Using and Designing Coordinate Frames¶
In astropy.coordinates
, as outlined in the
Overview of astropy.coordinates concepts, subclasses of BaseCoordinateFrame
(“frame
classes”) define particular coordinate frames. They can (but do not
have to) contain representation objects storing the actual coordinate
data. The actual coordinate transformations are defined as functions
that transform representations between frame classes. This approach
serves to separate high-level user functionality (see Using the SkyCoord High-level Class)
and details of how the coordinates are actually stored (see
Using and Designing Coordinate Representations) from the definition of frames and how they are
transformed.
Using Frame Objects¶
Frames without Data¶
Frame objects have two distinct (but related) uses. The first is storing the information needed to uniquely define a frame (e.g., equinox, observation time). This information is stored on the frame objects as (read-only) Python attributes, which are set when the object is first created:
>>> from astropy.coordinates import ICRS, FK5
>>> FK5(equinox='J1975')
<FK5 Frame (equinox=J1975.000)>
>>> ICRS() # has no attributes
<ICRS Frame>
>>> FK5() # uses default equinox
<FK5 Frame (equinox=J2000.000)>
The specific names of attributes available for a particular frame (and
their default values) are available as the class method
get_frame_attr_names
:
>>> FK5.get_frame_attr_names()
OrderedDict([('equinox', <Time object: scale='utc' format='jyear_str' value=J2000.000>)])
You can access any of the attributes on a frame by using standard Python
attribute access. Note that for cases like equinox
, which are time
inputs, if you pass in any unambiguous time string, it will be converted
into an Time
object with UTC scale (see
Inferring input format):
>>> f = FK5(equinox='J1975')
>>> f.equinox
<Time object: scale='utc' format='jyear_str' value=J1975.000>
>>> f = FK5(equinox='2011-05-15T12:13:14')
>>> f.equinox
<Time object: scale='utc' format='isot' value=2011-05-15T12:13:14.000>
Frames with Data¶
The second use for frame objects is to store actual realized coordinate
data for frames like those described above. In this use, it is similar
to the SkyCoord
class, and in fact, the SkyCoord
class internally
uses the frame classes as its implementation. However, the frame
classes have fewer “convenience” features, thereby keeping the
implementation of frame classes simple. As such, they are created
similarly to SkyCoord
object. The simplest way is to use
with keywords appropriate for the frame (e.g. ra
and dec
for
equatorial systems):
>>> from astropy import units as u
>>> ICRS(ra=1.1*u.deg, dec=2.2*u.deg)
<ICRS Coordinate: (ra, dec) in deg
(1.1, 2.2)>
>>> FK5(ra=1.1*u.deg, dec=2.2*u.deg, equinox='J1975')
<FK5 Coordinate (equinox=J1975.000): (ra, dec) in deg
(1.1, 2.2)>
These same attributes can be used to access the data in the frames, as
Angle
objects (or Angle
subclasses):
>>> coo = ICRS(ra=1.1*u.deg, dec=2.2*u.deg)
>>> coo.ra
<Longitude 1.1 deg>
>>> coo.ra.value
1.1
>>> coo.ra.to(u.hourangle)
<Longitude 0.07333333 hourangle>
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 attribute name on the representation
class:
>>> import astropy.units as u
>>> icrs = ICRS(1*u.deg, 2*u.deg)
>>> icrs.representation_type
<class 'astropy.coordinates.representation.SphericalRepresentation'>
>>> icrs.representation_component_names
OrderedDict([('ra', 'lon'), ('dec', 'lat'), ('distance', 'distance')])
One can get the data in a different representation if needed:
>>> icrs.represent_as('cartesian')
<CartesianRepresentation (x, y, z) [dimensionless]
(0.99923861, 0.01744177, 0.0348995)>
Note
In previous versions of Astropy, both the frame attribute and the argument
to frame classes that are now named representation_type
used to be
simply representation
. The name of this attribute/argument is confusing
as it points to the representation class, not the object containing the
underlying frame data (this is accessed via the frame attribute .data
).
To clarify, we have renamed representation
to representation_type
.
In this version 3.0, we have only changed the references to this attribute
in the documentation. In the next major version, we will issue a deprecation
warning. In two major versions, we will remove the .representation
attribute and representation=
argument.
