.. _astropy-coordinates-high-level: Using the SkyCoord High-Level Class *********************************** The |SkyCoord| class provides a simple and flexible user interface for celestial coordinate representation, manipulation, and transformation between coordinate frames. This is a high-level class that serves as a wrapper around the low-level coordinate frame classes like `~astropy.coordinates.ICRS` and `~astropy.coordinates.FK5` which do most of the heavy lifting. The key distinctions between |SkyCoord| and the low-level classes (:doc:`frames`) are as follows: - The |SkyCoord| object can maintain the union of frame attributes for all built-in and user-defined coordinate frames in the ``astropy.coordinates.frame_transform_graph``. Individual frame classes hold only the required attributes (e.g., equinox, observation time, or observer location) for that frame. This means that a transformation from `~astropy.coordinates.FK4` (with equinox and observation time) to `~astropy.coordinates.ICRS` (with neither) and back to `~astropy.coordinates.FK4` via the low-level classes would not remember the original equinox and observation time. Since the |SkyCoord| object stores all attributes, such a round-trip transformation will return to the same coordinate object. - The |SkyCoord| class is more flexible with inputs to accommodate a wide variety of user preferences and available data formats, whereas the frame classes expect to receive quantity-like objects with angular units. - The |SkyCoord| class has a number of convenience methods that are useful in typical analysis. - At present, |SkyCoord| objects can use only coordinate frames that have transformations defined in the ``astropy.coordinates.frame_transform_graph`` transform graph object. Creating SkyCoord Objects ========================= The |SkyCoord| class accepts a wide variety of inputs for initialization. At a minimum, these must provide one or more celestial coordinate values with unambiguous units. Typically you must also specify the coordinate frame, though this is not required. Common patterns are shown below. In this description the values in upper case like ``COORD`` or ``FRAME`` represent inputs which are described in detail in the `Initialization Syntax`_ section. Elements in square brackets like ``[unit=UNIT]`` are optional. :: SkyCoord(COORD, [FRAME], keyword_args ...) SkyCoord(LON, LAT, [frame=FRAME], [unit=UNIT], keyword_args ...) SkyCoord([FRAME], =LON, =LAT, keyword_args ...) The examples below illustrate common ways of initializing a |SkyCoord| object. These all reflect initializing using spherical coordinates, which is the default for all built-in frames. In order to understand working with coordinates using a different representation, such as Cartesian or cylindrical, see the section on `Representations`_. First, some imports:: >>> from astropy.coordinates import SkyCoord # High-level coordinates >>> from astropy.coordinates import ICRS, Galactic, FK4, FK5 # Low-level frames >>> from astropy.coordinates import Angle, Latitude, Longitude # Angles >>> import astropy.units as u >>> import numpy as np Examples -------- .. EXAMPLE START Initializing SkyCoord Objects Using Spherical Coordinates The coordinate values and frame specification can be provided using positional and keyword arguments. First we show positional arguments for RA and Dec:: >>> SkyCoord(10, 20, unit='deg') # Defaults to ICRS # doctest: +FLOAT_CMP >>> SkyCoord([1, 2, 3], [-30, 45, 8], frame='icrs', unit='deg') # doctest: +FLOAT_CMP Notice that the first example above does not explicitly give a frame. In this case, the default is taken to be the ICRS system (approximately correct for "J2000" equatorial coordinates). It is always better to explicitly specify the frame when it is known to be ICRS, however, as anyone reading the code will be better able to understand the intent. String inputs in common formats are acceptable, and the frame can be supplied as either a class type like `~astropy.coordinates.FK4`, an instance of a frame class, a `~astropy.coordinates.SkyCoord` instance (from which the frame will be extracted), or the lowercase version of a frame name as a string, for example, ``"fk4"``:: >>> coords = ["1:12:43.2 +1:12:43", "1 12 43.2 +1 12 43"] >>> sc = SkyCoord(coords, frame=FK4, unit=(u.hourangle, u.deg), obstime="J1992.21") >>> sc = SkyCoord(coords, frame=FK4(obstime="J1992.21"), unit=(u.hourangle, u.deg)) >>> sc = SkyCoord(coords, frame='fk4', unit='hourangle,deg', obstime="J1992.21") >>> sc = SkyCoord("1h12m43.2s", "+1d12m43s", frame=Galactic) # Units from strings >>> sc = SkyCoord("1h12m43.2s +1d12m43s", frame=Galactic) # Units from string >>> sc = SkyCoord(l="1h12m43.2s", b="+1d12m43s", frame='galactic') >>> sc = SkyCoord("1h12.72m +1d12.71m", frame='galactic') Note that frame instances with data and `~astropy.coordinates.SkyCoord` instances can only be passed as frames using the ``frame=`` keyword argument and not as positional arguments. For representations that have ``ra`` and ``dec`` attributes you can supply a coordinate string in a number of other common formats. Examples include:: >>> sc = SkyCoord("15h17+89d15") >>> sc = SkyCoord("275d11m15.6954s+17d59m59.876s") >>> sc = SkyCoord("8 00 -5 00.6", unit=(u.hour, u.deg)) >>> sc = SkyCoord("J080000.00-050036.00", unit=(u.hour, u.deg)) >>> sc = SkyCoord("J1874221.31+122328.03", unit=u.deg) Astropy `~astropy.units.Quantity`-type objects are acceptable and encouraged as a form of input:: >>> ra = Longitude([1, 2, 