Source Code for Module geometry.subspaces.subspaces

 1  from . import np, contract 
 2  from .. import assert_allclose 
 3   
 4   
 5  @contract(A='array[NxK]') 
 6 -def normalize_columns(A): 
 7      A = A.copy() 
 8      _, k = A.shape 
 9      for j in range(k): 
10          A[:, j] = A[:, j] / np.linalg.norm(A[:, j]) 
11      return A 
12   
13   
14  @contract(A='array[NxK]') 
15 -def proj_from_subspace(A): 
16      An = normalize_columns(A) 
17      return np.dot(An, An.T) 
18   
19   
20 -def get_random_proj(n, k): 
21      A = np.random.randn(n, k) 
22      return proj_from_subspace(A) 
23   
24   
25  @contract(P='array[NxN]') 
26 -def assert_projection(P): 
27      assert_allclose(P.T, P) 
28      assert_allclose(np.dot(P, P), P) 
29   
30   
31 -def check(): 
32      # XXX 
33      n = 6 
34      P1 = get_random_proj(n, 1) 
35      P2 = get_random_proj(n, 1) 
36   
37      C = np.dot(P1, P2) 
38      assert_projection(P1) 
39      assert_projection(P2) 
40   
41      assert_projection(C) 
42