Source Code for Module geometry.manifolds.todo.grassman

 1  from . import contract 
 2   
 3   
 4 -def Grassman(DifferentiableManifold): 
 5      '''  
 6          INCOMPLETE -- The Grassman manifold Grass(n,p) is the set of rank-p  
 7          subspaces in R^n. It is seen here as Grass(n,p) = ST(n,p)/GL_p. 
 8       
 9          For a reference, see the paper by Absil, Mahony, and Sepulchre (2004) 
10          where all these operations are explained. Also their book should 
11          contain essentially the same info, but with more background. 
12           
13      ''' 
14      @contract(n='N,N>0', p='P,P>0,P<=N') 
15      def __init__(self, p, n): 
16          '''  
17              Initializes the manifold structure.  
18               
19              :param n: dimension of space 
20              :param p: rank of subspace 
21          ''' 
22          self.n = n 
23          self.p = p 
24   
25      def belongs(self, a): 
26          assert False 
27   
28      def distance(self, a, b): 
29          assert False 
30   
31      def logmap(self, a, b): 
32          assert False 
33   
34      def expmap(self, a, vel): 
35          assert False 
36   
37      def project_ts(self, base, vx): 
38          assert False 
39   
40      def sample_uniform(self): 
41          assert False 
42   
43      def normalize(self, x): 
44          assert False 
45