Source Code for Module geometry.manifolds.matrix_lie_group_tangent

 1  from . import DifferentiableManifold, MatrixLieGroup, contract 
 2   
 3   
 4 -class MatrixLieGroupTangent(DifferentiableManifold): 
 5      ''' This class represents the tangent bundle of a matrix Lie group 
 6          using a tuble (base, v0), where v0 is in the algebra. 
 7           
 8          Compare with the generic TangentBundle that uses the representation 
 9          (base, vel) where vel is tangent at base (it holds that vel=base*v0). 
10           
11          (MatrixLieGroup has different representation) 
12      ''' 
13      # TODO: the tangent bundle of a matrix Lie group has more properties than 
14      # this. 
15      # TODO: create tests for all of this 
16   
17 -    def __init__(self, base_group): 
18          assert isinstance(base_group, MatrixLieGroup) 
19          self.base = base_group 
20          dimension = 2 * base_group.get_dimension() 
21          DifferentiableManifold.__init__(self, dimension=dimension) 
22   
23 -    def __str__(self): 
24          return "T%se" % self.base 
25   
26      @contract(x='tuple[2]') 
27 -    def belongs(self, x): 
28          self.base.belongs(x[0]) 
29          self.base.get_algebra().belongs(x[1]) 
30   
31 -    def belongs_ts(self, bv): 
32          # TODO: implement 
33          raise ValueError('Not supported') 
34   
35 -    def project_ts(self, bv): # TODO: test 
36          # TODO: implement 
37          raise ValueError('Not supported') 
38   
39      @contract(a='belongs', b='belongs', returns='>=0') 
40 -    def distance(self, a, b): 
41          # TODO: implement 
42          raise ValueError('Not supported') 
43   
44      @contract(base='belongs', p='belongs', returns='belongs_ts') 
45 -    def logmap(self, base, p): 
46          raise ValueError('Not supported') 
47   
48      @contract(bv='belongs_ts', returns='belongs') 
49 -    def expmap(self, bv): 
50          raise ValueError('Not supported') 
51   
52      @contract(returns='list(belongs)') 
53 -    def interesting_points(self): 
54          # TODO: write this 
55          return [] 
56   
57      @contract(a='belongs') 
58 -    def friendly(self, a): 
59          '''  
60              Returns a friendly description string for a point on the manifold.  
61          ''' 
62          v = self.base.get_algebra().vector_from_algebra(a[1]) 
63          return "V(%s,%s)" % (self.base.friendly(a[0]), v.tolist()) 
64