src/Tests/Grid.hs

   1 module Tests.Grid
   2 where
   3
   4 import Data.Maybe (fromJust)
   5 import Test.HUnit
   6 import Test.QuickCheck
   7
   8 import Assertions
   9 import Comparisons
  10 import Cube
  11 import Examples
  12 import FunctionValues (value_at)
  13 import Grid
  14 import Tetrahedron
  15
  16
  17 instance Arbitrary Grid where
  18     arbitrary = do
  19       (Positive h') <- arbitrary :: Gen (Positive Double)
  20       fvs <- arbitrary :: Gen [[[Double]]]
  21       return (make_grid h' fvs)
  22
  23
  24 -- | Check the value of c0030 for tetrahedron0 belonging to the
  25 --   cube centered on (1,1,1) with a grid constructed from the
  26 --   trilinear values. See example one in the paper.
  27 test_trilinear_c0030 :: Assertion
  28 test_trilinear_c0030 =
  29     assertAlmostEqual "c0030 is correct" (c t 0 0 3 0) (17/8)
  30       where
  31         g = make_grid 1 trilinear
  32         cube = fromJust $ cube_at g 1 1 1
  33         t = tetrahedron0 cube
  34
  35
  36 -- | Check the value of c0003 for tetrahedron0 belonging to the
  37 --   cube centered on (1,1,1) with a grid constructed from the
  38 --   trilinear values. See example one in the paper.
  39 test_trilinear_c0003 :: Assertion
  40 test_trilinear_c0003 =
  41     assertAlmostEqual "c0003 is correct" (c t 0 0 0 3) (27/8)
  42       where
  43         g = make_grid 1 trilinear
  44         cube = fromJust $ cube_at g 1 1 1
  45         t = tetrahedron0 cube
  46
  47
  48 -- | Check the value of c0021 for tetrahedron0 belonging to the
  49 --   cube centered on (1,1,1) with a grid constructed from the
  50 --   trilinear values. See example one in the paper.
  51 test_trilinear_c0021 :: Assertion
  52 test_trilinear_c0021 =
  53     assertAlmostEqual "c0021 is correct" (c t 0 0 2 1) (61/24)
  54       where
  55         g = make_grid 1 trilinear
  56         cube = fromJust $ cube_at g 1 1 1
  57         t = tetrahedron0 cube
  58
  59
  60 -- | Check the value of c0012 for tetrahedron0 belonging to the
  61 --   cube centered on (1,1,1) with a grid constructed from the
  62 --   trilinear values. See example one in the paper.
  63 test_trilinear_c0012 :: Assertion
  64 test_trilinear_c0012 =
  65     assertAlmostEqual "c0012 is correct" (c t 0 0 1 2) (71/24)
  66       where
  67         g = make_grid 1 trilinear
  68         cube = fromJust $ cube_at g 1 1 1
  69         t = tetrahedron0 cube
  70
  71
  72 -- | Check the value of c0120 for tetrahedron0 belonging to the
  73 --   cube centered on (1,1,1) with a grid constructed from the
  74 --   trilinear values. See example one in the paper.
  75 test_trilinear_c0120 :: Assertion
  76 test_trilinear_c0120 =
  77     assertAlmostEqual "c0120 is correct" (c t 0 1 2 0) (55/24)
  78       where
  79         g = make_grid 1 trilinear
  80         cube = fromJust $ cube_at g 1 1 1
  81         t = tetrahedron0 cube
  82
  83
  84 -- | Check the value of c0102 for tetrahedron0 belonging to the
  85 --   cube centered on (1,1,1) with a grid constructed from the
  86 --   trilinear values. See example one in the paper.
  87 test_trilinear_c0102 :: Assertion
  88 test_trilinear_c0102 =
  89     assertAlmostEqual "c0102 is correct" (c t 0 1 0 2) (73/24)
  90       where
  91         g = make_grid 1 trilinear
  92         cube = fromJust $ cube_at g 1 1 1
  93         t = tetrahedron0 cube
  94
  95
  96 -- | Check the value of c0111 for tetrahedron0 belonging to the
  97 --   cube centered on (1,1,1) with a grid constructed from the
  98 --   trilinear values. See example one in the paper.
  99 test_trilinear_c0111 :: Assertion
 100 test_trilinear_c0111 =
 101     assertAlmostEqual "c0111 is correct" (c t 0 1 1 1) (8/3)
 102       where
 103         g = make_grid 1 trilinear
 104         cube = fromJust $ cube_at g 1 1 1
 105         t = tetrahedron0 cube
 106
 107
 108 -- | Check the value of c0210 for tetrahedron0 belonging to the
 109 --   cube centered on (1,1,1) with a grid constructed from the
 110 --   trilinear values. See example one in the paper.
 111 test_trilinear_c0210 :: Assertion
 112 test_trilinear_c0210 =
 113     assertAlmostEqual "c0210 is correct" (c t 0 2 1 0) (29/12)
 114       where
 115         g = make_grid 1 trilinear
 116         cube = fromJust $ cube_at g 1 1 1
 117         t = tetrahedron0 cube
 118
 119
 120 -- | Check the value of c0201 for tetrahedron0 belonging to the
 121 --   cube centered on (1,1,1) with a grid constructed from the
 122 --   trilinear values. See example one in the paper.
