src/Tests/Cube.hs

   1 module Tests.Cube
   2 where
   3
   4 import Debug.Trace (trace)
   5 import Test.QuickCheck
   6
   7 import Comparisons
   8 import Cube
   9 import FunctionValues (FunctionValues)
  10 import Tests.FunctionValues ()
  11 import Tetrahedron (b0, b1, b2, b3, c,
  12                     Tetrahedron(Tetrahedron),
  13                     v0, v1, v2, v3, volume)
  14
  15 instance Arbitrary Cube where
  16     arbitrary = do
  17       (Positive h') <- arbitrary :: Gen (Positive Double)
  18       i' <- choose (coordmin, coordmax)
  19       j' <- choose (coordmin, coordmax)
  20       k' <- choose (coordmin, coordmax)
  21       fv' <- arbitrary :: Gen FunctionValues
  22       return (Cube h' i' j' k' fv')
  23         where
  24           coordmin = -268435456 -- -(2^29 / 2)
  25           coordmax = 268435456  -- +(2^29 / 2)
  26
  27
  28 -- Quickcheck tests.
  29
  30 -- | Since the grid size is necessarily positive, all tetrahedrons
  31 --   (which comprise cubes of positive volume) must have positive volume
  32 --   as well.
  33 prop_all_volumes_positive :: Cube -> Bool
  34 prop_all_volumes_positive c =
  35     null nonpositive_volumes
  36     where
  37       ts = tetrahedrons c
  38       volumes = map volume ts
  39       nonpositive_volumes = filter (<= 0) volumes
  40
  41 -- | In fact, since all of the tetrahedra are identical, we should
  42 --   already know their volumes. There's 24 tetrahedra to a cube, so
  43 --   we'd expect the volume of each one to be (1/24)*h^3.
  44 prop_tetrahedron0_volumes_exact :: Cube -> Bool
  45 prop_tetrahedron0_volumes_exact c =
  46     volume (tetrahedron0 c) ~= (1/24)*(delta^(3::Int))
  47     where
  48       delta = h c
  49
  50 -- | In fact, since all of the tetrahedra are identical, we should
  51 --   already know their volumes. There's 24 tetrahedra to a cube, so
  52 --   we'd expect the volume of each one to be (1/24)*h^3.
  53 prop_tetrahedron1_volumes_exact :: Cube -> Bool
  54 prop_tetrahedron1_volumes_exact c =
  55     volume (tetrahedron1 c) ~= (1/24)*(delta^(3::Int))
  56     where
  57       delta = h c
  58
  59 -- | In fact, since all of the tetrahedra are identical, we should
  60 --   already know their volumes. There's 24 tetrahedra to a cube, so
  61 --   we'd expect the volume of each one to be (1/24)*h^3.
  62 prop_tetrahedron2_volumes_exact :: Cube -> Bool
  63 prop_tetrahedron2_volumes_exact c =
  64     volume (tetrahedron2 c) ~= (1/24)*(delta^(3::Int))
  65     where
  66       delta = h c
  67
  68 -- | In fact, since all of the tetrahedra are identical, we should
  69 --   already know their volumes. There's 24 tetrahedra to a cube, so
  70 --   we'd expect the volume of each one to be (1/24)*h^3.
  71 prop_tetrahedron3_volumes_exact :: Cube -> Bool
  72 prop_tetrahedron3_volumes_exact c =
  73     volume (tetrahedron3 c) ~= (1/24)*(delta^(3::Int))
  74     where
  75       delta = h c
  76
  77 -- | In fact, since all of the tetrahedra are identical, we should
  78 --   already know their volumes. There's 24 tetrahedra to a cube, so
  79 --   we'd expect the volume of each one to be (1/24)*h^3.
