B q\3@sdZddlZddlZddlmZddlmZddlm Z m Z ddl m Z ddlmZdd lmZmZd d d d gZGdddZGdd d eeZGdddeeZGdd d eZGdd d eZGdd d eZdS)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)Model) Parameter)rotation_matrixmatrix_product)units) deprecated) _to_radian _to_orig_unitRotateCelestial2NativeRotateNative2Celestial Rotation2DEulerAngleRotationc@speZdZdZdZddZeddZeddZe d ed d Z d d Z dZ dZ eddZeddZdS)_EulerRotationz7 Base class which does the actual computation. Fc Cshg}xLt|||g|D]8\}}t|tjr0|j}|}|t||tjdqWt |ddd}|S)N)unit) zip isinstanceuQuantityvalueitemappendrradr) selfphithetapsi axes_orderZmatricesangleZaxisresultr!9lib/python3.7/site-packages/astropy/modeling/rotations.py_create_matrix,s z_EulerRotation._create_matrixcCsVt|}t|}t|t|}t|t|}t|}t|||gS)N)npZdeg2radcossinarray)alphadeltaxyzr!r!r"spherical2cartesian6s    z"_EulerRotation.spherical2cartesiancCs8t||}tt||}tt||}||fS)N)r$ZhypotZrad2degZarctan2)r*r+r,hr(r)r!r!r"cartesian2spherical?s z"_EulerRotation.cartesian2sphericalg@cCs0tt|t|gt| t|ggS)z Clockwise rotation matrix. Parameters ---------- angle : float Rotation angle in radians. )r$r'mathr%r&)rr!r!r"rotation_matrix_from_angleFs z)_EulerRotation.rotation_matrix_from_anglec Csd}t|tjr0|jdkr0|}|}|j}|||}|||||} t| |} |j | \} } |dk rz|| _|| _| | fS)N) rr$ndarrayndimflattenshaper-r#dotr/) rr(r)rrrrr6ZinpZmatrixr abr!r!r"evaluateTs  z_EulerRotation.evaluateTcCstjtjdS)z Input units. )r(r))rdeg)rr!r!r" input_unitsgsz_EulerRotation.input_unitscCstjtjdS)z Output units. )r(r))rr;)rr!r!r" return_unitslsz_EulerRotation.return_unitsN)__name__ __module__ __qualname____doc__ _separabler# staticmethodr-r/rr1r:Z_input_units_strictZ _input_units_allow_dimensionlesspropertyr<r=r!r!r!r"r%s   rcsfeZdZdZdZdZedeedZ edeedZ edeedZ fddZ ddZ fd d ZZS) ra' Implements Euler angle intrinsic rotations. Rotates one coordinate system into another (fixed) coordinate system. All coordinate systems are right-handed. The sign of the angles is determined by the right-hand rule.. Parameters ---------- phi, theta, psi : float or `~astropy.units.Quantity` "proper" Euler angles in deg. If floats, they should be in deg. axes_order : str A 3 character string, a combination of 'x', 'y' and 'z', where each character denotes an axis in 3D space. )r(r)r)defaultgettersetterc sdddg|_t|dkr&td|t||j}|rLtd||j||_dd|||gD}t|r~t |s~td t j f|||d |dS) Nr*r+r,zBExpected axes_order to be a character sequence of length 3,got {0}z2Unrecognized axis label {0}; should be one of {1} cSsg|]}t|tjqSr!)rrr).0parr!r!r" sz/EulerAngleRotation.__init__..z>All parameters should be of the same type - float or Quantity.)rrr) Zaxeslen TypeErrorformatset difference ValueErrorranyallsuper__init__)rrrrrkwargsZ unrecognizedqs) __class__r!r"rUs   zEulerAngleRotation.__init__cCs*|j|j |j |j |jddddS)Nr)rrrr)rXrrrr)rr!r!r"inverses zEulerAngleRotation.inversecs$t||||||j\}}||fS)N)rTr:r)rr(r)rrrr8r9)rXr!r"r:szEulerAngleRotation.evaluate)r>r?r@rAinputsoutputsrr r rrrrUrYr: __classcell__r!r!)rXr"rrs csVeZdZdZedeedZedeedZedeedZ fddZ fddZ Z S) _SkyRotationzK Base class for RotateNative2Celestial and RotateCelestial2Native. r)rErFrGc sJdd|||gD}t|r,t|s,tdtj|||f|d|_dS)NcSsg|]}t|tjqSr!)rrr)rIrJr!r!r"rKsz)_SkyRotation.__init__..z>All parameters should be of the same type - float or Quantity.Zzxz)rRrSrMrTrUr)rlonlatlon_polerVrW)rXr!r"rUs z_SkyRotation.