 123 test_trilinear_c0201 :: Assertion
 124 test_trilinear_c0201 =
 125     assertAlmostEqual "c0201 is correct" (c t 0 2 0 1) (11/4)
 126       where
 127         g = make_grid 1 trilinear
 128         cube = fromJust $ cube_at g 1 1 1
 129         t = tetrahedron0 cube
 130
 131
 132 -- | Check the value of c0300 for tetrahedron0 belonging to the
 133 --   cube centered on (1,1,1) with a grid constructed from the
 134 --   trilinear values. See example one in the paper.
 135 test_trilinear_c0300 :: Assertion
 136 test_trilinear_c0300 =
 137     assertAlmostEqual "c0300 is correct" (c t 0 3 0 0) (5/2)
 138       where
 139         g = make_grid 1 trilinear
 140         cube = fromJust $ cube_at g 1 1 1
 141         t = tetrahedron0 cube
 142
 143
 144 -- | Check the value of c1020 for tetrahedron0 belonging to the
 145 --   cube centered on (1,1,1) with a grid constructed from the
 146 --   trilinear values. See example one in the paper.
 147 test_trilinear_c1020 :: Assertion
 148 test_trilinear_c1020 =
 149     assertAlmostEqual "c1020 is correct" (c t 1 0 2 0) (8/3)
 150       where
 151         g = make_grid 1 trilinear
 152         cube = fromJust $ cube_at g 1 1 1
 153         t = tetrahedron0 cube
 154
 155
 156 -- | Check the value of c1002 for tetrahedron0 belonging to the
 157 --   cube centered on (1,1,1) with a grid constructed from the
 158 --   trilinear values. See example one in the paper.
 159 test_trilinear_c1002 :: Assertion
 160 test_trilinear_c1002 =
 161     assertAlmostEqual "c1002 is correct" (c t 1 0 0 2) (23/6)
 162       where
 163         g = make_grid 1 trilinear
 164         cube = fromJust $ cube_at g 1 1 1
 165         t = tetrahedron0 cube
 166
 167
 168 -- | Check the value of c1011 for tetrahedron0 belonging to the
 169 --   cube centered on (1,1,1) with a grid constructed from the
 170 --   trilinear values. See example one in the paper.
 171 test_trilinear_c1011 :: Assertion
 172 test_trilinear_c1011 =
 173     assertAlmostEqual "c1011 is correct" (c t 1 0 1 1) (13/4)
 174       where
 175         g = make_grid 1 trilinear
 176         cube = fromJust $ cube_at g 1 1 1
 177         t = tetrahedron0 cube
 178
 179
 180 -- | Check the value of c1110 for tetrahedron0 belonging to the
 181 --   cube centered on (1,1,1) with a grid constructed from the
 182 --   trilinear values. See example one in the paper.
 183 test_trilinear_c1110 :: Assertion
 184 test_trilinear_c1110 =
 185     assertAlmostEqual "c1110 is correct" (c t 1 1 1 0) (23/8)
 186       where
 187         g = make_grid 1 trilinear
 188         cube = fromJust $ cube_at g 1 1 1
 189         t = tetrahedron0 cube
 190
 191
 192 -- | Check the value of c1101 for tetrahedron0 belonging to the
 193 --   cube centered on (1,1,1) with a grid constructed from the
 194 --   trilinear values. See example one in the paper.
 195 test_trilinear_c1101 :: Assertion
 196 test_trilinear_c1101 =
 197     assertAlmostEqual "c1101 is correct" (c t 1 1 0 1) (27/8)
 198       where
 199         g = make_grid 1 trilinear
 200         cube = fromJust $ cube_at g 1 1 1
 201         t = tetrahedron0 cube
 202
 203
 204 -- | Check the value of c1200 for tetrahedron0 belonging to the
 205 --   cube centered on (1,1,1) with a grid constructed from the
 206 --   trilinear values. See example one in the paper.
 207 test_trilinear_c1200 :: Assertion
 208 test_trilinear_c1200 =
 209     assertAlmostEqual "c1200 is correct" (c t 1 2 0 0) 3
 210       where
 211         g = make_grid 1 trilinear
 212         cube = fromJust $ cube_at g 1 1 1
 213         t = tetrahedron0 cube
 214
 215
 216 -- | Check the value of c2010 for tetrahedron0 belonging to the
 217 --   cube centered on (1,1,1) with a grid constructed from the
 218 --   trilinear values. See example one in the paper.
 219 test_trilinear_c2010 :: Assertion
 220 test_trilinear_c2010 =
 221     assertAlmostEqual "c2010 is correct" (c t 2 0 1 0) (10/3)
 222       where
 223         g = make_grid 1 trilinear
 224         cube = fromJust $ cube_at g 1 1 1
 225         t = tetrahedron0 cube
 226
 227
 228 -- | Check the value of c2001 for tetrahedron0 belonging to the
 229 --   cube centered on (1,1,1) with a grid constructed from the
 230 --   trilinear values. See example one in the paper.
