a ߙfbWD@sdZddlZddlZddlmZmZddlmZ ddl m Z ddl m Z ddlmZmZgd Zd d Zd d ZddZGddde ZGdddeZGdddZGdddee ZGdddee ZGdddeZGdddeZGddde ZdS) a Implements rotations, including spherical rotations as defined in WCS Paper II [1]_ `RotateNative2Celestial` and `RotateCelestial2Native` follow the convention in WCS Paper II to rotate to/from a native sphere and the celestial sphere. The implementation uses `EulerAngleRotation`. The model parameters are three angles: the longitude (``lon``) and latitude (``lat``) of the fiducial point in the celestial system (``CRVAL`` keywords in FITS), and the longitude of the celestial pole in the native system (``lon_pole``). The Euler angles are ``lon+90``, ``90-lat`` and ``-(lon_pole-90)``. References ---------- .. [1] Calabretta, M.R., Greisen, E.W., 2002, A&A, 395, 1077 (Paper II) N)rotation_matrixmatrix_product)units)Model) Parameter) _to_radian _to_orig_unit)RotateCelestial2NativeRotateNative2Celestial Rotation2DEulerAngleRotationRotationSequence3DSphericalRotationSequencecCs^g}t||D]8\}}t|tjr(|j}|}|t||tjdqt |ddd}|S)Nunit) zip isinstanceuQuantityvalueitemappendrradr)angles axes_orderZmatricesangleZaxisresultr9lib/python3.9/site-packages/astropy/modeling/rotations.py_create_matrix%s r!cCsVt|}t|}t|t|}t|t|}t|}t|||gSN)npZdeg2radcossinarray)alphadeltaxyzrrr spherical2cartesian0s    r,cCs8t||}tt||}tt||}||fSr")r#ZhypotZrad2degZarctan2)r)r*r+hr'r(rrr cartesian2spherical9s r.csVeZdZdZdZdZdZdZege e ddZ d fdd Z e d d Zd d ZZS)ra Perform a series of rotations about different axis in 3D space. Positive angles represent a counter-clockwise rotation. Parameters ---------- angles : array-like Angles of rotation in deg in the order of axes_order. axes_order : str A sequence of 'x', 'y', 'z' corresponding to axis of rotation. Examples -------- >>> model = RotationSequence3D([1.1, 2.1, 3.1, 4.1], axes_order='xyzx') Fz4Angles of rotation in deg in the order of axes_orderdefaultgettersetterZ descriptionNcs~gd|_t||j}|r0td||j||_t|t|kr^tdt|t|tj||dd|_ d|_ dS)Nr)r*r+z2Unrecognized axis label {0}; should be one of {1} z=The number of angles {0} should match the number of axes {1}.)name) axesset difference ValueErrorformatrlensuper__init___inputs_outputs)selfrrr5 unrecognized __class__rr r=Ys  zRotationSequence3D.__init__cCs0|jjdddd}|j||jddddS)Inverse rotation.Nr)r)rrrCr)r@rrrr inversehszRotationSequence3D.inversecCs|j|jks|j|jkr td|jp(d}t|||g}tt|d|j|}|d|d|d}}}||_|_|_|||fS)zJ Apply the rotation to a set of 3D Cartesian coordinates. ,Expected input arrays to have the same shaperrr)shaper9r#r&flattendotr!r)r@r)r*r+r orig_shapeinarrrrrr evaluatens zRotationSequence3D.evaluate)N)__name__ __module__ __qualname____doc__Zstandard_broadcasting _separablen_inputs n_outputsrr rrr=propertyrErN __classcell__rrrBr r@s rcsFeZdZdZd fdd ZeddZeddZfd d ZZ S) ra\ Perform a sequence of rotations about arbitrary number of axes in spherical coordinates. Parameters ---------- angles : list A sequence of angles (in deg). axes_order : str A sequence of characters ('x', 'y', or 'z') corresponding to the axis of rotation and matching the order in ``angles``. Nc s6d|_d|_tj|f||d|d|_d|_dS)NrH)rr5)lonlat) _n_inputs _n_outputsr<r=r>r?)r@rrr5kwargsrBrr r=s z"SphericalRotationSequence.