-- function used to build the interpolation.
module Grid (
cube_at,
+ grid_properties,
grid_tests,
slow_tests,
- zoom
- )
+ zoom )
where
-import qualified Data.Array.Repa as R
-import qualified Data.Array.Repa.Operators.Traversal as R (unsafeTraverse)
-import Test.HUnit (Assertion, assertEqual)
-import Test.Framework (Test, testGroup)
-import Test.Framework.Providers.HUnit (testCase)
-import Test.Framework.Providers.QuickCheck2 (testProperty)
-import Test.QuickCheck ((==>),
- Arbitrary(..),
- Gen,
- Property,
- choose)
-import Assertions (assertAlmostEqual, assertTrue)
-import Comparisons ((~=))
-import Cube (Cube(Cube),
- find_containing_tetrahedron,
- tetrahedra,
- tetrahedron)
-import Examples (trilinear, trilinear9x9x9, zeros)
-import FunctionValues (make_values, value_at)
-import Point (Point(..))
-import ScaleFactor (ScaleFactor)
+import Data.Array.Repa (
+ (:.)( (:.) ),
+ DIM3,
+ Z( Z ),
+ computeUnboxedP,
+ fromListUnboxed )
+import Data.Array.Repa.Operators.Traversal ( unsafeTraverse )
+import Test.Tasty ( TestTree, testGroup )
+import Test.Tasty.HUnit ( Assertion, assertEqual, testCase )
+import Test.Tasty.QuickCheck (
+ Arbitrary( arbitrary ),
+ Gen,
+ Property,
+ (==>),
+ choose,
+ vectorOf,
+ testProperty )
+
+import Assertions ( assertAlmostEqual, assertTrue )
+import Comparisons ( (~=) )
+import Cube (
+ Cube( Cube ),
+ find_containing_tetrahedron,
+ tetrahedra,
+ tetrahedron )
+import Examples ( trilinear, trilinear9x9x9, zeros )
+import FunctionValues ( make_values, value_at )
+import Point ( Point(Point) )
+import ScaleFactor ( ScaleFactor )
import Tetrahedron (
- Tetrahedron(v0,v1,v2,v3),
+ Tetrahedron( v0, v1, v2, v3 ),
c,
- polynomial,
- )
-import Values (Values3D, dims, empty3d, zoom_shape)
+ polynomial )
+import Values ( Values3D, dims, empty3d, zoom_shape )
-- | Our problem is defined on a Grid. The grid size is given by the
-- performance reasons (and simplicity). The function values are the
-- values of the function at the grid points, which are distance h=1
-- from one another in each direction (x,y,z).
-data Grid = Grid { function_values :: Values3D }
- deriving (Show)
+--
+newtype Grid = Grid { function_values :: Values3D }
+ deriving (Show)
instance Arbitrary Grid where
arbitrary = do
- fvs <- arbitrary :: Gen Values3D
+ x_dim <- choose (1, 27)
+ y_dim <- choose (1, 27)
+ z_dim <- choose (1, 27)
+ elements <- vectorOf (x_dim * y_dim * z_dim) (arbitrary :: Gen Double)
+ let new_shape = (Z :. x_dim :. y_dim :. z_dim)
+ let fvs = fromListUnboxed new_shape elements
return $ Grid fvs
where
fvs = function_values g
fvs' = make_values fvs i j k
- tet_vol = 1/24
+ tet_vol = (1/24) :: Double
-- The first cube along any axis covers (-1/2, 1/2). The second
| otherwise = (ceiling (coord + offset)) - 1
where
(xsize, ysize, zsize) = dims (function_values g)
- offset = 1/2
+ offset = (1/2) :: Double
-- | Takes a 'Grid', and returns a 'Cube' containing the given 'Point'.
k = calculate_containing_cube_coordinate g z
-zoom_lookup :: Values3D -> ScaleFactor -> a -> (R.DIM3 -> Double)
+zoom_lookup :: Values3D -> ScaleFactor -> a -> (DIM3 -> Double)
zoom_lookup v3d scale_factor _ =
zoom_result v3d scale_factor
-zoom_result :: Values3D -> ScaleFactor -> R.DIM3 -> Double
-zoom_result v3d (sfx, sfy, sfz) (R.Z R.:. m R.:. n R.:. o) =
+zoom_result :: Values3D -> ScaleFactor -> DIM3 -> Double
+zoom_result v3d (sfx, sfy, sfz) (Z :. m :. n :. o) =
f p
where
g = Grid v3d
- offset = 1/2
+ offset = (1/2) :: Double
m' = (fromIntegral m) / (fromIntegral sfx) - offset
n' = (fromIntegral n) / (fromIntegral sfy) - offset
o' = (fromIntegral o) / (fromIntegral sfz) - offset
f = polynomial t
-zoom :: Values3D -> ScaleFactor -> Values3D
+--
+-- Instead of IO, we could get away with a generic monad 'm'
+-- here. However, /we/ only call this function from within IO.
