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PyGeometry
Package geometry :: Package manifolds :: Module matrix_linear_space :: Class MatrixLinearSpace
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Class MatrixLinearSpace

source code

Nested Classes [hide private]

Inherited from differentiable_manifold.DifferentiableManifold: Embedding, Isomorphism, __metaclass__

Instance Methods [hide private]
 
__init__(self, dimension, shape)
Note dimension is the intrinsic dimension.		 source code
 
belongs(self, x)
:param x: :type x: ``array``		 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)
Computes the geodesic distance between two points.		 source code
 
expmap(self, bv)
:param bv: :type bv: ``belongs_ts``		 source code
 
logmap(self, base, target)
:param base: :type base: ``belongs``		 source code
 
norm(self, v)
Return the norm of a vector in the algebra.		 source code
 
project(self, v)
Projects a vector onto this Lie Algebra.		 source code
 
project_ts(self, bv)
Projects a vector *v_ambient* in the ambient space to the tangent space at point *base*.		 source code
 
zero(self)
Returns the zero element for this algebra.		 source code

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 [hide private]

Inherited from differentiable_manifold.DifferentiableManifold: embedding, isomorphism

Class Variables [hide private]
  __abstractmethods__ = frozenset(['project'])
  _abc_cache = <_weakrefset.WeakSet object at 0x23aa1d0>

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, dimension, shape)
(Constructor)

source code 

Note dimension is the intrinsic dimension.

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

Overrides: object.__init__

belongs(self, x)

source code 

:param x: :type x: ``array``

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  

           Computes the geodesic distance between two points.  
       


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

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

:rtype:  ``>=0``
Overrides: differentiable_manifold.DifferentiableManifold.distance
(inherited documentation)

expmap(self, bv)

source code 

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

Overrides: differentiable_manifold.DifferentiableManifold.expmap

logmap(self, base, target)

source code 

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

:param target: :type target: ``belongs``

:rtype: ``belongs_ts``

Overrides: differentiable_manifold.DifferentiableManifold.logmap

norm(self, v)

source code 

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.

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)

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