  80 prop_tetrahedron4_volumes_exact :: Cube -> Bool
  81 prop_tetrahedron4_volumes_exact c =
  82     volume (tetrahedron4 c) ~= (1/24)*(delta^(3::Int))
  83     where
  84       delta = h c
  85
  86 -- | In fact, since all of the tetrahedra are identical, we should
  87 --   already know their volumes. There's 24 tetrahedra to a cube, so
  88 --   we'd expect the volume of each one to be (1/24)*h^3.
  89 prop_tetrahedron5_volumes_exact :: Cube -> Bool
  90 prop_tetrahedron5_volumes_exact c =
  91     volume (tetrahedron5 c) ~= (1/24)*(delta^(3::Int))
  92     where
  93       delta = h c
  94
  95 -- | In fact, since all of the tetrahedra are identical, we should
  96 --   already know their volumes. There's 24 tetrahedra to a cube, so
  97 --   we'd expect the volume of each one to be (1/24)*h^3.
  98 prop_tetrahedron6_volumes_exact :: Cube -> Bool
  99 prop_tetrahedron6_volumes_exact c =
 100     volume (tetrahedron6 c) ~= (1/24)*(delta^(3::Int))
 101     where
 102       delta = h c
 103
 104 -- | In fact, since all of the tetrahedra are identical, we should
 105 --   already know their volumes. There's 24 tetrahedra to a cube, so
 106 --   we'd expect the volume of each one to be (1/24)*h^3.
 107 prop_tetrahedron7_volumes_exact :: Cube -> Bool
 108 prop_tetrahedron7_volumes_exact c =
 109     volume (tetrahedron7 c) ~= (1/24)*(delta^(3::Int))
 110     where
 111       delta = h c
 112
 113 -- | All tetrahedron should have their v0 located at the center of the cube.
 114 prop_v0_all_equal :: Cube -> Bool
 115 prop_v0_all_equal c = (v0 t0) == (v0 t1)
 116     where
 117       t0 = head (tetrahedrons c) -- Doesn't matter which two we choose.
 118       t1 = head $ tail (tetrahedrons c)
 119
 120
 121 -- | This pretty much repeats the prop_all_volumes_positive property,
 122 --   but will let me know which tetrahedrons's vertices are disoriented.
 123 prop_tetrahedron0_volumes_positive :: Cube -> Bool
 124 prop_tetrahedron0_volumes_positive c =
 125     volume (tetrahedron0 c) > 0
 126
 127 -- | This pretty much repeats the prop_all_volumes_positive property,
 128 --   but will let me know which tetrahedrons's vertices are disoriented.
 129 prop_tetrahedron1_volumes_positive :: Cube -> Bool
 130 prop_tetrahedron1_volumes_positive c =
 131     volume (tetrahedron1 c) > 0
 132
 133 -- | This pretty much repeats the prop_all_volumes_positive property,
 134 --   but will let me know which tetrahedrons's vertices are disoriented.
 135 prop_tetrahedron2_volumes_positive :: Cube -> Bool
 136 prop_tetrahedron2_volumes_positive c =
 137     volume (tetrahedron2 c) > 0
 138
 139 -- | This pretty much repeats the prop_all_volumes_positive property,
 140 --   but will let me know which tetrahedrons's vertices are disoriented.
 141 prop_tetrahedron3_volumes_positive :: Cube -> Bool
 142 prop_tetrahedron3_volumes_positive c =
 143     volume (tetrahedron3 c) > 0
 144
 145 -- | This pretty much repeats the prop_all_volumes_positive property,
 146 --   but will let me know which tetrahedrons's vertices are disoriented.
 147 prop_tetrahedron4_volumes_positive :: Cube -> Bool
 148 prop_tetrahedron4_volumes_positive c =
 149     volume (tetrahedron4 c) > 0
 150
 151 -- | This pretty much repeats the prop_all_volumes_positive property,
 152 --   but will let me know which tetrahedrons's vertices are disoriented.