__init__cCs|jSr")rZr@rrr rTsz"SphericalRotationSequence.n_inputscCs|jSr")r[r]rrr rUsz#SphericalRotationSequence.n_outputsc s@t||\}}}t||||\}}} t||| \}}||fSr")r,r<rNr.) r@rXrYrr)r*r+Zx1Zy1Zz1rBrr rNsz"SphericalRotationSequence.evaluate)N) rOrPrQrRr=rVrTrUrNrWrrrBr r~s   rc@s<eZdZdZdZddZdZdZeddZ edd Z d S) _EulerRotationz7 Base class which does the actual computation. Fc Cstd}t|tjr&|}|}|j}t||}t|||g|} t| |} t| \} } |durl|| _|| _| | fSr") rr#ndarrayrJrIr,r!rKr.) r@r'r(phithetapsirrIZinpZmatrixrabrrr rNs    z_EulerRotation.evaluateTcCs|jdtj|jdtjiSz Input units. rrinputsrdegr]rrr input_unitss  z_EulerRotation.input_unitscCs|jdtj|jdtjiSz Output units. rroutputsrrhr]rrr return_unitss  z_EulerRotation.return_unitsN) rOrPrQrRrSrNZ_input_units_strictZ _input_units_allow_dimensionlessrVrirmrrrr r^s r^cspeZdZdZdZdZedeeddZ edeeddZ edeeddZ fdd Z e d d Zfd d ZZS)r a1 Implements Euler angle intrinsic rotations. Rotates one coordinate system into another (fixed) coordinate system. All coordinate systems are right-handed. The sign of the angles is determined by the right-hand rule.. Parameters ---------- phi, theta, psi : float or `~astropy.units.Quantity` ['angle'] "proper" Euler angles in deg. If floats, they should be in deg. axes_order : str A 3 character string, a combination of 'x', 'y' and 'z', where each character denotes an axis in 3D space. rHrz*1st Euler angle (Quantity or value in deg)r0z*2nd Euler angle (Quantity or value in deg)z*3rd Euler angle (Quantity or value in deg)c sgd|_t|dkr$td|t||j}|rJtd||j||_dd|||fD}t|r|t |s|tdt j f|||d|d |_ d |_ dS) Nr4r/zBExpected axes_order to be a character sequence of length 3, got {}z0Unrecognized axis label {}; should be one of {} cSsg|]}t|tjqSrrrr.0Zparrrr z/EulerAngleRotation.__init__..>All parameters should be of the same type - float or Quantity.)r`rarb)r'r()r6r; TypeErrorr:r7r8r9ranyallr<r=r>r?)r@r`rarbrr\rAqsrBrr r=s&  zEulerAngleRotation.__init__cCs*|j|j |j |j |jddddS)Nr)r`rarbr)rCrbrar`rr]rrr rEs  zEulerAngleRotation.inversecs$t||||||j\}}||fSr")r<rNr)r@r'r(r`rarbrcrdrBrr rNszEulerAngleRotation.evaluate)rOrPrQrRrTrUrr rr`rarbr=rVrErNrWrrrBr r s   r cs\eZdZdZedeeddZedeeddZedeeddZ fddZ fd d Z Z S) _SkyRotationzK Base class for RotateNative2Celestial and RotateCelestial2Native. rZLatituder0Z LongtitudezLongitude of a polec sNdd|||fD}t|r,t|s,tdtj|||fi|d|_dS)NcSsg|]}t|tjqSrrnrorrr rqrrz)_SkyRotation.__init__..rsZzxz)rurvrtr<r=r)r@rXrYlon_poler\rwrBrr r= s z_SkyRotation.__init__c sRt||||||j\}}|dk}t|tjrB||d7<n|d7}||fS)Nrih)r<rNrrr#r_) r@r`rarXrYryr'r(maskrBrr _evaluates z_SkyRotation._evaluate) rOrPrQrRrr rrXrYryr=r{rWrrrBr rxs  rxcsXeZdZdZdZdZeddZeddZfddZ fd d Z ed d Z Z S) r a~ Transform from Native to Celestial Spherical Coordinates. Parameters ---------- lon : float or `~astropy.units.Quantity` ['angle'] Celestial longitude of the fiducial point. lat : float or `~astropy.units.Quantity` ['angle'] Celestial latitude of the fiducial point. lon_pole : float or `~astropy.units.Quantity` ['angle'] Longitude of the celestial pole in the native system. Notes ----- If ``lon``, ``lat`` and ``lon_pole`` are numerical values they should be in units of deg. Inputs are angles on the native sphere. Outputs are angles on the celestial sphere. rHcCs|jdtj|jdtjiSrerfr]rrr ri6s  z"RotateNative2Celestial.input_unitscCs|jdtj|jdtjiSrjrkr]rrr rm<sz#RotateNative2Celestial.return_unitsc s(tj|||fi|d|_d|_dS)Nphi_Ntheta_Nalpha_Cdelta_Cr<r=rgrlr@rXrYryr\rBrr r=AszRotateNative2Celestial.