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PyGeometry
Package geometry :: Package manifolds :: Module special_orthogonal_algebra :: Class so_algebra
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Class so_algebra

source code

This is the Lie algebra of skew-symmetric matrices so(n), for the Special Orthogonal group SO(n).

Nested Classes [hide private]

Inherited from differentiable_manifold.DifferentiableManifold: Embedding, Isomorphism, __metaclass__

Instance Methods [hide private]
 
__init__(self, n)
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
 
project(self, v)
Projects *v* to the closest skew-symmetric matrix.		 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, norm, 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 [hide private]

Inherited from differentiable_manifold.DifferentiableManifold: embedding, isomorphism

Class Variables [hide private]
  __abstractmethods__ = frozenset([])
  _abc_cache = <_weakrefset.WeakSet object at 0x24a24d0>

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, n)
(Constructor)

source code 

Note dimension is the intrinsic dimension.

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

Overrides: object.__init__
(inherited documentation)

__repr__(self)
(Representation operator)

source code 

repr(x)

Overrides: object.__repr__
(inherited documentation)

algebra_from_vector(self, v)

source code 

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

Overrides: matrix_lie_algebra.MatrixLieAlgebra.algebra_from_vector

interesting_points(self)

source code  

           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)

project(self, v)

source code 

Projects *v* to the closest skew-symmetric matrix.

Overrides: matrix_linear_space.MatrixLinearSpace.project

vector_from_algebra(self, a)

source code 

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

Overrides: matrix_lie_algebra.MatrixLieAlgebra.vector_from_algebra

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