3], unit=u.deg) # Could also use Angle >>> dec = np.array([4.5, 5.2, 6.3]) * u.deg # Astropy Quantity >>> sc = SkyCoord(ra, dec, frame='icrs') >>> sc = SkyCoord(ra=ra, dec=dec, frame=ICRS, obstime='2001-01-02T12:34:56') Finally, it is possible to initialize from a low-level coordinate frame object. >>> c = FK4(1 * u.deg, 2 * u.deg) >>> sc = SkyCoord(c, obstime='J2010.11', equinox='B1965') # Override defaults A key subtlety highlighted here is that when low-level objects are created they have certain default attribute values. For instance, the `~astropy.coordinates.FK4` frame uses ``equinox='B1950.0`` and ``obstime=equinox`` as defaults. If this object is used to initialize a |SkyCoord| it is possible to override the low-level object attributes that were not explicitly set. If the coordinate above were created with ``c = FK4(1 * u.deg, 2 * u.deg, equinox='B1960')`` then creating a |SkyCoord| with a different ``equinox`` would raise an exception. .. EXAMPLE END Initialization Syntax --------------------- For spherical representations, which are the most common and are the default input format for all built-in frames, the syntax for |SkyCoord| is given below:: SkyCoord(COORD, [FRAME | frame=FRAME], [unit=UNIT], keyword_args ...) SkyCoord(LON, LAT, [DISTANCE], [FRAME | frame=FRAME], [unit=UNIT], keyword_args ...) SkyCoord([FRAME | frame=FRAME], =LON, =LAT, [unit=UNIT], keyword_args ...) In the above description, elements in all capital letters (e.g., ``FRAME``) describe a user input of that element type. Elements in square brackets are optional. For nonspherical inputs, see the `Representations`_ section. **LON**, **LAT** Longitude and latitude value can be specified as separate positional arguments. The following options are available for longitude and latitude: - Single angle value: - |Quantity| object - Plain numeric value with ``unit`` keyword specifying the unit - Angle string which is formatted for :ref:`angle-creation` of |Longitude| or |Latitude| objects - List or |Quantity| array, or NumPy array of angle values - |Angle|, |Longitude|, or |Latitude| object, which can be scalar or array-valued .. note:: While |SkyCoord| is flexible with respect to specifying longitude and latitude component inputs, the frame classes expect to receive |Quantity|-like objects with angular units (i.e., |Angle| or |Quantity|). For example, when specifying components, the frame classes (e.g., ``ICRS``) must be created as >>> ICRS(0 * u.deg, 0 * u.deg) # doctest: +FLOAT_CMP and other methods of flexible initialization (that work with |SkyCoord|) will not work >>> ICRS(0, 0, unit=u.deg) # doctest: +SKIP UnitTypeError: Longitude instances require units equivalent to 'rad', but no unit was given. **DISTANCE** The distance to the object from the frame center can be optionally specified: - Single distance value: - |Quantity| or `~astropy.coordinates.Distance` object - Plain numeric value for a dimensionless distance - Plain numeric value with ``unit`` keyword specifying the unit - List, or |Quantity|, or `~astropy.coordinates.Distance` array, or NumPy array of angle values **COORD** This input form uses a single object to supply coordinate data. For the case of spherical coordinate frames, the coordinate can include one or more longitude and latitude pairs in one of the following ways: - Single coordinate string with a LON and LAT value separated by a space. The respective values can be any string which is formatted for :ref:`angle-creation` of |Longitude| or |Latitude| objects, respectively. - List or NumPy array of such coordinate strings. - List of (LON, LAT) tuples, where each LON and LAT are scalars (not arrays). - ``N x 2`` NumPy or |Quantity| array of values where the first column is longitude and the second column is latitude, for example, ``[[270, -30], [355, +85]] * u.deg``. - List of (LON, LAT, DISTANCE) tuples. - ``N x 3`` NumPy or |Quantity| array of values where columns are longitude, latitude, and distance, respectively. The input can also be more generalized objects that are not necessarily represented in the standard spherical coordinates: - Coordinate frame object (e.g., ``FK4(1*u.deg, 2*u.deg, obstime='J2012.2')``). - |SkyCoord| object (which just makes a copy of the object). - `~astropy.coordinates.BaseRepresentation` subclass object like `~astropy.coordinates.SphericalRepresentation`, `~astropy.coordinates.CylindricalRepresentation`, or `~astropy.coordinates.CartesianRepresentation`. **FRAME** This can be a `~astropy.coordinates.BaseCoordinateFrame` frame class, an instance of such a class, or the corresponding string alias. The frame classes that are built in to Astropy are `~astropy.coordinates.ICRS`, `~astropy.coordinates.FK5`, `~astropy.coordinates.FK4`, `~astropy.coordinates.FK4NoETerms`, `~astropy.coordinates.Galactic`, and `~astropy.coordinates.AltAz`. The string aliases are lowercase versions of the class name. If the frame is not supplied then you will see a special ``ICRS`` identifier. This indicates that the frame is unspecified and operations that require comparing coordinates (even within that object) are not allowed. **unit=UNIT** The unit specifier can be one of the following: - `~astropy.units.Unit` object, which is an angular unit that is equivalent to ``Unit('radian')``. - Single string with a valid angular unit name. - 2-tuple of `~astropy.units.Unit` objects or string unit names specifying the LON and LAT unit, respectively (e.g., ``('hourangle', 'degree')``). - Single string with two unit names separated