = 90^\circ - 2 \sin^{-1} \left(\frac{\pi R_\theta}{360^\circ}\right) cCstS)N)r#)rrrrrfsz!Pix2Sky_ZenithalEqualArea.inversecCs t||S)N)rZzeax2s)rrrrrrrjsz"Pix2Sky_ZenithalEqualArea.evaluateN)rrrrrrrrrrrrr"[s  c@s(eZdZdZeddZeddZdS)r#a^ Zenithal equidistant projection - sky to pixel. Corresponds to the ``ZEA`` projection in FITS WCS. See `Zenithal` for a definition of the full transformation. .. math:: R_\theta &= \frac{180^\circ}{\pi} \sqrt{2(1 - \sin\theta)} \\ &= \frac{360^\circ}{\pi} \sin\left(\frac{90^\circ - \theta}{2}\right) cCstS)N)r")rrrrr~sz!Sky2Pix_ZenithalEqualArea.inversecCs t||S)N)rZzeas2x)rrrrrrrsz"Sky2Pix_ZenithalEqualArea.evaluateN)rrrrrrrrrrrrr#rs  c@s2eZdZdZeddZeddZeddZ dS) r$uA Airy projection - pixel to sky. Corresponds to the ``AIR`` projection in FITS WCS. See `Zenithal` for a definition of the full transformation. Parameters ---------- theta_b : float The latitude :math:`\theta_b` at which to minimize the error, in degrees. Default is 90°. gV@)rcCs t|jjS)N)r%theta_br)rrrrrszPix2Sky_Airy.inversecCst|||S)N)rZairx2s)rrrrrrrrszPix2Sky_Airy.evaluateN) rrrrrrrrrrrrrrr$s   c@s2eZdZdZeddZeddZeddZ dS) r%uE Airy - sky to pixel. Corresponds to the ``AIR`` projection in FITS WCS. See `Zenithal` for a definition of the full transformation. .. math:: R_\theta = -2 \frac{180^\circ}{\pi}\left(\frac{\ln(\cos \xi)}{\tan \xi} + \frac{\ln(\cos \xi_b)}{\tan^2 \xi_b} \tan \xi \right) where: .. math:: \xi &= \frac{90^\circ - \theta}{2} \\ \xi_b &= \frac{90^\circ - \theta_b}{2} Parameters ---------- theta_b : float The latitude :math:`\theta_b` at which to minimize the error, in degrees. Default is 90°. gV@)rcCs t|jjS)N)r$rr)rrrrrszSky2Pix_Airy.inversecCst|||S)N)rZairs2x)rrrrrrrrszSky2Pix_Airy.evaluateN) rrrrrrrrrrrrrrr%s  c@seZdZdZdZdS)rzBase class for Cylindrical projections. Cylindrical projections are so-named because the surface of projection is a cylinder. TN)rrrrrrrrrrsc@sXeZdZdZeddZeddZejddZejddZedd Z e d d Z d S) r&uZ Cylindrical perspective - pixel to sky. Corresponds to the ``CYP`` projection in FITS WCS. .. math:: \phi &= \frac{x}{\lambda} \\ \theta &= \arg(1, \eta) + \sin{-1}\left(\frac{\eta \mu}{\sqrt{\eta^2 + 1}}\right) where: .. math:: \eta = \frac{\pi}{180^{\circ}}\frac{y}{\mu + \lambda} Parameters ---------- mu : float Distance from center of sphere in the direction opposite the projected surface, in spherical radii, μ. Default is 1. lam : float Radius of the cylinder in spherical radii, λ. Default is 1. g?)rcCst||j krtddS)Nz.CYP projection is not defined for mu = -lambda)rrlamr)rrrrrrsz!Pix2Sky_CylindricalPerspective.mucCst||j krtddS)Nz.CYP projection is not defined for lambda = -mu)rrrr)rrrrrrsz"Pix2Sky_CylindricalPerspective.lamcCst|jj|jjS)N)r'rrr)rrrrrsz&Pix2Sky_CylindricalPerspective.inversecCst||||S)N)rZcypx2s)rrrrrrrrrsz'Pix2Sky_CylindricalPerspective.evaluateN) rrrrrrrrrrrrrrrrr&s   c@sXeZdZdZeddZeddZejddZejddZedd Z e d d Z d S) r'u Cylindrical Perspective - sky to pixel. Corresponds to the ``CYP`` projection in FITS WCS. .. math:: x &= \lambda \phi \\ y &= \frac{180^{\circ}}{\pi}\left(\frac{\mu + \lambda}{\mu + \cos \theta}\right)\sin \theta Parameters ---------- mu : float Distance from center of sphere in the direction opposite the projected surface, in spherical radii, μ. Default is 0. lam : float Radius of the cylinder in spherical radii, λ. Default is 0. g?)rcCst||j krtddS)Nz.CYP projection is not defined for mu = -lambda)rrrr)rrrrrrsz!Sky2Pix_CylindricalPerspective.mucCst||j krtddS)Nz.CYP projection is not defined for lambda = -mu)rrrr)rrrrrr%sz"Sky2Pix_CylindricalPerspective.lamcCst|j|jS)N)r&rr)rrrrr+sz&Sky2Pix_CylindricalPerspective.inversecCst||||S)N)rZcyps2x)rrrrrrrrr/sz'Sky2Pix_CylindricalPerspective.evaluateN) rrrrrrrrrrrrrrrrr's   c@s2eZdZdZeddZeddZeddZ dS) r(uU Cylindrical equal area projection - pixel to sky. Corresponds to the ``CEA`` projection in FITS WCS. .. math:: \phi &= x \\ \theta &= \sin^{-1}\left(\frac{\pi}{180^{\circ}}\lambda y\right) Parameters ---------- lam : float Radius of the cylinder in spherical radii, λ. Default is 1. r)rcCs t|jS)N)r)r)rrrrrIsz$Pix2Sky_CylindricalEqualArea.inversecCst|||S)N)rZceax2s)rrrrrrrrMsz%Pix2Sky_CylindricalEqualArea.evaluateN) rrrrrrrrrrrrrrr(7s  c@s2eZdZdZeddZeddZeddZ dS) r)uL Cylindrical equal area projection - sky to pixel. Corresponds to the ``CEA`` projection in FITS WCS. .. math:: x &= \phi \\ y &= \frac{180^{\circ}}{\pi}\frac{\sin \theta}{\lambda} Parameters ---------- lam : float Radius of the cylinder in spherical radii, λ. Default is 0. r)rcCs t|jS)N)r(r)rrrrrgsz$Sky2Pix_CylindricalEqualArea.inversecCst|||S)N)rZceas2x)rrrrrrrrksz%Sky2Pix_CylindricalEqualArea.evaluateN) rrrrrrrrrrrrrrr)Us  c@s(eZdZdZeddZeddZdS)r*u Plate carrée projection - pixel to sky. Corresponds to the ``CAR`` projection in FITS WCS. .. math:: \phi &= x \\ \theta &= y cCstS)N)r+)rrrrr~szPix2Sky_PlateCarree.inversecCs$tj|dd}tj|dd}||fS)NT)copy)rarray)rrrrrrrrszPix2Sky_PlateCarree.evaluateN)rrrrrr staticmethodrrrrrr*ss  c@s(eZdZdZeddZeddZdS)r+u Plate carrée projection - sky to pixel. Corresponds to the ``CAR`` projection in FITS WCS. .. math:: x &= \phi \\ y &= \theta cCstS)N)r*)rrrrrszSky2Pix_PlateCarree.inversecCs$tj|dd}tj|dd}||fS)NT)r)rr)rrrrrrrrszSky2Pix_PlateCarree.evaluateN)rrrrrrrrrrrrr+s  c@s(eZdZdZeddZeddZdS)r,z Mercator - pixel to sky. Corresponds to the ``MER`` projection in FITS WCS. .. math:: \phi &= x \\ \theta &= 2 \tan^{-1}\left(e^{y \pi / 180^{\circ}}\right)-90^{\circ} cCstS)N)r-)rrrrrszPix2Sky_Mercator.inversecCs t||S)N)rZmerx2s)rrrrrrrszPix2Sky_Mercator.evaluateN)rrrrrrrrrrrrr,s  c@s(eZdZdZeddZeddZdS)r-z Mercator - sky to pixel. Corresponds to the ``MER`` projection in FITS WCS. .. math:: x &= \phi \\ y &= \frac{180^{\circ}}{\pi}\ln \tan \left(\frac{90^{\circ} + \theta}{2}\right) cCstS)N)r,)rrrrrszSky2Pix_Mercator.inversecCs t||S)N)rZmers2x)rrrrrrrszSky2Pix_Mercator.evaluateN)rrrrrrrrrrrrr-s  c@seZdZdZdZdS)ra7Base class for pseudocylindrical projections. Pseudocylindrical projections are like cylindrical projections except the parallels of latitude are projected at diminishing lengths toward the polar regions in order to reduce lateral distortion there. Consequently, the meridians are curved. TN)rrrrrrrrrrsc@s(eZdZdZeddZeddZdS)r.z Sanson-Flamsteed projection - pixel to sky. Corresponds to the ``SFL`` projection in FITS WCS. .. math:: \phi &= \frac{x}{\cos y} \\ \theta &= y cCstS)N)r/)rrrrrszPix2Sky_SansonFlamsteed.inversecCs t||S)N)rZsflx2s)rrrrrrrsz Pix2Sky_SansonFlamsteed.evaluateN)rrrrrrrrrrrrr.s  c@s(eZdZdZeddZeddZdS)r/z Sanson-Flamsteed projection - sky to pixel. Corresponds to the ``SFL`` projection in FITS WCS. .. math:: x &= \phi \cos \theta \\ y &= \theta cCstS)N)r.)rrrrrszSky2Pix_SansonFlamsteed.inversecCs t||S)N)rZsfls2x)rrrrrrr sz Sky2Pix_SansonFlamsteed.evaluateN)rrrrrrrrrrrrr/s  c@s,eZdZdZdZeddZeddZdS)r0z Parabolic projection - pixel to sky. Corresponds to the ``PAR`` projection in FITS WCS. .. math:: \phi &= \frac{180^\circ}{\pi} \frac{x}{1 - 4(y / 180^\circ)^2} \\ \theta &= 3 \sin^{-1}\left(\frac{y}{180^\circ}\right) FcCstS)N)r1)rrrrrszPix2Sky_Parabolic.inversecCs t||S)N)rZparx2s)rrrrrrr"szPix2Sky_Parabolic.evaluateN) rrrrrrrrrrrrrr0s  c@s,eZdZdZdZeddZeddZdS)r1z Parabolic projection - sky to pixel. Corresponds to the ``PAR`` projection in FITS WCS. .. math:: x &= \phi \left(2\cos\frac{2\theta}{3} - 1\right) \\ y &= 180^\circ \sin \frac{\theta}{3} FcCstS)N)r0)rrrrr7szSky2Pix_Parabolic.inversecCs t||S)N)rZpars2x)rrrrrrr;szSky2Pix_Parabolic.evaluateN) rrrrrrrrrrrrrr1*s  c@s,eZdZdZdZeddZeddZdS)r2a Molleweide's projection - pixel to sky. Corresponds to the ``MOL`` projection in FITS WCS. .. math:: \phi &= \frac{\pi x}{2 \sqrt{2 - \left(\frac{\pi}{180^\circ}y\right)^2}} \\ \theta &= \sin^{-1}\left(\frac{1}{90^\circ}\sin^{-1}\left(\frac{\pi}{180^\circ}\frac{y}{\sqrt{2}}\right) + \frac{y}{180^\circ}\sqrt{2 - \left(\frac{\pi}{180^\circ}y\right)^2}\right) FcCstS)N)r3)rrrrrPszPix2Sky_Molleweide.inversecCs t||S)N)rZmolx2s)rrrrrrrTszPix2Sky_Molleweide.evaluateN) rrrrrrrrrrrrrr2Cs  c@s,eZdZdZdZeddZeddZdS)r3a Molleweide's projection - sky to pixel. Corresponds to the ``MOL`` projection in FITS WCS. .. math:: x &= \frac{2 \sqrt{2}}{\pi} \phi \cos \gamma \\ y &= \sqrt{2} \frac{180^\circ}{\pi} \sin \gamma where :math:`\gamma` is defined as the solution of the transcendental equation: .. math:: \sin \theta = \frac{\gamma}{90^\circ} + \frac{\sin 2 \gamma}{\pi} FcCstS)N)r2)rrrrrpszSky2Pix_Molleweide.inversecCs t||S)N)rZmols2x)rrrrrrrtszSky2Pix_Molleweide.evaluateN) rrrrrrrrrrrrrr3\s c@s,eZdZdZdZeddZeddZdS)r4a  Hammer-Aitoff projection - pixel to sky. Corresponds to the ``AIT`` projection in FITS WCS. .. math:: \phi &= 2 \arg \left(2Z^2 - 1, \frac{\pi}{180^\circ} \frac{Z}{2}x\right) \\ \theta &= \sin^{-1}\left(\frac{\pi}{180^\circ}yZ\right) FcCstS)N)r5)rrrrrszPix2Sky_HammerAitoff.inversecCs t||S)N)rZaitx2s)rrrrrrrszPix2Sky_HammerAitoff.evaluateN) rrrrrrrrrrrrrr4|s  c@s,eZdZdZdZeddZeddZdS)r5aD Hammer-Aitoff projection - sky to pixel. Corresponds to the ``AIT`` projection in FITS WCS. .. math:: x &= 2 \gamma \cos \theta \sin \frac{\phi}{2} \\ y &= \gamma \sin \theta where: .. math:: \gamma = \frac{180^\circ}{\pi} \sqrt{\frac{2}{1 + \cos \theta \cos(\phi / 2)}} FcCstS)N)r4)rrrrrszSky2Pix_HammerAitoff.inversecCs t||S)N)rZaits2x)rrrrrrrszSky2Pix_HammerAitoff.evaluateN) rrrrrrrrrrrrrr5s c@s0eZdZdZedeedZedeedZdZ dS)raBase class for conic projections. In conic projections, the sphere is