src/Tests/Grid.hs

   1 module Tests.Grid
   2 where
   3
   4 import Data.Maybe (fromJust)
   5 import Debug.Trace (trace)
   6 import Test.HUnit
   7 import Test.QuickCheck
   8
   9 import Assertions
  10 import Comparisons
  11 import Cube hiding (i, j, k)
  12 import Examples
  13 import FunctionValues (value_at)
  14 import Grid
  15 import Tetrahedron
  16
  17
  18 instance Arbitrary Grid where
  19     arbitrary = do
  20       (Positive h') <- arbitrary :: Gen (Positive Double)
  21       fvs <- arbitrary :: Gen [[[Double]]]
  22       return (make_grid h' fvs)
  23
  24
  25 -- | Check the value of c0030 for tetrahedron0 belonging to the
  26 --   cube centered on (1,1,1) with a grid constructed from the
  27 --   trilinear values. See example one in the paper.
  28 test_trilinear_c0030 :: Assertion
  29 test_trilinear_c0030 =
  30     assertAlmostEqual "c0030 is correct" (c t 0 0 3 0) (17/8)
  31       where
  32         g = make_grid 1 trilinear
  33         cube = fromJust $ cube_at g 1 1 1
  34         t = tetrahedron0 cube
  35
  36
  37 -- | Check the value of c0003 for tetrahedron0 belonging to the
  38 --   cube centered on (1,1,1) with a grid constructed from the
  39 --   trilinear values. See example one in the paper.
  40 test_trilinear_c0003 :: Assertion
  41 test_trilinear_c0003 =
  42     assertAlmostEqual "c0003 is correct" (c t 0 0 0 3) (27/8)
  43       where
  44         g = make_grid 1 trilinear
  45         cube = fromJust $ cube_at g 1 1 1
  46         t = tetrahedron0 cube
  47
  48
  49 -- | Check the value of c0021 for tetrahedron0 belonging to the
  50 --   cube centered on (1,1,1) with a grid constructed from the
  51 --   trilinear values. See example one in the paper.
  52 test_trilinear_c0021 :: Assertion
  53 test_trilinear_c0021 =
  54     assertAlmostEqual "c0021 is correct" (c t 0 0 2 1) (61/24)
  55       where
  56         g = make_grid 1 trilinear
  57         cube = fromJust $ cube_at g 1 1 1
  58         t = tetrahedron0 cube
  59
  60
  61 -- | Check the value of c0012 for tetrahedron0 belonging to the
  62 --   cube centered on (1,1,1) with a grid constructed from the
  63 --   trilinear values. See example one in the paper.
  64 test_trilinear_c0012 :: Assertion
  65 test_trilinear_c0012 =
  66     assertAlmostEqual "c0012 is correct" (c t 0 0 1 2) (71/24)
  67       where
  68         g = make_grid 1 trilinear
  69         cube = fromJust $ cube_at g 1 1 1
  70         t = tetrahedron0 cube
  71
  72
  73 -- | Check the value of c0120 for tetrahedron0 belonging to the
  74 --   cube centered on (1,1,1) with a grid constructed from the
  75 --   trilinear values. See example one in the paper.
  76 test_trilinear_c0120 :: Assertion
  77 test_trilinear_c0120 =
  78     assertAlmostEqual "c0120 is correct" (c t 0 1 2 0) (55/24)
  79       where
  80         g = make_grid 1 trilinear
  81         cube = fromJust $ cube_at g 1 1 1
  82         t = tetrahedron0 cube
  83
  84
  85 -- | Check the value of c0102 for tetrahedron0 belonging to the
  86 --   cube centered on (1,1,1) with a grid constructed from the
  87 --   trilinear values. See example one in the paper.
  88 test_trilinear_c0102 :: Assertion
  89 test_trilinear_c0102 =
  90     assertAlmostEqual "c0102 is correct" (c t 0 1 0 2) (73/24)
  91       where
  92         g = make_grid 1 trilinear
  93         cube = fromJust $ cube_at g 1 1 1
  94         t = tetrahedron0 cube
  95
  96
  97 -- | Check the value of c0111 for tetrahedron0 belonging to the
  98 --   cube centered on (1,1,1) with a grid constructed from the
  99 --   trilinear values. See example one in the paper.
