IR-e EbdZddlZddlmZddlZddlmZddl m Z ddl m Z ddl mZdd lmZmZgd Zd Zd Zd ZGdde ZGddeZGddZGddee ZGddee ZGddeZGddeZGdde ZdS)aImplements 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)reduce)units)rotation_matrix)Model) Parameter) _to_orig_unit _to_radian)RotateCelestial2NativeRotateNative2Celestial Rotation2DEulerAngleRotationRotationSequence3DSphericalRotationSequencec@g}t||D]i\}}t|tjr|j}|}|t||tjjttj |dddS)N)unit) zip isinstanceuQuantityvalueitemappendrradrnpmatmul)angles axes_ordermatricesangleaxiss :lib/python3.11/site-packages/astropy/modeling/rotations.py_create_matrixr$+sH6:..BB t eQZ ( ( KE t!%@@@AAAA ")Xddd^ , ,,cLtj|}tj|}tj|tj|z}tj|tj|z}tj|}tj|||gSN)rdeg2radcossinarray)alphadeltaxyzs r#spherical2cartesianr15sw Ju  E Ju  E u u %A u u %A u A 8Q1I  r%ctj||}tjtj||}tjtj||}||fSr')rhypotrad2degarctan2)r.r/r0hr,r-s r#cartesian2sphericalr7>sQ AA Jrz!Q'' ( (E Jrz!Q'' ( (E %<r%cneZdZdZdZdZdZdZege e dZ d fd Z e dZd ZxZS) ra Perform a series of rotations about different axis in 3D space. Positive angles represent a counter-clockwise rotation. Parameters ---------- angles : array-like Angles of rotation in deg in the order of axes_order. axes_order : str A sequence of 'x', 'y', 'z' corresponding to axis of rotation. Examples -------- >>> model = RotationSequence3D([1.1, 2.1, 3.1, 4.1], axes_order='xyzx') Fz4Angles of rotation in deg in the order of axes_orderdefaultgettersetter descriptionNcgd|_t||j}|rtd|d|jd||_t |t |kr0tdt |dt |dt ||d|_d|_ dS) Nr.r/r0Unrecognized axis label ; should be one of  zThe number of angles z! should match the number of axes .)name) axesset difference ValueErrorrlensuper__init___inputs_outputs)selfrrrE unrecognized __class__s r#rLzRotationSequence3D.__init__ds#OO :11$)<<  X<XXDIXXX % v;;#j// ) )9F 99&)*oo999  d+++& ' r%c||jjddddz}|||jdddS)Inverse rotation.Nr)r)rrrQr)rOrs r#inversezRotationSequence3D.inverseusA"44R4(2-~~f21F~GGGr%c|j|jks|j|jkrtd|jpd}tj|||g}tjt |d|j|}|d|d|d}}}|x|_x|_|_|||fS)zJ Apply the rotation to a set of 3D Cartesian coordinates. ,Expected input arrays to have the same shaperrr)shaperIrr+flattendotr$r)rOr.r/r0r orig_shapeinarrresults r#evaluatezRotationSequence3D.evaluate{s 7ag  AG!3!3KLL LW_ !))++qyy{{AIIKK@AAvay$/BBEJJ)VAYq a1&000!'AG!Qwr%r')__name__ __module__ __qualname____doc__standard_broadcasting _separablen_inputs n_outputsrr r rrLpropertyrTr_ __classcell__rQs@r#rrEs$"JHI YJ F(((((("HHXH       r%rcZeZdZdZdfd ZedZedZfdZxZ S)ra\ Perform a sequence of rotations about arbitrary number of axes in spherical coordinates. Parameters ---------- angles : list A sequence of angles (in deg). axes_order : str A sequence of characters ('x', 'y', or 'z') corresponding to the axis of rotation and matching the order in ``angles``. Nc zd|_d|_tj|f||d|d|_d|_dS)NrX)rrE)lonlat) _n_inputs _n_outputsrKrLrMrN)rOrrrEkwargsrQs r#rLz"SphericalRotationSequence.