import Test.QuickCheck
import Assertions
+import Comparisons
import Cube
+import Examples
+import FunctionValues (value_at)
import Grid
import Tetrahedron
return (make_grid h' fvs)
--- | Values of the function f(x,y,z) = 1 + x + xy + xyz taken at nine
--- points (hi, hj, jk) with h = 1. From example one in the paper.
--- Used in the next bunch of tests.
-trilinear :: [[[Double]]]
-trilinear = [ [ [ 1, 2, 3 ],
- [ 1, 3, 5 ],
- [ 1, 4, 7 ] ],
- [ [ 1, 2, 3 ],
- [ 1, 4, 7 ],
- [ 1, 6, 11 ] ],
- [ [ 1, 2, 3 ],
- [ 1, 5, 9 ],
- [ 1, 8, 15 ]]]
-
-- | Check the value of c0030 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c0030 :: Test
+test_trilinear_c0030 :: Assertion
test_trilinear_c0030 =
- TestCase $ assertAlmostEqual "c0030 is correct" (c t 0 0 3 0) (17/8)
+ assertAlmostEqual "c0030 is correct" (c t 0 0 3 0) (17/8)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c0003 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c0003 :: Test
+test_trilinear_c0003 :: Assertion
test_trilinear_c0003 =
- TestCase $ assertAlmostEqual "c0003 is correct" (c t 0 0 0 3) (27/8)
+ assertAlmostEqual "c0003 is correct" (c t 0 0 0 3) (27/8)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c0021 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c0021 :: Test
+test_trilinear_c0021 :: Assertion
test_trilinear_c0021 =
- TestCase $ assertAlmostEqual "c0021 is correct" (c t 0 0 2 1) (61/24)
+ assertAlmostEqual "c0021 is correct" (c t 0 0 2 1) (61/24)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c0012 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c0012 :: Test
+test_trilinear_c0012 :: Assertion
test_trilinear_c0012 =
- TestCase $ assertAlmostEqual "c0012 is correct" (c t 0 0 1 2) (71/24)
+ assertAlmostEqual "c0012 is correct" (c t 0 0 1 2) (71/24)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c0120 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c0120 :: Test
+test_trilinear_c0120 :: Assertion
test_trilinear_c0120 =
- TestCase $ assertAlmostEqual "c0120 is correct" (c t 0 1 2 0) (55/24)
+ assertAlmostEqual "c0120 is correct" (c t 0 1 2 0) (55/24)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c0102 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c0102 :: Test
+test_trilinear_c0102 :: Assertion
test_trilinear_c0102 =
- TestCase $ assertAlmostEqual "c0102 is correct" (c t 0 1 0 2) (73/24)
+ assertAlmostEqual "c0102 is correct" (c t 0 1 0 2) (73/24)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c0111 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c0111 :: Test
+test_trilinear_c0111 :: Assertion
test_trilinear_c0111 =
- TestCase $ assertAlmostEqual "c0111 is correct" (c t 0 1 1 1) (8/3)
+ assertAlmostEqual "c0111 is correct" (c t 0 1 1 1) (8/3)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c0210 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c0210 :: Test
+test_trilinear_c0210 :: Assertion
test_trilinear_c0210 =
- TestCase $ assertAlmostEqual "c0210 is correct" (c t 0 2 1 0) (29/12)
+ assertAlmostEqual "c0210 is correct" (c t 0 2 1 0) (29/12)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c0201 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c0201 :: Test
+test_trilinear_c0201 :: Assertion
test_trilinear_c0201 =
- TestCase $ assertAlmostEqual "c0201 is correct" (c t 0 2 0 1) (11/4)
+ assertAlmostEqual "c0201 is correct" (c t 0 2 0 1) (11/4)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c0300 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c0300 :: Test
+test_trilinear_c0300 :: Assertion
test_trilinear_c0300 =
- TestCase $ assertAlmostEqual "c0300 is correct" (c t 0 3 0 0) (5/2)
+ assertAlmostEqual "c0300 is correct" (c t 0 3 0 0) (5/2)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c1020 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c1020 :: Test