 153 prop_tetrahedron5_volumes_positive :: Cube -> Bool
 154 prop_tetrahedron5_volumes_positive c =
 155     volume (tetrahedron5 c) > 0
 156
 157 -- | This pretty much repeats the prop_all_volumes_positive property,
 158 --   but will let me know which tetrahedrons's vertices are disoriented.
 159 prop_tetrahedron6_volumes_positive :: Cube -> Bool
 160 prop_tetrahedron6_volumes_positive c =
 161     volume (tetrahedron6 c) > 0
 162
 163 -- | This pretty much repeats the prop_all_volumes_positive property,
 164 --   but will let me know which tetrahedrons's vertices are disoriented.
 165 prop_tetrahedron7_volumes_positive :: Cube -> Bool
 166 prop_tetrahedron7_volumes_positive c =
 167     volume (tetrahedron7 c) > 0
 168
 169 -- | This pretty much repeats the prop_all_volumes_positive property,
 170 --   but will let me know which tetrahedrons's vertices are disoriented.
 171 prop_tetrahedron8_volumes_positive :: Cube -> Bool
 172 prop_tetrahedron8_volumes_positive c =
 173     volume (tetrahedron8 c) > 0
 174
 175 -- | This pretty much repeats the prop_all_volumes_positive property,
 176 --   but will let me know which tetrahedrons's vertices are disoriented.
 177 prop_tetrahedron9_volumes_positive :: Cube -> Bool
 178 prop_tetrahedron9_volumes_positive c =
 179     volume (tetrahedron9 c) > 0
 180
 181 -- | This pretty much repeats the prop_all_volumes_positive property,
 182 --   but will let me know which tetrahedrons's vertices are disoriented.
 183 prop_tetrahedron10_volumes_positive :: Cube -> Bool
 184 prop_tetrahedron10_volumes_positive c =
 185     volume (tetrahedron10 c) > 0
 186
 187 -- | This pretty much repeats the prop_all_volumes_positive property,
 188 --   but will let me know which tetrahedrons's vertices are disoriented.
 189 prop_tetrahedron11_volumes_positive :: Cube -> Bool
 190 prop_tetrahedron11_volumes_positive c =
 191     volume (tetrahedron11 c) > 0
 192
 193 -- | This pretty much repeats the prop_all_volumes_positive property,
 194 --   but will let me know which tetrahedrons's vertices are disoriented.
 195 prop_tetrahedron12_volumes_positive :: Cube -> Bool
 196 prop_tetrahedron12_volumes_positive c =
 197     volume (tetrahedron12 c) > 0
 198
 199 -- | This pretty much repeats the prop_all_volumes_positive property,
 200 --   but will let me know which tetrahedrons's vertices are disoriented.
 201 prop_tetrahedron13_volumes_positive :: Cube -> Bool
 202 prop_tetrahedron13_volumes_positive c =
 203     volume (tetrahedron13 c) > 0
 204
 205 -- | This pretty much repeats the prop_all_volumes_positive property,
 206 --   but will let me know which tetrahedrons's vertices are disoriented.
 207 prop_tetrahedron14_volumes_positive :: Cube -> Bool
 208 prop_tetrahedron14_volumes_positive c =
 209     volume (tetrahedron14 c) > 0
 210
 211 -- | This pretty much repeats the prop_all_volumes_positive property,
 212 --   but will let me know which tetrahedrons's vertices are disoriented.
 213 prop_tetrahedron15_volumes_positive :: Cube -> Bool
 214 prop_tetrahedron15_volumes_positive c =
 215     volume (tetrahedron15 c) > 0
 216
 217 -- | This pretty much repeats the prop_all_volumes_positive property,
 218 --   but will let me know which tetrahedrons's vertices are disoriented.
 219 prop_tetrahedron16_volumes_positive :: Cube -> Bool
 220 prop_tetrahedron16_volumes_positive c =
 221     volume (tetrahedron16 c) > 0
 222
 223 -- | This pretty much repeats the prop_all_volumes_positive property,
 224 --   but will let me know which tetrahedrons's vertices are disoriented.
