Package geometry :: Package manifolds :: Module matrix_lie_algebra :: Class MatrixLieAlgebra

Class MatrixLieAlgebra

This is the base class for Matrix Lie Algebra.

It is understood that it is composed by square matrices.

The only function that *has* to be implemented is the :py:func:`project` function that projects a square matrix onto the algebra. This function is used both for checking that a vector is in the algebra (see :py:func:`belongs`) and to mitigate the numerical errors.

You probably also want to implement :py:func:`norm` if the default is not what you want.

Nested Classes

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Inherited from differentiable_manifold.DifferentiableManifold: Embedding, Isomorphism, __metaclass__

Instance Methods

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__init__(self, n, dimension)
Note dimension is the intrinsic dimension.

source code

algebra_from_vector(self, v)
Isomorphism from elements of the algebra to vectors.

source code

vector_from_algebra(self, a)
Isomorphism from elements of the algebra to vectors.

source code

Inherited from matrix_linear_space.MatrixLinearSpace: belongs, belongs_ts, distance, expmap, logmap, norm, project, project_ts, zero

Inherited from differentiable_manifold.DifferentiableManifold: assert_close, can_convert_to, can_represent, convert_to, embed_in, embeddable_in, friendly, from_yaml, geodesic, get_dimension, interesting_points, project_from, project_to, relations_descriptions, tangent_bundle, to_yaml

Inherited from object: __delattr__, __format__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__, __subclasshook__

Static Methods

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Inherited from differentiable_manifold.DifferentiableManifold: embedding, isomorphism

Class Variables

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__abstractmethods__ = frozenset(['algebra_from_vector', 'proje...

_abc_cache = <_weakrefset.WeakSet object at 0x23cf410>

Inherited from differentiable_manifold.DifferentiableManifold (private): _abc_negative_cache, _abc_negative_cache_version, _abc_registry

Properties

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Inherited from object: __class__

Method Details

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init(self, n, dimension)
(Constructor)

source code

Note dimension is the intrinsic dimension.

:param dimension: :type dimension: ``int,>0``

Overrides: object.__init__: (inherited documentation)

algebra_from_vector(self, v)

source code

Isomorphism from elements of the algebra to vectors.
       (For example, so(3) <==> R^3).
        


:param v: 
:type v:  ``array[K]``

:rtype:  ``belongs``

vector_from_algebra(self, a)

source code

Isomorphism from elements of the algebra to vectors.
       (For example, so(3) <==> R^3).
        


:param a: 
:type a:  ``belongs``

:rtype:  ``array[K]``

Class Variable Details

[hide private]

abstractmethods

Value:

frozenset(['algebra_from_vector', 'project', 'vector_from_algebra'])

Class MatrixLieAlgebra

__init__(self, n, dimension) (Constructor)

algebra_from_vector(self, v)

vector_from_algebra(self, a)

__abstractmethods__

init(self, n, dimension)
(Constructor)

abstractmethods