Source Code for Module geometry.manifolds.special_orthogonal_algebra

 1  from . import np, MatrixLieAlgebra, contract 
 2  from .. import hat_map, hat_map_2d, map_hat_2d, map_hat 
 3   
 4   
 5 -class so_algebra(MatrixLieAlgebra): 
 6      '''  
 7          This is the Lie algebra of skew-symmetric matrices so(n), 
 8          for the Special Orthogonal group SO(n). 
 9      ''' 
10   
11 -    def __init__(self, n): 
12          dimension = {2: 1, 3: 3}[n] 
13          MatrixLieAlgebra.__init__(self, n=n, dimension=dimension) 
14   
15 -    def project(self, v): 
16          ''' Projects *v* to the closest skew-symmetric matrix. ''' 
17          return 0.5 * (v - v.T) 
18   
19 -    def __repr__(self): 
20          return 'so%s' % (self.n) 
21   
22 -    def interesting_points(self): 
23          points = [] 
24          points.append(self.zero()) 
25          if self.n == 2: 
26              points.append(hat_map_2d(np.pi)) 
27              points.append(hat_map_2d(np.pi / 2)) 
28              points.append(hat_map_2d(-np.pi)) 
29          elif self.n == 3: 
30              points.append(hat_map(np.array([0, 0, 1]) * np.pi / 2)) 
31              points.append(hat_map(np.array([0, 0, 1]) * np.pi)) 
32              points.append(hat_map(np.array([0, 1, 0]) * np.pi / 2)) 
33              points.append(hat_map(np.array([0, 1, 0]) * np.pi)) 
34              points.append(hat_map(np.array([1, 0, 0]) * np.pi / 2)) 
35              points.append(hat_map(np.array([1, 0, 0]) * np.pi)) 
36          else: 
37              assert False, 'Not implemented for n=%s' % self.n 
38          return points 
39   
40      @contract(a='belongs') 
41 -    def vector_from_algebra(self, a): 
42          if self.n == 2: 
43              return np.array([map_hat_2d(a)]) 
44          elif self.n == 3: 
45              return map_hat(a) 
46          else: 
47              assert False, 'Not implemented for n=%s.' % self.n 
48   
49      @contract(v='array[N]') 
50 -    def algebra_from_vector(self, v): 
51          if self.n == 2: 
52              return hat_map_2d(v[0]) 
53          elif self.n == 3: 
54              return hat_map(v) 
55          else: 
56              assert False, 'Not implemented for n=%s.' % self.n 
57