NDCartesianRepresentation

class gala.dynamics.NDCartesianRepresentation(x, differentials=None, unit=None, copy=True)[source]

Bases: gala.dynamics.representation_nd.NDMixin, astropy.coordinates.CartesianRepresentation

Representation of points in ND cartesian coordinates.

Parameters:
x : Quantity or array

The Cartesian coordinates of the point(s). If not quantity, unit should be set.

differentials : dict, NDCartesianDifferential (optional)

Any differential classes that should be associated with this representation.

unit : Unit or str

If given, the coordinates will be converted to this unit (or taken to be in this unit if not given.

copy : bool, optional

If True (default), arrays will be copied rather than referenced.

Attributes Summary

T Return an instance with the data transposed.
attr_classes
components A tuple with the in-order names of the coordinate components.
differentials A dictionary of differential class instances.
isscalar
ndim The number of dimensions of the instance and underlying arrays.
recommended_units

Deprecated since version 3.0.
shape The shape of the instance and underlying arrays.
size The size of the object, as calculated from its shape.
x The ‘x’ component of the points(s).
xyz Return a vector array of the x, y, and z coordinates.
y The ‘y’ component of the points(s).
z The ‘z’ component of the points(s).

Methods Summary

copy(*args, **kwargs) Return an instance containing copies of the internal data.
cross(other) Cross product of two representations.
diagonal(*args, **kwargs) Return an instance with the specified diagonals.
dot(other) Dot product of two representations.
flatten(*args, **kwargs) Return a copy with the array collapsed into one dimension.
from_cartesian(other) Create a representation of this class from a supplied Cartesian one.
from_representation(representation) Create a new instance of this representation from another one.
get_name() Name of the representation or differential.
get_xyz([xyz_axis]) Return a vector array of the x, y, and z coordinates.
mean(*args, **kwargs) Vector mean.
norm() Vector norm.
ravel(*args, **kwargs) Return an instance with the array collapsed into one dimension.
represent_as(other_class[, differential_class]) Convert coordinates to another representation.
reshape(*args, **kwargs) Returns an instance containing the same data with a new shape.
scale_factors() Scale factors for each component’s direction.
squeeze(*args, **kwargs) Return an instance with single-dimensional shape entries removed
sum(*args, **kwargs) Vector sum.
swapaxes(*args, **kwargs) Return an instance with the given axes interchanged.
take(indices[, axis, mode]) Return a new instance formed from the elements at the given indices.
to_cartesian() Convert the representation to its Cartesian form.
transform(matrix) Transform the cartesian coordinates using a 3x3 matrix.
transpose(*args, **kwargs) Return an instance with the data transposed.
unit_vectors() 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.
without_differentials() Return a copy of the representation without attached differentials.

Attributes Documentation

T

Return an instance with the data transposed.

Parameters are as for T. All internal data are views of the data of the original.

attr_classes = {}
components

A tuple with the in-order names of the coordinate components.

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.

isscalar
ndim

The number of dimensions of the instance and underlying arrays.

recommended_units

Deprecated since version 3.0: The recommended_units attribute is deprecated and may be removed in a future version.

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 the reshape method.

Raises:
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 in-place).
size

The size of the object, as calculated from its shape.

x

The ‘x’ component of the points(s).

xyz

Return a vector array of the x, y, and z coordinates.

Parameters:
xyz_axis : int, optional

The axis in the final array along which the x, y, z components should be stored (default: 0).
Returns:
xs : Quantity

With dimension 3 along xyz_axis.
y

The ‘y’ component of the points(s).

z

The ‘z’ component of the points(s).

Methods Documentation

copy(*args, **kwargs)

Return an instance containing copies of the internal data.

Parameters are as for copy().

cross(other)

Cross product of two representations.

Parameters:
other : representation

If not already cartesian, it is converted.
Returns:
cross_product : CartesianRepresentation

With vectors perpendicular to both self and other.
diagonal(*args, **kwargs)

Return an instance with the specified diagonals.