__init__c slt|tjr|j}|j}|j}|tjd}tjd| }tjd| }t|||||\} } | | fS)a Parameters ---------- phi_N, theta_N : float or `~astropy.units.Quantity` ['angle'] Angles in the Native coordinate system. it is assumed that numerical only inputs are in degrees. If float, assumed in degrees. lon, lat, lon_pole : float or `~astropy.units.Quantity` ['angle'] Parameter values when the model was initialized. If float, assumed in degrees. Returns ------- alpha_C, delta_C : float or `~astropy.units.Quantity` ['angle'] Angles on the Celestial sphere. If float, in degrees. rHrrrrr#Zpir<r{) r@r}r~rXrYryr`rarbrrrBrr rNFs zRotateNative2Celestial.evaluatecCst|j|j|jSr")r rXrYryr]rrr rEdszRotateNative2Celestial.inverse rOrPrQrRrTrUrVrirmr=rNrErWrrrBr r s    r csXeZdZdZdZdZeddZeddZfddZ fd d Z ed d Z Z S) r a~ Transform from Celestial to Native Spherical Coordinates. Parameters ---------- lon : float or `~astropy.units.Quantity` ['angle'] Celestial longitude of the fiducial point. lat : float or `~astropy.units.Quantity` ['angle'] Celestial latitude of the fiducial point. lon_pole : float or `~astropy.units.Quantity` ['angle'] Longitude of the celestial pole in the native system. Notes ----- If ``lon``, ``lat`` and ``lon_pole`` are numerical values they should be in units of deg. Inputs are angles on the celestial sphere. Outputs are angles on the native sphere. rHcCs|jdtj|jdtjiSrerfr]rrr ris  z"RotateCelestial2Native.input_unitscCs|jdtj|jdtjiSrjrkr]rrr rms  z#RotateCelestial2Native.return_unitsc s(tj|||fi|d|_d|_dS)Nrr|rrrBrr r=szRotateCelestial2Native.__init__c sjt|tjr|j}|j}|j}tjd|}tjd|}|tjd }t|||||\} } | | fS)a; Parameters ---------- alpha_C, delta_C : float or `~astropy.units.Quantity` ['angle'] Angles in the Celestial coordinate frame. If float, assumed in degrees. lon, lat, lon_pole : float or `~astropy.units.Quantity` ['angle'] Parameter values when the model was initialized. If float, assumed in degrees. Returns ------- phi_N, theta_N : float or `~astropy.units.Quantity` ['angle'] Angles on the Native sphere. If float, in degrees. rHr) r@rrrXrYryr`rarbr}r~rBrr rNs zRotateCelestial2Native.evaluatecCst|j|j|jSr")r rXrYryr]rrr rEszRotateCelestial2Native.inverserrrrBr r js    r csdeZdZdZdZdZdZedee ddZ e ffdd Z e d d Z ed d Zed dZZS)r a  Perform a 2D rotation given an angle. Positive angles represent a counter-clockwise rotation and vice-versa. Parameters ---------- angle : float or `~astropy.units.Quantity` ['angle'] Angle of rotation (if float it should be in deg). rHFgz,Angle of rotation (Quantity or value in deg)r0c s&tjfd|i|d|_d|_dS)Nr)r)r*)r<r=r>r?)r@rr\rBrr r=szRotation2D.__init__cCs|j|j dS)rDr)rCrr]rrr rEszRotation2D.inversec Cs|j|jkrtdt|dd}t|dd}|duo:|du}||krl|rb||rb||}|}n td|jptd}t| | g}t |tj r| tj }t|||} | d| d}}||_|_|rtj ||dtj ||dfS||fS) a Rotate (x, y) about ``angle``. Parameters ---------- x, y : array-like Input quantities angle : float or `~astropy.units.Quantity` ['angle'] Angle of rotations. If float, assumed in degrees. rFrNz"x and y must have compatible unitsrGrrr)rIr9getattrZ is_equivalenttorZ UnitsErrorr#r&rJrrZto_valuerrK_compute_matrix) clsr)r*rZx_unitZy_unitZ has_unitsrLrMrrrr rNs(         zRotation2D.evaluatecCs6tjt|t| gt|t|ggtjdS)N)Zdtype)r#r&mathr$r%Zfloat64rrrr rs zRotation2D._compute_matrix)rOrPrQrRrTrUrSrr rrr=rVrE classmethodrN staticmethodrrWrrrBr r s   )r )rRrZnumpyr#Z$astropy.coordinates.matrix_utilitiesrrZastropyrrcorer parametersrZutilsrr __all__r!r,r.rrr^r rxr r r rrrr s&     >$';KM