The representation of the coordinate object can also be changed directly, 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: (1) the object prints itself in accord with the new representation,
and (2) 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.:
>>> from astropy.coordinates import CartesianRepresentation
>>> icrs.representation_type = CartesianRepresentation
>>> icrs
<ICRS Coordinate: (x, y, z) [dimensionless]
(0.99923861, 0.01744177, 0.0348995)>
>>> icrs.x
<Quantity 0.99923861>
The representation can also be set at the time of creating a coordinate and affects the set of keywords used to supply the coordinate data. For example to create a coordinate with cartesian data do:
>>> ICRS(x=1*u.kpc, y=2*u.kpc, z=3*u.kpc, representation_type='cartesian')
<ICRS Coordinate: (x, y, z) in kpc
(1., 2., 3.)>
For more information about the use of representations in coordinates see the Representations section, and for details about the representations themselves see Using and Designing Coordinate Representations.
There are two other ways to create frame classes with coordinates. A representation class can be passed in directly at creation, along with any frame attributes required:
>>> from astropy.coordinates import SphericalRepresentation
>>> rep = SphericalRepresentation(lon=1.1*u.deg, lat=2.2*u.deg, distance=3.3*u.kpc)
>>> FK5(rep, equinox='J1975')
<FK5 Coordinate (equinox=J1975.000): (ra, dec, distance) in (deg, deg, kpc)
(1.1, 2.2, 3.3)>
A final way is to create a frame object from an already existing frame
(either one with or without data), using the realize_frame
method. This
will yield a frame with the same attributes, but new data:
>>> f1 = FK5(equinox='J1975')
>>> f1
<FK5 Frame (equinox=J1975.000)>
>>> rep = SphericalRepresentation(lon=1.1*u.deg, lat=2.2*u.deg, distance=3.3*u.kpc)
>>> f1.realize_frame(rep)
<FK5 Coordinate (equinox=J1975.000): (ra, dec, distance) in (deg, deg, kpc)
(1.1, 2.2, 3.3)>
You can check if a frame object has data using the has_data
attribute, and
if it is preset, it can be accessed from the data
attribute:
>>> ICRS().has_data
False
>>> cooi = ICRS(ra=1.1*u.deg, dec=2.2*u.deg)
>>> cooi.has_data
True
>>> cooi.data
<UnitSphericalRepresentation (lon, lat) in deg
(1.1, 2.2)>
All of the above methods can also accept array data (in the form of
class:Quantity
, or other Python sequences) to create arrays of
coordinates:
>>> ICRS(ra=[1.5, 2.5]*u.deg, dec=[3.5, 4.5]*u.deg)
<ICRS Coordinate: (ra, dec) in deg
[(1.5, 3.5), (2.5, 4.5)]>
If you pass in mixed arrays and scalars, the arrays will be broadcast over the scalars appropriately:
>>> ICRS(ra=[1.5, 2.5]*u.deg, dec=[3.5, 4.5]*u.deg, distance=5*u.kpc)
<ICRS Coordinate: (ra, dec, distance) in (deg, deg, kpc)
[(1.5, 3.5, 5.), (2.5, 4.5, 5.)]>
Similar broadcasting happens if you transform to another frame. E.g.:
>>> import numpy as np
>>> from astropy.coordinates import EarthLocation, AltAz
>>> coo = ICRS(ra=180.*u.deg, dec=51.477811*u.deg)
>>> lf = AltAz(location=EarthLocation.of_site('greenwich'),
... obstime=['2012-03-21T00:00:00', '2012-06-21T00:00:00'])
>>> lcoo = coo.transform_to(lf) # this can load finals2000A.all
>>> lcoo
<AltAz Coordinate (obstime=['2012-03-21T00:00:00.000' '2012-06-21T00:00:00.000'], location=(3980608.9024681724, -102.47522910648239, 4966861.273100675) m, pressure=0.0 hPa, temperature=0.0 deg_C, relative_humidity=0.0, obswl=1.0 micron): (az, alt) in deg
[( 94.71264944, 89.21424252), (307.69488825, 37.98077771)]>
Above, the shapes – ()
for coo
and (2,)
for lf
– were
broadcast against each other. If you wished to determine the positions for a
set of coordinates, you’d need to make sure that the shapes allowed this:
>>> coo2 = ICRS(ra=[180., 225., 270.]*u.deg, dec=[51.5, 0., 51.5]*u.deg)
>>> coo2.transform_to(lf)
Traceback (most recent call last):
...