+test_trilinear_c1020 :: Assertion
test_trilinear_c1020 =
- TestCase $ assertAlmostEqual "c1020 is correct" (c t 1 0 2 0) (8/3)
+ assertAlmostEqual "c1020 is correct" (c t 1 0 2 0) (8/3)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c1002 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c1002 :: Test
+test_trilinear_c1002 :: Assertion
test_trilinear_c1002 =
- TestCase $ assertAlmostEqual "c1002 is correct" (c t 1 0 0 2) (23/6)
+ assertAlmostEqual "c1002 is correct" (c t 1 0 0 2) (23/6)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c1011 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c1011 :: Test
+test_trilinear_c1011 :: Assertion
test_trilinear_c1011 =
- TestCase $ assertAlmostEqual "c1011 is correct" (c t 1 0 1 1) (13/4)
+ assertAlmostEqual "c1011 is correct" (c t 1 0 1 1) (13/4)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c1110 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c1110 :: Test
+test_trilinear_c1110 :: Assertion
test_trilinear_c1110 =
- TestCase $ assertAlmostEqual "c1110 is correct" (c t 1 1 1 0) (23/8)
+ assertAlmostEqual "c1110 is correct" (c t 1 1 1 0) (23/8)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c1101 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c1101 :: Test
+test_trilinear_c1101 :: Assertion
test_trilinear_c1101 =
- TestCase $ assertAlmostEqual "c1101 is correct" (c t 1 1 0 1) (27/8)
+ assertAlmostEqual "c1101 is correct" (c t 1 1 0 1) (27/8)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c1200 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c1200 :: Test
+test_trilinear_c1200 :: Assertion
test_trilinear_c1200 =
- TestCase $ assertAlmostEqual "c1200 is correct" (c t 1 2 0 0) 3
+ assertAlmostEqual "c1200 is correct" (c t 1 2 0 0) 3
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c2010 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c2010 :: Test
+test_trilinear_c2010 :: Assertion
test_trilinear_c2010 =
- TestCase $ assertAlmostEqual "c2010 is correct" (c t 2 0 1 0) (10/3)
+ assertAlmostEqual "c2010 is correct" (c t 2 0 1 0) (10/3)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c2001 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c2001 :: Test
+test_trilinear_c2001 :: Assertion
test_trilinear_c2001 =
- TestCase $ assertAlmostEqual "c2001 is correct" (c t 2 0 0 1) 4
+ assertAlmostEqual "c2001 is correct" (c t 2 0 0 1) 4
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c2100 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c2100 :: Test
+test_trilinear_c2100 :: Assertion
test_trilinear_c2100 =
- TestCase $ assertAlmostEqual "c2100 is correct" (c t 2 1 0 0) (7/2)
+ assertAlmostEqual "c2100 is correct" (c t 2 1 0 0) (7/2)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Check the value of c3000 for tetrahedron0 belonging to the
-- cube centered on (1,1,1) with a grid constructed from the
-- trilinear values. See example one in the paper.
-test_trilinear_c3000 :: Test
+test_trilinear_c3000 :: Assertion
test_trilinear_c3000 =
- TestCase $ assertAlmostEqual "c3000 is correct" (c t 3 0 0 0) 4
+ assertAlmostEqual "c3000 is correct" (c t 3 0 0 0) 4
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Make sure that v0 of tetrahedron0 belonging to the cube centered
-- on (1,1,1) with a grid constructed from the trilinear values
-- winds up in the right place. See example one in the paper.
-test_trilinear_f0_t0_v0 :: Test
+test_trilinear_f0_t0_v0 :: Assertion
test_trilinear_f0_t0_v0 =
- TestCase $ assertEqual "v0 is correct" (v0 t) (1, 1, 1)
+ assertEqual "v0 is correct" (v0 t) (1, 1, 1)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Make sure that v1 of tetrahedron0 belonging to the cube centered
-- on (1,1,1) with a grid constructed from the trilinear values
-- winds up in the right place. See example one in the paper.