by a comma (e.g., ``'hourangle,degree'``). If only a single unit is provided then it applies to both LON and LAT. **Other keyword arguments** In lieu of positional arguments to specify the longitude and latitude, the frame-specific names can be used as keyword arguments: *ra*, *dec*: **LON**, **LAT** values, optional RA and Dec for frames where these are representation, including [FIXME] `~astropy.coordinates.ICRS`, `~astropy.coordinates.FK5`, `~astropy.coordinates.FK4`, and `~astropy.coordinates.FK4NoETerms`. *l*, *b*: **LON**, **LAT** values, optional Galactic ``l`` and ``b`` for the `~astropy.coordinates.Galactic` frame. The following keywords can be specified for any frame: *distance*: distance quantity-like, optional Distance from reference from center to source *obstime*: time-like, optional Time of observation *equinox*: time-like, optional Coordinate frame equinox If custom user-defined frames are included in the transform graph and they have additional frame attributes, then those attributes can also be set via corresponding keyword arguments in the |SkyCoord| initialization. .. _astropy-coordinates-array-operations: Array Operations ================ It is possible to store arrays of coordinates in a |SkyCoord| object, and manipulations done in this way will be orders of magnitude faster than looping over a list of individual |SkyCoord| objects. Examples -------- .. EXAMPLE START Storing Arrays of Coordinates in a SkyCoord Object To store arrays of coordinates in a |SkyCoord| object:: >>> ra = np.linspace(0, 36000, 1001) * u.deg >>> dec = np.linspace(-90, 90, 1001) * u.deg >>> sc_list = [SkyCoord(r, d, frame='icrs') for r, d in zip(ra, dec)] # doctest: +SKIP >>> timeit sc_gal_list = [c.galactic for c in sc_list] # doctest: +SKIP 1 loops, best of 3: 20.4 s per loop >>> sc = SkyCoord(ra, dec, frame='icrs') >>> timeit sc_gal = sc.galactic # doctest: +SKIP 100 loops, best of 3: 21.8 ms per loop .. EXAMPLE END .. EXAMPLE START Array Operations Using SkyCoord In addition to vectorized transformations, you can do the usual array slicing, dicing, and selection using the same methods and attributes that you use for `~numpy.ndarray` instances. Corresponding functions, as well as others that affect the shape, such as `~numpy.atleast_1d` and `~numpy.rollaxis`, work as expected. (The relevant functions have to be explicitly enabled in ``astropy`` source code; let us know if a ``numpy`` function is not supported that you think should work.):: >>> north_mask = sc.dec > 0 >>> sc_north = sc[north_mask] >>> len(sc_north) 500 >>> sc[2:4] # doctest: +FLOAT_CMP >>> sc[500] >>> sc[0:-1:100].reshape(2, 5) >>> np.roll(sc[::100], 1) Note that similarly to the `~numpy.ndarray` methods, all but ``flatten`` try to use new views of the data, with the data copied only if that is impossible (as discussed, for example, in the documentation for NumPy :func:`~numpy.reshape`). .. EXAMPLE END .. _astropy-coordinates-modifying-in-place: Modifying Coordinate Objects In-place ------------------------------------- Coordinate values in a array-valued |SkyCoord| object can be modified in-place (added in astropy 4.1). This requires that the new values be set from an another |SkyCoord| object that is equivalent in all ways except for the actual coordinate data values. In this way, no frame transformations are required and the item setting operation is extremely robust. Specifically, the right hand ``value`` must be strictly consistent with the object being modified: - Identical class - Equivalent frames (`~astropy.coordinates.BaseCoordinateFrame.is_equivalent_frame`) - Identical representation_types - Identical representation differentials keys - Identical frame attributes - Identical "extra" frame attributes (e.g., ``obstime`` for an ICRS coord) .. EXAMPLE START Modifying an Array of Coordinates in a SkyCoord Object To modify an array of coordinates in a |SkyCoord| object use the same syntax for a numpy array:: >>> sc1 = SkyCoord([1, 2] * u.deg, [3, 4] * u.deg) >>> sc2 = SkyCoord(10 * u.deg, 20 * u.deg) >>> sc1[0] = sc2 >>> sc1 .. EXAMPLE END .. EXAMPLE START Inserting Coordinates into a SkyCoord Object You can insert a scalar or array-valued |SkyCoord| object into another compatible |SkyCoord| object:: >>> sc1 = SkyCoord([1, 2] * u.deg, [3, 4] * u.deg) >>> sc2 = SkyCoord(10 * u.deg, 20 * u.deg) >>> sc1.insert(1, sc2) .. EXAMPLE END With the ability to modify a |SkyCoord| object in-place, all of the :ref:`table_operations` such as joining, stacking, and inserting are functional with |SkyCoord| mixin columns (so long as no masking is required). These methods are relatively slow because they require setting from an existing |SkyCoord| object and they perform extensive validation to ensure that the operation is valid. For some applications it may be necessary to take a different lower-level approach which is described in the section :ref:`astropy-coordinates-fast-in-place`. .. warning:: You may be tempted to try an apparently obvious way of modifying a coordinate object in place by updating the component attributes directly, for example ``sc1.ra[1] = 40 * u.deg``. However, while this will *appear* to give a correct result it does not actually modify the underlying representation data. This is related to the current implementation of performance-based caching. The current cache implementation is similarly unable to handle in-place changes to the representation (``.data``) or frame attributes such as ``.obstime``. Attributes ========== The |SkyCoord| object