[c@`sydZddlmZmZmZmZddlZddlZddlZddl m Z ddl Z ddl Z ddljZddlmZmZmZddlmZdd lmZdd lmZmZdd lmZdd lmZm Z dd l!m"Z"m#Z#ddddddddddddddddddd gZ$iZ%iZ&d!d"Z'dd#Z(d$efd%YZ)d&Z*d'eej+fd(YZ,ej-e,d)e)fd*YZ.d+e.fd,YZ/d-e.fd.YZ0d/e.fd0YZ1d1e.fd2YZ2d3e.fd4YZ3d5e.fd6YZ4d7eej+fd8YZ5ej-e5d9e)fd:YZ6d;e6fd<YZ7d=e6fd>YZ8d?e8fd@YZ9dAe8fdBYZ:dCe6fdDYZ;dEe;fdFYZ<dGe;fdHYZ=dIe6fdJYZ>dKe6fdLYZ?dMe6fdNYZ@dS(Ou In this module, we define the coordinate representation classes, which are used to represent low-level cartesian, spherical, cylindrical, and other coordinates. i(tabsolute_importtdivisiontprint_functiontunicode_literalsN(t OrderedDicti(tAnglet LongitudetLatitude(tDistancei(tsix(tShapedLikeNDArrayt classproperty(tInheritDocstrings(t NUMPY_LT_1_12t NUMPY_LT_1_14(tbroadcast_arrayst broadcast_tou BaseRepresentationOrDifferentialuBaseRepresentationuCartesianRepresentationuSphericalRepresentationuUnitSphericalRepresentationuRadialRepresentationuPhysicsSphericalRepresentationuCylindricalRepresentationuBaseDifferentialuCartesianDifferentialuBaseSphericalDifferentialuBaseSphericalCosLatDifferentialuSphericalDifferentialuSphericalCosLatDifferentialuUnitSphericalDifferentialuUnitSphericalCosLatDifferentialuRadialDifferentialuCylindricalDifferentialuPhysicsSphericalDifferentialuc `sidd6|d6}trddlm}tj}g|jjD]9}|tj||jd|dd|d ^qCfd }i|d 6|d <||d =s(tformattjointzip(tx(tformat_functions(sAlib/python2.7/site-packages/astropy/coordinates/representation.pytfmt<sunumpystru formatterustyle( R tnumpy.core.arrayprintRtnptget_printoptionstdtypetnamest atleast_1dtravelRtreprt array2string(tvaluestprefixtkwargsRtoptst componentR((RsAlib/python2.7/site-packages/astropy/coordinates/representation.pyt _array2string/s I   c C`s |jd}| |ko%|knsEtdj||n|dkr^||7}n|j}|||jdt}|||jdt}|j}|| d||}tjg|||fD]}|j |j ^qd|}||d|jdtS(u  Combine components ``x``, ``y``, ``z`` into a single Quantity array. Parameters ---------- x, y, z : `~astropy.units.Quantity` The individual x, y, and z components. xyz_axis : int, optional The axis in the final array along which the x, y, z components should be stored (default: 0). Returns ------- xyz : `~astropy.units.Quantity` With dimension 3 along ``xyz_axis``, i.e., using the default of ``0``, the shape will be ``(3,) + x.shape``. iu&xyz_axis {0} out of bounds [-{1}, {1})itcopytaxistunit(i( tndimt IndexErrorRt __class__R.tFalsetshapeRt concatenatetreshapetvalue( Rtytztxyz_axist result_ndimtclstshtct xyz_value((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt _combine_xyzMs      4 t BaseRepresentationOrDifferentialcB`sIeZdZdZdZedZejdZ ejdZ e dZ dZ e dZejd Zejd Zd Zd Zd ZdZdZdZejedZdZdZdZdZe dZe dZe dZdZ dZ!RS(u3D coordinate representations and differentials. Parameters ---------- comp1, comp2, comp3 : `~astropy.units.Quantity` or subclass The components of the 3D point or differential. The names are the keys and the subclasses the values of the ``attr_classes`` attribute. copy : bool, optional If `True` (default), arrays will be copied rather than referenced. iPc O`st|}|j}g}xf|D]^}y/|j|rF|jdn |j|Wq"tk rtdj|q"Xq"W|r|jdn|jdt}|rtdj|n|rx2|D]*}||krtdj|qqWtdj|ngt||D]%\}}|j ||d|^q,}yt dt|}Wnit k rt |d krd j |}nd j |d d |d }t d j|nXx1t||D] \}}t|d||qWdS(Niu8__init__() missing 1 required positional argument: {0!r}ucopyuunexpected arguments: {0}u1__init__() got multiple values for argument {0!r}u!unexpected keyword arguments: {0}R,tsubokiu and u, u, and u(Input parameters {0} cannot be broadcastu_(tlistt componentstappendtpoptKeyErrort TypeErrorRtTrueRt attr_classesRt ValueErrortlenRtsetattr( tselftargsR(RCtattrsR*R,tattrtc_str((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt__init__s<   /  '   8  cC`sK|jj}|jdr+|d }n|jdrG|d }n|S(uName of the representation or differential. In lower case, with any trailing 'representation' or 'differential' removed. (E.g., 'spherical' for `~astropy.coordinates.SphericalRepresentation` or `~astropy.coordinates.SphericalDifferential`.) urepresentationiu differentiali(t__name__tlowertendswith(R;tname((sAlib/python2.7/site-packages/astropy/coordinates/representation.pytget_names   cC`s tdS(u[Create a representation of this class from a supplied Cartesian one. Parameters ---------- other : `CartesianRepresentation` The representation to turn into this class Returns ------- representation : object of this class A new representation of this class's type. N(tNotImplementedError(RMtother((sAlib/python2.7/site-packages/astropy/coordinates/representation.pytfrom_cartesianscC`s tdS(uConvert the representation to its Cartesian form. Note that any differentials get dropped. Returns ------- cartrepr : `CartesianRepresentation` The representation in Cartesian form. N(RX(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt to_cartesians cC`s t|jS(u=A tuple with the in-order names of the coordinate components.(ttupleRI(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRCsc `sqtr$fd}ntj}|jdtg|jD]}|t||^qOS(uECreate a new representation or differential with ``method`` applied to the component data. In typical usage, the method is any of the shape-changing methods for `~numpy.ndarray` (``reshape``, ``swapaxes``, etc.), as well as those picking particular elements (``__getitem__``, ``take``, etc.), which are all defined in `~astropy.utils.misc.ShapedLikeNDArray`. It will be applied to the underlying arrays (e.g., ``x``, ``y``, and ``z`` for `~astropy.coordinates.CartesianRepresentation`), with the results used to create a new instance. Internally, it is also used to apply functions to the components (in particular, `~numpy.broadcast_to`). Parameters ---------- method : str or callable If str, it is the name of a method that is applied to the internal ``components``. If callable, the function is applied. args : tuple Any positional arguments for ``method``. kwargs : dict Any keyword arguments for ``method``. c`s|S(N((tarray(RNR(tmethod(sAlib/python2.7/site-packages/astropy/coordinates/representation.pytsR,(tcallabletoperatort methodcallerR1R2RCtgetattr(RMR^RNR(t apply_methodR*((RNR(R^sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt_applys   cC`st||jdjS(uThe shape of the instance and underlying arrays. Like `~numpy.ndarray.shape`, can be set to a new shape by assigning a tuple. Note that if different instances share some but not all underlying data, setting the shape of one instance can make the other instance unusable. Hence, it is strongly recommended to get new, reshaped instances with the ``reshape`` method. Raises ------ AttributeError If the shape of any of the components cannot be changed without the arrays being copied. For these