# Licensed under a 3-clause BSD style license - see LICENSE.rst # It gets to be really tedious to type long docstrings in ANSI C # syntax (since multi-line string literals are not valid). # Therefore, the docstrings are written here in doc/docstrings.py, # which are then converted by setup.py into docstrings.h, which is # included by pywcs.c __all__ = ['TWO_OR_MORE_ARGS', 'RETURNS', 'ORIGIN', 'RA_DEC_ORDER'] def _fix(content, indent=0): lines = content.split('\n') indent = '\n' + ' ' * indent return indent.join(lines) def TWO_OR_MORE_ARGS(naxis, indent=0): return _fix( f"""*args There are two accepted forms for the positional arguments: - 2 arguments: An *N* x *{naxis}* array of coordinates, and an *origin*. - more than 2 arguments: An array for each axis, followed by an *origin*. These arrays must be broadcastable to one another. Here, *origin* is the coordinate in the upper left corner of the image. In FITS and Fortran standards, this is 1. In Numpy and C standards this is 0. """, indent) def RETURNS(out_type, indent=0): return _fix(f"""result : array Returns the {out_type}. If the input was a single array and origin, a single array is returned, otherwise a tuple of arrays is returned.""", indent) def ORIGIN(indent=0): return _fix( """ origin : int Specifies the origin of pixel values. The Fortran and FITS standards use an origin of 1. Numpy and C use array indexing with origin at 0. """, indent) def RA_DEC_ORDER(indent=0): return _fix( """ ra_dec_order : bool, optional When `True` will ensure that world coordinates are always given and returned in as (*ra*, *dec*) pairs, regardless of the order of the axes specified by the in the ``CTYPE`` keywords. Default is `False`. """, indent) a = """ ``double array[a_order+1][a_order+1]`` Focal plane transformation matrix. The `SIP`_ ``A_i_j`` matrix used for pixel to focal plane transformation. Its values may be changed in place, but it may not be resized, without creating a new `~astropy.wcs.Sip` object. """ a_order = """ ``int`` (read-only) Order of the polynomial (``A_ORDER``). """ all_pix2world = """ all_pix2world(pixcrd, origin) -> ``double array[ncoord][nelem]`` Transforms pixel coordinates to world coordinates. Does the following: - Detector to image plane correction (if present) - SIP distortion correction (if present) - FITS WCS distortion correction (if present) - wcslib "core" WCS transformation The first three (the distortion corrections) are done in parallel. Parameters ---------- pixcrd : ndarray Array of pixel coordinates as ``double array[ncoord][nelem]``. {} Returns ------- world : ndarray Returns an array of world coordinates as ``double array[ncoord][nelem]``. Raises ------ MemoryError Memory allocation failed. SingularMatrixError Linear transformation matrix is singular. InconsistentAxisTypesError Inconsistent or unrecognized coordinate axis types. ValueError Invalid parameter value. ValueError Invalid coordinate transformation parameters. ValueError x- and y-coordinate arrays are not the same size. InvalidTransformError Invalid coordinate transformation. InvalidTransformError Ill-conditioned coordinate transformation parameters. """.format(ORIGIN()) alt = """ ``str`` Character code for alternate coordinate descriptions. For example, the ``"a"`` in keyword names such as ``CTYPEia``. This is a space character for the primary coordinate description, or one of the 26 upper-case letters, A-Z. """ ap = """ ``double array[ap_order+1][ap_order+1]`` Focal plane to pixel transformation matrix. The `SIP`_ ``AP_i_j`` matrix used for focal plane to pixel transformation. Its values may be changed in place, but it may not be resized, without creating a new `~astropy.wcs.Sip` object. """ ap_order = """ ``int`` (read-only) Order of the polynomial (``AP_ORDER``). """ cel = """ `~astropy.wcs.Celprm` Information required to transform celestial coordinates. """ Celprm = """ Class that contains information required to transform celestial coordinates. It consists of certain members that must be set by the user (given) and others that are set by the WCSLIB routines (returned). Some of the latter are supplied for informational purposes and others are for internal use only. """ Prjprm = """ Class that contains information needed to project or deproject native spherical coordinates. It consists of certain members that must be set by the user (given) and others that are set by the WCSLIB routines (returned). Some of the latter are supplied for informational purposes and others are for internal use only. """ aux = """ `~astropy.wcs.Auxprm` Auxiliary coordinate system information of a specialist nature. """ Auxprm = """ Class that contains auxiliary coordinate system information of a specialist nature. This class can not be constructed directly from Python, but instead is returned from `~astropy.wcs.Wcsprm.aux`. """ axis_types = """ ``int array[naxis]`` An array of four-digit type codes for each axis. - First digit (i.e. 1000s): - 0: Non-specific coordinate type. - 1: Stokes coordinate. - 2: Celestial coordinate (including ``CUBEFACE``). - 3: Spectral coordinate. - Second digit (i.e. 100s): - 0: Linear axis. - 1: Quantized axis (``STOKES``, ``CUBEFACE``). - 2: Non-linear celestial axis. - 3: Non-linear spectral axis. - 4: Logarithmic axis. - 5: Tabular axis. - Third digit (i.e. 10s): - 0: Group number, e.g. lookup table number - The fourth digit is used as a qualifier depending on the axis type. - For celestial axes: - 0: Longitude coordinate. - 1: Latitude coordinate. - 2: ``CUBEFACE`` number. - For lookup tables: the axis number in a multidimensional table. ``CTYPEia`` in ``"4-3"`` form with unrecognized algorithm code will have its type set to -1 and generate an error. """ b = """ ``double array[b_order+1][b_order+1]`` Pixel to focal plane transformation matrix. The `SIP`_ ``B_i_j`` matrix used for pixel to focal plane transformation. Its values may be changed in place, but it may not be resized, without creating a new `~astropy.wcs.Sip` object. """ b_order = """ ``int`` (read-only) Order of the polynomial (``B_ORDER``). """ bounds_check = """ bounds_check(pix2world, world2pix) Enable/disable bounds checking. Parameters ---------- pix2world : bool, optional When `True`, enable bounds checking for the pixel-to-world (p2x) transformations. Default is `True`. world2pix : bool, optional When `True`, enable bounds checking for the world-to-pixel (s2x) transformations. Default is `True`. Notes ----- Note that by default (without calling `bounds_check`) strict bounds checking is enabled. """ bp = """ ``double array[bp_order+1][bp_order+1]`` Focal plane to pixel transformation matrix. The `SIP`_ ``BP_i_j`` matrix used for focal plane to pixel transformation. Its values may be changed in place, but it may not be resized, without creating a new `~astropy.wcs.Sip` object. """ bp_order = """ ``int`` (read-only) Order of the polynomial (``BP_ORDER``). """ cd = """ ``double array[naxis][naxis]`` The ``CDi_ja`` linear transformation matrix. For historical compatibility, three alternate specifications of the linear transformations are available in wcslib. The canonical ``PCi_ja`` with ``CDELTia``, ``CDi_ja``, and the deprecated ``CROTAia`` keywords. Although the latter may not formally co-exist with ``PCi_ja``, the approach here is simply to ignore them if given in conjunction with ``PCi_ja``. `~astropy.wcs.Wcsprm.has_pc`, `~astropy.wcs.Wcsprm.has_cd` and `~astropy.wcs.Wcsprm.has_crota` can be used to determine which of these alternatives are present in the header. These alternate specifications of the linear transformation matrix are translated immediately to ``PCi_ja`` by `~astropy.wcs.Wcsprm.set` and are nowhere visible to the lower-level routines. In particular, `~astropy.wcs.Wcsprm.set` resets `~astropy.wcs.Wcsprm.cdelt` to unity if ``CDi_ja`` is present (and no ``PCi_ja``). If no ``CROTAia`` is associated with the latitude axis, `~astropy.wcs.Wcsprm.set` reverts to a unity ``PCi_ja`` matrix. """ cdelt = """ ``double array[naxis]`` Coordinate increments (``CDELTia``) for each coord axis. If a ``CDi_ja`` linear transformation matrix is present, a warning is raised and `~astropy.wcs.Wcsprm.cdelt` is ignored. The ``CDi_ja`` matrix may be deleted by:: del wcs.wcs.cd An undefined value is represented by NaN. """ cdfix = """ cdfix() Fix erroneously omitted ``CDi_ja`` keywords. Sets the diagonal element of the ``CDi_ja`` matrix to unity if all ``CDi_ja`` keywords associated with a given axis were omitted. According to Paper I, if any ``CDi_ja`` keywords at all are given in a FITS header then those not given default to zero. This results in a singular matrix with an intersecting row and column of zeros. Returns ------- success : int Returns ``0`` for success; ``-1`` if no change required. """ cel_offset = """ ``boolean`` Is there an offset? If `True`, an offset will be applied to ``(x, y)`` to force ``(x, y) = (0, 0)`` at the fiducial point, (phi_0, theta_0). Default is `False`. """ celprm_phi0 = r""" `float`, `None`. The native longitude, :math:`\phi_0`, in degrees of the fiducial point, i.e., the point whose celestial coordinates are given in ''Celprm.ref[0:1]''. If `None` or ``nan``, the initialization routine, ``celset()``, will set this to a projection-specific default. """ celprm_theta0 = r""" `float`, `None`. The native latitude, :math:`\theta_0`, in degrees of the fiducial point, i.e. the point whose celestial coordinates are given in ``Celprm:ref[0:1]``. If `None` or ``nan``, the initialization routine, ``celset()``, will set this to a projection-specific default. """ celprm_ref = """ ``numpy.ndarray`` with 4 elements. (Given) The first pair of values should be set to the celestial longitude and latitude of the fiducial point in degrees - typically right ascension and