has a number of useful attributes which come in handy. By digging through these we will learn a little bit about |SkyCoord| and how it works. To begin, one of the most important tools for learning about attributes and methods of objects is "TAB-discovery." From within IPython you can type an object name, the period, and then the key to see what is available. This can often be faster than reading the documentation:: >>> sc = SkyCoord(1, 2, frame='icrs', unit='deg', obstime='2013-01-02 14:25:36') >>> sc. # doctest: +SKIP sc.T sc.match_to_catalog_3d sc.altaz sc.match_to_catalog_sky sc.barycentrictrueecliptic sc.name sc.cartesian sc.ndim sc.cirs sc.obsgeoloc sc.copy sc.obsgeovel sc.data sc.obstime sc.dec sc.obswl sc.default_representation sc.position_angle sc.diagonal sc.precessedgeocentric sc.distance sc.pressure sc.equinox sc.ra sc.fk4 sc.ravel sc.fk4noeterms sc.realize_frame sc.fk5 sc.relative_humidity sc.flatten sc.represent_as sc.frame sc.representation_component_names sc.frame_attributes sc.representation_component_units sc.frame_specific_representation_info sc.representation_info sc.from_name sc.reshape sc.from_pixel sc.roll sc.galactic sc.search_around_3d sc.galactocentric sc.search_around_sky sc.galcen_distance sc.separation sc.gcrs sc.separation_3d sc.geocentrictrueecliptic sc.shape sc.get_constellation sc.size sc.get_frame_attr_names sc.skyoffset_frame sc.guess_from_table sc.spherical sc.has_data sc.spherical_offsets_to sc.hcrs sc.squeeze sc.heliocentrictrueecliptic sc.supergalactic sc.icrs sc.swapaxes sc.info sc.take sc.is_equivalent_frame sc.temperature sc.is_frame_attr_default sc.to_pixel sc.is_transformable_to sc.to_string sc.isscalar sc.transform_to sc.itrs sc.transpose sc.location sc.z_sun Here we see many attributes and methods. The most recognizable may be the longitude and latitude attributes which are named ``ra`` and ``dec`` for the ``ICRS`` frame:: >>> sc.ra # doctest: +FLOAT_CMP >>> sc.dec # doctest: +FLOAT_CMP Next, notice that all of the built-in frame names ``icrs``, ``galactic``, ``fk5``, ``fk4``, and ``fk4noeterms`` are there. Through the magic of Python properties, accessing these attributes calls the object `~astropy.coordinates.SkyCoord.transform_to` method appropriately and returns a new |SkyCoord| object in the requested frame:: >>> sc_gal = sc.galactic >>> sc_gal # doctest: +FLOAT_CMP Other attributes you may recognize are ``distance``, ``equinox``, ``obstime``, and ``shape``. Digging Deeper -------------- *[Casual users can skip this section]* After transforming to Galactic, the longitude and latitude values are now labeled ``l`` and ``b``, following the normal convention for Galactic coordinates. How does the object know what to call its values? The answer lies in some less obvious attributes:: >>> sc_gal.representation_component_names {'l': 'lon', 'b': 'lat', 'distance': 'distance'} >>> sc_gal.representation_component_units {'l': Unit("deg"), 'b': Unit("deg")} >>> sc_gal.representation_type Together these tell the object that ``l`` and ``b`` are the longitude and latitude, and that they should both be displayed in units of degrees as a spherical-type coordinate (and not, for example, a Cartesian coordinate). Furthermore, the frame's ``representation_component_names`` attribute defines the coordinate keyword arguments that |SkyCoord| will accept. Another important attribute is ``frame_attributes``, which defines the additional attributes that are required to fully define the frame:: >>> sc_fk4 = SkyCoord(1, 2, frame='fk4', unit='deg') >>> sc_fk4.frame_attributes # doctest: +ELLIPSIS {'equinox': <...TimeAttribute ...>, 'obstime': <...TimeAttribute ...>} This example shows that the `~astropy.coordinates.FK4` frame has two attributes, ``equinox`` and ``obstime``, that are required to fully define the frame. Some trickery is happening here because many of these attributes are actually owned by the underlying coordinate ``frame`` object which does much of the real work. This is the middle layer in the three-tiered system of objects: representation (spherical, Cartesian, etc.), frame (a.k.a. low-level frame class), and |SkyCoord| (a.k.a. high-level class; see :ref:`astropy-coordinates-overview` and :ref:`astropy-coordinates-definitions`):: >>> sc.frame # doctest: +FLOAT_CMP >>> sc.has_data is sc.frame.has_data True >>> sc.frame. # doctest: +SKIP sc.frame.T sc.frame.ra sc.frame.cartesian sc.frame.ravel sc.frame.copy sc.frame.realize_frame sc.frame.data sc.frame.represent_as sc.frame.dec sc.frame.representation sc.frame.default_representation sc.frame.representation_component_names sc.frame.diagonal sc.frame.representation_component_units sc.frame.distance sc.frame.representation_info sc.frame.flatten sc.frame.reshape sc.frame.frame_attributes sc.frame.separation sc.frame.frame_specific_representation_info sc.frame.separation_3d sc.frame.get_frame_attr_names sc.frame.shape sc.frame.has_data sc.frame.size sc.frame.is_equivalent_frame sc.frame.spherical sc.frame.is_frame_attr_default sc.frame.squeeze sc.frame.is_transformable_to sc.frame.swapaxes sc.frame.isscalar sc.frame.take sc.frame.name sc.frame.transform_to sc.frame.ndim sc.frame.transpose >>> sc.frame.name 'icrs' The |SkyCoord| object exposes the ``frame`` object attributes as its own. Though it might seem a tad confusing at first, this is a good thing because it makes |SkyCoord| objects and `~astropy.coordinates.BaseCoordinateFrame` objects behave very similarly and most routines can accept either one as input without much