-test_trilinear_f0_t0_v1 :: Test
+test_trilinear_f0_t0_v1 :: Assertion
test_trilinear_f0_t0_v1 =
- TestCase $ assertEqual "v1 is correct" (v1 t) (0.5, 1, 1)
+ assertEqual "v1 is correct" (v1 t) (0.5, 1, 1)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Make sure that v2 of tetrahedron0 belonging to the cube centered
-- on (1,1,1) with a grid constructed from the trilinear values
-- winds up in the right place. See example one in the paper.
-test_trilinear_f0_t0_v2 :: Test
+test_trilinear_f0_t0_v2 :: Assertion
test_trilinear_f0_t0_v2 =
- TestCase $ assertEqual "v2 is correct" (v2 t) (0.5, 0.5, 1.5)
+ assertEqual "v2 is correct" (v2 t) (0.5, 0.5, 1.5)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
-- | Make sure that v3 of tetrahedron0 belonging to the cube centered
-- on (1,1,1) with a grid constructed from the trilinear values
-- winds up in the right place. See example one in the paper.
-test_trilinear_f0_t0_v3 :: Test
+test_trilinear_f0_t0_v3 :: Assertion
test_trilinear_f0_t0_v3 =
- TestCase $ assertClose "v3 is correct" (v3 t) (0.5, 1.5, 1.5)
+ assertClose "v3 is correct" (v3 t) (0.5, 1.5, 1.5)
where
g = make_grid 1 trilinear
cube = fromJust $ cube_at g 1 1 1
t = tetrahedron0 cube
--- | A list of all HUnit tests defined in this module.
-grid_tests :: [Test]
-grid_tests =
- [test_trilinear_c0030,
- test_trilinear_c0003,
- test_trilinear_c0021,
- test_trilinear_c0012,
- test_trilinear_c0120,
- test_trilinear_c0102,
- test_trilinear_c0111,
- test_trilinear_c0210,
- test_trilinear_c0201,
- test_trilinear_c0300,
- test_trilinear_c1020,
- test_trilinear_c1002,
- test_trilinear_c1011,
- test_trilinear_c1110,
- test_trilinear_c1101,
- test_trilinear_c1200,
- test_trilinear_c2010,
- test_trilinear_c2001,
- test_trilinear_c2100,
- test_trilinear_c3000,
- test_trilinear_f0_t0_v0,
- test_trilinear_f0_t0_v1,
- test_trilinear_f0_t0_v2,
- test_trilinear_f0_t0_v3]
+test_trilinear_reproduced :: Assertion
+test_trilinear_reproduced =
+ assertTrue "trilinears are reproduced correctly" $
+ and [p (i', j', k') ~= value_at trilinear i j k
+ | i <- [0..2],
+ j <- [0..2],
+ k <- [0..2],
+ let i' = fromIntegral i,
+ let j' = fromIntegral j,
+ let k' = fromIntegral k]
+ where
+ g = make_grid 1 trilinear
+ c0 = fromJust $ cube_at g 1 1 1
+ t0 = tetrahedron0 c0
+ p = polynomial t0
+
+
+test_zeros_reproduced :: Assertion
+test_zeros_reproduced =
+ assertTrue "the zero function is reproduced correctly" $
+ and [p (i', j', k') ~= value_at zeros i j k
+ | i <- [0..2],
+ j <- [0..2],
+ k <- [0..2],
+ let i' = fromIntegral i,
+ let j' = fromIntegral j,
+ let k' = fromIntegral k]
+ where
+ g = make_grid 1 zeros
+ c0 = fromJust $ cube_at g 1 1 1
+ t0 = tetrahedron0 c0
+ p = polynomial t0
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