cases, use the ``reshape`` method (which copies any arrays that cannot be reshaped in-place). i(RcRCR3(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR3 scC`sg}|j}x}|jD]r}t||}|jdkry ||_Wn.tk rzx|D]}||_qaWqX|j|qqWdS(Ni(R3RCRctsizetAttributeErrorRD(RMR3treshapedtoldshapeR*tvaltval2((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR3s     cG`s tdS(N(RX(RMtopRN((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt_scale_operation1scC`s|jtj|S(N(RmRatmul(RMRY((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt__mul__5scC`s |j|S(N(Ro(RMRY((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt__rmul__8scC`s|jtj|S(N(RmRattruediv(RMRY((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt __truediv__;scC`s|jtj|S(N(RmRaRq(RMRY((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt__div__>scC`s|jtjS(N(RmRatneg(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt__neg__AscC`s |jS(N(R,(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt__pos__EscC`s tdS(N(RX(RMRlRYtreverse((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt_combine_operationJscC`s|jtj|S(N(RxRatadd(RMRY((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt__add__NscC`s|jtj|dtS(NRw(RxRaRyRH(RMRY((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt__radd__QscC`s|jtj|S(N(RxRatsub(RMRY((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt__sub__TscC`s|jtj|dtS(NRw(RxRaR|RH(RMRY((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt__rsub__WscC`sg|jD]!}t|t||f^q }tj|jg|D]\}}||jf^qD}x!|D]\}}|j||( R+RRctNoneRRt differentialstkeysR$RR1RSRC(RMt prefixstrtarrstrtdiffstrtkeyR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt__repr__|s7("RSt __module__t__doc__t__array_priority__RRt classmethodRWtabctabstractmethodRZR[tpropertyRCReR3tsetterRmRoRpRrRsRuRvR2RxRzR{R}R~RRRRR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR@vs8  * !            c`sdfd}|S(uMake an attribute getter for use in a property. Parameters ---------- component : str The name of the component that should be accessed. This assumes the actual value is stored in an attribute of that name prefixed by '_'. u_c`s t|S(N(Rc(RM(R*(sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt get_components((R*R((R*sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt _make_getters tMetaBaseRepresentationcB`seZdZRS(c C`stt|j||||jdkr/dSd|krJtdn|j}|tkrztdj|n|t|bs (Rtsqrtt functoolstreduceRaRyRIR(RM((RMsAlib/python2.7/site-packages/astropy/coordinates/representation.pytnormSs cO`s,|jd|j|jj||S(uBVector mean. Averaging is done by converting the representation to cartesian, and taking the mean of the x, y, and z components. The result is converted back to the same representation as the input. Refer to `~numpy.mean` for full documentation of the arguments, noting that ``axis`` is the entry in the ``shape`` of the representation, and that the ``out`` argument cannot be used. Returns ------- mean : representation Vector mean, in the same representation as that of the input. umean(RRZR[tmean(RMRNR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRfs cO`s,|jd|j|jj||S(u0Vector sum. Adding is done by converting the representation to cartesian, and summing the x, y, and z components. The result is converted back to the same representation as the input. Refer to `~numpy.sum` for full documentation of the arguments, noting that ``axis`` is the entry in the ``shape`` of the representation, and that the ``out`` argument cannot be used. Returns ------- sum : representation Vector sum, in the same representation as that of the input. usum(RRZR[tsum(RMRNR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRys cC`s|jj|S(uDot product of two representations. The calculation is done by converting both ``self`` and ``other`` to `~astropy.coordinates.CartesianRepresentation`. Note that any associated differentials will be dropped during this operation. Parameters ---------- other : `~astropy.coordinates.BaseRepresentation` The representation to take the dot product with. Returns ------- dot_product : `~astropy.units.Quantity` The sum of the product of the x, y, and z components of the cartesian representations of ``self`` and ``other``. (R[tdot(RMRY((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRscC`s)|jd|j|jj|S(u]Vector cross product of two representations. The calculation is done by converting both ``self`` and ``other`` to `~astropy.coordinates.CartesianRepresentation`, and converting the result back to the type of representation of ``self``. Parameters ---------- other : representation The representation to take the cross product with. Returns ------- cross_product : representation With vectors perpendicular to both ``self`` and ``other``, in the same type of representation as ``self``. ucross(RRZR[tcross(RMRY((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs N(RSRRtrecommended_unitsRRRRRRRRRRRRRRRRReRmR2RxR@R3RRRRRR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs."  =    0 ! !        tCartesianRepresentationcB`seZdZedejfdejfdejfgZdddddedZ dZ dZ ddZ e e Zed Zd Zd Zed Zd ZdZdZdZRS(u Representation of points in 3D cartesian coordinates. Parameters ---------- x, y, z : `~astropy.units.Quantity` or array The x, y, and z coordinates of the point(s). If ``x``, ``y``, and ``z`` have different shapes, they should be broadcastable. If not quantity, ``unit`` should be set. If only ``x`` is given, it is assumed that it contains an array with the 3 coordinates stored along ``xyz_axis``. unit : `~astropy.units.Unit` or str If given, the coordinates will be converted to this unit (or taken to be in this unit if not given. xyz_axis : int, optional The axis along which the coordinates are stored when a single array is provided rather than distinct ``x``, ``y``, and ``z`` (default: 0). differentials : dict, `CartesianDifferential`, optional Any differential classes that should be associated with this representation. The input must either be a single `CartesianDifferential` instance, or a dictionary of `CartesianDifferential` s with keys set to a string representation of the SI unit with which the differential (derivative) is taken. For example, for a velocity differential on a positional representation, the key would be ``'s'`` for seconds, indicating that the derivative is a time derivative. copy : bool, optional If `True` (default), arrays will be copied rather than referenced. uxuyuzcC`s|dkrZ|dkrZ|dk rH|dkrHtj||d}n|\}}}ni|dk rutdnN|dkr|dk s|dk r|dkrtdj|jjn|dk r2tj||d|dt }tj||d|dt }tj||d|dt }t }nt t |j |||d|d||jjj|jjjko|jjjknstjdndS(Niu|xyz_axis should only be set if x, y, and z are in a single array