bother (duck typing!). The lowest layer in the stack is the abstract `~astropy.coordinates.UnitSphericalRepresentation` object: >>> sc_gal.frame.data # doctest: +FLOAT_CMP Transformations =============== The topic of transformations is covered in detail in the section on :ref:`astropy-coordinates-transforming`. For completeness, here we will give some examples. Once you have defined your coordinates and the reference frame, you can transform from that frame to another frame. You can do this in a few different ways: if you only want the default version of that frame, you can use attribute-style access (as mentioned previously). For more control, you can use the `~astropy.coordinates.SkyCoord.transform_to` method, which accepts a frame name, frame class, frame instance, or |SkyCoord|. Examples -------- .. EXAMPLE START Transforming Between Frames To transform from one frame to another:: >>> from astropy.coordinates import FK5 >>> sc = SkyCoord(1, 2, frame='icrs', unit='deg') >>> sc.galactic # doctest: +FLOAT_CMP >>> sc.transform_to('fk5') # Same as sc.fk5 and sc.transform_to(FK5) # doctest: +FLOAT_CMP >>> sc.transform_to(FK5(equinox='J1975')) # Transform to FK5 with a different equinox # doctest: +FLOAT_CMP Transforming to a |SkyCoord| instance is a convenient way of ensuring that two coordinates are in the exact same reference frame:: >>> sc2 = SkyCoord(3, 4, frame='fk4', unit='deg', obstime='J1978.123', equinox='B1960.0') >>> sc.transform_to(sc2) # doctest: +FLOAT_CMP .. EXAMPLE END .. _astropy-skycoord-representations: Representations =============== So far we have been using a spherical coordinate representation in all of the examples, and this is the default for the built-in frames. Frequently it is convenient to initialize or work with a coordinate using a different representation such as Cartesian or cylindrical. In this section, we discuss how to initialize an object using a different representation and how to change the representation of an object. For more information about representation objects themselves, see :ref:`astropy-coordinates-representations`. Initialization -------------- Most of what you need to know can be inferred from the examples below and by extrapolating the previous documentation for spherical representations. Initialization requires setting the ``representation_type`` keyword and supplying the corresponding components for that representation. Examples ^^^^^^^^ .. EXAMPLE START Initialization of a SkyCoord Object Using Different Representations To initialize an object using a representation type other than spherical:: >>> c = SkyCoord(x=1, y=2, z=3, unit='kpc', representation_type='cartesian') >>> c # doctest: +FLOAT_CMP >>> c.x, c.y, c.z # doctest: +FLOAT_CMP (, , ) Other variations include:: >>> SkyCoord(1, 2*u.deg, 3, representation_type='cylindrical') # doctest: +FLOAT_CMP >>> SkyCoord(rho=1*u.km, phi=2*u.deg, z=3*u.m, representation_type='cylindrical') # doctest: +FLOAT_CMP >>> SkyCoord(rho=1, phi=2, z=3, unit=(u.km, u.deg, u.m), representation_type='cylindrical') # doctest: +FLOAT_CMP >>> SkyCoord(1, 2, 3, unit=(None, u.deg, None), representation_type='cylindrical') # doctest: +FLOAT_CMP In general terms, the allowed syntax is as follows:: SkyCoord(COORD, [FRAME | frame=FRAME], [unit=UNIT], [representation_type=REPRESENTATION], keyword_args ...) SkyCoord(COMP1, COMP2, [COMP3], [FRAME | frame=FRAME], [unit=UNIT], [representation_type=REPRESENTATION], keyword_args ...) SkyCoord([FRAME | frame=FRAME], =COMP1, =COMP2, =COMP3, [representation_type=REPRESENTATION], [unit=UNIT], keyword_args ...) In this case, the ``keyword_args`` now includes the element ``representation_type=REPRESENTATION``. In the above description, elements in all capital letters (e.g., ``FRAME``) describe a user input of that element type. Elements in square brackets are optional. .. EXAMPLE END **COMP1**, **COMP2**, **COMP3** Component values can be specified as separate positional arguments or as keyword arguments. In this formalism the exact type of allowed input depends on the details of the representation. In general, the following input forms are supported: - Single value: - Component class object - Plain numeric value with ``unit`` keyword specifying the unit - List or component class array, or NumPy array of values Each representation component has a specified class (the "component class") which is used to convert generic input data into a predefined object class with a certain unit. These component classes are expected to be subclasses of the `~astropy.units.Quantity` class. **COORD** This input form uses a single object to supply coordinate data. The coordinate can specify one or more coordinate positions as follows: - List of ``(COMP1, .., COMP)`` tuples, where each component is a scalar (not array) and there are ``M`` components in the representation. Typically there are three components, but some (e.g., `~astropy.coordinates.UnitSphericalRepresentation`) can have fewer. - ``N x M`` NumPy or |Quantity| array of values, where ``N`` is the number of coordinates and ``M`` is the number of components. **REPRESENTATION** The representation can be supplied either as a `~astropy.coordinates.representation.BaseRepresentation` class (e.g., `~astropy.coordinates.CartesianRepresentation`) or as a string name that is simply the class name in lowercase without the ``'representation'`` suffix (e.g., ``'cartesian'``). The rest of the inputs for creating a |SkyCoord| object in the general case are the same as for