 100 test_trilinear_c0111 :: Assertion
 101 test_trilinear_c0111 =
 102     assertAlmostEqual "c0111 is correct" (c t 0 1 1 1) (8/3)
 103       where
 104         g = make_grid 1 trilinear
 105         cube = fromJust $ cube_at g 1 1 1
 106         t = tetrahedron0 cube
 107
 108
 109 -- | Check the value of c0210 for tetrahedron0 belonging to the
 110 --   cube centered on (1,1,1) with a grid constructed from the
 111 --   trilinear values. See example one in the paper.
 112 test_trilinear_c0210 :: Assertion
 113 test_trilinear_c0210 =
 114     assertAlmostEqual "c0210 is correct" (c t 0 2 1 0) (29/12)
 115       where
 116         g = make_grid 1 trilinear
 117         cube = fromJust $ cube_at g 1 1 1
 118         t = tetrahedron0 cube
 119
 120
 121 -- | Check the value of c0201 for tetrahedron0 belonging to the
 122 --   cube centered on (1,1,1) with a grid constructed from the
 123 --   trilinear values. See example one in the paper.
 124 test_trilinear_c0201 :: Assertion
 125 test_trilinear_c0201 =
 126     assertAlmostEqual "c0201 is correct" (c t 0 2 0 1) (11/4)
 127       where
 128         g = make_grid 1 trilinear
 129         cube = fromJust $ cube_at g 1 1 1
 130         t = tetrahedron0 cube
 131
 132
 133 -- | Check the value of c0300 for tetrahedron0 belonging to the
 134 --   cube centered on (1,1,1) with a grid constructed from the
 135 --   trilinear values. See example one in the paper.
 136 test_trilinear_c0300 :: Assertion
 137 test_trilinear_c0300 =
 138     assertAlmostEqual "c0300 is correct" (c t 0 3 0 0) (5/2)
 139       where
 140         g = make_grid 1 trilinear
 141         cube = fromJust $ cube_at g 1 1 1
 142         t = tetrahedron0 cube
 143
 144
 145 -- | Check the value of c1020 for tetrahedron0 belonging to the
 146 --   cube centered on (1,1,1) with a grid constructed from the
 147 --   trilinear values. See example one in the paper.
 148 test_trilinear_c1020 :: Assertion
 149 test_trilinear_c1020 =
 150     assertAlmostEqual "c1020 is correct" (c t 1 0 2 0) (8/3)
 151       where
 152         g = make_grid 1 trilinear
 153         cube = fromJust $ cube_at g 1 1 1
 154         t = tetrahedron0 cube
 155
 156
 157 -- | Check the value of c1002 for tetrahedron0 belonging to the
 158 --   cube centered on (1,1,1) with a grid constructed from the
 159 --   trilinear values. See example one in the paper.
 160 test_trilinear_c1002 :: Assertion
 161 test_trilinear_c1002 =
 162     assertAlmostEqual "c1002 is correct" (c t 1 0 0 2) (23/6)
 163       where
 164         g = make_grid 1 trilinear
 165         cube = fromJust $ cube_at g 1 1 1
 166         t = tetrahedron0 cube
 167
 168
 169 -- | Check the value of c1011 for tetrahedron0 belonging to the
 170 --   cube centered on (1,1,1) with a grid constructed from the
 171 --   trilinear values. See example one in the paper.
 172 test_trilinear_c1011 :: Assertion
 173 test_trilinear_c1011 =
 174     assertAlmostEqual "c1011 is correct" (c t 1 0 1 1) (13/4)
 175       where
 176         g = make_grid 1 trilinear
 177         cube = fromJust $ cube_at g 1 1 1
 178         t = tetrahedron0 cube
 179
 180
 181 -- | Check the value of c1110 for tetrahedron0 belonging to the
 182 --   cube centered on (1,1,1) with a grid constructed from the
 183 --   trilinear values. See example one in the paper.
 184 test_trilinear_c1110 :: Assertion
 185 test_trilinear_c1110 =
 186     assertAlmostEqual "c1110 is correct" (c t 1 1 1 0) (23/8)
 187       where
 188         g = make_grid 1 trilinear
 189         cube = fromJust $ cube_at g 1 1 1
 190         t = tetrahedron0 cube
 191
 192
 193 -- | Check the value of c1101 for tetrahedron0 belonging to the
 194 --   cube centered on (1,1,1) with a grid constructed from the
 195 --   trilinear values. See example one in the paper.
