CartesianRepresentation¶

class
astropy.coordinates.
CartesianRepresentation
(x, y=None, z=None, unit=None, xyz_axis=None, differentials=None, copy=True)[source]¶ Bases:
astropy.coordinates.BaseRepresentation
Representation of points in 3D cartesian coordinates.
 Parameters
 x, y, z
Quantity
or array The x, y, and z coordinates of the point(s). If
x
,y
, andz
have different shapes, they should be broadcastable. If not quantity,unit
should be set. If onlyx
is given, it is assumed that it contains an array with the 3 coordinates stored alongxyz_axis
. unit
Unit
or str If given, the coordinates will be converted to this unit (or taken to be in this unit if not given.
 xyz_axisint, optional
The axis along which the coordinates are stored when a single array is provided rather than distinct
x
,y
, andz
(default: 0). differentialsdict,
CartesianDifferential
, optional Any differential classes that should be associated with this representation. The input must either be a single
CartesianDifferential
instance, or a dictionary ofCartesianDifferential
s with keys set to a string representation of the SI unit with which the differential (derivative) is taken. For example, for a velocity differential on a positional representation, the key would be's'
for seconds, indicating that the derivative is a time derivative. copybool, optional
If
True
(default), arrays will be copied. IfFalse
, arrays will be references, though possibly broadcast to ensure matching shapes.
 x, y, z
Attributes Summary
The ‘x’ component of the points(s).
Return a vector array of the x, y, and z coordinates.
The ‘y’ component of the points(s).
The ‘z’ component of the points(s).
Methods Summary
cross
(other)Cross product of two representations.
dot
(other)Dot product of two representations.
from_cartesian
(other)Create a representation of this class from a supplied Cartesian one.
get_xyz
([xyz_axis])Return a vector array of the x, y, and z coordinates.
mean
(*args, **kwargs)Vector mean.
norm
()Vector norm.
Scale factors for each component’s direction.
sum
(*args, **kwargs)Vector sum.
Convert the representation to its Cartesian form.
transform
(matrix)Transform the cartesian coordinates using a 3x3 matrix.
Cartesian unit vectors in the direction of each component.
Attributes Documentation

attr_classes
= {'x': <class 'astropy.units.quantity.Quantity'>, 'y': <class 'astropy.units.quantity.Quantity'>, 'z': <class 'astropy.units.quantity.Quantity'>}¶

x
¶ The ‘x’ component of the points(s).

xyz
¶ Return a vector array of the x, y, and z coordinates.
 Parameters
 xyz_axisint, optional
The axis in the final array along which the x, y, z components should be stored (default: 0).
 Returns
 xyz
Quantity
With dimension 3 along
xyz_axis
. Note that, if possible, this will be a view.
 xyz

y
¶ The ‘y’ component of the points(s).

z
¶ The ‘z’ component of the points(s).
Methods Documentation

cross
(other)[source]¶ Cross product of two representations.
 Parameters
 otherrepresentation
If not already cartesian, it is converted.
 Returns
 cross_product
CartesianRepresentation
With vectors perpendicular to both
self
andother
.
 cross_product

dot
(other)[source]¶ Dot product of two representations.
Note that any associated differentials will be dropped during this operation.
 Parameters
 otherrepresentation
If not already cartesian, it is converted.
 Returns
 dot_product
Quantity
The sum of the product of the x, y, and z components of
self
andother
.
 dot_product

classmethod
from_cartesian
(other)[source]¶ Create a representation of this class from a supplied Cartesian one.
 Parameters
 other
CartesianRepresentation
The representation to turn into this class
 other
 Returns
 representationobject of this class
A new representation of this class’s type.

get_xyz
(xyz_axis=0)[source]¶ Return a vector array of the x, y, and z coordinates.
 Parameters
 xyz_axisint, optional
The axis in the final array along which the x, y, z components should be stored (default: 0).
 Returns
 xyz
Quantity
With dimension 3 along
xyz_axis
. Note that, if possible, this will be a view.
 xyz

mean
(*args, **kwargs)[source]¶ Vector mean.
Returns a new CartesianRepresentation instance with the means of the x, y, and z components.
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.

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

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 \(\delta c \times f_c \times \hat{e}_c\).
 Returns
 scale_factorsdict of
Quantity
The keys are the component names.
 scale_factorsdict of

sum
(*args, **kwargs)[source]¶ Vector sum.
Returns a new CartesianRepresentation instance with the sums of the x, y, and z components.
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.

to_cartesian
()[source]¶ Convert the representation to its Cartesian form.
Note that any differentials get dropped.
 Returns
 cartrepr
CartesianRepresentation
The representation in Cartesian form.
 cartrepr

transform
(matrix)[source]¶ Transform the cartesian coordinates using a 3x3 matrix.
This returns a new representation and does not modify the original one. Any differentials attached to this representation will also be transformed.
 Parameters
 matrix
ndarray
A 3x3 transformation matrix, such as a rotation matrix.
 matrix
Examples
We can start off by creating a cartesian representation object:
>>> from astropy import units as u >>> from astropy.coordinates import CartesianRepresentation >>> rep = CartesianRepresentation([1, 2] * u.pc, ... [2, 3] * u.pc, ... [3, 4] * u.pc)
We now create a rotation matrix around the z axis:
>>> from astropy.coordinates.matrix_utilities import rotation_matrix >>> rotation = rotation_matrix(30 * u.deg, axis='z')
Finally, we can apply this transformation:
>>> rep_new = rep.transform(rotation) >>> rep_new.xyz <Quantity [[ 1.8660254 , 3.23205081], [ 1.23205081, 1.59807621], [ 3. , 4. ]] pc>

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_vectorsdict of
CartesianRepresentation
The keys are the component names.
 unit_vectorsdict of