BaseRepresentation¶

class
astropy.coordinates.
BaseRepresentation
(*args, differentials=None, **kwargs)[source]¶ Bases:
astropy.coordinates.BaseRepresentationOrDifferential
Base for representing a point in a 3D coordinate system.
 Parameters
 comp1, comp2, comp3
Quantity
or subclass The components of the 3D points. The names are the keys and the subclasses the values of the
attr_classes
attribute. differentials
dict
,BaseDifferential
, optional Any differential classes that should be associated with this representation. The input must either be a single
BaseDifferential
subclass instance, or a dictionary with keys set to a string representation of the SI unit with which the differential (derivative) is taken. For example, for a velocity differential on a positional representation, the key would be's'
for seconds, indicating that the derivative is a time derivative. copybool, optional
If
True
(default), arrays will be copied. IfFalse
, arrays will be references, though possibly broadcast to ensure matching shapes.
 comp1, comp2, comp3
Notes
All representation classes should subclass this base representation class, and define an
attr_classes
attribute, adict
which maps component names to the class that creates them. They must also define ato_cartesian
method and afrom_cartesian
class method. By default, transformations are done via the cartesian system, but classes that want to define a smarter transformation path can overload therepresent_as
method. If one wants to use an associated differential class, one should also defineunit_vectors
andscale_factors
methods (see those methods for details).Attributes Summary
A dictionary of differential class instances.
The shape of the instance and underlying arrays.
Methods Summary
cross
(other)Vector cross product of two representations.
dot
(other)Dot product of two representations.
from_representation
(representation)Create a new instance of this representation from another one.
mean
(*args, **kwargs)Vector mean.
norm
()Vector norm.
represent_as
(other_class[, differential_class])Convert coordinates to another representation.
Scale factors for each component’s direction.
sum
(*args, **kwargs)Vector sum.
transform
(matrix)Transform coordinates using a 3x3 matrix in a Cartesian basis.
Cartesian unit vectors in the direction of each component.
with_differentials
(differentials)Create a new representation with the same positions as this representation, but with these new differentials.
Return a copy of the representation without attached differentials.
Attributes Documentation

differentials
¶ A dictionary of differential class instances.
The keys of this dictionary must be a string representation of the SI unit with which the differential (derivative) is taken. For example, for a velocity differential on a positional representation, the key would be
's'
for seconds, indicating that the derivative is a time derivative.

info
¶

shape
¶ The shape of the instance and underlying arrays.
Like
shape
, can be set to a new shape by assigning a tuple. Note that if different instances share some but not all underlying data, setting the shape of one instance can make the other instance unusable. Hence, it is strongly recommended to get new, reshaped instances with thereshape
method. Raises
ValueError
If the new shape has the wrong total number of elements.
AttributeError
If the shape of any of the components cannot be changed without the arrays being copied. For these cases, use the
reshape
method (which copies any arrays that cannot be reshaped inplace).
Methods Documentation

cross
(other)[source]¶ Vector cross product of two representations.
The calculation is done by converting both
self
andother
toCartesianRepresentation
, and converting the result back to the type of representation ofself
. Parameters
 other
BaseRepresentation
subclass instance The representation to take the cross product with.
 other
 Returns
 cross_product
BaseRepresentation
subclass instance With vectors perpendicular to both
self
andother
, in the same type of representation asself
.
 cross_product

dot
(other)[source]¶ Dot product of two representations.
The calculation is done by converting both
self
andother
toCartesianRepresentation
.Note that any associated differentials will be dropped during this operation.
 Parameters
 other
BaseRepresentation
The representation to take the dot product with.
 other
 Returns
 dot_product
Quantity
The sum of the product of the x, y, and z components of the cartesian representations of
self
andother
.
 dot_product

classmethod
from_representation
(representation)[source]¶ Create a new instance of this representation from another one.
 Parameters
 representation
BaseRepresentation
instance The presentation that should be converted to this class.
 representation

mean
(*args, **kwargs)[source]¶ Vector mean.
Averaging is done by converting the representation to cartesian, and taking the mean of the x, y, and z components. The result is converted back to the same representation as the input.
Refer to
mean
for full documentation of the arguments, noting thataxis
is the entry in theshape
of the representation, and that theout
argument cannot be used. Returns
 mean
BaseRepresentation
subclass instance Vector mean, in the same representation as that of the input.
 mean

norm
()[source]¶ Vector norm.
The norm is the standard Frobenius norm, i.e., the square root of the sum of the squares of all components with nonangular units.
Note that any associated differentials will be dropped during this operation.
 Returns
 norm
astropy.units.Quantity
Vector norm, with the same shape as the representation.
 norm

represent_as
(other_class, differential_class=None)[source]¶ Convert coordinates to another representation.
If the instance is of the requested class, it is returned unmodified. By default, conversion is done via Cartesian coordinates. Also note that orientation information at the origin is not preserved by conversions through Cartesian coordinates. See the docstring for
to_cartesian()
for an example. Parameters
 other_class
BaseRepresentation
subclass The type of representation to turn the coordinates into.
 differential_class
dict
ofBaseDifferential
, optional Classes in which the differentials should be represented. Can be a single class if only a single differential is attached, otherwise it should be a
dict
keyed by the same keys as the differentials.
 other_class

scale_factors
()[source]¶ Scale factors for each component’s direction.
Given unit vectors \(\hat{e}_c\) and scale factors \(f_c\), a change in one component of \(\delta c\) corresponds to a change in representation of \(\delta c \times f_c \times \hat{e}_c\).

sum
(*args, **kwargs)[source]¶ Vector sum.
Adding is done by converting the representation to cartesian, and summing the x, y, and z components. The result is converted back to the same representation as the input.
Refer to
sum
for full documentation of the arguments, noting thataxis
is the entry in theshape
of the representation, and that theout
argument cannot be used. Returns
 sum
BaseRepresentation
subclass instance Vector sum, in the same representation as that of the input.
 sum

transform
(matrix)[source]¶ Transform coordinates using a 3x3 matrix in a Cartesian basis.
This returns a new representation and does not modify the original one. Any differentials attached to this representation will also be transformed.
 Parameters
 matrix(3,3) array_like
A 3x3 (or stack thereof) matrix, such as a rotation matrix.

unit_vectors
()[source]¶ Cartesian unit vectors in the direction of each component.
Given unit vectors \(\hat{e}_c\) and scale factors \(f_c\), a change in one component of \(\delta c\) corresponds to a change in representation of \(\delta c \times f_c \times \hat{e}_c\).
 Returns
 unit_vectors
dict
ofCartesianRepresentation
The keys are the component names.
 unit_vectors

with_differentials
(differentials)[source]¶ Create a new representation with the same positions as this representation, but with these new differentials.
Differential keys that already exist in this object’s differential dict are overwritten.
 Parameters
 differentialssequence of
BaseDifferential
subclass instance The differentials for the new representation to have.
 differentialssequence of
 Returns
BaseRepresentation
subclass instanceA copy of this representation, but with the
differentials
as its differentials.

without_differentials
()[source]¶ Return a copy of the representation without attached differentials.
 Returns
BaseRepresentation
subclass instanceA shallow copy of this representation, without any differentials. If no differentials were present, no copy is made.