passed in through x, i.e., y and z should not be not given.u+x, y, and z are required to instantiate {0}R,RARu/x, y, and z should have matching physical types(RRtrollaxisRJRR1RStutQuantityRHR2RRRRt_xR.t physical_typet_yt_zt UnitsError(RMRR7R8R.R9RR,((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRRs& 0   ! +c C`stdtj|jdt}tdtj|jdt}tdt|||dtfdt|||dtfdt|||dtffS(Ng?RAguxR,uyuz(RRtoneR3RHRRR2(RMtlto((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs cC`sDtdtj|jdt}td|fd|fd|ffS(Ng?RAuxuyuz(RRRR3RHR(RMR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRsicC`st|j|j|jd|S(uvReturn a vector array of the x, y, and z coordinates. Parameters ---------- xyz_axis : int, optional The axis in the final array along which the x, y, z components should be stored (default: 0). Returns ------- xyz : `~astropy.units.Quantity` With dimension 3 along ``xyz_axis``. R9(R?RRR(RMR9((sAlib/python2.7/site-packages/astropy/coordinates/representation.pytget_xyzscC`s|S(N((R;RY((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRZscC`s|S(N((RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR[sc`s=y j}Wn)tk r8tjj}nX|dd krXtdn|j}|jr|d rj|j}nHtj dkrtj d|jdt }ntj d|j}t j ||jdt }|jrtfd|jjD}nd }|jdt d ||S( u" Transform the cartesian coordinates using a 3x3 matrix. This returns a new representation and does not modify the original one. Any differentials attached to this representation will also be transformed. Parameters ---------- matrix : `~numpy.ndarray` A 3x3 transformation matrix, such as a rotation matrix. Examples -------- We can start off by creating a cartesian representation object: >>> from astropy import units as u >>> from astropy.coordinates import CartesianRepresentation >>> rep = CartesianRepresentation([1, 2] * u.pc, ... [2, 3] * u.pc, ... [3, 4] * u.pc) We now create a rotation matrix around the z axis: >>> from astropy.coordinates.matrix_utilities import rotation_matrix >>> rotation = rotation_matrix(30 * u.deg, axis='z') Finally, we can apply this transformation: >>> rep_new = rep.transform(rotation) >>> rep_new.xyz # doctest: +FLOAT_CMP iiuGtried to do matrix multiplication with an array that doesn't end in 3x3u1.14.0u...ij,j...->i...toptimizeR,c3`s9|]/\}}||j|jjfVqdS(N(RZR[t transform(RRtd(tmatrix(sAlib/python2.7/site-packages/astropy/coordinates/representation.pys isR(iiN(R3RgRR]RJtxyztisscalarRR6t __version__teinsumR2RRR.RRRRR1(RMRt matrix_shapetoldxyztnewxyzR((RsAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs*(       c`s|jjy|j}Wntk r4tSX|sG||fn ||f\|jfdjDS(Nc3`s0|]&}t|t|VqdS(N(Rc(RR*(tfirstRltsecond(sAlib/python2.7/site-packages/astropy/coordinates/representation.pys zs(RRSR[RRR1RC(RMRlRYRwtother_c((RRlRsAlib/python2.7/site-packages/astropy/coordinates/representation.pyRxps cO`s |jd|jd||S(uTVector mean. Returns a new CartesianRepresentation instance with the means of the x, y, and z components. Refer to `~numpy.mean` for full documentation of the arguments, noting that ``axis`` is the entry in the ``shape`` of the representation, and that the ``out`` argument cannot be used. umean(RRe(RMRNR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR~s cO`s |jd|jd||S(uQVector sum. Returns a new CartesianRepresentation instance with the sums of the x, y, and z components. Refer to `~numpy.sum` for full documentation of the arguments, noting that ``axis`` is the entry in the ``shape`` of the representation, and that the ``out`` argument cannot be used. usum(RRe(RMRNR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs c`shy|jWn,tk r>tdjt|nXtjtjfdj DS(uDot product of two representations. Note that any associated differentials will be dropped during this operation. Parameters ---------- other : representation If not already cartesian, it is converted. Returns ------- dot_product : `~astropy.units.Quantity` The sum of the product of the x, y, and z components of ``self`` and ``other``. uMcannot only take dot product with another representation, not a {0} instance.c3`s+|]!}t|t|VqdS(N(Rc(RR*(RRM(sAlib/python2.7/site-packages/astropy/coordinates/representation.pys s( R[RRGRRRRRaRyRC(RMRY((RRMsAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs   cC`s|jdy|j}Wn,tk rKtdjt|nX|j|j|j|j|j|j|j |j |j|j |j|j|j S(uZCross product of two representations. Parameters ---------- other : representation If not already cartesian, it is converted. Returns ------- cross_product : `~astropy.coordinates.CartesianRepresentation` With vectors perpendicular to both ``self`` and ``other``. ucrossuOcannot only take cross product with another representation, not a {0} instance.( RR[RRGRRR1R7R8R(RMRYR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs   !N(RSRRRRRRIRRHRRRRRRRRRZR[RR2RxRRRR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs$        T  RcB`seZdZedefdefgZiejd6ejd6Z e dZ de dZedZedZedZdZed Zd Zed Zdd Zd ZdZdZdZedZdZdZ dZ!RS(u Representation of points on a unit sphere. Parameters ---------- lon, lat : `~astropy.units.Quantity` or str The longitude and latitude of the point(s), in angular units. The latitude should be between -90 and 90 degrees, and the longitude will be wrapped to an angle between 0 and 360 degrees. These can also be instances of `~astropy.coordinates.Angle`, `~astropy.coordinates.Longitude`, or `~astropy.coordinates.Latitude`. differentials : dict, `BaseDifferential`, optional Any differential classes that should be associated with this representation. The input must either be a single `BaseDifferential` instance (see `._compatible_differentials` for valid types), or a dictionary of of differential instances with keys set to a string representation of the SI unit with which the differential (derivative) is taken. For example, for a velocity differential on a positional representation, the key would be ``'s'`` for seconds, indicating that the derivative is a time derivative. copy : bool, optional If `True` (default), arrays will be copied rather than referenced. ulonulatcC`stS(N(tSphericalRepresentation(R;((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt_dimensional_representationscC`s)tt|j||d|d|dS(NRR,(RRRR(RMtlontlatRR,((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRRscC`stttttgS(N(tUnitSphericalDifferentialtUnitSphericalCosLatDifferentialtSphericalDifferentialtSphericalCosLatDifferentialR(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRscC`s|jS(u0 The longitude of the point(s). (t_lon(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRscC`s|jS(u/ The latitude of the point(s). (t_lat(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRsc C`stj|jtj|j}}tj|jtj|j}}tdt| |ddtfdt| || ||dtffS(NulongR,ulat(RtsinRtcosRRRR2(RMtsinlontcoslontsinlattcoslat((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR s %%cC`s`tdtj|jdt}|r+|ntj|jtj}td|fd|ffS(Ng?RAulonulat( RRtradianR3RHRRRR(RMt omit_coslattsf_lattsf_lon((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs% c C`sutj|jtj|j}tj|jtj|j}tj|j}td|d|d|dtS(ug Converts spherical polar coordinates to 3D rectangular cartesian coordinates. RR7R8R,(RRRRRRR2(RMRR7R8((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR[s""cC`s^tj|j|j}tj|j|j}tj|j|}|d|d|dtS(ug Converts 3D rectangular cartesian coordinates to spherical polar coordinates. RRR,(RthypotRR7tarctan2R8R2(R;tcarttsRR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRZ#sc C`stj|r| rt|trU|d|jddtj|jdddtSt|t r|d|jd|jd ddtSnt t |j ||S( NtphitthetaiZtrg?R,RRtdistance( RRRtPhysicsSphericalRepresentationRRtdegRR2RRRR(RMRR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR1s) cC`s3|jd|jd|jd|jdd|S(NumultiplicationRRRg?