B zd@sddlZddlZedZddlmZddlmZddl m Z ddl m Z ddl m Z d d d d Zed \ZZZdZeeeeedddjjZeeeeedddjjZGdddeZedkrddlZej deedGddde!Z"d9ddZ#d:ddZ$d;d d!Z%dd,d-Z+d?d/d0Z,d1d2Z-d@d3d4Z.dAd5d6Z/d7d8Z0dS)BNZhealpy)SkyCoord)deprecated_renamed_argument) pixelfunc)sphtfunc) rotate_almZGalacticZEcliptic Equatorial)GECZBarycentricMeanEclipticZ cartesian)xyzframeZrepresentation_typeZgalacticZfk5c@seZdZdZdS)ConsistencyWarningz.Warns for a problem in the consistency of dataN)__name__ __module__ __qualname____doc__rr[/work/yifan.wang/ringdown/master-ringdown-env/lib/python3.7/site-packages/healpy/rotator.pyr?sr__main__always)categorymodulec@s eZdZdZdZd9ddZdd Zd d Zeed d Z ddZ ddZ ddZ ddZ ddZddZddZeddZeddZed d!Zed"d#Zed$d%Zed&d'Zed(d)Zd*d+Zd,d-Zd:d/d0Zed1dd2d;d3d4Zd5d6Zd7d8ZeZdS)<Rotatora&Rotation operator, including astronomical coordinate systems. This class provides tools for spherical rotations. It is meant to be used in the healpy library for plotting, and for this reason reflects the convention used in the Healpix IDL library. Parameters ---------- rot : None or sequence Describe the rotation by its euler angle. See :func:`euler_matrix_new`. coord : None or sequence of str Describe the coordinate system transform. If *rot* is also given, the coordinate transform is applied first, and then the rotation. inv : bool If True, the inverse rotation is defined. (Default: False) deg : bool If True, angles are assumed to be in degree. (Default: True) eulertype : str The Euler angle convention used. See :func:`euler_matrix_new`. Attributes ---------- mat coordin coordout coordinstr coordoutstr rots coords Examples -------- >>> r = Rotator(coord=['G','E']) # Transforms galactic to ecliptic coordinates >>> theta_gal, phi_gal = np.pi/2., 0. >>> theta_ecl, phi_ecl = r(theta_gal, phi_gal) # Apply the conversion >>> print(theta_ecl) 1.66742347999 >>> print(phi_ecl) -1.6259571125 >>> theta_ecl, phi_ecl = Rotator(coord='ge')(theta_gal, phi_gal) # In one line >>> print(theta_ecl) 1.66742347999 >>> print(phi_ecl) -1.6259571125 >>> vec_gal = np.array([1, 0, 0]) #Using vectors >>> vec_ecl = r(vec_gal) >>> print(vec_ecl) [-0.05487563 -0.99382135 -0.09647686] z?rot and coord must be single elements or sequence of same size.NTZYXcCsxt|dot|dd}t|do>t|ddo>t|dtk }|rn|rnt|t|krdttjq|}|} n0|sv|r|dk r|dk rttjn |g}|g} t|d} | rt|t|krtd|} n|gt|} |dkr||_nd|_g|_g|_ g|_ xXt || | D]H\} } }t | |d}t | }|j||j ||j t|qW|jsltd|dS) a|Create a rotator with given parameters. - rot: a float, a tuple of 1,2 or 3 floats or a sequence of tuples. If it is a sequence of tuple, it must have the same length as coord. - coord: a string or a tuple of 1 or 2 strings or a sequence of tuple If it is a sequence of tuple, it must have same length as rot. - inv: whether to use inverse rotation or not - deg: if True, angles in rot are assumed in degree (default: True) - eulertype: the convention for Euler angles in rot. Note: the coord system conversion is applied first, then the rotation. __len__rNz-inv must have same length as rot and/or coord)rXYr)degz5The chain of coord system rotations is not consistent)hasattrtypestrlen ValueErrorrErrMessWrongPar_eultype_rots_coords_invszip normalise_rotnormalise_coordappendbool consistentlogwarning_update_matrix)selfrotcoordinvr! eulertypeZ rot_is_seqZ coord_is_seqrotscoordsZ inv_is_seqinvsrciZrnZcnrrr__init__sD         zRotator.