ValueError: operands could not be broadcast together...
>>> coo2.shape
(3,)
>>> lf.shape
(2,)
>>> lf2 = lf[:, np.newaxis]
>>> lf2.shape
(2, 1)
>>> coo2.transform_to(lf2)
<AltAz Coordinate (obstime=[['2012-03-21T00:00:00.000' '2012-03-21T00:00:00.000'
'2012-03-21T00:00:00.000']
['2012-06-21T00:00:00.000' '2012-06-21T00:00:00.000'
'2012-06-21T00:00:00.000']], location=(3980608.9024681724, -102.47522910648239, 4966861.273100675) m, pressure=0.0 hPa, temperature=0.0 deg_C, relative_humidity=0.0, obswl=1.0 micron): (az, alt) in deg
[[( 93.09845202, 89.21613119), (126.85789652, 25.46600543),
( 51.37993229, 37.18532521)],
[(307.71713699, 37.99437658), (231.37407871, 26.36768329),
( 85.42187335, 89.69297997)]]>
Note
One sees that frames without data have a shape
that is determined by
their frame attributes. For frames with data the shape
always is that
of the data; any non-scalar attributes are broadcast to have matching shape
(as can be seen for obstime
in the last line above).
Transforming between Frames¶
To transform a frame object with data into another frame, use the
transform_to
method of an object, and provide it the frame you wish to
transform to. This frame can either be a frame class, in which case
the default attributes will be used, or a frame object (with or without
data):
>>> cooi = ICRS(1.5*u.deg, 2.5*u.deg)
>>> cooi.transform_to(FK5)
<FK5 Coordinate (equinox=J2000.000): (ra, dec) in deg
(1.50000661, 2.50000238)>
>>> cooi.transform_to(FK5(equinox='J1975'))
<FK5 Coordinate (equinox=J1975.000): (ra, dec) in deg
(1.17960348, 2.36085321)>
The Reference/API includes a list of all of the frames built
into astropy.coordinates
, as well as the defined transformations between
them. Any transformation that has a valid path, even if it passes through
other frames, can be transformed to. To programmatically check for or
manipulate transformations, see the TransformGraph
documentation.
Defining a New Frame¶
Users can add new coordinate frames by creating new classes that are subclasses
of BaseCoordinateFrame
. Detailed instructions for
subclassing are in the docstrings for that class. The key aspects are to
define the class attributes default_representation
and
frame_specific_representation_info
along with frame attributes as
Attribute
class instances (or subclasses like
TimeAttribute
). If these are
defined, there is often no need to define an __init__
function, as the
initializer in BaseCoordinateFrame
will probably behave
the way you want. As an example:
>>> from astropy.coordinates import BaseCoordinateFrame, Attribute, TimeAttribute, RepresentationMapping
>>> import astropy.coordinates.representation as r
>>> class MyFrame(BaseCoordinateFrame):
... # Specify how coordinate values are represented when outputted
... default_representation = r.SphericalRepresentation
...
... # Specify overrides to the default names and units for all available
... # representations (subclasses of BaseRepresentation).
... frame_specific_representation_info = {
... r.SphericalRepresentation: [RepresentationMapping(reprname='lon', framename='R', defaultunit=u.rad),
... RepresentationMapping(reprname='lat', framename='D', defaultunit=u.rad),
... RepresentationMapping(reprname='distance', framename='DIST', defaultunit=None)],
... r.UnitSphericalRepresentation: [RepresentationMapping(reprname='lon', framename='R', defaultunit=u.rad),
... RepresentationMapping(reprname='lat', framename='D', defaultunit=u.rad)],
... r.CartesianRepresentation: [RepresentationMapping(reprname='x', framename='X'),
... RepresentationMapping(reprname='y', framename='Y'),
... RepresentationMapping(reprname='z', framename='Z')]
... }
...
... # Specify frame attributes required to fully specify the frame
... location = Attribute(default=None)
... equinox = TimeAttribute(default='B1950')
... obstime = TimeAttribute(default=None, secondary_attribute='equinox')
>>> c = MyFrame(R=10*u.deg, D=20*u.deg)
>>> c
<MyFrame Coordinate (location=None, equinox=B1950.000, obstime=B1950.000): (R, D) in rad
(0.17453293, 0.34906585)>
>>> c.equinox
<Time object: scale='utc' format='byear_str' value=B1950.000>
If you also want to support velocity data in your coordinate frame, see the velocities documentation at Creating frame objects with velocity data.