 196 test_trilinear_c1101 :: Assertion
 197 test_trilinear_c1101 =
 198     assertAlmostEqual "c1101 is correct" (c t 1 1 0 1) (27/8)
 199       where
 200         g = make_grid 1 trilinear
 201         cube = fromJust $ cube_at g 1 1 1
 202         t = tetrahedron0 cube
 203
 204
 205 -- | Check the value of c1200 for tetrahedron0 belonging to the
 206 --   cube centered on (1,1,1) with a grid constructed from the
 207 --   trilinear values. See example one in the paper.
 208 test_trilinear_c1200 :: Assertion
 209 test_trilinear_c1200 =
 210     assertAlmostEqual "c1200 is correct" (c t 1 2 0 0) 3
 211       where
 212         g = make_grid 1 trilinear
 213         cube = fromJust $ cube_at g 1 1 1
 214         t = tetrahedron0 cube
 215
 216
 217 -- | Check the value of c2010 for tetrahedron0 belonging to the
 218 --   cube centered on (1,1,1) with a grid constructed from the
 219 --   trilinear values. See example one in the paper.
 220 test_trilinear_c2010 :: Assertion
 221 test_trilinear_c2010 =
 222     assertAlmostEqual "c2010 is correct" (c t 2 0 1 0) (10/3)
 223       where
 224         g = make_grid 1 trilinear
 225         cube = fromJust $ cube_at g 1 1 1
 226         t = tetrahedron0 cube
 227
 228
 229 -- | Check the value of c2001 for tetrahedron0 belonging to the
 230 --   cube centered on (1,1,1) with a grid constructed from the
 231 --   trilinear values. See example one in the paper.
 232 test_trilinear_c2001 :: Assertion
 233 test_trilinear_c2001 =
 234     assertAlmostEqual "c2001 is correct" (c t 2 0 0 1) 4
 235       where
 236         g = make_grid 1 trilinear
 237         cube = fromJust $ cube_at g 1 1 1
 238         t = tetrahedron0 cube
 239
 240
 241 -- | Check the value of c2100 for tetrahedron0 belonging to the
 242 --   cube centered on (1,1,1) with a grid constructed from the
 243 --   trilinear values. See example one in the paper.
 244 test_trilinear_c2100 :: Assertion
 245 test_trilinear_c2100 =
 246     assertAlmostEqual "c2100 is correct" (c t 2 1 0 0) (7/2)
 247       where
 248         g = make_grid 1 trilinear
 249         cube = fromJust $ cube_at g 1 1 1
 250         t = tetrahedron0 cube
 251
 252
 253 -- | Check the value of c3000 for tetrahedron0 belonging to the
 254 --   cube centered on (1,1,1) with a grid constructed from the
 255 --   trilinear values. See example one in the paper.
 256 test_trilinear_c3000 :: Assertion
 257 test_trilinear_c3000 =
 258     assertAlmostEqual "c3000 is correct" (c t 3 0 0 0) 4
 259       where
 260         g = make_grid 1 trilinear
 261         cube = fromJust $ cube_at g 1 1 1
 262         t = tetrahedron0 cube
 263
 264
 265 -- | Make sure that v0 of tetrahedron0 belonging to the cube centered
 266 --   on (1,1,1) with a grid constructed from the trilinear values
 267 --   winds up in the right place. See example one in the paper.
 268 test_trilinear_f0_t0_v0 :: Assertion
 269 test_trilinear_f0_t0_v0 =
 270     assertEqual "v0 is correct" (v0 t) (1, 1, 1)
 271       where
 272         g = make_grid 1 trilinear
 273         cube = fromJust $ cube_at g 1 1 1
 274         t = tetrahedron0 cube
 275
 276
 277 -- | Make sure that v1 of tetrahedron0 belonging to the cube centered
 278 --   on (1,1,1) with a grid constructed from the trilinear values
 279 --   winds up in the right place. See example one in the paper.
 280 test_trilinear_f0_t0_v1 :: Assertion
 281 test_trilinear_f0_t0_v1 =
 282     assertEqual "v1 is correct" (v1 t) (0.5, 1, 1)
 283       where
 284         g = make_grid 1 trilinear
 285         cube = fromJust $ cube_at g 1 1 1
 286         t = tetrahedron0 cube
 287
 288
 289 -- | Make sure that v2 of tetrahedron0 belonging to the cube centered
 290 --   on (1,1,1) with a grid constructed from the trilinear values
 291 --   winds up in the right place. See example one in the paper.