thought to be projected onto the surface of a cone which is then opened out. In a general sense, the pixel-to-sky transformation is defined as: .. math:: \phi &= \arg\left(\frac{Y_0 - y}{R_\theta}, \frac{x}{R_\theta}\right) / C \\ R_\theta &= \mathrm{sign} \theta_a \sqrt{x^2 + (Y_0 - y)^2} and the inverse (sky-to-pixel) is defined as: .. math:: x &= R_\theta \sin (C \phi) \\ y &= R_\theta \cos (C \phi) + Y_0 where :math:`C` is the "constant of the cone": .. math:: C = \frac{180^\circ \cos \theta}{\pi R_\theta} gV@)rrrgFN) rrrrrr rsigmadeltarrrrrrsc@s(eZdZdZeddZeddZdS)r6aB Colles' conic perspective projection - pixel to sky. Corresponds to the ``COP`` projection in FITS WCS. See `Conic` for a description of the entire equation. The projection formulae are: .. math:: C &= \sin \theta_a \\ R_\theta &= \frac{180^\circ}{\pi} \cos \eta [ \cot \theta_a - \tan(\theta - \theta_a)] \\ Y_0 &= \frac{180^\circ}{\pi} \cos \eta \cot \theta_a Parameters ---------- sigma : float :math:`(\theta_1 + \theta_2) / 2`, where :math:`\theta_1` and :math:`\theta_2` are the latitudes of the standard parallels, in degrees. Default is 90. delta : float :math:`(\theta_1 - \theta_2) / 2`, where :math:`\theta_1` and :math:`\theta_2` are the latitudes of the standard parallels, in degrees. Default is 0. cCst|jj|jjS)N)r7rrr)rrrrrsz Pix2Sky_ConicPerspective.inversecCst||t|t|S)N)rZcopx2sr )rrrrrrrrrsz!Pix2Sky_ConicPerspective.evaluateN)rrrrrrrrrrrrr6s c@s(eZdZdZeddZeddZdS)r7aB Colles' conic perspective projection - sky to pixel. Corresponds to the ``COP`` projection in FITS WCS. See `Conic` for a description of the entire equation. The projection formulae are: .. math:: C &= \sin \theta_a \\ R_\theta &= \frac{180^\circ}{\pi} \cos \eta [ \cot \theta_a - \tan(\theta - \theta_a)] \\ Y_0 &= \frac{180^\circ}{\pi} \cos \eta \cot \theta_a Parameters ---------- sigma : float :math:`(\theta_1 + \theta_2) / 2`, where :math:`\theta_1` and :math:`\theta_2` are the latitudes of the standard parallels, in degrees. Default is 90. delta : float :math:`(\theta_1 - \theta_2) / 2`, where :math:`\theta_1` and :math:`\theta_2` are the latitudes of the standard parallels, in degrees. Default is 0. cCst|jj|jjS)N)r6rrr)rrrrrsz Sky2Pix_ConicPerspective.inversecCst||t|t|S)N)rZcops2xr )rrrrrrrrrsz!Sky2Pix_ConicPerspective.evaluateN)rrrrrrrrrrrrr7s c@s(eZdZdZeddZeddZdS)r8a Alber's conic equal area projection - pixel to sky. Corresponds to the ``COE`` projection in FITS WCS. See `Conic` for a description of the entire equation. The projection formulae are: .. math:: C &= \gamma / 2 \\ R_\theta &= \frac{180^\circ}{\pi} \frac{2}{\gamma} \sqrt{1 + \sin \theta_1 \sin \theta_2 - \gamma \sin \theta} \\ Y_0 &= \frac{180^\circ}{\pi} \frac{2}{\gamma} \sqrt{1 + \sin \theta_1 \sin \theta_2 - \gamma \sin((\theta_1 + \theta_2)/2)} where: .. math:: \gamma = \sin \theta_1 + \sin \theta_2 Parameters ---------- sigma : float :math:`(\theta_1 + \theta_2) / 2`, where :math:`\theta_1` and :math:`\theta_2` are the latitudes of the standard parallels, in degrees. Default is 90. delta : float :math:`(\theta_1 - \theta_2) / 2`, where :math:`\theta_1` and :math:`\theta_2` are