spherical. Details ------- The available set of representations is dynamic and may change depending on what representation classes have been defined. The built-in representations are: ===================== ======================================================= Name Class ===================== ======================================================= ``spherical`` `~astropy.coordinates.SphericalRepresentation` ``unitspherical`` `~astropy.coordinates.UnitSphericalRepresentation` ``physicsspherical`` `~astropy.coordinates.PhysicsSphericalRepresentation` ``cartesian`` `~astropy.coordinates.CartesianRepresentation` ``cylindrical`` `~astropy.coordinates.CylindricalRepresentation` ===================== ======================================================= Each frame knows about all of the available representations, but different frames may use different names for the same components. A common example is that the `~astropy.coordinates.Galactic` frame uses ``l`` and ``b`` instead of ``ra`` and ``dec`` for the ``lon`` and ``lat`` components of the `~astropy.coordinates.SphericalRepresentation`. For a particular frame, in order to see the full list of representations and how it names all of the components, first make an instance of that frame without any data, and then print the ``representation_info`` property:: >>> ICRS().representation_info # doctest: +SKIP {astropy.coordinates.representation.CartesianRepresentation: {'names': ('x', 'y', 'z'), 'units': (None, None, None)}, astropy.coordinates.representation.SphericalRepresentation: {'names': ('ra', 'dec', 'distance'), 'units': (Unit("deg"), Unit("deg"), None)}, astropy.coordinates.representation.UnitSphericalRepresentation: {'names': ('ra', 'dec'), 'units': (Unit("deg"), Unit("deg"))}, astropy.coordinates.representation.PhysicsSphericalRepresentation: {'names': ('phi', 'theta', 'r'), 'units': (Unit("deg"), Unit("deg"), None)}, astropy.coordinates.representation.CylindricalRepresentation: {'names': ('rho', 'phi', 'z'), 'units': (None, Unit("deg"), None)} } This is a bit messy but it shows that for each representation there is a ``dict`` with two keys: - ``names``: defines how each component is named in that frame. - ``units``: defines the units of each component when output, where ``None`` means to not force a particular unit. For a particular coordinate instance you can use the ``representation_type`` attribute in conjunction with the ``representation_component_names`` attribute to figure out what keywords are accepted by a particular class object. The former will be the representation class the system is expressed in (e.g., spherical for equatorial frames), and the latter will be a dictionary mapping names for that frame to the component name on the representation class:: >>> import astropy.units as u >>> icrs = ICRS(1*u.deg, 2*u.deg) >>> icrs.representation_type >>> icrs.representation_component_names {'ra': 'lon', 'dec': 'lat', 'distance': 'distance'} Changing Representation ----------------------- The representation of the coordinate object can be changed, as shown below. This actually does *nothing* to the object internal data which stores the coordinate values, but it changes the external view of that data in two ways: - The object prints itself in accord with the new representation. - The available attributes change to match those of the new representation (e.g., from ``ra, dec, distance`` to ``x, y, z``). Setting the ``representation_type`` thus changes a *property* of the object (how it appears) without changing the intrinsic object itself which represents a point in 3D space. Examples ^^^^^^^^ .. EXAMPLE START Changing the Representation of a Coordinate Object To change the representation of a coordinate object by setting the ``representation_type`` :: >>> c = SkyCoord(x=1, y=2, z=3, unit='kpc', representation_type='cartesian') >>> c # doctest: +FLOAT_CMP >>> c.representation_type = 'cylindrical' >>> c # doctest: +FLOAT_CMP >>> c.phi.to(u.deg) # doctest: +FLOAT_CMP >>> c.x Traceback (most recent call last): ... AttributeError: 'SkyCoord' object has no attribute 'x' >>> c.representation_type = 'spherical' >>> c # doctest: +FLOAT_CMP >>> c.representation_type = 'unitspherical' >>> c # doctest: +FLOAT_CMP You can also use any representation class to set the representation:: >>> from astropy.coordinates import CartesianRepresentation >>> c.representation_type = CartesianRepresentation Note that if all you want is a particular representation without changing the state of the |SkyCoord| object, you should instead use the ``astropy.coordinates.SkyCoord.represent_as()`` method:: >>> c.representation_type = 'spherical' >>> cart = c.represent_as(CartesianRepresentation) >>> cart # doctest: +FLOAT_CMP >>> c.representation_type .. EXAMPLE END Example 1: Plotting random data in Aitoff projection ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. EXAMPLE START Plotting Random Data in Aitoff Projection This is an example of how to make a plot in the Aitoff projection using data in a |SkyCoord| object. Here, a randomly generated data set will be used. First we need to import the required packages. We use `matplotlib `_ here for plotting and `numpy `_ to get the value of pi and to generate our random data. >>> from astropy import units as u >>> from astropy.coordinates import SkyCoord >>> import numpy as np We now generate random data for visualization. For RA this is done in the range of 0 and 360 degrees (``ra_random``), for DEC between -90 and +90 degrees (``dec_random``). Finally, we