Source Code for Module geometry.manifolds.matrix_linear_space

 1  from . import np, DifferentiableManifold, contract 
 2  from .. import assert_allclose 
 3  from abc import abstractmethod 
 4  from contracts import check 
 5   
 6   
 7 -class MatrixLinearSpace(DifferentiableManifold): 
 8   
 9      @contract(dimension='int,>0') 
10 -    def __init__(self, dimension, shape): 
11          ''' Note dimension is the intrinsic dimension. ''' 
12          # TODO: give basis? 
13          self.shape = shape 
14          DifferentiableManifold.__init__(self, dimension=dimension) 
15   
16 -    def zero(self): 
17          ''' Returns the zero element for this algebra. ''' 
18          return np.zeros(self.shape) 
19   
20 -    def norm(self, v): 
21          ''' Return the norm of a vector in the algebra. 
22              This is used in :py:class:`MatrixLieGroup` to measure 
23              distances between points in the Lie group.  
24          ''' 
25          return np.linalg.norm(v, 2) 
26   
27      # Manifolds methods 
28 -    def distance(self, a, b): 
29          return self.norm(a - b) 
30   
31      @contract(bv='belongs_ts') 
32 -    def expmap(self, bv): 
33          base, vel = bv 
34          return base + vel 
35   
36      @contract(base='belongs', target='belongs', returns='belongs_ts') 
37 -    def logmap(self, base, target): 
38          return base, target - base 
39   
40      @contract(x='array') 
41 -    def belongs(self, x): 
42          if x.shape != self.shape: 
43              raise ValueError('Expected shape %r, not %r.' % 
44                               (self.shape, x.shape)) 
45   
46          # TODO: make contract 
47          assert np.all(np.isreal(x)), "Expected real vector" 
48          proj = self.project(x) 
49          assert_allclose(proj, x, atol=1e-8) # XXX: tol 
50   
51 -    def belongs_ts(self, bv): 
52  #        formatm('bv', bv) 
53          check('tuple(shape(x),shape(x))', bv, x=self.shape) 
54          base, vel = bv 
55          self.belongs(base) 
56          self.belongs(vel) 
57   
58      @abstractmethod 
59 -    def project(self, v): #@UnusedVariable 
60          ''' Projects a vector onto this Lie Algebra. ''' 
61   
62 -    def project_ts(self, bv): 
63          base, vel = bv 
64          return base, self.project(vel) 
65