__init__c sRt||||||j\}}|dk}t|tjrB||d7<n|d7}||fS)Nrih)rTr:rrr$r3) rrrr^r_r`r(r)mask)rXr!r" _evaluates  z_SkyRotation._evaluate) r>r?r@rArr r r^r_r`rUrbr\r!r!)rXr"r]s  r]csXeZdZdZdZdZeddZeddZfdd Z fd d Z ed d Z Z S)r a  Transform from Native to Celestial Spherical Coordinates. Parameters ---------- lon : float or or `~astropy.units.Quantity` Celestial longitude of the fiducial point. lat : float or or `~astropy.units.Quantity` Celestial latitude of the fiducial point. lon_pole : float or or `~astropy.units.Quantity` Longitude of the celestial pole in the native system. Notes ----- If ``lon``, ``lat`` and ``lon_pole`` are numerical values they should be in units of deg. )phi_Ntheta_N)alpha_Cdelta_CcCstjtjdS)z Input units. )rcrd)rr;)rr!r!r"r<sz"RotateNative2Celestial.input_unitscCstjtjdS)z Output units. )rerf)rr;)rr!r!r"r=sz#RotateNative2Celestial.return_unitsc stj|||f|dS)N)rTrU)rr^r_r`rV)rXr!r"rUszRotateNative2Celestial.__init__c slt|tjr|j}|j}|j}|tjd}tjd| }tjd| }t|||||\} } | | fS)a Parameters ---------- phi_N, theta_N : float (deg) or `~astropy.units.Quantity` Angles in the Native coordinate system. lon, lat, lon_pole : float (in deg) or `~astropy.units.Quantity` Parameter values when the model was initialized. Returns ------- alpha_C, delta_C : float (deg) or `~astropy.units.Quantity` Angles on the Celestial sphere. r2)rrrrr$pirTrb) rrcrdr^r_r`rrrrerf)rXr!r"r:s zRotateNative2Celestial.evaluatecCst|j|j|jS)N)r r^r_r`)rr!r!r"rYszRotateNative2Celestial.inverse) r>r?r@rArZr[rDr<r=rUr:rYr\r!r!)rXr"r s    csXeZdZdZdZdZeddZeddZfdd Z fd d Z ed d Z Z S)r a  Transform from Celestial to Native Spherical Coordinates. Parameters ---------- lon : float or or `~astropy.units.Quantity` Celestial longitude of the fiducial point. lat : float or or `~astropy.units.Quantity` Celestial latitude of the fiducial point. lon_pole : float or or `~astropy.units.Quantity` 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. )rerf)rcrdcCstjtjdS)z Input units. )rerf)rr;)rr!r!r"r<sz"RotateCelestial2Native.input_unitscCstjtjdS)z Output units. )rcrd)rr;)rr!r!r"r=$sz#RotateCelestial2Native.return_unitsc stj|||f|dS)N)rTrU)rr^r_r`rV)rXr!r"rU)szRotateCelestial2Native.__init__c sjt|tjr|j}|j}|j}tjd|}tjd|}|tjd }t|||||\} } | | fS)a Parameters ---------- alpha_C, delta_C : float (deg) or `~astropy.units.Quantity` Angles in the Celestial coordinate frame. lon, lat, lon_pole : float (deg) or `~astropy.units.Quantity` Parameter values when the model was initialized. Returns ------- phi_N, theta_N : float (deg) or `~astropy.units.Quantity` Angles on the Native sphere. r2)rrrrr$rgrTrb) rrerfr^r_r`rrrrcrd)rXr!r"r:,s zRotateCelestial2Native.evaluatecCst|j|j|jS)N)r r^r_r`)rr!r!r"rYGszRotateCelestial2Native.inverse) r>r?r@rArZr[rDr<r=rUr:rYr\r!r!)rXr"r s    c@sNeZdZdZdZdZdZedee dZ e ddZ e dd Zed d Zd S) 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 of rotation (if float it should be in deg). )r*r+Fg)rErFrGcCs|j|j dS)zInverse rotation.)r)rXr)rr!r!r"rY^szRotation2D.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 ||dtj ||dfS||fSdS) z Rotate (x, y) about ``angle``. Parameters ---------- x, y : ndarray-like Input quantities angle : float (deg) or `~astropy.units.Quantity` Angle of rotations. z,Expected input arrays to have the same shaperNz"x and y must have compatible units)rrr)r)r6rQgetattrZ is_equivalenttorZ UnitsErrorr$r'r5rrZto_valuerr7_compute_matrix) clsr*r+rZx_unitZy_unitZ has_unitsZ orig_shapeZinarrr r!r!r"r:ds(         zRotation2D.evaluatecCs6tjt|t| gt|t|ggtjdS)N)Zdtype)r$r'r0r%r&Zfloat64)rr!r!r"rjszRotation2D._compute_matrixN)r>r?r@rArZr[rBrr r rrDrY classmethodr:rCrjr!r!r!r"r Ls   *)rAr0Znumpyr$ZcorerZ parametersrZ$astropy.coordinates.matrix_utilitiesrrZastropyrrZastropy.utils.decoratorsrZutilsr r __all__rrr]r r r r!r!r!r"s     M5EE