+--
+zoom :: Values3D -> ScaleFactor -> IO Values3D
zoom v3d scale_factor
- | xsize == 0 || ysize == 0 || zsize == 0 = empty3d
+ | xsize == 0 || ysize == 0 || zsize == 0 = return empty3d
| otherwise =
- R.computeS $ R.unsafeTraverse v3d transExtent f
- where
- (xsize, ysize, zsize) = dims v3d
- transExtent = zoom_shape scale_factor
- f = zoom_lookup v3d scale_factor
+ computeUnboxedP $ unsafeTraverse v3d transExtent f
+ where
+ (xsize, ysize, zsize) = dims v3d
+ transExtent = zoom_shape scale_factor
+ f = zoom_lookup v3d scale_factor :: (DIM3 -> Double) -> DIM3 -> Double
-- | Check all coefficients of tetrahedron0 belonging to the cube
-- We also verify that the four vertices on face0 of the cube are
-- in the correct location.
--
-trilinear_c0_t0_tests :: Test.Framework.Test
+trilinear_c0_t0_tests :: TestTree
trilinear_c0_t0_tests =
testGroup "trilinear c0 t0"
[testGroup "coefficients"
c0 <- cs,
t <- tetrahedra c0,
let p = polynomial t,
- let i' = fromIntegral i,
- let j' = fromIntegral j,
- let k' = fromIntegral k]
+ let i' = fromIntegral i :: Double,
+ let j' = fromIntegral j :: Double,
+ let k' = fromIntegral k :: Double]
where
g = Grid trilinear
cs = [ cube_at g ci cj ck | ci <- [0..2], cj <- [0..2], ck <- [0..2] ]
| i <- [0..2],
j <- [0..2],
k <- [0..2],
- let i' = fromIntegral i,
- let j' = fromIntegral j,
- let k' = fromIntegral k,
+ let i' = fromIntegral i :: Double,
+ let j' = fromIntegral j :: Double,
+ let k' = fromIntegral k :: Double,
c0 <- cs,
t0 <- tetrahedra c0,
let p = polynomial t0 ]
k <- [0..8],
t <- tetrahedra c0,
let p = polynomial t,
- let i' = (fromIntegral i) * 0.5,
- let j' = (fromIntegral j) * 0.5,
- let k' = (fromIntegral k) * 0.5]
+ let i' = (fromIntegral i) * 0.5 :: Double,
+ let j' = (fromIntegral j) * 0.5 :: Double,
+ let k' = (fromIntegral k) * 0.5 :: Double]
where
g = Grid trilinear
c0 = cube_at g 1 1 1
prop_cube_indices_never_go_out_of_bounds :: Grid -> Gen Bool
prop_cube_indices_never_go_out_of_bounds g =
do
- let coordmin = negate (1/2)
+ let coordmin = negate (1/2) :: Double
let (xsize, ysize, zsize) = dims $ function_values g
- let xmax = (fromIntegral xsize) - (1/2)
- let ymax = (fromIntegral ysize) - (1/2)
- let zmax = (fromIntegral zsize) - (1/2)
+ let xmax = (fromIntegral xsize) - (1/2) :: Double
+ let ymax = (fromIntegral ysize) - (1/2) :: Double
+ let zmax = (fromIntegral zsize) - (1/2) :: Double
x <- choose (coordmin, xmax)
y <- choose (coordmin, ymax)
-- | All of the properties from Section (2.9), p. 80. These require a
-- grid since they refer to two adjacent cubes.
-p80_29_properties :: Test.Framework.Test
+p80_29_properties :: TestTree
p80_29_properties =
- testGroup "p. 80, Section (2.9) Properties" [
+ testGroup "p. 80, Section (2.9) properties" [
testProperty "c0120 identity" prop_c0120_identity,
testProperty "c0111 identity" prop_c0111_identity,
testProperty "c0201 identity" prop_c0201_identity,
testProperty "c0300 identity" prop_c0300_identity ]
-grid_tests :: Test.Framework.Test
+grid_tests :: TestTree
grid_tests =
- testGroup "Grid Tests" [
- trilinear_c0_t0_tests,
- p80_29_properties,
- testProperty "cube indices within bounds"
- prop_cube_indices_never_go_out_of_bounds ]
+ testGroup "Grid tests" [ trilinear_c0_t0_tests ]
+
+grid_properties :: TestTree
+grid_properties =
+ testGroup "Grid properties"
+ [ p80_29_properties,
+ testProperty "cube indices within bounds"
+ prop_cube_indices_never_go_out_of_bounds ]
-- Do the slow tests last so we can stop paying attention.
-slow_tests :: Test.Framework.Test
+slow_tests :: TestTree
slow_tests =
- testGroup "Slow Tests" [
+ testGroup "Slow tests" [
testCase "trilinear reproduced" test_trilinear_reproduced,
testCase "trilinear9x9x9 reproduced" test_trilinear9x9x9_reproduced,
testCase "zeros reproduced" test_zeros_reproduced ]
projects / spline3.git / blobdiff