the latitudes of the standard parallels, in degrees. Default is 0. cCst|jj|jjS)N)r9rrr)rrrrr@szPix2Sky_ConicEqualArea.inversecCst||t|t|S)N)rZcoex2sr )rrrrrrrrrDszPix2Sky_ConicEqualArea.evaluateN)rrrrrrrrrrrrr8 s c@s(eZdZdZeddZeddZdS)r9a Alber's conic equal area projection - sky to pixel. Corresponds to the ``COE`` projection in FITS WCS. See `Conic` for a description of the entire equation. The projection formulae are: .. math:: C &= \gamma / 2 \\ R_\theta &= \frac{180^\circ}{\pi} \frac{2}{\gamma} \sqrt{1 + \sin \theta_1 \sin \theta_2 - \gamma \sin \theta} \\ Y_0 &= \frac{180^\circ}{\pi} \frac{2}{\gamma} \sqrt{1 + \sin \theta_1 \sin \theta_2 - \gamma \sin((\theta_1 + \theta_2)/2)} where: .. math:: \gamma = \sin \theta_1 + \sin \theta_2 Parameters ---------- sigma : float :math:`(\theta_1 + \theta_2) / 2`, where :math:`\theta_1` and :math:`\theta_2` are the latitudes of the standard parallels, in degrees. Default is 90. delta : float :math:`(\theta_1 - \theta_2) / 2`, where :math:`\theta_1` and :math:`\theta_2` are the latitudes of the standard parallels, in degrees. Default is 0. cCst|jj|jjS)N)r8rrr)rrrrrlszSky2Pix_ConicEqualArea.inversecCst||t|t|S)N)rZcoes2xr )rrrrrrrrrpszSky2Pix_ConicEqualArea.evaluateN)rrrrrrrrrrrrr9Ls c@s(eZdZdZeddZeddZdS)r:a1 Conic equidistant projection - pixel to sky. Corresponds to the ``COD`` projection in FITS WCS. See `Conic` for a description of the entire equation. The projection formulae are: .. math:: C &= \frac{180^\circ}{\pi} \frac{\sin\theta_a\sin\eta}{\eta} \\ R_\theta &= \theta_a - \theta + \eta\cot\eta\cot\theta_a \\ Y_0 = \eta\cot\eta\cot\theta_a Parameters ---------- sigma : float :math:`(\theta_1 + \theta_2) / 2`, where :math:`\theta_1` and :math:`\theta_2` are the latitudes of the standard parallels, in degrees. Default is 90. delta : float :math:`(\theta_1 - \theta_2) / 2`, where :math:`\theta_1` and :math:`\theta_2` are the latitudes of the standard parallels, in degrees. Default is 0. cCst|jj|jjS)N)r;rrr)rrrrrsz Pix2Sky_ConicEquidistant.inversecCst||t|t|S)N)rZcodx2sr )rrrrrrrrrsz!Pix2Sky_ConicEquidistant.evaluateN)rrrrrrrrrrrrr:ys c@s(eZdZdZeddZeddZdS)r;a1 Conic equidistant projection - sky to pixel. Corresponds to the ``COD`` projection in FITS WCS. See `Conic` for a description of the entire equation. The projection formulae are: .. math:: C &= \frac{180^\circ}{\pi} \frac{\sin\theta_a\sin\eta}{\eta} \\ R_\theta &= \theta_a - \theta + \eta\cot\eta\cot\theta_a \\ Y_0 = \eta\cot\eta\cot\theta_a Parameters ---------- sigma : float :math:`(\theta_1 + \theta_2) / 2`, where :math:`\theta_1` and :math:`\theta_2` are the latitudes of the standard parallels, in degrees. Default is 90. delta : float :math:`(\theta_1 - \theta_2) / 2`, where :math:`\theta_1` and :math:`\theta_2` are the latitudes of the standard parallels, in degrees. Default is 0. cCst|jj|jjS)N)r:rrr)rrrrrsz Sky2Pix_ConicEquidistant.inversecCst||t|t|S)N)rZcods2xr )rrrrrrrrrsz!Sky2Pix_ConicEquidistant.evaluateN)rrrrrrrrrrrrr;s c@s(eZdZdZeddZeddZdS)r<a Conic orthomorphic projection - pixel to sky. Corresponds to the ``COO`` projection in FITS WCS. See `Conic` for a description of the entire