BaseDifferential¶

class astropy.coordinates.BaseDifferential(*args, **kwargs)[source]

A base class representing differentials of representations.

These represent differences or derivatives along each component. E.g., for physics spherical coordinates, these would be $$\delta r, \delta \theta, \delta \phi$$.

Parameters
d_comp1, d_comp2, d_comp3Quantity or subclass

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

copybool, optional

If True (default), arrays will be copied. If False, arrays will be references, though possibly broadcast to ensure matching shapes.

Notes

All differential representation classes should subclass this base class, and define an base_representation attribute with the class of the regular BaseRepresentation for which differential coordinates are provided. This will set up a default attr_classes instance with names equal to the base component names prefixed by d_, and all classes set to Quantity, plus properties to access those, and a default __init__ for initialization.

Methods Summary

 from_cartesian(other, base) Convert the differential from 3D rectangular cartesian coordinates to the desired class. from_representation(representation, base) Create a new instance of this representation from another one. norm([base]) Vector norm. represent_as(other_class, base) Convert coordinates to another representation. to_cartesian(base) Convert the differential to 3D rectangular cartesian coordinates. transform(matrix, base, transformed_base) Transform differential using a 3x3 matrix in a Cartesian basis.

Methods Documentation

classmethod from_cartesian(other, base)[source]

Convert the differential from 3D rectangular cartesian coordinates to the desired class.

Parameters
other

The object to convert into this differential.

baseBaseRepresentation

The points for which the differentials are to be converted: each of the components is multiplied by its unit vectors and scale factors. Will be converted to cls.base_representation if needed.

Returns
BaseDifferential subclass instance

A new differential object that is this class’ type.

classmethod from_representation(representation, base)[source]

Create a new instance of this representation from another one.

Parameters
representationBaseRepresentation instance

The presentation that should be converted to this class.

baseinstance of cls.base_representation

The base relative to which the differentials will be defined. If the representation is a differential itself, the base will be converted to its base_representation to help convert it.

norm(base=None)[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 non-angular units.

Parameters
baseinstance of self.base_representation

Base relative to which the differentials are defined. This is required to calculate the physical size of the differential for all but Cartesian differentials or radial differentials.

Returns
normastropy.units.Quantity

Vector norm, with the same shape as the representation.

represent_as(other_class, base)[source]

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_classBaseRepresentation subclass

The type of representation to turn the coordinates into.

baseinstance of self.base_representation

Base relative to which the differentials are defined. If the other class is a differential representation, the base will be converted to its base_representation.

to_cartesian(base)[source]

Convert the differential to 3D rectangular cartesian coordinates.

Parameters
baseinstance of self.base_representation

The points for which the differentials are to be converted: each of the components is multiplied by its unit vectors and scale factors.

Returns
CartesianDifferential

This object, converted.

transform(matrix, base, transformed_base)[source]

Transform differential using a 3x3 matrix in a Cartesian basis.

This returns a new differential and does not modify the original one.

Parameters
matrix(3,3) array_like

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

baseinstance of cls.base_representation

Base relative to which the differentials are defined. If the other class is a differential representation, the base will be converted to its base_representation.

transformed_baseinstance of cls.base_representation

Base relative to which the transformed differentials are defined. If the other class is a differential representation, the base will be converted to its base_representation.