__init__c Cstd|_d|_xxt|j|j|jD]b\}}}t||j d\}}}t |\}}} t ||}|rh|j }t |j||_|jp|p||_q&WdS)Nr F)r9) npidentity_matrix _do_rotationr,r)r*r+get_rotation_matrixr(get_coordconv_matrixdotT) r5r=r>r?rotmatdo_rotZrotnormZconvmatdo_convZ coordnormrrrr4s  zRotator._update_matrixcCsnxt|j|jD] \}}PqWxJt|jdd|jddD](\}}|||| kr\dS||}}q>WdS)NrFT)r,r*r+)r5r>r?ZcnextZinextrrr_is_coords_consistents(zRotator._is_coords_consistentz)consistency of the coords transform chain)doccCsRt|t|k rdSddt|j|jD}t|oP|j|jkoP|j|jkS)NFcSs"g|]\}}tj||dddqS)rgV瞯<)rtolatol)rAallclose).0r rrrr sz"Rotator.__eq__..)r#r,r)rAarrayallr*r+)r5avrrr__eq__s  zRotator.__eq__cOs|ddr|jj}n|j}|dd}t|dkr|d}t|dr^t|dks^t|dkrftd t|dkrt||d|d|j|d St||d|d|d|jSn\t|dkrt||d|d|j|d St|dkrt||d|d|d|jStd d S) aUse the rotator to rotate either spherical coordinates (theta, phi) or a vector (x,y,z). You can use lonla keyword to use longitude, latitude (in degree) instead of theta, phi (in radian). In this case, returns longitude, latitude in degree. Accepted forms: r(x,y,z) # x,y,z either scalars or arrays r(theta,phi) # theta, phi scalars or arrays r(lon,lat,lonlat=True) # lon, lat scalars or arrays r(vec) # vec 1-D array with 3 elements, or 2-D array 3xN r(direction) # direction 1-D array with 2 elements, or 2xN array Parameters ---------- vec_or_dir : array or multiple arrays The direction to rotate. See above for accepted formats. lonlat : bool, optional If True, assumes the input direction is longitude/latitude in degrees. Otherwise, assumes co-latitude/longitude in radians. Default: False inv : bool, optional If True, applies the inverse rotation. Default: False. r8Flonlatrrrr z.Argument must be a sequence of 2 or 3 elements)rXz#Either 1, 2 or 3 arguments acceptedN) poprCrHr%r" TypeErrorrotateDirectionrD rotateVector)r5argskwdsmrXargrrr__call__s$    "   zRotator.__call__cCsFt|tstd|j|j}|j|j}|j|j}t|||ddS)zComposition of rotation.zFA Rotator can only multiply another Rotator (composition of rotations)F)r6r7r8r!) isinstancerr[r)r*r+)r5rUr:r;r<rrr__mul__ s    zRotator.__mul__cCsFt|tstd|j|j}|j|j}|j|j}t|||ddS)NzNA Rotator can only be multiplied by another Rotator (composition of rotations)F)r6r7r8r!)rcrr[r)r*r+)r5br:r;r<rrr__rmul__s    zRotator.__rmul__cCs|jS)N)rD)r5rrr __nonzero__#szRotator.__nonzero__cCsJ|jddd}|jddd}dd|jdddD}t|||ddS)NcSsg|] }| qSrr)rQr?rrrrR)sz'Rotator.get_inverse..F)r6r7r8r!)r)r*r+r)r5r:r;r<rrr get_inverse&szRotator.get_inversecOsd|d<|j||S)zqRotate the given vector or direction using the inverse matrix. rot.I(vec) <==> rot(vec,inv=True) Tr8)rb)r5r^r_rrrI/sz Rotator.IcCs t|jS)z%The matrix representing the rotation.)rAasarrayrC)r5rrrmat6sz Rotator.matcCs.