BaseRepresentation

class astropy.coordinates.BaseRepresentation(*args, differentials=None, **kwargs)

Bases: BaseRepresentationOrDifferential

Base for representing a point in a 3D coordinate system.

Parameters:

comp1, comp2, comp3Quantity or subclass

The components of the 3D points. The names are the keys and the subclasses the values of the attr_classes attribute.

differentialspython: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. If False, arrays will be references, though possibly broadcast to ensure matching shapes.

Notes

All representation classes should subclass this base representation class, and define an attr_classes attribute, a dict which maps component names to the class that creates them. They must also define a to_cartesian method and a from_cartesian class method. By default, transformations are done via the cartesian system, but classes that want to define a smarter transformation path can overload the represent_as method. If one wants to use an associated differential class, one should also define unit_vectors and scale_factors methods (see those methods for details).

Attributes Summary

differentials	A dictionary of differential class instances.
info
shape	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()	Scale factors for each component's direction.
sum(*args, **kwargs)	Vector sum.
transform(matrix)	Transform coordinates using a 3x3 matrix in a Cartesian basis.
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

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 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).

Methods Documentation

cross(other)

Vector cross product of two representations.

The calculation is done by converting both self and other to CartesianRepresentation, and converting the result back to the type of representation of self.

Parameters:

otherBaseRepresentation subclass instance

The representation to take the cross product with.

Returns:

cross_productBaseRepresentation subclass instance

With vectors perpendicular to both self and other, in the same type of representation as self.

dot(other)

Dot product of two representations.

The calculation is done by converting both self and other to CartesianRepresentation.

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

Parameters:

otherBaseRepresentation

The representation to take the dot product with.

Returns:

dot_productQuantity

The sum of the product of the x, y, and z components of the cartesian representations of self and other.

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.

mean(*args, **kwargs)

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

Returns:

meanBaseRepresentation subclass instance

Vector mean, in the same representation as that of the input.

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.

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_classpython: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.

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_factorspython:dict of Quantity

The keys are the component names.

sum(*args, **kwargs)

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

Returns:

sumBaseRepresentation subclass instance

Vector sum, in the same representation as that of the input.

transform(matrix)

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) numpy:array_like

A 3x3 (or stack thereof) matrix, such as a rotation matrix.

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_vectorspython: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:

differentialspython:sequence 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.