multiply these values by degrees to get a `~astropy.units.Quantity` with units of degrees. >>> rng = np.random.default_rng() >>> ra_random = rng.uniform(0, 360, 100) * u.degree >>> dec_random = rng.uniform(-90, 90, 100) * u.degree As the next step, those coordinates are transformed into an `astropy.coordinates` |SkyCoord| object. >>> c = SkyCoord(ra=ra_random, dec=dec_random, frame='icrs') Because matplotlib needs the coordinates in radians and between :math:`-\pi` and :math:`\pi`, not 0 and :math:`2\pi`, we have to convert them. For this purpose the `astropy.coordinates.Angle` object provides a special method, which we use here to wrap at 180: >>> ra_rad = c.ra.wrap_at(180 * u.deg).radian >>> dec_rad = c.dec.radian As a last step, we set up the plotting environment with matplotlib using the Aitoff projection with a specific title, a grid, filled circles as markers with a marker size of 2, and an alpha value of 0.3. We use a figure with an x-y ratio that is well suited for such a projection and we move the title upwards from its usual position to avoid overlap with the axis labels. .. doctest-skip:: >>> import matplotlib.pyplot as plt >>> plt.figure(figsize=(8,4.2)) >>> plt.subplot(111, projection="aitoff") >>> plt.title("Aitoff projection of our random data") >>> plt.grid(True) >>> plt.plot(ra_rad, dec_rad, 'o', markersize=2, alpha=0.3) >>> plt.subplots_adjust(top=0.95,bottom=0.0) >>> plt.show() .. plot:: # This is an example how to make a plot in the Aitoff projection using data # in a SkyCoord object. Here a randomly generated data set will be used. The # final script can be found below. # First we need to import the required packages. We use # `matplotlib `_ here for # plotting and `numpy `_ to get the value of pi and to # generate our random data. from astropy import units as u from astropy.coordinates import SkyCoord import matplotlib.pyplot as plt import numpy as np # We now generate random data for visualization. For RA this is done in the range # of 0 and 360 degrees (``ra_random``), for DEC between -90 and +90 degrees # (``dec_random``). Finally, we multiply these values by degrees to get a # `~astropy.units.Quantity` with units of degrees. rng = np.random.default_rng() ra_random = rng.uniform(0, 360, 100) * u.degree dec_random = rng.uniform(-90, 90, 100) * u.degree # As the next step, those coordinates are transformed into an astropy.coordinates # astropy.coordinates.SkyCoord object. c = SkyCoord(ra=ra_random, dec=dec_random, frame='icrs') # Because matplotlib needs the coordinates in radians and between :math:`-\pi` # and :math:`\pi`, not 0 and :math:`2\pi`, we have to convert them. # For this purpose the `astropy.coordinates.Angle` object provides a special method, # which we use here to wrap at 180: ra_rad = c.ra.wrap_at(180 * u.deg).radian dec_rad = c.dec.radian # As a last step we set up the plotting environment with matplotlib using the # Aitoff projection with a specific title, a grid, filled circles as markers with # a marker size of 2, and an alpha value of 0.3. plt.figure(figsize=(8,4.2)) plt.subplot(111, projection="aitoff") plt.title("Aitoff projection of our random data", y=1.08) plt.grid(True) plt.plot(ra_rad, dec_rad, 'o', markersize=2, alpha=0.3) plt.subplots_adjust(top=0.95, bottom=0.0) plt.show() .. EXAMPLE END Example 2: Plotting star positions in bulge and disk ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. EXAMPLE START Plotting Star Positions in Bulge and Disk This is a more realistic example of how to make a plot in the Aitoff projection using data in a |SkyCoord| object. Here, a randomly generated data set (multivariate normal distribution) for both stars in the bulge and in the disk of a galaxy will be used. Both types will be plotted with different number counts. As in the last example, we first import the required packages. >>> from astropy import units as u >>> from astropy.coordinates import SkyCoord >>> import numpy as np We now generate random data for visualization using ``numpy.random.Generator.multivariate_normal``. >>> rng = np.random.default_rng() >>> disk = rng.multivariate_normal(mean=[0,0,0], cov=np.diag([1,1,0.5]), size=5000) >>> bulge = rng.multivariate_normal(mean=[0,0,0], cov=np.diag([1,1,1]), size=500) >>> galaxy = np.concatenate([disk, bulge]) As the next step, those coordinates are transformed into an `astropy.coordinates` |SkyCoord| object. >>> c_gal = SkyCoord(galaxy, representation_type='cartesian', frame='galactic') >>> c_gal_icrs = c_gal.icrs Again, as in the last example, we need to convert the coordinates in radians and make sure they are between :math:`-\pi` and :math:`\pi`: >>> ra_rad = c_gal_icrs.ra.wrap_at(180 * u.deg).radian >>> dec_rad = c_gal_icrs.dec.radian We use the same plotting setup as in the last example: .. doctest-skip:: >>> import matplotlib.pyplot as plt >>> plt.figure(figsize=(8,4.2)) >>> plt.subplot(111, projection="aitoff") >>> plt.title("Aitoff projection of our random data") >>> plt.grid(True) >>> plt.plot(ra_rad, dec_rad, 'o', markersize=2, alpha=0.3) >>> plt.subplots_adjust(top=0.95,bottom=0.0) >>> plt.show() .. plot:: # This is more realistic example how to make a plot in the Aitoff projection # using data in a SkyCoord object. # Here a randomly generated data set (multivariate normal distribution) # for both stars in the bulge and in the disk of a galaxy # will be used. Both types will be plotted with different number counts. The # final script can be found below. # As in the last example, we first import the