 225 prop_tetrahedron17_volumes_positive :: Cube -> Bool
 226 prop_tetrahedron17_volumes_positive c =
 227     volume (tetrahedron17 c) > 0
 228
 229 -- | This pretty much repeats the prop_all_volumes_positive property,
 230 --   but will let me know which tetrahedrons's vertices are disoriented.
 231 prop_tetrahedron18_volumes_positive :: Cube -> Bool
 232 prop_tetrahedron18_volumes_positive c =
 233     volume (tetrahedron18 c) > 0
 234
 235 -- | This pretty much repeats the prop_all_volumes_positive property,
 236 --   but will let me know which tetrahedrons's vertices are disoriented.
 237 prop_tetrahedron19_volumes_positive :: Cube -> Bool
 238 prop_tetrahedron19_volumes_positive c =
 239     volume (tetrahedron19 c) > 0
 240
 241 -- | This pretty much repeats the prop_all_volumes_positive property,
 242 --   but will let me know which tetrahedrons's vertices are disoriented.
 243 prop_tetrahedron20_volumes_positive :: Cube -> Bool
 244 prop_tetrahedron20_volumes_positive c =
 245     volume (tetrahedron20 c) > 0
 246
 247 -- | This pretty much repeats the prop_all_volumes_positive property,
 248 --   but will let me know which tetrahedrons's vertices are disoriented.
 249 prop_tetrahedron21_volumes_positive :: Cube -> Bool
 250 prop_tetrahedron21_volumes_positive c =
 251     volume (tetrahedron21 c) > 0
 252
 253 -- | This pretty much repeats the prop_all_volumes_positive property,
 254 --   but will let me know which tetrahedrons's vertices are disoriented.
 255 prop_tetrahedron22_volumes_positive :: Cube -> Bool
 256 prop_tetrahedron22_volumes_positive c =
 257     volume (tetrahedron22 c) > 0
 258
 259 -- | This pretty much repeats the prop_all_volumes_positive property,
 260 --   but will let me know which tetrahedrons's vertices are disoriented.
 261 prop_tetrahedron23_volumes_positive :: Cube -> Bool
 262 prop_tetrahedron23_volumes_positive c =
 263     volume (tetrahedron23 c) > 0
 264
 265
 266 -- | Given in Sorokina and Zeilfelder, p. 79.
 267 --prop_c0120_identity1 :: Cube -> Bool
 268 --prop_c0120_identity1 cube =
 269 --   c0 ~= (c1 + c2) / 2
 270 --     where
 271 --       c0 = trace ("c0 :" ++ (show (c t0 0 1 2 0))) (c t0 0 1 2 0)
 272 --       c1 = trace ("c1 :" ++ (show (c t0 0 0 2 1))) (c t0 0 0 2 1)
 273 --       c2 = trace ("c2 :" ++ (show (c t1 0 0 2 1))) (c t1 0 0 2 1)
 274 --       t0 = tetrahedron0 cube
 275 --       t1 = tetrahedron1 cube
 276
 277
 278 -- | Given in Sorokina and Zeilfelder, p. 78.
 279 -- prop_cijk1_identity :: Cube -> Bool
 280 -- prop_cijk1_identity cube =
 281 --      and [ c t0 i j k 1 ~=
 282 --                  (c t1 (i+1) j k 0) * ((b0 t0) (v3 t1)) +
 283 --                  (c t1 i (j+1) k 0) * ((b1 t0) (v3 t1)) +
 284 --                  (c t1 i j (k+1) 0) * ((b2 t0) (v3 t1)) +
 285 --                  (c t1 i j k 1) * ((b3 t0) (v3 t1)) | i <- [0..2],
 286 --                                                       j <- [0..2],
 287 --                                                       k <- [0..2],
 288 --                                                       i + j + k == 2]
 289 --       where
 290 --         t0 = tetrahedron0 cube
 291 --         t1 = tetrahedron1 cube