__init__sILJTLLVLLL% & r%c|jSr')rorOs r#rfz"SphericalRotationSequence.n_inputss ~r%c|jSr')rprss r#rgz#SphericalRotationSequence.n_outputss r%ct||\}}}t||||\}}} t||| \}}||fSr')r1rKr_r7) rOrmrnrr.r/r0x1y1z1rQs r#r_z"SphericalRotationSequence.evaluatesY%c3//1aWW%%aAv66 B&r2r22SCxr%r') r`rarbrcrLrhrfrgr_rirjs@r#rrs  ''''''XXr%rcPeZdZdZdZdZdZdZedZ edZ dS)_EulerRotationz7 Base class which does the actual computation. FcHd}t|tjr/|}|}|j}t ||}t |||g|} tj| |} t| \} } ||| _|| _| | fSr') rrndarrayrZrYr1r$r[r7) rOr,r-phithetapsirrYinpmatrixr^abs r#r_z_EulerRotation.evaluates eRZ ( ( MMOOEMMOOEKE!%//eS 1:>>$$"F+1  AGAG!t r%Tcb|jdtj|jdtjiSz Input units.rrinputsrdegrss r# input_unitsz_EulerRotation.input_units# At{1~qu==r%cb|jdtj|jdtjiSz Output units.rroutputsrrrss r# return_unitsz_EulerRotation.return_units# Q Q??r%N) r`rarbrcrer__input_units_strict _input_units_allow_dimensionlessrhrrr%r#rzrzs{J   '+$ >>X>@@X@@@r%rzceZdZdZdZdZedeedZ edeedZ edeedZ fdZ e d Zfd ZxZS) ra1 Implements Euler angle intrinsic rotations. Rotates one coordinate system into another (fixed) coordinate system. All coordinate systems are right-handed. The sign of the angles is determined by the right-hand rule.. Parameters ---------- phi, theta, psi : float or `~astropy.units.Quantity` ['angle'] "proper" Euler angles in deg. If floats, they should be in deg. axes_order : str A 3 character string, a combination of 'x', 'y' and 'z', where each character denotes an axis in 3D space. rXrz*1st Euler angle (Quantity or value in deg)r:z*2nd Euler angle (Quantity or value in deg)z*3rd Euler angle (Quantity or value in deg)c gd|_t|dkrtd|t||j}|rt d|d|j||_d|||fD}t|rt|stdtj d |||d|d |_ d |_ dS) Nr@r9z@Expected axes_order to be a character sequence of length 3, got rArBcBg|]}t|tjSrrrr.0pars r# z/EulerAngleRotation.__init__.. s$ G G Gcjaj)) G G Gr%>All parameters should be of the same type - float or Quantity.)r}r~r)r,r-r) rFrJ TypeErrorrGrHrIranyallrKrLrMrN) rOr}r~rrrqrPqsrQs r#rLzEulerAngleRotation.__init__s#OO z??a  $!$$ :11$)<<  W<WWDIWW % G Gc5#5F G G G r77 3r77 P  AS3AA&AAA) * r%c t||j |j |j |jdddS)Nr)r}r~rr)rQrr~r}rrss r#rTzEulerAngleRotation.inversesB~~ :+ ttt,    r%cht||||||j\}}||fSr')rKr_r) rOr,r-r}r~rrrrQs r#r_zEulerAngleRotation.evaluates3wwuc5#tOO1!t r%)r`rarbrcrfrgrr r r}r~rrLrhrTr_rirjs@r#rrs"HI )@    C I@    E )@    C+++++.  X r%rceZdZdZedeedZedeedZedeedZ fdZ fdZ xZ S) _SkyRotationzK Base class for RotateNative2Celestial and RotateCelestial2Native. rLatituder: LongtitudezLongitude of a polec d|||fD}t|rt|stdtj|||fi|d|_dS)NcBg|]}t|tjSrrrs r#rz)_SkyRotation.__init__..5s$ J J Jcjaj)) J J Jr%rzxz)rrrrKrLr)rOrmrnlon_polerqrrQs r#rLz_SkyRotation.__init__4s} J Jc35I J J J r77 3r77 P  c866v666r%ct||||||j\}}|dk}t|tjr||xxdz cc<n|dz }||fS)Nrih)rKr_rrrr|) rOr}r~rmrnrr,r-maskrQs r# _evaluatez_SkyRotation._evaluate=srww''UChXX uqy dBJ ' '  $KKK3 KKKK SLEe|r%) r`rarbrcrr r rmrnrrLrrirjs@r#rr"s )-    C )-    Cy) H     r%rcveZdZdZdZdZedZedZfdZ fdZ edZ xZ S)r a~ Transform from Native to Celestial Spherical Coordinates. Parameters ---------- lon : float or `~astropy.units.Quantity` ['angle'] Celestial longitude of the fiducial point. lat : float or `~astropy.units.Quantity` ['angle'] Celestial latitude of the fiducial point. lon_pole : float or `~astropy.units.Quantity` ['angle'] Longitude of the celestial pole in the native system. Notes ----- If ``lon``, ``lat`` and ``lon_pole`` are numerical values they should be in units of deg. Inputs are angles on the native sphere. Outputs are angles on the celestial sphere. rXcb|jdtj|jdtjiSrrrss r#rz"RotateNative2Celestial.input_units^rr%cb|jdtj|jdtjiSrrrss r#rz#RotateNative2Celestial.return_unitscrr%c \tj|||fi|d|_d|_dS)Nphi_Ntheta_Nalpha_Cdelta_CrKrLrrrOrmrnrrqrQs r#rLzRotateNative2Celestial.