(RRRR(RMRY((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRoAs cC`s3|jd|jd|jd|jdd|S(NudivisionRRRg?(RRRR(RMRY((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRrFs cC`s5|jd|j|jdtj|j dtS(Nunegationgf@R,(RR1RRRRR2(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRuKs cC`s%tjtj|jtjdtS(u|Vector norm. The norm is the standard Frobenius norm, i.e., the square root of the sum of the squares of all components with non-angular units, which is always unity for vectors on the unit sphere. Returns ------- norm : `~astropy.units.Quantity` Dimensionless ones, with the same shape as the representation. R,(RRRtonesR3tdimensionless_unscaledR2(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyROs cC`sO|j|j|jj|||}|tkr;tS|jj|SdS(N(RRSR[RxRRRZ(RMRlRYRwR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRx^s  cO`s/|jd|jj|jj||S(uVector mean. The representation is converted to cartesian, the means of the x, y, and z components are calculated, and the result is converted to a `~astropy.coordinates.SphericalRepresentation`. Refer to `~numpy.mean` for full documentation of the arguments, noting that ``axis`` is the entry in the ``shape`` of the representation, and that the ``out`` argument cannot be used. umean(RRRZR[R(RMRNR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRgs  cO`s/|jd|jj|jj||S(uVector sum. The representation is converted to cartesian, the sums of the x, y, and z components are calculated, and the result is converted to a `~astropy.coordinates.SphericalRepresentation`. Refer to `~numpy.sum` for full documentation of the arguments, noting that ``axis`` is the entry in the ``shape`` of the representation, and that the ``out`` argument cannot be used. usum(RRRZR[R(RMRNR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRvs  cC`s,|jd|jj|jj|S(uBCross product of two representations. The calculation is done by converting both ``self`` and ``other`` to `~astropy.coordinates.CartesianRepresentation`, and converting the result back to `~astropy.coordinates.SphericalRepresentation`. Parameters ---------- other : representation The representation to take the cross product with. Returns ------- cross_product : `~astropy.coordinates.SphericalRepresentation` With vectors perpendicular to both ``self`` and ``other``. ucross(RRRZR[R(RMRY((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs  N("RSRRRRRRIRRRR RRRHRRRRRRRR2RR[RRZRRoRrRuRRxRRR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs,           tRadialRepresentationcB`seZdZedejfgZd edZ e dZ dZ dZ dZedZdZd Zed ZRS( u. Representation of the distance of points from the origin. Note that this is mostly intended as an internal helper representation. It can do little else but being used as a scale in multiplication. Parameters ---------- distance : `~astropy.units.Quantity` The distance of the point(s) from the origin. differentials : dict, `BaseDifferential`, optional Any differential classes that should be associated with this representation. The input must either be a single `BaseDifferential` instance (see `._compatible_differentials` for valid types), or a dictionary of of differential instances with keys set to a string representation of the SI unit with which the differential (derivative) is taken. For example, for a velocity differential on a positional representation, the key would be ``'s'`` for seconds, indicating that the derivative is a time derivative. copy : bool, optional If `True` (default), arrays will be copied rather than referenced. udistancecC`s&tt|j|d|d|dS(NR,R(RRRR(RMRRR,((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRRscC`s|jS(u? The distance from the origin to the point(s). (t _distance(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRscC`stdj|jdS(u?Cartesian unit vectors are undefined for radial representation.u6Cartesian unit vectors are undefined for {0} instancesN(RXRR1(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs cC`s2tdtj|jdt}td|ffS(Ng?RAudistance(RRRR3RHR(RMR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRscC`stdj|jdS(u2Cannot convert radial representation to cartesian.u)cannot convert {0} instance to cartesian.N(RXRR1(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR[s cC`s|d|jdtS(uU Converts 3D rectangular cartesian coordinates to radial coordinate. RR,(RR2(R;R ((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRZscG`s |j|j||j|S(N(RRSR(RMRlRN((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRmscC`s|jS(uVector norm. Just the distance itself. Returns ------- norm : `~astropy.units.Quantity` Dimensionless ones, with the same shape as the representation. (R(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs cC`stS(N(R(RMRlRYRw((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRxsN(RSRRRRRRIRRHRRRRRRR[RRZRmRR2Rx(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs     RcB`seZdZedefdefdejfgZiej d6ej d6Z e Z dedZedZedZedZedZd Zed Zdd Zd Zed ZdZRS(u Representation of points in 3D spherical coordinates. Parameters ---------- lon, lat : `~astropy.units.Quantity` The longitude and latitude of the point(s), in angular units. The latitude should be between -90 and 90 degrees, and the longitude will be wrapped to an angle between 0 and 360 degrees. These can also be instances of `~astropy.coordinates.Angle`, `~astropy.coordinates.Longitude`, or `~astropy.coordinates.Latitude`. distance : `~astropy.units.Quantity` The distance to the point(s). If the distance is a length, it is passed to the :class:`~astropy.coordinates.Distance` class, otherwise it is passed to the :class:`~astropy.units.Quantity` class. differentials : dict, `BaseDifferential`, optional Any differential classes that