|js dSxt|j|jD]\}}qW||S)zThe input coordinate system.N)r1r,r*r+)r5r>r?rrrcoordin;s zRotator.coordincCs0|js dSxt|j|jD]\}}qW|| S)zThe output coordinate system.N)r1r,r*r+)r5r>r?rrrcoordoutDs zRotator.coordoutcCst|jdS)z#The input coordinate system in str.) coordnamegetrm)r5rrr coordinstrMszRotator.coordinstrcCst|jdS)z$The output coordinate system in str.ro)rprqrn)r5rrr coordoutstrRszRotator.coordoutstrcCs|jS)z+The sequence of rots defining the rotation.)r))r5rrrr:Wsz Rotator.rotscCs|jS)z-The sequence of coords defining the rotation.)r*)r5rrrr;\szRotator.coordscCs tj|j|tdddd S)z4Returns True if rotation is not (close to) identity.r ggV瞯<)rNrO)rArPr:zeros)r5r?rrrrJaszRotator.do_rotc Os(|}|dd}|dd}t|dkr|d}t|drRt|dksRt|dkrZtd t|dkr~t|d|d|d }q|}n>t|dkrt|d|d|d }nt|dkr|}ntd |||d }|d d dg|d } | d|d| d|d} | d|dt| |} t| | S)aCompute the angle between transverse reference direction of initial and final frames For example, if angle of polarisation is psi in initial frame, it will be psi+angle_ref in final frame. Parameters ---------- dir_or_vec : array Direction or vector (see Rotator.__call__) lonlat: bool, optional If True, assume input is longitude,latitude in degrees. Otherwise, theta,phi in radian. Default: False inv : bool, optional If True, use the inverse transforms. Default: False Returns ------- angle : float, scalar or array Angle in radian (a scalar or an array if input is a sequence of direction/vector) rXFr8rrrrYr z.Argument must be a sequence of 2 or 3 elements)rXz#Either 1, 2 or 3 arguments accepted)r8gg?)rqr%r"r[dir2vecrArGarctan2) r5r^r_RrXr8rarVZvpZ north_poleZsinalphaZcosalpharrr angle_refes(   "     zRotator.angle_refFcCs0|s|}n|}t||j||d|s,|SdS)zRotate Alms with the transform defined in the Rotator object see the docstring of the rotate_alm function defined in the healpy package, this function **returns** the rotated alms, does not rotate in place)matrixlmaxmmaxN)copyrrl)r5almrzr{Zinplace rotated_almrrrrs  zRotator.rotate_almverbosez1.15.0c Cs<tj|||||d}|j|||d}tj|||t|dS)aRotate a HEALPix map to a new reference frame in spherical harmonics space This is generally the best strategy to rotate/change reference frame of maps. If the input map is band-limited, i.e. it can be represented exactly by a spherical harmonics transform under a specific lmax, the map rotation will be invertible. Parameters ---------- m : np.ndarray Input map, single array is considered I, array with 3 rows:[I,Q,U] other arguments : see map2alm Returns ------- m_rotated : np.ndarray Map in the new reference frame )use_pixel_weightsrzr{datapath)rzr{)rzr{nside)rZmap2almrZalm2maprZ get_nside) r5r`rrzr{rrr}r~rrrrotate_map_almsszRotator.rotate_map_almscst|dkr|g}t|d}t|}tj|t|d\}}|||\fdd|D}t|dkr|d|ddtd | }t ||d<t ||d<n|d}|S) aRotate a HEALPix map to a new reference frame in pixel space It is generally better to rotate in spherical harmonics space, see the rotate_map_alms method. A case where pixel space rotation is better is for heavily masked maps where the spherical harmonics transform is not well defined. This function first rotates the pixels centers of the new reference frame to the original reference frame, then uses hp.get_interp_val to interpolate bilinearly the pixel values, finally fixes Q and U polarization by the modification to the psi angle caused by the Rotator using Rotator.angle_ref. Due to interpolation, this function generally suppresses the signal at high angular scales. Parameters ---------- m : np.ndarray Input map, 1 map is considered I, 2 maps:[Q,U], 3 maps:[I,Q,U] Returns ------- m_rotated : np.ndarray Map in the new reference frame r)rZipixcsg|]}t|qSr)rZget_interp_val)rQZeach)phi_pix_center_rottheta_pix_center_rotrrrRsz,Rotator.rotate_map_pixel..rrhy?y@) rZmaptyper%Z npix2nsideZpix2angrAZarangerjexprxrealimag)r5r`ZnpixrZtheta_pix_centerZphi_pix_centerZ m_rotatedZL_mapr)rrrrotate_map_pixels"     zRotator.rotate_map_pixelcCs*ddt|jt|jt|jgdS)Nz[ z, z ])joinr$r*r)r+)r5rrr__repr__ szRotator.