U e{jD@sdZddlZddlmZddlZddlmZddl m Z ddl m Z ddl mZdd lmZmZd d d d ddgZddZddZddZGddde ZGdddeZGdddZGdd d ee ZGdddee ZGdd d eZGdd d eZGdd d e 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)reduce)units)rotation_matrix)Model) Parameter) _to_orig_unit _to_radianRotateCelestial2NativeRotateNative2Celestial Rotation2DEulerAngleRotationRotationSequence3DSphericalRotationSequencecCs^g}t||D]8\}}t|tjr(|j}|}|t||tjdqt t j |dddS)N)unit) zip isinstanceuQuantityvalueitemappendrradrnpmatmul)angles axes_orderZmatricesangleZaxisrY/var/www/html/bwave/python/venv/lib/python3.8/site-packages/astropy/modeling/rotations.py_create_matrix-s r!cCsVt|}t|}t|t|}t|t|}t|}t|||gSN)rZdeg2radcossinarray)alphadeltaxyzrrr spherical2cartesian7s    r+cCs8t||}tt||}tt||}||fSr")rhypotZrad2degZarctan2)r(r)r*hr&r'rrr cartesian2spherical@s 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_orderdefaultgettersetter descriptionNcsdddg|_t||j}|r8td|d|jd||_t|t|krltdt|dt|d tj||d d |_d |_ dS) Nr(r)r*Unrecognized axis label ; should be one of  zThe number of angles z! should match the number of axes .)name)r(r)r*) axesset difference ValueErrorrlensuper__init___inputs_outputs)selfrrr9 unrecognized __class__rr r@fs zRotationSequence3D.__init__cCs0|jjdddd}|j||jddddS)Inverse rotation.Nr)r)rrrFr)rCrrrr inversewszRotationSequence3D.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)shaper=rr%flattendotr!r)rCr(r)r*r orig_shapeinarrresultrrr evaluate}s zRotationSequence3D.evaluate)N)__name__ __module__ __qualname____doc__Zstandard_broadcasting _separablen_inputs n_outputsrrr rr@propertyrHrR __classcell__rrrEr rGs csFeZdZdZd 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)NrK)rr9)lonlat) _n_inputs _n_outputsr?r@rArB)rCrrr9kwargsrErr r@s z"SphericalRotationSequence.__init__cCs|jSr")r^rCrrr rXsz"SphericalRotationSequence.n_inputscCs|jSr")r_rarrr rYsz#SphericalRotationSequence.n_outputsc s@t||\}}}t||||\}}} t||| \}}||fSr")r+r?rRr.) rCr\r]rr(r)r*x1y1Zz1rErr rRsz"SphericalRotationSequence.evaluate)N) rSrTrUrVr@rZrXrYrRr[rrrEr rs  c@s<eZdZdZdZddZdZdZeddZ edd Z d S) _EulerRotationz7 Base class which does the actual computation. Fc Cstd}t|tjr&|}|}|j}t||}t|||g|} t| |} t| \} } |dk rl|| _|| _| | fSr") rrndarrayrMrLr+r!rNr.) rCr&r'phithetapsirrLZinpmatrixrQabrrr rRs    z_EulerRotation.evaluateTcCs|jdtj|jdtjiSz Input units.rrinputsrdegrarrr input_unitssz_EulerRotation.input_unitscCs|jdtj|jdtjiSz Output units.rroutputsrrorarrr return_unitssz_EulerRotation.return_unitsN) rSrTrUrVrWrRZ_input_units_strictZ _input_units_allow_dimensionlessrZrprtrrrr rds rdcspeZdZdZdZdZedeeddZ 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. rKrz*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 sdddg|_t|dkr&td|t||j}|rPtd|d|j||_dd |||fD}t|rt|std t j f|||d |d |_ d |_ dS) Nr(r)r*r/z@Expected axes_order to be a character sequence of length 3, got r5r6cSsg|]}t|tjqSrrrr.0Zparrrr sz/EulerAngleRotation.__init__..>All parameters should be of the same type - float or Quantity.)rfrgrh)r&r') r:r> TypeErrorr;r<r=ranyallr?r@rArB)rCrfrgrhrr`rDqsrErr r@s&  zEulerAngleRotation.__init__cCs*|j|j |j |j |jddddS)Nr)rfrgrhr)rFrhrgrfrrarrr rHs zEulerAngleRotation.inversecs$t||||||j\}}||fSr")r?rRr)rCr&r'rfrgrhrjrkrErr rRszEulerAngleRotation.evaluate)rSrTrUrVrXrYrrr rfrgrhr@rZrHrRr[rrrEr r s2  cs\eZdZdZedeeddZedeeddZedeeddZ fddZ fd d Z Z S) _SkyRotationzK Base class for RotateNative2Celestial and RotateCelestial2Native. rZLatituder0Z LongtitudezLongitude of a polec sJdd|||fD}t|r,t|s,tdtj|||f|d|_dS)NcSsg|]}t|tjqSrrurvrrr rx7sz)_SkyRotation.