should be associated with this representation. The input must either be a single `BaseDifferential` instance (see `._compatible_differentials` for valid types), or a dictionary of of differential instances with keys set to a string representation of the SI unit with which the differential (derivative) is taken. For example, for a velocity differential on a positional representation, the key would be ``'s'`` for seconds, indicating that the derivative is a time derivative. copy : bool, optional If `True` (default), arrays will be copied rather than referenced. ulonulatudistancecC`sYtt|j|||d|d||jjjdkrU|jjt|_ndS(NR,Rulength(RRRRRR.RtviewR(RMRRRRR,((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRRs cC`stttttgS(N(RRRRR(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRscC`s|jS(u0 The longitude of the point(s). (R(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRscC`s|jS(u/ The latitude of the point(s). (R(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR%scC`s|jS(u? The distance from the origin to the point(s). (R(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR,sc C`stj|jtj|j}}tj|jtj|j}}tdt| |ddtfdt| || ||dtfdt|||||dtffS(NulongR,ulatudistance(RRRRRRRR2(RMRRRR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR3s%%cC`sv|jtj}|r|n|tj|j}tdtj|jdt }t d|fd|fd|ffS(Ng?RAulonulatudistance( RRRRRRRRR3RHR(RMRRRt sf_distance((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR=s "  c C`stj|r| rt|trX|d|jddtj|jd|jdt St|t r|d|jd|jdt Snt t |j ||S(NR RiZRR,RR(RRRRRRRRRR2RRRR(RMRR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyREs#"c C`st|jtr*|jjtj}n |j}|tj|jtj|j }|tj|jtj |j }|tj |j}t d|d|d|dt S(ug Converts spherical polar coordinates to 3D rectangular cartesian coordinates. RR7R8R,( RRRRRRRRRRRRR2(RMRRR7R8((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR[Ts &&c C`sytj|j|j}tj||j}tj|j|j}tj|j|}|d|d|d|dtS(ug Converts 3D rectangular cartesian coordinates to spherical polar coordinates. RRRR,(RR RR7R8R R2(R;R R RRR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRZfs cC`stj|jS(uVector norm. The norm is the standard Frobenius norm, i.e., the square root of the sum of the squares of all components with non-angular units. For spherical coordinates, this is just the absolute value of the distance. Returns ------- norm : `astropy.units.Quantity` Vector norm, with the same shape as the representation. (RtabsR(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRus N(RSRRRRRRRRIRRRt_unit_representationRRHRRRRRRRRR2RRR[RRZR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs"     RcB`seZdZedefdefdejfgZiejd6ejd6Z de dZ e dZe dZe dZdZd Zdd Zd Zed Zd ZRS(u9 Representation of points in 3D spherical coordinates (using the physics convention of using ``phi`` and ``theta`` for azimuth and inclination from the pole). Parameters ---------- phi, theta : `~astropy.units.Quantity` or str The azimuth and inclination of the point(s), in angular units. The inclination should be between 0 and 180 degrees, and the azimuth will be wrapped to an angle between 0 and 360 degrees. These can also be instances of `~astropy.coordinates.Angle`. If ``copy`` is False, `phi` will be changed inplace if it is not between 0 and 360 degrees. r : `~astropy.units.Quantity` The distance to the point(s). If the distance is a length, it is passed to the :class:`~astropy.coordinates.Distance` class, otherwise it is passed to the :class:`~astropy.units.Quantity` class. differentials : dict, `PhysicsSphericalDifferential`, optional Any differential classes that should be associated with this representation. The input must either be a single `PhysicsSphericalDifferential` instance, or a dictionary of of differential instances with keys set to a string representation of the SI unit with which the differential (derivative) is taken. For example, for a velocity differential on a positional representation, the key would be ``'s'`` for seconds, indicating that the derivative is a time derivative. copy : bool, optional If `True` (default), arrays will be copied rather than referenced. uphiuthetaurcC`stt|j|||d|d||rM|jjdtj|_n|jjdtjdttj |j dtjkstj |j dtjkrt dj |j tjn|jjjdkr|jjt|_ndS( NR,Rihtinplaceggf@uFInclination angle(s) must be within 0 deg <= angle <= 180 deg, got {0}ulength(RRRRt_phitwrap_atRRRHRtanyt_thetaRJRttotdegreet_rR.RRR(RMR RRRR,((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRRs> cC`s|jS(u. The azimuth of the point(s). (R(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR scC`s|jS(u0 The elevation of the point(s). (R(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRscC`s|jS(u? The distance from the origin to the point(s). (R"(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRsc C`stj|jtj|j}}tj|jtj|j}}tdt| |ddtfdt||||| dtfdt|||||dtffS(NuphigR,uthetaur(RRR RRRRR2(RMtsinphitcosphitsinthetatcostheta((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs%% cC`sj|jtj}tj|j}tdtj|jdt }t d||fd|fd|ffS(Ng?RAuphiuthetaur( RRRRRRRRR3RHR(RMRR%R((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs  cC`stj|r| rt|trR|d|jddtj|jd|jSt|t r|d|jddtj|jSnt t |j ||S(NRRiZR( RRRRR RRRRRRRR(RMRR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs# 'c C`st|jtr*|jjtj}n |j}|tj|jtj |j }|tj|jtj|j }|tj |j}t d|d|d|dt S(ug Converts spherical polar coordinates to 3D rectangular cartesian coordinates. RR7R8R,( RRRRRRRRRRR RR2(RMRRR7R8((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR[s &&c C`sytj|j|j}tj||j}tj|j|j}tj||j}|d|d|d|dtS(ug Converts 3D rectangular cartesian coordinates to spherical polar coordinates. R RRR,(RR RR7R8R R2(R;R R RR R((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRZs cC`stj|jS(uVector norm. The norm is the standard Frobenius norm, i.e., the square root of the sum of the squares of all components with non-angular units. For spherical coordinates, this is just the absolute value of the radius. Returns ------- norm : `astropy.units.Quantity` Vector norm, with the same shape as the representation. (RRR(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs N(RSRRRRRRRIRRRRHRRRR RRRRRR[RRZR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs      tCylindricalRepresentationcB`seZdZedejfdefdejfgZiejd6Z d e dZ e dZe dZe dZdZd Zed Zd ZRS( u Representation of points in 3D cylindrical coordinates. Parameters ---------- rho : `~astropy.units.Quantity` The distance from the z axis to the point(s). phi : `~astropy.units.Quantity` or str The azimuth of the point(s), in angular units, which will be wrapped to an angle between 0 and 360 degrees. This can also be instances of `~astropy.coordinates.Angle`, z : `~astropy.units.Quantity` The