__init__hs8c866v666* - r%c*t|tjr|j}|j}|j}|tjdz z }tjdz |z }tjdz |z }t |||||\} } | | fS)a Parameters ---------- phi_N, theta_N : float or `~astropy.units.Quantity` ['angle'] Angles in the Native coordinate system. it is assumed that numerical only inputs are in degrees. If float, assumed in degrees. lon, lat, lon_pole : float or `~astropy.units.Quantity` ['angle'] Parameter values when the model was initialized. If float, assumed in degrees. Returns ------- alpha_C, delta_C : float or `~astropy.units.Quantity` ['angle'] Angles on the Celestial sphere. If float, in degrees. rXrrrrrpirKr) rOrrrmrnrr}r~rrrrQs r#r_zRotateNative2Celestial.evaluatems& c1: & & &)C)C~H"%!)c/" C  77,,UGS%MMr%cBt|j|j|jSr')r rmrnrrss r#rTzRotateNative2Celestial.inverses&dh$-HHHr% r`rarbrcrfrgrhrrrLr_rTrirjs@r#r r Gs&HI >>X>@@X@.....      <IIXIIIIIr%r cveZdZdZdZdZedZedZfdZ fdZ edZ xZ 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. rXcb|jdtj|jdtjiSrrrss r#rz"RotateCelestial2Native.input_unitsrr%cb|jdtj|jdtjiSrrrss r#rz#RotateCelestial2Native.return_unitsrr%c \tj|||fi|d|_d|_dS)Nrrrrs r#rLzRotateCelestial2Native.__init__s:c866v666- + r%c(t|tjr|j}|j}|j}tjdz |z}tjdz |z }|tjdz z }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. rXr) rOrrrmrnrr}r~rrrrQs r#r_zRotateCelestial2Native.evaluates$ c1: & & &)C)C~Heai#o C2519$%**7GS%MMwg~r%cBt|j|j|jSr')r rmrnrrss r#rTzRotateCelestial2Native.inverses%dh$-HHHr%rrjs@r#r r s&HI >>X>@@X@,,,,,<IIXIIIIIr%r ceZdZdZdZdZdZedee dZ e ffd Z e dZ ed Zed ZxZS) 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). rXFgz,Angle of rotation (Quantity or value in deg)r:c Ztjdd|i|d|_d|_dS)Nr!)r.r/r)rKrLrMrN)rOr!rqrQs r#rLzRotation2D.__init__s7//u////! " r%c:||j S)rSr!)rQr!rss r#rTzRotation2D.inverses~~TZK~000r%c|j|jkrtdt|dd}t|dd}|duo|du}||krC|r-||r||}|}nt jd|jpd}tj| | g}t|t j r| t j }tj|||} | d| d}}|x|_|_|r.t j ||d t j ||d fS||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. rVrNz"x and y must have compatible unitsrWrrT)rsubok)rYrIgetattr is_equivalenttor UnitsErrorrr+rZrrto_valuerr[_compute_matrix) clsr.r/r!x_unity_unit has_unitsr\r]r^s r#r_zRotation2D.evaluates 7ag  KLL LFD))FD))$&=6+= V   IV11&99 IDDLLl#GHHHW_ !))++qyy{{344 eQZ ( ( *NN15))E++E22E::ay&)1&&!'  :afD9991:d<<< !t r%ctj|s|d}tjtj|tj| gtj|tj|ggtjS)Nr)dtype)risscalarr+mathr)r*float64rs r#rzRotation2D._compute_matrix*sp{5!! !HExhuoo/ 048E??DHUOO2T U*    r%)r`rarbrcrfrgrerr r r!rLrhrT classmethodr_ staticmethodrrirjs@r#r r s  HIJ IB    E####### 11X1(([(T  \     r%r )rcr functoolsrnumpyrastropyrr$astropy.coordinates.matrix_utilitiesrcorer parametersrutilsr r __all__r$r1r7rrrzrrr r r rr%r#rs|$ @@@@@@!!!!!!,,,,,,,,   ---CCCCCCCCL""""" 2"""J"@"@"@"@"@"@"@"@JJJJJJJJJZ""""">5"""JGIGIGIGIGI\GIGIGITIIIIIIIIII\IIIIIIXT T T T T T T T T T r%