 292 test_trilinear_f0_t0_v2 :: Assertion
 293 test_trilinear_f0_t0_v2 =
 294     assertEqual "v2 is correct" (v2 t) (0.5, 0.5, 1.5)
 295       where
 296         g = make_grid 1 trilinear
 297         cube = fromJust $ cube_at g 1 1 1
 298         t = tetrahedron0 cube
 299
 300
 301 -- | Make sure that v3 of tetrahedron0 belonging to the cube centered
 302 --   on (1,1,1) with a grid constructed from the trilinear values
 303 --   winds up in the right place. See example one in the paper.
 304 test_trilinear_f0_t0_v3 :: Assertion
 305 test_trilinear_f0_t0_v3 =
 306     assertClose "v3 is correct" (v3 t) (0.5, 1.5, 1.5)
 307       where
 308         g = make_grid 1 trilinear
 309         cube = fromJust $ cube_at g 1 1 1
 310         t = tetrahedron0 cube
 311
 312
 313 test_trilinear_reproduced_t0 :: Assertion
 314 test_trilinear_reproduced_t0 =
 315     assertTrue "trilinears are reproduced correctly" $
 316              and [p (i', j', k') ~= value_at trilinear i j k
 317                     | i <- [0..2],
 318                       j <- [0..2],
 319                       k <- [0..2],
 320                       let i' = fromIntegral i,
 321                       let j' = fromIntegral j,
 322                       let k' = fromIntegral k]
 323     where
 324       g = make_grid 1 trilinear
 325       c0 = fromJust $ cube_at g 1 1 1
 326       t0 = tetrahedron0 c0
 327       p = polynomial t0
 328
 329 test_trilinear_reproduced_t1 :: Assertion
 330 test_trilinear_reproduced_t1 =
 331     assertTrue "trilinears are reproduced correctly" $
 332              and [p (i', j', k') ~= value_at trilinear 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 trilinear
 341       c0 = fromJust $ cube_at g 1 1 1
 342       t1 = tetrahedron1 c0
 343       p = polynomial t1
 344
 345 test_trilinear_reproduced_t2 :: Assertion
 346 test_trilinear_reproduced_t2 =
 347     assertTrue "trilinears are reproduced correctly" $
 348              and [p (i', j', k') ~= value_at trilinear i j k
 349                     | i <- [0..2],
 350                       j <- [0..2],
 351                       k <- [0..2],
 352                       let i' = fromIntegral i,
 353                       let j' = fromIntegral j,
 354                       let k' = fromIntegral k]
 355     where
 356       g = make_grid 1 trilinear
 357       c0 = fromJust $ cube_at g 1 1 1
 358       t2 = tetrahedron2 c0
 359       p = polynomial t2
 360
 361 test_trilinear_reproduced_t3 :: Assertion
 362 test_trilinear_reproduced_t3 =
 363     assertTrue "trilinears are reproduced correctly" $
 364              and [p (i', j', k') ~= value_at trilinear i j k
 365                     | i <- [0..2],
 366                       j <- [0..2],
 367                       k <- [0..2],
 368                       let i' = fromIntegral i,
 369                       let j' = fromIntegral j,
 370                       let k' = fromIntegral k]
 371     where
 372       g = make_grid 1 trilinear
 373       c0 = fromJust $ cube_at g 1 1 1
 374       t3 = tetrahedron3 c0
 375       p = polynomial t3
 376
 377 test_trilinear_reproduced_t4 :: Assertion
 378 test_trilinear_reproduced_t4 =
 379     assertTrue "trilinears are reproduced correctly" $
 380              and [p (i', j', k') ~= value_at trilinear i j k
 381                     | i <- [0..2],
 382                       j <- [0..2],
 383                       k <- [0..2],
 384                       let i' = fromIntegral i,
 385                       let j' = fromIntegral j,
 386                       let k' = fromIntegral k]
 387     where
 388       g = make_grid 1 trilinear
 389       c0 = fromJust $ cube_at g 1 1 1
 390       t4 = tetrahedron4 c0
 391       p = polynomial t4
 392
 393 test_trilinear_reproduced_t5 :: Assertion
 394 test_trilinear_reproduced_t5 =
 395     assertTrue "trilinears are reproduced correctly" $
 396              and [p (i', j', k') ~= value_at trilinear i j k
 397                     | i <- [0..2],
 398                       j <- [0..2],
 399                       k <- [0..2],
 400                       let i' = fromIntegral i,
 401                       let j' = fromIntegral j,