z coordinate(s) of the point(s) differentials : dict, `CylindricalDifferential`, optional Any differential classes that should be associated with this representation. The input must either be a single `CylindricalDifferential` instance, or a dictionary of of differential instances with keys set to a string representation of the SI unit with which the differential (derivative) is taken. For example, for a velocity differential on a positional representation, the key would be ``'s'`` for seconds, indicating that the derivative is a time derivative. copy : bool, optional If `True` (default), arrays will be copied rather than referenced. urhouphiuzcC`sYtt|j|||d|d||jjj|jjsUtjdndS(NR,Ru-rho and z should have matching physical types( RR'RRt_rhoR.t is_equivalentRRR(RMtrhoR R8RR,((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRRJs cC`s|jS(u? The distance of the point(s) from the z-axis. (R((RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR*RscC`s|jS(u. The azimuth of the point(s). (R(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR YscC`s|jS(u- The height of the point(s). (R(RM((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR8`sc C`stj|jtj|j}}td|j}tdt||ddtfdt| |ddtfdtdd|dt j dtffS(Ng?urhoiR,uphiuzR.( RRR RRR3RRR2RR(RMR#R$R((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRgs %cC`sT|jtj}tdtj|jdt}td|fd|fd|ffS(Ng?RAurhouphiuz(R*RRRRR3RHR(RMR*R((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRos   c C`sXtj|j|j}tj|j|j}|j}|d|d|d|dtS(ui Converts 3D rectangular cartesian coordinates to cylindrical polar coordinates. R*R R8R,(RR RR7R R8R2(R;R R*R R8((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRZvs c C`sZ|jtj|j}|jtj|j}|j}td|d|d|dtS(ui Converts cylindrical polar coordinates to 3D rectangular cartesian coordinates. RR7R8R,(R*RRR RR8RR2(RMRR7R8((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR[s N(RSRRRRRRRIRRRRHRRRR*R R8RRRRZR[(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR'&s    tMetaBaseDifferentialcB`seZdZdZRS(uSet default ``attr_classes`` and component getters on a Differential. For these, the components are those of the base representation prefixed by 'd_', and the class is `~astropy.units.Quantity`. c C`s&tt|j||||jd kr/dSd|krJtdnt|ds|jj}tg|D]}d|t j f^qo|_n|j }|t krt dj|n|t |s(R3RRRaRyRRC(RMR((R5R6RMsAlib/python2.7/site-packages/astropy/coordinates/representation.pyR[ s c`sA|j|\}|dtfdtj|DS(uConvert the differential from 3D rectangular cartesian coordinates to the desired class. Parameters ---------- other : The object to convert into this differential. base : instance of ``self.base_representation`` The points for which the differentials are to be converted: each of the components is multiplied by its unit vectors and scale factors. Returns ------- A new differential object that is this class' type. R,c3`s,|]"\}}j||VqdS(N(R(RR*te(R6RY(sAlib/python2.7/site-packages/astropy/coordinates/representation.pys .s(R3R2R t iteritems(R;RYRR5((R6RYsAlib/python2.7/site-packages/astropy/coordinates/representation.pyRZscC`sd||jkr|S|j|}t|trS|j|j}|j||S|j|SdS(uConvert coordinates to another representation. If the instance is of the requested class, it is returned unmodified. By default, conversion is done via cartesian coordinates. Parameters ---------- other_class : `~astropy.coordinates.BaseRepresentation` subclass The type of representation to turn the coordinates into. base : instance of ``self.base_representation``, optional Base relative to which the differentials are defined. If the other class is a differential representation, the base will be converted to its ``base_representation``. N(R1R[RRRR,RZ(RMRRtself_cartesian((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR1scC`sIt|tr-|j|j|j}n |j}|j||S(uCreate a new instance of this representation from another one. Parameters ---------- representation : `~astropy.coordinates.BaseRepresentation` instance The presentation that should be converted to this class. base : instance of ``cls.base_representation`` The base relative to which the differentials will be defined. If the representation is a differential itself, the base will be converted to its ``base_representation`` to help convert it. (RRR[RR,RZ(R;RRt cartesian((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRKs  cG`sAg|jD]}|t|||^q }|jdt|S(u9Scale all components. Parameters ---------- op : `~operator` callable Operator to apply (e.g., `~operator.mul`, `~operator.neg`, etc. *args Any arguments required for the operator (typically, what is to be multiplied with, divided by). R,(RCRcR1R2(RMRlRNR=t scaled_attrs((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRm`s .cC`st|t|rw|s'||fn ||f\}}|jg|jD]'}|t||t||^qISy|j|}Wntk rtSX|j||| SdS(uCombine two differentials, or a differential with a representation. If ``other`` is of the same differential type as ``self``, the components will simply be combined. If ``other`` is a representation, it will be used as a base for which to evaluate the differential, and the result is a new representation. Parameters ---------- op : `~operator` callable Operator to apply (e.g., `~operator.add`, `~operator.sub`, etc. other : `~astropy.coordinates.BaseRepresentation` instance The other differential or representation. reverse : bool Whether the operands should be reversed (e.g., as we got here via ``self.__rsub__`` because ``self`` is a subclass of ``other``). N( RRR1RCRcR[RGRRx(RMRlRYRwRRR=R9((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRxns$ 5 cC`s)t|trtStt|j|S(N(RRRRRR}(RMRY((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR}scC`s|j|jS(uXVector norm. The norm is the standard Frobenius norm, i.e., the square root of the sum of the squares of all components with non-angular units. Parameters ---------- base : instance of ``self.base_representation`` Base relative to which the differentials are defined. This is required to calculate the physical size of the differential for all but cartesian differentials. Returns ------- norm : `astropy.units.Quantity` Vector norm, with the same shape as the representation. (R[R(RMR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRsN(RSRRRRRRR3R[RZRRRmR2RxR}RR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRs      tCartesianDifferentialcB`sbeZdZeZddddedZddZe ddZ ddZ e e Z RS(uDifferentials in of points in 3D cartesian coordinates. Parameters ---------- d_x, d_y, d_z : `~astropy.units.Quantity` or array The x, y, and z coordinates of the differentials. If ``d_x``, ``d_y``, and ``d_z`` have different shapes, they should be broadcastable. If not quantities, ``unit`` should be set. If only ``d_x`` is given, it is assumed that it contains an array with the 3 coordinates stored along ``xyz_axis``. unit : `~astropy.units.Unit` or str If given, the differentials will be converted to this unit (or taken to be in this unit if not given. xyz_axis : int, optional The axis along which the coordinates are stored when a single array is provided instead of distinct ``d_x``, ``d_y``, and ``d_z`` (default: 0). copy : bool, optional If `True` (default), arrays will be copied rather than referenced. cC`s|dkrZ|dkrZ|dk rH|dkrHtj||d}n|\}}}ni|dk rutdnN|dkr|dk s|dk r|dkrtdj|jjn|dk r2tj||d|dt }tj||d|dt }tj||d|dt }t }nt t |j |||d||jjj|jjo|jjj|jjstjdndS(Niuxyz_axis should only be set if d_x, d_y, and d_z are in a single array passed in through d_x, i.e., d_y and d_z should not be not given.u1d_x, d_y, and d_z are required to instantiate {0}R,RAu.d_x, d_y and d_z should have equivalent units.