B dB@sdZddlZddlZddlmZmZddlmZ ddl m Z ddl m Z ddlmZmZd d d d d dgZddZddZddZGdd d e 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)rotation_matrixmatrix_product)units)Model) Parameter) _to_radian _to_orig_unitRotateCelestial2NativeRotateNative2Celestial Rotation2DEulerAngleRotationRotationSequence3DSphericalRotationSequencecCsbg}xFt||D]8\}}t|tjr*|j}|}|t||tjdqWt |ddd}|S)N)unit) zip isinstanceuQuantityvalueitemappendrradr)angles axes_orderZmatricesangleZaxisresultrg/work/yifan.wang/ringdown/master-ringdown-env/lib/python3.7/site-packages/astropy/modeling/rotations.py_create_matrix%s r cCsVt|}t|}t|t|}t|t|}t|}t|||gS)N)npZdeg2radcossinarray)alphadeltaxyzrrrspherical2cartesian0s    r*cCs8t||}tt||}tt||}||fS)N)r!hypotZrad2degZarctan2)r'r(r)hr%r&rrrcartesian2spherical9s r-csTeZdZdZdZdZdZdZege e dZ d fdd Z e dd 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') F)defaultgettersetterNcsdddg|_t||j}|r2td||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)r'r(r)) axesset difference ValueErrorformatrlensuper__init___inputs_outputs)selfrrr2 unrecognized) __class__rrr:Ys    zRotationSequence3D.__init__cCs0|jjdddd}|j||jddddS)zInverse rotation.Nr)r)rrr?r)r=rrrrinverseiszRotationSequence3D.inversecCs|j|jkr|jkr&nntd|jp.d}t|||g}tt|d|j|}|d|d|d}}}||_|_|_|||fS)zJ Apply the rotation to a set of 3D Cartesian coordinates. z,Expected input arrays to have the same shape)rrr)shaper6r!r$flattendotr r)r=r'r(r)r orig_shapeinarrrrrrevaluateos zRotationSequence3D.evaluate)N)__name__ __module__ __qualname____doc__Zstandard_broadcasting _separablen_inputs n_outputsrr rrr:propertyr@rG __classcell__rr)r?rr@s 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)NrA)rr2)lonlat) _n_inputs _n_outputsr9r:r;r<)r=rrr2kwargs)r?rrr:s z"SphericalRotationSequence.__init__cCs|jS)N)rS)r=rrrrMsz"SphericalRotationSequence.n_inputscCs|jS)N)rT)r=rrrrNsz#SphericalRotationSequence.n_outputsc s@t||\}}}t||||\}}} t||| \}}||fS)N)r*r9rGr-) r=rQrRrr'r(r)x1y1Zz1)r?rrrGsz"SphericalRotationSequence.evaluate)N) rHrIrJrKr:rOrMrNrGrPrr)r?rrs    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|| _|| _| | fS)N) rr!ndarrayrCrBr*r rDr-) r=r%r&phithetapsirrBZinpmatrixrabrrrrGs    z_EulerRotation.evaluateTcCs|jdtj|jdtjiS)z Input units. rr)inputsrdeg)r=rrr input_unitss z_EulerRotation.input_unitscCs|jdtj|jdtjiS)z Output units. rr)outputsrra)r=rrr return_unitss z_EulerRotation.return_unitsN) rHrIrJrKrLrGZ_input_units_strictZ _input_units_allow_dimensionlessrOrbrdrrrrrXs rXcsjeZdZdZdZdZedeedZ edeedZ edeedZ fddZ e ddZfd 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. rAr)r/r0r1c sdddg|_t|dkr&td|t||j}|rLtd||j||_dd|||gD}t|r~t |s~td t j f|||d |d |_ d |_ dS) Nr'r(r)r.zAExpected axes_order to be a character sequence of length 3,got {}z0Unrecognized axis label {}; should be one of {} cSsg|]}t|tjqSr)rrr).0parrrr sz/EulerAngleRotation.__init__..z>All parameters should be of the same type - float or Quantity.)rZr[r\)r%r&)r3r8 TypeErrorr7r4r5r6ranyallr9r:r;r<)r=rZr[r\rrUr>qs)r?rrr:s    zEulerAngleRotation.__init__cCs*|j|j |j |j |jddddS)Nr)rZr[r\r)r?r\r[rZr)r=rrrr@s zEulerAngleRotation.inversecs$t||||||j\}}||fS)N)r9rGr)r=r%r&rZr[r\r^r_)r?rrrGszEulerAngleRotation.evaluate)rHrIrJrKrMrNrr rrZr[r\r:rOr@rGrPrr)r?rr s  csVeZdZdZedeedZedeedZedeedZ fddZ fddZ Z S) _SkyRotationzK Base class for RotateNative2Celestial and RotateCelestial2Native. r)r/r0r1c sJdd|||gD}t|r,t|s,tdtj|||f|d|_dS)NcSsg|]}t|tjqSr)rrr)rerfrrrrg sz)_SkyRotation.__init__..z>All parameters should be of the same type - float or Quantity.Zzxz)rirjrhr9r:r)r=rQrRlon_polerUrk)r?rrr: s z_SkyRotation.