mjo/cone/tests.py

   1 """
   2 Additional tests for the mjo.cone.cone module. These are extra
   3 properties that we'd like to check, but which are overkill for inclusion
   4 into Sage.
   5 """
   6
   7 # Sage doesn't load ~/.sage/init.sage during testing (sage -t), so we
   8 # have to explicitly mangle our sitedir here so that "mjo.cone"
   9 # resolves.
  10 from os.path import abspath
  11 from site import addsitedir
  12 addsitedir(abspath('../../'))
  13
  14 from sage.all import *
  15
  16 # The double-import is needed to get the underscore methods.
  17 from mjo.cone.cone import *
  18 from mjo.cone.cone import _basically_the_same, _restrict_to_space
  19
  20 #
  21 # Tests for _restrict_to_space.
  22 #
  23 """
  24 Apply _restrict_to_space according to our paper (to obtain our main
  25 result). Test all four parameter combinations::
  26
  27     sage: set_random_seed()
  28     sage: K = random_cone(max_ambient_dim = 8,
  29     ....:                 strictly_convex=False,
  30     ....:                 solid=False)
  31     sage: K_S = _restrict_to_space(K, K.span())
  32     sage: K_SP = _restrict_to_space(K_S.dual(), K_S.dual().span()).dual()
  33     sage: K_SP.is_proper()
  34     True
  35     sage: K_SP = _restrict_to_space(K_S, K_S.dual().span())
  36     sage: K_SP.is_proper()
  37     True
  38
  39 ::
  40
  41     sage: set_random_seed()
  42     sage: K = random_cone(max_ambient_dim = 8,
  43     ....:                 strictly_convex=True,
  44     ....:                 solid=False)
  45     sage: K_S = _restrict_to_space(K, K.span())
  46     sage: K_SP = _restrict_to_space(K_S.dual(), K_S.dual().span()).dual()
  47     sage: K_SP.is_proper()
  48     True
  49     sage: K_SP = _restrict_to_space(K_S, K_S.dual().span())
  50     sage: K_SP.is_proper()
  51     True
  52
  53 ::
  54
  55     sage: set_random_seed()
  56     sage: K = random_cone(max_ambient_dim = 8,
  57     ....:                 strictly_convex=False,
  58     ....:                 solid=True)
  59     sage: K_S = _restrict_to_space(K, K.span())
  60     sage: K_SP = _restrict_to_space(K_S.dual(), K_S.dual().span()).dual()
  61     sage: K_SP.is_proper()
  62     True
  63     sage: K_SP = _restrict_to_space(K_S, K_S.dual().span())
  64     sage: K_SP.is_proper()
  65     True
  66
  67 ::
  68
  69     sage: set_random_seed()
  70     sage: K = random_cone(max_ambient_dim = 8,
  71     ....:                 strictly_convex=True,
  72     ....:                 solid=True)
  73     sage: K_S = _restrict_to_space(K, K.span())
  74     sage: K_SP = _restrict_to_space(K_S.dual(), K_S.dual().span()).dual()
  75     sage: K_SP.is_proper()
  76     True
  77     sage: K_SP = _restrict_to_space(K_S, K_S.dual().span())
  78     sage: K_SP.is_proper()
  79     True
  80
  81 Test the proposition in our paper concerning the duals and
  82 restrictions. Generate a random cone, then create a subcone of
  83 it. The operation of dual-taking should then commute with rho. Test
  84 all parameter combinations::
  85
  86
  87     sage: set_random_seed()
  88     sage: J = random_cone(max_ambient_dim = 8,
  89     ....:                 solid=False,
  90     ....:                 strictly_convex=False)
  91     sage: K = Cone(random_sublist(J.rays(), 0.5), lattice=J.lattice())
  92     sage: K_W_star = _restrict_to_space(K, J.span()).dual()
  93     sage: K_star_W = _restrict_to_space(K.dual(), J.span())
  94     sage: _basically_the_same(K_W_star, K_star_W)
  95     True
  96
  97 ::
  98
  99     sage: set_random_seed()
 100     sage: J = random_cone(max_ambient_dim = 8,
 101     ....:                 solid=True,
 102     ....:                 strictly_convex=False)
 103     sage: K = Cone(random_sublist(J.rays(), 0.5), lattice=J.lattice())
 104     sage: K_W_star = _restrict_to_space(K, J.span()).dual()
 105     sage: K_star_W = _restrict_to_space(K.dual(), J.span())
 106     sage: _basically_the_same(K_W_star, K_star_W)
 107     True
 108
 109 ::
 110
 111     sage: set_random_seed()
 112     sage: J = random_cone(max_ambient_dim = 8,
 113     ....:                 solid=False,
 114     ....:                 strictly_convex=True)
 115     sage: K = Cone(random_sublist(J.rays(), 0.5), lattice=J.lattice())
 116     sage: K_W_star = _restrict_to_space(K, J.span()).dual()
 117     sage: K_star_W = _restrict_to_space(K.dual(), J.span())
 118     sage: _basically_the_same(K_W_star, K_star_W)
 119     True
 120
 121 ::
 122
 123     sage: set_random_seed()