declination. These are given by the ``CRVALia`` keywords in ``FITS``. (Given and returned) The second pair of values are the native longitude, ``phi_p`` (in degrees), and latitude, ``theta_p`` (in degrees), of the celestial pole (the latter is the same as the celestial latitude of the native pole, ``delta_p``) and these are given by the ``FITS`` keywords ``LONPOLEa`` and ``LATPOLEa`` (or by ``PVi_2a`` and ``PVi_3a`` attached to the longitude axis which take precedence if defined). ``LONPOLEa`` defaults to ``phi0`` if the celestial latitude of the fiducial point of the projection is greater than or equal to the native latitude, otherwise ``phi0 + 180`` (degrees). (This is the condition for the celestial latitude to increase in the same direction as the native latitude at the fiducial point.) ``ref[2]`` may be set to `None` or ``numpy.nan`` or 999.0 to indicate that the correct default should be substituted. ``theta_p``, the native latitude of the celestial pole (or equally the celestial latitude of the native pole, ``delta_p``) is often determined uniquely by ``CRVALia`` and ``LONPOLEa`` in which case ``LATPOLEa`` is ignored. However, in some circumstances there are two valid solutions for ``theta_p`` and ``LATPOLEa`` is used to choose between them. ``LATPOLEa`` is set in ``ref[3]`` and the solution closest to this value is used to reset ``ref[3]``. It is therefore legitimate, for example, to set ``ref[3]`` to ``+90.0`` to choose the more northerly solution - the default if the ``LATPOLEa`` keyword is omitted from the ``FITS`` header. For the special case where the fiducial point of the projection is at native latitude zero, its celestial latitude is zero, and ``LONPOLEa`` = ``+/- 90.0`` then the celestial latitude of the native pole is not determined by the first three reference values and ``LATPOLEa`` specifies it completely. The returned value, celprm.latpreq, specifies how ``LATPOLEa`` was actually used.""" celprm_euler = """ *Read-only* ``numpy.ndarray`` with 5 elements. Euler angles and associated intermediaries derived from the coordinate reference values. The first three values are the ``Z-``, ``X-``, and ``Z``-Euler angles in degrees, and the remaining two are the cosine and sine of the ``X``-Euler angle. """ celprm_latpreq = """ ``int``, *read-only*. For informational purposes, this indicates how the ``LATPOLEa`` keyword was used: - 0: Not required, ``theta_p == delta_p`` was determined uniquely by the ``CRVALia`` and ``LONPOLEa`` keywords. - 1: Required to select between two valid solutions of ``theta_p``. - 2: ``theta_p`` was specified solely by ``LATPOLEa``. """ celprm_isolat = """ ``bool``, *read-only*. True if the spherical rotation preserves the magnitude of the latitude, which occurs if the axes of the native and celestial coordinates are coincident. It signals an opportunity to cache intermediate calculations common to all elements in a vector computation. """ celprm_prj = """ *Read-only* Celestial transformation parameters. Some members of `Prjprm` are read-write, i.e., can be set by the user. For more details, see documentation for `Prjprm`. """ prjprm_r0 = r""" The radius of the generating sphere for the projection, a linear scaling parameter. If this is zero, it will be reset to its default value of :math:`180^\circ/\pi` (the value for FITS WCS). """ prjprm_code = """ Three-letter projection code defined by the FITS standard. """ prjprm_pv = """ Projection parameters. These correspond to the ``PVi_ma`` keywords in FITS, so ``pv[0]`` is ``PVi_0a``, ``pv[1]`` is ``PVi_1a``, etc., where ``i`` denotes the latitude-like axis. Many projections use ``pv[1]`` (``PVi_1a``), some also use ``pv[2]`` (``PVi_2a``) and ``SZP`` uses ``pv[3]`` (``PVi_3a``). ``ZPN`` is currently the only projection that uses any of the others. When setting ``pv`` values using lists or ``numpy.ndarray``, elements set to `None` will be left unchanged while those set to ``numpy.nan`` will be set to ``WCSLIB``'s ``UNDEFINED`` special value. For efficiency purposes, if supplied list or ``numpy.ndarray`` is shorter than the length of the ``pv`` member, then remaining values in ``pv`` will be left unchanged. .. note:: When retrieving ``pv``, a copy of the ``prjprm.pv`` array is returned. Modifying this array values will not modify underlying ``WCSLIB``'s ``prjprm.pv`` data. """ prjprm_pvi = """ Set/Get projection parameters for specific index. These correspond to the ``PVi_ma`` keywords in FITS, so ``pv[0]`` is ``PVi_0a``, ``pv[1]`` is ``PVi_1a``, etc., where ``i`` denotes the latitude-like axis. Many projections use ``pv[1]`` (``PVi_1a``), some also use ``pv[2]`` (``PVi_2a``) and ``SZP`` uses ``pv[3]`` (``PVi_3a``). ``ZPN`` is currently the only projection that uses any of the others. Setting a ``pvi`` value to `None` will reset the corresponding ``WCSLIB``'s ``prjprm.pv`` element to the default value as set by ``WCSLIB``'s ``prjini()``. Setting a ``pvi`` value to ``numpy.nan`` will set the corresponding ``WCSLIB``'s ``prjprm.pv`` element to ``WCSLIB``'s ``UNDEFINED`` special value. """ prjprm_phi0 = r""" The native longitude, :math:`\phi_0` (in degrees) of the reference point, i.e. the point ``(x,y) = (0,0)``. If undefined the initialization routine will set this to a projection-specific default. """ prjprm_theta0 = r""" the native latitude, :math:`\theta_0` (in degrees) of the reference point, i.e. the point ``(x,y) = (0,0)``. If undefined the initialization routine will set this to a projection-specific default. """ prjprm_bounds = """ Controls bounds checking. If ``bounds&1`` then enable strict bounds checking for the spherical-to-Cartesian (``s2x``) transformation for the ``AZP``, ``SZP``, ``TAN``, ``SIN``, ``ZPN``, and ``COP`` projections. If ``bounds&2`` then enable strict bounds checking for the Cartesian-to-spherical transformation (``x2s``) for the ``HPX`` and ``XPH`` projections. If ``bounds&4`` then the Cartesian- to-spherical transformations (``x2s``) will invoke WCSLIB's ``prjbchk()`` to perform bounds checking on the computed native coordinates, with a tolerance set to suit each projection. bounds is set to 7 during initialization by default which enables all checks. Zero it to disable all checking. It is not necessary to reset the ``Prjprm`` struct (via ``Prjprm.set()``) when ``bounds`` is changed. """ prjprm_name = """ *Read-only.* Long name of the projection. """ prjprm_category = """ *Read-only.* Projection category matching the value of the relevant ``wcs`` module constants: PRJ_ZENITHAL, PRJ_CYLINDRICAL, PRJ_PSEUDOCYLINDRICAL, PRJ_CONVENTIONAL, PRJ_CONIC, PRJ_POLYCONIC, PRJ_QUADCUBE, and PRJ_HEALPIX. """ prjprm_w = """ *Read-only.* Intermediate floating-point values derived from the projection parameters, cached here to save recomputation. .. note:: When retrieving ``w``, a copy of the ``prjprm.w`` array is returned. Modifying this array values will not modify underlying ``WCSLIB``'s ``prjprm.w`` data. """ prjprm_pvrange = """ *Read-only.* Range of projection parameter indices: 100 times the first allowed index plus the number of parameters, e.g. ``TAN`` is 0 (no parameters), ``SZP`` is 103 (1 to 3), and ``ZPN`` is 30 (0 to 29). """ prjprm_simplezen = """ *Read-only.* True if the projection is a radially-symmetric zenithal projection. """ prjprm_equiareal = """ *Read-only.* True if the projection is equal area. """ prjprm_conformal = """ *Read-only.* True if the projection is conformal. """ prjprm_global_projection = """ *Read-only.* True if the projection can represent the whole sphere in a finite, non-overlapped mapping. """ prjprm_divergent = """ *Read-only.* True if the projection diverges in latitude. """ prjprm_x0 = r""" *Read-only.* The offset in ``x`` used to force :math:`(x,y) = (0,0)` at :math:`(\phi_0, \theta_0)`. """ prjprm_y0 = r""" *Read-only.* The offset in ``y`` used to force :math:`(x,y) = (0,0)` at :math:`(\phi_0, \theta_0)`. """ prjprm_m = """ *Read-only.* Intermediate integer value (used only for the ``ZPN`` and ``HPX`` projections). """ prjprm_n = """ *Read-only.* Intermediate integer value (used only for the ``ZPN`` and ``HPX`` projections). """ prjprm_set = """ This method sets up a ``Prjprm`` object according to information supplied within it. Note that this routine need not be called directly; it will be invoked by `prjx2s` and `prjs2x` if ``Prjprm.flag`` is anything other than a predefined magic value. The one important property of ``set()`` is that the projection code must be defined in the ``Prjprm`` in order for ``set()`` to identify the required projection. Raises ------ MemoryError Null ``prjprm`` pointer passed to WCSLIB routines. InvalidPrjParametersError Invalid projection parameters. InvalidCoordinateError One or more of the ``(x,y)`` or ``(lon,lat)`` coordinates were invalid. """ prjprm_prjx2s = r""" Deproject Cartesian ``(x,y)`` coordinates in the plane of projection to native spherical coordinates :math:`(\phi,\theta)`. The projection is that specified by ``Prjprm.code``. Parameters ---------- x, y : numpy.ndarray Arrays corresponding to the first (``x``) and second (``y``) projected coordinates. Returns ------- phi, theta : tuple of numpy.ndarray Longitude and latitude :math:`(\phi,\theta)` of the projected point in native spherical coordinates (in degrees). Values corresponding to invalid ``(x,y)`` coordinates are set to ``numpy.nan``. Raises ------ MemoryError Null ``prjprm`` pointer passed to WCSLIB routines. InvalidPrjParametersError Invalid projection parameters. """ prjprm_prjs2x = r""" Project native spherical coordinates :math:`(\phi,\theta)` to Cartesian ``(x,y)`` coordinates in the plane of projection. The projection is that specified by ``Prjprm.code``. Parameters ---------- phi : numpy.ndarray Array corresponding to the longitude :math:`\phi` of the