__init__c sRt||||||j\}}|dk}t|tjrB||d7<n|d7}||fS)Nrih)r9rGrrr!rY) r=rZr[rQrRrmr%r&mask)r?rr _evaluates  z_SkyRotation._evaluate) rHrIrJrKrr rrQrRrmr:rorPrr)r?rrls  rlcsXeZdZdZdZdZeddZeddZfddZ fd d Z ed d Z Z S) r a~ Transform from Native to Celestial Spherical Coordinates. Parameters ---------- lon : float or `~astropy.units.Quantity` ['angle'] Celestial longitude of the fiducial point. lat : float or `~astropy.units.Quantity` ['angle'] Celestial latitude of the fiducial point. lon_pole : float or `~astropy.units.Quantity` ['angle'] Longitude of the celestial pole in the native system. Notes ----- If ``lon``, ``lat`` and ``lon_pole`` are numerical values they should be in units of deg. Inputs are angles on the native sphere. Outputs are angles on the celestial sphere. rAcCs|jdtj|jdtjiS)z Input units. rr)r`rra)r=rrrrb4s z"RotateNative2Celestial.input_unitscCs|jdtj|jdtjiS)z Output units. rr)rcrra)r=rrrrd:sz#RotateNative2Celestial.return_unitsc s$tj|||f|d|_d|_dS)N)phi_Ntheta_N)alpha_Cdelta_C)r9r:r`rc)r=rQrRrmrU)r?rrr:?szRotateNative2Celestial.__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. rA)rrrrr!pir9ro) r=rprqrQrRrmrZr[r\rrrs)r?rrrGDs zRotateNative2Celestial.evaluatecCst|j|j|jS)N)r rQrRrm)r=rrrr@bszRotateNative2Celestial.inverse) rHrIrJrKrMrNrOrbrdr:rGr@rPrr)r?rr s    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. rAcCs|jdtj|jdtjiS)z Input units. rr)r`rra)r=rrrrb~s z"RotateCelestial2Native.input_unitscCs|jdtj|jdtjiS)z Output units. rr)rcrra)r=rrrrds z#RotateCelestial2Native.return_unitsc s$tj|||f|d|_d|_dS)N)rrrs)rprq)r9r:r`rc)r=rQrRrmrU)r?rrr:szRotateCelestial2Native.__init__c sjt|tjr|j}|j}|j}tjd|}tjd|}|tjd }t|||||\} } | | fS)a; Parameters ---------- alpha_C, delta_C : float or `~astropy.units.Quantity` ['angle'] Angles in the Celestial coordinate frame. If float, assumed in degrees. lon, lat, lon_pole : float or `~astropy.units.Quantity` ['angle'] Parameter values when the model was initialized. If float, assumed in degrees. Returns ------- phi_N, theta_N : float or `~astropy.units.Quantity` ['angle'] Angles on the Native sphere. If float, in degrees. rA)rrrrr!rtr9ro) r=rrrsrQrRrmrZr[r\rprq)r?rrrGs zRotateCelestial2Native.evaluatecCst|j|j|jS)N)r rQrRrm)r=rrrr@szRotateCelestial2Native.inverse) rHrIrJrKrMrNrOrbrdr:rGr@rPrr)r?rr hs    csbeZdZdZdZdZdZedee dZ e ffdd Z e dd Z ed d Zed d ZZS)r a  Perform a 2D rotation given an angle. Positive angles represent a counter-clockwise rotation and vice-versa. Parameters ---------- angle : float or `~astropy.units.Quantity` ['angle'] Angle of rotation (if float it should be in deg). rAFg)r/r0r1c s&tjfd|i|d|_d|_dS)Nr)r'r()r9r:r;r<)r=rrU)r?rrr:szRotation2D.__init__cCs|j|j dS)zInverse rotation.)r)r?r)r=rrrr@szRotation2D.inversec Cs|j|jkrtdt|dd}t|dd}|dk o:|dk }||krl|rb||rb||}|}n td|jptd}t| | g}t |tj r| tj }t|||} | d| d}}||_|_|rtj ||dtj ||dfS||fS) a Rotate (x, y) about ``angle``. Parameters ---------- x, y : array-like Input quantities angle : float or `~astropy.units.Quantity` ['angle'] Angle of rotations. If float, assumed in degrees. z,Expected input arrays to have the same shaperNz"x and y must have compatible units)rrr)r)rBr6getattrZ is_equivalenttorZ UnitsErrorr!r$rCrrZto_valuerrD_compute_matrix) clsr'r(rZx_unitZy_unitZ has_unitsrErFrrrrrGs(         zRotation2D.evaluatecCs6tjt|t| gt|t|ggtjdS)N)Zdtype)r!r$mathr"r#Zfloat64)rrrrrwszRotation2D._compute_matrix)rHrIrJrKrMrNrLrr rrr:rOr@ classmethodrG staticmethodrwrPrr)r?rr s   *)rKrynumpyr!Z$astropy.coordinates.matrix_utilitiesrrZastropyrrcorer parametersrutilsrr __all__r r*r-rrrXr rlr r r rrrrs(      ?$'8KM