(RRRRJRR1RSRRRHR2RR<RRt_d_xR.R)t_d_yt_d_zR(RMtd_xtd_ytd_zR.R9R,((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRRs&    "cC`s)tg|jD]}t||^q S(N(RRCRc(RMRR=((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR[scC`s)|g|jD]}t||^q S(N(RCRc(R;RYRR=((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRZsicC`st|j|j|jd|S(uvReturn a vector array of the x, y, and z coordinates. Parameters ---------- xyz_axis : int, optional The axis in the final array along which the x, y, z components should be stored (default: 0). Returns ------- xyz : `~astropy.units.Quantity` With dimension 3 along ``xyz_axis``. R9(R?R=R>R?(RMR9((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt get_d_xyzsN(RSRRRR,RRHRRR[RRZRCRtd_xyz(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR<s    tBaseSphericalDifferentialcB`s,eZdZedZedZRS(cC`s$|j||jtj|jS(uConvert longitude differential d_lon to d_lon_coslat. Parameters ---------- base : instance of ``cls.base_representation`` The base from which the latitude will be taken. (Rtd_lonRRR(RMR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt _d_lon_coslats cC`s!|j||tj|jS(uHConvert longitude differential d_lon_coslat to d_lon. Parameters ---------- d_lon_coslat : `~astropy.units.Quantity` Longitude differential that includes ``cos(lat)``. base : instance of ``cls.base_representation`` The base from which the latitude will be taken. (RRRR(R;t d_lon_coslatR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt _get_d_lons c`st|tr%t|t| s4t|trt|jt|jB}|sb||fn ||f\fd|D}t|Stt|j||S(uCombine two differentials, or a differential with a representation. If ``other`` is of the same differential type as ``self``, the components will simply be combined. If both are different parts of a `~astropy.coordinates.SphericalDifferential` (e.g., a `~astropy.coordinates.UnitSphericalDifferential` and a `~astropy.coordinates.RadialDifferential`), they will combined appropriately. If ``other`` is a representation, it will be used as a base for which to evaluate the differential, and the result is a new representation. Parameters ---------- op : `~operator` callable Operator to apply (e.g., `~operator.add`, `~operator.sub`, etc. other : `~astropy.coordinates.BaseRepresentation` instance The other differential or representation. reverse : bool Whether the operands should be reversed (e.g., as we got here via ``self.__rsub__`` because ``self`` is a subclass of ``other``). c`s:i|]0}t|dt|d|qS(g(Rc(RR=(RRlR(sAlib/python2.7/site-packages/astropy/coordinates/representation.pys ) s ( RRERRRRCRRRx(RMRlRYRwtall_componentst result_args((RRlRsAlib/python2.7/site-packages/astropy/coordinates/representation.pyRx s$  (RSRRGRRIR2Rx(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyREs RcB`sVeZdZeZedZedZdZ ddZ e ddZ RS(uDifferential(s) of points on a unit sphere. Parameters ---------- d_lon, d_lat : `~astropy.units.Quantity` The longitude and latitude of the differentials. copy : bool, optional If `True` (default), arrays will be copied rather than referenced. cC`stS(N(R(R;((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt_dimensional_differential= scC`sPtt|j||d||jjj|jjsLtjdndS(NR,u-d_lon and d_lat should have equivalent units.( RRRRt_d_lonR.R)t_d_latRR(RMRFtd_latR,((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRRA scC`sut|tr|j}n1t|tr6|j}ntt|j|S|jt }|tt|j|S(N( RRRRRRRR[RR(RMRtscale((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR[G s  cC`sAt|tr(||j||jStt|j||S(N(RRRGRORRR(RMRR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRR scC`st|tr"||j|jSt|ttfr\|j|j|}|||jSt|tr||j |j St t |j ||S(N(RRRFRORRRIRHtPhysicsSphericalDifferentialtd_phitd_thetaRRR(R;RRRF((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRZ s  N(RSRRRR,R RLRHRRR[RRRR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR1 s   RcB`sDeZdZeZeZedZddZ e ddZ RS(ukDifferential(s) of points in 3D spherical coordinates. Parameters ---------- d_lon, d_lat : `~astropy.units.Quantity` The differential longitude and latitude. d_distance : `~astropy.units.Quantity` The differential distance. copy : bool, optional If `True` (default), arrays will be copied rather than referenced. cC`sStt|j|||d||jjj|jjsOtjdndS(NR,u-d_lon and d_lat should have equivalent units.( RRRRRMR.R)RNRR(RMRFROt d_distanceR,((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRRz scC`st|tr"||j|jSt|tr>||jSt|trl||j||j|jSt|tr||j||jSt|t r||j|j |jSt t |j ||SdS(N( RRRFRORRTRRGRRQRRR(RMRR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR s  cC`s|t|tr:|j|j|}|||j|jSt|trc||j|j |j St t |j ||S(N( RRRIRHRORTRQRRRStd_rRRR(R;RRRF((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR s N( RSRRRR,Rt_unit_differentialRHRRRRRR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRk s   tBaseSphericalCosLatDifferentialcB`sAeZdZedZdZedZedZRS(uDiffertials from points on a spherical base representation. With cos(lat) assumed to be included in the longitude differential. cC`s)|j||j|jdtfS(uGet unit vectors and scale factors from (unit)spherical base. Parameters ---------- base : instance of ``self.base_representation`` The points for which the unit vectors and scale factors should be retrieved. Returns ------- unit_vectors : dict of `CartesianRepresentation` In the directions of the coordinates of base. scale_factors : dict of `~astropy.units.Quantity` Scale factors for each of the coordinates. The scale factor for longitude does not include the cos(lat) factor. Raises ------ TypeError : if the base is not of the correct type R(RRRRH(R;R((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR3 s cC`s$|j||jtj|jS(uConvert longitude differential with cos(lat) to one without. Parameters ---------- base : instance of ``cls.base_representation`` The base from which the latitude will be taken. (RRHRRR(RMR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRM s cC`s!