Package geometry :: Package manifolds :: Module matrix_lie_group_tangent :: Class MatrixLieGroupTangent

Class MatrixLieGroupTangent

This class represents the tangent bundle of a matrix Lie group using a tuble (base, v0), where v0 is in the algebra.

Compare with the generic TangentBundle that uses the representation (base, vel) where vel is tangent at base (it holds that vel=base*v0).

(MatrixLieGroup has different representation)

Nested Classes

[hide private]

Inherited from differentiable_manifold.DifferentiableManifold: Embedding, Isomorphism, __metaclass__

Instance Methods

[hide private]

__init__(self, base_group)
x.__init__(...) initializes x; see help(type(x)) for signature

source code

__str__(self)
str(x)

source code

belongs(self, x)
:param x: :type x: ``tuple[2]``

source code

belongs_ts(self, bv)
Checks that a vector *vx* belongs to the tangent space at the given point *base*.

source code

distance(self, a, b)
:param a: :type a: ``belongs``

source code

expmap(self, bv)
:param bv: :type bv: ``belongs_ts``

source code

friendly(self, a)
Returns a friendly description string for a point on the manifold.

source code

interesting_points(self)
:rtype: ``list(belongs)``

source code

logmap(self, base, p)
:param p: :type p: ``belongs``

source code

project_ts(self, bv)
Projects a vector *v_ambient* in the ambient space to the tangent space at point *base*.

source code

Inherited from differentiable_manifold.DifferentiableManifold: assert_close, can_convert_to, can_represent, convert_to, embed_in, embeddable_in, 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__, __repr__, __setattr__, __sizeof__, __subclasshook__

Static Methods

[hide private]

Inherited from differentiable_manifold.DifferentiableManifold: embedding, isomorphism

Class Variables

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__abstractmethods__ = frozenset([])

_abc_cache = <_weakrefset.WeakSet object at 0x23d2fd0>

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

Properties

[hide private]

Inherited from object: __class__

Method Details

[hide private]

init(self, base_group)
(Constructor)

source code

x.__init__(...) initializes x; see help(type(x)) for signature

Overrides: object.__init__: (inherited documentation)

str(self)
(Informal representation operator)

source code

str(x)

Overrides: object.__str__: (inherited documentation)

belongs(self, x)

source code

:param x: :type x: ``tuple[2]``

Overrides: differentiable_manifold.DifferentiableManifold.belongs

belongs_ts(self, bv)

source code


           Checks that a vector *vx* belongs to the tangent space
           at the given point *base*.

       


:param bv: 
:type bv:  ``tuple(belongs,*)``

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

distance(self, a, b)

source code

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

:param b: :type b: ``belongs``

:rtype: ``>=0``

Overrides: differentiable_manifold.DifferentiableManifold.distance

expmap(self, bv)

source code

:param bv: :type bv: ``belongs_ts``

:rtype: ``belongs``

Overrides: differentiable_manifold.DifferentiableManifold.expmap

friendly(self, a)

source code


           Returns a friendly description string for a point on the manifold. 
       


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

Overrides: differentiable_manifold.DifferentiableManifold.friendly

interesting_points(self)

source code

:rtype: ``list(belongs)``

Overrides: differentiable_manifold.DifferentiableManifold.interesting_points

logmap(self, base, p)

source code

:param p: :type p: ``belongs``

:param base: :type base: ``belongs``

:rtype: ``belongs_ts``

Overrides: differentiable_manifold.DifferentiableManifold.logmap

project_ts(self, bv)

source code


           Projects a vector *v_ambient* in the ambient space
           to the tangent space at point *base*.
       


:param bv: 
:type bv:  ``tuple(belongs,*)``

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

Class MatrixLieGroupTangent

__init__(self, base_group) (Constructor)

__str__(self) (Informal representation operator)

belongs(self, x)

belongs_ts(self, bv)

distance(self, a, b)

expmap(self, bv)

friendly(self, a)

interesting_points(self)

logmap(self, base, p)

project_ts(self, bv)

init(self, base_group)
(Constructor)

str(self)
(Informal representation operator)