UnitSphericalRepresentation

class astropy.coordinates.UnitSphericalRepresentation(lon, lat=None, differentials=None, copy=True)

Bases: BaseRepresentation

Representation of points on a unit sphere.

Parameters:

lon, latQuantity [:ref: ‘angle’] or python:str

The longitude and latitude of the point(s), in angular units. The latitude should be between -90 and 90 degrees, and the longitude will be wrapped to an angle between 0 and 360 degrees. These can also be instances of Angle, Longitude, or Latitude.

differentialspython:dict, BaseDifferential, optional

Any differential classes that should be associated with this representation. The input must either be a single BaseDifferential instance (see _compatible_differentials for valid types), or a dictionary of of differential instances 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.

Attributes Summary

attr_classes
lat	The latitude of the point(s).
lon	The longitude of the point(s).

Methods Summary

cross(other)	Cross product of two representations.
from_cartesian(cart)	Converts 3D rectangular cartesian coordinates to spherical polar coordinates.
mean(*args, **kwargs)	Vector mean.
norm()	Vector norm.
represent_as(other_class[, differential_class])	Convert coordinates to another representation.
scale_factors([omit_coslat])	Scale factors for each component's direction.
sum(*args, **kwargs)	Vector sum.
to_cartesian()	Converts spherical polar coordinates to 3D rectangular cartesian coordinates.
transform(matrix)	Transform the unit-spherical coordinates using a 3x3 matrix.
unit_vectors()	Cartesian unit vectors in the direction of each component.

Attributes Documentation

attr_classes = {'lat': <class 'astropy.coordinates.angles.Latitude'>, 'lon': <class 'astropy.coordinates.angles.Longitude'>}

lat

The latitude of the point(s).

lon

The longitude of the point(s).

Methods Documentation

cross(other)

Cross product of two representations.

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

Parameters:

otherBaseRepresentation subclass instance

The representation to take the cross product with.

Returns:

cross_productSphericalRepresentation

With vectors perpendicular to both self and other.

classmethod from_cartesian(cart)

Converts 3D rectangular cartesian coordinates to spherical polar coordinates.

mean(*args, **kwargs)

Vector mean.

The representation is converted to cartesian, the means of the x, y, and z components are calculated, and the result is converted to a SphericalRepresentation.

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, which is always unity for vectors on the unit sphere.

Returns:

normQuantity [:ref: ‘dimensionless’]

Dimensionless ones, 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(omit_coslat=False)

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.

The representation is converted to cartesian, the sums of the x, y, and z components are calculated, and the result is converted to a SphericalRepresentation.

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.

to_cartesian()

Converts spherical polar coordinates to 3D rectangular cartesian coordinates.

transform(matrix)

Transform the unit-spherical 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(3,3) numpy:array_like

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

Returns:

UnitSphericalRepresentation or SphericalRepresentation

If matrix is O(3) – \(M \dot M^T = I\) – like a rotation, then the result is a UnitSphericalRepresentation. All other matrices will change the distance, so the dimensional representation is used instead.

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.