Source Code for Module geometry.manifolds.matrix_lie_algebra

 1  from . import MatrixLinearSpace, contract 
 2  from abc import abstractmethod 
 3   
 4   
 5 -class MatrixLieAlgebra(MatrixLinearSpace): 
 6      ''' This is the base class for Matrix Lie Algebra. 
 7       
 8          It is understood that it is composed by square matrices. 
 9           
10          The only function that *has* to be implemented is the  
11          :py:func:`project` function that projects a square matrix 
12          onto the algebra. This function is used both for checking 
13          that a vector is in the algebra (see :py:func:`belongs`) 
14          and to mitigate the numerical errors. 
15           
16          You probably also want to implement :py:func:`norm` if 
17          the default is not what you want.   
18      ''' 
19   
20 -    def __init__(self, n, dimension): 
21          MatrixLinearSpace.__init__(self, dimension=dimension, 
22                                     shape=(n, n)) 
23          self.n = n 
24   
25      @abstractmethod 
26      @contract(a='belongs', returns='array[K]') 
27 -    def vector_from_algebra(self, a): 
28          ''' Isomorphism from elements of the algebra to vectors. 
29          (For example, so(3) <==> R^3). 
30           ''' 
31          #raise ValueError('Not implemented for %s.' % self) 
32   
33      @abstractmethod 
34      @contract(returns='belongs', v='array[K]') 
35 -    def algebra_from_vector(self, v): 
36          ''' Isomorphism from elements of the algebra to vectors. 
37          (For example, so(3) <==> R^3). 
38           ''' 
39          #raise ValueError('Not implemented for %s.' % self) 
40   
41      # TODO: bracket 
42