Package geometry :: Package manifolds :: Module special_euclidean_algebra :: Class se_algebra

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Class se_algebra

This is the Lie algebra se(n) for the Special Euclidean group SE(n).

Note that you have to supply a coefficient *alpha* that weights rotation and translation when defining distances.

Nested Classes

Inherited from differentiable_manifold.DifferentiableManifold: Embedding, Isomorphism, __metaclass__

Instance Methods

__init__(self, N, alpha)
Note dimension is the intrinsic dimension.

source code

__repr__(self)
repr(x)

source code

algebra_from_vector(self, v)
:param v: :type v: ``array[N]``

source code

interesting_points(self)
Returns a list of "interesting points" on this manifold that should be used for testing various properties.

source code

norm(self, X)
Return the norm of a vector in the algebra.

source code

project(self, X)
Projects a vector onto this Lie Algebra.

source code

vector_from_algebra(self, a)
:param a: :type a: ``belongs``

source code

Inherited from matrix_linear_space.MatrixLinearSpace: belongs, belongs_ts, distance, expmap, logmap, 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, project_from, project_to, relations_descriptions, tangent_bundle, to_yaml

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

Static Methods

Inherited from differentiable_manifold.DifferentiableManifold: embedding, isomorphism

Class Variables

__abstractmethods__ = frozenset([])

_abc_cache = <_weakrefset.WeakSet object at 0x24a2d90>

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

Properties

Inherited from object: __class__

Method Details

init(self, N, alpha)
(Constructor)

Note dimension is the intrinsic dimension.

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

Overrides: object.__init__: (inherited documentation)

repr(self)
(Representation operator)

repr(x)

Overrides: object.__repr__: (inherited documentation)

algebra_from_vector(self, v)

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

:rtype: ``belongs``

Overrides: matrix_lie_algebra.MatrixLieAlgebra.algebra_from_vector

interesting_points(self)


           Returns a list of "interesting points" on this manifold that
           should be used for testing various properties. 
       


:rtype:  ``list(belongs)``

Overrides: differentiable_manifold.DifferentiableManifold.interesting_points: (inherited documentation)

norm(self, X)

Return the norm of a vector in the algebra. This is used in :py:class:`MatrixLieGroup` to measure distances between points in the Lie group.

Overrides: matrix_linear_space.MatrixLinearSpace.norm: (inherited documentation)

project(self, X)

Projects a vector onto this Lie Algebra.

Overrides: matrix_linear_space.MatrixLinearSpace.project: (inherited documentation)

vector_from_algebra(self, a)

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

Overrides: matrix_lie_algebra.MatrixLieAlgebra.vector_from_algebra