 402                       let k' = fromIntegral k]
 403     where
 404       g = make_grid 1 trilinear
 405       c0 = fromJust $ cube_at g 1 1 1
 406       t5 = tetrahedron5 c0
 407       p = polynomial t5
 408
 409 test_trilinear_reproduced_t6 :: Assertion
 410 test_trilinear_reproduced_t6 =
 411     assertTrue "trilinears are reproduced correctly" $
 412              and [p (i', j', k') ~= value_at trilinear i j k
 413                     | i <- [0..2],
 414                       j <- [0..2],
 415                       k <- [0..2],
 416                       let i' = fromIntegral i,
 417                       let j' = fromIntegral j,
 418                       let k' = fromIntegral k]
 419     where
 420       g = make_grid 1 trilinear
 421       c0 = fromJust $ cube_at g 1 1 1
 422       t6 = tetrahedron6 c0
 423       p = polynomial t6
 424
 425 test_trilinear_reproduced_t7 :: Assertion
 426 test_trilinear_reproduced_t7 =
 427     assertTrue "trilinears are reproduced correctly" $
 428              and [p (i', j', k') ~= value_at trilinear i j k
 429                     | i <- [0..2],
 430                       j <- [0..2],
 431                       k <- [0..2],
 432                       let i' = fromIntegral i,
 433                       let j' = fromIntegral j,
 434                       let k' = fromIntegral k]
 435     where
 436       g = make_grid 1 trilinear
 437       c0 = fromJust $ cube_at g 1 1 1
 438       t7 = tetrahedron7 c0
 439       p = polynomial t7
 440
 441 test_trilinear_reproduced_t8 :: Assertion
 442 test_trilinear_reproduced_t8 =
 443     assertTrue "trilinears are reproduced correctly" $
 444              and [p (i', j', k') ~= value_at trilinear i j k
 445                     | i <- [0..2],
 446                       j <- [0..2],
 447                       k <- [0..2],
 448                       let i' = fromIntegral i,
 449                       let j' = fromIntegral j,
 450                       let k' = fromIntegral k]
 451     where
 452       g = make_grid 1 trilinear
 453       c0 = fromJust $ cube_at g 1 1 1
 454       t8 = tetrahedron8 c0
 455       p = polynomial t8
 456
 457 test_trilinear_reproduced_t9 :: Assertion
 458 test_trilinear_reproduced_t9 =
 459     assertTrue "trilinears are reproduced correctly" $
 460              and [p (i', j', k') ~= value_at trilinear i j k
 461                     | i <- [0..2],
 462                       j <- [0..2],
 463                       k <- [0..2],
 464                       let i' = fromIntegral i,
 465                       let j' = fromIntegral j,
 466                       let k' = fromIntegral k]
 467     where
 468       g = make_grid 1 trilinear
 469       c0 = fromJust $ cube_at g 1 1 1
 470       t9 = tetrahedron9 c0
 471       p = polynomial t9
 472
 473 test_trilinear_reproduced_t10 :: Assertion
 474 test_trilinear_reproduced_t10 =
 475     assertTrue "trilinears are reproduced correctly" $
 476              and [p (i', j', k') ~= value_at trilinear i j k
 477                     | i <- [0..2],
 478                       j <- [0..2],
 479                       k <- [0..2],
 480                       let i' = fromIntegral i,
 481                       let j' = fromIntegral j,
 482                       let k' = fromIntegral k]
 483     where
 484       g = make_grid 1 trilinear
 485       c0 = fromJust $ cube_at g 1 1 1
 486       t10 = tetrahedron10 c0
 487       p = polynomial t10
 488
 489 test_trilinear_reproduced_t11 :: Assertion
 490 test_trilinear_reproduced_t11 =
 491     assertTrue "trilinears are reproduced correctly" $
 492              and [p (i', j', k') ~= value_at trilinear i j k
 493                     | i <- [0..2],
 494                       j <- [0..2],
 495                       k <- [0..2],
 496                       let i' = fromIntegral i,
 497                       let j' = fromIntegral j,
 498                       let k' = fromIntegral k]
 499     where
 500       g = make_grid 1 trilinear
 501       c0 = fromJust $ cube_at g 1 1 1
 502       t11 = tetrahedron11 c0
 503       p = polynomial t11
 504
 505 test_trilinear_reproduced_t12 :: Assertion
 506 test_trilinear_reproduced_t12 =