Parameters are as for diagonal(). All internal data are views of the data of the original.

dot(other)

Dot product of two representations.

Note that any associated differentials will be dropped during this operation.

Parameters:
other : representation

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 and other.
flatten(*args, **kwargs)

Return a copy with the array collapsed into one dimension.

Parameters are as for flatten().

classmethod from_cartesian(other)

Create a representation of this class from a supplied Cartesian one.

Parameters:
other : CartesianRepresentation

The representation to turn into this class
Returns:
representation : object of this class

A new representation of this class’s type.
classmethod from_representation(representation)

Create a new instance of this representation from another one.

Parameters:
representation : BaseRepresentation instance

The presentation that should be converted to this class.
classmethod get_name()

Name of the representation or differential.

In lower case, with any trailing ‘representation’ or ‘differential’ removed. (E.g., ‘spherical’ for SphericalRepresentation or SphericalDifferential.)

get_xyz(xyz_axis=0)[source]

Return a vector array of the x, y, and z coordinates.

Parameters:
xyz_axis : int, optional

The axis in the final array along which the x, y, z components should be stored (default: 0).
Returns:
xs : Quantity

With dimension 3 along xyz_axis.
mean(*args, **kwargs)

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 that axis is the entry in the shape of the representation, and that the out argument cannot be used.

norm()

Vector norm.

The norm is the standard Frobenius norm, i.e., the square root of the sum of the squares of all components with non-angular 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.
ravel(*args, **kwargs)

Return an instance with the array collapsed into one dimension.

Parameters are as for ravel(). Note that it is not always possible to unravel an array without copying the data. If you want an error to be raise if the data is copied, you should should assign shape (-1,) to the shape attribute.

represent_as(other_class, differential_class=None)

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.

Parameters:
other_class : BaseRepresentation subclass

The type of representation to turn the coordinates into.

differential_class : dict of BaseDifferential, 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.
reshape(*args, **kwargs)

Returns an instance containing the same data with a new shape.

Parameters are as for reshape(). Note that it is not always possible to change the shape of an array without copying the data (see reshape() documentation). If you want an error to be raise if the data is copied, you should assign the new shape to the shape attribute (note: this may not be implemented for all classes using ShapedLikeNDArray).

scale_factors()

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_factors : dict of Quantity

The keys are the component names.
squeeze(*args, **kwargs)

Return an instance with single-dimensional shape entries removed

Parameters are as for squeeze(). All internal data are views of the data of the original.

sum(*args, **kwargs)

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 that axis is the entry in the shape of the representation, and that the out argument cannot be used.

swapaxes(*args, **kwargs)

Return an instance with the given axes interchanged.

Parameters are as for swapaxes(): axis1, axis2. All internal data are views of the data of the original.

take(indices, axis=None, mode='raise')

Return a new instance formed from the elements at the given indices.

Parameters are as for take(), except that, obviously, no output array can be given.

to_cartesian()

Convert the representation to its Cartesian form.

Note that any differentials get dropped.

Returns:
cartrepr : CartesianRepresentation

The representation in Cartesian form.
transform(matrix)

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.

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  # doctest: +FLOAT_CMP
<Quantity [[ 1.8660254 , 3.23205081],
           [ 1.23205081, 1.59807621],
           [ 3.        , 4.        ]] pc>
transpose(*args, **kwargs)

Return an instance with the data transposed.

Parameters are as for transpose(). All internal data are views of the data of the original.

unit_vectors()

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 of CartesianRepresentation

The keys are the component names.
with_differentials(differentials)

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:
differentials : Sequence of BaseDifferential

The differentials for the new representation to have.
Returns:
newrepr

A copy of this representation, but with the differentials as its differentials.
without_differentials()

Return a copy of the representation without attached differentials.

Returns:
newrepr

A shallow copy of this representation, without any differentials. If no differentials were present, no copy is made.