Source Code for Module geometry.manifolds.torus

 1  from . import DifferentiableManifold, np, contract 
 2  from .. import normalize_pi 
 3  from contracts import check 
 4   
 5   
 6 -class Torus(DifferentiableManifold): 
 7   
 8 -    def __init__(self, n): 
 9          DifferentiableManifold.__init__(self, dimension=n) 
10          self.n = n 
11   
12 -    def belongs(self, a): 
13          check('array[N](>=-pi,<pi)', a, N=self.n) 
14   
15      @contract(a='belongs', b='belongs', returns='>=0') 
16 -    def distance(self, a, b): 
17          b = self.normalize(b - a) 
18          return np.linalg.norm(b) 
19   
20      @contract(a='belongs', b='belongs', returns='belongs_ts') 
21 -    def logmap(self, a, b): 
22          vel = self.normalize(b - a) 
23          return a, vel 
24   
25      @contract(bv='belongs_ts', returns='belongs') 
26 -    def expmap(self, bv): 
27          a, vel = bv 
28          b = self.normalize(a + vel) 
29          return b 
30   
31      @contract(bv='tuple(belongs, *)') 
32 -    def project_ts(self, bv): 
33          return bv # XXX: more checks 
34   
35      @contract(returns='belongs') 
36 -    def sample_uniform(self): 
37          return np.random.rand(self.n) * 2 * np.pi - np.pi 
38   
39 -    def normalize(self, x): 
40          return normalize_pi(x) 
41   
42 -    def friendly(self, a): 
43          return 'point(%s)' % a 
44   
45      @contract(returns='list(belongs)') 
46 -    def interesting_points(self): 
47          o = np.ones(self.n) 
48          return [np.zeros(self.n), o * -np.pi] 
49   
50 -    def __repr__(self): 
51          #return 'Torus(%s)' % self.n 
52          return 'T%s' % self.n 
53