 507     assertTrue "trilinears are reproduced correctly" $
 508              and [p (i', j', k') ~= value_at trilinear i j k
 509                     | i <- [0..2],
 510                       j <- [0..2],
 511                       k <- [0..2],
 512                       let i' = fromIntegral i,
 513                       let j' = fromIntegral j,
 514                       let k' = fromIntegral k]
 515     where
 516       g = make_grid 1 trilinear
 517       c0 = fromJust $ cube_at g 1 1 1
 518       t12 = tetrahedron12 c0
 519       p = polynomial t12
 520
 521 test_trilinear_reproduced_t13 :: Assertion
 522 test_trilinear_reproduced_t13 =
 523     assertTrue "trilinears are reproduced correctly" $
 524              and [p (i', j', k') ~= value_at trilinear i j k
 525                     | i <- [0..2],
 526                       j <- [0..2],
 527                       k <- [0..2],
 528                       let i' = fromIntegral i,
 529                       let j' = fromIntegral j,
 530                       let k' = fromIntegral k]
 531     where
 532       g = make_grid 1 trilinear
 533       c0 = fromJust $ cube_at g 1 1 1
 534       t13 = tetrahedron13 c0
 535       p = polynomial t13
 536
 537
 538 test_trilinear_reproduced_t14 :: Assertion
 539 test_trilinear_reproduced_t14 =
 540     assertTrue "trilinears are reproduced correctly" $
 541              and [p (i', j', k') ~= value_at trilinear i j k
 542                     | i <- [0..2],
 543                       j <- [0..2],
 544                       k <- [0..2],
 545                       let i' = fromIntegral i,
 546                       let j' = fromIntegral j,
 547                       let k' = fromIntegral k]
 548     where
 549       g = make_grid 1 trilinear
 550       c0 = fromJust $ cube_at g 1 1 1
 551       t14 = tetrahedron14 c0
 552       p = polynomial t14
 553
 554 test_trilinear_reproduced_t15 :: Assertion
 555 test_trilinear_reproduced_t15 =
 556     assertTrue "trilinears are reproduced correctly" $
 557              and [p (i', j', k') ~= value_at trilinear i j k
 558                     | i <- [0..2],
 559                       j <- [0..2],
 560                       k <- [0..2],
 561                       let i' = fromIntegral i,
 562                       let j' = fromIntegral j,
 563                       let k' = fromIntegral k]
 564     where
 565       g = make_grid 1 trilinear
 566       c0 = fromJust $ cube_at g 1 1 1
 567       t15 = tetrahedron15 c0
 568       p = polynomial t15
 569
 570 test_trilinear_reproduced_t16 :: Assertion
 571 test_trilinear_reproduced_t16 =
 572     assertTrue "trilinears are reproduced correctly" $
 573              and [p (i', j', k') ~= value_at trilinear i j k
 574                     | i <- [0..2],
 575                       j <- [0..2],
 576                       k <- [0..2],
 577                       let i' = fromIntegral i,
 578                       let j' = fromIntegral j,
 579                       let k' = fromIntegral k]
 580     where
 581       g = make_grid 1 trilinear
 582       c0 = fromJust $ cube_at g 1 1 1
 583       t16 = tetrahedron16 c0
 584       p = polynomial t16
 585
 586 test_trilinear_reproduced_t17 :: Assertion
 587 test_trilinear_reproduced_t17 =
 588     assertTrue "trilinears are reproduced correctly" $
 589              and [p (i', j', k') ~= value_at trilinear i j k
 590                     | i <- [0..2],
 591                       j <- [0..2],
 592                       k <- [0..2],
 593                       let i' = fromIntegral i,
 594                       let j' = fromIntegral j,
 595                       let k' = fromIntegral k]
 596     where
 597       g = make_grid 1 trilinear
 598       c0 = fromJust $ cube_at g 1 1 1
 599       t17 = tetrahedron17 c0
 600       p = polynomial t17
 601
 602 test_trilinear_reproduced_t18 :: Assertion
 603 test_trilinear_reproduced_t18 =
 604     assertTrue "trilinears are reproduced correctly" $
 605              and [p (i', j', k') ~= value_at trilinear i j k
 606                     | i <- [0..2],
 607                       j <- [0..2],
 608                       k <- [0..2],
 609                       let i' = fromIntegral i,