projected point in native spherical coordinates (in degrees). theta : numpy.ndarray Array corresponding to the longitude :math:`\theta` of the projected point in native spherical coordinatess (in degrees). Values corresponding to invalid :math:`(\phi, \theta)` coordinates are set to ``numpy.nan``. Returns ------- x, y : tuple of numpy.ndarray Projected coordinates. Raises ------ MemoryError Null ``prjprm`` pointer passed to WCSLIB routines. InvalidPrjParametersError Invalid projection parameters. """ celfix = """ Translates AIPS-convention celestial projection types, ``-NCP`` and ``-GLS``. Returns ------- success : int Returns ``0`` for success; ``-1`` if no change required. """ cname = """ ``list of strings`` A list of the coordinate axis names, from ``CNAMEia``. """ colax = """ ``int array[naxis]`` An array recording the column numbers for each axis in a pixel list. """ colnum = """ ``int`` Column of FITS binary table associated with this WCS. Where the coordinate representation is associated with an image-array column in a FITS binary table, this property may be used to record the relevant column number. It should be set to zero for an image header or pixel list. """ compare = """ compare(other, cmp=0, tolerance=0.0) Compare two Wcsprm objects for equality. Parameters ---------- other : Wcsprm The other Wcsprm object to compare to. cmp : int, optional A bit field controlling the strictness of the comparison. When 0, (the default), all fields must be identical. The following constants, defined in the `astropy.wcs` module, may be or'ed together to loosen the comparison. - ``WCSCOMPARE_ANCILLARY``: Ignores ancillary keywords that don't change the WCS transformation, such as ``XPOSURE`` or ``EQUINOX``. Note that this also ignores ``DATE-OBS``, which does change the WCS transformation in some cases. - ``WCSCOMPARE_TILING``: Ignore integral differences in ``CRPIXja``. This is the 'tiling' condition, where two WCSes cover different regions of the same map projection and align on the same map grid. - ``WCSCOMPARE_CRPIX``: Ignore any differences at all in ``CRPIXja``. The two WCSes cover different regions of the same map projection but may not align on the same grid map. Overrides ``WCSCOMPARE_TILING``. tolerance : float, optional The amount of tolerance required. For example, for a value of 1e-6, all floating-point values in the objects must be equal to the first 6 decimal places. The default value of 0.0 implies exact equality. Returns ------- equal : bool """ convert = """ convert(array) Perform the unit conversion on the elements of the given *array*, returning an array of the same shape. """ coord = """ ``double array[K_M]...[K_2][K_1][M]`` The tabular coordinate array. Has the dimensions:: (K_M, ... K_2, K_1, M) (see `~astropy.wcs.Tabprm.K`) i.e. with the `M` dimension varying fastest so that the `M` elements of a coordinate vector are stored contiguously in memory. """ copy = """ Creates a deep copy of the WCS object. """ cpdis1 = """ `~astropy.wcs.DistortionLookupTable` The pre-linear transformation distortion lookup table, ``CPDIS1``. """ cpdis2 = """ `~astropy.wcs.DistortionLookupTable` The pre-linear transformation distortion lookup table, ``CPDIS2``. """ crder = """ ``double array[naxis]`` The random error in each coordinate axis, ``CRDERia``. An undefined value is represented by NaN. """ crln_obs = """ ``double`` Carrington heliographic longitude of the observer (deg). If undefined, this is set to `None`. """ crota = """ ``double array[naxis]`` ``CROTAia`` keyvalues for each coordinate axis. For historical compatibility, three alternate specifications of the linear transformations are available in wcslib. The canonical ``PCi_ja`` with ``CDELTia``, ``CDi_ja``, and the deprecated ``CROTAia`` keywords. Although the latter may not formally co-exist with ``PCi_ja``, the approach here is simply to ignore them if given in conjunction with ``PCi_ja``. `~astropy.wcs.Wcsprm.has_pc`, `~astropy.wcs.Wcsprm.has_cd` and `~astropy.wcs.Wcsprm.has_crota` can be used to determine which of these alternatives are present in the header. These alternate specifications of the linear transformation matrix are translated immediately to ``PCi_ja`` by `~astropy.wcs.Wcsprm.set` and are nowhere visible to the lower-level routines. In particular, `~astropy.wcs.Wcsprm.set` resets `~astropy.wcs.Wcsprm.cdelt` to unity if ``CDi_ja`` is present (and no ``PCi_ja``). If no ``CROTAia`` is associated with the latitude axis, `~astropy.wcs.Wcsprm.set` reverts to a unity ``PCi_ja`` matrix. """ crpix = """ ``double array[naxis]`` Coordinate reference pixels (``CRPIXja``) for each pixel axis. """ crval = """ ``double array[naxis]`` Coordinate reference values (``CRVALia``) for each coordinate axis. """ crval_tabprm = """ ``double array[M]`` Index values for the reference pixel for each of the tabular coord axes. """ csyer = """ ``double array[naxis]`` The systematic error in the coordinate value axes, ``CSYERia``. An undefined value is represented by NaN. """ ctype = """ ``list of strings[naxis]`` List of ``CTYPEia`` keyvalues. The `~astropy.wcs.Wcsprm.ctype` keyword values must be in upper case and there must be zero or one pair of matched celestial axis types, and zero or one spectral axis. """ cubeface = """ ``int`` Index into the ``pixcrd`` (pixel coordinate) array for the ``CUBEFACE`` axis. This is used for quadcube projections where the cube faces are stored on a separate axis. The quadcube projections (``TSC``, ``CSC``, ``QSC``) may be represented in FITS in either of two ways: - The six faces may be laid out in one plane and numbered as follows:: 0 4 3 2 1 4 3 2 5 Faces 2, 3 and 4 may appear on one side or the other (or both). The world-to-pixel routines map faces 2, 3 and 4 to the left but the pixel-to-world routines accept them on either side. - The ``COBE`` convention in which the six faces are stored in a three-dimensional structure using a ``CUBEFACE`` axis indexed from 0 to 5 as above. These routines support both methods; `~astropy.wcs.Wcsprm.set` determines which is being used by the presence or absence of a ``CUBEFACE`` axis in `~astropy.wcs.Wcsprm.ctype`. `~astropy.wcs.Wcsprm.p2s` and `~astropy.wcs.Wcsprm.s2p` translate the ``CUBEFACE`` axis representation to the single plane representation understood by the lower-level projection routines. """ cunit = """ ``list of astropy.UnitBase[naxis]`` List of ``CUNITia`` keyvalues as `astropy.units.UnitBase` instances. These define the units of measurement of the ``CRVALia``, ``CDELTia`` and ``CDi_ja`` keywords. As ``CUNITia`` is an optional header keyword, `~astropy.wcs.Wcsprm.cunit` may be left blank but otherwise is expected to contain a standard units specification as defined by WCS Paper I. `~astropy.wcs.Wcsprm.unitfix` is available to translate commonly used non-standard units specifications but this must be done as a separate step before invoking `~astropy.wcs.Wcsprm.set`. For celestial axes, if `~astropy.wcs.Wcsprm.cunit` is not blank, `~astropy.wcs.Wcsprm.set` uses ``wcsunits`` to parse it and scale `~astropy.wcs.Wcsprm.cdelt`, `~astropy.wcs.Wcsprm.crval`, and `~astropy.wcs.Wcsprm.cd` to decimal degrees. It then resets `~astropy.wcs.Wcsprm.cunit` to ``"deg"``. For spectral axes, if `~astropy.wcs.Wcsprm.cunit` is not blank, `~astropy.wcs.Wcsprm.set` uses ``wcsunits`` to parse it and scale `~astropy.wcs.Wcsprm.cdelt`, `~astropy.wcs.Wcsprm.crval`, and `~astropy.wcs.Wcsprm.cd` to SI units. It then resets `~astropy.wcs.Wcsprm.cunit` accordingly. `~astropy.wcs.Wcsprm.set` ignores `~astropy.wcs.Wcsprm.cunit` for other coordinate types; `~astropy.wcs.Wcsprm.cunit` may be used to label coordinate values. """ cylfix = """ cylfix() Fixes WCS keyvalues for malformed cylindrical projections. Returns ------- success : int Returns ``0`` for success; ``-1`` if no change required. """ data = """ ``float array`` The array data for the `~astropy.wcs.DistortionLookupTable`. """ data_wtbarr = """ ``double array`` The array data for the BINTABLE. """ dateavg = """ ``string`` Representative mid-point of the date of observation. In ISO format, ``yyyy-mm-ddThh:mm:ss``. See also -------- astropy.wcs.Wcsprm.dateobs """ dateobs = """ ``string`` Start of the date of observation. In ISO format, ``yyyy-mm-ddThh:mm:ss``. See also -------- astropy.wcs.Wcsprm.dateavg """ datfix = """ datfix() Translates the old ``DATE-OBS`` date format to year-2000 standard form ``(yyyy-mm-ddThh:mm:ss)`` and derives ``MJD-OBS`` from it if not already set. Alternatively, if `~astropy.wcs.Wcsprm.mjdobs` is set and `~astropy.wcs.Wcsprm.dateobs` isn't, then `~astropy.wcs.Wcsprm.datfix` derives `~astropy.wcs.Wcsprm.dateobs` from it. If both are set but disagree by more than half a day then `ValueError` is raised. Returns ------- success : int Returns ``0`` for success; ``-1`` if no change required. """ delta = """ ``double array[M]`` (read-only) Interpolated indices into the coord array. Array of interpolated indices into the coordinate array such that Upsilon_m, as defined in Paper III, is equal to (`~astropy.wcs.Tabprm.p0` [m] + 1) + delta[m]. """ det2im = """ Convert detector coordinates to image plane coordinates. """ det2im1 = """ A `~astropy.wcs.DistortionLookupTable` object for detector to image plane correction in the *x*-axis. """ det2im2 = """ A `~astropy.wcs.DistortionLookupTable` object for detector to image plane correction in the *y*-axis. """ dims = """ ``int array[ndim]`` (read-only) The dimensions of the tabular array `~astropy.wcs.Wtbarr.data`. """ DistortionLookupTable = """ DistortionLookupTable(*table*, *crpix*, *crval*, *cdelt*) Represents a single lookup table for a `distortion paper`_ transformation. Parameters ---------- table : 2-dimensional array The distortion lookup table. crpix : 2-tuple The distortion array reference pixel crval : 2-tuple The image array pixel coordinate cdelt : 2-tuple The grid step size """ dsun_obs = """ ``double`` Distance between the centre of the Sun and the observer (m). If undefined, this is set to `None`. """ equinox = """ ``double`` The equinox associated with dynamical equatorial or ecliptic coordinate systems. ``EQUINOXa`` (or ``EPOCH`` in older headers). Not applicable to ICRS equatorial or ecliptic coordinates. An undefined value is represented by NaN. """ extlev = """ ``int`` (read-only) ``EXTLEV`` identifying the binary table extension. """ extnam = """ ``str`` (read-only) ``EXTNAME`` identifying the binary table extension. """ extrema = """ ``double array[K_M]...