Source Code for Module geometry.manifolds.tests.manifold_tests

  1  from geometry import (tran1, tran2, tran3, so2, so3, se2, se3, S1, SE2, SE3, 
  2                        S2, 
  3      Tran1, Tran2, Tran3, T1, T2, T3, R1, R2, SO2, SO3, R3, RandomManifold, 
  4      assert_allclose) 
  5  from nose.plugins.attrib import attr 
  6  import itertools 
  7  import numpy as np 
  8   
  9   
 10 -def check_geodesic_consistency(M, a, b, divisions=5): 
 11      '''  
 12          Check that there is consistency in the geodesics.  
 13       
 14          This is a test that  
 15           
 16              x(t) = geodesic( a, b, t)  
 17               
 18          interpolates between a and b, checking  
 19               
 20              d(a, x(t)) + d(x(t), b) = d(a,b) 
 21       
 22      ''' 
 23      check_geodesic_consistency.description = ( 
 24          '%s: Checking geodesic consistency. ' 
 25          '(a: %s, b: %s)' 
 26          % (M, M.friendly(a), M.friendly(b))) 
 27   
 28      d = M.distance(a, b) 
 29   
 30      ts = np.linspace(0, 1, divisions) 
 31      for t in ts: 
 32          c = M.geodesic(a, b, t) 
 33          M.belongs(c) 
 34          d1 = M.distance(a, c) 
 35          d2 = M.distance(c, b) 
 36   
 37          assert_allclose(d1 + d2, d, atol=1e-7) 
 38   
 39   
 40 -def check_logmap1(M, a, b): 
 41      ''' This is a test that: 
 42       
 43              Exp_a( Log_a(b) ) = b 
 44               
 45      ''' 
 46      check_logmap1.description = ( 
 47          '%s: Checking that logmap/expmap work. ' 
 48          '(a: %s, b: %s)' 
 49          % (M, M.friendly(a), M.friendly(b))) 
 50   
 51      bv = M.logmap(a, b) 
 52      b2 = M.expmap(bv) 
 53      assert_allclose(M.distance(b, b2), 0, atol=1e-7) 
 54   
 55   
 56 -def check_logmap3(M, a, b): 
 57      check_logmap3.description = ( 
 58          '%s: Checking that distance is consistent with logmap/expmap ' 
 59          '(a: %s, b: %s)' 
 60          % (M, M.friendly(a), M.friendly(b))) 
 61   
 62      d = M.distance(a, b) 
 63      base, vel = M.logmap(a, b) 
 64      ratios = [0.5, 0.3] 
 65      for ratio in ratios: 
 66          b2 = M.expmap((base, vel * ratio)) 
 67          d2 = M.distance(a, b2) 
 68          assert_allclose(d * ratio, d2, atol=1e-7) 
 69   
 70   
 71 -def check_friendly(M, a): 
 72      M.friendly(a) 
 73   
 74   
 75 -def check_interesting_point_in_manifold(M, p): 
 76      check_interesting_point_in_manifold.description = '%s: %s' % (M, p) 
 77      M.belongs(p) 
 78   
 79   
 80 -def check_enough_points(M): 
 81      points = list(M.interesting_points()) 
 82      if not points: 
 83          raise ValueError('No test points for %s.' % M) 
 84   
 85   
 86 -def check_manifold_suite(M, num_random=5): 
 87   
 88      yield check_enough_points, M 
 89   
 90      points = M.interesting_points() 
 91   
 92      if isinstance(M, RandomManifold): 
 93          for i in range(num_random): #@UnusedVariable 
 94              points.append(M.sample_uniform()) 
 95   
 96      one_point_functions = [check_friendly, check_interesting_point_in_manifold] 
 97      two_point_functions = [check_geodesic_consistency, check_logmap1, 
 98                             check_logmap3] 
 99   
100      for f in one_point_functions: 
101          for a in points: 
102              yield f, M, a 
103   
104      for f in two_point_functions: 
105          for a, b in itertools.product(points, points): 
106              yield f, M, a, b 
107   
108   
109 -def manifolds_to_check(): 
110  # import warnings 
111  #    warnings.warn('Some checks disabled') 
112      return  [ 
113          SO3, SO2, 
114          R1, R2, R3, 
115          T1, T2, T3, 
116          Tran1, Tran2, Tran3, 
117          SE2, SE3, 
118          S1, S2, 
119          se2, se3, 
120          so2, so3, 
121          tran1, tran2, tran3, 
122      ] 
123   
124   
125 -def test_dimensions(): 
126      x = [ 
127          (SO3, 3), 
128          (SO2, 1), 
129          (R1, 1), 
130          (R2, 2), 
131          (R3, 3), 
132          (T1, 1), (T2, 2), (T3, 3), 
133          (Tran1, 1), (Tran2, 2), (Tran3, 3), 
134          (SE2, 3), (SE3, 6), 
135          (S1, 1), (S2, 2), 
136          (se2, 3), (se3, 6), 
137          (so2, 1), (so3, 3), 
138          (tran1, 1), (tran2, 2), (tran3, 3) 
139      ] 
140   
141      for M, dim in x: 
142          actual = M.get_dimension() 
143          msg = 'Expected %d for %s, got %d ' % (dim, M, actual) 
144          assert actual == dim, msg 
145   
146   
147  @attr('manifolds') 
148 -def test_manifolds(): 
149      for M in manifolds_to_check(): 
150          #print('Testing %s' % M) 
151          for x in check_manifold_suite(M): 
152              yield x 
153   
154   
155  if __name__ == '__main__': 
156      test_manifolds() 
157