__init__..ryZzxz)r{r|rzr?r@r)rCr\r]lon_poler`r}rErr r@6sz_SkyRotation.__init__c sRt||||||j\}}|dk}t|tjrB||d7<n|d7}||fS)Nrih)r?rRrrrre) rCrfrgr\r]rr&r'maskrErr _evaluate?s  z_SkyRotation._evaluate) rSrTrUrVrrr r\r]rr@rr[rrrEr r~$s* r~csXeZdZdZdZdZeddZeddZfddZ 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. rKcCs|jdtj|jdtjiSrlrmrarrr rp`sz"RotateNative2Celestial.input_unitscCs|jdtj|jdtjiSrqrrrarrr rtesz#RotateNative2Celestial.return_unitsc s$tj|||f|d|_d|_dS)Nphi_Ntheta_Nalpha_Cdelta_Cr?r@rnrsrCr\r]rr`rErr r@jszRotateNative2Celestial.__init__c slt|tjr|j}|j}|j}|tjd}tjd| }tjd| }t|||||\} } | | fS)a Parameters ---------- phi_N, theta_N : float or `~astropy.units.Quantity` ['angle'] Angles in the Native coordinate system. it is assumed that numerical only inputs are in degrees. If float, assumed in degrees. lon, lat, lon_pole : float or `~astropy.units.Quantity` ['angle'] Parameter values when the model was initialized. If float, assumed in degrees. Returns ------- alpha_C, delta_C : float or `~astropy.units.Quantity` ['angle'] Angles on the Celestial sphere. If float, in degrees. rKrrrrrpir?r) rCrrr\r]rrfrgrhrrrErr rRos zRotateNative2Celestial.evaluatecCst|j|j|jSr")r r\r]rrarrr rHszRotateNative2Celestial.inverse rSrTrUrVrXrYrZrprtr@rRrHr[rrrEr r Is    csXeZdZdZdZdZeddZeddZfddZ fd d Z ed d Z Z S) r a~ Transform from Celestial to Native Spherical Coordinates. Parameters ---------- lon : float or `~astropy.units.Quantity` ['angle'] Celestial longitude of the fiducial point. lat : float or `~astropy.units.Quantity` ['angle'] Celestial latitude of the fiducial point. lon_pole : float or `~astropy.units.Quantity` ['angle'] Longitude of the celestial pole in the native system. Notes ----- If ``lon``, ``lat`` and ``lon_pole`` are numerical values they should be in units of deg. Inputs are angles on the celestial sphere. Outputs are angles on the native sphere. rKcCs|jdtj|jdtjiSrlrmrarrr rpsz"RotateCelestial2Native.input_unitscCs|jdtj|jdtjiSrqrrrarrr rtsz#RotateCelestial2Native.return_unitsc s$tj|||f|d|_d|_dS)NrrrrrErr 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. rKr) rCrrr\r]rrfrgrhrrrErr rRs zRotateCelestial2Native.evaluatecCst|j|j|jSr")r r\r]rrarrr rHszRotateCelestial2Native.inverserrrrEr r s    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). rKFgz,Angle of rotation (Quantity or value in deg)r0c s&tjfd|i|d|_d|_dS)Nr)r(r))r?r@rArB)rCrr`rErr r@szRotation2D.__init__cCs|j|j dS)rGr)rFrrarrr rHszRotation2D.inversec Cs|j|jkrtdt|dd}t|dd}|dk o:|dk }||krl|rb||rb||}|}n td|jptd}t| | g}t |tj r| tj }t|||} | d| d}}||_|_|rtj ||dd tj ||dd 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. rIrNz"x and y must have compatible unitsrJrrT)rZsubok)rLr=getattrZ is_equivalenttorZ UnitsErrorrr%rMrrZto_valuerrN_compute_matrix) clsr(r)rZx_unitZy_unitZ has_unitsrOrPrQrrr rRs0         zRotation2D.evaluatecCs6tjt|t| gt|t|ggtjdS)N)Zdtype)rr%mathr#r$Zfloat64rrrr r.s(zRotation2D._compute_matrix)rSrTrUrVrXrYrWrrr rr@rZrH classmethodrR staticmethodrr[rrrEr r s"   +)rVr functoolsrnumpyrZastropyrrZ$astropy.coordinates.matrix_utilitiesrcorer parametersrutilsrr __all__r!r+r.rrrdr r~r r r rrrr s4        F%%M%JL