[K_2][2][M]`` (read-only) An array recording the minimum and maximum value of each element of the coordinate vector in each row of the coordinate array, with the dimensions:: (K_M, ... K_2, 2, M) (see `~astropy.wcs.Tabprm.K`). The minimum is recorded in the first element of the compressed K_1 dimension, then the maximum. This array is used by the inverse table lookup function to speed up table searches. """ extver = """ ``int`` (read-only) ``EXTVER`` identifying the binary table extension. """ find_all_wcs = """ find_all_wcs(relax=0, keysel=0) Find all WCS transformations in the header. Parameters ---------- header : str The raw FITS header data. relax : bool or int Degree of permissiveness: - `False`: Recognize only FITS keywords defined by the published WCS standard. - `True`: Admit all recognized informal extensions of the WCS standard. - `int`: a bit field selecting specific extensions to accept. See :ref:`astropy:relaxread` for details. keysel : sequence of flags Used to restrict the keyword types considered: - ``WCSHDR_IMGHEAD``: Image header keywords. - ``WCSHDR_BIMGARR``: Binary table image array. - ``WCSHDR_PIXLIST``: Pixel list keywords. If zero, there is no restriction. If -1, `wcspih` is called, rather than `wcstbh`. Returns ------- wcs_list : list of `~astropy.wcs.Wcsprm` """ fix = """ fix(translate_units='', naxis=0) Applies all of the corrections handled separately by `~astropy.wcs.Wcsprm.datfix`, `~astropy.wcs.Wcsprm.unitfix`, `~astropy.wcs.Wcsprm.celfix`, `~astropy.wcs.Wcsprm.spcfix`, `~astropy.wcs.Wcsprm.cylfix` and `~astropy.wcs.Wcsprm.cdfix`. Parameters ---------- translate_units : str, optional Specify which potentially unsafe translations of non-standard unit strings to perform. By default, performs all. Although ``"S"`` is commonly used to represent seconds, its translation to ``"s"`` is potentially unsafe since the standard recognizes ``"S"`` formally as Siemens, however rarely that may be used. The same applies to ``"H"`` for hours (Henry), and ``"D"`` for days (Debye). This string controls what to do in such cases, and is case-insensitive. - If the string contains ``"s"``, translate ``"S"`` to ``"s"``. - If the string contains ``"h"``, translate ``"H"`` to ``"h"``. - If the string contains ``"d"``, translate ``"D"`` to ``"d"``. Thus ``''`` doesn't do any unsafe translations, whereas ``'shd'`` does all of them. naxis : int array, optional Image axis lengths. If this array is set to zero or ``None``, then `~astropy.wcs.Wcsprm.cylfix` will not be invoked. Returns ------- status : dict Returns a dictionary containing the following keys, each referring to a status string for each of the sub-fix functions that were called: - `~astropy.wcs.Wcsprm.cdfix` - `~astropy.wcs.Wcsprm.datfix` - `~astropy.wcs.Wcsprm.unitfix` - `~astropy.wcs.Wcsprm.celfix` - `~astropy.wcs.Wcsprm.spcfix` - `~astropy.wcs.Wcsprm.cylfix` """ get_offset = """ get_offset(x, y) -> (x, y) Returns the offset as defined in the distortion lookup table. Returns ------- coordinate : (2,) tuple The offset from the distortion table for pixel point (*x*, *y*). """ get_cdelt = """ get_cdelt() -> numpy.ndarray Coordinate increments (``CDELTia``) for each coord axis as ``double array[naxis]``. Returns the ``CDELT`` offsets in read-only form. Unlike the `~astropy.wcs.Wcsprm.cdelt` property, this works even when the header specifies the linear transformation matrix in one of the alternative ``CDi_ja`` or ``CROTAia`` forms. This is useful when you want access to the linear transformation matrix, but don't care how it was specified in the header. """ get_pc = """ get_pc() -> numpy.ndarray Returns the ``PC`` matrix in read-only form as ``double array[naxis][naxis]``. Unlike the `~astropy.wcs.Wcsprm.pc` property, this works even when the header specifies the linear transformation matrix in one of the alternative ``CDi_ja`` or ``CROTAia`` forms. This is useful when you want access to the linear transformation matrix, but don't care how it was specified in the header. """ get_ps = """ get_ps() -> list Returns ``PSi_ma`` keywords for each *i* and *m* as list of tuples. Returns ------- ps : list Returned as a list of tuples of the form (*i*, *m*, *value*): - *i*: int. Axis number, as in ``PSi_ma``, (i.e. 1-relative) - *m*: int. Parameter number, as in ``PSi_ma``, (i.e. 0-relative) - *value*: string. Parameter value. See also -------- astropy.wcs.Wcsprm.set_ps : Set ``PSi_ma`` values """ get_pv = """ get_pv() -> list Returns ``PVi_ma`` keywords for each *i* and *m* as list of tuples. Returns ------- sequence of tuple Returned as a list of tuples of the form (*i*, *m*, *value*): - *i*: int. Axis number, as in ``PVi_ma``, (i.e. 1-relative) - *m*: int. Parameter number, as in ``PVi_ma``, (i.e. 0-relative) - *value*: string. Parameter value. See also -------- astropy.wcs.Wcsprm.set_pv : Set ``PVi_ma`` values Notes ----- Note that, if they were not given, `~astropy.wcs.Wcsprm.set` resets the entries for ``PVi_1a``, ``PVi_2a``, ``PVi_3a``, and ``PVi_4a`` for longitude axis *i* to match (``phi_0``, ``theta_0``), the native longitude and latitude of the reference point given by ``LONPOLEa`` and ``LATPOLEa``. """ has_cd = """ has_cd() -> bool Returns `True` if ``CDi_ja`` is present. ``CDi_ja`` is an alternate specification of the linear transformation matrix, maintained for historical compatibility. Matrix elements in the IRAF convention are equivalent to the product ``CDi_ja = CDELTia * PCi_ja``, but the defaults differ from that of the ``PCi_ja`` matrix. If one or more ``CDi_ja`` keywords are present then all unspecified ``CDi_ja`` default to zero. If no ``CDi_ja`` (or ``CROTAia``) keywords are present, then the header is assumed to be in ``PCi_ja`` form whether or not any ``PCi_ja`` keywords are present since this results in an interpretation of ``CDELTia`` consistent with the original FITS specification. While ``CDi_ja`` may not formally co-exist with ``PCi_ja``, it may co-exist with ``CDELTia`` and ``CROTAia`` which are to be ignored. See also -------- astropy.wcs.Wcsprm.cd : Get the raw ``CDi_ja`` values. """ has_cdi_ja = """ has_cdi_ja() -> bool Alias for `~astropy.wcs.Wcsprm.has_cd`. Maintained for backward compatibility. """ has_crota = """ has_crota() -> bool Returns `True` if ``CROTAia`` is present. ``CROTAia`` is an alternate specification of the linear transformation matrix, maintained for historical compatibility. In the AIPS convention, ``CROTAia`` may only be associated with the latitude axis of a celestial axis pair. It specifies a rotation in the image plane that is applied *after* the ``CDELTia``; any other ``CROTAia`` keywords are ignored. ``CROTAia`` may not formally co-exist with ``PCi_ja``. ``CROTAia`` and ``CDELTia`` may formally co-exist with ``CDi_ja`` but if so are to be ignored. See also -------- astropy.wcs.Wcsprm.crota : Get the raw ``CROTAia`` values """ has_crotaia = """ has_crotaia() -> bool Alias for `~astropy.wcs.Wcsprm.has_crota`. Maintained for backward compatibility. """ has_pc = """ has_pc() -> bool Returns `True` if ``PCi_ja`` is present. ``PCi_ja`` is the recommended way to specify the linear transformation matrix. See also -------- astropy.wcs.Wcsprm.pc : Get the raw ``PCi_ja`` values """ has_pci_ja = """ has_pci_ja() -> bool Alias for `~astropy.wcs.Wcsprm.has_pc`. Maintained for backward compatibility. """ hgln_obs = """ ``double`` Stonyhurst heliographic longitude of the observer. If undefined, this is set to `None`. """ hglt_obs = """ ``double`` Heliographic latitude (Carrington or Stonyhurst) of the observer (deg). If undefined, this is set to `None`. """ i = """ ``int`` (read-only) Image axis number. """ imgpix_matrix = """ ``double array[2][2]`` (read-only) Inverse of the ``CDELT`` or ``PC`` matrix. Inverse containing the product of the ``CDELTia`` diagonal matrix and the ``PCi_ja`` matrix. """ is_unity = """ is_unity() -> bool Returns `True` if the linear transformation matrix (`~astropy.wcs.Wcsprm.cd`) is unity. """ K = """ ``int array[M]`` (read-only) The lengths of the axes of the coordinate array. An array of length `M` whose elements record the lengths of the axes of the coordinate array and of each indexing vector. """ kind = """ ``str`` (read-only) ``wcstab`` array type. Character identifying the ``wcstab`` array type: - ``'c'``: coordinate array, - ``'i'``: index vector. """ lat = """ ``int`` (read-only) The index into the world coord array containing latitude values. """ latpole = """ ``double`` The native latitude of the celestial pole, ``LATPOLEa`` (deg). """ lattyp = """ ``string`` (read-only) Celestial axis type for latitude. For example, "RA", "DEC", "GLON", "GLAT", etc. extracted from "RA--", "DEC-", "GLON", "GLAT", etc. in the first four characters of ``CTYPEia`` but with trailing dashes removed. """ lng = """ ``int`` (read-only) The index into the world coord array containing longitude values. """ lngtyp = """ ``string`` (read-only) Celestial axis type for longitude. For example, "RA", "DEC", "GLON", "GLAT", etc. extracted from "RA--", "DEC-", "GLON", "GLAT", etc. in the first four