__repr__)NNNTr)NNF)TNNNN) rrrrr'r@r4rLpropertyr1rWrbrdrfrgrirjrlrmrnrrrsr:r;rJrxrrrrr__str__rrrrrJsB1 7    0        ,   $=rTcCsr|dkr*|dkr*|r$tj||ddS|SnD|dk rf|dk rf|rZtj|t|||gddS|||fSntddS)aRotate a vector (or a list of vectors) using the rotation matrix given as first argument. Parameters ---------- rotmat : float, array-like shape (3,3) The rotation matrix vec : float, scalar or array-like The vector to transform (shape (3,) or (3,N)), or x component (scalar or shape (N,)) if vy and vz are given vy : float, scalar or array-like, optional The y component of the vector (scalar or shape (N,)) vz : float, scalar or array-like, optional The z component of the vector (scalar or shape (N,)) do_rot : bool, optional if True, really perform the operation, if False do nothing. Returns ------- vec : float, array The component of the rotated vector(s). See Also -------- Rotator N)rr)Zaxesz:You must give either vec only or vec, vy and vz parameters)rAZ tensordotrSr[)rIvecvyvzrJrrrr]s r]FcCs.t|t|||d|d\}}}t||||dS)aTRotate the vector described by angles theta,phi using the rotation matrix given as first argument. Parameters ---------- rotmat : float, array-like shape (3,3) The rotation matrix theta : float, scalar or array-like The angle theta (scalar or shape (N,)) or both angles (scalar or shape (2, N)) if phi is not given. phi : float, scalar or array-like, optionnal The angle phi (scalar or shape (N,)). do_rot : bool, optional if True, really perform the operation, if False do nothing. lonlat : bool If True, input angles are assumed to be longitude and latitude in degree, otherwise, they are co-latitude and longitude in radians. Returns ------- angles : float, array The angles of describing the rotated vector(s). See Also -------- Rotator )rX)rJ)r]ruvec2dir)rIthetaphirJrXvxrrrrrr\Bsr\cCs(tt|rtjtjfS|dkr8|dkr8|\}}}n|dk rN|dk rN|}ntdt|d|d|d}td|jf}t|||dddf<t |||dddf<|rt |}t |dddf|dddf|dddfd7<|dddddf S| SdS)ayTransform a vector to angle given by theta,phi. Parameters ---------- vec : float, scalar or array-like The vector to transform (shape (3,) or (3,N)), or x component (scalar or shape (N,)) if vy and vz are given vy : float, scalar or array-like, optional The y component of the vector (scalar or shape (N,)) vz : float, scalar or array-like, optional The z component of the vector (scalar or shape (N,)) lonlat : bool, optional If True, return angles will be longitude and latitude in degree, otherwise, angles will be longitude and co-latitude in radians (default) Returns ------- angles : float, array The angles (unit depending on *lonlat*) in an array of shape (2,) (if scalar input) or (2, N) See Also -------- :func:`dir2vec`, :func:`pixelfunc.ang2vec`, :func:`pixelfunc.vec2ang` Nz3You must either give both vy and vz or none of