equation. The projection formulae are: .. math:: C &= \frac{\ln \left( \frac{\cos\theta_2}{\cos\theta_1} \right)} {\ln \left[ \frac{\tan\left(\frac{90^\circ-\theta_2}{2}\right)} {\tan\left(\frac{90^\circ-\theta_1}{2}\right)} \right] } \\ R_\theta &= \psi \left[ \tan \left( \frac{90^\circ - \theta}{2} \right) \right]^C \\ Y_0 &= \psi \left[ \tan \left( \frac{90^\circ - \theta_a}{2} \right) \right]^C where: .. math:: \psi = \frac{180^\circ}{\pi} \frac{\cos \theta} {C\left[\tan\left(\frac{90^\circ-\theta}{2}\right)\right]^C} Parameters ---------- sigma : float :math:`(\theta_1 + \theta_2) / 2`, where :math:`\theta_1` and :math:`\theta_2` are the latitudes of the standard parallels, in degrees. Default is 90. delta : float :math:`(\theta_1 - \theta_2) / 2`, where :math:`\theta_1` and :math:`\theta_2` are the latitudes of the standard parallels, in degrees. Default is 0. cCst|jj|jjS)N)r=rrr)rrrrrsz!Pix2Sky_ConicOrthomorphic.inversecCst||t|t|S)N)rZcoox2sr )rrrrrrrrrsz"Pix2Sky_ConicOrthomorphic.evaluateN)rrrrrrrrrrrrr<s$ c@s(eZdZdZeddZeddZdS)r=a Conic orthomorphic projection - sky to pixel. Corresponds to the ``COO`` projection in FITS WCS. See `Conic` for a description of the entire equation. The projection formulae are: .. math:: C &= \frac{\ln \left( \frac{\cos\theta_2}{\cos\theta_1} \right)} {\ln \left[ \frac{\tan\left(\frac{90^\circ-\theta_2}{2}\right)} {\tan\left(\frac{90^\circ-\theta_1}{2}\right)} \right] } \\ R_\theta &= \psi \left[ \tan \left( \frac{90^\circ - \theta}{2} \right) \right]^C \\ Y_0 &= \psi \left[ \tan \left( \frac{90^\circ - \theta_a}{2} \right) \right]^C where: .. math:: \psi = \frac{180^\circ}{\pi} \frac{\cos \theta} {C\left[\tan\left(\frac{90^\circ-\theta}{2}\right)\right]^C} Parameters ---------- sigma : float :math:`(\theta_1 + \theta_2) / 2`, where :math:`\theta_1` and :math:`\theta_2` are the latitudes of the standard parallels, in degrees. Default is 90. delta : float :math:`(\theta_1 - \theta_2) / 2`, where :math:`\theta_1` and :math:`\theta_2` are the latitudes of the standard parallels, in degrees. Default is 0. cCst|jj|jjS)N)r<rrr)rrrrr sz!Sky2Pix_ConicOrthomorphic.inversecCst||t|t|S)N)rZcoos2xr )rrrrrrrrr$sz"Sky2Pix_ConicOrthomorphic.evaluateN)rrrrrrrrrrrrr=s$ c@seZdZdZdS)rzrBase class for pseudoconic projections. Pseudoconics are a subclass of conics with concentric parallels. N)rrrrrrrrr-sc@s:eZdZdZedeedZdZe ddZ e ddZ d S) r>a Bonne's equal area pseudoconic projection - pixel to sky. Corresponds to the ``BON`` projection in FITS WCS. .. math:: \phi &= \frac{\pi}{180^\circ} A_\phi R_\theta / \cos \theta \\ \theta &= Y_0 - R_\theta where: .. math:: R_\theta &= \mathrm{sign} \theta_1 \sqrt{x^2 + (Y_0 - y)^2} \\ A_\phi &= \arg\left(\frac{Y_0 - y}{R_\theta}, \frac{x}{R_\theta}\right) Parameters ---------- theta1 : float Bonne conformal latitude, in degrees. g)rrrTcCs t|jjS)N)r?theta1r)rrrrrNszPix2Sky_BonneEqualArea.inversecCst||t|S)N)rZbonx2sr )rrrrrrrrRszPix2Sky_BonneEqualArea.evaluateN) rrrrrr rrrrrrrrrrrr>4s  c@s:eZdZdZedeedZdZe ddZ e ddZ d S) r?a Bonne's equal area pseudoconic projection - sky to pixel. Corresponds to the ``BON`` projection in FITS