characters of ``CTYPEia`` but with trailing dashes removed. """ lonpole = """ ``double`` The native longitude of the celestial pole. ``LONPOLEa`` (deg). """ M = """ ``int`` (read-only) Number of tabular coordinate axes. """ m = """ ``int`` (read-only) ``wcstab`` axis number for index vectors. """ map = """ ``int array[M]`` Association between axes. A vector of length `~astropy.wcs.Tabprm.M` that defines the association between axis *m* in the *M*-dimensional coordinate array (1 <= *m* <= *M*) and the indices of the intermediate world coordinate and world coordinate arrays. When the intermediate and world coordinate arrays contain the full complement of coordinate elements in image-order, as will usually be the case, then ``map[m-1] == i-1`` for axis *i* in the *N*-dimensional image (1 <= *i* <= *N*). In terms of the FITS keywords:: map[PVi_3a - 1] == i - 1. However, a different association may result if the intermediate coordinates, for example, only contains a (relevant) subset of intermediate world coordinate elements. For example, if *M* == 1 for an image with *N* > 1, it is possible to fill the intermediate coordinates with the relevant coordinate element with ``nelem`` set to 1. In this case ``map[0] = 0`` regardless of the value of *i*. """ mix = """ mix(mixpix, mixcel, vspan, vstep, viter, world, pixcrd, origin) Given either the celestial longitude or latitude plus an element of the pixel coordinate, solves for the remaining elements by iterating on the unknown celestial coordinate element using `~astropy.wcs.Wcsprm.s2p`. Parameters ---------- mixpix : int Which element on the pixel coordinate is given. mixcel : int Which element of the celestial coordinate is given. If *mixcel* = ``1``, celestial longitude is given in ``world[self.lng]``, latitude returned in ``world[self.lat]``. If *mixcel* = ``2``, celestial latitude is given in ``world[self.lat]``, longitude returned in ``world[self.lng]``. vspan : (float, float) Solution interval for the celestial coordinate, in degrees. The ordering of the two limits is irrelevant. Longitude ranges may be specified with any convenient normalization, for example ``(-120,+120)`` is the same as ``(240,480)``, except that the solution will be returned with the same normalization, i.e. lie within the interval specified. vstep : float Step size for solution search, in degrees. If ``0``, a sensible, although perhaps non-optimal default will be used. viter : int If a solution is not found then the step size will be halved and the search recommenced. *viter* controls how many times the step size is halved. The allowed range is 5 - 10. world : ndarray World coordinate elements as ``double array[naxis]``. ``world[self.lng]`` and ``world[self.lat]`` are the celestial longitude and latitude, in degrees. Which is given and which returned depends on the value of *mixcel*. All other elements are given. The results will be written to this array in-place. pixcrd : ndarray Pixel coordinates as ``double array[naxis]``. The element indicated by *mixpix* is given and the remaining elements will be written in-place. {} Returns ------- result : dict Returns a dictionary with the following keys: - *phi* (``double array[naxis]``) - *theta* (``double array[naxis]``) - Longitude and latitude in the native coordinate system of the projection, in degrees. - *imgcrd* (``double array[naxis]``) - Image coordinate elements. ``imgcrd[self.lng]`` and ``imgcrd[self.lat]`` are the projected *x*- and *y*-coordinates, in decimal degrees. - *world* (``double array[naxis]``) - Another reference to the *world* argument passed in. Raises ------ MemoryError Memory allocation failed. SingularMatrixError Linear transformation matrix is singular. InconsistentAxisTypesError Inconsistent or unrecognized coordinate axis types. ValueError Invalid parameter value. InvalidTransformError Invalid coordinate transformation parameters. InvalidTransformError Ill-conditioned coordinate transformation parameters. InvalidCoordinateError Invalid world coordinate. NoSolutionError No solution found in the specified interval. See also -------- astropy.wcs.Wcsprm.lat, astropy.wcs.Wcsprm.lng Get the axes numbers for latitude and longitude Notes ----- Initially, the specified solution interval is checked to see if it's a \"crossing\" interval. If it isn't, a search is made for a crossing solution by iterating on the unknown celestial coordinate starting at the upper limit of the solution interval and decrementing by the specified step size. A crossing is indicated if the trial value of the pixel coordinate steps through the value specified. If a crossing interval is found then the solution is determined by a modified form of \"regula falsi\" division of the crossing interval. If no crossing interval was found within the specified solution interval then a search is made for a \"non-crossing\" solution as may arise from a point of tangency. The process is complicated by having to make allowance for the discontinuities that occur in all map projections. Once one solution has been determined others may be found by subsequent invocations of `~astropy.wcs.Wcsprm.mix` with suitably restricted solution intervals. Note the circumstance that arises when the solution point lies at a native pole of a projection in which the pole is represented as a finite curve, for example the zenithals and conics. In such cases two or more valid solutions may exist but `~astropy.wcs.Wcsprm.mix` only ever returns one. Because of its generality, `~astropy.wcs.Wcsprm.mix` is very compute-intensive. For compute-limited applications, more efficient special-case solvers could be written for simple projections, for example non-oblique cylindrical projections. """.format(ORIGIN()) mjdavg = """ ``double`` Modified Julian Date corresponding to ``DATE-AVG``. ``(MJD = JD - 2400000.5)``. An undefined value is represented by NaN. See also -------- astropy.wcs.Wcsprm.mjdobs """ mjdobs = """ ``double`` Modified Julian Date corresponding to ``DATE-OBS``. ``(MJD = JD - 2400000.5)``. An undefined value is represented by NaN. See also -------- astropy.wcs.Wcsprm.mjdavg """ name = """ ``string`` The name given to the coordinate representation ``WCSNAMEa``. """ naxis = """ ``int`` (read-only) The number of axes (pixel and coordinate). Given by the ``NAXIS`` or ``WCSAXESa`` keyvalues. The number of coordinate axes is determined at parsing time, and can not be subsequently changed. It is determined from the highest of the following: 1. ``NAXIS`` 2. ``WCSAXESa`` 3. The highest axis number in any parameterized WCS keyword. The keyvalue, as well as the keyword, must be syntactically valid otherwise it will not be considered. If none of these keyword types is present, i.e. if the header only contains auxiliary WCS keywords for a particular coordinate representation, then no coordinate description is constructed for it. This value may differ for different coordinate representations of the same image. """ nc = """ ``int`` (read-only) Total number of coord vectors in the coord array. Total number of coordinate vectors in the coordinate array being the product K_1 * K_2 * ... * K_M. """ ndim = """ ``int`` (read-only) Expected dimensionality of the ``wcstab`` array. """ obsgeo = """ ``double array[3]`` Location of the observer in a standard terrestrial reference frame. ``OBSGEO-X``, ``OBSGEO-Y``, ``OBSGEO-Z`` (in meters). An undefined value is represented by NaN. """ p0 = """ ``int array[M]`` Interpolated indices into the coordinate array. Vector of length `~astropy.wcs.Tabprm.M` of interpolated indices into the coordinate array such that Upsilon_m, as defined in Paper III, is equal to ``(p0[m] + 1) + delta[m]``. """ p2s = """ p2s(pixcrd, origin) Converts pixel to world coordinates. Parameters ---------- pixcrd : ndarray Array of pixel coordinates as ``double array[ncoord][nelem]``. {} Returns ------- result : dict Returns a dictionary with the following keys: - *imgcrd*: ndarray - Array of intermediate world coordinates as ``double array[ncoord][nelem]``. For celestial axes, ``imgcrd[][self.lng]`` and ``imgcrd[][self.lat]`` are the projected *x*-, and *y*-coordinates, in pseudo degrees. For spectral axes, ``imgcrd[][self.spec]`` is the intermediate spectral coordinate, in SI units. - *phi*: ndarray - Array as ``double array[ncoord]``. - *theta*: ndarray - Longitude and latitude in the native coordinate system of the projection, in degrees, as ``double array[ncoord]``. - *world*: ndarray - Array of world coordinates as ``double array[ncoord][nelem]``. For celestial axes, ``world[][self.lng]`` and ``world[][self.lat]`` are the celestial longitude and latitude, in degrees. For spectral axes, ``world[][self.spec]`` is the intermediate spectral coordinate, in SI units. - *stat*: ndarray - Status return value for each coordinate as ``int array[ncoord]``. ``0`` for success, ``1+`` for invalid pixel coordinate. Raises ------ MemoryError Memory allocation failed. SingularMatrixError Linear transformation matrix is singular. InconsistentAxisTypesError Inconsistent or unrecognized coordinate axis types. ValueError Invalid parameter value. ValueError *x*- and *y*-coordinate arrays are not the same size. InvalidTransformError Invalid coordinate transformation parameters. InvalidTransformError Ill-conditioned coordinate transformation parameters. See also -------- astropy.wcs.Wcsprm.lat, astropy.wcs.Wcsprm.lng Definition of the latitude and longitude axes """.format(ORIGIN()) p4_pix2foc = """ p4_pix2foc(*pixcrd, origin*) -> ``double array[ncoord][nelem]`` Convert pixel coordinates to focal plane coordinates using `distortion paper`_ lookup-table correction. Parameters ---------- pixcrd : ndarray Array of pixel coordinates as ``double array[ncoord][nelem]``. {} Returns ------- foccrd : ndarray