themrYrrgV@rh) rAanyisnannanr[sqrtemptysizearccosrvdegreesnegativesqueeze)rrrrXrr=angrrrrbs"   $rc Cs|dkr|\}}|r>||}}tjdt|t|}}t|t|t|t|f\}}}}td|jftj} ||| dddf<||| dddf<|| dddf<| S)aTransform a direction theta,phi to a unit vector. Parameters ---------- theta : float, scalar or array-like The angle theta (scalar or shape (N,)) or both angles (scalar or shape (2, N)) if phi is not given. phi : float, scalar or array-like, optionnal The angle phi (scalar or shape (N,)). lonlat : bool If True, input angles are assumed to be longitude and latitude in degree, otherwise, they are co-latitude and longitude in radians. Returns ------- vec : array The vector(s) corresponding to given angles, shape is (3,) or (3, N). See Also -------- :func:`vec2dir`, :func:`pixelfunc.ang2vec`, :func:`pixelfunc.vec2ang` Ng@r rrrY) rApiradianscossinrrfloat64r) rrrXZlonZlatctstcpsprrrrrus  ,ruc Cszt|dr t|dkr |\}}n|}}t|}t|}|jdkrx|jddkrbt||d}qt|d}t|}nB|jdkr|jddkrtt||dd}nt|d}t|}|jdkr|jddkrt||d}nt|d}t|}nF|jdkr<|jddkr(tt||dd}nt|d}t|}t t |j |j dj dd}||j dd}t ||S) aReturns the angular distance between dir1 and dir2. Parameters ---------- dir1, dir2 : float, array-like The directions between which computing the angular distance. Angular if len(dir) == 2 or vector if len(dir) == 3. See *lonlat* for unit lonlat : bool, scalar or sequence If True, angles are assumed to be longitude and latitude in degree, otherwise they are interpreted as colatitude and longitude in radian. If a sequence, lonlat[0] applies to dir1 and lonlat[1] applies to dir2. Returns ------- angles : float, scalar or array-like The angle(s) between dir1 and dir2 in radian. Examples -------- >>> import healpy as hp >>> hp.rotator.angdist([.2,0], [.2, 1e-6]) array([ 1.98669331e-07]) rrYr)rX)r rhr)r r)axis)r"r%rArkndimshaperuZreshape normalize_vecrcrossrHsumrv) Zdir1Zdir2rXZlonlat1Zlonlat2Zvec1Zvec2Zvec_prodZ scal_prodrrrangdists8             "rcCs2t|tj}ttj|ddd}||}|S)aNormalize the vector(s) *vec* (in-place if it is a ndarray). Parameters ---------- vec : float, array-like of shape (D,) or (D, N) The D-vector(s) to normalize. Returns ------- vec_normed : float, array Normalized vec, shape (D,) or (D, N) rYr)r)rArSrrr)rr=rrrrs rcCs||dkr |St|tstd|ddkr4d}nD|ddkrR|dkrRd}n&|ddksj|dkrpd}ntd|S) zCheck if parameter is a valid coord system. Raise a TypeError exception if it is not, otherwise returns the normalized coordinate system name. NzYCoordinate must be a string (G[alactic], E[cliptic], C[elestial] or Equatorial=Celestial)rr r rr zUWrong coordinate (either G[alactic], E[cliptic], C[elestial] or Equatorial=Celestial))rcr$r[upperr&)r>r rrr check_coord s rcCsjg}|dkrd}t|}t|dkr,tdx|D]}|t|q2Wt|dkrb||dt|S)aHNormalise the coord argument. Coord sys are either 'E','G', 'C' or 'X' if undefined. Input: either a string or a sequence of string. Output: a tuple of two strings, each being one of the norm coord sys name above. eg, 'E' -> ['E','E'], ['Ecliptic','G'] -> ['E','G'] None -> ['X','X'] etc. N)NNrYz^Coordinate must be a string (G[alactic], E[cliptic] or C[elestial]) or a sequence of 2 stringsr)tupler%r[r/r)r7 coord_normr rrrr.)s    r.cCsP|rtjd}nd}|dkr(td}n$t|tj|}|jddd|S)zReturn rot possibly completed with