 124     sage: J = random_cone(max_ambient_dim = 8,
 125     ....:                 solid=True,
 126     ....:                 strictly_convex=True)
 127     sage: K = Cone(random_sublist(J.rays(), 0.5), lattice=J.lattice())
 128     sage: K_W_star = _restrict_to_space(K, J.span()).dual()
 129     sage: K_star_W = _restrict_to_space(K.dual(), J.span())
 130     sage: _basically_the_same(K_W_star, K_star_W)
 131     True
 132
 133 """
 134
 135
 136 #
 137 # Lyapunov rank tests
 138 #
 139 """
 140
 141 The Lyapunov rank is invariant under a linear isomorphism. Check all
 142 combinations of parameters::
 143
 144     sage: K1 = random_cone(max_ambient_dim=8,
 145     ....:                  strictly_convex=True,
 146     ....:                  solid=True)
 147     sage: A = random_matrix(QQ, K1.lattice_dim(), algorithm='unimodular')
 148     sage: K2 = Cone( [ A*r for r in K1.rays() ], lattice=K1.lattice())
 149     sage: lyapunov_rank(K1) == lyapunov_rank(K2)
 150     True
 151
 152 ::
 153
 154     sage: K1 = random_cone(max_ambient_dim=8,
 155     ....:                  strictly_convex=True,
 156     ....:                  solid=False)
 157     sage: A = random_matrix(QQ, K1.lattice_dim(), algorithm='unimodular')
 158     sage: K2 = Cone( [ A*r for r in K1.rays() ], lattice=K1.lattice())
 159     sage: lyapunov_rank(K1) == lyapunov_rank(K2)
 160     True
 161
 162 ::
 163
 164     sage: K1 = random_cone(max_ambient_dim=8,
 165     ....:                  strictly_convex=False,
 166     ....:                  solid=True)
 167     sage: A = random_matrix(QQ, K1.lattice_dim(), algorithm='unimodular')
 168     sage: K2 = Cone( [ A*r for r in K1.rays() ], lattice=K1.lattice())
 169     sage: lyapunov_rank(K1) == lyapunov_rank(K2)
 170     True
 171
 172 ::
 173
 174     sage: K1 = random_cone(max_ambient_dim=8,
 175     ....:                  strictly_convex=False,
 176     ....:                  solid=False)
 177     sage: A = random_matrix(QQ, K1.lattice_dim(), algorithm='unimodular')
 178     sage: K2 = Cone( [ A*r for r in K1.rays() ], lattice=K1.lattice())
 179     sage: lyapunov_rank(K1) == lyapunov_rank(K2)
 180     True
 181
 182 The Lyapunov rank of a dual cone should be the same as the original
 183 cone. Check all combinations of parameters::
 184
 185     sage: set_random_seed()
 186     sage: K = random_cone(max_ambient_dim=8,
 187     ....:                 strictly_convex=False,
 188     ....:                 solid=False)
 189     sage: lyapunov_rank(K) == lyapunov_rank(K.dual())
 190     True
 191
 192 ::
 193
 194     sage: set_random_seed()
 195     sage: K = random_cone(max_ambient_dim=8,
 196     ....:                 strictly_convex=False,
 197     ....:                 solid=True)
 198     sage: lyapunov_rank(K) == lyapunov_rank(K.dual())
 199     True
 200
 201 ::
 202
 203     sage: set_random_seed()
 204     sage: K = random_cone(max_ambient_dim=8,
 205     ....:                 strictly_convex=True,
 206     ....:                 solid=False)
 207     sage: lyapunov_rank(K) == lyapunov_rank(K.dual())
 208     True
 209
 210 ::
 211
 212     sage: set_random_seed()
 213     sage: K = random_cone(max_ambient_dim=8,
 214     ....:                 strictly_convex=True,
 215     ....:                 solid=True)
 216     sage: lyapunov_rank(K) == lyapunov_rank(K.dual())
 217     True
 218
 219 The Lyapunov rank of a cone ``K`` is the dimension of ``LL(K)``. Check
 220 all combinations of parameters::
 221
 222     sage: set_random_seed()
 223     sage: K = random_cone(max_ambient_dim=8,
 224     ....:                 strictly_convex=True,
 225     ....:                 solid=True)
 226     sage: lyapunov_rank(K) == len(LL(K))
 227     True
 228
 229 ::
 230
 231     sage: set_random_seed()
 232     sage: K = random_cone(max_ambient_dim=8,
 233     ....:                 strictly_convex=True,
 234     ....:                 solid=False)
 235     sage: lyapunov_rank(K) == len(LL(K))
 236     True
 237
 238 ::
 239
 240     sage: set_random_seed()
 241     sage: K = random_cone(max_ambient_dim=8,
 242     ....:                 strictly_convex=False,
 243     ....:                 solid=True)
 244     sage: lyapunov_rank(K) == len(LL(K))
 245     True
 246
 247 ::
 248
 249     sage: set_random_seed()
 250     sage: K = random_cone(max_ambient_dim=8,
 251     ....:                 strictly_convex=False,
 252     ....:                 solid=False)
 253     sage: lyapunov_rank(K) == len(LL(K))
 254     True
 255
 256 """