Returns an array of focal plane coordinates as ``double array[ncoord][nelem]``. Raises ------ MemoryError Memory allocation failed. ValueError Invalid coordinate transformation parameters. """.format(ORIGIN()) pc = """ ``double array[naxis][naxis]`` The ``PCi_ja`` (pixel coordinate) transformation matrix. The order is:: [[PC1_1, PC1_2], [PC2_1, PC2_2]] For historical compatibility, three alternate specifications of the linear transformations are available in wcslib. The canonical ``PCi_ja`` with ``CDELTia``, ``CDi_ja``, and the deprecated ``CROTAia`` keywords. Although the latter may not formally co-exist with ``PCi_ja``, the approach here is simply to ignore them if given in conjunction with ``PCi_ja``. `~astropy.wcs.Wcsprm.has_pc`, `~astropy.wcs.Wcsprm.has_cd` and `~astropy.wcs.Wcsprm.has_crota` can be used to determine which of these alternatives are present in the header. These alternate specifications of the linear transformation matrix are translated immediately to ``PCi_ja`` by `~astropy.wcs.Wcsprm.set` and are nowhere visible to the lower-level routines. In particular, `~astropy.wcs.Wcsprm.set` resets `~astropy.wcs.Wcsprm.cdelt` to unity if ``CDi_ja`` is present (and no ``PCi_ja``). If no ``CROTAia`` is associated with the latitude axis, `~astropy.wcs.Wcsprm.set` reverts to a unity ``PCi_ja`` matrix. """ phi0 = """ ``double`` The native latitude of the fiducial point. The point whose celestial coordinates are given in ``ref[1:2]``. If undefined (NaN) the initialization routine, `~astropy.wcs.Wcsprm.set`, will set this to a projection-specific default. See also -------- astropy.wcs.Wcsprm.theta0 """ pix2foc = """ pix2foc(*pixcrd, origin*) -> ``double array[ncoord][nelem]`` Perform both `SIP`_ polynomial and `distortion paper`_ lookup-table correction in parallel. Parameters ---------- pixcrd : ndarray Array of pixel coordinates as ``double array[ncoord][nelem]``. {} Returns ------- foccrd : ndarray Returns an array of focal plane coordinates as ``double array[ncoord][nelem]``. Raises ------ MemoryError Memory allocation failed. ValueError Invalid coordinate transformation parameters. """.format(ORIGIN()) piximg_matrix = """ ``double array[2][2]`` (read-only) Matrix containing the product of the ``CDELTia`` diagonal matrix and the ``PCi_ja`` matrix. """ print_contents = """ print_contents() Print the contents of the `~astropy.wcs.Wcsprm` object to stdout. Probably only useful for debugging purposes, and may be removed in the future. To get a string of the contents, use `repr`. """ print_contents_tabprm = """ print_contents() Print the contents of the `~astropy.wcs.Tabprm` object to stdout. Probably only useful for debugging purposes, and may be removed in the future. To get a string of the contents, use `repr`. """ print_contents_wtbarr = """ print_contents() Print the contents of the `~astropy.wcs.Wtbarr` object to stdout. Probably only useful for debugging purposes, and may be removed in the future. To get a string of the contents, use `repr`. """ radesys = """ ``string`` The equatorial or ecliptic coordinate system type, ``RADESYSa``. """ restfrq = """ ``double`` Rest frequency (Hz) from ``RESTFRQa``. An undefined value is represented by NaN. """ restwav = """ ``double`` Rest wavelength (m) from ``RESTWAVa``. An undefined value is represented by NaN. """ row = """ ``int`` (read-only) Table row number. """ rsun_ref = """ ``double`` Reference radius of the Sun used in coordinate calculations (m). If undefined, this is set to `None`. """ s2p = """ s2p(world, origin) Transforms world coordinates to pixel coordinates. Parameters ---------- world : ndarray Array of world coordinates, in decimal degrees, as ``double array[ncoord][nelem]``. {} Returns ------- result : dict Returns a dictionary with the following keys: - *phi*: ``double array[ncoord]`` - *theta*: ``double array[ncoord]`` - Longitude and latitude in the native coordinate system of the projection, in degrees. - *imgcrd*: ``double array[ncoord][nelem]`` - Array of intermediate world coordinates. For celestial axes, ``imgcrd[][self.lng]`` and ``imgcrd[][self.lat]`` are the projected *x*-, and *y*-coordinates, in pseudo \"degrees\". For quadcube projections with a ``CUBEFACE`` axis, the face number is also returned in ``imgcrd[][self.cubeface]``. For spectral axes, ``imgcrd[][self.spec]`` is the intermediate spectral coordinate, in SI units. - *pixcrd*: ``double array[ncoord][nelem]`` - Array of pixel coordinates. Pixel coordinates are zero-based. - *stat*: ``int array[ncoord]`` - Status return value for each coordinate. ``0`` for success, ``1+`` for invalid pixel coordinate. Raises ------ MemoryError Memory allocation failed. SingularMatrixError Linear transformation matrix is singular. InconsistentAxisTypesError Inconsistent or unrecognized coordinate axis types. ValueError Invalid parameter value. InvalidTransformError Invalid coordinate transformation parameters. InvalidTransformError Ill-conditioned coordinate transformation parameters. See also -------- astropy.wcs.Wcsprm.lat, astropy.wcs.Wcsprm.lng Definition of the latitude and longitude axes """.format(ORIGIN()) sense = """ ``int array[M]`` +1 if monotonically increasing, -1 if decreasing. A vector of length `~astropy.wcs.Tabprm.M` whose elements indicate whether the corresponding indexing vector is monotonically increasing (+1), or decreasing (-1). """ set = """ set() Sets up a WCS object for use according to information supplied within it. Note that this routine need not be called directly; it will be invoked by `~astropy.wcs.Wcsprm.p2s` and `~astropy.wcs.Wcsprm.s2p` if necessary. Some attributes that are based on other attributes (such as `~astropy.wcs.Wcsprm.lattyp` on `~astropy.wcs.Wcsprm.ctype`) may not be correct until after `~astropy.wcs.Wcsprm.set` is called. `~astropy.wcs.Wcsprm.set` strips off trailing blanks in all string members. `~astropy.wcs.Wcsprm.set` recognizes the ``NCP`` projection and converts it to the equivalent ``SIN`` projection and it also recognizes ``GLS`` as a synonym for ``SFL``. It does alias translation for the AIPS spectral types (``FREQ-LSR``, ``FELO-HEL``, etc.) but without changing the input header keywords. Raises ------ MemoryError Memory allocation failed. SingularMatrixError Linear transformation matrix is singular. InconsistentAxisTypesError Inconsistent or unrecognized coordinate axis types. ValueError Invalid parameter value. InvalidTransformError Invalid coordinate transformation parameters. InvalidTransformError Ill-conditioned coordinate transformation parameters. """ set_tabprm = """ set() Allocates memory for work arrays. Also sets up the class according to information supplied within it. Note that this routine need not be called directly; it will be invoked by functions that need it. Raises ------ MemoryError Memory allocation failed. InvalidTabularParametersError Invalid tabular parameters. """ set_celprm = """ set() Sets up a ``celprm`` struct according to information supplied within it. Note that this routine need not be called directly; it will be invoked by functions that need it. Raises ------ MemoryError Memory allocation failed. InvalidPrjParametersError Invalid celestial parameters. """ set_ps = """ set_ps(ps) Sets ``PSi_ma`` keywords for each *i* and *m*. Parameters ---------- ps : sequence of tuple The input must be a sequence of tuples of the form (*i*, *m*, *value*): - *i*: int. Axis number, as in ``PSi_ma``, (i.e. 1-relative) - *m*: int. Parameter number, as in ``PSi_ma``, (i.e. 0-relative) - *value*: string. Parameter value. See also -------- astropy.wcs.Wcsprm.get_ps """ set_pv = """ set_pv(pv) Sets ``PVi_ma`` keywords for each *i* and *m*. Parameters ---------- pv : list of tuple The input must be a sequence of tuples of the form (*i*, *m*, *value*): - *i*: int. Axis number, as in ``PVi_ma``, (i.e. 1-relative) - *m*: int. Parameter number, as in ``PVi_ma``, (i.e. 0-relative) - *value*: float. Parameter value. See also -------- astropy.wcs.Wcsprm.get_pv """ sip = """ Get/set the `~astropy.wcs.Sip` object for performing `SIP`_ distortion correction. """ Sip = """ Sip(*a, b, ap, bp, crpix*) The `~astropy.wcs.Sip` class performs polynomial distortion correction using the `SIP`_ convention in both directions. Parameters ---------- a : ndarray The ``A_i_j`` polynomial for pixel to focal plane transformation as ``double array[m+1][m+1]``. Its size must be (*m* + 1, *m* + 1) where *m* = ``A_ORDER``. b : ndarray The ``B_i_j`` polynomial for pixel to focal plane transformation as ``double array[m+1][m+1]``. Its size must be (*m* + 1, *m* + 1) where *m* = ``B_ORDER``. ap : ndarray The ``AP_i_j`` polynomial for pixel to focal plane transformation as ``double array[m+1][m+1]``. Its size must be (*m* + 1, *m* + 1) where *m* = ``AP_ORDER``. bp : ndarray The ``BP_i_j`` polynomial for pixel to focal plane transformation as ``double array[m+1][m+1]``. Its size must be (*m* + 1, *m* + 1) where *m* = ``BP_ORDER``. crpix : ndarray The reference pixel as ``double array[2]``. Notes ----- Shupe, D. L., M. Moshir, J. Li, D. Makovoz and R. Narron. 