NDCartesianRepresentation#

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

Bases: NDMixin, CartesianRepresentation

Representation of points in ND cartesian coordinates.

Parameters:

xQuantity or array: The Cartesian coordinates of the point(s). If not quantity, unit should be set.
differentialsdict, NDCartesianDifferential (optional): Any differential classes that should be associated with this representation.
unitUnit or str: If given, the coordinates will be converted to this unit (or taken to be in this unit if not given.
copybool, 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.
`info`
`isscalar`
`ndim`	The number of dimensions of the instance and underlying arrays.
`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, out, 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.

info#

isscalar#

ndim#: The number of dimensions of the instance and underlying arrays.

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:

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

Returns:

xsQuantity: 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:

otherBaseRepresentation subclass instance: If not already cartesian, it is converted.

Returns:

cross_productCartesianRepresentation: 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:

otherBaseRepresentation subclass instance: If not already cartesian, it is converted.

Returns:

dot_productQuantity: 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:

otherCartesianRepresentation: The representation to turn into this class

Returns:

representationBaseRepresentation subclass instance: A new representation of this class’s type.

classmethod from_representation(representation)#

Create a new instance of this representation from another one.

Parameters:

representationBaseRepresentation 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_axisint, optional: The axis in the final array along which the x, y, z components should be stored (default: 0).

Returns:

xsQuantity: 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:

normastropy.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. 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_classBaseRepresentation subclass: The type of representation to turn the coordinates into.
differential_classdict 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 NDArrayShapeMethods).

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_factorsdict 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, out=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. Also note that orientation information at the origin is not preserved by conversions through Cartesian coordinates. For example, transforming an angular position defined at distance=0 through cartesian coordinates and back will lose the original angular coordinates:

>>> import astropy.units as u
>>> import astropy.coordinates as coord
>>> rep = coord.SphericalRepresentation(
...     lon=15*u.deg,
...     lat=-11*u.deg,
...     distance=0*u.pc)
>>> rep.to_cartesian().represent_as(coord.SphericalRepresentation)
<SphericalRepresentation (lon, lat, distance) in (rad, rad, pc)
    (0., 0., 0.)>

Returns:

cartreprCartesianRepresentation: 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:

matrixndarray: 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  
<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_vectorsdict 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:

differentialssequence of BaseDifferential subclass instance: The differentials for the new representation to have.

Returns:

BaseRepresentation subclass instance: A copy of this representation, but with the differentials as its differentials.

without_differentials()#

Return a copy of the representation without attached differentials.

Returns:

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