WCS. .. math:: x &= R_\theta \sin A_\phi \\ y &= -R_\theta \cos A_\phi + Y_0 where: .. math:: A_\phi &= \frac{180^\circ}{\pi R_\theta} \phi \cos \theta \\ R_\theta &= Y_0 - \theta \\ Y_0 &= \frac{180^\circ}{\pi} \cot \theta_1 + \theta_1 Parameters ---------- theta1 : float Bonne conformal latitude, in degrees. g)rrrTcCs t|jjS)N)r>rr)rrrrrsszSky2Pix_BonneEqualArea.inversecCst||t|S)N)rZbons2xr )rrrrrrrrwszSky2Pix_BonneEqualArea.evaluateN) rrrrrr rrrrrrrrrrrr?Zs  c@s,eZdZdZdZeddZeddZdS)r@zf Polyconic projection - pixel to sky. Corresponds to the ``PCO`` projection in FITS WCS. FcCstS)N)rA)rrrrrszPix2Sky_Polyconic.inversecCs t||S)N)rZpcox2s)rrrrrrrszPix2Sky_Polyconic.evaluateN) rrrrrrrrrrrrrr@s c@s,eZdZdZdZeddZeddZdS)rAzf Polyconic projection - sky to pixel. Corresponds to the ``PCO`` projection in FITS WCS. FcCstS)N)r@)rrrrrszSky2Pix_Polyconic.inversecCs t||S)N)rZpcos2x)rrrrrrrszSky2Pix_Polyconic.evaluateN) rrrrrrrrrrrrrrAs c@seZdZdZdS)rawBase class for quad cube projections. Quadrilateralized spherical cube (quad-cube) projections belong to the class of polyhedral projections in which the sphere is projected onto the surface of an enclosing polyhedron. The six faces of the quad-cube projections are numbered and laid out as:: 0 4 3 2 1 4 3 2 5 N)rrrrrrrrrsc@s,eZdZdZdZeddZeddZdS)rBzv Tangential spherical cube projection - pixel to sky. Corresponds to the ``TSC`` projection in FITS WCS. FcCstS)N)rC)rrrrrsz'Pix2Sky_TangentialSphericalCube.inversecCs t||S)N)rZtscx2s)rrrrrrrsz(Pix2Sky_TangentialSphericalCube.evaluateN) rrrrrrrrrrrrrrBs c@s,eZdZdZdZeddZeddZdS)rCzv Tangential spherical cube projection - sky to pixel. Corresponds to the ``PCO`` projection in FITS WCS. FcCstS)N)rB)rrrrrsz'Sky2Pix_TangentialSphericalCube.inversecCs t||S)N)rZtscs2x)rrrrrrrsz(Sky2Pix_TangentialSphericalCube.evaluateN) rrrrrrrrrrrrrrCs c@s,eZdZdZdZeddZeddZdS)rDz COBE quadrilateralized spherical cube projection - pixel to sky. Corresponds to the ``CSC`` projection in FITS WCS. FcCstS)N)rE)rrrrrsz%Pix2Sky_COBEQuadSphericalCube.inversecCs t||S)N)rZcscx2s)rrrrrrrsz&Pix2Sky_COBEQuadSphericalCube.evaluateN) rrrrrrrrrrrrrrDs c@s,eZdZdZdZeddZeddZdS)rEz COBE quadrilateralized spherical cube projection - sky to pixel. Corresponds to the ``CSC`` projection in FITS WCS. FcCstS)N)rD)rrrrrsz%Sky2Pix_COBEQuadSphericalCube.inversecCs t||S)N)rZcscs2x)rrrrrrrsz&Sky2Pix_COBEQuadSphericalCube.evaluateN) rrrrrrrrrrrrrrEs c@s,eZdZdZdZeddZeddZdS)rFz} Quadrilateralized spherical cube projection - pixel to sky. Corresponds to the ``QSC`` projection in FITS WCS. FcCstS)N)rG)rrrrrsz!Pix2Sky_QuadSphericalCube.inversecCs t||S)N)rZqscx2s)rrrrrrrsz"Pix2Sky_QuadSphericalCube.evaluateN) rrrrrrrrrrrrrrF s c@s,eZdZdZdZeddZeddZdS)rGz} Quadrilateralized spherical cube projection - sky to pixel. Corresponds to the ``QSC`` projection in FITS WCS. FcCstS)N)rF)rrrrr%sz!Sky2Pix_QuadSphericalCube.inversecCs t||S)N)rZqscs2x)rrrrrrr)sz"Sky2Pix_QuadSphericalCube.evaluateN) rrrrrrrrrrrrrrGs c@seZdZdZdS)rz(Base class for HEALPix projections. N)rrrrrrrrr1sc@s@eZdZdZdZeddZeddZeddZ e dd Z d S) rHz HEALPix - pixel to sky. Corresponds to the ``HPX`` projection in FITS WCS. Parameters ---------- H : float The number of facets in longitude direction. X : float The number of facets in latitude direction. Tg@)rg@cCst|jj|jjS)N)rIHrX)rrrrrIszPix2Sky_HEALPix.inversecCst||||S)N)rZhpxx2s)rrrrrrrrrMszPix2Sky_HEALPix.evaluateN) rrrrrrrrrrrrrrrrrH6s     c@s@eZdZdZdZeddZeddZeddZ e dd Z d S) rIa  HEALPix projection - sky to pixel. Corresponds to the ``HPX`` projection in FITS WCS. Parameters ---------- H : float The number of facets in longitude direction. X : float The number of facets in latitude direction. Tg@)rg@cCst|jj|jjS)N)rHrrr)rrrrrhszSky2Pix_HEALPix.inversecCst||||S)N)rhpxs2x)rrrrrrrrrlszSky2Pix_HEALPix.evaluateN) rrrrrrrrrrrrrrrrrIUs     c@s,eZdZdZdZeddZeddZdS)rJz{ HEALPix polar, aka "butterfly" projection - pixel to sky. Corresponds to the ``XPH`` projection in FITS WCS. FcCstS)N)rI)rrrrr|szPix2Sky_HEALPixPolar.inversecCs t||S)N)rZxphx2s)rrrrrrrszPix2Sky_HEALPixPolar.evaluateN) rrrrrrrrrrrrrrJts c@s,eZdZdZdZeddZeddZdS)rKz{ HEALPix polar, aka "butterfly" projection - pixel to sky. Corresponds to the ``XPH`` projection in FITS WCS. FcCstS)N)rH)rrrrrszSky2Pix_HEALPixPolar.inversecCs t||S)N)rr)rrrrrrrszSky2Pix_HEALPixPolar.evaluateN) rrrrrrrrrrrrrrKs cseZdZdZdZdZdZdZeddgddggdZ eddgdZ e j ddZ e j d d Z e e ffd d Z e d dZeddZeddZe ddZZS)raP Perform an affine transformation in 2 dimensions. Parameters ---------- matrix : array A 2x2 matrix specifying the linear transformation to apply to the inputs translation : array A 2D vector (given as either a 2x1 or 1x2 array) specifying a translation to apply to the inputs rFg?g)rcCst|dkrtddS)z2Validates that the input matrix is a 2x2 2D array.)rrz0Expected transformation matrix to be a 2x2 arrayN)rshaper)rrrrrmatrixszAffineTransformation2D.matrixcCsDt|dkrt|dks@t|dkr8t|dks@tddS)z Validates that the translation vector is a 2D vector. This allows either a "row" vector or a "column" vector where in the latter case the resultant Numpy array has ``ndim=2`` but the shape is ``(1, 2)``. r)rr)rrzHExpected translation vector to be a 2 element row or column vector arrayN)rndimrr)rrrrr translationsz"AffineTransformation2D.translationc s(tjf||d|d|_d|_dS)N)rr)rr)rrrr)rrrr)rrrrszAffineTransformation2D.__init__cCsrtj|jj}|dkr*td|jjtj |jj}|jj dk rR||jj }t ||j j }|j||dS)z Inverse transformation. Raises `~astropy.modeling.InputParameterError` if the transformation cannot be inverted. rzDTransformation matrix is singular; {} model does not have an inverseN)rr) rZlinalgdetrrrformatrrinvunitdotr)rrrrrrrrs   zAffineTransformation2D.inversec Cs|j|jkrtd|jpd}tt|t|t|j|jg}|jddksf|j dkrntd| ||}t ||}|d|d}}||_|_||fS)a, Apply the transformation to a set of 2D Cartesian coordinates given as two lists--one for the x coordinates and one for a y coordinates--or a single coordinate pair. Parameters ---------- x, y : array, float x and y coordinates z,Expected input arrays to have the same shape)rrrzIncompatible input shapesr) rrrZvstackrZravelZonessizedtyper_create_augmented_matrixr) rrrrrrZinarraugmented_matrixresultrrrrs      zAffineTransformation2D.evaluatecCsd}tt|dt|dgr\tt|dt|dgsrtr?rur@rvrArwrrBrxrCryrDrzrEr{rFr|rGr}rrHr~rIrrJrrKrrrrrrsx   2,*)*!" 1, $%)*%&./##