zeroes to reach size 3. If rot is None, return a vector of 0. If deg is True, convert from degree to radian, otherwise assume input is in radian. gf@g?Nr F)Zrefcheck)rArrtrSrflattenresize)r6r!convertrrrr-Fs  r-rcCst||d}tj|tdddds*d}nd}|dkrVt|d |d  |d dd }nF|d kr~t|d |d  |d dd}nt|d |d  |d dd}|||fS)aReturn the rotation matrix corresponding to angles given in rot. Usage: matrot,do_rot,normrot = get_rotation_matrix(rot) Input: - rot: either None, an angle or a tuple of 1,2 or 3 angles corresponding to Euler angles. Output: - matrot: 3x3 rotation matrix - do_rot: True if rotation is not identity, False otherwise - normrot: the normalized version of the input rot. )r!r ggV瞯<)rNrOTFrrrrY)rr )r )r)r-rArPrteuler_matrix_new)r6r!r9rJZmatrotrrrrEXs   rEcCst|}|d|dkr(td}d}ntjt}tt|}tjt}tt|}|dkrft}nP|dkrt|}nB|dkrt}n4|dkr|}n&|d kr|}n|d kr|}n td |d }|||fS) aReturn the rotation matrix corresponding to coord systems given in coord. Usage: matconv,do_conv,normcoord = get_coordconv_matrix(coord) Input: - coord: a tuple with initial and final coord systems. See normalise_coord. Output: - matconv: the euler matrix for coord sys conversion - do_conv: True if matconv is not identity, False otherwise - normcoord: the tuple of initial and final coord sys. History: adapted from CGIS IDL library. rrr F)r r )r r )r r )r r )r r )r r zWrong coord transform :T) r.rArBZlinalgr8e2grGe2qr&)r7rZmatconvrKZg2eZg2qZq2eZq2grrrrFts.      rFcCshtj}d|}d|}d|}|dkrld}ddddd d g} d d d dddg} ddddddg} ddddd d g} nDd}ddddddg} ddddddg} ddd d d!d!g} ddddddg} |d} ||| | }||}t|}t|}|t|}| |  || | |}t||}t| | || | ||t|}t|| | |||}||fS)"a NAME: euler PURPOSE: Transform between Galactic, celestial, and ecliptic coordinates. EXPLANATION: Use the procedure ASTRO to use this routine interactively CALLING SEQUENCE: EULER, AI, BI, AO, BO, [ SELECT, /FK4, SELECT = ] INPUTS: AI - Input Longitude in DEGREES, scalar or vector. If only two parameters are supplied, then AI and BI will be modified to contain the output longitude and latitude. BI - Input Latitude in DEGREES OPTIONAL INPUT: SELECT - Integer (1-6) specifying type of coordinate transformation. SELECT From To | SELECT From To 1 RA-Dec (2000) Galactic | 4 Ecliptic RA-Dec 2 Galactic RA-DEC | 5 Ecliptic Galactic 3 RA-Dec Ecliptic | 6 Galactic Ecliptic If not supplied as a parameter or keyword, then EULER will prompt for the value of SELECT Celestial coordinates (RA, Dec) should be given in equinox J2000 unless the /FK4 keyword is set. OUTPUTS: AO - Output Longitude in DEGREES BO - Output Latitude in DEGREES INPUT KEYWORD: /FK4 - If this keyword is set and non-zero, then input and output celestial and ecliptic coordinates should be given in equinox B1950. /SELECT - The coordinate conversion integer (1-6) may alternatively be specified as a keyword NOTES: EULER was changed in December 1998 to use J2000 coordinates as the default, ** and may be incompatible with earlier versions***. REVISION HISTORY: Written W. Landsman, February 1987 Adapted from Fortran by Daryl Yentis NRL Converted to IDL V5.0 W. Landsman September 1997 Made J2000 the default, added /FK4 keyword W. Landsman December 1998 Add option to specify SELECT as a keyword W. Landsman March 2003 Converted to python by K. Ganga December 2007 g@g@gf@rz(B1950)g"d@n?gtk@ggݤĉ}?gSGY@gsh?gshgXv?gXvٿgk?gkggPs?gF[?g/2c?z(J2000)g+d?g~*P@gG8h?gt @gI1Lz?gI1Lzg,P.u?g,P.uٿgu*?gu*gnj.?g;hW\?gotB?)rArrrZarcsinrvfmod)ZaiZbiselectZFK4ZPIZtwopiZfourpiZ deg_to_radZequinoxpsiZsthetaZcthetarr?rUresbcbZcbsaZboZaorrreulers?   *rcCsd}|r|d}|r|d}|dkr,tdd}|r>tjd}t||} t||} t||} t||} t||} t||}|rt| | dg| | dgdddgg}t| d| gdddg| d| gg}tdddgd| | gd|| gg}n|rzt| | dg| | dgdddgg}t| d| gdddg| d| gg}t| | dg|| dgdddgg}nlt| | dg| | dgdddgg}tdddgd| | gd| | gg}t| | dg|| dgdddgg}t|jt|j|j}|S)aG NAME: euler_matrix_new PURPOSE: computes the Euler matrix of an arbitrary rotation described by 3 Euler angles correct bugs present in Euler_Matrix CALLING SEQUENCE: result = euler_matrix_new (a1, a2, a3 [,X, Y, ZYX, DEG ]) INPUTS: a1, a2, a3 = Euler angles, scalar (in radian by default, in degree if DEG is set) all the angles are measured counterclockwise correspond to x, y, zyx-conventions (see Goldstein) the default is x KEYWORD PARAMETERS: DEG : if set the angle are measured in degree X : rotation a1 around original Z rotation a2 around interm X rotation a3 around final Z DEFAULT, classical mechanics convention Y : rotation a1 around original Z rotation a2 around interm Y rotation a3 around final Z quantum mechanics convention (override X) ZYX : rotation a1 around original Z rotation a2 around interm Y rotation a3 around final X aeronautics convention (override X) * these last three keywords are obviously mutually exclusive * OUTPUTS: result is a 3x3 matrix USAGE: if vec is an Nx3 array containing N 3D vectors, vec # euler_matrix_new(a1,a2,a3,/Y) will be the rotated vectors MODIFICATION HISTORY: March 2002, EH, Caltech, rewritting of euler_matrix convention euler_matrix_new euler_matrix X: M_new(a,b,c,/X) = M_old(-a,-b,-c,/X) = Transpose( M_old(c, b, a,/X)) Y: M_new(a,b,c,/Y) = M_old(-a, b,-c,/Y) = Transpose( M_old(c,-b, a,/Y)) ZYX: M_new(a,b,c,/Z) = M_old(-a, b,-c,/Z) rrz$Choose either X, Y or ZYX conventiong?gf@)r&rArrrrSrGrH)Za1Za2a3rr rr!Zt_krc1s1c2s2c3Zs3m1m2Zm3Mrrrrjs:9 $$&$$&$$$rc Cst|}|d|dkr*td\}}}ntd\}}}t|d}||||gj\} } } | tt| | } | tt| | } | tt| | } t| d| d }t t|| }t| d| d}|||fS)aReturn the ZYZ Euler angles corresponding to a rotation between the two coordinate systems. The angles can be used in rotate_alm. Parameters ---------- coord : a tuple with initial and final coord systems. See normalise_coord. Returns ------- psi, theta, phi : floats The Euler angles defining a ZYZ rotation between the coordinate systems. Examples -------- >>> np.array(coordsys2euler_zyz('GE')) array([ 1.4593747 , 1.05048844, -3.14118737]) >>> np.array(coordsys2euler_zyz('CG')) array([-0.22444029, 1.09731902, 2.14556673]) >>> np.array(coordsys2euler_zyz('E')) array([ 0., 0., 0.]) rrr )r7rY) r.rArteyerrHrrGrvr) r7rrrrZxinZyinZzinr6ZxoutZyoutZzoutrrrcoordsys2euler_zyzs r)NNT)NTF)NNF)NF)F)F)Fr)r)TFFF)1numpyrAlogging getLoggerr2Zastropy.coordinatesrZastropy.utils.decoratorsrrorrZ _sphtoolsrrprr rrZastropy_ecliptic_framelowerZ transform_todataZ to_cartesianZget_xyzvaluerrWarningrrwarningsfilterwarningsobjectrr]r\rrurrrr.r-rErFrrrrrrrs^       R ) / $ ?  R % g