required packages. from astropy import units as u from astropy.coordinates import SkyCoord import matplotlib.pyplot as plt import numpy as np # We now generate random data for visualization with # np.random.Generator.multivariate_normal. rng = np.random.default_rng() disk = rng.multivariate_normal(mean=[0,0,0], cov=np.diag([1,1,0.5]), size=5000) bulge = rng.multivariate_normal(mean=[0,0,0], cov=np.diag([1,1,1]), size=500) galaxy = np.concatenate([disk, bulge]) # As the next step, those coordinates are transformed into an astropy.coordinates # astropy.coordinates.SkyCoord object. c_gal = SkyCoord(galaxy, representation_type='cartesian', frame='galactic') c_gal_icrs = c_gal.icrs # Again, as in the last example, we need to convert the coordinates in radians # and make sure they are between :math:`-\pi` and :math:`\pi`: ra_rad = c_gal_icrs.ra.wrap_at(180 * u.deg).radian dec_rad = c_gal_icrs.dec.radian # We use the same plotting setup as in the last example: plt.figure(figsize=(8,4.2)) plt.subplot(111, projection="aitoff") plt.title("Aitoff projection of our random data", y=1.08) plt.grid(True) plt.plot(ra_rad, dec_rad, 'o', markersize=2, alpha=0.3) plt.subplots_adjust(top=0.95,bottom=0.0) plt.show() .. EXAMPLE END .. _coordinates-skycoord-comparing: Comparing SkyCoord Objects ========================== There are two primary ways to compare |SkyCoord| objects to each other. First is checking if the coordinates are within a specified distance of each other. This is what most users should do in their science or processing analysis work because it allows for a tolerance due to floating point representation issues. The second is checking for exact equivalence of two objects down to the bit, which is most useful for developers writing tests. The example below illustrates the floating point issue using the exact equality comparison, where we do a roundtrip transformation FK4 => ICRS => FK4 and then compare:: >>> sc1 = SkyCoord(1*u.deg, 2*u.deg, frame='fk4') >>> sc1.icrs.fk4 == sc1 False Matching Within Tolerance ------------------------- To test if coordinates are within a certain angular distance of one other, use the `~astropy.coordinates.SkyCoord.separation` method:: >>> sc1.icrs.fk4.separation(sc1).to(u.arcsec) # doctest: +SKIP >>> sc1.icrs.fk4.separation(sc1) < 1e-9 * u.arcsec True Exact Equality -------------- Astropy also provides an exact equality operator for coordinates. For example, when comparing, e.g., two |SkyCoord| objects:: >>> left_skycoord == right_skycoord # doctest: +SKIP the right object must be strictly consistent with the left object for comparison: - Identical class - Equivalent frames (`~astropy.coordinates.BaseCoordinateFrame.is_equivalent_frame`) - Identical representation_types - Identical representation differentials keys - Identical frame attributes - Identical "extra" frame attributes (e.g., ``obstime`` for an ICRS coord) In the first example we show simple comparisons using array-valued coordinates:: >>> sc1 = SkyCoord([1, 2]*u.deg, [3, 4]*u.deg) >>> sc2 = SkyCoord([1, 20]*u.deg, [3, 4]*u.deg) >>> sc1 == sc2 # Array-valued comparison array([ True, False]) >>> sc2 == sc2[1] # Broadcasting comparison with a scalar array([False, True]) >>> sc2[0] == sc2[1] # Scalar to scalar comparison False >>> sc1 != sc2 # Not equal array([False, True]) In addition to numerically comparing the representation component data (which may include velocities), the equality comparison includes strict tests that all of the frame attributes like ``equinox`` or ``obstime`` are exactly equal. Any mismatch in attributes will result in an exception being raised. For example:: >>> sc1 = SkyCoord([1, 2]*u.deg, [3, 4]*u.deg) >>> sc2 = SkyCoord([1, 20]*u.deg, [3, 4]*u.deg, obstime='2020-01-01') >>> sc1 == sc2 # doctest: +SKIP ... ValueError: cannot compare: extra frame attribute 'obstime' is not equivalent (perhaps compare the frames directly to avoid this exception) In this example the ``obstime`` attribute is a so-called "extra" frame attribute that does not apply directly to the ICRS coordinate frame. So we could compare with the following, this time using the ``!=`` operator for variety:: >>> sc1.frame != sc2.frame array([False, True]) One slightly special case is comparing two frames that both have no data, where the return value is the same as ``frame1.is_equivalent_frame(frame2)``. For example:: >>> from astropy.coordinates import FK4 >>> FK4() == FK4(obstime='2020-01-01') False .. _skycoord-table-conversion: Converting a SkyCoord to a Table ================================ A |SkyCoord| object can be converted to a |QTable| using its :meth:`~astropy.coordinates.SkyCoord.to_table` method. The attributes of the |SkyCoord| are converted to columns of the table or added to its metadata depending on whether or not they have the same length as the |SkyCoord|. This means that attributes such as ``obstime`` can become columns or metadata:: >>> from astropy.coordinates import SkyCoord >>> from astropy.time import Time >>> sc = SkyCoord(ra=[15, 30], dec=[-70, -50], unit=u.deg, ... obstime=Time([2000, 2010], format='jyear')) >>> t = sc.to_table() >>> t ra dec obstime deg deg float64 float64 Time ------- ------- ------- 15.0 -70.0 2000.0 30.0 -50.0 2010.0 >>> t.meta {'representation_type': 'spherical', 'frame': 'icrs'} >>> sc = SkyCoord(l=[0, 20], b=[20, 0], unit=u.deg, frame='galactic', ... obstime=Time(2000, format='jyear')) >>> t = sc.to_table() >>> t l b deg deg float64 float64 ------- ------- 0.0 20.0 20.0 0.0 >>> t.meta {'obstime':