 231 test_trilinear_c2001 :: Assertion
 232 test_trilinear_c2001 =
 233     assertAlmostEqual "c2001 is correct" (c t 2 0 0 1) 4
 234       where
 235         g = make_grid 1 trilinear
 236         cube = fromJust $ cube_at g 1 1 1
 237         t = tetrahedron0 cube
 238
 239
 240 -- | Check the value of c2100 for tetrahedron0 belonging to the
 241 --   cube centered on (1,1,1) with a grid constructed from the
 242 --   trilinear values. See example one in the paper.
 243 test_trilinear_c2100 :: Assertion
 244 test_trilinear_c2100 =
 245     assertAlmostEqual "c2100 is correct" (c t 2 1 0 0) (7/2)
 246       where
 247         g = make_grid 1 trilinear
 248         cube = fromJust $ cube_at g 1 1 1
 249         t = tetrahedron0 cube
 250
 251
 252 -- | Check the value of c3000 for tetrahedron0 belonging to the
 253 --   cube centered on (1,1,1) with a grid constructed from the
 254 --   trilinear values. See example one in the paper.
 255 test_trilinear_c3000 :: Assertion
 256 test_trilinear_c3000 =
 257     assertAlmostEqual "c3000 is correct" (c t 3 0 0 0) 4
 258       where
 259         g = make_grid 1 trilinear
 260         cube = fromJust $ cube_at g 1 1 1
 261         t = tetrahedron0 cube
 262
 263
 264 -- | Make sure that v0 of tetrahedron0 belonging to the cube centered
 265 --   on (1,1,1) with a grid constructed from the trilinear values
 266 --   winds up in the right place. See example one in the paper.
 267 test_trilinear_f0_t0_v0 :: Assertion
 268 test_trilinear_f0_t0_v0 =
 269     assertEqual "v0 is correct" (v0 t) (1, 1, 1)
 270       where
 271         g = make_grid 1 trilinear
 272         cube = fromJust $ cube_at g 1 1 1
 273         t = tetrahedron0 cube
 274
 275
 276 -- | Make sure that v1 of tetrahedron0 belonging to the cube centered
 277 --   on (1,1,1) with a grid constructed from the trilinear values
 278 --   winds up in the right place. See example one in the paper.
 279 test_trilinear_f0_t0_v1 :: Assertion
 280 test_trilinear_f0_t0_v1 =
 281     assertEqual "v1 is correct" (v1 t) (0.5, 1, 1)
 282       where
 283         g = make_grid 1 trilinear
 284         cube = fromJust $ cube_at g 1 1 1
 285         t = tetrahedron0 cube
 286
 287
 288 -- | Make sure that v2 of tetrahedron0 belonging to the cube centered
 289 --   on (1,1,1) with a grid constructed from the trilinear values
 290 --   winds up in the right place. See example one in the paper.
 291 test_trilinear_f0_t0_v2 :: Assertion
 292 test_trilinear_f0_t0_v2 =
 293     assertEqual "v2 is correct" (v2 t) (0.5, 0.5, 1.5)
 294       where
 295         g = make_grid 1 trilinear
 296         cube = fromJust $ cube_at g 1 1 1
 297         t = tetrahedron0 cube
 298
 299
 300 -- | Make sure that v3 of tetrahedron0 belonging to the cube centered
 301 --   on (1,1,1) with a grid constructed from the trilinear values
 302 --   winds up in the right place. See example one in the paper.
 303 test_trilinear_f0_t0_v3 :: Assertion
 304 test_trilinear_f0_t0_v3 =
 305     assertClose "v3 is correct" (v3 t) (0.5, 1.5, 1.5)
 306       where
 307         g = make_grid 1 trilinear
 308         cube = fromJust $ cube_at g 1 1 1
 309         t = tetrahedron0 cube
 310
 311
 312 test_trilinear_reproduced :: Assertion
 313 test_trilinear_reproduced =
 314     assertTrue "trilinears are reproduced correctly" $
 315              and [p (i', j', k') ~= value_at trilinear i j k
 316                     | i <- [0..2],
 317                       j <- [0..2],
 318                       k <- [0..2],
 319                       let i' = fromIntegral i,
 320                       let j' = fromIntegral j,
 321                       let k' = fromIntegral k]
 322     where
 323       g = make_grid 1 trilinear
 324       c0 = fromJust $ cube_at g 1 1 1
 325       t0 = tetrahedron0 c0
 326       p = polynomial t0
 327
 328
 329 test_zeros_reproduced :: Assertion
 330 test_zeros_reproduced =
 331     assertTrue "the zero function is reproduced correctly" $
 332              and [p (i', j', k') ~= value_at zeros i j k
 333                     | i <- [0..2],
 334                       j <- [0..2],
 335                       k <- [0..2],
 336                       let i' = fromIntegral i,
 337                       let j' = fromIntegral j,
 338                       let k' = fromIntegral k]
 339     where
 340       g = make_grid 1 zeros
 341       c0 = fromJust $ cube_at g 1 1 1
 342       t0 = tetrahedron0 c0
 343       p = polynomial t0