ó šßÈ[c@`s\dZddlmZmZmZmZddlZddlZddl m Z ddl m Z ddl mZdd lmZmZdd lmZdd lmZdd lmZmZd dddgZdefd„ƒYZdee fd„ƒYZdee fd„ƒYZdefd„ƒYZdefd„ƒYZ de fd„ƒYZ!dS(u° 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) i(tabsolute_importtunicode_literalstdivisiontprint_functionNi(tModel(t Parameteri(tzip(trotation_matrixtmatrix_product(tunits(t deprecated(t _to_radiant _to_orig_unituRotateCelestial2NativeuRotateNative2Celestialu Rotation2DuEulerAngleRotationt_EulerRotationcB`sƒeZdZd„Zed„ƒZed„ƒZedƒed„ƒƒZd„Z e Z e Z e d„ƒZe d„ƒZRS( u7 Base class which does the actual computation. c C`s•g}xot|||g|ƒD]U\}}t|tjƒrI|j}n|jƒ}|jt||dtjƒƒqWt |ddd…Œ}|S(Ntunitiÿÿÿÿ( Rt isinstancetutQuantitytvaluetitemtappendRtradR( tselftphitthetatpsit axes_ordertmatricestangletaxistresult((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyt_create_matrix.s%  #cC`s{tj|ƒ}tj|ƒ}tj|ƒtj|ƒ}tj|ƒtj|ƒ}tj|ƒ}tj|||gƒS(N(tnptdeg2radtcostsintarray(talphatdeltatxtytz((s9lib/python2.7/site-packages/astropy/modeling/rotations.pytspherical2cartesian8s cC`sRtj||ƒ}tjtj||ƒƒ}tjtj||ƒƒ}||fS(N(R thypottrad2degtarctan2(R'R(R)thR%R&((s9lib/python2.7/site-packages/astropy/modeling/rotations.pytcartesian2sphericalAsg@cC`sDtjtj|ƒtj|ƒgtj|ƒ tj|ƒggƒS(u Clockwise rotation matrix. Parameters ---------- angle : float Rotation angle in radians. (R R$tmathR"R#(R((s9lib/python2.7/site-packages/astropy/modeling/rotations.pytrotation_matrix_from_angleHs !c C`sÇd}t|tjƒrK|jdkrK|jƒ}|jƒ}|j}n|j||ƒ}|j||||ƒ} tj | |ƒ} |j | Œ\} } |dk r½|| _|| _n| | fS(Ni( tNoneRR tndarraytndimtflattentshapeR*RtdotR/( RR%R&RRRRR6tinptmatrixRtatb((s9lib/python2.7/site-packages/astropy/modeling/rotations.pytevaluateVs!      cC`sitjd6tjd6S(u Input units. ualphaudelta(Rtdeg(R((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyt input_unitsiscC`sitjd6tjd6S(u Output units. ualphaudelta(RR=(R((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyt return_unitsns(t__name__t __module__t__doc__Rt staticmethodR*R/R R1R<tTruetinput_units_stricttinput_units_allow_dimensionlesstpropertyR>R?(((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyR )s    tEulerAngleRotationcB`s†eZdZd Zd ZedddedeƒZedddedeƒZ edddedeƒZ d„Z d„Z d „Z RS( u' 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. ualphaudeltatdefaultitgettertsetterc K`sdddg|_t|ƒdkr<tdj|ƒƒ‚nt|ƒj|jƒ}|rxtdj||jƒƒ‚n||_g|||gD]}t|t j ƒ^q‘}t |ƒr×t |ƒ r×tdƒ‚nt t|ƒjd|d |d ||dS( NuxuyuziuBExpected axes_order to be a character sequence of length 3,got {0}u2Unrecognized axis label {0}; should be one of {1} u>All parameters should be of the same type - float or Quantity.RRR(taxestlent TypeErrortformattsett differencet ValueErrorRRRRtanytalltsuperRHt__init__( RRRRRtkwargst unrecognizedtpartqs((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyRVs  .c C`s>|jd|j d|j d|j d|jddd…ƒS(NRRRRiÿÿÿÿ(t __class__RRRR(R((s9lib/python2.7/site-packages/astropy/modeling/rotations.pytinversežs  cC`s:tt|ƒj||||||jƒ\}}||fS(N(RURHR<R(RR%R&RRRR:R;((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyR<¤s0(ualphaudelta(ualphaudelta(R@RARBtinputstoutputsRR R RRRRVR\R<(((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyRHts  t _SkyRotationcB`sqeZdZedddedeƒZedddedeƒZedddedeƒZd„Z d„Z RS(uK Base class for RotateNative2Celestial and RotateCelestial2Native. RIiRJRKcK`s‚g|||gD]}t|tjƒ^q}t|ƒrVt|ƒ rVtdƒ‚ntt|ƒj||||d|_ dS(Nu>All parameters should be of the same type - float or Quantity.uzxz( RRRRSRTRNRUR_RVR(Rtlontlattlon_poleRWRYRZ((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyRV²s .c C`sutt|ƒj||||||jƒ\}}|dk}t|tjƒra||cd7ÜscC`sitjd6tjd6S(u Output units. ualpha_Cudelta_C(RR=(R((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyR?áscK`s#tt|ƒj||||dS(N(RUReRV(RR`RaRbRW((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyRVæsc C`s™t|tjƒr0|j}|j}|j}n|tjd}tjd| }tjd| }tt|ƒj|||||ƒ\} } | | fS(u¼ 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. i( RRRRR tpiRUReRd( Rtphi_Nttheta_NR`RaRbRRRtalpha_Ctdelta_C((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyR<és   cC`st|j|j|jƒS(N(tRotateCelestial2NativeR`RaRb(R((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyR\s(uphi_Nutheta_N(ualpha_Cudelta_C( R@RARBR]R^RGR>R?RVR<R\(((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyReÄs  RkcB`sYeZdZd Zd Zed„ƒZed„ƒZd„Zd„Z ed „ƒZ RS( u  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. ualpha_Cudelta_Cuphi_Nutheta_NcC`sitjd6tjd6S(u Input units. ualpha_Cudelta_C(RR=(R((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyR>"scC`sitjd6tjd6S(u Output units. uphi_Nutheta_N(RR=(R((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyR?'scK`s#tt|ƒj||||dS(N(RURkRV(RR`RaRbRW((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyRV,sc C`s˜t|tjƒr0|j}|j}|j}ntjd|}tjd|}|tjd }tt|ƒj|||||ƒ\} } | | fS(u¹ 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. i( RRRRR RfRURkRd( RRiRjR`RaRbRRRRgRh((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyR</s   cC`st|j|j|jƒS(N(ReR`RaRb(R((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyR\Ks(ualpha_Cudelta_C(uphi_Nutheta_N( R@RARBR]R^RGR>R?RVR<R\(((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyRk s  t Rotation2DcB`sneZdZd Zd ZedddedeƒZe Z e Z e d„ƒZ ed„ƒZed „ƒZRS( u 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). uxuyRIgRJRKcC`s|jd|j ƒS(uInverse rotation.R(R[R(R((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyR\escC`s|j|jkr!tdƒ‚n|jp-d}t|tjƒrN|j}nd}tj|j ƒ|j ƒgƒ}t|tjƒr“|j }ntj |j |ƒ|ƒ}|d|d}}||_|_|dk rtj|d|ƒtj|d|ƒfS||fSdS(uê Rotate (x, y) about ``angle``. Parameters ---------- x, y : ndarray-like Input quantities angle : float (deg) or `~astropy.units.Quantity` Angle of rotations. u,Expected input arrays to have the same shapeiiRN(i( R6RRRRRRR2R R$R5RR7t_compute_matrix(tclsR'R(Rt orig_shapeRtinarrR((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyR<ks !  (cC`sMtjtj|ƒtj|ƒ gtj|ƒtj|ƒggdtjƒS(Ntdtype(R R$R0R"R#tfloat64(R((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyRmŽs"!(uxuy(uxuy(R@RARBR]R^RR R RRDRERFRGR\t classmethodR<RCRm(((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyRlPs #("RBt __future__RRRRR0tnumpyR tcoreRt parametersRtextern.six.movesRtcoordinates.matrix_utilitiesRRtR Rtutils.decoratorsR tutilsR R t__all__tobjectR RHR_ReRkRl(((s9lib/python2.7/site-packages/astropy/modeling/rotations.pyts$"    K5FF