2005. "The SIP Convention for Representing Distortion in FITS Image Headers." ADASS XIV. """ sip_foc2pix = """ sip_foc2pix(*foccrd, origin*) -> ``double array[ncoord][nelem]`` Convert focal plane coordinates to pixel coordinates using the `SIP`_ polynomial distortion convention. Parameters ---------- foccrd : ndarray Array of focal plane coordinates as ``double array[ncoord][nelem]``. {} Returns ------- pixcrd : ndarray Returns an array of pixel coordinates as ``double array[ncoord][nelem]``. Raises ------ MemoryError Memory allocation failed. ValueError Invalid coordinate transformation parameters. """.format(ORIGIN()) sip_pix2foc = """ sip_pix2foc(*pixcrd, origin*) -> ``double array[ncoord][nelem]`` Convert pixel coordinates to focal plane coordinates using the `SIP`_ polynomial distortion convention. Parameters ---------- pixcrd : ndarray Array of pixel coordinates as ``double array[ncoord][nelem]``. {} Returns ------- foccrd : ndarray Returns an array of focal plane coordinates as ``double array[ncoord][nelem]``. Raises ------ MemoryError Memory allocation failed. ValueError Invalid coordinate transformation parameters. """.format(ORIGIN()) spcfix = """ spcfix() -> int Translates AIPS-convention spectral coordinate types. {``FREQ``, ``VELO``, ``FELO``}-{``OBS``, ``HEL``, ``LSR``} (e.g. ``FREQ-LSR``, ``VELO-OBS``, ``FELO-HEL``) Returns ------- success : int Returns ``0`` for success; ``-1`` if no change required. """ spec = """ ``int`` (read-only) The index containing the spectral axis values. """ specsys = """ ``string`` Spectral reference frame (standard of rest), ``SPECSYSa``. See also -------- astropy.wcs.Wcsprm.ssysobs, astropy.wcs.Wcsprm.velosys """ sptr = """ sptr(ctype, i=-1) Translates the spectral axis in a WCS object. For example, a ``FREQ`` axis may be translated into ``ZOPT-F2W`` and vice versa. Parameters ---------- ctype : str Required spectral ``CTYPEia``, maximum of 8 characters. The first four characters are required to be given and are never modified. The remaining four, the algorithm code, are completely determined by, and must be consistent with, the first four characters. Wildcarding may be used, i.e. if the final three characters are specified as ``\"???\"``, or if just the eighth character is specified as ``\"?\"``, the correct algorithm code will be substituted and returned. i : int Index of the spectral axis (0-relative). If ``i < 0`` (or not provided), it will be set to the first spectral axis identified from the ``CTYPE`` keyvalues in the FITS header. Raises ------ MemoryError Memory allocation failed. SingularMatrixError Linear transformation matrix is singular. InconsistentAxisTypesError Inconsistent or unrecognized coordinate axis types. ValueError Invalid parameter value. InvalidTransformError Invalid coordinate transformation parameters. InvalidTransformError Ill-conditioned coordinate transformation parameters. InvalidSubimageSpecificationError Invalid subimage specification (no spectral axis). """ ssysobs = """ ``string`` Spectral reference frame. The spectral reference frame in which there is no differential variation in the spectral coordinate across the field-of-view, ``SSYSOBSa``. See also -------- astropy.wcs.Wcsprm.specsys, astropy.wcs.Wcsprm.velosys """ ssyssrc = """ ``string`` Spectral reference frame for redshift. The spectral reference frame (standard of rest) in which the redshift was measured, ``SSYSSRCa``. """ sub = """ sub(axes) Extracts the coordinate description for a subimage from a `~astropy.wcs.WCS` object. The world coordinate system of the subimage must be separable in the sense that the world coordinates at any point in the subimage must depend only on the pixel coordinates of the axes extracted. In practice, this means that the ``PCi_ja`` matrix of the original image must not contain non-zero off-diagonal terms that associate any of the subimage axes with any of the non-subimage axes. `sub` can also add axes to a wcsprm object. The new axes will be created using the defaults set by the Wcsprm constructor which produce a simple, unnamed, linear axis with world coordinates equal to the pixel coordinate. These default values can be changed before invoking `set`. Parameters ---------- axes : int or a sequence. - If an int, include the first *N* axes in their original order. - If a sequence, may contain a combination of image axis numbers (1-relative) or special axis identifiers (see below). Order is significant; ``axes[0]`` is the axis number of the input image that corresponds to the first axis in the subimage, etc. Use an axis number of 0 to create a new axis using the defaults. - If ``0``, ``[]`` or ``None``, do a deep copy. Coordinate axes types may be specified using either strings or special integer constants. The available types are: - ``'longitude'`` / ``WCSSUB_LONGITUDE``: Celestial longitude - ``'latitude'`` / ``WCSSUB_LATITUDE``: Celestial latitude - ``'cubeface'`` / ``WCSSUB_CUBEFACE``: Quadcube ``CUBEFACE`` axis - ``'spectral'`` / ``WCSSUB_SPECTRAL``: Spectral axis - ``'stokes'`` / ``WCSSUB_STOKES``: Stokes axis - ``'temporal'`` / ``WCSSUB_TIME``: Time axis (requires ``WCSLIB`` version 7.8 or greater) - ``'celestial'`` / ``WCSSUB_CELESTIAL``: An alias for the combination of ``'longitude'``, ``'latitude'`` and ``'cubeface'``. Returns ------- new_wcs : `~astropy.wcs.WCS` object Raises ------ MemoryError Memory allocation failed. InvalidSubimageSpecificationError Invalid subimage specification (no spectral axis). NonseparableSubimageCoordinateSystemError Non-separable subimage coordinate system. Notes ----- Combinations of subimage axes of particular types may be extracted in the same order as they occur in the input image by combining the integer constants with the 'binary or' (``|``) operator. For example:: wcs.sub([WCSSUB_LONGITUDE | WCSSUB_LATITUDE | WCSSUB_SPECTRAL]) would extract the longitude, latitude, and spectral axes in the same order as the input image. If one of each were present, the resulting object would have three dimensions. For convenience, ``WCSSUB_CELESTIAL`` is defined as the combination ``WCSSUB_LONGITUDE | WCSSUB_LATITUDE | WCSSUB_CUBEFACE``. The codes may also be negated to extract all but the types specified, for example:: wcs.sub([ WCSSUB_LONGITUDE, WCSSUB_LATITUDE, WCSSUB_CUBEFACE, -(WCSSUB_SPECTRAL | WCSSUB_STOKES)]) The last of these specifies all axis types other than spectral or Stokes. Extraction is done in the order specified by ``axes``, i.e. a longitude axis (if present) would be extracted first (via ``axes[0]``) and not subsequently (via ``axes[3]``). Likewise for the latitude and cubeface axes in this example. The number of dimensions in the returned object may be less than or greater than the length of ``axes``. However, it will never exceed the number of axes in the input image. """ tab = """ ``list of Tabprm`` Tabular coordinate objects. A list of tabular coordinate objects associated with this WCS. """ Tabprm = """ A class to store the information related to tabular coordinates, i.e., coordinates that are defined via a lookup table. This class can not be constructed directly from Python, but instead is returned from `~astropy.wcs.Wcsprm.tab`. """ theta0 = """ ``double`` The native longitude of the fiducial point. The point whose celestial coordinates are given in ``ref[1:2]``. If undefined (NaN) the initialization routine, `~astropy.wcs.Wcsprm.set`, will set this to a projection-specific default. See also -------- astropy.wcs.Wcsprm.phi0 """ to_header = """ to_header(relax=False) `to_header` translates a WCS object into a FITS header. The details of the header depends on context: - If the `~astropy.wcs.Wcsprm.colnum` member is non-zero then a binary table image array header will be produced. - Otherwise, if the `~astropy.wcs.Wcsprm.colax` member is set non-zero then a pixel list header will be produced. - Otherwise, a primary image or image extension header will be produced. The output header will almost certainly differ from the input in a number of respects: 1. The output header only contains WCS-related keywords. In particular, it does not contain syntactically-required keywords such as ``SIMPLE``, ``NAXIS``, ``BITPIX``, or ``END``. 2. Deprecated (e.g. ``CROTAn``) or non-standard usage will be translated to standard (this is partially dependent on whether ``fix`` was applied). 3. Quantities will be converted to the units used internally, basically SI with the addition of degrees. 4. Floating-point quantities may be given to a different decimal precision. 5. Elements of the ``PCi_j`` matrix will be written if and only if they differ from the unit matrix. Thus, if the matrix is unity then no elements will be written. 6. Additional keywords such as ``WCSAXES``, ``CUNITia``, ``LONPOLEa`` and ``LATPOLEa`` may appear. 7. The original keycomments will be lost, although `~astropy.wcs.Wcsprm.to_header` tries hard to write meaningful comments. 8. Keyword order may be changed. Keywords can be translated between the image array, binary table, and pixel lists forms by manipulating the `~astropy.wcs.Wcsprm.colnum` or `~astropy.wcs.Wcsprm.colax` members of the `~astropy.wcs.WCS` object. Parameters ---------- relax : bool or int Degree of permissiveness: - `False`: Recognize only FITS keywords defined by the published WCS standard. - `True`: Admit all recognized informal extensions of the WCS standard. - `int`: a bit field selecting specific extensions to write. See :ref:`astropy:relaxwrite` for details. Returns ------- header : str Raw FITS header as a string. """ ttype = """ ``str`` (read-only) ``TTYPEn`` identifying the column of the binary table that contains the wcstab array. """ unitfix = """ unitfix(translate_units='') Translates non-standard ``CUNITia`` keyvalues. For example, ``DEG`` -> ``deg``, also stripping off unnecessary whitespace. Parameters ---------- translate_units : str, optional Do potentially unsafe translations of non-standard unit strings. Although ``\"S\"`` is commonly used to represent seconds, its recognizes ``\"S\"`` formally as Siemens, however rarely that may be translation to ``\"s\"`` is potentially unsafe since the standard used. The same applies to ``\"H\"`` for hours (Henry), and ``\"D\"`` for days (Debye). This string controls what to do in such cases, and is case-insensitive. - If the string contains ``\"s\"``, translate ``\"S\"`` to ``\"s\"``. - If the string contains ``\"h\"``, translate ``\"H\"`` to ``\"h\"``. - If the string contains ``\"d\"``, translate ``\"D\"`` to ``\"d\"``. Thus ``''`` doesn't do any unsafe translations, whereas ``'shd'`` does all of them. Returns ------- success : int Returns ``0`` for success; ``-1`` if no change required. """ velangl = """ ``double`` Velocity angle. The angle in degrees that should be used to decompose an observed velocity into radial and transverse components. An undefined value is represented by NaN. """ velosys = """ ``double`` Relative radial velocity. The relative radial velocity (m/s) between the observer and the selected standard of rest in the direction of the celestial reference coordinate, ``VELOSYSa``. An undefined value is represented by NaN. See also -------- astropy.wcs.Wcsprm.specsys, astropy.wcs.Wcsprm.ssysobs """ velref = """ ``int`` AIPS velocity code. From ``VELREF`` keyword. """ wcs = """ A `~astropy.wcs.Wcsprm` object to perform the basic `wcslib`_ WCS transformation. """ Wcs = """ Wcs(*sip, cpdis, wcsprm, det2im*) Wcs objects amalgamate basic WCS (as provided by `wcslib`_), with `SIP`_ and `distortion paper`_ operations. To perform all distortion corrections and WCS transformation, use ``all_pix2world``. Parameters ---------- sip : `~astropy.wcs.Sip` object or None cpdis : (2,) tuple of `~astropy.wcs.DistortionLookupTable` or None wcsprm : `~astropy.wcs.Wcsprm` det2im : (2,) tuple of `~astropy.wcs.DistortionLookupTable` or None """ Wcsprm = """ Wcsprm(header=None, key=' ', relax=False, naxis=2, keysel=0, colsel=None) `~astropy.wcs.Wcsprm` performs the core WCS transformations. .. note:: The members of this object correspond roughly to the key/value pairs in the FITS header. However, they are adjusted and normalized in a number of ways that make performing the WCS transformation easier. Therefore, they can not be relied upon to get the original values in the header. For that, use `astropy.io.fits.Header` directly. The FITS header parsing enforces correct FITS "keyword = value" syntax with regard to the equals sign occurring in columns 9 and 10. However, it does recognize free-format character (NOST 100-2.0, Sect. 5.2.1), integer (Sect. 5.2.3), and floating-point values (Sect. 5.2.4) for all keywords. .. warning:: Many of the attributes of this class require additional processing when modifying underlying C structure. When needed, this additional processing is implemented in attribute setters. Therefore, for mutable attributes, one should always set the attribute rather than a slice of its current value (or its individual elements) since the latter may lead the class instance to be in an invalid state. For example, attribute ``crpix`` of a 2D WCS' ``Wcsprm`` object ``wcs`` should be set as ``wcs.crpix = [crpix1, crpix2]`` instead of ``wcs.crpix[0] = crpix1; wcs.crpix[1] = crpix2]``. Parameters ---------- header : `~astropy.io.fits.Header`, str, or None. If ``None``, the object will be initialized to default values. key : str, optional The key referring to a particular WCS transform in the header. This may be either ``' '`` or ``'A'``-``'Z'`` and corresponds to the ``\"a\"`` part of ``\"CTYPEia\"``. (*key* may only be provided if *header* is also provided.) relax : bool or int, optional Degree of permissiveness: - `False`: Recognize only FITS keywords defined by the published WCS standard. - `True`: Admit all recognized informal extensions of the WCS standard. - `int`: a bit field selecting specific extensions to accept. See :ref:`astropy:relaxread` for details. naxis : int, optional The number of world coordinates axes for the object. (*naxis* may only be provided if *header* is `None`.) keysel : sequence of flag bits, optional Vector of flag bits that may be used to restrict the keyword types considered: - ``WCSHDR_IMGHEAD``: Image header keywords. - ``WCSHDR_BIMGARR``: Binary table image array. - ``WCSHDR_PIXLIST``: Pixel list keywords. If zero, there is no restriction. If -1, the underlying wcslib function ``wcspih()`` is called, rather than ``wcstbh()``. colsel : sequence of int A sequence of table column numbers used to restrict the keywords considered. `None` indicates no restriction. Raises ------ MemoryError Memory allocation failed. ValueError Invalid key. KeyError Key not found in FITS header. """ wtb = """ ``list of Wtbarr`` objects to construct coordinate lookup tables from BINTABLE. """ Wtbarr = """ Classes to construct coordinate lookup tables from a binary table extension (BINTABLE). This class can not be constructed directly from Python, but instead is returned from `~astropy.wcs.Wcsprm.wtb`. """ zsource = """ ``double`` The redshift, ``ZSOURCEa``, of the source. An undefined value is represented by NaN. """ WcsError = """ Base class of all invalid WCS errors. """ SingularMatrix = """ SingularMatrixError() The linear transformation matrix is singular. """ InconsistentAxisTypes = """ InconsistentAxisTypesError() The WCS header inconsistent or unrecognized coordinate axis type(s). """ InvalidTransform = """ InvalidTransformError() The WCS transformation is invalid, or the transformation parameters are invalid. """ InvalidCoordinate = """ InvalidCoordinateError() One or more of the world coordinates is invalid. """ NoSolution = """ NoSolutionError() No solution can be found in the given interval. """ InvalidSubimageSpecification = """ InvalidSubimageSpecificationError() The subimage specification is invalid. """ NonseparableSubimageCoordinateSystem = """ NonseparableSubimageCoordinateSystemError() Non-separable subimage coordinate system. """ NoWcsKeywordsFound = """ NoWcsKeywordsFoundError() No WCS keywords were found in the given header. """ InvalidTabularParameters = """ InvalidTabularParametersError() The given tabular parameters are invalid. """ InvalidPrjParameters = """ InvalidPrjParametersError() The given projection parameters are invalid. """ mjdbeg = """ ``double`` Modified Julian Date corresponding to ``DATE-BEG``. ``(MJD = JD - 2400000.5)``. An undefined value is represented by NaN. See also -------- astropy.wcs.Wcsprm.mjdbeg """ mjdend = """ ``double`` Modified Julian Date corresponding to ``DATE-END``. ``(MJD = JD - 2400000.5)``. An undefined value is represented by NaN. See also -------- astropy.wcs.Wcsprm.mjdend """ mjdref = """ ``double`` Modified Julian Date corresponding to ``DATE-REF``. ``(MJD = JD - 2400000.5)``. An undefined value is represented by NaN. See also -------- astropy.wcs.Wcsprm.dateref """ bepoch = """ ``double`` Equivalent to ``DATE-OBS``. Expressed as a Besselian epoch. See also -------- astropy.wcs.Wcsprm.dateobs """ jepoch = """ ``double`` Equivalent to ``DATE-OBS``. Expressed as a Julian epoch. See also -------- astropy.wcs.Wcsprm.dateobs """ datebeg = """ ``string`` Date at the start of the observation. In ISO format, ``yyyy-mm-ddThh:mm:ss``. See also -------- astropy.wcs.Wcsprm.datebeg """ dateend = """ ``string`` Date at the end of the observation. In ISO format, ``yyyy-mm-ddThh:mm:ss``. See also -------- astropy.wcs.Wcsprm.dateend """ dateref = """ ``string`` Date of a reference epoch relative to which other time measurements refer. See also -------- astropy.wcs.Wcsprm.dateref """ timesys = """ ``string`` Time scale (UTC, TAI, etc.) in which all other time-related auxiliary header values are recorded. Also defines the time scale for an image axis with CTYPEia set to 'TIME'. See also -------- astropy.wcs.Wcsprm.timesys """ trefpos = """ ``string`` Location in space where the recorded time is valid. See also -------- astropy.wcs.Wcsprm.trefpos """ trefdir = """ ``string`` Reference direction used in calculating a pathlength delay. See also -------- astropy.wcs.Wcsprm.trefdir """ timeunit = """ ``string`` Time units in which the following header values are expressed: ``TSTART``, ``TSTOP``, ``TIMEOFFS``, ``TIMSYER``, ``TIMRDER``, ``TIMEDEL``. It also provides the default value for ``CUNITia`` for time axes. See also -------- astropy.wcs.Wcsprm.trefdir """ plephem = """ ``string`` The Solar System ephemeris used for calculating a pathlength delay. See also -------- astropy.wcs.Wcsprm.plephem """ tstart = """ ``double`` equivalent to DATE-BEG expressed as a time in units of TIMEUNIT relative to DATEREF+TIMEOFFS. See also -------- astropy.wcs.Wcsprm.tstop """ tstop = """ ``double`` equivalent to DATE-END expressed as a time in units of TIMEUNIT relative to DATEREF+TIMEOFFS. See also -------- astropy.wcs.Wcsprm.tstart """ telapse = """ ``double`` equivalent to the elapsed time between DATE-BEG and DATE-END, in units of TIMEUNIT. See also -------- astropy.wcs.Wcsprm.tstart """ timeoffs = """ ``double`` Time offset, which may be used, for example, to provide a uniform clock correction for times referenced to DATEREF. See also -------- astropy.wcs.Wcsprm.timeoffs """ timsyer = """ ``double`` the absolute error of the time values, in units of TIMEUNIT. See also -------- astropy.wcs.Wcsprm.timrder """ timrder = """ ``double`` the accuracy of time stamps relative to each other, in units of TIMEUNIT. See also -------- astropy.wcs.Wcsprm.timsyer """ timedel = """ ``double`` the resolution of the time stamps. See also -------- astropy.wcs.Wcsprm.timedel """ timepixr = """ ``double`` relative position of the time stamps in binned time intervals, a value between 0.0 and 1.0. See also -------- astropy.wcs.Wcsprm.timepixr """ obsorbit = """ ``string`` URI, URL, or name of an orbit ephemeris file giving spacecraft coordinates relating to TREFPOS. See also -------- astropy.wcs.Wcsprm.trefpos """ xposure = """ ``double`` effective exposure time in units of TIMEUNIT. See also -------- astropy.wcs.Wcsprm.timeunit """ czphs = """ ``double array[naxis]`` The time at the zero point of a phase axis, ``CSPHSia``. An undefined value is represented by NaN. """ cperi = """ ``double array[naxis]`` period of a phase axis, CPERIia. An undefined value is represented by NaN. """