|j||tj|jS(uHConvert longitude differential d_lon to d_lon_coslat. Parameters ---------- d_lon : `~astropy.units.Quantity` Value of the longitude differential without ``cos(lat)``. base : instance of ``cls.base_representation`` The base from which the latitude will be taken. (RRRR(R;RFR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyt_get_d_lon_coslat s c`st|tr%t|t| s4t|trt|jt|jB}|sb||fn ||f\fd|D}t|Stt|j||S(uCombine two differentials, or a differential with a representation. If ``other`` is of the same differential type as ``self``, the components will simply be combined. If both are different parts of a `~astropy.coordinates.SphericalDifferential` (e.g., a `~astropy.coordinates.UnitSphericalDifferential` and a `~astropy.coordinates.RadialDifferential`), they will combined appropriately. If ``other`` is a representation, it will be used as a base for which to evaluate the differential, and the result is a new representation. Parameters ---------- op : `~operator` callable Operator to apply (e.g., `~operator.add`, `~operator.sub`, etc. other : `~astropy.coordinates.BaseRepresentation` instance The other differential or representation. reverse : bool Whether the operands should be reversed (e.g., as we got here via ``self.__rsub__`` because ``self`` is a subclass of ``other``). c`s:i|]0}t|dt|d|qS(g(Rc(RR=(RRlR(sAlib/python2.7/site-packages/astropy/coordinates/representation.pys s ( RRWRRRRCRRRx(RMRlRYRwRJRK((RRlRsAlib/python2.7/site-packages/astropy/coordinates/representation.pyRx s$  ( RSRRRR3RMRXR2Rx(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRW s  RcB`szeZdZeZedejfdejfgZe dZ e dZ dZ ddZeddZRS( u!Differential(s) of points on a unit sphere. Parameters ---------- d_lon_coslat, d_lat : `~astropy.units.Quantity` The longitude and latitude of the differentials. copy : bool, optional If `True` (default), arrays will be copied rather than referenced. u d_lon_coslatud_latcC`stS(N(R(R;((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRL scC`sPtt|j||d||jjj|jjsLtjdndS(NR,u4d_lon_coslat and d_lat should have equivalent units.( RRRRRGR.R)RNRR(RMRHROR,((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRR scC`sut|tr|j}n1t|tr6|j}ntt|j|S|jt }|tt|j|S(N( RRRRRRRR[RR(RMRRP((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR[ s   cC`sAt|tr(||j||jStt|j||S(N(RRRMRORRR(RMRR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR" scC`st|tr"||j|jSt|ttfr\|j|j|}|||jSt|tr|j|j |}|||j St t|j ||S(N( RRRHRORRRXRFRQRRRSRR(R;RRRH((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR* s  N(RSRRRR,RRRRIR RLRHRRR[RRRR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR s   RcB`steZdZeZeZedej fdej fdej fgZ e dZ ddZeddZRS(uDifferential(s) of points in 3D spherical coordinates. Parameters ---------- d_lon_coslat, d_lat : `~astropy.units.Quantity` The differential longitude (with cos(lat) included) and latitude. d_distance : `~astropy.units.Quantity` The differential distance. copy : bool, optional If `True` (default), arrays will be copied rather than referenced. u d_lon_coslatud_latu d_distancecC`sStt|j|||d||jjj|jjsOtjdndS(NR,u4d_lon_coslat and d_lat should have equivalent units.( RRRRRGR.R)RNRR(RMRHRORTR,((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRRN scC`st|tr"||j|jSt|tr>||jSt|trl||j||j|jSt|tr||j||jSt|t r||j||j |jSt t |j ||S(N( RRRHRORRTRRMRRQRRR(RMRR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRU s  cC`st|tr:|j|j|}|||j|jSt|tru|j|j|}|||j |j St t |j ||S(N( RRRXRFRORTRQRRRSRURRR(R;RRRH((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRf s    N(RSRRRR,RRVRRRRIRHRRRRRR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR< s    RcB`sJeZdZeZdZedZeddZ e dZ RS(uDifferential(s) of radial distances. Parameters ---------- d_distance : `~astropy.units.Quantity` The differential distance. copy : bool, optional If `True` (default), arrays will be copied rather than referenced. cC`s|j|jtjS(N(RTRRR[(RMR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR[ s cC`s"||j|jtdtS(NR,(RRRR2(R;RYR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRZ scC`s[t|ttfr"||jSt|tr>||jStt|j||SdS(N( RRRRTRQRURRR(R;RR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR s    c`st||jr]|r.|j|jn|j|j|jdtSt|ttfrt|j t|j B}|s||fn ||f\fd|D}t |St t |j ||SdS(NR,c`s:i|]0}t|dt|d|qS(g(Rc(RR=(RRlR(sAlib/python2.7/site-packages/astropy/coordinates/representation.pys s (RR,RRTR1R2RERWRRCRRRRx(RMRlRYRwRJRK((RRlRsAlib/python2.7/site-packages/astropy/coordinates/representation.pyRx s  $  N( RSRRRR,R[RRZRRR2Rx(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRw s   RQcB`s>eZdZeZedZddZe ddZ RS(u}Differential(s) of 3D spherical coordinates using physics convention. Parameters ---------- d_phi, d_theta : `~astropy.units.Quantity` The differential azimuth and inclination. d_r : `~astropy.units.Quantity` The differential radial distance. copy : bool, optional If `True` (default), arrays will be copied rather than referenced. cC`sStt|j|||d||jjj|jjsOtjdndS(NR,u/d_phi and d_theta should have equivalent units.( RRQRRt_d_phiR.R)t_d_thetaRR(RMRRRSRUR,((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRR scC`st|tr)||j|j |jSt|trL||j|j St|tr|j||jtj |j }|||j |jSt|t r|j||jtj |j }|||j St|t r||jSt t|j||S(N(RRRRRSRURRRRRRRRRRQR(RMRRRH((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR s    cC`st|tr)||j|j |jSt|tru|j||jtj |j }|||j |jSt t |j ||S(N(RRRFRORTRRRHRRRRRQR(R;RRRR((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR s  N( RSRRRR,RHRRRRRR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRQ s    tCylindricalDifferentialcB`s eZdZeZedZRS(uDifferential(s) of points in cylindrical coordinates. Parameters ---------- d_rho : `~astropy.units.Quantity` The differential cylindrical radius. d_phi : `~astropy.units.Quantity` The differential azimuth. d_z : `~astropy.units.Quantity` The differential height. copy : bool, optional If `True` (default), arrays will be copied rather than referenced. cC`sStt|j|||d||jjj|jjsOtjdndS(NR,u+d_rho and d_z should have equivalent units.( RR[RRt_d_rhoR.R)R?RR(RMtd_rhoRRRBR,((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyRR s(RSRRR'R,R2RR(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pyR[ s (ARt __future__RRRRRRRat collectionsRRtnumpyRt astropy.unitstunitsRtanglesRRRt distancesRtexternR tutilsR R t utils.miscR t utils.compatR Rtutils.compat.numpyRRt__all__RRR+R?R@RtABCMetaRt add_metaclassRRRRRRR'R+RR<RERRRWRRRRQR[(((sAlib/python2.7/site-packages/astropy/coordinates/representation.pytsp"        ) Pi(L>:6[@;4<