 610                       let j' = fromIntegral j,
 611                       let k' = fromIntegral k]
 612     where
 613       g = make_grid 1 trilinear
 614       c0 = fromJust $ cube_at g 1 1 1
 615       t18 = tetrahedron18 c0
 616       p = polynomial t18
 617
 618 test_trilinear_reproduced_t19 :: Assertion
 619 test_trilinear_reproduced_t19 =
 620     assertTrue "trilinears are reproduced correctly" $
 621              and [p (i', j', k') ~= value_at trilinear i j k
 622                     | i <- [0..2],
 623                       j <- [0..2],
 624                       k <- [0..2],
 625                       let i' = fromIntegral i,
 626                       let j' = fromIntegral j,
 627                       let k' = fromIntegral k]
 628     where
 629       g = make_grid 1 trilinear
 630       c0 = fromJust $ cube_at g 1 1 1
 631       t19 = tetrahedron19 c0
 632       p = polynomial t19
 633
 634 test_trilinear_reproduced_t20 :: Assertion
 635 test_trilinear_reproduced_t20 =
 636     assertTrue "trilinears are reproduced correctly" $
 637              and [p (i', j', k') ~= value_at trilinear i j k
 638                     | i <- [0..2],
 639                       j <- [0..2],
 640                       k <- [0..2],
 641                       let i' = fromIntegral i,
 642                       let j' = fromIntegral j,
 643                       let k' = fromIntegral k]
 644     where
 645       g = make_grid 1 trilinear
 646       c0 = fromJust $ cube_at g 1 1 1
 647       t20 = tetrahedron20 c0
 648       p = polynomial t20
 649
 650
 651 test_trilinear_reproduced_t21 :: Assertion
 652 test_trilinear_reproduced_t21 =
 653     assertTrue "trilinears are reproduced correctly" $
 654              and [p (i', j', k') ~= value_at trilinear i j k
 655                     | i <- [0..2],
 656                       j <- [0..2],
 657                       k <- [0..2],
 658                       let i' = fromIntegral i,
 659                       let j' = fromIntegral j,
 660                       let k' = fromIntegral k]
 661     where
 662       g = make_grid 1 trilinear
 663       c0 = fromJust $ cube_at g 1 1 1
 664       t21 = tetrahedron21 c0
 665       p = polynomial t21
 666
 667 test_trilinear_reproduced_t22 :: Assertion
 668 test_trilinear_reproduced_t22 =
 669     assertTrue "trilinears are reproduced correctly" $
 670              and [p (i', j', k') ~= value_at trilinear i j k
 671                     | i <- [0..2],
 672                       j <- [0..2],
 673                       k <- [0..2],
 674                       let i' = fromIntegral i,
 675                       let j' = fromIntegral j,
 676                       let k' = fromIntegral k]
 677     where
 678       g = make_grid 1 trilinear
 679       c0 = fromJust $ cube_at g 1 1 1
 680       t22 = tetrahedron22 c0
 681       p = polynomial t22
 682
 683
 684 test_trilinear_reproduced_t23 :: Assertion
 685 test_trilinear_reproduced_t23 =
 686     assertTrue "trilinears are reproduced correctly" $
 687              and [p (i', j', k') ~= value_at trilinear i j k
 688                     | i <- [0..2],
 689                       j <- [0..2],
 690                       k <- [0..2],
 691                       let i' = fromIntegral i,
 692                       let j' = fromIntegral j,
 693                       let k' = fromIntegral k]
 694     where
 695       g = make_grid 1 trilinear
 696       c0 = fromJust $ cube_at g 1 1 1
 697       t19 = tetrahedron19 c0
 698       p = polynomial t19
 699
 700
 701 test_zeros_reproduced :: Assertion
 702 test_zeros_reproduced =
 703     assertTrue "the zero function is reproduced correctly" $
 704              and [p (i', j', k') ~= value_at zeros i j k
 705                     | i <- [0..2],
 706                       j <- [0..2],
 707                       k <- [0..2],
 708                       let i' = fromIntegral i,
 709                       let j' = fromIntegral j,
 710                       let k' = fromIntegral k]
 711     where
 712       g = make_grid 1 zeros
 713       c0 = fromJust $ cube_at g 1 1 1
 714       t0 = tetrahedron0 c0
 715       p = polynomial t0