module Tests.Grid
where

import Data.Maybe (fromJust)
import Test.HUnit
import Test.QuickCheck

import Assertions
import Comparisons
import Cube
import Examples
import FunctionValues (value_at)
import Grid
import Tetrahedron


instance Arbitrary Grid where
    arbitrary = do
      (Positive h') <- arbitrary :: Gen (Positive Double)
      fvs <- arbitrary :: Gen [[[Double]]]
      return (make_grid h' fvs)


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ assertEqual "v0 is correct" (v0 t) (1, 1, 1)
      where
        g = make_grid 1 trilinear
        cube = fromJust $ cube_at g 1 1 1
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ assertEqual "v1 is correct" (v1 t) (0.5, 1, 1)
      where
        g = make_grid 1 trilinear
        cube = fromJust $ cube_at g 1 1 1
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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
        t = tetrahedron0 cube


-- | 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 =
    TestCase $ 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


test_trilinear_reproduced :: Test
test_trilinear_reproduced =
    TestCase $ 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 :: Test
test_zeros_reproduced =
    TestCase $ 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


-- | 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,
     test_zeros_reproduced]