You can also define arbitrary methods for any added functionality you
want your frame to have that’s unique to that frame. These methods will
be available in any SkyCoord
that is created using your user-defined
frame.
For examples of defining frame classes, the first place to look is
probably the source code for the frames that are included in astropy
(available at astropy.coordinates.builtin_frames
). These are not
“magic” in any way, and use all the same API and features available to
user-created frames.
Examples:
See also Create a new coordinate class (for the Sagittarius stream) for a more annotated example of defining a new coordinate frame.
Customizing Display of Attributes¶
While the default repr
for coordinate frames is suitable for most cases, you may want
to customize how frame attributes are displayed in certain cases. To do this you can
define a method named _astropy_repr_in_frame
. This method should be defined on the
the object that’s set to the frame attribute itself, not the
Attribute
descriptor.
For example, you could have an object Spam
which you have as an attribute of your frame:
>>> class Spam:
... def _astropy_repr_in_frame(self):
... return "<A can of Spam>"
If your frame has this class as an attribute:
>>> class Egg(BaseCoordinateFrame):
... can = Attribute(default=Spam())
When it is displayed by the frame it will use the result of _astropy_repr_in_frame
:
>>> Egg()
<Egg Frame (can=<A can of Spam>)>
Defining Transformations¶
A frame may not be too useful without a way to transform coordinates
defined in it to or from other frames. Fortunately,
astropy.coordinates
provides a framework to do just that. The key
concept for these transformations is the frame transform graph,
available as astropy.coordinates.frame_transform_graph
, an instance of
the TransformGraph
class. This graph (in the
“graph theory” sense, not “plot”), stores all the transformations
between all of the builtin frames, as well as tools for finding shortest
paths through this graph to transform from any frame to any other. All
of the power of this graph is available to user-created frames as well, meaning
that once you define even one transform from your frame to some frame in
the graph, coordinates defined in your frame can be transformed to
any other frame in the graph.
The transforms themselves are represented as
CoordinateTransform
objects or their subclasses. The useful
subclasses/types of transformations are:
-
A transform that is defined as a function that takes a frame object of one frame class and returns an object of another class.
-
A transformation that includes a linear matrix operation and a translation (vector offset). These transformations are defined by a 3x3 matrix and a 3-vector for the offset (supplied as a Cartesian representation). The transformation is applied to the Cartesian representation of one frame and transforms into the Cartesian representation of the target frame.
-
The matrix transforms are
AffineTransform
’s without a translation, i.e. a rotation. The static version is for the case where the matrix is independent of the frame attributes (e.g., the ICRS->FK5 transformation, because ICRS has no frame attributes). The dynamic case is for transformations where the transformation matrix depends on the frame attributes of either the to or from frame.
Generally, it is not necessary to use these classes directly. Instead,
use methods on frame_transform_graph
that can be used as function
decorators. Then just define functions that either do the actual
transformation (for FunctionTransform), or that compute the necessary
transformation matrices to transform. Then decorate the functions to
register these transformations with the frame transform graph:
from astropy.coordinates import frame_transform_graph
@frame_transform_graph.transform(DynamicMatrixTransform, ICRS, FK5)
def icrs_to_fk5(icrscoord, fk5frame):
...
@frame_transform_graph.transform(DynamicMatrixTransform, FK5, ICRS)
def fk5_to_icrs(fk5coord, icrsframe):
...
If the transformation to your coordinate frame of interest is not
representable by a matrix operation, you can also specify a function to do
the actual transformation, and pass the
FunctionTransform
class to the transform graph
decorator instead:
@frame_transform_graph.transform(FunctionTransform, FK4NoETerms, FK4)
def fk4_no_e_to_fk4(fk4noecoord, fk4frame):
...
Furthermore, the frame_transform_graph
does some caching and
optimization to speed up transformations after the first attempt to go
from one frame to another, and shortcuts steps where relevant (for
example, combining multiple static matrix transforms into a single
matrix). Hence, in general, it is better to define whatever are the
most natural transformations for a user-defined frame, rather than
worrying about optimizing or caching a transformation to speed up the
process.
For a demonstration of how to define transformation functions that also work for transforming velocity components, see Transforming frames with velocities.