Package geometry :: Package manifolds :: Module tangent_bundle :: Class TangentBundle

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Class TangentBundle

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This class represents the tangent bundle of a generic manifold using a tuple (base, vel) where vel is tangent at base.

(MatrixLieGroup has different representation)

Nested Classes

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Inherited from differentiable_manifold.DifferentiableManifold: Embedding, Isomorphism, __metaclass__

Instance Methods

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

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__str__(self)
str(x)

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belongs(self, x)
Raises an Exception if the point does not belong to this manifold.

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

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

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

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

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

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

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

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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

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Inherited from differentiable_manifold.DifferentiableManifold: embedding, isomorphism

Class Variables

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__abstractmethods__ = frozenset([])

_abc_cache = <_weakrefset.WeakSet object at 0x23ced90>

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, base_manifold)
(Constructor)

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

Overrides: object.__init__: (inherited documentation)

str(self)
(Informal representation operator)

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str(x)

Overrides: object.__str__: (inherited documentation)

belongs(self, x)

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Raises an Exception if the point does not belong to this manifold.

This function wraps some checks around :py:func:`belongs_`, which is implemented by the subclasses.

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

belongs_ts(self, bv)

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           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)

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

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

:rtype: ``>=0``

Overrides: differentiable_manifold.DifferentiableManifold.distance

expmap(self, bv)

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

:rtype: ``belongs``

Overrides: differentiable_manifold.DifferentiableManifold.expmap

friendly(self, a)

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


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

Overrides: differentiable_manifold.DifferentiableManifold.friendly

interesting_points(self)

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:rtype: ``list(belongs)``

Overrides: differentiable_manifold.DifferentiableManifold.interesting_points

logmap(self, base, p)

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

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

:rtype: ``belongs_ts``

Overrides: differentiable_manifold.DifferentiableManifold.logmap

project_ts(self, bv)

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           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 TangentBundle

__init__(self, base_manifold) (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_manifold)
(Constructor)

str(self)
(Informal representation operator)